From 0abdf2aa36d94abfaba030ba9c59736c441441d0 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 8 Aug 2011 09:21:20 +0000 Subject: [PATCH 001/256] Initial checkin of experimental bignum type. [SVN r73607] --- .gitattributes | 96 ++ include/boost/math/big_number.hpp | 1165 +++++++++++++++++ include/boost/math/big_number/gmp.hpp | 691 ++++++++++ .../math/concepts/big_number_architypes.hpp | 309 +++++ math/test/big_number_concept_check.cpp | 38 + math/test/test_arithmetic.cpp | 443 +++++++ 6 files changed, 2742 insertions(+) create mode 100644 .gitattributes create mode 100644 include/boost/math/big_number.hpp create mode 100644 include/boost/math/big_number/gmp.hpp create mode 100644 include/boost/math/concepts/big_number_architypes.hpp create mode 100644 math/test/big_number_concept_check.cpp create mode 100644 math/test/test_arithmetic.cpp diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 00000000..3e84d7c7 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,96 @@ +* text=auto !eol svneol=native#text/plain +*.gitattributes text svneol=native#text/plain + +# Scriptish formats +*.bat text svneol=native#text/plain +*.bsh text svneol=native#text/x-beanshell +*.cgi text svneol=native#text/plain +*.cmd text svneol=native#text/plain +*.js text svneol=native#text/javascript +*.php text svneol=native#text/x-php +*.pl text svneol=native#text/x-perl +*.pm text svneol=native#text/x-perl +*.py text svneol=native#text/x-python +*.sh eol=lf svneol=LF#text/x-sh +configure eol=lf svneol=LF#text/x-sh + +# Image formats +*.bmp binary svneol=unset#image/bmp +*.gif binary svneol=unset#image/gif +*.ico binary svneol=unset#image/ico +*.jpeg binary svneol=unset#image/jpeg +*.jpg binary svneol=unset#image/jpeg +*.png binary svneol=unset#image/png +*.tif binary svneol=unset#image/tiff +*.tiff binary svneol=unset#image/tiff +*.svg text svneol=native#image/svg%2Bxml + +# Data formats +*.pdf binary svneol=unset#application/pdf +*.avi binary svneol=unset#video/avi +*.doc binary svneol=unset#application/msword +*.dsp text svneol=crlf#text/plain +*.dsw text svneol=crlf#text/plain +*.eps binary svneol=unset#application/postscript +*.gz binary svneol=unset#application/gzip +*.mov binary svneol=unset#video/quicktime +*.mp3 binary svneol=unset#audio/mpeg +*.ppt binary svneol=unset#application/vnd.ms-powerpoint +*.ps binary svneol=unset#application/postscript +*.psd binary svneol=unset#application/photoshop +*.rdf binary svneol=unset#text/rdf +*.rss text svneol=unset#text/xml +*.rtf binary svneol=unset#text/rtf +*.sln text svneol=native#text/plain +*.swf binary svneol=unset#application/x-shockwave-flash +*.tgz binary svneol=unset#application/gzip +*.vcproj text svneol=native#text/xml +*.vcxproj text svneol=native#text/xml +*.vsprops text svneol=native#text/xml +*.wav binary svneol=unset#audio/wav +*.xls binary svneol=unset#application/vnd.ms-excel +*.zip binary svneol=unset#application/zip + +# Text formats +.htaccess text svneol=native#text/plain +*.bbk text svneol=native#text/xml +*.cmake text svneol=native#text/plain +*.css text svneol=native#text/css +*.dtd text svneol=native#text/xml +*.htm text svneol=native#text/html +*.html text svneol=native#text/html +*.ini text svneol=native#text/plain +*.log text svneol=native#text/plain +*.mak text svneol=native#text/plain +*.qbk text svneol=native#text/plain +*.rst text svneol=native#text/plain +*.sql text svneol=native#text/x-sql +*.txt text svneol=native#text/plain +*.xhtml text svneol=native#text/xhtml%2Bxml +*.xml text svneol=native#text/xml +*.xsd text svneol=native#text/xml +*.xsl text svneol=native#text/xml +*.xslt text svneol=native#text/xml +*.xul text svneol=native#text/xul +*.yml text svneol=native#text/plain +boost-no-inspect text svneol=native#text/plain +CHANGES text svneol=native#text/plain +COPYING text svneol=native#text/plain +INSTALL text svneol=native#text/plain +Jamfile text svneol=native#text/plain +Jamroot text svneol=native#text/plain +Jamfile.v2 text svneol=native#text/plain +Jamrules text svneol=native#text/plain +Makefile* text svneol=native#text/plain +README text svneol=native#text/plain +TODO text svneol=native#text/plain + +# Code formats +*.c text svneol=native#text/plain +*.cpp text svneol=native#text/plain +*.h text svneol=native#text/plain +*.hpp text svneol=native#text/plain +*.ipp text svneol=native#text/plain +*.tpp text svneol=native#text/plain +*.jam text svneol=native#text/plain +*.java text svneol=native#text/plain diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp new file mode 100644 index 00000000..632c7b72 --- /dev/null +++ b/include/boost/math/big_number.hpp @@ -0,0 +1,1165 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_EXTENDED_REAL_HPP +#define BOOST_MATH_EXTENDED_REAL_HPP + +#include +#include +#include +#include +#include +#include +#include + +namespace boost{ namespace math{ + +template +class big_number; + +namespace detail{ + +// Forward-declare an expression wrapper +template +struct big_number_exp; +// +// Declare our grammars: +// +struct big_number_grammar + : proto::or_< + proto::terminal< proto::_ > + , proto::plus< big_number_grammar, big_number_grammar > + , proto::multiplies< big_number_grammar, big_number_grammar > + , proto::minus< big_number_grammar, big_number_grammar > + , proto::divides< big_number_grammar, big_number_grammar > + , proto::unary_plus< big_number_grammar > + , proto::negate< big_number_grammar > + , proto::modulus + > +{}; + +// Define a calculator domain. Expression within +// the calculator domain will be wrapped in the +// calculator<> expression wrapper. +struct big_number_domain + : proto::domain< proto::generator, big_number_grammar> +{}; + +template +struct big_number_exp + : proto::extends, big_number_domain> +{ + typedef + proto::extends, big_number_domain> base_type; + + big_number_exp(Expr const &expr = Expr()) + : base_type(expr) + {} + template + big_number_exp(const Other& o) + : base_type(o) + {} +}; + +struct CalcDepth + : proto::or_< + proto::when< proto::terminal, + mpl::int_<0>() + > + , proto::when< proto::unary_expr, + CalcDepth(proto::_child) + > + , proto::when< proto::binary_expr, + mpl::plus, mpl::int_<1> >() + > + > +{}; + +template +struct has_enough_bits +{ + template + struct type : public mpl::bool_::digits >= b>{}; +}; + +template +struct canonical_imp +{ + typedef Val type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::signed_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::unsigned_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::real_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef const char* type; +}; + +template +struct canonical +{ + typedef typename mpl::if_< + is_signed, + mpl::int_<0>, + typename mpl::if_< + is_unsigned, + mpl::int_<1>, + typename mpl::if_< + is_floating_point, + mpl::int_<2>, + typename mpl::if_< + mpl::or_< + is_convertible, + is_same + >, + mpl::int_<3>, + mpl::int_<4> + >::type + >::type + >::type + >::type tag_type; + + typedef typename canonical_imp::type type; +}; + +} // namespace detail + +// +// Traits class, lets us know whether a backend is an integer type, otherwise assumed to be a real number type: +// +template +struct is_extended_integer : public mpl::false_ {}; +template +struct is_extended_integer > : public is_extended_integer{}; + +template +class big_number : public detail::big_number_exp*>::type > +{ + typedef detail::big_number_exp*>::type > base_type; + typedef big_number self_type; +public: + big_number() + { + proto::value(*this) = this; + BOOST_ASSERT(proto::value(*this) == this); + } + big_number(const big_number& e) : m_backend(e.m_backend) + { + proto::value(*this) = this; + BOOST_ASSERT(proto::value(*this) == this); + } + template + big_number(V v, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) + { + proto::value(*this) = this; + BOOST_ASSERT(proto::value(*this) == this); + m_backend = canonical_value(v); + } + /* + big_number(unsigned digits10, typename enable_if_c::type* dummy = 0) + : base_type(digits10) + { + proto::value(*this) = this; + BOOST_ASSERT(proto::value(*this) == this); + }*/ + big_number(const big_number& e, unsigned digits10) : m_backend(e.m_backend, digits10) + { + proto::value(*this) = this; + BOOST_ASSERT(proto::value(*this) == this); + } + template + big_number(V v, unsigned digits10, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) + : base_type(digits10) + { + proto::value(*this) = this; + BOOST_ASSERT(proto::value(*this) == this); + m_backend = canonical_value(v); + } + + template + big_number& operator=(const detail::big_number_exp& e) + { + do_assign(e, typename proto::tag_of::type()); + return *this; + } + + big_number& operator=(const big_number& e) + { + m_backend = e.m_backend; + return *this; + } + + template + typename enable_if, is_same, is_convertible >, big_number& >::type + operator=(const V& v) + { + m_backend = canonical_value(v); + return *this; + } + + template + big_number(const detail::big_number_exp& e) + { + proto::value(*this) = this; + BOOST_ASSERT(proto::value(*this) == this); + do_assign(e, typename proto::tag_of::type()); + } + + template + big_number& operator+=(const detail::big_number_exp& e) + { + // Create a copy if e contains this, but not if we're just doing a + // x *= x + if(contains_self(e) && !is_self(e)) + { + self_type temp(e); + do_add(temp, typename proto::tag_of::type()); + } + else + { + do_add(e, typename proto::tag_of::type()); + } + return *this; + } + + template + typename enable_if, big_number& >::type + operator+=(const V& v) + { + do_add_value(canonical_value(v), mpl::false_()); + return *this; + } + + template + big_number& operator-=(const detail::big_number_exp& e) + { + // Create a copy if e contains this, but not if we're just doing a + if(contains_self(e)) + { + self_type temp(e); + do_subtract(temp, typename proto::tag_of::type()); + } + else + { + do_subtract(e, typename proto::tag_of::type()); + } + return *this; + } + + template + typename enable_if, big_number& >::type + operator-=(const V& v) + { + do_subtract_value(canonical_value(v), mpl::false_()); + return *this; + } + + template + big_number& operator*=(const detail::big_number_exp& e) + { + // Create a temporary if the RHS references *this, but not + // if we're just doing an x += x; + if(contains_self(e) && !is_self(e)) + { + self_type temp(e); + do_multiplies(temp, typename proto::tag_of::type()); + } + else + { + do_multiplies(e, typename proto::tag_of::type()); + } + return *this; + } + + template + typename enable_if, big_number& >::type + operator*=(const V& v) + { + do_multiplies_value(canonical_value(v), mpl::false_()); + return *this; + } + + template + big_number& operator%=(const detail::big_number_exp& e) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + // Create a temporary if the RHS references *this: + if(contains_self(e)) + { + self_type temp(e); + do_modulus(temp, typename proto::tag_of::type()); + } + else + { + do_modulus(e, typename proto::tag_of::type()); + } + return *this; + } + + template + typename enable_if, big_number& >::type + operator%=(const V& v) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + do_modulus_value(canonical_value(v), mpl::false_()); + return *this; + } + + template + big_number& operator/=(const detail::big_number_exp& e) + { + // Create a temporary if the RHS references *this: + if(contains_self(e)) + { + self_type temp(e); + do_divide(temp, typename proto::tag_of::type()); + } + else + { + do_divide(e, typename proto::tag_of::type()); + } + return *this; + } + + template + typename enable_if, big_number& >::type + operator/=(const V& v) + { + do_divide_value(canonical_value(v), mpl::false_()); + return *this; + } + + // + // String conversion functions: + // + std::string str()const + { + return m_backend.str(); + } + // + // Default precision: + // + static unsigned default_precision() + { + return Backend::default_precision(); + } + static void default_precision(unsigned digits10) + { + Backend::default_precision(digits10); + } + unsigned precision()const + { + return m_backend.precision(); + } + void precision(unsigned digits10) + { + m_backend.precision(digits10); + } + // + // Comparison: + // + int compare(const big_number& o)const + { + return m_backend.compare(o.m_backend); + } + template + typename enable_if, int>::type compare(const V& o)const + { + return m_backend.compare(canonical_value(o)); + } +private: + template + void do_assign(const Exp& e, const proto::tag::unary_plus&) + { + typedef typename proto::result_of::left::type left_type; + do_assign(proto::left(e), typename proto::tag_of::type()); + } + + template + void do_assign(const Exp& e, const proto::tag::negate&) + { + typedef typename proto::result_of::left::type left_type; + do_assign(proto::left(e), typename proto::tag_of::type()); + m_backend.negate(); + } + + template + void do_assign(const Exp& e, const proto::tag::plus&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + + static int const left_depth = boost::result_of::type::value; + static int const right_depth = boost::result_of::type::value; + + bool bl = contains_self(proto::left(e)); + bool br = contains_self(proto::right(e)); + + if(bl && is_self(proto::left(e))) + { + // Ignore the left node, it's *this, just add the right: + do_add(proto::right(e), typename proto::tag_of::type()); + } + else if(br && is_self(proto::right(e))) + { + // Ignore the right node, it's *this, just add the left: + do_add(proto::left(e), typename proto::tag_of::type()); + } + else if(bl || br) + { + self_type temp(e); + temp.m_backend.swap(this->m_backend); + } + else if(left_depth >= right_depth) + { + do_assign(proto::left(e), typename proto::tag_of::type()); + do_add(proto::right(e), typename proto::tag_of::type()); + } + else + { + do_assign(proto::right(e), typename proto::tag_of::type()); + do_add(proto::left(e), typename proto::tag_of::type()); + } + } + template + void do_assign(const Exp& e, const proto::tag::minus&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + + static int const left_depth = boost::result_of::type::value; + static int const right_depth = boost::result_of::type::value; + + bool bl = contains_self(proto::left(e)); + bool br = contains_self(proto::right(e)); + + if(bl && is_self(proto::left(e))) + { + // Ignore the left node, it's *this, just subtract the right: + do_subtract(proto::right(e), typename proto::tag_of::type()); + } + else if(br && is_self(proto::right(e))) + { + // Ignore the right node, it's *this, just subtract the left and negate the result: + do_subtract(proto::left(e), typename proto::tag_of::type()); + m_backend.negate(); + } + else if(bl || br) + { + self_type temp(e); + temp.m_backend.swap(this->m_backend); + } + else if(left_depth >= right_depth) + { + do_assign(proto::left(e), typename proto::tag_of::type()); + do_subtract(proto::right(e), typename proto::tag_of::type()); + } + else + { + do_assign(proto::right(e), typename proto::tag_of::type()); + do_subtract(proto::left(e), typename proto::tag_of::type()); + m_backend.negate(); + } + } + template + void do_assign(const Exp& e, const proto::tag::multiplies&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + + static int const left_depth = boost::result_of::type::value; + static int const right_depth = boost::result_of::type::value; + + bool bl = contains_self(proto::left(e)); + bool br = contains_self(proto::right(e)); + + if(bl && is_self(proto::left(e))) + { + // Ignore the left node, it's *this, just add the right: + do_multiplies(proto::right(e), typename proto::tag_of::type()); + } + else if(br && is_self(proto::right(e))) + { + // Ignore the right node, it's *this, just add the left: + do_multiplies(proto::left(e), typename proto::tag_of::type()); + } + else if(bl || br) + { + self_type temp(e); + temp.m_backend.swap(this->m_backend); + } + else if(left_depth >= right_depth) + { + do_assign(proto::left(e), typename proto::tag_of::type()); + do_multiplies(proto::right(e), typename proto::tag_of::type()); + } + else + { + do_assign(proto::right(e), typename proto::tag_of::type()); + do_multiplies(proto::left(e), typename proto::tag_of::type()); + } + } + template + void do_assign(const Exp& e, const proto::tag::divides&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + + static int const left_depth = boost::result_of::type::value; + static int const right_depth = boost::result_of::type::value; + + bool bl = contains_self(proto::left(e)); + bool br = contains_self(proto::right(e)); + + if(bl && is_self(proto::left(e))) + { + // Ignore the left node, it's *this, just add the right: + do_divide(proto::right(e), typename proto::tag_of::type()); + } + else if(bl || br) + { + self_type temp(e); + temp.m_backend.swap(this->m_backend); + } + else + { + do_assign(proto::left(e), typename proto::tag_of::type()); + do_divide(proto::right(e), typename proto::tag_of::type()); + } + } + template + void do_assign(const Exp& e, const proto::tag::modulus&) + { + // + // This operation is only valid for integer backends: + // + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + + static int const left_depth = boost::result_of::type::value; + static int const right_depth = boost::result_of::type::value; + + bool bl = contains_self(proto::left(e)); + bool br = contains_self(proto::right(e)); + + if(bl && is_self(proto::left(e))) + { + // Ignore the left node, it's *this, just add the right: + do_modulus(proto::right(e), typename proto::tag_of::type()); + } + else if(bl || br) + { + self_type temp(e); + temp.m_backend.swap(this->m_backend); + } + else + { + do_assign(proto::left(e), typename proto::tag_of::type()); + do_modulus(proto::right(e), typename proto::tag_of::type()); + } + } + template + void do_assign(const Exp& e, const proto::tag::terminal&) + { + if(!is_self(e)) + { + m_backend = canonical_value(proto::value(e)); + } + } + + template + void do_add(const Exp& e, const proto::tag::terminal&) + { + typedef typename proto::result_of::value::type t1; + typedef typename remove_reference::type t2; + typedef typename remove_cv::type t3; + typedef typename detail::canonical::type t4; + typedef typename is_convertible::type tag; + do_add_value(canonical_value(proto::value(e)), tag()); + } + + template + void do_add_value(const V& v, const mpl::false_&) + { + m_backend += v; + } + template + void do_add_value(const V& v, const mpl::true_&) + { + self_type temp(v); + m_backend += temp.m_backend; + } + + template + void do_add(const Exp& e, const proto::tag::unary_plus&) + { + typedef typename proto::result_of::left::type left_type; + do_add(proto::left(e), typename proto::tag_of::type()); + } + + template + void do_add(const Exp& e, const proto::tag::negate&) + { + typedef typename proto::result_of::left::type left_type; + do_subtract(proto::left(e), typename proto::tag_of::type()); + } + + template + void do_add(const Exp& e, const proto::tag::plus&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_add(proto::left(e), typename proto::tag_of::type()); + do_add(proto::right(e), typename proto::tag_of::type()); + } + + template + void do_add(const Exp& e, const proto::tag::minus&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_add(proto::left(e), typename proto::tag_of::type()); + do_subtract(proto::right(e), typename proto::tag_of::type()); + } + + template + void do_add(const Exp& e, const unknown&) + { + self_type temp(e); + do_add(temp, proto::tag::terminal()); + } + + template + void do_subtract(const Exp& e, const proto::tag::terminal&) + { + typedef typename proto::result_of::value::type t1; + typedef typename remove_reference::type t2; + typedef typename remove_cv::type t3; + typedef typename detail::canonical::type t4; + typedef typename is_convertible::type tag; + do_subtract_value(canonical_value(proto::value(e)), tag()); + } + + template + void do_subtract_value(const V& v, const mpl::false_&) + { + m_backend -= v; + } + template + void do_subtract_value(const V& v, const mpl::true_&) + { + self_type temp(v); + m_backend -= temp.m_backend; + } + + template + void do_subtract(const Exp& e, const proto::tag::unary_plus&) + { + typedef typename proto::result_of::left::type left_type; + do_subtract(proto::left(e), typename proto::tag_of::type()); + } + + template + void do_subtract(const Exp& e, const proto::tag::negate&) + { + typedef typename proto::result_of::left::type left_type; + do_add(proto::left(e), typename proto::tag_of::type()); + } + + template + void do_subtract(const Exp& e, const proto::tag::plus&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_subtract(proto::left(e), typename proto::tag_of::type()); + do_subtract(proto::right(e), typename proto::tag_of::type()); + } + + template + void do_subtract(const Exp& e, const proto::tag::minus&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_subtract(proto::left(e), typename proto::tag_of::type()); + do_add(proto::right(e), typename proto::tag_of::type()); + } + + template + void do_subtract(const Exp& e, const unknown&) + { + self_type temp(e); + do_subtract(temp, proto::tag::terminal()); + } + + template + void do_multiplies(const Exp& e, const proto::tag::terminal&) + { + typedef typename proto::result_of::value::type t1; + typedef typename remove_reference::type t2; + typedef typename remove_cv::type t3; + typedef typename detail::canonical::type t4; + typedef typename is_convertible::type tag; + do_multiplies_value(canonical_value(proto::value(e)), tag()); + } + + template + void do_multiplies_value(const Val& v, const mpl::false_&) + { + m_backend *= v; + } + + template + void do_multiplies_value(const Val& e, const mpl::true_&) + { + self_type temp(e); + m_backend *= temp.m_backend; + } + + template + void do_multiplies(const Exp& e, const proto::tag::unary_plus&) + { + typedef typename proto::result_of::left::type left_type; + do_multiplies(proto::left(e), typename proto::tag_of::type()); + } + + template + void do_multiplies(const Exp& e, const proto::tag::negate&) + { + typedef typename proto::result_of::left::type left_type; + do_multiplies(proto::left(e), typename proto::tag_of::type()); + m_backend.negate(); + } + + template + void do_multiplies(const Exp& e, const proto::tag::multiplies&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_multiplies(proto::left(e), typename proto::tag_of::type()); + do_multiplies(proto::right(e), typename proto::tag_of::type()); + } + + template + void do_multiplies(const Exp& e, const proto::tag::divides&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_multiplies(proto::left(e), typename proto::tag_of::type()); + do_divide(proto::right(e), typename proto::tag_of::type()); + } + + template + void do_multiplies(const Exp& e, const unknown&) + { + self_type temp(e); + m_backend *= temp.m_backend; + } + + template + void do_divide(const Exp& e, const proto::tag::terminal&) + { + typedef typename proto::result_of::value::type t1; + typedef typename remove_reference::type t2; + typedef typename remove_cv::type t3; + typedef typename detail::canonical::type t4; + typedef typename is_convertible::type tag; + do_divide_value(canonical_value(proto::value(e)), tag()); + } + + template + void do_divide_value(const Val& v, const mpl::false_&) + { + m_backend /= v; + } + + template + void do_divide_value(const Val& e, const mpl::true_&) + { + self_type temp(e); + m_backend /= temp.m_backend; + } + + template + void do_divide(const Exp& e, const proto::tag::unary_plus&) + { + typedef typename proto::result_of::left::type left_type; + do_divide(proto::left(e), typename proto::tag_of::type()); + } + + template + void do_divide(const Exp& e, const proto::tag::negate&) + { + typedef typename proto::result_of::left::type left_type; + do_divide(proto::left(e), typename proto::tag_of::type()); + m_backend.negate(); + } + + template + void do_divide(const Exp& e, const proto::tag::multiplies&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_divide(proto::left(e), typename proto::tag_of::type()); + do_divide(proto::right(e), typename proto::tag_of::type()); + } + + template + void do_divide(const Exp& e, const proto::tag::divides&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_divide(proto::left(e), typename proto::tag_of::type()); + do_multiplies(proto::right(e), typename proto::tag_of::type()); + } + + template + void do_divide(const Exp& e, const unknown&) + { + self_type temp(e); + m_backend /= temp.m_backend; + } + + template + void do_modulus(const Exp& e, const proto::tag::terminal&) + { + typedef typename proto::result_of::value::type t1; + typedef typename remove_reference::type t2; + typedef typename remove_cv::type t3; + typedef typename detail::canonical::type t4; + typedef typename is_convertible::type tag; + do_modulus_value(canonical_value(proto::value(e)), tag()); + } + + template + void do_modulus_value(const Val& v, const mpl::false_&) + { + m_backend %= v; + } + + template + void do_modulus_value(const Val& e, const mpl::true_&) + { + self_type temp(e); + m_backend %= temp.m_backend; + } + + template + void do_modulus(const Exp& e, const Unknown&) + { + self_type temp(e); + do_modulus_value(canonical_value(proto::value(temp)), mpl::false_()); + } + + // Tests if the expression contains a reference to *this: + template + bool contains_self(const Exp& e)const + { + return contains_self(e, mpl::int_::value>()); + } + template + bool contains_self(const Exp& e, mpl::int_<0> const&)const + { + return is_really_self(proto::value(e)); + } + template + bool contains_self(const Exp& e, mpl::int_<1> const&)const + { + typedef typename proto::result_of::child_c::type child_type; + return contains_self(proto::child_c<0>(e), mpl::int_::value>()); + } + template + bool contains_self(const Exp& e, mpl::int_<2> const&)const + { + typedef typename proto::result_of::child_c::type child0_type; + typedef typename proto::result_of::child_c::type child1_type; + return contains_self(proto::child_c<0>(e), mpl::int_::value>()) || contains_self(proto::child_c<1>(e), mpl::int_::value>()); + } + + // Test if the expression is a reference to *this: + template + bool is_self(const Exp& e)const + { + return is_self(e, mpl::int_::value>()); + } + template + bool is_self(const Exp& e, mpl::int_<0> const&)const + { + return is_really_self(proto::value(e)); + } + template + bool is_self(const Exp& e, mpl::int_ const&)const + { + return false; + } + + template + bool is_really_self(const Val&)const { return false; } + bool is_really_self(const self_type* v)const + { + return v == this; + } + bool is_really_self(self_type* v)const + { + return v == this; + } + + static const Backend& canonical_value(const self_type& v){ return v.m_backend; } + static const Backend& canonical_value(const self_type* v){ return v->m_backend; } + static const Backend& canonical_value(self_type* v){ return v->m_backend; } + template + static typename detail::canonical::type canonical_value(const V& v){ return v; } + static typename detail::canonical::type canonical_value(const std::string& v){ return v.c_str(); } + + Backend m_backend; +}; + +namespace detail +{ + +template +struct combine_expression_type +{ + typedef void type; +}; + +template +struct combine_expression_type, boost::math::big_number > +{ + typedef boost::math::big_number type; +}; + +template +struct combine_expression_type, Exp> +{ + typedef boost::math::big_number type; +}; + +template +struct combine_expression_type > +{ + typedef boost::math::big_number type; +}; + +template +struct is_big_number : public mpl::false_{}; +template +struct is_big_number > : public mpl::true_{}; +template +struct is_big_number_exp : public mpl::false_{}; +template +struct is_big_number_exp > : public mpl::true_{}; + + +template +struct expression_type_imp; + +template +struct expression_type_imp +{ + typedef typename remove_pointer::type>::type type; +}; + +template +struct expression_type_imp +{ + typedef typename proto::result_of::left::type nested_type; + typedef typename expression_type_imp::value>::type type; +}; + +template +struct expression_type_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename expression_type_imp::value>::type left_result; + typedef typename expression_type_imp::value>::type right_result; + typedef typename combine_expression_type::type type; +}; + +template +struct expression_type +{ + typedef typename expression_type_imp::value>::type type; +}; + +template +inline int big_number_compare(const big_number& a, const big_number& b) +{ + return a.compare(b); +} + +template +inline int big_number_compare(const big_number& a, const big_number_exp& b) +{ + return a.compare(big_number(b)); +} + +template +inline int big_number_compare(const big_number_exp& a, const big_number& b) +{ + return -b.compare(big_number(a)); +} + +template +inline int big_number_compare(const big_number& a, const Val b) +{ + return a.compare(b); +} + +template +inline int big_number_compare(const Val a, const big_number& b) +{ + return -b.compare(a); +} + +template +inline int big_number_compare(const big_number_exp& a, const big_number_exp& b) +{ + typedef typename expression_type::type real1; + typedef typename expression_type::type real2; + return real1(a).compare(real2(b)); +} + +template +inline typename enable_if, int>::type big_number_compare(const big_number_exp& a, const Val b) +{ + typedef typename expression_type::type real; + real t(a); + return t.compare(b); +} + +template +inline typename enable_if, int>::type big_number_compare(const Val a, const big_number_exp& b) +{ + typedef typename expression_type::type real; + return -real(b).compare(a); +} + +template +struct is_valid_comparison_imp +{ + typedef typename mpl::or_< + is_big_number, + is_big_number_exp + >::type is1; + typedef typename mpl::or_< + is_big_number, + is_big_number_exp + >::type is2; + typedef typename mpl::or_< + mpl::and_< + is1, + mpl::or_< + is2, + is_arithmetic + > + >, + mpl::and_< + is2, + mpl::or_< + is1, + is_arithmetic + > + > + >::type type; +}; + +template +struct is_valid_comparison : public boost::math::detail::is_valid_comparison_imp::type {}; + +} + + +template +inline typename boost::enable_if, bool>::type + operator == (const Exp1& a, const Exp2& b) +{ + return 0 == detail::big_number_compare(a, b); +} + +template +inline typename boost::enable_if, bool>::type + operator != (const Exp1& a, const Exp2& b) +{ + return 0 != detail::big_number_compare(a, b); +} + +template +inline typename boost::enable_if, bool>::type + operator <= (const Exp1& a, const Exp2& b) +{ + return 0 >= detail::big_number_compare(a, b); +} + +template +inline typename boost::enable_if, bool>::type + operator < (const Exp1& a, const Exp2& b) +{ + return 0 > detail::big_number_compare(a, b); +} + +template +inline typename boost::enable_if, bool>::type + operator >= (const Exp1& a, const Exp2& b) +{ + return 0 <= detail::big_number_compare(a, b); +} + +template +inline typename boost::enable_if, bool>::type + operator > (const Exp1& a, const Exp2& b) +{ + return 0 < detail::big_number_compare(a, b); +} + +template +std::ostream& operator << (std::ostream& os, const big_number& r) +{ + return os << r.str(); +} + +template +std::istream& operator >> (std::istream& is, big_number& r) +{ + std::string s; + is >> s; + r = s; + return is; +} + +}} // namespaces + +#endif diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp new file mode 100644 index 00000000..a82674e5 --- /dev/null +++ b/include/boost/math/big_number/gmp.hpp @@ -0,0 +1,691 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_ER_GMP_BACKEND_HPP +#define BOOST_MATH_ER_GMP_BACKEND_HPP + +#include +#include +#include +#include +#include +#include + +namespace boost{ namespace math{ + +template +struct gmp_real; + +namespace detail{ + +template +struct gmp_real_imp +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + gmp_real_imp(){} + + gmp_real_imp(const gmp_real_imp& o) + { + mpf_init_set(m_data, o.m_data); + } + gmp_real_imp& operator = (const gmp_real_imp& o) + { + mpf_set(m_data, o.m_data); + return *this; + } + gmp_real_imp& operator = (boost::uintmax_t i) + { + boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned shift = 0; + mpf_t t; + mpf_init2(m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_init2(t, ((digits10 + 1) * 1000L) / 301L); + while(i) + { + mpf_set_ui(t, static_cast(i & mask)); + if(shift) + mpf_mul_2exp(t, t, shift); + mpf_add(m_data, m_data, t); + shift += std::numeric_limits::digits; + i >>= std::numeric_limits::digits; + } + mpf_clear(t); + return *this; + } + gmp_real_imp& operator = (boost::intmax_t i) + { + bool neg = i < 0; + *this = static_cast(std::abs(i)); + if(neg) + mpf_neg(m_data, m_data); + return *this; + } + gmp_real_imp& operator = (unsigned long i) + { + mpf_set_ui(m_data, i); + return *this; + } + gmp_real_imp& operator = (long i) + { + mpf_set_si(m_data, i); + return *this; + } + gmp_real_imp& operator = (double d) + { + mpf_set_d(m_data, d); + return *this; + } + gmp_real_imp& operator = (long double a) + { + using std::frexp; + using std::ldexp; + using std::floor; + + if (a == 0) { + mpf_set_si(m_data, 0); + return *this; + } + + if (a == 1) { + mpf_set_si(m_data, 1); + return *this; + } + + BOOST_ASSERT(!(boost::math::isinf)(a)); + BOOST_ASSERT(!(boost::math::isnan)(a)); + + int e; + long double f, term; + mpf_init_set_ui(m_data, 0u); + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + mpf_mul_2exp(m_data, m_data, shift); + if(term > 0) + mpf_add_ui(m_data, m_data, static_cast(term)); + else + mpf_sub_ui(m_data, m_data, static_cast(-term)); + f -= term; + } + if(e > 0) + mpf_mul_2exp(m_data, m_data, e); + else if(e < 0) + mpf_div_2exp(m_data, m_data, -e); + return *this; + } + gmp_real_imp& operator = (const char* s) + { + mpf_set_str(m_data, s, 10); + return *this; + } + gmp_real_imp& operator += (const gmp_real& o) + { + mpf_add(m_data, m_data, o.m_data); + return *this; + } + template + gmp_real_imp& operator += (V v) + { + gmp_real d; + d = v; + return *this += d; + } + gmp_real_imp& operator -= (const gmp_real& o) + { + mpf_sub(m_data, m_data, o.m_data); + return *this; + } + template + gmp_real_imp& operator -= (V v) + { + gmp_real d; + d = v; + return *this -= d; + } + gmp_real_imp& operator *= (const gmp_real& o) + { + mpf_mul(m_data, m_data, o.m_data); + return *this; + } + template + gmp_real_imp& operator *= (V v) + { + gmp_real d; + d = v; + return *this *= d; + } + gmp_real_imp& operator /= (const gmp_real& o) + { + mpf_div(m_data, m_data, o.m_data); + return *this; + } + template + gmp_real_imp& operator /= (V v) + { + gmp_real d; + d = v; + return *this /= d; + } + gmp_real_imp& operator += (unsigned long i) + { + mpf_add_ui(m_data, m_data, i); + return *this; + } + gmp_real_imp& operator -= (unsigned long i) + { + mpf_sub_ui(m_data, m_data, i); + return *this; + } + gmp_real_imp& operator *= (unsigned long i) + { + mpf_mul_ui(m_data, m_data, i); + return *this; + } + gmp_real_imp& operator /= (unsigned long i) + { + mpf_div_ui(m_data, m_data, i); + return *this; + } + gmp_real_imp& operator += (long i) + { + if(i > 0) + mpf_add_ui(m_data, m_data, i); + else + mpf_sub_ui(m_data, m_data, std::abs(i)); + return *this; + } + gmp_real_imp& operator -= (long i) + { + if(i > 0) + mpf_sub_ui(m_data, m_data, i); + else + mpf_add_ui(m_data, m_data, std::abs(i)); + return *this; + } + gmp_real_imp& operator *= (long i) + { + mpf_mul_ui(m_data, m_data, std::abs(i)); + if(i < 0) + mpf_neg(m_data, m_data); + return *this; + } + gmp_real_imp& operator /= (long i) + { + mpf_div_ui(m_data, m_data, std::abs(i)); + if(i < 0) + mpf_neg(m_data, m_data); + return *this; + } + void swap(gmp_real_imp& o) + { + mpf_swap(m_data, o.m_data); + } + std::string str()const + { + mp_exp_t e; + void *(*alloc_func_ptr) (size_t); + void *(*realloc_func_ptr) (void *, size_t, size_t); + void (*free_func_ptr) (void *, size_t); + const char* ps = mpf_get_str (0, &e, 10, 0, m_data); + std::string s("0."); + if(ps[0] == '-') + { + s.insert(0, ps, 1); + s += ps + 1; + } + else + { + s += ps; + } + s += "e"; + s += boost::lexical_cast(e); + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); + return s; + } + ~gmp_real_imp() + { + mpf_clear(m_data); + } + void negate() + { + mpf_neg(m_data, m_data); + } + int compare(const gmp_real& o)const + { + return mpf_cmp(m_data, o.m_data); + } + int compare(long i)const + { + return mpf_cmp_si(m_data, i); + } + int compare(unsigned long i)const + { + return mpf_cmp_ui(m_data, i); + } + template + int compare(V v)const + { + gmp_real d; + d = v; + return compare(d); + } +protected: + mpf_t m_data; +}; + +} // namespace detail + +template +struct gmp_real : public detail::gmp_real_imp +{ + gmp_real() + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + } + gmp_real(const gmp_real& o) : gmp_real_imp(o) {} + + gmp_real& operator=(const gmp_real& o) + { + *static_cast*>(this) = static_cast const&>(o); + return *this; + } + + template + gmp_real& operator=(const V& v) + { + *static_cast*>(this) = v; + return *this; + } +}; + +template <> +struct gmp_real<0> : public detail::gmp_real_imp<0> +{ + gmp_real() + { + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + } + gmp_real(unsigned digits10) + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + } + gmp_real(const gmp_real& o) : gmp_real_imp(o) {} + gmp_real(const gmp_real& o, unsigned digits10) + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + *this = o; + } + + gmp_real& operator=(const gmp_real& o) + { + *static_cast*>(this) = static_cast const&>(o); + return *this; + } + + template + gmp_real& operator=(const V& v) + { + *static_cast*>(this) = v; + return *this; + } + static unsigned default_precision() + { + return get_default_precision(); + } + static void default_precision(unsigned v) + { + get_default_precision() = v; + } + unsigned precision()const + { + return mpf_get_prec(this->m_data) * 301L / 1000 - 1; + } + void precision(unsigned digits10) + { + mpf_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); + } +private: + static unsigned& get_default_precision() + { + static unsigned val = 50; + return val; + } +}; + +struct gmp_int +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + gmp_int() + { + mpz_init(this->m_data); + } + gmp_int(const gmp_int& o) + { + mpz_init_set(m_data, o.m_data); + } + gmp_int& operator = (const gmp_int& o) + { + mpz_set(m_data, o.m_data); + return *this; + } + gmp_int& operator = (boost::uintmax_t i) + { + boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned shift = 0; + mpz_t t; + mpz_init(m_data); + mpz_init(t); + while(i) + { + mpz_set_ui(t, static_cast(i & mask)); + if(shift) + mpz_mul_2exp(t, t, shift); + mpz_add(m_data, m_data, t); + shift += std::numeric_limits::digits; + i >>= std::numeric_limits::digits; + } + mpz_clear(t); + return *this; + } + gmp_int& operator = (boost::intmax_t i) + { + bool neg = i < 0; + *this = static_cast(std::abs(i)); + if(neg) + mpz_neg(m_data, m_data); + return *this; + } + gmp_int& operator = (unsigned long i) + { + mpz_set_ui(m_data, i); + return *this; + } + gmp_int& operator = (long i) + { + mpz_set_si(m_data, i); + return *this; + } + gmp_int& operator = (double d) + { + mpz_set_d(m_data, d); + return *this; + } + gmp_int& operator = (long double a) + { + using std::frexp; + using std::ldexp; + using std::floor; + + if (a == 0) { + mpz_set_si(m_data, 0); + return *this; + } + + if (a == 1) { + mpz_set_si(m_data, 1); + return *this; + } + + BOOST_ASSERT(!(boost::math::isinf)(a)); + BOOST_ASSERT(!(boost::math::isnan)(a)); + + int e; + long double f, term; + mpz_init_set_ui(m_data, 0u); + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + mpz_mul_2exp(m_data, m_data, shift); + if(term > 0) + mpz_add_ui(m_data, m_data, static_cast(term)); + else + mpz_sub_ui(m_data, m_data, static_cast(-term)); + f -= term; + } + if(e > 0) + mpz_mul_2exp(m_data, m_data, e); + else if(e < 0) + mpz_div_2exp(m_data, m_data, -e); + return *this; + } + gmp_int& operator = (const char* s) + { + mpz_set_str(m_data, s, 10); + return *this; + } + gmp_int& operator += (const gmp_int& o) + { + mpz_add(m_data, m_data, o.m_data); + return *this; + } + template + gmp_int& operator += (V v) + { + gmp_int d; + d = v; + return *this += d; + } + gmp_int& operator -= (const gmp_int& o) + { + mpz_sub(m_data, m_data, o.m_data); + return *this; + } + template + gmp_int& operator -= (V v) + { + gmp_int d; + d = v; + return *this -= d; + } + gmp_int& operator *= (const gmp_int& o) + { + mpz_mul(m_data, m_data, o.m_data); + return *this; + } + template + gmp_int& operator *= (V v) + { + gmp_int d; + d = v; + return *this *= d; + } + gmp_int& operator /= (const gmp_int& o) + { + mpz_div(m_data, m_data, o.m_data); + return *this; + } + template + gmp_int& operator /= (V v) + { + gmp_int d; + d = v; + return *this /= d; + } + gmp_int& operator %= (const gmp_int& o) + { + bool neg = mpz_sgn(m_data) < 0; + bool neg2 = mpz_sgn(o.m_data) < 0; + mpz_mod(m_data, m_data, o.m_data); + if(neg) + { + if(!neg2) + negate(); + mpz_add(m_data, m_data, o.m_data); + if(!neg2) + negate(); + } + return *this; + } + template + gmp_int& operator %= (V v) + { + gmp_int d; + d = v; + return *this %= d; + } + gmp_int& operator += (unsigned long i) + { + mpz_add_ui(m_data, m_data, i); + return *this; + } + gmp_int& operator -= (unsigned long i) + { + mpz_sub_ui(m_data, m_data, i); + return *this; + } + gmp_int& operator *= (unsigned long i) + { + mpz_mul_ui(m_data, m_data, i); + return *this; + } + gmp_int& operator %= (unsigned long i) + { + bool neg = mpz_sgn(m_data) < 0; + mpz_mod_ui(m_data, m_data, i); + if(neg) + { + negate(); + mpz_add_ui(m_data, m_data, i); + negate(); + } + return *this; + } + gmp_int& operator /= (unsigned long i) + { + mpz_div_ui(m_data, m_data, i); + return *this; + } + gmp_int& operator += (long i) + { + if(i > 0) + mpz_add_ui(m_data, m_data, i); + else + mpz_sub_ui(m_data, m_data, std::abs(i)); + return *this; + } + gmp_int& operator -= (long i) + { + if(i > 0) + mpz_sub_ui(m_data, m_data, i); + else + mpz_add_ui(m_data, m_data, std::abs(i)); + return *this; + } + gmp_int& operator *= (long i) + { + mpz_mul_ui(m_data, m_data, std::abs(i)); + if(i < 0) + mpz_neg(m_data, m_data); + return *this; + } + gmp_int& operator %= (long i) + { + bool neg = mpz_sgn(m_data) < 0; + bool neg2 = i < 0; + mpz_mod_ui(m_data, m_data, std::abs(i)); + if(neg) + { + if(!neg2) + { + negate(); + mpz_add_ui(m_data, m_data, std::abs(i)); + negate(); + } + else + { + mpz_sub_ui(m_data, m_data, std::abs(i)); + } + } + return *this; + } + gmp_int& operator /= (long i) + { + mpz_div_ui(m_data, m_data, std::abs(i)); + if(i < 0) + mpz_neg(m_data, m_data); + return *this; + } + void swap(gmp_int& o) + { + mpz_swap(m_data, o.m_data); + } + std::string str()const + { + void *(*alloc_func_ptr) (size_t); + void *(*realloc_func_ptr) (void *, size_t, size_t); + void (*free_func_ptr) (void *, size_t); + const char* ps = mpz_get_str (0, 10, m_data); + std::string s = ps; + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); + return s; + } + ~gmp_int() + { + mpz_clear(m_data); + } + void negate() + { + mpz_neg(m_data, m_data); + } + int compare(const gmp_int& o)const + { + return mpz_cmp(m_data, o.m_data); + } + int compare(long i)const + { + return mpz_cmp_si(m_data, i); + } + int compare(unsigned long i)const + { + return mpz_cmp_ui(m_data, i); + } + template + int compare(V v)const + { + gmp_int d; + d = v; + return compare(d); + } +protected: + mpz_t m_data; +}; + +template<> +struct is_extended_integer : public mpl::true_ {}; + +typedef big_number > mpf_real_50; +typedef big_number > mpf_real_100; +typedef big_number > mpf_real_500; +typedef big_number > mpf_real_1000; +typedef big_number > mpf_real; +typedef big_number mpz_int; + +}} // namespaces + +#endif diff --git a/include/boost/math/concepts/big_number_architypes.hpp b/include/boost/math/concepts/big_number_architypes.hpp new file mode 100644 index 00000000..f7c196e1 --- /dev/null +++ b/include/boost/math/concepts/big_number_architypes.hpp @@ -0,0 +1,309 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MATH_CONCEPTS_ER_HPP +#define BOOST_MATH_CONCEPTS_ER_HPP + +#include +#include +#include +#include +#include + +namespace boost{ +namespace math{ +namespace concepts{ + +struct big_number_backend_real_architype +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + big_number_backend_real_architype() + { + std::cout << "Default construct" << std::endl; + } + big_number_backend_real_architype(const big_number_backend_real_architype& o) + { + std::cout << "Copy construct" << std::endl; + m_value = o.m_value; + } + big_number_backend_real_architype& operator = (const big_number_backend_real_architype& o) + { + m_value = o.m_value; + std::cout << "Assignment (" << m_value << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (boost::uintmax_t i) + { + m_value = i; + std::cout << "UInt Assignment (" << i << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (boost::intmax_t i) + { + m_value = i; + std::cout << "Int Assignment (" << i << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (unsigned i) + { + m_value = i; + std::cout << "UInt Assignment (" << i << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (int i) + { + m_value = i; + std::cout << "Int Assignment (" << i << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (double d) + { + m_value = d; + std::cout << "double Assignment (" << d << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (long double d) + { + m_value = d; + std::cout << "long double Assignment (" << d << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (const char* s) + { + m_value = boost::lexical_cast(s); + std::cout << "const char* Assignment (" << s << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator += (const big_number_backend_real_architype& o) + { + std::cout << "Addition (" << m_value << " += " << o.m_value << ")" << std::endl; + m_value += o.m_value; + return *this; + } + big_number_backend_real_architype& operator -= (const big_number_backend_real_architype& o) + { + std::cout << "Subtraction (" << m_value << " -= " << o.m_value << ")" << std::endl; + m_value -= o.m_value; + return *this; + } + big_number_backend_real_architype& operator *= (const big_number_backend_real_architype& o) + { + std::cout << "Multiplication (" << m_value << " *= " << o.m_value << ")" << std::endl; + m_value *= o.m_value; + return *this; + } + big_number_backend_real_architype& operator /= (const big_number_backend_real_architype& o) + { + std::cout << "Division (" << m_value << " /= " << o.m_value << ")" << std::endl; + m_value /= o.m_value; + return *this; + } + big_number_backend_real_architype& operator += (boost::uintmax_t i) + { + std::cout << "UIntmax_t Addition (" << m_value << " += " << i << ")" << std::endl; + m_value += i; + return *this; + } + big_number_backend_real_architype& operator -= (boost::uintmax_t i) + { + std::cout << "UIntmax_t Subtraction (" << m_value << " -= " << i << ")" << std::endl; + m_value -= i; + return *this; + } + big_number_backend_real_architype& operator *= (boost::uintmax_t i) + { + std::cout << "UIntmax_t Multiplication (" << m_value << " *= " << i << ")" << std::endl; + m_value *= i; + return *this; + } + big_number_backend_real_architype& operator /= (boost::uintmax_t i) + { + std::cout << "UIntmax_t Division (" << m_value << " /= " << i << ")" << std::endl; + m_value /= i; + return *this; + } + big_number_backend_real_architype& operator += (boost::intmax_t i) + { + std::cout << "Intmax_t Addition (" << m_value << " += " << i << ")" << std::endl; + m_value += i; + return *this; + } + big_number_backend_real_architype& operator -= (boost::intmax_t i) + { + std::cout << "Intmax_t Subtraction (" << m_value << " -= " << i << ")" << std::endl; + m_value -= i; + return *this; + } + big_number_backend_real_architype& operator *= (boost::intmax_t i) + { + std::cout << "Intmax_t Multiplication (" << m_value << " *= " << i << ")" << std::endl; + m_value *= i; + return *this; + } + big_number_backend_real_architype& operator /= (boost::intmax_t i) + { + std::cout << "Intmax_t Division (" << m_value << " /= " << i << ")" << std::endl; + m_value /= i; + return *this; + } + big_number_backend_real_architype& operator += (unsigned i) + { + std::cout << "UInt Addition (" << m_value << " += " << i << ")" << std::endl; + m_value += i; + return *this; + } + big_number_backend_real_architype& operator -= (unsigned i) + { + std::cout << "UInt Subtraction (" << m_value << " -= " << i << ")" << std::endl; + m_value -= i; + return *this; + } + big_number_backend_real_architype& operator *= (unsigned i) + { + std::cout << "UInt Multiplication (" << m_value << " *= " << i << ")" << std::endl; + m_value *= i; + return *this; + } + big_number_backend_real_architype& operator /= (unsigned i) + { + std::cout << "UInt Division (" << m_value << " /= " << i << ")" << std::endl; + m_value /= i; + return *this; + } + big_number_backend_real_architype& operator += (int i) + { + std::cout << "Int Addition (" << m_value << " += " << i << ")" << std::endl; + m_value += i; + return *this; + } + big_number_backend_real_architype& operator -= (int i) + { + std::cout << "Int Subtraction (" << m_value << " -= " << i << ")" << std::endl; + m_value -= i; + return *this; + } + big_number_backend_real_architype& operator *= (int i) + { + std::cout << "Int Multiplication (" << m_value << " *= " << i << ")" << std::endl; + m_value *= i; + return *this; + } + big_number_backend_real_architype& operator /= (int i) + { + std::cout << "Int Division (" << m_value << " /= " << i << ")" << std::endl; + m_value /= i; + return *this; + } + big_number_backend_real_architype& operator += (double d) + { + std::cout << "double Addition (" << m_value << " += " << d << ")" << std::endl; + m_value += d; + return *this; + } + big_number_backend_real_architype& operator -= (double d) + { + std::cout << "double Subtraction (" << m_value << " -= " << d << ")" << std::endl; + m_value -= d; + return *this; + } + big_number_backend_real_architype& operator *= (double d) + { + std::cout << "double Multiplication (" << m_value << " *= " << d << ")" << std::endl; + m_value *= d; + return *this; + } + big_number_backend_real_architype& operator /= (double d) + { + std::cout << "double Division (" << m_value << " /= " << d << ")" << std::endl; + m_value /= d; + return *this; + } + big_number_backend_real_architype& operator += (long double d) + { + std::cout << "long double Addition (" << m_value << " += " << d << ")" << std::endl; + m_value += d; + return *this; + } + big_number_backend_real_architype& operator -= (long double d) + { + std::cout << "long double Subtraction (" << m_value << " -= " << d << ")" << std::endl; + m_value -= d; + return *this; + } + big_number_backend_real_architype& operator *= (long double d) + { + std::cout << "long double Multiplication (" << m_value << " *= " << d << ")" << std::endl; + m_value *= d; + return *this; + } + big_number_backend_real_architype& operator /= (long double d) + { + std::cout << "long double Division (" << m_value << " /= " << d << ")" << std::endl; + m_value /= d; + return *this; + } + void swap(big_number_backend_real_architype& o) + { + std::cout << "Swapping (" << m_value << " with " << o.m_value << ")" << std::endl; + std::swap(m_value, o.m_value); + } + std::string str()const + { + std::string s(boost::lexical_cast(m_value)); + std::cout << "Converting to string (" << s << ")" << std::endl; + return s; + } + void negate() + { + std::cout << "Negating (" << m_value << ")" << std::endl; + m_value = -m_value; + } + int compare(const big_number_backend_real_architype& o)const + { + std::cout << "Comparison" << std::endl; + return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); + } + int compare(int i)const + { + std::cout << "Comparison with int" << std::endl; + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(unsigned i)const + { + std::cout << "Comparison with unsigned" << std::endl; + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(boost::intmax_t i)const + { + std::cout << "Comparison with int" << std::endl; + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(boost::uintmax_t i)const + { + std::cout << "Comparison with unsigned" << std::endl; + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(double d)const + { + std::cout << "Comparison with double" << std::endl; + return m_value > d ? 1 : (m_value < d ? -1 : 0); + } + int compare(long double d)const + { + std::cout << "Comparison with long double" << std::endl; + return m_value > d ? 1 : (m_value < d ? -1 : 0); + } +private: + long double m_value; +}; + +typedef boost::math::big_number big_number_real_architype; + +}}} // namespaces + +#endif diff --git a/math/test/big_number_concept_check.cpp b/math/test/big_number_concept_check.cpp new file mode 100644 index 00000000..f4eaba6e --- /dev/null +++ b/math/test/big_number_concept_check.cpp @@ -0,0 +1,38 @@ + +// Copyright John Maddock 2011. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests two things: that e_float meets our +// conceptual requirements, and that we can instantiate +// all our distributions and special functions on this type. +// +#define BOOST_MATH_ASSERT_UNDEFINED_POLICY false +#define TEST_MPFR + +#ifdef _MSC_VER +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#include + +#include +//#include "compile_test/instantiate.hpp" +/* +void foo() +{ + instantiate(boost::math::ef::e_float()); +} +*/ +int main() +{ + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +} + + diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp new file mode 100644 index 00000000..1109c3d3 --- /dev/null +++ b/math/test/test_arithmetic.cpp @@ -0,0 +1,443 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) +# define TEST_MPF50 +# define TEST_MPF +# define TEST_BACKEND +# define TEST_MPZ +#endif + +template +void test_integer_ops(const boost::mpl::false_&){} + +template +void test_integer_ops(const boost::mpl::true_&) +{ + Real a(20); + Real b(7); + BOOST_TEST(a % b == 20 % 7); + BOOST_TEST(a % 7 == 20 % 7); + BOOST_TEST(a % 7u == 20 % 7); + BOOST_TEST(-a % b == -20 % 7); + BOOST_TEST(-a % -b == -20 % -7); + BOOST_TEST(a % -b == 20 % -7); + BOOST_TEST(-a % 7 == -20 % 7); + BOOST_TEST(-a % -7 == -20 % -7); + BOOST_TEST(a % -7 == 20 % -7); + BOOST_TEST(-a % 7u == -20 % 7); + + a = 20; + a %= b; + BOOST_TEST(a == 20 % 7); + a = -20; + a %= b; + BOOST_TEST(a == -20 % 7); + a = 20; + a %= -b; + BOOST_TEST(a == 20 % -7); + a = -20; + a %= -b; + BOOST_TEST(a == -20 % -7); + + a = 20; + a %= 7; + BOOST_TEST(a == 20 % 7); + a = -20; + a %= 7; + BOOST_TEST(a == -20 % 7); + a = 20; + a %= -7; + BOOST_TEST(a == 20 % -7); + a = -20; + a %= -7; + BOOST_TEST(a == -20 % -7); +} + +template +void test_negative_mixed(boost::mpl::true_ const&) +{ + std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; + Num n1 = -static_cast(1uLL << (std::numeric_limits::digits - 1)); + Num n2 = -1; + Num n3 = 0; + Num n4 = -20; + Num n5 = -8; + // Default construct: + BOOST_TEST(Real(n1) == n1); + BOOST_TEST(Real(n2) == n2); + BOOST_TEST(Real(n3) == n3); + BOOST_TEST(Real(n4) == n4); + BOOST_TEST(n1 == Real(n1)); + BOOST_TEST(n2 == Real(n2)); + BOOST_TEST(n3 == Real(n3)); + BOOST_TEST(n4 == Real(n4)); + BOOST_TEST(n1 == boost::lexical_cast(Real(n1))); + BOOST_TEST(n2 == boost::lexical_cast(Real(n2))); + BOOST_TEST(n3 == boost::lexical_cast(Real(n3))); + BOOST_TEST(n4 == boost::lexical_cast(Real(n4))); + // Assignment: + Real r(0); + BOOST_TEST(r != n1); + r = n1; + BOOST_TEST(r == n1); + r = n2; + BOOST_TEST(r == n2); + r = n3; + BOOST_TEST(r == n3); + r = n4; + BOOST_TEST(r == n4); + // Addition: + r = n2; + BOOST_TEST(r + n4 == n2 + n4); + BOOST_TEST(Real(r + n4) == n2 + n4); + r += n4; + BOOST_TEST(r == n2 + n4); + // subtraction: + r = n4; + BOOST_TEST(r - n5 == n4 - n5); + BOOST_TEST(Real(r - n5) == n4 - n5); + r -= n5; + BOOST_TEST(r == n4 - n5); + // Multiplication: + r = n2; + BOOST_TEST(r * n4 == n2 * n4); + BOOST_TEST(Real(r * n4) == n2 * n4); + r *= n4; + BOOST_TEST(r == n2 * n4); + // Division: + r = n1; + BOOST_TEST(r / n5 == n1 / n5); + BOOST_TEST(Real(r / n5) == n1 / n5); + r /= n5; + BOOST_TEST(r == n1 / n5); +} + +template +void test_negative_mixed(boost::mpl::false_ const&) +{ +} + +template +void test_mixed() +{ + std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; + Num n1 = static_cast(1uLL << (std::numeric_limits::digits - 1)); + Num n2 = 1; + Num n3 = 0; + Num n4 = 20; + Num n5 = 8; + // Default construct: + BOOST_TEST(Real(n1) == n1); + BOOST_TEST(Real(n2) == n2); + BOOST_TEST(Real(n3) == n3); + BOOST_TEST(Real(n4) == n4); + BOOST_TEST(n1 == Real(n1)); + BOOST_TEST(n2 == Real(n2)); + BOOST_TEST(n3 == Real(n3)); + BOOST_TEST(n4 == Real(n4)); + BOOST_TEST(n1 == boost::lexical_cast(Real(n1))); + BOOST_TEST(n2 == boost::lexical_cast(Real(n2))); + BOOST_TEST(n3 == boost::lexical_cast(Real(n3))); + BOOST_TEST(n4 == boost::lexical_cast(Real(n4))); + // Assignment: + Real r(0); + BOOST_TEST(r != n1); + r = n1; + BOOST_TEST(r == n1); + r = n2; + BOOST_TEST(r == n2); + r = n3; + BOOST_TEST(r == n3); + r = n4; + BOOST_TEST(r == n4); + // Addition: + r = n2; + BOOST_TEST(r + n4 == n2 + n4); + BOOST_TEST(Real(r + n4) == n2 + n4); + r += n4; + BOOST_TEST(r == n2 + n4); + // subtraction: + r = n4; + BOOST_TEST(r - n5 == n4 - n5); + BOOST_TEST(Real(r - n5) == n4 - n5); + r -= n5; + BOOST_TEST(r == n4 - n5); + // Multiplication: + r = n2; + BOOST_TEST(r * n4 == n2 * n4); + BOOST_TEST(Real(r * n4) == n2 * n4); + r *= n4; + BOOST_TEST(r == n2 * n4); + // Division: + r = n1; + BOOST_TEST(r / n5 == n1 / n5); + BOOST_TEST(Real(r / n5) == n1 / n5); + r /= n5; + BOOST_TEST(r == n1 / n5); + + test_negative_mixed(boost::mpl::bool_::is_signed>()); +} + +template +void test() +{ + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); +#ifdef BOOST_HAS_LONG_LONG + test_mixed(); + test_mixed(); +#endif + test_mixed(); + test_mixed(); + test_mixed(); + // + // Integer only functions: + // + test_integer_ops(boost::math::is_extended_integer()); + // + // Test basic arithmetic: + // + Real a(8); + Real b(64); + Real c(500); + Real d(1024); + BOOST_TEST(a + b == 72); + a += b; + BOOST_TEST(a == 72); + BOOST_TEST(a - b == 8); + a -= b; + BOOST_TEST(a == 8); + BOOST_TEST(a * b == 8*64L); + a *= b; + BOOST_TEST(a == 8*64L); + BOOST_TEST(a / b == 8); + a /= b; + BOOST_TEST(a == 8); + + Real ac(a); + BOOST_TEST(ac == a); + BOOST_TEST(-a == -8); + + ac = a * c; + BOOST_TEST(ac == 8*500L); + + ac = ac + b + c; + BOOST_TEST(ac == 8*500L+64+500); + ac = a; + ac = b + c + ac; + BOOST_TEST(ac == 8+64+500); + ac = ac - b + c; + BOOST_TEST(ac == 8+64+500-64+500); + ac = a; + ac = b + c - ac; + BOOST_TEST(ac == -8+64+500); + ac = a; + ac = ac * b; + BOOST_TEST(ac == 8*64); + ac = a; + ac *= b * ac; + BOOST_TEST(ac == 8*8*64); + ac = b; + ac = ac / a; + BOOST_TEST(ac == 64/8); + ac = b; + ac /= ac / a; + BOOST_TEST(ac == 64 / (64/8)); + ac = a; + ac = b + ac * a; + BOOST_TEST(ac == 64 * 2); + ac = a; + ac = b - ac * a; + BOOST_TEST(ac == 0); + ac = a; + ac = b * (ac + a); + BOOST_TEST(ac == 64 * (16)); + ac = a; + ac = b / (ac * 1); + BOOST_TEST(ac == 64 / 8); + ac = a; + ac = ac + b; + BOOST_TEST(ac == 8 + 64); + ac = a; + ac = a + ac; + BOOST_TEST(ac == 16); + ac = a; + ac = ac - b; + BOOST_TEST(ac == 8 - 64); + ac = a; + ac = a - ac; + BOOST_TEST(ac == 0); + ac = a; + ac += a + b; + BOOST_TEST(ac == 80); + ac = a; + ac += b + a; + BOOST_TEST(ac == 80); + ac = a; + ac -= a + b; + BOOST_TEST(ac == -64); + ac = a; + ac -= b - a; + BOOST_TEST(ac == 16 - 64); + ac = +a; + BOOST_TEST(ac == 8); + ac = -a; + BOOST_TEST(ac == -8); + ac = 8; + ac = a * ac; + BOOST_TEST(ac == 8*8); + ac = a; + ac = ac + "8"; + BOOST_TEST(ac == 16); + ac = a; + ac += +a; + BOOST_TEST(ac == 16); + ac = a; + ac += -a; + BOOST_TEST(ac == 0); + ac = a; + ac += b - a; + BOOST_TEST(ac == 8 + 64-8); + ac = a; + ac += b*c; + BOOST_TEST(ac == 8 + 64 * 500); + ac = a; + ac = ac - "8"; + BOOST_TEST(ac == 0); + ac = a; + ac -= +a; + BOOST_TEST(ac == 0); + ac = a; + ac -= -a; + BOOST_TEST(ac == 16); + ac = a; + ac -= c - b; + BOOST_TEST(ac == 8 - (500-64)); + ac = a; + ac -= b*c; + BOOST_TEST(ac == 8 - 500*64); + ac = a; + ac += ac * b; + BOOST_TEST(ac == 8 + 8 * 64); + ac = a; + ac -= ac * b; + BOOST_TEST(ac == 8 - 8 * 64); + ac = a * "8"; + BOOST_TEST(ac == 64); + ac *= +a; + BOOST_TEST(ac == 64 * 8); + ac = a; + ac *= -a; + BOOST_TEST(ac == -64); + ac = a; + ac *= b * c; + BOOST_TEST(ac == 8 * 64 * 500); + ac = a; + ac *= b / a; + BOOST_TEST(ac == 8 * 64 / 8); + ac = a; + ac *= b + c; + BOOST_TEST(ac == 8 * (64 + 500)); + ac = b / "8"; + BOOST_TEST(ac == 8); + ac = b; + ac /= +a; + BOOST_TEST(ac == 8); + ac = b; + ac /= -a; + BOOST_TEST(ac == -8); + ac = b; + ac /= b / a; + BOOST_TEST(ac == 64 / (64/8)); + ac = b; + ac /= a + Real(0); + BOOST_TEST(ac == 8); + ac = a + std::string("8"); + BOOST_TEST(ac == 16); + // + // Comparisons: + // + BOOST_TEST((a == b) == false); + BOOST_TEST((a != b) == true); + BOOST_TEST((a <= b) == true); + BOOST_TEST((a < b) == true); + BOOST_TEST((a >= b) == false); + BOOST_TEST((a > b) == false); + + BOOST_TEST((a+b == b) == false); + BOOST_TEST((a+b != b) == true); + BOOST_TEST((a+b >= b) == true); + BOOST_TEST((a+b > b) == true); + BOOST_TEST((a+b <= b) == false); + BOOST_TEST((a+b < b) == false); + + BOOST_TEST((a == b+a) == false); + BOOST_TEST((a != b+a) == true); + BOOST_TEST((a <= b+a) == true); + BOOST_TEST((a < b+a) == true); + BOOST_TEST((a >= b+a) == false); + BOOST_TEST((a > b+a) == false); + + BOOST_TEST((a+b == b+a) == true); + BOOST_TEST((a+b != b+a) == false); + BOOST_TEST((a+b <= b+a) == true); + BOOST_TEST((a+b < b+a) == false); + BOOST_TEST((a+b >= b+a) == true); + BOOST_TEST((a+b > b+a) == false); + + BOOST_TEST((8 == b+a) == false); + BOOST_TEST((8 != b+a) == true); + BOOST_TEST((8 <= b+a) == true); + BOOST_TEST((8 < b+a) == true); + BOOST_TEST((8 >= b+a) == false); + BOOST_TEST((8 > b+a) == false); + BOOST_TEST((800 == b+a) == false); + BOOST_TEST((800 != b+a) == true); + BOOST_TEST((800 >= b+a) == true); + BOOST_TEST((800 > b+a) == true); + BOOST_TEST((800 <= b+a) == false); + BOOST_TEST((800 < b+a) == false); + BOOST_TEST((72 == b+a) == true); + BOOST_TEST((72 != b+a) == false); + BOOST_TEST((72 <= b+a) == true); + BOOST_TEST((72 < b+a) == false); + BOOST_TEST((72 >= b+a) == true); + BOOST_TEST((72 > b+a) == false); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); +#endif +#ifdef TEST_MPF + boost::math::mpf_real::default_precision(1000); + boost::math::mpf_real r; + r.precision(50); + BOOST_TEST(r.precision() >= 50); + BOOST_TEST(boost::math::mpf_real::default_precision() == 1000); + test(); +#endif +#ifdef TEST_MPZ + test(); +#endif + return boost::report_errors(); +} From 136e7b67afb6924fbf95bb2e68ca1b5f3b02aadd Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 8 Aug 2011 12:27:46 +0000 Subject: [PATCH 002/256] Add a few non-member functions for real-valued types. Add minimal docs. [SVN r73608] --- include/boost/math/big_number.hpp | 49 ++ include/boost/math/big_number/gmp.hpp | 48 ++ math/Jamroot.jam | 9 + math/boost-build.jam | 72 +++ math/doc/Jamfile.v2 | 67 ++ math/doc/big_number.qbk | 207 ++++++ math/doc/html/boost_bignumbers/intro.html | 44 ++ math/doc/html/boost_bignumbers/ref.html | 40 ++ .../boost_bignumbers/ref/backendconc.html | 38 ++ .../doc/html/boost_bignumbers/ref/bignum.html | 151 +++++ math/doc/html/boost_bignumbers/tut.html | 44 ++ math/doc/html/boost_bignumbers/tut/ints.html | 146 +++++ math/doc/html/boost_bignumbers/tut/reals.html | 158 +++++ math/doc/html/boostbook.css | 588 ++++++++++++++++++ math/doc/html/images/blank.png | Bin 0 -> 374 bytes math/doc/html/images/caution.png | Bin 0 -> 1250 bytes math/doc/html/images/caution.svg | 68 ++ math/doc/html/images/draft.png | Bin 0 -> 17454 bytes math/doc/html/images/home.png | Bin 0 -> 358 bytes math/doc/html/images/home.svg | 26 + math/doc/html/images/important.png | Bin 0 -> 722 bytes math/doc/html/images/important.svg | 25 + math/doc/html/images/next.png | Bin 0 -> 336 bytes math/doc/html/images/next.svg | 19 + math/doc/html/images/next_disabled.png | Bin 0 -> 1110 bytes math/doc/html/images/note.png | Bin 0 -> 490 bytes math/doc/html/images/note.svg | 33 + math/doc/html/images/prev.png | Bin 0 -> 334 bytes math/doc/html/images/prev.svg | 19 + math/doc/html/images/prev_disabled.png | Bin 0 -> 1109 bytes math/doc/html/images/tip.png | Bin 0 -> 449 bytes math/doc/html/images/tip.svg | 84 +++ math/doc/html/images/toc-blank.png | Bin 0 -> 318 bytes math/doc/html/images/toc-minus.png | Bin 0 -> 259 bytes math/doc/html/images/toc-plus.png | Bin 0 -> 264 bytes math/doc/html/images/up.png | Bin 0 -> 370 bytes math/doc/html/images/up.svg | 19 + math/doc/html/images/up_disabled.png | Bin 0 -> 1115 bytes math/doc/html/images/warning.png | Bin 0 -> 1241 bytes math/doc/html/images/warning.svg | 23 + math/doc/html/index.html | 53 ++ math/test/test_arithmetic.cpp | 23 + 42 files changed, 2053 insertions(+) create mode 100644 math/Jamroot.jam create mode 100644 math/boost-build.jam create mode 100644 math/doc/Jamfile.v2 create mode 100644 math/doc/big_number.qbk create mode 100644 math/doc/html/boost_bignumbers/intro.html create mode 100644 math/doc/html/boost_bignumbers/ref.html create mode 100644 math/doc/html/boost_bignumbers/ref/backendconc.html create mode 100644 math/doc/html/boost_bignumbers/ref/bignum.html create mode 100644 math/doc/html/boost_bignumbers/tut.html create mode 100644 math/doc/html/boost_bignumbers/tut/ints.html create mode 100644 math/doc/html/boost_bignumbers/tut/reals.html create mode 100644 math/doc/html/boostbook.css create mode 100644 math/doc/html/images/blank.png create mode 100644 math/doc/html/images/caution.png create mode 100644 math/doc/html/images/caution.svg create mode 100644 math/doc/html/images/draft.png create mode 100644 math/doc/html/images/home.png create mode 100644 math/doc/html/images/home.svg create mode 100644 math/doc/html/images/important.png create mode 100644 math/doc/html/images/important.svg create mode 100644 math/doc/html/images/next.png create mode 100644 math/doc/html/images/next.svg create mode 100644 math/doc/html/images/next_disabled.png create mode 100644 math/doc/html/images/note.png create mode 100644 math/doc/html/images/note.svg create mode 100644 math/doc/html/images/prev.png create mode 100644 math/doc/html/images/prev.svg create mode 100644 math/doc/html/images/prev_disabled.png create mode 100644 math/doc/html/images/tip.png create mode 100644 math/doc/html/images/tip.svg create mode 100644 math/doc/html/images/toc-blank.png create mode 100644 math/doc/html/images/toc-minus.png create mode 100644 math/doc/html/images/toc-plus.png create mode 100644 math/doc/html/images/up.png create mode 100644 math/doc/html/images/up.svg create mode 100644 math/doc/html/images/up_disabled.png create mode 100644 math/doc/html/images/warning.png create mode 100644 math/doc/html/images/warning.svg create mode 100644 math/doc/html/index.html diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index 632c7b72..ab3fabe7 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -398,6 +398,14 @@ public: { return m_backend.compare(canonical_value(o)); } + Backend& backend() + { + return m_backend; + } + const Backend& backend()const + { + return m_backend; + } private: template void do_assign(const Exp& e, const proto::tag::unary_plus&) @@ -1160,6 +1168,47 @@ std::istream& operator >> (std::istream& is, big_number& r) return is; } +// +// Non-member functions accepting an expression-template as argument: +// +#undef sqrt +template +typename boost::math::detail::expression_type::type sqrt(const detail::big_number_exp& val) +{ + typedef typename detail::expression_type::type result_type; + return sqrt(result_type(val)); +} +template +typename detail::expression_type::type abs(const detail::big_number_exp& val) +{ + typedef typename detail::expression_type::type result_type; + return abs(result_type(val)); +} +template +typename detail::expression_type::type fabs(const detail::big_number_exp& val) +{ + typedef typename detail::expression_type::type result_type; + return fabs(result_type(val)); +} +template +typename detail::expression_type::type ceil(const detail::big_number_exp& val) +{ + typedef typename detail::expression_type::type result_type; + return ceil(result_type(val)); +} +template +typename detail::expression_type::type floor(const detail::big_number_exp& val) +{ + typedef typename detail::expression_type::type result_type; + return floor(result_type(val)); +} +template +typename detail::expression_type::type trunc(const detail::big_number_exp& val) +{ + typedef typename detail::expression_type::type result_type; + return trunc(result_type(val)); +} + }} // namespaces #endif diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index a82674e5..374c7594 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -283,6 +283,8 @@ struct gmp_real_imp d = v; return compare(d); } + mpf_t& data() { return m_data; } + const mpf_t& data()const { return m_data; } protected: mpf_t m_data; }; @@ -366,6 +368,52 @@ private: } }; +// +// Native non-member operations: +// +template +big_number > sqrt(const big_number >& val) +{ + big_number > result; + mpf_sqrt(result.backend().data(), val.backend().data()); + return result; +} +template +big_number > abs(const big_number >& val) +{ + big_number > result; + mpf_abs(result.backend().data(), val.backend().data()); + return result; +} +template +big_number > fabs(const big_number >& val) +{ + big_number > result; + mpf_abs(result.backend().data(), val.backend().data()); + return result; +} +template +big_number > ceil(const big_number >& val) +{ + big_number > result; + mpf_ceil(result.backend().data(), val.backend().data()); + return result; +} +template +big_number > floor(const big_number >& val) +{ + big_number > result; + mpf_floor(result.backend().data(), val.backend().data()); + return result; +} +template +big_number > trunc(const big_number >& val) +{ + big_number > result; + mpf_trunc(result.backend().data(), val.backend().data()); + return result; +} + struct gmp_int { typedef mpl::list signed_types; diff --git a/math/Jamroot.jam b/math/Jamroot.jam new file mode 100644 index 00000000..c8019258 --- /dev/null +++ b/math/Jamroot.jam @@ -0,0 +1,9 @@ + +import modules ; + +local boost = [ modules.peek : BOOST ] ; + +project sandbox : requirements $(boost) ; + +# This seems to prevent some Boost.Build errors that otherwise occur :-( +use-project /boost : $(boost) ; diff --git a/math/boost-build.jam b/math/boost-build.jam new file mode 100644 index 00000000..02b750a1 --- /dev/null +++ b/math/boost-build.jam @@ -0,0 +1,72 @@ +# Copyright Rene Rivera 2007. +# +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt) + +# For instructions see Jamfile.v2, or "bjam --help". + +local rule if-has-file ( file + : dir * ) +{ + local result ; + if $(dir) + { + result = [ GLOB $(dir) : $(file) ] ; + } + return $(result[1]:P) ; +} + +#~ Attempts to find the Boost source tree... + +local boost-src = [ if-has-file LICENSE_1_0.txt : + [ MATCH --boost=(.*) : $(ARGV) ] + $(BOOST) + $(BOOST_ROOT) + $(.boost-build-file:D)/../boost + $(.boost-build-file:D)/../Trunk + ] ; + +# error handling: +if ! $(boost-src) +{ + ECHO Unable to find the Boost source tree in the locations searched. ; + ECHO Try setting the environment variable BOOST to point to your ; + ECHO Boost tree, or else invoke bjam with the --boost=path option. ; + ECHO The Boost include path will not be automatically set. ; + ECHO The paths searched were [ MATCH --boost=(.*) : $(ARGV) ] $(BOOST) $(.boost-build-file:D)/../boost $(.boost-build-file:D)/../Trunk ; + ECHO But the file LICENSE_1_0.txt was not found in any of them ; +} + +#~ Attempts to find the Boost.Build files... + +local boost-build-src = [ if-has-file bootstrap.jam : + [ MATCH --boost-build=(.*) : $(ARGV) ] + $(BOOST_BUILD_PATH) + $(BOOST_BUILD) + $(boost-src)/tools/build/v2 + ] ; + +# error handling: +if ! $(boost-build-src) +{ + ECHO Unable to find the Boost.Build source tree in the locations searched. ; + ECHO Try setting the environment variable BOOST_BUILD to point to your ; + ECHO Boost.Build tree, or else invoke bjam with the --boost-build=path option. ; + ECHO The paths searched were [ MATCH --boost-build=(.*) : $(ARGV) ] $(BOOST_BUILD_PATH) $(BOOST_BUILD) $(boost-src)/tools/build/v2 ; + ECHO But bootstrap.jam was not found in any of these ; + ECHO More failures will very likely follow... ; +} + +#~ Set some common vars to refer to the Boost sources... + +BOOST ?= $(boost-src) ; +BOOST_ROOT ?= $(boost-src) ; + +#~ And load up Boost.Build... + +boost-build $(boost-build-src) ; + + + + + diff --git a/math/doc/Jamfile.v2 b/math/doc/Jamfile.v2 new file mode 100644 index 00000000..2f00f026 --- /dev/null +++ b/math/doc/Jamfile.v2 @@ -0,0 +1,67 @@ + +# Copyright John Maddock 2011. Use, modification, and distribution are +# subject to the Boost Software License, Version 1.0. (See accompanying +# file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +using quickbook ; + +path-constant images_location : html ; + +xml big_number : big_number.qbk ; +boostbook standalone + : + big_number + : + # Path for links to Boost: + #boost.root=../../../../.. + + # Some general style settings: + table.footnote.number.format=1 + footnote.number.format=1 + html.stylesheet=boostbook.css + + # HTML options first: + # Use graphics not text for navigation: + navig.graphics=1 + # How far down we chunk nested sections, basically all of them: + chunk.section.depth=10 + # Don't put the first section on the same page as the TOC: + chunk.first.sections=10 + # How far down sections get TOC's + toc.section.depth=10 + # Max depth in each TOC: + toc.max.depth=4 + # How far down we go with TOC's + #generate.section.toc.level=10 + # Index on type: + index.on.type=1 + + # PDF Options: + # TOC Generation: this is needed for FOP-0.9 and later: + fop1.extensions=0 + pdf:xep.extensions=1 + # TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9! + pdf:fop.extensions=0 + pdf:fop1.extensions=0 + # No indent on body text: + pdf:body.start.indent=0pt + # Margin size: + pdf:page.margin.inner=0.5in + # Margin size: + pdf:page.margin.outer=0.5in + # Paper type = A4 + pdf:paper.type=A4 + # Yes, we want graphics for admonishments: + admon.graphics=1 + # Set this one for PDF generation *only*: + # default pnd graphics are awful in PDF form, + # better use SVG's instead: + pdf:admon.graphics.extension=".svg" + pdf:use.role.for.mediaobject=1 + pdf:preferred.mediaobject.role=print + pdf:img.src.path=$(images_location)/ + pdf:draft.mode="no" + pdf:boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/sf_and_dist/html + ; + +install pdf-install : standalone : . PDF ; diff --git a/math/doc/big_number.qbk b/math/doc/big_number.qbk new file mode 100644 index 00000000..4ccfb199 --- /dev/null +++ b/math/doc/big_number.qbk @@ -0,0 +1,207 @@ +[/ + Copyright 2011 John Maddock. + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt). +] + +[library Boost.BigNumbers + [quickbook 1.5] + [copyright 2011 John Maddock] + [purpose Big Number library] + [license + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + [@http://www.boost.org/LICENSE_1_0.txt]) + ] + [authors [authors, various]] + [last-revision $Date: 2011-07-08 18:51:46 +0100 (Fri, 08 Jul 2011) $] +] + +[section:intro Introduction] + +The Big Number library comes in two distinct parts: an expression template enabled front end `big_number` +that handles all the operator overloading, expression evaluation optimization, and code reduction, and +a selection of backends that implement the actual arithmetic operations, and need conform only to the +reduced interface requirements of the front end. + +[endsect] + +[section:tut Tutorial] + +In order to use this library you need to make two choices: what kind of number do I want, and +which backend do I want to perform the actual arithmetic? + +[section:ints Integer Types] + +The following backends provide integer arithmetic: + +[table +[[Backend Type][Header][Radix][Dependencies][Pros][Cons]] +[[`gmp_int`][boost/math/big_number/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] +] + +[h4 gmp_int] + + namespace boost{ namespace math{ + + class gmp_int; + + typedef big_number mpz_int; + + }} // namespaces + +The `gmp_int` backend is used via the typedef `boost::math::mpz_int`. It acts as a thin wrapper around the GMP `mpz_t` +to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. + +[h5 Example:] + + #include + + boost::math::mpz_int v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + + std::cout << i << std::endl; // prints 1000! + +[endsect] + +[section:reals Real Numbers] + +The following backends provide real number arithmetic: + +[table +[[Backend Type][Header][Radix][Dependencies][Pros][Cons]] +[[`gmp_real`][boost/math/big_number/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] +] + +[h4 gmp_real] + + namespace boost{ namespace math{ + + template + class gmp_real; + + typedef big_number > mpf_real_50; + typedef big_number > mpf_real_100; + typedef big_number > mpf_real_500; + typedef big_number > mpf_real_1000; + typedef big_number > mpf_real; + + }} // namespaces + +The `gmp_real` backend is used in conjunction with `big_number`: It acts as a thin wrapper around the GMP `mpf_t` +to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision. + +Type `gmp_real` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or +at variable precision by setting the template argument to zero. The typedefs mpf_real_50, mpf_real_100, +mpf_real_500, mpf_real_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision +respectively. The typedef mpf_real provides a variable precision type whose precision can be controlled via the +`big_number`'s member functions. + +[h5 example:] + + #include + + boost::math::gmp_real a = 2; + boost::math::gmp_real::default_precision(1000); + std::cout << boost::math::gmp_real::default_precision() << std::endl; + std::cout << sqrt(a) << std::endl; // print root-2 + +[endsect] + +[endsect] + +[section:ref Reference] + +[section:bignum big_number] + +[h4 Synopsis] + + namespace boost{ namespace math{ + + template + class big_number + { + big_number(); + big_number(see-below); + big_number& operator=(see-below); + /* Other number-type operators here */ + // string conversion: + std::string str()const; + // precision control: + static unsigned default_precision(); + static void default_precision(unsigned digits10); + unsigned precision()const; + void precision(unsigned digits10); + // Comparison: + int compare(const big_number& o)const; + template + typename enable_if, int>::type compare(const V& o)const; + }; + + }} // namespaces + +[h4 Description] + + big_number(); + big_number(see-below); + big_number& operator=(see-below); + +Type `big_number` is default constructible, and copy both constructible and assignable from: + +* Itself. +* An expression template which is the result of one of the arithmetic operators. +* Any builtin arithmetic type. +* A `std::string` or any type which is convertible to `const char*`. + + /* Other number-type operators here */ + +The following arithmetic operations are support for real-numbered types: + +* Binary +, -, *, /, +=, -=, *=, /=, ==, !=, <=, >=, <, >. +* Unary +, -. + +For integer types the following operators are also supported: + +Binary %, %=. + +(More to follow!!) + +Note that the result of the binary +, -, *, / and % operations is an expression template of "unmentionable type". + + std::string str()const; + +Returns the number formatted as a string (TODO: enable custom precision). + + static unsigned default_precision(); + static void default_precision(unsigned digits10); + unsigned precision()const; + void precision(unsigned digits10); + +These functions are only available if the Backend template parameter supports runtime changes to precision. They get and set +the default precision and the precision of *this respectively. + + int compare(const big_number& o)const; + template + typename enable_if, int>::type compare(const V& other)const; + +Returns: + +* A value less that 0 for *this < other +* A value greater that 0 for *this > other +* Zero for *this == other + +[endsect] + +[section:backendconc Backend Requirements] + +TODO, big boring job!! + +[endsect] + +[endsect] + diff --git a/math/doc/html/boost_bignumbers/intro.html b/math/doc/html/boost_bignumbers/intro.html new file mode 100644 index 00000000..ee77f4b1 --- /dev/null +++ b/math/doc/html/boost_bignumbers/intro.html @@ -0,0 +1,44 @@ + + + +Introduction + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+

+ The Big Number library comes in two distinct parts: an expression template + enabled front end big_number + that handles all the operator overloading, expression evaluation optimization, + and code reduction, and a selection of backends that implement the actual arithmetic + operations, and need conform only to the reduced interface requirements of + the front end. +

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/math/doc/html/boost_bignumbers/ref.html b/math/doc/html/boost_bignumbers/ref.html new file mode 100644 index 00000000..c6a81e2f --- /dev/null +++ b/math/doc/html/boost_bignumbers/ref.html @@ -0,0 +1,40 @@ + + + +Reference + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+
+
big_number
+
Backend Requirements
+
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/math/doc/html/boost_bignumbers/ref/backendconc.html b/math/doc/html/boost_bignumbers/ref/backendconc.html new file mode 100644 index 00000000..44dd13af --- /dev/null +++ b/math/doc/html/boost_bignumbers/ref/backendconc.html @@ -0,0 +1,38 @@ + + + +Backend Requirements + + + + + + + +
+
+
+PrevUpHome +
+
+
+

+ TODO, big boring job!! +

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHome +
+ + diff --git a/math/doc/html/boost_bignumbers/ref/bignum.html b/math/doc/html/boost_bignumbers/ref/bignum.html new file mode 100644 index 00000000..bcf3ef57 --- /dev/null +++ b/math/doc/html/boost_bignumbers/ref/bignum.html @@ -0,0 +1,151 @@ + + + +big_number + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+
+ + Synopsis +
+
namespace boost{ namespace math{
+
+template <class Backend>
+class big_number
+{
+   big_number();
+   big_number(see-below);
+   big_number& operator=(see-below);
+   /* Other number-type operators here */
+   // string conversion:
+   std::string str()const;
+   // precision control:
+   static unsigned default_precision();
+   static void default_precision(unsigned digits10);
+   unsigned precision()const;
+   void precision(unsigned digits10);
+   // Comparison:
+   int compare(const big_number<Backend>& o)const;
+   template <class V>
+   typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
+};
+
+}} // namespaces
+
+
+ + Description +
+
big_number();
+big_number(see-below);
+big_number& operator=(see-below);
+
+

+ Type big_number is default + constructible, and copy both constructible and assignable from: +

+
    +
  • + Itself. +
    • +
  • + An expression template which is the result of one of the arithmetic operators. +
    • +
  • + Any builtin arithmetic type. +
    • +
  • + A std::string or any type which is convertible + to const char*. +
    • +
+
/* Other number-type operators here */
+
+

+ The following arithmetic operations are support for real-numbered types: +

+
    +
  • + Binary +, -, *, /, +, -, *, /, + ==, !, <, >=, <, >. +
    • +
  • + Unary +, -. +
    • +
+

+ For integer types the following operators are also supported: +

+

+ Binary %, %=. +

+

+ (More to follow!!) +

+

+ Note that the result of the binary +, -, *, / and % operations is an expression + template of "unmentionable type". +

+
std::string str()const;
+
+

+ Returns the number formatted as a string (TODO: enable custom precision). +

+
static unsigned default_precision();
+static void default_precision(unsigned digits10);
+unsigned precision()const;
+void precision(unsigned digits10);
+
+

+ These functions are only available if the Backend template parameter supports + runtime changes to precision. They get and set the default precision and + the precision of *this respectively. +

+
int compare(const big_number<Backend>& o)const;
+template <class V>
+typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
+
+

+ Returns: +

+
    +
  • + A value less that 0 for *this < other +
    • +
  • + A value greater that 0 for *this > other +
    • +
  • + Zero for *this == other +
    • +
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/math/doc/html/boost_bignumbers/tut.html b/math/doc/html/boost_bignumbers/tut.html new file mode 100644 index 00000000..92e58b08 --- /dev/null +++ b/math/doc/html/boost_bignumbers/tut.html @@ -0,0 +1,44 @@ + + + +Tutorial + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+
+
Integer Types
+
Real Numbers
+
+

+ In order to use this library you need to make two choices: what kind of number + do I want, and which backend do I want to perform the actual arithmetic? +

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/math/doc/html/boost_bignumbers/tut/ints.html b/math/doc/html/boost_bignumbers/tut/ints.html new file mode 100644 index 00000000..b2dbce57 --- /dev/null +++ b/math/doc/html/boost_bignumbers/tut/ints.html @@ -0,0 +1,146 @@ + + + +Integer Types + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+

+ The following backends provide integer arithmetic: +

+
++++++++ + + + + + + + + + + + + + + + + +
+

+ Backend Type +

+ 		+

+ Header +

+ 		+

+ Radix +

+ 		+

+ Dependencies +

+ 		+

+ Pros +

+ 		+

+ Cons +

+
+

+ gmp_int +

+ 		+

+ boost/math/big_number/gmp.hpp +

+ 		+

+ 2 +

+ 		+

+ GMP +

+ 		+

+ Very fast and efficient backend. +

+ 		+

+ Dependency on GNU licenced GMP library. +

+
+
+ + gmp_int +
+
namespace boost{ namespace math{
+
+class gmp_int;
+
+typedef big_number<gmp_int >         mpz_int;
+
+}} // namespaces
+
+

+ The gmp_int backend is used + via the typedef boost::math::mpz_int. It acts as a thin wrapper around + the GMP mpz_t to provide + an integer type that is a drop-in replacement for the native C++ integer + types, but with unlimited precision. +

+
+ + Example: +
+
#include <boost/math/big_number/gmp.hpp>
+
+boost::math::mpz_int v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+
+std::cout << i << std::endl; // prints 1000!
+
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/math/doc/html/boost_bignumbers/tut/reals.html b/math/doc/html/boost_bignumbers/tut/reals.html new file mode 100644 index 00000000..cd08e445 --- /dev/null +++ b/math/doc/html/boost_bignumbers/tut/reals.html @@ -0,0 +1,158 @@ + + + +Real Numbers + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+

+ The following backends provide real number arithmetic: +

+
++++++++ + + + + + + + + + + + + + + + + +
+

+ Backend Type +

+ 		+

+ Header +

+ 		+

+ Radix +

+ 		+

+ Dependencies +

+ 		+

+ Pros +

+ 		+

+ Cons +

+
+

+ gmp_real<N> +

+ 		+

+ boost/math/big_number/gmp.hpp +

+ 		+

+ 2 +

+ 		+

+ GMP +

+ 		+

+ Very fast and efficient backend. +

+ 		+

+ Dependency on GNU licenced GMP library. +

+
+
+ + gmp_real +
+
namespace boost{ namespace math{
+
+template <unsigned Digits10>
+class gmp_real;
+
+typedef big_number<gmp_real<50> >    mpf_real_50;
+typedef big_number<gmp_real<100> >   mpf_real_100;
+typedef big_number<gmp_real<500> >   mpf_real_500;
+typedef big_number<gmp_real<1000> >  mpf_real_1000;
+typedef big_number<gmp_real<0> >     mpf_real;
+
+}} // namespaces
+
+

+ The gmp_real backend is used + in conjunction with big_number: + It acts as a thin wrapper around the GMP mpf_t + to provide an real-number type that is a drop-in replacement for the native + C++ floating-point types, but with much greater precision. +

+

+ Type gmp_real can be used + at fixed precision by specifying a non-zero Digits10 + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpf_real_50, mpf_real_100, mpf_real_500, mpf_real_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpf_real provides a variable precision type whose + precision can be controlled via the big_number's + member functions. +

+
+ + example: +
+
#include <boost/math/big_number/gmp.hpp>
+
+boost::math::gmp_real a = 2;
+boost::math::gmp_real::default_precision(1000);
+std::cout << boost::math::gmp_real::default_precision() << std::endl;
+std::cout << sqrt(a) << std::endl; // print root-2
+
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
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(See accompany- + ing file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +=============================================================================*/ + +/*============================================================================= + Body defaults +=============================================================================*/ + + body + { + margin: 1em; + font-family: sans-serif; + } + +/*============================================================================= + Paragraphs +=============================================================================*/ + + p + { + text-align: left; + font-size: 10pt; + line-height: 1.15; + } + +/*============================================================================= + Program listings +=============================================================================*/ + + /* Code on paragraphs */ + p tt.computeroutput + { + font-size: 9pt; + } + + pre.synopsis + { + font-size: 90%; + margin: 1pc 4% 0pc 4%; + padding: 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border: 1px solid #DCDCDC; + } + + div.informaltable table tr th, + div.table table tr th + { + background-color: #F0F0F0; + border: 1px solid #DCDCDC; + } + + .copyright-footer + { + color: #8F8F8F; + } + + /* Misc */ + span.highlight + { + color: #00A000; + } + } + + @media print + { + /* Links */ + a + { + color: black; + } + + a:visited + { + color: black; + } + + .spirit-nav + { + display: none; + } + + /* Program listing */ + pre.synopsis + { + border: 1px solid gray; + } + + .programlisting, + .screen + { + border: 1px solid gray; + } + + td .programlisting, + td .screen + { + border: 0px solid #DCDCDC; + } + + /* Table of contents */ + .toc + { + border: 1px solid gray; + } + + .informaltable table, + .table table + { + border: 1px solid gray; + border-collapse: collapse; + } + + /* Tables */ + div.informaltable table tr td, + div.table table tr td + { + border: 1px solid gray; + } + + div.informaltable table tr th, + div.table table tr th + { + border: 1px solid gray; + } + + table.simplelist tr td + { + border: none !important; + } + + /* Misc */ + span.highlight + { + font-weight: bold; + } + } + +/*============================================================================= + Images +=============================================================================*/ + + span.inlinemediaobject img + { + vertical-align: middle; + } + +/*============================================================================== + Super and Subscript: style so that line spacing isn't effected, see + http://www.adobe.com/cfusion/communityengine/index.cfm?event=showdetails&productId=1&postId=5341 +==============================================================================*/ + +sup, +sub { + height: 0; + line-height: 1; + vertical-align: baseline; + _vertical-align: bottom; + position: relative; + +} + +sup { + bottom: 1ex; +} + +sub { + top: .5ex; +} + diff --git a/math/doc/html/images/blank.png b/math/doc/html/images/blank.png new file mode 100644 index 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+ + +
+
+
Next
+
+
+

+Chapter 1. Boost.BigNumbers

+

+various authors +

+

Copyright © 2011 John Maddock

+
+

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+

Table of Contents

+
+
Introduction
+
Tutorial
+
+
Integer Types
+
Real Numbers
+
+
Reference
+
+
big_number
+
Backend Requirements
+
+
+
+
+ + + +

Last revised: July 08, 2011 at 18:51:46 +0100

+
+
Next
+ + diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 1109c3d3..421df04a 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -60,6 +60,25 @@ void test_integer_ops(const boost::mpl::true_&) BOOST_TEST(a == -20 % -7); } +template +void test_real_ops(const boost::mpl::false_&){} + +template +void test_real_ops(const boost::mpl::true_&) +{ + std::cout << "Root2 = " << sqrt(Real(2)) << std::endl; + BOOST_TEST(abs(Real(2)) == 2); + BOOST_TEST(abs(Real(-2)) == 2); + BOOST_TEST(fabs(Real(2)) == 2); + BOOST_TEST(fabs(Real(-2)) == 2); + BOOST_TEST(floor(Real(5) / 2) == 2); + BOOST_TEST(ceil(Real(5) / 2) == 3); + BOOST_TEST(floor(Real(-5) / 2) == -3); + BOOST_TEST(ceil(Real(-5) / 2) == -2); + BOOST_TEST(trunc(Real(5) / 2) == 2); + BOOST_TEST(trunc(Real(-5) / 2) == -2); +} + template void test_negative_mixed(boost::mpl::true_ const&) { @@ -209,6 +228,10 @@ void test() // test_integer_ops(boost::math::is_extended_integer()); // + // Real number only functions: + // + test_real_ops(boost::mpl::bool_::value >()); + // // Test basic arithmetic: // Real a(8); From 41bee8c1421c7bac2342c390473885278a28322e Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 8 Aug 2011 16:15:37 +0000 Subject: [PATCH 003/256] Add some build warnings. [SVN r73610] --- math/test/test_arithmetic.cpp | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 421df04a..e09d7f59 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -12,6 +12,14 @@ # define TEST_MPF # define TEST_BACKEND # define TEST_MPZ + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + #endif template From 53d0691ac950b88572f7ca00a03c5feb97645e88 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 8 Aug 2011 17:13:50 +0000 Subject: [PATCH 004/256] Add ldexp and frexp. [SVN r73612] --- include/boost/math/big_number/gmp.hpp | 24 ++++++++++++++++++++++++ math/test/test_arithmetic.cpp | 15 +++++++++++++++ 2 files changed, 39 insertions(+) diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index 374c7594..aaa5a068 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -413,6 +413,30 @@ big_number > trunc(const big_number >& val mpf_trunc(result.backend().data(), val.backend().data()); return result; } +template +big_number > ldexp(const big_number >& val, long e) +{ + big_number > result; + if(e > 0) + mpf_mul_2exp(result.backend().data(), val.backend().data(), e); + else if(e < 0) + mpf_div_2exp(result.backend().data(), val.backend().data(), -e); + return result; +} +template +big_number > frexp(const big_number >& val, int* e) +{ + long v; + mpf_get_d_2exp(&v, val.backend().data()); + *e = v; + return ldexp(val, -v); +} +template +big_number > frexp(const big_number >& val, long* e) +{ + mpf_get_d_2exp(e, val.backend().data()); + return ldexp(val, -*v); +} struct gmp_int { diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index e09d7f59..fa2fc9c6 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -85,6 +85,21 @@ void test_real_ops(const boost::mpl::true_&) BOOST_TEST(ceil(Real(-5) / 2) == -2); BOOST_TEST(trunc(Real(5) / 2) == 2); BOOST_TEST(trunc(Real(-5) / 2) == -2); + + // + // ldexp and frexp, these pretty much have to implemented by each backend: + // + BOOST_TEST(ldexp(Real(2), 5) == 64); + BOOST_TEST(ldexp(Real(2), -5) == Real(2) / 32); + Real v(512); + int exp; + Real r = frexp(v, &exp); + BOOST_TEST(r == 0.5); + BOOST_TEST(exp == 10); + v = 1 / v; + r = frexp(v, &exp); + BOOST_TEST(r == 0.5); + BOOST_TEST(exp == -8); } template From 0fa9745248e1ffde53fb429bd72825a59497422b Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 9 Aug 2011 16:25:39 +0000 Subject: [PATCH 005/256] Add missing #includes. [SVN r73626] --- include/boost/math/big_number.hpp | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index ab3fabe7..af00ec74 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -11,8 +11,12 @@ #include #include #include +#include #include #include +#include +#include +#include namespace boost{ namespace math{ From 30fbb4d528ad0b46880086dfbd4fbec1624f4746 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 11 Aug 2011 11:28:11 +0000 Subject: [PATCH 006/256] Add rvalue reference support. Add LINPACK benchmark test. Update arithmetic tests to work with types other than big_number. Fix precision of ostream& operator<<. [SVN r73649] --- include/boost/math/big_number.hpp | 26 +- include/boost/math/big_number/gmp.hpp | 46 +- .../math/concepts/big_number_architypes.hpp | 2 +- math/test/linpack-benchmark.cpp | 1258 +++++++++++++++++ math/test/test_arithmetic.cpp | 34 +- 5 files changed, 1345 insertions(+), 21 deletions(-) create mode 100644 math/test/linpack-benchmark.cpp diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index af00ec74..f9a7c98b 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -190,13 +190,6 @@ public: BOOST_ASSERT(proto::value(*this) == this); m_backend = canonical_value(v); } - /* - big_number(unsigned digits10, typename enable_if_c::type* dummy = 0) - : base_type(digits10) - { - proto::value(*this) = this; - BOOST_ASSERT(proto::value(*this) == this); - }*/ big_number(const big_number& e, unsigned digits10) : m_backend(e.m_backend, digits10) { proto::value(*this) = this; @@ -240,6 +233,19 @@ public: do_assign(e, typename proto::tag_of::type()); } +#ifndef BOOST_NO_RVALUE_REFERENCES + big_number(big_number&& r) : m_backend(r.m_backend) + { + proto::value(*this) = this; + BOOST_ASSERT(proto::value(*this) == this); + } + big_number& operator=(big_number&& r) + { + m_backend.swap(r.m_backend); + return *this; + } +#endif + template big_number& operator+=(const detail::big_number_exp& e) { @@ -367,9 +373,9 @@ public: // // String conversion functions: // - std::string str()const + std::string str(unsigned digits = 0)const { - return m_backend.str(); + return m_backend.str(digits); } // // Default precision: @@ -1160,7 +1166,7 @@ inline typename boost::enable_if, bool>: template std::ostream& operator << (std::ostream& os, const big_number& r) { - return os << r.str(); + return os << r.str(static_cast(os.precision())); } template diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index aaa5a068..cba6ed56 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -33,11 +33,25 @@ struct gmp_real_imp { mpf_init_set(m_data, o.m_data); } +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real_imp(gmp_real_imp&& o) + { + m_data[0] = o.m_data[0]; + o.m_data[0]._mp_d = 0; + } +#endif gmp_real_imp& operator = (const gmp_real_imp& o) { mpf_set(m_data, o.m_data); return *this; } +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real_imp& operator = (gmp_real_imp&& o) + { + mpf_swap(m_data, o.m_data); + return *this; + } +#endif gmp_real_imp& operator = (boost::uintmax_t i) { boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); @@ -233,13 +247,13 @@ struct gmp_real_imp { mpf_swap(m_data, o.m_data); } - std::string str()const + std::string str(unsigned digits)const { mp_exp_t e; void *(*alloc_func_ptr) (size_t); void *(*realloc_func_ptr) (void *, size_t, size_t); void (*free_func_ptr) (void *, size_t); - const char* ps = mpf_get_str (0, &e, 10, 0, m_data); + const char* ps = mpf_get_str (0, &e, 10, digits, m_data); std::string s("0."); if(ps[0] == '-') { @@ -258,7 +272,8 @@ struct gmp_real_imp } ~gmp_real_imp() { - mpf_clear(m_data); + if(m_data[0]._mp_d) + mpf_clear(m_data); } void negate() { @@ -299,13 +314,21 @@ struct gmp_real : public detail::gmp_real_imp mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } gmp_real(const gmp_real& o) : gmp_real_imp(o) {} - +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real(gmp_real&& o) : gmp_real_imp(o) {} +#endif gmp_real& operator=(const gmp_real& o) { *static_cast*>(this) = static_cast const&>(o); return *this; } - +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real& operator=(gmp_real&& o) + { + *static_cast*>(this) = static_cast&&>(o); + return *this; + } +#endif template gmp_real& operator=(const V& v) { @@ -326,6 +349,9 @@ struct gmp_real<0> : public detail::gmp_real_imp<0> mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } gmp_real(const gmp_real& o) : gmp_real_imp(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real(gmp_real&& o) : gmp_real_imp(o) {} +#endif gmp_real(const gmp_real& o, unsigned digits10) { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); @@ -337,7 +363,13 @@ struct gmp_real<0> : public detail::gmp_real_imp<0> *static_cast*>(this) = static_cast const&>(o); return *this; } - +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real& operator=(gmp_real&& o) + { + *static_cast*>(this) = static_cast &&>(o); + return *this; + } +#endif template gmp_real& operator=(const V& v) { @@ -706,7 +738,7 @@ struct gmp_int { mpz_swap(m_data, o.m_data); } - std::string str()const + std::string str(unsigned)const { void *(*alloc_func_ptr) (size_t); void *(*realloc_func_ptr) (void *, size_t, size_t); diff --git a/include/boost/math/concepts/big_number_architypes.hpp b/include/boost/math/concepts/big_number_architypes.hpp index f7c196e1..31b4d992 100644 --- a/include/boost/math/concepts/big_number_architypes.hpp +++ b/include/boost/math/concepts/big_number_architypes.hpp @@ -252,7 +252,7 @@ struct big_number_backend_real_architype std::cout << "Swapping (" << m_value << " with " << o.m_value << ")" << std::endl; std::swap(m_value, o.m_value); } - std::string str()const + std::string str(unsigned)const { std::string s(boost::lexical_cast(m_value)); std::cout << "Converting to string (" << s << ")" << std::endl; diff --git a/math/test/linpack-benchmark.cpp b/math/test/linpack-benchmark.cpp new file mode 100644 index 00000000..c2c1d054 --- /dev/null +++ b/math/test/linpack-benchmark.cpp @@ -0,0 +1,1258 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +/* 1000d.f -- translated by f2c (version 20050501). +You must link the resulting object file with libf2c: +on Microsoft Windows system, link with libf2c.lib; +on Linux or Unix systems, link with .../path/to/libf2c.a -lm +or, if you install libf2c.a in a standard place, with -lf2c -lm +-- in that order, at the end of the command line, as in +cc *.o -lf2c -lm +Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + +http://www.netlib.org/f2c/libf2c.zip +*/ +#include +#include +#include +#ifdef TEST_BIG_NUMBER +#include +typedef boost::math::mpf_real_100 real_type; +#elif defined(TEST_GMPXX) +#include +typedef mpf_class real_type; +#elif defined(TEST_EF_GMP) +#define E_FLOAT_TYPE_GMP +#include +typedef e_float real_type; +#define CAST_TO_RT(x) real_type(x) +#elif defined(TEST_MATH_EF) +#define E_FLOAT_TYPE_GMP +#include +typedef boost::math::ef::e_float real_type; +//#define CAST_TO_RT(x) real_type(x) +#else +typedef double real_type; +#endif + +#ifndef CAST_TO_RT +# define CAST_TO_RT(x) x +#endif + +extern "C" { +#include "f2c.h" + integer s_wsfe(cilist *), e_wsfe(void), do_fio(integer *, char *, ftnlen), + s_wsle(cilist *), do_lio(integer *, integer *, char *, ftnlen), + e_wsle(void); + /* Subroutine */ int s_stop(char *, ftnlen); + +#undef abs +#undef dabs +#define dabs abs +#undef min +#undef max +#undef dmin +#undef dmax +#define dmin min +#define dmax max + +} +#include + + +#if defined(TEST_EF_GMP) +#include +using namespace ef; +#endif + +using std::min; +using std::max; + +/* Table of constant values */ + +static integer c__0 = 0; +static real_type c_b7 = CAST_TO_RT(1); +static integer c__1 = 1; +static integer c__9 = 9; + +inline double second_(void) +{ + return ((double)(clock())) / CLOCKS_PER_SEC; +} + + +int main() +{ +#ifdef TEST_BIG_NUMBER + std::cout << "Testing big_number >" << std::endl; +#elif defined(TEST_GMPXX) + std::cout << "Testing mpfr_class at 100 decimal degits" << std::endl; + mpf_set_default_prec(((100 + 1) * 1000L) / 301L); +#elif defined(TEST_EF_GMP) + std::cout << "Testing gmp::e_float" << std::endl; +#elif defined(TEST_MATH_EF) + std::cout << "Testing boost::math::ef::e_float" << std::endl; +#else + std::cout << "Testing double" << std::endl; +#endif + + + /* Format strings */ + static char fmt_1[] = "(\002 Please send the results of this run to:\002" + "//\002 Jack J. Dongarra\002/\002 Computer Science Department\002/" + "\002 University of Tennessee\002/\002 Knoxville, Tennessee 37996" + "-1300\002//\002 Fax: 615-974-8296\002//\002 Internet: dongarra@c" + "s.utk.edu\002/)"; + static char fmt_40[] = "(\002 norm. resid resid mac" + "hep\002,\002 x(1) x(n)\002)"; + static char fmt_50[] = "(1p5e16.8)"; + static char fmt_60[] = "(//\002 times are reported for matrices of or" + "der \002,i5)"; + static char fmt_70[] = "(6x,\002factor\002,5x,\002solve\002,6x,\002tota" + "l\002,5x,\002mflops\002,7x,\002unit\002,6x,\002ratio\002)"; + static char fmt_80[] = "(\002 times for array with leading dimension o" + "f\002,i4)"; + static char fmt_110[] = "(6(1pe11.3))"; + + /* System generated locals */ + integer i__1; + real_type d__1, d__2, d__3; + + /* Builtin functions */ + + /* Local variables */ + static real_type a[1001000] /* was [1001][1000] */, b[1000]; + static integer i__, n; + static real_type x[1000]; + static double t1; + static integer lda; + static double ops; + static real_type eps; + static integer info; + static double time[6], cray, total; + static integer ipvt[1000]; + extern /* Subroutine */ int dgefa_(real_type *, integer *, integer *, + integer *, integer *), dgesl_(real_type *, integer *, integer *, + integer *, real_type *, integer *); + static real_type resid, norma; + extern /* Subroutine */ int dmxpy_(integer *, real_type *, integer *, + integer *, real_type *, real_type *); + static real_type normx; + extern /* Subroutine */ int matgen_(real_type *, integer *, integer *, + real_type *, real_type *); + static real_type residn; + extern real_type epslon_(real_type *); + + /* Fortran I/O blocks */ + static cilist io___4 = { 0, 6, 0, fmt_1, 0 }; + static cilist io___20 = { 0, 6, 0, fmt_40, 0 }; + static cilist io___21 = { 0, 6, 0, fmt_50, 0 }; + static cilist io___22 = { 0, 6, 0, fmt_60, 0 }; + static cilist io___23 = { 0, 6, 0, fmt_70, 0 }; + static cilist io___24 = { 0, 6, 0, fmt_80, 0 }; + static cilist io___25 = { 0, 6, 0, fmt_110, 0 }; + static cilist io___26 = { 0, 6, 0, 0, 0 }; + + + lda = 1001; + + /* this program was updated on 10/12/92 to correct a */ + /* problem with the random number generator. The previous */ + /* random number generator had a short period and produced */ + /* singular matrices occasionally. */ + + n = 1000; + cray = .056f; + s_wsfe(&io___4); + e_wsfe(); + /* Computing 3rd power */ + d__1 = (real_type) n; + /* Computing 2nd power */ + d__2 = (real_type) n; + ops = boost::lexical_cast(real_type(d__1 * (d__1 * d__1) * 2. / 3. + d__2 * d__2 * 2.)); + + matgen_(a, &lda, &n, b, &norma); + + /* ****************************************************************** */ + /* ****************************************************************** */ + /* you should replace the call to dgefa and dgesl */ + /* by calls to your linear equation solver. */ + /* ****************************************************************** */ + /* ****************************************************************** */ + + t1 = second_(); + dgefa_(a, &lda, &n, ipvt, &info); + time[0] = second_() - t1; + t1 = second_(); + dgesl_(a, &lda, &n, ipvt, b, &c__0); + time[1] = second_() - t1; + total = time[0] + time[1]; + /* ****************************************************************** */ + /* ****************************************************************** */ + + /* compute a residual to verify results. */ + + i__1 = n; + for (i__ = 1; i__ <= i__1; ++i__) { + x[i__ - 1] = b[i__ - 1]; + /* L10: */ + } + matgen_(a, &lda, &n, b, &norma); + i__1 = n; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ - 1] = -b[i__ - 1]; + /* L20: */ + } + dmxpy_(&n, b, &n, &lda, x, a); + resid = CAST_TO_RT(0); + normx = CAST_TO_RT(0); + i__1 = n; + for (i__ = 1; i__ <= i__1; ++i__) { + /* Computing MAX */ + d__2 = resid, d__3 = (d__1 = b[i__ - 1], abs(d__1)); + resid = max(d__2,d__3); + /* Computing MAX */ + d__2 = normx, d__3 = (d__1 = x[i__ - 1], abs(d__1)); + normx = max(d__2,d__3); + /* L30: */ + } + eps = epslon_(&c_b7); + residn = resid / (n * norma * normx * eps); + s_wsfe(&io___20); + e_wsfe(); + s_wsfe(&io___21); + /* + do_fio(&c__1, (char *)&residn, (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&resid, (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&eps, (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&x[0], (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&x[n - 1], (ftnlen)sizeof(real_type)); + */ + std::cout << std::setw(12) << std::setprecision(5) << residn << " " << resid << " " << eps << " " << x[0] << " " << x[n-1] << std::endl; + e_wsfe(); + + s_wsfe(&io___22); + do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); + e_wsfe(); + s_wsfe(&io___23); + e_wsfe(); + + time[2] = total; + time[3] = ops / (total * 1e6); + time[4] = 2. / time[3]; + time[5] = total / cray; + s_wsfe(&io___24); + do_fio(&c__1, (char *)&lda, (ftnlen)sizeof(integer)); + e_wsfe(); + s_wsfe(&io___25); + for (i__ = 1; i__ <= 6; ++i__) { + // do_fio(&c__1, (char *)&time[i__ - 1], (ftnlen)sizeof(real_type)); + std::cout << std::setw(12) << std::setprecision(5) << time[i__ - 1]; + } + e_wsfe(); + s_wsle(&io___26); + do_lio(&c__9, &c__1, " end of tests -- this version dated 10/12/92", ( + ftnlen)44); + e_wsle(); + + s_stop("", (ftnlen)0); + return 0; +} /* MAIN__ */ + +/* Subroutine */ int matgen_(real_type *a, integer *lda, integer *n, + real_type *b, real_type *norma) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + real_type d__1, d__2; + + /* Local variables */ + static integer i__, j; + extern real_type ran_(integer *); + static integer init[4]; + + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --b; + + /* Function Body */ + init[0] = 1; + init[1] = 2; + init[2] = 3; + init[3] = 1325; + *norma = CAST_TO_RT(0); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = ran_(init) - .5f; + /* Computing MAX */ + d__2 = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + *norma = max(d__2,*norma); + /* L20: */ + } + /* L30: */ + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__] = CAST_TO_RT(0); + /* L35: */ + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__] += a[i__ + j * a_dim1]; + /* L40: */ + } + /* L50: */ + } + return 0; +} /* matgen_ */ + +/* Subroutine */ int dgefa_(real_type *a, integer *lda, integer *n, integer * + ipvt, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + static integer j, k, l; + static real_type t; + static integer kp1, nm1; + extern /* Subroutine */ int dscal_(integer *, real_type *, real_type *, + integer *), daxpy_(integer *, real_type *, real_type *, integer + *, real_type *, integer *); + extern integer idamax_(integer *, real_type *, integer *); + + + /* dgefa factors a double precision matrix by gaussian elimination. */ + + /* dgefa is usually called by dgeco, but it can be called */ + /* directly with a saving in time if rcond is not needed. */ + /* (time for dgeco) = (1 + 9/n)*(time for dgefa) . */ + + /* on entry */ + + /* a double precision(lda, n) */ + /* the matrix to be factored. */ + + /* lda integer */ + /* the leading dimension of the array a . */ + + /* n integer */ + /* the order of the matrix a . */ + + /* on return */ + + /* a an upper triangular matrix and the multipliers */ + /* which were used to obtain it. */ + /* the factorization can be written a = l*u where */ + /* l is a product of permutation and unit lower */ + /* triangular matrices and u is upper triangular. */ + + /* ipvt integer(n) */ + /* an integer vector of pivot indices. */ + + /* info integer */ + /* = 0 normal value. */ + /* = k if u(k,k) .eq. 0.0 . this is not an error */ + /* condition for this subroutine, but it does */ + /* indicate that dgesl or dgedi will divide by zero */ + /* if called. use rcond in dgeco for a reliable */ + /* indication of singularity. */ + + /* linpack. this version dated 08/14/78 . */ + /* cleve moler, university of new mexico, argonne national lab. */ + + /* subroutines and functions */ + + /* blas daxpy,dscal,idamax */ + + /* internal variables */ + + + + /* gaussian elimination with partial pivoting */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipvt; + + /* Function Body */ + *info = 0; + nm1 = *n - 1; + if (nm1 < 1) { + goto L70; + } + i__1 = nm1; + for (k = 1; k <= i__1; ++k) { + kp1 = k + 1; + + /* find l = pivot index */ + + i__2 = *n - k + 1; + l = idamax_(&i__2, &a[k + k * a_dim1], &c__1) + k - 1; + ipvt[k] = l; + + /* zero pivot implies this column already triangularized */ + + if (a[l + k * a_dim1] == 0.) { + goto L40; + } + + /* interchange if necessary */ + + if (l == k) { + goto L10; + } + t = a[l + k * a_dim1]; + a[l + k * a_dim1] = a[k + k * a_dim1]; + a[k + k * a_dim1] = t; +L10: + + /* compute multipliers */ + + t = -1. / a[k + k * a_dim1]; + i__2 = *n - k; + dscal_(&i__2, &t, &a[k + 1 + k * a_dim1], &c__1); + + /* row elimination with column indexing */ + + i__2 = *n; + for (j = kp1; j <= i__2; ++j) { + t = a[l + j * a_dim1]; + if (l == k) { + goto L20; + } + a[l + j * a_dim1] = a[k + j * a_dim1]; + a[k + j * a_dim1] = t; +L20: + i__3 = *n - k; + daxpy_(&i__3, &t, &a[k + 1 + k * a_dim1], &c__1, &a[k + 1 + j * + a_dim1], &c__1); + /* L30: */ + } + goto L50; +L40: + *info = k; +L50: + /* L60: */ + ; + } +L70: + ipvt[*n] = *n; + if (a[*n + *n * a_dim1] == 0.) { + *info = *n; + } + return 0; +} /* dgefa_ */ + +/* Subroutine */ int dgesl_(real_type *a, integer *lda, integer *n, integer * + ipvt, real_type *b, integer *job) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + static integer k, l; + static real_type t; + static integer kb, nm1; + extern real_type ddot_(integer *, real_type *, integer *, real_type *, + integer *); + extern /* Subroutine */ int daxpy_(integer *, real_type *, real_type *, + integer *, real_type *, integer *); + + + /* dgesl solves the double precision system */ + /* a * x = b or trans(a) * x = b */ + /* using the factors computed by dgeco or dgefa. */ + + /* on entry */ + + /* a double precision(lda, n) */ + /* the output from dgeco or dgefa. */ + + /* lda integer */ + /* the leading dimension of the array a . */ + + /* n integer */ + /* the order of the matrix a . */ + + /* ipvt integer(n) */ + /* the pivot vector from dgeco or dgefa. */ + + /* b double precision(n) */ + /* the right hand side vector. */ + + /* job integer */ + /* = 0 to solve a*x = b , */ + /* = nonzero to solve trans(a)*x = b where */ + /* trans(a) is the transpose. */ + + /* on return */ + + /* b the solution vector x . */ + + /* error condition */ + + /* a division by zero will occur if the input factor contains a */ + /* zero on the diagonal. technically this indicates singularity */ + /* but it is often caused by improper arguments or improper */ + /* setting of lda . it will not occur if the subroutines are */ + /* called correctly and if dgeco has set rcond .gt. 0.0 */ + /* or dgefa has set info .eq. 0 . */ + + /* to compute inverse(a) * c where c is a matrix */ + /* with p columns */ + /* call dgeco(a,lda,n,ipvt,rcond,z) */ + /* if (rcond is too small) go to ... */ + /* do 10 j = 1, p */ + /* call dgesl(a,lda,n,ipvt,c(1,j),0) */ + /* 10 continue */ + + /* linpack. this version dated 08/14/78 . */ + /* cleve moler, university of new mexico, argonne national lab. */ + + /* subroutines and functions */ + + /* blas daxpy,ddot */ + + /* internal variables */ + + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipvt; + --b; + + /* Function Body */ + nm1 = *n - 1; + if (*job != 0) { + goto L50; + } + + /* job = 0 , solve a * x = b */ + /* first solve l*y = b */ + + if (nm1 < 1) { + goto L30; + } + i__1 = nm1; + for (k = 1; k <= i__1; ++k) { + l = ipvt[k]; + t = b[l]; + if (l == k) { + goto L10; + } + b[l] = b[k]; + b[k] = t; +L10: + i__2 = *n - k; + daxpy_(&i__2, &t, &a[k + 1 + k * a_dim1], &c__1, &b[k + 1], &c__1); + /* L20: */ + } +L30: + + /* now solve u*x = y */ + + i__1 = *n; + for (kb = 1; kb <= i__1; ++kb) { + k = *n + 1 - kb; + b[k] /= a[k + k * a_dim1]; + t = -b[k]; + i__2 = k - 1; + daxpy_(&i__2, &t, &a[k * a_dim1 + 1], &c__1, &b[1], &c__1); + /* L40: */ + } + goto L100; +L50: + + /* job = nonzero, solve trans(a) * x = b */ + /* first solve trans(u)*y = b */ + + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + i__2 = k - 1; + t = ddot_(&i__2, &a[k * a_dim1 + 1], &c__1, &b[1], &c__1); + b[k] = (b[k] - t) / a[k + k * a_dim1]; + /* L60: */ + } + + /* now solve trans(l)*x = y */ + + if (nm1 < 1) { + goto L90; + } + i__1 = nm1; + for (kb = 1; kb <= i__1; ++kb) { + k = *n - kb; + i__2 = *n - k; + b[k] += ddot_(&i__2, &a[k + 1 + k * a_dim1], &c__1, &b[k + 1], &c__1); + l = ipvt[k]; + if (l == k) { + goto L70; + } + t = b[l]; + b[l] = b[k]; + b[k] = t; +L70: + /* L80: */ + ; + } +L90: +L100: + return 0; +} /* dgesl_ */ + +/* Subroutine */ int daxpy_(integer *n, real_type *da, real_type *dx, + integer *incx, real_type *dy, integer *incy) +{ + /* System generated locals */ + integer i__1; + + /* Local variables */ + static integer i__, m, ix, iy, mp1; + + + /* constant times a vector plus a vector. */ + /* uses unrolled loops for increments equal to one. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*da == 0.) { + return 0; + } + if (*incx == 1 && *incy == 1) { + goto L20; + } + + /* code for unequal increments or equal increments */ + /* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[iy] += *da * dx[ix]; + ix += *incx; + iy += *incy; + /* L10: */ + } + return 0; + + /* code for both increments equal to 1 */ + + + /* clean-up loop */ + +L20: + m = *n % 4; + if (m == 0) { + goto L40; + } + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[i__] += *da * dx[i__]; + /* L30: */ + } + if (*n < 4) { + return 0; + } +L40: + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 4) { + dy[i__] += *da * dx[i__]; + dy[i__ + 1] += *da * dx[i__ + 1]; + dy[i__ + 2] += *da * dx[i__ + 2]; + dy[i__ + 3] += *da * dx[i__ + 3]; + /* L50: */ + } + return 0; +} /* daxpy_ */ + +real_type ddot_(integer *n, real_type *dx, integer *incx, real_type *dy, + integer *incy) +{ + /* System generated locals */ + integer i__1; + real_type ret_val; + + /* Local variables */ + static integer i__, m, ix, iy, mp1; + static real_type dtemp; + + + /* forms the dot product of two vectors. */ + /* uses unrolled loops for increments equal to one. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + ret_val = CAST_TO_RT(0); + dtemp = CAST_TO_RT(0); + if (*n <= 0) { + return ret_val; + } + if (*incx == 1 && *incy == 1) { + goto L20; + } + + /* code for unequal increments or equal increments */ + /* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[ix] * dy[iy]; + ix += *incx; + iy += *incy; + /* L10: */ + } + ret_val = dtemp; + return ret_val; + + /* code for both increments equal to 1 */ + + + /* clean-up loop */ + +L20: + m = *n % 5; + if (m == 0) { + goto L40; + } + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[i__] * dy[i__]; + /* L30: */ + } + if (*n < 5) { + goto L60; + } +L40: + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 5) { + dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + dx[ + i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + dx[i__ + + 4] * dy[i__ + 4]; + /* L50: */ + } +L60: + ret_val = dtemp; + return ret_val; +} /* ddot_ */ + +/* Subroutine */ int dscal_(integer *n, real_type *da, real_type *dx, + integer *incx) +{ + /* System generated locals */ + integer i__1, i__2; + + /* Local variables */ + static integer i__, m, mp1, nincx; + + + /* scales a vector by a constant. */ + /* uses unrolled loops for increment equal to one. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*incx == 1) { + goto L20; + } + + /* code for increment not equal to 1 */ + + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + dx[i__] = *da * dx[i__]; + /* L10: */ + } + return 0; + + /* code for increment equal to 1 */ + + + /* clean-up loop */ + +L20: + m = *n % 5; + if (m == 0) { + goto L40; + } + i__2 = m; + for (i__ = 1; i__ <= i__2; ++i__) { + dx[i__] = *da * dx[i__]; + /* L30: */ + } + if (*n < 5) { + return 0; + } +L40: + mp1 = m + 1; + i__2 = *n; + for (i__ = mp1; i__ <= i__2; i__ += 5) { + dx[i__] = *da * dx[i__]; + dx[i__ + 1] = *da * dx[i__ + 1]; + dx[i__ + 2] = *da * dx[i__ + 2]; + dx[i__ + 3] = *da * dx[i__ + 3]; + dx[i__ + 4] = *da * dx[i__ + 4]; + /* L50: */ + } + return 0; +} /* dscal_ */ + +integer idamax_(integer *n, real_type *dx, integer *incx) +{ + /* System generated locals */ + integer ret_val, i__1; + real_type d__1; + + /* Local variables */ + static integer i__, ix; + static real_type dmax__; + + + /* finds the index of element having max. dabsolute value. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dx; + + /* Function Body */ + ret_val = 0; + if (*n < 1) { + return ret_val; + } + ret_val = 1; + if (*n == 1) { + return ret_val; + } + if (*incx == 1) { + goto L20; + } + + /* code for increment not equal to 1 */ + + ix = 1; + dmax__ = abs(dx[1]); + ix += *incx; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[ix], abs(d__1)) <= dmax__) { + goto L5; + } + ret_val = i__; + dmax__ = (d__1 = dx[ix], abs(d__1)); +L5: + ix += *incx; + /* L10: */ + } + return ret_val; + + /* code for increment equal to 1 */ + +L20: + dmax__ = abs(dx[1]); + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[i__], abs(d__1)) <= dmax__) { + goto L30; + } + ret_val = i__; + dmax__ = (d__1 = dx[i__], abs(d__1)); +L30: + ; + } + return ret_val; +} /* idamax_ */ + +real_type epslon_(real_type *x) +{ +#ifdef TEST_BIG_NUMBER + return ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); +#elif defined(TEST_GMPXX) + return ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); +#else + return CAST_TO_RT(std::numeric_limits::epsilon()); +#endif +} /* epslon_ */ + +/* Subroutine */ int mm_(real_type *a, integer *lda, integer *n1, integer * + n3, real_type *b, integer *ldb, integer *n2, real_type *c__, + integer *ldc) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2; + + /* Local variables */ + static integer i__, j; + extern /* Subroutine */ int dmxpy_(integer *, real_type *, integer *, + integer *, real_type *, real_type *); + + + /* purpose: */ + /* multiply matrix b times matrix c and store the result in matrix a. */ + + /* parameters: */ + + /* a double precision(lda,n3), matrix of n1 rows and n3 columns */ + + /* lda integer, leading dimension of array a */ + + /* n1 integer, number of rows in matrices a and b */ + + /* n3 integer, number of columns in matrices a and c */ + + /* b double precision(ldb,n2), matrix of n1 rows and n2 columns */ + + /* ldb integer, leading dimension of array b */ + + /* n2 integer, number of columns in matrix b, and number of rows in */ + /* matrix c */ + + /* c double precision(ldc,n3), matrix of n2 rows and n3 columns */ + + /* ldc integer, leading dimension of array c */ + + /* ---------------------------------------------------------------------- */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + + /* Function Body */ + i__1 = *n3; + for (j = 1; j <= i__1; ++j) { + i__2 = *n1; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = CAST_TO_RT(0); + /* L10: */ + } + dmxpy_(n2, &a[j * a_dim1 + 1], n1, ldb, &c__[j * c_dim1 + 1], &b[ + b_offset]); + /* L20: */ + } + + return 0; +} /* mm_ */ + +/* Subroutine */ int dmxpy_(integer *n1, real_type *y, integer *n2, integer * + ldm, real_type *x, real_type *m) +{ + /* System generated locals */ + integer m_dim1, m_offset, i__1, i__2; + + /* Local variables */ + static integer i__, j, jmin; + + + /* purpose: */ + /* multiply matrix m times vector x and add the result to vector y. */ + + /* parameters: */ + + /* n1 integer, number of elements in vector y, and number of rows in */ + /* matrix m */ + + /* y double precision(n1), vector of length n1 to which is added */ + /* the product m*x */ + + /* n2 integer, number of elements in vector x, and number of columns */ + /* in matrix m */ + + /* ldm integer, leading dimension of array m */ + + /* x double precision(n2), vector of length n2 */ + + /* m double precision(ldm,n2), matrix of n1 rows and n2 columns */ + + /* ---------------------------------------------------------------------- */ + + /* cleanup odd vector */ + + /* Parameter adjustments */ + --y; + m_dim1 = *ldm; + m_offset = 1 + m_dim1; + m -= m_offset; + --x; + + /* Function Body */ + j = *n2 % 2; + if (j >= 1) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] += x[j] * m[i__ + j * m_dim1]; + /* L10: */ + } + } + + /* cleanup odd group of two vectors */ + + j = *n2 % 4; + if (j >= 2) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = y[i__] + x[j - 1] * m[i__ + (j - 1) * m_dim1] + x[j] * m[ + i__ + j * m_dim1]; + /* L20: */ + } + } + + /* cleanup odd group of four vectors */ + + j = *n2 % 8; + if (j >= 4) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = y[i__] + x[j - 3] * m[i__ + (j - 3) * m_dim1] + x[j - 2] + * m[i__ + (j - 2) * m_dim1] + x[j - 1] * m[i__ + (j - 1) * + m_dim1] + x[j] * m[i__ + j * m_dim1]; + /* L30: */ + } + } + + /* cleanup odd group of eight vectors */ + + j = *n2 % 16; + if (j >= 8) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = y[i__] + x[j - 7] * m[i__ + (j - 7) * m_dim1] + x[j - 6] + * m[i__ + (j - 6) * m_dim1] + x[j - 5] * m[i__ + (j - 5) * + m_dim1] + x[j - 4] * m[i__ + (j - 4) * m_dim1] + x[j - 3] + * m[i__ + (j - 3) * m_dim1] + x[j - 2] * m[i__ + (j - 2) + * m_dim1] + x[j - 1] * m[i__ + (j - 1) * m_dim1] + x[j] * + m[i__ + j * m_dim1]; + /* L40: */ + } + } + + /* main loop - groups of sixteen vectors */ + + jmin = j + 16; + i__1 = *n2; + for (j = jmin; j <= i__1; j += 16) { + i__2 = *n1; + for (i__ = 1; i__ <= i__2; ++i__) { + y[i__] = y[i__] + x[j - 15] * m[i__ + (j - 15) * m_dim1] + x[j - + 14] * m[i__ + (j - 14) * m_dim1] + x[j - 13] * m[i__ + (j + - 13) * m_dim1] + x[j - 12] * m[i__ + (j - 12) * m_dim1] + + x[j - 11] * m[i__ + (j - 11) * m_dim1] + x[j - 10] * m[ + i__ + (j - 10) * m_dim1] + x[j - 9] * m[i__ + (j - 9) * + m_dim1] + x[j - 8] * m[i__ + (j - 8) * m_dim1] + x[j - 7] + * m[i__ + (j - 7) * m_dim1] + x[j - 6] * m[i__ + (j - 6) * + m_dim1] + x[j - 5] * m[i__ + (j - 5) * m_dim1] + x[j - 4] + * m[i__ + (j - 4) * m_dim1] + x[j - 3] * m[i__ + (j - 3) + * m_dim1] + x[j - 2] * m[i__ + (j - 2) * m_dim1] + x[j - + 1] * m[i__ + (j - 1) * m_dim1] + x[j] * m[i__ + j * + m_dim1]; + /* L50: */ + } + /* L60: */ + } + return 0; +} /* dmxpy_ */ + +real_type ran_(integer *iseed) +{ + /* System generated locals */ + real_type ret_val; + + /* Local variables */ + static integer it1, it2, it3, it4; + + + /* modified from the LAPACK auxiliary routine 10/12/92 JD */ + /* -- LAPACK auxiliary routine (version 1.0) -- */ + /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */ + /* Courant Institute, Argonne National Lab, and Rice University */ + /* February 29, 1992 */ + + /* .. Array Arguments .. */ + /* .. */ + + /* Purpose */ + /* ======= */ + + /* DLARAN returns a random double number from a uniform (0,1) */ + /* distribution. */ + + /* Arguments */ + /* ========= */ + + /* ISEED (input/output) INTEGER array, dimension (4) */ + /* On entry, the seed of the random number generator; the array */ + /* elements must be between 0 and 4095, and ISEED(4) must be */ + /* odd. */ + /* On exit, the seed is updated. */ + + /* Further Details */ + /* =============== */ + + /* This routine uses a multiplicative congruential method with modulus */ + /* 2**48 and multiplier 33952834046453 (see G.S.Fishman, */ + /* 'Multiplicative congruential random number generators with modulus */ + /* 2**b: an exhaustive analysis for b = 32 and a partial analysis for */ + /* b = 48', Math. Comp. 189, pp 331-344, 1990). */ + + /* 48-bit integers are stored in 4 integer array elements with 12 bits */ + /* per element. Hence the routine is portable across machines with */ + /* integers of 32 bits or more. */ + + /* .. Parameters .. */ + /* .. */ + /* .. Local Scalars .. */ + /* .. */ + /* .. Intrinsic Functions .. */ + /* .. */ + /* .. Executable Statements .. */ + + /* multiply the seed by the multiplier modulo 2**48 */ + + /* Parameter adjustments */ + --iseed; + + /* Function Body */ + it4 = iseed[4] * 2549; + it3 = it4 / 4096; + it4 -= it3 << 12; + it3 = it3 + iseed[3] * 2549 + iseed[4] * 2508; + it2 = it3 / 4096; + it3 -= it2 << 12; + it2 = it2 + iseed[2] * 2549 + iseed[3] * 2508 + iseed[4] * 322; + it1 = it2 / 4096; + it2 -= it1 << 12; + it1 = it1 + iseed[1] * 2549 + iseed[2] * 2508 + iseed[3] * 322 + iseed[4] + * 494; + it1 %= 4096; + + /* return updated seed */ + + iseed[1] = it1; + iseed[2] = it2; + iseed[3] = it3; + iseed[4] = it4; + + /* convert 48-bit integer to a double number in the interval (0,1) */ + + ret_val = ((real_type) it1 + ((real_type) it2 + ((real_type) it3 + ( + real_type) it4 * 2.44140625e-4) * 2.44140625e-4) * 2.44140625e-4) + * 2.44140625e-4; + return ret_val; + + /* End of RAN */ + +} /* ran_ */ + +/* + +Double results: +~~~~~~~~~~~~~~ + +norm. resid resid machep x(1) x(n) +6.4915 7.207e-013 2.2204e-016 1 1 + + + +times are reported for matrices of order 1000 +factor solve total mflops unit ratio +times for array with leading dimension of1001 +1.443 0.003 1.446 462.43 0.004325 25.821 + + +mpf_class results: +~~~~~~~~~~~~~~~~~~ + +norm. resid resid machep x(1) x(n) +3.6575e-05 5.2257e-103 2.8575e-101 1 1 + + + +times are reported for matrices of order 1000 +factor solve total mflops unit ratio +times for array with leading dimension of1001 +266.45 0.798 267.24 2.5021 0.79933 4772.2 + + +big_number >: +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + + norm. resid resid machep x(1) x(n) + 0.36575e-4 0.52257e-102 0.28575e-100 0.1e1 0.1e1 + + + + times are reported for matrices of order 1000 + factor solve total mflops unit ratio + times for array with leading dimension of1001 + 279.96 0.84 280.8 2.3813 0.83988 5014.3 + +boost::math::ef::e_float: +~~~~~~~~~~~~~~~~~~~~~~~~~ + + norm. resid resid machep x(1) x(n) + 2.551330735e-16 1.275665107e-112 1e-99 1 1 + + + + times are reported for matrices of order 1000 + factor solve total mflops unit ratio + times for array with leading dimension of1001 + 363.89 1.074 364.97 1.8321 1.0916 6517.3 +*/ diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index fa2fc9c6..99436325 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -4,10 +4,8 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ #include -#include -#include -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) # define TEST_MPF50 # define TEST_MPF # define TEST_BACKEND @@ -22,6 +20,17 @@ #endif +#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#include +#endif + template void test_integer_ops(const boost::mpl::false_&){} @@ -83,9 +92,12 @@ void test_real_ops(const boost::mpl::true_&) BOOST_TEST(ceil(Real(5) / 2) == 3); BOOST_TEST(floor(Real(-5) / 2) == -3); BOOST_TEST(ceil(Real(-5) / 2) == -2); +#ifndef TEST_E_FLOAT BOOST_TEST(trunc(Real(5) / 2) == 2); BOOST_TEST(trunc(Real(-5) / 2) == -2); +#endif +#ifndef TEST_E_FLOAT // // ldexp and frexp, these pretty much have to implemented by each backend: // @@ -100,6 +112,7 @@ void test_real_ops(const boost::mpl::true_&) r = frexp(v, &exp); BOOST_TEST(r == 0.5); BOOST_TEST(exp == -8); +#endif } template @@ -347,8 +360,10 @@ void test() ac = a * ac; BOOST_TEST(ac == 8*8); ac = a; +#ifndef TEST_E_FLOAT ac = ac + "8"; BOOST_TEST(ac == 16); +#endif ac = a; ac += +a; BOOST_TEST(ac == 16); @@ -362,8 +377,10 @@ void test() ac += b*c; BOOST_TEST(ac == 8 + 64 * 500); ac = a; +#ifndef TEST_E_FLOAT ac = ac - "8"; BOOST_TEST(ac == 0); +#endif ac = a; ac -= +a; BOOST_TEST(ac == 0); @@ -382,8 +399,12 @@ void test() ac = a; ac -= ac * b; BOOST_TEST(ac == 8 - 8 * 64); +#ifndef TEST_E_FLOAT ac = a * "8"; BOOST_TEST(ac == 64); +#else + ac = a * 8; +#endif ac *= +a; BOOST_TEST(ac == 64 * 8); ac = a; @@ -398,8 +419,10 @@ void test() ac = a; ac *= b + c; BOOST_TEST(ac == 8 * (64 + 500)); +#ifndef TEST_E_FLOAT ac = b / "8"; BOOST_TEST(ac == 8); +#endif ac = b; ac /= +a; BOOST_TEST(ac == 8); @@ -412,8 +435,10 @@ void test() ac = b; ac /= a + Real(0); BOOST_TEST(ac == 8); +#ifndef TEST_E_FLOAT ac = a + std::string("8"); BOOST_TEST(ac == 16); +#endif // // Comparisons: // @@ -484,6 +509,9 @@ int main() #endif #ifdef TEST_MPZ test(); +#endif +#ifdef TEST_E_FLOAT + test(); #endif return boost::report_errors(); } From dc54f251a4b4aa141294cdf5a6ab4c636e7db13b Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 11 Aug 2011 16:09:23 +0000 Subject: [PATCH 007/256] Fix code to compile with GCC. [SVN r73660] --- include/boost/math/big_number/gmp.hpp | 10 +++---- math/test/linpack-benchmark.cpp | 38 +++++++++++---------------- 2 files changed, 21 insertions(+), 27 deletions(-) diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index cba6ed56..95fddb04 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -313,9 +313,9 @@ struct gmp_real : public detail::gmp_real_imp { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } - gmp_real(const gmp_real& o) : gmp_real_imp(o) {} + gmp_real(const gmp_real& o) : detail::gmp_real_imp(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real(gmp_real&& o) : gmp_real_imp(o) {} + gmp_real(gmp_real&& o) : detail::gmp_real_imp(o) {} #endif gmp_real& operator=(const gmp_real& o) { @@ -348,9 +348,9 @@ struct gmp_real<0> : public detail::gmp_real_imp<0> { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } - gmp_real(const gmp_real& o) : gmp_real_imp(o) {} + gmp_real(const gmp_real& o) : detail::gmp_real_imp<0>(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real(gmp_real&& o) : gmp_real_imp(o) {} + gmp_real(gmp_real&& o) : detail::gmp_real_imp<0>(o) {} #endif gmp_real(const gmp_real& o, unsigned digits10) { @@ -467,7 +467,7 @@ template big_number > frexp(const big_number >& val, long* e) { mpf_get_d_2exp(e, val.backend().data()); - return ldexp(val, -*v); + return ldexp(val, -*e); } struct gmp_int diff --git a/math/test/linpack-benchmark.cpp b/math/test/linpack-benchmark.cpp index c2c1d054..bf5300fb 100644 --- a/math/test/linpack-benchmark.cpp +++ b/math/test/linpack-benchmark.cpp @@ -17,6 +17,7 @@ http://www.netlib.org/f2c/libf2c.zip #include #include #include +#include #ifdef TEST_BIG_NUMBER #include typedef boost::math::mpf_real_100 real_type; @@ -82,8 +83,20 @@ inline double second_(void) return ((double)(clock())) / CLOCKS_PER_SEC; } +int dgefa_(real_type *, integer *, integer *, integer *, integer *), dgesl_(real_type *, integer *, integer *, integer *, real_type *, integer *); +int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type *); +int matgen_(real_type *, integer *, integer *, real_type *, real_type *); +real_type epslon_(real_type *); +real_type ran_(integer *); +int dscal_(integer *, real_type *, real_type *, integer *); +int daxpy_(integer *, real_type *, real_type *, integer *, real_type *, integer *); +integer idamax_(integer *, real_type *, integer *); +real_type ddot_(integer *, real_type *, integer *, real_type *, integer *); +int daxpy_(integer *, real_type *, real_type *, integer *, real_type *, integer *); +int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type *); -int main() + +extern "C" int MAIN__() { #ifdef TEST_BIG_NUMBER std::cout << "Testing big_number >" << std::endl; @@ -133,17 +146,9 @@ int main() static integer info; static double time[6], cray, total; static integer ipvt[1000]; - extern /* Subroutine */ int dgefa_(real_type *, integer *, integer *, - integer *, integer *), dgesl_(real_type *, integer *, integer *, - integer *, real_type *, integer *); static real_type resid, norma; - extern /* Subroutine */ int dmxpy_(integer *, real_type *, integer *, - integer *, real_type *, real_type *); static real_type normx; - extern /* Subroutine */ int matgen_(real_type *, integer *, integer *, - real_type *, real_type *); static real_type residn; - extern real_type epslon_(real_type *); /* Fortran I/O blocks */ static cilist io___4 = { 0, 6, 0, fmt_1, 0 }; @@ -270,7 +275,6 @@ int main() /* Local variables */ static integer i__, j; - extern real_type ran_(integer *); static integer init[4]; @@ -325,10 +329,6 @@ int main() static integer j, k, l; static real_type t; static integer kp1, nm1; - extern /* Subroutine */ int dscal_(integer *, real_type *, real_type *, - integer *), daxpy_(integer *, real_type *, real_type *, integer - *, real_type *, integer *); - extern integer idamax_(integer *, real_type *, integer *); /* dgefa factors a double precision matrix by gaussian elimination. */ @@ -465,10 +465,6 @@ L70: static integer k, l; static real_type t; static integer kb, nm1; - extern real_type ddot_(integer *, real_type *, integer *, real_type *, - integer *); - extern /* Subroutine */ int daxpy_(integer *, real_type *, real_type *, - integer *, real_type *, integer *); /* dgesl solves the double precision system */ @@ -917,9 +913,9 @@ L30: real_type epslon_(real_type *x) { #ifdef TEST_BIG_NUMBER - return ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); + return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); #elif defined(TEST_GMPXX) - return ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); + return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); #else return CAST_TO_RT(std::numeric_limits::epsilon()); #endif @@ -934,8 +930,6 @@ real_type epslon_(real_type *x) /* Local variables */ static integer i__, j; - extern /* Subroutine */ int dmxpy_(integer *, real_type *, integer *, - integer *, real_type *, real_type *); /* purpose: */ From 4760f643cd7d05326489b341ccd1439ea3de9297 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 16 Aug 2011 18:02:03 +0000 Subject: [PATCH 008/256] Change backend concepts to allow for easier default implementations, plus out-of-place arithmetic as well as in-place. Change non-member functions to use expression templates with result value passed to the function as "workspace". [SVN r73819] --- include/boost/math/big_number.hpp | 564 +++++-------- .../boost/math/big_number/big_number_base.hpp | 463 +++++++++++ include/boost/math/big_number/default_ops.hpp | 302 +++++++ include/boost/math/big_number/gmp.hpp | 779 +++++++++++------- .../math/concepts/big_number_architypes.hpp | 248 +----- math/test/linpack-benchmark.cpp | 1 + math/test/test_arithmetic.cpp | 97 ++- 7 files changed, 1562 insertions(+), 892 deletions(-) create mode 100644 include/boost/math/big_number/big_number_base.hpp create mode 100644 include/boost/math/big_number/default_ops.hpp diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index f9a7c98b..434ddb79 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -17,156 +17,10 @@ #include #include #include +#include namespace boost{ namespace math{ -template -class big_number; - -namespace detail{ - -// Forward-declare an expression wrapper -template -struct big_number_exp; -// -// Declare our grammars: -// -struct big_number_grammar - : proto::or_< - proto::terminal< proto::_ > - , proto::plus< big_number_grammar, big_number_grammar > - , proto::multiplies< big_number_grammar, big_number_grammar > - , proto::minus< big_number_grammar, big_number_grammar > - , proto::divides< big_number_grammar, big_number_grammar > - , proto::unary_plus< big_number_grammar > - , proto::negate< big_number_grammar > - , proto::modulus - > -{}; - -// Define a calculator domain. Expression within -// the calculator domain will be wrapped in the -// calculator<> expression wrapper. -struct big_number_domain - : proto::domain< proto::generator, big_number_grammar> -{}; - -template -struct big_number_exp - : proto::extends, big_number_domain> -{ - typedef - proto::extends, big_number_domain> base_type; - - big_number_exp(Expr const &expr = Expr()) - : base_type(expr) - {} - template - big_number_exp(const Other& o) - : base_type(o) - {} -}; - -struct CalcDepth - : proto::or_< - proto::when< proto::terminal, - mpl::int_<0>() - > - , proto::when< proto::unary_expr, - CalcDepth(proto::_child) - > - , proto::when< proto::binary_expr, - mpl::plus, mpl::int_<1> >() - > - > -{}; - -template -struct has_enough_bits -{ - template - struct type : public mpl::bool_::digits >= b>{}; -}; - -template -struct canonical_imp -{ - typedef Val type; -}; -template -struct canonical_imp > -{ - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - typename Backend::signed_types, - pred_type - >::type iter_type; - typedef typename mpl::deref::type type; -}; -template -struct canonical_imp > -{ - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - typename Backend::unsigned_types, - pred_type - >::type iter_type; - typedef typename mpl::deref::type type; -}; -template -struct canonical_imp > -{ - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - typename Backend::real_types, - pred_type - >::type iter_type; - typedef typename mpl::deref::type type; -}; -template -struct canonical_imp > -{ - typedef const char* type; -}; - -template -struct canonical -{ - typedef typename mpl::if_< - is_signed, - mpl::int_<0>, - typename mpl::if_< - is_unsigned, - mpl::int_<1>, - typename mpl::if_< - is_floating_point, - mpl::int_<2>, - typename mpl::if_< - mpl::or_< - is_convertible, - is_same - >, - mpl::int_<3>, - mpl::int_<4> - >::type - >::type - >::type - >::type tag_type; - - typedef typename canonical_imp::type type; -}; - -} // namespace detail - -// -// Traits class, lets us know whether a backend is an integer type, otherwise assumed to be a real number type: -// -template -struct is_extended_integer : public mpl::false_ {}; -template -struct is_extended_integer > : public is_extended_integer{}; - template class big_number : public detail::big_number_exp*>::type > { @@ -207,7 +61,7 @@ public: template big_number& operator=(const detail::big_number_exp& e) { - do_assign(e, typename proto::tag_of::type()); + do_assign(e, typename detail::assign_and_eval::type()); return *this; } @@ -230,7 +84,7 @@ public: { proto::value(*this) = this; BOOST_ASSERT(proto::value(*this) == this); - do_assign(e, typename proto::tag_of::type()); + do_assign(e, typename detail::assign_and_eval::type()); } #ifndef BOOST_NO_RVALUE_REFERENCES @@ -267,7 +121,8 @@ public: typename enable_if, big_number& >::type operator+=(const V& v) { - do_add_value(canonical_value(v), mpl::false_()); + using big_num_default_ops::add; + add(m_backend, canonical_value(v)); return *this; } @@ -291,7 +146,8 @@ public: typename enable_if, big_number& >::type operator-=(const V& v) { - do_subtract_value(canonical_value(v), mpl::false_()); + using big_num_default_ops::subtract; + subtract(m_backend, canonical_value(v)); return *this; } @@ -316,7 +172,8 @@ public: typename enable_if, big_number& >::type operator*=(const V& v) { - do_multiplies_value(canonical_value(v), mpl::false_()); + using big_num_default_ops::multiply; + multiply(m_backend, canonical_value(v)); return *this; } @@ -342,7 +199,8 @@ public: operator%=(const V& v) { BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); - do_modulus_value(canonical_value(v), mpl::false_()); + using big_num_default_ops::modulus; + modulus(m_backend, canonical_value(v)); return *this; } @@ -366,16 +224,17 @@ public: typename enable_if, big_number& >::type operator/=(const V& v) { - do_divide_value(canonical_value(v), mpl::false_()); + using big_num_default_ops::divide; + divide(m_backend, canonical_value(v)); return *this; } // // String conversion functions: // - std::string str(unsigned digits = 0)const + std::string str(unsigned digits = 0, bool scientific = true)const { - return m_backend.str(digits); + return m_backend.str(digits, scientific); } // // Default precision: @@ -417,18 +276,103 @@ public: return m_backend; } private: + template + void do_assign(const Exp& e, const detail::add_immediates&) + { + using big_num_default_ops::add; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + add(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + } + + template + void do_assign(const Exp& e, const detail::add_and_negate_immediates&) + { + using big_num_default_ops::add; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + add(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + m_backend.negate(); + } + + template + void do_assign(const Exp& e, const detail::subtract_immediates&) + { + using big_num_default_ops::subtract; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + subtract(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + } + + template + void do_assign(const Exp& e, const detail::subtract_and_negate_immediates&) + { + using big_num_default_ops::subtract; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + subtract(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + m_backend.negate(); + } + + template + void do_assign(const Exp& e, const detail::multiply_immediates&) + { + using big_num_default_ops::multiply; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + multiply(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + } + + template + void do_assign(const Exp& e, const detail::multiply_and_negate_immediates&) + { + using big_num_default_ops::multiply; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + multiply(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + m_backend.negate(); + } + + template + void do_assign(const Exp& e, const detail::divide_immediates&) + { + using big_num_default_ops::divide; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + divide(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + } + + template + void do_assign(const Exp& e, const detail::divide_and_negate_immediates&) + { + using big_num_default_ops::divide; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + divide(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + m_backend.negate(); + } + + template + void do_assign(const Exp& e, const detail::modulus_immediates&) + { + using big_num_default_ops::modulus; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + modulus(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + } + template void do_assign(const Exp& e, const proto::tag::unary_plus&) { typedef typename proto::result_of::left::type left_type; - do_assign(proto::left(e), typename proto::tag_of::type()); + do_assign(proto::left(e), typename detail::assign_and_eval::type()); } template void do_assign(const Exp& e, const proto::tag::negate&) { typedef typename proto::result_of::left::type left_type; - do_assign(proto::left(e), typename proto::tag_of::type()); + do_assign(proto::left(e), typename detail::assign_and_eval::type()); m_backend.negate(); } @@ -461,12 +405,12 @@ private: } else if(left_depth >= right_depth) { - do_assign(proto::left(e), typename proto::tag_of::type()); + do_assign(proto::left(e), typename detail::assign_and_eval::type()); do_add(proto::right(e), typename proto::tag_of::type()); } else { - do_assign(proto::right(e), typename proto::tag_of::type()); + do_assign(proto::right(e), typename detail::assign_and_eval::type()); do_add(proto::left(e), typename proto::tag_of::type()); } } @@ -500,12 +444,12 @@ private: } else if(left_depth >= right_depth) { - do_assign(proto::left(e), typename proto::tag_of::type()); + do_assign(proto::left(e), typename detail::assign_and_eval::type()); do_subtract(proto::right(e), typename proto::tag_of::type()); } else { - do_assign(proto::right(e), typename proto::tag_of::type()); + do_assign(proto::right(e), typename detail::assign_and_eval::type()); do_subtract(proto::left(e), typename proto::tag_of::type()); m_backend.negate(); } @@ -539,12 +483,12 @@ private: } else if(left_depth >= right_depth) { - do_assign(proto::left(e), typename proto::tag_of::type()); + do_assign(proto::left(e), typename detail::assign_and_eval::type()); do_multiplies(proto::right(e), typename proto::tag_of::type()); } else { - do_assign(proto::right(e), typename proto::tag_of::type()); + do_assign(proto::right(e), typename detail::assign_and_eval::type()); do_multiplies(proto::left(e), typename proto::tag_of::type()); } } @@ -572,7 +516,7 @@ private: } else { - do_assign(proto::left(e), typename proto::tag_of::type()); + do_assign(proto::left(e), typename detail::assign_and_eval::type()); do_divide(proto::right(e), typename proto::tag_of::type()); } } @@ -605,7 +549,7 @@ private: } else { - do_assign(proto::left(e), typename proto::tag_of::type()); + do_assign(proto::left(e), typename detail::assign_and_eval::type()); do_modulus(proto::right(e), typename proto::tag_of::type()); } } @@ -617,28 +561,55 @@ private: m_backend = canonical_value(proto::value(e)); } } + template + void do_assign(const Exp& e, const proto::tag::function&) + { + typedef typename proto::arity_of::type tag_type; + do_assign_function(e, tag_type()); + } + template + void do_assign_function(const Exp& e, const mpl::long_<1>&) + { + proto::value(proto::left(e))(&m_backend); + } + template + void do_assign_function(const Exp& e, const mpl::long_<2>&) + { + typedef typename proto::result_of::right::type right_type; + typedef typename proto::tag_of::type tag_type; + do_assign_function_1(proto::value(proto::left(e)), proto::right(e), tag_type()); + } + template + void do_assign_function_1(const F& f, const Exp& val, const proto::tag::terminal&) + { + f(&m_backend, canonical_value(proto::value(val))); + } + template + void do_assign_function_1(const F& f, const Exp& val, const Tag&) + { + big_number t(val); + f(&m_backend, t.backend()); + } + template + void do_assign_function(const Exp& e, const mpl::long_<3>&) + { + typedef typename proto::result_of::right::type right_type; + typedef typename proto::tag_of::type tag_type; + typedef typename proto::result_of::child_c::type end_type; + typedef typename proto::tag_of::type end_tag; + do_assign_function_2(proto::value(proto::left(e)), proto::right(e), proto::child_c<2>(e), tag_type(), end_tag()); + } + template + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const proto::tag::terminal&, const proto::tag::terminal&) + { + f(&m_backend, canonical_value(proto::value(val1)), canonical_value(proto::value(val2))); + } template void do_add(const Exp& e, const proto::tag::terminal&) { - typedef typename proto::result_of::value::type t1; - typedef typename remove_reference::type t2; - typedef typename remove_cv::type t3; - typedef typename detail::canonical::type t4; - typedef typename is_convertible::type tag; - do_add_value(canonical_value(proto::value(e)), tag()); - } - - template - void do_add_value(const V& v, const mpl::false_&) - { - m_backend += v; - } - template - void do_add_value(const V& v, const mpl::true_&) - { - self_type temp(v); - m_backend += temp.m_backend; + using big_num_default_ops::add; + add(m_backend, canonical_value(proto::value(e))); } template @@ -683,24 +654,8 @@ private: template void do_subtract(const Exp& e, const proto::tag::terminal&) { - typedef typename proto::result_of::value::type t1; - typedef typename remove_reference::type t2; - typedef typename remove_cv::type t3; - typedef typename detail::canonical::type t4; - typedef typename is_convertible::type tag; - do_subtract_value(canonical_value(proto::value(e)), tag()); - } - - template - void do_subtract_value(const V& v, const mpl::false_&) - { - m_backend -= v; - } - template - void do_subtract_value(const V& v, const mpl::true_&) - { - self_type temp(v); - m_backend -= temp.m_backend; + using big_num_default_ops::subtract; + subtract(m_backend, canonical_value(proto::value(e))); } template @@ -745,25 +700,8 @@ private: template void do_multiplies(const Exp& e, const proto::tag::terminal&) { - typedef typename proto::result_of::value::type t1; - typedef typename remove_reference::type t2; - typedef typename remove_cv::type t3; - typedef typename detail::canonical::type t4; - typedef typename is_convertible::type tag; - do_multiplies_value(canonical_value(proto::value(e)), tag()); - } - - template - void do_multiplies_value(const Val& v, const mpl::false_&) - { - m_backend *= v; - } - - template - void do_multiplies_value(const Val& e, const mpl::true_&) - { - self_type temp(e); - m_backend *= temp.m_backend; + using big_num_default_ops::multiply; + multiply(m_backend, canonical_value(proto::value(e))); } template @@ -802,32 +740,16 @@ private: template void do_multiplies(const Exp& e, const unknown&) { + using big_num_default_ops::multiply; self_type temp(e); - m_backend *= temp.m_backend; + multiply(m_backend, temp.m_backend); } template void do_divide(const Exp& e, const proto::tag::terminal&) { - typedef typename proto::result_of::value::type t1; - typedef typename remove_reference::type t2; - typedef typename remove_cv::type t3; - typedef typename detail::canonical::type t4; - typedef typename is_convertible::type tag; - do_divide_value(canonical_value(proto::value(e)), tag()); - } - - template - void do_divide_value(const Val& v, const mpl::false_&) - { - m_backend /= v; - } - - template - void do_divide_value(const Val& e, const mpl::true_&) - { - self_type temp(e); - m_backend /= temp.m_backend; + using big_num_default_ops::divide; + divide(m_backend, canonical_value(proto::value(e))); } template @@ -866,39 +788,24 @@ private: template void do_divide(const Exp& e, const unknown&) { + using big_num_default_ops::multiply; self_type temp(e); - m_backend /= temp.m_backend; + divide(m_backend, temp.m_backend); } template void do_modulus(const Exp& e, const proto::tag::terminal&) { - typedef typename proto::result_of::value::type t1; - typedef typename remove_reference::type t2; - typedef typename remove_cv::type t3; - typedef typename detail::canonical::type t4; - typedef typename is_convertible::type tag; - do_modulus_value(canonical_value(proto::value(e)), tag()); - } - - template - void do_modulus_value(const Val& v, const mpl::false_&) - { - m_backend %= v; - } - - template - void do_modulus_value(const Val& e, const mpl::true_&) - { - self_type temp(e); - m_backend %= temp.m_backend; + using big_num_default_ops::modulus; + modulus(m_backend, canonical_value(proto::value(e))); } template void do_modulus(const Exp& e, const Unknown&) { + using big_num_default_ops::modulus; self_type temp(e); - do_modulus_value(canonical_value(proto::value(temp)), mpl::false_()); + modulus(m_backend, canonical_value(proto::value(temp))); } // Tests if the expression contains a reference to *this: @@ -953,6 +860,19 @@ private: { return v == this; } + template + static typename detail::underlying_result::type underlying_value(const big_number_exp& e, const proto::tag::terminal&) + { + return proto::value(e); + } + template + static typename detail::underlying_result::type + underlying_value(const big_number_exp& e, const tag&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::tag_of::type tag_type; + return underlying_value(proto::left(e), tag_type()); + } static const Backend& canonical_value(const self_type& v){ return v.m_backend; } static const Backend& canonical_value(const self_type* v){ return v->m_backend; } @@ -967,72 +887,6 @@ private: namespace detail { -template -struct combine_expression_type -{ - typedef void type; -}; - -template -struct combine_expression_type, boost::math::big_number > -{ - typedef boost::math::big_number type; -}; - -template -struct combine_expression_type, Exp> -{ - typedef boost::math::big_number type; -}; - -template -struct combine_expression_type > -{ - typedef boost::math::big_number type; -}; - -template -struct is_big_number : public mpl::false_{}; -template -struct is_big_number > : public mpl::true_{}; -template -struct is_big_number_exp : public mpl::false_{}; -template -struct is_big_number_exp > : public mpl::true_{}; - - -template -struct expression_type_imp; - -template -struct expression_type_imp -{ - typedef typename remove_pointer::type>::type type; -}; - -template -struct expression_type_imp -{ - typedef typename proto::result_of::left::type nested_type; - typedef typename expression_type_imp::value>::type type; -}; - -template -struct expression_type_imp -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename expression_type_imp::value>::type left_result; - typedef typename expression_type_imp::value>::type right_result; - typedef typename combine_expression_type::type type; -}; - -template -struct expression_type -{ - typedef typename expression_type_imp::value>::type type; -}; - template inline int big_number_compare(const big_number& a, const big_number& b) { @@ -1164,13 +1018,20 @@ inline typename boost::enable_if, bool>: } template -std::ostream& operator << (std::ostream& os, const big_number& r) +inline std::ostream& operator << (std::ostream& os, const big_number& r) { - return os << r.str(static_cast(os.precision())); + return os << r.str(static_cast(os.precision(), os.flags() & os.scientific)); +} +template +inline std::ostream& operator << (std::ostream& os, const detail::big_number_exp& r) +{ + typedef typename detail::expression_type::type value_type; + value_type temp(r); + return os << temp; } template -std::istream& operator >> (std::istream& is, big_number& r) +inline std::istream& operator >> (std::istream& is, big_number& r) { std::string s; is >> s; @@ -1178,47 +1039,6 @@ std::istream& operator >> (std::istream& is, big_number& r) return is; } -// -// Non-member functions accepting an expression-template as argument: -// -#undef sqrt -template -typename boost::math::detail::expression_type::type sqrt(const detail::big_number_exp& val) -{ - typedef typename detail::expression_type::type result_type; - return sqrt(result_type(val)); -} -template -typename detail::expression_type::type abs(const detail::big_number_exp& val) -{ - typedef typename detail::expression_type::type result_type; - return abs(result_type(val)); -} -template -typename detail::expression_type::type fabs(const detail::big_number_exp& val) -{ - typedef typename detail::expression_type::type result_type; - return fabs(result_type(val)); -} -template -typename detail::expression_type::type ceil(const detail::big_number_exp& val) -{ - typedef typename detail::expression_type::type result_type; - return ceil(result_type(val)); -} -template -typename detail::expression_type::type floor(const detail::big_number_exp& val) -{ - typedef typename detail::expression_type::type result_type; - return floor(result_type(val)); -} -template -typename detail::expression_type::type trunc(const detail::big_number_exp& val) -{ - typedef typename detail::expression_type::type result_type; - return trunc(result_type(val)); -} - }} // namespaces #endif diff --git a/include/boost/math/big_number/big_number_base.hpp b/include/boost/math/big_number/big_number_base.hpp new file mode 100644 index 00000000..b3caed30 --- /dev/null +++ b/include/boost/math/big_number/big_number_base.hpp @@ -0,0 +1,463 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_BIG_NUM_BASE_HPP +#define BOOST_MATH_BIG_NUM_BASE_HPP + +namespace boost{ namespace math{ + +template +class big_number; + +namespace detail{ + +// Forward-declare an expression wrapper +template +struct big_number_exp; +// +// Declare our grammars: +// +struct big_number_grammar + : proto::or_< + proto::terminal< proto::_ > + , proto::plus< big_number_grammar, big_number_grammar > + , proto::multiplies< big_number_grammar, big_number_grammar > + , proto::minus< big_number_grammar, big_number_grammar > + , proto::divides< big_number_grammar, big_number_grammar > + , proto::unary_plus< big_number_grammar > + , proto::negate< big_number_grammar > + , proto::modulus + > +{}; + +// Define a calculator domain. Expression within +// the calculator domain will be wrapped in the +// calculator<> expression wrapper. +struct big_number_domain + : proto::domain< proto::generator, big_number_grammar> +{}; + +template +struct big_number_exp + : proto::extends, big_number_domain> +{ + typedef + proto::extends, big_number_domain> base_type; + + big_number_exp(Expr const &expr = Expr()) + : base_type(expr) + {} + template + big_number_exp(const Other& o) + : base_type(o) + {} +}; + +struct CalcDepth + : proto::or_< + proto::when< proto::terminal, + mpl::int_<0>() + > + , proto::when< proto::unary_expr, + CalcDepth(proto::_child) + > + , proto::when< proto::binary_expr, + mpl::plus, mpl::int_<1> >() + > + > +{}; + +template +struct has_enough_bits +{ + template + struct type : public mpl::bool_::digits >= b>{}; +}; + +template +struct canonical_imp +{ + typedef Val type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::signed_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::unsigned_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::real_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef const char* type; +}; + +template +struct canonical +{ + typedef typename mpl::if_< + is_signed, + mpl::int_<0>, + typename mpl::if_< + is_unsigned, + mpl::int_<1>, + typename mpl::if_< + is_floating_point, + mpl::int_<2>, + typename mpl::if_< + mpl::or_< + is_convertible, + is_same + >, + mpl::int_<3>, + mpl::int_<4> + >::type + >::type + >::type + >::type tag_type; + + typedef typename canonical_imp::type type; +}; + +template +struct assign_and_eval_imp +{ + typedef tag type; +}; + +struct add_immediates{}; +struct add_and_negate_immediates{}; +struct subtract_immediates{}; +struct subtract_and_negate_immediates{}; +struct multiply_immediates{}; +struct multiply_and_negate_immediates{}; +struct divide_immediates{}; +struct divide_and_negate_immediates{}; +struct modulus_immediates{}; + +struct immediate{}; +struct negative_immediate{}; + +template +struct immediate_type +{ + typedef tag type; +}; +template +struct immediate_type +{ + typedef immediate type; +}; +template +struct immediate_type +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::tag_of::type left_tag; + typedef typename mpl::if_< + is_same, + immediate, + left_tag + >::type type; +}; +template +struct immediate_type +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::tag_of::type left_tag; + typedef typename immediate_type::type tag; + typedef typename mpl::if_< + is_same, + negative_immediate, + tag + >::type type; +}; + +template +struct assign_and_eval_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::tag_of::type left_tag; + typedef typename proto::tag_of::type right_tag; + typedef typename immediate_type::type left_imm; + typedef typename immediate_type::type right_imm; + typedef typename mpl::if_< + mpl::and_, is_same >, + add_immediates, + typename mpl::if_< + mpl::and_, is_same >, + subtract_immediates, + typename mpl::if_< + mpl::and_, is_same >, + subtract_and_negate_immediates, + typename mpl::if_< + mpl::and_, is_same >, + add_and_negate_immediates, + proto::tag::plus + >::type + >::type + >::type + >::type type; +}; + +template +struct assign_and_eval_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::tag_of::type left_tag; + typedef typename proto::tag_of::type right_tag; + typedef typename immediate_type::type left_imm; + typedef typename immediate_type::type right_imm; + typedef typename mpl::if_< + mpl::and_, is_same >, + subtract_immediates, + typename mpl::if_< + mpl::and_, is_same >, + add_immediates, + typename mpl::if_< + mpl::and_, is_same >, + add_and_negate_immediates, + typename mpl::if_< + mpl::and_, is_same >, + subtract_and_negate_immediates, + proto::tag::minus + >::type + >::type + >::type + >::type type; +}; + +template +struct assign_and_eval_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::tag_of::type left_tag; + typedef typename proto::tag_of::type right_tag; + typedef typename immediate_type::type left_imm; + typedef typename immediate_type::type right_imm; + typedef typename mpl::if_< + mpl::and_, is_same >, + multiply_immediates, + typename mpl::if_< + mpl::and_, is_same >, + multiply_and_negate_immediates, + typename mpl::if_< + mpl::and_, is_same >, + multiply_and_negate_immediates, + typename mpl::if_< + mpl::and_, is_same >, + multiply_immediates, + proto::tag::multiplies + >::type + >::type + >::type + >::type type; +}; + +template +struct assign_and_eval_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::tag_of::type left_tag; + typedef typename proto::tag_of::type right_tag; + typedef typename immediate_type::type left_imm; + typedef typename immediate_type::type right_imm; + typedef typename mpl::if_< + mpl::and_, is_same >, + divide_immediates, + typename mpl::if_< + mpl::and_, is_same >, + divide_and_negate_immediates, + typename mpl::if_< + mpl::and_, is_same >, + divide_and_negate_immediates, + typename mpl::if_< + mpl::and_, is_same >, + divide_immediates, + proto::tag::divides + >::type + >::type + >::type + >::type type; +}; + +template +struct assign_and_eval_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::tag_of::type left_tag; + typedef typename proto::tag_of::type right_tag; + typedef typename immediate_type::type left_imm; + typedef typename immediate_type::type right_imm; + typedef typename mpl::if_< + mpl::and_, is_same >, + modulus_immediates, + proto::tag::modulus + >::type type; +}; + +template +struct assign_and_eval +{ + typedef typename proto::tag_of::type tag_type; + typedef typename assign_and_eval_imp::type type; +}; + +template +struct underlying_result_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::tag_of::type tag_type; + typedef typename underlying_result_imp::type type; +}; + +template +struct underlying_result_imp +{ + typedef typename proto::result_of::value::type type; +}; + +template +struct underlying_result +{ + typedef typename proto::tag_of::type tag_type; + typedef typename underlying_result_imp::type type; +}; + +template +struct combine_expression_type +{ + typedef void type; +}; + +template +struct combine_expression_type, boost::math::big_number > +{ + typedef boost::math::big_number type; +}; + +template +struct combine_expression_type, Exp> +{ + typedef boost::math::big_number type; +}; + +template +struct combine_expression_type > +{ + typedef boost::math::big_number type; +}; + +template +struct is_big_number : public mpl::false_{}; +template +struct is_big_number > : public mpl::true_{}; +template +struct is_big_number_exp : public mpl::false_{}; +template +struct is_big_number_exp > : public mpl::true_{}; + + +template +struct expression_type_imp; + +template +struct expression_type_imp +{ + typedef typename remove_pointer::type>::type type; +}; + +template +struct expression_type_imp +{ + typedef typename proto::result_of::left::type nested_type; + typedef typename expression_type_imp::value>::type type; +}; + +template +struct expression_type_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename expression_type_imp::value>::type left_result; + typedef typename expression_type_imp::value>::type right_result; + typedef typename combine_expression_type::type type; +}; + +template +struct expression_type_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::result_of::child_c::type end_type; + typedef typename expression_type_imp::value>::type left_result; + typedef typename expression_type_imp::value>::type right_result; + typedef typename expression_type_imp::value>::type end_result; + typedef typename combine_expression_type::type>::type type; +}; + +template +struct expression_type +{ + typedef typename expression_type_imp::value>::type type; +}; + +template +struct backend_type +{ + typedef typename expression_type::type num_type; + typedef typename backend_type::type type; +}; + +template +struct backend_type > +{ + typedef Backend type; +}; + +} // namespace detail + +// +// Traits class, lets us know whether a backend is an integer type, otherwise assumed to be a real number type: +// +template +struct is_extended_integer : public mpl::false_ {}; +template +struct is_extended_integer > : public is_extended_integer{}; + + +}} // namespaces + +#endif // BOOST_MATH_BIG_NUM_BASE_HPP + + diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp new file mode 100644 index 00000000..569a32f6 --- /dev/null +++ b/include/boost/math/big_number/default_ops.hpp @@ -0,0 +1,302 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_BIG_NUM_DEF_OPS +#define BOOST_MATH_BIG_NUM_DEF_OPS + +#include + +namespace boost{ namespace math{ namespace big_num_default_ops{ + +// +// Default versions of mixed arithmetic, these just construct a temporary +// from the arithmetic value and then do the arithmetic on that: +// +template +inline typename enable_if, is_convertible, is_same > >::type + add(T& result, V const& v) +{ + T t; + t = v; + add(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + subtract(T& result, V const& v) +{ + T t; + t = v; + subtract(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + multiply(T& result, V const& v) +{ + T t; + t = v; + multiply(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + divide(T& result, V const& v) +{ + T t; + t = v; + divide(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + modulus(T& result, V const& v) +{ + T t; + t = v; + mudulus(result, t); +} + +template +inline bool is_same_object(const T& u, const T&v) +{ return &u == &v; } +template +inline bool is_same_object(const T& u, const U&v) +{ return false; } + +// +// Default versions of 3-arg arithmetic functions, these just forward to the 2 arg versions: +// +template +inline void add(T& t, const U& u, const V& v) +{ + if(is_same_object(t, v)) + { + add(t, u); + } + else if(is_same_object(t, u)) + { + add(t, v); + } + else + { + t = u; + add(t, v); + } +} +template +inline void subtract(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + subtract(t, v); + else if(is_same_object(t, v)) + { + subtract(t, u); + t.negate(); + } + else + { + t = u; + subtract(t, v); + } +} +template +inline void multiply(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + multiply(t, v); + else if(is_same_object(t, v)) + multiply(t, u); + else + { + t = u; + multiply(t, v); + } +} +template +inline void divide(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + divide(t, v); + else if(is_same_object(t, v)) + { + T temp = t; + divide(temp, u, v); + temp.swap(t); + } + else + { + t = u; + divide(t, v); + } +} +template +inline void modulus(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + modulus(t, v); + else if(is_same_object(t, v)) + { + T temp; + modulus(temp, u, v); + temp.swap(t); + } + else + { + t = u; + modulus(t, v); + } +} + +// +// Functions: +// +template +void abs(T* result, const T& arg) +{ + typedef typename T::signed_types type_list; + typedef typename mpl::front::type front; + *result = arg; + if(arg.compare(front(0)) < 0) + result->negate(); +} +template +void fabs(T* result, const T& arg) +{ + typedef typename T::signed_types type_list; + typedef typename mpl::front::type front; + *result = arg; + if(arg.compare(front(0)) < 0) + result->negate(); +} + +// +// These have to implemented by the backend, declared here so that our macro generated code compiles OK. +// +template +typename enable_if_c::type floor(); +template +typename enable_if_c::type ceil(); +template +typename enable_if_c::type trunc(); +template +typename enable_if_c::type sqrt(); +template +typename enable_if_c::type ldexp(); +template +typename enable_if_c::type frexp(); + +} + + +template +class big_number; + +namespace detail{ + +template +struct big_number_exp; + +} + +#define UNARY_OP_FUNCTOR(func)\ +namespace detail{\ +template \ +struct BOOST_JOIN(func, _funct)\ +{\ + void operator()(Backend* result, const Backend& arg)const\ + {\ + using big_num_default_ops::func;\ + func(result, arg);\ + }\ +};\ +\ +}\ +\ +template \ +typename proto::result_of::make_expr<\ + proto::tag::function\ + , detail::BOOST_JOIN(func, _funct)::type>\ + , detail::big_number_exp\ +>::type const \ +func(const detail::big_number_exp& arg)\ +{\ + return proto::make_expr(\ + detail::BOOST_JOIN(func, _funct)::type>() \ + , arg \ + );\ +}\ +template \ +typename proto::result_of::make_expr<\ + proto::tag::function\ + , detail::BOOST_JOIN(func, _funct)\ + , detail::big_number_exp*>::type>\ +>::type const \ +func(const big_number& arg)\ +{\ + return proto::make_expr(\ + detail::BOOST_JOIN(func, _funct)() \ + , static_cast*>::type>&>(arg) \ + );\ +} + +#define BINARY_OP_FUNCTOR(func)\ +namespace detail{\ +template \ +struct BOOST_JOIN(func, _funct)\ +{\ + template \ + void operator()(Backend* result, const Backend& arg, const A2& a)const\ + {\ + using big_num_default_ops::func;\ + func(result, arg, a);\ + }\ +};\ +\ +}\ +\ +template \ +typename proto::result_of::make_expr<\ + proto::tag::function\ + , detail::BOOST_JOIN(func, _funct)::type>\ + , detail::big_number_exp\ + , typename proto::result_of::as_child::type\ +>::type const \ +func(const detail::big_number_exp& arg, const A2& a)\ +{\ + return proto::make_expr(\ + detail::BOOST_JOIN(func, _funct)::type>() \ + , arg, proto::as_child(a) \ + );\ +}\ +template \ +typename proto::result_of::make_expr<\ + proto::tag::function\ + , detail::BOOST_JOIN(func, _funct)\ + , detail::big_number_exp*>::type>\ + , typename proto::result_of::as_child::type\ +>::type const \ +func(const big_number& arg, const A2& a)\ +{\ + return proto::make_expr(\ + detail::BOOST_JOIN(func, _funct)() \ + , static_cast*>::type>&>(arg),\ + proto::as_child(a)\ + );\ +} + +UNARY_OP_FUNCTOR(abs) +UNARY_OP_FUNCTOR(fabs) +UNARY_OP_FUNCTOR(sqrt) +UNARY_OP_FUNCTOR(floor) +UNARY_OP_FUNCTOR(ceil) +UNARY_OP_FUNCTOR(trunc) + +BINARY_OP_FUNCTOR(ldexp) +BINARY_OP_FUNCTOR(frexp) + +#undef BINARY_OP_FUNCTOR +#undef UNARY_OP_FUNCTOR + +}} // namespaces + +#endif + diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index 95fddb04..20dc9203 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -145,130 +145,45 @@ struct gmp_real_imp mpf_set_str(m_data, s, 10); return *this; } - gmp_real_imp& operator += (const gmp_real& o) - { - mpf_add(m_data, m_data, o.m_data); - return *this; - } - template - gmp_real_imp& operator += (V v) - { - gmp_real d; - d = v; - return *this += d; - } - gmp_real_imp& operator -= (const gmp_real& o) - { - mpf_sub(m_data, m_data, o.m_data); - return *this; - } - template - gmp_real_imp& operator -= (V v) - { - gmp_real d; - d = v; - return *this -= d; - } - gmp_real_imp& operator *= (const gmp_real& o) - { - mpf_mul(m_data, m_data, o.m_data); - return *this; - } - template - gmp_real_imp& operator *= (V v) - { - gmp_real d; - d = v; - return *this *= d; - } - gmp_real_imp& operator /= (const gmp_real& o) - { - mpf_div(m_data, m_data, o.m_data); - return *this; - } - template - gmp_real_imp& operator /= (V v) - { - gmp_real d; - d = v; - return *this /= d; - } - gmp_real_imp& operator += (unsigned long i) - { - mpf_add_ui(m_data, m_data, i); - return *this; - } - gmp_real_imp& operator -= (unsigned long i) - { - mpf_sub_ui(m_data, m_data, i); - return *this; - } - gmp_real_imp& operator *= (unsigned long i) - { - mpf_mul_ui(m_data, m_data, i); - return *this; - } - gmp_real_imp& operator /= (unsigned long i) - { - mpf_div_ui(m_data, m_data, i); - return *this; - } - gmp_real_imp& operator += (long i) - { - if(i > 0) - mpf_add_ui(m_data, m_data, i); - else - mpf_sub_ui(m_data, m_data, std::abs(i)); - return *this; - } - gmp_real_imp& operator -= (long i) - { - if(i > 0) - mpf_sub_ui(m_data, m_data, i); - else - mpf_add_ui(m_data, m_data, std::abs(i)); - return *this; - } - gmp_real_imp& operator *= (long i) - { - mpf_mul_ui(m_data, m_data, std::abs(i)); - if(i < 0) - mpf_neg(m_data, m_data); - return *this; - } - gmp_real_imp& operator /= (long i) - { - mpf_div_ui(m_data, m_data, std::abs(i)); - if(i < 0) - mpf_neg(m_data, m_data); - return *this; - } void swap(gmp_real_imp& o) { mpf_swap(m_data, o.m_data); } - std::string str(unsigned digits)const + std::string str(unsigned digits, bool scientific)const { + std::string result; mp_exp_t e; void *(*alloc_func_ptr) (size_t); void *(*realloc_func_ptr) (void *, size_t, size_t); void (*free_func_ptr) (void *, size_t); const char* ps = mpf_get_str (0, &e, 10, digits, m_data); - std::string s("0."); - if(ps[0] == '-') + std::ptrdiff_t sl = std::strlen(ps); + if(sl == 0) + return "0"; + if(*ps == '-') + --sl; // number of digits excluding sign. + if(!scientific + && (sl <= std::numeric_limits::digits10 + 1) + && (e >= sl) + && (sl <= std::numeric_limits::digits10 + 1)) { - s.insert(0, ps, 1); - s += ps + 1; + result = ps; + result.append(e-sl, '0'); } else { - s += ps; + result = ps; + if(ps[0] == '-') + result.insert(2, 1, '.'); + else + result.insert(1, 1, '.'); + --e; + if(e) + result += "e" + lexical_cast(e); } - s += "e"; - s += boost::lexical_cast(e); mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); - return s; + return result; } ~gmp_real_imp() { @@ -400,74 +315,280 @@ private: } }; +template +inline void add(gmp_real& result, const gmp_real& o) +{ + mpf_add(result.data(), result.data(), o.data()); +} +template +inline void subtract(gmp_real& result, const gmp_real& o) +{ + mpf_sub(result.data(), result.data(), o.data()); +} +template +inline void multiply(gmp_real& result, const gmp_real& o) +{ + mpf_mul(result.data(), result.data(), o.data()); +} +template +inline void divide(gmp_real& result, const gmp_real& o) +{ + mpf_div(result.data(), result.data(), o.data()); +} +template +inline void add(gmp_real& result, unsigned long i) +{ + mpf_add_ui(result.data(), result.data(), i); +} +template +inline void subtract(gmp_real& result, unsigned long i) +{ + mpf_sub_ui(result.data(), result.data(), i); +} +template +inline void multiply(gmp_real& result, unsigned long i) +{ + mpf_mul_ui(result.data(), result.data(), i); +} +template +inline void divide(gmp_real& result, unsigned long i) +{ + mpf_div_ui(result.data(), result.data(), i); +} +template +inline void add(gmp_real& result, long i) +{ + if(i > 0) + mpf_add_ui(result.data(), result.data(), i); + else + mpf_sub_ui(result.data(), result.data(), std::abs(i)); +} +template +inline void subtract(gmp_real& result, long i) +{ + if(i > 0) + mpf_sub_ui(result.data(), result.data(), i); + else + mpf_add_ui(result.data(), result.data(), std::abs(i)); +} +template +inline void multiply(gmp_real& result, long i) +{ + mpf_mul_ui(result.data(), result.data(), std::abs(i)); + if(i < 0) + mpf_neg(result.data(), result.data()); +} +template +inline void divide(gmp_real& result, long i) +{ + mpf_div_ui(result.data(), result.data(), std::abs(i)); + if(i < 0) + mpf_neg(result.data(), result.data()); +} +// +// Specialised 3 arg versions of the basic operators: +// +template +inline void add(gmp_real& a, const gmp_real& x, const gmp_real& y) +{ + mpf_add(a.data(), x.data(), y.data()); +} +template +inline void add(gmp_real& a, const gmp_real& x, unsigned long y) +{ + mpf_add_ui(a.data(), x.data(), y); +} +template +inline void add(gmp_real& a, const gmp_real& x, long y) +{ + if(y < 0) + mpf_sub_ui(a.data(), x.data(), -y); + else + mpf_add_ui(a.data(), x.data(), y); +} +template +inline void add(gmp_real& a, unsigned long x, const gmp_real& y) +{ + mpf_add_ui(a.data(), y.data(), x); +} +template +inline void add(gmp_real& a, long x, const gmp_real& y) +{ + if(x < 0) + { + mpf_ui_sub(a.data(), -x, y.data()); + mpf_neg(a.data(), a.data()); + } + else + mpf_add_ui(a.data(), y.data(), x); +} +template +inline void subtract(gmp_real& a, const gmp_real& x, const gmp_real& y) +{ + mpf_sub(a.data(), x.data(), y.data()); +} +template +inline void subtract(gmp_real& a, const gmp_real& x, unsigned long y) +{ + mpf_sub_ui(a.data(), x.data(), y); +} +template +inline void subtract(gmp_real& a, const gmp_real& x, long y) +{ + if(y < 0) + mpf_add_ui(a.data(), x.data(), -y); + else + mpf_sub_ui(a.data(), x.data(), y); +} +template +inline void subtract(gmp_real& a, unsigned long x, const gmp_real& y) +{ + mpf_ui_sub(a.data(), x, y.data()); +} +template +inline void subtract(gmp_real& a, long x, const gmp_real& y) +{ + if(x < 0) + { + mpf_add_ui(a.data(), y.data(), -x); + mpf_neg(a.data(), a.data()); + } + else + mpf_ui_sub(a.data(), x, y.data()); +} + +template +inline void multiply(gmp_real& a, const gmp_real& x, const gmp_real& y) +{ + mpf_mul(a.data(), x.data(), y.data()); +} +template +inline void multiply(gmp_real& a, const gmp_real& x, unsigned long y) +{ + mpf_mul_ui(a.data(), x.data(), y); +} +template +inline void multiply(gmp_real& a, const gmp_real& x, long y) +{ + if(y < 0) + { + mpf_mul_ui(a.data(), x.data(), -y); + a.negate(); + } + else + mpf_mul_ui(a.data(), x.data(), y); +} +template +inline void multiply(gmp_real& a, unsigned long x, const gmp_real& y) +{ + mpf_mul_ui(a.data(), y.data(), x); +} +template +inline void multiply(gmp_real& a, long x, const gmp_real& y) +{ + if(x < 0) + { + mpf_mul_ui(a.data(), y.data(), -x); + mpf_neg(a.data(), a.data()); + } + else + mpf_mul_ui(a.data(), y.data(), x); +} + +template +inline void divide(gmp_real& a, const gmp_real& x, const gmp_real& y) +{ + mpf_div(a.data(), x.data(), y.data()); +} +template +inline void divide(gmp_real& a, const gmp_real& x, unsigned long y) +{ + mpf_div_ui(a.data(), x.data(), y); +} +template +inline void divide(gmp_real& a, const gmp_real& x, long y) +{ + if(y < 0) + { + mpf_div_ui(a.data(), x.data(), -y); + a.negate(); + } + else + mpf_div_ui(a.data(), x.data(), y); +} +template +inline void divide(gmp_real& a, unsigned long x, const gmp_real& y) +{ + mpf_ui_div(a.data(), x, y.data()); +} +template +inline void divide(gmp_real& a, long x, const gmp_real& y) +{ + if(x < 0) + { + mpf_ui_div(a.data(), -x, y.data()); + mpf_neg(a.data(), a.data()); + } + else + mpf_ui_div(a.data(), x, y.data()); +} + // // Native non-member operations: // template -big_number > sqrt(const big_number >& val) +inline void sqrt(gmp_real* result, const gmp_real& val) { - big_number > result; - mpf_sqrt(result.backend().data(), val.backend().data()); - return result; + mpf_sqrt(result->data(), val.data()); +} + +template +inline void abs(gmp_real* result, const gmp_real& val) +{ + mpf_abs(result->data(), val.data()); +} + +template +inline void fabs(gmp_real* result, const gmp_real& val) +{ + mpf_abs(result->data(), val.data()); } template -big_number > abs(const big_number >& val) +inline void ceil(gmp_real* result, const gmp_real& val) { - big_number > result; - mpf_abs(result.backend().data(), val.backend().data()); - return result; + mpf_ceil(result->data(), val.data()); } template -big_number > fabs(const big_number >& val) +inline void floor(gmp_real* result, const gmp_real& val) { - big_number > result; - mpf_abs(result.backend().data(), val.backend().data()); - return result; + mpf_floor(result->data(), val.data()); } template -big_number > ceil(const big_number >& val) +inline void trunc(gmp_real* result, const gmp_real& val) { - big_number > result; - mpf_ceil(result.backend().data(), val.backend().data()); - return result; + mpf_trunc(result->data(), val.data()); } template -big_number > floor(const big_number >& val) +inline void ldexp(gmp_real* result, const gmp_real& val, long e) { - big_number > result; - mpf_floor(result.backend().data(), val.backend().data()); - return result; -} -template -big_number > trunc(const big_number >& val) -{ - big_number > result; - mpf_trunc(result.backend().data(), val.backend().data()); - return result; -} -template -big_number > ldexp(const big_number >& val, long e) -{ - big_number > result; if(e > 0) - mpf_mul_2exp(result.backend().data(), val.backend().data(), e); + mpf_mul_2exp(result->data(), val.data(), e); else if(e < 0) - mpf_div_2exp(result.backend().data(), val.backend().data(), -e); - return result; + mpf_div_2exp(result->data(), val.data(), -e); } template -big_number > frexp(const big_number >& val, int* e) +inline void frexp(gmp_real* result, const gmp_real& val, int* e) { long v; - mpf_get_d_2exp(&v, val.backend().data()); + mpf_get_d_2exp(&v, val.data()); *e = v; - return ldexp(val, -v); + return ldexp(result, val, -v); } template -big_number > frexp(const big_number >& val, long* e) +inline void frexp(gmp_real* result, const gmp_real& val, long* e) { - mpf_get_d_2exp(e, val.backend().data()); - return ldexp(val, -*e); + mpf_get_d_2exp(e, val.data()); + return ldexp(result, val, -*e); } struct gmp_int @@ -582,163 +703,11 @@ struct gmp_int mpz_set_str(m_data, s, 10); return *this; } - gmp_int& operator += (const gmp_int& o) - { - mpz_add(m_data, m_data, o.m_data); - return *this; - } - template - gmp_int& operator += (V v) - { - gmp_int d; - d = v; - return *this += d; - } - gmp_int& operator -= (const gmp_int& o) - { - mpz_sub(m_data, m_data, o.m_data); - return *this; - } - template - gmp_int& operator -= (V v) - { - gmp_int d; - d = v; - return *this -= d; - } - gmp_int& operator *= (const gmp_int& o) - { - mpz_mul(m_data, m_data, o.m_data); - return *this; - } - template - gmp_int& operator *= (V v) - { - gmp_int d; - d = v; - return *this *= d; - } - gmp_int& operator /= (const gmp_int& o) - { - mpz_div(m_data, m_data, o.m_data); - return *this; - } - template - gmp_int& operator /= (V v) - { - gmp_int d; - d = v; - return *this /= d; - } - gmp_int& operator %= (const gmp_int& o) - { - bool neg = mpz_sgn(m_data) < 0; - bool neg2 = mpz_sgn(o.m_data) < 0; - mpz_mod(m_data, m_data, o.m_data); - if(neg) - { - if(!neg2) - negate(); - mpz_add(m_data, m_data, o.m_data); - if(!neg2) - negate(); - } - return *this; - } - template - gmp_int& operator %= (V v) - { - gmp_int d; - d = v; - return *this %= d; - } - gmp_int& operator += (unsigned long i) - { - mpz_add_ui(m_data, m_data, i); - return *this; - } - gmp_int& operator -= (unsigned long i) - { - mpz_sub_ui(m_data, m_data, i); - return *this; - } - gmp_int& operator *= (unsigned long i) - { - mpz_mul_ui(m_data, m_data, i); - return *this; - } - gmp_int& operator %= (unsigned long i) - { - bool neg = mpz_sgn(m_data) < 0; - mpz_mod_ui(m_data, m_data, i); - if(neg) - { - negate(); - mpz_add_ui(m_data, m_data, i); - negate(); - } - return *this; - } - gmp_int& operator /= (unsigned long i) - { - mpz_div_ui(m_data, m_data, i); - return *this; - } - gmp_int& operator += (long i) - { - if(i > 0) - mpz_add_ui(m_data, m_data, i); - else - mpz_sub_ui(m_data, m_data, std::abs(i)); - return *this; - } - gmp_int& operator -= (long i) - { - if(i > 0) - mpz_sub_ui(m_data, m_data, i); - else - mpz_add_ui(m_data, m_data, std::abs(i)); - return *this; - } - gmp_int& operator *= (long i) - { - mpz_mul_ui(m_data, m_data, std::abs(i)); - if(i < 0) - mpz_neg(m_data, m_data); - return *this; - } - gmp_int& operator %= (long i) - { - bool neg = mpz_sgn(m_data) < 0; - bool neg2 = i < 0; - mpz_mod_ui(m_data, m_data, std::abs(i)); - if(neg) - { - if(!neg2) - { - negate(); - mpz_add_ui(m_data, m_data, std::abs(i)); - negate(); - } - else - { - mpz_sub_ui(m_data, m_data, std::abs(i)); - } - } - return *this; - } - gmp_int& operator /= (long i) - { - mpz_div_ui(m_data, m_data, std::abs(i)); - if(i < 0) - mpz_neg(m_data, m_data); - return *this; - } void swap(gmp_int& o) { mpz_swap(m_data, o.m_data); } - std::string str(unsigned)const + std::string str(unsigned /*digits*/, bool /*scientific*/)const { void *(*alloc_func_ptr) (size_t); void *(*realloc_func_ptr) (void *, size_t, size_t); @@ -776,10 +745,218 @@ struct gmp_int d = v; return compare(d); } + mpz_t& data() { return m_data; } + const mpz_t& data()const { return m_data; } protected: mpz_t m_data; }; +inline void add(gmp_int& t, const gmp_int& o) +{ + mpz_add(t.data(), t.data(), o.data()); +} +inline void subtract(gmp_int& t, const gmp_int& o) +{ + mpz_sub(t.data(), t.data(), o.data()); +} +inline void multiply(gmp_int& t, const gmp_int& o) +{ + mpz_mul(t.data(), t.data(), o.data()); +} +inline void divide(gmp_int& t, const gmp_int& o) +{ + mpz_div(t.data(), t.data(), o.data()); +} +inline void modulus(gmp_int& t, const gmp_int& o) +{ + bool neg = mpz_sgn(t.data()) < 0; + bool neg2 = mpz_sgn(o.data()) < 0; + mpz_mod(t.data(), t.data(), o.data()); + if(neg) + { + if(!neg2) + t.negate(); + mpz_add(t.data(), t.data(), o.data()); + if(!neg2) + t.negate(); + } +} +inline void add(gmp_int& t, unsigned long i) +{ + mpz_add_ui(t.data(), t.data(), i); +} +inline void subtract(gmp_int& t, unsigned long i) +{ + mpz_sub_ui(t.data(), t.data(), i); +} +inline void multiply(gmp_int& t, unsigned long i) +{ + mpz_mul_ui(t.data(), t.data(), i); +} +inline void modulus(gmp_int& t, unsigned long i) +{ + bool neg = mpz_sgn(t.data()) < 0; + mpz_mod_ui(t.data(), t.data(), i); + if(neg) + { + t.negate(); + mpz_add_ui(t.data(), t.data(), i); + t.negate(); + } +} +inline void divide(gmp_int& t, unsigned long i) +{ + mpz_div_ui(t.data(), t.data(), i); +} +inline void add(gmp_int& t, long i) +{ + if(i > 0) + mpz_add_ui(t.data(), t.data(), i); + else + mpz_sub_ui(t.data(), t.data(), -i); +} +inline void subtract(gmp_int& t, long i) +{ + if(i > 0) + mpz_sub_ui(t.data(), t.data(), i); + else + mpz_add_ui(t.data(), t.data(), -i); +} +inline void multiply(gmp_int& t, long i) +{ + mpz_mul_ui(t.data(), t.data(), std::abs(i)); + if(i < 0) + mpz_neg(t.data(), t.data()); +} +inline void modulus(gmp_int& t, long i) +{ + bool neg = mpz_sgn(t.data()) < 0; + bool neg2 = i < 0; + mpz_mod_ui(t.data(), t.data(), std::abs(i)); + if(neg) + { + if(!neg2) + { + t.negate(); + mpz_add_ui(t.data(), t.data(), std::abs(i)); + t.negate(); + } + else + { + mpz_sub_ui(t.data(), t.data(), std::abs(i)); + } + } +} +inline void divide(gmp_int& t, long i) +{ + mpz_div_ui(t.data(), t.data(), std::abs(i)); + if(i < 0) + mpz_neg(t.data(), t.data()); +} + +inline void add(gmp_int& t, const gmp_int& p, const gmp_int& o) +{ + mpz_add(t.data(), p.data(), o.data()); +} +inline void subtract(gmp_int& t, const gmp_int& p, const gmp_int& o) +{ + mpz_sub(t.data(), p.data(), o.data()); +} +inline void multiply(gmp_int& t, const gmp_int& p, const gmp_int& o) +{ + mpz_mul(t.data(), p.data(), o.data()); +} +inline void divide(gmp_int& t, const gmp_int& p, const gmp_int& o) +{ + mpz_div(t.data(), p.data(), o.data()); +} +inline void modulus(gmp_int& t, const gmp_int& p, const gmp_int& o) +{ + bool neg = mpz_sgn(p.data()) < 0; + bool neg2 = mpz_sgn(o.data()) < 0; + mpz_mod(t.data(), p.data(), o.data()); + if(neg) + { + if(!neg2) + t.negate(); + mpz_add(t.data(), t.data(), o.data()); + if(!neg2) + t.negate(); + } +} +inline void add(gmp_int& t, const gmp_int& p, unsigned long i) +{ + mpz_add_ui(t.data(), p.data(), i); +} +inline void subtract(gmp_int& t, const gmp_int& p, unsigned long i) +{ + mpz_sub_ui(t.data(), p.data(), i); +} +inline void multiply(gmp_int& t, const gmp_int& p, unsigned long i) +{ + mpz_mul_ui(t.data(), p.data(), i); +} +inline void modulus(gmp_int& t, const gmp_int& p, unsigned long i) +{ + bool neg = mpz_sgn(p.data()) < 0; + mpz_mod_ui(t.data(), p.data(), i); + if(neg) + { + t.negate(); + mpz_add_ui(t.data(), t.data(), i); + t.negate(); + } +} +inline void divide(gmp_int& t, const gmp_int& p, unsigned long i) +{ + mpz_div_ui(t.data(), p.data(), i); +} +inline void add(gmp_int& t, const gmp_int& p, long i) +{ + if(i > 0) + mpz_add_ui(t.data(), p.data(), i); + else + mpz_sub_ui(t.data(), p.data(), -i); +} +inline void subtract(gmp_int& t, const gmp_int& p, long i) +{ + if(i > 0) + mpz_sub_ui(t.data(), p.data(), i); + else + mpz_add_ui(t.data(), p.data(), -i); +} +inline void multiply(gmp_int& t, const gmp_int& p, long i) +{ + mpz_mul_ui(t.data(), p.data(), std::abs(i)); + if(i < 0) + mpz_neg(t.data(), t.data()); +} +inline void modulus(gmp_int& t, const gmp_int& p, long i) +{ + bool neg = mpz_sgn(p.data()) < 0; + bool neg2 = i < 0; + mpz_mod_ui(t.data(), p.data(), std::abs(i)); + if(neg) + { + if(!neg2) + { + t.negate(); + mpz_add_ui(t.data(), t.data(), std::abs(i)); + t.negate(); + } + else + { + mpz_sub_ui(t.data(), t.data(), std::abs(i)); + } + } +} +inline void divide(gmp_int& t, const gmp_int& p, long i) +{ + mpz_div_ui(t.data(), p.data(), std::abs(i)); + if(i < 0) + mpz_neg(t.data(), t.data()); +} + template<> struct is_extended_integer : public mpl::true_ {}; diff --git a/include/boost/math/concepts/big_number_architypes.hpp b/include/boost/math/concepts/big_number_architypes.hpp index 31b4d992..6067b6e6 100644 --- a/include/boost/math/concepts/big_number_architypes.hpp +++ b/include/boost/math/concepts/big_number_architypes.hpp @@ -18,9 +18,9 @@ namespace concepts{ struct big_number_backend_real_architype { - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list real_types; + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; big_number_backend_real_architype() { @@ -49,24 +49,6 @@ struct big_number_backend_real_architype std::cout << "Int Assignment (" << i << ")" << std::endl; return *this; } - big_number_backend_real_architype& operator = (unsigned i) - { - m_value = i; - std::cout << "UInt Assignment (" << i << ")" << std::endl; - return *this; - } - big_number_backend_real_architype& operator = (int i) - { - m_value = i; - std::cout << "Int Assignment (" << i << ")" << std::endl; - return *this; - } - big_number_backend_real_architype& operator = (double d) - { - m_value = d; - std::cout << "double Assignment (" << d << ")" << std::endl; - return *this; - } big_number_backend_real_architype& operator = (long double d) { m_value = d; @@ -79,182 +61,29 @@ struct big_number_backend_real_architype std::cout << "const char* Assignment (" << s << ")" << std::endl; return *this; } - big_number_backend_real_architype& operator += (const big_number_backend_real_architype& o) - { - std::cout << "Addition (" << m_value << " += " << o.m_value << ")" << std::endl; - m_value += o.m_value; - return *this; - } - big_number_backend_real_architype& operator -= (const big_number_backend_real_architype& o) - { - std::cout << "Subtraction (" << m_value << " -= " << o.m_value << ")" << std::endl; - m_value -= o.m_value; - return *this; - } - big_number_backend_real_architype& operator *= (const big_number_backend_real_architype& o) - { - std::cout << "Multiplication (" << m_value << " *= " << o.m_value << ")" << std::endl; - m_value *= o.m_value; - return *this; - } - big_number_backend_real_architype& operator /= (const big_number_backend_real_architype& o) - { - std::cout << "Division (" << m_value << " /= " << o.m_value << ")" << std::endl; - m_value /= o.m_value; - return *this; - } - big_number_backend_real_architype& operator += (boost::uintmax_t i) - { - std::cout << "UIntmax_t Addition (" << m_value << " += " << i << ")" << std::endl; - m_value += i; - return *this; - } - big_number_backend_real_architype& operator -= (boost::uintmax_t i) - { - std::cout << "UIntmax_t Subtraction (" << m_value << " -= " << i << ")" << std::endl; - m_value -= i; - return *this; - } - big_number_backend_real_architype& operator *= (boost::uintmax_t i) - { - std::cout << "UIntmax_t Multiplication (" << m_value << " *= " << i << ")" << std::endl; - m_value *= i; - return *this; - } - big_number_backend_real_architype& operator /= (boost::uintmax_t i) - { - std::cout << "UIntmax_t Division (" << m_value << " /= " << i << ")" << std::endl; - m_value /= i; - return *this; - } - big_number_backend_real_architype& operator += (boost::intmax_t i) - { - std::cout << "Intmax_t Addition (" << m_value << " += " << i << ")" << std::endl; - m_value += i; - return *this; - } - big_number_backend_real_architype& operator -= (boost::intmax_t i) - { - std::cout << "Intmax_t Subtraction (" << m_value << " -= " << i << ")" << std::endl; - m_value -= i; - return *this; - } - big_number_backend_real_architype& operator *= (boost::intmax_t i) - { - std::cout << "Intmax_t Multiplication (" << m_value << " *= " << i << ")" << std::endl; - m_value *= i; - return *this; - } - big_number_backend_real_architype& operator /= (boost::intmax_t i) - { - std::cout << "Intmax_t Division (" << m_value << " /= " << i << ")" << std::endl; - m_value /= i; - return *this; - } - big_number_backend_real_architype& operator += (unsigned i) - { - std::cout << "UInt Addition (" << m_value << " += " << i << ")" << std::endl; - m_value += i; - return *this; - } - big_number_backend_real_architype& operator -= (unsigned i) - { - std::cout << "UInt Subtraction (" << m_value << " -= " << i << ")" << std::endl; - m_value -= i; - return *this; - } - big_number_backend_real_architype& operator *= (unsigned i) - { - std::cout << "UInt Multiplication (" << m_value << " *= " << i << ")" << std::endl; - m_value *= i; - return *this; - } - big_number_backend_real_architype& operator /= (unsigned i) - { - std::cout << "UInt Division (" << m_value << " /= " << i << ")" << std::endl; - m_value /= i; - return *this; - } - big_number_backend_real_architype& operator += (int i) - { - std::cout << "Int Addition (" << m_value << " += " << i << ")" << std::endl; - m_value += i; - return *this; - } - big_number_backend_real_architype& operator -= (int i) - { - std::cout << "Int Subtraction (" << m_value << " -= " << i << ")" << std::endl; - m_value -= i; - return *this; - } - big_number_backend_real_architype& operator *= (int i) - { - std::cout << "Int Multiplication (" << m_value << " *= " << i << ")" << std::endl; - m_value *= i; - return *this; - } - big_number_backend_real_architype& operator /= (int i) - { - std::cout << "Int Division (" << m_value << " /= " << i << ")" << std::endl; - m_value /= i; - return *this; - } - big_number_backend_real_architype& operator += (double d) - { - std::cout << "double Addition (" << m_value << " += " << d << ")" << std::endl; - m_value += d; - return *this; - } - big_number_backend_real_architype& operator -= (double d) - { - std::cout << "double Subtraction (" << m_value << " -= " << d << ")" << std::endl; - m_value -= d; - return *this; - } - big_number_backend_real_architype& operator *= (double d) - { - std::cout << "double Multiplication (" << m_value << " *= " << d << ")" << std::endl; - m_value *= d; - return *this; - } - big_number_backend_real_architype& operator /= (double d) - { - std::cout << "double Division (" << m_value << " /= " << d << ")" << std::endl; - m_value /= d; - return *this; - } - big_number_backend_real_architype& operator += (long double d) - { - std::cout << "long double Addition (" << m_value << " += " << d << ")" << std::endl; - m_value += d; - return *this; - } - big_number_backend_real_architype& operator -= (long double d) - { - std::cout << "long double Subtraction (" << m_value << " -= " << d << ")" << std::endl; - m_value -= d; - return *this; - } - big_number_backend_real_architype& operator *= (long double d) - { - std::cout << "long double Multiplication (" << m_value << " *= " << d << ")" << std::endl; - m_value *= d; - return *this; - } - big_number_backend_real_architype& operator /= (long double d) - { - std::cout << "long double Division (" << m_value << " /= " << d << ")" << std::endl; - m_value /= d; - return *this; - } void swap(big_number_backend_real_architype& o) { std::cout << "Swapping (" << m_value << " with " << o.m_value << ")" << std::endl; std::swap(m_value, o.m_value); } - std::string str(unsigned)const + std::string str(unsigned digits, bool scientific)const { - std::string s(boost::lexical_cast(m_value)); + std::stringstream ss; + if(scientific) + ss.setf(ss.scientific); + if(digits) + ss.precision(digits); + else + ss.precision(std::numeric_limits::digits10 + 2); + boost::intmax_t i = m_value; + boost::uintmax_t u = m_value; + if(!scientific && m_value == i) + ss << i; + else if(!scientific && m_value == u) + ss << u; + else + ss << m_value; + std::string s = ss.str(); std::cout << "Converting to string (" << s << ")" << std::endl; return s; } @@ -268,16 +97,6 @@ struct big_number_backend_real_architype std::cout << "Comparison" << std::endl; return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); } - int compare(int i)const - { - std::cout << "Comparison with int" << std::endl; - return m_value > i ? 1 : (m_value < i ? -1 : 0); - } - int compare(unsigned i)const - { - std::cout << "Comparison with unsigned" << std::endl; - return m_value > i ? 1 : (m_value < i ? -1 : 0); - } int compare(boost::intmax_t i)const { std::cout << "Comparison with int" << std::endl; @@ -288,20 +107,35 @@ struct big_number_backend_real_architype std::cout << "Comparison with unsigned" << std::endl; return m_value > i ? 1 : (m_value < i ? -1 : 0); } - int compare(double d)const - { - std::cout << "Comparison with double" << std::endl; - return m_value > d ? 1 : (m_value < d ? -1 : 0); - } int compare(long double d)const { std::cout << "Comparison with long double" << std::endl; return m_value > d ? 1 : (m_value < d ? -1 : 0); } -private: long double m_value; }; +inline void add(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +{ + std::cout << "Addition (" << result.m_value << " += " << o.m_value << ")" << std::endl; + result.m_value += o.m_value; +} +inline void subtract(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +{ + std::cout << "Subtraction (" << result.m_value << " -= " << o.m_value << ")" << std::endl; + result.m_value -= o.m_value; +} +inline void multiply(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +{ + std::cout << "Multiplication (" << result.m_value << " *= " << o.m_value << ")" << std::endl; + result.m_value *= o.m_value; +} +inline void divide(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +{ + std::cout << "Division (" << result.m_value << " /= " << o.m_value << ")" << std::endl; + result.m_value /= o.m_value; +} + typedef boost::math::big_number big_number_real_architype; }}} // namespaces diff --git a/math/test/linpack-benchmark.cpp b/math/test/linpack-benchmark.cpp index bf5300fb..89ba6099 100644 --- a/math/test/linpack-benchmark.cpp +++ b/math/test/linpack-benchmark.cpp @@ -18,6 +18,7 @@ http://www.netlib.org/f2c/libf2c.zip #include #include #include + #ifdef TEST_BIG_NUMBER #include typedef boost::math::mpf_real_100 real_type; diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 99436325..9aeefdb2 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -50,6 +50,16 @@ void test_integer_ops(const boost::mpl::true_&) BOOST_TEST(a % -7 == 20 % -7); BOOST_TEST(-a % 7u == -20 % 7); + b = -b; + BOOST_TEST(a % b == 20 % -7); + a = -a; + BOOST_TEST(a % b == -20 % -7); + BOOST_TEST(a % -7 == -20 % -7); + b = 7; + BOOST_TEST(a % b == -20 % 7); + BOOST_TEST(a % 7 == -20 % 7); + BOOST_TEST(a % 7u == -20 % 7); + a = 20; a %= b; BOOST_TEST(a == 20 % 7); @@ -83,6 +93,7 @@ void test_real_ops(const boost::mpl::false_&){} template void test_real_ops(const boost::mpl::true_&) { +#if defined(TEST_MPF) || defined(TEST_MPF_50) std::cout << "Root2 = " << sqrt(Real(2)) << std::endl; BOOST_TEST(abs(Real(2)) == 2); BOOST_TEST(abs(Real(-2)) == 2); @@ -92,12 +103,8 @@ void test_real_ops(const boost::mpl::true_&) BOOST_TEST(ceil(Real(5) / 2) == 3); BOOST_TEST(floor(Real(-5) / 2) == -3); BOOST_TEST(ceil(Real(-5) / 2) == -2); -#ifndef TEST_E_FLOAT BOOST_TEST(trunc(Real(5) / 2) == 2); BOOST_TEST(trunc(Real(-5) / 2) == -2); -#endif - -#ifndef TEST_E_FLOAT // // ldexp and frexp, these pretty much have to implemented by each backend: // @@ -108,6 +115,7 @@ void test_real_ops(const boost::mpl::true_&) Real r = frexp(v, &exp); BOOST_TEST(r == 0.5); BOOST_TEST(exp == 10); + BOOST_TEST(v == 512); v = 1 / v; r = frexp(v, &exp); BOOST_TEST(r == 0.5); @@ -115,9 +123,24 @@ void test_real_ops(const boost::mpl::true_&) #endif } +template +struct lexical_cast_target_type +{ + typedef typename boost::mpl::if_< + boost::is_signed, + boost::intmax_t, + typename boost::mpl::if_< + boost::is_unsigned, + boost::uintmax_t, + T + >::type + >::type type; +}; + template void test_negative_mixed(boost::mpl::true_ const&) { + typedef typename lexical_cast_target_type::type target_type; std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; Num n1 = -static_cast(1uLL << (std::numeric_limits::digits - 1)); Num n2 = -1; @@ -133,10 +156,10 @@ void test_negative_mixed(boost::mpl::true_ const&) BOOST_TEST(n2 == Real(n2)); BOOST_TEST(n3 == Real(n3)); BOOST_TEST(n4 == Real(n4)); - BOOST_TEST(n1 == boost::lexical_cast(Real(n1))); - BOOST_TEST(n2 == boost::lexical_cast(Real(n2))); - BOOST_TEST(n3 == boost::lexical_cast(Real(n3))); - BOOST_TEST(n4 == boost::lexical_cast(Real(n4))); + BOOST_TEST(n1 == boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value))); + BOOST_TEST(n2 == boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value))); + BOOST_TEST(n3 == boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value))); + BOOST_TEST(n4 == boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value))); // Assignment: Real r(0); BOOST_TEST(r != n1); @@ -172,6 +195,21 @@ void test_negative_mixed(boost::mpl::true_ const&) BOOST_TEST(Real(r / n5) == n1 / n5); r /= n5; BOOST_TEST(r == n1 / n5); + // + // Extra cases for full coverage: + // + r = Real(n4) + n5; + BOOST_TEST(r == n4 + n5); + r = n4 + Real(n5); + BOOST_TEST(r == n4 + n5); + r = Real(n4) - n5; + BOOST_TEST(r == n4 - n5); + r = n4 - Real(n5); + BOOST_TEST(r == n4 - n5); + r = n4 * Real(n5); + BOOST_TEST(r == n4 * n5); + r = (4 * n4) / Real(4); + BOOST_TEST(r == n4); } template @@ -182,6 +220,7 @@ void test_negative_mixed(boost::mpl::false_ const&) template void test_mixed() { + typedef typename lexical_cast_target_type::type target_type; std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; Num n1 = static_cast(1uLL << (std::numeric_limits::digits - 1)); Num n2 = 1; @@ -197,10 +236,10 @@ void test_mixed() BOOST_TEST(n2 == Real(n2)); BOOST_TEST(n3 == Real(n3)); BOOST_TEST(n4 == Real(n4)); - BOOST_TEST(n1 == boost::lexical_cast(Real(n1))); - BOOST_TEST(n2 == boost::lexical_cast(Real(n2))); - BOOST_TEST(n3 == boost::lexical_cast(Real(n3))); - BOOST_TEST(n4 == boost::lexical_cast(Real(n4))); + BOOST_TEST(n1 == boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value))); + BOOST_TEST(n2 == boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value))); + BOOST_TEST(n3 == boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value))); + BOOST_TEST(n4 == boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value))); // Assignment: Real r(0); BOOST_TEST(r != n1); @@ -237,6 +276,18 @@ void test_mixed() r /= n5; BOOST_TEST(r == n1 / n5); + // + // special cases for full coverage: + // + r = n5 + Real(n4); + BOOST_TEST(r == n4 + n5); + r = n4 - Real(n5); + BOOST_TEST(r == n4 - n5); + r = n4 * Real(n5); + BOOST_TEST(r == n4 * n5); + r = (4 * n4) / Real(4); + BOOST_TEST(r == n4); + test_negative_mixed(boost::mpl::bool_::is_signed>()); } @@ -439,6 +490,28 @@ void test() ac = a + std::string("8"); BOOST_TEST(ac == 16); #endif + // + // simple tests with immediate values, these calls can be optimised in many backends: + // + ac = a + b; + BOOST_TEST(ac == 72); + ac = a + +b; + BOOST_TEST(ac == 72); + ac = +a + b; + BOOST_TEST(ac == 72); + ac = +a + +b; + BOOST_TEST(ac == 72); + ac = a + -b; + BOOST_TEST(ac == 8 - 64); + ac = -a + b; + BOOST_TEST(ac == -8+64); + ac = -a + -b; + BOOST_TEST(ac == -72); + ac = a + - + -b; // lots of unary operators!! + BOOST_TEST(ac == 72); + ac = a; + ac = b / ac; + BOOST_TEST(ac == b / a); // // Comparisons: // From acc0bbe5111089d22035239b8c000a0c25645360 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 17 Aug 2011 08:38:17 +0000 Subject: [PATCH 009/256] Add some more modulus tests, fix regressions and add abs function for gmp_int backend. [SVN r73840] --- include/boost/math/big_number/default_ops.hpp | 2 +- include/boost/math/big_number/gmp.hpp | 5 ++++ math/test/test_arithmetic.cpp | 25 +++++++++++++++++++ 3 files changed, 31 insertions(+), 1 deletion(-) diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index 569a32f6..86a2aa09 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -52,7 +52,7 @@ inline typename enable_if, is_convertible diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index 20dc9203..ff74c39d 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -957,6 +957,11 @@ inline void divide(gmp_int& t, const gmp_int& p, long i) mpz_neg(t.data(), t.data()); } +inline void abs(gmp_int* result, const gmp_int& val) +{ + mpz_abs(result->data(), val.data()); +} + template<> struct is_extended_integer : public mpl::true_ {}; diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 9aeefdb2..c87f94c0 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -85,6 +85,31 @@ void test_integer_ops(const boost::mpl::true_&) a = -20; a %= -7; BOOST_TEST(a == -20 % -7); +#ifndef BOOST_NO_LONG_LONG + a = 20; + a %= 7uLL; + BOOST_TEST(a == 20 % 7); + a = -20; + a %= 7uLL; + BOOST_TEST(a == -20 % 7); + a = 20; + a %= -7LL; + BOOST_TEST(a == 20 % -7); + a = -20; + a %= -7LL; + BOOST_TEST(a == -20 % -7); +#endif + // + // Non-member functions: + // + a = -20; + BOOST_TEST(abs(a) == 20); + BOOST_TEST(abs(-a) == 20); + BOOST_TEST(abs(+a) == 20); + a = 20; + BOOST_TEST(abs(a) == 20); + BOOST_TEST(abs(-a) == 20); + BOOST_TEST(abs(+a) == 20); } template From a21103c7b7a9e47ea3d88911fb1774a700cf1e55 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 19 Aug 2011 17:24:39 +0000 Subject: [PATCH 010/256] Fix buglets in GMP support, add MPFR support. [SVN r73922] --- include/boost/math/big_number/gmp.hpp | 13 +- include/boost/math/big_number/mpfr.hpp | 613 +++++++++++++++++++++++++ math/test/linpack-benchmark.cpp | 21 +- math/test/test_arithmetic.cpp | 24 +- 4 files changed, 661 insertions(+), 10 deletions(-) create mode 100644 include/boost/math/big_number/mpfr.hpp diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index ff74c39d..e9811c28 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -31,7 +31,14 @@ struct gmp_real_imp gmp_real_imp(const gmp_real_imp& o) { - mpf_init_set(m_data, o.m_data); + // + // We have to do an init followed by a set here, otherwise *this may be at + // a lower precision than o: seems like mpf_init_set copies just enough bits + // to get the right value, but if it's then used in further calculations + // things go badly wrong!! + // + mpf_init2(m_data, (((digits10 ? digits10 : gmp_real<0>::default_precision()) + 1) * 1000L) / 301L); + mpf_set(m_data, o.m_data); } #ifndef BOOST_NO_RVALUE_REFERENCES gmp_real_imp(gmp_real_imp&& o) @@ -57,8 +64,8 @@ struct gmp_real_imp boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpf_t t; - mpf_init2(m_data, ((digits10 + 1) * 1000L) / 301L); - mpf_init2(t, ((digits10 + 1) * 1000L) / 301L); + mpf_init2(t, (((digits10 ? digits10 : gmp_real<0>::default_precision()) + 1) * 1000L) / 301L); + mpf_set_ui(m_data, 0); while(i) { mpf_set_ui(t, static_cast(i & mask)); diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp new file mode 100644 index 00000000..4589f68f --- /dev/null +++ b/include/boost/math/big_number/mpfr.hpp @@ -0,0 +1,613 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_BN_MPFR_HPP +#define BOOST_MATH_BN_MPFR_HPP + +#include +#include +#include +#include +#include +#include +#include + +namespace boost{ namespace math{ + +template +struct mpfr_real_backend; + +namespace detail{ + +template +struct mpfr_real_imp +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + mpfr_real_imp(){} + + mpfr_real_imp(const mpfr_real_imp& o) + { + mpfr_init2(m_data, (((digits10 ? digits10 : mpfr_real_backend<0>::default_precision()) + 1) * 1000L) / 301L); + mpfr_set(m_data, o.m_data, MPFR_RNDN); + } +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_imp(mpfr_real_imp&& o) + { + m_data[0] = o.m_data[0]; + o.m_data[0]._mpfr_d = 0; + } +#endif + mpfr_real_imp& operator = (const mpfr_real_imp& o) + { + mpfr_set(m_data, o.m_data, MPFR_RNDN); + return *this; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_imp& operator = (mpfr_real_imp&& o) + { + mpfr_swap(m_data, o.m_data); + return *this; + } +#endif + mpfr_real_imp& operator = (boost::uintmax_t i) + { + boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned shift = 0; + mpfr_t t; + mpfr_init2(t, (std::max)(static_cast(std::numeric_limits::digits), static_cast(((digits10 + 1) * 1000L) / 301L))); + mpfr_set_ui(m_data, 0, MPFR_RNDN); + while(i) + { + mpfr_set_ui(t, static_cast(i & mask), MPFR_RNDN); + long e; + const char* ps = mpfr_get_str (0, &e, 10, 0, t, MPFR_RNDN); + if(shift) + mpfr_mul_2exp(t, t, shift, MPFR_RNDN); + ps = mpfr_get_str (0, &e, 10, 0, t, MPFR_RNDN); + mpfr_add(m_data, m_data, t, MPFR_RNDN); + ps = mpfr_get_str (0, &e, 10, 0, m_data, MPFR_RNDN); + shift += std::numeric_limits::digits; + i >>= std::numeric_limits::digits; + } + mpfr_clear(t); + return *this; + } + mpfr_real_imp& operator = (boost::intmax_t i) + { + bool neg = i < 0; + *this = static_cast(std::abs(i)); + if(neg) + mpfr_neg(m_data, m_data, MPFR_RNDN); + return *this; + } + mpfr_real_imp& operator = (unsigned long i) + { + mpfr_set_ui(m_data, i, MPFR_RNDN); + return *this; + } + mpfr_real_imp& operator = (long i) + { + mpfr_set_si(m_data, i, MPFR_RNDN); + return *this; + } + mpfr_real_imp& operator = (double d) + { + mpfr_set_d(m_data, d, MPFR_RNDN); + return *this; + } + mpfr_real_imp& operator = (long double a) + { + using std::frexp; + using std::ldexp; + using std::floor; + + if (a == 0) { + mpfr_set_si(m_data, 0, MPFR_RNDN); + return *this; + } + + if (a == 1) { + mpfr_set_si(m_data, 1, MPFR_RNDN); + return *this; + } + + BOOST_ASSERT(!(boost::math::isinf)(a)); + BOOST_ASSERT(!(boost::math::isnan)(a)); + + int e; + long double f, term; + mpfr_init_set_ui(m_data, 0u, MPFR_RNDN); + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + mpfr_mul_2exp(m_data, m_data, shift, MPFR_RNDN); + if(term > 0) + mpfr_add_ui(m_data, m_data, static_cast(term), MPFR_RNDN); + else + mpfr_sub_ui(m_data, m_data, static_cast(-term), MPFR_RNDN); + f -= term; + } + if(e > 0) + mpfr_mul_2exp(m_data, m_data, e, MPFR_RNDN); + else if(e < 0) + mpfr_div_2exp(m_data, m_data, -e, MPFR_RNDN); + return *this; + } + mpfr_real_imp& operator = (const char* s) + { + mpfr_set_str(m_data, s, 10, MPFR_RNDN); + return *this; + } + void swap(mpfr_real_imp& o) + { + mpfr_swap(m_data, o.m_data); + } + std::string str(unsigned digits, bool scientific)const + { + std::string result; + mp_exp_t e; + void *(*alloc_func_ptr) (size_t); + void *(*realloc_func_ptr) (void *, size_t, size_t); + void (*free_func_ptr) (void *, size_t); + const char* ps = mpfr_get_str (0, &e, 10, digits, m_data, MPFR_RNDN); + std::ptrdiff_t sl = std::strlen(ps); + unsigned chars = sl; + if(sl == 0) + return "0"; + while(ps[chars-1] == '0') + --chars; + if(*ps == '-') + --chars; // number of digits excluding sign. + if(chars == 0) + return "0"; + if(!scientific + && (chars <= std::numeric_limits::digits10 + 1) + && (e >= (int)chars) + && (chars <= std::numeric_limits::digits10 + 1)) + { + result.assign(ps, (*ps == '-' ? chars+1 : chars)); + result.append(e-chars, '0'); + } + else + { + result = ps; + if(ps[0] == '-') + result.insert(2, 1, '.'); + else + result.insert(1, 1, '.'); + --e; + if(e) + result += "e" + lexical_cast(e); + } + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + (*free_func_ptr)((void*)ps, sl + 1); + return result; + } + ~mpfr_real_imp() + { + if(m_data[0]._mpfr_d) + mpfr_clear(m_data); + } + void negate() + { + mpfr_neg(m_data, m_data, MPFR_RNDN); + } + int compare(const mpfr_real_backend& o)const + { + return mpfr_cmp(m_data, o.m_data); + } + int compare(long i)const + { + return mpfr_cmp_si(m_data, i); + } + int compare(unsigned long i)const + { + return mpfr_cmp_ui(m_data, i); + } + template + int compare(V v)const + { + mpfr_real_backend d; + d = v; + return compare(d); + } + mpfr_t& data() { return m_data; } + const mpfr_t& data()const { return m_data; } +protected: + mpfr_t m_data; +}; + +} // namespace detail + +template +struct mpfr_real_backend : public detail::mpfr_real_imp +{ + mpfr_real_backend() + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + } + mpfr_real_backend(const mpfr_real_backend& o) : detail::mpfr_real_imp(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_backend(mpfr_real_backend&& o) : detail::mpfr_real_imp(o) {} +#endif + mpfr_real_backend& operator=(const mpfr_real_backend& o) + { + *static_cast*>(this) = static_cast const&>(o); + return *this; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_backend& operator=(mpfr_real_backend&& o) + { + *static_cast*>(this) = static_cast&&>(o); + return *this; + } +#endif + template + mpfr_real_backend& operator=(const V& v) + { + *static_cast*>(this) = v; + return *this; + } +}; + +template <> +struct mpfr_real_backend<0> : public detail::mpfr_real_imp<0> +{ + mpfr_real_backend() + { + mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + } + mpfr_real_backend(unsigned digits10) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + } + mpfr_real_backend(const mpfr_real_backend& o) : detail::mpfr_real_imp<0>(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_backend(mpfr_real_backend&& o) : detail::mpfr_real_imp<0>(o) {} +#endif + mpfr_real_backend(const mpfr_real_backend& o, unsigned digits10) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + *this = o; + } + + mpfr_real_backend& operator=(const mpfr_real_backend& o) + { + *static_cast*>(this) = static_cast const&>(o); + return *this; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_backend& operator=(mpfr_real_backend&& o) + { + *static_cast*>(this) = static_cast &&>(o); + return *this; + } +#endif + template + mpfr_real_backend& operator=(const V& v) + { + *static_cast*>(this) = v; + return *this; + } + static unsigned default_precision() + { + return get_default_precision(); + } + static void default_precision(unsigned v) + { + get_default_precision() = v; + } + unsigned precision()const + { + return mpfr_get_prec(this->m_data) * 301L / 1000 - 1; + } + void precision(unsigned digits10) + { + mpfr_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); + } +private: + static unsigned& get_default_precision() + { + static unsigned val = 50; + return val; + } +}; + +template +inline void add(mpfr_real_backend& result, const mpfr_real_backend& o) +{ + mpfr_add(result.data(), result.data(), o.data(), MPFR_RNDN); +} +template +inline void subtract(mpfr_real_backend& result, const mpfr_real_backend& o) +{ + mpfr_sub(result.data(), result.data(), o.data(), MPFR_RNDN); +} +template +inline void multiply(mpfr_real_backend& result, const mpfr_real_backend& o) +{ + mpfr_mul(result.data(), result.data(), o.data(), MPFR_RNDN); +} +template +inline void divide(mpfr_real_backend& result, const mpfr_real_backend& o) +{ + mpfr_div(result.data(), result.data(), o.data(), MPFR_RNDN); +} +template +inline void add(mpfr_real_backend& result, unsigned long i) +{ + mpfr_add_ui(result.data(), result.data(), i, MPFR_RNDN); +} +template +inline void subtract(mpfr_real_backend& result, unsigned long i) +{ + mpfr_sub_ui(result.data(), result.data(), i, MPFR_RNDN); +} +template +inline void multiply(mpfr_real_backend& result, unsigned long i) +{ + mpfr_mul_ui(result.data(), result.data(), i, MPFR_RNDN); +} +template +inline void divide(mpfr_real_backend& result, unsigned long i) +{ + mpfr_div_ui(result.data(), result.data(), i, MPFR_RNDN); +} +template +inline void add(mpfr_real_backend& result, long i) +{ + if(i > 0) + mpfr_add_ui(result.data(), result.data(), i, MPFR_RNDN); + else + mpfr_sub_ui(result.data(), result.data(), std::abs(i), MPFR_RNDN); +} +template +inline void subtract(mpfr_real_backend& result, long i) +{ + if(i > 0) + mpfr_sub_ui(result.data(), result.data(), i, MPFR_RNDN); + else + mpfr_add_ui(result.data(), result.data(), std::abs(i), MPFR_RNDN); +} +template +inline void multiply(mpfr_real_backend& result, long i) +{ + mpfr_mul_ui(result.data(), result.data(), std::abs(i), MPFR_RNDN); + if(i < 0) + mpfr_neg(result.data(), result.data(), MPFR_RNDN); +} +template +inline void divide(mpfr_real_backend& result, long i) +{ + mpfr_div_ui(result.data(), result.data(), std::abs(i), MPFR_RNDN); + if(i < 0) + mpfr_neg(result.data(), result.data(), MPFR_RNDN); +} +// +// Specialised 3 arg versions of the basic operators: +// +template +inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +{ + mpfr_add(a.data(), x.data(), y.data(), MPFR_RNDN); +} +template +inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +{ + mpfr_add_ui(a.data(), x.data(), y, MPFR_RNDN); +} +template +inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +{ + if(y < 0) + mpfr_sub_ui(a.data(), x.data(), -y, MPFR_RNDN); + else + mpfr_add_ui(a.data(), x.data(), y, MPFR_RNDN); +} +template +inline void add(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +{ + mpfr_add_ui(a.data(), y.data(), x, MPFR_RNDN); +} +template +inline void add(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +{ + if(x < 0) + { + mpfr_ui_sub(a.data(), -x, y.data(), MPFR_RNDN); + mpfr_neg(a.data(), a.data(), MPFR_RNDN); + } + else + mpfr_add_ui(a.data(), y.data(), x, MPFR_RNDN); +} +template +inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +{ + mpfr_sub(a.data(), x.data(), y.data(), MPFR_RNDN); +} +template +inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +{ + mpfr_sub_ui(a.data(), x.data(), y, MPFR_RNDN); +} +template +inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +{ + if(y < 0) + mpfr_add_ui(a.data(), x.data(), -y, MPFR_RNDN); + else + mpfr_sub_ui(a.data(), x.data(), y, MPFR_RNDN); +} +template +inline void subtract(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +{ + mpfr_ui_sub(a.data(), x, y.data(), MPFR_RNDN); +} +template +inline void subtract(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +{ + if(x < 0) + { + mpfr_add_ui(a.data(), y.data(), -x, MPFR_RNDN); + mpfr_neg(a.data(), a.data(), MPFR_RNDN); + } + else + mpfr_ui_sub(a.data(), x, y.data(), MPFR_RNDN); +} + +template +inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +{ + mpfr_mul(a.data(), x.data(), y.data(), MPFR_RNDN); +} +template +inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +{ + mpfr_mul_ui(a.data(), x.data(), y, MPFR_RNDN); +} +template +inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +{ + if(y < 0) + { + mpfr_mul_ui(a.data(), x.data(), -y, MPFR_RNDN); + a.negate(); + } + else + mpfr_mul_ui(a.data(), x.data(), y, MPFR_RNDN); +} +template +inline void multiply(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +{ + mpfr_mul_ui(a.data(), y.data(), x, MPFR_RNDN); +} +template +inline void multiply(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +{ + if(x < 0) + { + mpfr_mul_ui(a.data(), y.data(), -x, MPFR_RNDN); + mpfr_neg(a.data(), a.data(), MPFR_RNDN); + } + else + mpfr_mul_ui(a.data(), y.data(), x, MPFR_RNDN); +} + +template +inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +{ + mpfr_div(a.data(), x.data(), y.data(), MPFR_RNDN); +} +template +inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +{ + mpfr_div_ui(a.data(), x.data(), y, MPFR_RNDN); +} +template +inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +{ + if(y < 0) + { + mpfr_div_ui(a.data(), x.data(), -y, MPFR_RNDN); + a.negate(); + } + else + mpfr_div_ui(a.data(), x.data(), y, MPFR_RNDN); +} +template +inline void divide(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +{ + mpfr_ui_div(a.data(), x, y.data(), MPFR_RNDN); +} +template +inline void divide(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +{ + if(x < 0) + { + mpfr_ui_div(a.data(), -x, y.data(), MPFR_RNDN); + mpfr_neg(a.data(), a.data(), MPFR_RNDN); + } + else + mpfr_ui_div(a.data(), x, y.data(), MPFR_RNDN); +} + +// +// Native non-member operations: +// +template +inline void sqrt(mpfr_real_backend* result, const mpfr_real_backend& val) +{ + mpfr_sqrt(result->data(), val.data(), MPFR_RNDN); +} + +template +inline void abs(mpfr_real_backend* result, const mpfr_real_backend& val) +{ + mpfr_abs(result->data(), val.data(), MPFR_RNDN); +} + +template +inline void fabs(mpfr_real_backend* result, const mpfr_real_backend& val) +{ + mpfr_abs(result->data(), val.data(), MPFR_RNDN); +} +template +inline void ceil(mpfr_real_backend* result, const mpfr_real_backend& val) +{ + mpfr_ceil(result->data(), val.data()); +} +template +inline void floor(mpfr_real_backend* result, const mpfr_real_backend& val) +{ + mpfr_floor(result->data(), val.data()); +} +template +inline void trunc(mpfr_real_backend* result, const mpfr_real_backend& val) +{ + mpfr_trunc(result->data(), val.data()); +} +template +inline void ldexp(mpfr_real_backend* result, const mpfr_real_backend& val, long e) +{ + if(e > 0) + mpfr_mul_2exp(result->data(), val.data(), e, MPFR_RNDN); + else if(e < 0) + mpfr_div_2exp(result->data(), val.data(), -e, MPFR_RNDN); +} +template +inline void frexp(mpfr_real_backend* result, const mpfr_real_backend& val, int* e) +{ + long v; + mpfr_get_d_2exp(&v, val.data(), MPFR_RNDN); + *e = v; + return ldexp(result, val, -v); +} +template +inline void frexp(mpfr_real_backend* result, const mpfr_real_backend& val, long* e) +{ + mpfr_get_d_2exp(e, val.data(), MPFR_RNDN); + return ldexp(result, val, -*e); +} + +typedef big_number > mpfr_real_50; +typedef big_number > mpfr_real_100; +typedef big_number > mpfr_real_500; +typedef big_number > mpfr_real_1000; +typedef big_number > mpfr_real; + +}} // namespaces + +#endif diff --git a/math/test/linpack-benchmark.cpp b/math/test/linpack-benchmark.cpp index 89ba6099..0511f863 100644 --- a/math/test/linpack-benchmark.cpp +++ b/math/test/linpack-benchmark.cpp @@ -19,12 +19,18 @@ http://www.netlib.org/f2c/libf2c.zip #include #include -#ifdef TEST_BIG_NUMBER +#ifdef TEST_MPF_100 #include typedef boost::math::mpf_real_100 real_type; +#elif defined(TEST_MPFR_100) +#include +typedef boost::math::mpfr_real_100 real_type; #elif defined(TEST_GMPXX) #include typedef mpf_class real_type; +#elif defined(TEST_MPFRXX) +#include +typedef mpfr_class real_type; #elif defined(TEST_EF_GMP) #define E_FLOAT_TYPE_GMP #include @@ -99,11 +105,16 @@ int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type extern "C" int MAIN__() { -#ifdef TEST_BIG_NUMBER +#ifdef TEST_MPF_100 + std::cout << "Testing big_number >" << std::endl; +#elif defined(TEST_MPFR_100) std::cout << "Testing big_number >" << std::endl; #elif defined(TEST_GMPXX) - std::cout << "Testing mpfr_class at 100 decimal degits" << std::endl; + std::cout << "Testing mpf_class at 100 decimal degits" << std::endl; mpf_set_default_prec(((100 + 1) * 1000L) / 301L); +#elif defined(TEST_MPFRXX) + std::cout << "Testing mpfr_class at 100 decimal degits" << std::endl; + mpfr_set_default_prec(((100 + 1) * 1000L) / 301L); #elif defined(TEST_EF_GMP) std::cout << "Testing gmp::e_float" << std::endl; #elif defined(TEST_MATH_EF) @@ -913,9 +924,7 @@ L30: real_type epslon_(real_type *x) { -#ifdef TEST_BIG_NUMBER - return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); -#elif defined(TEST_GMPXX) +#if defined(TEST_MPF_100) || defined(TEST_MPFR_100) || defined(TEST_GMPXX) || defined(TEST_MPFRXX) return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); #else return CAST_TO_RT(std::numeric_limits::epsilon()); diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index c87f94c0..9e7261a8 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -5,11 +5,13 @@ #include -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) # define TEST_MPF50 # define TEST_MPF # define TEST_BACKEND # define TEST_MPZ +# define TEST_MPFR +# define TEST_MPFR_50 #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -30,6 +32,9 @@ #include #include #endif +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) +#include +#endif template void test_integer_ops(const boost::mpl::false_&){} @@ -599,9 +604,11 @@ int main() #endif #ifdef TEST_MPF boost::math::mpf_real::default_precision(1000); + /* boost::math::mpf_real r; r.precision(50); BOOST_TEST(r.precision() >= 50); + */ BOOST_TEST(boost::math::mpf_real::default_precision() == 1000); test(); #endif @@ -610,6 +617,21 @@ int main() #endif #ifdef TEST_E_FLOAT test(); +#endif +#ifdef TEST_MPFR + test(); +#endif +#ifdef TEST_MPFR_50 + test(); #endif return boost::report_errors(); } + +namespace boost +{ + void assertion_failed(char const * expr, + char const * function, char const * file, long line) + { + std::cout << "Failed assertion in expression: " << expr << " in function: " << function << " in file: " << file << " at line: " << line < Date: Mon, 22 Aug 2011 12:03:49 +0000 Subject: [PATCH 011/256] Added new backend adapter type, plus tentative e_float support. Added numeric_limits support, plus embryonic test program. [SVN r74004] --- include/boost/math/big_number.hpp | 8 + .../math/big_number/arithmetic_backend.hpp | 147 ++++++++++++ include/boost/math/big_number/e_float.hpp | 33 +++ include/boost/math/big_number/gmp.hpp | 212 ++++++++++++++++++ include/boost/math/big_number/mpfr.hpp | 188 ++++++++++++++++ .../math/concepts/big_number_architypes.hpp | 38 ++++ math/test/linpack-benchmark.cpp | 35 ++- math/test/test_arithmetic.cpp | 14 +- math/test/test_numeric_limits.cpp | 117 ++++++++++ 9 files changed, 761 insertions(+), 31 deletions(-) create mode 100644 include/boost/math/big_number/arithmetic_backend.hpp create mode 100644 include/boost/math/big_number/e_float.hpp create mode 100644 math/test/test_numeric_limits.cpp diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index 434ddb79..b140dbf7 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -58,6 +58,14 @@ public: m_backend = canonical_value(v); } + template + big_number(V v, typename enable_if, mpl::not_ > > >::type* dummy1 = 0) + : m_backend(v) + { + proto::value(*this) = this; + BOOST_ASSERT(proto::value(*this) == this); + } + template big_number& operator=(const detail::big_number_exp& e) { diff --git a/include/boost/math/big_number/arithmetic_backend.hpp b/include/boost/math/big_number/arithmetic_backend.hpp new file mode 100644 index 00000000..ba8d7165 --- /dev/null +++ b/include/boost/math/big_number/arithmetic_backend.hpp @@ -0,0 +1,147 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MATH_ARITH_BACKEND_HPP +#define BOOST_MATH_ARITH_BACKEND_HPP + +#include +#include +#include +#include +#include + +namespace boost{ +namespace math{ + +template +struct arithmetic_backend +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + arithmetic_backend(){} + arithmetic_backend(const arithmetic_backend& o) + { + m_value = o.m_value; + } + arithmetic_backend(const Arithmetic& o) : m_value(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + arithmetic_backend(arithmetic_backend&& o) : m_value(o.m_value) {} + arithmetic_backend(Arithmetic&& o) : m_value(o) {} +#endif + arithmetic_backend& operator = (const arithmetic_backend& o) + { + m_value = o.m_value; + return *this; + } + arithmetic_backend& operator = (boost::uintmax_t i) + { + m_value = i; + return *this; + } + arithmetic_backend& operator = (boost::intmax_t i) + { + m_value = i; + return *this; + } + arithmetic_backend& operator = (long double d) + { + m_value = d; + return *this; + } + arithmetic_backend& operator = (const char* s) + { + m_value = boost::lexical_cast(s); + return *this; + } + void swap(arithmetic_backend& o) + { + std::swap(m_value, o.m_value); + } + std::string str(unsigned digits, bool scientific)const + { + return boost::lexical_cast(m_value); + } + void negate() + { + m_value = -m_value; + } + int compare(const arithmetic_backend& o)const + { + return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); + } + int compare(boost::intmax_t i)const + { + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(boost::uintmax_t i)const + { + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(long double d)const + { + return m_value > d ? 1 : (m_value < d ? -1 : 0); + } + Arithmetic& data() { return m_value; } + const Arithmetic& data()const { return m_value; } +private: + Arithmetic m_value; +}; + +template +inline void add(arithmetic_backend& result, const arithmetic_backend& o) +{ + result.data() += o.data(); +} +template +inline void subtract(arithmetic_backend& result, const arithmetic_backend& o) +{ + result.data() -= o.data(); +} +template +inline void multiply(arithmetic_backend& result, const arithmetic_backend& o) +{ + result.data() *= o.data(); +} +template +inline void divide(arithmetic_backend& result, const arithmetic_backend& o) +{ + result.data() /= o.data(); +} + +}} // namespaces + + +namespace std{ + +#ifdef BOOST_NO_NOEXCEPT +# define noexcept +#endif + +template +class numeric_limits > > : public std::numeric_limits +{ + typedef std::numeric_limits base_type; + typedef boost::math::big_number > number_type; +public: + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return base_type::denorm_min(); } +}; + +#ifdef BOOST_NO_NOEXCEPT +# undef noexcept +#endif + +} + +#endif diff --git a/include/boost/math/big_number/e_float.hpp b/include/boost/math/big_number/e_float.hpp new file mode 100644 index 00000000..b531fa08 --- /dev/null +++ b/include/boost/math/big_number/e_float.hpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MATH_EFX_BACKEND_HPP +#define BOOST_MATH_EFX_BACKEND_HPP + +#include +#include +#include +#include + +namespace boost{ +namespace math{ + +typedef big_number > e_float; + +template<> +inline void arithmetic_backend::negate() +{ + m_value.negate(); +} + +inline void abs(arithmetic_backend* result, const arithmetic_backend& arg) +{ + result->data() = ef::fabs(arg.data()); +} + + +}} // namespaces + +#endif diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index e9811c28..b137cf52 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -12,6 +12,8 @@ #include #include #include +#include +#include namespace boost{ namespace math{ @@ -981,4 +983,214 @@ typedef big_number mpz_int; }} // namespaces +namespace std{ + +#ifdef BOOST_NO_NOEXCEPT +# define noexcept +#endif + +// +// numeric_limits [partial] specializations for the types declared in this header: +// +template +class numeric_limits > > +{ + typedef boost::math::big_number > number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), LONG_MAX); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpf_mul_2exp(value.second.backend().data(), value.second.backend().data(), LONG_MAX - 1); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept + { + return -(max)(); + } + BOOST_STATIC_CONSTEXPR int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); + BOOST_STATIC_CONSTEXPR int digits10 = Digits10; + // Is this really correct??? + BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 1; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR int radix = 2; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits::digits - 1); + } + return value.second; + } + // What value should this be???? + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept + { + // returns epsilon/2 + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), digits); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR long min_exponent = LONG_MIN; + BOOST_STATIC_CONSTEXPR long min_exponent10 = (LONG_MIN / 1000) * 301L; + BOOST_STATIC_CONSTEXPR long max_exponent = LONG_MAX; + BOOST_STATIC_CONSTEXPR long max_exponent10 = (LONG_MAX / 1000) * 301L; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = true; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = true; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest; + +private: + struct data_initializer + { + data_initializer() + { + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + std::numeric_limits > >::min(); + std::numeric_limits > >::max(); + } + void do_nothing()const{} + }; + static const data_initializer initializer; +}; + +template +const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; + +template<> +class numeric_limits > > +{ + typedef boost::math::big_number > number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = false; + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR int digits = 0; + BOOST_STATIC_CONSTEXPR int digits10 = 0; + BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR bool is_signed = false; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR int radix = 0; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = false; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + +template<> +class numeric_limits +{ + typedef boost::math::mpz_int number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + // + // Largest and smallest numbers are bounded only by available memory, set + // to zero: + // + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + { + return number_type(); + } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + { + return number_type(); + } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return (min)(); } + // Digits are unbounded, use zero for now: + BOOST_STATIC_CONSTEXPR int digits = 0; + BOOST_STATIC_CONSTEXPR int digits10 = 0; + BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = true; + BOOST_STATIC_CONSTEXPR bool is_exact = true; + BOOST_STATIC_CONSTEXPR int radix = 2; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = false; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + +#ifdef BOOST_NO_NOEXCEPT +# undef noexcept +#endif + +} // namespace std + #endif diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp index 4589f68f..1aa60cae 100644 --- a/include/boost/math/big_number/mpfr.hpp +++ b/include/boost/math/big_number/mpfr.hpp @@ -610,4 +610,192 @@ typedef big_number > mpfr_real; }} // namespaces +namespace std{ + +#ifdef BOOST_NO_NOEXCEPT +# define noexcept +#endif + +// +// numeric_limits [partial] specializations for the types declared in this header: +// +template +class numeric_limits > > +{ + typedef boost::math::big_number > number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 0.5; + mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), -mpfr_get_emin(), MPFR_RNDN); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 0.5; + mpfr_mul_2exp(value.second.backend().data(), value.second.backend().data(), mpfr_get_emax(), MPFR_RNDN); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept + { + return -(max)(); + } + BOOST_STATIC_CONSTEXPR int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); + BOOST_STATIC_CONSTEXPR int digits10 = Digits10; + // Is this really correct??? + BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 1; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR int radix = 2; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits::digits - 1, MPFR_RNDN); + } + return value.second; + } + // What value should this be???? + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept + { + // returns epsilon/2 + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), digits, MPFR_RNDN); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR long min_exponent = MPFR_EMIN_DEFAULT; + BOOST_STATIC_CONSTEXPR long min_exponent10 = (MPFR_EMIN_DEFAULT / 1000) * 301L; + BOOST_STATIC_CONSTEXPR long max_exponent = MPFR_EMAX_DEFAULT; + BOOST_STATIC_CONSTEXPR long max_exponent10 = (MPFR_EMAX_DEFAULT / 1000) * 301L; + BOOST_STATIC_CONSTEXPR bool has_infinity = true; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept + { + // returns epsilon/2 + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpfr_set_inf(value.second.backend().data(), 1); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept + { + // returns epsilon/2 + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpfr_set_nan(value.second.backend().data()); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept + { + return number_type(0); + } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = true; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = true; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest; + +private: + struct data_initializer + { + data_initializer() + { + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + std::numeric_limits > >::min(); + std::numeric_limits > >::max(); + std::numeric_limits > >::infinity(); + std::numeric_limits > >::quiet_NaN(); + } + void do_nothing()const{} + }; + static const data_initializer initializer; +}; + +template +const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; + +template<> +class numeric_limits > > +{ + typedef boost::math::big_number > number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = false; + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR int digits = 0; + BOOST_STATIC_CONSTEXPR int digits10 = 0; + BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR bool is_signed = false; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR int radix = 0; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = false; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + +#ifdef noexcept +#undef noexcept +#endif + +} // namespace std #endif diff --git a/include/boost/math/concepts/big_number_architypes.hpp b/include/boost/math/concepts/big_number_architypes.hpp index 6067b6e6..fc85bfa3 100644 --- a/include/boost/math/concepts/big_number_architypes.hpp +++ b/include/boost/math/concepts/big_number_architypes.hpp @@ -16,6 +16,11 @@ namespace boost{ namespace math{ namespace concepts{ +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4244) +#endif + struct big_number_backend_real_architype { typedef mpl::list signed_types; @@ -140,4 +145,37 @@ typedef boost::math::big_number big_number_re }}} // namespaces +namespace std{ + +#ifdef BOOST_NO_NOEXCEPT +# define noexcept +#endif + +template <> +class numeric_limits : public std::numeric_limits +{ + typedef std::numeric_limits base_type; + typedef boost::math::concepts::big_number_real_architype number_type; +public: + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return base_type::denorm_min(); } +}; + +#ifdef BOOST_NO_NOEXCEPT +# undef noexcept +#endif + +} + +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + #endif diff --git a/math/test/linpack-benchmark.cpp b/math/test/linpack-benchmark.cpp index 0511f863..99c8c87b 100644 --- a/math/test/linpack-benchmark.cpp +++ b/math/test/linpack-benchmark.cpp @@ -31,16 +31,15 @@ typedef mpf_class real_type; #elif defined(TEST_MPFRXX) #include typedef mpfr_class real_type; -#elif defined(TEST_EF_GMP) -#define E_FLOAT_TYPE_GMP -#include -typedef e_float real_type; -#define CAST_TO_RT(x) real_type(x) -#elif defined(TEST_MATH_EF) -#define E_FLOAT_TYPE_GMP -#include -typedef boost::math::ef::e_float real_type; -//#define CAST_TO_RT(x) real_type(x) +#elif defined(TEST_E_FLOAT) +#include +#include +#include +typedef ::efx::e_float real_type; +using ef::abs; +#elif defined(TEST_E_FLOAT_BN) +#include +typedef boost::math::e_float real_type; #else typedef double real_type; #endif @@ -69,12 +68,6 @@ extern "C" { } #include - -#if defined(TEST_EF_GMP) -#include -using namespace ef; -#endif - using std::min; using std::max; @@ -115,10 +108,10 @@ extern "C" int MAIN__() #elif defined(TEST_MPFRXX) std::cout << "Testing mpfr_class at 100 decimal degits" << std::endl; mpfr_set_default_prec(((100 + 1) * 1000L) / 301L); -#elif defined(TEST_EF_GMP) - std::cout << "Testing gmp::e_float" << std::endl; -#elif defined(TEST_MATH_EF) - std::cout << "Testing boost::math::ef::e_float" << std::endl; +#elif defined(TEST_E_FLOAT) + std::cout << "Testing boost::ef::e_float" << std::endl; +#elif defined(TEST_E_FLOAT_BN) + std::cout << "Testing boost::math::e_float" << std::endl; #else std::cout << "Testing double" << std::endl; #endif @@ -926,6 +919,8 @@ real_type epslon_(real_type *x) { #if defined(TEST_MPF_100) || defined(TEST_MPFR_100) || defined(TEST_GMPXX) || defined(TEST_MPFRXX) return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); +#elif defined(TEST_E_FLOAT_BN) + return std::pow(10.0, 1-std::numeric_limits::digits10); #else return CAST_TO_RT(std::numeric_limits::epsilon()); #endif diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 9e7261a8..8df99829 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -12,6 +12,7 @@ # define TEST_MPZ # define TEST_MPFR # define TEST_MPFR_50 +# define TEST_E_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -29,8 +30,7 @@ #include #endif #ifdef TEST_E_FLOAT -#include -#include +#include #endif #if defined(TEST_MPFR) || defined(TEST_MPFR_50) #include @@ -616,7 +616,7 @@ int main() test(); #endif #ifdef TEST_E_FLOAT - test(); + test(); #endif #ifdef TEST_MPFR test(); @@ -627,11 +627,3 @@ int main() return boost::report_errors(); } -namespace boost -{ - void assertion_failed(char const * expr, - char const * function, char const * file, long line) - { - std::cout << "Failed assertion in expression: " << expr << " in function: " << function << " in file: " << file << " at line: " << line < + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) +# define TEST_MPF50 +# define TEST_MPF +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR +# define TEST_MPFR_50 +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) +#include +#endif + +#define PRINT(x)\ + std::cout << BOOST_STRINGIZE(x) << " = " << std::numeric_limits::x << std::endl; + +template +void test() +{ + // + // Note really a test just yet, but we can at least print out all the values: + // + std::cout << "numeric_limits values for type " << typeid(Number).name() << std::endl; + + PRINT(is_specialized); + PRINT(min()); + PRINT(max()); + PRINT(lowest()); + PRINT(digits); + PRINT(digits10); + PRINT(max_digits10); + PRINT(is_signed); + PRINT(is_integer); + PRINT(is_exact); + PRINT(radix); + PRINT(epsilon()); + PRINT(round_error()); + PRINT(min_exponent); + PRINT(min_exponent10); + PRINT(max_exponent); + PRINT(max_exponent10); + PRINT(has_infinity); + PRINT(has_quiet_NaN); + PRINT(has_signaling_NaN); + PRINT(has_denorm); + PRINT(has_denorm_loss); + PRINT(infinity()); + PRINT(quiet_NaN()); + PRINT(signaling_NaN()); + PRINT(denorm_min()); + PRINT(is_iec559); + PRINT(is_bounded); + PRINT(is_modulo); + PRINT(traps); + PRINT(tinyness_before); + PRINT(round_style); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); +#endif +#ifdef TEST_MPF + boost::math::mpf_real::default_precision(1000); + /* + boost::math::mpf_real r; + r.precision(50); + BOOST_TEST(r.precision() >= 50); + */ + BOOST_TEST(boost::math::mpf_real::default_precision() == 1000); + test(); +#endif +#ifdef TEST_MPZ + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif +#ifdef TEST_MPFR + test(); +#endif +#ifdef TEST_MPFR_50 + test(); +#endif + return boost::report_errors(); +} + From cdcf165e309d9cfa51477c2f141bd12f3af47e1f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 23 Aug 2011 18:31:03 +0000 Subject: [PATCH 012/256] Add increment, decrement and bitwise-shift operators. [SVN r74024] --- include/boost/math/big_number.hpp | 154 ++++++++++++++++++ .../boost/math/big_number/big_number_base.hpp | 2 + include/boost/math/big_number/default_ops.hpp | 28 ++++ include/boost/math/big_number/gmp.hpp | 24 ++- include/boost/math/big_number/mpfr.hpp | 4 +- math/test/test_arithmetic.cpp | 40 +++++ 6 files changed, 248 insertions(+), 4 deletions(-) diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index b140dbf7..082c95b6 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -17,6 +17,9 @@ #include #include #include +#include +#include +#include #include namespace boost{ namespace math{ @@ -201,6 +204,65 @@ public: } return *this; } + // + // These operators are *not* proto-ized. + // The issue is that the increment/decrement must happen + // even if the result of the operator *is never used*. + // Possibly we could modify our expression wrapper to + // execute the increment/decrement on destruction, but + // correct implemetation will be tricky, so defered for now... + // + big_number& operator++() + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The increment operation is only valid for integer types"); + using big_num_default_ops::increment; + increment(m_backend); + return *this; + } + + big_number& operator--() + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The increment operation is only valid for integer types"); + using big_num_default_ops::decrement; + decrement(m_backend); + return *this; + } + + big_number operator++(int) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The increment operation is only valid for integer types"); + using big_num_default_ops::increment; + self_type temp(*this); + increment(m_backend); + return temp; + } + + big_number operator--(int) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The increment operation is only valid for integer types"); + using big_num_default_ops::decrement; + self_type temp(*this); + decrement(m_backend); + return temp; + } + + template + typename enable_if, big_number&>::type operator <<= (V val) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The left-shift operation is only valid for integer types"); + check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); + left_shift(m_backend, canonical_value(val)); + return *this; + } + + template + typename enable_if, big_number&>::type operator >>= (V val) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The right-shift operation is only valid for integer types"); + check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); + right_shift(m_backend, canonical_value(val)); + return *this; + } template typename enable_if, big_number& >::type @@ -237,6 +299,14 @@ public: return *this; } + // + // swap: + // + void swap(self_type& other) + { + m_backend.swap(other.backend()); + } + // // String conversion functions: // @@ -284,6 +354,29 @@ public: return m_backend; } private: + template + void check_shift_range(V val, const mpl::true_&, const mpl::true_&) + { + if(val > std::numeric_limits::max()) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); + if(val < 0) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); + } + template + void check_shift_range(V val, const mpl::false_&, const mpl::true_&) + { + if(val < 0) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); + } + template + void check_shift_range(V val, const mpl::true_&, const mpl::false_&) + { + if(val > std::numeric_limits::max()) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); + } + template + void check_shift_range(V val, const mpl::false_&, const mpl::false_&){} + template void do_assign(const Exp& e, const detail::add_immediates&) { @@ -363,6 +456,7 @@ private: template void do_assign(const Exp& e, const detail::modulus_immediates&) { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); using big_num_default_ops::modulus; typedef typename proto::tag_of::type>::type left_tag; typedef typename proto::tag_of::type>::type right_tag; @@ -575,6 +669,64 @@ private: typedef typename proto::arity_of::type tag_type; do_assign_function(e, tag_type()); } + template + void do_assign(const Exp& e, const proto::tag::shift_left&) + { + // We can only shift by an integer value, not an arbitrary expression: + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::arity_of::type right_arity; + BOOST_STATIC_ASSERT_MSG(right_arity::value == 0, "The left shift operator requires an integer value for the shift operand."); + typedef typename proto::result_of::value::type right_value_type; + BOOST_STATIC_ASSERT_MSG(is_integral::value, "The left shift operator requires an integer value for the shift operand."); + typedef typename proto::tag_of::type tag_type; + do_assign_left_shift(proto::left(e), canonical_value(proto::value(proto::right(e))), tag_type()); + } + + template + void do_assign(const Exp& e, const proto::tag::shift_right&) + { + // We can only shift by an integer value, not an arbitrary expression: + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::arity_of::type right_arity; + BOOST_STATIC_ASSERT_MSG(right_arity::value == 0, "The left shift operator requires an integer value for the shift operand."); + typedef typename proto::result_of::value::type right_value_type; + BOOST_STATIC_ASSERT_MSG(is_integral::value, "The left shift operator requires an integer value for the shift operand."); + typedef typename proto::tag_of::type tag_type; + do_assign_right_shift(proto::left(e), canonical_value(proto::value(proto::right(e))), tag_type()); + } + + template + void do_assign_right_shift(const Exp& e, const Val& val, const proto::tag::terminal&) + { + using big_num_default_ops::right_shift; + right_shift(m_backend, canonical_value(proto::value(e)), val); + } + + template + void do_assign_left_shift(const Exp& e, const Val& val, const proto::tag::terminal&) + { + using big_num_default_ops::left_shift; + left_shift(m_backend, canonical_value(proto::value(e)), val); + } + + template + void do_assign_right_shift(const Exp& e, const Val& val, const Tag&) + { + using big_num_default_ops::right_shift; + self_type temp(e); + right_shift(m_backend, temp.backend(), val); + } + + template + void do_assign_left_shift(const Exp& e, const Val& val, const Tag&) + { + using big_num_default_ops::left_shift; + self_type temp(e); + left_shift(m_backend, temp.backend(), val); + } + template void do_assign_function(const Exp& e, const mpl::long_<1>&) { @@ -804,6 +956,7 @@ private: template void do_modulus(const Exp& e, const proto::tag::terminal&) { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); using big_num_default_ops::modulus; modulus(m_backend, canonical_value(proto::value(e))); } @@ -811,6 +964,7 @@ private: template void do_modulus(const Exp& e, const Unknown&) { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); using big_num_default_ops::modulus; self_type temp(e); modulus(m_backend, canonical_value(proto::value(temp))); diff --git a/include/boost/math/big_number/big_number_base.hpp b/include/boost/math/big_number/big_number_base.hpp index b3caed30..5a75e71d 100644 --- a/include/boost/math/big_number/big_number_base.hpp +++ b/include/boost/math/big_number/big_number_base.hpp @@ -29,6 +29,8 @@ struct big_number_grammar , proto::unary_plus< big_number_grammar > , proto::negate< big_number_grammar > , proto::modulus + , proto::shift_left + , proto::shift_right > {}; diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index 86a2aa09..c5b3f581 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -146,6 +146,34 @@ inline void modulus(T& t, const U& u, const V& v) } } +template +inline void increment(T& val) +{ + typedef typename mpl::front::type ui_type; + add(val, static_cast(1u)); +} + +template +inline void decrement(T& val) +{ + typedef typename mpl::front::type ui_type; + subtract(val, static_cast(1u)); +} + +template +inline void left_shift(T& result, const T& arg, const V val) +{ + result = arg; + left_shift(result, val); +} + +template +inline void right_shift(T& result, const T& arg, const V val) +{ + result = arg; + right_shift(result, val); +} + // // Functions: // diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index b137cf52..6397d354 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -862,6 +862,26 @@ inline void divide(gmp_int& t, long i) if(i < 0) mpz_neg(t.data(), t.data()); } +template +inline void left_shift(gmp_int& t, UI i) +{ + mpz_mul_2exp(t.data(), t.data(), static_cast(i)); +} +template +inline void right_shift(gmp_int& t, UI i) +{ + mpz_fdiv_q_2exp(t.data(), t.data(), static_cast(i)); +} +template +inline void left_shift(gmp_int& t, const gmp_int& v, UI i) +{ + mpz_mul_2exp(t.data(), v.data(), static_cast(i)); +} +template +inline void right_shift(gmp_int& t, const gmp_int& v, UI i) +{ + mpz_fdiv_q_2exp(t.data(), v.data(), static_cast(i)); +} inline void add(gmp_int& t, const gmp_int& p, const gmp_int& o) { @@ -1087,8 +1107,8 @@ private: { std::numeric_limits > >::epsilon(); std::numeric_limits > >::round_error(); - std::numeric_limits > >::min(); - std::numeric_limits > >::max(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); } void do_nothing()const{} }; diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp index 1aa60cae..380e4eaa 100644 --- a/include/boost/math/big_number/mpfr.hpp +++ b/include/boost/math/big_number/mpfr.hpp @@ -741,8 +741,8 @@ private: { std::numeric_limits > >::epsilon(); std::numeric_limits > >::round_error(); - std::numeric_limits > >::min(); - std::numeric_limits > >::max(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); std::numeric_limits > >::infinity(); std::numeric_limits > >::quiet_NaN(); } diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 8df99829..70c44787 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -36,6 +36,11 @@ #include #endif +#define BOOST_TEST_THROW(x, EX)\ + try { x; BOOST_ERROR("Expected exception not thrown"); } \ + catch(const EX&){}\ + catch(...){ BOOST_ERROR("Incorrect exception type thrown"); } + template void test_integer_ops(const boost::mpl::false_&){} @@ -104,6 +109,41 @@ void test_integer_ops(const boost::mpl::true_&) a %= -7LL; BOOST_TEST(a == -20 % -7); #endif + a = 20; + BOOST_TEST(++a == 21); + BOOST_TEST(--a == 20); + BOOST_TEST(a++ == 20); + BOOST_TEST(a == 21); + BOOST_TEST(a-- == 21); + BOOST_TEST(a == 20); + a = 2000; + a <<= 20; + BOOST_TEST(a == 2000L << 20); + a >>= 20; + BOOST_TEST(a == 2000); + a <<= 20u; + BOOST_TEST(a == 2000L << 20); + a >>= 20u; + BOOST_TEST(a == 2000); + BOOST_TEST_THROW(a <<= -20, std::out_of_range); + BOOST_TEST_THROW(a >>= -20, std::out_of_range); +#ifndef BOOST_NO_LONG_LONG + if(sizeof(long long) > sizeof(std::size_t)) + { + // extreme values should trigger an exception: + BOOST_TEST_THROW(a >>= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_TEST_THROW(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + } +#endif + a = 20; + b = a << 20; + BOOST_TEST(b == (20 << 20)); + b = a >> 2; + BOOST_TEST(b == (20 >> 2)); + b = (a + 2) << 10; + BOOST_TEST(b == (22 << 10)); + b = (a + 3) >> 3; + BOOST_TEST(b == (23 >> 3)); // // Non-member functions: // From b1986d204d0d69f2fe124d530a7f9df08ec8b4bd Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 24 Aug 2011 11:27:08 +0000 Subject: [PATCH 013/256] Add sign and is_zero functions. Add use in boolean context. [SVN r74042] --- include/boost/math/big_number.hpp | 14 +++- .../boost/math/big_number/big_number_base.hpp | 65 ++++++++++++++----- include/boost/math/big_number/default_ops.hpp | 13 ++++ include/boost/math/big_number/e_float.hpp | 11 ++++ include/boost/math/big_number/gmp.hpp | 20 ++++++ include/boost/math/big_number/mpfr.hpp | 11 ++++ math/test/test_arithmetic.cpp | 49 ++++++++++++++ 7 files changed, 166 insertions(+), 17 deletions(-) diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index 082c95b6..d5bb02f6 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -306,7 +306,19 @@ public: { m_backend.swap(other.backend()); } - + // + // Zero and sign: + // + bool is_zero() + { + using big_num_default_ops::is_zero; + return is_zero(m_backend); + } + int sign() + { + using big_num_default_ops::get_sign; + return get_sign(m_backend); + } // // String conversion functions: // diff --git a/include/boost/math/big_number/big_number_base.hpp b/include/boost/math/big_number/big_number_base.hpp index 5a75e71d..9c432a6c 100644 --- a/include/boost/math/big_number/big_number_base.hpp +++ b/include/boost/math/big_number/big_number_base.hpp @@ -41,22 +41,6 @@ struct big_number_domain : proto::domain< proto::generator, big_number_grammar> {}; -template -struct big_number_exp - : proto::extends, big_number_domain> -{ - typedef - proto::extends, big_number_domain> base_type; - - big_number_exp(Expr const &expr = Expr()) - : base_type(expr) - {} - template - big_number_exp(const Other& o) - : base_type(o) - {} -}; - struct CalcDepth : proto::or_< proto::when< proto::terminal, @@ -447,6 +431,55 @@ struct backend_type > typedef Backend type; }; +template +struct big_number_exp + : proto::extends, big_number_domain> +{ +private: + typedef proto::extends, big_number_domain> base_type; + typedef big_number_exp self_type; + typedef typename expression_type::type number_type; + typedef void (self_type::*unmentionable_type)(); + void unmentionable_proc(){} + unmentionable_type boolean_context_from_terminal(const number_type* pval)const + { + return pval->is_zero() ? 0 : &self_type::unmentionable_proc; + } + unmentionable_type boolean_context_from_terminal(number_type* pval)const + { + return pval->is_zero() ? 0 : &self_type::unmentionable_proc; + } + template + unmentionable_type boolean_context_from_terminal(const Terminal& val)const + { + return val ? 0 : &self_type::unmentionable_proc; + } + unmentionable_type boolean_context(const proto::tag::terminal&)const + { + return boolean_context_from_terminal(proto::value(*this)); + } + template + unmentionable_type boolean_context(const Tag&)const + { + // we have to evaluate the expression template: + number_type result(*this); + return result.is_zero() ? 0 : &self_type::unmentionable_proc; + } +public: + big_number_exp(Expr const &expr = Expr()) + : base_type(expr) + {} + template + big_number_exp(const Other& o) + : base_type(o) + {} + + operator unmentionable_type()const + { + return boolean_context(typename proto::tag_of::type()); + } +}; + } // namespace detail // diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index c5b3f581..be28df3c 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -174,6 +174,19 @@ inline void right_shift(T& result, const T& arg, const V val) right_shift(result, val); } +template +inline bool is_zero(const T& val) +{ + typedef typename mpl::front::type ui_type; + return val.compare(static_cast(0)) == 0; +} +template +inline int get_sign(const T& val) +{ + typedef typename mpl::front::type ui_type; + return val.compare(static_cast(0)); +} + // // Functions: // diff --git a/include/boost/math/big_number/e_float.hpp b/include/boost/math/big_number/e_float.hpp index b531fa08..977d613d 100644 --- a/include/boost/math/big_number/e_float.hpp +++ b/include/boost/math/big_number/e_float.hpp @@ -27,6 +27,17 @@ inline void abs(arithmetic_backend* result, const arithmetic_backe result->data() = ef::fabs(arg.data()); } +inline bool is_zero(const arithmetic_backend& val) +{ + return val.data().iszero(); +} +inline int get_sign(const arithmetic_backend& val) +{ + return val.data().isneg() ? -1 : val.data().iszero() ? 0 : 1; +} + + + }} // namespaces diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index 6397d354..53d648b1 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -542,6 +542,17 @@ inline void divide(gmp_real& a, long x, const gmp_real& y) mpf_ui_div(a.data(), x, y.data()); } +template +inline bool is_zero(const gmp_real& val) +{ + return mpf_sgn(val.data()) == 0; +} +template +inline int get_sign(const gmp_real& val) +{ + return mpf_sgn(val.data()); +} + // // Native non-member operations: // @@ -986,6 +997,15 @@ inline void divide(gmp_int& t, const gmp_int& p, long i) mpz_neg(t.data(), t.data()); } +inline bool is_zero(const gmp_int& val) +{ + return mpz_sgn(val.data()) == 0; +} +inline int get_sign(const gmp_int& val) +{ + return mpz_sgn(val.data()); +} + inline void abs(gmp_int* result, const gmp_int& val) { mpz_abs(result->data(), val.data()); diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp index 380e4eaa..5e015d53 100644 --- a/include/boost/math/big_number/mpfr.hpp +++ b/include/boost/math/big_number/mpfr.hpp @@ -544,6 +544,17 @@ inline void divide(mpfr_real_backend& a, long x, const mpfr_real_backe mpfr_ui_div(a.data(), x, y.data(), MPFR_RNDN); } +template +inline bool is_zero(const mpfr_real_backend& val) +{ + return 0 != mpfr_zero_p(val.data()); +} +template +inline int get_sign(const mpfr_real_backend& val) +{ + return mpfr_sgn(val.data()); +} + // // Native non-member operations: // diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 70c44787..327a575f 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -41,6 +41,16 @@ catch(const EX&){}\ catch(...){ BOOST_ERROR("Incorrect exception type thrown"); } +#undef BOOST_TEST +#define BOOST_TEST(x)\ + try {\ + if(x){}else{ BOOST_ERROR("Value was zero: "); }\ + }\ + catch(const std::exception& e){ \ + BOOST_ERROR("Unexpected exception: ");\ + BOOST_LIGHTWEIGHT_TEST_OSTREAM << e.what() << std::endl;\ + } + template void test_integer_ops(const boost::mpl::false_&){} @@ -631,6 +641,45 @@ void test() BOOST_TEST((72 < b+a) == false); BOOST_TEST((72 >= b+a) == true); BOOST_TEST((72 > b+a) == false); + // + // Test sign and zero functions, plus use in boolian context: + // + a = 20; + BOOST_TEST(a.sign() > 0); + BOOST_TEST(!a.is_zero()); + a = -20; + BOOST_TEST(a.sign() < 0); + BOOST_TEST(!a.is_zero()); + a = 0; + BOOST_TEST(a.sign() == 0); + BOOST_TEST(a.is_zero()); + if(a) + { + BOOST_ERROR("Unexpected non-zero result"); + } + if(!a){} + else + { + BOOST_ERROR("Unexpected zero result"); + } + b = 2; + if(!b) + { + BOOST_ERROR("Unexpected zero result"); + } + if(b){} + else + { + BOOST_ERROR("Unexpected non-zero result"); + } + if(a && b) + { + BOOST_ERROR("Unexpected zero result"); + } + if(!(a || b)) + { + BOOST_ERROR("Unexpected zero result"); + } } From 32ad75f48b5e1faa7d66adbd50029200ba391d14 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 24 Aug 2011 11:57:52 +0000 Subject: [PATCH 014/256] Add test cases for expression-template used in boolean context. [SVN r74043] --- math/test/test_arithmetic.cpp | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 327a575f..35bc6682 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -680,6 +680,15 @@ void test() { BOOST_ERROR("Unexpected zero result"); } + if(a + b){} + else + { + BOOST_ERROR("Unexpected zero result"); + } + if(b - 2) + { + BOOST_ERROR("Unexpected non-zero result"); + } } From b48a341d164749a289c2fdb8b3b1ca3e56f63a15 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 25 Aug 2011 16:09:57 +0000 Subject: [PATCH 015/256] Add conversion routines. Add Jamfile. Fix broken stream operators. [SVN r74057] --- include/boost/math/big_number.hpp | 49 +++++- .../boost/math/big_number/big_number_base.hpp | 6 +- include/boost/math/big_number/default_ops.hpp | 60 +++++++ include/boost/math/big_number/e_float.hpp | 28 +++ include/boost/math/big_number/gmp.hpp | 28 +++ include/boost/math/big_number/mpfr.hpp | 41 ++++- math/config/Jamfile.v2 | 45 +++++ math/config/has_e_float.cpp | 17 ++ math/config/has_gcc_visibility.cpp | 13 ++ math/config/has_gmp.cpp | 7 + math/config/has_gmpxx.cpp | 7 + math/config/has_long_double_support.cpp | 10 ++ math/config/has_mpfr.cpp | 7 + math/config/has_mpfr_class.cpp | 14 ++ math/config/has_mpreal.cpp | 14 ++ math/config/has_ntl_rr.cpp | 12 ++ math/test/Jamfile.v2 | 166 ++++++++++++++++++ math/test/test_arithmetic.cpp | 31 +++- 18 files changed, 537 insertions(+), 18 deletions(-) create mode 100644 math/config/Jamfile.v2 create mode 100644 math/config/has_e_float.cpp create mode 100644 math/config/has_gcc_visibility.cpp create mode 100644 math/config/has_gmp.cpp create mode 100644 math/config/has_gmpxx.cpp create mode 100644 math/config/has_long_double_support.cpp create mode 100644 math/config/has_mpfr.cpp create mode 100644 math/config/has_mpfr_class.cpp create mode 100644 math/config/has_mpreal.cpp create mode 100644 math/config/has_ntl_rr.cpp create mode 100644 math/test/Jamfile.v2 diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index d5bb02f6..d8dae762 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -326,6 +326,14 @@ public: { return m_backend.str(digits, scientific); } + template + T convert_to()const + { + using big_num_default_ops::convert_to; + T result; + convert_to(&result, m_backend); + return result; + } // // Default precision: // @@ -1190,22 +1198,47 @@ inline typename boost::enable_if, bool>: { return 0 < detail::big_number_compare(a, b); } - -template -inline std::ostream& operator << (std::ostream& os, const big_number& r) +// +// Because proto overloads these << operators, we need version that accept both +// const and non-const RHS values, otherwise the proto version will be found +// with unpleasant results... not only that, but the stream parameter has to be a template +// otherwise the LHS of the expression would have to be *exactly* of type std::ostream +// for the overload to be found (ie doesn't work for std::fstream etc unless we do this...) +// +template +inline typename enable_if, std::ostream&>::type operator << (Stream& os, const big_number& r) { return os << r.str(static_cast(os.precision(), os.flags() & os.scientific)); } -template -inline std::ostream& operator << (std::ostream& os, const detail::big_number_exp& r) + +template +inline typename enable_if, std::ostream&>::type operator << (Stream& os, big_number& r) { - typedef typename detail::expression_type::type value_type; + return os << r.str(static_cast(os.precision(), os.flags() & os.scientific)); +} + +namespace detail{ + +template +inline typename enable_if, std::ostream&>::type operator << (Stream& os, const big_number_exp& r) +{ + typedef typename expression_type >::type value_type; value_type temp(r); return os << temp; } -template -inline std::istream& operator >> (std::istream& is, big_number& r) +template +inline typename enable_if, std::ostream&>::type operator << (Stream& os, big_number_exp& r) +{ + typedef typename expression_type >::type value_type; + value_type temp(r); + return os << temp; +} + +} + +template +inline typename enable_if, std::istream&>::type operator >> (Stream& is, big_number& r) { std::string s; is >> s; diff --git a/include/boost/math/big_number/big_number_base.hpp b/include/boost/math/big_number/big_number_base.hpp index 9c432a6c..83e635a2 100644 --- a/include/boost/math/big_number/big_number_base.hpp +++ b/include/boost/math/big_number/big_number_base.hpp @@ -436,9 +436,9 @@ struct big_number_exp : proto::extends, big_number_domain> { private: - typedef proto::extends, big_number_domain> base_type; - typedef big_number_exp self_type; - typedef typename expression_type::type number_type; + typedef proto::extends, big_number_domain> base_type; + typedef big_number_exp self_type; + typedef typename remove_reference::type>::type number_type; typedef void (self_type::*unmentionable_type)(); void unmentionable_proc(){} unmentionable_type boolean_context_from_terminal(const number_type* pval)const diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index be28df3c..57fcf2ba 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -187,6 +187,66 @@ inline int get_sign(const T& val) return val.compare(static_cast(0)); } +template +struct has_enough_bits +{ + template + struct type : public mpl::and_ >, mpl::bool_::digits >= b> >{}; +}; + +template +struct terminal +{ + terminal(const R& v) : value(v){} + terminal(){} + terminal& operator = (R val) { value = val; } + R value; + operator R()const { return value; } +}; + +template +struct calculate_next_larger_type +{ + typedef typename mpl::if_< + is_signed, + typename B::signed_types, + typename mpl::if_< + is_unsigned, + typename B::unsigned_types, + typename B::real_types + >::type + >::type list_type; + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + list_type, + pred_type + >::type iter_type; + typedef typename mpl::eval_if< + is_same::type, iter_type>, + mpl::identity >, + mpl::deref + >::type type; +}; + +template +inline void convert_to(R* result, const B& backend) +{ + typedef calculate_next_larger_type::type next_type; + next_type n; + convert_to(&n, backend); + *result = static_cast(n); +} + +template +inline void convert_to(terminal* result, const B& backend) +{ + // + // We ran out of types to try for the convertion, try + // a lexical_cast and hope for the best: + // + result->value = boost::lexical_cast(backend.str(0, false)); +} + // // Functions: // diff --git a/include/boost/math/big_number/e_float.hpp b/include/boost/math/big_number/e_float.hpp index 977d613d..402c4379 100644 --- a/include/boost/math/big_number/e_float.hpp +++ b/include/boost/math/big_number/e_float.hpp @@ -10,6 +10,7 @@ #include #include #include +#include namespace boost{ namespace math{ @@ -21,6 +22,17 @@ inline void arithmetic_backend::negate() { m_value.negate(); } +template<> +inline std::string arithmetic_backend::str(unsigned digits, bool scientific)const +{ + std::fstream os; + os << std::setprecision(digits ? digits : efx::e_float::ef_digits + 5); + if(scientific) + os << std::scientific; + std::string result; + this->data().wr_string(result, os); + return result; +} inline void abs(arithmetic_backend* result, const arithmetic_backend& arg) { @@ -36,6 +48,22 @@ inline int get_sign(const arithmetic_backend& val) return val.data().isneg() ? -1 : val.data().iszero() ? 0 : 1; } +inline void convert_to(boost::uintmax_t* result, const arithmetic_backend& val) +{ + *result = val.data().extract_unsigned_long_long(); +} +inline void convert_to(boost::intmax_t* result, const arithmetic_backend& val) +{ + *result = val.data().extract_signed_long_long(); +} +inline void convert_to(double* result, const arithmetic_backend& val) +{ + *result = val.data().extract_double(); +} +inline void convert_to(long double* result, const arithmetic_backend& val) +{ + *result = val.data().extract_long_double(); +} diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index 53d648b1..51d35fe0 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -553,6 +553,22 @@ inline int get_sign(const gmp_real& val) return mpf_sgn(val.data()); } +template +inline void convert_to(unsigned long* result, const gmp_real& val) +{ + *result = mpf_get_ui(val.data()); +} +template +inline void convert_to(long* result, const gmp_real& val) +{ + *result = mpf_get_si(val.data()); +} +template +inline void convert_to(double* result, const gmp_real& val) +{ + *result = mpf_get_d(val.data()); +} + // // Native non-member operations: // @@ -1005,6 +1021,18 @@ inline int get_sign(const gmp_int& val) { return mpz_sgn(val.data()); } +inline void convert_to(unsigned long* result, const gmp_int& val) +{ + *result = mpz_get_ui(val.data()); +} +inline void convert_to(long* result, const gmp_int& val) +{ + *result = mpz_get_si(val.data()); +} +inline void convert_to(double* result, const gmp_int& val) +{ + *result = mpz_get_d(val.data()); +} inline void abs(gmp_int* result, const gmp_int& val) { diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp index 5e015d53..a9aeac6f 100644 --- a/include/boost/math/big_number/mpfr.hpp +++ b/include/boost/math/big_number/mpfr.hpp @@ -159,10 +159,7 @@ struct mpfr_real_imp { std::string result; mp_exp_t e; - void *(*alloc_func_ptr) (size_t); - void *(*realloc_func_ptr) (void *, size_t, size_t); - void (*free_func_ptr) (void *, size_t); - const char* ps = mpfr_get_str (0, &e, 10, digits, m_data, MPFR_RNDN); + char* ps = mpfr_get_str (0, &e, 10, digits, m_data, MPFR_RNDN); std::ptrdiff_t sl = std::strlen(ps); unsigned chars = sl; if(sl == 0) @@ -192,8 +189,7 @@ struct mpfr_real_imp if(e) result += "e" + lexical_cast(e); } - mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); - (*free_func_ptr)((void*)ps, sl + 1); + mpfr_free_str(ps); return result; } ~mpfr_real_imp() @@ -555,6 +551,39 @@ inline int get_sign(const mpfr_real_backend& val) return mpfr_sgn(val.data()); } +template +inline void convert_to(unsigned long* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_ui(val.data(), MPFR_RNDN); +} +template +inline void convert_to(long* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_si(val.data(), MPFR_RNDN); +} +#ifdef _MPFR_H_HAVE_INTMAX_T +template +inline void convert_to(boost::uintmax_t* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_uj(val.data(), MPFR_RNDN); +} +template +inline void convert_to(boost::intmax_t* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_sj(val.data(), MPFR_RNDN); +} +#endif +template +inline void convert_to(double* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_d(val.data(), MPFR_RNDN); +} +template +inline void convert_to(long double* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_ld(val.data(), MPFR_RNDN); +} + // // Native non-member operations: // diff --git a/math/config/Jamfile.v2 b/math/config/Jamfile.v2 new file mode 100644 index 00000000..832e2936 --- /dev/null +++ b/math/config/Jamfile.v2 @@ -0,0 +1,45 @@ +# copyright John Maddock 2008 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + +import modules ; +import path ; + +local ntl-path = [ modules.peek : NTL_PATH ] ; +local gmp_path = [ modules.peek : GMP_PATH ] ; +local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local e_float_path = [ modules.peek : BOOST_E_FLOAT_PATH ] ; + +if ! $(e_float_path) +{ + e_float_path = ../../../../e_float ; +} + +ECHO $(BOOST_E_FLOAT_PATH) + +obj has_long_double_support : has_long_double_support.cpp ; +obj has_mpfr_class : has_mpfr_class.cpp : + $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; +obj has_mpreal : has_mpreal.cpp : + $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/mpfrc++ ; +obj has_ntl_rr : has_ntl_rr.cpp : $(ntl-path)/include ; +obj has_gmpxx : has_gmpxx.cpp : + $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; +obj has_gcc_visibility : has_gcc_visibility.cpp : + gcc:-fvisibility=hidden gcc:-Werror ; +obj has_e_float : has_e_float.cpp : $(e_float_path) ; +obj has_gmp : has_gmp.cpp : + $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; +obj has_mpfr : has_mpfr.cpp : + $(mpfr_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; + +explicit has_long_double_support ; +explicit has_mpfr_class ; +explicit has_mpreal ; +explicit has_ntl_rr ; +explicit has_gmpxx ; +explicit has_gcc_visibility ; +explicit has_e_float ; +explicit has_gmp ; +explicit has_mpfr ; diff --git a/math/config/has_e_float.cpp b/math/config/has_e_float.cpp new file mode 100644 index 00000000..8cadc5c6 --- /dev/null +++ b/math/config/has_e_float.cpp @@ -0,0 +1,17 @@ +// Copyright John Maddock 2011. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + + +#ifdef _MSC_VER +# pragma warning (disable : 4100) // unreferenced formal parameter +#endif + +#define E_FLOAT_TYPE_EFX + +#include +#include +#include + + diff --git a/math/config/has_gcc_visibility.cpp b/math/config/has_gcc_visibility.cpp new file mode 100644 index 00000000..6c7d6f91 --- /dev/null +++ b/math/config/has_gcc_visibility.cpp @@ -0,0 +1,13 @@ +// Copyright John Maddock 20010. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef __GNUC__ +# error "This is a GCC specific test case". +#endif + +int main() +{ + return 0; +} diff --git a/math/config/has_gmp.cpp b/math/config/has_gmp.cpp new file mode 100644 index 00000000..582f0027 --- /dev/null +++ b/math/config/has_gmp.cpp @@ -0,0 +1,7 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + diff --git a/math/config/has_gmpxx.cpp b/math/config/has_gmpxx.cpp new file mode 100644 index 00000000..edf62d8c --- /dev/null +++ b/math/config/has_gmpxx.cpp @@ -0,0 +1,7 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + diff --git a/math/config/has_long_double_support.cpp b/math/config/has_long_double_support.cpp new file mode 100644 index 00000000..d314cf38 --- /dev/null +++ b/math/config/has_long_double_support.cpp @@ -0,0 +1,10 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS +#error "long double support is not supported by Boost.Math on this Plaform: the long double version of the TR1 library will not be built." +#endif diff --git a/math/config/has_mpfr.cpp b/math/config/has_mpfr.cpp new file mode 100644 index 00000000..49d12a0b --- /dev/null +++ b/math/config/has_mpfr.cpp @@ -0,0 +1,7 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + diff --git a/math/config/has_mpfr_class.cpp b/math/config/has_mpfr_class.cpp new file mode 100644 index 00000000..8eb3c7b2 --- /dev/null +++ b/math/config/has_mpfr_class.cpp @@ -0,0 +1,14 @@ +// Copyright John Maddock 2008. +// Copyright Paul A. Britow 2009 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4127) // conditional expression is constant +# pragma warning (disable : 4800) // 'int' : forcing value to bool 'true' or 'false' (performance warning) +# pragma warning (disable : 4512) // assignment operator could not be generated +#endif + +#include + diff --git a/math/config/has_mpreal.cpp b/math/config/has_mpreal.cpp new file mode 100644 index 00000000..8ee8897d --- /dev/null +++ b/math/config/has_mpreal.cpp @@ -0,0 +1,14 @@ +// Copyright John Maddock 2008. +// Copyright Paul A. Britow 2009 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4127) // conditional expression is constant +# pragma warning (disable : 4800) // 'int' : forcing value to bool 'true' or 'false' (performance warning) +# pragma warning (disable : 4512) // assignment operator could not be generated +#endif + +#include + diff --git a/math/config/has_ntl_rr.cpp b/math/config/has_ntl_rr.cpp new file mode 100644 index 00000000..f3844217 --- /dev/null +++ b/math/config/has_ntl_rr.cpp @@ -0,0 +1,12 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + + +#ifdef _MSC_VER +# pragma warning (disable : 4100) // unreferenced formal parameter +#endif + +#include + diff --git a/math/test/Jamfile.v2 b/math/test/Jamfile.v2 new file mode 100644 index 00000000..16b71922 --- /dev/null +++ b/math/test/Jamfile.v2 @@ -0,0 +1,166 @@ +# copyright John Maddock 2008 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + +import modules ; +import path ; + +local ntl-path = [ modules.peek : NTL_PATH ] ; +local gmp_path = [ modules.peek : GMP_PATH ] ; +local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local e_float_path = [ modules.peek : BOOST_E_FLOAT_PATH ] ; + +if ! $(e_float_path) +{ + e_float_path = ../../../../e_float ; +} + +project : requirements + $(gmp_path) + $(gmp_path)/mpfr + $(gmp_path)/gmpfrxx + $(mpfr_path) + ../../.. + $(e_float_path) + $(gmp_path) + $(mpfr_path) + $(mpfr_path)/build.vc10/lib/Win32/Debug + msvc:static + E_FLOAT_DIGITS10=100 + E_FLOAT_TYPE_EFX + ; + +lib gmp ; +lib mpfr ; + +E_FLOAT_SRC = [ GLOB $(e_float_path)/libs/e_float/src/e_float : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/e_float/efx : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/constants : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/elementary : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/gamma : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/integer : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/tables : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/zeta : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/generic_functions/constants : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/generic_functions/elementary : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/utility : *.cpp ] + ; + +lib e_float : $(E_FLOAT_SRC) + : + [ check-target-builds ../config//has_e_float : : no ] + ; + +run test_arithmetic.cpp + : # command line + : # input files + : # requirements + TEST_BACKEND + : test_arithmetic_backend_concept ; + +run test_arithmetic.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_arithmetic_mpf50 ; + +run test_arithmetic.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF + [ check-target-builds ../config//has_gmp : : no ] + : test_arithmetic_mpf ; + +run test_arithmetic.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPZ + [ check-target-builds ../config//has_gmp : : no ] + : test_arithmetic_mpz ; + +run test_arithmetic.cpp mpfr gmp + : # command line + : # input files + : # requirements + TEST_MPFR + [ check-target-builds ../config//has_mpfr : : no ] + : test_arithmetic_mpfr ; + +run test_arithmetic.cpp mpfr gmp + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_arithmetic_mpfr_50 ; + +run test_arithmetic.cpp $(E_FLOAT_SRC) + : # command line + : # input files + : # requirements + TEST_E_FLOAT + [ check-target-builds ../config//has_e_float : : no ] + : test_arithmetic_e_float ; + +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + TEST_BACKEND + : test_numeric_limits_backend_concept ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_numeric_limits_mpf50 ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF + [ check-target-builds ../config//has_gmp : : no ] + : test_numeric_limits_mpf ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPZ + [ check-target-builds ../config//has_gmp : : no ] + : test_numeric_limits_mpz ; + +run test_numeric_limits.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR + [ check-target-builds ../config//has_mpfr : : no ] + : test_numeric_limits_mpfr ; + +run test_numeric_limits.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_numeric_limits_mpfr_50 ; + +run test_numeric_limits.cpp $(E_FLOAT_SRC) + : # command line + : # input files + : # requirements + TEST_E_FLOAT + [ check-target-builds ../config//has_e_float : : no ] + : test_numeric_limits_e_float ; + + + diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 35bc6682..74111c7b 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -174,7 +174,6 @@ template void test_real_ops(const boost::mpl::true_&) { #if defined(TEST_MPF) || defined(TEST_MPF_50) - std::cout << "Root2 = " << sqrt(Real(2)) << std::endl; BOOST_TEST(abs(Real(2)) == 2); BOOST_TEST(abs(Real(-2)) == 2); BOOST_TEST(fabs(Real(2)) == 2); @@ -203,6 +202,16 @@ void test_real_ops(const boost::mpl::true_&) #endif } +#ifdef TEST_E_FLOAT + +template +struct lexical_cast_target_type +{ + typedef long double type; +}; + +#else + template struct lexical_cast_target_type { @@ -217,6 +226,8 @@ struct lexical_cast_target_type >::type type; }; +#endif + template void test_negative_mixed(boost::mpl::true_ const&) { @@ -312,6 +323,10 @@ void test_mixed() BOOST_TEST(Real(n2) == n2); BOOST_TEST(Real(n3) == n3); BOOST_TEST(Real(n4) == n4); + BOOST_TEST(Real(n1).template convert_to() == n1); + BOOST_TEST(Real(n2).template convert_to() == n2); + BOOST_TEST(Real(n3).template convert_to() == n3); + BOOST_TEST(Real(n4).template convert_to() == n4); BOOST_TEST(n1 == Real(n1)); BOOST_TEST(n2 == Real(n2)); BOOST_TEST(n3 == Real(n3)); @@ -689,6 +704,20 @@ void test() { BOOST_ERROR("Unexpected non-zero result"); } + // + // Test iostreams: + // + std::stringstream ss; + a = 20; + b = 2; + ss << a; + ss >> c; + BOOST_TEST(a == c); + ss.clear(); + ss << a + b; + ss >> c; + BOOST_TEST(c == 22); + BOOST_TEST(c == a + b); } From 439ae1589f9a04e8953d73e7a1f2a83574570c75 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 27 Aug 2011 16:37:01 +0000 Subject: [PATCH 016/256] Add bitwise integer ops. Reorganise proto grammar. [SVN r74089] --- include/boost/math/big_number.hpp | 353 +++++++++++++++--- .../boost/math/big_number/big_number_base.hpp | 181 ++++++++- include/boost/math/big_number/default_ops.hpp | 74 ++++ include/boost/math/big_number/gmp.hpp | 35 ++ math/test/test_arithmetic.cpp | 83 ++++ 5 files changed, 668 insertions(+), 58 deletions(-) diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index d8dae762..cd21fff5 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -204,6 +204,16 @@ public: } return *this; } + template + typename enable_if, big_number& >::type + operator%=(const V& v) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + using big_num_default_ops::modulus; + modulus(m_backend, canonical_value(v)); + return *this; + } + // // These operators are *not* proto-ized. // The issue is that the increment/decrement must happen @@ -264,16 +274,6 @@ public: return *this; } - template - typename enable_if, big_number& >::type - operator%=(const V& v) - { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); - using big_num_default_ops::modulus; - modulus(m_backend, canonical_value(v)); - return *this; - } - template big_number& operator/=(const detail::big_number_exp& e) { @@ -299,6 +299,82 @@ public: return *this; } + template + big_number& operator&=(const detail::big_number_exp& e) + { + // Create a temporary if the RHS references *this, but not + // if we're just doing an x &= x; + if(contains_self(e) && !is_self(e)) + { + self_type temp(e); + do_bitwise_and(temp, typename proto::tag_of::type()); + } + else + { + do_bitwise_and(e, typename proto::tag_of::type()); + } + return *this; + } + + template + typename enable_if, big_number& >::type + operator&=(const V& v) + { + using big_num_default_ops::bitwise_and; + bitwise_and(m_backend, canonical_value(v)); + return *this; + } + + template + big_number& operator|=(const detail::big_number_exp& e) + { + // Create a temporary if the RHS references *this, but not + // if we're just doing an x |= x; + if(contains_self(e) && !is_self(e)) + { + self_type temp(e); + do_bitwise_or(temp, typename proto::tag_of::type()); + } + else + { + do_bitwise_or(e, typename proto::tag_of::type()); + } + return *this; + } + + template + typename enable_if, big_number& >::type + operator|=(const V& v) + { + using big_num_default_ops::bitwise_or; + bitwise_or(m_backend, canonical_value(v)); + return *this; + } + + template + big_number& operator^=(const detail::big_number_exp& e) + { + if(contains_self(e)) + { + self_type temp(e); + do_bitwise_xor(temp, typename proto::tag_of::type()); + } + else + { + do_bitwise_xor(e, typename proto::tag_of::type()); + } + return *this; + } + + template + typename enable_if, big_number& >::type + operator^=(const V& v) + { + using big_num_default_ops::bitwise_xor; + bitwise_xor(m_backend, canonical_value(v)); + return *this; + } + // // swap: // @@ -473,16 +549,6 @@ private: m_backend.negate(); } - template - void do_assign(const Exp& e, const detail::modulus_immediates&) - { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); - using big_num_default_ops::modulus; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - modulus(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); - } - template void do_assign(const Exp& e, const proto::tag::unary_plus&) { @@ -675,6 +741,142 @@ private: do_modulus(proto::right(e), typename proto::tag_of::type()); } } + template + void do_assign(const Exp& e, const detail::modulus_immediates&) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + using big_num_default_ops::modulus; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + modulus(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + } + + template + void do_assign(const Exp& e, const proto::tag::bitwise_and&) + { + // + // This operation is only valid for integer backends: + // + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + + static int const left_depth = boost::result_of::type::value; + static int const right_depth = boost::result_of::type::value; + + bool bl = contains_self(proto::left(e)); + bool br = contains_self(proto::right(e)); + + if(bl && is_self(proto::left(e))) + { + // Ignore the left node, it's *this, just add the right: + do_bitwise_and(proto::right(e), typename proto::tag_of::type()); + } + else if(br && is_self(proto::right(e))) + { + do_bitwise_and(proto::left(e), typename proto::tag_of::type()); + } + else + { + do_assign(proto::left(e), typename detail::assign_and_eval::type()); + do_bitwise_and(proto::right(e), typename proto::tag_of::type()); + } + } + template + void do_assign(const Exp& e, const detail::bitwise_and_immediates&) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + using big_num_default_ops::bitwise_and; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + bitwise_and(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + } + + template + void do_assign(const Exp& e, const proto::tag::bitwise_or&) + { + // + // This operation is only valid for integer backends: + // + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + + static int const left_depth = boost::result_of::type::value; + static int const right_depth = boost::result_of::type::value; + + bool bl = contains_self(proto::left(e)); + bool br = contains_self(proto::right(e)); + + if(bl && is_self(proto::left(e))) + { + // Ignore the left node, it's *this, just add the right: + do_bitwise_or(proto::right(e), typename proto::tag_of::type()); + } + else if(br && is_self(proto::right(e))) + { + do_bitwise_or(proto::left(e), typename proto::tag_of::type()); + } + else + { + do_assign(proto::left(e), typename detail::assign_and_eval::type()); + do_bitwise_or(proto::right(e), typename proto::tag_of::type()); + } + } + template + void do_assign(const Exp& e, const detail::bitwise_or_immediates&) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + using big_num_default_ops::bitwise_or; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + bitwise_or(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + } + + template + void do_assign(const Exp& e, const proto::tag::bitwise_xor&) + { + // + // This operation is only valid for integer backends: + // + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + + static int const left_depth = boost::result_of::type::value; + static int const right_depth = boost::result_of::type::value; + + bool bl = contains_self(proto::left(e)); + bool br = contains_self(proto::right(e)); + + if(bl && is_self(proto::left(e))) + { + // Ignore the left node, it's *this, just add the right: + do_bitwise_xor(proto::right(e), typename proto::tag_of::type()); + } + else if(br && is_self(proto::right(e))) + { + do_bitwise_xor(proto::left(e), typename proto::tag_of::type()); + } + else + { + do_assign(proto::left(e), typename detail::assign_and_eval::type()); + do_bitwise_xor(proto::right(e), typename proto::tag_of::type()); + } + } + template + void do_assign(const Exp& e, const detail::bitwise_xor_immediates&) + { + BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + using big_num_default_ops::bitwise_xor; + typedef typename proto::tag_of::type>::type left_tag; + typedef typename proto::tag_of::type>::type right_tag; + bitwise_xor(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + } + template void do_assign(const Exp& e, const proto::tag::terminal&) { @@ -717,6 +919,21 @@ private: do_assign_right_shift(proto::left(e), canonical_value(proto::value(proto::right(e))), tag_type()); } + template + void do_assign(const Exp& e, const proto::tag::complement&) + { + using big_num_default_ops::complement; + self_type temp(proto::left(e)); + complement(m_backend, temp.backend()); + } + + template + void do_assign(const Exp& e, const detail::complement_immediates&) + { + using big_num_default_ops::complement; + complement(m_backend, canonical_value(proto::left(e))); + } + template void do_assign_right_shift(const Exp& e, const Val& val, const proto::tag::terminal&) { @@ -990,6 +1207,72 @@ private: modulus(m_backend, canonical_value(proto::value(temp))); } + template + void do_bitwise_and(const Exp& e, const proto::tag::terminal&) + { + using big_num_default_ops::bitwise_and; + bitwise_and(m_backend, canonical_value(proto::value(e))); + } + template + void do_bitwise_and(const Exp& e, const proto::tag::bitwise_and&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_bitwise_and(proto::left(e), typename proto::tag_of::type()); + do_bitwise_and(proto::right(e), typename proto::tag_of::type()); + } + template + void do_bitwise_and(const Exp& e, const unknown&) + { + using big_num_default_ops::bitwise_and; + self_type temp(e); + bitwise_and(m_backend, temp.m_backend); + } + + template + void do_bitwise_or(const Exp& e, const proto::tag::terminal&) + { + using big_num_default_ops::bitwise_or; + bitwise_or(m_backend, canonical_value(proto::value(e))); + } + template + void do_bitwise_or(const Exp& e, const proto::tag::bitwise_or&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_bitwise_or(proto::left(e), typename proto::tag_of::type()); + do_bitwise_or(proto::right(e), typename proto::tag_of::type()); + } + template + void do_bitwise_or(const Exp& e, const unknown&) + { + using big_num_default_ops::bitwise_or; + self_type temp(e); + bitwise_or(m_backend, temp.m_backend); + } + + template + void do_bitwise_xor(const Exp& e, const proto::tag::terminal&) + { + using big_num_default_ops::bitwise_xor; + bitwise_xor(m_backend, canonical_value(proto::value(e))); + } + template + void do_bitwise_xor(const Exp& e, const proto::tag::bitwise_xor&) + { + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + do_bitwise_xor(proto::left(e), typename proto::tag_of::type()); + do_bitwise_xor(proto::right(e), typename proto::tag_of::type()); + } + template + void do_bitwise_xor(const Exp& e, const unknown&) + { + using big_num_default_ops::bitwise_xor; + self_type temp(e); + bitwise_xor(m_backend, temp.m_backend); + } + // Tests if the expression contains a reference to *this: template bool contains_self(const Exp& e)const @@ -1198,44 +1481,24 @@ inline typename boost::enable_if, bool>: { return 0 < detail::big_number_compare(a, b); } -// -// Because proto overloads these << operators, we need version that accept both -// const and non-const RHS values, otherwise the proto version will be found -// with unpleasant results... not only that, but the stream parameter has to be a template -// otherwise the LHS of the expression would have to be *exactly* of type std::ostream -// for the overload to be found (ie doesn't work for std::fstream etc unless we do this...) -// -template -inline typename enable_if, std::ostream&>::type operator << (Stream& os, const big_number& r) -{ - return os << r.str(static_cast(os.precision(), os.flags() & os.scientific)); -} -template -inline typename enable_if, std::ostream&>::type operator << (Stream& os, big_number& r) +template +inline std::ostream& operator << (std::ostream& os, const big_number& r) { return os << r.str(static_cast(os.precision(), os.flags() & os.scientific)); } namespace detail{ -template -inline typename enable_if, std::ostream&>::type operator << (Stream& os, const big_number_exp& r) +template +inline std::ostream& operator << (std::ostream& os, const big_number_exp& r) { typedef typename expression_type >::type value_type; value_type temp(r); return os << temp; } -template -inline typename enable_if, std::ostream&>::type operator << (Stream& os, big_number_exp& r) -{ - typedef typename expression_type >::type value_type; - value_type temp(r); - return os << temp; -} - -} +} // namespace detail template inline typename enable_if, std::istream&>::type operator >> (Stream& is, big_number& r) diff --git a/include/boost/math/big_number/big_number_base.hpp b/include/boost/math/big_number/big_number_base.hpp index 83e635a2..c579d71e 100644 --- a/include/boost/math/big_number/big_number_base.hpp +++ b/include/boost/math/big_number/big_number_base.hpp @@ -19,21 +19,111 @@ struct big_number_exp; // // Declare our grammars: // -struct big_number_grammar - : proto::or_< - proto::terminal< proto::_ > - , proto::plus< big_number_grammar, big_number_grammar > - , proto::multiplies< big_number_grammar, big_number_grammar > - , proto::minus< big_number_grammar, big_number_grammar > - , proto::divides< big_number_grammar, big_number_grammar > - , proto::unary_plus< big_number_grammar > - , proto::negate< big_number_grammar > - , proto::modulus - , proto::shift_left - , proto::shift_right - > +struct integer_terminal : public +proto::and_< + proto::terminal< proto::_ >, + proto::if_ < boost::is_integral< proto::_value >() > + > {}; +struct big_number_grammar; + +template +struct is_big_number_ptr : mpl::false_ {}; + +template +struct is_big_number_ptr*> : mpl::true_ {}; + + +struct big_number_grammar_cases +{ + // The primary template matches nothing: + template + struct case_ + : proto::not_ + {}; +}; + +template<> +struct big_number_grammar_cases::case_ + : proto::and_< + proto::terminal, + proto::or_< + proto::if_ < is_big_number_ptr< proto::_value >() >, + proto::if_ < is_arithmetic< proto::_value >() >, + proto::if_ < is_same< proto::_value, std::string>() >, + proto::if_ < is_convertible< proto::_value, const char*>() > + > + > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::plus< big_number_grammar, big_number_grammar > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::multiplies< big_number_grammar, big_number_grammar > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::minus< big_number_grammar, big_number_grammar > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::divides< big_number_grammar, big_number_grammar > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::unary_plus< big_number_grammar> +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::negate< big_number_grammar> +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::modulus< big_number_grammar, big_number_grammar > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::bitwise_and< big_number_grammar, big_number_grammar > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::bitwise_or< big_number_grammar, big_number_grammar > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::bitwise_xor< big_number_grammar, big_number_grammar > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::shift_left< big_number_grammar, integer_terminal > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::shift_right< big_number_grammar, integer_terminal > +{}; + +template<> +struct big_number_grammar_cases::case_ + : proto::complement +{}; + +struct big_number_grammar : proto::switch_{}; + // Define a calculator domain. Expression within // the calculator domain will be wrapped in the // calculator<> expression wrapper. @@ -146,6 +236,10 @@ struct multiply_and_negate_immediates{}; struct divide_immediates{}; struct divide_and_negate_immediates{}; struct modulus_immediates{}; +struct bitwise_and_immediates{}; +struct bitwise_or_immediates{}; +struct bitwise_xor_immediates{}; +struct complement_immediates{}; struct immediate{}; struct negative_immediate{}; @@ -312,6 +406,67 @@ struct assign_and_eval_imp >::type type; }; +template +struct assign_and_eval_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::tag_of::type left_tag; + typedef typename proto::tag_of::type right_tag; + typedef typename immediate_type::type left_imm; + typedef typename immediate_type::type right_imm; + typedef typename mpl::if_< + mpl::and_, is_same >, + bitwise_and_immediates, + proto::tag::bitwise_and + >::type type; +}; + +template +struct assign_and_eval_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::tag_of::type left_tag; + typedef typename proto::tag_of::type right_tag; + typedef typename immediate_type::type left_imm; + typedef typename immediate_type::type right_imm; + typedef typename mpl::if_< + mpl::and_, is_same >, + bitwise_or_immediates, + proto::tag::bitwise_or + >::type type; +}; + +template +struct assign_and_eval_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::result_of::right::type right_type; + typedef typename proto::tag_of::type left_tag; + typedef typename proto::tag_of::type right_tag; + typedef typename immediate_type::type left_imm; + typedef typename immediate_type::type right_imm; + typedef typename mpl::if_< + mpl::and_, is_same >, + bitwise_xor_immediates, + proto::tag::bitwise_xor + >::type type; +}; + +template +struct assign_and_eval_imp +{ + typedef typename proto::result_of::left::type left_type; + typedef typename proto::tag_of::type left_tag; + typedef typename immediate_type::type left_imm; + typedef typename mpl::if_< + is_same, + complement_immediates, + proto::tag::complement + >::type type; +}; + template struct assign_and_eval { diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index 57fcf2ba..79da094b 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -54,6 +54,39 @@ inline typename enable_if, is_convertible +inline typename enable_if, is_convertible, is_same > >::type + bitwise_and(T& result, V const& v) +{ + T t; + t = v; + bitwise_and(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + bitwise_or(T& result, V const& v) +{ + T t; + t = v; + bitwise_or(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + bitwise_xor(T& result, V const& v) +{ + T t; + t = v; + bitwise_xor(result, t); +} + +template +inline typename enable_if, is_convertible, is_same > >::type + complement(T& result, V const& v) +{ + T t; + t = v; + complement(result, t); +} template inline bool is_same_object(const T& u, const T&v) @@ -145,6 +178,47 @@ inline void modulus(T& t, const U& u, const V& v) modulus(t, v); } } +template +inline void bitwise_and(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + bitwise_and(t, v); + else if(is_same_object(t, v)) + bitwise_and(t, u); + else + { + t = u; + bitwise_and(t, v); + } +} + +template +inline void bitwise_or(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + bitwise_or(t, v); + else if(is_same_object(t, v)) + bitwise_or(t, u); + else + { + t = u; + bitwise_or(t, v); + } +} + +template +inline void bitwise_xor(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + bitwise_xor(t, v); + else if(is_same_object(t, v)) + bitwise_xor(t, u); + else + { + t = u; + bitwise_xor(t, v); + } +} template inline void increment(T& val) diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index 51d35fe0..40bde812 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -910,6 +910,21 @@ inline void right_shift(gmp_int& t, const gmp_int& v, UI i) mpz_fdiv_q_2exp(t.data(), v.data(), static_cast(i)); } +inline void bitwise_and(gmp_int& result, const gmp_int& v) +{ + mpz_and(result.data(), result.data(), v.data()); +} + +inline void bitwise_or(gmp_int& result, const gmp_int& v) +{ + mpz_ior(result.data(), result.data(), v.data()); +} + +inline void bitwise_xor(gmp_int& result, const gmp_int& v) +{ + mpz_xor(result.data(), result.data(), v.data()); +} + inline void add(gmp_int& t, const gmp_int& p, const gmp_int& o) { mpz_add(t.data(), p.data(), o.data()); @@ -1013,6 +1028,26 @@ inline void divide(gmp_int& t, const gmp_int& p, long i) mpz_neg(t.data(), t.data()); } +inline void bitwise_and(gmp_int& result, const gmp_int& u, const gmp_int& v) +{ + mpz_and(result.data(), u.data(), v.data()); +} + +inline void bitwise_or(gmp_int& result, const gmp_int& u, const gmp_int& v) +{ + mpz_ior(result.data(), u.data(), v.data()); +} + +inline void bitwise_xor(gmp_int& result, const gmp_int& u, const gmp_int& v) +{ + mpz_xor(result.data(), u.data(), v.data()); +} + +inline void complement(gmp_int& result, const gmp_int& u) +{ + mpz_com(result.data(), u.data()); +} + inline bool is_zero(const gmp_int& val) { return mpz_sgn(val.data()) == 0; diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 74111c7b..927376cd 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -59,6 +59,7 @@ void test_integer_ops(const boost::mpl::true_&) { Real a(20); Real b(7); + Real c; BOOST_TEST(a % b == 20 % 7); BOOST_TEST(a % 7 == 20 % 7); BOOST_TEST(a % 7u == 20 % 7); @@ -154,6 +155,86 @@ void test_integer_ops(const boost::mpl::true_&) BOOST_TEST(b == (22 << 10)); b = (a + 3) >> 3; BOOST_TEST(b == (23 >> 3)); + // + // Bit fiddling: + // + int i = 1020304; + int j = 56789123; + int k = 4523187; + a = i; + b = j; + c = a; + c &= b; + BOOST_TEST(c == (i & j)); + c = a; + c &= j; + BOOST_TEST(c == (i & j)); + c = a; + c &= a + b; + BOOST_TEST(c == (i & (i + j))); + BOOST_TEST((a & b) == (i & j)); + c = k; + a = a & (b + k); + BOOST_TEST(a == (i & (j + k))); + a = i; + a = (b + k) & a; + BOOST_TEST(a == (i & (j + k))); + a = i; + c = a & b & k; + BOOST_TEST(c == (i&j&k)); + + a = i; + b = j; + c = a; + c |= b; + BOOST_TEST(c == (i | j)); + c = a; + c |= j; + BOOST_TEST(c == (i | j)); + c = a; + c |= a + b; + BOOST_TEST(c == (i | (i + j))); + BOOST_TEST((a | b) == (i | j)); + c = k; + a = a | (b + k); + BOOST_TEST(a == (i | (j + k))); + a = i; + a = (b + k) | a; + BOOST_TEST(a == (i | (j + k))); + a = i; + c = a | b | k; + BOOST_TEST(c == (i|j|k)); + + a = i; + b = j; + c = a; + c ^= b; + BOOST_TEST(c == (i ^ j)); + c = a; + c ^= j; + BOOST_TEST(c == (i ^ j)); + c = a; + c ^= a + b; + BOOST_TEST(c == (i ^ (i + j))); + BOOST_TEST((a ^ b) == (i ^ j)); + c = k; + a = a ^ (b + k); + BOOST_TEST(a == (i ^ (j + k))); + a = i; + a = (b + k) ^ a; + BOOST_TEST(a == (i ^ (j + k))); + a = i; + c = a ^ b ^ k; + BOOST_TEST(c == (i^j^k)); + a = i; + b = j; + c = k; + BOOST_TEST(~a == ~i); + c = a & ~b; + BOOST_TEST(c == (i & ~j)); + c = ~(a | b); + BOOST_TEST(c == ~(i | j)); + // // Non-member functions: // @@ -389,6 +470,7 @@ void test_mixed() template void test() { +#ifndef NO_MIXED_OPS test_mixed(); test_mixed(); test_mixed(); @@ -405,6 +487,7 @@ void test() test_mixed(); test_mixed(); test_mixed(); +#endif // // Integer only functions: // From 0b6e68579954aef5a8ce51ad80e39a2c5615f463 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 30 Aug 2011 17:00:05 +0000 Subject: [PATCH 017/256] Change function evaluation calling convention and naming. Add integer-powers support. [SVN r74166] --- include/boost/math/big_number.hpp | 6 +-- include/boost/math/big_number/default_ops.hpp | 33 ++++++++------- include/boost/math/big_number/e_float.hpp | 9 +++- include/boost/math/big_number/gmp.hpp | 42 +++++++++---------- include/boost/math/big_number/mpfr.hpp | 36 ++++++++-------- .../math/concepts/big_number_architypes.hpp | 42 +++++++++++++++++++ math/test/test_arithmetic.cpp | 27 +++++++++++- 7 files changed, 136 insertions(+), 59 deletions(-) diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index cd21fff5..1a8ed194 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -979,13 +979,13 @@ private: template void do_assign_function_1(const F& f, const Exp& val, const proto::tag::terminal&) { - f(&m_backend, canonical_value(proto::value(val))); + f(m_backend, canonical_value(proto::value(val))); } template void do_assign_function_1(const F& f, const Exp& val, const Tag&) { big_number t(val); - f(&m_backend, t.backend()); + f(m_backend, t.backend()); } template void do_assign_function(const Exp& e, const mpl::long_<3>&) @@ -999,7 +999,7 @@ private: template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const proto::tag::terminal&, const proto::tag::terminal&) { - f(&m_backend, canonical_value(proto::value(val1)), canonical_value(proto::value(val2))); + f(m_backend, canonical_value(proto::value(val1)), canonical_value(proto::value(val2))); } template diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index 79da094b..bb9bba69 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -325,7 +325,7 @@ inline void convert_to(terminal* result, const B& backend) // Functions: // template -void abs(T* result, const T& arg) +void eval_abs(T* result, const T& arg) { typedef typename T::signed_types type_list; typedef typename mpl::front::type front; @@ -334,7 +334,7 @@ void abs(T* result, const T& arg) result->negate(); } template -void fabs(T* result, const T& arg) +void eval_fabs(T* result, const T& arg) { typedef typename T::signed_types type_list; typedef typename mpl::front::type front; @@ -347,17 +347,21 @@ void fabs(T* result, const T& arg) // These have to implemented by the backend, declared here so that our macro generated code compiles OK. // template -typename enable_if_c::type floor(); +typename enable_if_c::type eval_floor(); template -typename enable_if_c::type ceil(); +typename enable_if_c::type eval_ceil(); template -typename enable_if_c::type trunc(); +typename enable_if_c::type eval_trunc(); template -typename enable_if_c::type sqrt(); +typename enable_if_c::type eval_sqrt(); template -typename enable_if_c::type ldexp(); +typename enable_if_c::type eval_ldexp(); template -typename enable_if_c::type frexp(); +typename enable_if_c::type eval_frexp(); +// +// These functions are implemented in separate files, but expanded inline here: +// +#include } @@ -377,10 +381,10 @@ namespace detail{\ template \ struct BOOST_JOIN(func, _funct)\ {\ - void operator()(Backend* result, const Backend& arg)const\ + void operator()(Backend& result, const Backend& arg)const\ {\ - using big_num_default_ops::func;\ - func(result, arg);\ + using big_num_default_ops::BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result, arg);\ }\ };\ \ @@ -419,10 +423,10 @@ template \ struct BOOST_JOIN(func, _funct)\ {\ template \ - void operator()(Backend* result, const Backend& arg, const A2& a)const\ + void operator()(Backend& result, const Backend& arg, const A2& a)const\ {\ - using big_num_default_ops::func;\ - func(result, arg, a);\ + using big_num_default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result, arg, a);\ }\ };\ \ @@ -467,6 +471,7 @@ UNARY_OP_FUNCTOR(trunc) BINARY_OP_FUNCTOR(ldexp) BINARY_OP_FUNCTOR(frexp) +BINARY_OP_FUNCTOR(pow) #undef BINARY_OP_FUNCTOR #undef UNARY_OP_FUNCTOR diff --git a/include/boost/math/big_number/e_float.hpp b/include/boost/math/big_number/e_float.hpp index 402c4379..2cc4c8ee 100644 --- a/include/boost/math/big_number/e_float.hpp +++ b/include/boost/math/big_number/e_float.hpp @@ -34,9 +34,14 @@ inline std::string arithmetic_backend::str(unsigned digits, bool s return result; } -inline void abs(arithmetic_backend* result, const arithmetic_backend& arg) +inline void eval_abs(arithmetic_backend& result, const arithmetic_backend& arg) { - result->data() = ef::fabs(arg.data()); + result.data() = ef::fabs(arg.data()); +} + +inline void eval_fabs(arithmetic_backend& result, const arithmetic_backend& arg) +{ + result.data() = ef::fabs(arg.data()); } inline bool is_zero(const arithmetic_backend& val) diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index 40bde812..c4a08f88 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -573,58 +573,58 @@ inline void convert_to(double* result, const gmp_real& val) // Native non-member operations: // template -inline void sqrt(gmp_real* result, const gmp_real& val) +inline void eval_sqrt(gmp_real& result, const gmp_real& val) { - mpf_sqrt(result->data(), val.data()); + mpf_sqrt(result.data(), val.data()); } template -inline void abs(gmp_real* result, const gmp_real& val) +inline void eval_abs(gmp_real& result, const gmp_real& val) { - mpf_abs(result->data(), val.data()); + mpf_abs(result.data(), val.data()); } template -inline void fabs(gmp_real* result, const gmp_real& val) +inline void eval_fabs(gmp_real& result, const gmp_real& val) { - mpf_abs(result->data(), val.data()); + mpf_abs(result.data(), val.data()); } template -inline void ceil(gmp_real* result, const gmp_real& val) +inline void eval_ceil(gmp_real& result, const gmp_real& val) { - mpf_ceil(result->data(), val.data()); + mpf_ceil(result.data(), val.data()); } template -inline void floor(gmp_real* result, const gmp_real& val) +inline void eval_floor(gmp_real& result, const gmp_real& val) { - mpf_floor(result->data(), val.data()); + mpf_floor(result.data(), val.data()); } template -inline void trunc(gmp_real* result, const gmp_real& val) +inline void eval_trunc(gmp_real& result, const gmp_real& val) { - mpf_trunc(result->data(), val.data()); + mpf_trunc(result.data(), val.data()); } template -inline void ldexp(gmp_real* result, const gmp_real& val, long e) +inline void eval_ldexp(gmp_real& result, const gmp_real& val, long e) { if(e > 0) - mpf_mul_2exp(result->data(), val.data(), e); + mpf_mul_2exp(result.data(), val.data(), e); else if(e < 0) - mpf_div_2exp(result->data(), val.data(), -e); + mpf_div_2exp(result.data(), val.data(), -e); } template -inline void frexp(gmp_real* result, const gmp_real& val, int* e) +inline void eval_frexp(gmp_real& result, const gmp_real& val, int* e) { long v; mpf_get_d_2exp(&v, val.data()); *e = v; - return ldexp(result, val, -v); + eval_ldexp(result, val, -v); } template -inline void frexp(gmp_real* result, const gmp_real& val, long* e) +inline void eval_frexp(gmp_real& result, const gmp_real& val, long* e) { mpf_get_d_2exp(e, val.data()); - return ldexp(result, val, -*e); + eval_ldexp(result, val, -*e); } struct gmp_int @@ -1069,9 +1069,9 @@ inline void convert_to(double* result, const gmp_int& val) *result = mpz_get_d(val.data()); } -inline void abs(gmp_int* result, const gmp_int& val) +inline void eval_abs(gmp_int& result, const gmp_int& val) { - mpz_abs(result->data(), val.data()); + mpz_abs(result.data(), val.data()); } template<> diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp index a9aeac6f..afa2b953 100644 --- a/include/boost/math/big_number/mpfr.hpp +++ b/include/boost/math/big_number/mpfr.hpp @@ -588,55 +588,55 @@ inline void convert_to(long double* result, const mpfr_real_backend& v // Native non-member operations: // template -inline void sqrt(mpfr_real_backend* result, const mpfr_real_backend& val) +inline void eval_sqrt(mpfr_real_backend& result, const mpfr_real_backend& val) { - mpfr_sqrt(result->data(), val.data(), MPFR_RNDN); + mpfr_sqrt(result.data(), val.data(), MPFR_RNDN); } template -inline void abs(mpfr_real_backend* result, const mpfr_real_backend& val) +inline void eval_abs(mpfr_real_backend& result, const mpfr_real_backend& val) { - mpfr_abs(result->data(), val.data(), MPFR_RNDN); + mpfr_abs(result.data(), val.data(), MPFR_RNDN); } template -inline void fabs(mpfr_real_backend* result, const mpfr_real_backend& val) +inline void eval_fabs(mpfr_real_backend& result, const mpfr_real_backend& val) { - mpfr_abs(result->data(), val.data(), MPFR_RNDN); + mpfr_abs(result.data(), val.data(), MPFR_RNDN); } template -inline void ceil(mpfr_real_backend* result, const mpfr_real_backend& val) +inline void eval_ceil(mpfr_real_backend& result, const mpfr_real_backend& val) { - mpfr_ceil(result->data(), val.data()); + mpfr_ceil(result.data(), val.data()); } template -inline void floor(mpfr_real_backend* result, const mpfr_real_backend& val) +inline void eval_floor(mpfr_real_backend& result, const mpfr_real_backend& val) { - mpfr_floor(result->data(), val.data()); + mpfr_floor(result.data(), val.data()); } template -inline void trunc(mpfr_real_backend* result, const mpfr_real_backend& val) +inline void eval_trunc(mpfr_real_backend& result, const mpfr_real_backend& val) { - mpfr_trunc(result->data(), val.data()); + mpfr_trunc(result.data(), val.data()); } template -inline void ldexp(mpfr_real_backend* result, const mpfr_real_backend& val, long e) +inline void eval_ldexp(mpfr_real_backend& result, const mpfr_real_backend& val, long e) { if(e > 0) - mpfr_mul_2exp(result->data(), val.data(), e, MPFR_RNDN); + mpfr_mul_2exp(result.data(), val.data(), e, MPFR_RNDN); else if(e < 0) - mpfr_div_2exp(result->data(), val.data(), -e, MPFR_RNDN); + mpfr_div_2exp(result.data(), val.data(), -e, MPFR_RNDN); } template -inline void frexp(mpfr_real_backend* result, const mpfr_real_backend& val, int* e) +inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, int* e) { long v; mpfr_get_d_2exp(&v, val.data(), MPFR_RNDN); *e = v; - return ldexp(result, val, -v); + ldexp(result, val, -v); } template -inline void frexp(mpfr_real_backend* result, const mpfr_real_backend& val, long* e) +inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, long* e) { mpfr_get_d_2exp(e, val.data(), MPFR_RNDN); return ldexp(result, val, -*e); diff --git a/include/boost/math/concepts/big_number_architypes.hpp b/include/boost/math/concepts/big_number_architypes.hpp index fc85bfa3..29b53493 100644 --- a/include/boost/math/concepts/big_number_architypes.hpp +++ b/include/boost/math/concepts/big_number_architypes.hpp @@ -8,9 +8,11 @@ #include #include +#include #include #include #include +#include namespace boost{ namespace math{ @@ -141,6 +143,46 @@ inline void divide(big_number_backend_real_architype& result, const big_number_b result.m_value /= o.m_value; } +inline void eval_frexp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg, int* exp) +{ + result = std::frexp(arg.m_value, exp); +} + +inline void eval_ldexp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg, int exp) +{ + result = std::ldexp(arg.m_value, exp); +} + +inline void eval_floor(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::floor(arg.m_value); +} + +inline void eval_ceil(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::ceil(arg.m_value); +} + +inline void eval_trunc(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = boost::math::trunc(arg.m_value); +} + +inline void eval_sqrt(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::sqrt(arg.m_value); +} + +inline void eval_abs(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::abs(arg.m_value); +} + +inline void eval_fabs(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::fabs(arg.m_value); +} + typedef boost::math::big_number big_number_real_architype; }}} // namespaces diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 927376cd..1c80628b 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -4,6 +4,7 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ #include +#include #if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) # define TEST_MPF50 @@ -254,7 +255,7 @@ void test_real_ops(const boost::mpl::false_&){} template void test_real_ops(const boost::mpl::true_&) { -#if defined(TEST_MPF) || defined(TEST_MPF_50) +#if defined(TEST_MPF) || defined(TEST_MPF_50) || defined(TEST_BACKEND) BOOST_TEST(abs(Real(2)) == 2); BOOST_TEST(abs(Real(-2)) == 2); BOOST_TEST(fabs(Real(2)) == 2); @@ -280,6 +281,30 @@ void test_real_ops(const boost::mpl::true_&) r = frexp(v, &exp); BOOST_TEST(r == 0.5); BOOST_TEST(exp == -8); + // + // pow and exp: + // + v = 3.25; + r = pow(v, 0); + BOOST_TEST(r == 1); + r = pow(v, 1); + BOOST_TEST(r == 3.25); + r = pow(v, 2); + BOOST_TEST(r == boost::math::pow<2>(3.25)); + r = pow(v, 3); + BOOST_TEST(r == boost::math::pow<3>(3.25)); + r = pow(v, 4); + BOOST_TEST(r == boost::math::pow<4>(3.25)); + r = pow(v, 5); + BOOST_TEST(r == boost::math::pow<5>(3.25)); + r = pow(v, 6); + BOOST_TEST(r == boost::math::pow<6>(3.25)); + r = pow(v, 25); + BOOST_TEST(r == boost::math::pow<25>(Real(3.25))); + /* + r = pow(v, 56); + BOOST_TEST(r == boost::math::pow<56>(Real(3.25))); + */ #endif } From 821405e5469b5801bbc063bb8be44a4644669955 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 30 Aug 2011 18:08:56 +0000 Subject: [PATCH 018/256] Added fpclassify routines. [SVN r74167] --- include/boost/math/big_number/default_ops.hpp | 67 +++++++++++++++++++ include/boost/math/big_number/e_float.hpp | 5 +- include/boost/math/big_number/mpfr.hpp | 6 ++ .../math/concepts/big_number_architypes.hpp | 5 ++ math/test/test_numeric_limits.cpp | 48 +++++++++++++ 5 files changed, 130 insertions(+), 1 deletion(-) diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index bb9bba69..de1bf552 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -7,6 +7,7 @@ #define BOOST_MATH_BIG_NUM_DEF_OPS #include +#include namespace boost{ namespace math{ namespace big_num_default_ops{ @@ -343,6 +344,11 @@ void eval_fabs(T* result, const T& arg) result->negate(); } +template +inline int eval_fpclassify(const Backend& arg) +{ + return is_zero(arg) ? FP_ZERO : FP_NORMAL; +} // // These have to implemented by the backend, declared here so that our macro generated code compiles OK. // @@ -376,6 +382,67 @@ struct big_number_exp; } +// +// Default versions of floating point classification routines: +// +template +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& arg) +{ + using big_num_default_ops::eval_fpclassify; + return eval_fpclassify(arg.backend()); +} +template +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) +{ + typedef typename expression_type::type value_type; + return fpclassify(value_type(arg)); +} +template +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& arg) +{ + int v = fpclassify(arg); + return (v != FP_INFINITE) && (v != FP_NAN); +} +template +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) +{ + typedef typename expression_type::type value_type; + return isfinite(value_type(arg)); +} +template +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& arg) +{ + return fpclassify(arg) == FP_NAN; +} +template +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) +{ + typedef typename expression_type::type value_type; + return isnan(value_type(arg)); +} +template +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& arg) +{ + return fpclassify(arg) == FP_INFINITE; +} +template +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) +{ + typedef typename expression_type::type value_type; + return isinf(value_type(arg)); +} +template +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& arg) +{ + return fpclassify(arg) == FP_NORMAL; +} +template +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) +{ + typedef typename expression_type::type value_type; + return isnormal(value_type(arg)); +} + #define UNARY_OP_FUNCTOR(func)\ namespace detail{\ template \ diff --git a/include/boost/math/big_number/e_float.hpp b/include/boost/math/big_number/e_float.hpp index 2cc4c8ee..9ce737c4 100644 --- a/include/boost/math/big_number/e_float.hpp +++ b/include/boost/math/big_number/e_float.hpp @@ -69,7 +69,10 @@ inline void convert_to(long double* result, const arithmetic_backend& val) +{ + return val.data().isinf() ? FP_INFINITE : val.data().isnan() ? FP_NAN : val.data().iszero() ? FP_ZERO : FP_NORMAL; +} }} // namespaces diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp index afa2b953..cdd562dc 100644 --- a/include/boost/math/big_number/mpfr.hpp +++ b/include/boost/math/big_number/mpfr.hpp @@ -642,6 +642,12 @@ inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_back return ldexp(result, val, -*e); } +template +inline int eval_fpclassify(const mpfr_real_backend& val) +{ + return mpfr_inf_p(val.data()) ? FP_INFINITE : mpfr_nan_p(val.data()) ? FP_NAN : mpfr_zero_p(val.data()) ? FP_ZERO : FP_NORMAL; +} + typedef big_number > mpfr_real_50; typedef big_number > mpfr_real_100; typedef big_number > mpfr_real_500; diff --git a/include/boost/math/concepts/big_number_architypes.hpp b/include/boost/math/concepts/big_number_architypes.hpp index 29b53493..66d79fc4 100644 --- a/include/boost/math/concepts/big_number_architypes.hpp +++ b/include/boost/math/concepts/big_number_architypes.hpp @@ -183,6 +183,11 @@ inline void eval_fabs(big_number_backend_real_architype& result, const big_numbe result = std::fabs(arg.m_value); } +inline int eval_fpclassify(const big_number_backend_real_architype& arg) +{ + return boost::math::fpclassify(arg.m_value); +} + typedef boost::math::big_number big_number_real_architype; }}} // namespaces diff --git a/math/test/test_numeric_limits.cpp b/math/test/test_numeric_limits.cpp index 35227e0c..8f3ecdcc 100644 --- a/math/test/test_numeric_limits.cpp +++ b/math/test/test_numeric_limits.cpp @@ -79,6 +79,54 @@ void test() PRINT(traps); PRINT(tinyness_before); PRINT(round_style); + + if(std::numeric_limits::is_specialized) + { + if(std::numeric_limits::has_quiet_NaN) + { + BOOST_TEST((boost::math::isnan)(std::numeric_limits::quiet_NaN())); + BOOST_TEST(FP_NAN == (boost::math::fpclassify)(std::numeric_limits::quiet_NaN())); + BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits::quiet_NaN())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::quiet_NaN())); + BOOST_TEST(!(boost::math::isinf)(std::numeric_limits::quiet_NaN())); + } + if(std::numeric_limits::has_signaling_NaN) + { + BOOST_TEST((boost::math::isnan)(std::numeric_limits::signaling_NaN())); + BOOST_TEST(FP_NAN == (boost::math::fpclassify)(std::numeric_limits::signaling_NaN())); + BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits::signaling_NaN())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::signaling_NaN())); + BOOST_TEST(!(boost::math::isinf)(std::numeric_limits::signaling_NaN())); + } + if(std::numeric_limits::has_infinity) + { + BOOST_TEST((boost::math::isinf)(std::numeric_limits::infinity())); + BOOST_TEST(FP_INFINITE == (boost::math::fpclassify)(std::numeric_limits::infinity())); + BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits::infinity())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::infinity())); + BOOST_TEST(!(boost::math::isnan)(std::numeric_limits::infinity())); + } + if(std::numeric_limits::has_denorm) + { + BOOST_TEST(FP_SUBNORMAL == (boost::math::fpclassify)(std::numeric_limits::denorm_min())); + BOOST_TEST((boost::math::isfinite)(std::numeric_limits::denorm_min())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::denorm_min())); + BOOST_TEST(!(boost::math::isinf)(std::numeric_limits::denorm_min())); + BOOST_TEST(!(boost::math::isnan)(std::numeric_limits::denorm_min())); + } + } + Number n = 0; + BOOST_TEST((boost::math::fpclassify)(n) == FP_ZERO); + BOOST_TEST((boost::math::isfinite)(n)); + BOOST_TEST(!(boost::math::isnormal)(n)); + BOOST_TEST(!(boost::math::isinf)(n)); + BOOST_TEST(!(boost::math::isnan)(n)); + n = 2; + BOOST_TEST((boost::math::fpclassify)(n) == FP_NORMAL); + BOOST_TEST((boost::math::isfinite)(n)); + BOOST_TEST((boost::math::isnormal)(n)); + BOOST_TEST(!(boost::math::isinf)(n)); + BOOST_TEST(!(boost::math::isnan)(n)); } From 4af7f865b06419e12569771ef9c6ceb28f8e71a5 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 12 Sep 2011 08:35:42 +0000 Subject: [PATCH 019/256] Bring mpfr backend into line with Boost.Math's requirements. Fix input streaming. Add MPQ support. Mostly fix gcc compiler issues. [SVN r74354] --- include/boost/math/big_number.hpp | 68 +++- .../boost/math/big_number/big_number_base.hpp | 26 +- include/boost/math/big_number/default_ops.hpp | 347 ++++++++++++++++-- include/boost/math/big_number/gmp.hpp | 233 +++++++++++- include/boost/math/big_number/mpfr.hpp | 281 +++++++++----- math/test/Jamfile.v2 | 16 + math/test/big_number_concept_check.cpp | 140 ++++++- math/test/test_arithmetic.cpp | 10 +- math/test/test_numeric_limits.cpp | 8 +- 9 files changed, 960 insertions(+), 169 deletions(-) diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index 1a8ed194..664aec72 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -453,7 +453,7 @@ private: template void check_shift_range(V val, const mpl::true_&, const mpl::true_&) { - if(val > std::numeric_limits::max()) + if(val > (std::numeric_limits::max)()) BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); if(val < 0) BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); @@ -467,7 +467,7 @@ private: template void check_shift_range(V val, const mpl::true_&, const mpl::false_&) { - if(val > std::numeric_limits::max()) + if(val > (std::numeric_limits::max)()) BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); } template @@ -686,9 +686,6 @@ private: typedef typename proto::result_of::left::type left_type; typedef typename proto::result_of::right::type right_type; - static int const left_depth = boost::result_of::type::value; - static int const right_depth = boost::result_of::type::value; - bool bl = contains_self(proto::left(e)); bool br = contains_self(proto::right(e)); @@ -719,9 +716,6 @@ private: typedef typename proto::result_of::left::type left_type; typedef typename proto::result_of::right::type right_type; - static int const left_depth = boost::result_of::type::value; - static int const right_depth = boost::result_of::type::value; - bool bl = contains_self(proto::left(e)); bool br = contains_self(proto::right(e)); @@ -777,11 +771,16 @@ private: { do_bitwise_and(proto::left(e), typename proto::tag_of::type()); } - else + else if(left_depth >= right_depth) { do_assign(proto::left(e), typename detail::assign_and_eval::type()); do_bitwise_and(proto::right(e), typename proto::tag_of::type()); } + else + { + do_assign(proto::right(e), typename detail::assign_and_eval::type()); + do_bitwise_and(proto::left(e), typename proto::tag_of::type()); + } } template void do_assign(const Exp& e, const detail::bitwise_and_immediates&) @@ -819,11 +818,16 @@ private: { do_bitwise_or(proto::left(e), typename proto::tag_of::type()); } - else + else if(left_depth >= right_depth) { do_assign(proto::left(e), typename detail::assign_and_eval::type()); do_bitwise_or(proto::right(e), typename proto::tag_of::type()); } + else + { + do_assign(proto::right(e), typename detail::assign_and_eval::type()); + do_bitwise_or(proto::left(e), typename proto::tag_of::type()); + } } template void do_assign(const Exp& e, const detail::bitwise_or_immediates&) @@ -861,11 +865,16 @@ private: { do_bitwise_xor(proto::left(e), typename proto::tag_of::type()); } - else + else if(left_depth >= right_depth) { do_assign(proto::left(e), typename detail::assign_and_eval::type()); do_bitwise_xor(proto::right(e), typename proto::tag_of::type()); } + else + { + do_assign(proto::right(e), typename detail::assign_and_eval::type()); + do_bitwise_xor(proto::left(e), typename proto::tag_of::type()); + } } template void do_assign(const Exp& e, const detail::bitwise_xor_immediates&) @@ -1001,6 +1010,25 @@ private: { f(m_backend, canonical_value(proto::value(val1)), canonical_value(proto::value(val2))); } + template + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const proto::tag::terminal&) + { + self_type temp1(val1); + f(m_backend, temp1.backend(), canonical_value(proto::value(val2))); + } + template + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const proto::tag::terminal&, const Tag2&) + { + self_type temp2(val2); + f(m_backend, canonical_value(proto::value(val1)), temp2.backend()); + } + template + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const Tag2&) + { + self_type temp1(val1); + self_type temp2(val2); + f(m_backend, temp1.backend(), temp2.backend()); + } template void do_add(const Exp& e, const proto::tag::terminal&) @@ -1297,6 +1325,16 @@ private: typedef typename proto::result_of::child_c::type child1_type; return contains_self(proto::child_c<0>(e), mpl::int_::value>()) || contains_self(proto::child_c<1>(e), mpl::int_::value>()); } + template + bool contains_self(const Exp& e, mpl::int_<3> const&)const + { + typedef typename proto::result_of::child_c::type child0_type; + typedef typename proto::result_of::child_c::type child1_type; + typedef typename proto::result_of::child_c::type child2_type; + return contains_self(proto::child_c<0>(e), mpl::int_::value>()) + || contains_self(proto::child_c<1>(e), mpl::int_::value>()) + || contains_self(proto::child_c<2>(e), mpl::int_::value>()); + } // Test if the expression is a reference to *this: template @@ -1326,13 +1364,13 @@ private: return v == this; } template - static typename detail::underlying_result::type underlying_value(const big_number_exp& e, const proto::tag::terminal&) + static typename detail::underlying_result::type underlying_value(const detail::big_number_exp& e, const proto::tag::terminal&) { return proto::value(e); } template static typename detail::underlying_result::type - underlying_value(const big_number_exp& e, const tag&) + underlying_value(const detail::big_number_exp& e, const tag&) { typedef typename proto::result_of::left::type left_type; typedef typename proto::tag_of::type tag_type; @@ -1500,8 +1538,8 @@ inline std::ostream& operator << (std::ostream& os, const big_number_exp& r } // namespace detail -template -inline typename enable_if, std::istream&>::type operator >> (Stream& is, big_number& r) +template +inline std::istream& operator >> (std::istream& is, big_number& r) { std::string s; is >> s; diff --git a/include/boost/math/big_number/big_number_base.hpp b/include/boost/math/big_number/big_number_base.hpp index c579d71e..5356c6a3 100644 --- a/include/boost/math/big_number/big_number_base.hpp +++ b/include/boost/math/big_number/big_number_base.hpp @@ -6,6 +6,8 @@ #ifndef BOOST_MATH_BIG_NUM_BASE_HPP #define BOOST_MATH_BIG_NUM_BASE_HPP +#include + namespace boost{ namespace math{ template @@ -122,6 +124,14 @@ struct big_number_grammar_cases::case_ : proto::complement {}; +template<> +struct big_number_grammar_cases::case_ + : proto::or_< + proto::function< proto::_, big_number_grammar >, + proto::function< proto::_, big_number_grammar, proto::_ > + > +{}; + struct big_number_grammar : proto::switch_{}; // Define a calculator domain. Expression within @@ -625,7 +635,7 @@ public: : base_type(expr) {} template - big_number_exp(const Other& o) + big_number_exp(const Other& o, typename enable_if >::type const* = 0) : base_type(o) {} @@ -645,9 +655,21 @@ struct is_extended_integer : public mpl::false_ {}; template struct is_extended_integer > : public is_extended_integer{}; - }} // namespaces +namespace boost{ namespace math{ namespace tools{ + +template +struct promote_arg; + +template +struct promote_arg > +{ + typedef typename boost::math::detail::expression_type::type type; +}; + +}}} + #endif // BOOST_MATH_BIG_NUM_BASE_HPP diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index de1bf552..ca14a806 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -6,8 +6,10 @@ #ifndef BOOST_MATH_BIG_NUM_DEF_OPS #define BOOST_MATH_BIG_NUM_DEF_OPS +#include #include #include +#include namespace boost{ namespace math{ namespace big_num_default_ops{ @@ -306,7 +308,7 @@ struct calculate_next_larger_type template inline void convert_to(R* result, const B& backend) { - typedef calculate_next_larger_type::type next_type; + typedef typename calculate_next_larger_type::type next_type; next_type n; convert_to(&n, backend); *result = static_cast(n); @@ -365,6 +367,31 @@ typename enable_if_c::type eval_ldexp(); template typename enable_if_c::type eval_frexp(); // +// TODO: implement default versions of these: +// +template +typename enable_if_c::type eval_exp(); +template +typename enable_if_c::type eval_log(); +template +typename enable_if_c::type eval_sin(); +template +typename enable_if_c::type eval_cos(); +template +typename enable_if_c::type eval_tan(); +template +typename enable_if_c::type eval_asin(); +template +typename enable_if_c::type eval_acos(); +template +typename enable_if_c::type eval_atan(); +template +typename enable_if_c::type eval_sinh(); +template +typename enable_if_c::type eval_cosh(); +template +typename enable_if_c::type eval_tanh(); +// // These functions are implemented in separate files, but expanded inline here: // #include @@ -394,7 +421,7 @@ inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number template inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) { - typedef typename expression_type::type value_type; + typedef typename detail::expression_type::type value_type; return fpclassify(value_type(arg)); } template @@ -406,7 +433,7 @@ inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& template inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) { - typedef typename expression_type::type value_type; + typedef typename detail::expression_type::type value_type; return isfinite(value_type(arg)); } template @@ -417,7 +444,7 @@ inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& ar template inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) { - typedef typename expression_type::type value_type; + typedef typename detail::expression_type::type value_type; return isnan(value_type(arg)); } template @@ -428,7 +455,7 @@ inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& ar template inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) { - typedef typename expression_type::type value_type; + typedef typename detail::expression_type::type value_type; return isinf(value_type(arg)); } template @@ -439,13 +466,150 @@ inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& template inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) { - typedef typename expression_type::type value_type; + typedef typename detail::expression_type::type value_type; return isnormal(value_type(arg)); } +template +inline int itrunc(const detail::big_number_exp& v, const Policy& pol) +{ + typedef typename detail::expression_type::type number_type; + number_type r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return r.template convert_to(); +} +template +inline int itrunc(const big_number& v, const Policy& pol) +{ + big_number r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long ltrunc(const detail::big_number_exp& v, const Policy& pol) +{ + typedef typename detail::expression_type::type number_type; + number_type r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long ltrunc(const big_number& v, const Policy& pol) +{ + big_number r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return r.template convert_to(); +} +#ifndef BOOST_NO_LONG_LONG +template +inline long long lltrunc(const detail::big_number_exp& v, const Policy& pol) +{ + typedef typename detail::expression_type::type number_type; + number_type r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long long lltrunc(const big_number& v, const Policy& pol) +{ + big_number r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return r.template convert_to(); +} +#endif +template +inline int iround(const detail::big_number_exp& v, const Policy& pol) +{ + typedef typename detail::expression_type::type number_type; + number_type r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return r.template convert_to(); +} +template +inline int iround(const big_number& v, const Policy& pol) +{ + big_number r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long lround(const detail::big_number_exp& v, const Policy& pol) +{ + typedef typename detail::expression_type::type number_type; + number_type r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long lround(const big_number& v, const Policy& pol) +{ + big_number r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return r.template convert_to(); +} +#ifndef BOOST_NO_LONG_LONG +template +inline long long llround(const detail::big_number_exp& v, const Policy& pol) +{ + typedef typename detail::expression_type::type number_type; + number_type r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long long llround(const big_number& v, const Policy& pol) +{ + big_number r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return r.template convert_to(); +} +#endif +// +// Overload of Boost.Math functions that find the wrong overload when used with big_number: +// +namespace detail{ + template T sinc_pi_imp(T); + template T sinhc_pi_imp(T); +} +template +inline big_number sinc_pi(const big_number& x) +{ + return detail::sinc_pi_imp(x); +} + +template +inline big_number sinc_pi(const big_number& x, const Policy&) +{ + return detail::sinc_pi_imp(x); +} + +template +inline big_number sinhc_pi(const big_number& x) +{ + return detail::sinhc_pi_imp(x); +} + +template +inline big_number sinhc_pi(const big_number& x, const Policy&) +{ + return boost::math::sinhc_pi(x); +} + #define UNARY_OP_FUNCTOR(func)\ namespace detail{\ -template \ +template \ struct BOOST_JOIN(func, _funct)\ {\ void operator()(Backend& result, const Backend& arg)const\ @@ -457,11 +621,11 @@ struct BOOST_JOIN(func, _funct)\ \ }\ \ -template \ +template \ typename proto::result_of::make_expr<\ proto::tag::function\ - , detail::BOOST_JOIN(func, _funct)::type>\ - , detail::big_number_exp\ + , detail::BOOST_JOIN(func, _funct)::type> \ + , detail::big_number_exp \ >::type const \ func(const detail::big_number_exp& arg)\ {\ @@ -470,11 +634,11 @@ func(const detail::big_number_exp& arg)\ , arg \ );\ }\ -template \ +template \ typename proto::result_of::make_expr<\ proto::tag::function\ - , detail::BOOST_JOIN(func, _funct)\ - , detail::big_number_exp*>::type>\ + , detail::BOOST_JOIN(func, _funct) \ + , detail::big_number_exp*>::type> \ >::type const \ func(const big_number& arg)\ {\ @@ -486,11 +650,125 @@ func(const big_number& arg)\ #define BINARY_OP_FUNCTOR(func)\ namespace detail{\ -template \ +template \ struct BOOST_JOIN(func, _funct)\ {\ - template \ - void operator()(Backend& result, const Backend& arg, const A2& a)const\ + void operator()(Backend& result, const Backend& arg, const Backend& a)const\ + {\ + using big_num_default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result, arg, a);\ + }\ + template \ + void operator()(Backend& result, const Backend& arg, const Arithmetic& a)const\ + {\ + using big_num_default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result, arg, a);\ + }\ +};\ +\ +}\ +template \ +typename proto::result_of::make_expr<\ + proto::tag::function\ + , detail::BOOST_JOIN(func, _funct) \ + , detail::big_number_exp*>::type> \ + , detail::big_number_exp*>::type> \ +>::type const \ +func(const big_number& arg, const big_number& a)\ +{\ + return proto::make_expr(\ + detail::BOOST_JOIN(func, _funct)() \ + , static_cast*>::type>&>(arg),\ + static_cast*>::type>&>(a)\ + );\ +}\ +template \ +typename proto::result_of::make_expr<\ + proto::tag::function\ + , detail::BOOST_JOIN(func, _funct) \ + , detail::big_number_exp*>::type> \ + , detail::big_number_exp \ +>::type const \ +func(const big_number& arg, const detail::big_number_exp& a)\ +{\ + return proto::make_expr(\ + detail::BOOST_JOIN(func, _funct)() \ + , static_cast*>::type>&>(arg),\ + a\ + );\ +}\ +template \ +typename proto::result_of::make_expr<\ + proto::tag::function\ + , detail::BOOST_JOIN(func, _funct) \ + , detail::big_number_exp \ + , detail::big_number_exp*>::type > \ +>::type const \ +func(const detail::big_number_exp& arg, const big_number& a)\ +{\ + return proto::make_expr(\ + detail::BOOST_JOIN(func, _funct)() \ + , arg,\ + static_cast*>::type>&>(a)\ + );\ +}\ +template \ +typename proto::result_of::make_expr<\ + proto::tag::function\ + , detail::BOOST_JOIN(func, _funct)::type> \ + , detail::big_number_exp \ + , detail::big_number_exp \ +>::type const \ +func(const detail::big_number_exp& arg, const detail::big_number_exp& a)\ +{\ + return proto::make_expr(\ + detail::BOOST_JOIN(func, _funct)::type>() \ + , arg,\ + a\ + );\ +}\ +template \ +typename enable_if<\ + is_arithmetic,\ + typename proto::result_of::make_expr<\ + proto::tag::function\ + , detail::BOOST_JOIN(func, _funct) \ + , detail::big_number_exp*>::type> \ + , typename proto::result_of::as_child::type\ +>::type>::type const \ +func(const big_number& arg, const Arithmetic& a)\ +{\ + return proto::make_expr(\ + detail::BOOST_JOIN(func, _funct)() \ + , static_cast*>::type>&>(arg),\ + proto::as_child(a)\ + );\ +}\ +template \ +typename enable_if<\ + is_arithmetic,\ + typename proto::result_of::make_expr<\ + proto::tag::function\ + , detail::BOOST_JOIN(func, _funct)::type> \ + , detail::big_number_exp \ + , typename proto::result_of::as_child::type\ +>::type>::type const \ +func(const detail::big_number_exp& arg, const Arithmetic& a)\ +{\ + return proto::make_expr(\ + detail::BOOST_JOIN(func, _funct)::type>() \ + , arg,\ + proto::as_child(a)\ + );\ +}\ + + +#define HETERO_BINARY_OP_FUNCTOR(func, Arg2)\ +namespace detail{\ +template \ +struct BOOST_JOIN(func, _funct)\ +{\ + void operator()(Backend& result, Backend const& arg, Arg2 a)const\ {\ using big_num_default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result, arg, a);\ @@ -499,35 +777,35 @@ struct BOOST_JOIN(func, _funct)\ \ }\ \ -template \ +template \ typename proto::result_of::make_expr<\ proto::tag::function\ - , detail::BOOST_JOIN(func, _funct)::type>\ - , detail::big_number_exp\ - , typename proto::result_of::as_child::type\ + , detail::BOOST_JOIN(func, _funct)::type> \ + , detail::big_number_exp \ + , typename proto::result_of::as_child::type \ >::type const \ -func(const detail::big_number_exp& arg, const A2& a)\ +func(const detail::big_number_exp& arg, Arg2 const& a)\ {\ return proto::make_expr(\ detail::BOOST_JOIN(func, _funct)::type>() \ , arg, proto::as_child(a) \ );\ }\ -template \ +template \ typename proto::result_of::make_expr<\ proto::tag::function\ - , detail::BOOST_JOIN(func, _funct)\ - , detail::big_number_exp*>::type>\ - , typename proto::result_of::as_child::type\ + , detail::BOOST_JOIN(func, _funct) \ + , detail::big_number_exp*>::type> \ + , typename proto::result_of::as_child::type \ >::type const \ -func(const big_number& arg, const A2& a)\ +func(const big_number& arg, Arg2 const& a)\ {\ return proto::make_expr(\ detail::BOOST_JOIN(func, _funct)() \ , static_cast*>::type>&>(arg),\ proto::as_child(a)\ );\ -} +}\ UNARY_OP_FUNCTOR(abs) UNARY_OP_FUNCTOR(fabs) @@ -535,9 +813,20 @@ UNARY_OP_FUNCTOR(sqrt) UNARY_OP_FUNCTOR(floor) UNARY_OP_FUNCTOR(ceil) UNARY_OP_FUNCTOR(trunc) +UNARY_OP_FUNCTOR(exp) +UNARY_OP_FUNCTOR(log) +UNARY_OP_FUNCTOR(cos) +UNARY_OP_FUNCTOR(sin) +UNARY_OP_FUNCTOR(tan) +UNARY_OP_FUNCTOR(asin) +UNARY_OP_FUNCTOR(acos) +UNARY_OP_FUNCTOR(atan) +UNARY_OP_FUNCTOR(cosh) +UNARY_OP_FUNCTOR(sinh) +UNARY_OP_FUNCTOR(tanh) -BINARY_OP_FUNCTOR(ldexp) -BINARY_OP_FUNCTOR(frexp) +HETERO_BINARY_OP_FUNCTOR(ldexp, int) +HETERO_BINARY_OP_FUNCTOR(frexp, int*) BINARY_OP_FUNCTOR(pow) #undef BINARY_OP_FUNCTOR diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index c4a08f88..cfb114aa 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -39,7 +39,7 @@ struct gmp_real_imp // to get the right value, but if it's then used in further calculations // things go badly wrong!! // - mpf_init2(m_data, (((digits10 ? digits10 : gmp_real<0>::default_precision()) + 1) * 1000L) / 301L); + mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpf_set(m_data, o.m_data); } #ifndef BOOST_NO_RVALUE_REFERENCES @@ -66,7 +66,7 @@ struct gmp_real_imp boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpf_t t; - mpf_init2(t, (((digits10 ? digits10 : gmp_real<0>::default_precision()) + 1) * 1000L) / 301L); + mpf_init2(t, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpf_set_ui(m_data, 0); while(i) { @@ -226,6 +226,11 @@ struct gmp_real_imp const mpf_t& data()const { return m_data; } protected: mpf_t m_data; + static unsigned& get_default_precision() + { + static unsigned val = 50; + return val; + } }; } // namespace detail @@ -316,12 +321,6 @@ struct gmp_real<0> : public detail::gmp_real_imp<0> { mpf_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); } -private: - static unsigned& get_default_precision() - { - static unsigned val = 50; - return val; - } }; template @@ -892,22 +891,22 @@ inline void divide(gmp_int& t, long i) template inline void left_shift(gmp_int& t, UI i) { - mpz_mul_2exp(t.data(), t.data(), static_cast(i)); + mpz_mul_2exp(t.data(), t.data(), static_cast(i)); } template inline void right_shift(gmp_int& t, UI i) { - mpz_fdiv_q_2exp(t.data(), t.data(), static_cast(i)); + mpz_fdiv_q_2exp(t.data(), t.data(), static_cast(i)); } template inline void left_shift(gmp_int& t, const gmp_int& v, UI i) { - mpz_mul_2exp(t.data(), v.data(), static_cast(i)); + mpz_mul_2exp(t.data(), v.data(), static_cast(i)); } template inline void right_shift(gmp_int& t, const gmp_int& v, UI i) { - mpz_fdiv_q_2exp(t.data(), v.data(), static_cast(i)); + mpz_fdiv_q_2exp(t.data(), v.data(), static_cast(i)); } inline void bitwise_and(gmp_int& result, const gmp_int& v) @@ -1074,6 +1073,215 @@ inline void eval_abs(gmp_int& result, const gmp_int& val) mpz_abs(result.data(), val.data()); } +struct gmp_rational; +void add(gmp_rational& t, const gmp_rational& o); + +struct gmp_rational +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + gmp_rational() + { + mpq_init(this->m_data); + } + gmp_rational(const gmp_rational& o) + { + mpq_init(m_data); + mpq_set(m_data, o.m_data); + } + gmp_rational& operator = (const gmp_rational& o) + { + mpq_set(m_data, o.m_data); + return *this; + } + gmp_rational& operator = (boost::uintmax_t i) + { + boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned shift = 0; + mpq_t t; + mpq_init(m_data); + mpq_init(t); + while(i) + { + mpq_set_ui(t, static_cast(i & mask), 1); + if(shift) + mpq_mul_2exp(t, t, shift); + mpq_add(m_data, m_data, t); + shift += std::numeric_limits::digits; + i >>= std::numeric_limits::digits; + } + mpq_clear(t); + return *this; + } + gmp_rational& operator = (boost::intmax_t i) + { + bool neg = i < 0; + *this = static_cast(std::abs(i)); + if(neg) + mpq_neg(m_data, m_data); + return *this; + } + gmp_rational& operator = (unsigned long i) + { + mpq_set_ui(m_data, i, 1); + return *this; + } + gmp_rational& operator = (long i) + { + mpq_set_si(m_data, i, 1); + return *this; + } + gmp_rational& operator = (double d) + { + mpq_set_d(m_data, d); + return *this; + } + gmp_rational& operator = (long double a) + { + using std::frexp; + using std::ldexp; + using std::floor; + using big_num_default_ops::add; + using big_num_default_ops::subtract; + + if (a == 0) { + mpq_set_si(m_data, 0, 1); + return *this; + } + + if (a == 1) { + mpq_set_si(m_data, 1, 1); + return *this; + } + + BOOST_ASSERT(!(boost::math::isinf)(a)); + BOOST_ASSERT(!(boost::math::isnan)(a)); + + int e; + long double f, term; + mpq_init(m_data); + mpq_set_ui(m_data, 0u, 1); + gmp_rational t; + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + mpq_mul_2exp(m_data, m_data, shift); + t = static_cast(term); + add(*this, t); + f -= term; + } + if(e > 0) + mpq_mul_2exp(m_data, m_data, e); + else if(e < 0) + mpq_div_2exp(m_data, m_data, -e); + return *this; + } + gmp_rational& operator = (const char* s) + { + mpq_set_str(m_data, s, 10); + return *this; + } + void swap(gmp_rational& o) + { + mpq_swap(m_data, o.m_data); + } + std::string str(unsigned /*digits*/, bool /*scientific*/)const + { + void *(*alloc_func_ptr) (size_t); + void *(*realloc_func_ptr) (void *, size_t, size_t); + void (*free_func_ptr) (void *, size_t); + const char* ps = mpq_get_str (0, 10, m_data); + std::string s = ps; + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); + return s; + } + ~gmp_rational() + { + mpq_clear(m_data); + } + void negate() + { + mpq_neg(m_data, m_data); + } + int compare(const gmp_rational& o)const + { + return mpq_cmp(m_data, o.m_data); + } + template + int compare(V v)const + { + gmp_rational d; + d = v; + return compare(d); + } + mpq_t& data() { return m_data; } + const mpq_t& data()const { return m_data; } +protected: + mpq_t m_data; +}; + +inline void add(gmp_rational& t, const gmp_rational& o) +{ + mpq_add(t.data(), t.data(), o.data()); +} +inline void subtract(gmp_rational& t, const gmp_rational& o) +{ + mpq_sub(t.data(), t.data(), o.data()); +} +inline void multiply(gmp_rational& t, const gmp_rational& o) +{ + mpq_mul(t.data(), t.data(), o.data()); +} +inline void divide(gmp_rational& t, const gmp_rational& o) +{ + mpq_div(t.data(), t.data(), o.data()); +} +inline void add(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +{ + mpq_add(t.data(), p.data(), o.data()); +} +inline void subtract(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +{ + mpq_sub(t.data(), p.data(), o.data()); +} +inline void multiply(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +{ + mpq_mul(t.data(), p.data(), o.data()); +} +inline void divide(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +{ + mpq_div(t.data(), p.data(), o.data()); +} + +inline bool is_zero(const gmp_rational& val) +{ + return mpq_sgn(val.data()) == 0; +} +inline int get_sign(const gmp_rational& val) +{ + return mpq_sgn(val.data()); +} +inline void convert_to(double* result, const gmp_rational& val) +{ + *result = mpq_get_d(val.data()); +} + +inline void eval_abs(gmp_rational& result, const gmp_rational& val) +{ + mpq_abs(result.data(), val.data()); +} + template<> struct is_extended_integer : public mpl::true_ {}; @@ -1083,6 +1291,7 @@ typedef big_number > mpf_real_500; typedef big_number > mpf_real_1000; typedef big_number > mpf_real; typedef big_number mpz_int; +typedef big_number mpq_rational; }} // namespaces diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp index cdd562dc..3020edf5 100644 --- a/include/boost/math/big_number/mpfr.hpp +++ b/include/boost/math/big_number/mpfr.hpp @@ -21,6 +21,8 @@ struct mpfr_real_backend; namespace detail{ +long get_default_precision() { return 50; } + template struct mpfr_real_imp { @@ -32,8 +34,8 @@ struct mpfr_real_imp mpfr_real_imp(const mpfr_real_imp& o) { - mpfr_init2(m_data, (((digits10 ? digits10 : mpfr_real_backend<0>::default_precision()) + 1) * 1000L) / 301L); - mpfr_set(m_data, o.m_data, MPFR_RNDN); + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_set(m_data, o.m_data, GMP_RNDN); } #ifndef BOOST_NO_RVALUE_REFERENCES mpfr_real_imp(mpfr_real_imp&& o) @@ -44,7 +46,7 @@ struct mpfr_real_imp #endif mpfr_real_imp& operator = (const mpfr_real_imp& o) { - mpfr_set(m_data, o.m_data, MPFR_RNDN); + mpfr_set(m_data, o.m_data, GMP_RNDN); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES @@ -60,17 +62,17 @@ struct mpfr_real_imp unsigned shift = 0; mpfr_t t; mpfr_init2(t, (std::max)(static_cast(std::numeric_limits::digits), static_cast(((digits10 + 1) * 1000L) / 301L))); - mpfr_set_ui(m_data, 0, MPFR_RNDN); + mpfr_set_ui(m_data, 0, GMP_RNDN); while(i) { - mpfr_set_ui(t, static_cast(i & mask), MPFR_RNDN); + mpfr_set_ui(t, static_cast(i & mask), GMP_RNDN); long e; - const char* ps = mpfr_get_str (0, &e, 10, 0, t, MPFR_RNDN); + const char* ps = mpfr_get_str (0, &e, 10, 0, t, GMP_RNDN); if(shift) - mpfr_mul_2exp(t, t, shift, MPFR_RNDN); - ps = mpfr_get_str (0, &e, 10, 0, t, MPFR_RNDN); - mpfr_add(m_data, m_data, t, MPFR_RNDN); - ps = mpfr_get_str (0, &e, 10, 0, m_data, MPFR_RNDN); + mpfr_mul_2exp(t, t, shift, GMP_RNDN); + ps = mpfr_get_str (0, &e, 10, 0, t, GMP_RNDN); + mpfr_add(m_data, m_data, t, GMP_RNDN); + ps = mpfr_get_str (0, &e, 10, 0, m_data, GMP_RNDN); shift += std::numeric_limits::digits; i >>= std::numeric_limits::digits; } @@ -82,22 +84,22 @@ struct mpfr_real_imp bool neg = i < 0; *this = static_cast(std::abs(i)); if(neg) - mpfr_neg(m_data, m_data, MPFR_RNDN); + mpfr_neg(m_data, m_data, GMP_RNDN); return *this; } mpfr_real_imp& operator = (unsigned long i) { - mpfr_set_ui(m_data, i, MPFR_RNDN); + mpfr_set_ui(m_data, i, GMP_RNDN); return *this; } mpfr_real_imp& operator = (long i) { - mpfr_set_si(m_data, i, MPFR_RNDN); + mpfr_set_si(m_data, i, GMP_RNDN); return *this; } mpfr_real_imp& operator = (double d) { - mpfr_set_d(m_data, d, MPFR_RNDN); + mpfr_set_d(m_data, d, GMP_RNDN); return *this; } mpfr_real_imp& operator = (long double a) @@ -107,12 +109,12 @@ struct mpfr_real_imp using std::floor; if (a == 0) { - mpfr_set_si(m_data, 0, MPFR_RNDN); + mpfr_set_si(m_data, 0, GMP_RNDN); return *this; } if (a == 1) { - mpfr_set_si(m_data, 1, MPFR_RNDN); + mpfr_set_si(m_data, 1, GMP_RNDN); return *this; } @@ -121,7 +123,7 @@ struct mpfr_real_imp int e; long double f, term; - mpfr_init_set_ui(m_data, 0u, MPFR_RNDN); + mpfr_init_set_ui(m_data, 0u, GMP_RNDN); f = frexp(a, &e); @@ -133,22 +135,22 @@ struct mpfr_real_imp f = ldexp(f, shift); term = floor(f); e -= shift; - mpfr_mul_2exp(m_data, m_data, shift, MPFR_RNDN); + mpfr_mul_2exp(m_data, m_data, shift, GMP_RNDN); if(term > 0) - mpfr_add_ui(m_data, m_data, static_cast(term), MPFR_RNDN); + mpfr_add_ui(m_data, m_data, static_cast(term), GMP_RNDN); else - mpfr_sub_ui(m_data, m_data, static_cast(-term), MPFR_RNDN); + mpfr_sub_ui(m_data, m_data, static_cast(-term), GMP_RNDN); f -= term; } if(e > 0) - mpfr_mul_2exp(m_data, m_data, e, MPFR_RNDN); + mpfr_mul_2exp(m_data, m_data, e, GMP_RNDN); else if(e < 0) - mpfr_div_2exp(m_data, m_data, -e, MPFR_RNDN); + mpfr_div_2exp(m_data, m_data, -e, GMP_RNDN); return *this; } mpfr_real_imp& operator = (const char* s) { - mpfr_set_str(m_data, s, 10, MPFR_RNDN); + mpfr_set_str(m_data, s, 10, GMP_RNDN); return *this; } void swap(mpfr_real_imp& o) @@ -159,7 +161,7 @@ struct mpfr_real_imp { std::string result; mp_exp_t e; - char* ps = mpfr_get_str (0, &e, 10, digits, m_data, MPFR_RNDN); + char* ps = mpfr_get_str (0, &e, 10, digits, m_data, GMP_RNDN); std::ptrdiff_t sl = std::strlen(ps); unsigned chars = sl; if(sl == 0) @@ -199,7 +201,7 @@ struct mpfr_real_imp } void negate() { - mpfr_neg(m_data, m_data, MPFR_RNDN); + mpfr_neg(m_data, m_data, GMP_RNDN); } int compare(const mpfr_real_backend& o)const { @@ -224,6 +226,11 @@ struct mpfr_real_imp const mpfr_t& data()const { return m_data; } protected: mpfr_t m_data; + static unsigned& get_default_precision() + { + static unsigned val = 50; + return val; + } }; } // namespace detail @@ -314,83 +321,77 @@ struct mpfr_real_backend<0> : public detail::mpfr_real_imp<0> { mpfr_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); } -private: - static unsigned& get_default_precision() - { - static unsigned val = 50; - return val; - } }; template inline void add(mpfr_real_backend& result, const mpfr_real_backend& o) { - mpfr_add(result.data(), result.data(), o.data(), MPFR_RNDN); + mpfr_add(result.data(), result.data(), o.data(), GMP_RNDN); } template inline void subtract(mpfr_real_backend& result, const mpfr_real_backend& o) { - mpfr_sub(result.data(), result.data(), o.data(), MPFR_RNDN); + mpfr_sub(result.data(), result.data(), o.data(), GMP_RNDN); } template inline void multiply(mpfr_real_backend& result, const mpfr_real_backend& o) { - mpfr_mul(result.data(), result.data(), o.data(), MPFR_RNDN); + mpfr_mul(result.data(), result.data(), o.data(), GMP_RNDN); } template inline void divide(mpfr_real_backend& result, const mpfr_real_backend& o) { - mpfr_div(result.data(), result.data(), o.data(), MPFR_RNDN); + mpfr_div(result.data(), result.data(), o.data(), GMP_RNDN); } template inline void add(mpfr_real_backend& result, unsigned long i) { - mpfr_add_ui(result.data(), result.data(), i, MPFR_RNDN); + mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); } template inline void subtract(mpfr_real_backend& result, unsigned long i) { - mpfr_sub_ui(result.data(), result.data(), i, MPFR_RNDN); + mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); } template inline void multiply(mpfr_real_backend& result, unsigned long i) { - mpfr_mul_ui(result.data(), result.data(), i, MPFR_RNDN); + mpfr_mul_ui(result.data(), result.data(), i, GMP_RNDN); } template inline void divide(mpfr_real_backend& result, unsigned long i) { - mpfr_div_ui(result.data(), result.data(), i, MPFR_RNDN); + mpfr_div_ui(result.data(), result.data(), i, GMP_RNDN); } template inline void add(mpfr_real_backend& result, long i) { if(i > 0) - mpfr_add_ui(result.data(), result.data(), i, MPFR_RNDN); + mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); else - mpfr_sub_ui(result.data(), result.data(), std::abs(i), MPFR_RNDN); + mpfr_sub_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); } template inline void subtract(mpfr_real_backend& result, long i) { if(i > 0) - mpfr_sub_ui(result.data(), result.data(), i, MPFR_RNDN); + mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); else - mpfr_add_ui(result.data(), result.data(), std::abs(i), MPFR_RNDN); + mpfr_add_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); } template inline void multiply(mpfr_real_backend& result, long i) { - mpfr_mul_ui(result.data(), result.data(), std::abs(i), MPFR_RNDN); + mpfr_mul_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); if(i < 0) - mpfr_neg(result.data(), result.data(), MPFR_RNDN); + mpfr_neg(result.data(), result.data(), GMP_RNDN); } template inline void divide(mpfr_real_backend& result, long i) { - mpfr_div_ui(result.data(), result.data(), std::abs(i), MPFR_RNDN); + mpfr_div_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); if(i < 0) - mpfr_neg(result.data(), result.data(), MPFR_RNDN); + mpfr_neg(result.data(), result.data(), GMP_RNDN); } // // Specialised 3 arg versions of the basic operators: @@ -398,146 +399,146 @@ inline void divide(mpfr_real_backend& result, long i) template inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) { - mpfr_add(a.data(), x.data(), y.data(), MPFR_RNDN); + mpfr_add(a.data(), x.data(), y.data(), GMP_RNDN); } template inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) { - mpfr_add_ui(a.data(), x.data(), y, MPFR_RNDN); + mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); } template inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, long y) { if(y < 0) - mpfr_sub_ui(a.data(), x.data(), -y, MPFR_RNDN); + mpfr_sub_ui(a.data(), x.data(), -y, GMP_RNDN); else - mpfr_add_ui(a.data(), x.data(), y, MPFR_RNDN); + mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); } template inline void add(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) { - mpfr_add_ui(a.data(), y.data(), x, MPFR_RNDN); + mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } template inline void add(mpfr_real_backend& a, long x, const mpfr_real_backend& y) { if(x < 0) { - mpfr_ui_sub(a.data(), -x, y.data(), MPFR_RNDN); - mpfr_neg(a.data(), a.data(), MPFR_RNDN); + mpfr_ui_sub(a.data(), -x, y.data(), GMP_RNDN); + mpfr_neg(a.data(), a.data(), GMP_RNDN); } else - mpfr_add_ui(a.data(), y.data(), x, MPFR_RNDN); + mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } template inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) { - mpfr_sub(a.data(), x.data(), y.data(), MPFR_RNDN); + mpfr_sub(a.data(), x.data(), y.data(), GMP_RNDN); } template inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) { - mpfr_sub_ui(a.data(), x.data(), y, MPFR_RNDN); + mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); } template inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, long y) { if(y < 0) - mpfr_add_ui(a.data(), x.data(), -y, MPFR_RNDN); + mpfr_add_ui(a.data(), x.data(), -y, GMP_RNDN); else - mpfr_sub_ui(a.data(), x.data(), y, MPFR_RNDN); + mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); } template inline void subtract(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) { - mpfr_ui_sub(a.data(), x, y.data(), MPFR_RNDN); + mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); } template inline void subtract(mpfr_real_backend& a, long x, const mpfr_real_backend& y) { if(x < 0) { - mpfr_add_ui(a.data(), y.data(), -x, MPFR_RNDN); - mpfr_neg(a.data(), a.data(), MPFR_RNDN); + mpfr_add_ui(a.data(), y.data(), -x, GMP_RNDN); + mpfr_neg(a.data(), a.data(), GMP_RNDN); } else - mpfr_ui_sub(a.data(), x, y.data(), MPFR_RNDN); + mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); } template inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) { - mpfr_mul(a.data(), x.data(), y.data(), MPFR_RNDN); + mpfr_mul(a.data(), x.data(), y.data(), GMP_RNDN); } template inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) { - mpfr_mul_ui(a.data(), x.data(), y, MPFR_RNDN); + mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); } template inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, long y) { if(y < 0) { - mpfr_mul_ui(a.data(), x.data(), -y, MPFR_RNDN); + mpfr_mul_ui(a.data(), x.data(), -y, GMP_RNDN); a.negate(); } else - mpfr_mul_ui(a.data(), x.data(), y, MPFR_RNDN); + mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); } template inline void multiply(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) { - mpfr_mul_ui(a.data(), y.data(), x, MPFR_RNDN); + mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); } template inline void multiply(mpfr_real_backend& a, long x, const mpfr_real_backend& y) { if(x < 0) { - mpfr_mul_ui(a.data(), y.data(), -x, MPFR_RNDN); - mpfr_neg(a.data(), a.data(), MPFR_RNDN); + mpfr_mul_ui(a.data(), y.data(), -x, GMP_RNDN); + mpfr_neg(a.data(), a.data(), GMP_RNDN); } else - mpfr_mul_ui(a.data(), y.data(), x, MPFR_RNDN); + mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); } template inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) { - mpfr_div(a.data(), x.data(), y.data(), MPFR_RNDN); + mpfr_div(a.data(), x.data(), y.data(), GMP_RNDN); } template inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) { - mpfr_div_ui(a.data(), x.data(), y, MPFR_RNDN); + mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); } template inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, long y) { if(y < 0) { - mpfr_div_ui(a.data(), x.data(), -y, MPFR_RNDN); + mpfr_div_ui(a.data(), x.data(), -y, GMP_RNDN); a.negate(); } else - mpfr_div_ui(a.data(), x.data(), y, MPFR_RNDN); + mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); } template inline void divide(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) { - mpfr_ui_div(a.data(), x, y.data(), MPFR_RNDN); + mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); } template inline void divide(mpfr_real_backend& a, long x, const mpfr_real_backend& y) { if(x < 0) { - mpfr_ui_div(a.data(), -x, y.data(), MPFR_RNDN); - mpfr_neg(a.data(), a.data(), MPFR_RNDN); + mpfr_ui_div(a.data(), -x, y.data(), GMP_RNDN); + mpfr_neg(a.data(), a.data(), GMP_RNDN); } else - mpfr_ui_div(a.data(), x, y.data(), MPFR_RNDN); + mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); } template @@ -554,34 +555,34 @@ inline int get_sign(const mpfr_real_backend& val) template inline void convert_to(unsigned long* result, const mpfr_real_backend& val) { - *result = mpfr_get_ui(val.data(), MPFR_RNDN); + *result = mpfr_get_ui(val.data(), GMP_RNDN); } template inline void convert_to(long* result, const mpfr_real_backend& val) { - *result = mpfr_get_si(val.data(), MPFR_RNDN); + *result = mpfr_get_si(val.data(), GMP_RNDN); } #ifdef _MPFR_H_HAVE_INTMAX_T template inline void convert_to(boost::uintmax_t* result, const mpfr_real_backend& val) { - *result = mpfr_get_uj(val.data(), MPFR_RNDN); + *result = mpfr_get_uj(val.data(), GMP_RNDN); } template inline void convert_to(boost::intmax_t* result, const mpfr_real_backend& val) { - *result = mpfr_get_sj(val.data(), MPFR_RNDN); + *result = mpfr_get_sj(val.data(), GMP_RNDN); } #endif template inline void convert_to(double* result, const mpfr_real_backend& val) { - *result = mpfr_get_d(val.data(), MPFR_RNDN); + *result = mpfr_get_d(val.data(), GMP_RNDN); } template inline void convert_to(long double* result, const mpfr_real_backend& val) { - *result = mpfr_get_ld(val.data(), MPFR_RNDN); + *result = mpfr_get_ld(val.data(), GMP_RNDN); } // @@ -590,19 +591,19 @@ inline void convert_to(long double* result, const mpfr_real_backend& v template inline void eval_sqrt(mpfr_real_backend& result, const mpfr_real_backend& val) { - mpfr_sqrt(result.data(), val.data(), MPFR_RNDN); + mpfr_sqrt(result.data(), val.data(), GMP_RNDN); } template inline void eval_abs(mpfr_real_backend& result, const mpfr_real_backend& val) { - mpfr_abs(result.data(), val.data(), MPFR_RNDN); + mpfr_abs(result.data(), val.data(), GMP_RNDN); } template inline void eval_fabs(mpfr_real_backend& result, const mpfr_real_backend& val) { - mpfr_abs(result.data(), val.data(), MPFR_RNDN); + mpfr_abs(result.data(), val.data(), GMP_RNDN); } template inline void eval_ceil(mpfr_real_backend& result, const mpfr_real_backend& val) @@ -623,23 +624,23 @@ template inline void eval_ldexp(mpfr_real_backend& result, const mpfr_real_backend& val, long e) { if(e > 0) - mpfr_mul_2exp(result.data(), val.data(), e, MPFR_RNDN); + mpfr_mul_2exp(result.data(), val.data(), e, GMP_RNDN); else if(e < 0) - mpfr_div_2exp(result.data(), val.data(), -e, MPFR_RNDN); + mpfr_div_2exp(result.data(), val.data(), -e, GMP_RNDN); } template inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, int* e) { long v; - mpfr_get_d_2exp(&v, val.data(), MPFR_RNDN); + mpfr_get_d_2exp(&v, val.data(), GMP_RNDN); *e = v; - ldexp(result, val, -v); + eval_ldexp(result, val, -v); } template inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, long* e) { - mpfr_get_d_2exp(e, val.data(), MPFR_RNDN); - return ldexp(result, val, -*e); + mpfr_get_d_2exp(e, val.data(), GMP_RNDN); + return eval_ldexp(result, val, -*e); } template @@ -648,6 +649,90 @@ inline int eval_fpclassify(const mpfr_real_backend& val) return mpfr_inf_p(val.data()) ? FP_INFINITE : mpfr_nan_p(val.data()) ? FP_NAN : mpfr_zero_p(val.data()) ? FP_ZERO : FP_NORMAL; } +template +inline void eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const mpfr_real_backend& e) +{ + mpfr_pow(result.data(), b.data(), e.data(), GMP_RNDN); +} + +template +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const Integer& e) +{ + mpfr_pow_si(result.data(), b.data(), e, GMP_RNDN); +} + +template +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const Integer& e) +{ + mpfr_pow_ui(result.data(), b.data(), e, GMP_RNDN); +} + +template +inline void eval_exp(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_exp(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_log(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_log(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_sin(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_sin(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_cos(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_cos(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_tan(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_tan(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_asin(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_asin(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_acos(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_acos(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_atan(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_atan(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_sinh(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_sinh(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_cosh(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_cosh(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_tanh(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_tanh(result.data(), arg.data(), GMP_RNDN); +} + typedef big_number > mpfr_real_50; typedef big_number > mpfr_real_100; typedef big_number > mpfr_real_500; @@ -679,7 +764,7 @@ public: { value.first = true; value.second = 0.5; - mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), -mpfr_get_emin(), MPFR_RNDN); + mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), -mpfr_get_emin(), GMP_RNDN); } return value.second; } @@ -691,7 +776,7 @@ public: { value.first = true; value.second = 0.5; - mpfr_mul_2exp(value.second.backend().data(), value.second.backend().data(), mpfr_get_emax(), MPFR_RNDN); + mpfr_mul_2exp(value.second.backend().data(), value.second.backend().data(), mpfr_get_emax(), GMP_RNDN); } return value.second; } @@ -715,7 +800,7 @@ public: { value.first = true; value.second = 1; - mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits::digits - 1, MPFR_RNDN); + mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits::digits - 1, GMP_RNDN); } return value.second; } @@ -729,7 +814,7 @@ public: { value.first = true; value.second = 1; - mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), digits, MPFR_RNDN); + mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), digits, GMP_RNDN); } return value.second; } diff --git a/math/test/Jamfile.v2 b/math/test/Jamfile.v2 index 16b71922..b37662be 100644 --- a/math/test/Jamfile.v2 +++ b/math/test/Jamfile.v2 @@ -83,6 +83,14 @@ run test_arithmetic.cpp gmp [ check-target-builds ../config//has_gmp : : no ] : test_arithmetic_mpz ; +run test_arithmetic.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPQ + [ check-target-builds ../config//has_gmp : : no ] + : test_arithmetic_mpq ; + run test_arithmetic.cpp mpfr gmp : # command line : # input files @@ -138,6 +146,14 @@ run test_numeric_limits.cpp gmp [ check-target-builds ../config//has_gmp : : no ] : test_numeric_limits_mpz ; +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPQ + [ check-target-builds ../config//has_gmp : : no ] + : test_numeric_limits_mpq ; + run test_numeric_limits.cpp mpfr : # command line : # input files diff --git a/math/test/big_number_concept_check.cpp b/math/test/big_number_concept_check.cpp index f4eaba6e..764cd3b4 100644 --- a/math/test/big_number_concept_check.cpp +++ b/math/test/big_number_concept_check.cpp @@ -10,7 +10,7 @@ // all our distributions and special functions on this type. // #define BOOST_MATH_ASSERT_UNDEFINED_POLICY false -#define TEST_MPFR +#define BOOST_MATH_INSTANTIATE_MINIMUM #ifdef _MSC_VER # pragma warning(disable:4800) @@ -20,19 +20,143 @@ # pragma warning(disable:4503) // decorated name length exceeded, name was truncated #endif -#include +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) +# define TEST_MPF50 +# define TEST_MPF +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR +# define TEST_MPFR_50 +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) +#include +#endif #include -//#include "compile_test/instantiate.hpp" -/* +#include "libs/math/test/compile_test/instantiate.hpp" + +void a() +{ + using namespace boost; + using namespace boost::math; + using namespace boost::math::concepts; + + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); +} + +void b() +{ + using namespace boost; + using namespace boost::math; + using namespace boost::math::concepts; + + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); +} + +void c() +{ + using namespace boost; + using namespace boost::math; + using namespace boost::math::concepts; + + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); +} + +void d() +{ + using namespace boost; + using namespace boost::math; + using namespace boost::math::concepts; + + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); +} + void foo() { - instantiate(boost::math::ef::e_float()); +#ifdef TEST_BACKEND + instantiate(boost::math::big_number_real_architype()); +#endif +#ifdef TEST_MPF_50 + instantiate(boost::math::mpf_real_50()); +#endif +#ifdef TEST_MPF + instantiate(boost::math::mpf_real()); +#endif +#ifdef TEST_MPFR_50 + instantiate(boost::math::mpfr_real_50()); +#endif +#ifdef TEST_MPFR + instantiate(boost::math::mpfr_real()); +#endif +#ifdef TEST_E_FLOAT + instantiate(boost::math::e_float()); +#endif } -*/ + int main() { +#ifdef TEST_BACKEND BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif +#ifdef TEST_MPF_50 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif +#ifdef TEST_MPF + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif +#ifdef TEST_MPFR_50 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif +#ifdef TEST_MPFR + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif +#ifdef TEST_E_FLOAT + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif + } - - diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 1c80628b..a8635716 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -6,7 +6,7 @@ #include #include -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 # define TEST_MPF # define TEST_BACKEND @@ -14,6 +14,7 @@ # define TEST_MPFR # define TEST_MPFR_50 # define TEST_E_FLOAT +# define TEST_MPQ #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -24,7 +25,7 @@ #endif -#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) +#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) #include #endif #ifdef TEST_BACKEND @@ -255,7 +256,7 @@ void test_real_ops(const boost::mpl::false_&){} template void test_real_ops(const boost::mpl::true_&) { -#if defined(TEST_MPF) || defined(TEST_MPF_50) || defined(TEST_BACKEND) +#if defined(TEST_MPF) || defined(TEST_MPF_50) || defined(TEST_BACKEND) || defined(TEST_MPFR) BOOST_TEST(abs(Real(2)) == 2); BOOST_TEST(abs(Real(-2)) == 2); BOOST_TEST(fabs(Real(2)) == 2); @@ -850,6 +851,9 @@ int main() #ifdef TEST_MPZ test(); #endif +#ifdef TEST_MPQ + test(); +#endif #ifdef TEST_E_FLOAT test(); #endif diff --git a/math/test/test_numeric_limits.cpp b/math/test/test_numeric_limits.cpp index 8f3ecdcc..00bb19e2 100644 --- a/math/test/test_numeric_limits.cpp +++ b/math/test/test_numeric_limits.cpp @@ -5,7 +5,7 @@ #include -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 # define TEST_MPF # define TEST_BACKEND @@ -13,6 +13,7 @@ # define TEST_MPFR # define TEST_MPFR_50 # define TEST_E_FLOAT +# define TEST_MPQ #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -23,7 +24,7 @@ #endif -#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) +#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) #include #endif #ifdef TEST_BACKEND @@ -151,6 +152,9 @@ int main() #ifdef TEST_MPZ test(); #endif +#ifdef TEST_MPQ + test(); +#endif #ifdef TEST_E_FLOAT test(); #endif From c3d0d2beadf01fa2b92279c29efbc574768b2633 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 20 Sep 2011 12:36:22 +0000 Subject: [PATCH 020/256] Optimise comparison to zero. Remove unnecessary static asserts - even floats are incrementable. Fix some of the default function methods, and add fmod. Add mpq comparison and conversion routines. Add mpfr lanczos support. Add std lib function support for big_number_architype. Update comparison tests. [SVN r74479] --- include/boost/math/big_number.hpp | 7 +- include/boost/math/big_number/default_ops.hpp | 25 ++++++- include/boost/math/big_number/gmp.hpp | 22 +++++++ include/boost/math/big_number/mpfr.hpp | 24 +++++++ .../math/concepts/big_number_architypes.hpp | 65 +++++++++++++++++++ math/test/test_arithmetic.cpp | 24 +++++++ 6 files changed, 161 insertions(+), 6 deletions(-) diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index 664aec72..b2f2612a 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -224,7 +224,6 @@ public: // big_number& operator++() { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The increment operation is only valid for integer types"); using big_num_default_ops::increment; increment(m_backend); return *this; @@ -232,7 +231,6 @@ public: big_number& operator--() { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The increment operation is only valid for integer types"); using big_num_default_ops::decrement; decrement(m_backend); return *this; @@ -240,7 +238,6 @@ public: big_number operator++(int) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The increment operation is only valid for integer types"); using big_num_default_ops::increment; self_type temp(*this); increment(m_backend); @@ -249,7 +246,6 @@ public: big_number operator--(int) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The increment operation is only valid for integer types"); using big_num_default_ops::decrement; self_type temp(*this); decrement(m_backend); @@ -439,6 +435,8 @@ public: template typename enable_if, int>::type compare(const V& o)const { + if(o == 0) + return get_sign(m_backend); return m_backend.compare(canonical_value(o)); } Backend& backend() @@ -1380,6 +1378,7 @@ private: static const Backend& canonical_value(const self_type& v){ return v.m_backend; } static const Backend& canonical_value(const self_type* v){ return v->m_backend; } static const Backend& canonical_value(self_type* v){ return v->m_backend; } + static const Backend& canonical_value(self_type& v){ return v.m_backend; } template static typename detail::canonical::type canonical_value(const V& v){ return v; } static typename detail::canonical::type canonical_value(const std::string& v){ return v.c_str(); } diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index ca14a806..da2df385 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -328,7 +328,7 @@ inline void convert_to(terminal* result, const B& backend) // Functions: // template -void eval_abs(T* result, const T& arg) +void eval_abs(T& result, const T& arg) { typedef typename T::signed_types type_list; typedef typename mpl::front::type front; @@ -337,7 +337,7 @@ void eval_abs(T* result, const T& arg) result->negate(); } template -void eval_fabs(T* result, const T& arg) +void eval_fabs(T& result, const T& arg) { typedef typename T::signed_types type_list; typedef typename mpl::front::type front; @@ -351,6 +351,26 @@ inline int eval_fpclassify(const Backend& arg) { return is_zero(arg) ? FP_ZERO : FP_NORMAL; } + +template +inline void eval_fmod(T& result, const T& a, const T& b) +{ + if((&result == &a) || (&result == &b)) + { + T temp; + eval_fmod(temp, a, b); + result = temp; + } + T n; + divide(result, a, b); + if(get_sign(a) < 0) + eval_ceil(n, result); + else + eval_floor(n, result); + multiply(n, b); + subtract(result, a, n); +} + // // These have to implemented by the backend, declared here so that our macro generated code compiles OK. // @@ -828,6 +848,7 @@ UNARY_OP_FUNCTOR(tanh) HETERO_BINARY_OP_FUNCTOR(ldexp, int) HETERO_BINARY_OP_FUNCTOR(frexp, int*) BINARY_OP_FUNCTOR(pow) +BINARY_OP_FUNCTOR(fmod) #undef BINARY_OP_FUNCTOR #undef UNARY_OP_FUNCTOR diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index cfb114aa..3c32b4ea 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -1225,6 +1225,14 @@ struct gmp_rational d = v; return compare(d); } + int compare(unsigned long v) + { + return mpq_cmp_ui(m_data, v, 1); + } + int compare(long v) + { + return mpq_cmp_si(m_data, v, 1); + } mpq_t& data() { return m_data; } const mpq_t& data()const { return m_data; } protected: @@ -1277,6 +1285,20 @@ inline void convert_to(double* result, const gmp_rational& val) *result = mpq_get_d(val.data()); } +inline void convert_to(long* result, const gmp_rational& val) +{ + double r; + convert_to(&r, val); + *result = r; +} + +inline void convert_to(unsigned long* result, const gmp_rational& val) +{ + double r; + convert_to(&r, val); + *result = r; +} + inline void eval_abs(gmp_rational& result, const gmp_rational& val) { mpq_abs(result.data(), val.data()); diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp index 3020edf5..e03f05da 100644 --- a/include/boost/math/big_number/mpfr.hpp +++ b/include/boost/math/big_number/mpfr.hpp @@ -10,6 +10,7 @@ #include #include #include +#include #include #include #include @@ -739,6 +740,29 @@ typedef big_number > mpfr_real_500; typedef big_number > mpfr_real_1000; typedef big_number > mpfr_real; +namespace lanczos{ + +template +struct lanczos >, Policy> +{ + typedef typename mpl::if_c< + Digits10 <= 36, + lanczos22UDT, + typename mpl::if_c< + Digits10 <= 50, + lanczos31UDT, + typename mpl::if_c< + Digits10 <= 110, + lanczos61UDT, + undefined_lanczos + >::type + >::type + >::type type; +}; + +} // namespace lanczos + + }} // namespaces namespace std{ diff --git a/include/boost/math/concepts/big_number_architypes.hpp b/include/boost/math/concepts/big_number_architypes.hpp index 66d79fc4..26a7a4b6 100644 --- a/include/boost/math/concepts/big_number_architypes.hpp +++ b/include/boost/math/concepts/big_number_architypes.hpp @@ -188,6 +188,71 @@ inline int eval_fpclassify(const big_number_backend_real_architype& arg) return boost::math::fpclassify(arg.m_value); } +inline void eval_pow(big_number_backend_real_architype& result, const big_number_backend_real_architype& b, const big_number_backend_real_architype& e) +{ + result = std::pow(b.m_value, e.m_value); +} + +inline void eval_pow(big_number_backend_real_architype& result, const big_number_backend_real_architype& b, int e) +{ + result = std::pow(b.m_value, e); +} + +inline void eval_exp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::exp(arg.m_value); +} + +inline void eval_log(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::log(arg.m_value); +} + +inline void eval_sin(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::sin(arg.m_value); +} + +inline void eval_cos(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::cos(arg.m_value); +} + +inline void eval_tan(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::tan(arg.m_value); +} + +inline void eval_asin(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::asin(arg.m_value); +} + +inline void eval_acos(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::acos(arg.m_value); +} + +inline void eval_atan(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::atan(arg.m_value); +} + +inline void eval_sinh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::sinh(arg.m_value); +} + +inline void eval_cosh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::cosh(arg.m_value); +} + +inline void eval_tanh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::tanh(arg.m_value); +} + typedef boost::math::big_number big_number_real_architype; }}} // namespaces diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index a8635716..fa795461 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -345,6 +345,18 @@ void test_negative_mixed(boost::mpl::true_ const&) Num n3 = 0; Num n4 = -20; Num n5 = -8; + BOOST_TEST((Real(n2) < 0) == true); + BOOST_TEST((Real(n2) <= 0) == true); + BOOST_TEST((Real(n2) > 0) == false); + BOOST_TEST((Real(n2) >= 0) == false); + BOOST_TEST((Real(n2) == 0) == false); + BOOST_TEST((Real(n2) != 0) == true); + BOOST_TEST((Real(n2) == n2) == true); + BOOST_TEST((Real(n2) != n2) == false); + BOOST_TEST((Real(n2) >= n2) == true); + BOOST_TEST((Real(n2) <= n2) == true); + BOOST_TEST((Real(n2) > n2) == false); + BOOST_TEST((Real(n2) < n2) == false); // Default construct: BOOST_TEST(Real(n1) == n1); BOOST_TEST(Real(n2) == n2); @@ -425,6 +437,18 @@ void test_mixed() Num n3 = 0; Num n4 = 20; Num n5 = 8; + BOOST_TEST((Real(n2) < 0) == false); + BOOST_TEST((Real(n2) <= 0) == false); + BOOST_TEST((Real(n2) > 0) == true); + BOOST_TEST((Real(n2) >= 0) == true); + BOOST_TEST((Real(n2) == 0) == false); + BOOST_TEST((Real(n2) != 0) == true); + BOOST_TEST((Real(n2) == n2) == true); + BOOST_TEST((Real(n2) != n2) == false); + BOOST_TEST((Real(n2) >= n2) == true); + BOOST_TEST((Real(n2) <= n2) == true); + BOOST_TEST((Real(n2) > n2) == false); + BOOST_TEST((Real(n2) < n2) == false); // Default construct: BOOST_TEST(Real(n1) == n1); BOOST_TEST(Real(n2) == n2); From 4783bd83e63f5684c96c95ab55f05a784d323f42 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 24 Sep 2011 11:07:59 +0000 Subject: [PATCH 021/256] First cut at removing proto dependency - concept check now builds with msvc and mpfr_real_50. [SVN r74545] --- include/boost/math/big_number.hpp | 923 ++++++------ .../boost/math/big_number/big_number_base.hpp | 1319 ++++++++++------- include/boost/math/big_number/default_ops.hpp | 282 ++-- include/boost/math/big_number/gmp.hpp | 4 +- math/test/big_number_concept_check.cpp | 62 - math/test/test_arithmetic.cpp | 44 +- 6 files changed, 1458 insertions(+), 1176 deletions(-) diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index b2f2612a..86a9ad1e 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -6,7 +6,6 @@ #ifndef BOOST_MATH_EXTENDED_REAL_HPP #define BOOST_MATH_EXTENDED_REAL_HPP -#include #include #include #include @@ -25,54 +24,33 @@ namespace boost{ namespace math{ template -class big_number : public detail::big_number_exp*>::type > +class big_number { - typedef detail::big_number_exp*>::type > base_type; typedef big_number self_type; public: - big_number() - { - proto::value(*this) = this; - BOOST_ASSERT(proto::value(*this) == this); - } - big_number(const big_number& e) : m_backend(e.m_backend) - { - proto::value(*this) = this; - BOOST_ASSERT(proto::value(*this) == this); - } + big_number(){} + big_number(const big_number& e) : m_backend(e.m_backend){} template big_number(V v, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) { - proto::value(*this) = this; - BOOST_ASSERT(proto::value(*this) == this); m_backend = canonical_value(v); } - big_number(const big_number& e, unsigned digits10) : m_backend(e.m_backend, digits10) - { - proto::value(*this) = this; - BOOST_ASSERT(proto::value(*this) == this); - } + big_number(const big_number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} template big_number(V v, unsigned digits10, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) - : base_type(digits10) { - proto::value(*this) = this; - BOOST_ASSERT(proto::value(*this) == this); + m_backend.precision(digits10); m_backend = canonical_value(v); } template big_number(V v, typename enable_if, mpl::not_ > > >::type* dummy1 = 0) - : m_backend(v) - { - proto::value(*this) = this; - BOOST_ASSERT(proto::value(*this) == this); - } + : m_backend(v){} - template - big_number& operator=(const detail::big_number_exp& e) + template + big_number& operator=(const detail::big_number_exp& e) { - do_assign(e, typename detail::assign_and_eval::type()); + do_assign(e, tag()); return *this; } @@ -90,20 +68,14 @@ public: return *this; } - template - big_number(const detail::big_number_exp& e) + template + big_number(const detail::big_number_exp& e) { - proto::value(*this) = this; - BOOST_ASSERT(proto::value(*this) == this); - do_assign(e, typename detail::assign_and_eval::type()); + do_assign(e, tag()); } #ifndef BOOST_NO_RVALUE_REFERENCES - big_number(big_number&& r) : m_backend(r.m_backend) - { - proto::value(*this) = this; - BOOST_ASSERT(proto::value(*this) == this); - } + big_number(big_number&& r) : m_backend(r.m_backend){} big_number& operator=(big_number&& r) { m_backend.swap(r.m_backend); @@ -111,19 +83,25 @@ public: } #endif - template - big_number& operator+=(const detail::big_number_exp& e) + big_number& operator+=(const self_type& val) + { + do_add(detail::big_number_exp(val), detail::terminal()); + return *this; + } + + template + big_number& operator+=(const detail::big_number_exp& e) { // Create a copy if e contains this, but not if we're just doing a // x *= x if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_add(temp, typename proto::tag_of::type()); + do_add(detail::big_number_exp(temp), detail::terminal()); } else { - do_add(e, typename proto::tag_of::type()); + do_add(e, tag()); } return *this; } @@ -137,6 +115,12 @@ public: return *this; } + big_number& operator-=(const self_type& val) + { + do_subtract(detail::big_number_exp(val), detail::terminal()); + return *this; + } + template big_number& operator-=(const detail::big_number_exp& e) { @@ -144,11 +128,11 @@ public: if(contains_self(e)) { self_type temp(e); - do_subtract(temp, typename proto::tag_of::type()); + do_subtract(temp, typename detail_of::type()); } else { - do_subtract(e, typename proto::tag_of::type()); + do_subtract(e, typename Exp::tag_type()); } return *this; } @@ -162,6 +146,13 @@ public: return *this; } + + big_number& operator *= (const self_type& e) + { + do_multiplies(detail::big_number_exp(e), detail::terminal()); + return *this; + } + template big_number& operator*=(const detail::big_number_exp& e) { @@ -170,11 +161,11 @@ public: if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_multiplies(temp, typename proto::tag_of::type()); + do_multiplies(detail::big_number_exp(temp), detail::terminal()); } else { - do_multiplies(e, typename proto::tag_of::type()); + do_multiplies(e, typename Exp::tag_type()); } return *this; } @@ -188,19 +179,25 @@ public: return *this; } + big_number& operator%=(const self_type& e) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); + do_modulus(detail::big_number_exp(e), detail::terminal()); + return *this; + } template big_number& operator%=(const detail::big_number_exp& e) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); // Create a temporary if the RHS references *this: if(contains_self(e)) { self_type temp(e); - do_modulus(temp, typename proto::tag_of::type()); + do_modulus(temp, typename detail_of::type()); } else { - do_modulus(e, typename proto::tag_of::type()); + do_modulus(e, typename Exp::tag_type()); } return *this; } @@ -208,7 +205,7 @@ public: typename enable_if, big_number& >::type operator%=(const V& v) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); using big_num_default_ops::modulus; modulus(m_backend, canonical_value(v)); return *this; @@ -255,7 +252,7 @@ public: template typename enable_if, big_number&>::type operator <<= (V val) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The left-shift operation is only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left-shift operation is only valid for integer types"); check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); left_shift(m_backend, canonical_value(val)); return *this; @@ -264,12 +261,18 @@ public: template typename enable_if, big_number&>::type operator >>= (V val) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The right-shift operation is only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right-shift operation is only valid for integer types"); check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); right_shift(m_backend, canonical_value(val)); return *this; } + big_number& operator /= (const self_type& e) + { + do_divide(detail::big_number_exp(e), detail::terminal()); + return *this; + } + template big_number& operator/=(const detail::big_number_exp& e) { @@ -277,11 +280,11 @@ public: if(contains_self(e)) { self_type temp(e); - do_divide(temp, typename proto::tag_of::type()); + do_divide(detail::big_number_exp(temp), typename detail_of::type()); } else { - do_divide(e, typename proto::tag_of::type()); + do_divide(e, typename Exp::tag_type()); } return *this; } @@ -295,6 +298,12 @@ public: return *this; } + big_number& operator&=(const self_type& e) + { + do_bitwise_and(detail::big_number_exp(e), detail::terminal()); + return *this; + } + template big_number& operator&=(const detail::big_number_exp& e) { @@ -303,11 +312,11 @@ public: if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_bitwise_and(temp, typename proto::tag_of::type()); + do_bitwise_and(temp, typename detail_of::type()); } else { - do_bitwise_and(e, typename proto::tag_of::type()); + do_bitwise_and(e, typename Exp::tag_type()); } return *this; } @@ -321,6 +330,12 @@ public: return *this; } + big_number& operator|=(const self_type& e) + { + do_bitwise_or(detail::big_number_exp(e), detail::terminal()); + return *this; + } + template big_number& operator|=(const detail::big_number_exp& e) { @@ -329,11 +344,11 @@ public: if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_bitwise_or(temp, typename proto::tag_of::type()); + do_bitwise_or(temp, typename detail_of::type()); } else { - do_bitwise_or(e, typename proto::tag_of::type()); + do_bitwise_or(e, typename Exp::tag_type()); } return *this; } @@ -347,17 +362,23 @@ public: return *this; } + big_number& operator^=(const self_type& e) + { + do_bitwise_xor(detail::big_number_exp(e), detail::terminal()); + return *this; + } + template big_number& operator^=(const detail::big_number_exp& e) { if(contains_self(e)) { self_type temp(e); - do_bitwise_xor(temp, typename proto::tag_of::type()); + do_bitwise_xor(temp, typename detail_of::type()); } else { - do_bitwise_xor(e, typename proto::tag_of::type()); + do_bitwise_xor(e, typename Exp::tag_type()); } return *this; } @@ -370,6 +391,15 @@ public: bitwise_xor(m_backend, canonical_value(v)); return *this; } + // + // Use in boolean context: + // + typedef bool (self_type::*unmentionable_type)()const; + + operator unmentionable_type()const + { + return is_zero() ? 0 : &self_type::is_zero; + } // // swap: @@ -381,12 +411,12 @@ public: // // Zero and sign: // - bool is_zero() + bool is_zero()const { using big_num_default_ops::is_zero; return is_zero(m_backend); } - int sign() + int sign()const { using big_num_default_ops::get_sign; return get_sign(m_backend); @@ -435,6 +465,7 @@ public: template typename enable_if, int>::type compare(const V& o)const { + using big_num_default_ops::get_sign; if(o == 0) return get_sign(m_backend); return m_backend.compare(canonical_value(o)); @@ -475,114 +506,99 @@ private: void do_assign(const Exp& e, const detail::add_immediates&) { using big_num_default_ops::add; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - add(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } - +/* template void do_assign(const Exp& e, const detail::add_and_negate_immediates&) { using big_num_default_ops::add; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - add(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); m_backend.negate(); } - +*/ template void do_assign(const Exp& e, const detail::subtract_immediates&) { using big_num_default_ops::subtract; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - subtract(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } - + /* template void do_assign(const Exp& e, const detail::subtract_and_negate_immediates&) { using big_num_default_ops::subtract; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - subtract(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); m_backend.negate(); } - + */ template void do_assign(const Exp& e, const detail::multiply_immediates&) { using big_num_default_ops::multiply; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - multiply(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); - } - - template - void do_assign(const Exp& e, const detail::multiply_and_negate_immediates&) - { - using big_num_default_ops::multiply; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - multiply(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); - m_backend.negate(); + multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template void do_assign(const Exp& e, const detail::divide_immediates&) { using big_num_default_ops::divide; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - divide(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + } + +#if 0 + template + void do_assign(const Exp& e, const detail::multiply_and_negate_immediates&) + { + using big_num_default_ops::multiply; + multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + m_backend.negate(); } template void do_assign(const Exp& e, const detail::divide_and_negate_immediates&) { using big_num_default_ops::divide; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - divide(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); m_backend.negate(); } template - void do_assign(const Exp& e, const proto::tag::unary_plus&) + void do_assign(const Exp& e, const detail::unary_plus&) { - typedef typename proto::result_of::left::type left_type; - do_assign(proto::left(e), typename detail::assign_and_eval::type()); + typedef typename Exp::left_type left_type; + do_assign(e.left(), typename left_type::tag_type()); } +#endif template - void do_assign(const Exp& e, const proto::tag::negate&) + void do_assign(const Exp& e, const detail::negate&) { - typedef typename proto::result_of::left::type left_type; - do_assign(proto::left(e), typename detail::assign_and_eval::type()); + typedef typename Exp::left_type left_type; + do_assign(e.left(), typename left_type::tag_type()); m_backend.negate(); } - template - void do_assign(const Exp& e, const proto::tag::plus&) + void do_assign(const Exp& e, const detail::plus&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; - static int const left_depth = boost::result_of::type::value; - static int const right_depth = boost::result_of::type::value; + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; - bool bl = contains_self(proto::left(e)); - bool br = contains_self(proto::right(e)); + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); - if(bl && is_self(proto::left(e))) + if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: - do_add(proto::right(e), typename proto::tag_of::type()); + do_add(e.right(), typename right_type::tag_type()); } - else if(br && is_self(proto::right(e))) + else if(br && is_self(e.right())) { // Ignore the right node, it's *this, just add the left: - do_add(proto::left(e), typename proto::tag_of::type()); + do_add(e.left(), typename left_type::tag_type()); } else if(bl || br) { @@ -591,36 +607,36 @@ private: } else if(left_depth >= right_depth) { - do_assign(proto::left(e), typename detail::assign_and_eval::type()); - do_add(proto::right(e), typename proto::tag_of::type()); + do_assign(e.left(), typename left_type::tag_type()); + do_add(e.right(), typename right_type::tag_type()); } else { - do_assign(proto::right(e), typename detail::assign_and_eval::type()); - do_add(proto::left(e), typename proto::tag_of::type()); + do_assign(e.right(), typename right_type::tag_type()); + do_add(e.left(), typename left_type::tag_type()); } } template - void do_assign(const Exp& e, const proto::tag::minus&) + void do_assign(const Exp& e, const detail::minus&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; - static int const left_depth = boost::result_of::type::value; - static int const right_depth = boost::result_of::type::value; + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; - bool bl = contains_self(proto::left(e)); - bool br = contains_self(proto::right(e)); + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); - if(bl && is_self(proto::left(e))) + if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just subtract the right: - do_subtract(proto::right(e), typename proto::tag_of::type()); + do_subtract(e.right(), typename right_type::tag_type()); } - else if(br && is_self(proto::right(e))) + else if(br && is_self(e.right())) { // Ignore the right node, it's *this, just subtract the left and negate the result: - do_subtract(proto::left(e), typename proto::tag_of::type()); + do_subtract(e.left(), typename left_type::tag_type()); m_backend.negate(); } else if(bl || br) @@ -630,37 +646,37 @@ private: } else if(left_depth >= right_depth) { - do_assign(proto::left(e), typename detail::assign_and_eval::type()); - do_subtract(proto::right(e), typename proto::tag_of::type()); + do_assign(e.left(), typename left_type::tag_type()); + do_subtract(e.right(), typename right_type::tag_type()); } else { - do_assign(proto::right(e), typename detail::assign_and_eval::type()); - do_subtract(proto::left(e), typename proto::tag_of::type()); + do_assign(e.right(), typename right_type::tag_type()); + do_subtract(e.left(), typename left_type::tag_type()); m_backend.negate(); } } template - void do_assign(const Exp& e, const proto::tag::multiplies&) + void do_assign(const Exp& e, const detail::multiplies&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; - static int const left_depth = boost::result_of::type::value; - static int const right_depth = boost::result_of::type::value; + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; - bool bl = contains_self(proto::left(e)); - bool br = contains_self(proto::right(e)); + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); - if(bl && is_self(proto::left(e))) + if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: - do_multiplies(proto::right(e), typename proto::tag_of::type()); + do_multiplies(e.right(), typename right_type::tag_type()); } - else if(br && is_self(proto::right(e))) + else if(br && is_self(e.right())) { // Ignore the right node, it's *this, just add the left: - do_multiplies(proto::left(e), typename proto::tag_of::type()); + do_multiplies(e.left(), typename left_type::tag_type()); } else if(bl || br) { @@ -669,28 +685,28 @@ private: } else if(left_depth >= right_depth) { - do_assign(proto::left(e), typename detail::assign_and_eval::type()); - do_multiplies(proto::right(e), typename proto::tag_of::type()); + do_assign(e.left(), typename left_type::tag_type()); + do_multiplies(e.right(), typename right_type::tag_type()); } else { - do_assign(proto::right(e), typename detail::assign_and_eval::type()); - do_multiplies(proto::left(e), typename proto::tag_of::type()); + do_assign(e.right(), typename right_type::tag_type()); + do_multiplies(e.left(), typename left_type::tag_type()); } } template - void do_assign(const Exp& e, const proto::tag::divides&) + void do_assign(const Exp& e, const detail::divides&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; - bool bl = contains_self(proto::left(e)); - bool br = contains_self(proto::right(e)); + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); - if(bl && is_self(proto::left(e))) + if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: - do_divide(proto::right(e), typename proto::tag_of::type()); + do_divide(e.right(), typename right_type::tag_type()); } else if(bl || br) { @@ -699,28 +715,28 @@ private: } else { - do_assign(proto::left(e), typename detail::assign_and_eval::type()); - do_divide(proto::right(e), typename proto::tag_of::type()); + do_assign(e.left(), typename left_type::tag_type()); + do_divide(e.right(), typename right_type::tag_type()); } } template - void do_assign(const Exp& e, const proto::tag::modulus&) + void do_assign(const Exp& e, const detail::modulus&) { // // This operation is only valid for integer backends: // - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; - bool bl = contains_self(proto::left(e)); - bool br = contains_self(proto::right(e)); + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); - if(bl && is_self(proto::left(e))) + if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: - do_modulus(proto::right(e), typename proto::tag_of::type()); + do_modulus(e.right(), typename right_type::tag_type()); } else if(bl || br) { @@ -729,208 +745,199 @@ private: } else { - do_assign(proto::left(e), typename detail::assign_and_eval::type()); - do_modulus(proto::right(e), typename proto::tag_of::type()); + do_assign(e.left(), typename left_type::tag_type()); + do_modulus(e.right(), typename right_type::tag_type()); } } template void do_assign(const Exp& e, const detail::modulus_immediates&) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); using big_num_default_ops::modulus; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - modulus(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + modulus(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template - void do_assign(const Exp& e, const proto::tag::bitwise_and&) + void do_assign(const Exp& e, const detail::bitwise_and&) { // // This operation is only valid for integer backends: // - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; - static int const left_depth = boost::result_of::type::value; - static int const right_depth = boost::result_of::type::value; + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; - bool bl = contains_self(proto::left(e)); - bool br = contains_self(proto::right(e)); + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); - if(bl && is_self(proto::left(e))) + if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: - do_bitwise_and(proto::right(e), typename proto::tag_of::type()); + do_bitwise_and(e.right(), typename right_type::tag_type()); } - else if(br && is_self(proto::right(e))) + else if(br && is_self(e.right())) { - do_bitwise_and(proto::left(e), typename proto::tag_of::type()); + do_bitwise_and(e.left(), typename left_type::tag_type()); } else if(left_depth >= right_depth) { - do_assign(proto::left(e), typename detail::assign_and_eval::type()); - do_bitwise_and(proto::right(e), typename proto::tag_of::type()); + do_assign(e.left(), typename left_type::tag_type()); + do_bitwise_and(e.right(), typename right_type::tag_type()); } else { - do_assign(proto::right(e), typename detail::assign_and_eval::type()); - do_bitwise_and(proto::left(e), typename proto::tag_of::type()); + do_assign(e.right(), typename right_type::tag_type()); + do_bitwise_and(e.left(), typename left_type::tag_type()); } } template void do_assign(const Exp& e, const detail::bitwise_and_immediates&) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); using big_num_default_ops::bitwise_and; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - bitwise_and(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + bitwise_and(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template - void do_assign(const Exp& e, const proto::tag::bitwise_or&) + void do_assign(const Exp& e, const detail::bitwise_or&) { // // This operation is only valid for integer backends: // - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; - static int const left_depth = boost::result_of::type::value; - static int const right_depth = boost::result_of::type::value; + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; - bool bl = contains_self(proto::left(e)); - bool br = contains_self(proto::right(e)); + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); - if(bl && is_self(proto::left(e))) + if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: - do_bitwise_or(proto::right(e), typename proto::tag_of::type()); + do_bitwise_or(e.right(), typename right_type::tag_type()); } - else if(br && is_self(proto::right(e))) + else if(br && is_self(e.right())) { - do_bitwise_or(proto::left(e), typename proto::tag_of::type()); + do_bitwise_or(e.left(), typename left_type::tag_type()); } else if(left_depth >= right_depth) { - do_assign(proto::left(e), typename detail::assign_and_eval::type()); - do_bitwise_or(proto::right(e), typename proto::tag_of::type()); + do_assign(e.left(), typename left_type::tag_type()); + do_bitwise_or(e.right(), typename right_type::tag_type()); } else { - do_assign(proto::right(e), typename detail::assign_and_eval::type()); - do_bitwise_or(proto::left(e), typename proto::tag_of::type()); + do_assign(e.right(), typename right_type::tag_type()); + do_bitwise_or(e.left(), typename left_type::tag_type()); } } template void do_assign(const Exp& e, const detail::bitwise_or_immediates&) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); using big_num_default_ops::bitwise_or; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - bitwise_or(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + bitwise_or(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template - void do_assign(const Exp& e, const proto::tag::bitwise_xor&) + void do_assign(const Exp& e, const detail::bitwise_xor&) { // // This operation is only valid for integer backends: // - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; - static int const left_depth = boost::result_of::type::value; - static int const right_depth = boost::result_of::type::value; + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; - bool bl = contains_self(proto::left(e)); - bool br = contains_self(proto::right(e)); + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); - if(bl && is_self(proto::left(e))) + if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: - do_bitwise_xor(proto::right(e), typename proto::tag_of::type()); + do_bitwise_xor(e.right(), typename right_type::tag_type()); } - else if(br && is_self(proto::right(e))) + else if(br && is_self(e.right())) { - do_bitwise_xor(proto::left(e), typename proto::tag_of::type()); + do_bitwise_xor(e.left(), typename left_type::tag_type()); } else if(left_depth >= right_depth) { - do_assign(proto::left(e), typename detail::assign_and_eval::type()); - do_bitwise_xor(proto::right(e), typename proto::tag_of::type()); + do_assign(e.left(), typename left_type::tag_type()); + do_bitwise_xor(e.right(), typename right_type::tag_type()); } else { - do_assign(proto::right(e), typename detail::assign_and_eval::type()); - do_bitwise_xor(proto::left(e), typename proto::tag_of::type()); + do_assign(e.right(), typename right_type::tag_type()); + do_bitwise_xor(e.left(), typename left_type::tag_type()); } } template void do_assign(const Exp& e, const detail::bitwise_xor_immediates&) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "Bitwise operations are only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); using big_num_default_ops::bitwise_xor; - typedef typename proto::tag_of::type>::type left_tag; - typedef typename proto::tag_of::type>::type right_tag; - bitwise_xor(m_backend, canonical_value(underlying_value(proto::left(e), left_tag())), canonical_value(underlying_value(proto::right(e), right_tag()))); + bitwise_xor(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } - template - void do_assign(const Exp& e, const proto::tag::terminal&) + void do_assign(const Exp& e, const detail::terminal&) { if(!is_self(e)) { - m_backend = canonical_value(proto::value(e)); + m_backend = canonical_value(e.value()); } } template - void do_assign(const Exp& e, const proto::tag::function&) + void do_assign(const Exp& e, const detail::function&) { - typedef typename proto::arity_of::type tag_type; + typedef typename Exp::arity tag_type; do_assign_function(e, tag_type()); } template - void do_assign(const Exp& e, const proto::tag::shift_left&) + void do_assign(const Exp& e, const detail::shift_left&) { // We can only shift by an integer value, not an arbitrary expression: - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::arity_of::type right_arity; + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + typedef typename right_type::arity right_arity; BOOST_STATIC_ASSERT_MSG(right_arity::value == 0, "The left shift operator requires an integer value for the shift operand."); - typedef typename proto::result_of::value::type right_value_type; + typedef typename right_type::result_type right_value_type; BOOST_STATIC_ASSERT_MSG(is_integral::value, "The left shift operator requires an integer value for the shift operand."); - typedef typename proto::tag_of::type tag_type; - do_assign_left_shift(proto::left(e), canonical_value(proto::value(proto::right(e))), tag_type()); + typedef typename left_type::tag_type tag_type; + do_assign_left_shift(e.left(), canonical_value(e.right().value()), tag_type()); } template - void do_assign(const Exp& e, const proto::tag::shift_right&) + void do_assign(const Exp& e, const detail::shift_right&) { // We can only shift by an integer value, not an arbitrary expression: - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::arity_of::type right_arity; + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + typedef typename right_type::arity right_arity; BOOST_STATIC_ASSERT_MSG(right_arity::value == 0, "The left shift operator requires an integer value for the shift operand."); - typedef typename proto::result_of::value::type right_value_type; + typedef typename right_type::result_type right_value_type; BOOST_STATIC_ASSERT_MSG(is_integral::value, "The left shift operator requires an integer value for the shift operand."); - typedef typename proto::tag_of::type tag_type; - do_assign_right_shift(proto::left(e), canonical_value(proto::value(proto::right(e))), tag_type()); + typedef typename left_type::tag_type tag_type; + do_assign_right_shift(e.left(), canonical_value(e.right().value()), tag_type()); } template - void do_assign(const Exp& e, const proto::tag::complement&) + void do_assign(const Exp& e, const detail::bitwise_complement&) { using big_num_default_ops::complement; - self_type temp(proto::left(e)); + self_type temp(e.left()); complement(m_backend, temp.backend()); } @@ -938,21 +945,21 @@ private: void do_assign(const Exp& e, const detail::complement_immediates&) { using big_num_default_ops::complement; - complement(m_backend, canonical_value(proto::left(e))); + complement(m_backend, canonical_value(e.left().value())); } template - void do_assign_right_shift(const Exp& e, const Val& val, const proto::tag::terminal&) + void do_assign_right_shift(const Exp& e, const Val& val, const detail::terminal&) { using big_num_default_ops::right_shift; - right_shift(m_backend, canonical_value(proto::value(e)), val); + right_shift(m_backend, canonical_value(e.value()), val); } template - void do_assign_left_shift(const Exp& e, const Val& val, const proto::tag::terminal&) + void do_assign_left_shift(const Exp& e, const Val& val, const detail::terminal&) { using big_num_default_ops::left_shift; - left_shift(m_backend, canonical_value(proto::value(e)), val); + left_shift(m_backend, canonical_value(e.value()), val); } template @@ -972,21 +979,21 @@ private: } template - void do_assign_function(const Exp& e, const mpl::long_<1>&) + void do_assign_function(const Exp& e, const mpl::int_<1>&) { - proto::value(proto::left(e))(&m_backend); + e.left().value()(&m_backend); } template - void do_assign_function(const Exp& e, const mpl::long_<2>&) + void do_assign_function(const Exp& e, const mpl::int_<2>&) { - typedef typename proto::result_of::right::type right_type; - typedef typename proto::tag_of::type tag_type; - do_assign_function_1(proto::value(proto::left(e)), proto::right(e), tag_type()); + typedef typename Exp::right_type right_type; + typedef typename right_type::tag_type tag_type; + do_assign_function_1(e.left().value(), e.right(), tag_type()); } template - void do_assign_function_1(const F& f, const Exp& val, const proto::tag::terminal&) + void do_assign_function_1(const F& f, const Exp& val, const detail::terminal&) { - f(m_backend, canonical_value(proto::value(val))); + f(m_backend, canonical_value(val.value())); } template void do_assign_function_1(const F& f, const Exp& val, const Tag&) @@ -995,30 +1002,30 @@ private: f(m_backend, t.backend()); } template - void do_assign_function(const Exp& e, const mpl::long_<3>&) + void do_assign_function(const Exp& e, const mpl::int_<3>&) { - typedef typename proto::result_of::right::type right_type; - typedef typename proto::tag_of::type tag_type; - typedef typename proto::result_of::child_c::type end_type; - typedef typename proto::tag_of::type end_tag; - do_assign_function_2(proto::value(proto::left(e)), proto::right(e), proto::child_c<2>(e), tag_type(), end_tag()); + typedef typename Exp::middle_type middle_type; + typedef typename middle_type::tag_type tag_type; + typedef typename Exp::right_type end_type; + typedef typename end_type::tag_type end_tag; + do_assign_function_2(e.left().value(), e.middle(), e.right(), tag_type(), end_tag()); } template - void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const proto::tag::terminal&, const proto::tag::terminal&) + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const detail::terminal&) { - f(m_backend, canonical_value(proto::value(val1)), canonical_value(proto::value(val2))); + f(m_backend, canonical_value(val1.value()), canonical_value(val2.value())); } template - void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const proto::tag::terminal&) + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const detail::terminal&) { self_type temp1(val1); - f(m_backend, temp1.backend(), canonical_value(proto::value(val2))); + f(m_backend, temp1.backend(), canonical_value(val2.value())); } template - void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const proto::tag::terminal&, const Tag2&) + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const Tag2&) { self_type temp2(val2); - f(m_backend, canonical_value(proto::value(val1)), temp2.backend()); + f(m_backend, canonical_value(val1.value()), temp2.backend()); } template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const Tag2&) @@ -1029,137 +1036,160 @@ private: } template - void do_add(const Exp& e, const proto::tag::terminal&) + void do_add(const Exp& e, const detail::terminal&) { using big_num_default_ops::add; - add(m_backend, canonical_value(proto::value(e))); + add(m_backend, canonical_value(e.value())); } template - void do_add(const Exp& e, const proto::tag::unary_plus&) + void do_add(const Exp& e, const detail::negate&) { - typedef typename proto::result_of::left::type left_type; - do_add(proto::left(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + do_subtract(e.left(), typename left_type::tag_type()); } template - void do_add(const Exp& e, const proto::tag::negate&) + void do_add(const Exp& e, const detail::plus&) { - typedef typename proto::result_of::left::type left_type; - do_subtract(proto::left(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_add(e.left(), typename left_type::tag_type()); + do_add(e.right(), typename right_type::tag_type()); } template - void do_add(const Exp& e, const proto::tag::plus&) + void do_add(const Exp& e, const detail::minus&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_add(proto::left(e), typename proto::tag_of::type()); - do_add(proto::right(e), typename proto::tag_of::type()); - } - - template - void do_add(const Exp& e, const proto::tag::minus&) - { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_add(proto::left(e), typename proto::tag_of::type()); - do_subtract(proto::right(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_add(e.left(), typename left_type::tag_type()); + do_subtract(e.right(), typename right_type::tag_type()); } template void do_add(const Exp& e, const unknown&) { self_type temp(e); - do_add(temp, proto::tag::terminal()); + do_add(detail::big_number_exp(temp), detail::terminal()); } template - void do_subtract(const Exp& e, const proto::tag::terminal&) + void do_add(const Exp& e, const detail::add_immediates&) + { + using big_num_default_ops::add; + add(m_backend, canonical_value(e.left().value())); + add(m_backend, canonical_value(e.right().value())); + } + template + void do_add(const Exp& e, const detail::subtract_immediates&) + { + using big_num_default_ops::add; + using big_num_default_ops::subtract; + add(m_backend, canonical_value(e.left().value())); + subtract(m_backend, canonical_value(e.right().value())); + } + template + void do_subtract(const Exp& e, const detail::terminal&) { using big_num_default_ops::subtract; - subtract(m_backend, canonical_value(proto::value(e))); + subtract(m_backend, canonical_value(e.value())); } template - void do_subtract(const Exp& e, const proto::tag::unary_plus&) + void do_subtract(const Exp& e, const detail::negate&) { - typedef typename proto::result_of::left::type left_type; - do_subtract(proto::left(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + do_add(e.left(), typename left_type::tag_type()); } template - void do_subtract(const Exp& e, const proto::tag::negate&) + void do_subtract(const Exp& e, const detail::plus&) { - typedef typename proto::result_of::left::type left_type; - do_add(proto::left(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_subtract(e.left(), typename left_type::tag_type()); + do_subtract(e.right(), typename right_type::tag_type()); } template - void do_subtract(const Exp& e, const proto::tag::plus&) + void do_subtract(const Exp& e, const detail::minus&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_subtract(proto::left(e), typename proto::tag_of::type()); - do_subtract(proto::right(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_subtract(e.left(), typename left_type::tag_type()); + do_add(e.right(), typename right_type::tag_type()); } - template - void do_subtract(const Exp& e, const proto::tag::minus&) + void do_subtract(const Exp& e, const detail::add_immediates&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_subtract(proto::left(e), typename proto::tag_of::type()); - do_add(proto::right(e), typename proto::tag_of::type()); + using big_num_default_ops::subtract; + subtract(m_backend, canonical_value(e.left().value())); + subtract(m_backend, canonical_value(e.right().value())); + } + template + void do_subtract(const Exp& e, const detail::subtract_immediates&) + { + using big_num_default_ops::add; + using big_num_default_ops::subtract; + subtract(m_backend, canonical_value(e.left().value())); + add(m_backend, canonical_value(e.right().value())); } - template void do_subtract(const Exp& e, const unknown&) { self_type temp(e); - do_subtract(temp, proto::tag::terminal()); + do_subtract(detail::big_number_exp(temp), detail::terminal()); } template - void do_multiplies(const Exp& e, const proto::tag::terminal&) + void do_multiplies(const Exp& e, const detail::terminal&) { using big_num_default_ops::multiply; - multiply(m_backend, canonical_value(proto::value(e))); + multiply(m_backend, canonical_value(e.value())); } template - void do_multiplies(const Exp& e, const proto::tag::unary_plus&) + void do_multiplies(const Exp& e, const detail::negate&) { - typedef typename proto::result_of::left::type left_type; - do_multiplies(proto::left(e), typename proto::tag_of::type()); - } - - template - void do_multiplies(const Exp& e, const proto::tag::negate&) - { - typedef typename proto::result_of::left::type left_type; - do_multiplies(proto::left(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + do_multiplies(e.left(), typename left_type::tag_type()); m_backend.negate(); } template - void do_multiplies(const Exp& e, const proto::tag::multiplies&) + void do_multiplies(const Exp& e, const detail::multiplies&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_multiplies(proto::left(e), typename proto::tag_of::type()); - do_multiplies(proto::right(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_multiplies(e.left(), typename left_type::tag_type()); + do_multiplies(e.right(), typename right_type::tag_type()); } template - void do_multiplies(const Exp& e, const proto::tag::divides&) + void do_multiplies(const Exp& e, const detail::divides&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_multiplies(proto::left(e), typename proto::tag_of::type()); - do_divide(proto::right(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_multiplies(e.left(), typename left_type::tag_type()); + do_divide(e.right(), typename right_type::tag_type()); } + template + void do_multiplies(const Exp& e, const detail::multiply_immediates&) + { + using big_num_default_ops::multiply; + multiply(m_backend, canonical_value(e.left().value())); + multiply(m_backend, canonical_value(e.right().value())); + } + template + void do_multiplies(const Exp& e, const detail::divide_immediates&) + { + using big_num_default_ops::multiply; + using big_num_default_ops::divide; + multiply(m_backend, canonical_value(e.left().value())); + divide(m_backend, canonical_value(e.right().value())); + } template void do_multiplies(const Exp& e, const unknown&) { @@ -1169,43 +1199,52 @@ private: } template - void do_divide(const Exp& e, const proto::tag::terminal&) + void do_divide(const Exp& e, const detail::terminal&) { using big_num_default_ops::divide; - divide(m_backend, canonical_value(proto::value(e))); + divide(m_backend, canonical_value(e.value())); } template - void do_divide(const Exp& e, const proto::tag::unary_plus&) + void do_divide(const Exp& e, const detail::negate&) { - typedef typename proto::result_of::left::type left_type; - do_divide(proto::left(e), typename proto::tag_of::type()); - } - - template - void do_divide(const Exp& e, const proto::tag::negate&) - { - typedef typename proto::result_of::left::type left_type; - do_divide(proto::left(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + do_divide(e.left(), typename left_type::tag_type()); m_backend.negate(); } template - void do_divide(const Exp& e, const proto::tag::multiplies&) + void do_divide(const Exp& e, const detail::multiplies&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_divide(proto::left(e), typename proto::tag_of::type()); - do_divide(proto::right(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_divide(e.left(), typename left_type::tag_type()); + do_divide(e.right(), typename right_type::tag_type()); } template - void do_divide(const Exp& e, const proto::tag::divides&) + void do_divide(const Exp& e, const detail::divides&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_divide(proto::left(e), typename proto::tag_of::type()); - do_multiplies(proto::right(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_divide(e.left(), typename left_type::tag_type()); + do_multiplies(e.right(), typename right_type::tag_type()); + } + + template + void do_divides(const Exp& e, const detail::multiply_immediates&) + { + using big_num_default_ops::divide; + divide(m_backend, canonical_value(e.left().value())); + divide(m_backend, canonical_value(e.right().value())); + } + template + void do_divides(const Exp& e, const detail::divide_immediates&) + { + using big_num_default_ops::multiply; + using big_num_default_ops::divide; + divide(m_backend, canonical_value(e.left().value())); + mutiply(m_backend, canonical_value(e.right().value())); } template @@ -1217,35 +1256,35 @@ private: } template - void do_modulus(const Exp& e, const proto::tag::terminal&) + void do_modulus(const Exp& e, const detail::terminal&) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); using big_num_default_ops::modulus; - modulus(m_backend, canonical_value(proto::value(e))); + modulus(m_backend, canonical_value(e.value())); } template void do_modulus(const Exp& e, const Unknown&) { - BOOST_STATIC_ASSERT_MSG(is_extended_integer::value, "The modulus operation is only valid for integer types"); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); using big_num_default_ops::modulus; self_type temp(e); - modulus(m_backend, canonical_value(proto::value(temp))); + modulus(m_backend, canonical_value(temp)); } template - void do_bitwise_and(const Exp& e, const proto::tag::terminal&) + void do_bitwise_and(const Exp& e, const detail::terminal&) { using big_num_default_ops::bitwise_and; - bitwise_and(m_backend, canonical_value(proto::value(e))); + bitwise_and(m_backend, canonical_value(e.value())); } template - void do_bitwise_and(const Exp& e, const proto::tag::bitwise_and&) + void do_bitwise_and(const Exp& e, const detail::bitwise_and&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_bitwise_and(proto::left(e), typename proto::tag_of::type()); - do_bitwise_and(proto::right(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_bitwise_and(e.left(), typename left_type::tag_type()); + do_bitwise_and(e.right(), typename right_type::tag_type()); } template void do_bitwise_and(const Exp& e, const unknown&) @@ -1256,18 +1295,18 @@ private: } template - void do_bitwise_or(const Exp& e, const proto::tag::terminal&) + void do_bitwise_or(const Exp& e, const detail::terminal&) { using big_num_default_ops::bitwise_or; - bitwise_or(m_backend, canonical_value(proto::value(e))); + bitwise_or(m_backend, canonical_value(e.value())); } template - void do_bitwise_or(const Exp& e, const proto::tag::bitwise_or&) + void do_bitwise_or(const Exp& e, const detail::bitwise_or&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_bitwise_or(proto::left(e), typename proto::tag_of::type()); - do_bitwise_or(proto::right(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_bitwise_or(e.left(), typename left_type::tag_type()); + do_bitwise_or(e.right(), typename right_type::tag_type()); } template void do_bitwise_or(const Exp& e, const unknown&) @@ -1278,18 +1317,18 @@ private: } template - void do_bitwise_xor(const Exp& e, const proto::tag::terminal&) + void do_bitwise_xor(const Exp& e, const detail::terminal&) { using big_num_default_ops::bitwise_xor; - bitwise_xor(m_backend, canonical_value(proto::value(e))); + bitwise_xor(m_backend, canonical_value(e.value())); } template - void do_bitwise_xor(const Exp& e, const proto::tag::bitwise_xor&) + void do_bitwise_xor(const Exp& e, const detail::bitwise_xor&) { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - do_bitwise_xor(proto::left(e), typename proto::tag_of::type()); - do_bitwise_xor(proto::right(e), typename proto::tag_of::type()); + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_bitwise_xor(e.left(), typename left_type::tag_type()); + do_bitwise_xor(e.right(), typename right_type::tag_type()); } template void do_bitwise_xor(const Exp& e, const unknown&) @@ -1303,47 +1342,48 @@ private: template bool contains_self(const Exp& e)const { - return contains_self(e, mpl::int_::value>()); + return contains_self(e, typename Exp::arity()); } template bool contains_self(const Exp& e, mpl::int_<0> const&)const { - return is_really_self(proto::value(e)); + return is_really_self(e.value()); } template bool contains_self(const Exp& e, mpl::int_<1> const&)const { - typedef typename proto::result_of::child_c::type child_type; - return contains_self(proto::child_c<0>(e), mpl::int_::value>()); + typedef typename Exp::left_type child_type; + return contains_self(e.left(), typename child_type::arity()); } template bool contains_self(const Exp& e, mpl::int_<2> const&)const { - typedef typename proto::result_of::child_c::type child0_type; - typedef typename proto::result_of::child_c::type child1_type; - return contains_self(proto::child_c<0>(e), mpl::int_::value>()) || contains_self(proto::child_c<1>(e), mpl::int_::value>()); + typedef typename Exp::left_type child0_type; + typedef typename Exp::right_type child1_type; + return contains_self(e.left(), typename child0_type::arity()) + || contains_self(e.right(), typename child1_type::arity()); } template bool contains_self(const Exp& e, mpl::int_<3> const&)const { - typedef typename proto::result_of::child_c::type child0_type; - typedef typename proto::result_of::child_c::type child1_type; - typedef typename proto::result_of::child_c::type child2_type; - return contains_self(proto::child_c<0>(e), mpl::int_::value>()) - || contains_self(proto::child_c<1>(e), mpl::int_::value>()) - || contains_self(proto::child_c<2>(e), mpl::int_::value>()); + typedef typename Exp::left_type child0_type; + typedef typename Exp::middle_type child1_type; + typedef typename Exp::right_type child2_type; + return contains_self(e.left(), typename child0_type::arity()) + || contains_self(e.middle(), typename child1_type::arity()) + || contains_self(e.right(), typename child2_type::arity()); } // Test if the expression is a reference to *this: template bool is_self(const Exp& e)const { - return is_self(e, mpl::int_::value>()); + return is_self(e, typename Exp::arity()); } template bool is_self(const Exp& e, mpl::int_<0> const&)const { - return is_really_self(proto::value(e)); + return is_really_self(e.value()); } template bool is_self(const Exp& e, mpl::int_ const&)const @@ -1353,36 +1393,15 @@ private: template bool is_really_self(const Val&)const { return false; } - bool is_really_self(const self_type* v)const - { - return v == this; - } - bool is_really_self(self_type* v)const - { - return v == this; - } - template - static typename detail::underlying_result::type underlying_value(const detail::big_number_exp& e, const proto::tag::terminal&) - { - return proto::value(e); - } - template - static typename detail::underlying_result::type - underlying_value(const detail::big_number_exp& e, const tag&) - { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::tag_of::type tag_type; - return underlying_value(proto::left(e), tag_type()); - } + bool is_really_self(const self_type& v)const { return &v == this; } static const Backend& canonical_value(const self_type& v){ return v.m_backend; } - static const Backend& canonical_value(const self_type* v){ return v->m_backend; } - static const Backend& canonical_value(self_type* v){ return v->m_backend; } - static const Backend& canonical_value(self_type& v){ return v.m_backend; } + //static const Backend& canonical_value(const self_type* v){ return v->m_backend; } + //static const Backend& canonical_value(self_type* v){ return v->m_backend; } + //static const Backend& canonical_value(self_type& v){ return v.m_backend; } template static typename detail::canonical::type canonical_value(const V& v){ return v; } static typename detail::canonical::type canonical_value(const std::string& v){ return v.c_str(); } - Backend m_backend; }; @@ -1395,14 +1414,14 @@ inline int big_number_compare(const big_number& a, const big_number -inline int big_number_compare(const big_number& a, const big_number_exp& b) +template +inline int big_number_compare(const big_number& a, const big_number_exp& b) { return a.compare(big_number(b)); } -template -inline int big_number_compare(const big_number_exp& a, const big_number& b) +template +inline int big_number_compare(const big_number_exp& a, const big_number& b) { return -b.compare(big_number(a)); } @@ -1419,26 +1438,26 @@ inline int big_number_compare(const Val a, const big_number& b) return -b.compare(a); } -template -inline int big_number_compare(const big_number_exp& a, const big_number_exp& b) +template +inline int big_number_compare(const big_number_exp& a, const big_number_exp& b) { - typedef typename expression_type::type real1; - typedef typename expression_type::type real2; + typedef typename big_number_exp::result_type real1; + typedef typename big_number_exp::result_type real2; return real1(a).compare(real2(b)); } -template -inline typename enable_if, int>::type big_number_compare(const big_number_exp& a, const Val b) +template +inline typename enable_if, int>::type big_number_compare(const big_number_exp& a, const Val b) { - typedef typename expression_type::type real; + typedef typename big_number_exp::result_type real; real t(a); return t.compare(b); } -template -inline typename enable_if, int>::type big_number_compare(const Val a, const big_number_exp& b) +template +inline typename enable_if, int>::type big_number_compare(const Val a, const big_number_exp& b) { - typedef typename expression_type::type real; + typedef typename big_number_exp::result_type real; return -real(b).compare(a); } @@ -1527,10 +1546,10 @@ inline std::ostream& operator << (std::ostream& os, const big_number& r namespace detail{ -template -inline std::ostream& operator << (std::ostream& os, const big_number_exp& r) +template +inline std::ostream& operator << (std::ostream& os, const big_number_exp& r) { - typedef typename expression_type >::type value_type; + typedef typename big_number_exp::result_type value_type; value_type temp(r); return os << temp; } diff --git a/include/boost/math/big_number/big_number_base.hpp b/include/boost/math/big_number/big_number_base.hpp index 5356c6a3..4053c0b8 100644 --- a/include/boost/math/big_number/big_number_base.hpp +++ b/include/boost/math/big_number/big_number_base.hpp @@ -7,6 +7,8 @@ #define BOOST_MATH_BIG_NUM_BASE_HPP #include +#include +#include namespace boost{ namespace math{ @@ -16,145 +18,8 @@ class big_number; namespace detail{ // Forward-declare an expression wrapper -template +template struct big_number_exp; -// -// Declare our grammars: -// -struct integer_terminal : public -proto::and_< - proto::terminal< proto::_ >, - proto::if_ < boost::is_integral< proto::_value >() > - > -{}; - -struct big_number_grammar; - -template -struct is_big_number_ptr : mpl::false_ {}; - -template -struct is_big_number_ptr*> : mpl::true_ {}; - - -struct big_number_grammar_cases -{ - // The primary template matches nothing: - template - struct case_ - : proto::not_ - {}; -}; - -template<> -struct big_number_grammar_cases::case_ - : proto::and_< - proto::terminal, - proto::or_< - proto::if_ < is_big_number_ptr< proto::_value >() >, - proto::if_ < is_arithmetic< proto::_value >() >, - proto::if_ < is_same< proto::_value, std::string>() >, - proto::if_ < is_convertible< proto::_value, const char*>() > - > - > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::plus< big_number_grammar, big_number_grammar > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::multiplies< big_number_grammar, big_number_grammar > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::minus< big_number_grammar, big_number_grammar > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::divides< big_number_grammar, big_number_grammar > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::unary_plus< big_number_grammar> -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::negate< big_number_grammar> -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::modulus< big_number_grammar, big_number_grammar > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::bitwise_and< big_number_grammar, big_number_grammar > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::bitwise_or< big_number_grammar, big_number_grammar > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::bitwise_xor< big_number_grammar, big_number_grammar > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::shift_left< big_number_grammar, integer_terminal > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::shift_right< big_number_grammar, integer_terminal > -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::complement -{}; - -template<> -struct big_number_grammar_cases::case_ - : proto::or_< - proto::function< proto::_, big_number_grammar >, - proto::function< proto::_, big_number_grammar, proto::_ > - > -{}; - -struct big_number_grammar : proto::switch_{}; - -// Define a calculator domain. Expression within -// the calculator domain will be wrapped in the -// calculator<> expression wrapper. -struct big_number_domain - : proto::domain< proto::generator, big_number_grammar> -{}; - -struct CalcDepth - : proto::or_< - proto::when< proto::terminal, - mpl::int_<0>() - > - , proto::when< proto::unary_expr, - CalcDepth(proto::_child) - > - , proto::when< proto::binary_expr, - mpl::plus, mpl::int_<1> >() - > - > -{}; template struct has_enough_bits @@ -231,303 +96,45 @@ struct canonical typedef typename canonical_imp::type type; }; -template -struct assign_and_eval_imp -{ - typedef tag type; -}; - +struct terminal{}; +struct negate{}; +struct plus{}; +struct minus{}; +struct multiplies{}; +struct divides{}; +struct modulus{}; +struct shift_left{}; +struct shift_right{}; +struct bitwise_and{}; +struct bitwise_or{}; +struct bitwise_xor{}; +struct bitwise_complement{}; struct add_immediates{}; -struct add_and_negate_immediates{}; struct subtract_immediates{}; -struct subtract_and_negate_immediates{}; struct multiply_immediates{}; -struct multiply_and_negate_immediates{}; struct divide_immediates{}; -struct divide_and_negate_immediates{}; struct modulus_immediates{}; struct bitwise_and_immediates{}; struct bitwise_or_immediates{}; struct bitwise_xor_immediates{}; struct complement_immediates{}; +struct function{}; -struct immediate{}; -struct negative_immediate{}; +template +struct backend_type; -template -struct immediate_type +template +struct backend_type > { - typedef tag type; -}; -template -struct immediate_type -{ - typedef immediate type; -}; -template -struct immediate_type -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::tag_of::type left_tag; - typedef typename mpl::if_< - is_same, - immediate, - left_tag - >::type type; -}; -template -struct immediate_type -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::tag_of::type left_tag; - typedef typename immediate_type::type tag; - typedef typename mpl::if_< - is_same, - negative_immediate, - tag - >::type type; + typedef T type; }; -template -struct assign_and_eval_imp +template +struct backend_type > { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::tag_of::type left_tag; - typedef typename proto::tag_of::type right_tag; - typedef typename immediate_type::type left_imm; - typedef typename immediate_type::type right_imm; - typedef typename mpl::if_< - mpl::and_, is_same >, - add_immediates, - typename mpl::if_< - mpl::and_, is_same >, - subtract_immediates, - typename mpl::if_< - mpl::and_, is_same >, - subtract_and_negate_immediates, - typename mpl::if_< - mpl::and_, is_same >, - add_and_negate_immediates, - proto::tag::plus - >::type - >::type - >::type - >::type type; + typedef typename backend_type::result_type>::type type; }; -template -struct assign_and_eval_imp -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::tag_of::type left_tag; - typedef typename proto::tag_of::type right_tag; - typedef typename immediate_type::type left_imm; - typedef typename immediate_type::type right_imm; - typedef typename mpl::if_< - mpl::and_, is_same >, - subtract_immediates, - typename mpl::if_< - mpl::and_, is_same >, - add_immediates, - typename mpl::if_< - mpl::and_, is_same >, - add_and_negate_immediates, - typename mpl::if_< - mpl::and_, is_same >, - subtract_and_negate_immediates, - proto::tag::minus - >::type - >::type - >::type - >::type type; -}; - -template -struct assign_and_eval_imp -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::tag_of::type left_tag; - typedef typename proto::tag_of::type right_tag; - typedef typename immediate_type::type left_imm; - typedef typename immediate_type::type right_imm; - typedef typename mpl::if_< - mpl::and_, is_same >, - multiply_immediates, - typename mpl::if_< - mpl::and_, is_same >, - multiply_and_negate_immediates, - typename mpl::if_< - mpl::and_, is_same >, - multiply_and_negate_immediates, - typename mpl::if_< - mpl::and_, is_same >, - multiply_immediates, - proto::tag::multiplies - >::type - >::type - >::type - >::type type; -}; - -template -struct assign_and_eval_imp -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::tag_of::type left_tag; - typedef typename proto::tag_of::type right_tag; - typedef typename immediate_type::type left_imm; - typedef typename immediate_type::type right_imm; - typedef typename mpl::if_< - mpl::and_, is_same >, - divide_immediates, - typename mpl::if_< - mpl::and_, is_same >, - divide_and_negate_immediates, - typename mpl::if_< - mpl::and_, is_same >, - divide_and_negate_immediates, - typename mpl::if_< - mpl::and_, is_same >, - divide_immediates, - proto::tag::divides - >::type - >::type - >::type - >::type type; -}; - -template -struct assign_and_eval_imp -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::tag_of::type left_tag; - typedef typename proto::tag_of::type right_tag; - typedef typename immediate_type::type left_imm; - typedef typename immediate_type::type right_imm; - typedef typename mpl::if_< - mpl::and_, is_same >, - modulus_immediates, - proto::tag::modulus - >::type type; -}; - -template -struct assign_and_eval_imp -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::tag_of::type left_tag; - typedef typename proto::tag_of::type right_tag; - typedef typename immediate_type::type left_imm; - typedef typename immediate_type::type right_imm; - typedef typename mpl::if_< - mpl::and_, is_same >, - bitwise_and_immediates, - proto::tag::bitwise_and - >::type type; -}; - -template -struct assign_and_eval_imp -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::tag_of::type left_tag; - typedef typename proto::tag_of::type right_tag; - typedef typename immediate_type::type left_imm; - typedef typename immediate_type::type right_imm; - typedef typename mpl::if_< - mpl::and_, is_same >, - bitwise_or_immediates, - proto::tag::bitwise_or - >::type type; -}; - -template -struct assign_and_eval_imp -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::tag_of::type left_tag; - typedef typename proto::tag_of::type right_tag; - typedef typename immediate_type::type left_imm; - typedef typename immediate_type::type right_imm; - typedef typename mpl::if_< - mpl::and_, is_same >, - bitwise_xor_immediates, - proto::tag::bitwise_xor - >::type type; -}; - -template -struct assign_and_eval_imp -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::tag_of::type left_tag; - typedef typename immediate_type::type left_imm; - typedef typename mpl::if_< - is_same, - complement_immediates, - proto::tag::complement - >::type type; -}; - -template -struct assign_and_eval -{ - typedef typename proto::tag_of::type tag_type; - typedef typename assign_and_eval_imp::type type; -}; - -template -struct underlying_result_imp -{ - typedef typename proto::result_of::left::type left_type; - typedef typename proto::tag_of::type tag_type; - typedef typename underlying_result_imp::type type; -}; - -template -struct underlying_result_imp -{ - typedef typename proto::result_of::value::type type; -}; - -template -struct underlying_result -{ - typedef typename proto::tag_of::type tag_type; - typedef typename underlying_result_imp::type type; -}; - -template -struct combine_expression_type -{ - typedef void type; -}; - -template -struct combine_expression_type, boost::math::big_number > -{ - typedef boost::math::big_number type; -}; - -template -struct combine_expression_type, Exp> -{ - typedef boost::math::big_number type; -}; - -template -struct combine_expression_type > -{ - typedef boost::math::big_number type; -}; template struct is_big_number : public mpl::false_{}; @@ -535,125 +142,823 @@ template struct is_big_number > : public mpl::true_{}; template struct is_big_number_exp : public mpl::false_{}; +template +struct is_big_number_exp > : public mpl::true_{}; + +template +struct combine_expression; + +template +struct combine_expression, T2> +{ + typedef big_number type; +}; + +template +struct combine_expression > +{ + typedef big_number type; +}; + template -struct is_big_number_exp > : public mpl::true_{}; - - -template -struct expression_type_imp; - -template -struct expression_type_imp +struct combine_expression, big_number > { - typedef typename remove_pointer::type>::type type; + typedef big_number type; }; -template -struct expression_type_imp +template +struct arg_type { - typedef typename proto::result_of::left::type nested_type; - typedef typename expression_type_imp::value>::type type; + typedef big_number_exp type; }; -template -struct expression_type_imp +template +struct arg_type > { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename expression_type_imp::value>::type left_result; - typedef typename expression_type_imp::value>::type right_result; - typedef typename combine_expression_type::type type; + typedef big_number_exp type; }; -template -struct expression_type_imp +template +void unmentionable_proc(){} + +typedef void (*unmentionable_type)(); + +template +struct big_number_exp_storage { - typedef typename proto::result_of::left::type left_type; - typedef typename proto::result_of::right::type right_type; - typedef typename proto::result_of::child_c::type end_type; - typedef typename expression_type_imp::value>::type left_result; - typedef typename expression_type_imp::value>::type right_result; - typedef typename expression_type_imp::value>::type end_result; - typedef typename combine_expression_type::type>::type type; + typedef const T& type; }; -template -struct expression_type +template +struct big_number_exp_storage { - typedef typename expression_type_imp::value>::type type; + typedef T* type; }; -template -struct backend_type +template +struct big_number_exp_storage { - typedef typename expression_type::type num_type; - typedef typename backend_type::type type; + typedef const T* type; }; -template -struct backend_type > +template +struct big_number_exp_storage > { - typedef Backend type; + typedef big_number_exp type; }; -template -struct big_number_exp - : proto::extends, big_number_domain> +template +struct big_number_exp { + typedef mpl::int_<1> arity; + typedef typename arg_type::type left_type; + typedef typename left_type::result_type result_type; + typedef tag tag_type; + + big_number_exp(const Arg1& a) : arg(a) {} + + left_type left()const { return arg; } + + const Arg1& left_ref()const{ return arg; } + + static const unsigned depth = left_type::depth + 1; + + operator unmentionable_type()const + { + result_type r(*this); + return r ? unmentionable_proc : 0; + } + private: - typedef proto::extends, big_number_domain> base_type; - typedef big_number_exp self_type; - typedef typename remove_reference::type>::type number_type; - typedef void (self_type::*unmentionable_type)(); - void unmentionable_proc(){} - unmentionable_type boolean_context_from_terminal(const number_type* pval)const - { - return pval->is_zero() ? 0 : &self_type::unmentionable_proc; - } - unmentionable_type boolean_context_from_terminal(number_type* pval)const - { - return pval->is_zero() ? 0 : &self_type::unmentionable_proc; - } - template - unmentionable_type boolean_context_from_terminal(const Terminal& val)const - { - return val ? 0 : &self_type::unmentionable_proc; - } - unmentionable_type boolean_context(const proto::tag::terminal&)const - { - return boolean_context_from_terminal(proto::value(*this)); - } - template - unmentionable_type boolean_context(const Tag&)const - { - // we have to evaluate the expression template: - number_type result(*this); - return result.is_zero() ? 0 : &self_type::unmentionable_proc; - } -public: - big_number_exp(Expr const &expr = Expr()) - : base_type(expr) - {} - template - big_number_exp(const Other& o, typename enable_if >::type const* = 0) - : base_type(o) - {} + typename big_number_exp_storage::type arg; +}; - operator unmentionable_type()const - { - return boolean_context(typename proto::tag_of::type()); - } +template +struct big_number_exp +{ + typedef mpl::int_<0> arity; + typedef Arg1 result_type; + typedef terminal tag_type; + + big_number_exp(const Arg1& a) : arg(a) {} + + const Arg1& value()const { return arg; } + + static const unsigned depth = 0; + + operator unmentionable_type()const + { + return arg ? unmentionable_proc : 0; + } + +private: + typename big_number_exp_storage::type arg; +}; + +template +struct big_number_exp +{ + typedef mpl::int_<2> arity; + typedef typename arg_type::type left_type; + typedef typename arg_type::type right_type; + typedef typename left_type::result_type left_result_type; + typedef typename right_type::result_type right_result_type; + typedef typename combine_expression::type result_type; + typedef tag tag_type; + + big_number_exp(const Arg1& a1, const Arg2& a2) : arg1(a1), arg2(a2) {} + + left_type left()const { return arg1; } + right_type right()const { return arg2; } + const Arg1& left_ref()const{ return arg1; } + const Arg2& right_ref()const{ return arg2; } + + operator unmentionable_type()const + { + result_type r(*this); + return r ? unmentionable_proc : 0; + } + + static const unsigned left_depth = left_type::depth + 1; + static const unsigned right_depth = right_type::depth + 1; + static const unsigned depth = left_depth > right_depth ? left_depth : right_depth; +private: + typename big_number_exp_storage::type arg1; + typename big_number_exp_storage::type arg2; +}; + +template +struct big_number_exp +{ + typedef mpl::int_<3> arity; + typedef typename arg_type::type left_type; + typedef typename arg_type::type middle_type; + typedef typename arg_type::type right_type; + typedef typename left_type::result_type left_result_type; + typedef typename middle_type::result_type middle_result_type; + typedef typename right_type::result_type right_result_type; + typedef typename combine_expression< + left_result_type, + typename combine_expression::type + >::type result_type; + typedef tag tag_type; + + big_number_exp(const Arg1& a1, const Arg2& a2, const Arg3& a3) : arg1(a1), arg2(a2), arg3(a3) {} + + left_type left()const { return arg1; } + middle_type middle()const { return arg2; } + right_type right()const { return arg3; } + const Arg1& left_ref()const{ return arg1; } + const Arg2& middle_ref()const{ return arg2; } + const Arg3& right_ref()const{ return arg3; } + + operator unmentionable_type()const + { + result_type r(*this); + return r ? unmentionable_proc : 0; + } + + static const unsigned left_depth = left_type::depth + 1; + static const unsigned middle_depth = middle_type::depth + 1; + static const unsigned right_depth = right_type::depth + 1; + static const unsigned depth = left_depth > right_depth ? (left_depth > middle_depth ? left_depth : middle_depth) : (right_depth > middle_depth ? right_depth : middle_depth); +private: + typename big_number_exp_storage::type arg1; + typename big_number_exp_storage::type arg2; + typename big_number_exp_storage::type arg3; }; } // namespace detail // -// Traits class, lets us know whether a backend is an integer type, otherwise assumed to be a real number type: +// Non-member operators for big_number: // +// Unary operators first: +// +template +inline const big_number& operator + (const big_number& v) { return v; } +template +inline const detail::big_number_exp& operator + (const detail::big_number_exp& v) { return v; } +template +inline detail::big_number_exp > operator - (const big_number& v) { return v; } +template +inline detail::big_number_exp > operator - (const detail::big_number_exp& v) { return v; } +template +inline detail::big_number_exp > operator ~ (const big_number& v) { return v; } +template +inline detail::big_number_exp > operator ~ (const detail::big_number_exp& v) { return v; } +// +// Then addition: +// +template +inline detail::big_number_exp, big_number > + operator + (const big_number& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator + (const big_number& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator + (const V& a, const big_number& b) +{ + return detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator + (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, big_number > + operator + (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator + (const detail::big_number_exp& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator + (const detail::big_number_exp& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator + (const V& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::big_number_exp, typename detail::big_number_exp::left_type > + operator + (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, typename detail::big_number_exp::left_type >(a, b.left_ref()); +} +template +inline detail::big_number_exp, typename detail::big_number_exp::left_type > + operator + (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, typename detail::big_number_exp::left_type >(b, a.left_ref()); +} +template +inline detail::big_number_exp, big_number > + operator + (const big_number& a, const detail::big_number_exp >& b) +{ + return detail::big_number_exp, big_number >(a, b.left_ref()); +} +template +inline detail::big_number_exp, big_number > + operator + (const detail::big_number_exp >& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(b, a.left_ref()); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator + (const detail::big_number_exp >& a, const V& b) +{ + return detail::big_number_exp >(b, a.left_ref()); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator + (const V& a, const detail::big_number_exp >& b) +{ + return detail::big_number_exp, big_number >(a, b.left_ref()); +} +// +// Subtraction: +// +template +inline detail::big_number_exp, big_number > + operator - (const big_number& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator - (const big_number& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator - (const V& a, const big_number& b) +{ + return detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator - (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, big_number > + operator - (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator - (const detail::big_number_exp& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator - (const detail::big_number_exp& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator - (const V& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::big_number_exp, typename detail::big_number_exp::left_type > + operator - (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, typename detail::big_number_exp::left_type >(a, b.left_ref()); +} +template +inline detail::big_number_exp, typename detail::big_number_exp::left_type > > + operator - (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, typename detail::big_number_exp::left_type >(b, a.left_ref()); +} +template +inline detail::big_number_exp, big_number > + operator - (const big_number& a, const detail::big_number_exp >& b) +{ + return detail::big_number_exp, big_number >(a, b.left_ref()); +} +template +inline detail::big_number_exp, big_number > > + operator - (const detail::big_number_exp >& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(b, a.left_ref()); +} +template +inline typename enable_if, detail::big_number_exp, V > > >::type + operator - (const detail::big_number_exp >& a, const V& b) +{ + return detail::big_number_exp >(b, a.left_ref()); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator - (const V& a, const detail::big_number_exp >& b) +{ + return detail::big_number_exp >(a, b.left_ref()); +} +// +// Multiplication: +// +template +inline detail::big_number_exp, big_number > + operator * (const big_number& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator * (const big_number& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator * (const V& a, const big_number& b) +{ + return detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator * (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, big_number > + operator * (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator * (const detail::big_number_exp& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator * (const detail::big_number_exp& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator * (const V& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::big_number_exp, typename detail::big_number_exp::left_type > > + operator * (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, typename detail::big_number_exp::left_type > (a, b.left_ref()); +} +template +inline detail::big_number_exp, typename detail::big_number_exp::left_type > > + operator * (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, typename detail::big_number_exp::left_type >(b, a.left_ref()); +} +template +inline detail::big_number_exp, big_number > > + operator * (const big_number& a, const detail::big_number_exp >& b) +{ + return detail::big_number_exp, big_number >(a, b.left_ref()); +} +template +inline detail::big_number_exp, big_number > > + operator * (const detail::big_number_exp >& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(b, a.left_ref()); +} +template +inline typename enable_if, detail::big_number_exp, V > > >::type + operator * (const detail::big_number_exp >& a, const V& b) +{ + return detail::big_number_exp, V >(a.left_ref(), b); +} +template +inline typename enable_if, detail::big_number_exp, V > > >::type + operator * (const V& a, const detail::big_number_exp >& b) +{ + return detail::big_number_exp, V >(b.left_ref(), a); +} +// +// Division: +// +template +inline detail::big_number_exp, big_number > + operator / (const big_number& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator / (const big_number& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator / (const V& a, const big_number& b) +{ + return detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator / (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, big_number > + operator / (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator / (const detail::big_number_exp& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator / (const detail::big_number_exp& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator / (const V& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::big_number_exp, typename detail::big_number_exp::left_type > > + operator / (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, typename detail::big_number_exp::left_type >(a, b.left_ref()); +} +template +inline detail::big_number_exp::left_type, big_number > > + operator / (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp::left_type, big_number >(a.left_ref(), b); +} +template +inline detail::big_number_exp, big_number > > + operator / (const big_number& a, const detail::big_number_exp >& b) +{ + return detail::big_number_exp, big_number >(a, b.left_ref()); +} +template +inline detail::big_number_exp, big_number > > + operator / (const detail::big_number_exp >& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a.left_ref(), b); +} +template +inline typename enable_if, detail::big_number_exp, V > > >::type + operator / (const detail::big_number_exp >& a, const V& b) +{ + return detail::big_number_exp, V>(a.left_ref(), b); +} +template +inline typename enable_if, detail::big_number_exp > > >::type + operator / (const V& a, const detail::big_number_exp >& b) +{ + return detail::big_number_exp >(a, b.left_ref()); +} +// +// Modulus: +// +template +inline detail::big_number_exp, big_number > + operator % (const big_number& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator % (const big_number& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator % (const V& a, const big_number& b) +{ + return detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator % (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, big_number > + operator % (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator % (const detail::big_number_exp& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator % (const detail::big_number_exp& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator % (const V& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp >(a, b); +} +// +// Left shift: +// +template +inline typename enable_if, detail::big_number_exp, I > >::type + operator << (const big_number& a, const I& b) +{ + return detail::big_number_exp, I>(a, b); +} +template +inline typename enable_if, detail::big_number_exp, I> >::type + operator << (const detail::big_number_exp& a, const I& b) +{ + return detail::big_number_exp, I>(a, b); +} +// +// Right shift: +// +template +inline typename enable_if, detail::big_number_exp, I > >::type + operator >> (const big_number& a, const I& b) +{ + return detail::big_number_exp, I>(a, b); +} +template +inline typename enable_if, detail::big_number_exp, I> >::type + operator >> (const detail::big_number_exp& a, const I& b) +{ + return detail::big_number_exp, I>(a, b); +} +// +// Bitwise AND: +// +template +inline detail::big_number_exp, big_number > + operator & (const big_number& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator & (const big_number& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator & (const V& a, const big_number& b) +{ + return detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator & (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, big_number > + operator & (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator & (const detail::big_number_exp& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator & (const detail::big_number_exp& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator & (const V& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp >(a, b); +} +// +// Bitwise OR: +// +template +inline detail::big_number_exp, big_number > + operator| (const big_number& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator| (const big_number& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator| (const V& a, const big_number& b) +{ + return detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator| (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, big_number > + operator| (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator| (const detail::big_number_exp& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator| (const detail::big_number_exp& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator| (const V& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp >(a, b); +} +// +// Bitwise XOR: +// +template +inline detail::big_number_exp, big_number > + operator^ (const big_number& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator^ (const big_number& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator^ (const V& a, const big_number& b) +{ + return detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator^ (const big_number& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline detail::big_number_exp, big_number > + operator^ (const detail::big_number_exp& a, const big_number& b) +{ + return detail::big_number_exp, big_number >(a, b); +} +template +inline detail::big_number_exp, detail::big_number_exp > + operator^ (const detail::big_number_exp& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp, detail::big_number_exp >(a, b); +} +template +inline typename enable_if, detail::big_number_exp, V > >::type + operator^ (const detail::big_number_exp& a, const V& b) +{ + return detail::big_number_exp, V >(a, b); +} +template +inline typename enable_if, detail::big_number_exp > >::type + operator^ (const V& a, const detail::big_number_exp& b) +{ + return detail::big_number_exp >(a, b); +} + +// +// Traits class, lets us know what kind of number we have, defaults to a floating point type: +// +enum number_category_type +{ + number_kind_integer = 0, + number_kind_floating_point = 1, + number_kind_rational = 2, + number_kind_fixed_point = 3 +}; + template -struct is_extended_integer : public mpl::false_ {}; +struct number_category : public mpl::int_ {}; template -struct is_extended_integer > : public is_extended_integer{}; +struct number_category > : public number_category{}; +template +struct number_category > : public number_category::result_type>{}; }} // namespaces @@ -662,10 +967,10 @@ namespace boost{ namespace math{ namespace tools{ template struct promote_arg; -template -struct promote_arg > +template +struct promote_arg > { - typedef typename boost::math::detail::expression_type::type type; + typedef typename boost::math::detail::big_number_exp::result_type type; }; }}} diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index da2df385..52047256 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -10,6 +10,8 @@ #include #include #include +#include +#include namespace boost{ namespace math{ namespace big_num_default_ops{ @@ -418,17 +420,9 @@ typename enable_if_c::type eval_tanh(); } - template class big_number; -namespace detail{ - -template -struct big_number_exp; - -} - // // Default versions of floating point classification routines: // @@ -438,10 +432,10 @@ inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number using big_num_default_ops::eval_fpclassify; return eval_fpclassify(arg.backend()); } -template -inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) +template +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) { - typedef typename detail::expression_type::type value_type; + typedef typename detail::big_number_exp::result_type value_type; return fpclassify(value_type(arg)); } template @@ -450,10 +444,10 @@ inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& int v = fpclassify(arg); return (v != FP_INFINITE) && (v != FP_NAN); } -template -inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) +template +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) { - typedef typename detail::expression_type::type value_type; + typedef typename detail::big_number_exp::result_type value_type; return isfinite(value_type(arg)); } template @@ -461,10 +455,10 @@ inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& ar { return fpclassify(arg) == FP_NAN; } -template -inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) +template +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) { - typedef typename detail::expression_type::type value_type; + typedef typename detail::big_number_exp::result_type value_type; return isnan(value_type(arg)); } template @@ -472,10 +466,10 @@ inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& ar { return fpclassify(arg) == FP_INFINITE; } -template -inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) +template +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) { - typedef typename detail::expression_type::type value_type; + typedef typename detail::big_number_exp::result_type value_type; return isinf(value_type(arg)); } template @@ -483,17 +477,17 @@ inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& { return fpclassify(arg) == FP_NORMAL; } -template -inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) +template +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) { - typedef typename detail::expression_type::type value_type; + typedef typename detail::big_number_exp::result_type value_type; return isnormal(value_type(arg)); } -template -inline int itrunc(const detail::big_number_exp& v, const Policy& pol) +template +inline int itrunc(const detail::big_number_exp& v, const Policy& pol) { - typedef typename detail::expression_type::type number_type; + typedef typename detail::big_number_exp::result_type number_type; number_type r = trunc(v, pol); if(fabs(r) > (std::numeric_limits::max)()) return policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); @@ -641,30 +635,38 @@ struct BOOST_JOIN(func, _funct)\ \ }\ \ -template \ -typename proto::result_of::make_expr<\ - proto::tag::function\ - , detail::BOOST_JOIN(func, _funct)::type> \ - , detail::big_number_exp \ ->::type const \ -func(const detail::big_number_exp& arg)\ +template \ +detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::big_number_exp \ +> \ +func(const detail::big_number_exp& arg)\ {\ - return proto::make_expr(\ - detail::BOOST_JOIN(func, _funct)::type>() \ + return detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::big_number_exp \ +> (\ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg \ );\ }\ template \ -typename proto::result_of::make_expr<\ - proto::tag::function\ +detail::big_number_exp<\ + detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , detail::big_number_exp*>::type> \ ->::type const \ + , big_number\ +> \ func(const big_number& arg)\ {\ - return proto::make_expr(\ + return detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , big_number\ + >(\ detail::BOOST_JOIN(func, _funct)() \ - , static_cast*>::type>&>(arg) \ + , arg \ );\ } @@ -688,61 +690,81 @@ struct BOOST_JOIN(func, _funct)\ \ }\ template \ -typename proto::result_of::make_expr<\ - proto::tag::function\ +detail::big_number_exp<\ + detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , detail::big_number_exp*>::type> \ - , detail::big_number_exp*>::type> \ ->::type const \ + , big_number \ + , big_number \ +> \ func(const big_number& arg, const big_number& a)\ {\ - return proto::make_expr(\ - detail::BOOST_JOIN(func, _funct)() \ - , static_cast*>::type>&>(arg),\ - static_cast*>::type>&>(a)\ - );\ -}\ -template \ -typename proto::result_of::make_expr<\ - proto::tag::function\ + return detail::big_number_exp<\ + detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , detail::big_number_exp*>::type> \ - , detail::big_number_exp \ ->::type const \ -func(const big_number& arg, const detail::big_number_exp& a)\ -{\ - return proto::make_expr(\ + , big_number \ + , big_number \ + >(\ detail::BOOST_JOIN(func, _funct)() \ - , static_cast*>::type>&>(arg),\ + , arg,\ a\ );\ }\ -template \ -typename proto::result_of::make_expr<\ - proto::tag::function\ +template \ +detail::big_number_exp<\ + detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , detail::big_number_exp \ - , detail::big_number_exp*>::type > \ ->::type const \ -func(const detail::big_number_exp& arg, const big_number& a)\ + , big_number \ + , detail::big_number_exp \ +> \ +func(const big_number& arg, const detail::big_number_exp& a)\ {\ - return proto::make_expr(\ + return detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , big_number \ + , detail::big_number_exp \ + >(\ detail::BOOST_JOIN(func, _funct)() \ , arg,\ - static_cast*>::type>&>(a)\ + a\ );\ }\ -template \ -typename proto::result_of::make_expr<\ - proto::tag::function\ - , detail::BOOST_JOIN(func, _funct)::type> \ - , detail::big_number_exp \ - , detail::big_number_exp \ ->::type const \ -func(const detail::big_number_exp& arg, const detail::big_number_exp& a)\ +template \ +detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , detail::big_number_exp \ + , big_number\ +>\ +func(const detail::big_number_exp& arg, const big_number& a)\ {\ - return proto::make_expr(\ - detail::BOOST_JOIN(func, _funct)::type>() \ + return detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , detail::big_number_exp \ + , big_number\ + >(\ + detail::BOOST_JOIN(func, _funct)() \ + , arg,\ + a\ + );\ +}\ +template \ +detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::big_number_exp \ + , detail::big_number_exp \ +>\ +func(const detail::big_number_exp& arg, const detail::big_number_exp& a)\ +{\ + return detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::big_number_exp \ + , detail::big_number_exp \ + >(\ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg,\ a\ );\ @@ -750,35 +772,47 @@ func(const detail::big_number_exp& arg, const detail::big_number_exp template \ typename enable_if<\ is_arithmetic,\ - typename proto::result_of::make_expr<\ - proto::tag::function\ + detail::big_number_exp<\ + detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , detail::big_number_exp*>::type> \ - , typename proto::result_of::as_child::type\ ->::type>::type const \ + , big_number\ + , Arithmetic\ + > \ +>::type \ func(const big_number& arg, const Arithmetic& a)\ {\ - return proto::make_expr(\ + return detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , big_number\ + , Arithmetic\ + >(\ detail::BOOST_JOIN(func, _funct)() \ - , static_cast*>::type>&>(arg),\ - proto::as_child(a)\ + , arg,\ + a\ );\ }\ -template \ +template \ typename enable_if<\ is_arithmetic,\ - typename proto::result_of::make_expr<\ - proto::tag::function\ - , detail::BOOST_JOIN(func, _funct)::type> \ - , detail::big_number_exp \ - , typename proto::result_of::as_child::type\ ->::type>::type const \ -func(const detail::big_number_exp& arg, const Arithmetic& a)\ + detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::big_number_exp \ + , Arithmetic\ + > \ +>::type \ +func(const detail::big_number_exp& arg, const Arithmetic& a)\ {\ - return proto::make_expr(\ - detail::BOOST_JOIN(func, _funct)::type>() \ + return detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::big_number_exp \ + , Arithmetic\ + >(\ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg,\ - proto::as_child(a)\ + a\ );\ }\ @@ -797,33 +831,43 @@ struct BOOST_JOIN(func, _funct)\ \ }\ \ -template \ -typename proto::result_of::make_expr<\ - proto::tag::function\ - , detail::BOOST_JOIN(func, _funct)::type> \ - , detail::big_number_exp \ - , typename proto::result_of::as_child::type \ ->::type const \ -func(const detail::big_number_exp& arg, Arg2 const& a)\ +template \ +detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::big_number_exp \ + , Arg2\ +>\ +func(const detail::big_number_exp& arg, Arg2 const& a)\ {\ - return proto::make_expr(\ - detail::BOOST_JOIN(func, _funct)::type>() \ - , arg, proto::as_child(a) \ + return detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::big_number_exp \ + , Arg2\ + >(\ + detail::BOOST_JOIN(func, _funct) >::type>() \ + , arg, a \ );\ }\ template \ -typename proto::result_of::make_expr<\ - proto::tag::function\ +detail::big_number_exp<\ + detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , detail::big_number_exp*>::type> \ - , typename proto::result_of::as_child::type \ ->::type const \ + , big_number\ + , Arg2\ +>\ func(const big_number& arg, Arg2 const& a)\ {\ - return proto::make_expr(\ + return detail::big_number_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , big_number\ + , Arg2\ + >(\ detail::BOOST_JOIN(func, _funct)() \ - , static_cast*>::type>&>(arg),\ - proto::as_child(a)\ + , arg,\ + a\ );\ }\ diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp index 3c32b4ea..3ee95512 100644 --- a/include/boost/math/big_number/gmp.hpp +++ b/include/boost/math/big_number/gmp.hpp @@ -1305,7 +1305,9 @@ inline void eval_abs(gmp_rational& result, const gmp_rational& val) } template<> -struct is_extended_integer : public mpl::true_ {}; +struct number_category : public mpl::int_{}; +template<> +struct number_category : public mpl::int_{}; typedef big_number > mpf_real_50; typedef big_number > mpf_real_100; diff --git a/math/test/big_number_concept_check.cpp b/math/test/big_number_concept_check.cpp index 764cd3b4..e2745897 100644 --- a/math/test/big_number_concept_check.cpp +++ b/math/test/big_number_concept_check.cpp @@ -54,68 +54,6 @@ #include #include "libs/math/test/compile_test/instantiate.hpp" -void a() -{ - using namespace boost; - using namespace boost::math; - using namespace boost::math::concepts; - - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); -} - -void b() -{ - using namespace boost; - using namespace boost::math; - using namespace boost::math::concepts; - - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); -} - -void c() -{ - using namespace boost; - using namespace boost::math; - using namespace boost::math::concepts; - - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); -} - -void d() -{ - using namespace boost; - using namespace boost::math; - using namespace boost::math::concepts; - - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); -} - void foo() { #ifdef TEST_BACKEND diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index fa795461..559ec81c 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -53,11 +53,11 @@ BOOST_LIGHTWEIGHT_TEST_OSTREAM << e.what() << std::endl;\ } -template -void test_integer_ops(const boost::mpl::false_&){} +template +void test_integer_ops(const boost::mpl::int_&){} template -void test_integer_ops(const boost::mpl::true_&) +void test_integer_ops(const boost::mpl::int_&) { Real a(20); Real b(7); @@ -236,7 +236,6 @@ void test_integer_ops(const boost::mpl::true_&) BOOST_TEST(c == (i & ~j)); c = ~(a | b); BOOST_TEST(c == ~(i | j)); - // // Non-member functions: // @@ -250,11 +249,11 @@ void test_integer_ops(const boost::mpl::true_&) BOOST_TEST(abs(+a) == 20); } -template -void test_real_ops(const boost::mpl::false_&){} +template +void test_real_ops(const boost::mpl::int_&){} template -void test_real_ops(const boost::mpl::true_&) +void test_real_ops(const boost::mpl::int_&) { #if defined(TEST_MPF) || defined(TEST_MPF_50) || defined(TEST_BACKEND) || defined(TEST_MPFR) BOOST_TEST(abs(Real(2)) == 2); @@ -501,7 +500,6 @@ void test_mixed() BOOST_TEST(Real(r / n5) == n1 / n5); r /= n5; BOOST_TEST(r == n1 / n5); - // // special cases for full coverage: // @@ -513,7 +511,6 @@ void test_mixed() BOOST_TEST(r == n4 * n5); r = (4 * n4) / Real(4); BOOST_TEST(r == n4); - test_negative_mixed(boost::mpl::bool_::is_signed>()); } @@ -541,11 +538,11 @@ void test() // // Integer only functions: // - test_integer_ops(boost::math::is_extended_integer()); + test_integer_ops(boost::math::number_category()); // // Real number only functions: // - test_real_ops(boost::mpl::bool_::value >()); + test_real_ops(boost::math::number_category()); // // Test basic arithmetic: // @@ -565,14 +562,12 @@ void test() BOOST_TEST(a / b == 8); a /= b; BOOST_TEST(a == 8); - Real ac(a); BOOST_TEST(ac == a); BOOST_TEST(-a == -8); - ac = a * c; BOOST_TEST(ac == 8*500L); - + ac = 8*500L; ac = ac + b + c; BOOST_TEST(ac == 8*500L+64+500); ac = a; @@ -639,10 +634,6 @@ void test() ac = a * ac; BOOST_TEST(ac == 8*8); ac = a; -#ifndef TEST_E_FLOAT - ac = ac + "8"; - BOOST_TEST(ac == 16); -#endif ac = a; ac += +a; BOOST_TEST(ac == 16); @@ -656,10 +647,6 @@ void test() ac += b*c; BOOST_TEST(ac == 8 + 64 * 500); ac = a; -#ifndef TEST_E_FLOAT - ac = ac - "8"; - BOOST_TEST(ac == 0); -#endif ac = a; ac -= +a; BOOST_TEST(ac == 0); @@ -678,12 +665,7 @@ void test() ac = a; ac -= ac * b; BOOST_TEST(ac == 8 - 8 * 64); -#ifndef TEST_E_FLOAT - ac = a * "8"; - BOOST_TEST(ac == 64); -#else ac = a * 8; -#endif ac *= +a; BOOST_TEST(ac == 64 * 8); ac = a; @@ -698,10 +680,6 @@ void test() ac = a; ac *= b + c; BOOST_TEST(ac == 8 * (64 + 500)); -#ifndef TEST_E_FLOAT - ac = b / "8"; - BOOST_TEST(ac == 8); -#endif ac = b; ac /= +a; BOOST_TEST(ac == 8); @@ -714,10 +692,6 @@ void test() ac = b; ac /= a + Real(0); BOOST_TEST(ac == 8); -#ifndef TEST_E_FLOAT - ac = a + std::string("8"); - BOOST_TEST(ac == 16); -#endif // // simple tests with immediate values, these calls can be optimised in many backends: // From 23bc9e5f5067a6783b4c4603a6b890d48e1df027 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 25 Sep 2011 11:11:14 +0000 Subject: [PATCH 022/256] Fix coding errors undetected by MSVC, get everything compiling with GCC. [SVN r74559] --- include/boost/math/big_number.hpp | 12 ++--- .../boost/math/big_number/big_number_base.hpp | 13 +++-- include/boost/math/big_number/default_ops.hpp | 54 +++++++++---------- math/test/Jamfile.v2 | 9 +++- math/test/test_arithmetic.cpp | 46 +++++++++++----- math/test/test_numeric_limits.cpp | 4 ++ 6 files changed, 85 insertions(+), 53 deletions(-) diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp index 86a9ad1e..6b84e39b 100644 --- a/include/boost/math/big_number.hpp +++ b/include/boost/math/big_number.hpp @@ -128,7 +128,7 @@ public: if(contains_self(e)) { self_type temp(e); - do_subtract(temp, typename detail_of::type()); + do_subtract(temp, typename self_type::tag_type()); } else { @@ -193,7 +193,7 @@ public: if(contains_self(e)) { self_type temp(e); - do_modulus(temp, typename detail_of::type()); + do_modulus(temp, typename self_type::tag_type()); } else { @@ -280,7 +280,7 @@ public: if(contains_self(e)) { self_type temp(e); - do_divide(detail::big_number_exp(temp), typename detail_of::type()); + do_divide(detail::big_number_exp(temp), typename self_type::tag_type()); } else { @@ -312,7 +312,7 @@ public: if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_bitwise_and(temp, typename detail_of::type()); + do_bitwise_and(temp, typename self_type::tag_type()); } else { @@ -344,7 +344,7 @@ public: if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_bitwise_or(temp, typename detail_of::type()); + do_bitwise_or(temp, typename self_type::tag_type()); } else { @@ -374,7 +374,7 @@ public: if(contains_self(e)) { self_type temp(e); - do_bitwise_xor(temp, typename detail_of::type()); + do_bitwise_xor(temp, typename self_type::tag_type()); } else { diff --git a/include/boost/math/big_number/big_number_base.hpp b/include/boost/math/big_number/big_number_base.hpp index 4053c0b8..8eef7048 100644 --- a/include/boost/math/big_number/big_number_base.hpp +++ b/include/boost/math/big_number/big_number_base.hpp @@ -179,7 +179,10 @@ struct arg_type > }; template -void unmentionable_proc(){} +struct unmentionable +{ + static void proc(){} +}; typedef void (*unmentionable_type)(); @@ -226,7 +229,7 @@ struct big_number_exp operator unmentionable_type()const { result_type r(*this); - return r ? unmentionable_proc : 0; + return r ? &unmentionable::proc : 0; } private: @@ -248,7 +251,7 @@ struct big_number_exp operator unmentionable_type()const { - return arg ? unmentionable_proc : 0; + return arg ? &unmentionable::proc : 0; } private: @@ -276,7 +279,7 @@ struct big_number_exp operator unmentionable_type()const { result_type r(*this); - return r ? unmentionable_proc : 0; + return r ? &unmentionable::proc : 0; } static const unsigned left_depth = left_type::depth + 1; @@ -315,7 +318,7 @@ struct big_number_exp operator unmentionable_type()const { result_type r(*this); - return r ? unmentionable_proc : 0; + return r ? &unmentionable::proc : 0; } static const unsigned left_depth = left_type::depth + 1; diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp index 52047256..ea034e00 100644 --- a/include/boost/math/big_number/default_ops.hpp +++ b/include/boost/math/big_number/default_ops.hpp @@ -501,10 +501,10 @@ inline int itrunc(const big_number& v, const Policy& pol) return policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } -template -inline long ltrunc(const detail::big_number_exp& v, const Policy& pol) +template +inline long ltrunc(const detail::big_number_exp& v, const Policy& pol) { - typedef typename detail::expression_type::type number_type; + typedef typename detail::big_number_exp::result_result number_type; number_type r = trunc(v, pol); if(fabs(r) > (std::numeric_limits::max)()) return policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); @@ -519,10 +519,10 @@ inline long ltrunc(const big_number& v, const Policy& pol) return r.template convert_to(); } #ifndef BOOST_NO_LONG_LONG -template -inline long long lltrunc(const detail::big_number_exp& v, const Policy& pol) +template +inline long long lltrunc(const detail::big_number_exp& v, const Policy& pol) { - typedef typename detail::expression_type::type number_type; + typedef typename detail::big_number_exp::result_result number_type; number_type r = trunc(v, pol); if(fabs(r) > (std::numeric_limits::max)()) return policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); @@ -537,10 +537,10 @@ inline long long lltrunc(const big_number& v, const Policy& pol) return r.template convert_to(); } #endif -template -inline int iround(const detail::big_number_exp& v, const Policy& pol) +template +inline int iround(const detail::big_number_exp& v, const Policy& pol) { - typedef typename detail::expression_type::type number_type; + typedef typename detail::big_number_exp::result_result number_type; number_type r = round(v, pol); if(fabs(r) > (std::numeric_limits::max)()) return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); @@ -554,10 +554,10 @@ inline int iround(const big_number& v, const Policy& pol) return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } -template -inline long lround(const detail::big_number_exp& v, const Policy& pol) +template +inline long lround(const detail::big_number_exp& v, const Policy& pol) { - typedef typename detail::expression_type::type number_type; + typedef typename detail::big_number_exp::result_result number_type; number_type r = round(v, pol); if(fabs(r) > (std::numeric_limits::max)()) return policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); @@ -572,10 +572,10 @@ inline long lround(const big_number& v, const Policy& pol) return r.template convert_to(); } #ifndef BOOST_NO_LONG_LONG -template -inline long long llround(const detail::big_number_exp& v, const Policy& pol) +template +inline long long llround(const detail::big_number_exp& v, const Policy& pol) { - typedef typename detail::expression_type::type number_type; + typedef typename detail::big_number_exp::result_result number_type; number_type r = round(v, pol); if(fabs(r) > (std::numeric_limits::max)()) return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); @@ -656,14 +656,14 @@ template \ detail::big_number_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , big_number\ + , big_number \ > \ func(const big_number& arg)\ {\ return detail::big_number_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , big_number\ + , big_number \ >(\ detail::BOOST_JOIN(func, _funct)() \ , arg \ @@ -734,15 +734,15 @@ detail::big_number_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , detail::big_number_exp \ - , big_number\ ->\ + , big_number \ +> \ func(const detail::big_number_exp& arg, const big_number& a)\ {\ return detail::big_number_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , detail::big_number_exp \ - , big_number\ + , big_number \ >(\ detail::BOOST_JOIN(func, _funct)() \ , arg,\ @@ -755,7 +755,7 @@ detail::big_number_exp<\ , detail::BOOST_JOIN(func, _funct) >::type> \ , detail::big_number_exp \ , detail::big_number_exp \ ->\ +> \ func(const detail::big_number_exp& arg, const detail::big_number_exp& a)\ {\ return detail::big_number_exp<\ @@ -775,7 +775,7 @@ typename enable_if<\ detail::big_number_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , big_number\ + , big_number \ , Arithmetic\ > \ >::type \ @@ -784,7 +784,7 @@ func(const big_number& arg, const Arithmetic& a)\ return detail::big_number_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , big_number\ + , big_number \ , Arithmetic\ >(\ detail::BOOST_JOIN(func, _funct)() \ @@ -837,7 +837,7 @@ detail::big_number_exp<\ , detail::BOOST_JOIN(func, _funct) >::type> \ , detail::big_number_exp \ , Arg2\ ->\ +> \ func(const detail::big_number_exp& arg, Arg2 const& a)\ {\ return detail::big_number_exp<\ @@ -854,15 +854,15 @@ template \ detail::big_number_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , big_number\ + , big_number \ , Arg2\ ->\ +> \ func(const big_number& arg, Arg2 const& a)\ {\ return detail::big_number_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , big_number\ + , big_number \ , Arg2\ >(\ detail::BOOST_JOIN(func, _funct)() \ diff --git a/math/test/Jamfile.v2 b/math/test/Jamfile.v2 index b37662be..24b697e7 100644 --- a/math/test/Jamfile.v2 +++ b/math/test/Jamfile.v2 @@ -170,6 +170,7 @@ run test_numeric_limits.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : test_numeric_limits_mpfr_50 ; + run test_numeric_limits.cpp $(E_FLOAT_SRC) : # command line : # input files @@ -178,5 +179,11 @@ run test_numeric_limits.cpp $(E_FLOAT_SRC) [ check-target-builds ../config//has_e_float : : no ] : test_numeric_limits_e_float ; - +run big_number_concept_check.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : big_number_concept_check_mpfr_50 ; diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 559ec81c..5bca68e6 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -53,8 +53,25 @@ BOOST_LIGHTWEIGHT_TEST_OSTREAM << e.what() << std::endl;\ } -template -void test_integer_ops(const boost::mpl::int_&){} +bool isfloat(float){ return true; } +bool isfloat(double){ return true; } +bool isfloat(long double){ return true; } +template bool isfloat(T){ return false; } + +#define BOOST_TEST_CLOSE(x, y, tol)\ + if(x == 0){\ + BOOST_TEST(y == 0); }\ + else if(!isfloat(x)){\ + BOOST_TEST(x == y); }\ + else if((x != y) && (::fabsl(static_cast((x-y)/x)) > tol))\ + {\ + BOOST_ERROR("Expected tolerance was exceeded: ");\ + BOOST_LIGHTWEIGHT_TEST_OSTREAM << std::setprecision(34) << "(x-y)/x = " << ::fabsl(static_cast((x-y)/x)) \ + << " tolerance = " << tol << std::endl;\ + } + +template +void test_integer_ops(const T&){} template void test_integer_ops(const boost::mpl::int_&) @@ -249,8 +266,8 @@ void test_integer_ops(const boost::mpl::int_&) BOOST_TEST(abs(+a) == 20); } -template -void test_real_ops(const boost::mpl::int_&){} +template +void test_real_ops(const T&){} template void test_real_ops(const boost::mpl::int_&) @@ -365,10 +382,10 @@ void test_negative_mixed(boost::mpl::true_ const&) BOOST_TEST(n2 == Real(n2)); BOOST_TEST(n3 == Real(n3)); BOOST_TEST(n4 == Real(n4)); - BOOST_TEST(n1 == boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value))); - BOOST_TEST(n2 == boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value))); - BOOST_TEST(n3 == boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value))); - BOOST_TEST(n4 == boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value))); + BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), 3 * std::numeric_limits::epsilon()); + BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); + BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); + BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); // Assignment: Real r(0); BOOST_TEST(r != n1); @@ -461,10 +478,11 @@ void test_mixed() BOOST_TEST(n2 == Real(n2)); BOOST_TEST(n3 == Real(n3)); BOOST_TEST(n4 == Real(n4)); - BOOST_TEST(n1 == boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value))); - BOOST_TEST(n2 == boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value))); - BOOST_TEST(n3 == boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value))); - BOOST_TEST(n4 == boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value))); + std::cout << Real(n1).str(0, boost::is_floating_point::value) << std::endl; + BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), 3 * std::numeric_limits::epsilon()); + BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); + BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); + BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); // Assignment: Real r(0); BOOST_TEST(r != n1); @@ -538,11 +556,11 @@ void test() // // Integer only functions: // - test_integer_ops(boost::math::number_category()); + test_integer_ops(typename boost::math::number_category::type()); // // Real number only functions: // - test_real_ops(boost::math::number_category()); + test_real_ops(typename boost::math::number_category::type()); // // Test basic arithmetic: // diff --git a/math/test/test_numeric_limits.cpp b/math/test/test_numeric_limits.cpp index 00bb19e2..08d1c32f 100644 --- a/math/test/test_numeric_limits.cpp +++ b/math/test/test_numeric_limits.cpp @@ -51,10 +51,14 @@ void test() PRINT(is_specialized); PRINT(min()); PRINT(max()); +#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST PRINT(lowest()); +#endif PRINT(digits); PRINT(digits10); +#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST PRINT(max_digits10); +#endif PRINT(is_signed); PRINT(is_integer); PRINT(is_exact); From 377971fae44d8d161deed9560f58a7a0fd26dc14 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 25 Sep 2011 12:35:40 +0000 Subject: [PATCH 023/256] Fix remaining GCC test failures, plus a few warnings. [SVN r74562] --- include/boost/math/big_number/mpfr.hpp | 4 ---- math/test/test_arithmetic.cpp | 26 ++++++++++++++++++-------- 2 files changed, 18 insertions(+), 12 deletions(-) diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp index e03f05da..31165841 100644 --- a/include/boost/math/big_number/mpfr.hpp +++ b/include/boost/math/big_number/mpfr.hpp @@ -67,13 +67,9 @@ struct mpfr_real_imp while(i) { mpfr_set_ui(t, static_cast(i & mask), GMP_RNDN); - long e; - const char* ps = mpfr_get_str (0, &e, 10, 0, t, GMP_RNDN); if(shift) mpfr_mul_2exp(t, t, shift, GMP_RNDN); - ps = mpfr_get_str (0, &e, 10, 0, t, GMP_RNDN); mpfr_add(m_data, m_data, t, GMP_RNDN); - ps = mpfr_get_str (0, &e, 10, 0, m_data, GMP_RNDN); shift += std::numeric_limits::digits; i >>= std::numeric_limits::digits; } diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp index 5bca68e6..5e267eba 100644 --- a/math/test/test_arithmetic.cpp +++ b/math/test/test_arithmetic.cpp @@ -382,10 +382,15 @@ void test_negative_mixed(boost::mpl::true_ const&) BOOST_TEST(n2 == Real(n2)); BOOST_TEST(n3 == Real(n3)); BOOST_TEST(n4 == Real(n4)); - BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), 3 * std::numeric_limits::epsilon()); - BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); - BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); - BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) + Num tol = 10 * std::numeric_limits::epsilon(); +#else + Num tol = 0; +#endif + BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), tol); + BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), 0); + BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), 0); + BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), 0); // Assignment: Real r(0); BOOST_TEST(r != n1); @@ -479,10 +484,15 @@ void test_mixed() BOOST_TEST(n3 == Real(n3)); BOOST_TEST(n4 == Real(n4)); std::cout << Real(n1).str(0, boost::is_floating_point::value) << std::endl; - BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), 3 * std::numeric_limits::epsilon()); - BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); - BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); - BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), std::numeric_limits::epsilon()); +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) + Num tol = 10 * std::numeric_limits::epsilon(); +#else + Num tol = 0; +#endif + BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), tol); + BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), 0); + BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), 0); + BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), 0); // Assignment: Real r(0); BOOST_TEST(r != n1); From 09e1fd8f771138fba4f7c2014adee1c8c73b2411 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 26 Sep 2011 16:29:44 +0000 Subject: [PATCH 024/256] Giant file and directory rename: changed directory name from math to multiprecision and updated code to match. [SVN r74578] --- .../multiprecision/arithmetic_backend.hpp | 147 ++ .../multiprecision/backends/functions/pow.hpp | 97 + .../concepts/big_number_architypes.hpp | 293 +++ .../multiprecision/detail/big_number_base.hpp | 983 +++++++++++ .../multiprecision/detail/default_ops.hpp | 903 ++++++++++ include/boost/multiprecision/e_float.hpp | 80 + include/boost/multiprecision/gmp.hpp | 1532 ++++++++++++++++ include/boost/multiprecision/mp_number.hpp | 1570 +++++++++++++++++ include/boost/multiprecision/mpfr.hpp | 952 ++++++++++ 9 files changed, 6557 insertions(+) create mode 100644 include/boost/multiprecision/arithmetic_backend.hpp create mode 100644 include/boost/multiprecision/backends/functions/pow.hpp create mode 100644 include/boost/multiprecision/concepts/big_number_architypes.hpp create mode 100644 include/boost/multiprecision/detail/big_number_base.hpp create mode 100644 include/boost/multiprecision/detail/default_ops.hpp create mode 100644 include/boost/multiprecision/e_float.hpp create mode 100644 include/boost/multiprecision/gmp.hpp create mode 100644 include/boost/multiprecision/mp_number.hpp create mode 100644 include/boost/multiprecision/mpfr.hpp diff --git a/include/boost/multiprecision/arithmetic_backend.hpp b/include/boost/multiprecision/arithmetic_backend.hpp new file mode 100644 index 00000000..54d452ec --- /dev/null +++ b/include/boost/multiprecision/arithmetic_backend.hpp @@ -0,0 +1,147 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MATH_ARITH_BACKEND_HPP +#define BOOST_MATH_ARITH_BACKEND_HPP + +#include +#include +#include +#include +#include + +namespace boost{ +namespace math{ + +template +struct arithmetic_backend +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + arithmetic_backend(){} + arithmetic_backend(const arithmetic_backend& o) + { + m_value = o.m_value; + } + arithmetic_backend(const Arithmetic& o) : m_value(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + arithmetic_backend(arithmetic_backend&& o) : m_value(o.m_value) {} + arithmetic_backend(Arithmetic&& o) : m_value(o) {} +#endif + arithmetic_backend& operator = (const arithmetic_backend& o) + { + m_value = o.m_value; + return *this; + } + arithmetic_backend& operator = (boost::uintmax_t i) + { + m_value = i; + return *this; + } + arithmetic_backend& operator = (boost::intmax_t i) + { + m_value = i; + return *this; + } + arithmetic_backend& operator = (long double d) + { + m_value = d; + return *this; + } + arithmetic_backend& operator = (const char* s) + { + m_value = boost::lexical_cast(s); + return *this; + } + void swap(arithmetic_backend& o) + { + std::swap(m_value, o.m_value); + } + std::string str(unsigned digits, bool scientific)const + { + return boost::lexical_cast(m_value); + } + void negate() + { + m_value = -m_value; + } + int compare(const arithmetic_backend& o)const + { + return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); + } + int compare(boost::intmax_t i)const + { + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(boost::uintmax_t i)const + { + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(long double d)const + { + return m_value > d ? 1 : (m_value < d ? -1 : 0); + } + Arithmetic& data() { return m_value; } + const Arithmetic& data()const { return m_value; } +private: + Arithmetic m_value; +}; + +template +inline void add(arithmetic_backend& result, const arithmetic_backend& o) +{ + result.data() += o.data(); +} +template +inline void subtract(arithmetic_backend& result, const arithmetic_backend& o) +{ + result.data() -= o.data(); +} +template +inline void multiply(arithmetic_backend& result, const arithmetic_backend& o) +{ + result.data() *= o.data(); +} +template +inline void divide(arithmetic_backend& result, const arithmetic_backend& o) +{ + result.data() /= o.data(); +} + +}} // namespaces + + +namespace std{ + +#ifdef BOOST_NO_NOEXCEPT +# define noexcept +#endif + +template +class numeric_limits > > : public std::numeric_limits +{ + typedef std::numeric_limits base_type; + typedef boost::math::mp_number > number_type; +public: + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return base_type::denorm_min(); } +}; + +#ifdef BOOST_NO_NOEXCEPT +# undef noexcept +#endif + +} + +#endif diff --git a/include/boost/multiprecision/backends/functions/pow.hpp b/include/boost/multiprecision/backends/functions/pow.hpp new file mode 100644 index 00000000..48d10c15 --- /dev/null +++ b/include/boost/multiprecision/backends/functions/pow.hpp @@ -0,0 +1,97 @@ + +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Distributed under the Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) + +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +// +// This file has no include guards or namespaces - it's expanded inline inside default_ops.hpp +// + +template +inline void eval_pow(T& result, const T& t, const T& p) +{ +} + +namespace detail{ + +template +inline T pow_imp(T& result, const T& t, const U& p, const mpl::false_&) +{ + T temp(p); + eval_pow(result, t, p); +} + +template +inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) +{ + // Compute the pure power of typename T t^p. Binary splitting of the power is + // used. The resulting computational complexity has the order of log2[abs(p)]. + + typedef typename mpl::front::type int_type; + + if(p < 0) + { + T temp; + temp = static_cast(1); + T denom; + pow_imp(denom, t, -p, mpl::true_()); + divide(result, temp, denom); + } + + switch(p) + { + case 0: + result = static_cast(1); + break; + case 1: + result = t; + break; + case 2: + multiply(result, t, t); + break; + case 3: + multiply(result, t, t); + multiply(result, t); + break; + case 4: + multiply(result, t, t); + multiply(result, result); + break; + default: + { + result = t; + U n; + + for(n = static_cast(1); n <= static_cast(p / static_cast(2)); n *= static_cast(2)) + { + multiply(result, result); + } + + const U p_minus_n = static_cast(p - n); + + // Call the function recursively for computing the remaining power of n. + if(p_minus_n) + { + T temp; + pow_imp(temp, t, p_minus_n, mpl::true_()); + multiply(result, temp); + } + } + } +} + +} // namespace detail + +template +inline void eval_pow(T& result, const T& t, const U& p) +{ + typedef typename is_integral::type tag_type; + detail::pow_imp(result, t, p, tag_type()); +} + + diff --git a/include/boost/multiprecision/concepts/big_number_architypes.hpp b/include/boost/multiprecision/concepts/big_number_architypes.hpp new file mode 100644 index 00000000..f13c2c7e --- /dev/null +++ b/include/boost/multiprecision/concepts/big_number_architypes.hpp @@ -0,0 +1,293 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MATH_CONCEPTS_ER_HPP +#define BOOST_MATH_CONCEPTS_ER_HPP + +#include +#include +#include +#include +#include +#include +#include + +namespace boost{ +namespace math{ +namespace concepts{ + +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4244) +#endif + +struct big_number_backend_real_architype +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + big_number_backend_real_architype() + { + std::cout << "Default construct" << std::endl; + } + big_number_backend_real_architype(const big_number_backend_real_architype& o) + { + std::cout << "Copy construct" << std::endl; + m_value = o.m_value; + } + big_number_backend_real_architype& operator = (const big_number_backend_real_architype& o) + { + m_value = o.m_value; + std::cout << "Assignment (" << m_value << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (boost::uintmax_t i) + { + m_value = i; + std::cout << "UInt Assignment (" << i << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (boost::intmax_t i) + { + m_value = i; + std::cout << "Int Assignment (" << i << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (long double d) + { + m_value = d; + std::cout << "long double Assignment (" << d << ")" << std::endl; + return *this; + } + big_number_backend_real_architype& operator = (const char* s) + { + m_value = boost::lexical_cast(s); + std::cout << "const char* Assignment (" << s << ")" << std::endl; + return *this; + } + void swap(big_number_backend_real_architype& o) + { + std::cout << "Swapping (" << m_value << " with " << o.m_value << ")" << std::endl; + std::swap(m_value, o.m_value); + } + std::string str(unsigned digits, bool scientific)const + { + std::stringstream ss; + if(scientific) + ss.setf(ss.scientific); + if(digits) + ss.precision(digits); + else + ss.precision(std::numeric_limits::digits10 + 2); + boost::intmax_t i = m_value; + boost::uintmax_t u = m_value; + if(!scientific && m_value == i) + ss << i; + else if(!scientific && m_value == u) + ss << u; + else + ss << m_value; + std::string s = ss.str(); + std::cout << "Converting to string (" << s << ")" << std::endl; + return s; + } + void negate() + { + std::cout << "Negating (" << m_value << ")" << std::endl; + m_value = -m_value; + } + int compare(const big_number_backend_real_architype& o)const + { + std::cout << "Comparison" << std::endl; + return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); + } + int compare(boost::intmax_t i)const + { + std::cout << "Comparison with int" << std::endl; + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(boost::uintmax_t i)const + { + std::cout << "Comparison with unsigned" << std::endl; + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(long double d)const + { + std::cout << "Comparison with long double" << std::endl; + return m_value > d ? 1 : (m_value < d ? -1 : 0); + } + long double m_value; +}; + +inline void add(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +{ + std::cout << "Addition (" << result.m_value << " += " << o.m_value << ")" << std::endl; + result.m_value += o.m_value; +} +inline void subtract(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +{ + std::cout << "Subtraction (" << result.m_value << " -= " << o.m_value << ")" << std::endl; + result.m_value -= o.m_value; +} +inline void multiply(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +{ + std::cout << "Multiplication (" << result.m_value << " *= " << o.m_value << ")" << std::endl; + result.m_value *= o.m_value; +} +inline void divide(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +{ + std::cout << "Division (" << result.m_value << " /= " << o.m_value << ")" << std::endl; + result.m_value /= o.m_value; +} + +inline void eval_frexp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg, int* exp) +{ + result = std::frexp(arg.m_value, exp); +} + +inline void eval_ldexp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg, int exp) +{ + result = std::ldexp(arg.m_value, exp); +} + +inline void eval_floor(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::floor(arg.m_value); +} + +inline void eval_ceil(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::ceil(arg.m_value); +} + +inline void eval_trunc(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = boost::math::trunc(arg.m_value); +} + +inline void eval_sqrt(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::sqrt(arg.m_value); +} + +inline void eval_abs(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::abs(arg.m_value); +} + +inline void eval_fabs(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::fabs(arg.m_value); +} + +inline int eval_fpclassify(const big_number_backend_real_architype& arg) +{ + return boost::math::fpclassify(arg.m_value); +} + +inline void eval_pow(big_number_backend_real_architype& result, const big_number_backend_real_architype& b, const big_number_backend_real_architype& e) +{ + result = std::pow(b.m_value, e.m_value); +} + +inline void eval_pow(big_number_backend_real_architype& result, const big_number_backend_real_architype& b, int e) +{ + result = std::pow(b.m_value, e); +} + +inline void eval_exp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::exp(arg.m_value); +} + +inline void eval_log(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::log(arg.m_value); +} + +inline void eval_sin(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::sin(arg.m_value); +} + +inline void eval_cos(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::cos(arg.m_value); +} + +inline void eval_tan(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::tan(arg.m_value); +} + +inline void eval_asin(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::asin(arg.m_value); +} + +inline void eval_acos(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::acos(arg.m_value); +} + +inline void eval_atan(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::atan(arg.m_value); +} + +inline void eval_sinh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::sinh(arg.m_value); +} + +inline void eval_cosh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::cosh(arg.m_value); +} + +inline void eval_tanh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +{ + result = std::tanh(arg.m_value); +} + +typedef boost::math::mp_number big_number_real_architype; + +}}} // namespaces + +namespace std{ + +#ifdef BOOST_NO_NOEXCEPT +# define noexcept +#endif + +template <> +class numeric_limits : public std::numeric_limits +{ + typedef std::numeric_limits base_type; + typedef boost::math::concepts::big_number_real_architype number_type; +public: + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return base_type::denorm_min(); } +}; + +#ifdef BOOST_NO_NOEXCEPT +# undef noexcept +#endif + +} + +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + +#endif diff --git a/include/boost/multiprecision/detail/big_number_base.hpp b/include/boost/multiprecision/detail/big_number_base.hpp new file mode 100644 index 00000000..c8fcd9cf --- /dev/null +++ b/include/boost/multiprecision/detail/big_number_base.hpp @@ -0,0 +1,983 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_BIG_NUM_BASE_HPP +#define BOOST_MATH_BIG_NUM_BASE_HPP + +#include +#include +#include + +namespace boost{ namespace math{ + +template +class mp_number; + +namespace detail{ + +// Forward-declare an expression wrapper +template +struct mp_exp; + +template +struct has_enough_bits +{ + template + struct type : public mpl::bool_::digits >= b>{}; +}; + +template +struct canonical_imp +{ + typedef Val type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::signed_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::unsigned_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::real_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef const char* type; +}; + +template +struct canonical +{ + typedef typename mpl::if_< + is_signed, + mpl::int_<0>, + typename mpl::if_< + is_unsigned, + mpl::int_<1>, + typename mpl::if_< + is_floating_point, + mpl::int_<2>, + typename mpl::if_< + mpl::or_< + is_convertible, + is_same + >, + mpl::int_<3>, + mpl::int_<4> + >::type + >::type + >::type + >::type tag_type; + + typedef typename canonical_imp::type type; +}; + +struct terminal{}; +struct negate{}; +struct plus{}; +struct minus{}; +struct multiplies{}; +struct divides{}; +struct modulus{}; +struct shift_left{}; +struct shift_right{}; +struct bitwise_and{}; +struct bitwise_or{}; +struct bitwise_xor{}; +struct bitwise_complement{}; +struct add_immediates{}; +struct subtract_immediates{}; +struct multiply_immediates{}; +struct divide_immediates{}; +struct modulus_immediates{}; +struct bitwise_and_immediates{}; +struct bitwise_or_immediates{}; +struct bitwise_xor_immediates{}; +struct complement_immediates{}; +struct function{}; + +template +struct backend_type; + +template +struct backend_type > +{ + typedef T type; +}; + +template +struct backend_type > +{ + typedef typename backend_type::result_type>::type type; +}; + + +template +struct is_big_number : public mpl::false_{}; +template +struct is_big_number > : public mpl::true_{}; +template +struct is_big_number_exp : public mpl::false_{}; +template +struct is_big_number_exp > : public mpl::true_{}; + +template +struct combine_expression; + +template +struct combine_expression, T2> +{ + typedef mp_number type; +}; + +template +struct combine_expression > +{ + typedef mp_number type; +}; + +template +struct combine_expression, mp_number > +{ + typedef mp_number type; +}; + +template +struct arg_type +{ + typedef mp_exp type; +}; + +template +struct arg_type > +{ + typedef mp_exp type; +}; + +template +struct unmentionable +{ + static void proc(){} +}; + +typedef void (*unmentionable_type)(); + +template +struct big_number_exp_storage +{ + typedef const T& type; +}; + +template +struct big_number_exp_storage +{ + typedef T* type; +}; + +template +struct big_number_exp_storage +{ + typedef const T* type; +}; + +template +struct big_number_exp_storage > +{ + typedef mp_exp type; +}; + +template +struct mp_exp +{ + typedef mpl::int_<1> arity; + typedef typename arg_type::type left_type; + typedef typename left_type::result_type result_type; + typedef tag tag_type; + + mp_exp(const Arg1& a) : arg(a) {} + + left_type left()const { return arg; } + + const Arg1& left_ref()const{ return arg; } + + static const unsigned depth = left_type::depth + 1; + + operator unmentionable_type()const + { + result_type r(*this); + return r ? &unmentionable::proc : 0; + } + +private: + typename big_number_exp_storage::type arg; +}; + +template +struct mp_exp +{ + typedef mpl::int_<0> arity; + typedef Arg1 result_type; + typedef terminal tag_type; + + mp_exp(const Arg1& a) : arg(a) {} + + const Arg1& value()const { return arg; } + + static const unsigned depth = 0; + + operator unmentionable_type()const + { + return arg ? &unmentionable::proc : 0; + } + +private: + typename big_number_exp_storage::type arg; +}; + +template +struct mp_exp +{ + typedef mpl::int_<2> arity; + typedef typename arg_type::type left_type; + typedef typename arg_type::type right_type; + typedef typename left_type::result_type left_result_type; + typedef typename right_type::result_type right_result_type; + typedef typename combine_expression::type result_type; + typedef tag tag_type; + + mp_exp(const Arg1& a1, const Arg2& a2) : arg1(a1), arg2(a2) {} + + left_type left()const { return arg1; } + right_type right()const { return arg2; } + const Arg1& left_ref()const{ return arg1; } + const Arg2& right_ref()const{ return arg2; } + + operator unmentionable_type()const + { + result_type r(*this); + return r ? &unmentionable::proc : 0; + } + + static const unsigned left_depth = left_type::depth + 1; + static const unsigned right_depth = right_type::depth + 1; + static const unsigned depth = left_depth > right_depth ? left_depth : right_depth; +private: + typename big_number_exp_storage::type arg1; + typename big_number_exp_storage::type arg2; +}; + +template +struct mp_exp +{ + typedef mpl::int_<3> arity; + typedef typename arg_type::type left_type; + typedef typename arg_type::type middle_type; + typedef typename arg_type::type right_type; + typedef typename left_type::result_type left_result_type; + typedef typename middle_type::result_type middle_result_type; + typedef typename right_type::result_type right_result_type; + typedef typename combine_expression< + left_result_type, + typename combine_expression::type + >::type result_type; + typedef tag tag_type; + + mp_exp(const Arg1& a1, const Arg2& a2, const Arg3& a3) : arg1(a1), arg2(a2), arg3(a3) {} + + left_type left()const { return arg1; } + middle_type middle()const { return arg2; } + right_type right()const { return arg3; } + const Arg1& left_ref()const{ return arg1; } + const Arg2& middle_ref()const{ return arg2; } + const Arg3& right_ref()const{ return arg3; } + + operator unmentionable_type()const + { + result_type r(*this); + return r ? &unmentionable::proc : 0; + } + + static const unsigned left_depth = left_type::depth + 1; + static const unsigned middle_depth = middle_type::depth + 1; + static const unsigned right_depth = right_type::depth + 1; + static const unsigned depth = left_depth > right_depth ? (left_depth > middle_depth ? left_depth : middle_depth) : (right_depth > middle_depth ? right_depth : middle_depth); +private: + typename big_number_exp_storage::type arg1; + typename big_number_exp_storage::type arg2; + typename big_number_exp_storage::type arg3; +}; + +} // namespace detail + +// +// Non-member operators for mp_number: +// +// Unary operators first: +// +template +inline const mp_number& operator + (const mp_number& v) { return v; } +template +inline const detail::mp_exp& operator + (const detail::mp_exp& v) { return v; } +template +inline detail::mp_exp > operator - (const mp_number& v) { return v; } +template +inline detail::mp_exp > operator - (const detail::mp_exp& v) { return v; } +template +inline detail::mp_exp > operator ~ (const mp_number& v) { return v; } +template +inline detail::mp_exp > operator ~ (const detail::mp_exp& v) { return v; } +// +// Then addition: +// +template +inline detail::mp_exp, mp_number > + operator + (const mp_number& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator + (const mp_number& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator + (const V& a, const mp_number& b) +{ + return detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator + (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, mp_number > + operator + (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator + (const detail::mp_exp& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator + (const detail::mp_exp& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator + (const V& a, const detail::mp_exp& b) +{ + return detail::mp_exp >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::mp_exp, typename detail::mp_exp::left_type > + operator + (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); +} +template +inline detail::mp_exp, typename detail::mp_exp::left_type > + operator + (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref()); +} +template +inline detail::mp_exp, mp_number > + operator + (const mp_number& a, const detail::mp_exp >& b) +{ + return detail::mp_exp, mp_number >(a, b.left_ref()); +} +template +inline detail::mp_exp, mp_number > + operator + (const detail::mp_exp >& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(b, a.left_ref()); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator + (const detail::mp_exp >& a, const V& b) +{ + return detail::mp_exp >(b, a.left_ref()); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator + (const V& a, const detail::mp_exp >& b) +{ + return detail::mp_exp, mp_number >(a, b.left_ref()); +} +// +// Subtraction: +// +template +inline detail::mp_exp, mp_number > + operator - (const mp_number& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator - (const mp_number& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator - (const V& a, const mp_number& b) +{ + return detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator - (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, mp_number > + operator - (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator - (const detail::mp_exp& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator - (const detail::mp_exp& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator - (const V& a, const detail::mp_exp& b) +{ + return detail::mp_exp >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::mp_exp, typename detail::mp_exp::left_type > + operator - (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); +} +template +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator - (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref()); +} +template +inline detail::mp_exp, mp_number > + operator - (const mp_number& a, const detail::mp_exp >& b) +{ + return detail::mp_exp, mp_number >(a, b.left_ref()); +} +template +inline detail::mp_exp, mp_number > > + operator - (const detail::mp_exp >& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(b, a.left_ref()); +} +template +inline typename enable_if, detail::mp_exp, V > > >::type + operator - (const detail::mp_exp >& a, const V& b) +{ + return detail::mp_exp >(b, a.left_ref()); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator - (const V& a, const detail::mp_exp >& b) +{ + return detail::mp_exp >(a, b.left_ref()); +} +// +// Multiplication: +// +template +inline detail::mp_exp, mp_number > + operator * (const mp_number& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator * (const mp_number& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator * (const V& a, const mp_number& b) +{ + return detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator * (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, mp_number > + operator * (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator * (const detail::mp_exp& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator * (const detail::mp_exp& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator * (const V& a, const detail::mp_exp& b) +{ + return detail::mp_exp >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator * (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, typename detail::mp_exp::left_type > (a, b.left_ref()); +} +template +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator * (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref()); +} +template +inline detail::mp_exp, mp_number > > + operator * (const mp_number& a, const detail::mp_exp >& b) +{ + return detail::mp_exp, mp_number >(a, b.left_ref()); +} +template +inline detail::mp_exp, mp_number > > + operator * (const detail::mp_exp >& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(b, a.left_ref()); +} +template +inline typename enable_if, detail::mp_exp, V > > >::type + operator * (const detail::mp_exp >& a, const V& b) +{ + return detail::mp_exp, V >(a.left_ref(), b); +} +template +inline typename enable_if, detail::mp_exp, V > > >::type + operator * (const V& a, const detail::mp_exp >& b) +{ + return detail::mp_exp, V >(b.left_ref(), a); +} +// +// Division: +// +template +inline detail::mp_exp, mp_number > + operator / (const mp_number& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator / (const mp_number& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator / (const V& a, const mp_number& b) +{ + return detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator / (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, mp_number > + operator / (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator / (const detail::mp_exp& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator / (const detail::mp_exp& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator / (const V& a, const detail::mp_exp& b) +{ + return detail::mp_exp >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator / (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); +} +template +inline detail::mp_exp::left_type, mp_number > > + operator / (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp::left_type, mp_number >(a.left_ref(), b); +} +template +inline detail::mp_exp, mp_number > > + operator / (const mp_number& a, const detail::mp_exp >& b) +{ + return detail::mp_exp, mp_number >(a, b.left_ref()); +} +template +inline detail::mp_exp, mp_number > > + operator / (const detail::mp_exp >& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a.left_ref(), b); +} +template +inline typename enable_if, detail::mp_exp, V > > >::type + operator / (const detail::mp_exp >& a, const V& b) +{ + return detail::mp_exp, V>(a.left_ref(), b); +} +template +inline typename enable_if, detail::mp_exp > > >::type + operator / (const V& a, const detail::mp_exp >& b) +{ + return detail::mp_exp >(a, b.left_ref()); +} +// +// Modulus: +// +template +inline detail::mp_exp, mp_number > + operator % (const mp_number& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator % (const mp_number& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator % (const V& a, const mp_number& b) +{ + return detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator % (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, mp_number > + operator % (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator % (const detail::mp_exp& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator % (const detail::mp_exp& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator % (const V& a, const detail::mp_exp& b) +{ + return detail::mp_exp >(a, b); +} +// +// Left shift: +// +template +inline typename enable_if, detail::mp_exp, I > >::type + operator << (const mp_number& a, const I& b) +{ + return detail::mp_exp, I>(a, b); +} +template +inline typename enable_if, detail::mp_exp, I> >::type + operator << (const detail::mp_exp& a, const I& b) +{ + return detail::mp_exp, I>(a, b); +} +// +// Right shift: +// +template +inline typename enable_if, detail::mp_exp, I > >::type + operator >> (const mp_number& a, const I& b) +{ + return detail::mp_exp, I>(a, b); +} +template +inline typename enable_if, detail::mp_exp, I> >::type + operator >> (const detail::mp_exp& a, const I& b) +{ + return detail::mp_exp, I>(a, b); +} +// +// Bitwise AND: +// +template +inline detail::mp_exp, mp_number > + operator & (const mp_number& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator & (const mp_number& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator & (const V& a, const mp_number& b) +{ + return detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator & (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, mp_number > + operator & (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator & (const detail::mp_exp& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator & (const detail::mp_exp& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator & (const V& a, const detail::mp_exp& b) +{ + return detail::mp_exp >(a, b); +} +// +// Bitwise OR: +// +template +inline detail::mp_exp, mp_number > + operator| (const mp_number& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator| (const mp_number& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator| (const V& a, const mp_number& b) +{ + return detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator| (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, mp_number > + operator| (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator| (const detail::mp_exp& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator| (const detail::mp_exp& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator| (const V& a, const detail::mp_exp& b) +{ + return detail::mp_exp >(a, b); +} +// +// Bitwise XOR: +// +template +inline detail::mp_exp, mp_number > + operator^ (const mp_number& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator^ (const mp_number& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator^ (const V& a, const mp_number& b) +{ + return detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator^ (const mp_number& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline detail::mp_exp, mp_number > + operator^ (const detail::mp_exp& a, const mp_number& b) +{ + return detail::mp_exp, mp_number >(a, b); +} +template +inline detail::mp_exp, detail::mp_exp > + operator^ (const detail::mp_exp& a, const detail::mp_exp& b) +{ + return detail::mp_exp, detail::mp_exp >(a, b); +} +template +inline typename enable_if, detail::mp_exp, V > >::type + operator^ (const detail::mp_exp& a, const V& b) +{ + return detail::mp_exp, V >(a, b); +} +template +inline typename enable_if, detail::mp_exp > >::type + operator^ (const V& a, const detail::mp_exp& b) +{ + return detail::mp_exp >(a, b); +} + +// +// Traits class, lets us know what kind of number we have, defaults to a floating point type: +// +enum number_category_type +{ + number_kind_integer = 0, + number_kind_floating_point = 1, + number_kind_rational = 2, + number_kind_fixed_point = 3 +}; + +template +struct number_category : public mpl::int_ {}; +template +struct number_category > : public number_category{}; +template +struct number_category > : public number_category::result_type>{}; + +}} // namespaces + +namespace boost{ namespace math{ namespace tools{ + +template +struct promote_arg; + +template +struct promote_arg > +{ + typedef typename boost::math::detail::mp_exp::result_type type; +}; + +}}} + +#endif // BOOST_MATH_BIG_NUM_BASE_HPP + + diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp new file mode 100644 index 00000000..262b3ee7 --- /dev/null +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -0,0 +1,903 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_BIG_NUM_DEF_OPS +#define BOOST_MATH_BIG_NUM_DEF_OPS + +#include +#include +#include +#include +#include +#include + +namespace boost{ namespace math{ namespace big_num_default_ops{ + +// +// Default versions of mixed arithmetic, these just construct a temporary +// from the arithmetic value and then do the arithmetic on that: +// +template +inline typename enable_if, is_convertible, is_same > >::type + add(T& result, V const& v) +{ + T t; + t = v; + add(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + subtract(T& result, V const& v) +{ + T t; + t = v; + subtract(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + multiply(T& result, V const& v) +{ + T t; + t = v; + multiply(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + divide(T& result, V const& v) +{ + T t; + t = v; + divide(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + modulus(T& result, V const& v) +{ + T t; + t = v; + modulus(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + bitwise_and(T& result, V const& v) +{ + T t; + t = v; + bitwise_and(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + bitwise_or(T& result, V const& v) +{ + T t; + t = v; + bitwise_or(result, t); +} +template +inline typename enable_if, is_convertible, is_same > >::type + bitwise_xor(T& result, V const& v) +{ + T t; + t = v; + bitwise_xor(result, t); +} + +template +inline typename enable_if, is_convertible, is_same > >::type + complement(T& result, V const& v) +{ + T t; + t = v; + complement(result, t); +} + +template +inline bool is_same_object(const T& u, const T&v) +{ return &u == &v; } +template +inline bool is_same_object(const T& u, const U&v) +{ return false; } + +// +// Default versions of 3-arg arithmetic functions, these just forward to the 2 arg versions: +// +template +inline void add(T& t, const U& u, const V& v) +{ + if(is_same_object(t, v)) + { + add(t, u); + } + else if(is_same_object(t, u)) + { + add(t, v); + } + else + { + t = u; + add(t, v); + } +} +template +inline void subtract(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + subtract(t, v); + else if(is_same_object(t, v)) + { + subtract(t, u); + t.negate(); + } + else + { + t = u; + subtract(t, v); + } +} +template +inline void multiply(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + multiply(t, v); + else if(is_same_object(t, v)) + multiply(t, u); + else + { + t = u; + multiply(t, v); + } +} +template +inline void divide(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + divide(t, v); + else if(is_same_object(t, v)) + { + T temp = t; + divide(temp, u, v); + temp.swap(t); + } + else + { + t = u; + divide(t, v); + } +} +template +inline void modulus(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + modulus(t, v); + else if(is_same_object(t, v)) + { + T temp; + modulus(temp, u, v); + temp.swap(t); + } + else + { + t = u; + modulus(t, v); + } +} +template +inline void bitwise_and(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + bitwise_and(t, v); + else if(is_same_object(t, v)) + bitwise_and(t, u); + else + { + t = u; + bitwise_and(t, v); + } +} + +template +inline void bitwise_or(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + bitwise_or(t, v); + else if(is_same_object(t, v)) + bitwise_or(t, u); + else + { + t = u; + bitwise_or(t, v); + } +} + +template +inline void bitwise_xor(T& t, const U& u, const V& v) +{ + if(is_same_object(t, u)) + bitwise_xor(t, v); + else if(is_same_object(t, v)) + bitwise_xor(t, u); + else + { + t = u; + bitwise_xor(t, v); + } +} + +template +inline void increment(T& val) +{ + typedef typename mpl::front::type ui_type; + add(val, static_cast(1u)); +} + +template +inline void decrement(T& val) +{ + typedef typename mpl::front::type ui_type; + subtract(val, static_cast(1u)); +} + +template +inline void left_shift(T& result, const T& arg, const V val) +{ + result = arg; + left_shift(result, val); +} + +template +inline void right_shift(T& result, const T& arg, const V val) +{ + result = arg; + right_shift(result, val); +} + +template +inline bool is_zero(const T& val) +{ + typedef typename mpl::front::type ui_type; + return val.compare(static_cast(0)) == 0; +} +template +inline int get_sign(const T& val) +{ + typedef typename mpl::front::type ui_type; + return val.compare(static_cast(0)); +} + +template +struct has_enough_bits +{ + template + struct type : public mpl::and_ >, mpl::bool_::digits >= b> >{}; +}; + +template +struct terminal +{ + terminal(const R& v) : value(v){} + terminal(){} + terminal& operator = (R val) { value = val; } + R value; + operator R()const { return value; } +}; + +template +struct calculate_next_larger_type +{ + typedef typename mpl::if_< + is_signed, + typename B::signed_types, + typename mpl::if_< + is_unsigned, + typename B::unsigned_types, + typename B::real_types + >::type + >::type list_type; + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + list_type, + pred_type + >::type iter_type; + typedef typename mpl::eval_if< + is_same::type, iter_type>, + mpl::identity >, + mpl::deref + >::type type; +}; + +template +inline void convert_to(R* result, const B& backend) +{ + typedef typename calculate_next_larger_type::type next_type; + next_type n; + convert_to(&n, backend); + *result = static_cast(n); +} + +template +inline void convert_to(terminal* result, const B& backend) +{ + // + // We ran out of types to try for the convertion, try + // a lexical_cast and hope for the best: + // + result->value = boost::lexical_cast(backend.str(0, false)); +} + +// +// Functions: +// +template +void eval_abs(T& result, const T& arg) +{ + typedef typename T::signed_types type_list; + typedef typename mpl::front::type front; + *result = arg; + if(arg.compare(front(0)) < 0) + result->negate(); +} +template +void eval_fabs(T& result, const T& arg) +{ + typedef typename T::signed_types type_list; + typedef typename mpl::front::type front; + *result = arg; + if(arg.compare(front(0)) < 0) + result->negate(); +} + +template +inline int eval_fpclassify(const Backend& arg) +{ + return is_zero(arg) ? FP_ZERO : FP_NORMAL; +} + +template +inline void eval_fmod(T& result, const T& a, const T& b) +{ + if((&result == &a) || (&result == &b)) + { + T temp; + eval_fmod(temp, a, b); + result = temp; + } + T n; + divide(result, a, b); + if(get_sign(a) < 0) + eval_ceil(n, result); + else + eval_floor(n, result); + multiply(n, b); + subtract(result, a, n); +} + +// +// These have to implemented by the backend, declared here so that our macro generated code compiles OK. +// +template +typename enable_if_c::type eval_floor(); +template +typename enable_if_c::type eval_ceil(); +template +typename enable_if_c::type eval_trunc(); +template +typename enable_if_c::type eval_sqrt(); +template +typename enable_if_c::type eval_ldexp(); +template +typename enable_if_c::type eval_frexp(); +// +// TODO: implement default versions of these: +// +template +typename enable_if_c::type eval_exp(); +template +typename enable_if_c::type eval_log(); +template +typename enable_if_c::type eval_sin(); +template +typename enable_if_c::type eval_cos(); +template +typename enable_if_c::type eval_tan(); +template +typename enable_if_c::type eval_asin(); +template +typename enable_if_c::type eval_acos(); +template +typename enable_if_c::type eval_atan(); +template +typename enable_if_c::type eval_sinh(); +template +typename enable_if_c::type eval_cosh(); +template +typename enable_if_c::type eval_tanh(); +// +// These functions are implemented in separate files, but expanded inline here: +// +#include + +} + +template +class mp_number; + +// +// Default versions of floating point classification routines: +// +template +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const mp_number& arg) +{ + using big_num_default_ops::eval_fpclassify; + return eval_fpclassify(arg.backend()); +} +template +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::mp_exp& arg) +{ + typedef typename detail::mp_exp::result_type value_type; + return fpclassify(value_type(arg)); +} +template +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const mp_number& arg) +{ + int v = fpclassify(arg); + return (v != FP_INFINITE) && (v != FP_NAN); +} +template +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::mp_exp& arg) +{ + typedef typename detail::mp_exp::result_type value_type; + return isfinite(value_type(arg)); +} +template +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const mp_number& arg) +{ + return fpclassify(arg) == FP_NAN; +} +template +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::mp_exp& arg) +{ + typedef typename detail::mp_exp::result_type value_type; + return isnan(value_type(arg)); +} +template +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const mp_number& arg) +{ + return fpclassify(arg) == FP_INFINITE; +} +template +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::mp_exp& arg) +{ + typedef typename detail::mp_exp::result_type value_type; + return isinf(value_type(arg)); +} +template +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const mp_number& arg) +{ + return fpclassify(arg) == FP_NORMAL; +} +template +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::mp_exp& arg) +{ + typedef typename detail::mp_exp::result_type value_type; + return isnormal(value_type(arg)); +} + +template +inline int itrunc(const detail::mp_exp& v, const Policy& pol) +{ + typedef typename detail::mp_exp::result_type number_type; + number_type r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return r.template convert_to(); +} +template +inline int itrunc(const mp_number& v, const Policy& pol) +{ + mp_number r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long ltrunc(const detail::mp_exp& v, const Policy& pol) +{ + typedef typename detail::mp_exp::result_result number_type; + number_type r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long ltrunc(const mp_number& v, const Policy& pol) +{ + mp_number r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return r.template convert_to(); +} +#ifndef BOOST_NO_LONG_LONG +template +inline long long lltrunc(const detail::mp_exp& v, const Policy& pol) +{ + typedef typename detail::mp_exp::result_result number_type; + number_type r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long long lltrunc(const mp_number& v, const Policy& pol) +{ + mp_number r = trunc(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return r.template convert_to(); +} +#endif +template +inline int iround(const detail::mp_exp& v, const Policy& pol) +{ + typedef typename detail::mp_exp::result_result number_type; + number_type r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return r.template convert_to(); +} +template +inline int iround(const mp_number& v, const Policy& pol) +{ + mp_number r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long lround(const detail::mp_exp& v, const Policy& pol) +{ + typedef typename detail::mp_exp::result_result number_type; + number_type r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long lround(const mp_number& v, const Policy& pol) +{ + mp_number r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return r.template convert_to(); +} +#ifndef BOOST_NO_LONG_LONG +template +inline long long llround(const detail::mp_exp& v, const Policy& pol) +{ + typedef typename detail::mp_exp::result_result number_type; + number_type r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return r.template convert_to(); +} +template +inline long long llround(const mp_number& v, const Policy& pol) +{ + mp_number r = round(v, pol); + if(fabs(r) > (std::numeric_limits::max)()) + return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return r.template convert_to(); +} +#endif +// +// Overload of Boost.Math functions that find the wrong overload when used with mp_number: +// +namespace detail{ + template T sinc_pi_imp(T); + template T sinhc_pi_imp(T); +} +template +inline mp_number sinc_pi(const mp_number& x) +{ + return detail::sinc_pi_imp(x); +} + +template +inline mp_number sinc_pi(const mp_number& x, const Policy&) +{ + return detail::sinc_pi_imp(x); +} + +template +inline mp_number sinhc_pi(const mp_number& x) +{ + return detail::sinhc_pi_imp(x); +} + +template +inline mp_number sinhc_pi(const mp_number& x, const Policy&) +{ + return boost::math::sinhc_pi(x); +} + +#define UNARY_OP_FUNCTOR(func)\ +namespace detail{\ +template \ +struct BOOST_JOIN(func, _funct)\ +{\ + void operator()(Backend& result, const Backend& arg)const\ + {\ + using big_num_default_ops::BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result, arg);\ + }\ +};\ +\ +}\ +\ +template \ +detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ +> \ +func(const detail::mp_exp& arg)\ +{\ + return detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ +> (\ + detail::BOOST_JOIN(func, _funct) >::type>() \ + , arg \ + );\ +}\ +template \ +detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , mp_number \ +> \ +func(const mp_number& arg)\ +{\ + return detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , mp_number \ + >(\ + detail::BOOST_JOIN(func, _funct)() \ + , arg \ + );\ +} + +#define BINARY_OP_FUNCTOR(func)\ +namespace detail{\ +template \ +struct BOOST_JOIN(func, _funct)\ +{\ + void operator()(Backend& result, const Backend& arg, const Backend& a)const\ + {\ + using big_num_default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result, arg, a);\ + }\ + template \ + void operator()(Backend& result, const Backend& arg, const Arithmetic& a)const\ + {\ + using big_num_default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result, arg, a);\ + }\ +};\ +\ +}\ +template \ +detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , mp_number \ + , mp_number \ +> \ +func(const mp_number& arg, const mp_number& a)\ +{\ + return detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , mp_number \ + , mp_number \ + >(\ + detail::BOOST_JOIN(func, _funct)() \ + , arg,\ + a\ + );\ +}\ +template \ +detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , mp_number \ + , detail::mp_exp \ +> \ +func(const mp_number& arg, const detail::mp_exp& a)\ +{\ + return detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , mp_number \ + , detail::mp_exp \ + >(\ + detail::BOOST_JOIN(func, _funct)() \ + , arg,\ + a\ + );\ +}\ +template \ +detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , detail::mp_exp \ + , mp_number \ +> \ +func(const detail::mp_exp& arg, const mp_number& a)\ +{\ + return detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , detail::mp_exp \ + , mp_number \ + >(\ + detail::BOOST_JOIN(func, _funct)() \ + , arg,\ + a\ + );\ +}\ +template \ +detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ + , detail::mp_exp \ +> \ +func(const detail::mp_exp& arg, const detail::mp_exp& a)\ +{\ + return detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ + , detail::mp_exp \ + >(\ + detail::BOOST_JOIN(func, _funct) >::type>() \ + , arg,\ + a\ + );\ +}\ +template \ +typename enable_if<\ + is_arithmetic,\ + detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , mp_number \ + , Arithmetic\ + > \ +>::type \ +func(const mp_number& arg, const Arithmetic& a)\ +{\ + return detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , mp_number \ + , Arithmetic\ + >(\ + detail::BOOST_JOIN(func, _funct)() \ + , arg,\ + a\ + );\ +}\ +template \ +typename enable_if<\ + is_arithmetic,\ + detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ + , Arithmetic\ + > \ +>::type \ +func(const detail::mp_exp& arg, const Arithmetic& a)\ +{\ + return detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ + , Arithmetic\ + >(\ + detail::BOOST_JOIN(func, _funct) >::type>() \ + , arg,\ + a\ + );\ +}\ + + +#define HETERO_BINARY_OP_FUNCTOR(func, Arg2)\ +namespace detail{\ +template \ +struct BOOST_JOIN(func, _funct)\ +{\ + void operator()(Backend& result, Backend const& arg, Arg2 a)const\ + {\ + using big_num_default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result, arg, a);\ + }\ +};\ +\ +}\ +\ +template \ +detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ + , Arg2\ +> \ +func(const detail::mp_exp& arg, Arg2 const& a)\ +{\ + return detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ + , Arg2\ + >(\ + detail::BOOST_JOIN(func, _funct) >::type>() \ + , arg, a \ + );\ +}\ +template \ +detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , mp_number \ + , Arg2\ +> \ +func(const mp_number& arg, Arg2 const& a)\ +{\ + return detail::mp_exp<\ + detail::function\ + , detail::BOOST_JOIN(func, _funct) \ + , mp_number \ + , Arg2\ + >(\ + detail::BOOST_JOIN(func, _funct)() \ + , arg,\ + a\ + );\ +}\ + +UNARY_OP_FUNCTOR(abs) +UNARY_OP_FUNCTOR(fabs) +UNARY_OP_FUNCTOR(sqrt) +UNARY_OP_FUNCTOR(floor) +UNARY_OP_FUNCTOR(ceil) +UNARY_OP_FUNCTOR(trunc) +UNARY_OP_FUNCTOR(exp) +UNARY_OP_FUNCTOR(log) +UNARY_OP_FUNCTOR(cos) +UNARY_OP_FUNCTOR(sin) +UNARY_OP_FUNCTOR(tan) +UNARY_OP_FUNCTOR(asin) +UNARY_OP_FUNCTOR(acos) +UNARY_OP_FUNCTOR(atan) +UNARY_OP_FUNCTOR(cosh) +UNARY_OP_FUNCTOR(sinh) +UNARY_OP_FUNCTOR(tanh) + +HETERO_BINARY_OP_FUNCTOR(ldexp, int) +HETERO_BINARY_OP_FUNCTOR(frexp, int*) +BINARY_OP_FUNCTOR(pow) +BINARY_OP_FUNCTOR(fmod) + +#undef BINARY_OP_FUNCTOR +#undef UNARY_OP_FUNCTOR + +}} // namespaces + +#endif + diff --git a/include/boost/multiprecision/e_float.hpp b/include/boost/multiprecision/e_float.hpp new file mode 100644 index 00000000..4f9d4aa2 --- /dev/null +++ b/include/boost/multiprecision/e_float.hpp @@ -0,0 +1,80 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MATH_EFX_BACKEND_HPP +#define BOOST_MATH_EFX_BACKEND_HPP + +#include +#include +#include +#include +#include + +namespace boost{ +namespace math{ + +typedef mp_number > e_float; + +template<> +inline void arithmetic_backend::negate() +{ + m_value.negate(); +} +template<> +inline std::string arithmetic_backend::str(unsigned digits, bool scientific)const +{ + std::fstream os; + os << std::setprecision(digits ? digits : efx::e_float::ef_digits + 5); + if(scientific) + os << std::scientific; + std::string result; + this->data().wr_string(result, os); + return result; +} + +inline void eval_abs(arithmetic_backend& result, const arithmetic_backend& arg) +{ + result.data() = ef::fabs(arg.data()); +} + +inline void eval_fabs(arithmetic_backend& result, const arithmetic_backend& arg) +{ + result.data() = ef::fabs(arg.data()); +} + +inline bool is_zero(const arithmetic_backend& val) +{ + return val.data().iszero(); +} +inline int get_sign(const arithmetic_backend& val) +{ + return val.data().isneg() ? -1 : val.data().iszero() ? 0 : 1; +} + +inline void convert_to(boost::uintmax_t* result, const arithmetic_backend& val) +{ + *result = val.data().extract_unsigned_long_long(); +} +inline void convert_to(boost::intmax_t* result, const arithmetic_backend& val) +{ + *result = val.data().extract_signed_long_long(); +} +inline void convert_to(double* result, const arithmetic_backend& val) +{ + *result = val.data().extract_double(); +} +inline void convert_to(long double* result, const arithmetic_backend& val) +{ + *result = val.data().extract_long_double(); +} +inline int eval_fpclassify(const arithmetic_backend& val) +{ + return val.data().isinf() ? FP_INFINITE : val.data().isnan() ? FP_NAN : val.data().iszero() ? FP_ZERO : FP_NORMAL; +} + + +}} // namespaces + +#endif diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp new file mode 100644 index 00000000..2cf5991d --- /dev/null +++ b/include/boost/multiprecision/gmp.hpp @@ -0,0 +1,1532 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_ER_GMP_BACKEND_HPP +#define BOOST_MATH_ER_GMP_BACKEND_HPP + +#include +#include +#include +#include +#include +#include +#include +#include + +namespace boost{ namespace math{ + +template +struct gmp_real; + +namespace detail{ + +template +struct gmp_real_imp +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + gmp_real_imp(){} + + gmp_real_imp(const gmp_real_imp& o) + { + // + // We have to do an init followed by a set here, otherwise *this may be at + // a lower precision than o: seems like mpf_init_set copies just enough bits + // to get the right value, but if it's then used in further calculations + // things go badly wrong!! + // + mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_set(m_data, o.m_data); + } +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real_imp(gmp_real_imp&& o) + { + m_data[0] = o.m_data[0]; + o.m_data[0]._mp_d = 0; + } +#endif + gmp_real_imp& operator = (const gmp_real_imp& o) + { + mpf_set(m_data, o.m_data); + return *this; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real_imp& operator = (gmp_real_imp&& o) + { + mpf_swap(m_data, o.m_data); + return *this; + } +#endif + gmp_real_imp& operator = (boost::uintmax_t i) + { + boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned shift = 0; + mpf_t t; + mpf_init2(t, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_set_ui(m_data, 0); + while(i) + { + mpf_set_ui(t, static_cast(i & mask)); + if(shift) + mpf_mul_2exp(t, t, shift); + mpf_add(m_data, m_data, t); + shift += std::numeric_limits::digits; + i >>= std::numeric_limits::digits; + } + mpf_clear(t); + return *this; + } + gmp_real_imp& operator = (boost::intmax_t i) + { + bool neg = i < 0; + *this = static_cast(std::abs(i)); + if(neg) + mpf_neg(m_data, m_data); + return *this; + } + gmp_real_imp& operator = (unsigned long i) + { + mpf_set_ui(m_data, i); + return *this; + } + gmp_real_imp& operator = (long i) + { + mpf_set_si(m_data, i); + return *this; + } + gmp_real_imp& operator = (double d) + { + mpf_set_d(m_data, d); + return *this; + } + gmp_real_imp& operator = (long double a) + { + using std::frexp; + using std::ldexp; + using std::floor; + + if (a == 0) { + mpf_set_si(m_data, 0); + return *this; + } + + if (a == 1) { + mpf_set_si(m_data, 1); + return *this; + } + + BOOST_ASSERT(!(boost::math::isinf)(a)); + BOOST_ASSERT(!(boost::math::isnan)(a)); + + int e; + long double f, term; + mpf_init_set_ui(m_data, 0u); + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + mpf_mul_2exp(m_data, m_data, shift); + if(term > 0) + mpf_add_ui(m_data, m_data, static_cast(term)); + else + mpf_sub_ui(m_data, m_data, static_cast(-term)); + f -= term; + } + if(e > 0) + mpf_mul_2exp(m_data, m_data, e); + else if(e < 0) + mpf_div_2exp(m_data, m_data, -e); + return *this; + } + gmp_real_imp& operator = (const char* s) + { + mpf_set_str(m_data, s, 10); + return *this; + } + void swap(gmp_real_imp& o) + { + mpf_swap(m_data, o.m_data); + } + std::string str(unsigned digits, bool scientific)const + { + std::string result; + mp_exp_t e; + void *(*alloc_func_ptr) (size_t); + void *(*realloc_func_ptr) (void *, size_t, size_t); + void (*free_func_ptr) (void *, size_t); + const char* ps = mpf_get_str (0, &e, 10, digits, m_data); + std::ptrdiff_t sl = std::strlen(ps); + if(sl == 0) + return "0"; + if(*ps == '-') + --sl; // number of digits excluding sign. + if(!scientific + && (sl <= std::numeric_limits::digits10 + 1) + && (e >= sl) + && (sl <= std::numeric_limits::digits10 + 1)) + { + result = ps; + result.append(e-sl, '0'); + } + else + { + result = ps; + if(ps[0] == '-') + result.insert(2, 1, '.'); + else + result.insert(1, 1, '.'); + --e; + if(e) + result += "e" + lexical_cast(e); + } + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); + return result; + } + ~gmp_real_imp() + { + if(m_data[0]._mp_d) + mpf_clear(m_data); + } + void negate() + { + mpf_neg(m_data, m_data); + } + int compare(const gmp_real& o)const + { + return mpf_cmp(m_data, o.m_data); + } + int compare(long i)const + { + return mpf_cmp_si(m_data, i); + } + int compare(unsigned long i)const + { + return mpf_cmp_ui(m_data, i); + } + template + int compare(V v)const + { + gmp_real d; + d = v; + return compare(d); + } + mpf_t& data() { return m_data; } + const mpf_t& data()const { return m_data; } +protected: + mpf_t m_data; + static unsigned& get_default_precision() + { + static unsigned val = 50; + return val; + } +}; + +} // namespace detail + +template +struct gmp_real : public detail::gmp_real_imp +{ + gmp_real() + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + } + gmp_real(const gmp_real& o) : detail::gmp_real_imp(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real(gmp_real&& o) : detail::gmp_real_imp(o) {} +#endif + gmp_real& operator=(const gmp_real& o) + { + *static_cast*>(this) = static_cast const&>(o); + return *this; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real& operator=(gmp_real&& o) + { + *static_cast*>(this) = static_cast&&>(o); + return *this; + } +#endif + template + gmp_real& operator=(const V& v) + { + *static_cast*>(this) = v; + return *this; + } +}; + +template <> +struct gmp_real<0> : public detail::gmp_real_imp<0> +{ + gmp_real() + { + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + } + gmp_real(unsigned digits10) + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + } + gmp_real(const gmp_real& o) : detail::gmp_real_imp<0>(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real(gmp_real&& o) : detail::gmp_real_imp<0>(o) {} +#endif + gmp_real(const gmp_real& o, unsigned digits10) + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + *this = o; + } + + gmp_real& operator=(const gmp_real& o) + { + *static_cast*>(this) = static_cast const&>(o); + return *this; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_real& operator=(gmp_real&& o) + { + *static_cast*>(this) = static_cast &&>(o); + return *this; + } +#endif + template + gmp_real& operator=(const V& v) + { + *static_cast*>(this) = v; + return *this; + } + static unsigned default_precision() + { + return get_default_precision(); + } + static void default_precision(unsigned v) + { + get_default_precision() = v; + } + unsigned precision()const + { + return mpf_get_prec(this->m_data) * 301L / 1000 - 1; + } + void precision(unsigned digits10) + { + mpf_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); + } +}; + +template +inline void add(gmp_real& result, const gmp_real& o) +{ + mpf_add(result.data(), result.data(), o.data()); +} +template +inline void subtract(gmp_real& result, const gmp_real& o) +{ + mpf_sub(result.data(), result.data(), o.data()); +} +template +inline void multiply(gmp_real& result, const gmp_real& o) +{ + mpf_mul(result.data(), result.data(), o.data()); +} +template +inline void divide(gmp_real& result, const gmp_real& o) +{ + mpf_div(result.data(), result.data(), o.data()); +} +template +inline void add(gmp_real& result, unsigned long i) +{ + mpf_add_ui(result.data(), result.data(), i); +} +template +inline void subtract(gmp_real& result, unsigned long i) +{ + mpf_sub_ui(result.data(), result.data(), i); +} +template +inline void multiply(gmp_real& result, unsigned long i) +{ + mpf_mul_ui(result.data(), result.data(), i); +} +template +inline void divide(gmp_real& result, unsigned long i) +{ + mpf_div_ui(result.data(), result.data(), i); +} +template +inline void add(gmp_real& result, long i) +{ + if(i > 0) + mpf_add_ui(result.data(), result.data(), i); + else + mpf_sub_ui(result.data(), result.data(), std::abs(i)); +} +template +inline void subtract(gmp_real& result, long i) +{ + if(i > 0) + mpf_sub_ui(result.data(), result.data(), i); + else + mpf_add_ui(result.data(), result.data(), std::abs(i)); +} +template +inline void multiply(gmp_real& result, long i) +{ + mpf_mul_ui(result.data(), result.data(), std::abs(i)); + if(i < 0) + mpf_neg(result.data(), result.data()); +} +template +inline void divide(gmp_real& result, long i) +{ + mpf_div_ui(result.data(), result.data(), std::abs(i)); + if(i < 0) + mpf_neg(result.data(), result.data()); +} +// +// Specialised 3 arg versions of the basic operators: +// +template +inline void add(gmp_real& a, const gmp_real& x, const gmp_real& y) +{ + mpf_add(a.data(), x.data(), y.data()); +} +template +inline void add(gmp_real& a, const gmp_real& x, unsigned long y) +{ + mpf_add_ui(a.data(), x.data(), y); +} +template +inline void add(gmp_real& a, const gmp_real& x, long y) +{ + if(y < 0) + mpf_sub_ui(a.data(), x.data(), -y); + else + mpf_add_ui(a.data(), x.data(), y); +} +template +inline void add(gmp_real& a, unsigned long x, const gmp_real& y) +{ + mpf_add_ui(a.data(), y.data(), x); +} +template +inline void add(gmp_real& a, long x, const gmp_real& y) +{ + if(x < 0) + { + mpf_ui_sub(a.data(), -x, y.data()); + mpf_neg(a.data(), a.data()); + } + else + mpf_add_ui(a.data(), y.data(), x); +} +template +inline void subtract(gmp_real& a, const gmp_real& x, const gmp_real& y) +{ + mpf_sub(a.data(), x.data(), y.data()); +} +template +inline void subtract(gmp_real& a, const gmp_real& x, unsigned long y) +{ + mpf_sub_ui(a.data(), x.data(), y); +} +template +inline void subtract(gmp_real& a, const gmp_real& x, long y) +{ + if(y < 0) + mpf_add_ui(a.data(), x.data(), -y); + else + mpf_sub_ui(a.data(), x.data(), y); +} +template +inline void subtract(gmp_real& a, unsigned long x, const gmp_real& y) +{ + mpf_ui_sub(a.data(), x, y.data()); +} +template +inline void subtract(gmp_real& a, long x, const gmp_real& y) +{ + if(x < 0) + { + mpf_add_ui(a.data(), y.data(), -x); + mpf_neg(a.data(), a.data()); + } + else + mpf_ui_sub(a.data(), x, y.data()); +} + +template +inline void multiply(gmp_real& a, const gmp_real& x, const gmp_real& y) +{ + mpf_mul(a.data(), x.data(), y.data()); +} +template +inline void multiply(gmp_real& a, const gmp_real& x, unsigned long y) +{ + mpf_mul_ui(a.data(), x.data(), y); +} +template +inline void multiply(gmp_real& a, const gmp_real& x, long y) +{ + if(y < 0) + { + mpf_mul_ui(a.data(), x.data(), -y); + a.negate(); + } + else + mpf_mul_ui(a.data(), x.data(), y); +} +template +inline void multiply(gmp_real& a, unsigned long x, const gmp_real& y) +{ + mpf_mul_ui(a.data(), y.data(), x); +} +template +inline void multiply(gmp_real& a, long x, const gmp_real& y) +{ + if(x < 0) + { + mpf_mul_ui(a.data(), y.data(), -x); + mpf_neg(a.data(), a.data()); + } + else + mpf_mul_ui(a.data(), y.data(), x); +} + +template +inline void divide(gmp_real& a, const gmp_real& x, const gmp_real& y) +{ + mpf_div(a.data(), x.data(), y.data()); +} +template +inline void divide(gmp_real& a, const gmp_real& x, unsigned long y) +{ + mpf_div_ui(a.data(), x.data(), y); +} +template +inline void divide(gmp_real& a, const gmp_real& x, long y) +{ + if(y < 0) + { + mpf_div_ui(a.data(), x.data(), -y); + a.negate(); + } + else + mpf_div_ui(a.data(), x.data(), y); +} +template +inline void divide(gmp_real& a, unsigned long x, const gmp_real& y) +{ + mpf_ui_div(a.data(), x, y.data()); +} +template +inline void divide(gmp_real& a, long x, const gmp_real& y) +{ + if(x < 0) + { + mpf_ui_div(a.data(), -x, y.data()); + mpf_neg(a.data(), a.data()); + } + else + mpf_ui_div(a.data(), x, y.data()); +} + +template +inline bool is_zero(const gmp_real& val) +{ + return mpf_sgn(val.data()) == 0; +} +template +inline int get_sign(const gmp_real& val) +{ + return mpf_sgn(val.data()); +} + +template +inline void convert_to(unsigned long* result, const gmp_real& val) +{ + *result = mpf_get_ui(val.data()); +} +template +inline void convert_to(long* result, const gmp_real& val) +{ + *result = mpf_get_si(val.data()); +} +template +inline void convert_to(double* result, const gmp_real& val) +{ + *result = mpf_get_d(val.data()); +} + +// +// Native non-member operations: +// +template +inline void eval_sqrt(gmp_real& result, const gmp_real& val) +{ + mpf_sqrt(result.data(), val.data()); +} + +template +inline void eval_abs(gmp_real& result, const gmp_real& val) +{ + mpf_abs(result.data(), val.data()); +} + +template +inline void eval_fabs(gmp_real& result, const gmp_real& val) +{ + mpf_abs(result.data(), val.data()); +} +template +inline void eval_ceil(gmp_real& result, const gmp_real& val) +{ + mpf_ceil(result.data(), val.data()); +} +template +inline void eval_floor(gmp_real& result, const gmp_real& val) +{ + mpf_floor(result.data(), val.data()); +} +template +inline void eval_trunc(gmp_real& result, const gmp_real& val) +{ + mpf_trunc(result.data(), val.data()); +} +template +inline void eval_ldexp(gmp_real& result, const gmp_real& val, long e) +{ + if(e > 0) + mpf_mul_2exp(result.data(), val.data(), e); + else if(e < 0) + mpf_div_2exp(result.data(), val.data(), -e); +} +template +inline void eval_frexp(gmp_real& result, const gmp_real& val, int* e) +{ + long v; + mpf_get_d_2exp(&v, val.data()); + *e = v; + eval_ldexp(result, val, -v); +} +template +inline void eval_frexp(gmp_real& result, const gmp_real& val, long* e) +{ + mpf_get_d_2exp(e, val.data()); + eval_ldexp(result, val, -*e); +} + +struct gmp_int +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + gmp_int() + { + mpz_init(this->m_data); + } + gmp_int(const gmp_int& o) + { + mpz_init_set(m_data, o.m_data); + } + gmp_int& operator = (const gmp_int& o) + { + mpz_set(m_data, o.m_data); + return *this; + } + gmp_int& operator = (boost::uintmax_t i) + { + boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned shift = 0; + mpz_t t; + mpz_init(m_data); + mpz_init(t); + while(i) + { + mpz_set_ui(t, static_cast(i & mask)); + if(shift) + mpz_mul_2exp(t, t, shift); + mpz_add(m_data, m_data, t); + shift += std::numeric_limits::digits; + i >>= std::numeric_limits::digits; + } + mpz_clear(t); + return *this; + } + gmp_int& operator = (boost::intmax_t i) + { + bool neg = i < 0; + *this = static_cast(std::abs(i)); + if(neg) + mpz_neg(m_data, m_data); + return *this; + } + gmp_int& operator = (unsigned long i) + { + mpz_set_ui(m_data, i); + return *this; + } + gmp_int& operator = (long i) + { + mpz_set_si(m_data, i); + return *this; + } + gmp_int& operator = (double d) + { + mpz_set_d(m_data, d); + return *this; + } + gmp_int& operator = (long double a) + { + using std::frexp; + using std::ldexp; + using std::floor; + + if (a == 0) { + mpz_set_si(m_data, 0); + return *this; + } + + if (a == 1) { + mpz_set_si(m_data, 1); + return *this; + } + + BOOST_ASSERT(!(boost::math::isinf)(a)); + BOOST_ASSERT(!(boost::math::isnan)(a)); + + int e; + long double f, term; + mpz_init_set_ui(m_data, 0u); + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + mpz_mul_2exp(m_data, m_data, shift); + if(term > 0) + mpz_add_ui(m_data, m_data, static_cast(term)); + else + mpz_sub_ui(m_data, m_data, static_cast(-term)); + f -= term; + } + if(e > 0) + mpz_mul_2exp(m_data, m_data, e); + else if(e < 0) + mpz_div_2exp(m_data, m_data, -e); + return *this; + } + gmp_int& operator = (const char* s) + { + mpz_set_str(m_data, s, 10); + return *this; + } + void swap(gmp_int& o) + { + mpz_swap(m_data, o.m_data); + } + std::string str(unsigned /*digits*/, bool /*scientific*/)const + { + void *(*alloc_func_ptr) (size_t); + void *(*realloc_func_ptr) (void *, size_t, size_t); + void (*free_func_ptr) (void *, size_t); + const char* ps = mpz_get_str (0, 10, m_data); + std::string s = ps; + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); + return s; + } + ~gmp_int() + { + mpz_clear(m_data); + } + void negate() + { + mpz_neg(m_data, m_data); + } + int compare(const gmp_int& o)const + { + return mpz_cmp(m_data, o.m_data); + } + int compare(long i)const + { + return mpz_cmp_si(m_data, i); + } + int compare(unsigned long i)const + { + return mpz_cmp_ui(m_data, i); + } + template + int compare(V v)const + { + gmp_int d; + d = v; + return compare(d); + } + mpz_t& data() { return m_data; } + const mpz_t& data()const { return m_data; } +protected: + mpz_t m_data; +}; + +inline void add(gmp_int& t, const gmp_int& o) +{ + mpz_add(t.data(), t.data(), o.data()); +} +inline void subtract(gmp_int& t, const gmp_int& o) +{ + mpz_sub(t.data(), t.data(), o.data()); +} +inline void multiply(gmp_int& t, const gmp_int& o) +{ + mpz_mul(t.data(), t.data(), o.data()); +} +inline void divide(gmp_int& t, const gmp_int& o) +{ + mpz_div(t.data(), t.data(), o.data()); +} +inline void modulus(gmp_int& t, const gmp_int& o) +{ + bool neg = mpz_sgn(t.data()) < 0; + bool neg2 = mpz_sgn(o.data()) < 0; + mpz_mod(t.data(), t.data(), o.data()); + if(neg) + { + if(!neg2) + t.negate(); + mpz_add(t.data(), t.data(), o.data()); + if(!neg2) + t.negate(); + } +} +inline void add(gmp_int& t, unsigned long i) +{ + mpz_add_ui(t.data(), t.data(), i); +} +inline void subtract(gmp_int& t, unsigned long i) +{ + mpz_sub_ui(t.data(), t.data(), i); +} +inline void multiply(gmp_int& t, unsigned long i) +{ + mpz_mul_ui(t.data(), t.data(), i); +} +inline void modulus(gmp_int& t, unsigned long i) +{ + bool neg = mpz_sgn(t.data()) < 0; + mpz_mod_ui(t.data(), t.data(), i); + if(neg) + { + t.negate(); + mpz_add_ui(t.data(), t.data(), i); + t.negate(); + } +} +inline void divide(gmp_int& t, unsigned long i) +{ + mpz_div_ui(t.data(), t.data(), i); +} +inline void add(gmp_int& t, long i) +{ + if(i > 0) + mpz_add_ui(t.data(), t.data(), i); + else + mpz_sub_ui(t.data(), t.data(), -i); +} +inline void subtract(gmp_int& t, long i) +{ + if(i > 0) + mpz_sub_ui(t.data(), t.data(), i); + else + mpz_add_ui(t.data(), t.data(), -i); +} +inline void multiply(gmp_int& t, long i) +{ + mpz_mul_ui(t.data(), t.data(), std::abs(i)); + if(i < 0) + mpz_neg(t.data(), t.data()); +} +inline void modulus(gmp_int& t, long i) +{ + bool neg = mpz_sgn(t.data()) < 0; + bool neg2 = i < 0; + mpz_mod_ui(t.data(), t.data(), std::abs(i)); + if(neg) + { + if(!neg2) + { + t.negate(); + mpz_add_ui(t.data(), t.data(), std::abs(i)); + t.negate(); + } + else + { + mpz_sub_ui(t.data(), t.data(), std::abs(i)); + } + } +} +inline void divide(gmp_int& t, long i) +{ + mpz_div_ui(t.data(), t.data(), std::abs(i)); + if(i < 0) + mpz_neg(t.data(), t.data()); +} +template +inline void left_shift(gmp_int& t, UI i) +{ + mpz_mul_2exp(t.data(), t.data(), static_cast(i)); +} +template +inline void right_shift(gmp_int& t, UI i) +{ + mpz_fdiv_q_2exp(t.data(), t.data(), static_cast(i)); +} +template +inline void left_shift(gmp_int& t, const gmp_int& v, UI i) +{ + mpz_mul_2exp(t.data(), v.data(), static_cast(i)); +} +template +inline void right_shift(gmp_int& t, const gmp_int& v, UI i) +{ + mpz_fdiv_q_2exp(t.data(), v.data(), static_cast(i)); +} + +inline void bitwise_and(gmp_int& result, const gmp_int& v) +{ + mpz_and(result.data(), result.data(), v.data()); +} + +inline void bitwise_or(gmp_int& result, const gmp_int& v) +{ + mpz_ior(result.data(), result.data(), v.data()); +} + +inline void bitwise_xor(gmp_int& result, const gmp_int& v) +{ + mpz_xor(result.data(), result.data(), v.data()); +} + +inline void add(gmp_int& t, const gmp_int& p, const gmp_int& o) +{ + mpz_add(t.data(), p.data(), o.data()); +} +inline void subtract(gmp_int& t, const gmp_int& p, const gmp_int& o) +{ + mpz_sub(t.data(), p.data(), o.data()); +} +inline void multiply(gmp_int& t, const gmp_int& p, const gmp_int& o) +{ + mpz_mul(t.data(), p.data(), o.data()); +} +inline void divide(gmp_int& t, const gmp_int& p, const gmp_int& o) +{ + mpz_div(t.data(), p.data(), o.data()); +} +inline void modulus(gmp_int& t, const gmp_int& p, const gmp_int& o) +{ + bool neg = mpz_sgn(p.data()) < 0; + bool neg2 = mpz_sgn(o.data()) < 0; + mpz_mod(t.data(), p.data(), o.data()); + if(neg) + { + if(!neg2) + t.negate(); + mpz_add(t.data(), t.data(), o.data()); + if(!neg2) + t.negate(); + } +} +inline void add(gmp_int& t, const gmp_int& p, unsigned long i) +{ + mpz_add_ui(t.data(), p.data(), i); +} +inline void subtract(gmp_int& t, const gmp_int& p, unsigned long i) +{ + mpz_sub_ui(t.data(), p.data(), i); +} +inline void multiply(gmp_int& t, const gmp_int& p, unsigned long i) +{ + mpz_mul_ui(t.data(), p.data(), i); +} +inline void modulus(gmp_int& t, const gmp_int& p, unsigned long i) +{ + bool neg = mpz_sgn(p.data()) < 0; + mpz_mod_ui(t.data(), p.data(), i); + if(neg) + { + t.negate(); + mpz_add_ui(t.data(), t.data(), i); + t.negate(); + } +} +inline void divide(gmp_int& t, const gmp_int& p, unsigned long i) +{ + mpz_div_ui(t.data(), p.data(), i); +} +inline void add(gmp_int& t, const gmp_int& p, long i) +{ + if(i > 0) + mpz_add_ui(t.data(), p.data(), i); + else + mpz_sub_ui(t.data(), p.data(), -i); +} +inline void subtract(gmp_int& t, const gmp_int& p, long i) +{ + if(i > 0) + mpz_sub_ui(t.data(), p.data(), i); + else + mpz_add_ui(t.data(), p.data(), -i); +} +inline void multiply(gmp_int& t, const gmp_int& p, long i) +{ + mpz_mul_ui(t.data(), p.data(), std::abs(i)); + if(i < 0) + mpz_neg(t.data(), t.data()); +} +inline void modulus(gmp_int& t, const gmp_int& p, long i) +{ + bool neg = mpz_sgn(p.data()) < 0; + bool neg2 = i < 0; + mpz_mod_ui(t.data(), p.data(), std::abs(i)); + if(neg) + { + if(!neg2) + { + t.negate(); + mpz_add_ui(t.data(), t.data(), std::abs(i)); + t.negate(); + } + else + { + mpz_sub_ui(t.data(), t.data(), std::abs(i)); + } + } +} +inline void divide(gmp_int& t, const gmp_int& p, long i) +{ + mpz_div_ui(t.data(), p.data(), std::abs(i)); + if(i < 0) + mpz_neg(t.data(), t.data()); +} + +inline void bitwise_and(gmp_int& result, const gmp_int& u, const gmp_int& v) +{ + mpz_and(result.data(), u.data(), v.data()); +} + +inline void bitwise_or(gmp_int& result, const gmp_int& u, const gmp_int& v) +{ + mpz_ior(result.data(), u.data(), v.data()); +} + +inline void bitwise_xor(gmp_int& result, const gmp_int& u, const gmp_int& v) +{ + mpz_xor(result.data(), u.data(), v.data()); +} + +inline void complement(gmp_int& result, const gmp_int& u) +{ + mpz_com(result.data(), u.data()); +} + +inline bool is_zero(const gmp_int& val) +{ + return mpz_sgn(val.data()) == 0; +} +inline int get_sign(const gmp_int& val) +{ + return mpz_sgn(val.data()); +} +inline void convert_to(unsigned long* result, const gmp_int& val) +{ + *result = mpz_get_ui(val.data()); +} +inline void convert_to(long* result, const gmp_int& val) +{ + *result = mpz_get_si(val.data()); +} +inline void convert_to(double* result, const gmp_int& val) +{ + *result = mpz_get_d(val.data()); +} + +inline void eval_abs(gmp_int& result, const gmp_int& val) +{ + mpz_abs(result.data(), val.data()); +} + +struct gmp_rational; +void add(gmp_rational& t, const gmp_rational& o); + +struct gmp_rational +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + gmp_rational() + { + mpq_init(this->m_data); + } + gmp_rational(const gmp_rational& o) + { + mpq_init(m_data); + mpq_set(m_data, o.m_data); + } + gmp_rational& operator = (const gmp_rational& o) + { + mpq_set(m_data, o.m_data); + return *this; + } + gmp_rational& operator = (boost::uintmax_t i) + { + boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned shift = 0; + mpq_t t; + mpq_init(m_data); + mpq_init(t); + while(i) + { + mpq_set_ui(t, static_cast(i & mask), 1); + if(shift) + mpq_mul_2exp(t, t, shift); + mpq_add(m_data, m_data, t); + shift += std::numeric_limits::digits; + i >>= std::numeric_limits::digits; + } + mpq_clear(t); + return *this; + } + gmp_rational& operator = (boost::intmax_t i) + { + bool neg = i < 0; + *this = static_cast(std::abs(i)); + if(neg) + mpq_neg(m_data, m_data); + return *this; + } + gmp_rational& operator = (unsigned long i) + { + mpq_set_ui(m_data, i, 1); + return *this; + } + gmp_rational& operator = (long i) + { + mpq_set_si(m_data, i, 1); + return *this; + } + gmp_rational& operator = (double d) + { + mpq_set_d(m_data, d); + return *this; + } + gmp_rational& operator = (long double a) + { + using std::frexp; + using std::ldexp; + using std::floor; + using big_num_default_ops::add; + using big_num_default_ops::subtract; + + if (a == 0) { + mpq_set_si(m_data, 0, 1); + return *this; + } + + if (a == 1) { + mpq_set_si(m_data, 1, 1); + return *this; + } + + BOOST_ASSERT(!(boost::math::isinf)(a)); + BOOST_ASSERT(!(boost::math::isnan)(a)); + + int e; + long double f, term; + mpq_init(m_data); + mpq_set_ui(m_data, 0u, 1); + gmp_rational t; + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + mpq_mul_2exp(m_data, m_data, shift); + t = static_cast(term); + add(*this, t); + f -= term; + } + if(e > 0) + mpq_mul_2exp(m_data, m_data, e); + else if(e < 0) + mpq_div_2exp(m_data, m_data, -e); + return *this; + } + gmp_rational& operator = (const char* s) + { + mpq_set_str(m_data, s, 10); + return *this; + } + void swap(gmp_rational& o) + { + mpq_swap(m_data, o.m_data); + } + std::string str(unsigned /*digits*/, bool /*scientific*/)const + { + void *(*alloc_func_ptr) (size_t); + void *(*realloc_func_ptr) (void *, size_t, size_t); + void (*free_func_ptr) (void *, size_t); + const char* ps = mpq_get_str (0, 10, m_data); + std::string s = ps; + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); + return s; + } + ~gmp_rational() + { + mpq_clear(m_data); + } + void negate() + { + mpq_neg(m_data, m_data); + } + int compare(const gmp_rational& o)const + { + return mpq_cmp(m_data, o.m_data); + } + template + int compare(V v)const + { + gmp_rational d; + d = v; + return compare(d); + } + int compare(unsigned long v) + { + return mpq_cmp_ui(m_data, v, 1); + } + int compare(long v) + { + return mpq_cmp_si(m_data, v, 1); + } + mpq_t& data() { return m_data; } + const mpq_t& data()const { return m_data; } +protected: + mpq_t m_data; +}; + +inline void add(gmp_rational& t, const gmp_rational& o) +{ + mpq_add(t.data(), t.data(), o.data()); +} +inline void subtract(gmp_rational& t, const gmp_rational& o) +{ + mpq_sub(t.data(), t.data(), o.data()); +} +inline void multiply(gmp_rational& t, const gmp_rational& o) +{ + mpq_mul(t.data(), t.data(), o.data()); +} +inline void divide(gmp_rational& t, const gmp_rational& o) +{ + mpq_div(t.data(), t.data(), o.data()); +} +inline void add(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +{ + mpq_add(t.data(), p.data(), o.data()); +} +inline void subtract(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +{ + mpq_sub(t.data(), p.data(), o.data()); +} +inline void multiply(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +{ + mpq_mul(t.data(), p.data(), o.data()); +} +inline void divide(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +{ + mpq_div(t.data(), p.data(), o.data()); +} + +inline bool is_zero(const gmp_rational& val) +{ + return mpq_sgn(val.data()) == 0; +} +inline int get_sign(const gmp_rational& val) +{ + return mpq_sgn(val.data()); +} +inline void convert_to(double* result, const gmp_rational& val) +{ + *result = mpq_get_d(val.data()); +} + +inline void convert_to(long* result, const gmp_rational& val) +{ + double r; + convert_to(&r, val); + *result = r; +} + +inline void convert_to(unsigned long* result, const gmp_rational& val) +{ + double r; + convert_to(&r, val); + *result = r; +} + +inline void eval_abs(gmp_rational& result, const gmp_rational& val) +{ + mpq_abs(result.data(), val.data()); +} + +template<> +struct number_category : public mpl::int_{}; +template<> +struct number_category : public mpl::int_{}; + +typedef mp_number > mpf_real_50; +typedef mp_number > mpf_real_100; +typedef mp_number > mpf_real_500; +typedef mp_number > mpf_real_1000; +typedef mp_number > mpf_real; +typedef mp_number mpz_int; +typedef mp_number mpq_rational; + +}} // namespaces + +namespace std{ + +#ifdef BOOST_NO_NOEXCEPT +# define noexcept +#endif + +// +// numeric_limits [partial] specializations for the types declared in this header: +// +template +class numeric_limits > > +{ + typedef boost::math::mp_number > number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), LONG_MAX); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpf_mul_2exp(value.second.backend().data(), value.second.backend().data(), LONG_MAX - 1); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept + { + return -(max)(); + } + BOOST_STATIC_CONSTEXPR int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); + BOOST_STATIC_CONSTEXPR int digits10 = Digits10; + // Is this really correct??? + BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 1; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR int radix = 2; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits::digits - 1); + } + return value.second; + } + // What value should this be???? + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept + { + // returns epsilon/2 + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), digits); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR long min_exponent = LONG_MIN; + BOOST_STATIC_CONSTEXPR long min_exponent10 = (LONG_MIN / 1000) * 301L; + BOOST_STATIC_CONSTEXPR long max_exponent = LONG_MAX; + BOOST_STATIC_CONSTEXPR long max_exponent10 = (LONG_MAX / 1000) * 301L; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = true; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = true; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest; + +private: + struct data_initializer + { + data_initializer() + { + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); + } + void do_nothing()const{} + }; + static const data_initializer initializer; +}; + +template +const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; + +template<> +class numeric_limits > > +{ + typedef boost::math::mp_number > number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = false; + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR int digits = 0; + BOOST_STATIC_CONSTEXPR int digits10 = 0; + BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR bool is_signed = false; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR int radix = 0; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = false; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + +template<> +class numeric_limits +{ + typedef boost::math::mpz_int number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + // + // Largest and smallest numbers are bounded only by available memory, set + // to zero: + // + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + { + return number_type(); + } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + { + return number_type(); + } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return (min)(); } + // Digits are unbounded, use zero for now: + BOOST_STATIC_CONSTEXPR int digits = 0; + BOOST_STATIC_CONSTEXPR int digits10 = 0; + BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = true; + BOOST_STATIC_CONSTEXPR bool is_exact = true; + BOOST_STATIC_CONSTEXPR int radix = 2; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = false; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + +#ifdef BOOST_NO_NOEXCEPT +# undef noexcept +#endif + +} // namespace std + +#endif diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp new file mode 100644 index 00000000..fc2f2f75 --- /dev/null +++ b/include/boost/multiprecision/mp_number.hpp @@ -0,0 +1,1570 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_EXTENDED_REAL_HPP +#define BOOST_MATH_EXTENDED_REAL_HPP + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +namespace boost{ namespace math{ + +template +class mp_number +{ + typedef mp_number self_type; +public: + mp_number(){} + mp_number(const mp_number& e) : m_backend(e.m_backend){} + template + mp_number(V v, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) + { + m_backend = canonical_value(v); + } + mp_number(const mp_number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} + template + mp_number(V v, unsigned digits10, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) + { + m_backend.precision(digits10); + m_backend = canonical_value(v); + } + + template + mp_number(V v, typename enable_if, mpl::not_ > > >::type* dummy1 = 0) + : m_backend(v){} + + template + mp_number& operator=(const detail::mp_exp& e) + { + do_assign(e, tag()); + return *this; + } + + mp_number& operator=(const mp_number& e) + { + m_backend = e.m_backend; + return *this; + } + + template + typename enable_if, is_same, is_convertible >, mp_number& >::type + operator=(const V& v) + { + m_backend = canonical_value(v); + return *this; + } + + template + mp_number(const detail::mp_exp& e) + { + do_assign(e, tag()); + } + +#ifndef BOOST_NO_RVALUE_REFERENCES + mp_number(mp_number&& r) : m_backend(r.m_backend){} + mp_number& operator=(mp_number&& r) + { + m_backend.swap(r.m_backend); + return *this; + } +#endif + + mp_number& operator+=(const self_type& val) + { + do_add(detail::mp_exp(val), detail::terminal()); + return *this; + } + + template + mp_number& operator+=(const detail::mp_exp& e) + { + // Create a copy if e contains this, but not if we're just doing a + // x *= x + if(contains_self(e) && !is_self(e)) + { + self_type temp(e); + do_add(detail::mp_exp(temp), detail::terminal()); + } + else + { + do_add(e, tag()); + } + return *this; + } + + template + typename enable_if, mp_number& >::type + operator+=(const V& v) + { + using big_num_default_ops::add; + add(m_backend, canonical_value(v)); + return *this; + } + + mp_number& operator-=(const self_type& val) + { + do_subtract(detail::mp_exp(val), detail::terminal()); + return *this; + } + + template + mp_number& operator-=(const detail::mp_exp& e) + { + // Create a copy if e contains this, but not if we're just doing a + if(contains_self(e)) + { + self_type temp(e); + do_subtract(temp, typename self_type::tag_type()); + } + else + { + do_subtract(e, typename Exp::tag_type()); + } + return *this; + } + + template + typename enable_if, mp_number& >::type + operator-=(const V& v) + { + using big_num_default_ops::subtract; + subtract(m_backend, canonical_value(v)); + return *this; + } + + + mp_number& operator *= (const self_type& e) + { + do_multiplies(detail::mp_exp(e), detail::terminal()); + return *this; + } + + template + mp_number& operator*=(const detail::mp_exp& e) + { + // Create a temporary if the RHS references *this, but not + // if we're just doing an x += x; + if(contains_self(e) && !is_self(e)) + { + self_type temp(e); + do_multiplies(detail::mp_exp(temp), detail::terminal()); + } + else + { + do_multiplies(e, typename Exp::tag_type()); + } + return *this; + } + + template + typename enable_if, mp_number& >::type + operator*=(const V& v) + { + using big_num_default_ops::multiply; + multiply(m_backend, canonical_value(v)); + return *this; + } + + mp_number& operator%=(const self_type& e) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); + do_modulus(detail::mp_exp(e), detail::terminal()); + return *this; + } + template + mp_number& operator%=(const detail::mp_exp& e) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); + // Create a temporary if the RHS references *this: + if(contains_self(e)) + { + self_type temp(e); + do_modulus(temp, typename self_type::tag_type()); + } + else + { + do_modulus(e, typename Exp::tag_type()); + } + return *this; + } + template + typename enable_if, mp_number& >::type + operator%=(const V& v) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); + using big_num_default_ops::modulus; + modulus(m_backend, canonical_value(v)); + return *this; + } + + // + // These operators are *not* proto-ized. + // The issue is that the increment/decrement must happen + // even if the result of the operator *is never used*. + // Possibly we could modify our expression wrapper to + // execute the increment/decrement on destruction, but + // correct implemetation will be tricky, so defered for now... + // + mp_number& operator++() + { + using big_num_default_ops::increment; + increment(m_backend); + return *this; + } + + mp_number& operator--() + { + using big_num_default_ops::decrement; + decrement(m_backend); + return *this; + } + + mp_number operator++(int) + { + using big_num_default_ops::increment; + self_type temp(*this); + increment(m_backend); + return temp; + } + + mp_number operator--(int) + { + using big_num_default_ops::decrement; + self_type temp(*this); + decrement(m_backend); + return temp; + } + + template + typename enable_if, mp_number&>::type operator <<= (V val) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left-shift operation is only valid for integer types"); + check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); + left_shift(m_backend, canonical_value(val)); + return *this; + } + + template + typename enable_if, mp_number&>::type operator >>= (V val) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right-shift operation is only valid for integer types"); + check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); + right_shift(m_backend, canonical_value(val)); + return *this; + } + + mp_number& operator /= (const self_type& e) + { + do_divide(detail::mp_exp(e), detail::terminal()); + return *this; + } + + template + mp_number& operator/=(const detail::mp_exp& e) + { + // Create a temporary if the RHS references *this: + if(contains_self(e)) + { + self_type temp(e); + do_divide(detail::mp_exp(temp), typename self_type::tag_type()); + } + else + { + do_divide(e, typename Exp::tag_type()); + } + return *this; + } + + template + typename enable_if, mp_number& >::type + operator/=(const V& v) + { + using big_num_default_ops::divide; + divide(m_backend, canonical_value(v)); + return *this; + } + + mp_number& operator&=(const self_type& e) + { + do_bitwise_and(detail::mp_exp(e), detail::terminal()); + return *this; + } + + template + mp_number& operator&=(const detail::mp_exp& e) + { + // Create a temporary if the RHS references *this, but not + // if we're just doing an x &= x; + if(contains_self(e) && !is_self(e)) + { + self_type temp(e); + do_bitwise_and(temp, typename self_type::tag_type()); + } + else + { + do_bitwise_and(e, typename Exp::tag_type()); + } + return *this; + } + + template + typename enable_if, mp_number& >::type + operator&=(const V& v) + { + using big_num_default_ops::bitwise_and; + bitwise_and(m_backend, canonical_value(v)); + return *this; + } + + mp_number& operator|=(const self_type& e) + { + do_bitwise_or(detail::mp_exp(e), detail::terminal()); + return *this; + } + + template + mp_number& operator|=(const detail::mp_exp& e) + { + // Create a temporary if the RHS references *this, but not + // if we're just doing an x |= x; + if(contains_self(e) && !is_self(e)) + { + self_type temp(e); + do_bitwise_or(temp, typename self_type::tag_type()); + } + else + { + do_bitwise_or(e, typename Exp::tag_type()); + } + return *this; + } + + template + typename enable_if, mp_number& >::type + operator|=(const V& v) + { + using big_num_default_ops::bitwise_or; + bitwise_or(m_backend, canonical_value(v)); + return *this; + } + + mp_number& operator^=(const self_type& e) + { + do_bitwise_xor(detail::mp_exp(e), detail::terminal()); + return *this; + } + + template + mp_number& operator^=(const detail::mp_exp& e) + { + if(contains_self(e)) + { + self_type temp(e); + do_bitwise_xor(temp, typename self_type::tag_type()); + } + else + { + do_bitwise_xor(e, typename Exp::tag_type()); + } + return *this; + } + + template + typename enable_if, mp_number& >::type + operator^=(const V& v) + { + using big_num_default_ops::bitwise_xor; + bitwise_xor(m_backend, canonical_value(v)); + return *this; + } + // + // Use in boolean context: + // + typedef bool (self_type::*unmentionable_type)()const; + + operator unmentionable_type()const + { + return is_zero() ? 0 : &self_type::is_zero; + } + + // + // swap: + // + void swap(self_type& other) + { + m_backend.swap(other.backend()); + } + // + // Zero and sign: + // + bool is_zero()const + { + using big_num_default_ops::is_zero; + return is_zero(m_backend); + } + int sign()const + { + using big_num_default_ops::get_sign; + return get_sign(m_backend); + } + // + // String conversion functions: + // + std::string str(unsigned digits = 0, bool scientific = true)const + { + return m_backend.str(digits, scientific); + } + template + T convert_to()const + { + using big_num_default_ops::convert_to; + T result; + convert_to(&result, m_backend); + return result; + } + // + // Default precision: + // + static unsigned default_precision() + { + return Backend::default_precision(); + } + static void default_precision(unsigned digits10) + { + Backend::default_precision(digits10); + } + unsigned precision()const + { + return m_backend.precision(); + } + void precision(unsigned digits10) + { + m_backend.precision(digits10); + } + // + // Comparison: + // + int compare(const mp_number& o)const + { + return m_backend.compare(o.m_backend); + } + template + typename enable_if, int>::type compare(const V& o)const + { + using big_num_default_ops::get_sign; + if(o == 0) + return get_sign(m_backend); + return m_backend.compare(canonical_value(o)); + } + Backend& backend() + { + return m_backend; + } + const Backend& backend()const + { + return m_backend; + } +private: + template + void check_shift_range(V val, const mpl::true_&, const mpl::true_&) + { + if(val > (std::numeric_limits::max)()) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); + if(val < 0) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); + } + template + void check_shift_range(V val, const mpl::false_&, const mpl::true_&) + { + if(val < 0) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); + } + template + void check_shift_range(V val, const mpl::true_&, const mpl::false_&) + { + if(val > (std::numeric_limits::max)()) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); + } + template + void check_shift_range(V val, const mpl::false_&, const mpl::false_&){} + + template + void do_assign(const Exp& e, const detail::add_immediates&) + { + using big_num_default_ops::add; + add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + } +/* + template + void do_assign(const Exp& e, const detail::add_and_negate_immediates&) + { + using big_num_default_ops::add; + add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + m_backend.negate(); + } +*/ + template + void do_assign(const Exp& e, const detail::subtract_immediates&) + { + using big_num_default_ops::subtract; + subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + } + /* + template + void do_assign(const Exp& e, const detail::subtract_and_negate_immediates&) + { + using big_num_default_ops::subtract; + subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + m_backend.negate(); + } + */ + template + void do_assign(const Exp& e, const detail::multiply_immediates&) + { + using big_num_default_ops::multiply; + multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + } + + template + void do_assign(const Exp& e, const detail::divide_immediates&) + { + using big_num_default_ops::divide; + divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + } + +#if 0 + template + void do_assign(const Exp& e, const detail::multiply_and_negate_immediates&) + { + using big_num_default_ops::multiply; + multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + m_backend.negate(); + } + + template + void do_assign(const Exp& e, const detail::divide_and_negate_immediates&) + { + using big_num_default_ops::divide; + divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + m_backend.negate(); + } + + template + void do_assign(const Exp& e, const detail::unary_plus&) + { + typedef typename Exp::left_type left_type; + do_assign(e.left(), typename left_type::tag_type()); + } + +#endif + template + void do_assign(const Exp& e, const detail::negate&) + { + typedef typename Exp::left_type left_type; + do_assign(e.left(), typename left_type::tag_type()); + m_backend.negate(); + } + template + void do_assign(const Exp& e, const detail::plus&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; + + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); + + if(bl && is_self(e.left())) + { + // Ignore the left node, it's *this, just add the right: + do_add(e.right(), typename right_type::tag_type()); + } + else if(br && is_self(e.right())) + { + // Ignore the right node, it's *this, just add the left: + do_add(e.left(), typename left_type::tag_type()); + } + else if(bl || br) + { + self_type temp(e); + temp.m_backend.swap(this->m_backend); + } + else if(left_depth >= right_depth) + { + do_assign(e.left(), typename left_type::tag_type()); + do_add(e.right(), typename right_type::tag_type()); + } + else + { + do_assign(e.right(), typename right_type::tag_type()); + do_add(e.left(), typename left_type::tag_type()); + } + } + template + void do_assign(const Exp& e, const detail::minus&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; + + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); + + if(bl && is_self(e.left())) + { + // Ignore the left node, it's *this, just subtract the right: + do_subtract(e.right(), typename right_type::tag_type()); + } + else if(br && is_self(e.right())) + { + // Ignore the right node, it's *this, just subtract the left and negate the result: + do_subtract(e.left(), typename left_type::tag_type()); + m_backend.negate(); + } + else if(bl || br) + { + self_type temp(e); + temp.m_backend.swap(this->m_backend); + } + else if(left_depth >= right_depth) + { + do_assign(e.left(), typename left_type::tag_type()); + do_subtract(e.right(), typename right_type::tag_type()); + } + else + { + do_assign(e.right(), typename right_type::tag_type()); + do_subtract(e.left(), typename left_type::tag_type()); + m_backend.negate(); + } + } + template + void do_assign(const Exp& e, const detail::multiplies&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; + + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); + + if(bl && is_self(e.left())) + { + // Ignore the left node, it's *this, just add the right: + do_multiplies(e.right(), typename right_type::tag_type()); + } + else if(br && is_self(e.right())) + { + // Ignore the right node, it's *this, just add the left: + do_multiplies(e.left(), typename left_type::tag_type()); + } + else if(bl || br) + { + self_type temp(e); + temp.m_backend.swap(this->m_backend); + } + else if(left_depth >= right_depth) + { + do_assign(e.left(), typename left_type::tag_type()); + do_multiplies(e.right(), typename right_type::tag_type()); + } + else + { + do_assign(e.right(), typename right_type::tag_type()); + do_multiplies(e.left(), typename left_type::tag_type()); + } + } + template + void do_assign(const Exp& e, const detail::divides&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); + + if(bl && is_self(e.left())) + { + // Ignore the left node, it's *this, just add the right: + do_divide(e.right(), typename right_type::tag_type()); + } + else if(bl || br) + { + self_type temp(e); + temp.m_backend.swap(this->m_backend); + } + else + { + do_assign(e.left(), typename left_type::tag_type()); + do_divide(e.right(), typename right_type::tag_type()); + } + } + template + void do_assign(const Exp& e, const detail::modulus&) + { + // + // This operation is only valid for integer backends: + // + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); + + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); + + if(bl && is_self(e.left())) + { + // Ignore the left node, it's *this, just add the right: + do_modulus(e.right(), typename right_type::tag_type()); + } + else if(bl || br) + { + self_type temp(e); + temp.m_backend.swap(this->m_backend); + } + else + { + do_assign(e.left(), typename left_type::tag_type()); + do_modulus(e.right(), typename right_type::tag_type()); + } + } + template + void do_assign(const Exp& e, const detail::modulus_immediates&) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); + using big_num_default_ops::modulus; + modulus(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + } + + template + void do_assign(const Exp& e, const detail::bitwise_and&) + { + // + // This operation is only valid for integer backends: + // + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); + + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; + + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); + + if(bl && is_self(e.left())) + { + // Ignore the left node, it's *this, just add the right: + do_bitwise_and(e.right(), typename right_type::tag_type()); + } + else if(br && is_self(e.right())) + { + do_bitwise_and(e.left(), typename left_type::tag_type()); + } + else if(left_depth >= right_depth) + { + do_assign(e.left(), typename left_type::tag_type()); + do_bitwise_and(e.right(), typename right_type::tag_type()); + } + else + { + do_assign(e.right(), typename right_type::tag_type()); + do_bitwise_and(e.left(), typename left_type::tag_type()); + } + } + template + void do_assign(const Exp& e, const detail::bitwise_and_immediates&) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); + using big_num_default_ops::bitwise_and; + bitwise_and(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + } + + template + void do_assign(const Exp& e, const detail::bitwise_or&) + { + // + // This operation is only valid for integer backends: + // + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); + + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; + + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); + + if(bl && is_self(e.left())) + { + // Ignore the left node, it's *this, just add the right: + do_bitwise_or(e.right(), typename right_type::tag_type()); + } + else if(br && is_self(e.right())) + { + do_bitwise_or(e.left(), typename left_type::tag_type()); + } + else if(left_depth >= right_depth) + { + do_assign(e.left(), typename left_type::tag_type()); + do_bitwise_or(e.right(), typename right_type::tag_type()); + } + else + { + do_assign(e.right(), typename right_type::tag_type()); + do_bitwise_or(e.left(), typename left_type::tag_type()); + } + } + template + void do_assign(const Exp& e, const detail::bitwise_or_immediates&) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); + using big_num_default_ops::bitwise_or; + bitwise_or(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + } + + template + void do_assign(const Exp& e, const detail::bitwise_xor&) + { + // + // This operation is only valid for integer backends: + // + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); + + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + + static int const left_depth = left_type::depth; + static int const right_depth = right_type::depth; + + bool bl = contains_self(e.left()); + bool br = contains_self(e.right()); + + if(bl && is_self(e.left())) + { + // Ignore the left node, it's *this, just add the right: + do_bitwise_xor(e.right(), typename right_type::tag_type()); + } + else if(br && is_self(e.right())) + { + do_bitwise_xor(e.left(), typename left_type::tag_type()); + } + else if(left_depth >= right_depth) + { + do_assign(e.left(), typename left_type::tag_type()); + do_bitwise_xor(e.right(), typename right_type::tag_type()); + } + else + { + do_assign(e.right(), typename right_type::tag_type()); + do_bitwise_xor(e.left(), typename left_type::tag_type()); + } + } + template + void do_assign(const Exp& e, const detail::bitwise_xor_immediates&) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); + using big_num_default_ops::bitwise_xor; + bitwise_xor(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + } + template + void do_assign(const Exp& e, const detail::terminal&) + { + if(!is_self(e)) + { + m_backend = canonical_value(e.value()); + } + } + template + void do_assign(const Exp& e, const detail::function&) + { + typedef typename Exp::arity tag_type; + do_assign_function(e, tag_type()); + } + template + void do_assign(const Exp& e, const detail::shift_left&) + { + // We can only shift by an integer value, not an arbitrary expression: + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + typedef typename right_type::arity right_arity; + BOOST_STATIC_ASSERT_MSG(right_arity::value == 0, "The left shift operator requires an integer value for the shift operand."); + typedef typename right_type::result_type right_value_type; + BOOST_STATIC_ASSERT_MSG(is_integral::value, "The left shift operator requires an integer value for the shift operand."); + typedef typename left_type::tag_type tag_type; + do_assign_left_shift(e.left(), canonical_value(e.right().value()), tag_type()); + } + + template + void do_assign(const Exp& e, const detail::shift_right&) + { + // We can only shift by an integer value, not an arbitrary expression: + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + typedef typename right_type::arity right_arity; + BOOST_STATIC_ASSERT_MSG(right_arity::value == 0, "The left shift operator requires an integer value for the shift operand."); + typedef typename right_type::result_type right_value_type; + BOOST_STATIC_ASSERT_MSG(is_integral::value, "The left shift operator requires an integer value for the shift operand."); + typedef typename left_type::tag_type tag_type; + do_assign_right_shift(e.left(), canonical_value(e.right().value()), tag_type()); + } + + template + void do_assign(const Exp& e, const detail::bitwise_complement&) + { + using big_num_default_ops::complement; + self_type temp(e.left()); + complement(m_backend, temp.backend()); + } + + template + void do_assign(const Exp& e, const detail::complement_immediates&) + { + using big_num_default_ops::complement; + complement(m_backend, canonical_value(e.left().value())); + } + + template + void do_assign_right_shift(const Exp& e, const Val& val, const detail::terminal&) + { + using big_num_default_ops::right_shift; + right_shift(m_backend, canonical_value(e.value()), val); + } + + template + void do_assign_left_shift(const Exp& e, const Val& val, const detail::terminal&) + { + using big_num_default_ops::left_shift; + left_shift(m_backend, canonical_value(e.value()), val); + } + + template + void do_assign_right_shift(const Exp& e, const Val& val, const Tag&) + { + using big_num_default_ops::right_shift; + self_type temp(e); + right_shift(m_backend, temp.backend(), val); + } + + template + void do_assign_left_shift(const Exp& e, const Val& val, const Tag&) + { + using big_num_default_ops::left_shift; + self_type temp(e); + left_shift(m_backend, temp.backend(), val); + } + + template + void do_assign_function(const Exp& e, const mpl::int_<1>&) + { + e.left().value()(&m_backend); + } + template + void do_assign_function(const Exp& e, const mpl::int_<2>&) + { + typedef typename Exp::right_type right_type; + typedef typename right_type::tag_type tag_type; + do_assign_function_1(e.left().value(), e.right(), tag_type()); + } + template + void do_assign_function_1(const F& f, const Exp& val, const detail::terminal&) + { + f(m_backend, canonical_value(val.value())); + } + template + void do_assign_function_1(const F& f, const Exp& val, const Tag&) + { + mp_number t(val); + f(m_backend, t.backend()); + } + template + void do_assign_function(const Exp& e, const mpl::int_<3>&) + { + typedef typename Exp::middle_type middle_type; + typedef typename middle_type::tag_type tag_type; + typedef typename Exp::right_type end_type; + typedef typename end_type::tag_type end_tag; + do_assign_function_2(e.left().value(), e.middle(), e.right(), tag_type(), end_tag()); + } + template + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const detail::terminal&) + { + f(m_backend, canonical_value(val1.value()), canonical_value(val2.value())); + } + template + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const detail::terminal&) + { + self_type temp1(val1); + f(m_backend, temp1.backend(), canonical_value(val2.value())); + } + template + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const Tag2&) + { + self_type temp2(val2); + f(m_backend, canonical_value(val1.value()), temp2.backend()); + } + template + void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const Tag2&) + { + self_type temp1(val1); + self_type temp2(val2); + f(m_backend, temp1.backend(), temp2.backend()); + } + + template + void do_add(const Exp& e, const detail::terminal&) + { + using big_num_default_ops::add; + add(m_backend, canonical_value(e.value())); + } + + template + void do_add(const Exp& e, const detail::negate&) + { + typedef typename Exp::left_type left_type; + do_subtract(e.left(), typename left_type::tag_type()); + } + + template + void do_add(const Exp& e, const detail::plus&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_add(e.left(), typename left_type::tag_type()); + do_add(e.right(), typename right_type::tag_type()); + } + + template + void do_add(const Exp& e, const detail::minus&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_add(e.left(), typename left_type::tag_type()); + do_subtract(e.right(), typename right_type::tag_type()); + } + + template + void do_add(const Exp& e, const unknown&) + { + self_type temp(e); + do_add(detail::mp_exp(temp), detail::terminal()); + } + + template + void do_add(const Exp& e, const detail::add_immediates&) + { + using big_num_default_ops::add; + add(m_backend, canonical_value(e.left().value())); + add(m_backend, canonical_value(e.right().value())); + } + template + void do_add(const Exp& e, const detail::subtract_immediates&) + { + using big_num_default_ops::add; + using big_num_default_ops::subtract; + add(m_backend, canonical_value(e.left().value())); + subtract(m_backend, canonical_value(e.right().value())); + } + template + void do_subtract(const Exp& e, const detail::terminal&) + { + using big_num_default_ops::subtract; + subtract(m_backend, canonical_value(e.value())); + } + + template + void do_subtract(const Exp& e, const detail::negate&) + { + typedef typename Exp::left_type left_type; + do_add(e.left(), typename left_type::tag_type()); + } + + template + void do_subtract(const Exp& e, const detail::plus&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_subtract(e.left(), typename left_type::tag_type()); + do_subtract(e.right(), typename right_type::tag_type()); + } + + template + void do_subtract(const Exp& e, const detail::minus&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_subtract(e.left(), typename left_type::tag_type()); + do_add(e.right(), typename right_type::tag_type()); + } + template + void do_subtract(const Exp& e, const detail::add_immediates&) + { + using big_num_default_ops::subtract; + subtract(m_backend, canonical_value(e.left().value())); + subtract(m_backend, canonical_value(e.right().value())); + } + template + void do_subtract(const Exp& e, const detail::subtract_immediates&) + { + using big_num_default_ops::add; + using big_num_default_ops::subtract; + subtract(m_backend, canonical_value(e.left().value())); + add(m_backend, canonical_value(e.right().value())); + } + template + void do_subtract(const Exp& e, const unknown&) + { + self_type temp(e); + do_subtract(detail::mp_exp(temp), detail::terminal()); + } + + template + void do_multiplies(const Exp& e, const detail::terminal&) + { + using big_num_default_ops::multiply; + multiply(m_backend, canonical_value(e.value())); + } + + template + void do_multiplies(const Exp& e, const detail::negate&) + { + typedef typename Exp::left_type left_type; + do_multiplies(e.left(), typename left_type::tag_type()); + m_backend.negate(); + } + + template + void do_multiplies(const Exp& e, const detail::multiplies&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_multiplies(e.left(), typename left_type::tag_type()); + do_multiplies(e.right(), typename right_type::tag_type()); + } + + template + void do_multiplies(const Exp& e, const detail::divides&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_multiplies(e.left(), typename left_type::tag_type()); + do_divide(e.right(), typename right_type::tag_type()); + } + + template + void do_multiplies(const Exp& e, const detail::multiply_immediates&) + { + using big_num_default_ops::multiply; + multiply(m_backend, canonical_value(e.left().value())); + multiply(m_backend, canonical_value(e.right().value())); + } + template + void do_multiplies(const Exp& e, const detail::divide_immediates&) + { + using big_num_default_ops::multiply; + using big_num_default_ops::divide; + multiply(m_backend, canonical_value(e.left().value())); + divide(m_backend, canonical_value(e.right().value())); + } + template + void do_multiplies(const Exp& e, const unknown&) + { + using big_num_default_ops::multiply; + self_type temp(e); + multiply(m_backend, temp.m_backend); + } + + template + void do_divide(const Exp& e, const detail::terminal&) + { + using big_num_default_ops::divide; + divide(m_backend, canonical_value(e.value())); + } + + template + void do_divide(const Exp& e, const detail::negate&) + { + typedef typename Exp::left_type left_type; + do_divide(e.left(), typename left_type::tag_type()); + m_backend.negate(); + } + + template + void do_divide(const Exp& e, const detail::multiplies&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_divide(e.left(), typename left_type::tag_type()); + do_divide(e.right(), typename right_type::tag_type()); + } + + template + void do_divide(const Exp& e, const detail::divides&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_divide(e.left(), typename left_type::tag_type()); + do_multiplies(e.right(), typename right_type::tag_type()); + } + + template + void do_divides(const Exp& e, const detail::multiply_immediates&) + { + using big_num_default_ops::divide; + divide(m_backend, canonical_value(e.left().value())); + divide(m_backend, canonical_value(e.right().value())); + } + template + void do_divides(const Exp& e, const detail::divide_immediates&) + { + using big_num_default_ops::multiply; + using big_num_default_ops::divide; + divide(m_backend, canonical_value(e.left().value())); + mutiply(m_backend, canonical_value(e.right().value())); + } + + template + void do_divide(const Exp& e, const unknown&) + { + using big_num_default_ops::multiply; + self_type temp(e); + divide(m_backend, temp.m_backend); + } + + template + void do_modulus(const Exp& e, const detail::terminal&) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); + using big_num_default_ops::modulus; + modulus(m_backend, canonical_value(e.value())); + } + + template + void do_modulus(const Exp& e, const Unknown&) + { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); + using big_num_default_ops::modulus; + self_type temp(e); + modulus(m_backend, canonical_value(temp)); + } + + template + void do_bitwise_and(const Exp& e, const detail::terminal&) + { + using big_num_default_ops::bitwise_and; + bitwise_and(m_backend, canonical_value(e.value())); + } + template + void do_bitwise_and(const Exp& e, const detail::bitwise_and&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_bitwise_and(e.left(), typename left_type::tag_type()); + do_bitwise_and(e.right(), typename right_type::tag_type()); + } + template + void do_bitwise_and(const Exp& e, const unknown&) + { + using big_num_default_ops::bitwise_and; + self_type temp(e); + bitwise_and(m_backend, temp.m_backend); + } + + template + void do_bitwise_or(const Exp& e, const detail::terminal&) + { + using big_num_default_ops::bitwise_or; + bitwise_or(m_backend, canonical_value(e.value())); + } + template + void do_bitwise_or(const Exp& e, const detail::bitwise_or&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_bitwise_or(e.left(), typename left_type::tag_type()); + do_bitwise_or(e.right(), typename right_type::tag_type()); + } + template + void do_bitwise_or(const Exp& e, const unknown&) + { + using big_num_default_ops::bitwise_or; + self_type temp(e); + bitwise_or(m_backend, temp.m_backend); + } + + template + void do_bitwise_xor(const Exp& e, const detail::terminal&) + { + using big_num_default_ops::bitwise_xor; + bitwise_xor(m_backend, canonical_value(e.value())); + } + template + void do_bitwise_xor(const Exp& e, const detail::bitwise_xor&) + { + typedef typename Exp::left_type left_type; + typedef typename Exp::right_type right_type; + do_bitwise_xor(e.left(), typename left_type::tag_type()); + do_bitwise_xor(e.right(), typename right_type::tag_type()); + } + template + void do_bitwise_xor(const Exp& e, const unknown&) + { + using big_num_default_ops::bitwise_xor; + self_type temp(e); + bitwise_xor(m_backend, temp.m_backend); + } + + // Tests if the expression contains a reference to *this: + template + bool contains_self(const Exp& e)const + { + return contains_self(e, typename Exp::arity()); + } + template + bool contains_self(const Exp& e, mpl::int_<0> const&)const + { + return is_really_self(e.value()); + } + template + bool contains_self(const Exp& e, mpl::int_<1> const&)const + { + typedef typename Exp::left_type child_type; + return contains_self(e.left(), typename child_type::arity()); + } + template + bool contains_self(const Exp& e, mpl::int_<2> const&)const + { + typedef typename Exp::left_type child0_type; + typedef typename Exp::right_type child1_type; + return contains_self(e.left(), typename child0_type::arity()) + || contains_self(e.right(), typename child1_type::arity()); + } + template + bool contains_self(const Exp& e, mpl::int_<3> const&)const + { + typedef typename Exp::left_type child0_type; + typedef typename Exp::middle_type child1_type; + typedef typename Exp::right_type child2_type; + return contains_self(e.left(), typename child0_type::arity()) + || contains_self(e.middle(), typename child1_type::arity()) + || contains_self(e.right(), typename child2_type::arity()); + } + + // Test if the expression is a reference to *this: + template + bool is_self(const Exp& e)const + { + return is_self(e, typename Exp::arity()); + } + template + bool is_self(const Exp& e, mpl::int_<0> const&)const + { + return is_really_self(e.value()); + } + template + bool is_self(const Exp& e, mpl::int_ const&)const + { + return false; + } + + template + bool is_really_self(const Val&)const { return false; } + bool is_really_self(const self_type& v)const { return &v == this; } + + static const Backend& canonical_value(const self_type& v){ return v.m_backend; } + //static const Backend& canonical_value(const self_type* v){ return v->m_backend; } + //static const Backend& canonical_value(self_type* v){ return v->m_backend; } + //static const Backend& canonical_value(self_type& v){ return v.m_backend; } + template + static typename detail::canonical::type canonical_value(const V& v){ return v; } + static typename detail::canonical::type canonical_value(const std::string& v){ return v.c_str(); } + Backend m_backend; +}; + +namespace detail +{ + +template +inline int big_number_compare(const mp_number& a, const mp_number& b) +{ + return a.compare(b); +} + +template +inline int big_number_compare(const mp_number& a, const mp_exp& b) +{ + return a.compare(mp_number(b)); +} + +template +inline int big_number_compare(const mp_exp& a, const mp_number& b) +{ + return -b.compare(mp_number(a)); +} + +template +inline int big_number_compare(const mp_number& a, const Val b) +{ + return a.compare(b); +} + +template +inline int big_number_compare(const Val a, const mp_number& b) +{ + return -b.compare(a); +} + +template +inline int big_number_compare(const mp_exp& a, const mp_exp& b) +{ + typedef typename mp_exp::result_type real1; + typedef typename mp_exp::result_type real2; + return real1(a).compare(real2(b)); +} + +template +inline typename enable_if, int>::type big_number_compare(const mp_exp& a, const Val b) +{ + typedef typename mp_exp::result_type real; + real t(a); + return t.compare(b); +} + +template +inline typename enable_if, int>::type big_number_compare(const Val a, const mp_exp& b) +{ + typedef typename mp_exp::result_type real; + return -real(b).compare(a); +} + +template +struct is_valid_comparison_imp +{ + typedef typename mpl::or_< + is_big_number, + is_big_number_exp + >::type is1; + typedef typename mpl::or_< + is_big_number, + is_big_number_exp + >::type is2; + typedef typename mpl::or_< + mpl::and_< + is1, + mpl::or_< + is2, + is_arithmetic + > + >, + mpl::and_< + is2, + mpl::or_< + is1, + is_arithmetic + > + > + >::type type; +}; + +template +struct is_valid_comparison : public boost::math::detail::is_valid_comparison_imp::type {}; + +} + + +template +inline typename boost::enable_if, bool>::type + operator == (const Exp1& a, const Exp2& b) +{ + return 0 == detail::big_number_compare(a, b); +} + +template +inline typename boost::enable_if, bool>::type + operator != (const Exp1& a, const Exp2& b) +{ + return 0 != detail::big_number_compare(a, b); +} + +template +inline typename boost::enable_if, bool>::type + operator <= (const Exp1& a, const Exp2& b) +{ + return 0 >= detail::big_number_compare(a, b); +} + +template +inline typename boost::enable_if, bool>::type + operator < (const Exp1& a, const Exp2& b) +{ + return 0 > detail::big_number_compare(a, b); +} + +template +inline typename boost::enable_if, bool>::type + operator >= (const Exp1& a, const Exp2& b) +{ + return 0 <= detail::big_number_compare(a, b); +} + +template +inline typename boost::enable_if, bool>::type + operator > (const Exp1& a, const Exp2& b) +{ + return 0 < detail::big_number_compare(a, b); +} + +template +inline std::ostream& operator << (std::ostream& os, const mp_number& r) +{ + return os << r.str(static_cast(os.precision(), os.flags() & os.scientific)); +} + +namespace detail{ + +template +inline std::ostream& operator << (std::ostream& os, const mp_exp& r) +{ + typedef typename mp_exp::result_type value_type; + value_type temp(r); + return os << temp; +} + +} // namespace detail + +template +inline std::istream& operator >> (std::istream& is, mp_number& r) +{ + std::string s; + is >> s; + r = s; + return is; +} + +}} // namespaces + +#endif diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp new file mode 100644 index 00000000..ad018505 --- /dev/null +++ b/include/boost/multiprecision/mpfr.hpp @@ -0,0 +1,952 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_BN_MPFR_HPP +#define BOOST_MATH_BN_MPFR_HPP + +#include +#include +#include +#include +#include +#include +#include +#include + +namespace boost{ namespace math{ + +template +struct mpfr_real_backend; + +namespace detail{ + +long get_default_precision() { return 50; } + +template +struct mpfr_real_imp +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + + mpfr_real_imp(){} + + mpfr_real_imp(const mpfr_real_imp& o) + { + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_set(m_data, o.m_data, GMP_RNDN); + } +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_imp(mpfr_real_imp&& o) + { + m_data[0] = o.m_data[0]; + o.m_data[0]._mpfr_d = 0; + } +#endif + mpfr_real_imp& operator = (const mpfr_real_imp& o) + { + mpfr_set(m_data, o.m_data, GMP_RNDN); + return *this; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_imp& operator = (mpfr_real_imp&& o) + { + mpfr_swap(m_data, o.m_data); + return *this; + } +#endif + mpfr_real_imp& operator = (boost::uintmax_t i) + { + boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned shift = 0; + mpfr_t t; + mpfr_init2(t, (std::max)(static_cast(std::numeric_limits::digits), static_cast(((digits10 + 1) * 1000L) / 301L))); + mpfr_set_ui(m_data, 0, GMP_RNDN); + while(i) + { + mpfr_set_ui(t, static_cast(i & mask), GMP_RNDN); + if(shift) + mpfr_mul_2exp(t, t, shift, GMP_RNDN); + mpfr_add(m_data, m_data, t, GMP_RNDN); + shift += std::numeric_limits::digits; + i >>= std::numeric_limits::digits; + } + mpfr_clear(t); + return *this; + } + mpfr_real_imp& operator = (boost::intmax_t i) + { + bool neg = i < 0; + *this = static_cast(std::abs(i)); + if(neg) + mpfr_neg(m_data, m_data, GMP_RNDN); + return *this; + } + mpfr_real_imp& operator = (unsigned long i) + { + mpfr_set_ui(m_data, i, GMP_RNDN); + return *this; + } + mpfr_real_imp& operator = (long i) + { + mpfr_set_si(m_data, i, GMP_RNDN); + return *this; + } + mpfr_real_imp& operator = (double d) + { + mpfr_set_d(m_data, d, GMP_RNDN); + return *this; + } + mpfr_real_imp& operator = (long double a) + { + using std::frexp; + using std::ldexp; + using std::floor; + + if (a == 0) { + mpfr_set_si(m_data, 0, GMP_RNDN); + return *this; + } + + if (a == 1) { + mpfr_set_si(m_data, 1, GMP_RNDN); + return *this; + } + + BOOST_ASSERT(!(boost::math::isinf)(a)); + BOOST_ASSERT(!(boost::math::isnan)(a)); + + int e; + long double f, term; + mpfr_init_set_ui(m_data, 0u, GMP_RNDN); + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + mpfr_mul_2exp(m_data, m_data, shift, GMP_RNDN); + if(term > 0) + mpfr_add_ui(m_data, m_data, static_cast(term), GMP_RNDN); + else + mpfr_sub_ui(m_data, m_data, static_cast(-term), GMP_RNDN); + f -= term; + } + if(e > 0) + mpfr_mul_2exp(m_data, m_data, e, GMP_RNDN); + else if(e < 0) + mpfr_div_2exp(m_data, m_data, -e, GMP_RNDN); + return *this; + } + mpfr_real_imp& operator = (const char* s) + { + mpfr_set_str(m_data, s, 10, GMP_RNDN); + return *this; + } + void swap(mpfr_real_imp& o) + { + mpfr_swap(m_data, o.m_data); + } + std::string str(unsigned digits, bool scientific)const + { + std::string result; + mp_exp_t e; + char* ps = mpfr_get_str (0, &e, 10, digits, m_data, GMP_RNDN); + std::ptrdiff_t sl = std::strlen(ps); + unsigned chars = sl; + if(sl == 0) + return "0"; + while(ps[chars-1] == '0') + --chars; + if(*ps == '-') + --chars; // number of digits excluding sign. + if(chars == 0) + return "0"; + if(!scientific + && (chars <= std::numeric_limits::digits10 + 1) + && (e >= (int)chars) + && (chars <= std::numeric_limits::digits10 + 1)) + { + result.assign(ps, (*ps == '-' ? chars+1 : chars)); + result.append(e-chars, '0'); + } + else + { + result = ps; + if(ps[0] == '-') + result.insert(2, 1, '.'); + else + result.insert(1, 1, '.'); + --e; + if(e) + result += "e" + lexical_cast(e); + } + mpfr_free_str(ps); + return result; + } + ~mpfr_real_imp() + { + if(m_data[0]._mpfr_d) + mpfr_clear(m_data); + } + void negate() + { + mpfr_neg(m_data, m_data, GMP_RNDN); + } + int compare(const mpfr_real_backend& o)const + { + return mpfr_cmp(m_data, o.m_data); + } + int compare(long i)const + { + return mpfr_cmp_si(m_data, i); + } + int compare(unsigned long i)const + { + return mpfr_cmp_ui(m_data, i); + } + template + int compare(V v)const + { + mpfr_real_backend d; + d = v; + return compare(d); + } + mpfr_t& data() { return m_data; } + const mpfr_t& data()const { return m_data; } +protected: + mpfr_t m_data; + static unsigned& get_default_precision() + { + static unsigned val = 50; + return val; + } +}; + +} // namespace detail + +template +struct mpfr_real_backend : public detail::mpfr_real_imp +{ + mpfr_real_backend() + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + } + mpfr_real_backend(const mpfr_real_backend& o) : detail::mpfr_real_imp(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_backend(mpfr_real_backend&& o) : detail::mpfr_real_imp(o) {} +#endif + mpfr_real_backend& operator=(const mpfr_real_backend& o) + { + *static_cast*>(this) = static_cast const&>(o); + return *this; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_backend& operator=(mpfr_real_backend&& o) + { + *static_cast*>(this) = static_cast&&>(o); + return *this; + } +#endif + template + mpfr_real_backend& operator=(const V& v) + { + *static_cast*>(this) = v; + return *this; + } +}; + +template <> +struct mpfr_real_backend<0> : public detail::mpfr_real_imp<0> +{ + mpfr_real_backend() + { + mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + } + mpfr_real_backend(unsigned digits10) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + } + mpfr_real_backend(const mpfr_real_backend& o) : detail::mpfr_real_imp<0>(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_backend(mpfr_real_backend&& o) : detail::mpfr_real_imp<0>(o) {} +#endif + mpfr_real_backend(const mpfr_real_backend& o, unsigned digits10) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + *this = o; + } + + mpfr_real_backend& operator=(const mpfr_real_backend& o) + { + *static_cast*>(this) = static_cast const&>(o); + return *this; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + mpfr_real_backend& operator=(mpfr_real_backend&& o) + { + *static_cast*>(this) = static_cast &&>(o); + return *this; + } +#endif + template + mpfr_real_backend& operator=(const V& v) + { + *static_cast*>(this) = v; + return *this; + } + static unsigned default_precision() + { + return get_default_precision(); + } + static void default_precision(unsigned v) + { + get_default_precision() = v; + } + unsigned precision()const + { + return mpfr_get_prec(this->m_data) * 301L / 1000 - 1; + } + void precision(unsigned digits10) + { + mpfr_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); + } +}; + +template +inline void add(mpfr_real_backend& result, const mpfr_real_backend& o) +{ + mpfr_add(result.data(), result.data(), o.data(), GMP_RNDN); +} +template +inline void subtract(mpfr_real_backend& result, const mpfr_real_backend& o) +{ + mpfr_sub(result.data(), result.data(), o.data(), GMP_RNDN); +} +template +inline void multiply(mpfr_real_backend& result, const mpfr_real_backend& o) +{ + mpfr_mul(result.data(), result.data(), o.data(), GMP_RNDN); +} +template +inline void divide(mpfr_real_backend& result, const mpfr_real_backend& o) +{ + mpfr_div(result.data(), result.data(), o.data(), GMP_RNDN); +} +template +inline void add(mpfr_real_backend& result, unsigned long i) +{ + mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); +} +template +inline void subtract(mpfr_real_backend& result, unsigned long i) +{ + mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); +} +template +inline void multiply(mpfr_real_backend& result, unsigned long i) +{ + mpfr_mul_ui(result.data(), result.data(), i, GMP_RNDN); +} +template +inline void divide(mpfr_real_backend& result, unsigned long i) +{ + mpfr_div_ui(result.data(), result.data(), i, GMP_RNDN); +} +template +inline void add(mpfr_real_backend& result, long i) +{ + if(i > 0) + mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); + else + mpfr_sub_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); +} +template +inline void subtract(mpfr_real_backend& result, long i) +{ + if(i > 0) + mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); + else + mpfr_add_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); +} +template +inline void multiply(mpfr_real_backend& result, long i) +{ + mpfr_mul_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); + if(i < 0) + mpfr_neg(result.data(), result.data(), GMP_RNDN); +} +template +inline void divide(mpfr_real_backend& result, long i) +{ + mpfr_div_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); + if(i < 0) + mpfr_neg(result.data(), result.data(), GMP_RNDN); +} +// +// Specialised 3 arg versions of the basic operators: +// +template +inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +{ + mpfr_add(a.data(), x.data(), y.data(), GMP_RNDN); +} +template +inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +{ + mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); +} +template +inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +{ + if(y < 0) + mpfr_sub_ui(a.data(), x.data(), -y, GMP_RNDN); + else + mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); +} +template +inline void add(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +{ + mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); +} +template +inline void add(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +{ + if(x < 0) + { + mpfr_ui_sub(a.data(), -x, y.data(), GMP_RNDN); + mpfr_neg(a.data(), a.data(), GMP_RNDN); + } + else + mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); +} +template +inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +{ + mpfr_sub(a.data(), x.data(), y.data(), GMP_RNDN); +} +template +inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +{ + mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); +} +template +inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +{ + if(y < 0) + mpfr_add_ui(a.data(), x.data(), -y, GMP_RNDN); + else + mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); +} +template +inline void subtract(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +{ + mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); +} +template +inline void subtract(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +{ + if(x < 0) + { + mpfr_add_ui(a.data(), y.data(), -x, GMP_RNDN); + mpfr_neg(a.data(), a.data(), GMP_RNDN); + } + else + mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); +} + +template +inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +{ + mpfr_mul(a.data(), x.data(), y.data(), GMP_RNDN); +} +template +inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +{ + mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); +} +template +inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +{ + if(y < 0) + { + mpfr_mul_ui(a.data(), x.data(), -y, GMP_RNDN); + a.negate(); + } + else + mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); +} +template +inline void multiply(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +{ + mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); +} +template +inline void multiply(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +{ + if(x < 0) + { + mpfr_mul_ui(a.data(), y.data(), -x, GMP_RNDN); + mpfr_neg(a.data(), a.data(), GMP_RNDN); + } + else + mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); +} + +template +inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +{ + mpfr_div(a.data(), x.data(), y.data(), GMP_RNDN); +} +template +inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +{ + mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); +} +template +inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +{ + if(y < 0) + { + mpfr_div_ui(a.data(), x.data(), -y, GMP_RNDN); + a.negate(); + } + else + mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); +} +template +inline void divide(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +{ + mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); +} +template +inline void divide(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +{ + if(x < 0) + { + mpfr_ui_div(a.data(), -x, y.data(), GMP_RNDN); + mpfr_neg(a.data(), a.data(), GMP_RNDN); + } + else + mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); +} + +template +inline bool is_zero(const mpfr_real_backend& val) +{ + return 0 != mpfr_zero_p(val.data()); +} +template +inline int get_sign(const mpfr_real_backend& val) +{ + return mpfr_sgn(val.data()); +} + +template +inline void convert_to(unsigned long* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_ui(val.data(), GMP_RNDN); +} +template +inline void convert_to(long* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_si(val.data(), GMP_RNDN); +} +#ifdef _MPFR_H_HAVE_INTMAX_T +template +inline void convert_to(boost::uintmax_t* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_uj(val.data(), GMP_RNDN); +} +template +inline void convert_to(boost::intmax_t* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_sj(val.data(), GMP_RNDN); +} +#endif +template +inline void convert_to(double* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_d(val.data(), GMP_RNDN); +} +template +inline void convert_to(long double* result, const mpfr_real_backend& val) +{ + *result = mpfr_get_ld(val.data(), GMP_RNDN); +} + +// +// Native non-member operations: +// +template +inline void eval_sqrt(mpfr_real_backend& result, const mpfr_real_backend& val) +{ + mpfr_sqrt(result.data(), val.data(), GMP_RNDN); +} + +template +inline void eval_abs(mpfr_real_backend& result, const mpfr_real_backend& val) +{ + mpfr_abs(result.data(), val.data(), GMP_RNDN); +} + +template +inline void eval_fabs(mpfr_real_backend& result, const mpfr_real_backend& val) +{ + mpfr_abs(result.data(), val.data(), GMP_RNDN); +} +template +inline void eval_ceil(mpfr_real_backend& result, const mpfr_real_backend& val) +{ + mpfr_ceil(result.data(), val.data()); +} +template +inline void eval_floor(mpfr_real_backend& result, const mpfr_real_backend& val) +{ + mpfr_floor(result.data(), val.data()); +} +template +inline void eval_trunc(mpfr_real_backend& result, const mpfr_real_backend& val) +{ + mpfr_trunc(result.data(), val.data()); +} +template +inline void eval_ldexp(mpfr_real_backend& result, const mpfr_real_backend& val, long e) +{ + if(e > 0) + mpfr_mul_2exp(result.data(), val.data(), e, GMP_RNDN); + else if(e < 0) + mpfr_div_2exp(result.data(), val.data(), -e, GMP_RNDN); +} +template +inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, int* e) +{ + long v; + mpfr_get_d_2exp(&v, val.data(), GMP_RNDN); + *e = v; + eval_ldexp(result, val, -v); +} +template +inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, long* e) +{ + mpfr_get_d_2exp(e, val.data(), GMP_RNDN); + return eval_ldexp(result, val, -*e); +} + +template +inline int eval_fpclassify(const mpfr_real_backend& val) +{ + return mpfr_inf_p(val.data()) ? FP_INFINITE : mpfr_nan_p(val.data()) ? FP_NAN : mpfr_zero_p(val.data()) ? FP_ZERO : FP_NORMAL; +} + +template +inline void eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const mpfr_real_backend& e) +{ + mpfr_pow(result.data(), b.data(), e.data(), GMP_RNDN); +} + +template +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const Integer& e) +{ + mpfr_pow_si(result.data(), b.data(), e, GMP_RNDN); +} + +template +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const Integer& e) +{ + mpfr_pow_ui(result.data(), b.data(), e, GMP_RNDN); +} + +template +inline void eval_exp(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_exp(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_log(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_log(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_sin(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_sin(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_cos(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_cos(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_tan(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_tan(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_asin(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_asin(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_acos(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_acos(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_atan(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_atan(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_sinh(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_sinh(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_cosh(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_cosh(result.data(), arg.data(), GMP_RNDN); +} + +template +inline void eval_tanh(mpfr_real_backend& result, const mpfr_real_backend& arg) +{ + mpfr_tanh(result.data(), arg.data(), GMP_RNDN); +} + +typedef mp_number > mpfr_real_50; +typedef mp_number > mpfr_real_100; +typedef mp_number > mpfr_real_500; +typedef mp_number > mpfr_real_1000; +typedef mp_number > mpfr_real; + +namespace lanczos{ + +template +struct lanczos >, Policy> +{ + typedef typename mpl::if_c< + Digits10 <= 36, + lanczos22UDT, + typename mpl::if_c< + Digits10 <= 50, + lanczos31UDT, + typename mpl::if_c< + Digits10 <= 110, + lanczos61UDT, + undefined_lanczos + >::type + >::type + >::type type; +}; + +} // namespace lanczos + + +}} // namespaces + +namespace std{ + +#ifdef BOOST_NO_NOEXCEPT +# define noexcept +#endif + +// +// numeric_limits [partial] specializations for the types declared in this header: +// +template +class numeric_limits > > +{ + typedef boost::math::mp_number > number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 0.5; + mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), -mpfr_get_emin(), GMP_RNDN); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 0.5; + mpfr_mul_2exp(value.second.backend().data(), value.second.backend().data(), mpfr_get_emax(), GMP_RNDN); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept + { + return -(max)(); + } + BOOST_STATIC_CONSTEXPR int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); + BOOST_STATIC_CONSTEXPR int digits10 = Digits10; + // Is this really correct??? + BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 1; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR int radix = 2; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits::digits - 1, GMP_RNDN); + } + return value.second; + } + // What value should this be???? + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept + { + // returns epsilon/2 + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), digits, GMP_RNDN); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR long min_exponent = MPFR_EMIN_DEFAULT; + BOOST_STATIC_CONSTEXPR long min_exponent10 = (MPFR_EMIN_DEFAULT / 1000) * 301L; + BOOST_STATIC_CONSTEXPR long max_exponent = MPFR_EMAX_DEFAULT; + BOOST_STATIC_CONSTEXPR long max_exponent10 = (MPFR_EMAX_DEFAULT / 1000) * 301L; + BOOST_STATIC_CONSTEXPR bool has_infinity = true; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept + { + // returns epsilon/2 + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpfr_set_inf(value.second.backend().data(), 1); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept + { + // returns epsilon/2 + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + mpfr_set_nan(value.second.backend().data()); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept + { + return number_type(0); + } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = true; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = true; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest; + +private: + struct data_initializer + { + data_initializer() + { + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); + std::numeric_limits > >::infinity(); + std::numeric_limits > >::quiet_NaN(); + } + void do_nothing()const{} + }; + static const data_initializer initializer; +}; + +template +const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; + +template<> +class numeric_limits > > +{ + typedef boost::math::mp_number > number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = false; + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR int digits = 0; + BOOST_STATIC_CONSTEXPR int digits10 = 0; + BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR bool is_signed = false; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR int radix = 0; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = false; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + +#ifdef noexcept +#undef noexcept +#endif + +} // namespace std +#endif From 73960e2a46a54fbcdf792f834e28ffa48dff4306 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 26 Sep 2011 17:00:44 +0000 Subject: [PATCH 025/256] Giant file and directory rename: changed directory name from math to multiprecision and updated code to match. [SVN r74579] --- Jamroot.jam | 9 + boost-build.jam | 72 + config/Jamfile.v2 | 45 + config/has_e_float.cpp | 17 + config/has_gcc_visibility.cpp | 13 + config/has_gmp.cpp | 7 + config/has_gmpxx.cpp | 7 + config/has_long_double_support.cpp | 10 + config/has_mpfr.cpp | 7 + config/has_mpfr_class.cpp | 14 + config/has_mpreal.cpp | 14 + config/has_ntl_rr.cpp | 12 + doc/Jamfile.v2 | 67 + doc/big_number.qbk | 207 +++ doc/html/boost_bignumbers/intro.html | 44 + doc/html/boost_bignumbers/ref.html | 40 + .../boost_bignumbers/ref/backendconc.html | 38 + doc/html/boost_bignumbers/ref/bignum.html | 151 ++ doc/html/boost_bignumbers/tut.html | 44 + doc/html/boost_bignumbers/tut/ints.html | 146 ++ doc/html/boost_bignumbers/tut/reals.html | 158 +++ doc/html/boostbook.css | 588 ++++++++ doc/html/images/blank.png | Bin 0 -> 374 bytes doc/html/images/caution.png | Bin 0 -> 1250 bytes doc/html/images/caution.svg | 68 + doc/html/images/draft.png | Bin 0 -> 17454 bytes doc/html/images/home.png | Bin 0 -> 358 bytes doc/html/images/home.svg | 26 + doc/html/images/important.png | Bin 0 -> 722 bytes doc/html/images/important.svg | 25 + doc/html/images/next.png | Bin 0 -> 336 bytes doc/html/images/next.svg | 19 + doc/html/images/next_disabled.png | Bin 0 -> 1110 bytes doc/html/images/note.png | Bin 0 -> 490 bytes doc/html/images/note.svg | 33 + doc/html/images/prev.png | Bin 0 -> 334 bytes doc/html/images/prev.svg | 19 + doc/html/images/prev_disabled.png | Bin 0 -> 1109 bytes doc/html/images/tip.png | Bin 0 -> 449 bytes doc/html/images/tip.svg | 84 ++ doc/html/images/toc-blank.png | Bin 0 -> 318 bytes doc/html/images/toc-minus.png | Bin 0 -> 259 bytes doc/html/images/toc-plus.png | Bin 0 -> 264 bytes doc/html/images/up.png | Bin 0 -> 370 bytes doc/html/images/up.svg | 19 + doc/html/images/up_disabled.png | Bin 0 -> 1115 bytes doc/html/images/warning.png | Bin 0 -> 1241 bytes doc/html/images/warning.svg | 23 + doc/html/index.html | 53 + test/Jamfile.v2 | 189 +++ test/big_number_concept_check.cpp | 100 ++ test/linpack-benchmark.cpp | 1257 +++++++++++++++++ test/test_arithmetic.cpp | 894 ++++++++++++ test/test_numeric_limits.cpp | 173 +++ 54 files changed, 4692 insertions(+) create mode 100644 Jamroot.jam create mode 100644 boost-build.jam create mode 100644 config/Jamfile.v2 create mode 100644 config/has_e_float.cpp create mode 100644 config/has_gcc_visibility.cpp create mode 100644 config/has_gmp.cpp create mode 100644 config/has_gmpxx.cpp create mode 100644 config/has_long_double_support.cpp create mode 100644 config/has_mpfr.cpp create mode 100644 config/has_mpfr_class.cpp create mode 100644 config/has_mpreal.cpp create mode 100644 config/has_ntl_rr.cpp create mode 100644 doc/Jamfile.v2 create mode 100644 doc/big_number.qbk create mode 100644 doc/html/boost_bignumbers/intro.html create mode 100644 doc/html/boost_bignumbers/ref.html create mode 100644 doc/html/boost_bignumbers/ref/backendconc.html create mode 100644 doc/html/boost_bignumbers/ref/bignum.html create mode 100644 doc/html/boost_bignumbers/tut.html create mode 100644 doc/html/boost_bignumbers/tut/ints.html create mode 100644 doc/html/boost_bignumbers/tut/reals.html create mode 100644 doc/html/boostbook.css create mode 100644 doc/html/images/blank.png create mode 100644 doc/html/images/caution.png create mode 100644 doc/html/images/caution.svg create mode 100644 doc/html/images/draft.png create mode 100644 doc/html/images/home.png create mode 100644 doc/html/images/home.svg create mode 100644 doc/html/images/important.png create mode 100644 doc/html/images/important.svg create mode 100644 doc/html/images/next.png create mode 100644 doc/html/images/next.svg create mode 100644 doc/html/images/next_disabled.png create mode 100644 doc/html/images/note.png create mode 100644 doc/html/images/note.svg create mode 100644 doc/html/images/prev.png create mode 100644 doc/html/images/prev.svg create mode 100644 doc/html/images/prev_disabled.png create mode 100644 doc/html/images/tip.png create mode 100644 doc/html/images/tip.svg create mode 100644 doc/html/images/toc-blank.png create mode 100644 doc/html/images/toc-minus.png create mode 100644 doc/html/images/toc-plus.png create mode 100644 doc/html/images/up.png create mode 100644 doc/html/images/up.svg create mode 100644 doc/html/images/up_disabled.png create mode 100644 doc/html/images/warning.png create mode 100644 doc/html/images/warning.svg create mode 100644 doc/html/index.html create mode 100644 test/Jamfile.v2 create mode 100644 test/big_number_concept_check.cpp create mode 100644 test/linpack-benchmark.cpp create mode 100644 test/test_arithmetic.cpp create mode 100644 test/test_numeric_limits.cpp diff --git a/Jamroot.jam b/Jamroot.jam new file mode 100644 index 00000000..c8019258 --- /dev/null +++ b/Jamroot.jam @@ -0,0 +1,9 @@ + +import modules ; + +local boost = [ modules.peek : BOOST ] ; + +project sandbox : requirements $(boost) ; + +# This seems to prevent some Boost.Build errors that otherwise occur :-( +use-project /boost : $(boost) ; diff --git a/boost-build.jam b/boost-build.jam new file mode 100644 index 00000000..02b750a1 --- /dev/null +++ b/boost-build.jam @@ -0,0 +1,72 @@ +# Copyright Rene Rivera 2007. +# +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt) + +# For instructions see Jamfile.v2, or "bjam --help". + +local rule if-has-file ( file + : dir * ) +{ + local result ; + if $(dir) + { + result = [ GLOB $(dir) : $(file) ] ; + } + return $(result[1]:P) ; +} + +#~ Attempts to find the Boost source tree... + +local boost-src = [ if-has-file LICENSE_1_0.txt : + [ MATCH --boost=(.*) : $(ARGV) ] + $(BOOST) + $(BOOST_ROOT) + $(.boost-build-file:D)/../boost + $(.boost-build-file:D)/../Trunk + ] ; + +# error handling: +if ! $(boost-src) +{ + ECHO Unable to find the Boost source tree in the locations searched. ; + ECHO Try setting the environment variable BOOST to point to your ; + ECHO Boost tree, or else invoke bjam with the --boost=path option. ; + ECHO The Boost include path will not be automatically set. ; + ECHO The paths searched were [ MATCH --boost=(.*) : $(ARGV) ] $(BOOST) $(.boost-build-file:D)/../boost $(.boost-build-file:D)/../Trunk ; + ECHO But the file LICENSE_1_0.txt was not found in any of them ; +} + +#~ Attempts to find the Boost.Build files... + +local boost-build-src = [ if-has-file bootstrap.jam : + [ MATCH --boost-build=(.*) : $(ARGV) ] + $(BOOST_BUILD_PATH) + $(BOOST_BUILD) + $(boost-src)/tools/build/v2 + ] ; + +# error handling: +if ! $(boost-build-src) +{ + ECHO Unable to find the Boost.Build source tree in the locations searched. ; + ECHO Try setting the environment variable BOOST_BUILD to point to your ; + ECHO Boost.Build tree, or else invoke bjam with the --boost-build=path option. ; + ECHO The paths searched were [ MATCH --boost-build=(.*) : $(ARGV) ] $(BOOST_BUILD_PATH) $(BOOST_BUILD) $(boost-src)/tools/build/v2 ; + ECHO But bootstrap.jam was not found in any of these ; + ECHO More failures will very likely follow... ; +} + +#~ Set some common vars to refer to the Boost sources... + +BOOST ?= $(boost-src) ; +BOOST_ROOT ?= $(boost-src) ; + +#~ And load up Boost.Build... + +boost-build $(boost-build-src) ; + + + + + diff --git a/config/Jamfile.v2 b/config/Jamfile.v2 new file mode 100644 index 00000000..832e2936 --- /dev/null +++ b/config/Jamfile.v2 @@ -0,0 +1,45 @@ +# copyright John Maddock 2008 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + +import modules ; +import path ; + +local ntl-path = [ modules.peek : NTL_PATH ] ; +local gmp_path = [ modules.peek : GMP_PATH ] ; +local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local e_float_path = [ modules.peek : BOOST_E_FLOAT_PATH ] ; + +if ! $(e_float_path) +{ + e_float_path = ../../../../e_float ; +} + +ECHO $(BOOST_E_FLOAT_PATH) + +obj has_long_double_support : has_long_double_support.cpp ; +obj has_mpfr_class : has_mpfr_class.cpp : + $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; +obj has_mpreal : has_mpreal.cpp : + $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/mpfrc++ ; +obj has_ntl_rr : has_ntl_rr.cpp : $(ntl-path)/include ; +obj has_gmpxx : has_gmpxx.cpp : + $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; +obj has_gcc_visibility : has_gcc_visibility.cpp : + gcc:-fvisibility=hidden gcc:-Werror ; +obj has_e_float : has_e_float.cpp : $(e_float_path) ; +obj has_gmp : has_gmp.cpp : + $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; +obj has_mpfr : has_mpfr.cpp : + $(mpfr_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; + +explicit has_long_double_support ; +explicit has_mpfr_class ; +explicit has_mpreal ; +explicit has_ntl_rr ; +explicit has_gmpxx ; +explicit has_gcc_visibility ; +explicit has_e_float ; +explicit has_gmp ; +explicit has_mpfr ; diff --git a/config/has_e_float.cpp b/config/has_e_float.cpp new file mode 100644 index 00000000..8cadc5c6 --- /dev/null +++ b/config/has_e_float.cpp @@ -0,0 +1,17 @@ +// Copyright John Maddock 2011. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + + +#ifdef _MSC_VER +# pragma warning (disable : 4100) // unreferenced formal parameter +#endif + +#define E_FLOAT_TYPE_EFX + +#include +#include +#include + + diff --git a/config/has_gcc_visibility.cpp b/config/has_gcc_visibility.cpp new file mode 100644 index 00000000..6c7d6f91 --- /dev/null +++ b/config/has_gcc_visibility.cpp @@ -0,0 +1,13 @@ +// Copyright John Maddock 20010. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef __GNUC__ +# error "This is a GCC specific test case". +#endif + +int main() +{ + return 0; +} diff --git a/config/has_gmp.cpp b/config/has_gmp.cpp new file mode 100644 index 00000000..582f0027 --- /dev/null +++ b/config/has_gmp.cpp @@ -0,0 +1,7 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + diff --git a/config/has_gmpxx.cpp b/config/has_gmpxx.cpp new file mode 100644 index 00000000..edf62d8c --- /dev/null +++ b/config/has_gmpxx.cpp @@ -0,0 +1,7 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + diff --git a/config/has_long_double_support.cpp b/config/has_long_double_support.cpp new file mode 100644 index 00000000..d314cf38 --- /dev/null +++ b/config/has_long_double_support.cpp @@ -0,0 +1,10 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS +#error "long double support is not supported by Boost.Math on this Plaform: the long double version of the TR1 library will not be built." +#endif diff --git a/config/has_mpfr.cpp b/config/has_mpfr.cpp new file mode 100644 index 00000000..49d12a0b --- /dev/null +++ b/config/has_mpfr.cpp @@ -0,0 +1,7 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + diff --git a/config/has_mpfr_class.cpp b/config/has_mpfr_class.cpp new file mode 100644 index 00000000..8eb3c7b2 --- /dev/null +++ b/config/has_mpfr_class.cpp @@ -0,0 +1,14 @@ +// Copyright John Maddock 2008. +// Copyright Paul A. Britow 2009 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4127) // conditional expression is constant +# pragma warning (disable : 4800) // 'int' : forcing value to bool 'true' or 'false' (performance warning) +# pragma warning (disable : 4512) // assignment operator could not be generated +#endif + +#include + diff --git a/config/has_mpreal.cpp b/config/has_mpreal.cpp new file mode 100644 index 00000000..8ee8897d --- /dev/null +++ b/config/has_mpreal.cpp @@ -0,0 +1,14 @@ +// Copyright John Maddock 2008. +// Copyright Paul A. Britow 2009 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4127) // conditional expression is constant +# pragma warning (disable : 4800) // 'int' : forcing value to bool 'true' or 'false' (performance warning) +# pragma warning (disable : 4512) // assignment operator could not be generated +#endif + +#include + diff --git a/config/has_ntl_rr.cpp b/config/has_ntl_rr.cpp new file mode 100644 index 00000000..f3844217 --- /dev/null +++ b/config/has_ntl_rr.cpp @@ -0,0 +1,12 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + + +#ifdef _MSC_VER +# pragma warning (disable : 4100) // unreferenced formal parameter +#endif + +#include + diff --git a/doc/Jamfile.v2 b/doc/Jamfile.v2 new file mode 100644 index 00000000..2f00f026 --- /dev/null +++ b/doc/Jamfile.v2 @@ -0,0 +1,67 @@ + +# Copyright John Maddock 2011. Use, modification, and distribution are +# subject to the Boost Software License, Version 1.0. (See accompanying +# file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +using quickbook ; + +path-constant images_location : html ; + +xml big_number : big_number.qbk ; +boostbook standalone + : + big_number + : + # Path for links to Boost: + #boost.root=../../../../.. + + # Some general style settings: + table.footnote.number.format=1 + footnote.number.format=1 + html.stylesheet=boostbook.css + + # HTML options first: + # Use graphics not text for navigation: + navig.graphics=1 + # How far down we chunk nested sections, basically all of them: + chunk.section.depth=10 + # Don't put the first section on the same page as the TOC: + chunk.first.sections=10 + # How far down sections get TOC's + toc.section.depth=10 + # Max depth in each TOC: + toc.max.depth=4 + # How far down we go with TOC's + #generate.section.toc.level=10 + # Index on type: + index.on.type=1 + + # PDF Options: + # TOC Generation: this is needed for FOP-0.9 and later: + fop1.extensions=0 + pdf:xep.extensions=1 + # TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9! + pdf:fop.extensions=0 + pdf:fop1.extensions=0 + # No indent on body text: + pdf:body.start.indent=0pt + # Margin size: + pdf:page.margin.inner=0.5in + # Margin size: + pdf:page.margin.outer=0.5in + # Paper type = A4 + pdf:paper.type=A4 + # Yes, we want graphics for admonishments: + admon.graphics=1 + # Set this one for PDF generation *only*: + # default pnd graphics are awful in PDF form, + # better use SVG's instead: + pdf:admon.graphics.extension=".svg" + pdf:use.role.for.mediaobject=1 + pdf:preferred.mediaobject.role=print + pdf:img.src.path=$(images_location)/ + pdf:draft.mode="no" + pdf:boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/sf_and_dist/html + ; + +install pdf-install : standalone : . PDF ; diff --git a/doc/big_number.qbk b/doc/big_number.qbk new file mode 100644 index 00000000..4ccfb199 --- /dev/null +++ b/doc/big_number.qbk @@ -0,0 +1,207 @@ +[/ + Copyright 2011 John Maddock. + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt). +] + +[library Boost.BigNumbers + [quickbook 1.5] + [copyright 2011 John Maddock] + [purpose Big Number library] + [license + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + [@http://www.boost.org/LICENSE_1_0.txt]) + ] + [authors [authors, various]] + [last-revision $Date: 2011-07-08 18:51:46 +0100 (Fri, 08 Jul 2011) $] +] + +[section:intro Introduction] + +The Big Number library comes in two distinct parts: an expression template enabled front end `big_number` +that handles all the operator overloading, expression evaluation optimization, and code reduction, and +a selection of backends that implement the actual arithmetic operations, and need conform only to the +reduced interface requirements of the front end. + +[endsect] + +[section:tut Tutorial] + +In order to use this library you need to make two choices: what kind of number do I want, and +which backend do I want to perform the actual arithmetic? + +[section:ints Integer Types] + +The following backends provide integer arithmetic: + +[table +[[Backend Type][Header][Radix][Dependencies][Pros][Cons]] +[[`gmp_int`][boost/math/big_number/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] +] + +[h4 gmp_int] + + namespace boost{ namespace math{ + + class gmp_int; + + typedef big_number mpz_int; + + }} // namespaces + +The `gmp_int` backend is used via the typedef `boost::math::mpz_int`. It acts as a thin wrapper around the GMP `mpz_t` +to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. + +[h5 Example:] + + #include + + boost::math::mpz_int v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + + std::cout << i << std::endl; // prints 1000! + +[endsect] + +[section:reals Real Numbers] + +The following backends provide real number arithmetic: + +[table +[[Backend Type][Header][Radix][Dependencies][Pros][Cons]] +[[`gmp_real`][boost/math/big_number/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] +] + +[h4 gmp_real] + + namespace boost{ namespace math{ + + template + class gmp_real; + + typedef big_number > mpf_real_50; + typedef big_number > mpf_real_100; + typedef big_number > mpf_real_500; + typedef big_number > mpf_real_1000; + typedef big_number > mpf_real; + + }} // namespaces + +The `gmp_real` backend is used in conjunction with `big_number`: It acts as a thin wrapper around the GMP `mpf_t` +to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision. + +Type `gmp_real` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or +at variable precision by setting the template argument to zero. The typedefs mpf_real_50, mpf_real_100, +mpf_real_500, mpf_real_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision +respectively. The typedef mpf_real provides a variable precision type whose precision can be controlled via the +`big_number`'s member functions. + +[h5 example:] + + #include + + boost::math::gmp_real a = 2; + boost::math::gmp_real::default_precision(1000); + std::cout << boost::math::gmp_real::default_precision() << std::endl; + std::cout << sqrt(a) << std::endl; // print root-2 + +[endsect] + +[endsect] + +[section:ref Reference] + +[section:bignum big_number] + +[h4 Synopsis] + + namespace boost{ namespace math{ + + template + class big_number + { + big_number(); + big_number(see-below); + big_number& operator=(see-below); + /* Other number-type operators here */ + // string conversion: + std::string str()const; + // precision control: + static unsigned default_precision(); + static void default_precision(unsigned digits10); + unsigned precision()const; + void precision(unsigned digits10); + // Comparison: + int compare(const big_number& o)const; + template + typename enable_if, int>::type compare(const V& o)const; + }; + + }} // namespaces + +[h4 Description] + + big_number(); + big_number(see-below); + big_number& operator=(see-below); + +Type `big_number` is default constructible, and copy both constructible and assignable from: + +* Itself. +* An expression template which is the result of one of the arithmetic operators. +* Any builtin arithmetic type. +* A `std::string` or any type which is convertible to `const char*`. + + /* Other number-type operators here */ + +The following arithmetic operations are support for real-numbered types: + +* Binary +, -, *, /, +=, -=, *=, /=, ==, !=, <=, >=, <, >. +* Unary +, -. + +For integer types the following operators are also supported: + +Binary %, %=. + +(More to follow!!) + +Note that the result of the binary +, -, *, / and % operations is an expression template of "unmentionable type". + + std::string str()const; + +Returns the number formatted as a string (TODO: enable custom precision). + + static unsigned default_precision(); + static void default_precision(unsigned digits10); + unsigned precision()const; + void precision(unsigned digits10); + +These functions are only available if the Backend template parameter supports runtime changes to precision. They get and set +the default precision and the precision of *this respectively. + + int compare(const big_number& o)const; + template + typename enable_if, int>::type compare(const V& other)const; + +Returns: + +* A value less that 0 for *this < other +* A value greater that 0 for *this > other +* Zero for *this == other + +[endsect] + +[section:backendconc Backend Requirements] + +TODO, big boring job!! + +[endsect] + +[endsect] + diff --git a/doc/html/boost_bignumbers/intro.html b/doc/html/boost_bignumbers/intro.html new file mode 100644 index 00000000..ee77f4b1 --- /dev/null +++ b/doc/html/boost_bignumbers/intro.html @@ -0,0 +1,44 @@ + + + +Introduction + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+

+ The Big Number library comes in two distinct parts: an expression template + enabled front end big_number + that handles all the operator overloading, expression evaluation optimization, + and code reduction, and a selection of backends that implement the actual arithmetic + operations, and need conform only to the reduced interface requirements of + the front end. +

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_bignumbers/ref.html b/doc/html/boost_bignumbers/ref.html new file mode 100644 index 00000000..c6a81e2f --- /dev/null +++ b/doc/html/boost_bignumbers/ref.html @@ -0,0 +1,40 @@ + + + +Reference + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+
+
big_number
+
Backend Requirements
+
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_bignumbers/ref/backendconc.html b/doc/html/boost_bignumbers/ref/backendconc.html new file mode 100644 index 00000000..44dd13af --- /dev/null +++ b/doc/html/boost_bignumbers/ref/backendconc.html @@ -0,0 +1,38 @@ + + + +Backend Requirements + + + + + + + +
+
+
+PrevUpHome +
+
+
+

+ TODO, big boring job!! +

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHome +
+ + diff --git a/doc/html/boost_bignumbers/ref/bignum.html b/doc/html/boost_bignumbers/ref/bignum.html new file mode 100644 index 00000000..bcf3ef57 --- /dev/null +++ b/doc/html/boost_bignumbers/ref/bignum.html @@ -0,0 +1,151 @@ + + + +big_number + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+
+ + Synopsis +
+
namespace boost{ namespace math{
+
+template <class Backend>
+class big_number
+{
+   big_number();
+   big_number(see-below);
+   big_number& operator=(see-below);
+   /* Other number-type operators here */
+   // string conversion:
+   std::string str()const;
+   // precision control:
+   static unsigned default_precision();
+   static void default_precision(unsigned digits10);
+   unsigned precision()const;
+   void precision(unsigned digits10);
+   // Comparison:
+   int compare(const big_number<Backend>& o)const;
+   template <class V>
+   typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
+};
+
+}} // namespaces
+
+
+ + Description +
+
big_number();
+big_number(see-below);
+big_number& operator=(see-below);
+
+

+ Type big_number is default + constructible, and copy both constructible and assignable from: +

+
    +
  • + Itself. +
    • +
  • + An expression template which is the result of one of the arithmetic operators. +
    • +
  • + Any builtin arithmetic type. +
    • +
  • + A std::string or any type which is convertible + to const char*. +
    • +
+
/* Other number-type operators here */
+
+

+ The following arithmetic operations are support for real-numbered types: +

+
    +
  • + Binary +, -, *, /, +, -, *, /, + ==, !, <, >=, <, >. +
    • +
  • + Unary +, -. +
    • +
+

+ For integer types the following operators are also supported: +

+

+ Binary %, %=. +

+

+ (More to follow!!) +

+

+ Note that the result of the binary +, -, *, / and % operations is an expression + template of "unmentionable type". +

+
std::string str()const;
+
+

+ Returns the number formatted as a string (TODO: enable custom precision). +

+
static unsigned default_precision();
+static void default_precision(unsigned digits10);
+unsigned precision()const;
+void precision(unsigned digits10);
+
+

+ These functions are only available if the Backend template parameter supports + runtime changes to precision. They get and set the default precision and + the precision of *this respectively. +

+
int compare(const big_number<Backend>& o)const;
+template <class V>
+typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
+
+

+ Returns: +

+
    +
  • + A value less that 0 for *this < other +
    • +
  • + A value greater that 0 for *this > other +
    • +
  • + Zero for *this == other +
    • +
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_bignumbers/tut.html b/doc/html/boost_bignumbers/tut.html new file mode 100644 index 00000000..92e58b08 --- /dev/null +++ b/doc/html/boost_bignumbers/tut.html @@ -0,0 +1,44 @@ + + + +Tutorial + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+
+
Integer Types
+
Real Numbers
+
+

+ In order to use this library you need to make two choices: what kind of number + do I want, and which backend do I want to perform the actual arithmetic? +

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_bignumbers/tut/ints.html b/doc/html/boost_bignumbers/tut/ints.html new file mode 100644 index 00000000..b2dbce57 --- /dev/null +++ b/doc/html/boost_bignumbers/tut/ints.html @@ -0,0 +1,146 @@ + + + +Integer Types + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+

+ The following backends provide integer arithmetic: +

+
++++++++ + + + + + + + + + + + + + + + + +
+

+ Backend Type +

+ 		+

+ Header +

+ 		+

+ Radix +

+ 		+

+ Dependencies +

+ 		+

+ Pros +

+ 		+

+ Cons +

+
+

+ gmp_int +

+ 		+

+ boost/math/big_number/gmp.hpp +

+ 		+

+ 2 +

+ 		+

+ GMP +

+ 		+

+ Very fast and efficient backend. +

+ 		+

+ Dependency on GNU licenced GMP library. +

+
+
+ + gmp_int +
+
namespace boost{ namespace math{
+
+class gmp_int;
+
+typedef big_number<gmp_int >         mpz_int;
+
+}} // namespaces
+
+

+ The gmp_int backend is used + via the typedef boost::math::mpz_int. It acts as a thin wrapper around + the GMP mpz_t to provide + an integer type that is a drop-in replacement for the native C++ integer + types, but with unlimited precision. +

+
+ + Example: +
+
#include <boost/math/big_number/gmp.hpp>
+
+boost::math::mpz_int v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+
+std::cout << i << std::endl; // prints 1000!
+
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_bignumbers/tut/reals.html b/doc/html/boost_bignumbers/tut/reals.html new file mode 100644 index 00000000..cd08e445 --- /dev/null +++ b/doc/html/boost_bignumbers/tut/reals.html @@ -0,0 +1,158 @@ + + + +Real Numbers + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+

+ The following backends provide real number arithmetic: +

+
++++++++ + + + + + + + + + + + + + + + + +
+

+ Backend Type +

+ 		+

+ Header +

+ 		+

+ Radix +

+ 		+

+ Dependencies +

+ 		+

+ Pros +

+ 		+

+ Cons +

+
+

+ gmp_real<N> +

+ 		+

+ boost/math/big_number/gmp.hpp +

+ 		+

+ 2 +

+ 		+

+ GMP +

+ 		+

+ Very fast and efficient backend. +

+ 		+

+ Dependency on GNU licenced GMP library. +

+
+
+ + gmp_real +
+
namespace boost{ namespace math{
+
+template <unsigned Digits10>
+class gmp_real;
+
+typedef big_number<gmp_real<50> >    mpf_real_50;
+typedef big_number<gmp_real<100> >   mpf_real_100;
+typedef big_number<gmp_real<500> >   mpf_real_500;
+typedef big_number<gmp_real<1000> >  mpf_real_1000;
+typedef big_number<gmp_real<0> >     mpf_real;
+
+}} // namespaces
+
+

+ The gmp_real backend is used + in conjunction with big_number: + It acts as a thin wrapper around the GMP mpf_t + to provide an real-number type that is a drop-in replacement for the native + C++ floating-point types, but with much greater precision. +

+

+ Type gmp_real can be used + at fixed precision by specifying a non-zero Digits10 + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpf_real_50, mpf_real_100, mpf_real_500, mpf_real_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpf_real provides a variable precision type whose + precision can be controlled via the big_number's + member functions. +

+
+ + example: +
+
#include <boost/math/big_number/gmp.hpp>
+
+boost::math::gmp_real a = 2;
+boost::math::gmp_real::default_precision(1000);
+std::cout << boost::math::gmp_real::default_precision() << std::endl;
+std::cout << sqrt(a) << std::endl; // print root-2
+
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boostbook.css b/doc/html/boostbook.css new file mode 100644 index 00000000..252fa9ec --- /dev/null +++ b/doc/html/boostbook.css @@ -0,0 +1,588 @@ +/*============================================================================= + Copyright (c) 2004 Joel de Guzman + http://spirit.sourceforge.net/ + + Distributed under the Boost Software License, Version 1.0. (See accompany- + ing file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +=============================================================================*/ + +/*============================================================================= + Body defaults +=============================================================================*/ + + body + { + margin: 1em; + font-family: sans-serif; + } + +/*============================================================================= + Paragraphs +=============================================================================*/ + + p + { + text-align: left; + font-size: 10pt; + line-height: 1.15; + } + +/*============================================================================= + Program listings +=============================================================================*/ + + /* Code on paragraphs */ + p tt.computeroutput + { + font-size: 9pt; + } + + pre.synopsis + { + font-size: 90%; + margin: 1pc 4% 0pc 4%; + padding: 0.5pc 0.5pc 0.5pc 0.5pc; + } + + .programlisting, + .screen + { + font-size: 9pt; + display: block; + margin: 1pc 4% 0pc 4%; + padding: 0.5pc 0.5pc 0.5pc 0.5pc; + } + + /* Program listings in tables don't get borders */ + td .programlisting, + td .screen + { + margin: 0pc 0pc 0pc 0pc; + padding: 0pc 0pc 0pc 0pc; + } + +/*============================================================================= + Headings +=============================================================================*/ + + h1, h2, h3, h4, h5, h6 + { + text-align: left; + margin: 1em 0em 0.5em 0em; + font-weight: bold; + } + + h1 { font: 140% } + h2 { font: bold 140% } + h3 { font: bold 130% } + h4 { font: bold 120% } + h5 { font: italic 110% } + h6 { font: italic 100% } + + /* Top page titles */ + title, + h1.title, + h2.title + h3.title, + h4.title, + h5.title, + h6.title, + .refentrytitle + { + font-weight: bold; + margin-bottom: 1pc; + } + + h1.title { font-size: 140% } + h2.title { font-size: 140% } + h3.title { font-size: 130% } + h4.title { font-size: 120% } + h5.title { font-size: 110% } + h6.title { font-size: 100% } + + .section h1 + { + margin: 0em 0em 0.5em 0em; + font-size: 140%; + } + + .section h2 { font-size: 140% } + .section h3 { font-size: 130% } + .section h4 { font-size: 120% } + .section h5 { font-size: 110% } + .section h6 { font-size: 100% } + + /* Code on titles */ + h1 tt.computeroutput { font-size: 140% } + h2 tt.computeroutput { font-size: 140% } + h3 tt.computeroutput { font-size: 130% } + h4 tt.computeroutput { font-size: 120% } + h5 tt.computeroutput { font-size: 110% } + h6 tt.computeroutput { font-size: 100% } + +/*============================================================================= + Author +=============================================================================*/ + + h3.author + { + font-size: 100% + } + +/*============================================================================= + Lists 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table + { + padding: 4px; + } + + /* Table Cells */ + div.informaltable table tr td, + div.table table tr td + { + padding: 0.5em; + text-align: left; + font-size: 9pt; + } + + div.informaltable table tr th, + div.table table tr th + { + padding: 0.5em 0.5em 0.5em 0.5em; + border: 1pt solid white; + font-size: 80%; + } + + table.simplelist + { + width: auto !important; + margin: 0em !important; + padding: 0em !important; + border: none !important; + } + table.simplelist td + { + margin: 0em !important; + padding: 0em !important; + text-align: left !important; + font-size: 9pt !important; + border: none !important; + } + +/*============================================================================= + Blurbs +=============================================================================*/ + + div.note, + div.tip, + div.important, + div.caution, + div.warning, + p.blurb + { + font-size: 9pt; /* A little bit smaller than the main text */ + line-height: 1.2; + display: block; + margin: 1pc 4% 0pc 4%; + padding: 0.5pc 0.5pc 0.5pc 0.5pc; + } + + p.blurb img + { + padding: 1pt; + } + +/*============================================================================= + Variable Lists +=============================================================================*/ + + /* Make the terms in definition lists bold */ + div.variablelist dl dt, + span.term + { + font-weight: bold; + font-size: 10pt; + } + + div.variablelist table tbody tr td + { + text-align: left; + vertical-align: top; + padding: 0em 2em 0em 0em; + font-size: 10pt; + margin: 0em 0em 0.5em 0em; + line-height: 1; + } + + div.variablelist dl dt + { + margin-bottom: 0.2em; + } + + div.variablelist dl dd + { + margin: 0em 0em 0.5em 2em; + font-size: 10pt; + } + + div.variablelist table tbody tr td p, + div.variablelist dl dd p + { + margin: 0em 0em 0.5em 0em; + line-height: 1; + } + +/*============================================================================= + Misc +=============================================================================*/ + + /* Title of books and articles in bibliographies */ + span.title + { + font-style: italic; + } + + span.underline + { + text-decoration: underline; + } + + span.strikethrough + { + text-decoration: line-through; + } + + /* Copyright, Legal Notice */ + div div.legalnotice p + { + text-align: left + } + +/*============================================================================= + Colors +=============================================================================*/ + + @media screen + { + body { + background-color: #FFFFFF; + } + + /* Links */ + a + { + color: #005a9c; + } + + a:visited + { + color: #9c5a9c; + } + + h1 a, h2 a, h3 a, h4 a, h5 a, h6 a, + h1 a:hover, h2 a:hover, h3 a:hover, h4 a:hover, h5 a:hover, h6 a:hover, + h1 a:visited, h2 a:visited, h3 a:visited, h4 a:visited, h5 a:visited, h6 a:visited + { + text-decoration: none; /* no underline */ + color: #000000; + } + + /* Syntax Highlighting */ + .keyword { color: #0000AA; } + .identifier { color: #000000; } + .special { color: #707070; } + .preprocessor { color: #402080; } + .char { color: teal; } + .comment { color: #800000; } + .string { color: teal; } + .number { color: teal; } + .white_bkd { background-color: #FFFFFF; } + .dk_grey_bkd { background-color: #999999; } + + /* Copyright, Legal Notice */ + .copyright + { + color: #666666; + font-size: small; + } + + div div.legalnotice p + { + color: #666666; + } + + /* Program listing */ + pre.synopsis + { + border: 1px solid #DCDCDC; + } + + .programlisting, + .screen + { + border: 1px solid #DCDCDC; + } + + td .programlisting, + td .screen + { + border: 0px solid #DCDCDC; + } + + /* Blurbs */ + div.note, + div.tip, + div.important, + div.caution, + div.warning, + p.blurb + { + border: 1px solid #DCDCDC; + } + + /* Table of contents */ + .toc + { + border: 1px solid #DCDCDC; + } + + /* Tables */ + div.informaltable table tr td, + div.table table tr td + { + border: 1px solid #DCDCDC; + } + + div.informaltable table tr th, + div.table table tr th + { + background-color: #F0F0F0; + border: 1px solid #DCDCDC; + } + + .copyright-footer + { + color: #8F8F8F; + } + + /* Misc */ + span.highlight + { + color: #00A000; + } + } + + @media print + { + /* Links */ + a + { + color: black; + } + + a:visited + { + color: black; + } + + .spirit-nav + { + display: none; + } + + /* Program listing */ + pre.synopsis + { + border: 1px solid gray; + } + + .programlisting, + .screen + { + border: 1px solid gray; + } + + td .programlisting, + td .screen + { + border: 0px solid #DCDCDC; + } + + /* Table of contents */ + .toc + { + border: 1px solid gray; + } + + .informaltable table, + .table table + { + border: 1px solid gray; + border-collapse: collapse; + } + + /* Tables */ + div.informaltable table tr td, + div.table table tr td + { + border: 1px solid gray; + } + + div.informaltable table tr th, + div.table table tr th + { + border: 1px solid gray; + } + + table.simplelist tr td + { + border: none !important; + } + + /* Misc */ + span.highlight + { + font-weight: bold; + } + } + +/*============================================================================= + Images +=============================================================================*/ + + span.inlinemediaobject img + { + vertical-align: middle; + } + +/*============================================================================== + Super and Subscript: style so that line spacing isn't effected, see + http://www.adobe.com/cfusion/communityengine/index.cfm?event=showdetails&productId=1&postId=5341 +==============================================================================*/ + +sup, +sub { + height: 0; + line-height: 1; + vertical-align: baseline; + _vertical-align: bottom; + position: relative; + +} + +sup { + bottom: 1ex; +} + +sub { + top: .5ex; +} + diff --git a/doc/html/images/blank.png b/doc/html/images/blank.png new file mode 100644 index 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+
+
Next
+
+
+

+Chapter 1. Boost.BigNumbers

+

+various authors +

+

Copyright © 2011 John Maddock

+
+

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+

Table of Contents

+
+
Introduction
+
Tutorial
+
+
Integer Types
+
Real Numbers
+
+
Reference
+
+
big_number
+
Backend Requirements
+
+
+
+
+ + + +

Last revised: July 08, 2011 at 18:51:46 +0100

+
+
Next
+ + diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 new file mode 100644 index 00000000..24b697e7 --- /dev/null +++ b/test/Jamfile.v2 @@ -0,0 +1,189 @@ +# copyright John Maddock 2008 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + +import modules ; +import path ; + +local ntl-path = [ modules.peek : NTL_PATH ] ; +local gmp_path = [ modules.peek : GMP_PATH ] ; +local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local e_float_path = [ modules.peek : BOOST_E_FLOAT_PATH ] ; + +if ! $(e_float_path) +{ + e_float_path = ../../../../e_float ; +} + +project : requirements + $(gmp_path) + $(gmp_path)/mpfr + $(gmp_path)/gmpfrxx + $(mpfr_path) + ../../.. + $(e_float_path) + $(gmp_path) + $(mpfr_path) + $(mpfr_path)/build.vc10/lib/Win32/Debug + msvc:static + E_FLOAT_DIGITS10=100 + E_FLOAT_TYPE_EFX + ; + +lib gmp ; +lib mpfr ; + +E_FLOAT_SRC = [ GLOB $(e_float_path)/libs/e_float/src/e_float : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/e_float/efx : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/constants : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/elementary : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/gamma : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/integer : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/tables : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/functions/zeta : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/generic_functions/constants : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/generic_functions/elementary : *.cpp ] + [ GLOB $(e_float_path)/libs/e_float/src/utility : *.cpp ] + ; + +lib e_float : $(E_FLOAT_SRC) + : + [ check-target-builds ../config//has_e_float : : no ] + ; + +run test_arithmetic.cpp + : # command line + : # input files + : # requirements + TEST_BACKEND + : test_arithmetic_backend_concept ; + +run test_arithmetic.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_arithmetic_mpf50 ; + +run test_arithmetic.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF + [ check-target-builds ../config//has_gmp : : no ] + : test_arithmetic_mpf ; + +run test_arithmetic.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPZ + [ check-target-builds ../config//has_gmp : : no ] + : test_arithmetic_mpz ; + +run test_arithmetic.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPQ + [ check-target-builds ../config//has_gmp : : no ] + : test_arithmetic_mpq ; + +run test_arithmetic.cpp mpfr gmp + : # command line + : # input files + : # requirements + TEST_MPFR + [ check-target-builds ../config//has_mpfr : : no ] + : test_arithmetic_mpfr ; + +run test_arithmetic.cpp mpfr gmp + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_arithmetic_mpfr_50 ; + +run test_arithmetic.cpp $(E_FLOAT_SRC) + : # command line + : # input files + : # requirements + TEST_E_FLOAT + [ check-target-builds ../config//has_e_float : : no ] + : test_arithmetic_e_float ; + +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + TEST_BACKEND + : test_numeric_limits_backend_concept ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_numeric_limits_mpf50 ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF + [ check-target-builds ../config//has_gmp : : no ] + : test_numeric_limits_mpf ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPZ + [ check-target-builds ../config//has_gmp : : no ] + : test_numeric_limits_mpz ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPQ + [ check-target-builds ../config//has_gmp : : no ] + : test_numeric_limits_mpq ; + +run test_numeric_limits.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR + [ check-target-builds ../config//has_mpfr : : no ] + : test_numeric_limits_mpfr ; + +run test_numeric_limits.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_numeric_limits_mpfr_50 ; + + +run test_numeric_limits.cpp $(E_FLOAT_SRC) + : # command line + : # input files + : # requirements + TEST_E_FLOAT + [ check-target-builds ../config//has_e_float : : no ] + : test_numeric_limits_e_float ; + +run big_number_concept_check.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : big_number_concept_check_mpfr_50 ; + diff --git a/test/big_number_concept_check.cpp b/test/big_number_concept_check.cpp new file mode 100644 index 00000000..466af22f --- /dev/null +++ b/test/big_number_concept_check.cpp @@ -0,0 +1,100 @@ + +// Copyright John Maddock 2011. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests two things: that e_float meets our +// conceptual requirements, and that we can instantiate +// all our distributions and special functions on this type. +// +#define BOOST_MATH_ASSERT_UNDEFINED_POLICY false +#define BOOST_MATH_INSTANTIATE_MINIMUM + +#ifdef _MSC_VER +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) +# define TEST_MPF50 +# define TEST_MPF +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR +# define TEST_MPFR_50 +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) +#include +#endif + +#include +#include "libs/math/test/compile_test/instantiate.hpp" + +void foo() +{ +#ifdef TEST_BACKEND + instantiate(boost::math::big_number_real_architype()); +#endif +#ifdef TEST_MPF_50 + instantiate(boost::math::mpf_real_50()); +#endif +#ifdef TEST_MPF + instantiate(boost::math::mpf_real()); +#endif +#ifdef TEST_MPFR_50 + instantiate(boost::math::mpfr_real_50()); +#endif +#ifdef TEST_MPFR + instantiate(boost::math::mpfr_real()); +#endif +#ifdef TEST_E_FLOAT + instantiate(boost::math::e_float()); +#endif +} + +int main() +{ +#ifdef TEST_BACKEND + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif +#ifdef TEST_MPF_50 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif +#ifdef TEST_MPF + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif +#ifdef TEST_MPFR_50 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif +#ifdef TEST_MPFR + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif +#ifdef TEST_E_FLOAT + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif + +} diff --git a/test/linpack-benchmark.cpp b/test/linpack-benchmark.cpp new file mode 100644 index 00000000..27fdde3e --- /dev/null +++ b/test/linpack-benchmark.cpp @@ -0,0 +1,1257 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +/* 1000d.f -- translated by f2c (version 20050501). +You must link the resulting object file with libf2c: +on Microsoft Windows system, link with libf2c.lib; +on Linux or Unix systems, link with .../path/to/libf2c.a -lm +or, if you install libf2c.a in a standard place, with -lf2c -lm +-- in that order, at the end of the command line, as in +cc *.o -lf2c -lm +Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + +http://www.netlib.org/f2c/libf2c.zip +*/ +#include +#include +#include +#include + +#ifdef TEST_MPF_100 +#include +typedef boost::math::mpf_real_100 real_type; +#elif defined(TEST_MPFR_100) +#include +typedef boost::math::mpfr_real_100 real_type; +#elif defined(TEST_GMPXX) +#include +typedef mpf_class real_type; +#elif defined(TEST_MPFRXX) +#include +typedef mpfr_class real_type; +#elif defined(TEST_E_FLOAT) +#include +#include +#include +typedef ::efx::e_float real_type; +using ef::abs; +#elif defined(TEST_E_FLOAT_BN) +#include +typedef boost::math::e_float real_type; +#else +typedef double real_type; +#endif + +#ifndef CAST_TO_RT +# define CAST_TO_RT(x) x +#endif + +extern "C" { +#include "f2c.h" + integer s_wsfe(cilist *), e_wsfe(void), do_fio(integer *, char *, ftnlen), + s_wsle(cilist *), do_lio(integer *, integer *, char *, ftnlen), + e_wsle(void); + /* Subroutine */ int s_stop(char *, ftnlen); + +#undef abs +#undef dabs +#define dabs abs +#undef min +#undef max +#undef dmin +#undef dmax +#define dmin min +#define dmax max + +} +#include + +using std::min; +using std::max; + +/* Table of constant values */ + +static integer c__0 = 0; +static real_type c_b7 = CAST_TO_RT(1); +static integer c__1 = 1; +static integer c__9 = 9; + +inline double second_(void) +{ + return ((double)(clock())) / CLOCKS_PER_SEC; +} + +int dgefa_(real_type *, integer *, integer *, integer *, integer *), dgesl_(real_type *, integer *, integer *, integer *, real_type *, integer *); +int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type *); +int matgen_(real_type *, integer *, integer *, real_type *, real_type *); +real_type epslon_(real_type *); +real_type ran_(integer *); +int dscal_(integer *, real_type *, real_type *, integer *); +int daxpy_(integer *, real_type *, real_type *, integer *, real_type *, integer *); +integer idamax_(integer *, real_type *, integer *); +real_type ddot_(integer *, real_type *, integer *, real_type *, integer *); +int daxpy_(integer *, real_type *, real_type *, integer *, real_type *, integer *); +int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type *); + + +extern "C" int MAIN__() +{ +#ifdef TEST_MPF_100 + std::cout << "Testing mp_number >" << std::endl; +#elif defined(TEST_MPFR_100) + std::cout << "Testing mp_number >" << std::endl; +#elif defined(TEST_GMPXX) + std::cout << "Testing mpf_class at 100 decimal degits" << std::endl; + mpf_set_default_prec(((100 + 1) * 1000L) / 301L); +#elif defined(TEST_MPFRXX) + std::cout << "Testing mpfr_class at 100 decimal degits" << std::endl; + mpfr_set_default_prec(((100 + 1) * 1000L) / 301L); +#elif defined(TEST_E_FLOAT) + std::cout << "Testing boost::ef::e_float" << std::endl; +#elif defined(TEST_E_FLOAT_BN) + std::cout << "Testing boost::math::e_float" << std::endl; +#else + std::cout << "Testing double" << std::endl; +#endif + + + /* Format strings */ + static char fmt_1[] = "(\002 Please send the results of this run to:\002" + "//\002 Jack J. Dongarra\002/\002 Computer Science Department\002/" + "\002 University of Tennessee\002/\002 Knoxville, Tennessee 37996" + "-1300\002//\002 Fax: 615-974-8296\002//\002 Internet: dongarra@c" + "s.utk.edu\002/)"; + static char fmt_40[] = "(\002 norm. resid resid mac" + "hep\002,\002 x(1) x(n)\002)"; + static char fmt_50[] = "(1p5e16.8)"; + static char fmt_60[] = "(//\002 times are reported for matrices of or" + "der \002,i5)"; + static char fmt_70[] = "(6x,\002factor\002,5x,\002solve\002,6x,\002tota" + "l\002,5x,\002mflops\002,7x,\002unit\002,6x,\002ratio\002)"; + static char fmt_80[] = "(\002 times for array with leading dimension o" + "f\002,i4)"; + static char fmt_110[] = "(6(1pe11.3))"; + + /* System generated locals */ + integer i__1; + real_type d__1, d__2, d__3; + + /* Builtin functions */ + + /* Local variables */ + static real_type a[1001000] /* was [1001][1000] */, b[1000]; + static integer i__, n; + static real_type x[1000]; + static double t1; + static integer lda; + static double ops; + static real_type eps; + static integer info; + static double time[6], cray, total; + static integer ipvt[1000]; + static real_type resid, norma; + static real_type normx; + static real_type residn; + + /* Fortran I/O blocks */ + static cilist io___4 = { 0, 6, 0, fmt_1, 0 }; + static cilist io___20 = { 0, 6, 0, fmt_40, 0 }; + static cilist io___21 = { 0, 6, 0, fmt_50, 0 }; + static cilist io___22 = { 0, 6, 0, fmt_60, 0 }; + static cilist io___23 = { 0, 6, 0, fmt_70, 0 }; + static cilist io___24 = { 0, 6, 0, fmt_80, 0 }; + static cilist io___25 = { 0, 6, 0, fmt_110, 0 }; + static cilist io___26 = { 0, 6, 0, 0, 0 }; + + + lda = 1001; + + /* this program was updated on 10/12/92 to correct a */ + /* problem with the random number generator. The previous */ + /* random number generator had a short period and produced */ + /* singular matrices occasionally. */ + + n = 1000; + cray = .056f; + s_wsfe(&io___4); + e_wsfe(); + /* Computing 3rd power */ + d__1 = (real_type) n; + /* Computing 2nd power */ + d__2 = (real_type) n; + ops = boost::lexical_cast(real_type(d__1 * (d__1 * d__1) * 2. / 3. + d__2 * d__2 * 2.)); + + matgen_(a, &lda, &n, b, &norma); + + /* ****************************************************************** */ + /* ****************************************************************** */ + /* you should replace the call to dgefa and dgesl */ + /* by calls to your linear equation solver. */ + /* ****************************************************************** */ + /* ****************************************************************** */ + + t1 = second_(); + dgefa_(a, &lda, &n, ipvt, &info); + time[0] = second_() - t1; + t1 = second_(); + dgesl_(a, &lda, &n, ipvt, b, &c__0); + time[1] = second_() - t1; + total = time[0] + time[1]; + /* ****************************************************************** */ + /* ****************************************************************** */ + + /* compute a residual to verify results. */ + + i__1 = n; + for (i__ = 1; i__ <= i__1; ++i__) { + x[i__ - 1] = b[i__ - 1]; + /* L10: */ + } + matgen_(a, &lda, &n, b, &norma); + i__1 = n; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ - 1] = -b[i__ - 1]; + /* L20: */ + } + dmxpy_(&n, b, &n, &lda, x, a); + resid = CAST_TO_RT(0); + normx = CAST_TO_RT(0); + i__1 = n; + for (i__ = 1; i__ <= i__1; ++i__) { + /* Computing MAX */ + d__2 = resid, d__3 = (d__1 = b[i__ - 1], abs(d__1)); + resid = max(d__2,d__3); + /* Computing MAX */ + d__2 = normx, d__3 = (d__1 = x[i__ - 1], abs(d__1)); + normx = max(d__2,d__3); + /* L30: */ + } + eps = epslon_(&c_b7); + residn = resid / (n * norma * normx * eps); + s_wsfe(&io___20); + e_wsfe(); + s_wsfe(&io___21); + /* + do_fio(&c__1, (char *)&residn, (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&resid, (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&eps, (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&x[0], (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&x[n - 1], (ftnlen)sizeof(real_type)); + */ + std::cout << std::setw(12) << std::setprecision(5) << residn << " " << resid << " " << eps << " " << x[0] << " " << x[n-1] << std::endl; + e_wsfe(); + + s_wsfe(&io___22); + do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); + e_wsfe(); + s_wsfe(&io___23); + e_wsfe(); + + time[2] = total; + time[3] = ops / (total * 1e6); + time[4] = 2. / time[3]; + time[5] = total / cray; + s_wsfe(&io___24); + do_fio(&c__1, (char *)&lda, (ftnlen)sizeof(integer)); + e_wsfe(); + s_wsfe(&io___25); + for (i__ = 1; i__ <= 6; ++i__) { + // do_fio(&c__1, (char *)&time[i__ - 1], (ftnlen)sizeof(real_type)); + std::cout << std::setw(12) << std::setprecision(5) << time[i__ - 1]; + } + e_wsfe(); + s_wsle(&io___26); + do_lio(&c__9, &c__1, " end of tests -- this version dated 10/12/92", ( + ftnlen)44); + e_wsle(); + + s_stop("", (ftnlen)0); + return 0; +} /* MAIN__ */ + +/* Subroutine */ int matgen_(real_type *a, integer *lda, integer *n, + real_type *b, real_type *norma) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + real_type d__1, d__2; + + /* Local variables */ + static integer i__, j; + static integer init[4]; + + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --b; + + /* Function Body */ + init[0] = 1; + init[1] = 2; + init[2] = 3; + init[3] = 1325; + *norma = CAST_TO_RT(0); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = ran_(init) - .5f; + /* Computing MAX */ + d__2 = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + *norma = max(d__2,*norma); + /* L20: */ + } + /* L30: */ + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__] = CAST_TO_RT(0); + /* L35: */ + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__] += a[i__ + j * a_dim1]; + /* L40: */ + } + /* L50: */ + } + return 0; +} /* matgen_ */ + +/* Subroutine */ int dgefa_(real_type *a, integer *lda, integer *n, integer * + ipvt, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + static integer j, k, l; + static real_type t; + static integer kp1, nm1; + + + /* dgefa factors a double precision matrix by gaussian elimination. */ + + /* dgefa is usually called by dgeco, but it can be called */ + /* directly with a saving in time if rcond is not needed. */ + /* (time for dgeco) = (1 + 9/n)*(time for dgefa) . */ + + /* on entry */ + + /* a double precision(lda, n) */ + /* the matrix to be factored. */ + + /* lda integer */ + /* the leading dimension of the array a . */ + + /* n integer */ + /* the order of the matrix a . */ + + /* on return */ + + /* a an upper triangular matrix and the multipliers */ + /* which were used to obtain it. */ + /* the factorization can be written a = l*u where */ + /* l is a product of permutation and unit lower */ + /* triangular matrices and u is upper triangular. */ + + /* ipvt integer(n) */ + /* an integer vector of pivot indices. */ + + /* info integer */ + /* = 0 normal value. */ + /* = k if u(k,k) .eq. 0.0 . this is not an error */ + /* condition for this subroutine, but it does */ + /* indicate that dgesl or dgedi will divide by zero */ + /* if called. use rcond in dgeco for a reliable */ + /* indication of singularity. */ + + /* linpack. this version dated 08/14/78 . */ + /* cleve moler, university of new mexico, argonne national lab. */ + + /* subroutines and functions */ + + /* blas daxpy,dscal,idamax */ + + /* internal variables */ + + + + /* gaussian elimination with partial pivoting */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipvt; + + /* Function Body */ + *info = 0; + nm1 = *n - 1; + if (nm1 < 1) { + goto L70; + } + i__1 = nm1; + for (k = 1; k <= i__1; ++k) { + kp1 = k + 1; + + /* find l = pivot index */ + + i__2 = *n - k + 1; + l = idamax_(&i__2, &a[k + k * a_dim1], &c__1) + k - 1; + ipvt[k] = l; + + /* zero pivot implies this column already triangularized */ + + if (a[l + k * a_dim1] == 0.) { + goto L40; + } + + /* interchange if necessary */ + + if (l == k) { + goto L10; + } + t = a[l + k * a_dim1]; + a[l + k * a_dim1] = a[k + k * a_dim1]; + a[k + k * a_dim1] = t; +L10: + + /* compute multipliers */ + + t = -1. / a[k + k * a_dim1]; + i__2 = *n - k; + dscal_(&i__2, &t, &a[k + 1 + k * a_dim1], &c__1); + + /* row elimination with column indexing */ + + i__2 = *n; + for (j = kp1; j <= i__2; ++j) { + t = a[l + j * a_dim1]; + if (l == k) { + goto L20; + } + a[l + j * a_dim1] = a[k + j * a_dim1]; + a[k + j * a_dim1] = t; +L20: + i__3 = *n - k; + daxpy_(&i__3, &t, &a[k + 1 + k * a_dim1], &c__1, &a[k + 1 + j * + a_dim1], &c__1); + /* L30: */ + } + goto L50; +L40: + *info = k; +L50: + /* L60: */ + ; + } +L70: + ipvt[*n] = *n; + if (a[*n + *n * a_dim1] == 0.) { + *info = *n; + } + return 0; +} /* dgefa_ */ + +/* Subroutine */ int dgesl_(real_type *a, integer *lda, integer *n, integer * + ipvt, real_type *b, integer *job) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + static integer k, l; + static real_type t; + static integer kb, nm1; + + + /* dgesl solves the double precision system */ + /* a * x = b or trans(a) * x = b */ + /* using the factors computed by dgeco or dgefa. */ + + /* on entry */ + + /* a double precision(lda, n) */ + /* the output from dgeco or dgefa. */ + + /* lda integer */ + /* the leading dimension of the array a . */ + + /* n integer */ + /* the order of the matrix a . */ + + /* ipvt integer(n) */ + /* the pivot vector from dgeco or dgefa. */ + + /* b double precision(n) */ + /* the right hand side vector. */ + + /* job integer */ + /* = 0 to solve a*x = b , */ + /* = nonzero to solve trans(a)*x = b where */ + /* trans(a) is the transpose. */ + + /* on return */ + + /* b the solution vector x . */ + + /* error condition */ + + /* a division by zero will occur if the input factor contains a */ + /* zero on the diagonal. technically this indicates singularity */ + /* but it is often caused by improper arguments or improper */ + /* setting of lda . it will not occur if the subroutines are */ + /* called correctly and if dgeco has set rcond .gt. 0.0 */ + /* or dgefa has set info .eq. 0 . */ + + /* to compute inverse(a) * c where c is a matrix */ + /* with p columns */ + /* call dgeco(a,lda,n,ipvt,rcond,z) */ + /* if (rcond is too small) go to ... */ + /* do 10 j = 1, p */ + /* call dgesl(a,lda,n,ipvt,c(1,j),0) */ + /* 10 continue */ + + /* linpack. this version dated 08/14/78 . */ + /* cleve moler, university of new mexico, argonne national lab. */ + + /* subroutines and functions */ + + /* blas daxpy,ddot */ + + /* internal variables */ + + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipvt; + --b; + + /* Function Body */ + nm1 = *n - 1; + if (*job != 0) { + goto L50; + } + + /* job = 0 , solve a * x = b */ + /* first solve l*y = b */ + + if (nm1 < 1) { + goto L30; + } + i__1 = nm1; + for (k = 1; k <= i__1; ++k) { + l = ipvt[k]; + t = b[l]; + if (l == k) { + goto L10; + } + b[l] = b[k]; + b[k] = t; +L10: + i__2 = *n - k; + daxpy_(&i__2, &t, &a[k + 1 + k * a_dim1], &c__1, &b[k + 1], &c__1); + /* L20: */ + } +L30: + + /* now solve u*x = y */ + + i__1 = *n; + for (kb = 1; kb <= i__1; ++kb) { + k = *n + 1 - kb; + b[k] /= a[k + k * a_dim1]; + t = -b[k]; + i__2 = k - 1; + daxpy_(&i__2, &t, &a[k * a_dim1 + 1], &c__1, &b[1], &c__1); + /* L40: */ + } + goto L100; +L50: + + /* job = nonzero, solve trans(a) * x = b */ + /* first solve trans(u)*y = b */ + + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + i__2 = k - 1; + t = ddot_(&i__2, &a[k * a_dim1 + 1], &c__1, &b[1], &c__1); + b[k] = (b[k] - t) / a[k + k * a_dim1]; + /* L60: */ + } + + /* now solve trans(l)*x = y */ + + if (nm1 < 1) { + goto L90; + } + i__1 = nm1; + for (kb = 1; kb <= i__1; ++kb) { + k = *n - kb; + i__2 = *n - k; + b[k] += ddot_(&i__2, &a[k + 1 + k * a_dim1], &c__1, &b[k + 1], &c__1); + l = ipvt[k]; + if (l == k) { + goto L70; + } + t = b[l]; + b[l] = b[k]; + b[k] = t; +L70: + /* L80: */ + ; + } +L90: +L100: + return 0; +} /* dgesl_ */ + +/* Subroutine */ int daxpy_(integer *n, real_type *da, real_type *dx, + integer *incx, real_type *dy, integer *incy) +{ + /* System generated locals */ + integer i__1; + + /* Local variables */ + static integer i__, m, ix, iy, mp1; + + + /* constant times a vector plus a vector. */ + /* uses unrolled loops for increments equal to one. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*da == 0.) { + return 0; + } + if (*incx == 1 && *incy == 1) { + goto L20; + } + + /* code for unequal increments or equal increments */ + /* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[iy] += *da * dx[ix]; + ix += *incx; + iy += *incy; + /* L10: */ + } + return 0; + + /* code for both increments equal to 1 */ + + + /* clean-up loop */ + +L20: + m = *n % 4; + if (m == 0) { + goto L40; + } + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[i__] += *da * dx[i__]; + /* L30: */ + } + if (*n < 4) { + return 0; + } +L40: + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 4) { + dy[i__] += *da * dx[i__]; + dy[i__ + 1] += *da * dx[i__ + 1]; + dy[i__ + 2] += *da * dx[i__ + 2]; + dy[i__ + 3] += *da * dx[i__ + 3]; + /* L50: */ + } + return 0; +} /* daxpy_ */ + +real_type ddot_(integer *n, real_type *dx, integer *incx, real_type *dy, + integer *incy) +{ + /* System generated locals */ + integer i__1; + real_type ret_val; + + /* Local variables */ + static integer i__, m, ix, iy, mp1; + static real_type dtemp; + + + /* forms the dot product of two vectors. */ + /* uses unrolled loops for increments equal to one. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + ret_val = CAST_TO_RT(0); + dtemp = CAST_TO_RT(0); + if (*n <= 0) { + return ret_val; + } + if (*incx == 1 && *incy == 1) { + goto L20; + } + + /* code for unequal increments or equal increments */ + /* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[ix] * dy[iy]; + ix += *incx; + iy += *incy; + /* L10: */ + } + ret_val = dtemp; + return ret_val; + + /* code for both increments equal to 1 */ + + + /* clean-up loop */ + +L20: + m = *n % 5; + if (m == 0) { + goto L40; + } + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[i__] * dy[i__]; + /* L30: */ + } + if (*n < 5) { + goto L60; + } +L40: + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 5) { + dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + dx[ + i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + dx[i__ + + 4] * dy[i__ + 4]; + /* L50: */ + } +L60: + ret_val = dtemp; + return ret_val; +} /* ddot_ */ + +/* Subroutine */ int dscal_(integer *n, real_type *da, real_type *dx, + integer *incx) +{ + /* System generated locals */ + integer i__1, i__2; + + /* Local variables */ + static integer i__, m, mp1, nincx; + + + /* scales a vector by a constant. */ + /* uses unrolled loops for increment equal to one. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*incx == 1) { + goto L20; + } + + /* code for increment not equal to 1 */ + + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + dx[i__] = *da * dx[i__]; + /* L10: */ + } + return 0; + + /* code for increment equal to 1 */ + + + /* clean-up loop */ + +L20: + m = *n % 5; + if (m == 0) { + goto L40; + } + i__2 = m; + for (i__ = 1; i__ <= i__2; ++i__) { + dx[i__] = *da * dx[i__]; + /* L30: */ + } + if (*n < 5) { + return 0; + } +L40: + mp1 = m + 1; + i__2 = *n; + for (i__ = mp1; i__ <= i__2; i__ += 5) { + dx[i__] = *da * dx[i__]; + dx[i__ + 1] = *da * dx[i__ + 1]; + dx[i__ + 2] = *da * dx[i__ + 2]; + dx[i__ + 3] = *da * dx[i__ + 3]; + dx[i__ + 4] = *da * dx[i__ + 4]; + /* L50: */ + } + return 0; +} /* dscal_ */ + +integer idamax_(integer *n, real_type *dx, integer *incx) +{ + /* System generated locals */ + integer ret_val, i__1; + real_type d__1; + + /* Local variables */ + static integer i__, ix; + static real_type dmax__; + + + /* finds the index of element having max. dabsolute value. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dx; + + /* Function Body */ + ret_val = 0; + if (*n < 1) { + return ret_val; + } + ret_val = 1; + if (*n == 1) { + return ret_val; + } + if (*incx == 1) { + goto L20; + } + + /* code for increment not equal to 1 */ + + ix = 1; + dmax__ = abs(dx[1]); + ix += *incx; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[ix], abs(d__1)) <= dmax__) { + goto L5; + } + ret_val = i__; + dmax__ = (d__1 = dx[ix], abs(d__1)); +L5: + ix += *incx; + /* L10: */ + } + return ret_val; + + /* code for increment equal to 1 */ + +L20: + dmax__ = abs(dx[1]); + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[i__], abs(d__1)) <= dmax__) { + goto L30; + } + ret_val = i__; + dmax__ = (d__1 = dx[i__], abs(d__1)); +L30: + ; + } + return ret_val; +} /* idamax_ */ + +real_type epslon_(real_type *x) +{ +#if defined(TEST_MPF_100) || defined(TEST_MPFR_100) || defined(TEST_GMPXX) || defined(TEST_MPFRXX) + return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); +#elif defined(TEST_E_FLOAT_BN) + return std::pow(10.0, 1-std::numeric_limits::digits10); +#else + return CAST_TO_RT(std::numeric_limits::epsilon()); +#endif +} /* epslon_ */ + +/* Subroutine */ int mm_(real_type *a, integer *lda, integer *n1, integer * + n3, real_type *b, integer *ldb, integer *n2, real_type *c__, + integer *ldc) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2; + + /* Local variables */ + static integer i__, j; + + + /* purpose: */ + /* multiply matrix b times matrix c and store the result in matrix a. */ + + /* parameters: */ + + /* a double precision(lda,n3), matrix of n1 rows and n3 columns */ + + /* lda integer, leading dimension of array a */ + + /* n1 integer, number of rows in matrices a and b */ + + /* n3 integer, number of columns in matrices a and c */ + + /* b double precision(ldb,n2), matrix of n1 rows and n2 columns */ + + /* ldb integer, leading dimension of array b */ + + /* n2 integer, number of columns in matrix b, and number of rows in */ + /* matrix c */ + + /* c double precision(ldc,n3), matrix of n2 rows and n3 columns */ + + /* ldc integer, leading dimension of array c */ + + /* ---------------------------------------------------------------------- */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + + /* Function Body */ + i__1 = *n3; + for (j = 1; j <= i__1; ++j) { + i__2 = *n1; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = CAST_TO_RT(0); + /* L10: */ + } + dmxpy_(n2, &a[j * a_dim1 + 1], n1, ldb, &c__[j * c_dim1 + 1], &b[ + b_offset]); + /* L20: */ + } + + return 0; +} /* mm_ */ + +/* Subroutine */ int dmxpy_(integer *n1, real_type *y, integer *n2, integer * + ldm, real_type *x, real_type *m) +{ + /* System generated locals */ + integer m_dim1, m_offset, i__1, i__2; + + /* Local variables */ + static integer i__, j, jmin; + + + /* purpose: */ + /* multiply matrix m times vector x and add the result to vector y. */ + + /* parameters: */ + + /* n1 integer, number of elements in vector y, and number of rows in */ + /* matrix m */ + + /* y double precision(n1), vector of length n1 to which is added */ + /* the product m*x */ + + /* n2 integer, number of elements in vector x, and number of columns */ + /* in matrix m */ + + /* ldm integer, leading dimension of array m */ + + /* x double precision(n2), vector of length n2 */ + + /* m double precision(ldm,n2), matrix of n1 rows and n2 columns */ + + /* ---------------------------------------------------------------------- */ + + /* cleanup odd vector */ + + /* Parameter adjustments */ + --y; + m_dim1 = *ldm; + m_offset = 1 + m_dim1; + m -= m_offset; + --x; + + /* Function Body */ + j = *n2 % 2; + if (j >= 1) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] += x[j] * m[i__ + j * m_dim1]; + /* L10: */ + } + } + + /* cleanup odd group of two vectors */ + + j = *n2 % 4; + if (j >= 2) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = y[i__] + x[j - 1] * m[i__ + (j - 1) * m_dim1] + x[j] * m[ + i__ + j * m_dim1]; + /* L20: */ + } + } + + /* cleanup odd group of four vectors */ + + j = *n2 % 8; + if (j >= 4) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = y[i__] + x[j - 3] * m[i__ + (j - 3) * m_dim1] + x[j - 2] + * m[i__ + (j - 2) * m_dim1] + x[j - 1] * m[i__ + (j - 1) * + m_dim1] + x[j] * m[i__ + j * m_dim1]; + /* L30: */ + } + } + + /* cleanup odd group of eight vectors */ + + j = *n2 % 16; + if (j >= 8) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = y[i__] + x[j - 7] * m[i__ + (j - 7) * m_dim1] + x[j - 6] + * m[i__ + (j - 6) * m_dim1] + x[j - 5] * m[i__ + (j - 5) * + m_dim1] + x[j - 4] * m[i__ + (j - 4) * m_dim1] + x[j - 3] + * m[i__ + (j - 3) * m_dim1] + x[j - 2] * m[i__ + (j - 2) + * m_dim1] + x[j - 1] * m[i__ + (j - 1) * m_dim1] + x[j] * + m[i__ + j * m_dim1]; + /* L40: */ + } + } + + /* main loop - groups of sixteen vectors */ + + jmin = j + 16; + i__1 = *n2; + for (j = jmin; j <= i__1; j += 16) { + i__2 = *n1; + for (i__ = 1; i__ <= i__2; ++i__) { + y[i__] = y[i__] + x[j - 15] * m[i__ + (j - 15) * m_dim1] + x[j - + 14] * m[i__ + (j - 14) * m_dim1] + x[j - 13] * m[i__ + (j + - 13) * m_dim1] + x[j - 12] * m[i__ + (j - 12) * m_dim1] + + x[j - 11] * m[i__ + (j - 11) * m_dim1] + x[j - 10] * m[ + i__ + (j - 10) * m_dim1] + x[j - 9] * m[i__ + (j - 9) * + m_dim1] + x[j - 8] * m[i__ + (j - 8) * m_dim1] + x[j - 7] + * m[i__ + (j - 7) * m_dim1] + x[j - 6] * m[i__ + (j - 6) * + m_dim1] + x[j - 5] * m[i__ + (j - 5) * m_dim1] + x[j - 4] + * m[i__ + (j - 4) * m_dim1] + x[j - 3] * m[i__ + (j - 3) + * m_dim1] + x[j - 2] * m[i__ + (j - 2) * m_dim1] + x[j - + 1] * m[i__ + (j - 1) * m_dim1] + x[j] * m[i__ + j * + m_dim1]; + /* L50: */ + } + /* L60: */ + } + return 0; +} /* dmxpy_ */ + +real_type ran_(integer *iseed) +{ + /* System generated locals */ + real_type ret_val; + + /* Local variables */ + static integer it1, it2, it3, it4; + + + /* modified from the LAPACK auxiliary routine 10/12/92 JD */ + /* -- LAPACK auxiliary routine (version 1.0) -- */ + /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */ + /* Courant Institute, Argonne National Lab, and Rice University */ + /* February 29, 1992 */ + + /* .. Array Arguments .. */ + /* .. */ + + /* Purpose */ + /* ======= */ + + /* DLARAN returns a random double number from a uniform (0,1) */ + /* distribution. */ + + /* Arguments */ + /* ========= */ + + /* ISEED (input/output) INTEGER array, dimension (4) */ + /* On entry, the seed of the random number generator; the array */ + /* elements must be between 0 and 4095, and ISEED(4) must be */ + /* odd. */ + /* On exit, the seed is updated. */ + + /* Further Details */ + /* =============== */ + + /* This routine uses a multiplicative congruential method with modulus */ + /* 2**48 and multiplier 33952834046453 (see G.S.Fishman, */ + /* 'Multiplicative congruential random number generators with modulus */ + /* 2**b: an exhaustive analysis for b = 32 and a partial analysis for */ + /* b = 48', Math. Comp. 189, pp 331-344, 1990). */ + + /* 48-bit integers are stored in 4 integer array elements with 12 bits */ + /* per element. Hence the routine is portable across machines with */ + /* integers of 32 bits or more. */ + + /* .. Parameters .. */ + /* .. */ + /* .. Local Scalars .. */ + /* .. */ + /* .. Intrinsic Functions .. */ + /* .. */ + /* .. Executable Statements .. */ + + /* multiply the seed by the multiplier modulo 2**48 */ + + /* Parameter adjustments */ + --iseed; + + /* Function Body */ + it4 = iseed[4] * 2549; + it3 = it4 / 4096; + it4 -= it3 << 12; + it3 = it3 + iseed[3] * 2549 + iseed[4] * 2508; + it2 = it3 / 4096; + it3 -= it2 << 12; + it2 = it2 + iseed[2] * 2549 + iseed[3] * 2508 + iseed[4] * 322; + it1 = it2 / 4096; + it2 -= it1 << 12; + it1 = it1 + iseed[1] * 2549 + iseed[2] * 2508 + iseed[3] * 322 + iseed[4] + * 494; + it1 %= 4096; + + /* return updated seed */ + + iseed[1] = it1; + iseed[2] = it2; + iseed[3] = it3; + iseed[4] = it4; + + /* convert 48-bit integer to a double number in the interval (0,1) */ + + ret_val = ((real_type) it1 + ((real_type) it2 + ((real_type) it3 + ( + real_type) it4 * 2.44140625e-4) * 2.44140625e-4) * 2.44140625e-4) + * 2.44140625e-4; + return ret_val; + + /* End of RAN */ + +} /* ran_ */ + +/* + +Double results: +~~~~~~~~~~~~~~ + +norm. resid resid machep x(1) x(n) +6.4915 7.207e-013 2.2204e-016 1 1 + + + +times are reported for matrices of order 1000 +factor solve total mflops unit ratio +times for array with leading dimension of1001 +1.443 0.003 1.446 462.43 0.004325 25.821 + + +mpf_class results: +~~~~~~~~~~~~~~~~~~ + +norm. resid resid machep x(1) x(n) +3.6575e-05 5.2257e-103 2.8575e-101 1 1 + + + +times are reported for matrices of order 1000 +factor solve total mflops unit ratio +times for array with leading dimension of1001 +266.45 0.798 267.24 2.5021 0.79933 4772.2 + + +mp_number >: +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + + norm. resid resid machep x(1) x(n) + 0.36575e-4 0.52257e-102 0.28575e-100 0.1e1 0.1e1 + + + + times are reported for matrices of order 1000 + factor solve total mflops unit ratio + times for array with leading dimension of1001 + 279.96 0.84 280.8 2.3813 0.83988 5014.3 + +boost::math::ef::e_float: +~~~~~~~~~~~~~~~~~~~~~~~~~ + + norm. resid resid machep x(1) x(n) + 2.551330735e-16 1.275665107e-112 1e-99 1 1 + + + + times are reported for matrices of order 1000 + factor solve total mflops unit ratio + times for array with leading dimension of1001 + 363.89 1.074 364.97 1.8321 1.0916 6517.3 +*/ diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp new file mode 100644 index 00000000..3e82e749 --- /dev/null +++ b/test/test_arithmetic.cpp @@ -0,0 +1,894 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +# define TEST_MPF +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR +# define TEST_MPFR_50 +# define TEST_E_FLOAT +# define TEST_MPQ + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) +#include +#endif + +#define BOOST_TEST_THROW(x, EX)\ + try { x; BOOST_ERROR("Expected exception not thrown"); } \ + catch(const EX&){}\ + catch(...){ BOOST_ERROR("Incorrect exception type thrown"); } + +#undef BOOST_TEST +#define BOOST_TEST(x)\ + try {\ + if(x){}else{ BOOST_ERROR("Value was zero: "); }\ + }\ + catch(const std::exception& e){ \ + BOOST_ERROR("Unexpected exception: ");\ + BOOST_LIGHTWEIGHT_TEST_OSTREAM << e.what() << std::endl;\ + } + +bool isfloat(float){ return true; } +bool isfloat(double){ return true; } +bool isfloat(long double){ return true; } +template bool isfloat(T){ return false; } + +#define BOOST_TEST_CLOSE(x, y, tol)\ + if(x == 0){\ + BOOST_TEST(y == 0); }\ + else if(!isfloat(x)){\ + BOOST_TEST(x == y); }\ + else if((x != y) && (::fabsl(static_cast((x-y)/x)) > tol))\ + {\ + BOOST_ERROR("Expected tolerance was exceeded: ");\ + BOOST_LIGHTWEIGHT_TEST_OSTREAM << std::setprecision(34) << "(x-y)/x = " << ::fabsl(static_cast((x-y)/x)) \ + << " tolerance = " << tol << std::endl;\ + } + +template +void test_integer_ops(const T&){} + +template +void test_integer_ops(const boost::mpl::int_&) +{ + Real a(20); + Real b(7); + Real c; + BOOST_TEST(a % b == 20 % 7); + BOOST_TEST(a % 7 == 20 % 7); + BOOST_TEST(a % 7u == 20 % 7); + BOOST_TEST(-a % b == -20 % 7); + BOOST_TEST(-a % -b == -20 % -7); + BOOST_TEST(a % -b == 20 % -7); + BOOST_TEST(-a % 7 == -20 % 7); + BOOST_TEST(-a % -7 == -20 % -7); + BOOST_TEST(a % -7 == 20 % -7); + BOOST_TEST(-a % 7u == -20 % 7); + + b = -b; + BOOST_TEST(a % b == 20 % -7); + a = -a; + BOOST_TEST(a % b == -20 % -7); + BOOST_TEST(a % -7 == -20 % -7); + b = 7; + BOOST_TEST(a % b == -20 % 7); + BOOST_TEST(a % 7 == -20 % 7); + BOOST_TEST(a % 7u == -20 % 7); + + a = 20; + a %= b; + BOOST_TEST(a == 20 % 7); + a = -20; + a %= b; + BOOST_TEST(a == -20 % 7); + a = 20; + a %= -b; + BOOST_TEST(a == 20 % -7); + a = -20; + a %= -b; + BOOST_TEST(a == -20 % -7); + + a = 20; + a %= 7; + BOOST_TEST(a == 20 % 7); + a = -20; + a %= 7; + BOOST_TEST(a == -20 % 7); + a = 20; + a %= -7; + BOOST_TEST(a == 20 % -7); + a = -20; + a %= -7; + BOOST_TEST(a == -20 % -7); +#ifndef BOOST_NO_LONG_LONG + a = 20; + a %= 7uLL; + BOOST_TEST(a == 20 % 7); + a = -20; + a %= 7uLL; + BOOST_TEST(a == -20 % 7); + a = 20; + a %= -7LL; + BOOST_TEST(a == 20 % -7); + a = -20; + a %= -7LL; + BOOST_TEST(a == -20 % -7); +#endif + a = 20; + BOOST_TEST(++a == 21); + BOOST_TEST(--a == 20); + BOOST_TEST(a++ == 20); + BOOST_TEST(a == 21); + BOOST_TEST(a-- == 21); + BOOST_TEST(a == 20); + a = 2000; + a <<= 20; + BOOST_TEST(a == 2000L << 20); + a >>= 20; + BOOST_TEST(a == 2000); + a <<= 20u; + BOOST_TEST(a == 2000L << 20); + a >>= 20u; + BOOST_TEST(a == 2000); + BOOST_TEST_THROW(a <<= -20, std::out_of_range); + BOOST_TEST_THROW(a >>= -20, std::out_of_range); +#ifndef BOOST_NO_LONG_LONG + if(sizeof(long long) > sizeof(std::size_t)) + { + // extreme values should trigger an exception: + BOOST_TEST_THROW(a >>= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_TEST_THROW(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + } +#endif + a = 20; + b = a << 20; + BOOST_TEST(b == (20 << 20)); + b = a >> 2; + BOOST_TEST(b == (20 >> 2)); + b = (a + 2) << 10; + BOOST_TEST(b == (22 << 10)); + b = (a + 3) >> 3; + BOOST_TEST(b == (23 >> 3)); + // + // Bit fiddling: + // + int i = 1020304; + int j = 56789123; + int k = 4523187; + a = i; + b = j; + c = a; + c &= b; + BOOST_TEST(c == (i & j)); + c = a; + c &= j; + BOOST_TEST(c == (i & j)); + c = a; + c &= a + b; + BOOST_TEST(c == (i & (i + j))); + BOOST_TEST((a & b) == (i & j)); + c = k; + a = a & (b + k); + BOOST_TEST(a == (i & (j + k))); + a = i; + a = (b + k) & a; + BOOST_TEST(a == (i & (j + k))); + a = i; + c = a & b & k; + BOOST_TEST(c == (i&j&k)); + + a = i; + b = j; + c = a; + c |= b; + BOOST_TEST(c == (i | j)); + c = a; + c |= j; + BOOST_TEST(c == (i | j)); + c = a; + c |= a + b; + BOOST_TEST(c == (i | (i + j))); + BOOST_TEST((a | b) == (i | j)); + c = k; + a = a | (b + k); + BOOST_TEST(a == (i | (j + k))); + a = i; + a = (b + k) | a; + BOOST_TEST(a == (i | (j + k))); + a = i; + c = a | b | k; + BOOST_TEST(c == (i|j|k)); + + a = i; + b = j; + c = a; + c ^= b; + BOOST_TEST(c == (i ^ j)); + c = a; + c ^= j; + BOOST_TEST(c == (i ^ j)); + c = a; + c ^= a + b; + BOOST_TEST(c == (i ^ (i + j))); + BOOST_TEST((a ^ b) == (i ^ j)); + c = k; + a = a ^ (b + k); + BOOST_TEST(a == (i ^ (j + k))); + a = i; + a = (b + k) ^ a; + BOOST_TEST(a == (i ^ (j + k))); + a = i; + c = a ^ b ^ k; + BOOST_TEST(c == (i^j^k)); + a = i; + b = j; + c = k; + BOOST_TEST(~a == ~i); + c = a & ~b; + BOOST_TEST(c == (i & ~j)); + c = ~(a | b); + BOOST_TEST(c == ~(i | j)); + // + // Non-member functions: + // + a = -20; + BOOST_TEST(abs(a) == 20); + BOOST_TEST(abs(-a) == 20); + BOOST_TEST(abs(+a) == 20); + a = 20; + BOOST_TEST(abs(a) == 20); + BOOST_TEST(abs(-a) == 20); + BOOST_TEST(abs(+a) == 20); +} + +template +void test_real_ops(const T&){} + +template +void test_real_ops(const boost::mpl::int_&) +{ +#if defined(TEST_MPF) || defined(TEST_MPF_50) || defined(TEST_BACKEND) || defined(TEST_MPFR) + BOOST_TEST(abs(Real(2)) == 2); + BOOST_TEST(abs(Real(-2)) == 2); + BOOST_TEST(fabs(Real(2)) == 2); + BOOST_TEST(fabs(Real(-2)) == 2); + BOOST_TEST(floor(Real(5) / 2) == 2); + BOOST_TEST(ceil(Real(5) / 2) == 3); + BOOST_TEST(floor(Real(-5) / 2) == -3); + BOOST_TEST(ceil(Real(-5) / 2) == -2); + BOOST_TEST(trunc(Real(5) / 2) == 2); + BOOST_TEST(trunc(Real(-5) / 2) == -2); + // + // ldexp and frexp, these pretty much have to implemented by each backend: + // + BOOST_TEST(ldexp(Real(2), 5) == 64); + BOOST_TEST(ldexp(Real(2), -5) == Real(2) / 32); + Real v(512); + int exp; + Real r = frexp(v, &exp); + BOOST_TEST(r == 0.5); + BOOST_TEST(exp == 10); + BOOST_TEST(v == 512); + v = 1 / v; + r = frexp(v, &exp); + BOOST_TEST(r == 0.5); + BOOST_TEST(exp == -8); + // + // pow and exp: + // + v = 3.25; + r = pow(v, 0); + BOOST_TEST(r == 1); + r = pow(v, 1); + BOOST_TEST(r == 3.25); + r = pow(v, 2); + BOOST_TEST(r == boost::math::pow<2>(3.25)); + r = pow(v, 3); + BOOST_TEST(r == boost::math::pow<3>(3.25)); + r = pow(v, 4); + BOOST_TEST(r == boost::math::pow<4>(3.25)); + r = pow(v, 5); + BOOST_TEST(r == boost::math::pow<5>(3.25)); + r = pow(v, 6); + BOOST_TEST(r == boost::math::pow<6>(3.25)); + r = pow(v, 25); + BOOST_TEST(r == boost::math::pow<25>(Real(3.25))); + /* + r = pow(v, 56); + BOOST_TEST(r == boost::math::pow<56>(Real(3.25))); + */ +#endif +} + +#ifdef TEST_E_FLOAT + +template +struct lexical_cast_target_type +{ + typedef long double type; +}; + +#else + +template +struct lexical_cast_target_type +{ + typedef typename boost::mpl::if_< + boost::is_signed, + boost::intmax_t, + typename boost::mpl::if_< + boost::is_unsigned, + boost::uintmax_t, + T + >::type + >::type type; +}; + +#endif + +template +void test_negative_mixed(boost::mpl::true_ const&) +{ + typedef typename lexical_cast_target_type::type target_type; + std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; + Num n1 = -static_cast(1uLL << (std::numeric_limits::digits - 1)); + Num n2 = -1; + Num n3 = 0; + Num n4 = -20; + Num n5 = -8; + BOOST_TEST((Real(n2) < 0) == true); + BOOST_TEST((Real(n2) <= 0) == true); + BOOST_TEST((Real(n2) > 0) == false); + BOOST_TEST((Real(n2) >= 0) == false); + BOOST_TEST((Real(n2) == 0) == false); + BOOST_TEST((Real(n2) != 0) == true); + BOOST_TEST((Real(n2) == n2) == true); + BOOST_TEST((Real(n2) != n2) == false); + BOOST_TEST((Real(n2) >= n2) == true); + BOOST_TEST((Real(n2) <= n2) == true); + BOOST_TEST((Real(n2) > n2) == false); + BOOST_TEST((Real(n2) < n2) == false); + // Default construct: + BOOST_TEST(Real(n1) == n1); + BOOST_TEST(Real(n2) == n2); + BOOST_TEST(Real(n3) == n3); + BOOST_TEST(Real(n4) == n4); + BOOST_TEST(n1 == Real(n1)); + BOOST_TEST(n2 == Real(n2)); + BOOST_TEST(n3 == Real(n3)); + BOOST_TEST(n4 == Real(n4)); +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) + Num tol = 10 * std::numeric_limits::epsilon(); +#else + Num tol = 0; +#endif + BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), tol); + BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), 0); + BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), 0); + BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), 0); + // Assignment: + Real r(0); + BOOST_TEST(r != n1); + r = n1; + BOOST_TEST(r == n1); + r = n2; + BOOST_TEST(r == n2); + r = n3; + BOOST_TEST(r == n3); + r = n4; + BOOST_TEST(r == n4); + // Addition: + r = n2; + BOOST_TEST(r + n4 == n2 + n4); + BOOST_TEST(Real(r + n4) == n2 + n4); + r += n4; + BOOST_TEST(r == n2 + n4); + // subtraction: + r = n4; + BOOST_TEST(r - n5 == n4 - n5); + BOOST_TEST(Real(r - n5) == n4 - n5); + r -= n5; + BOOST_TEST(r == n4 - n5); + // Multiplication: + r = n2; + BOOST_TEST(r * n4 == n2 * n4); + BOOST_TEST(Real(r * n4) == n2 * n4); + r *= n4; + BOOST_TEST(r == n2 * n4); + // Division: + r = n1; + BOOST_TEST(r / n5 == n1 / n5); + BOOST_TEST(Real(r / n5) == n1 / n5); + r /= n5; + BOOST_TEST(r == n1 / n5); + // + // Extra cases for full coverage: + // + r = Real(n4) + n5; + BOOST_TEST(r == n4 + n5); + r = n4 + Real(n5); + BOOST_TEST(r == n4 + n5); + r = Real(n4) - n5; + BOOST_TEST(r == n4 - n5); + r = n4 - Real(n5); + BOOST_TEST(r == n4 - n5); + r = n4 * Real(n5); + BOOST_TEST(r == n4 * n5); + r = (4 * n4) / Real(4); + BOOST_TEST(r == n4); +} + +template +void test_negative_mixed(boost::mpl::false_ const&) +{ +} + +template +void test_mixed() +{ + typedef typename lexical_cast_target_type::type target_type; + std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; + Num n1 = static_cast(1uLL << (std::numeric_limits::digits - 1)); + Num n2 = 1; + Num n3 = 0; + Num n4 = 20; + Num n5 = 8; + BOOST_TEST((Real(n2) < 0) == false); + BOOST_TEST((Real(n2) <= 0) == false); + BOOST_TEST((Real(n2) > 0) == true); + BOOST_TEST((Real(n2) >= 0) == true); + BOOST_TEST((Real(n2) == 0) == false); + BOOST_TEST((Real(n2) != 0) == true); + BOOST_TEST((Real(n2) == n2) == true); + BOOST_TEST((Real(n2) != n2) == false); + BOOST_TEST((Real(n2) >= n2) == true); + BOOST_TEST((Real(n2) <= n2) == true); + BOOST_TEST((Real(n2) > n2) == false); + BOOST_TEST((Real(n2) < n2) == false); + // Default construct: + BOOST_TEST(Real(n1) == n1); + BOOST_TEST(Real(n2) == n2); + BOOST_TEST(Real(n3) == n3); + BOOST_TEST(Real(n4) == n4); + BOOST_TEST(Real(n1).template convert_to() == n1); + BOOST_TEST(Real(n2).template convert_to() == n2); + BOOST_TEST(Real(n3).template convert_to() == n3); + BOOST_TEST(Real(n4).template convert_to() == n4); + BOOST_TEST(n1 == Real(n1)); + BOOST_TEST(n2 == Real(n2)); + BOOST_TEST(n3 == Real(n3)); + BOOST_TEST(n4 == Real(n4)); + std::cout << Real(n1).str(0, boost::is_floating_point::value) << std::endl; +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) + Num tol = 10 * std::numeric_limits::epsilon(); +#else + Num tol = 0; +#endif + BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), tol); + BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), 0); + BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), 0); + BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), 0); + // Assignment: + Real r(0); + BOOST_TEST(r != n1); + r = n1; + BOOST_TEST(r == n1); + r = n2; + BOOST_TEST(r == n2); + r = n3; + BOOST_TEST(r == n3); + r = n4; + BOOST_TEST(r == n4); + // Addition: + r = n2; + BOOST_TEST(r + n4 == n2 + n4); + BOOST_TEST(Real(r + n4) == n2 + n4); + r += n4; + BOOST_TEST(r == n2 + n4); + // subtraction: + r = n4; + BOOST_TEST(r - n5 == n4 - n5); + BOOST_TEST(Real(r - n5) == n4 - n5); + r -= n5; + BOOST_TEST(r == n4 - n5); + // Multiplication: + r = n2; + BOOST_TEST(r * n4 == n2 * n4); + BOOST_TEST(Real(r * n4) == n2 * n4); + r *= n4; + BOOST_TEST(r == n2 * n4); + // Division: + r = n1; + BOOST_TEST(r / n5 == n1 / n5); + BOOST_TEST(Real(r / n5) == n1 / n5); + r /= n5; + BOOST_TEST(r == n1 / n5); + // + // special cases for full coverage: + // + r = n5 + Real(n4); + BOOST_TEST(r == n4 + n5); + r = n4 - Real(n5); + BOOST_TEST(r == n4 - n5); + r = n4 * Real(n5); + BOOST_TEST(r == n4 * n5); + r = (4 * n4) / Real(4); + BOOST_TEST(r == n4); + test_negative_mixed(boost::mpl::bool_::is_signed>()); +} + +template +void test() +{ +#ifndef NO_MIXED_OPS + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); + test_mixed(); +#ifdef BOOST_HAS_LONG_LONG + test_mixed(); + test_mixed(); +#endif + test_mixed(); + test_mixed(); + test_mixed(); +#endif + // + // Integer only functions: + // + test_integer_ops(typename boost::math::number_category::type()); + // + // Real number only functions: + // + test_real_ops(typename boost::math::number_category::type()); + // + // Test basic arithmetic: + // + Real a(8); + Real b(64); + Real c(500); + Real d(1024); + BOOST_TEST(a + b == 72); + a += b; + BOOST_TEST(a == 72); + BOOST_TEST(a - b == 8); + a -= b; + BOOST_TEST(a == 8); + BOOST_TEST(a * b == 8*64L); + a *= b; + BOOST_TEST(a == 8*64L); + BOOST_TEST(a / b == 8); + a /= b; + BOOST_TEST(a == 8); + Real ac(a); + BOOST_TEST(ac == a); + BOOST_TEST(-a == -8); + ac = a * c; + BOOST_TEST(ac == 8*500L); + ac = 8*500L; + ac = ac + b + c; + BOOST_TEST(ac == 8*500L+64+500); + ac = a; + ac = b + c + ac; + BOOST_TEST(ac == 8+64+500); + ac = ac - b + c; + BOOST_TEST(ac == 8+64+500-64+500); + ac = a; + ac = b + c - ac; + BOOST_TEST(ac == -8+64+500); + ac = a; + ac = ac * b; + BOOST_TEST(ac == 8*64); + ac = a; + ac *= b * ac; + BOOST_TEST(ac == 8*8*64); + ac = b; + ac = ac / a; + BOOST_TEST(ac == 64/8); + ac = b; + ac /= ac / a; + BOOST_TEST(ac == 64 / (64/8)); + ac = a; + ac = b + ac * a; + BOOST_TEST(ac == 64 * 2); + ac = a; + ac = b - ac * a; + BOOST_TEST(ac == 0); + ac = a; + ac = b * (ac + a); + BOOST_TEST(ac == 64 * (16)); + ac = a; + ac = b / (ac * 1); + BOOST_TEST(ac == 64 / 8); + ac = a; + ac = ac + b; + BOOST_TEST(ac == 8 + 64); + ac = a; + ac = a + ac; + BOOST_TEST(ac == 16); + ac = a; + ac = ac - b; + BOOST_TEST(ac == 8 - 64); + ac = a; + ac = a - ac; + BOOST_TEST(ac == 0); + ac = a; + ac += a + b; + BOOST_TEST(ac == 80); + ac = a; + ac += b + a; + BOOST_TEST(ac == 80); + ac = a; + ac -= a + b; + BOOST_TEST(ac == -64); + ac = a; + ac -= b - a; + BOOST_TEST(ac == 16 - 64); + ac = +a; + BOOST_TEST(ac == 8); + ac = -a; + BOOST_TEST(ac == -8); + ac = 8; + ac = a * ac; + BOOST_TEST(ac == 8*8); + ac = a; + ac = a; + ac += +a; + BOOST_TEST(ac == 16); + ac = a; + ac += -a; + BOOST_TEST(ac == 0); + ac = a; + ac += b - a; + BOOST_TEST(ac == 8 + 64-8); + ac = a; + ac += b*c; + BOOST_TEST(ac == 8 + 64 * 500); + ac = a; + ac = a; + ac -= +a; + BOOST_TEST(ac == 0); + ac = a; + ac -= -a; + BOOST_TEST(ac == 16); + ac = a; + ac -= c - b; + BOOST_TEST(ac == 8 - (500-64)); + ac = a; + ac -= b*c; + BOOST_TEST(ac == 8 - 500*64); + ac = a; + ac += ac * b; + BOOST_TEST(ac == 8 + 8 * 64); + ac = a; + ac -= ac * b; + BOOST_TEST(ac == 8 - 8 * 64); + ac = a * 8; + ac *= +a; + BOOST_TEST(ac == 64 * 8); + ac = a; + ac *= -a; + BOOST_TEST(ac == -64); + ac = a; + ac *= b * c; + BOOST_TEST(ac == 8 * 64 * 500); + ac = a; + ac *= b / a; + BOOST_TEST(ac == 8 * 64 / 8); + ac = a; + ac *= b + c; + BOOST_TEST(ac == 8 * (64 + 500)); + ac = b; + ac /= +a; + BOOST_TEST(ac == 8); + ac = b; + ac /= -a; + BOOST_TEST(ac == -8); + ac = b; + ac /= b / a; + BOOST_TEST(ac == 64 / (64/8)); + ac = b; + ac /= a + Real(0); + BOOST_TEST(ac == 8); + // + // simple tests with immediate values, these calls can be optimised in many backends: + // + ac = a + b; + BOOST_TEST(ac == 72); + ac = a + +b; + BOOST_TEST(ac == 72); + ac = +a + b; + BOOST_TEST(ac == 72); + ac = +a + +b; + BOOST_TEST(ac == 72); + ac = a + -b; + BOOST_TEST(ac == 8 - 64); + ac = -a + b; + BOOST_TEST(ac == -8+64); + ac = -a + -b; + BOOST_TEST(ac == -72); + ac = a + - + -b; // lots of unary operators!! + BOOST_TEST(ac == 72); + ac = a; + ac = b / ac; + BOOST_TEST(ac == b / a); + // + // Comparisons: + // + BOOST_TEST((a == b) == false); + BOOST_TEST((a != b) == true); + BOOST_TEST((a <= b) == true); + BOOST_TEST((a < b) == true); + BOOST_TEST((a >= b) == false); + BOOST_TEST((a > b) == false); + + BOOST_TEST((a+b == b) == false); + BOOST_TEST((a+b != b) == true); + BOOST_TEST((a+b >= b) == true); + BOOST_TEST((a+b > b) == true); + BOOST_TEST((a+b <= b) == false); + BOOST_TEST((a+b < b) == false); + + BOOST_TEST((a == b+a) == false); + BOOST_TEST((a != b+a) == true); + BOOST_TEST((a <= b+a) == true); + BOOST_TEST((a < b+a) == true); + BOOST_TEST((a >= b+a) == false); + BOOST_TEST((a > b+a) == false); + + BOOST_TEST((a+b == b+a) == true); + BOOST_TEST((a+b != b+a) == false); + BOOST_TEST((a+b <= b+a) == true); + BOOST_TEST((a+b < b+a) == false); + BOOST_TEST((a+b >= b+a) == true); + BOOST_TEST((a+b > b+a) == false); + + BOOST_TEST((8 == b+a) == false); + BOOST_TEST((8 != b+a) == true); + BOOST_TEST((8 <= b+a) == true); + BOOST_TEST((8 < b+a) == true); + BOOST_TEST((8 >= b+a) == false); + BOOST_TEST((8 > b+a) == false); + BOOST_TEST((800 == b+a) == false); + BOOST_TEST((800 != b+a) == true); + BOOST_TEST((800 >= b+a) == true); + BOOST_TEST((800 > b+a) == true); + BOOST_TEST((800 <= b+a) == false); + BOOST_TEST((800 < b+a) == false); + BOOST_TEST((72 == b+a) == true); + BOOST_TEST((72 != b+a) == false); + BOOST_TEST((72 <= b+a) == true); + BOOST_TEST((72 < b+a) == false); + BOOST_TEST((72 >= b+a) == true); + BOOST_TEST((72 > b+a) == false); + // + // Test sign and zero functions, plus use in boolian context: + // + a = 20; + BOOST_TEST(a.sign() > 0); + BOOST_TEST(!a.is_zero()); + a = -20; + BOOST_TEST(a.sign() < 0); + BOOST_TEST(!a.is_zero()); + a = 0; + BOOST_TEST(a.sign() == 0); + BOOST_TEST(a.is_zero()); + if(a) + { + BOOST_ERROR("Unexpected non-zero result"); + } + if(!a){} + else + { + BOOST_ERROR("Unexpected zero result"); + } + b = 2; + if(!b) + { + BOOST_ERROR("Unexpected zero result"); + } + if(b){} + else + { + BOOST_ERROR("Unexpected non-zero result"); + } + if(a && b) + { + BOOST_ERROR("Unexpected zero result"); + } + if(!(a || b)) + { + BOOST_ERROR("Unexpected zero result"); + } + if(a + b){} + else + { + BOOST_ERROR("Unexpected zero result"); + } + if(b - 2) + { + BOOST_ERROR("Unexpected non-zero result"); + } + // + // Test iostreams: + // + std::stringstream ss; + a = 20; + b = 2; + ss << a; + ss >> c; + BOOST_TEST(a == c); + ss.clear(); + ss << a + b; + ss >> c; + BOOST_TEST(c == 22); + BOOST_TEST(c == a + b); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); +#endif +#ifdef TEST_MPF + boost::math::mpf_real::default_precision(1000); + /* + boost::math::mpf_real r; + r.precision(50); + BOOST_TEST(r.precision() >= 50); + */ + BOOST_TEST(boost::math::mpf_real::default_precision() == 1000); + test(); +#endif +#ifdef TEST_MPZ + test(); +#endif +#ifdef TEST_MPQ + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif +#ifdef TEST_MPFR + test(); +#endif +#ifdef TEST_MPFR_50 + test(); +#endif + return boost::report_errors(); +} + diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp new file mode 100644 index 00000000..1cd7f695 --- /dev/null +++ b/test/test_numeric_limits.cpp @@ -0,0 +1,173 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +# define TEST_MPF +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR +# define TEST_MPFR_50 +# define TEST_E_FLOAT +# define TEST_MPQ + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) +#include +#endif + +#define PRINT(x)\ + std::cout << BOOST_STRINGIZE(x) << " = " << std::numeric_limits::x << std::endl; + +template +void test() +{ + // + // Note really a test just yet, but we can at least print out all the values: + // + std::cout << "numeric_limits values for type " << typeid(Number).name() << std::endl; + + PRINT(is_specialized); + PRINT(min()); + PRINT(max()); +#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST + PRINT(lowest()); +#endif + PRINT(digits); + PRINT(digits10); +#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST + PRINT(max_digits10); +#endif + PRINT(is_signed); + PRINT(is_integer); + PRINT(is_exact); + PRINT(radix); + PRINT(epsilon()); + PRINT(round_error()); + PRINT(min_exponent); + PRINT(min_exponent10); + PRINT(max_exponent); + PRINT(max_exponent10); + PRINT(has_infinity); + PRINT(has_quiet_NaN); + PRINT(has_signaling_NaN); + PRINT(has_denorm); + PRINT(has_denorm_loss); + PRINT(infinity()); + PRINT(quiet_NaN()); + PRINT(signaling_NaN()); + PRINT(denorm_min()); + PRINT(is_iec559); + PRINT(is_bounded); + PRINT(is_modulo); + PRINT(traps); + PRINT(tinyness_before); + PRINT(round_style); + + if(std::numeric_limits::is_specialized) + { + if(std::numeric_limits::has_quiet_NaN) + { + BOOST_TEST((boost::math::isnan)(std::numeric_limits::quiet_NaN())); + BOOST_TEST(FP_NAN == (boost::math::fpclassify)(std::numeric_limits::quiet_NaN())); + BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits::quiet_NaN())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::quiet_NaN())); + BOOST_TEST(!(boost::math::isinf)(std::numeric_limits::quiet_NaN())); + } + if(std::numeric_limits::has_signaling_NaN) + { + BOOST_TEST((boost::math::isnan)(std::numeric_limits::signaling_NaN())); + BOOST_TEST(FP_NAN == (boost::math::fpclassify)(std::numeric_limits::signaling_NaN())); + BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits::signaling_NaN())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::signaling_NaN())); + BOOST_TEST(!(boost::math::isinf)(std::numeric_limits::signaling_NaN())); + } + if(std::numeric_limits::has_infinity) + { + BOOST_TEST((boost::math::isinf)(std::numeric_limits::infinity())); + BOOST_TEST(FP_INFINITE == (boost::math::fpclassify)(std::numeric_limits::infinity())); + BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits::infinity())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::infinity())); + BOOST_TEST(!(boost::math::isnan)(std::numeric_limits::infinity())); + } + if(std::numeric_limits::has_denorm) + { + BOOST_TEST(FP_SUBNORMAL == (boost::math::fpclassify)(std::numeric_limits::denorm_min())); + BOOST_TEST((boost::math::isfinite)(std::numeric_limits::denorm_min())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::denorm_min())); + BOOST_TEST(!(boost::math::isinf)(std::numeric_limits::denorm_min())); + BOOST_TEST(!(boost::math::isnan)(std::numeric_limits::denorm_min())); + } + } + Number n = 0; + BOOST_TEST((boost::math::fpclassify)(n) == FP_ZERO); + BOOST_TEST((boost::math::isfinite)(n)); + BOOST_TEST(!(boost::math::isnormal)(n)); + BOOST_TEST(!(boost::math::isinf)(n)); + BOOST_TEST(!(boost::math::isnan)(n)); + n = 2; + BOOST_TEST((boost::math::fpclassify)(n) == FP_NORMAL); + BOOST_TEST((boost::math::isfinite)(n)); + BOOST_TEST((boost::math::isnormal)(n)); + BOOST_TEST(!(boost::math::isinf)(n)); + BOOST_TEST(!(boost::math::isnan)(n)); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); +#endif +#ifdef TEST_MPF + boost::math::mpf_real::default_precision(1000); + /* + boost::math::mpf_real r; + r.precision(50); + BOOST_TEST(r.precision() >= 50); + */ + BOOST_TEST(boost::math::mpf_real::default_precision() == 1000); + test(); +#endif +#ifdef TEST_MPZ + test(); +#endif +#ifdef TEST_MPQ + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif +#ifdef TEST_MPFR + test(); +#endif +#ifdef TEST_MPFR_50 + test(); +#endif + return boost::report_errors(); +} + From 440eb46de639f2fc4732838e99742fcf08c9ca8d Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 26 Sep 2011 17:01:23 +0000 Subject: [PATCH 026/256] Giant file and directory rename: changed directory name from math to multiprecision and updated code to match. 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math/doc/html/index.html | 53 - math/test/Jamfile.v2 | 189 --- math/test/big_number_concept_check.cpp | 100 -- math/test/linpack-benchmark.cpp | 1257 ----------------- math/test/test_arithmetic.cpp | 894 ------------ math/test/test_numeric_limits.cpp | 173 --- 54 files changed, 4692 deletions(-) delete mode 100644 math/Jamroot.jam delete mode 100644 math/boost-build.jam delete mode 100644 math/config/Jamfile.v2 delete mode 100644 math/config/has_e_float.cpp delete mode 100644 math/config/has_gcc_visibility.cpp delete mode 100644 math/config/has_gmp.cpp delete mode 100644 math/config/has_gmpxx.cpp delete mode 100644 math/config/has_long_double_support.cpp delete mode 100644 math/config/has_mpfr.cpp delete mode 100644 math/config/has_mpfr_class.cpp delete mode 100644 math/config/has_mpreal.cpp delete mode 100644 math/config/has_ntl_rr.cpp delete mode 100644 math/doc/Jamfile.v2 delete mode 100644 math/doc/big_number.qbk delete mode 100644 math/doc/html/boost_bignumbers/intro.html delete mode 100644 math/doc/html/boost_bignumbers/ref.html delete mode 100644 math/doc/html/boost_bignumbers/ref/backendconc.html delete mode 100644 math/doc/html/boost_bignumbers/ref/bignum.html delete mode 100644 math/doc/html/boost_bignumbers/tut.html delete mode 100644 math/doc/html/boost_bignumbers/tut/ints.html delete mode 100644 math/doc/html/boost_bignumbers/tut/reals.html delete mode 100644 math/doc/html/boostbook.css delete mode 100644 math/doc/html/images/blank.png delete mode 100644 math/doc/html/images/caution.png delete mode 100644 math/doc/html/images/caution.svg delete mode 100644 math/doc/html/images/draft.png delete mode 100644 math/doc/html/images/home.png delete mode 100644 math/doc/html/images/home.svg delete mode 100644 math/doc/html/images/important.png delete mode 100644 math/doc/html/images/important.svg delete mode 100644 math/doc/html/images/next.png delete mode 100644 math/doc/html/images/next.svg delete mode 100644 math/doc/html/images/next_disabled.png delete mode 100644 math/doc/html/images/note.png delete mode 100644 math/doc/html/images/note.svg delete mode 100644 math/doc/html/images/prev.png delete mode 100644 math/doc/html/images/prev.svg delete mode 100644 math/doc/html/images/prev_disabled.png delete mode 100644 math/doc/html/images/tip.png delete mode 100644 math/doc/html/images/tip.svg delete mode 100644 math/doc/html/images/toc-blank.png delete mode 100644 math/doc/html/images/toc-minus.png delete mode 100644 math/doc/html/images/toc-plus.png delete mode 100644 math/doc/html/images/up.png delete mode 100644 math/doc/html/images/up.svg delete mode 100644 math/doc/html/images/up_disabled.png delete mode 100644 math/doc/html/images/warning.png delete mode 100644 math/doc/html/images/warning.svg delete mode 100644 math/doc/html/index.html delete mode 100644 math/test/Jamfile.v2 delete mode 100644 math/test/big_number_concept_check.cpp delete mode 100644 math/test/linpack-benchmark.cpp delete mode 100644 math/test/test_arithmetic.cpp delete mode 100644 math/test/test_numeric_limits.cpp diff --git a/math/Jamroot.jam b/math/Jamroot.jam deleted file mode 100644 index c8019258..00000000 --- a/math/Jamroot.jam +++ /dev/null @@ -1,9 +0,0 @@ - -import modules ; - -local boost = [ modules.peek : BOOST ] ; - -project sandbox : requirements $(boost) ; - -# This seems to prevent some Boost.Build errors that otherwise occur :-( -use-project /boost : $(boost) ; diff --git a/math/boost-build.jam b/math/boost-build.jam deleted file mode 100644 index 02b750a1..00000000 --- a/math/boost-build.jam +++ /dev/null @@ -1,72 +0,0 @@ -# Copyright Rene Rivera 2007. -# -# Distributed under the Boost Software License, Version 1.0. -# (See accompanying file LICENSE_1_0.txt or copy at -# http://www.boost.org/LICENSE_1_0.txt) - -# For instructions see Jamfile.v2, or "bjam --help". - -local rule if-has-file ( file + : dir * ) -{ - local result ; - if $(dir) - { - result = [ GLOB $(dir) : $(file) ] ; - } - return $(result[1]:P) ; -} - -#~ Attempts to find the Boost source tree... - -local boost-src = [ if-has-file LICENSE_1_0.txt : - [ MATCH --boost=(.*) : $(ARGV) ] - $(BOOST) - $(BOOST_ROOT) - $(.boost-build-file:D)/../boost - $(.boost-build-file:D)/../Trunk - ] ; - -# error handling: -if ! $(boost-src) -{ - ECHO Unable to find the Boost source tree in the locations searched. ; - ECHO Try setting the environment variable BOOST to point to your ; - ECHO Boost tree, or else invoke bjam with the --boost=path option. ; - ECHO The Boost include path will not be automatically set. ; - ECHO The paths searched were [ MATCH --boost=(.*) : $(ARGV) ] $(BOOST) $(.boost-build-file:D)/../boost $(.boost-build-file:D)/../Trunk ; - ECHO But the file LICENSE_1_0.txt was not found in any of them ; -} - -#~ Attempts to find the Boost.Build files... - -local boost-build-src = [ if-has-file bootstrap.jam : - [ MATCH --boost-build=(.*) : $(ARGV) ] - $(BOOST_BUILD_PATH) - $(BOOST_BUILD) - $(boost-src)/tools/build/v2 - ] ; - -# error handling: -if ! $(boost-build-src) -{ - ECHO Unable to find the Boost.Build source tree in the locations searched. ; - ECHO Try setting the environment variable BOOST_BUILD to point to your ; - ECHO Boost.Build tree, or else invoke bjam with the --boost-build=path option. ; - ECHO The paths searched were [ MATCH --boost-build=(.*) : $(ARGV) ] $(BOOST_BUILD_PATH) $(BOOST_BUILD) $(boost-src)/tools/build/v2 ; - ECHO But bootstrap.jam was not found in any of these ; - ECHO More failures will very likely follow... ; -} - -#~ Set some common vars to refer to the Boost sources... - -BOOST ?= $(boost-src) ; -BOOST_ROOT ?= $(boost-src) ; - -#~ And load up Boost.Build... - -boost-build $(boost-build-src) ; - - - - - diff --git a/math/config/Jamfile.v2 b/math/config/Jamfile.v2 deleted file mode 100644 index 832e2936..00000000 --- a/math/config/Jamfile.v2 +++ /dev/null @@ -1,45 +0,0 @@ -# copyright John Maddock 2008 -# Distributed under the Boost Software License, Version 1.0. -# (See accompanying file LICENSE_1_0.txt or copy at -# http://www.boost.org/LICENSE_1_0.txt. - -import modules ; -import path ; - -local ntl-path = [ modules.peek : NTL_PATH ] ; -local gmp_path = [ modules.peek : GMP_PATH ] ; -local mpfr_path = [ modules.peek : MPFR_PATH ] ; -local e_float_path = [ modules.peek : BOOST_E_FLOAT_PATH ] ; - -if ! $(e_float_path) -{ - e_float_path = ../../../../e_float ; -} - -ECHO $(BOOST_E_FLOAT_PATH) - -obj has_long_double_support : has_long_double_support.cpp ; -obj has_mpfr_class : has_mpfr_class.cpp : - $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; -obj has_mpreal : has_mpreal.cpp : - $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/mpfrc++ ; -obj has_ntl_rr : has_ntl_rr.cpp : $(ntl-path)/include ; -obj has_gmpxx : has_gmpxx.cpp : - $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; -obj has_gcc_visibility : has_gcc_visibility.cpp : - gcc:-fvisibility=hidden gcc:-Werror ; -obj has_e_float : has_e_float.cpp : $(e_float_path) ; -obj has_gmp : has_gmp.cpp : - $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; -obj has_mpfr : has_mpfr.cpp : - $(mpfr_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; - -explicit has_long_double_support ; -explicit has_mpfr_class ; -explicit has_mpreal ; -explicit has_ntl_rr ; -explicit has_gmpxx ; -explicit has_gcc_visibility ; -explicit has_e_float ; -explicit has_gmp ; -explicit has_mpfr ; diff --git a/math/config/has_e_float.cpp b/math/config/has_e_float.cpp deleted file mode 100644 index 8cadc5c6..00000000 --- a/math/config/has_e_float.cpp +++ /dev/null @@ -1,17 +0,0 @@ -// Copyright John Maddock 2011. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - - -#ifdef _MSC_VER -# pragma warning (disable : 4100) // unreferenced formal parameter -#endif - -#define E_FLOAT_TYPE_EFX - -#include -#include -#include - - diff --git a/math/config/has_gcc_visibility.cpp b/math/config/has_gcc_visibility.cpp deleted file mode 100644 index 6c7d6f91..00000000 --- a/math/config/has_gcc_visibility.cpp +++ /dev/null @@ -1,13 +0,0 @@ -// Copyright John Maddock 20010. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef __GNUC__ -# error "This is a GCC specific test case". -#endif - -int main() -{ - return 0; -} diff --git a/math/config/has_gmp.cpp b/math/config/has_gmp.cpp deleted file mode 100644 index 582f0027..00000000 --- a/math/config/has_gmp.cpp +++ /dev/null @@ -1,7 +0,0 @@ -// Copyright John Maddock 2008. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#include - diff --git a/math/config/has_gmpxx.cpp b/math/config/has_gmpxx.cpp deleted file mode 100644 index edf62d8c..00000000 --- a/math/config/has_gmpxx.cpp +++ /dev/null @@ -1,7 +0,0 @@ -// Copyright John Maddock 2008. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#include - diff --git a/math/config/has_long_double_support.cpp b/math/config/has_long_double_support.cpp deleted file mode 100644 index d314cf38..00000000 --- a/math/config/has_long_double_support.cpp +++ /dev/null @@ -1,10 +0,0 @@ -// Copyright John Maddock 2008. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#include - -#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS -#error "long double support is not supported by Boost.Math on this Plaform: the long double version of the TR1 library will not be built." -#endif diff --git a/math/config/has_mpfr.cpp b/math/config/has_mpfr.cpp deleted file mode 100644 index 49d12a0b..00000000 --- a/math/config/has_mpfr.cpp +++ /dev/null @@ -1,7 +0,0 @@ -// Copyright John Maddock 2008. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#include - diff --git a/math/config/has_mpfr_class.cpp b/math/config/has_mpfr_class.cpp deleted file mode 100644 index 8eb3c7b2..00000000 --- a/math/config/has_mpfr_class.cpp +++ /dev/null @@ -1,14 +0,0 @@ -// Copyright John Maddock 2008. -// Copyright Paul A. Britow 2009 -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifdef _MSC_VER -# pragma warning (disable : 4127) // conditional expression is constant -# pragma warning (disable : 4800) // 'int' : forcing value to bool 'true' or 'false' (performance warning) -# pragma warning (disable : 4512) // assignment operator could not be generated -#endif - -#include - diff --git a/math/config/has_mpreal.cpp b/math/config/has_mpreal.cpp deleted file mode 100644 index 8ee8897d..00000000 --- a/math/config/has_mpreal.cpp +++ /dev/null @@ -1,14 +0,0 @@ -// Copyright John Maddock 2008. -// Copyright Paul A. Britow 2009 -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifdef _MSC_VER -# pragma warning (disable : 4127) // conditional expression is constant -# pragma warning (disable : 4800) // 'int' : forcing value to bool 'true' or 'false' (performance warning) -# pragma warning (disable : 4512) // assignment operator could not be generated -#endif - -#include - diff --git a/math/config/has_ntl_rr.cpp b/math/config/has_ntl_rr.cpp deleted file mode 100644 index f3844217..00000000 --- a/math/config/has_ntl_rr.cpp +++ /dev/null @@ -1,12 +0,0 @@ -// Copyright John Maddock 2008. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - - -#ifdef _MSC_VER -# pragma warning (disable : 4100) // unreferenced formal parameter -#endif - -#include - diff --git a/math/doc/Jamfile.v2 b/math/doc/Jamfile.v2 deleted file mode 100644 index 2f00f026..00000000 --- a/math/doc/Jamfile.v2 +++ /dev/null @@ -1,67 +0,0 @@ - -# Copyright John Maddock 2011. Use, modification, and distribution are -# subject to the Boost Software License, Version 1.0. (See accompanying -# file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -using quickbook ; - -path-constant images_location : html ; - -xml big_number : big_number.qbk ; -boostbook standalone - : - big_number - : - # Path for links to Boost: - #boost.root=../../../../.. - - # Some general style settings: - table.footnote.number.format=1 - footnote.number.format=1 - html.stylesheet=boostbook.css - - # HTML options first: - # Use graphics not text for navigation: - navig.graphics=1 - # How far down we chunk nested sections, basically all of them: - chunk.section.depth=10 - # Don't put the first section on the same page as the TOC: - chunk.first.sections=10 - # How far down sections get TOC's - toc.section.depth=10 - # Max depth in each TOC: - toc.max.depth=4 - # How far down we go with TOC's - #generate.section.toc.level=10 - # Index on type: - index.on.type=1 - - # PDF Options: - # TOC Generation: this is needed for FOP-0.9 and later: - fop1.extensions=0 - pdf:xep.extensions=1 - # TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9! - pdf:fop.extensions=0 - pdf:fop1.extensions=0 - # No indent on body text: - pdf:body.start.indent=0pt - # Margin size: - pdf:page.margin.inner=0.5in - # Margin size: - pdf:page.margin.outer=0.5in - # Paper type = A4 - pdf:paper.type=A4 - # Yes, we want graphics for admonishments: - admon.graphics=1 - # Set this one for PDF generation *only*: - # default pnd graphics are awful in PDF form, - # better use SVG's instead: - pdf:admon.graphics.extension=".svg" - pdf:use.role.for.mediaobject=1 - pdf:preferred.mediaobject.role=print - pdf:img.src.path=$(images_location)/ - pdf:draft.mode="no" - pdf:boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/sf_and_dist/html - ; - -install pdf-install : standalone : . PDF ; diff --git a/math/doc/big_number.qbk b/math/doc/big_number.qbk deleted file mode 100644 index 4ccfb199..00000000 --- a/math/doc/big_number.qbk +++ /dev/null @@ -1,207 +0,0 @@ -[/ - Copyright 2011 John Maddock. - Distributed under the Boost Software License, Version 1.0. - (See accompanying file LICENSE_1_0.txt or copy at - http://www.boost.org/LICENSE_1_0.txt). -] - -[library Boost.BigNumbers - [quickbook 1.5] - [copyright 2011 John Maddock] - [purpose Big Number library] - [license - Distributed under the Boost Software License, Version 1.0. - (See accompanying file LICENSE_1_0.txt or copy at - [@http://www.boost.org/LICENSE_1_0.txt]) - ] - [authors [authors, various]] - [last-revision $Date: 2011-07-08 18:51:46 +0100 (Fri, 08 Jul 2011) $] -] - -[section:intro Introduction] - -The Big Number library comes in two distinct parts: an expression template enabled front end `big_number` -that handles all the operator overloading, expression evaluation optimization, and code reduction, and -a selection of backends that implement the actual arithmetic operations, and need conform only to the -reduced interface requirements of the front end. - -[endsect] - -[section:tut Tutorial] - -In order to use this library you need to make two choices: what kind of number do I want, and -which backend do I want to perform the actual arithmetic? - -[section:ints Integer Types] - -The following backends provide integer arithmetic: - -[table -[[Backend Type][Header][Radix][Dependencies][Pros][Cons]] -[[`gmp_int`][boost/math/big_number/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] -] - -[h4 gmp_int] - - namespace boost{ namespace math{ - - class gmp_int; - - typedef big_number mpz_int; - - }} // namespaces - -The `gmp_int` backend is used via the typedef `boost::math::mpz_int`. It acts as a thin wrapper around the GMP `mpz_t` -to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. - -[h5 Example:] - - #include - - boost::math::mpz_int v = 1; - - // Do some arithmetic: - for(unsigned i = 1; i <= 1000; ++i) - v *= i; - - std::cout << i << std::endl; // prints 1000! - -[endsect] - -[section:reals Real Numbers] - -The following backends provide real number arithmetic: - -[table -[[Backend Type][Header][Radix][Dependencies][Pros][Cons]] -[[`gmp_real`][boost/math/big_number/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] -] - -[h4 gmp_real] - - namespace boost{ namespace math{ - - template - class gmp_real; - - typedef big_number > mpf_real_50; - typedef big_number > mpf_real_100; - typedef big_number > mpf_real_500; - typedef big_number > mpf_real_1000; - typedef big_number > mpf_real; - - }} // namespaces - -The `gmp_real` backend is used in conjunction with `big_number`: It acts as a thin wrapper around the GMP `mpf_t` -to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with -much greater precision. - -Type `gmp_real` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or -at variable precision by setting the template argument to zero. The typedefs mpf_real_50, mpf_real_100, -mpf_real_500, mpf_real_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision -respectively. The typedef mpf_real provides a variable precision type whose precision can be controlled via the -`big_number`'s member functions. - -[h5 example:] - - #include - - boost::math::gmp_real a = 2; - boost::math::gmp_real::default_precision(1000); - std::cout << boost::math::gmp_real::default_precision() << std::endl; - std::cout << sqrt(a) << std::endl; // print root-2 - -[endsect] - -[endsect] - -[section:ref Reference] - -[section:bignum big_number] - -[h4 Synopsis] - - namespace boost{ namespace math{ - - template - class big_number - { - big_number(); - big_number(see-below); - big_number& operator=(see-below); - /* Other number-type operators here */ - // string conversion: - std::string str()const; - // precision control: - static unsigned default_precision(); - static void default_precision(unsigned digits10); - unsigned precision()const; - void precision(unsigned digits10); - // Comparison: - int compare(const big_number& o)const; - template - typename enable_if, int>::type compare(const V& o)const; - }; - - }} // namespaces - -[h4 Description] - - big_number(); - big_number(see-below); - big_number& operator=(see-below); - -Type `big_number` is default constructible, and copy both constructible and assignable from: - -* Itself. -* An expression template which is the result of one of the arithmetic operators. -* Any builtin arithmetic type. -* A `std::string` or any type which is convertible to `const char*`. - - /* Other number-type operators here */ - -The following arithmetic operations are support for real-numbered types: - -* Binary +, -, *, /, +=, -=, *=, /=, ==, !=, <=, >=, <, >. -* Unary +, -. - -For integer types the following operators are also supported: - -Binary %, %=. - -(More to follow!!) - -Note that the result of the binary +, -, *, / and % operations is an expression template of "unmentionable type". - - std::string str()const; - -Returns the number formatted as a string (TODO: enable custom precision). - - static unsigned default_precision(); - static void default_precision(unsigned digits10); - unsigned precision()const; - void precision(unsigned digits10); - -These functions are only available if the Backend template parameter supports runtime changes to precision. They get and set -the default precision and the precision of *this respectively. - - int compare(const big_number& o)const; - template - typename enable_if, int>::type compare(const V& other)const; - -Returns: - -* A value less that 0 for *this < other -* A value greater that 0 for *this > other -* Zero for *this == other - -[endsect] - -[section:backendconc Backend Requirements] - -TODO, big boring job!! - -[endsect] - -[endsect] - diff --git a/math/doc/html/boost_bignumbers/intro.html b/math/doc/html/boost_bignumbers/intro.html deleted file mode 100644 index ee77f4b1..00000000 --- a/math/doc/html/boost_bignumbers/intro.html +++ /dev/null @@ -1,44 +0,0 @@ - - - -Introduction - - - - - - - - -
-
-
-PrevUpHomeNext -
-
-
-

- The Big Number library comes in two distinct parts: an expression template - enabled front end big_number - that handles all the operator overloading, expression evaluation optimization, - and code reduction, and a selection of backends that implement the actual arithmetic - operations, and need conform only to the reduced interface requirements of - the front end. -

-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHomeNext -
- - diff --git a/math/doc/html/boost_bignumbers/ref.html b/math/doc/html/boost_bignumbers/ref.html deleted file mode 100644 index c6a81e2f..00000000 --- a/math/doc/html/boost_bignumbers/ref.html +++ /dev/null @@ -1,40 +0,0 @@ - - - -Reference - - - - - - - - -
-
-
-PrevUpHomeNext -
-
-
-
-
big_number
-
Backend Requirements
-
-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHomeNext -
- - diff --git a/math/doc/html/boost_bignumbers/ref/backendconc.html b/math/doc/html/boost_bignumbers/ref/backendconc.html deleted file mode 100644 index 44dd13af..00000000 --- a/math/doc/html/boost_bignumbers/ref/backendconc.html +++ /dev/null @@ -1,38 +0,0 @@ - - - -Backend Requirements - - - - - - - -
-
-
-PrevUpHome -
-
-
-

- TODO, big boring job!! -

-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHome -
- - diff --git a/math/doc/html/boost_bignumbers/ref/bignum.html b/math/doc/html/boost_bignumbers/ref/bignum.html deleted file mode 100644 index bcf3ef57..00000000 --- a/math/doc/html/boost_bignumbers/ref/bignum.html +++ /dev/null @@ -1,151 +0,0 @@ - - - -big_number - - - - - - - - -
-
-
-PrevUpHomeNext -
-
-
-
- - Synopsis -
-
namespace boost{ namespace math{
-
-template <class Backend>
-class big_number
-{
-   big_number();
-   big_number(see-below);
-   big_number& operator=(see-below);
-   /* Other number-type operators here */
-   // string conversion:
-   std::string str()const;
-   // precision control:
-   static unsigned default_precision();
-   static void default_precision(unsigned digits10);
-   unsigned precision()const;
-   void precision(unsigned digits10);
-   // Comparison:
-   int compare(const big_number<Backend>& o)const;
-   template <class V>
-   typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
-};
-
-}} // namespaces
-
-
- - Description -
-
big_number();
-big_number(see-below);
-big_number& operator=(see-below);
-
-

- Type big_number is default - constructible, and copy both constructible and assignable from: -

-
    -
  • - Itself. -
    • -
  • - An expression template which is the result of one of the arithmetic operators. -
    • -
  • - Any builtin arithmetic type. -
    • -
  • - A std::string or any type which is convertible - to const char*. -
    • -
-
/* Other number-type operators here */
-
-

- The following arithmetic operations are support for real-numbered types: -

-
    -
  • - Binary +, -, *, /, +, -, *, /, - ==, !, <, >=, <, >. -
    • -
  • - Unary +, -. -
    • -
-

- For integer types the following operators are also supported: -

-

- Binary %, %=. -

-

- (More to follow!!) -

-

- Note that the result of the binary +, -, *, / and % operations is an expression - template of "unmentionable type". -

-
std::string str()const;
-
-

- Returns the number formatted as a string (TODO: enable custom precision). -

-
static unsigned default_precision();
-static void default_precision(unsigned digits10);
-unsigned precision()const;
-void precision(unsigned digits10);
-
-

- These functions are only available if the Backend template parameter supports - runtime changes to precision. They get and set the default precision and - the precision of *this respectively. -

-
int compare(const big_number<Backend>& o)const;
-template <class V>
-typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
-
-

- Returns: -

-
    -
  • - A value less that 0 for *this < other -
    • -
  • - A value greater that 0 for *this > other -
    • -
  • - Zero for *this == other -
    • -
-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHomeNext -
- - diff --git a/math/doc/html/boost_bignumbers/tut.html b/math/doc/html/boost_bignumbers/tut.html deleted file mode 100644 index 92e58b08..00000000 --- a/math/doc/html/boost_bignumbers/tut.html +++ /dev/null @@ -1,44 +0,0 @@ - - - -Tutorial - - - - - - - - -
-
-
-PrevUpHomeNext -
-
-
-
-
Integer Types
-
Real Numbers
-
-

- In order to use this library you need to make two choices: what kind of number - do I want, and which backend do I want to perform the actual arithmetic? -

-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHomeNext -
- - diff --git a/math/doc/html/boost_bignumbers/tut/ints.html b/math/doc/html/boost_bignumbers/tut/ints.html deleted file mode 100644 index b2dbce57..00000000 --- a/math/doc/html/boost_bignumbers/tut/ints.html +++ /dev/null @@ -1,146 +0,0 @@ - - - -Integer Types - - - - - - - - -
-
-
-PrevUpHomeNext -
-
-
-

- The following backends provide integer arithmetic: -

-
-------- - - - - - - - - - - - - - - - - -
-

- Backend Type -

- 		-

- Header -

- 		-

- Radix -

- 		-

- Dependencies -

- 		-

- Pros -

- 		-

- Cons -

-
-

- gmp_int -

- 		-

- boost/math/big_number/gmp.hpp -

- 		-

- 2 -

- 		-

- GMP -

- 		-

- Very fast and efficient backend. -

- 		-

- Dependency on GNU licenced GMP library. -

-
-
- - gmp_int -
-
namespace boost{ namespace math{
-
-class gmp_int;
-
-typedef big_number<gmp_int >         mpz_int;
-
-}} // namespaces
-
-

- The gmp_int backend is used - via the typedef boost::math::mpz_int. It acts as a thin wrapper around - the GMP mpz_t to provide - an integer type that is a drop-in replacement for the native C++ integer - types, but with unlimited precision. -

-
- - Example: -
-
#include <boost/math/big_number/gmp.hpp>
-
-boost::math::mpz_int v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-
-std::cout << i << std::endl; // prints 1000!
-
-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHomeNext -
- - diff --git a/math/doc/html/boost_bignumbers/tut/reals.html b/math/doc/html/boost_bignumbers/tut/reals.html deleted file mode 100644 index cd08e445..00000000 --- a/math/doc/html/boost_bignumbers/tut/reals.html +++ /dev/null @@ -1,158 +0,0 @@ - - - -Real Numbers - - - - - - - - -
-
-
-PrevUpHomeNext -
-
-
-

- The following backends provide real number arithmetic: -

-
-------- - - - - - - - - - - - - - - - - -
-

- Backend Type -

- 		-

- Header -

- 		-

- Radix -

- 		-

- Dependencies -

- 		-

- Pros -

- 		-

- Cons -

-
-

- gmp_real<N> -

- 		-

- boost/math/big_number/gmp.hpp -

- 		-

- 2 -

- 		-

- GMP -

- 		-

- Very fast and efficient backend. -

- 		-

- Dependency on GNU licenced GMP library. -

-
-
- - gmp_real -
-
namespace boost{ namespace math{
-
-template <unsigned Digits10>
-class gmp_real;
-
-typedef big_number<gmp_real<50> >    mpf_real_50;
-typedef big_number<gmp_real<100> >   mpf_real_100;
-typedef big_number<gmp_real<500> >   mpf_real_500;
-typedef big_number<gmp_real<1000> >  mpf_real_1000;
-typedef big_number<gmp_real<0> >     mpf_real;
-
-}} // namespaces
-
-

- The gmp_real backend is used - in conjunction with big_number: - It acts as a thin wrapper around the GMP mpf_t - to provide an real-number type that is a drop-in replacement for the native - C++ floating-point types, but with much greater precision. -

-

- Type gmp_real can be used - at fixed precision by specifying a non-zero Digits10 - template parameter, or at variable precision by setting the template argument - to zero. The typedefs mpf_real_50, mpf_real_100, mpf_real_500, mpf_real_1000 - provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision - respectively. The typedef mpf_real provides a variable precision type whose - precision can be controlled via the big_number's - member functions. -

-
- - example: -
-
#include <boost/math/big_number/gmp.hpp>
-
-boost::math::gmp_real a = 2;
-boost::math::gmp_real::default_precision(1000);
-std::cout << boost::math::gmp_real::default_precision() << std::endl;
-std::cout << sqrt(a) << std::endl; // print root-2
-
-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHomeNext -
- - diff --git a/math/doc/html/boostbook.css b/math/doc/html/boostbook.css deleted file mode 100644 index 252fa9ec..00000000 --- a/math/doc/html/boostbook.css +++ /dev/null @@ -1,588 +0,0 @@ -/*============================================================================= - Copyright (c) 2004 Joel de Guzman - http://spirit.sourceforge.net/ - - Distributed under the Boost Software License, Version 1.0. (See accompany- - ing file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -=============================================================================*/ - -/*============================================================================= - Body defaults -=============================================================================*/ - - body - { - margin: 1em; - font-family: sans-serif; - } - -/*============================================================================= - Paragraphs -=============================================================================*/ - - p - { - text-align: left; - font-size: 10pt; - line-height: 1.15; - } - -/*============================================================================= - Program listings -=============================================================================*/ - - /* Code on paragraphs */ - p tt.computeroutput - { - font-size: 9pt; - } - - pre.synopsis - { - font-size: 90%; - margin: 1pc 4% 0pc 4%; - padding: 0.5pc 0.5pc 0.5pc 0.5pc; - } - - .programlisting, - .screen - { - font-size: 9pt; - display: block; - margin: 1pc 4% 0pc 4%; - padding: 0.5pc 0.5pc 0.5pc 0.5pc; - } - - /* Program listings in tables don't get borders */ - td .programlisting, - td .screen - { - margin: 0pc 0pc 0pc 0pc; - padding: 0pc 0pc 0pc 0pc; - } - -/*============================================================================= - Headings -=============================================================================*/ - - h1, h2, h3, h4, h5, h6 - { - text-align: left; - margin: 1em 0em 0.5em 0em; - font-weight: bold; - } - - h1 { font: 140% } - h2 { font: bold 140% } - h3 { font: bold 130% } - h4 { font: bold 120% } - h5 { font: italic 110% } - h6 { font: italic 100% } - - /* Top page titles */ - title, - h1.title, - h2.title - h3.title, - h4.title, - h5.title, - h6.title, - .refentrytitle - { - font-weight: bold; - margin-bottom: 1pc; - } - - h1.title { font-size: 140% } - h2.title { font-size: 140% } - h3.title { 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- -Chapter 1. Boost.BigNumbers - - - - - - -
-
-
Next
-
-
-

-Chapter 1. Boost.BigNumbers

-

-various authors -

-

Copyright © 2011 John Maddock

-
-

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-

Table of Contents

-
-
Introduction
-
Tutorial
-
-
Integer Types
-
Real Numbers
-
-
Reference
-
-
big_number
-
Backend Requirements
-
-
-
-
- - - -

Last revised: July 08, 2011 at 18:51:46 +0100

-
-
Next
- - diff --git a/math/test/Jamfile.v2 b/math/test/Jamfile.v2 deleted file mode 100644 index 24b697e7..00000000 --- a/math/test/Jamfile.v2 +++ /dev/null @@ -1,189 +0,0 @@ -# copyright John Maddock 2008 -# Distributed under the Boost Software License, Version 1.0. -# (See accompanying file LICENSE_1_0.txt or copy at -# http://www.boost.org/LICENSE_1_0.txt. - -import modules ; -import path ; - -local ntl-path = [ modules.peek : NTL_PATH ] ; -local gmp_path = [ modules.peek : GMP_PATH ] ; -local mpfr_path = [ modules.peek : MPFR_PATH ] ; -local e_float_path = [ modules.peek : BOOST_E_FLOAT_PATH ] ; - -if ! $(e_float_path) -{ - e_float_path = ../../../../e_float ; -} - -project : requirements - $(gmp_path) - $(gmp_path)/mpfr - $(gmp_path)/gmpfrxx - $(mpfr_path) - ../../.. - $(e_float_path) - $(gmp_path) - $(mpfr_path) - $(mpfr_path)/build.vc10/lib/Win32/Debug - msvc:static - E_FLOAT_DIGITS10=100 - E_FLOAT_TYPE_EFX - ; - -lib gmp ; -lib mpfr ; - -E_FLOAT_SRC = [ GLOB $(e_float_path)/libs/e_float/src/e_float : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/e_float/efx : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/constants : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/elementary : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/gamma : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/integer : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/tables : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/zeta : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/generic_functions/constants : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/generic_functions/elementary : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/utility : *.cpp ] - ; - -lib e_float : $(E_FLOAT_SRC) - : - [ check-target-builds ../config//has_e_float : : no ] - ; - -run test_arithmetic.cpp - : # command line - : # input files - : # requirements - TEST_BACKEND - : test_arithmetic_backend_concept ; - -run test_arithmetic.cpp gmp - : # command line - : # input files - : # requirements - TEST_MPF50 - [ check-target-builds ../config//has_gmp : : no ] - : test_arithmetic_mpf50 ; - -run test_arithmetic.cpp gmp - : # command line - : # input files - : # requirements - TEST_MPF - [ check-target-builds ../config//has_gmp : : no ] - : test_arithmetic_mpf ; - -run test_arithmetic.cpp gmp - : # command line - : # input files - : # requirements - TEST_MPZ - [ check-target-builds ../config//has_gmp : : no ] - : test_arithmetic_mpz ; - -run test_arithmetic.cpp gmp - : # command line - : # input files - : # requirements - TEST_MPQ - [ check-target-builds ../config//has_gmp : : no ] - : test_arithmetic_mpq ; - -run test_arithmetic.cpp mpfr gmp - : # command line - : # input files - : # requirements - TEST_MPFR - [ check-target-builds ../config//has_mpfr : : no ] - : test_arithmetic_mpfr ; - -run test_arithmetic.cpp mpfr gmp - : # command line - : # input files - : # requirements - TEST_MPFR_50 - [ check-target-builds ../config//has_mpfr : : no ] - : test_arithmetic_mpfr_50 ; - -run test_arithmetic.cpp $(E_FLOAT_SRC) - : # command line - : # input files - : # requirements - TEST_E_FLOAT - [ check-target-builds ../config//has_e_float : : no ] - : test_arithmetic_e_float ; - -run test_numeric_limits.cpp - : # command line - : # input files - : # requirements - TEST_BACKEND - : test_numeric_limits_backend_concept ; - -run test_numeric_limits.cpp gmp - : # command line - : # input files - : # requirements - TEST_MPF50 - [ check-target-builds ../config//has_gmp : : no ] - : test_numeric_limits_mpf50 ; - -run test_numeric_limits.cpp gmp - : # command line - : # input files - : # requirements - TEST_MPF - [ check-target-builds ../config//has_gmp : : no ] - : test_numeric_limits_mpf ; - -run test_numeric_limits.cpp gmp - : # command line - : # input files - : # requirements - TEST_MPZ - [ check-target-builds ../config//has_gmp : : no ] - : test_numeric_limits_mpz ; - -run test_numeric_limits.cpp gmp - : # command line - : # input files - : # requirements - TEST_MPQ - [ check-target-builds ../config//has_gmp : : no ] - : test_numeric_limits_mpq ; - -run test_numeric_limits.cpp mpfr - : # command line - : # input files - : # requirements - TEST_MPFR - [ check-target-builds ../config//has_mpfr : : no ] - : test_numeric_limits_mpfr ; - -run test_numeric_limits.cpp mpfr - : # command line - : # input files - : # requirements - TEST_MPFR_50 - [ check-target-builds ../config//has_mpfr : : no ] - : test_numeric_limits_mpfr_50 ; - - -run test_numeric_limits.cpp $(E_FLOAT_SRC) - : # command line - : # input files - : # requirements - TEST_E_FLOAT - [ check-target-builds ../config//has_e_float : : no ] - : test_numeric_limits_e_float ; - -run big_number_concept_check.cpp mpfr - : # command line - : # input files - : # requirements - TEST_MPFR_50 - [ check-target-builds ../config//has_mpfr : : no ] - : big_number_concept_check_mpfr_50 ; - diff --git a/math/test/big_number_concept_check.cpp b/math/test/big_number_concept_check.cpp deleted file mode 100644 index e2745897..00000000 --- a/math/test/big_number_concept_check.cpp +++ /dev/null @@ -1,100 +0,0 @@ - -// Copyright John Maddock 2011. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -// -// This tests two things: that e_float meets our -// conceptual requirements, and that we can instantiate -// all our distributions and special functions on this type. -// -#define BOOST_MATH_ASSERT_UNDEFINED_POLICY false -#define BOOST_MATH_INSTANTIATE_MINIMUM - -#ifdef _MSC_VER -# pragma warning(disable:4800) -# pragma warning(disable:4512) -# pragma warning(disable:4127) -# pragma warning(disable:4512) -# pragma warning(disable:4503) // decorated name length exceeded, name was truncated -#endif - -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) -# define TEST_MPF50 -# define TEST_MPF -# define TEST_BACKEND -# define TEST_MPZ -# define TEST_MPFR -# define TEST_MPFR_50 -# define TEST_E_FLOAT - -#ifdef _MSC_VER -#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") -#endif -#ifdef __GNUC__ -#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" -#endif - -#endif - -#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) -#include -#endif -#ifdef TEST_BACKEND -#include -#endif -#ifdef TEST_E_FLOAT -#include -#endif -#if defined(TEST_MPFR) || defined(TEST_MPFR_50) -#include -#endif - -#include -#include "libs/math/test/compile_test/instantiate.hpp" - -void foo() -{ -#ifdef TEST_BACKEND - instantiate(boost::math::big_number_real_architype()); -#endif -#ifdef TEST_MPF_50 - instantiate(boost::math::mpf_real_50()); -#endif -#ifdef TEST_MPF - instantiate(boost::math::mpf_real()); -#endif -#ifdef TEST_MPFR_50 - instantiate(boost::math::mpfr_real_50()); -#endif -#ifdef TEST_MPFR - instantiate(boost::math::mpfr_real()); -#endif -#ifdef TEST_E_FLOAT - instantiate(boost::math::e_float()); -#endif -} - -int main() -{ -#ifdef TEST_BACKEND - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); -#endif -#ifdef TEST_MPF_50 - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); -#endif -#ifdef TEST_MPF - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); -#endif -#ifdef TEST_MPFR_50 - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); -#endif -#ifdef TEST_MPFR - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); -#endif -#ifdef TEST_E_FLOAT - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); -#endif - -} diff --git a/math/test/linpack-benchmark.cpp b/math/test/linpack-benchmark.cpp deleted file mode 100644 index 99c8c87b..00000000 --- a/math/test/linpack-benchmark.cpp +++ /dev/null @@ -1,1257 +0,0 @@ -/////////////////////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -/* 1000d.f -- translated by f2c (version 20050501). -You must link the resulting object file with libf2c: -on Microsoft Windows system, link with libf2c.lib; -on Linux or Unix systems, link with .../path/to/libf2c.a -lm -or, if you install libf2c.a in a standard place, with -lf2c -lm --- in that order, at the end of the command line, as in -cc *.o -lf2c -lm -Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - -http://www.netlib.org/f2c/libf2c.zip -*/ -#include -#include -#include -#include - -#ifdef TEST_MPF_100 -#include -typedef boost::math::mpf_real_100 real_type; -#elif defined(TEST_MPFR_100) -#include -typedef boost::math::mpfr_real_100 real_type; -#elif defined(TEST_GMPXX) -#include -typedef mpf_class real_type; -#elif defined(TEST_MPFRXX) -#include -typedef mpfr_class real_type; -#elif defined(TEST_E_FLOAT) -#include -#include -#include -typedef ::efx::e_float real_type; -using ef::abs; -#elif defined(TEST_E_FLOAT_BN) -#include -typedef boost::math::e_float real_type; -#else -typedef double real_type; -#endif - -#ifndef CAST_TO_RT -# define CAST_TO_RT(x) x -#endif - -extern "C" { -#include "f2c.h" - integer s_wsfe(cilist *), e_wsfe(void), do_fio(integer *, char *, ftnlen), - s_wsle(cilist *), do_lio(integer *, integer *, char *, ftnlen), - e_wsle(void); - /* Subroutine */ int s_stop(char *, ftnlen); - -#undef abs -#undef dabs -#define dabs abs -#undef min -#undef max -#undef dmin -#undef dmax -#define dmin min -#define dmax max - -} -#include - -using std::min; -using std::max; - -/* Table of constant values */ - -static integer c__0 = 0; -static real_type c_b7 = CAST_TO_RT(1); -static integer c__1 = 1; -static integer c__9 = 9; - -inline double second_(void) -{ - return ((double)(clock())) / CLOCKS_PER_SEC; -} - -int dgefa_(real_type *, integer *, integer *, integer *, integer *), dgesl_(real_type *, integer *, integer *, integer *, real_type *, integer *); -int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type *); -int matgen_(real_type *, integer *, integer *, real_type *, real_type *); -real_type epslon_(real_type *); -real_type ran_(integer *); -int dscal_(integer *, real_type *, real_type *, integer *); -int daxpy_(integer *, real_type *, real_type *, integer *, real_type *, integer *); -integer idamax_(integer *, real_type *, integer *); -real_type ddot_(integer *, real_type *, integer *, real_type *, integer *); -int daxpy_(integer *, real_type *, real_type *, integer *, real_type *, integer *); -int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type *); - - -extern "C" int MAIN__() -{ -#ifdef TEST_MPF_100 - std::cout << "Testing big_number >" << std::endl; -#elif defined(TEST_MPFR_100) - std::cout << "Testing big_number >" << std::endl; -#elif defined(TEST_GMPXX) - std::cout << "Testing mpf_class at 100 decimal degits" << std::endl; - mpf_set_default_prec(((100 + 1) * 1000L) / 301L); -#elif defined(TEST_MPFRXX) - std::cout << "Testing mpfr_class at 100 decimal degits" << std::endl; - mpfr_set_default_prec(((100 + 1) * 1000L) / 301L); -#elif defined(TEST_E_FLOAT) - std::cout << "Testing boost::ef::e_float" << std::endl; -#elif defined(TEST_E_FLOAT_BN) - std::cout << "Testing boost::math::e_float" << std::endl; -#else - std::cout << "Testing double" << std::endl; -#endif - - - /* Format strings */ - static char fmt_1[] = "(\002 Please send the results of this run to:\002" - "//\002 Jack J. Dongarra\002/\002 Computer Science Department\002/" - "\002 University of Tennessee\002/\002 Knoxville, Tennessee 37996" - "-1300\002//\002 Fax: 615-974-8296\002//\002 Internet: dongarra@c" - "s.utk.edu\002/)"; - static char fmt_40[] = "(\002 norm. resid resid mac" - "hep\002,\002 x(1) x(n)\002)"; - static char fmt_50[] = "(1p5e16.8)"; - static char fmt_60[] = "(//\002 times are reported for matrices of or" - "der \002,i5)"; - static char fmt_70[] = "(6x,\002factor\002,5x,\002solve\002,6x,\002tota" - "l\002,5x,\002mflops\002,7x,\002unit\002,6x,\002ratio\002)"; - static char fmt_80[] = "(\002 times for array with leading dimension o" - "f\002,i4)"; - static char fmt_110[] = "(6(1pe11.3))"; - - /* System generated locals */ - integer i__1; - real_type d__1, d__2, d__3; - - /* Builtin functions */ - - /* Local variables */ - static real_type a[1001000] /* was [1001][1000] */, b[1000]; - static integer i__, n; - static real_type x[1000]; - static double t1; - static integer lda; - static double ops; - static real_type eps; - static integer info; - static double time[6], cray, total; - static integer ipvt[1000]; - static real_type resid, norma; - static real_type normx; - static real_type residn; - - /* Fortran I/O blocks */ - static cilist io___4 = { 0, 6, 0, fmt_1, 0 }; - static cilist io___20 = { 0, 6, 0, fmt_40, 0 }; - static cilist io___21 = { 0, 6, 0, fmt_50, 0 }; - static cilist io___22 = { 0, 6, 0, fmt_60, 0 }; - static cilist io___23 = { 0, 6, 0, fmt_70, 0 }; - static cilist io___24 = { 0, 6, 0, fmt_80, 0 }; - static cilist io___25 = { 0, 6, 0, fmt_110, 0 }; - static cilist io___26 = { 0, 6, 0, 0, 0 }; - - - lda = 1001; - - /* this program was updated on 10/12/92 to correct a */ - /* problem with the random number generator. The previous */ - /* random number generator had a short period and produced */ - /* singular matrices occasionally. */ - - n = 1000; - cray = .056f; - s_wsfe(&io___4); - e_wsfe(); - /* Computing 3rd power */ - d__1 = (real_type) n; - /* Computing 2nd power */ - d__2 = (real_type) n; - ops = boost::lexical_cast(real_type(d__1 * (d__1 * d__1) * 2. / 3. + d__2 * d__2 * 2.)); - - matgen_(a, &lda, &n, b, &norma); - - /* ****************************************************************** */ - /* ****************************************************************** */ - /* you should replace the call to dgefa and dgesl */ - /* by calls to your linear equation solver. */ - /* ****************************************************************** */ - /* ****************************************************************** */ - - t1 = second_(); - dgefa_(a, &lda, &n, ipvt, &info); - time[0] = second_() - t1; - t1 = second_(); - dgesl_(a, &lda, &n, ipvt, b, &c__0); - time[1] = second_() - t1; - total = time[0] + time[1]; - /* ****************************************************************** */ - /* ****************************************************************** */ - - /* compute a residual to verify results. */ - - i__1 = n; - for (i__ = 1; i__ <= i__1; ++i__) { - x[i__ - 1] = b[i__ - 1]; - /* L10: */ - } - matgen_(a, &lda, &n, b, &norma); - i__1 = n; - for (i__ = 1; i__ <= i__1; ++i__) { - b[i__ - 1] = -b[i__ - 1]; - /* L20: */ - } - dmxpy_(&n, b, &n, &lda, x, a); - resid = CAST_TO_RT(0); - normx = CAST_TO_RT(0); - i__1 = n; - for (i__ = 1; i__ <= i__1; ++i__) { - /* Computing MAX */ - d__2 = resid, d__3 = (d__1 = b[i__ - 1], abs(d__1)); - resid = max(d__2,d__3); - /* Computing MAX */ - d__2 = normx, d__3 = (d__1 = x[i__ - 1], abs(d__1)); - normx = max(d__2,d__3); - /* L30: */ - } - eps = epslon_(&c_b7); - residn = resid / (n * norma * normx * eps); - s_wsfe(&io___20); - e_wsfe(); - s_wsfe(&io___21); - /* - do_fio(&c__1, (char *)&residn, (ftnlen)sizeof(real_type)); - do_fio(&c__1, (char *)&resid, (ftnlen)sizeof(real_type)); - do_fio(&c__1, (char *)&eps, (ftnlen)sizeof(real_type)); - do_fio(&c__1, (char *)&x[0], (ftnlen)sizeof(real_type)); - do_fio(&c__1, (char *)&x[n - 1], (ftnlen)sizeof(real_type)); - */ - std::cout << std::setw(12) << std::setprecision(5) << residn << " " << resid << " " << eps << " " << x[0] << " " << x[n-1] << std::endl; - e_wsfe(); - - s_wsfe(&io___22); - do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); - e_wsfe(); - s_wsfe(&io___23); - e_wsfe(); - - time[2] = total; - time[3] = ops / (total * 1e6); - time[4] = 2. / time[3]; - time[5] = total / cray; - s_wsfe(&io___24); - do_fio(&c__1, (char *)&lda, (ftnlen)sizeof(integer)); - e_wsfe(); - s_wsfe(&io___25); - for (i__ = 1; i__ <= 6; ++i__) { - // do_fio(&c__1, (char *)&time[i__ - 1], (ftnlen)sizeof(real_type)); - std::cout << std::setw(12) << std::setprecision(5) << time[i__ - 1]; - } - e_wsfe(); - s_wsle(&io___26); - do_lio(&c__9, &c__1, " end of tests -- this version dated 10/12/92", ( - ftnlen)44); - e_wsle(); - - s_stop("", (ftnlen)0); - return 0; -} /* MAIN__ */ - -/* Subroutine */ int matgen_(real_type *a, integer *lda, integer *n, - real_type *b, real_type *norma) -{ - /* System generated locals */ - integer a_dim1, a_offset, i__1, i__2; - real_type d__1, d__2; - - /* Local variables */ - static integer i__, j; - static integer init[4]; - - - /* Parameter adjustments */ - a_dim1 = *lda; - a_offset = 1 + a_dim1; - a -= a_offset; - --b; - - /* Function Body */ - init[0] = 1; - init[1] = 2; - init[2] = 3; - init[3] = 1325; - *norma = CAST_TO_RT(0); - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = ran_(init) - .5f; - /* Computing MAX */ - d__2 = (d__1 = a[i__ + j * a_dim1], abs(d__1)); - *norma = max(d__2,*norma); - /* L20: */ - } - /* L30: */ - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - b[i__] = CAST_TO_RT(0); - /* L35: */ - } - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__] += a[i__ + j * a_dim1]; - /* L40: */ - } - /* L50: */ - } - return 0; -} /* matgen_ */ - -/* Subroutine */ int dgefa_(real_type *a, integer *lda, integer *n, integer * - ipvt, integer *info) -{ - /* System generated locals */ - integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ - static integer j, k, l; - static real_type t; - static integer kp1, nm1; - - - /* dgefa factors a double precision matrix by gaussian elimination. */ - - /* dgefa is usually called by dgeco, but it can be called */ - /* directly with a saving in time if rcond is not needed. */ - /* (time for dgeco) = (1 + 9/n)*(time for dgefa) . */ - - /* on entry */ - - /* a double precision(lda, n) */ - /* the matrix to be factored. */ - - /* lda integer */ - /* the leading dimension of the array a . */ - - /* n integer */ - /* the order of the matrix a . */ - - /* on return */ - - /* a an upper triangular matrix and the multipliers */ - /* which were used to obtain it. */ - /* the factorization can be written a = l*u where */ - /* l is a product of permutation and unit lower */ - /* triangular matrices and u is upper triangular. */ - - /* ipvt integer(n) */ - /* an integer vector of pivot indices. */ - - /* info integer */ - /* = 0 normal value. */ - /* = k if u(k,k) .eq. 0.0 . this is not an error */ - /* condition for this subroutine, but it does */ - /* indicate that dgesl or dgedi will divide by zero */ - /* if called. use rcond in dgeco for a reliable */ - /* indication of singularity. */ - - /* linpack. this version dated 08/14/78 . */ - /* cleve moler, university of new mexico, argonne national lab. */ - - /* subroutines and functions */ - - /* blas daxpy,dscal,idamax */ - - /* internal variables */ - - - - /* gaussian elimination with partial pivoting */ - - /* Parameter adjustments */ - a_dim1 = *lda; - a_offset = 1 + a_dim1; - a -= a_offset; - --ipvt; - - /* Function Body */ - *info = 0; - nm1 = *n - 1; - if (nm1 < 1) { - goto L70; - } - i__1 = nm1; - for (k = 1; k <= i__1; ++k) { - kp1 = k + 1; - - /* find l = pivot index */ - - i__2 = *n - k + 1; - l = idamax_(&i__2, &a[k + k * a_dim1], &c__1) + k - 1; - ipvt[k] = l; - - /* zero pivot implies this column already triangularized */ - - if (a[l + k * a_dim1] == 0.) { - goto L40; - } - - /* interchange if necessary */ - - if (l == k) { - goto L10; - } - t = a[l + k * a_dim1]; - a[l + k * a_dim1] = a[k + k * a_dim1]; - a[k + k * a_dim1] = t; -L10: - - /* compute multipliers */ - - t = -1. / a[k + k * a_dim1]; - i__2 = *n - k; - dscal_(&i__2, &t, &a[k + 1 + k * a_dim1], &c__1); - - /* row elimination with column indexing */ - - i__2 = *n; - for (j = kp1; j <= i__2; ++j) { - t = a[l + j * a_dim1]; - if (l == k) { - goto L20; - } - a[l + j * a_dim1] = a[k + j * a_dim1]; - a[k + j * a_dim1] = t; -L20: - i__3 = *n - k; - daxpy_(&i__3, &t, &a[k + 1 + k * a_dim1], &c__1, &a[k + 1 + j * - a_dim1], &c__1); - /* L30: */ - } - goto L50; -L40: - *info = k; -L50: - /* L60: */ - ; - } -L70: - ipvt[*n] = *n; - if (a[*n + *n * a_dim1] == 0.) { - *info = *n; - } - return 0; -} /* dgefa_ */ - -/* Subroutine */ int dgesl_(real_type *a, integer *lda, integer *n, integer * - ipvt, real_type *b, integer *job) -{ - /* System generated locals */ - integer a_dim1, a_offset, i__1, i__2; - - /* Local variables */ - static integer k, l; - static real_type t; - static integer kb, nm1; - - - /* dgesl solves the double precision system */ - /* a * x = b or trans(a) * x = b */ - /* using the factors computed by dgeco or dgefa. */ - - /* on entry */ - - /* a double precision(lda, n) */ - /* the output from dgeco or dgefa. */ - - /* lda integer */ - /* the leading dimension of the array a . */ - - /* n integer */ - /* the order of the matrix a . */ - - /* ipvt integer(n) */ - /* the pivot vector from dgeco or dgefa. */ - - /* b double precision(n) */ - /* the right hand side vector. */ - - /* job integer */ - /* = 0 to solve a*x = b , */ - /* = nonzero to solve trans(a)*x = b where */ - /* trans(a) is the transpose. */ - - /* on return */ - - /* b the solution vector x . */ - - /* error condition */ - - /* a division by zero will occur if the input factor contains a */ - /* zero on the diagonal. technically this indicates singularity */ - /* but it is often caused by improper arguments or improper */ - /* setting of lda . it will not occur if the subroutines are */ - /* called correctly and if dgeco has set rcond .gt. 0.0 */ - /* or dgefa has set info .eq. 0 . */ - - /* to compute inverse(a) * c where c is a matrix */ - /* with p columns */ - /* call dgeco(a,lda,n,ipvt,rcond,z) */ - /* if (rcond is too small) go to ... */ - /* do 10 j = 1, p */ - /* call dgesl(a,lda,n,ipvt,c(1,j),0) */ - /* 10 continue */ - - /* linpack. this version dated 08/14/78 . */ - /* cleve moler, university of new mexico, argonne national lab. */ - - /* subroutines and functions */ - - /* blas daxpy,ddot */ - - /* internal variables */ - - - /* Parameter adjustments */ - a_dim1 = *lda; - a_offset = 1 + a_dim1; - a -= a_offset; - --ipvt; - --b; - - /* Function Body */ - nm1 = *n - 1; - if (*job != 0) { - goto L50; - } - - /* job = 0 , solve a * x = b */ - /* first solve l*y = b */ - - if (nm1 < 1) { - goto L30; - } - i__1 = nm1; - for (k = 1; k <= i__1; ++k) { - l = ipvt[k]; - t = b[l]; - if (l == k) { - goto L10; - } - b[l] = b[k]; - b[k] = t; -L10: - i__2 = *n - k; - daxpy_(&i__2, &t, &a[k + 1 + k * a_dim1], &c__1, &b[k + 1], &c__1); - /* L20: */ - } -L30: - - /* now solve u*x = y */ - - i__1 = *n; - for (kb = 1; kb <= i__1; ++kb) { - k = *n + 1 - kb; - b[k] /= a[k + k * a_dim1]; - t = -b[k]; - i__2 = k - 1; - daxpy_(&i__2, &t, &a[k * a_dim1 + 1], &c__1, &b[1], &c__1); - /* L40: */ - } - goto L100; -L50: - - /* job = nonzero, solve trans(a) * x = b */ - /* first solve trans(u)*y = b */ - - i__1 = *n; - for (k = 1; k <= i__1; ++k) { - i__2 = k - 1; - t = ddot_(&i__2, &a[k * a_dim1 + 1], &c__1, &b[1], &c__1); - b[k] = (b[k] - t) / a[k + k * a_dim1]; - /* L60: */ - } - - /* now solve trans(l)*x = y */ - - if (nm1 < 1) { - goto L90; - } - i__1 = nm1; - for (kb = 1; kb <= i__1; ++kb) { - k = *n - kb; - i__2 = *n - k; - b[k] += ddot_(&i__2, &a[k + 1 + k * a_dim1], &c__1, &b[k + 1], &c__1); - l = ipvt[k]; - if (l == k) { - goto L70; - } - t = b[l]; - b[l] = b[k]; - b[k] = t; -L70: - /* L80: */ - ; - } -L90: -L100: - return 0; -} /* dgesl_ */ - -/* Subroutine */ int daxpy_(integer *n, real_type *da, real_type *dx, - integer *incx, real_type *dy, integer *incy) -{ - /* System generated locals */ - integer i__1; - - /* Local variables */ - static integer i__, m, ix, iy, mp1; - - - /* constant times a vector plus a vector. */ - /* uses unrolled loops for increments equal to one. */ - /* jack dongarra, linpack, 3/11/78. */ - - - /* Parameter adjustments */ - --dy; - --dx; - - /* Function Body */ - if (*n <= 0) { - return 0; - } - if (*da == 0.) { - return 0; - } - if (*incx == 1 && *incy == 1) { - goto L20; - } - - /* code for unequal increments or equal increments */ - /* not equal to 1 */ - - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - dy[iy] += *da * dx[ix]; - ix += *incx; - iy += *incy; - /* L10: */ - } - return 0; - - /* code for both increments equal to 1 */ - - - /* clean-up loop */ - -L20: - m = *n % 4; - if (m == 0) { - goto L40; - } - i__1 = m; - for (i__ = 1; i__ <= i__1; ++i__) { - dy[i__] += *da * dx[i__]; - /* L30: */ - } - if (*n < 4) { - return 0; - } -L40: - mp1 = m + 1; - i__1 = *n; - for (i__ = mp1; i__ <= i__1; i__ += 4) { - dy[i__] += *da * dx[i__]; - dy[i__ + 1] += *da * dx[i__ + 1]; - dy[i__ + 2] += *da * dx[i__ + 2]; - dy[i__ + 3] += *da * dx[i__ + 3]; - /* L50: */ - } - return 0; -} /* daxpy_ */ - -real_type ddot_(integer *n, real_type *dx, integer *incx, real_type *dy, - integer *incy) -{ - /* System generated locals */ - integer i__1; - real_type ret_val; - - /* Local variables */ - static integer i__, m, ix, iy, mp1; - static real_type dtemp; - - - /* forms the dot product of two vectors. */ - /* uses unrolled loops for increments equal to one. */ - /* jack dongarra, linpack, 3/11/78. */ - - - /* Parameter adjustments */ - --dy; - --dx; - - /* Function Body */ - ret_val = CAST_TO_RT(0); - dtemp = CAST_TO_RT(0); - if (*n <= 0) { - return ret_val; - } - if (*incx == 1 && *incy == 1) { - goto L20; - } - - /* code for unequal increments or equal increments */ - /* not equal to 1 */ - - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - dtemp += dx[ix] * dy[iy]; - ix += *incx; - iy += *incy; - /* L10: */ - } - ret_val = dtemp; - return ret_val; - - /* code for both increments equal to 1 */ - - - /* clean-up loop */ - -L20: - m = *n % 5; - if (m == 0) { - goto L40; - } - i__1 = m; - for (i__ = 1; i__ <= i__1; ++i__) { - dtemp += dx[i__] * dy[i__]; - /* L30: */ - } - if (*n < 5) { - goto L60; - } -L40: - mp1 = m + 1; - i__1 = *n; - for (i__ = mp1; i__ <= i__1; i__ += 5) { - dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + dx[ - i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + dx[i__ + - 4] * dy[i__ + 4]; - /* L50: */ - } -L60: - ret_val = dtemp; - return ret_val; -} /* ddot_ */ - -/* Subroutine */ int dscal_(integer *n, real_type *da, real_type *dx, - integer *incx) -{ - /* System generated locals */ - integer i__1, i__2; - - /* Local variables */ - static integer i__, m, mp1, nincx; - - - /* scales a vector by a constant. */ - /* uses unrolled loops for increment equal to one. */ - /* jack dongarra, linpack, 3/11/78. */ - - - /* Parameter adjustments */ - --dx; - - /* Function Body */ - if (*n <= 0) { - return 0; - } - if (*incx == 1) { - goto L20; - } - - /* code for increment not equal to 1 */ - - nincx = *n * *incx; - i__1 = nincx; - i__2 = *incx; - for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - dx[i__] = *da * dx[i__]; - /* L10: */ - } - return 0; - - /* code for increment equal to 1 */ - - - /* clean-up loop */ - -L20: - m = *n % 5; - if (m == 0) { - goto L40; - } - i__2 = m; - for (i__ = 1; i__ <= i__2; ++i__) { - dx[i__] = *da * dx[i__]; - /* L30: */ - } - if (*n < 5) { - return 0; - } -L40: - mp1 = m + 1; - i__2 = *n; - for (i__ = mp1; i__ <= i__2; i__ += 5) { - dx[i__] = *da * dx[i__]; - dx[i__ + 1] = *da * dx[i__ + 1]; - dx[i__ + 2] = *da * dx[i__ + 2]; - dx[i__ + 3] = *da * dx[i__ + 3]; - dx[i__ + 4] = *da * dx[i__ + 4]; - /* L50: */ - } - return 0; -} /* dscal_ */ - -integer idamax_(integer *n, real_type *dx, integer *incx) -{ - /* System generated locals */ - integer ret_val, i__1; - real_type d__1; - - /* Local variables */ - static integer i__, ix; - static real_type dmax__; - - - /* finds the index of element having max. dabsolute value. */ - /* jack dongarra, linpack, 3/11/78. */ - - - /* Parameter adjustments */ - --dx; - - /* Function Body */ - ret_val = 0; - if (*n < 1) { - return ret_val; - } - ret_val = 1; - if (*n == 1) { - return ret_val; - } - if (*incx == 1) { - goto L20; - } - - /* code for increment not equal to 1 */ - - ix = 1; - dmax__ = abs(dx[1]); - ix += *incx; - i__1 = *n; - for (i__ = 2; i__ <= i__1; ++i__) { - if ((d__1 = dx[ix], abs(d__1)) <= dmax__) { - goto L5; - } - ret_val = i__; - dmax__ = (d__1 = dx[ix], abs(d__1)); -L5: - ix += *incx; - /* L10: */ - } - return ret_val; - - /* code for increment equal to 1 */ - -L20: - dmax__ = abs(dx[1]); - i__1 = *n; - for (i__ = 2; i__ <= i__1; ++i__) { - if ((d__1 = dx[i__], abs(d__1)) <= dmax__) { - goto L30; - } - ret_val = i__; - dmax__ = (d__1 = dx[i__], abs(d__1)); -L30: - ; - } - return ret_val; -} /* idamax_ */ - -real_type epslon_(real_type *x) -{ -#if defined(TEST_MPF_100) || defined(TEST_MPFR_100) || defined(TEST_GMPXX) || defined(TEST_MPFRXX) - return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); -#elif defined(TEST_E_FLOAT_BN) - return std::pow(10.0, 1-std::numeric_limits::digits10); -#else - return CAST_TO_RT(std::numeric_limits::epsilon()); -#endif -} /* epslon_ */ - -/* Subroutine */ int mm_(real_type *a, integer *lda, integer *n1, integer * - n3, real_type *b, integer *ldb, integer *n2, real_type *c__, - integer *ldc) -{ - /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2; - - /* Local variables */ - static integer i__, j; - - - /* purpose: */ - /* multiply matrix b times matrix c and store the result in matrix a. */ - - /* parameters: */ - - /* a double precision(lda,n3), matrix of n1 rows and n3 columns */ - - /* lda integer, leading dimension of array a */ - - /* n1 integer, number of rows in matrices a and b */ - - /* n3 integer, number of columns in matrices a and c */ - - /* b double precision(ldb,n2), matrix of n1 rows and n2 columns */ - - /* ldb integer, leading dimension of array b */ - - /* n2 integer, number of columns in matrix b, and number of rows in */ - /* matrix c */ - - /* c double precision(ldc,n3), matrix of n2 rows and n3 columns */ - - /* ldc integer, leading dimension of array c */ - - /* ---------------------------------------------------------------------- */ - - /* Parameter adjustments */ - a_dim1 = *lda; - a_offset = 1 + a_dim1; - a -= a_offset; - b_dim1 = *ldb; - b_offset = 1 + b_dim1; - b -= b_offset; - c_dim1 = *ldc; - c_offset = 1 + c_dim1; - c__ -= c_offset; - - /* Function Body */ - i__1 = *n3; - for (j = 1; j <= i__1; ++j) { - i__2 = *n1; - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = CAST_TO_RT(0); - /* L10: */ - } - dmxpy_(n2, &a[j * a_dim1 + 1], n1, ldb, &c__[j * c_dim1 + 1], &b[ - b_offset]); - /* L20: */ - } - - return 0; -} /* mm_ */ - -/* Subroutine */ int dmxpy_(integer *n1, real_type *y, integer *n2, integer * - ldm, real_type *x, real_type *m) -{ - /* System generated locals */ - integer m_dim1, m_offset, i__1, i__2; - - /* Local variables */ - static integer i__, j, jmin; - - - /* purpose: */ - /* multiply matrix m times vector x and add the result to vector y. */ - - /* parameters: */ - - /* n1 integer, number of elements in vector y, and number of rows in */ - /* matrix m */ - - /* y double precision(n1), vector of length n1 to which is added */ - /* the product m*x */ - - /* n2 integer, number of elements in vector x, and number of columns */ - /* in matrix m */ - - /* ldm integer, leading dimension of array m */ - - /* x double precision(n2), vector of length n2 */ - - /* m double precision(ldm,n2), matrix of n1 rows and n2 columns */ - - /* ---------------------------------------------------------------------- */ - - /* cleanup odd vector */ - - /* Parameter adjustments */ - --y; - m_dim1 = *ldm; - m_offset = 1 + m_dim1; - m -= m_offset; - --x; - - /* Function Body */ - j = *n2 % 2; - if (j >= 1) { - i__1 = *n1; - for (i__ = 1; i__ <= i__1; ++i__) { - y[i__] += x[j] * m[i__ + j * m_dim1]; - /* L10: */ - } - } - - /* cleanup odd group of two vectors */ - - j = *n2 % 4; - if (j >= 2) { - i__1 = *n1; - for (i__ = 1; i__ <= i__1; ++i__) { - y[i__] = y[i__] + x[j - 1] * m[i__ + (j - 1) * m_dim1] + x[j] * m[ - i__ + j * m_dim1]; - /* L20: */ - } - } - - /* cleanup odd group of four vectors */ - - j = *n2 % 8; - if (j >= 4) { - i__1 = *n1; - for (i__ = 1; i__ <= i__1; ++i__) { - y[i__] = y[i__] + x[j - 3] * m[i__ + (j - 3) * m_dim1] + x[j - 2] - * m[i__ + (j - 2) * m_dim1] + x[j - 1] * m[i__ + (j - 1) * - m_dim1] + x[j] * m[i__ + j * m_dim1]; - /* L30: */ - } - } - - /* cleanup odd group of eight vectors */ - - j = *n2 % 16; - if (j >= 8) { - i__1 = *n1; - for (i__ = 1; i__ <= i__1; ++i__) { - y[i__] = y[i__] + x[j - 7] * m[i__ + (j - 7) * m_dim1] + x[j - 6] - * m[i__ + (j - 6) * m_dim1] + x[j - 5] * m[i__ + (j - 5) * - m_dim1] + x[j - 4] * m[i__ + (j - 4) * m_dim1] + x[j - 3] - * m[i__ + (j - 3) * m_dim1] + x[j - 2] * m[i__ + (j - 2) - * m_dim1] + x[j - 1] * m[i__ + (j - 1) * m_dim1] + x[j] * - m[i__ + j * m_dim1]; - /* L40: */ - } - } - - /* main loop - groups of sixteen vectors */ - - jmin = j + 16; - i__1 = *n2; - for (j = jmin; j <= i__1; j += 16) { - i__2 = *n1; - for (i__ = 1; i__ <= i__2; ++i__) { - y[i__] = y[i__] + x[j - 15] * m[i__ + (j - 15) * m_dim1] + x[j - - 14] * m[i__ + (j - 14) * m_dim1] + x[j - 13] * m[i__ + (j - - 13) * m_dim1] + x[j - 12] * m[i__ + (j - 12) * m_dim1] - + x[j - 11] * m[i__ + (j - 11) * m_dim1] + x[j - 10] * m[ - i__ + (j - 10) * m_dim1] + x[j - 9] * m[i__ + (j - 9) * - m_dim1] + x[j - 8] * m[i__ + (j - 8) * m_dim1] + x[j - 7] - * m[i__ + (j - 7) * m_dim1] + x[j - 6] * m[i__ + (j - 6) * - m_dim1] + x[j - 5] * m[i__ + (j - 5) * m_dim1] + x[j - 4] - * m[i__ + (j - 4) * m_dim1] + x[j - 3] * m[i__ + (j - 3) - * m_dim1] + x[j - 2] * m[i__ + (j - 2) * m_dim1] + x[j - - 1] * m[i__ + (j - 1) * m_dim1] + x[j] * m[i__ + j * - m_dim1]; - /* L50: */ - } - /* L60: */ - } - return 0; -} /* dmxpy_ */ - -real_type ran_(integer *iseed) -{ - /* System generated locals */ - real_type ret_val; - - /* Local variables */ - static integer it1, it2, it3, it4; - - - /* modified from the LAPACK auxiliary routine 10/12/92 JD */ - /* -- LAPACK auxiliary routine (version 1.0) -- */ - /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */ - /* Courant Institute, Argonne National Lab, and Rice University */ - /* February 29, 1992 */ - - /* .. Array Arguments .. */ - /* .. */ - - /* Purpose */ - /* ======= */ - - /* DLARAN returns a random double number from a uniform (0,1) */ - /* distribution. */ - - /* Arguments */ - /* ========= */ - - /* ISEED (input/output) INTEGER array, dimension (4) */ - /* On entry, the seed of the random number generator; the array */ - /* elements must be between 0 and 4095, and ISEED(4) must be */ - /* odd. */ - /* On exit, the seed is updated. */ - - /* Further Details */ - /* =============== */ - - /* This routine uses a multiplicative congruential method with modulus */ - /* 2**48 and multiplier 33952834046453 (see G.S.Fishman, */ - /* 'Multiplicative congruential random number generators with modulus */ - /* 2**b: an exhaustive analysis for b = 32 and a partial analysis for */ - /* b = 48', Math. Comp. 189, pp 331-344, 1990). */ - - /* 48-bit integers are stored in 4 integer array elements with 12 bits */ - /* per element. Hence the routine is portable across machines with */ - /* integers of 32 bits or more. */ - - /* .. Parameters .. */ - /* .. */ - /* .. Local Scalars .. */ - /* .. */ - /* .. Intrinsic Functions .. */ - /* .. */ - /* .. Executable Statements .. */ - - /* multiply the seed by the multiplier modulo 2**48 */ - - /* Parameter adjustments */ - --iseed; - - /* Function Body */ - it4 = iseed[4] * 2549; - it3 = it4 / 4096; - it4 -= it3 << 12; - it3 = it3 + iseed[3] * 2549 + iseed[4] * 2508; - it2 = it3 / 4096; - it3 -= it2 << 12; - it2 = it2 + iseed[2] * 2549 + iseed[3] * 2508 + iseed[4] * 322; - it1 = it2 / 4096; - it2 -= it1 << 12; - it1 = it1 + iseed[1] * 2549 + iseed[2] * 2508 + iseed[3] * 322 + iseed[4] - * 494; - it1 %= 4096; - - /* return updated seed */ - - iseed[1] = it1; - iseed[2] = it2; - iseed[3] = it3; - iseed[4] = it4; - - /* convert 48-bit integer to a double number in the interval (0,1) */ - - ret_val = ((real_type) it1 + ((real_type) it2 + ((real_type) it3 + ( - real_type) it4 * 2.44140625e-4) * 2.44140625e-4) * 2.44140625e-4) - * 2.44140625e-4; - return ret_val; - - /* End of RAN */ - -} /* ran_ */ - -/* - -Double results: -~~~~~~~~~~~~~~ - -norm. resid resid machep x(1) x(n) -6.4915 7.207e-013 2.2204e-016 1 1 - - - -times are reported for matrices of order 1000 -factor solve total mflops unit ratio -times for array with leading dimension of1001 -1.443 0.003 1.446 462.43 0.004325 25.821 - - -mpf_class results: -~~~~~~~~~~~~~~~~~~ - -norm. resid resid machep x(1) x(n) -3.6575e-05 5.2257e-103 2.8575e-101 1 1 - - - -times are reported for matrices of order 1000 -factor solve total mflops unit ratio -times for array with leading dimension of1001 -266.45 0.798 267.24 2.5021 0.79933 4772.2 - - -big_number >: -~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - norm. resid resid machep x(1) x(n) - 0.36575e-4 0.52257e-102 0.28575e-100 0.1e1 0.1e1 - - - - times are reported for matrices of order 1000 - factor solve total mflops unit ratio - times for array with leading dimension of1001 - 279.96 0.84 280.8 2.3813 0.83988 5014.3 - -boost::math::ef::e_float: -~~~~~~~~~~~~~~~~~~~~~~~~~ - - norm. resid resid machep x(1) x(n) - 2.551330735e-16 1.275665107e-112 1e-99 1 1 - - - - times are reported for matrices of order 1000 - factor solve total mflops unit ratio - times for array with leading dimension of1001 - 363.89 1.074 364.97 1.8321 1.0916 6517.3 -*/ diff --git a/math/test/test_arithmetic.cpp b/math/test/test_arithmetic.cpp deleted file mode 100644 index 5e267eba..00000000 --- a/math/test/test_arithmetic.cpp +++ /dev/null @@ -1,894 +0,0 @@ -/////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ - -#include -#include - -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 -# define TEST_MPF -# define TEST_BACKEND -# define TEST_MPZ -# define TEST_MPFR -# define TEST_MPFR_50 -# define TEST_E_FLOAT -# define TEST_MPQ - -#ifdef _MSC_VER -#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") -#endif -#ifdef __GNUC__ -#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" -#endif - -#endif - -#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) -#include -#endif -#ifdef TEST_BACKEND -#include -#endif -#ifdef TEST_E_FLOAT -#include -#endif -#if defined(TEST_MPFR) || defined(TEST_MPFR_50) -#include -#endif - -#define BOOST_TEST_THROW(x, EX)\ - try { x; BOOST_ERROR("Expected exception not thrown"); } \ - catch(const EX&){}\ - catch(...){ BOOST_ERROR("Incorrect exception type thrown"); } - -#undef BOOST_TEST -#define BOOST_TEST(x)\ - try {\ - if(x){}else{ BOOST_ERROR("Value was zero: "); }\ - }\ - catch(const std::exception& e){ \ - BOOST_ERROR("Unexpected exception: ");\ - BOOST_LIGHTWEIGHT_TEST_OSTREAM << e.what() << std::endl;\ - } - -bool isfloat(float){ return true; } -bool isfloat(double){ return true; } -bool isfloat(long double){ return true; } -template bool isfloat(T){ return false; } - -#define BOOST_TEST_CLOSE(x, y, tol)\ - if(x == 0){\ - BOOST_TEST(y == 0); }\ - else if(!isfloat(x)){\ - BOOST_TEST(x == y); }\ - else if((x != y) && (::fabsl(static_cast((x-y)/x)) > tol))\ - {\ - BOOST_ERROR("Expected tolerance was exceeded: ");\ - BOOST_LIGHTWEIGHT_TEST_OSTREAM << std::setprecision(34) << "(x-y)/x = " << ::fabsl(static_cast((x-y)/x)) \ - << " tolerance = " << tol << std::endl;\ - } - -template -void test_integer_ops(const T&){} - -template -void test_integer_ops(const boost::mpl::int_&) -{ - Real a(20); - Real b(7); - Real c; - BOOST_TEST(a % b == 20 % 7); - BOOST_TEST(a % 7 == 20 % 7); - BOOST_TEST(a % 7u == 20 % 7); - BOOST_TEST(-a % b == -20 % 7); - BOOST_TEST(-a % -b == -20 % -7); - BOOST_TEST(a % -b == 20 % -7); - BOOST_TEST(-a % 7 == -20 % 7); - BOOST_TEST(-a % -7 == -20 % -7); - BOOST_TEST(a % -7 == 20 % -7); - BOOST_TEST(-a % 7u == -20 % 7); - - b = -b; - BOOST_TEST(a % b == 20 % -7); - a = -a; - BOOST_TEST(a % b == -20 % -7); - BOOST_TEST(a % -7 == -20 % -7); - b = 7; - BOOST_TEST(a % b == -20 % 7); - BOOST_TEST(a % 7 == -20 % 7); - BOOST_TEST(a % 7u == -20 % 7); - - a = 20; - a %= b; - BOOST_TEST(a == 20 % 7); - a = -20; - a %= b; - BOOST_TEST(a == -20 % 7); - a = 20; - a %= -b; - BOOST_TEST(a == 20 % -7); - a = -20; - a %= -b; - BOOST_TEST(a == -20 % -7); - - a = 20; - a %= 7; - BOOST_TEST(a == 20 % 7); - a = -20; - a %= 7; - BOOST_TEST(a == -20 % 7); - a = 20; - a %= -7; - BOOST_TEST(a == 20 % -7); - a = -20; - a %= -7; - BOOST_TEST(a == -20 % -7); -#ifndef BOOST_NO_LONG_LONG - a = 20; - a %= 7uLL; - BOOST_TEST(a == 20 % 7); - a = -20; - a %= 7uLL; - BOOST_TEST(a == -20 % 7); - a = 20; - a %= -7LL; - BOOST_TEST(a == 20 % -7); - a = -20; - a %= -7LL; - BOOST_TEST(a == -20 % -7); -#endif - a = 20; - BOOST_TEST(++a == 21); - BOOST_TEST(--a == 20); - BOOST_TEST(a++ == 20); - BOOST_TEST(a == 21); - BOOST_TEST(a-- == 21); - BOOST_TEST(a == 20); - a = 2000; - a <<= 20; - BOOST_TEST(a == 2000L << 20); - a >>= 20; - BOOST_TEST(a == 2000); - a <<= 20u; - BOOST_TEST(a == 2000L << 20); - a >>= 20u; - BOOST_TEST(a == 2000); - BOOST_TEST_THROW(a <<= -20, std::out_of_range); - BOOST_TEST_THROW(a >>= -20, std::out_of_range); -#ifndef BOOST_NO_LONG_LONG - if(sizeof(long long) > sizeof(std::size_t)) - { - // extreme values should trigger an exception: - BOOST_TEST_THROW(a >>= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); - BOOST_TEST_THROW(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); - } -#endif - a = 20; - b = a << 20; - BOOST_TEST(b == (20 << 20)); - b = a >> 2; - BOOST_TEST(b == (20 >> 2)); - b = (a + 2) << 10; - BOOST_TEST(b == (22 << 10)); - b = (a + 3) >> 3; - BOOST_TEST(b == (23 >> 3)); - // - // Bit fiddling: - // - int i = 1020304; - int j = 56789123; - int k = 4523187; - a = i; - b = j; - c = a; - c &= b; - BOOST_TEST(c == (i & j)); - c = a; - c &= j; - BOOST_TEST(c == (i & j)); - c = a; - c &= a + b; - BOOST_TEST(c == (i & (i + j))); - BOOST_TEST((a & b) == (i & j)); - c = k; - a = a & (b + k); - BOOST_TEST(a == (i & (j + k))); - a = i; - a = (b + k) & a; - BOOST_TEST(a == (i & (j + k))); - a = i; - c = a & b & k; - BOOST_TEST(c == (i&j&k)); - - a = i; - b = j; - c = a; - c |= b; - BOOST_TEST(c == (i | j)); - c = a; - c |= j; - BOOST_TEST(c == (i | j)); - c = a; - c |= a + b; - BOOST_TEST(c == (i | (i + j))); - BOOST_TEST((a | b) == (i | j)); - c = k; - a = a | (b + k); - BOOST_TEST(a == (i | (j + k))); - a = i; - a = (b + k) | a; - BOOST_TEST(a == (i | (j + k))); - a = i; - c = a | b | k; - BOOST_TEST(c == (i|j|k)); - - a = i; - b = j; - c = a; - c ^= b; - BOOST_TEST(c == (i ^ j)); - c = a; - c ^= j; - BOOST_TEST(c == (i ^ j)); - c = a; - c ^= a + b; - BOOST_TEST(c == (i ^ (i + j))); - BOOST_TEST((a ^ b) == (i ^ j)); - c = k; - a = a ^ (b + k); - BOOST_TEST(a == (i ^ (j + k))); - a = i; - a = (b + k) ^ a; - BOOST_TEST(a == (i ^ (j + k))); - a = i; - c = a ^ b ^ k; - BOOST_TEST(c == (i^j^k)); - a = i; - b = j; - c = k; - BOOST_TEST(~a == ~i); - c = a & ~b; - BOOST_TEST(c == (i & ~j)); - c = ~(a | b); - BOOST_TEST(c == ~(i | j)); - // - // Non-member functions: - // - a = -20; - BOOST_TEST(abs(a) == 20); - BOOST_TEST(abs(-a) == 20); - BOOST_TEST(abs(+a) == 20); - a = 20; - BOOST_TEST(abs(a) == 20); - BOOST_TEST(abs(-a) == 20); - BOOST_TEST(abs(+a) == 20); -} - -template -void test_real_ops(const T&){} - -template -void test_real_ops(const boost::mpl::int_&) -{ -#if defined(TEST_MPF) || defined(TEST_MPF_50) || defined(TEST_BACKEND) || defined(TEST_MPFR) - BOOST_TEST(abs(Real(2)) == 2); - BOOST_TEST(abs(Real(-2)) == 2); - BOOST_TEST(fabs(Real(2)) == 2); - BOOST_TEST(fabs(Real(-2)) == 2); - BOOST_TEST(floor(Real(5) / 2) == 2); - BOOST_TEST(ceil(Real(5) / 2) == 3); - BOOST_TEST(floor(Real(-5) / 2) == -3); - BOOST_TEST(ceil(Real(-5) / 2) == -2); - BOOST_TEST(trunc(Real(5) / 2) == 2); - BOOST_TEST(trunc(Real(-5) / 2) == -2); - // - // ldexp and frexp, these pretty much have to implemented by each backend: - // - BOOST_TEST(ldexp(Real(2), 5) == 64); - BOOST_TEST(ldexp(Real(2), -5) == Real(2) / 32); - Real v(512); - int exp; - Real r = frexp(v, &exp); - BOOST_TEST(r == 0.5); - BOOST_TEST(exp == 10); - BOOST_TEST(v == 512); - v = 1 / v; - r = frexp(v, &exp); - BOOST_TEST(r == 0.5); - BOOST_TEST(exp == -8); - // - // pow and exp: - // - v = 3.25; - r = pow(v, 0); - BOOST_TEST(r == 1); - r = pow(v, 1); - BOOST_TEST(r == 3.25); - r = pow(v, 2); - BOOST_TEST(r == boost::math::pow<2>(3.25)); - r = pow(v, 3); - BOOST_TEST(r == boost::math::pow<3>(3.25)); - r = pow(v, 4); - BOOST_TEST(r == boost::math::pow<4>(3.25)); - r = pow(v, 5); - BOOST_TEST(r == boost::math::pow<5>(3.25)); - r = pow(v, 6); - BOOST_TEST(r == boost::math::pow<6>(3.25)); - r = pow(v, 25); - BOOST_TEST(r == boost::math::pow<25>(Real(3.25))); - /* - r = pow(v, 56); - BOOST_TEST(r == boost::math::pow<56>(Real(3.25))); - */ -#endif -} - -#ifdef TEST_E_FLOAT - -template -struct lexical_cast_target_type -{ - typedef long double type; -}; - -#else - -template -struct lexical_cast_target_type -{ - typedef typename boost::mpl::if_< - boost::is_signed, - boost::intmax_t, - typename boost::mpl::if_< - boost::is_unsigned, - boost::uintmax_t, - T - >::type - >::type type; -}; - -#endif - -template -void test_negative_mixed(boost::mpl::true_ const&) -{ - typedef typename lexical_cast_target_type::type target_type; - std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; - Num n1 = -static_cast(1uLL << (std::numeric_limits::digits - 1)); - Num n2 = -1; - Num n3 = 0; - Num n4 = -20; - Num n5 = -8; - BOOST_TEST((Real(n2) < 0) == true); - BOOST_TEST((Real(n2) <= 0) == true); - BOOST_TEST((Real(n2) > 0) == false); - BOOST_TEST((Real(n2) >= 0) == false); - BOOST_TEST((Real(n2) == 0) == false); - BOOST_TEST((Real(n2) != 0) == true); - BOOST_TEST((Real(n2) == n2) == true); - BOOST_TEST((Real(n2) != n2) == false); - BOOST_TEST((Real(n2) >= n2) == true); - BOOST_TEST((Real(n2) <= n2) == true); - BOOST_TEST((Real(n2) > n2) == false); - BOOST_TEST((Real(n2) < n2) == false); - // Default construct: - BOOST_TEST(Real(n1) == n1); - BOOST_TEST(Real(n2) == n2); - BOOST_TEST(Real(n3) == n3); - BOOST_TEST(Real(n4) == n4); - BOOST_TEST(n1 == Real(n1)); - BOOST_TEST(n2 == Real(n2)); - BOOST_TEST(n3 == Real(n3)); - BOOST_TEST(n4 == Real(n4)); -#if defined(TEST_MPFR) || defined(TEST_MPFR_50) - Num tol = 10 * std::numeric_limits::epsilon(); -#else - Num tol = 0; -#endif - BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), tol); - BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), 0); - BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), 0); - BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), 0); - // Assignment: - Real r(0); - BOOST_TEST(r != n1); - r = n1; - BOOST_TEST(r == n1); - r = n2; - BOOST_TEST(r == n2); - r = n3; - BOOST_TEST(r == n3); - r = n4; - BOOST_TEST(r == n4); - // Addition: - r = n2; - BOOST_TEST(r + n4 == n2 + n4); - BOOST_TEST(Real(r + n4) == n2 + n4); - r += n4; - BOOST_TEST(r == n2 + n4); - // subtraction: - r = n4; - BOOST_TEST(r - n5 == n4 - n5); - BOOST_TEST(Real(r - n5) == n4 - n5); - r -= n5; - BOOST_TEST(r == n4 - n5); - // Multiplication: - r = n2; - BOOST_TEST(r * n4 == n2 * n4); - BOOST_TEST(Real(r * n4) == n2 * n4); - r *= n4; - BOOST_TEST(r == n2 * n4); - // Division: - r = n1; - BOOST_TEST(r / n5 == n1 / n5); - BOOST_TEST(Real(r / n5) == n1 / n5); - r /= n5; - BOOST_TEST(r == n1 / n5); - // - // Extra cases for full coverage: - // - r = Real(n4) + n5; - BOOST_TEST(r == n4 + n5); - r = n4 + Real(n5); - BOOST_TEST(r == n4 + n5); - r = Real(n4) - n5; - BOOST_TEST(r == n4 - n5); - r = n4 - Real(n5); - BOOST_TEST(r == n4 - n5); - r = n4 * Real(n5); - BOOST_TEST(r == n4 * n5); - r = (4 * n4) / Real(4); - BOOST_TEST(r == n4); -} - -template -void test_negative_mixed(boost::mpl::false_ const&) -{ -} - -template -void test_mixed() -{ - typedef typename lexical_cast_target_type::type target_type; - std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; - Num n1 = static_cast(1uLL << (std::numeric_limits::digits - 1)); - Num n2 = 1; - Num n3 = 0; - Num n4 = 20; - Num n5 = 8; - BOOST_TEST((Real(n2) < 0) == false); - BOOST_TEST((Real(n2) <= 0) == false); - BOOST_TEST((Real(n2) > 0) == true); - BOOST_TEST((Real(n2) >= 0) == true); - BOOST_TEST((Real(n2) == 0) == false); - BOOST_TEST((Real(n2) != 0) == true); - BOOST_TEST((Real(n2) == n2) == true); - BOOST_TEST((Real(n2) != n2) == false); - BOOST_TEST((Real(n2) >= n2) == true); - BOOST_TEST((Real(n2) <= n2) == true); - BOOST_TEST((Real(n2) > n2) == false); - BOOST_TEST((Real(n2) < n2) == false); - // Default construct: - BOOST_TEST(Real(n1) == n1); - BOOST_TEST(Real(n2) == n2); - BOOST_TEST(Real(n3) == n3); - BOOST_TEST(Real(n4) == n4); - BOOST_TEST(Real(n1).template convert_to() == n1); - BOOST_TEST(Real(n2).template convert_to() == n2); - BOOST_TEST(Real(n3).template convert_to() == n3); - BOOST_TEST(Real(n4).template convert_to() == n4); - BOOST_TEST(n1 == Real(n1)); - BOOST_TEST(n2 == Real(n2)); - BOOST_TEST(n3 == Real(n3)); - BOOST_TEST(n4 == Real(n4)); - std::cout << Real(n1).str(0, boost::is_floating_point::value) << std::endl; -#if defined(TEST_MPFR) || defined(TEST_MPFR_50) - Num tol = 10 * std::numeric_limits::epsilon(); -#else - Num tol = 0; -#endif - BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), tol); - BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), 0); - BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), 0); - BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), 0); - // Assignment: - Real r(0); - BOOST_TEST(r != n1); - r = n1; - BOOST_TEST(r == n1); - r = n2; - BOOST_TEST(r == n2); - r = n3; - BOOST_TEST(r == n3); - r = n4; - BOOST_TEST(r == n4); - // Addition: - r = n2; - BOOST_TEST(r + n4 == n2 + n4); - BOOST_TEST(Real(r + n4) == n2 + n4); - r += n4; - BOOST_TEST(r == n2 + n4); - // subtraction: - r = n4; - BOOST_TEST(r - n5 == n4 - n5); - BOOST_TEST(Real(r - n5) == n4 - n5); - r -= n5; - BOOST_TEST(r == n4 - n5); - // Multiplication: - r = n2; - BOOST_TEST(r * n4 == n2 * n4); - BOOST_TEST(Real(r * n4) == n2 * n4); - r *= n4; - BOOST_TEST(r == n2 * n4); - // Division: - r = n1; - BOOST_TEST(r / n5 == n1 / n5); - BOOST_TEST(Real(r / n5) == n1 / n5); - r /= n5; - BOOST_TEST(r == n1 / n5); - // - // special cases for full coverage: - // - r = n5 + Real(n4); - BOOST_TEST(r == n4 + n5); - r = n4 - Real(n5); - BOOST_TEST(r == n4 - n5); - r = n4 * Real(n5); - BOOST_TEST(r == n4 * n5); - r = (4 * n4) / Real(4); - BOOST_TEST(r == n4); - test_negative_mixed(boost::mpl::bool_::is_signed>()); -} - -template -void test() -{ -#ifndef NO_MIXED_OPS - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); -#ifdef BOOST_HAS_LONG_LONG - test_mixed(); - test_mixed(); -#endif - test_mixed(); - test_mixed(); - test_mixed(); -#endif - // - // Integer only functions: - // - test_integer_ops(typename boost::math::number_category::type()); - // - // Real number only functions: - // - test_real_ops(typename boost::math::number_category::type()); - // - // Test basic arithmetic: - // - Real a(8); - Real b(64); - Real c(500); - Real d(1024); - BOOST_TEST(a + b == 72); - a += b; - BOOST_TEST(a == 72); - BOOST_TEST(a - b == 8); - a -= b; - BOOST_TEST(a == 8); - BOOST_TEST(a * b == 8*64L); - a *= b; - BOOST_TEST(a == 8*64L); - BOOST_TEST(a / b == 8); - a /= b; - BOOST_TEST(a == 8); - Real ac(a); - BOOST_TEST(ac == a); - BOOST_TEST(-a == -8); - ac = a * c; - BOOST_TEST(ac == 8*500L); - ac = 8*500L; - ac = ac + b + c; - BOOST_TEST(ac == 8*500L+64+500); - ac = a; - ac = b + c + ac; - BOOST_TEST(ac == 8+64+500); - ac = ac - b + c; - BOOST_TEST(ac == 8+64+500-64+500); - ac = a; - ac = b + c - ac; - BOOST_TEST(ac == -8+64+500); - ac = a; - ac = ac * b; - BOOST_TEST(ac == 8*64); - ac = a; - ac *= b * ac; - BOOST_TEST(ac == 8*8*64); - ac = b; - ac = ac / a; - BOOST_TEST(ac == 64/8); - ac = b; - ac /= ac / a; - BOOST_TEST(ac == 64 / (64/8)); - ac = a; - ac = b + ac * a; - BOOST_TEST(ac == 64 * 2); - ac = a; - ac = b - ac * a; - BOOST_TEST(ac == 0); - ac = a; - ac = b * (ac + a); - BOOST_TEST(ac == 64 * (16)); - ac = a; - ac = b / (ac * 1); - BOOST_TEST(ac == 64 / 8); - ac = a; - ac = ac + b; - BOOST_TEST(ac == 8 + 64); - ac = a; - ac = a + ac; - BOOST_TEST(ac == 16); - ac = a; - ac = ac - b; - BOOST_TEST(ac == 8 - 64); - ac = a; - ac = a - ac; - BOOST_TEST(ac == 0); - ac = a; - ac += a + b; - BOOST_TEST(ac == 80); - ac = a; - ac += b + a; - BOOST_TEST(ac == 80); - ac = a; - ac -= a + b; - BOOST_TEST(ac == -64); - ac = a; - ac -= b - a; - BOOST_TEST(ac == 16 - 64); - ac = +a; - BOOST_TEST(ac == 8); - ac = -a; - BOOST_TEST(ac == -8); - ac = 8; - ac = a * ac; - BOOST_TEST(ac == 8*8); - ac = a; - ac = a; - ac += +a; - BOOST_TEST(ac == 16); - ac = a; - ac += -a; - BOOST_TEST(ac == 0); - ac = a; - ac += b - a; - BOOST_TEST(ac == 8 + 64-8); - ac = a; - ac += b*c; - BOOST_TEST(ac == 8 + 64 * 500); - ac = a; - ac = a; - ac -= +a; - BOOST_TEST(ac == 0); - ac = a; - ac -= -a; - BOOST_TEST(ac == 16); - ac = a; - ac -= c - b; - BOOST_TEST(ac == 8 - (500-64)); - ac = a; - ac -= b*c; - BOOST_TEST(ac == 8 - 500*64); - ac = a; - ac += ac * b; - BOOST_TEST(ac == 8 + 8 * 64); - ac = a; - ac -= ac * b; - BOOST_TEST(ac == 8 - 8 * 64); - ac = a * 8; - ac *= +a; - BOOST_TEST(ac == 64 * 8); - ac = a; - ac *= -a; - BOOST_TEST(ac == -64); - ac = a; - ac *= b * c; - BOOST_TEST(ac == 8 * 64 * 500); - ac = a; - ac *= b / a; - BOOST_TEST(ac == 8 * 64 / 8); - ac = a; - ac *= b + c; - BOOST_TEST(ac == 8 * (64 + 500)); - ac = b; - ac /= +a; - BOOST_TEST(ac == 8); - ac = b; - ac /= -a; - BOOST_TEST(ac == -8); - ac = b; - ac /= b / a; - BOOST_TEST(ac == 64 / (64/8)); - ac = b; - ac /= a + Real(0); - BOOST_TEST(ac == 8); - // - // simple tests with immediate values, these calls can be optimised in many backends: - // - ac = a + b; - BOOST_TEST(ac == 72); - ac = a + +b; - BOOST_TEST(ac == 72); - ac = +a + b; - BOOST_TEST(ac == 72); - ac = +a + +b; - BOOST_TEST(ac == 72); - ac = a + -b; - BOOST_TEST(ac == 8 - 64); - ac = -a + b; - BOOST_TEST(ac == -8+64); - ac = -a + -b; - BOOST_TEST(ac == -72); - ac = a + - + -b; // lots of unary operators!! - BOOST_TEST(ac == 72); - ac = a; - ac = b / ac; - BOOST_TEST(ac == b / a); - // - // Comparisons: - // - BOOST_TEST((a == b) == false); - BOOST_TEST((a != b) == true); - BOOST_TEST((a <= b) == true); - BOOST_TEST((a < b) == true); - BOOST_TEST((a >= b) == false); - BOOST_TEST((a > b) == false); - - BOOST_TEST((a+b == b) == false); - BOOST_TEST((a+b != b) == true); - BOOST_TEST((a+b >= b) == true); - BOOST_TEST((a+b > b) == true); - BOOST_TEST((a+b <= b) == false); - BOOST_TEST((a+b < b) == false); - - BOOST_TEST((a == b+a) == false); - BOOST_TEST((a != b+a) == true); - BOOST_TEST((a <= b+a) == true); - BOOST_TEST((a < b+a) == true); - BOOST_TEST((a >= b+a) == false); - BOOST_TEST((a > b+a) == false); - - BOOST_TEST((a+b == b+a) == true); - BOOST_TEST((a+b != b+a) == false); - BOOST_TEST((a+b <= b+a) == true); - BOOST_TEST((a+b < b+a) == false); - BOOST_TEST((a+b >= b+a) == true); - BOOST_TEST((a+b > b+a) == false); - - BOOST_TEST((8 == b+a) == false); - BOOST_TEST((8 != b+a) == true); - BOOST_TEST((8 <= b+a) == true); - BOOST_TEST((8 < b+a) == true); - BOOST_TEST((8 >= b+a) == false); - BOOST_TEST((8 > b+a) == false); - BOOST_TEST((800 == b+a) == false); - BOOST_TEST((800 != b+a) == true); - BOOST_TEST((800 >= b+a) == true); - BOOST_TEST((800 > b+a) == true); - BOOST_TEST((800 <= b+a) == false); - BOOST_TEST((800 < b+a) == false); - BOOST_TEST((72 == b+a) == true); - BOOST_TEST((72 != b+a) == false); - BOOST_TEST((72 <= b+a) == true); - BOOST_TEST((72 < b+a) == false); - BOOST_TEST((72 >= b+a) == true); - BOOST_TEST((72 > b+a) == false); - // - // Test sign and zero functions, plus use in boolian context: - // - a = 20; - BOOST_TEST(a.sign() > 0); - BOOST_TEST(!a.is_zero()); - a = -20; - BOOST_TEST(a.sign() < 0); - BOOST_TEST(!a.is_zero()); - a = 0; - BOOST_TEST(a.sign() == 0); - BOOST_TEST(a.is_zero()); - if(a) - { - BOOST_ERROR("Unexpected non-zero result"); - } - if(!a){} - else - { - BOOST_ERROR("Unexpected zero result"); - } - b = 2; - if(!b) - { - BOOST_ERROR("Unexpected zero result"); - } - if(b){} - else - { - BOOST_ERROR("Unexpected non-zero result"); - } - if(a && b) - { - BOOST_ERROR("Unexpected zero result"); - } - if(!(a || b)) - { - BOOST_ERROR("Unexpected zero result"); - } - if(a + b){} - else - { - BOOST_ERROR("Unexpected zero result"); - } - if(b - 2) - { - BOOST_ERROR("Unexpected non-zero result"); - } - // - // Test iostreams: - // - std::stringstream ss; - a = 20; - b = 2; - ss << a; - ss >> c; - BOOST_TEST(a == c); - ss.clear(); - ss << a + b; - ss >> c; - BOOST_TEST(c == 22); - BOOST_TEST(c == a + b); -} - - -int main() -{ -#ifdef TEST_BACKEND - test >(); -#endif -#ifdef TEST_MPF50 - test(); -#endif -#ifdef TEST_MPF - boost::math::mpf_real::default_precision(1000); - /* - boost::math::mpf_real r; - r.precision(50); - BOOST_TEST(r.precision() >= 50); - */ - BOOST_TEST(boost::math::mpf_real::default_precision() == 1000); - test(); -#endif -#ifdef TEST_MPZ - test(); -#endif -#ifdef TEST_MPQ - test(); -#endif -#ifdef TEST_E_FLOAT - test(); -#endif -#ifdef TEST_MPFR - test(); -#endif -#ifdef TEST_MPFR_50 - test(); -#endif - return boost::report_errors(); -} - diff --git a/math/test/test_numeric_limits.cpp b/math/test/test_numeric_limits.cpp deleted file mode 100644 index 08d1c32f..00000000 --- a/math/test/test_numeric_limits.cpp +++ /dev/null @@ -1,173 +0,0 @@ -/////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ - -#include - -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 -# define TEST_MPF -# define TEST_BACKEND -# define TEST_MPZ -# define TEST_MPFR -# define TEST_MPFR_50 -# define TEST_E_FLOAT -# define TEST_MPQ - -#ifdef _MSC_VER -#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") -#endif -#ifdef __GNUC__ -#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" -#endif - -#endif - -#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) -#include -#endif -#ifdef TEST_BACKEND -#include -#endif -#ifdef TEST_E_FLOAT -#include -#endif -#if defined(TEST_MPFR) || defined(TEST_MPFR_50) -#include -#endif - -#define PRINT(x)\ - std::cout << BOOST_STRINGIZE(x) << " = " << std::numeric_limits::x << std::endl; - -template -void test() -{ - // - // Note really a test just yet, but we can at least print out all the values: - // - std::cout << "numeric_limits values for type " << typeid(Number).name() << std::endl; - - PRINT(is_specialized); - PRINT(min()); - PRINT(max()); -#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST - PRINT(lowest()); -#endif - PRINT(digits); - PRINT(digits10); -#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST - PRINT(max_digits10); -#endif - PRINT(is_signed); - PRINT(is_integer); - PRINT(is_exact); - PRINT(radix); - PRINT(epsilon()); - PRINT(round_error()); - PRINT(min_exponent); - PRINT(min_exponent10); - PRINT(max_exponent); - PRINT(max_exponent10); - PRINT(has_infinity); - PRINT(has_quiet_NaN); - PRINT(has_signaling_NaN); - PRINT(has_denorm); - PRINT(has_denorm_loss); - PRINT(infinity()); - PRINT(quiet_NaN()); - PRINT(signaling_NaN()); - PRINT(denorm_min()); - PRINT(is_iec559); - PRINT(is_bounded); - PRINT(is_modulo); - PRINT(traps); - PRINT(tinyness_before); - PRINT(round_style); - - if(std::numeric_limits::is_specialized) - { - if(std::numeric_limits::has_quiet_NaN) - { - BOOST_TEST((boost::math::isnan)(std::numeric_limits::quiet_NaN())); - BOOST_TEST(FP_NAN == (boost::math::fpclassify)(std::numeric_limits::quiet_NaN())); - BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits::quiet_NaN())); - BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::quiet_NaN())); - BOOST_TEST(!(boost::math::isinf)(std::numeric_limits::quiet_NaN())); - } - if(std::numeric_limits::has_signaling_NaN) - { - BOOST_TEST((boost::math::isnan)(std::numeric_limits::signaling_NaN())); - BOOST_TEST(FP_NAN == (boost::math::fpclassify)(std::numeric_limits::signaling_NaN())); - BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits::signaling_NaN())); - BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::signaling_NaN())); - BOOST_TEST(!(boost::math::isinf)(std::numeric_limits::signaling_NaN())); - } - if(std::numeric_limits::has_infinity) - { - BOOST_TEST((boost::math::isinf)(std::numeric_limits::infinity())); - BOOST_TEST(FP_INFINITE == (boost::math::fpclassify)(std::numeric_limits::infinity())); - BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits::infinity())); - BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::infinity())); - BOOST_TEST(!(boost::math::isnan)(std::numeric_limits::infinity())); - } - if(std::numeric_limits::has_denorm) - { - BOOST_TEST(FP_SUBNORMAL == (boost::math::fpclassify)(std::numeric_limits::denorm_min())); - BOOST_TEST((boost::math::isfinite)(std::numeric_limits::denorm_min())); - BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits::denorm_min())); - BOOST_TEST(!(boost::math::isinf)(std::numeric_limits::denorm_min())); - BOOST_TEST(!(boost::math::isnan)(std::numeric_limits::denorm_min())); - } - } - Number n = 0; - BOOST_TEST((boost::math::fpclassify)(n) == FP_ZERO); - BOOST_TEST((boost::math::isfinite)(n)); - BOOST_TEST(!(boost::math::isnormal)(n)); - BOOST_TEST(!(boost::math::isinf)(n)); - BOOST_TEST(!(boost::math::isnan)(n)); - n = 2; - BOOST_TEST((boost::math::fpclassify)(n) == FP_NORMAL); - BOOST_TEST((boost::math::isfinite)(n)); - BOOST_TEST((boost::math::isnormal)(n)); - BOOST_TEST(!(boost::math::isinf)(n)); - BOOST_TEST(!(boost::math::isnan)(n)); -} - - -int main() -{ -#ifdef TEST_BACKEND - test >(); -#endif -#ifdef TEST_MPF50 - test(); -#endif -#ifdef TEST_MPF - boost::math::mpf_real::default_precision(1000); - /* - boost::math::mpf_real r; - r.precision(50); - BOOST_TEST(r.precision() >= 50); - */ - BOOST_TEST(boost::math::mpf_real::default_precision() == 1000); - test(); -#endif -#ifdef TEST_MPZ - test(); -#endif -#ifdef TEST_MPQ - test(); -#endif -#ifdef TEST_E_FLOAT - test(); -#endif -#ifdef TEST_MPFR - test(); -#endif -#ifdef TEST_MPFR_50 - test(); -#endif - return boost::report_errors(); -} - From 94d6513d38bc833fcb7009e6af1abd1fcbc9f36b Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 26 Sep 2011 17:03:55 +0000 Subject: [PATCH 027/256] Giant file and directory rename: changed directory name from math to multiprecision and updated code to match. [SVN r74582] --- include/boost/math/big_number.hpp | 1570 ----------------- .../math/big_number/arithmetic_backend.hpp | 147 -- .../boost/math/big_number/big_number_base.hpp | 983 ----------- include/boost/math/big_number/default_ops.hpp | 903 ---------- include/boost/math/big_number/e_float.hpp | 80 - include/boost/math/big_number/gmp.hpp | 1532 ---------------- include/boost/math/big_number/mpfr.hpp | 952 ---------- .../math/concepts/big_number_architypes.hpp | 293 --- 8 files changed, 6460 deletions(-) delete mode 100644 include/boost/math/big_number.hpp delete mode 100644 include/boost/math/big_number/arithmetic_backend.hpp delete mode 100644 include/boost/math/big_number/big_number_base.hpp delete mode 100644 include/boost/math/big_number/default_ops.hpp delete mode 100644 include/boost/math/big_number/e_float.hpp delete mode 100644 include/boost/math/big_number/gmp.hpp delete mode 100644 include/boost/math/big_number/mpfr.hpp delete mode 100644 include/boost/math/concepts/big_number_architypes.hpp diff --git a/include/boost/math/big_number.hpp b/include/boost/math/big_number.hpp deleted file mode 100644 index 6b84e39b..00000000 --- a/include/boost/math/big_number.hpp +++ /dev/null @@ -1,1570 +0,0 @@ -/////////////////////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_EXTENDED_REAL_HPP -#define BOOST_MATH_EXTENDED_REAL_HPP - -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include - -namespace boost{ namespace math{ - -template -class big_number -{ - typedef big_number self_type; -public: - big_number(){} - big_number(const big_number& e) : m_backend(e.m_backend){} - template - big_number(V v, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) - { - m_backend = canonical_value(v); - } - big_number(const big_number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} - template - big_number(V v, unsigned digits10, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) - { - m_backend.precision(digits10); - m_backend = canonical_value(v); - } - - template - big_number(V v, typename enable_if, mpl::not_ > > >::type* dummy1 = 0) - : m_backend(v){} - - template - big_number& operator=(const detail::big_number_exp& e) - { - do_assign(e, tag()); - return *this; - } - - big_number& operator=(const big_number& e) - { - m_backend = e.m_backend; - return *this; - } - - template - typename enable_if, is_same, is_convertible >, big_number& >::type - operator=(const V& v) - { - m_backend = canonical_value(v); - return *this; - } - - template - big_number(const detail::big_number_exp& e) - { - do_assign(e, tag()); - } - -#ifndef BOOST_NO_RVALUE_REFERENCES - big_number(big_number&& r) : m_backend(r.m_backend){} - big_number& operator=(big_number&& r) - { - m_backend.swap(r.m_backend); - return *this; - } -#endif - - big_number& operator+=(const self_type& val) - { - do_add(detail::big_number_exp(val), detail::terminal()); - return *this; - } - - template - big_number& operator+=(const detail::big_number_exp& e) - { - // Create a copy if e contains this, but not if we're just doing a - // x *= x - if(contains_self(e) && !is_self(e)) - { - self_type temp(e); - do_add(detail::big_number_exp(temp), detail::terminal()); - } - else - { - do_add(e, tag()); - } - return *this; - } - - template - typename enable_if, big_number& >::type - operator+=(const V& v) - { - using big_num_default_ops::add; - add(m_backend, canonical_value(v)); - return *this; - } - - big_number& operator-=(const self_type& val) - { - do_subtract(detail::big_number_exp(val), detail::terminal()); - return *this; - } - - template - big_number& operator-=(const detail::big_number_exp& e) - { - // Create a copy if e contains this, but not if we're just doing a - if(contains_self(e)) - { - self_type temp(e); - do_subtract(temp, typename self_type::tag_type()); - } - else - { - do_subtract(e, typename Exp::tag_type()); - } - return *this; - } - - template - typename enable_if, big_number& >::type - operator-=(const V& v) - { - using big_num_default_ops::subtract; - subtract(m_backend, canonical_value(v)); - return *this; - } - - - big_number& operator *= (const self_type& e) - { - do_multiplies(detail::big_number_exp(e), detail::terminal()); - return *this; - } - - template - big_number& operator*=(const detail::big_number_exp& e) - { - // Create a temporary if the RHS references *this, but not - // if we're just doing an x += x; - if(contains_self(e) && !is_self(e)) - { - self_type temp(e); - do_multiplies(detail::big_number_exp(temp), detail::terminal()); - } - else - { - do_multiplies(e, typename Exp::tag_type()); - } - return *this; - } - - template - typename enable_if, big_number& >::type - operator*=(const V& v) - { - using big_num_default_ops::multiply; - multiply(m_backend, canonical_value(v)); - return *this; - } - - big_number& operator%=(const self_type& e) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - do_modulus(detail::big_number_exp(e), detail::terminal()); - return *this; - } - template - big_number& operator%=(const detail::big_number_exp& e) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - // Create a temporary if the RHS references *this: - if(contains_self(e)) - { - self_type temp(e); - do_modulus(temp, typename self_type::tag_type()); - } - else - { - do_modulus(e, typename Exp::tag_type()); - } - return *this; - } - template - typename enable_if, big_number& >::type - operator%=(const V& v) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using big_num_default_ops::modulus; - modulus(m_backend, canonical_value(v)); - return *this; - } - - // - // These operators are *not* proto-ized. - // The issue is that the increment/decrement must happen - // even if the result of the operator *is never used*. - // Possibly we could modify our expression wrapper to - // execute the increment/decrement on destruction, but - // correct implemetation will be tricky, so defered for now... - // - big_number& operator++() - { - using big_num_default_ops::increment; - increment(m_backend); - return *this; - } - - big_number& operator--() - { - using big_num_default_ops::decrement; - decrement(m_backend); - return *this; - } - - big_number operator++(int) - { - using big_num_default_ops::increment; - self_type temp(*this); - increment(m_backend); - return temp; - } - - big_number operator--(int) - { - using big_num_default_ops::decrement; - self_type temp(*this); - decrement(m_backend); - return temp; - } - - template - typename enable_if, big_number&>::type operator <<= (V val) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left-shift operation is only valid for integer types"); - check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); - left_shift(m_backend, canonical_value(val)); - return *this; - } - - template - typename enable_if, big_number&>::type operator >>= (V val) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right-shift operation is only valid for integer types"); - check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); - right_shift(m_backend, canonical_value(val)); - return *this; - } - - big_number& operator /= (const self_type& e) - { - do_divide(detail::big_number_exp(e), detail::terminal()); - return *this; - } - - template - big_number& operator/=(const detail::big_number_exp& e) - { - // Create a temporary if the RHS references *this: - if(contains_self(e)) - { - self_type temp(e); - do_divide(detail::big_number_exp(temp), typename self_type::tag_type()); - } - else - { - do_divide(e, typename Exp::tag_type()); - } - return *this; - } - - template - typename enable_if, big_number& >::type - operator/=(const V& v) - { - using big_num_default_ops::divide; - divide(m_backend, canonical_value(v)); - return *this; - } - - big_number& operator&=(const self_type& e) - { - do_bitwise_and(detail::big_number_exp(e), detail::terminal()); - return *this; - } - - template - big_number& operator&=(const detail::big_number_exp& e) - { - // Create a temporary if the RHS references *this, but not - // if we're just doing an x &= x; - if(contains_self(e) && !is_self(e)) - { - self_type temp(e); - do_bitwise_and(temp, typename self_type::tag_type()); - } - else - { - do_bitwise_and(e, typename Exp::tag_type()); - } - return *this; - } - - template - typename enable_if, big_number& >::type - operator&=(const V& v) - { - using big_num_default_ops::bitwise_and; - bitwise_and(m_backend, canonical_value(v)); - return *this; - } - - big_number& operator|=(const self_type& e) - { - do_bitwise_or(detail::big_number_exp(e), detail::terminal()); - return *this; - } - - template - big_number& operator|=(const detail::big_number_exp& e) - { - // Create a temporary if the RHS references *this, but not - // if we're just doing an x |= x; - if(contains_self(e) && !is_self(e)) - { - self_type temp(e); - do_bitwise_or(temp, typename self_type::tag_type()); - } - else - { - do_bitwise_or(e, typename Exp::tag_type()); - } - return *this; - } - - template - typename enable_if, big_number& >::type - operator|=(const V& v) - { - using big_num_default_ops::bitwise_or; - bitwise_or(m_backend, canonical_value(v)); - return *this; - } - - big_number& operator^=(const self_type& e) - { - do_bitwise_xor(detail::big_number_exp(e), detail::terminal()); - return *this; - } - - template - big_number& operator^=(const detail::big_number_exp& e) - { - if(contains_self(e)) - { - self_type temp(e); - do_bitwise_xor(temp, typename self_type::tag_type()); - } - else - { - do_bitwise_xor(e, typename Exp::tag_type()); - } - return *this; - } - - template - typename enable_if, big_number& >::type - operator^=(const V& v) - { - using big_num_default_ops::bitwise_xor; - bitwise_xor(m_backend, canonical_value(v)); - return *this; - } - // - // Use in boolean context: - // - typedef bool (self_type::*unmentionable_type)()const; - - operator unmentionable_type()const - { - return is_zero() ? 0 : &self_type::is_zero; - } - - // - // swap: - // - void swap(self_type& other) - { - m_backend.swap(other.backend()); - } - // - // Zero and sign: - // - bool is_zero()const - { - using big_num_default_ops::is_zero; - return is_zero(m_backend); - } - int sign()const - { - using big_num_default_ops::get_sign; - return get_sign(m_backend); - } - // - // String conversion functions: - // - std::string str(unsigned digits = 0, bool scientific = true)const - { - return m_backend.str(digits, scientific); - } - template - T convert_to()const - { - using big_num_default_ops::convert_to; - T result; - convert_to(&result, m_backend); - return result; - } - // - // Default precision: - // - static unsigned default_precision() - { - return Backend::default_precision(); - } - static void default_precision(unsigned digits10) - { - Backend::default_precision(digits10); - } - unsigned precision()const - { - return m_backend.precision(); - } - void precision(unsigned digits10) - { - m_backend.precision(digits10); - } - // - // Comparison: - // - int compare(const big_number& o)const - { - return m_backend.compare(o.m_backend); - } - template - typename enable_if, int>::type compare(const V& o)const - { - using big_num_default_ops::get_sign; - if(o == 0) - return get_sign(m_backend); - return m_backend.compare(canonical_value(o)); - } - Backend& backend() - { - return m_backend; - } - const Backend& backend()const - { - return m_backend; - } -private: - template - void check_shift_range(V val, const mpl::true_&, const mpl::true_&) - { - if(val > (std::numeric_limits::max)()) - BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); - if(val < 0) - BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); - } - template - void check_shift_range(V val, const mpl::false_&, const mpl::true_&) - { - if(val < 0) - BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); - } - template - void check_shift_range(V val, const mpl::true_&, const mpl::false_&) - { - if(val > (std::numeric_limits::max)()) - BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); - } - template - void check_shift_range(V val, const mpl::false_&, const mpl::false_&){} - - template - void do_assign(const Exp& e, const detail::add_immediates&) - { - using big_num_default_ops::add; - add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - } -/* - template - void do_assign(const Exp& e, const detail::add_and_negate_immediates&) - { - using big_num_default_ops::add; - add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - m_backend.negate(); - } -*/ - template - void do_assign(const Exp& e, const detail::subtract_immediates&) - { - using big_num_default_ops::subtract; - subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - } - /* - template - void do_assign(const Exp& e, const detail::subtract_and_negate_immediates&) - { - using big_num_default_ops::subtract; - subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - m_backend.negate(); - } - */ - template - void do_assign(const Exp& e, const detail::multiply_immediates&) - { - using big_num_default_ops::multiply; - multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - } - - template - void do_assign(const Exp& e, const detail::divide_immediates&) - { - using big_num_default_ops::divide; - divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - } - -#if 0 - template - void do_assign(const Exp& e, const detail::multiply_and_negate_immediates&) - { - using big_num_default_ops::multiply; - multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - m_backend.negate(); - } - - template - void do_assign(const Exp& e, const detail::divide_and_negate_immediates&) - { - using big_num_default_ops::divide; - divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - m_backend.negate(); - } - - template - void do_assign(const Exp& e, const detail::unary_plus&) - { - typedef typename Exp::left_type left_type; - do_assign(e.left(), typename left_type::tag_type()); - } - -#endif - template - void do_assign(const Exp& e, const detail::negate&) - { - typedef typename Exp::left_type left_type; - do_assign(e.left(), typename left_type::tag_type()); - m_backend.negate(); - } - template - void do_assign(const Exp& e, const detail::plus&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - - static int const left_depth = left_type::depth; - static int const right_depth = right_type::depth; - - bool bl = contains_self(e.left()); - bool br = contains_self(e.right()); - - if(bl && is_self(e.left())) - { - // Ignore the left node, it's *this, just add the right: - do_add(e.right(), typename right_type::tag_type()); - } - else if(br && is_self(e.right())) - { - // Ignore the right node, it's *this, just add the left: - do_add(e.left(), typename left_type::tag_type()); - } - else if(bl || br) - { - self_type temp(e); - temp.m_backend.swap(this->m_backend); - } - else if(left_depth >= right_depth) - { - do_assign(e.left(), typename left_type::tag_type()); - do_add(e.right(), typename right_type::tag_type()); - } - else - { - do_assign(e.right(), typename right_type::tag_type()); - do_add(e.left(), typename left_type::tag_type()); - } - } - template - void do_assign(const Exp& e, const detail::minus&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - - static int const left_depth = left_type::depth; - static int const right_depth = right_type::depth; - - bool bl = contains_self(e.left()); - bool br = contains_self(e.right()); - - if(bl && is_self(e.left())) - { - // Ignore the left node, it's *this, just subtract the right: - do_subtract(e.right(), typename right_type::tag_type()); - } - else if(br && is_self(e.right())) - { - // Ignore the right node, it's *this, just subtract the left and negate the result: - do_subtract(e.left(), typename left_type::tag_type()); - m_backend.negate(); - } - else if(bl || br) - { - self_type temp(e); - temp.m_backend.swap(this->m_backend); - } - else if(left_depth >= right_depth) - { - do_assign(e.left(), typename left_type::tag_type()); - do_subtract(e.right(), typename right_type::tag_type()); - } - else - { - do_assign(e.right(), typename right_type::tag_type()); - do_subtract(e.left(), typename left_type::tag_type()); - m_backend.negate(); - } - } - template - void do_assign(const Exp& e, const detail::multiplies&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - - static int const left_depth = left_type::depth; - static int const right_depth = right_type::depth; - - bool bl = contains_self(e.left()); - bool br = contains_self(e.right()); - - if(bl && is_self(e.left())) - { - // Ignore the left node, it's *this, just add the right: - do_multiplies(e.right(), typename right_type::tag_type()); - } - else if(br && is_self(e.right())) - { - // Ignore the right node, it's *this, just add the left: - do_multiplies(e.left(), typename left_type::tag_type()); - } - else if(bl || br) - { - self_type temp(e); - temp.m_backend.swap(this->m_backend); - } - else if(left_depth >= right_depth) - { - do_assign(e.left(), typename left_type::tag_type()); - do_multiplies(e.right(), typename right_type::tag_type()); - } - else - { - do_assign(e.right(), typename right_type::tag_type()); - do_multiplies(e.left(), typename left_type::tag_type()); - } - } - template - void do_assign(const Exp& e, const detail::divides&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - - bool bl = contains_self(e.left()); - bool br = contains_self(e.right()); - - if(bl && is_self(e.left())) - { - // Ignore the left node, it's *this, just add the right: - do_divide(e.right(), typename right_type::tag_type()); - } - else if(bl || br) - { - self_type temp(e); - temp.m_backend.swap(this->m_backend); - } - else - { - do_assign(e.left(), typename left_type::tag_type()); - do_divide(e.right(), typename right_type::tag_type()); - } - } - template - void do_assign(const Exp& e, const detail::modulus&) - { - // - // This operation is only valid for integer backends: - // - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - - bool bl = contains_self(e.left()); - bool br = contains_self(e.right()); - - if(bl && is_self(e.left())) - { - // Ignore the left node, it's *this, just add the right: - do_modulus(e.right(), typename right_type::tag_type()); - } - else if(bl || br) - { - self_type temp(e); - temp.m_backend.swap(this->m_backend); - } - else - { - do_assign(e.left(), typename left_type::tag_type()); - do_modulus(e.right(), typename right_type::tag_type()); - } - } - template - void do_assign(const Exp& e, const detail::modulus_immediates&) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using big_num_default_ops::modulus; - modulus(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - } - - template - void do_assign(const Exp& e, const detail::bitwise_and&) - { - // - // This operation is only valid for integer backends: - // - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - - static int const left_depth = left_type::depth; - static int const right_depth = right_type::depth; - - bool bl = contains_self(e.left()); - bool br = contains_self(e.right()); - - if(bl && is_self(e.left())) - { - // Ignore the left node, it's *this, just add the right: - do_bitwise_and(e.right(), typename right_type::tag_type()); - } - else if(br && is_self(e.right())) - { - do_bitwise_and(e.left(), typename left_type::tag_type()); - } - else if(left_depth >= right_depth) - { - do_assign(e.left(), typename left_type::tag_type()); - do_bitwise_and(e.right(), typename right_type::tag_type()); - } - else - { - do_assign(e.right(), typename right_type::tag_type()); - do_bitwise_and(e.left(), typename left_type::tag_type()); - } - } - template - void do_assign(const Exp& e, const detail::bitwise_and_immediates&) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - using big_num_default_ops::bitwise_and; - bitwise_and(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - } - - template - void do_assign(const Exp& e, const detail::bitwise_or&) - { - // - // This operation is only valid for integer backends: - // - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - - static int const left_depth = left_type::depth; - static int const right_depth = right_type::depth; - - bool bl = contains_self(e.left()); - bool br = contains_self(e.right()); - - if(bl && is_self(e.left())) - { - // Ignore the left node, it's *this, just add the right: - do_bitwise_or(e.right(), typename right_type::tag_type()); - } - else if(br && is_self(e.right())) - { - do_bitwise_or(e.left(), typename left_type::tag_type()); - } - else if(left_depth >= right_depth) - { - do_assign(e.left(), typename left_type::tag_type()); - do_bitwise_or(e.right(), typename right_type::tag_type()); - } - else - { - do_assign(e.right(), typename right_type::tag_type()); - do_bitwise_or(e.left(), typename left_type::tag_type()); - } - } - template - void do_assign(const Exp& e, const detail::bitwise_or_immediates&) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - using big_num_default_ops::bitwise_or; - bitwise_or(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - } - - template - void do_assign(const Exp& e, const detail::bitwise_xor&) - { - // - // This operation is only valid for integer backends: - // - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - - static int const left_depth = left_type::depth; - static int const right_depth = right_type::depth; - - bool bl = contains_self(e.left()); - bool br = contains_self(e.right()); - - if(bl && is_self(e.left())) - { - // Ignore the left node, it's *this, just add the right: - do_bitwise_xor(e.right(), typename right_type::tag_type()); - } - else if(br && is_self(e.right())) - { - do_bitwise_xor(e.left(), typename left_type::tag_type()); - } - else if(left_depth >= right_depth) - { - do_assign(e.left(), typename left_type::tag_type()); - do_bitwise_xor(e.right(), typename right_type::tag_type()); - } - else - { - do_assign(e.right(), typename right_type::tag_type()); - do_bitwise_xor(e.left(), typename left_type::tag_type()); - } - } - template - void do_assign(const Exp& e, const detail::bitwise_xor_immediates&) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - using big_num_default_ops::bitwise_xor; - bitwise_xor(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - } - template - void do_assign(const Exp& e, const detail::terminal&) - { - if(!is_self(e)) - { - m_backend = canonical_value(e.value()); - } - } - template - void do_assign(const Exp& e, const detail::function&) - { - typedef typename Exp::arity tag_type; - do_assign_function(e, tag_type()); - } - template - void do_assign(const Exp& e, const detail::shift_left&) - { - // We can only shift by an integer value, not an arbitrary expression: - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - typedef typename right_type::arity right_arity; - BOOST_STATIC_ASSERT_MSG(right_arity::value == 0, "The left shift operator requires an integer value for the shift operand."); - typedef typename right_type::result_type right_value_type; - BOOST_STATIC_ASSERT_MSG(is_integral::value, "The left shift operator requires an integer value for the shift operand."); - typedef typename left_type::tag_type tag_type; - do_assign_left_shift(e.left(), canonical_value(e.right().value()), tag_type()); - } - - template - void do_assign(const Exp& e, const detail::shift_right&) - { - // We can only shift by an integer value, not an arbitrary expression: - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - typedef typename right_type::arity right_arity; - BOOST_STATIC_ASSERT_MSG(right_arity::value == 0, "The left shift operator requires an integer value for the shift operand."); - typedef typename right_type::result_type right_value_type; - BOOST_STATIC_ASSERT_MSG(is_integral::value, "The left shift operator requires an integer value for the shift operand."); - typedef typename left_type::tag_type tag_type; - do_assign_right_shift(e.left(), canonical_value(e.right().value()), tag_type()); - } - - template - void do_assign(const Exp& e, const detail::bitwise_complement&) - { - using big_num_default_ops::complement; - self_type temp(e.left()); - complement(m_backend, temp.backend()); - } - - template - void do_assign(const Exp& e, const detail::complement_immediates&) - { - using big_num_default_ops::complement; - complement(m_backend, canonical_value(e.left().value())); - } - - template - void do_assign_right_shift(const Exp& e, const Val& val, const detail::terminal&) - { - using big_num_default_ops::right_shift; - right_shift(m_backend, canonical_value(e.value()), val); - } - - template - void do_assign_left_shift(const Exp& e, const Val& val, const detail::terminal&) - { - using big_num_default_ops::left_shift; - left_shift(m_backend, canonical_value(e.value()), val); - } - - template - void do_assign_right_shift(const Exp& e, const Val& val, const Tag&) - { - using big_num_default_ops::right_shift; - self_type temp(e); - right_shift(m_backend, temp.backend(), val); - } - - template - void do_assign_left_shift(const Exp& e, const Val& val, const Tag&) - { - using big_num_default_ops::left_shift; - self_type temp(e); - left_shift(m_backend, temp.backend(), val); - } - - template - void do_assign_function(const Exp& e, const mpl::int_<1>&) - { - e.left().value()(&m_backend); - } - template - void do_assign_function(const Exp& e, const mpl::int_<2>&) - { - typedef typename Exp::right_type right_type; - typedef typename right_type::tag_type tag_type; - do_assign_function_1(e.left().value(), e.right(), tag_type()); - } - template - void do_assign_function_1(const F& f, const Exp& val, const detail::terminal&) - { - f(m_backend, canonical_value(val.value())); - } - template - void do_assign_function_1(const F& f, const Exp& val, const Tag&) - { - big_number t(val); - f(m_backend, t.backend()); - } - template - void do_assign_function(const Exp& e, const mpl::int_<3>&) - { - typedef typename Exp::middle_type middle_type; - typedef typename middle_type::tag_type tag_type; - typedef typename Exp::right_type end_type; - typedef typename end_type::tag_type end_tag; - do_assign_function_2(e.left().value(), e.middle(), e.right(), tag_type(), end_tag()); - } - template - void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const detail::terminal&) - { - f(m_backend, canonical_value(val1.value()), canonical_value(val2.value())); - } - template - void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const detail::terminal&) - { - self_type temp1(val1); - f(m_backend, temp1.backend(), canonical_value(val2.value())); - } - template - void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const Tag2&) - { - self_type temp2(val2); - f(m_backend, canonical_value(val1.value()), temp2.backend()); - } - template - void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const Tag2&) - { - self_type temp1(val1); - self_type temp2(val2); - f(m_backend, temp1.backend(), temp2.backend()); - } - - template - void do_add(const Exp& e, const detail::terminal&) - { - using big_num_default_ops::add; - add(m_backend, canonical_value(e.value())); - } - - template - void do_add(const Exp& e, const detail::negate&) - { - typedef typename Exp::left_type left_type; - do_subtract(e.left(), typename left_type::tag_type()); - } - - template - void do_add(const Exp& e, const detail::plus&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_add(e.left(), typename left_type::tag_type()); - do_add(e.right(), typename right_type::tag_type()); - } - - template - void do_add(const Exp& e, const detail::minus&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_add(e.left(), typename left_type::tag_type()); - do_subtract(e.right(), typename right_type::tag_type()); - } - - template - void do_add(const Exp& e, const unknown&) - { - self_type temp(e); - do_add(detail::big_number_exp(temp), detail::terminal()); - } - - template - void do_add(const Exp& e, const detail::add_immediates&) - { - using big_num_default_ops::add; - add(m_backend, canonical_value(e.left().value())); - add(m_backend, canonical_value(e.right().value())); - } - template - void do_add(const Exp& e, const detail::subtract_immediates&) - { - using big_num_default_ops::add; - using big_num_default_ops::subtract; - add(m_backend, canonical_value(e.left().value())); - subtract(m_backend, canonical_value(e.right().value())); - } - template - void do_subtract(const Exp& e, const detail::terminal&) - { - using big_num_default_ops::subtract; - subtract(m_backend, canonical_value(e.value())); - } - - template - void do_subtract(const Exp& e, const detail::negate&) - { - typedef typename Exp::left_type left_type; - do_add(e.left(), typename left_type::tag_type()); - } - - template - void do_subtract(const Exp& e, const detail::plus&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_subtract(e.left(), typename left_type::tag_type()); - do_subtract(e.right(), typename right_type::tag_type()); - } - - template - void do_subtract(const Exp& e, const detail::minus&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_subtract(e.left(), typename left_type::tag_type()); - do_add(e.right(), typename right_type::tag_type()); - } - template - void do_subtract(const Exp& e, const detail::add_immediates&) - { - using big_num_default_ops::subtract; - subtract(m_backend, canonical_value(e.left().value())); - subtract(m_backend, canonical_value(e.right().value())); - } - template - void do_subtract(const Exp& e, const detail::subtract_immediates&) - { - using big_num_default_ops::add; - using big_num_default_ops::subtract; - subtract(m_backend, canonical_value(e.left().value())); - add(m_backend, canonical_value(e.right().value())); - } - template - void do_subtract(const Exp& e, const unknown&) - { - self_type temp(e); - do_subtract(detail::big_number_exp(temp), detail::terminal()); - } - - template - void do_multiplies(const Exp& e, const detail::terminal&) - { - using big_num_default_ops::multiply; - multiply(m_backend, canonical_value(e.value())); - } - - template - void do_multiplies(const Exp& e, const detail::negate&) - { - typedef typename Exp::left_type left_type; - do_multiplies(e.left(), typename left_type::tag_type()); - m_backend.negate(); - } - - template - void do_multiplies(const Exp& e, const detail::multiplies&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_multiplies(e.left(), typename left_type::tag_type()); - do_multiplies(e.right(), typename right_type::tag_type()); - } - - template - void do_multiplies(const Exp& e, const detail::divides&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_multiplies(e.left(), typename left_type::tag_type()); - do_divide(e.right(), typename right_type::tag_type()); - } - - template - void do_multiplies(const Exp& e, const detail::multiply_immediates&) - { - using big_num_default_ops::multiply; - multiply(m_backend, canonical_value(e.left().value())); - multiply(m_backend, canonical_value(e.right().value())); - } - template - void do_multiplies(const Exp& e, const detail::divide_immediates&) - { - using big_num_default_ops::multiply; - using big_num_default_ops::divide; - multiply(m_backend, canonical_value(e.left().value())); - divide(m_backend, canonical_value(e.right().value())); - } - template - void do_multiplies(const Exp& e, const unknown&) - { - using big_num_default_ops::multiply; - self_type temp(e); - multiply(m_backend, temp.m_backend); - } - - template - void do_divide(const Exp& e, const detail::terminal&) - { - using big_num_default_ops::divide; - divide(m_backend, canonical_value(e.value())); - } - - template - void do_divide(const Exp& e, const detail::negate&) - { - typedef typename Exp::left_type left_type; - do_divide(e.left(), typename left_type::tag_type()); - m_backend.negate(); - } - - template - void do_divide(const Exp& e, const detail::multiplies&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_divide(e.left(), typename left_type::tag_type()); - do_divide(e.right(), typename right_type::tag_type()); - } - - template - void do_divide(const Exp& e, const detail::divides&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_divide(e.left(), typename left_type::tag_type()); - do_multiplies(e.right(), typename right_type::tag_type()); - } - - template - void do_divides(const Exp& e, const detail::multiply_immediates&) - { - using big_num_default_ops::divide; - divide(m_backend, canonical_value(e.left().value())); - divide(m_backend, canonical_value(e.right().value())); - } - template - void do_divides(const Exp& e, const detail::divide_immediates&) - { - using big_num_default_ops::multiply; - using big_num_default_ops::divide; - divide(m_backend, canonical_value(e.left().value())); - mutiply(m_backend, canonical_value(e.right().value())); - } - - template - void do_divide(const Exp& e, const unknown&) - { - using big_num_default_ops::multiply; - self_type temp(e); - divide(m_backend, temp.m_backend); - } - - template - void do_modulus(const Exp& e, const detail::terminal&) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using big_num_default_ops::modulus; - modulus(m_backend, canonical_value(e.value())); - } - - template - void do_modulus(const Exp& e, const Unknown&) - { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using big_num_default_ops::modulus; - self_type temp(e); - modulus(m_backend, canonical_value(temp)); - } - - template - void do_bitwise_and(const Exp& e, const detail::terminal&) - { - using big_num_default_ops::bitwise_and; - bitwise_and(m_backend, canonical_value(e.value())); - } - template - void do_bitwise_and(const Exp& e, const detail::bitwise_and&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_bitwise_and(e.left(), typename left_type::tag_type()); - do_bitwise_and(e.right(), typename right_type::tag_type()); - } - template - void do_bitwise_and(const Exp& e, const unknown&) - { - using big_num_default_ops::bitwise_and; - self_type temp(e); - bitwise_and(m_backend, temp.m_backend); - } - - template - void do_bitwise_or(const Exp& e, const detail::terminal&) - { - using big_num_default_ops::bitwise_or; - bitwise_or(m_backend, canonical_value(e.value())); - } - template - void do_bitwise_or(const Exp& e, const detail::bitwise_or&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_bitwise_or(e.left(), typename left_type::tag_type()); - do_bitwise_or(e.right(), typename right_type::tag_type()); - } - template - void do_bitwise_or(const Exp& e, const unknown&) - { - using big_num_default_ops::bitwise_or; - self_type temp(e); - bitwise_or(m_backend, temp.m_backend); - } - - template - void do_bitwise_xor(const Exp& e, const detail::terminal&) - { - using big_num_default_ops::bitwise_xor; - bitwise_xor(m_backend, canonical_value(e.value())); - } - template - void do_bitwise_xor(const Exp& e, const detail::bitwise_xor&) - { - typedef typename Exp::left_type left_type; - typedef typename Exp::right_type right_type; - do_bitwise_xor(e.left(), typename left_type::tag_type()); - do_bitwise_xor(e.right(), typename right_type::tag_type()); - } - template - void do_bitwise_xor(const Exp& e, const unknown&) - { - using big_num_default_ops::bitwise_xor; - self_type temp(e); - bitwise_xor(m_backend, temp.m_backend); - } - - // Tests if the expression contains a reference to *this: - template - bool contains_self(const Exp& e)const - { - return contains_self(e, typename Exp::arity()); - } - template - bool contains_self(const Exp& e, mpl::int_<0> const&)const - { - return is_really_self(e.value()); - } - template - bool contains_self(const Exp& e, mpl::int_<1> const&)const - { - typedef typename Exp::left_type child_type; - return contains_self(e.left(), typename child_type::arity()); - } - template - bool contains_self(const Exp& e, mpl::int_<2> const&)const - { - typedef typename Exp::left_type child0_type; - typedef typename Exp::right_type child1_type; - return contains_self(e.left(), typename child0_type::arity()) - || contains_self(e.right(), typename child1_type::arity()); - } - template - bool contains_self(const Exp& e, mpl::int_<3> const&)const - { - typedef typename Exp::left_type child0_type; - typedef typename Exp::middle_type child1_type; - typedef typename Exp::right_type child2_type; - return contains_self(e.left(), typename child0_type::arity()) - || contains_self(e.middle(), typename child1_type::arity()) - || contains_self(e.right(), typename child2_type::arity()); - } - - // Test if the expression is a reference to *this: - template - bool is_self(const Exp& e)const - { - return is_self(e, typename Exp::arity()); - } - template - bool is_self(const Exp& e, mpl::int_<0> const&)const - { - return is_really_self(e.value()); - } - template - bool is_self(const Exp& e, mpl::int_ const&)const - { - return false; - } - - template - bool is_really_self(const Val&)const { return false; } - bool is_really_self(const self_type& v)const { return &v == this; } - - static const Backend& canonical_value(const self_type& v){ return v.m_backend; } - //static const Backend& canonical_value(const self_type* v){ return v->m_backend; } - //static const Backend& canonical_value(self_type* v){ return v->m_backend; } - //static const Backend& canonical_value(self_type& v){ return v.m_backend; } - template - static typename detail::canonical::type canonical_value(const V& v){ return v; } - static typename detail::canonical::type canonical_value(const std::string& v){ return v.c_str(); } - Backend m_backend; -}; - -namespace detail -{ - -template -inline int big_number_compare(const big_number& a, const big_number& b) -{ - return a.compare(b); -} - -template -inline int big_number_compare(const big_number& a, const big_number_exp& b) -{ - return a.compare(big_number(b)); -} - -template -inline int big_number_compare(const big_number_exp& a, const big_number& b) -{ - return -b.compare(big_number(a)); -} - -template -inline int big_number_compare(const big_number& a, const Val b) -{ - return a.compare(b); -} - -template -inline int big_number_compare(const Val a, const big_number& b) -{ - return -b.compare(a); -} - -template -inline int big_number_compare(const big_number_exp& a, const big_number_exp& b) -{ - typedef typename big_number_exp::result_type real1; - typedef typename big_number_exp::result_type real2; - return real1(a).compare(real2(b)); -} - -template -inline typename enable_if, int>::type big_number_compare(const big_number_exp& a, const Val b) -{ - typedef typename big_number_exp::result_type real; - real t(a); - return t.compare(b); -} - -template -inline typename enable_if, int>::type big_number_compare(const Val a, const big_number_exp& b) -{ - typedef typename big_number_exp::result_type real; - return -real(b).compare(a); -} - -template -struct is_valid_comparison_imp -{ - typedef typename mpl::or_< - is_big_number, - is_big_number_exp - >::type is1; - typedef typename mpl::or_< - is_big_number, - is_big_number_exp - >::type is2; - typedef typename mpl::or_< - mpl::and_< - is1, - mpl::or_< - is2, - is_arithmetic - > - >, - mpl::and_< - is2, - mpl::or_< - is1, - is_arithmetic - > - > - >::type type; -}; - -template -struct is_valid_comparison : public boost::math::detail::is_valid_comparison_imp::type {}; - -} - - -template -inline typename boost::enable_if, bool>::type - operator == (const Exp1& a, const Exp2& b) -{ - return 0 == detail::big_number_compare(a, b); -} - -template -inline typename boost::enable_if, bool>::type - operator != (const Exp1& a, const Exp2& b) -{ - return 0 != detail::big_number_compare(a, b); -} - -template -inline typename boost::enable_if, bool>::type - operator <= (const Exp1& a, const Exp2& b) -{ - return 0 >= detail::big_number_compare(a, b); -} - -template -inline typename boost::enable_if, bool>::type - operator < (const Exp1& a, const Exp2& b) -{ - return 0 > detail::big_number_compare(a, b); -} - -template -inline typename boost::enable_if, bool>::type - operator >= (const Exp1& a, const Exp2& b) -{ - return 0 <= detail::big_number_compare(a, b); -} - -template -inline typename boost::enable_if, bool>::type - operator > (const Exp1& a, const Exp2& b) -{ - return 0 < detail::big_number_compare(a, b); -} - -template -inline std::ostream& operator << (std::ostream& os, const big_number& r) -{ - return os << r.str(static_cast(os.precision(), os.flags() & os.scientific)); -} - -namespace detail{ - -template -inline std::ostream& operator << (std::ostream& os, const big_number_exp& r) -{ - typedef typename big_number_exp::result_type value_type; - value_type temp(r); - return os << temp; -} - -} // namespace detail - -template -inline std::istream& operator >> (std::istream& is, big_number& r) -{ - std::string s; - is >> s; - r = s; - return is; -} - -}} // namespaces - -#endif diff --git a/include/boost/math/big_number/arithmetic_backend.hpp b/include/boost/math/big_number/arithmetic_backend.hpp deleted file mode 100644 index ba8d7165..00000000 --- a/include/boost/math/big_number/arithmetic_backend.hpp +++ /dev/null @@ -1,147 +0,0 @@ -/////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ - -#ifndef BOOST_MATH_ARITH_BACKEND_HPP -#define BOOST_MATH_ARITH_BACKEND_HPP - -#include -#include -#include -#include -#include - -namespace boost{ -namespace math{ - -template -struct arithmetic_backend -{ - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list real_types; - - arithmetic_backend(){} - arithmetic_backend(const arithmetic_backend& o) - { - m_value = o.m_value; - } - arithmetic_backend(const Arithmetic& o) : m_value(o) {} -#ifndef BOOST_NO_RVALUE_REFERENCES - arithmetic_backend(arithmetic_backend&& o) : m_value(o.m_value) {} - arithmetic_backend(Arithmetic&& o) : m_value(o) {} -#endif - arithmetic_backend& operator = (const arithmetic_backend& o) - { - m_value = o.m_value; - return *this; - } - arithmetic_backend& operator = (boost::uintmax_t i) - { - m_value = i; - return *this; - } - arithmetic_backend& operator = (boost::intmax_t i) - { - m_value = i; - return *this; - } - arithmetic_backend& operator = (long double d) - { - m_value = d; - return *this; - } - arithmetic_backend& operator = (const char* s) - { - m_value = boost::lexical_cast(s); - return *this; - } - void swap(arithmetic_backend& o) - { - std::swap(m_value, o.m_value); - } - std::string str(unsigned digits, bool scientific)const - { - return boost::lexical_cast(m_value); - } - void negate() - { - m_value = -m_value; - } - int compare(const arithmetic_backend& o)const - { - return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); - } - int compare(boost::intmax_t i)const - { - return m_value > i ? 1 : (m_value < i ? -1 : 0); - } - int compare(boost::uintmax_t i)const - { - return m_value > i ? 1 : (m_value < i ? -1 : 0); - } - int compare(long double d)const - { - return m_value > d ? 1 : (m_value < d ? -1 : 0); - } - Arithmetic& data() { return m_value; } - const Arithmetic& data()const { return m_value; } -private: - Arithmetic m_value; -}; - -template -inline void add(arithmetic_backend& result, const arithmetic_backend& o) -{ - result.data() += o.data(); -} -template -inline void subtract(arithmetic_backend& result, const arithmetic_backend& o) -{ - result.data() -= o.data(); -} -template -inline void multiply(arithmetic_backend& result, const arithmetic_backend& o) -{ - result.data() *= o.data(); -} -template -inline void divide(arithmetic_backend& result, const arithmetic_backend& o) -{ - result.data() /= o.data(); -} - -}} // namespaces - - -namespace std{ - -#ifdef BOOST_NO_NOEXCEPT -# define noexcept -#endif - -template -class numeric_limits > > : public std::numeric_limits -{ - typedef std::numeric_limits base_type; - typedef boost::math::big_number > number_type; -public: - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return -(max)(); } - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return base_type::epsilon(); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return epsilon() / 2; } - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return base_type::infinity(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return base_type::quiet_NaN(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return base_type::signaling_NaN(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return base_type::denorm_min(); } -}; - -#ifdef BOOST_NO_NOEXCEPT -# undef noexcept -#endif - -} - -#endif diff --git a/include/boost/math/big_number/big_number_base.hpp b/include/boost/math/big_number/big_number_base.hpp deleted file mode 100644 index 8eef7048..00000000 --- a/include/boost/math/big_number/big_number_base.hpp +++ /dev/null @@ -1,983 +0,0 @@ -/////////////////////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_BIG_NUM_BASE_HPP -#define BOOST_MATH_BIG_NUM_BASE_HPP - -#include -#include -#include - -namespace boost{ namespace math{ - -template -class big_number; - -namespace detail{ - -// Forward-declare an expression wrapper -template -struct big_number_exp; - -template -struct has_enough_bits -{ - template - struct type : public mpl::bool_::digits >= b>{}; -}; - -template -struct canonical_imp -{ - typedef Val type; -}; -template -struct canonical_imp > -{ - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - typename Backend::signed_types, - pred_type - >::type iter_type; - typedef typename mpl::deref::type type; -}; -template -struct canonical_imp > -{ - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - typename Backend::unsigned_types, - pred_type - >::type iter_type; - typedef typename mpl::deref::type type; -}; -template -struct canonical_imp > -{ - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - typename Backend::real_types, - pred_type - >::type iter_type; - typedef typename mpl::deref::type type; -}; -template -struct canonical_imp > -{ - typedef const char* type; -}; - -template -struct canonical -{ - typedef typename mpl::if_< - is_signed, - mpl::int_<0>, - typename mpl::if_< - is_unsigned, - mpl::int_<1>, - typename mpl::if_< - is_floating_point, - mpl::int_<2>, - typename mpl::if_< - mpl::or_< - is_convertible, - is_same - >, - mpl::int_<3>, - mpl::int_<4> - >::type - >::type - >::type - >::type tag_type; - - typedef typename canonical_imp::type type; -}; - -struct terminal{}; -struct negate{}; -struct plus{}; -struct minus{}; -struct multiplies{}; -struct divides{}; -struct modulus{}; -struct shift_left{}; -struct shift_right{}; -struct bitwise_and{}; -struct bitwise_or{}; -struct bitwise_xor{}; -struct bitwise_complement{}; -struct add_immediates{}; -struct subtract_immediates{}; -struct multiply_immediates{}; -struct divide_immediates{}; -struct modulus_immediates{}; -struct bitwise_and_immediates{}; -struct bitwise_or_immediates{}; -struct bitwise_xor_immediates{}; -struct complement_immediates{}; -struct function{}; - -template -struct backend_type; - -template -struct backend_type > -{ - typedef T type; -}; - -template -struct backend_type > -{ - typedef typename backend_type::result_type>::type type; -}; - - -template -struct is_big_number : public mpl::false_{}; -template -struct is_big_number > : public mpl::true_{}; -template -struct is_big_number_exp : public mpl::false_{}; -template -struct is_big_number_exp > : public mpl::true_{}; - -template -struct combine_expression; - -template -struct combine_expression, T2> -{ - typedef big_number type; -}; - -template -struct combine_expression > -{ - typedef big_number type; -}; - -template -struct combine_expression, big_number > -{ - typedef big_number type; -}; - -template -struct arg_type -{ - typedef big_number_exp type; -}; - -template -struct arg_type > -{ - typedef big_number_exp type; -}; - -template -struct unmentionable -{ - static void proc(){} -}; - -typedef void (*unmentionable_type)(); - -template -struct big_number_exp_storage -{ - typedef const T& type; -}; - -template -struct big_number_exp_storage -{ - typedef T* type; -}; - -template -struct big_number_exp_storage -{ - typedef const T* type; -}; - -template -struct big_number_exp_storage > -{ - typedef big_number_exp type; -}; - -template -struct big_number_exp -{ - typedef mpl::int_<1> arity; - typedef typename arg_type::type left_type; - typedef typename left_type::result_type result_type; - typedef tag tag_type; - - big_number_exp(const Arg1& a) : arg(a) {} - - left_type left()const { return arg; } - - const Arg1& left_ref()const{ return arg; } - - static const unsigned depth = left_type::depth + 1; - - operator unmentionable_type()const - { - result_type r(*this); - return r ? &unmentionable::proc : 0; - } - -private: - typename big_number_exp_storage::type arg; -}; - -template -struct big_number_exp -{ - typedef mpl::int_<0> arity; - typedef Arg1 result_type; - typedef terminal tag_type; - - big_number_exp(const Arg1& a) : arg(a) {} - - const Arg1& value()const { return arg; } - - static const unsigned depth = 0; - - operator unmentionable_type()const - { - return arg ? &unmentionable::proc : 0; - } - -private: - typename big_number_exp_storage::type arg; -}; - -template -struct big_number_exp -{ - typedef mpl::int_<2> arity; - typedef typename arg_type::type left_type; - typedef typename arg_type::type right_type; - typedef typename left_type::result_type left_result_type; - typedef typename right_type::result_type right_result_type; - typedef typename combine_expression::type result_type; - typedef tag tag_type; - - big_number_exp(const Arg1& a1, const Arg2& a2) : arg1(a1), arg2(a2) {} - - left_type left()const { return arg1; } - right_type right()const { return arg2; } - const Arg1& left_ref()const{ return arg1; } - const Arg2& right_ref()const{ return arg2; } - - operator unmentionable_type()const - { - result_type r(*this); - return r ? &unmentionable::proc : 0; - } - - static const unsigned left_depth = left_type::depth + 1; - static const unsigned right_depth = right_type::depth + 1; - static const unsigned depth = left_depth > right_depth ? left_depth : right_depth; -private: - typename big_number_exp_storage::type arg1; - typename big_number_exp_storage::type arg2; -}; - -template -struct big_number_exp -{ - typedef mpl::int_<3> arity; - typedef typename arg_type::type left_type; - typedef typename arg_type::type middle_type; - typedef typename arg_type::type right_type; - typedef typename left_type::result_type left_result_type; - typedef typename middle_type::result_type middle_result_type; - typedef typename right_type::result_type right_result_type; - typedef typename combine_expression< - left_result_type, - typename combine_expression::type - >::type result_type; - typedef tag tag_type; - - big_number_exp(const Arg1& a1, const Arg2& a2, const Arg3& a3) : arg1(a1), arg2(a2), arg3(a3) {} - - left_type left()const { return arg1; } - middle_type middle()const { return arg2; } - right_type right()const { return arg3; } - const Arg1& left_ref()const{ return arg1; } - const Arg2& middle_ref()const{ return arg2; } - const Arg3& right_ref()const{ return arg3; } - - operator unmentionable_type()const - { - result_type r(*this); - return r ? &unmentionable::proc : 0; - } - - static const unsigned left_depth = left_type::depth + 1; - static const unsigned middle_depth = middle_type::depth + 1; - static const unsigned right_depth = right_type::depth + 1; - static const unsigned depth = left_depth > right_depth ? (left_depth > middle_depth ? left_depth : middle_depth) : (right_depth > middle_depth ? right_depth : middle_depth); -private: - typename big_number_exp_storage::type arg1; - typename big_number_exp_storage::type arg2; - typename big_number_exp_storage::type arg3; -}; - -} // namespace detail - -// -// Non-member operators for big_number: -// -// Unary operators first: -// -template -inline const big_number& operator + (const big_number& v) { return v; } -template -inline const detail::big_number_exp& operator + (const detail::big_number_exp& v) { return v; } -template -inline detail::big_number_exp > operator - (const big_number& v) { return v; } -template -inline detail::big_number_exp > operator - (const detail::big_number_exp& v) { return v; } -template -inline detail::big_number_exp > operator ~ (const big_number& v) { return v; } -template -inline detail::big_number_exp > operator ~ (const detail::big_number_exp& v) { return v; } -// -// Then addition: -// -template -inline detail::big_number_exp, big_number > - operator + (const big_number& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator + (const big_number& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator + (const V& a, const big_number& b) -{ - return detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator + (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, big_number > - operator + (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator + (const detail::big_number_exp& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator + (const detail::big_number_exp& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator + (const V& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::big_number_exp, typename detail::big_number_exp::left_type > - operator + (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, typename detail::big_number_exp::left_type >(a, b.left_ref()); -} -template -inline detail::big_number_exp, typename detail::big_number_exp::left_type > - operator + (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, typename detail::big_number_exp::left_type >(b, a.left_ref()); -} -template -inline detail::big_number_exp, big_number > - operator + (const big_number& a, const detail::big_number_exp >& b) -{ - return detail::big_number_exp, big_number >(a, b.left_ref()); -} -template -inline detail::big_number_exp, big_number > - operator + (const detail::big_number_exp >& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(b, a.left_ref()); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator + (const detail::big_number_exp >& a, const V& b) -{ - return detail::big_number_exp >(b, a.left_ref()); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator + (const V& a, const detail::big_number_exp >& b) -{ - return detail::big_number_exp, big_number >(a, b.left_ref()); -} -// -// Subtraction: -// -template -inline detail::big_number_exp, big_number > - operator - (const big_number& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator - (const big_number& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator - (const V& a, const big_number& b) -{ - return detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator - (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, big_number > - operator - (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator - (const detail::big_number_exp& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator - (const detail::big_number_exp& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator - (const V& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::big_number_exp, typename detail::big_number_exp::left_type > - operator - (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, typename detail::big_number_exp::left_type >(a, b.left_ref()); -} -template -inline detail::big_number_exp, typename detail::big_number_exp::left_type > > - operator - (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, typename detail::big_number_exp::left_type >(b, a.left_ref()); -} -template -inline detail::big_number_exp, big_number > - operator - (const big_number& a, const detail::big_number_exp >& b) -{ - return detail::big_number_exp, big_number >(a, b.left_ref()); -} -template -inline detail::big_number_exp, big_number > > - operator - (const detail::big_number_exp >& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(b, a.left_ref()); -} -template -inline typename enable_if, detail::big_number_exp, V > > >::type - operator - (const detail::big_number_exp >& a, const V& b) -{ - return detail::big_number_exp >(b, a.left_ref()); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator - (const V& a, const detail::big_number_exp >& b) -{ - return detail::big_number_exp >(a, b.left_ref()); -} -// -// Multiplication: -// -template -inline detail::big_number_exp, big_number > - operator * (const big_number& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator * (const big_number& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator * (const V& a, const big_number& b) -{ - return detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator * (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, big_number > - operator * (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator * (const detail::big_number_exp& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator * (const detail::big_number_exp& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator * (const V& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::big_number_exp, typename detail::big_number_exp::left_type > > - operator * (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, typename detail::big_number_exp::left_type > (a, b.left_ref()); -} -template -inline detail::big_number_exp, typename detail::big_number_exp::left_type > > - operator * (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, typename detail::big_number_exp::left_type >(b, a.left_ref()); -} -template -inline detail::big_number_exp, big_number > > - operator * (const big_number& a, const detail::big_number_exp >& b) -{ - return detail::big_number_exp, big_number >(a, b.left_ref()); -} -template -inline detail::big_number_exp, big_number > > - operator * (const detail::big_number_exp >& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(b, a.left_ref()); -} -template -inline typename enable_if, detail::big_number_exp, V > > >::type - operator * (const detail::big_number_exp >& a, const V& b) -{ - return detail::big_number_exp, V >(a.left_ref(), b); -} -template -inline typename enable_if, detail::big_number_exp, V > > >::type - operator * (const V& a, const detail::big_number_exp >& b) -{ - return detail::big_number_exp, V >(b.left_ref(), a); -} -// -// Division: -// -template -inline detail::big_number_exp, big_number > - operator / (const big_number& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator / (const big_number& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator / (const V& a, const big_number& b) -{ - return detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator / (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, big_number > - operator / (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator / (const detail::big_number_exp& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator / (const detail::big_number_exp& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator / (const V& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::big_number_exp, typename detail::big_number_exp::left_type > > - operator / (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, typename detail::big_number_exp::left_type >(a, b.left_ref()); -} -template -inline detail::big_number_exp::left_type, big_number > > - operator / (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp::left_type, big_number >(a.left_ref(), b); -} -template -inline detail::big_number_exp, big_number > > - operator / (const big_number& a, const detail::big_number_exp >& b) -{ - return detail::big_number_exp, big_number >(a, b.left_ref()); -} -template -inline detail::big_number_exp, big_number > > - operator / (const detail::big_number_exp >& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a.left_ref(), b); -} -template -inline typename enable_if, detail::big_number_exp, V > > >::type - operator / (const detail::big_number_exp >& a, const V& b) -{ - return detail::big_number_exp, V>(a.left_ref(), b); -} -template -inline typename enable_if, detail::big_number_exp > > >::type - operator / (const V& a, const detail::big_number_exp >& b) -{ - return detail::big_number_exp >(a, b.left_ref()); -} -// -// Modulus: -// -template -inline detail::big_number_exp, big_number > - operator % (const big_number& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator % (const big_number& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator % (const V& a, const big_number& b) -{ - return detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator % (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, big_number > - operator % (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator % (const detail::big_number_exp& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator % (const detail::big_number_exp& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator % (const V& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp >(a, b); -} -// -// Left shift: -// -template -inline typename enable_if, detail::big_number_exp, I > >::type - operator << (const big_number& a, const I& b) -{ - return detail::big_number_exp, I>(a, b); -} -template -inline typename enable_if, detail::big_number_exp, I> >::type - operator << (const detail::big_number_exp& a, const I& b) -{ - return detail::big_number_exp, I>(a, b); -} -// -// Right shift: -// -template -inline typename enable_if, detail::big_number_exp, I > >::type - operator >> (const big_number& a, const I& b) -{ - return detail::big_number_exp, I>(a, b); -} -template -inline typename enable_if, detail::big_number_exp, I> >::type - operator >> (const detail::big_number_exp& a, const I& b) -{ - return detail::big_number_exp, I>(a, b); -} -// -// Bitwise AND: -// -template -inline detail::big_number_exp, big_number > - operator & (const big_number& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator & (const big_number& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator & (const V& a, const big_number& b) -{ - return detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator & (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, big_number > - operator & (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator & (const detail::big_number_exp& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator & (const detail::big_number_exp& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator & (const V& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp >(a, b); -} -// -// Bitwise OR: -// -template -inline detail::big_number_exp, big_number > - operator| (const big_number& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator| (const big_number& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator| (const V& a, const big_number& b) -{ - return detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator| (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, big_number > - operator| (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator| (const detail::big_number_exp& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator| (const detail::big_number_exp& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator| (const V& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp >(a, b); -} -// -// Bitwise XOR: -// -template -inline detail::big_number_exp, big_number > - operator^ (const big_number& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator^ (const big_number& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator^ (const V& a, const big_number& b) -{ - return detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator^ (const big_number& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline detail::big_number_exp, big_number > - operator^ (const detail::big_number_exp& a, const big_number& b) -{ - return detail::big_number_exp, big_number >(a, b); -} -template -inline detail::big_number_exp, detail::big_number_exp > - operator^ (const detail::big_number_exp& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp, detail::big_number_exp >(a, b); -} -template -inline typename enable_if, detail::big_number_exp, V > >::type - operator^ (const detail::big_number_exp& a, const V& b) -{ - return detail::big_number_exp, V >(a, b); -} -template -inline typename enable_if, detail::big_number_exp > >::type - operator^ (const V& a, const detail::big_number_exp& b) -{ - return detail::big_number_exp >(a, b); -} - -// -// Traits class, lets us know what kind of number we have, defaults to a floating point type: -// -enum number_category_type -{ - number_kind_integer = 0, - number_kind_floating_point = 1, - number_kind_rational = 2, - number_kind_fixed_point = 3 -}; - -template -struct number_category : public mpl::int_ {}; -template -struct number_category > : public number_category{}; -template -struct number_category > : public number_category::result_type>{}; - -}} // namespaces - -namespace boost{ namespace math{ namespace tools{ - -template -struct promote_arg; - -template -struct promote_arg > -{ - typedef typename boost::math::detail::big_number_exp::result_type type; -}; - -}}} - -#endif // BOOST_MATH_BIG_NUM_BASE_HPP - - diff --git a/include/boost/math/big_number/default_ops.hpp b/include/boost/math/big_number/default_ops.hpp deleted file mode 100644 index ea034e00..00000000 --- a/include/boost/math/big_number/default_ops.hpp +++ /dev/null @@ -1,903 +0,0 @@ -/////////////////////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_BIG_NUM_DEF_OPS -#define BOOST_MATH_BIG_NUM_DEF_OPS - -#include -#include -#include -#include -#include -#include - -namespace boost{ namespace math{ namespace big_num_default_ops{ - -// -// Default versions of mixed arithmetic, these just construct a temporary -// from the arithmetic value and then do the arithmetic on that: -// -template -inline typename enable_if, is_convertible, is_same > >::type - add(T& result, V const& v) -{ - T t; - t = v; - add(result, t); -} -template -inline typename enable_if, is_convertible, is_same > >::type - subtract(T& result, V const& v) -{ - T t; - t = v; - subtract(result, t); -} -template -inline typename enable_if, is_convertible, is_same > >::type - multiply(T& result, V const& v) -{ - T t; - t = v; - multiply(result, t); -} -template -inline typename enable_if, is_convertible, is_same > >::type - divide(T& result, V const& v) -{ - T t; - t = v; - divide(result, t); -} -template -inline typename enable_if, is_convertible, is_same > >::type - modulus(T& result, V const& v) -{ - T t; - t = v; - modulus(result, t); -} -template -inline typename enable_if, is_convertible, is_same > >::type - bitwise_and(T& result, V const& v) -{ - T t; - t = v; - bitwise_and(result, t); -} -template -inline typename enable_if, is_convertible, is_same > >::type - bitwise_or(T& result, V const& v) -{ - T t; - t = v; - bitwise_or(result, t); -} -template -inline typename enable_if, is_convertible, is_same > >::type - bitwise_xor(T& result, V const& v) -{ - T t; - t = v; - bitwise_xor(result, t); -} - -template -inline typename enable_if, is_convertible, is_same > >::type - complement(T& result, V const& v) -{ - T t; - t = v; - complement(result, t); -} - -template -inline bool is_same_object(const T& u, const T&v) -{ return &u == &v; } -template -inline bool is_same_object(const T& u, const U&v) -{ return false; } - -// -// Default versions of 3-arg arithmetic functions, these just forward to the 2 arg versions: -// -template -inline void add(T& t, const U& u, const V& v) -{ - if(is_same_object(t, v)) - { - add(t, u); - } - else if(is_same_object(t, u)) - { - add(t, v); - } - else - { - t = u; - add(t, v); - } -} -template -inline void subtract(T& t, const U& u, const V& v) -{ - if(is_same_object(t, u)) - subtract(t, v); - else if(is_same_object(t, v)) - { - subtract(t, u); - t.negate(); - } - else - { - t = u; - subtract(t, v); - } -} -template -inline void multiply(T& t, const U& u, const V& v) -{ - if(is_same_object(t, u)) - multiply(t, v); - else if(is_same_object(t, v)) - multiply(t, u); - else - { - t = u; - multiply(t, v); - } -} -template -inline void divide(T& t, const U& u, const V& v) -{ - if(is_same_object(t, u)) - divide(t, v); - else if(is_same_object(t, v)) - { - T temp = t; - divide(temp, u, v); - temp.swap(t); - } - else - { - t = u; - divide(t, v); - } -} -template -inline void modulus(T& t, const U& u, const V& v) -{ - if(is_same_object(t, u)) - modulus(t, v); - else if(is_same_object(t, v)) - { - T temp; - modulus(temp, u, v); - temp.swap(t); - } - else - { - t = u; - modulus(t, v); - } -} -template -inline void bitwise_and(T& t, const U& u, const V& v) -{ - if(is_same_object(t, u)) - bitwise_and(t, v); - else if(is_same_object(t, v)) - bitwise_and(t, u); - else - { - t = u; - bitwise_and(t, v); - } -} - -template -inline void bitwise_or(T& t, const U& u, const V& v) -{ - if(is_same_object(t, u)) - bitwise_or(t, v); - else if(is_same_object(t, v)) - bitwise_or(t, u); - else - { - t = u; - bitwise_or(t, v); - } -} - -template -inline void bitwise_xor(T& t, const U& u, const V& v) -{ - if(is_same_object(t, u)) - bitwise_xor(t, v); - else if(is_same_object(t, v)) - bitwise_xor(t, u); - else - { - t = u; - bitwise_xor(t, v); - } -} - -template -inline void increment(T& val) -{ - typedef typename mpl::front::type ui_type; - add(val, static_cast(1u)); -} - -template -inline void decrement(T& val) -{ - typedef typename mpl::front::type ui_type; - subtract(val, static_cast(1u)); -} - -template -inline void left_shift(T& result, const T& arg, const V val) -{ - result = arg; - left_shift(result, val); -} - -template -inline void right_shift(T& result, const T& arg, const V val) -{ - result = arg; - right_shift(result, val); -} - -template -inline bool is_zero(const T& val) -{ - typedef typename mpl::front::type ui_type; - return val.compare(static_cast(0)) == 0; -} -template -inline int get_sign(const T& val) -{ - typedef typename mpl::front::type ui_type; - return val.compare(static_cast(0)); -} - -template -struct has_enough_bits -{ - template - struct type : public mpl::and_ >, mpl::bool_::digits >= b> >{}; -}; - -template -struct terminal -{ - terminal(const R& v) : value(v){} - terminal(){} - terminal& operator = (R val) { value = val; } - R value; - operator R()const { return value; } -}; - -template -struct calculate_next_larger_type -{ - typedef typename mpl::if_< - is_signed, - typename B::signed_types, - typename mpl::if_< - is_unsigned, - typename B::unsigned_types, - typename B::real_types - >::type - >::type list_type; - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - list_type, - pred_type - >::type iter_type; - typedef typename mpl::eval_if< - is_same::type, iter_type>, - mpl::identity >, - mpl::deref - >::type type; -}; - -template -inline void convert_to(R* result, const B& backend) -{ - typedef typename calculate_next_larger_type::type next_type; - next_type n; - convert_to(&n, backend); - *result = static_cast(n); -} - -template -inline void convert_to(terminal* result, const B& backend) -{ - // - // We ran out of types to try for the convertion, try - // a lexical_cast and hope for the best: - // - result->value = boost::lexical_cast(backend.str(0, false)); -} - -// -// Functions: -// -template -void eval_abs(T& result, const T& arg) -{ - typedef typename T::signed_types type_list; - typedef typename mpl::front::type front; - *result = arg; - if(arg.compare(front(0)) < 0) - result->negate(); -} -template -void eval_fabs(T& result, const T& arg) -{ - typedef typename T::signed_types type_list; - typedef typename mpl::front::type front; - *result = arg; - if(arg.compare(front(0)) < 0) - result->negate(); -} - -template -inline int eval_fpclassify(const Backend& arg) -{ - return is_zero(arg) ? FP_ZERO : FP_NORMAL; -} - -template -inline void eval_fmod(T& result, const T& a, const T& b) -{ - if((&result == &a) || (&result == &b)) - { - T temp; - eval_fmod(temp, a, b); - result = temp; - } - T n; - divide(result, a, b); - if(get_sign(a) < 0) - eval_ceil(n, result); - else - eval_floor(n, result); - multiply(n, b); - subtract(result, a, n); -} - -// -// These have to implemented by the backend, declared here so that our macro generated code compiles OK. -// -template -typename enable_if_c::type eval_floor(); -template -typename enable_if_c::type eval_ceil(); -template -typename enable_if_c::type eval_trunc(); -template -typename enable_if_c::type eval_sqrt(); -template -typename enable_if_c::type eval_ldexp(); -template -typename enable_if_c::type eval_frexp(); -// -// TODO: implement default versions of these: -// -template -typename enable_if_c::type eval_exp(); -template -typename enable_if_c::type eval_log(); -template -typename enable_if_c::type eval_sin(); -template -typename enable_if_c::type eval_cos(); -template -typename enable_if_c::type eval_tan(); -template -typename enable_if_c::type eval_asin(); -template -typename enable_if_c::type eval_acos(); -template -typename enable_if_c::type eval_atan(); -template -typename enable_if_c::type eval_sinh(); -template -typename enable_if_c::type eval_cosh(); -template -typename enable_if_c::type eval_tanh(); -// -// These functions are implemented in separate files, but expanded inline here: -// -#include - -} - -template -class big_number; - -// -// Default versions of floating point classification routines: -// -template -inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& arg) -{ - using big_num_default_ops::eval_fpclassify; - return eval_fpclassify(arg.backend()); -} -template -inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) -{ - typedef typename detail::big_number_exp::result_type value_type; - return fpclassify(value_type(arg)); -} -template -inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& arg) -{ - int v = fpclassify(arg); - return (v != FP_INFINITE) && (v != FP_NAN); -} -template -inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) -{ - typedef typename detail::big_number_exp::result_type value_type; - return isfinite(value_type(arg)); -} -template -inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& arg) -{ - return fpclassify(arg) == FP_NAN; -} -template -inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) -{ - typedef typename detail::big_number_exp::result_type value_type; - return isnan(value_type(arg)); -} -template -inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& arg) -{ - return fpclassify(arg) == FP_INFINITE; -} -template -inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) -{ - typedef typename detail::big_number_exp::result_type value_type; - return isinf(value_type(arg)); -} -template -inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const big_number& arg) -{ - return fpclassify(arg) == FP_NORMAL; -} -template -inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::big_number_exp& arg) -{ - typedef typename detail::big_number_exp::result_type value_type; - return isnormal(value_type(arg)); -} - -template -inline int itrunc(const detail::big_number_exp& v, const Policy& pol) -{ - typedef typename detail::big_number_exp::result_type number_type; - number_type r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); - return r.template convert_to(); -} -template -inline int itrunc(const big_number& v, const Policy& pol) -{ - big_number r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); - return r.template convert_to(); -} -template -inline long ltrunc(const detail::big_number_exp& v, const Policy& pol) -{ - typedef typename detail::big_number_exp::result_result number_type; - number_type r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); - return r.template convert_to(); -} -template -inline long ltrunc(const big_number& v, const Policy& pol) -{ - big_number r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); - return r.template convert_to(); -} -#ifndef BOOST_NO_LONG_LONG -template -inline long long lltrunc(const detail::big_number_exp& v, const Policy& pol) -{ - typedef typename detail::big_number_exp::result_result number_type; - number_type r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); - return r.template convert_to(); -} -template -inline long long lltrunc(const big_number& v, const Policy& pol) -{ - big_number r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); - return r.template convert_to(); -} -#endif -template -inline int iround(const detail::big_number_exp& v, const Policy& pol) -{ - typedef typename detail::big_number_exp::result_result number_type; - number_type r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); - return r.template convert_to(); -} -template -inline int iround(const big_number& v, const Policy& pol) -{ - big_number r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); - return r.template convert_to(); -} -template -inline long lround(const detail::big_number_exp& v, const Policy& pol) -{ - typedef typename detail::big_number_exp::result_result number_type; - number_type r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); - return r.template convert_to(); -} -template -inline long lround(const big_number& v, const Policy& pol) -{ - big_number r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); - return r.template convert_to(); -} -#ifndef BOOST_NO_LONG_LONG -template -inline long long llround(const detail::big_number_exp& v, const Policy& pol) -{ - typedef typename detail::big_number_exp::result_result number_type; - number_type r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); - return r.template convert_to(); -} -template -inline long long llround(const big_number& v, const Policy& pol) -{ - big_number r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); - return r.template convert_to(); -} -#endif -// -// Overload of Boost.Math functions that find the wrong overload when used with big_number: -// -namespace detail{ - template T sinc_pi_imp(T); - template T sinhc_pi_imp(T); -} -template -inline big_number sinc_pi(const big_number& x) -{ - return detail::sinc_pi_imp(x); -} - -template -inline big_number sinc_pi(const big_number& x, const Policy&) -{ - return detail::sinc_pi_imp(x); -} - -template -inline big_number sinhc_pi(const big_number& x) -{ - return detail::sinhc_pi_imp(x); -} - -template -inline big_number sinhc_pi(const big_number& x, const Policy&) -{ - return boost::math::sinhc_pi(x); -} - -#define UNARY_OP_FUNCTOR(func)\ -namespace detail{\ -template \ -struct BOOST_JOIN(func, _funct)\ -{\ - void operator()(Backend& result, const Backend& arg)const\ - {\ - using big_num_default_ops::BOOST_JOIN(eval_,func);\ - BOOST_JOIN(eval_,func)(result, arg);\ - }\ -};\ -\ -}\ -\ -template \ -detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::big_number_exp \ -> \ -func(const detail::big_number_exp& arg)\ -{\ - return detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::big_number_exp \ -> (\ - detail::BOOST_JOIN(func, _funct) >::type>() \ - , arg \ - );\ -}\ -template \ -detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , big_number \ -> \ -func(const big_number& arg)\ -{\ - return detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , big_number \ - >(\ - detail::BOOST_JOIN(func, _funct)() \ - , arg \ - );\ -} - -#define BINARY_OP_FUNCTOR(func)\ -namespace detail{\ -template \ -struct BOOST_JOIN(func, _funct)\ -{\ - void operator()(Backend& result, const Backend& arg, const Backend& a)const\ - {\ - using big_num_default_ops:: BOOST_JOIN(eval_,func);\ - BOOST_JOIN(eval_,func)(result, arg, a);\ - }\ - template \ - void operator()(Backend& result, const Backend& arg, const Arithmetic& a)const\ - {\ - using big_num_default_ops:: BOOST_JOIN(eval_,func);\ - BOOST_JOIN(eval_,func)(result, arg, a);\ - }\ -};\ -\ -}\ -template \ -detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , big_number \ - , big_number \ -> \ -func(const big_number& arg, const big_number& a)\ -{\ - return detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , big_number \ - , big_number \ - >(\ - detail::BOOST_JOIN(func, _funct)() \ - , arg,\ - a\ - );\ -}\ -template \ -detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , big_number \ - , detail::big_number_exp \ -> \ -func(const big_number& arg, const detail::big_number_exp& a)\ -{\ - return detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , big_number \ - , detail::big_number_exp \ - >(\ - detail::BOOST_JOIN(func, _funct)() \ - , arg,\ - a\ - );\ -}\ -template \ -detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , detail::big_number_exp \ - , big_number \ -> \ -func(const detail::big_number_exp& arg, const big_number& a)\ -{\ - return detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , detail::big_number_exp \ - , big_number \ - >(\ - detail::BOOST_JOIN(func, _funct)() \ - , arg,\ - a\ - );\ -}\ -template \ -detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::big_number_exp \ - , detail::big_number_exp \ -> \ -func(const detail::big_number_exp& arg, const detail::big_number_exp& a)\ -{\ - return detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::big_number_exp \ - , detail::big_number_exp \ - >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ - , arg,\ - a\ - );\ -}\ -template \ -typename enable_if<\ - is_arithmetic,\ - detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , big_number \ - , Arithmetic\ - > \ ->::type \ -func(const big_number& arg, const Arithmetic& a)\ -{\ - return detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , big_number \ - , Arithmetic\ - >(\ - detail::BOOST_JOIN(func, _funct)() \ - , arg,\ - a\ - );\ -}\ -template \ -typename enable_if<\ - is_arithmetic,\ - detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::big_number_exp \ - , Arithmetic\ - > \ ->::type \ -func(const detail::big_number_exp& arg, const Arithmetic& a)\ -{\ - return detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::big_number_exp \ - , Arithmetic\ - >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ - , arg,\ - a\ - );\ -}\ - - -#define HETERO_BINARY_OP_FUNCTOR(func, Arg2)\ -namespace detail{\ -template \ -struct BOOST_JOIN(func, _funct)\ -{\ - void operator()(Backend& result, Backend const& arg, Arg2 a)const\ - {\ - using big_num_default_ops:: BOOST_JOIN(eval_,func);\ - BOOST_JOIN(eval_,func)(result, arg, a);\ - }\ -};\ -\ -}\ -\ -template \ -detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::big_number_exp \ - , Arg2\ -> \ -func(const detail::big_number_exp& arg, Arg2 const& a)\ -{\ - return detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::big_number_exp \ - , Arg2\ - >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ - , arg, a \ - );\ -}\ -template \ -detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , big_number \ - , Arg2\ -> \ -func(const big_number& arg, Arg2 const& a)\ -{\ - return detail::big_number_exp<\ - detail::function\ - , detail::BOOST_JOIN(func, _funct) \ - , big_number \ - , Arg2\ - >(\ - detail::BOOST_JOIN(func, _funct)() \ - , arg,\ - a\ - );\ -}\ - -UNARY_OP_FUNCTOR(abs) -UNARY_OP_FUNCTOR(fabs) -UNARY_OP_FUNCTOR(sqrt) -UNARY_OP_FUNCTOR(floor) -UNARY_OP_FUNCTOR(ceil) -UNARY_OP_FUNCTOR(trunc) -UNARY_OP_FUNCTOR(exp) -UNARY_OP_FUNCTOR(log) -UNARY_OP_FUNCTOR(cos) -UNARY_OP_FUNCTOR(sin) -UNARY_OP_FUNCTOR(tan) -UNARY_OP_FUNCTOR(asin) -UNARY_OP_FUNCTOR(acos) -UNARY_OP_FUNCTOR(atan) -UNARY_OP_FUNCTOR(cosh) -UNARY_OP_FUNCTOR(sinh) -UNARY_OP_FUNCTOR(tanh) - -HETERO_BINARY_OP_FUNCTOR(ldexp, int) -HETERO_BINARY_OP_FUNCTOR(frexp, int*) -BINARY_OP_FUNCTOR(pow) -BINARY_OP_FUNCTOR(fmod) - -#undef BINARY_OP_FUNCTOR -#undef UNARY_OP_FUNCTOR - -}} // namespaces - -#endif - diff --git a/include/boost/math/big_number/e_float.hpp b/include/boost/math/big_number/e_float.hpp deleted file mode 100644 index 9ce737c4..00000000 --- a/include/boost/math/big_number/e_float.hpp +++ /dev/null @@ -1,80 +0,0 @@ -/////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ - -#ifndef BOOST_MATH_EFX_BACKEND_HPP -#define BOOST_MATH_EFX_BACKEND_HPP - -#include -#include -#include -#include -#include - -namespace boost{ -namespace math{ - -typedef big_number > e_float; - -template<> -inline void arithmetic_backend::negate() -{ - m_value.negate(); -} -template<> -inline std::string arithmetic_backend::str(unsigned digits, bool scientific)const -{ - std::fstream os; - os << std::setprecision(digits ? digits : efx::e_float::ef_digits + 5); - if(scientific) - os << std::scientific; - std::string result; - this->data().wr_string(result, os); - return result; -} - -inline void eval_abs(arithmetic_backend& result, const arithmetic_backend& arg) -{ - result.data() = ef::fabs(arg.data()); -} - -inline void eval_fabs(arithmetic_backend& result, const arithmetic_backend& arg) -{ - result.data() = ef::fabs(arg.data()); -} - -inline bool is_zero(const arithmetic_backend& val) -{ - return val.data().iszero(); -} -inline int get_sign(const arithmetic_backend& val) -{ - return val.data().isneg() ? -1 : val.data().iszero() ? 0 : 1; -} - -inline void convert_to(boost::uintmax_t* result, const arithmetic_backend& val) -{ - *result = val.data().extract_unsigned_long_long(); -} -inline void convert_to(boost::intmax_t* result, const arithmetic_backend& val) -{ - *result = val.data().extract_signed_long_long(); -} -inline void convert_to(double* result, const arithmetic_backend& val) -{ - *result = val.data().extract_double(); -} -inline void convert_to(long double* result, const arithmetic_backend& val) -{ - *result = val.data().extract_long_double(); -} -inline int eval_fpclassify(const arithmetic_backend& val) -{ - return val.data().isinf() ? FP_INFINITE : val.data().isnan() ? FP_NAN : val.data().iszero() ? FP_ZERO : FP_NORMAL; -} - - -}} // namespaces - -#endif diff --git a/include/boost/math/big_number/gmp.hpp b/include/boost/math/big_number/gmp.hpp deleted file mode 100644 index 3ee95512..00000000 --- a/include/boost/math/big_number/gmp.hpp +++ /dev/null @@ -1,1532 +0,0 @@ -/////////////////////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_ER_GMP_BACKEND_HPP -#define BOOST_MATH_ER_GMP_BACKEND_HPP - -#include -#include -#include -#include -#include -#include -#include -#include - -namespace boost{ namespace math{ - -template -struct gmp_real; - -namespace detail{ - -template -struct gmp_real_imp -{ - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list real_types; - - gmp_real_imp(){} - - gmp_real_imp(const gmp_real_imp& o) - { - // - // We have to do an init followed by a set here, otherwise *this may be at - // a lower precision than o: seems like mpf_init_set copies just enough bits - // to get the right value, but if it's then used in further calculations - // things go badly wrong!! - // - mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); - mpf_set(m_data, o.m_data); - } -#ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real_imp(gmp_real_imp&& o) - { - m_data[0] = o.m_data[0]; - o.m_data[0]._mp_d = 0; - } -#endif - gmp_real_imp& operator = (const gmp_real_imp& o) - { - mpf_set(m_data, o.m_data); - return *this; - } -#ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real_imp& operator = (gmp_real_imp&& o) - { - mpf_swap(m_data, o.m_data); - return *this; - } -#endif - gmp_real_imp& operator = (boost::uintmax_t i) - { - boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); - unsigned shift = 0; - mpf_t t; - mpf_init2(t, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); - mpf_set_ui(m_data, 0); - while(i) - { - mpf_set_ui(t, static_cast(i & mask)); - if(shift) - mpf_mul_2exp(t, t, shift); - mpf_add(m_data, m_data, t); - shift += std::numeric_limits::digits; - i >>= std::numeric_limits::digits; - } - mpf_clear(t); - return *this; - } - gmp_real_imp& operator = (boost::intmax_t i) - { - bool neg = i < 0; - *this = static_cast(std::abs(i)); - if(neg) - mpf_neg(m_data, m_data); - return *this; - } - gmp_real_imp& operator = (unsigned long i) - { - mpf_set_ui(m_data, i); - return *this; - } - gmp_real_imp& operator = (long i) - { - mpf_set_si(m_data, i); - return *this; - } - gmp_real_imp& operator = (double d) - { - mpf_set_d(m_data, d); - return *this; - } - gmp_real_imp& operator = (long double a) - { - using std::frexp; - using std::ldexp; - using std::floor; - - if (a == 0) { - mpf_set_si(m_data, 0); - return *this; - } - - if (a == 1) { - mpf_set_si(m_data, 1); - return *this; - } - - BOOST_ASSERT(!(boost::math::isinf)(a)); - BOOST_ASSERT(!(boost::math::isnan)(a)); - - int e; - long double f, term; - mpf_init_set_ui(m_data, 0u); - - f = frexp(a, &e); - - static const int shift = std::numeric_limits::digits - 1; - - while(f) - { - // extract int sized bits from f: - f = ldexp(f, shift); - term = floor(f); - e -= shift; - mpf_mul_2exp(m_data, m_data, shift); - if(term > 0) - mpf_add_ui(m_data, m_data, static_cast(term)); - else - mpf_sub_ui(m_data, m_data, static_cast(-term)); - f -= term; - } - if(e > 0) - mpf_mul_2exp(m_data, m_data, e); - else if(e < 0) - mpf_div_2exp(m_data, m_data, -e); - return *this; - } - gmp_real_imp& operator = (const char* s) - { - mpf_set_str(m_data, s, 10); - return *this; - } - void swap(gmp_real_imp& o) - { - mpf_swap(m_data, o.m_data); - } - std::string str(unsigned digits, bool scientific)const - { - std::string result; - mp_exp_t e; - void *(*alloc_func_ptr) (size_t); - void *(*realloc_func_ptr) (void *, size_t, size_t); - void (*free_func_ptr) (void *, size_t); - const char* ps = mpf_get_str (0, &e, 10, digits, m_data); - std::ptrdiff_t sl = std::strlen(ps); - if(sl == 0) - return "0"; - if(*ps == '-') - --sl; // number of digits excluding sign. - if(!scientific - && (sl <= std::numeric_limits::digits10 + 1) - && (e >= sl) - && (sl <= std::numeric_limits::digits10 + 1)) - { - result = ps; - result.append(e-sl, '0'); - } - else - { - result = ps; - if(ps[0] == '-') - result.insert(2, 1, '.'); - else - result.insert(1, 1, '.'); - --e; - if(e) - result += "e" + lexical_cast(e); - } - mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); - (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); - return result; - } - ~gmp_real_imp() - { - if(m_data[0]._mp_d) - mpf_clear(m_data); - } - void negate() - { - mpf_neg(m_data, m_data); - } - int compare(const gmp_real& o)const - { - return mpf_cmp(m_data, o.m_data); - } - int compare(long i)const - { - return mpf_cmp_si(m_data, i); - } - int compare(unsigned long i)const - { - return mpf_cmp_ui(m_data, i); - } - template - int compare(V v)const - { - gmp_real d; - d = v; - return compare(d); - } - mpf_t& data() { return m_data; } - const mpf_t& data()const { return m_data; } -protected: - mpf_t m_data; - static unsigned& get_default_precision() - { - static unsigned val = 50; - return val; - } -}; - -} // namespace detail - -template -struct gmp_real : public detail::gmp_real_imp -{ - gmp_real() - { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - } - gmp_real(const gmp_real& o) : detail::gmp_real_imp(o) {} -#ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real(gmp_real&& o) : detail::gmp_real_imp(o) {} -#endif - gmp_real& operator=(const gmp_real& o) - { - *static_cast*>(this) = static_cast const&>(o); - return *this; - } -#ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real& operator=(gmp_real&& o) - { - *static_cast*>(this) = static_cast&&>(o); - return *this; - } -#endif - template - gmp_real& operator=(const V& v) - { - *static_cast*>(this) = v; - return *this; - } -}; - -template <> -struct gmp_real<0> : public detail::gmp_real_imp<0> -{ - gmp_real() - { - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); - } - gmp_real(unsigned digits10) - { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - } - gmp_real(const gmp_real& o) : detail::gmp_real_imp<0>(o) {} -#ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real(gmp_real&& o) : detail::gmp_real_imp<0>(o) {} -#endif - gmp_real(const gmp_real& o, unsigned digits10) - { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - *this = o; - } - - gmp_real& operator=(const gmp_real& o) - { - *static_cast*>(this) = static_cast const&>(o); - return *this; - } -#ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real& operator=(gmp_real&& o) - { - *static_cast*>(this) = static_cast &&>(o); - return *this; - } -#endif - template - gmp_real& operator=(const V& v) - { - *static_cast*>(this) = v; - return *this; - } - static unsigned default_precision() - { - return get_default_precision(); - } - static void default_precision(unsigned v) - { - get_default_precision() = v; - } - unsigned precision()const - { - return mpf_get_prec(this->m_data) * 301L / 1000 - 1; - } - void precision(unsigned digits10) - { - mpf_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); - } -}; - -template -inline void add(gmp_real& result, const gmp_real& o) -{ - mpf_add(result.data(), result.data(), o.data()); -} -template -inline void subtract(gmp_real& result, const gmp_real& o) -{ - mpf_sub(result.data(), result.data(), o.data()); -} -template -inline void multiply(gmp_real& result, const gmp_real& o) -{ - mpf_mul(result.data(), result.data(), o.data()); -} -template -inline void divide(gmp_real& result, const gmp_real& o) -{ - mpf_div(result.data(), result.data(), o.data()); -} -template -inline void add(gmp_real& result, unsigned long i) -{ - mpf_add_ui(result.data(), result.data(), i); -} -template -inline void subtract(gmp_real& result, unsigned long i) -{ - mpf_sub_ui(result.data(), result.data(), i); -} -template -inline void multiply(gmp_real& result, unsigned long i) -{ - mpf_mul_ui(result.data(), result.data(), i); -} -template -inline void divide(gmp_real& result, unsigned long i) -{ - mpf_div_ui(result.data(), result.data(), i); -} -template -inline void add(gmp_real& result, long i) -{ - if(i > 0) - mpf_add_ui(result.data(), result.data(), i); - else - mpf_sub_ui(result.data(), result.data(), std::abs(i)); -} -template -inline void subtract(gmp_real& result, long i) -{ - if(i > 0) - mpf_sub_ui(result.data(), result.data(), i); - else - mpf_add_ui(result.data(), result.data(), std::abs(i)); -} -template -inline void multiply(gmp_real& result, long i) -{ - mpf_mul_ui(result.data(), result.data(), std::abs(i)); - if(i < 0) - mpf_neg(result.data(), result.data()); -} -template -inline void divide(gmp_real& result, long i) -{ - mpf_div_ui(result.data(), result.data(), std::abs(i)); - if(i < 0) - mpf_neg(result.data(), result.data()); -} -// -// Specialised 3 arg versions of the basic operators: -// -template -inline void add(gmp_real& a, const gmp_real& x, const gmp_real& y) -{ - mpf_add(a.data(), x.data(), y.data()); -} -template -inline void add(gmp_real& a, const gmp_real& x, unsigned long y) -{ - mpf_add_ui(a.data(), x.data(), y); -} -template -inline void add(gmp_real& a, const gmp_real& x, long y) -{ - if(y < 0) - mpf_sub_ui(a.data(), x.data(), -y); - else - mpf_add_ui(a.data(), x.data(), y); -} -template -inline void add(gmp_real& a, unsigned long x, const gmp_real& y) -{ - mpf_add_ui(a.data(), y.data(), x); -} -template -inline void add(gmp_real& a, long x, const gmp_real& y) -{ - if(x < 0) - { - mpf_ui_sub(a.data(), -x, y.data()); - mpf_neg(a.data(), a.data()); - } - else - mpf_add_ui(a.data(), y.data(), x); -} -template -inline void subtract(gmp_real& a, const gmp_real& x, const gmp_real& y) -{ - mpf_sub(a.data(), x.data(), y.data()); -} -template -inline void subtract(gmp_real& a, const gmp_real& x, unsigned long y) -{ - mpf_sub_ui(a.data(), x.data(), y); -} -template -inline void subtract(gmp_real& a, const gmp_real& x, long y) -{ - if(y < 0) - mpf_add_ui(a.data(), x.data(), -y); - else - mpf_sub_ui(a.data(), x.data(), y); -} -template -inline void subtract(gmp_real& a, unsigned long x, const gmp_real& y) -{ - mpf_ui_sub(a.data(), x, y.data()); -} -template -inline void subtract(gmp_real& a, long x, const gmp_real& y) -{ - if(x < 0) - { - mpf_add_ui(a.data(), y.data(), -x); - mpf_neg(a.data(), a.data()); - } - else - mpf_ui_sub(a.data(), x, y.data()); -} - -template -inline void multiply(gmp_real& a, const gmp_real& x, const gmp_real& y) -{ - mpf_mul(a.data(), x.data(), y.data()); -} -template -inline void multiply(gmp_real& a, const gmp_real& x, unsigned long y) -{ - mpf_mul_ui(a.data(), x.data(), y); -} -template -inline void multiply(gmp_real& a, const gmp_real& x, long y) -{ - if(y < 0) - { - mpf_mul_ui(a.data(), x.data(), -y); - a.negate(); - } - else - mpf_mul_ui(a.data(), x.data(), y); -} -template -inline void multiply(gmp_real& a, unsigned long x, const gmp_real& y) -{ - mpf_mul_ui(a.data(), y.data(), x); -} -template -inline void multiply(gmp_real& a, long x, const gmp_real& y) -{ - if(x < 0) - { - mpf_mul_ui(a.data(), y.data(), -x); - mpf_neg(a.data(), a.data()); - } - else - mpf_mul_ui(a.data(), y.data(), x); -} - -template -inline void divide(gmp_real& a, const gmp_real& x, const gmp_real& y) -{ - mpf_div(a.data(), x.data(), y.data()); -} -template -inline void divide(gmp_real& a, const gmp_real& x, unsigned long y) -{ - mpf_div_ui(a.data(), x.data(), y); -} -template -inline void divide(gmp_real& a, const gmp_real& x, long y) -{ - if(y < 0) - { - mpf_div_ui(a.data(), x.data(), -y); - a.negate(); - } - else - mpf_div_ui(a.data(), x.data(), y); -} -template -inline void divide(gmp_real& a, unsigned long x, const gmp_real& y) -{ - mpf_ui_div(a.data(), x, y.data()); -} -template -inline void divide(gmp_real& a, long x, const gmp_real& y) -{ - if(x < 0) - { - mpf_ui_div(a.data(), -x, y.data()); - mpf_neg(a.data(), a.data()); - } - else - mpf_ui_div(a.data(), x, y.data()); -} - -template -inline bool is_zero(const gmp_real& val) -{ - return mpf_sgn(val.data()) == 0; -} -template -inline int get_sign(const gmp_real& val) -{ - return mpf_sgn(val.data()); -} - -template -inline void convert_to(unsigned long* result, const gmp_real& val) -{ - *result = mpf_get_ui(val.data()); -} -template -inline void convert_to(long* result, const gmp_real& val) -{ - *result = mpf_get_si(val.data()); -} -template -inline void convert_to(double* result, const gmp_real& val) -{ - *result = mpf_get_d(val.data()); -} - -// -// Native non-member operations: -// -template -inline void eval_sqrt(gmp_real& result, const gmp_real& val) -{ - mpf_sqrt(result.data(), val.data()); -} - -template -inline void eval_abs(gmp_real& result, const gmp_real& val) -{ - mpf_abs(result.data(), val.data()); -} - -template -inline void eval_fabs(gmp_real& result, const gmp_real& val) -{ - mpf_abs(result.data(), val.data()); -} -template -inline void eval_ceil(gmp_real& result, const gmp_real& val) -{ - mpf_ceil(result.data(), val.data()); -} -template -inline void eval_floor(gmp_real& result, const gmp_real& val) -{ - mpf_floor(result.data(), val.data()); -} -template -inline void eval_trunc(gmp_real& result, const gmp_real& val) -{ - mpf_trunc(result.data(), val.data()); -} -template -inline void eval_ldexp(gmp_real& result, const gmp_real& val, long e) -{ - if(e > 0) - mpf_mul_2exp(result.data(), val.data(), e); - else if(e < 0) - mpf_div_2exp(result.data(), val.data(), -e); -} -template -inline void eval_frexp(gmp_real& result, const gmp_real& val, int* e) -{ - long v; - mpf_get_d_2exp(&v, val.data()); - *e = v; - eval_ldexp(result, val, -v); -} -template -inline void eval_frexp(gmp_real& result, const gmp_real& val, long* e) -{ - mpf_get_d_2exp(e, val.data()); - eval_ldexp(result, val, -*e); -} - -struct gmp_int -{ - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list real_types; - - gmp_int() - { - mpz_init(this->m_data); - } - gmp_int(const gmp_int& o) - { - mpz_init_set(m_data, o.m_data); - } - gmp_int& operator = (const gmp_int& o) - { - mpz_set(m_data, o.m_data); - return *this; - } - gmp_int& operator = (boost::uintmax_t i) - { - boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); - unsigned shift = 0; - mpz_t t; - mpz_init(m_data); - mpz_init(t); - while(i) - { - mpz_set_ui(t, static_cast(i & mask)); - if(shift) - mpz_mul_2exp(t, t, shift); - mpz_add(m_data, m_data, t); - shift += std::numeric_limits::digits; - i >>= std::numeric_limits::digits; - } - mpz_clear(t); - return *this; - } - gmp_int& operator = (boost::intmax_t i) - { - bool neg = i < 0; - *this = static_cast(std::abs(i)); - if(neg) - mpz_neg(m_data, m_data); - return *this; - } - gmp_int& operator = (unsigned long i) - { - mpz_set_ui(m_data, i); - return *this; - } - gmp_int& operator = (long i) - { - mpz_set_si(m_data, i); - return *this; - } - gmp_int& operator = (double d) - { - mpz_set_d(m_data, d); - return *this; - } - gmp_int& operator = (long double a) - { - using std::frexp; - using std::ldexp; - using std::floor; - - if (a == 0) { - mpz_set_si(m_data, 0); - return *this; - } - - if (a == 1) { - mpz_set_si(m_data, 1); - return *this; - } - - BOOST_ASSERT(!(boost::math::isinf)(a)); - BOOST_ASSERT(!(boost::math::isnan)(a)); - - int e; - long double f, term; - mpz_init_set_ui(m_data, 0u); - - f = frexp(a, &e); - - static const int shift = std::numeric_limits::digits - 1; - - while(f) - { - // extract int sized bits from f: - f = ldexp(f, shift); - term = floor(f); - e -= shift; - mpz_mul_2exp(m_data, m_data, shift); - if(term > 0) - mpz_add_ui(m_data, m_data, static_cast(term)); - else - mpz_sub_ui(m_data, m_data, static_cast(-term)); - f -= term; - } - if(e > 0) - mpz_mul_2exp(m_data, m_data, e); - else if(e < 0) - mpz_div_2exp(m_data, m_data, -e); - return *this; - } - gmp_int& operator = (const char* s) - { - mpz_set_str(m_data, s, 10); - return *this; - } - void swap(gmp_int& o) - { - mpz_swap(m_data, o.m_data); - } - std::string str(unsigned /*digits*/, bool /*scientific*/)const - { - void *(*alloc_func_ptr) (size_t); - void *(*realloc_func_ptr) (void *, size_t, size_t); - void (*free_func_ptr) (void *, size_t); - const char* ps = mpz_get_str (0, 10, m_data); - std::string s = ps; - mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); - (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); - return s; - } - ~gmp_int() - { - mpz_clear(m_data); - } - void negate() - { - mpz_neg(m_data, m_data); - } - int compare(const gmp_int& o)const - { - return mpz_cmp(m_data, o.m_data); - } - int compare(long i)const - { - return mpz_cmp_si(m_data, i); - } - int compare(unsigned long i)const - { - return mpz_cmp_ui(m_data, i); - } - template - int compare(V v)const - { - gmp_int d; - d = v; - return compare(d); - } - mpz_t& data() { return m_data; } - const mpz_t& data()const { return m_data; } -protected: - mpz_t m_data; -}; - -inline void add(gmp_int& t, const gmp_int& o) -{ - mpz_add(t.data(), t.data(), o.data()); -} -inline void subtract(gmp_int& t, const gmp_int& o) -{ - mpz_sub(t.data(), t.data(), o.data()); -} -inline void multiply(gmp_int& t, const gmp_int& o) -{ - mpz_mul(t.data(), t.data(), o.data()); -} -inline void divide(gmp_int& t, const gmp_int& o) -{ - mpz_div(t.data(), t.data(), o.data()); -} -inline void modulus(gmp_int& t, const gmp_int& o) -{ - bool neg = mpz_sgn(t.data()) < 0; - bool neg2 = mpz_sgn(o.data()) < 0; - mpz_mod(t.data(), t.data(), o.data()); - if(neg) - { - if(!neg2) - t.negate(); - mpz_add(t.data(), t.data(), o.data()); - if(!neg2) - t.negate(); - } -} -inline void add(gmp_int& t, unsigned long i) -{ - mpz_add_ui(t.data(), t.data(), i); -} -inline void subtract(gmp_int& t, unsigned long i) -{ - mpz_sub_ui(t.data(), t.data(), i); -} -inline void multiply(gmp_int& t, unsigned long i) -{ - mpz_mul_ui(t.data(), t.data(), i); -} -inline void modulus(gmp_int& t, unsigned long i) -{ - bool neg = mpz_sgn(t.data()) < 0; - mpz_mod_ui(t.data(), t.data(), i); - if(neg) - { - t.negate(); - mpz_add_ui(t.data(), t.data(), i); - t.negate(); - } -} -inline void divide(gmp_int& t, unsigned long i) -{ - mpz_div_ui(t.data(), t.data(), i); -} -inline void add(gmp_int& t, long i) -{ - if(i > 0) - mpz_add_ui(t.data(), t.data(), i); - else - mpz_sub_ui(t.data(), t.data(), -i); -} -inline void subtract(gmp_int& t, long i) -{ - if(i > 0) - mpz_sub_ui(t.data(), t.data(), i); - else - mpz_add_ui(t.data(), t.data(), -i); -} -inline void multiply(gmp_int& t, long i) -{ - mpz_mul_ui(t.data(), t.data(), std::abs(i)); - if(i < 0) - mpz_neg(t.data(), t.data()); -} -inline void modulus(gmp_int& t, long i) -{ - bool neg = mpz_sgn(t.data()) < 0; - bool neg2 = i < 0; - mpz_mod_ui(t.data(), t.data(), std::abs(i)); - if(neg) - { - if(!neg2) - { - t.negate(); - mpz_add_ui(t.data(), t.data(), std::abs(i)); - t.negate(); - } - else - { - mpz_sub_ui(t.data(), t.data(), std::abs(i)); - } - } -} -inline void divide(gmp_int& t, long i) -{ - mpz_div_ui(t.data(), t.data(), std::abs(i)); - if(i < 0) - mpz_neg(t.data(), t.data()); -} -template -inline void left_shift(gmp_int& t, UI i) -{ - mpz_mul_2exp(t.data(), t.data(), static_cast(i)); -} -template -inline void right_shift(gmp_int& t, UI i) -{ - mpz_fdiv_q_2exp(t.data(), t.data(), static_cast(i)); -} -template -inline void left_shift(gmp_int& t, const gmp_int& v, UI i) -{ - mpz_mul_2exp(t.data(), v.data(), static_cast(i)); -} -template -inline void right_shift(gmp_int& t, const gmp_int& v, UI i) -{ - mpz_fdiv_q_2exp(t.data(), v.data(), static_cast(i)); -} - -inline void bitwise_and(gmp_int& result, const gmp_int& v) -{ - mpz_and(result.data(), result.data(), v.data()); -} - -inline void bitwise_or(gmp_int& result, const gmp_int& v) -{ - mpz_ior(result.data(), result.data(), v.data()); -} - -inline void bitwise_xor(gmp_int& result, const gmp_int& v) -{ - mpz_xor(result.data(), result.data(), v.data()); -} - -inline void add(gmp_int& t, const gmp_int& p, const gmp_int& o) -{ - mpz_add(t.data(), p.data(), o.data()); -} -inline void subtract(gmp_int& t, const gmp_int& p, const gmp_int& o) -{ - mpz_sub(t.data(), p.data(), o.data()); -} -inline void multiply(gmp_int& t, const gmp_int& p, const gmp_int& o) -{ - mpz_mul(t.data(), p.data(), o.data()); -} -inline void divide(gmp_int& t, const gmp_int& p, const gmp_int& o) -{ - mpz_div(t.data(), p.data(), o.data()); -} -inline void modulus(gmp_int& t, const gmp_int& p, const gmp_int& o) -{ - bool neg = mpz_sgn(p.data()) < 0; - bool neg2 = mpz_sgn(o.data()) < 0; - mpz_mod(t.data(), p.data(), o.data()); - if(neg) - { - if(!neg2) - t.negate(); - mpz_add(t.data(), t.data(), o.data()); - if(!neg2) - t.negate(); - } -} -inline void add(gmp_int& t, const gmp_int& p, unsigned long i) -{ - mpz_add_ui(t.data(), p.data(), i); -} -inline void subtract(gmp_int& t, const gmp_int& p, unsigned long i) -{ - mpz_sub_ui(t.data(), p.data(), i); -} -inline void multiply(gmp_int& t, const gmp_int& p, unsigned long i) -{ - mpz_mul_ui(t.data(), p.data(), i); -} -inline void modulus(gmp_int& t, const gmp_int& p, unsigned long i) -{ - bool neg = mpz_sgn(p.data()) < 0; - mpz_mod_ui(t.data(), p.data(), i); - if(neg) - { - t.negate(); - mpz_add_ui(t.data(), t.data(), i); - t.negate(); - } -} -inline void divide(gmp_int& t, const gmp_int& p, unsigned long i) -{ - mpz_div_ui(t.data(), p.data(), i); -} -inline void add(gmp_int& t, const gmp_int& p, long i) -{ - if(i > 0) - mpz_add_ui(t.data(), p.data(), i); - else - mpz_sub_ui(t.data(), p.data(), -i); -} -inline void subtract(gmp_int& t, const gmp_int& p, long i) -{ - if(i > 0) - mpz_sub_ui(t.data(), p.data(), i); - else - mpz_add_ui(t.data(), p.data(), -i); -} -inline void multiply(gmp_int& t, const gmp_int& p, long i) -{ - mpz_mul_ui(t.data(), p.data(), std::abs(i)); - if(i < 0) - mpz_neg(t.data(), t.data()); -} -inline void modulus(gmp_int& t, const gmp_int& p, long i) -{ - bool neg = mpz_sgn(p.data()) < 0; - bool neg2 = i < 0; - mpz_mod_ui(t.data(), p.data(), std::abs(i)); - if(neg) - { - if(!neg2) - { - t.negate(); - mpz_add_ui(t.data(), t.data(), std::abs(i)); - t.negate(); - } - else - { - mpz_sub_ui(t.data(), t.data(), std::abs(i)); - } - } -} -inline void divide(gmp_int& t, const gmp_int& p, long i) -{ - mpz_div_ui(t.data(), p.data(), std::abs(i)); - if(i < 0) - mpz_neg(t.data(), t.data()); -} - -inline void bitwise_and(gmp_int& result, const gmp_int& u, const gmp_int& v) -{ - mpz_and(result.data(), u.data(), v.data()); -} - -inline void bitwise_or(gmp_int& result, const gmp_int& u, const gmp_int& v) -{ - mpz_ior(result.data(), u.data(), v.data()); -} - -inline void bitwise_xor(gmp_int& result, const gmp_int& u, const gmp_int& v) -{ - mpz_xor(result.data(), u.data(), v.data()); -} - -inline void complement(gmp_int& result, const gmp_int& u) -{ - mpz_com(result.data(), u.data()); -} - -inline bool is_zero(const gmp_int& val) -{ - return mpz_sgn(val.data()) == 0; -} -inline int get_sign(const gmp_int& val) -{ - return mpz_sgn(val.data()); -} -inline void convert_to(unsigned long* result, const gmp_int& val) -{ - *result = mpz_get_ui(val.data()); -} -inline void convert_to(long* result, const gmp_int& val) -{ - *result = mpz_get_si(val.data()); -} -inline void convert_to(double* result, const gmp_int& val) -{ - *result = mpz_get_d(val.data()); -} - -inline void eval_abs(gmp_int& result, const gmp_int& val) -{ - mpz_abs(result.data(), val.data()); -} - -struct gmp_rational; -void add(gmp_rational& t, const gmp_rational& o); - -struct gmp_rational -{ - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list real_types; - - gmp_rational() - { - mpq_init(this->m_data); - } - gmp_rational(const gmp_rational& o) - { - mpq_init(m_data); - mpq_set(m_data, o.m_data); - } - gmp_rational& operator = (const gmp_rational& o) - { - mpq_set(m_data, o.m_data); - return *this; - } - gmp_rational& operator = (boost::uintmax_t i) - { - boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); - unsigned shift = 0; - mpq_t t; - mpq_init(m_data); - mpq_init(t); - while(i) - { - mpq_set_ui(t, static_cast(i & mask), 1); - if(shift) - mpq_mul_2exp(t, t, shift); - mpq_add(m_data, m_data, t); - shift += std::numeric_limits::digits; - i >>= std::numeric_limits::digits; - } - mpq_clear(t); - return *this; - } - gmp_rational& operator = (boost::intmax_t i) - { - bool neg = i < 0; - *this = static_cast(std::abs(i)); - if(neg) - mpq_neg(m_data, m_data); - return *this; - } - gmp_rational& operator = (unsigned long i) - { - mpq_set_ui(m_data, i, 1); - return *this; - } - gmp_rational& operator = (long i) - { - mpq_set_si(m_data, i, 1); - return *this; - } - gmp_rational& operator = (double d) - { - mpq_set_d(m_data, d); - return *this; - } - gmp_rational& operator = (long double a) - { - using std::frexp; - using std::ldexp; - using std::floor; - using big_num_default_ops::add; - using big_num_default_ops::subtract; - - if (a == 0) { - mpq_set_si(m_data, 0, 1); - return *this; - } - - if (a == 1) { - mpq_set_si(m_data, 1, 1); - return *this; - } - - BOOST_ASSERT(!(boost::math::isinf)(a)); - BOOST_ASSERT(!(boost::math::isnan)(a)); - - int e; - long double f, term; - mpq_init(m_data); - mpq_set_ui(m_data, 0u, 1); - gmp_rational t; - - f = frexp(a, &e); - - static const int shift = std::numeric_limits::digits - 1; - - while(f) - { - // extract int sized bits from f: - f = ldexp(f, shift); - term = floor(f); - e -= shift; - mpq_mul_2exp(m_data, m_data, shift); - t = static_cast(term); - add(*this, t); - f -= term; - } - if(e > 0) - mpq_mul_2exp(m_data, m_data, e); - else if(e < 0) - mpq_div_2exp(m_data, m_data, -e); - return *this; - } - gmp_rational& operator = (const char* s) - { - mpq_set_str(m_data, s, 10); - return *this; - } - void swap(gmp_rational& o) - { - mpq_swap(m_data, o.m_data); - } - std::string str(unsigned /*digits*/, bool /*scientific*/)const - { - void *(*alloc_func_ptr) (size_t); - void *(*realloc_func_ptr) (void *, size_t, size_t); - void (*free_func_ptr) (void *, size_t); - const char* ps = mpq_get_str (0, 10, m_data); - std::string s = ps; - mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); - (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); - return s; - } - ~gmp_rational() - { - mpq_clear(m_data); - } - void negate() - { - mpq_neg(m_data, m_data); - } - int compare(const gmp_rational& o)const - { - return mpq_cmp(m_data, o.m_data); - } - template - int compare(V v)const - { - gmp_rational d; - d = v; - return compare(d); - } - int compare(unsigned long v) - { - return mpq_cmp_ui(m_data, v, 1); - } - int compare(long v) - { - return mpq_cmp_si(m_data, v, 1); - } - mpq_t& data() { return m_data; } - const mpq_t& data()const { return m_data; } -protected: - mpq_t m_data; -}; - -inline void add(gmp_rational& t, const gmp_rational& o) -{ - mpq_add(t.data(), t.data(), o.data()); -} -inline void subtract(gmp_rational& t, const gmp_rational& o) -{ - mpq_sub(t.data(), t.data(), o.data()); -} -inline void multiply(gmp_rational& t, const gmp_rational& o) -{ - mpq_mul(t.data(), t.data(), o.data()); -} -inline void divide(gmp_rational& t, const gmp_rational& o) -{ - mpq_div(t.data(), t.data(), o.data()); -} -inline void add(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) -{ - mpq_add(t.data(), p.data(), o.data()); -} -inline void subtract(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) -{ - mpq_sub(t.data(), p.data(), o.data()); -} -inline void multiply(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) -{ - mpq_mul(t.data(), p.data(), o.data()); -} -inline void divide(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) -{ - mpq_div(t.data(), p.data(), o.data()); -} - -inline bool is_zero(const gmp_rational& val) -{ - return mpq_sgn(val.data()) == 0; -} -inline int get_sign(const gmp_rational& val) -{ - return mpq_sgn(val.data()); -} -inline void convert_to(double* result, const gmp_rational& val) -{ - *result = mpq_get_d(val.data()); -} - -inline void convert_to(long* result, const gmp_rational& val) -{ - double r; - convert_to(&r, val); - *result = r; -} - -inline void convert_to(unsigned long* result, const gmp_rational& val) -{ - double r; - convert_to(&r, val); - *result = r; -} - -inline void eval_abs(gmp_rational& result, const gmp_rational& val) -{ - mpq_abs(result.data(), val.data()); -} - -template<> -struct number_category : public mpl::int_{}; -template<> -struct number_category : public mpl::int_{}; - -typedef big_number > mpf_real_50; -typedef big_number > mpf_real_100; -typedef big_number > mpf_real_500; -typedef big_number > mpf_real_1000; -typedef big_number > mpf_real; -typedef big_number mpz_int; -typedef big_number mpq_rational; - -}} // namespaces - -namespace std{ - -#ifdef BOOST_NO_NOEXCEPT -# define noexcept -#endif - -// -// numeric_limits [partial] specializations for the types declared in this header: -// -template -class numeric_limits > > -{ - typedef boost::math::big_number > number_type; -public: - BOOST_STATIC_CONSTEXPR bool is_specialized = true; - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept - { - initializer.do_nothing(); - static std::pair value; - if(!value.first) - { - value.first = true; - value.second = 1; - mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), LONG_MAX); - } - return value.second; - } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept - { - initializer.do_nothing(); - static std::pair value; - if(!value.first) - { - value.first = true; - value.second = 1; - mpf_mul_2exp(value.second.backend().data(), value.second.backend().data(), LONG_MAX - 1); - } - return value.second; - } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept - { - return -(max)(); - } - BOOST_STATIC_CONSTEXPR int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); - BOOST_STATIC_CONSTEXPR int digits10 = Digits10; - // Is this really correct??? - BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 1; - BOOST_STATIC_CONSTEXPR bool is_signed = true; - BOOST_STATIC_CONSTEXPR bool is_integer = false; - BOOST_STATIC_CONSTEXPR bool is_exact = false; - BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept - { - initializer.do_nothing(); - static std::pair value; - if(!value.first) - { - value.first = true; - value.second = 1; - mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits::digits - 1); - } - return value.second; - } - // What value should this be???? - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept - { - // returns epsilon/2 - initializer.do_nothing(); - static std::pair value; - if(!value.first) - { - value.first = true; - value.second = 1; - mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), digits); - } - return value.second; - } - BOOST_STATIC_CONSTEXPR long min_exponent = LONG_MIN; - BOOST_STATIC_CONSTEXPR long min_exponent10 = (LONG_MIN / 1000) * 301L; - BOOST_STATIC_CONSTEXPR long max_exponent = LONG_MAX; - BOOST_STATIC_CONSTEXPR long max_exponent10 = (LONG_MAX / 1000) * 301L; - BOOST_STATIC_CONSTEXPR bool has_infinity = false; - BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; - BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; - BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; - BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR bool is_iec559 = false; - BOOST_STATIC_CONSTEXPR bool is_bounded = true; - BOOST_STATIC_CONSTEXPR bool is_modulo = false; - BOOST_STATIC_CONSTEXPR bool traps = true; - BOOST_STATIC_CONSTEXPR bool tinyness_before = false; - BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest; - -private: - struct data_initializer - { - data_initializer() - { - std::numeric_limits > >::epsilon(); - std::numeric_limits > >::round_error(); - (std::numeric_limits > >::min)(); - (std::numeric_limits > >::max)(); - } - void do_nothing()const{} - }; - static const data_initializer initializer; -}; - -template -const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; - -template<> -class numeric_limits > > -{ - typedef boost::math::big_number > number_type; -public: - BOOST_STATIC_CONSTEXPR bool is_specialized = false; - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR int digits = 0; - BOOST_STATIC_CONSTEXPR int digits10 = 0; - BOOST_STATIC_CONSTEXPR int max_digits10 = 0; - BOOST_STATIC_CONSTEXPR bool is_signed = false; - BOOST_STATIC_CONSTEXPR bool is_integer = false; - BOOST_STATIC_CONSTEXPR bool is_exact = false; - BOOST_STATIC_CONSTEXPR int radix = 0; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR int min_exponent = 0; - BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; - BOOST_STATIC_CONSTEXPR int max_exponent = 0; - BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; - BOOST_STATIC_CONSTEXPR bool has_infinity = false; - BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; - BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; - BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; - BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR bool is_iec559 = false; - BOOST_STATIC_CONSTEXPR bool is_bounded = false; - BOOST_STATIC_CONSTEXPR bool is_modulo = false; - BOOST_STATIC_CONSTEXPR bool traps = false; - BOOST_STATIC_CONSTEXPR bool tinyness_before = false; - BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; -}; - -template<> -class numeric_limits -{ - typedef boost::math::mpz_int number_type; -public: - BOOST_STATIC_CONSTEXPR bool is_specialized = true; - // - // Largest and smallest numbers are bounded only by available memory, set - // to zero: - // - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept - { - return number_type(); - } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept - { - return number_type(); - } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return (min)(); } - // Digits are unbounded, use zero for now: - BOOST_STATIC_CONSTEXPR int digits = 0; - BOOST_STATIC_CONSTEXPR int digits10 = 0; - BOOST_STATIC_CONSTEXPR int max_digits10 = 0; - BOOST_STATIC_CONSTEXPR bool is_signed = true; - BOOST_STATIC_CONSTEXPR bool is_integer = true; - BOOST_STATIC_CONSTEXPR bool is_exact = true; - BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR int min_exponent = 0; - BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; - BOOST_STATIC_CONSTEXPR int max_exponent = 0; - BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; - BOOST_STATIC_CONSTEXPR bool has_infinity = false; - BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; - BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; - BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; - BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR bool is_iec559 = false; - BOOST_STATIC_CONSTEXPR bool is_bounded = false; - BOOST_STATIC_CONSTEXPR bool is_modulo = false; - BOOST_STATIC_CONSTEXPR bool traps = false; - BOOST_STATIC_CONSTEXPR bool tinyness_before = false; - BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; -}; - -#ifdef BOOST_NO_NOEXCEPT -# undef noexcept -#endif - -} // namespace std - -#endif diff --git a/include/boost/math/big_number/mpfr.hpp b/include/boost/math/big_number/mpfr.hpp deleted file mode 100644 index 31165841..00000000 --- a/include/boost/math/big_number/mpfr.hpp +++ /dev/null @@ -1,952 +0,0 @@ -/////////////////////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_BN_MPFR_HPP -#define BOOST_MATH_BN_MPFR_HPP - -#include -#include -#include -#include -#include -#include -#include -#include - -namespace boost{ namespace math{ - -template -struct mpfr_real_backend; - -namespace detail{ - -long get_default_precision() { return 50; } - -template -struct mpfr_real_imp -{ - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list real_types; - - mpfr_real_imp(){} - - mpfr_real_imp(const mpfr_real_imp& o) - { - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); - mpfr_set(m_data, o.m_data, GMP_RNDN); - } -#ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_imp(mpfr_real_imp&& o) - { - m_data[0] = o.m_data[0]; - o.m_data[0]._mpfr_d = 0; - } -#endif - mpfr_real_imp& operator = (const mpfr_real_imp& o) - { - mpfr_set(m_data, o.m_data, GMP_RNDN); - return *this; - } -#ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_imp& operator = (mpfr_real_imp&& o) - { - mpfr_swap(m_data, o.m_data); - return *this; - } -#endif - mpfr_real_imp& operator = (boost::uintmax_t i) - { - boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); - unsigned shift = 0; - mpfr_t t; - mpfr_init2(t, (std::max)(static_cast(std::numeric_limits::digits), static_cast(((digits10 + 1) * 1000L) / 301L))); - mpfr_set_ui(m_data, 0, GMP_RNDN); - while(i) - { - mpfr_set_ui(t, static_cast(i & mask), GMP_RNDN); - if(shift) - mpfr_mul_2exp(t, t, shift, GMP_RNDN); - mpfr_add(m_data, m_data, t, GMP_RNDN); - shift += std::numeric_limits::digits; - i >>= std::numeric_limits::digits; - } - mpfr_clear(t); - return *this; - } - mpfr_real_imp& operator = (boost::intmax_t i) - { - bool neg = i < 0; - *this = static_cast(std::abs(i)); - if(neg) - mpfr_neg(m_data, m_data, GMP_RNDN); - return *this; - } - mpfr_real_imp& operator = (unsigned long i) - { - mpfr_set_ui(m_data, i, GMP_RNDN); - return *this; - } - mpfr_real_imp& operator = (long i) - { - mpfr_set_si(m_data, i, GMP_RNDN); - return *this; - } - mpfr_real_imp& operator = (double d) - { - mpfr_set_d(m_data, d, GMP_RNDN); - return *this; - } - mpfr_real_imp& operator = (long double a) - { - using std::frexp; - using std::ldexp; - using std::floor; - - if (a == 0) { - mpfr_set_si(m_data, 0, GMP_RNDN); - return *this; - } - - if (a == 1) { - mpfr_set_si(m_data, 1, GMP_RNDN); - return *this; - } - - BOOST_ASSERT(!(boost::math::isinf)(a)); - BOOST_ASSERT(!(boost::math::isnan)(a)); - - int e; - long double f, term; - mpfr_init_set_ui(m_data, 0u, GMP_RNDN); - - f = frexp(a, &e); - - static const int shift = std::numeric_limits::digits - 1; - - while(f) - { - // extract int sized bits from f: - f = ldexp(f, shift); - term = floor(f); - e -= shift; - mpfr_mul_2exp(m_data, m_data, shift, GMP_RNDN); - if(term > 0) - mpfr_add_ui(m_data, m_data, static_cast(term), GMP_RNDN); - else - mpfr_sub_ui(m_data, m_data, static_cast(-term), GMP_RNDN); - f -= term; - } - if(e > 0) - mpfr_mul_2exp(m_data, m_data, e, GMP_RNDN); - else if(e < 0) - mpfr_div_2exp(m_data, m_data, -e, GMP_RNDN); - return *this; - } - mpfr_real_imp& operator = (const char* s) - { - mpfr_set_str(m_data, s, 10, GMP_RNDN); - return *this; - } - void swap(mpfr_real_imp& o) - { - mpfr_swap(m_data, o.m_data); - } - std::string str(unsigned digits, bool scientific)const - { - std::string result; - mp_exp_t e; - char* ps = mpfr_get_str (0, &e, 10, digits, m_data, GMP_RNDN); - std::ptrdiff_t sl = std::strlen(ps); - unsigned chars = sl; - if(sl == 0) - return "0"; - while(ps[chars-1] == '0') - --chars; - if(*ps == '-') - --chars; // number of digits excluding sign. - if(chars == 0) - return "0"; - if(!scientific - && (chars <= std::numeric_limits::digits10 + 1) - && (e >= (int)chars) - && (chars <= std::numeric_limits::digits10 + 1)) - { - result.assign(ps, (*ps == '-' ? chars+1 : chars)); - result.append(e-chars, '0'); - } - else - { - result = ps; - if(ps[0] == '-') - result.insert(2, 1, '.'); - else - result.insert(1, 1, '.'); - --e; - if(e) - result += "e" + lexical_cast(e); - } - mpfr_free_str(ps); - return result; - } - ~mpfr_real_imp() - { - if(m_data[0]._mpfr_d) - mpfr_clear(m_data); - } - void negate() - { - mpfr_neg(m_data, m_data, GMP_RNDN); - } - int compare(const mpfr_real_backend& o)const - { - return mpfr_cmp(m_data, o.m_data); - } - int compare(long i)const - { - return mpfr_cmp_si(m_data, i); - } - int compare(unsigned long i)const - { - return mpfr_cmp_ui(m_data, i); - } - template - int compare(V v)const - { - mpfr_real_backend d; - d = v; - return compare(d); - } - mpfr_t& data() { return m_data; } - const mpfr_t& data()const { return m_data; } -protected: - mpfr_t m_data; - static unsigned& get_default_precision() - { - static unsigned val = 50; - return val; - } -}; - -} // namespace detail - -template -struct mpfr_real_backend : public detail::mpfr_real_imp -{ - mpfr_real_backend() - { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - } - mpfr_real_backend(const mpfr_real_backend& o) : detail::mpfr_real_imp(o) {} -#ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_backend(mpfr_real_backend&& o) : detail::mpfr_real_imp(o) {} -#endif - mpfr_real_backend& operator=(const mpfr_real_backend& o) - { - *static_cast*>(this) = static_cast const&>(o); - return *this; - } -#ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_backend& operator=(mpfr_real_backend&& o) - { - *static_cast*>(this) = static_cast&&>(o); - return *this; - } -#endif - template - mpfr_real_backend& operator=(const V& v) - { - *static_cast*>(this) = v; - return *this; - } -}; - -template <> -struct mpfr_real_backend<0> : public detail::mpfr_real_imp<0> -{ - mpfr_real_backend() - { - mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); - } - mpfr_real_backend(unsigned digits10) - { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - } - mpfr_real_backend(const mpfr_real_backend& o) : detail::mpfr_real_imp<0>(o) {} -#ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_backend(mpfr_real_backend&& o) : detail::mpfr_real_imp<0>(o) {} -#endif - mpfr_real_backend(const mpfr_real_backend& o, unsigned digits10) - { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - *this = o; - } - - mpfr_real_backend& operator=(const mpfr_real_backend& o) - { - *static_cast*>(this) = static_cast const&>(o); - return *this; - } -#ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_backend& operator=(mpfr_real_backend&& o) - { - *static_cast*>(this) = static_cast &&>(o); - return *this; - } -#endif - template - mpfr_real_backend& operator=(const V& v) - { - *static_cast*>(this) = v; - return *this; - } - static unsigned default_precision() - { - return get_default_precision(); - } - static void default_precision(unsigned v) - { - get_default_precision() = v; - } - unsigned precision()const - { - return mpfr_get_prec(this->m_data) * 301L / 1000 - 1; - } - void precision(unsigned digits10) - { - mpfr_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); - } -}; - -template -inline void add(mpfr_real_backend& result, const mpfr_real_backend& o) -{ - mpfr_add(result.data(), result.data(), o.data(), GMP_RNDN); -} -template -inline void subtract(mpfr_real_backend& result, const mpfr_real_backend& o) -{ - mpfr_sub(result.data(), result.data(), o.data(), GMP_RNDN); -} -template -inline void multiply(mpfr_real_backend& result, const mpfr_real_backend& o) -{ - mpfr_mul(result.data(), result.data(), o.data(), GMP_RNDN); -} -template -inline void divide(mpfr_real_backend& result, const mpfr_real_backend& o) -{ - mpfr_div(result.data(), result.data(), o.data(), GMP_RNDN); -} -template -inline void add(mpfr_real_backend& result, unsigned long i) -{ - mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); -} -template -inline void subtract(mpfr_real_backend& result, unsigned long i) -{ - mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); -} -template -inline void multiply(mpfr_real_backend& result, unsigned long i) -{ - mpfr_mul_ui(result.data(), result.data(), i, GMP_RNDN); -} -template -inline void divide(mpfr_real_backend& result, unsigned long i) -{ - mpfr_div_ui(result.data(), result.data(), i, GMP_RNDN); -} -template -inline void add(mpfr_real_backend& result, long i) -{ - if(i > 0) - mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); - else - mpfr_sub_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); -} -template -inline void subtract(mpfr_real_backend& result, long i) -{ - if(i > 0) - mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); - else - mpfr_add_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); -} -template -inline void multiply(mpfr_real_backend& result, long i) -{ - mpfr_mul_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); - if(i < 0) - mpfr_neg(result.data(), result.data(), GMP_RNDN); -} -template -inline void divide(mpfr_real_backend& result, long i) -{ - mpfr_div_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); - if(i < 0) - mpfr_neg(result.data(), result.data(), GMP_RNDN); -} -// -// Specialised 3 arg versions of the basic operators: -// -template -inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) -{ - mpfr_add(a.data(), x.data(), y.data(), GMP_RNDN); -} -template -inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) -{ - mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); -} -template -inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, long y) -{ - if(y < 0) - mpfr_sub_ui(a.data(), x.data(), -y, GMP_RNDN); - else - mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); -} -template -inline void add(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) -{ - mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); -} -template -inline void add(mpfr_real_backend& a, long x, const mpfr_real_backend& y) -{ - if(x < 0) - { - mpfr_ui_sub(a.data(), -x, y.data(), GMP_RNDN); - mpfr_neg(a.data(), a.data(), GMP_RNDN); - } - else - mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); -} -template -inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) -{ - mpfr_sub(a.data(), x.data(), y.data(), GMP_RNDN); -} -template -inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) -{ - mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); -} -template -inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, long y) -{ - if(y < 0) - mpfr_add_ui(a.data(), x.data(), -y, GMP_RNDN); - else - mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); -} -template -inline void subtract(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) -{ - mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); -} -template -inline void subtract(mpfr_real_backend& a, long x, const mpfr_real_backend& y) -{ - if(x < 0) - { - mpfr_add_ui(a.data(), y.data(), -x, GMP_RNDN); - mpfr_neg(a.data(), a.data(), GMP_RNDN); - } - else - mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); -} - -template -inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) -{ - mpfr_mul(a.data(), x.data(), y.data(), GMP_RNDN); -} -template -inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) -{ - mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); -} -template -inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, long y) -{ - if(y < 0) - { - mpfr_mul_ui(a.data(), x.data(), -y, GMP_RNDN); - a.negate(); - } - else - mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); -} -template -inline void multiply(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) -{ - mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); -} -template -inline void multiply(mpfr_real_backend& a, long x, const mpfr_real_backend& y) -{ - if(x < 0) - { - mpfr_mul_ui(a.data(), y.data(), -x, GMP_RNDN); - mpfr_neg(a.data(), a.data(), GMP_RNDN); - } - else - mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); -} - -template -inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) -{ - mpfr_div(a.data(), x.data(), y.data(), GMP_RNDN); -} -template -inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) -{ - mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); -} -template -inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, long y) -{ - if(y < 0) - { - mpfr_div_ui(a.data(), x.data(), -y, GMP_RNDN); - a.negate(); - } - else - mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); -} -template -inline void divide(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) -{ - mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); -} -template -inline void divide(mpfr_real_backend& a, long x, const mpfr_real_backend& y) -{ - if(x < 0) - { - mpfr_ui_div(a.data(), -x, y.data(), GMP_RNDN); - mpfr_neg(a.data(), a.data(), GMP_RNDN); - } - else - mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); -} - -template -inline bool is_zero(const mpfr_real_backend& val) -{ - return 0 != mpfr_zero_p(val.data()); -} -template -inline int get_sign(const mpfr_real_backend& val) -{ - return mpfr_sgn(val.data()); -} - -template -inline void convert_to(unsigned long* result, const mpfr_real_backend& val) -{ - *result = mpfr_get_ui(val.data(), GMP_RNDN); -} -template -inline void convert_to(long* result, const mpfr_real_backend& val) -{ - *result = mpfr_get_si(val.data(), GMP_RNDN); -} -#ifdef _MPFR_H_HAVE_INTMAX_T -template -inline void convert_to(boost::uintmax_t* result, const mpfr_real_backend& val) -{ - *result = mpfr_get_uj(val.data(), GMP_RNDN); -} -template -inline void convert_to(boost::intmax_t* result, const mpfr_real_backend& val) -{ - *result = mpfr_get_sj(val.data(), GMP_RNDN); -} -#endif -template -inline void convert_to(double* result, const mpfr_real_backend& val) -{ - *result = mpfr_get_d(val.data(), GMP_RNDN); -} -template -inline void convert_to(long double* result, const mpfr_real_backend& val) -{ - *result = mpfr_get_ld(val.data(), GMP_RNDN); -} - -// -// Native non-member operations: -// -template -inline void eval_sqrt(mpfr_real_backend& result, const mpfr_real_backend& val) -{ - mpfr_sqrt(result.data(), val.data(), GMP_RNDN); -} - -template -inline void eval_abs(mpfr_real_backend& result, const mpfr_real_backend& val) -{ - mpfr_abs(result.data(), val.data(), GMP_RNDN); -} - -template -inline void eval_fabs(mpfr_real_backend& result, const mpfr_real_backend& val) -{ - mpfr_abs(result.data(), val.data(), GMP_RNDN); -} -template -inline void eval_ceil(mpfr_real_backend& result, const mpfr_real_backend& val) -{ - mpfr_ceil(result.data(), val.data()); -} -template -inline void eval_floor(mpfr_real_backend& result, const mpfr_real_backend& val) -{ - mpfr_floor(result.data(), val.data()); -} -template -inline void eval_trunc(mpfr_real_backend& result, const mpfr_real_backend& val) -{ - mpfr_trunc(result.data(), val.data()); -} -template -inline void eval_ldexp(mpfr_real_backend& result, const mpfr_real_backend& val, long e) -{ - if(e > 0) - mpfr_mul_2exp(result.data(), val.data(), e, GMP_RNDN); - else if(e < 0) - mpfr_div_2exp(result.data(), val.data(), -e, GMP_RNDN); -} -template -inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, int* e) -{ - long v; - mpfr_get_d_2exp(&v, val.data(), GMP_RNDN); - *e = v; - eval_ldexp(result, val, -v); -} -template -inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, long* e) -{ - mpfr_get_d_2exp(e, val.data(), GMP_RNDN); - return eval_ldexp(result, val, -*e); -} - -template -inline int eval_fpclassify(const mpfr_real_backend& val) -{ - return mpfr_inf_p(val.data()) ? FP_INFINITE : mpfr_nan_p(val.data()) ? FP_NAN : mpfr_zero_p(val.data()) ? FP_ZERO : FP_NORMAL; -} - -template -inline void eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const mpfr_real_backend& e) -{ - mpfr_pow(result.data(), b.data(), e.data(), GMP_RNDN); -} - -template -inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const Integer& e) -{ - mpfr_pow_si(result.data(), b.data(), e, GMP_RNDN); -} - -template -inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const Integer& e) -{ - mpfr_pow_ui(result.data(), b.data(), e, GMP_RNDN); -} - -template -inline void eval_exp(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_exp(result.data(), arg.data(), GMP_RNDN); -} - -template -inline void eval_log(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_log(result.data(), arg.data(), GMP_RNDN); -} - -template -inline void eval_sin(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_sin(result.data(), arg.data(), GMP_RNDN); -} - -template -inline void eval_cos(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_cos(result.data(), arg.data(), GMP_RNDN); -} - -template -inline void eval_tan(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_tan(result.data(), arg.data(), GMP_RNDN); -} - -template -inline void eval_asin(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_asin(result.data(), arg.data(), GMP_RNDN); -} - -template -inline void eval_acos(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_acos(result.data(), arg.data(), GMP_RNDN); -} - -template -inline void eval_atan(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_atan(result.data(), arg.data(), GMP_RNDN); -} - -template -inline void eval_sinh(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_sinh(result.data(), arg.data(), GMP_RNDN); -} - -template -inline void eval_cosh(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_cosh(result.data(), arg.data(), GMP_RNDN); -} - -template -inline void eval_tanh(mpfr_real_backend& result, const mpfr_real_backend& arg) -{ - mpfr_tanh(result.data(), arg.data(), GMP_RNDN); -} - -typedef big_number > mpfr_real_50; -typedef big_number > mpfr_real_100; -typedef big_number > mpfr_real_500; -typedef big_number > mpfr_real_1000; -typedef big_number > mpfr_real; - -namespace lanczos{ - -template -struct lanczos >, Policy> -{ - typedef typename mpl::if_c< - Digits10 <= 36, - lanczos22UDT, - typename mpl::if_c< - Digits10 <= 50, - lanczos31UDT, - typename mpl::if_c< - Digits10 <= 110, - lanczos61UDT, - undefined_lanczos - >::type - >::type - >::type type; -}; - -} // namespace lanczos - - -}} // namespaces - -namespace std{ - -#ifdef BOOST_NO_NOEXCEPT -# define noexcept -#endif - -// -// numeric_limits [partial] specializations for the types declared in this header: -// -template -class numeric_limits > > -{ - typedef boost::math::big_number > number_type; -public: - BOOST_STATIC_CONSTEXPR bool is_specialized = true; - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept - { - initializer.do_nothing(); - static std::pair value; - if(!value.first) - { - value.first = true; - value.second = 0.5; - mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), -mpfr_get_emin(), GMP_RNDN); - } - return value.second; - } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept - { - initializer.do_nothing(); - static std::pair value; - if(!value.first) - { - value.first = true; - value.second = 0.5; - mpfr_mul_2exp(value.second.backend().data(), value.second.backend().data(), mpfr_get_emax(), GMP_RNDN); - } - return value.second; - } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept - { - return -(max)(); - } - BOOST_STATIC_CONSTEXPR int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); - BOOST_STATIC_CONSTEXPR int digits10 = Digits10; - // Is this really correct??? - BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 1; - BOOST_STATIC_CONSTEXPR bool is_signed = true; - BOOST_STATIC_CONSTEXPR bool is_integer = false; - BOOST_STATIC_CONSTEXPR bool is_exact = false; - BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept - { - initializer.do_nothing(); - static std::pair value; - if(!value.first) - { - value.first = true; - value.second = 1; - mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits::digits - 1, GMP_RNDN); - } - return value.second; - } - // What value should this be???? - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept - { - // returns epsilon/2 - initializer.do_nothing(); - static std::pair value; - if(!value.first) - { - value.first = true; - value.second = 1; - mpfr_div_2exp(value.second.backend().data(), value.second.backend().data(), digits, GMP_RNDN); - } - return value.second; - } - BOOST_STATIC_CONSTEXPR long min_exponent = MPFR_EMIN_DEFAULT; - BOOST_STATIC_CONSTEXPR long min_exponent10 = (MPFR_EMIN_DEFAULT / 1000) * 301L; - BOOST_STATIC_CONSTEXPR long max_exponent = MPFR_EMAX_DEFAULT; - BOOST_STATIC_CONSTEXPR long max_exponent10 = (MPFR_EMAX_DEFAULT / 1000) * 301L; - BOOST_STATIC_CONSTEXPR bool has_infinity = true; - BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true; - BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; - BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; - BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept - { - // returns epsilon/2 - initializer.do_nothing(); - static std::pair value; - if(!value.first) - { - value.first = true; - value.second = 1; - mpfr_set_inf(value.second.backend().data(), 1); - } - return value.second; - } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept - { - // returns epsilon/2 - initializer.do_nothing(); - static std::pair value; - if(!value.first) - { - value.first = true; - value.second = 1; - mpfr_set_nan(value.second.backend().data()); - } - return value.second; - } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept - { - return number_type(0); - } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR bool is_iec559 = false; - BOOST_STATIC_CONSTEXPR bool is_bounded = true; - BOOST_STATIC_CONSTEXPR bool is_modulo = false; - BOOST_STATIC_CONSTEXPR bool traps = true; - BOOST_STATIC_CONSTEXPR bool tinyness_before = false; - BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest; - -private: - struct data_initializer - { - data_initializer() - { - std::numeric_limits > >::epsilon(); - std::numeric_limits > >::round_error(); - (std::numeric_limits > >::min)(); - (std::numeric_limits > >::max)(); - std::numeric_limits > >::infinity(); - std::numeric_limits > >::quiet_NaN(); - } - void do_nothing()const{} - }; - static const data_initializer initializer; -}; - -template -const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; - -template<> -class numeric_limits > > -{ - typedef boost::math::big_number > number_type; -public: - BOOST_STATIC_CONSTEXPR bool is_specialized = false; - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR int digits = 0; - BOOST_STATIC_CONSTEXPR int digits10 = 0; - BOOST_STATIC_CONSTEXPR int max_digits10 = 0; - BOOST_STATIC_CONSTEXPR bool is_signed = false; - BOOST_STATIC_CONSTEXPR bool is_integer = false; - BOOST_STATIC_CONSTEXPR bool is_exact = false; - BOOST_STATIC_CONSTEXPR int radix = 0; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR int min_exponent = 0; - BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; - BOOST_STATIC_CONSTEXPR int max_exponent = 0; - BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; - BOOST_STATIC_CONSTEXPR bool has_infinity = false; - BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; - BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; - BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; - BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR bool is_iec559 = false; - BOOST_STATIC_CONSTEXPR bool is_bounded = false; - BOOST_STATIC_CONSTEXPR bool is_modulo = false; - BOOST_STATIC_CONSTEXPR bool traps = false; - BOOST_STATIC_CONSTEXPR bool tinyness_before = false; - BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; -}; - -#ifdef noexcept -#undef noexcept -#endif - -} // namespace std -#endif diff --git a/include/boost/math/concepts/big_number_architypes.hpp b/include/boost/math/concepts/big_number_architypes.hpp deleted file mode 100644 index 26a7a4b6..00000000 --- a/include/boost/math/concepts/big_number_architypes.hpp +++ /dev/null @@ -1,293 +0,0 @@ -/////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ - -#ifndef BOOST_MATH_CONCEPTS_ER_HPP -#define BOOST_MATH_CONCEPTS_ER_HPP - -#include -#include -#include -#include -#include -#include -#include - -namespace boost{ -namespace math{ -namespace concepts{ - -#ifdef BOOST_MSVC -#pragma warning(push) -#pragma warning(disable:4244) -#endif - -struct big_number_backend_real_architype -{ - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list real_types; - - big_number_backend_real_architype() - { - std::cout << "Default construct" << std::endl; - } - big_number_backend_real_architype(const big_number_backend_real_architype& o) - { - std::cout << "Copy construct" << std::endl; - m_value = o.m_value; - } - big_number_backend_real_architype& operator = (const big_number_backend_real_architype& o) - { - m_value = o.m_value; - std::cout << "Assignment (" << m_value << ")" << std::endl; - return *this; - } - big_number_backend_real_architype& operator = (boost::uintmax_t i) - { - m_value = i; - std::cout << "UInt Assignment (" << i << ")" << std::endl; - return *this; - } - big_number_backend_real_architype& operator = (boost::intmax_t i) - { - m_value = i; - std::cout << "Int Assignment (" << i << ")" << std::endl; - return *this; - } - big_number_backend_real_architype& operator = (long double d) - { - m_value = d; - std::cout << "long double Assignment (" << d << ")" << std::endl; - return *this; - } - big_number_backend_real_architype& operator = (const char* s) - { - m_value = boost::lexical_cast(s); - std::cout << "const char* Assignment (" << s << ")" << std::endl; - return *this; - } - void swap(big_number_backend_real_architype& o) - { - std::cout << "Swapping (" << m_value << " with " << o.m_value << ")" << std::endl; - std::swap(m_value, o.m_value); - } - std::string str(unsigned digits, bool scientific)const - { - std::stringstream ss; - if(scientific) - ss.setf(ss.scientific); - if(digits) - ss.precision(digits); - else - ss.precision(std::numeric_limits::digits10 + 2); - boost::intmax_t i = m_value; - boost::uintmax_t u = m_value; - if(!scientific && m_value == i) - ss << i; - else if(!scientific && m_value == u) - ss << u; - else - ss << m_value; - std::string s = ss.str(); - std::cout << "Converting to string (" << s << ")" << std::endl; - return s; - } - void negate() - { - std::cout << "Negating (" << m_value << ")" << std::endl; - m_value = -m_value; - } - int compare(const big_number_backend_real_architype& o)const - { - std::cout << "Comparison" << std::endl; - return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); - } - int compare(boost::intmax_t i)const - { - std::cout << "Comparison with int" << std::endl; - return m_value > i ? 1 : (m_value < i ? -1 : 0); - } - int compare(boost::uintmax_t i)const - { - std::cout << "Comparison with unsigned" << std::endl; - return m_value > i ? 1 : (m_value < i ? -1 : 0); - } - int compare(long double d)const - { - std::cout << "Comparison with long double" << std::endl; - return m_value > d ? 1 : (m_value < d ? -1 : 0); - } - long double m_value; -}; - -inline void add(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) -{ - std::cout << "Addition (" << result.m_value << " += " << o.m_value << ")" << std::endl; - result.m_value += o.m_value; -} -inline void subtract(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) -{ - std::cout << "Subtraction (" << result.m_value << " -= " << o.m_value << ")" << std::endl; - result.m_value -= o.m_value; -} -inline void multiply(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) -{ - std::cout << "Multiplication (" << result.m_value << " *= " << o.m_value << ")" << std::endl; - result.m_value *= o.m_value; -} -inline void divide(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) -{ - std::cout << "Division (" << result.m_value << " /= " << o.m_value << ")" << std::endl; - result.m_value /= o.m_value; -} - -inline void eval_frexp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg, int* exp) -{ - result = std::frexp(arg.m_value, exp); -} - -inline void eval_ldexp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg, int exp) -{ - result = std::ldexp(arg.m_value, exp); -} - -inline void eval_floor(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::floor(arg.m_value); -} - -inline void eval_ceil(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::ceil(arg.m_value); -} - -inline void eval_trunc(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = boost::math::trunc(arg.m_value); -} - -inline void eval_sqrt(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::sqrt(arg.m_value); -} - -inline void eval_abs(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::abs(arg.m_value); -} - -inline void eval_fabs(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::fabs(arg.m_value); -} - -inline int eval_fpclassify(const big_number_backend_real_architype& arg) -{ - return boost::math::fpclassify(arg.m_value); -} - -inline void eval_pow(big_number_backend_real_architype& result, const big_number_backend_real_architype& b, const big_number_backend_real_architype& e) -{ - result = std::pow(b.m_value, e.m_value); -} - -inline void eval_pow(big_number_backend_real_architype& result, const big_number_backend_real_architype& b, int e) -{ - result = std::pow(b.m_value, e); -} - -inline void eval_exp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::exp(arg.m_value); -} - -inline void eval_log(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::log(arg.m_value); -} - -inline void eval_sin(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::sin(arg.m_value); -} - -inline void eval_cos(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::cos(arg.m_value); -} - -inline void eval_tan(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::tan(arg.m_value); -} - -inline void eval_asin(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::asin(arg.m_value); -} - -inline void eval_acos(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::acos(arg.m_value); -} - -inline void eval_atan(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::atan(arg.m_value); -} - -inline void eval_sinh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::sinh(arg.m_value); -} - -inline void eval_cosh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::cosh(arg.m_value); -} - -inline void eval_tanh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) -{ - result = std::tanh(arg.m_value); -} - -typedef boost::math::big_number big_number_real_architype; - -}}} // namespaces - -namespace std{ - -#ifdef BOOST_NO_NOEXCEPT -# define noexcept -#endif - -template <> -class numeric_limits : public std::numeric_limits -{ - typedef std::numeric_limits base_type; - typedef boost::math::concepts::big_number_real_architype number_type; -public: - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return -(max)(); } - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return base_type::epsilon(); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return epsilon() / 2; } - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return base_type::infinity(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return base_type::quiet_NaN(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return base_type::signaling_NaN(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return base_type::denorm_min(); } -}; - -#ifdef BOOST_NO_NOEXCEPT -# undef noexcept -#endif - -} - -#ifdef BOOST_MSVC -#pragma warning(pop) -#endif - -#endif From b0de931cf10a650da845e949a3084fe8f1a6ff5a Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 26 Sep 2011 17:59:35 +0000 Subject: [PATCH 028/256] Giant file and directory rename: changed directory name from math to multiprecision and updated code to match. [SVN r74583] --- .../boost/multiprecision/{backends => detail}/functions/pow.hpp | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename include/boost/multiprecision/{backends => detail}/functions/pow.hpp (100%) diff --git a/include/boost/multiprecision/backends/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp similarity index 100% rename from include/boost/multiprecision/backends/functions/pow.hpp rename to include/boost/multiprecision/detail/functions/pow.hpp From 01173bc59c781aa04f574a666e9b064aab67a425 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 3 Oct 2011 16:56:24 +0000 Subject: [PATCH 029/256] Changed namespace to "multiprecision". Added some numberic constant calculations. Added exp function support and test case. [SVN r74669] --- .../multiprecision/arithmetic_backend.hpp | 6 +- .../concepts/big_number_architypes.hpp | 23 ++- .../multiprecision/detail/big_number_base.hpp | 10 +- .../multiprecision/detail/default_ops.hpp | 189 ++++++++++++------ .../detail/functions/constants.hpp | 116 +++++++++++ .../multiprecision/detail/functions/pow.hpp | 146 ++++++++++++++ include/boost/multiprecision/e_float.hpp | 2 +- include/boost/multiprecision/gmp.hpp | 90 +++++++-- include/boost/multiprecision/mp_number.hpp | 29 +-- include/boost/multiprecision/mpfr.hpp | 30 +-- test/Jamfile.v2 | 8 + test/big_number_concept_check.cpp | 22 +- test/linpack-benchmark.cpp | 10 +- test/test_arithmetic.cpp | 30 +-- test/test_exp.cpp | 129 ++++++++++++ test/test_numeric_limits.cpp | 22 +- 16 files changed, 691 insertions(+), 171 deletions(-) create mode 100644 include/boost/multiprecision/detail/functions/constants.hpp create mode 100644 test/test_exp.cpp diff --git a/include/boost/multiprecision/arithmetic_backend.hpp b/include/boost/multiprecision/arithmetic_backend.hpp index 54d452ec..f5429c48 100644 --- a/include/boost/multiprecision/arithmetic_backend.hpp +++ b/include/boost/multiprecision/arithmetic_backend.hpp @@ -13,7 +13,7 @@ #include namespace boost{ -namespace math{ +namespace multiprecision{ template struct arithmetic_backend @@ -122,10 +122,10 @@ namespace std{ #endif template -class numeric_limits > > : public std::numeric_limits +class numeric_limits > > : public std::numeric_limits { typedef std::numeric_limits base_type; - typedef boost::math::mp_number > number_type; + typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } diff --git a/include/boost/multiprecision/concepts/big_number_architypes.hpp b/include/boost/multiprecision/concepts/big_number_architypes.hpp index f13c2c7e..fbec67b3 100644 --- a/include/boost/multiprecision/concepts/big_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/big_number_architypes.hpp @@ -15,7 +15,7 @@ #include namespace boost{ -namespace math{ +namespace multiprecision{ namespace concepts{ #ifdef BOOST_MSVC @@ -64,7 +64,7 @@ struct big_number_backend_real_architype } big_number_backend_real_architype& operator = (const char* s) { - m_value = boost::lexical_cast(s); + m_value = boost::lexical_cast(s); std::cout << "const char* Assignment (" << s << ")" << std::endl; return *this; } @@ -143,6 +143,19 @@ inline void divide(big_number_backend_real_architype& result, const big_number_b result.m_value /= o.m_value; } +inline void convert_to(boost::uintmax_t* result, const big_number_backend_real_architype& val) +{ + *result = static_cast(val.m_value); +} +inline void convert_to(boost::intmax_t* result, const big_number_backend_real_architype& val) +{ + *result = static_cast(val.m_value); +} +inline void convert_to(long double* result, big_number_backend_real_architype& val) +{ + *result = val.m_value; +} + inline void eval_frexp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg, int* exp) { result = std::frexp(arg.m_value, exp); @@ -253,7 +266,7 @@ inline void eval_tanh(big_number_backend_real_architype& result, const big_numbe result = std::tanh(arg.m_value); } -typedef boost::math::mp_number big_number_real_architype; +typedef boost::multiprecision::mp_number big_number_real_architype; }}} // namespaces @@ -264,10 +277,10 @@ namespace std{ #endif template <> -class numeric_limits : public std::numeric_limits +class numeric_limits : public std::numeric_limits { typedef std::numeric_limits base_type; - typedef boost::math::concepts::big_number_real_architype number_type; + typedef boost::multiprecision::concepts::big_number_real_architype number_type; public: BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } diff --git a/include/boost/multiprecision/detail/big_number_base.hpp b/include/boost/multiprecision/detail/big_number_base.hpp index c8fcd9cf..6b85d7d4 100644 --- a/include/boost/multiprecision/detail/big_number_base.hpp +++ b/include/boost/multiprecision/detail/big_number_base.hpp @@ -10,7 +10,7 @@ #include #include -namespace boost{ namespace math{ +namespace boost{ namespace multiprecision{ template class mp_number; @@ -139,11 +139,11 @@ struct backend_type > template struct is_big_number : public mpl::false_{}; template -struct is_big_number > : public mpl::true_{}; +struct is_big_number > : public mpl::true_{}; template struct is_big_number_exp : public mpl::false_{}; template -struct is_big_number_exp > : public mpl::true_{}; +struct is_big_number_exp > : public mpl::true_{}; template struct combine_expression; @@ -971,9 +971,9 @@ template struct promote_arg; template -struct promote_arg > +struct promote_arg > { - typedef typename boost::math::detail::mp_exp::result_type type; + typedef typename boost::multiprecision::detail::mp_exp::result_type type; }; }}} diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 262b3ee7..da8780e8 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -12,8 +12,9 @@ #include #include #include +#include -namespace boost{ namespace math{ namespace big_num_default_ops{ +namespace boost{ namespace multiprecision{ namespace big_num_default_ops{ // // Default versions of mixed arithmetic, these just construct a temporary @@ -372,6 +373,29 @@ inline void eval_fmod(T& result, const T& a, const T& b) multiply(n, b); subtract(result, a, n); } +template +inline void eval_trunc(T& result, const T& a) +{ + if(get_sign(a) < 0) + eval_ceil(result, a); + else + eval_floor(result, a); +} + +template +inline void eval_round(T& result, const T& a) +{ + if(get_sign(a) < 0) + { + subtract(result, a, 0.5f); + eval_ceil(result, result); + } + else + { + add(result, a, 0.5f); + eval_floor(result, result); + } +} // // These have to implemented by the backend, declared here so that our macro generated code compiles OK. @@ -414,8 +438,10 @@ typename enable_if_c::type eval_cosh(); template typename enable_if_c::type eval_tanh(); // -// These functions are implemented in separate files, but expanded inline here: +// These functions are implemented in separate files, but expanded inline here, +// DO NOT CHANGE THE ORDER OF THESE INCLUDES: // +#include #include } @@ -423,74 +449,95 @@ typename enable_if_c::type eval_tanh(); template class mp_number; +} // namespace multiprecision +namespace math{ // // Default versions of floating point classification routines: // template -inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const mp_number& arg) +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { - using big_num_default_ops::eval_fpclassify; + using multiprecision::big_num_default_ops::eval_fpclassify; return eval_fpclassify(arg.backend()); } template -inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::mp_exp& arg) +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) { - typedef typename detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::mp_exp::result_type value_type; return fpclassify(value_type(arg)); } template -inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const mp_number& arg) +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { int v = fpclassify(arg); return (v != FP_INFINITE) && (v != FP_NAN); } template -inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::mp_exp& arg) +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) { - typedef typename detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::mp_exp::result_type value_type; return isfinite(value_type(arg)); } template -inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const mp_number& arg) +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { return fpclassify(arg) == FP_NAN; } template -inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::mp_exp& arg) +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) { - typedef typename detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::mp_exp::result_type value_type; return isnan(value_type(arg)); } template -inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const mp_number& arg) +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { return fpclassify(arg) == FP_INFINITE; } template -inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::mp_exp& arg) +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) { - typedef typename detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::mp_exp::result_type value_type; return isinf(value_type(arg)); } template -inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const mp_number& arg) +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { return fpclassify(arg) == FP_NORMAL; } template -inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const detail::mp_exp& arg) +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) { - typedef typename detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::mp_exp::result_type value_type; return isnormal(value_type(arg)); } +} // namespace math +namespace multiprecision{ + +template +inline typename detail::mp_exp::result_type trunc(const detail::mp_exp& v, const Policy& pol) +{ + typedef typename detail::mp_exp::result_type number_type; + return trunc(v, pol); +} + +template +inline mp_number trunc(const mp_number& v, const Policy& pol) +{ + using big_num_default_ops::eval_trunc; + mp_number result; + eval_trunc(result.backend(), v.backend()); + return result; +} + template inline int itrunc(const detail::mp_exp& v, const Policy& pol) { typedef typename detail::mp_exp::result_type number_type; number_type r = trunc(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } template @@ -498,7 +545,7 @@ inline int itrunc(const mp_number& v, const Policy& pol) { mp_number r = trunc(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } template @@ -507,7 +554,7 @@ inline long ltrunc(const detail::mp_exp& v, const Policy& pol) typedef typename detail::mp_exp::result_result number_type; number_type r = trunc(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } template @@ -515,7 +562,7 @@ inline long ltrunc(const mp_number& v, const Policy& pol) { mp_number r = trunc(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } #ifndef BOOST_NO_LONG_LONG @@ -525,7 +572,7 @@ inline long long lltrunc(const detail::mp_exp& v, const Policy& typedef typename detail::mp_exp::result_result number_type; number_type r = trunc(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } template @@ -533,17 +580,32 @@ inline long long lltrunc(const mp_number& v, const Policy& pol) { mp_number r = trunc(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } #endif +template +inline typename detail::mp_exp::result_result round(const detail::mp_exp& v, const Policy& pol) +{ + typedef typename detail::mp_exp::result_result number_type; + return round(static_cast(v), pol); +} +template +inline mp_number round(const mp_number& v, const Policy& pol) +{ + using big_num_default_ops::eval_round; + mp_number result; + eval_round(result.backend(), v.backend()); + return result; +} + template inline int iround(const detail::mp_exp& v, const Policy& pol) { typedef typename detail::mp_exp::result_result number_type; number_type r = round(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } template @@ -551,7 +613,7 @@ inline int iround(const mp_number& v, const Policy& pol) { mp_number r = round(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } template @@ -560,7 +622,7 @@ inline long lround(const detail::mp_exp& v, const Policy& pol) typedef typename detail::mp_exp::result_result number_type; number_type r = round(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } template @@ -568,7 +630,7 @@ inline long lround(const mp_number& v, const Policy& pol) { mp_number r = round(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } #ifndef BOOST_NO_LONG_LONG @@ -578,7 +640,7 @@ inline long long llround(const detail::mp_exp& v, const Policy& typedef typename detail::mp_exp::result_result number_type; number_type r = round(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } template @@ -586,40 +648,10 @@ inline long long llround(const mp_number& v, const Policy& pol) { mp_number r = round(v, pol); if(fabs(r) > (std::numeric_limits::max)()) - return policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } #endif -// -// Overload of Boost.Math functions that find the wrong overload when used with mp_number: -// -namespace detail{ - template T sinc_pi_imp(T); - template T sinhc_pi_imp(T); -} -template -inline mp_number sinc_pi(const mp_number& x) -{ - return detail::sinc_pi_imp(x); -} - -template -inline mp_number sinc_pi(const mp_number& x, const Policy&) -{ - return detail::sinc_pi_imp(x); -} - -template -inline mp_number sinhc_pi(const mp_number& x) -{ - return detail::sinhc_pi_imp(x); -} - -template -inline mp_number sinhc_pi(const mp_number& x, const Policy&) -{ - return boost::math::sinhc_pi(x); -} #define UNARY_OP_FUNCTOR(func)\ namespace detail{\ @@ -897,7 +929,42 @@ BINARY_OP_FUNCTOR(fmod) #undef BINARY_OP_FUNCTOR #undef UNARY_OP_FUNCTOR -}} // namespaces +} //namespace multiprecision + +namespace math{ +// +// Overload of Boost.Math functions that find the wrong overload when used with mp_number: +// +namespace detail{ + template T sinc_pi_imp(T); + template T sinhc_pi_imp(T); +} +template +inline multiprecision::mp_number sinc_pi(const multiprecision::mp_number& x) +{ + return detail::sinc_pi_imp(x); +} + +template +inline multiprecision::mp_number sinc_pi(const multiprecision::mp_number& x, const Policy&) +{ + return detail::sinc_pi_imp(x); +} + +template +inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x) +{ + return detail::sinhc_pi_imp(x); +} + +template +inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x, const Policy&) +{ + return boost::multiprecision::sinhc_pi(x); +} + +} // namespace math +} // namespace boost #endif diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp new file mode 100644 index 00000000..60a3bfe8 --- /dev/null +++ b/include/boost/multiprecision/detail/functions/constants.hpp @@ -0,0 +1,116 @@ +// Copyright 2011 John Maddock. Distributed under the Boost +// Distributed under the Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// This file has no include guards or namespaces - it's expanded inline inside default_ops.hpp +// + +template +void calc_log2(T& num, unsigned digits) +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename T::unsigned_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type ui_type; + typedef typename mpl::front::type si_type; + + num = static_cast(1180509120u); + T denom, next_term, temp; + denom = static_cast(1277337600u); + next_term = static_cast(120u); + si_type sign = -1; + + ui_type limit = digits / 3 + 1; + + for(ui_type n = 6; n < limit; ++n) + { + temp = static_cast(2); + multiply(temp, ui_type(2 * n)); + multiply(temp, ui_type(2 * n + 1)); + multiply(num, temp); + multiply(denom, temp); + sign = -sign; + multiply(next_term, n); + multiply(temp, next_term, next_term); + multiply(temp, sign); + add(num, temp); + } + multiply(denom, ui_type(4)); + multiply(num, ui_type(3)); + divide(num, denom); +} + +template +void calc_e(T& result, unsigned digits) +{ + typedef typename mpl::front::type ui_type; + typedef typename mpl::front::type real_type; + T lim; + lim = ui_type(1); + eval_ldexp(lim, lim, digits); + + result = ui_type(2); + T denom; + denom = ui_type(1); + ui_type i = 2; + do{ + multiply(denom, i); + multiply(result, i); + add(result, ui_type(1)); + ++i; + }while(denom.compare(lim) <= 0); + divide(result, denom); +} + + +template +struct constant_initializer +{ + static void do_nothing() + { + init.do_nothing(); + } +private: + struct initializer + { + initializer() + { + F(); + } + void do_nothing()const{} + }; + static const initializer init; +}; + +template +typename constant_initializer::initializer const constant_initializer::init; + +template +const T& get_constant_ln2() +{ + static T result; + static bool b = false; + if(!b) + calc_log2(result, std::numeric_limits >::digits); + + constant_initializer >::do_nothing(); + + return result; +} + +template +const T& get_constant_e() +{ + static T result; + static bool b = false; + if(!b) + calc_e(result, std::numeric_limits >::digits); + + constant_initializer >::do_nothing(); + + return result; +} + diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 48d10c15..de5b2b4e 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -94,4 +94,150 @@ inline void eval_pow(T& result, const T& t, const U& p) detail::pow_imp(result, t, p, tag_type()); } +template +void hyp0F0(T& H0F0, const T& x) +{ + // Compute the series representation of Hypergeometric0F0 taken from + // http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric0F0/06/01/ + // There are no checks on input range or parameter boundaries. + + typedef typename mpl::front::type ui_type; + + long tol = std::numeric_limits >::digits; + T t; + + T x_pow_n_div_n_fact(x); + + add(H0F0, x_pow_n_div_n_fact, ui_type(1)); + + ui_type n; + + // Series expansion of hyperg_0f0(; ; x). + for(n = 2; n < 300; ++n) + { + multiply(x_pow_n_div_n_fact, x); + divide(x_pow_n_div_n_fact, n); + + if(n > 20) + { + eval_ldexp(t, H0F0, -tol); + if(t.compare(x_pow_n_div_n_fact) >= 0) + { + break; + } + } + + add(H0F0, x_pow_n_div_n_fact); + } + if(n >= 300) + throw std::runtime_error("H0F0 failed to converge"); +} + + +template +void eval_exp(T& result, const T& x) +{ + if(&x == &result) + { + T temp; + eval_exp(temp, x); + result = temp; + } + typedef typename mpl::front::type ui_type; + // Handle special arguments. + int type = eval_fpclassify(x); + bool isneg = get_sign(x) < 0; + if(type == FP_NAN) + { + result = std::numeric_limits >::quiet_NaN().backend(); + return; + } + else if(type == FP_INFINITE) + { + result = x; + if(isneg) + result = ui_type(0u); + else + result = x; + return; + } + else if(type == FP_ZERO) + { + result = ui_type(1); + return; + } + + // Get local copy of argument and force it to be positive. + T xx = x; + T exp_series; + if(isneg) + xx.negate(); + + // Check the range of the argument. + static const boost::intmax_t maximum_arg_for_exp = std::numeric_limits >::max_exponent == 0 ? std::numeric_limits::max() : std::numeric_limits >::max_exponent; + + if(xx.compare(maximum_arg_for_exp) >= 0) + { + // Overflow / underflow + if(isneg) + result = ui_type(0); + else + result = std::numeric_limits >::has_infinity ? std::numeric_limits >::infinity().backend() : (std::numeric_limits >::max)().backend(); + return; + } + + // Check for pure-integer arguments which can be either signed or unsigned. + boost::intmax_t ll; + eval_trunc(exp_series, x); + convert_to(&ll, exp_series); + if(x.compare(ll) == 0) + { + detail::pow_imp(result, get_constant_e(), ll, mpl::true_()); + return; + } + + // The algorithm for exp has been taken from MPFUN. + // exp(t) = [ (1 + r + r^2/2! + r^3/3! + r^4/4! ...)^p2 ] * 2^n + // where p2 is a power of 2 such as 2048, r = t_prime / p2, and + // t_prime = t - n*ln2, with n chosen to minimize the absolute + // value of t_prime. In the resulting Taylor series, which is + // implemented as a hypergeometric function, |r| is bounded by + // ln2 / p2. For small arguments, no scaling is done. + + typedef typename mpl::front::type float_type; + + const bool b_scale = (xx.compare(float_type(1e-4)) > 0); + + // Compute the exponential series of the (possibly) scaled argument. + + if(b_scale) + { + divide(result, xx, get_constant_ln2()); + boost::intmax_t n; + convert_to(&n, result); + + // The scaling is 2^11 = 2048. + static const long long p2 = static_cast(boost::uint32_t(1u) << 11); + + multiply(exp_series, get_constant_ln2(), n); + subtract(exp_series, xx); + divide(exp_series, p2); + exp_series.negate(); + hyp0F0(result, exp_series); + + detail::pow_imp(exp_series, result, p2, mpl::true_()); + result = ui_type(1); + eval_ldexp(result, result, n); + multiply(exp_series, result); + } + else + { + hyp0F0(exp_series, xx); + } + + if(isneg) + divide(result, ui_type(1), exp_series); + else + result = exp_series; +} diff --git a/include/boost/multiprecision/e_float.hpp b/include/boost/multiprecision/e_float.hpp index 4f9d4aa2..68931334 100644 --- a/include/boost/multiprecision/e_float.hpp +++ b/include/boost/multiprecision/e_float.hpp @@ -13,7 +13,7 @@ #include namespace boost{ -namespace math{ +namespace multiprecision{ typedef mp_number > e_float; diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 2cf5991d..bcaaf1e0 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -15,7 +15,7 @@ #include #include -namespace boost{ namespace math{ +namespace boost{ namespace multiprecision{ template struct gmp_real; @@ -567,6 +567,68 @@ inline void convert_to(double* result, const gmp_real& val) { *result = mpf_get_d(val.data()); } +#ifdef BOOST_HAS_LONG_LONG +template +inline void convert_to(long long* result, const gmp_real& val) +{ + gmp_real t(val); + if(get_sign(t) < 0) + t.negate(); + + long digits = std::numeric_limits::digits - std::numeric_limits::digits; + + if(digits > 0) + mpf_div_2exp(t.data(), t.data(), digits); + + if(!mpf_fits_slong_p(t.data())) + { + *result = (std::numeric_limits::max)(); + return; + }; + + *result = mpf_get_si(t.data()); + while(digits > 0) + { + *result <<= digits; + digits -= std::numeric_limits::digits; + mpf_mul_2exp(t.data(), t.data(), digits >= 0 ? std::numeric_limits::digits : std::numeric_limits::digits + digits); + unsigned long l = mpf_get_ui(t.data()); + if(digits < 0) + l >>= -digits; + *result |= l; + } + if(get_sign(val) < 0) + *result = -*result; +} +template +inline void convert_to(unsigned long long* result, const gmp_real& val) +{ + gmp_real t(val); + + long digits = std::numeric_limits::digits - std::numeric_limits::digits; + + if(digits > 0) + mpf_div_2exp(t.data(), t.data(), digits); + + if(!mpf_fits_ulong_p(t.data())) + { + *result = (std::numeric_limits::max)(); + return; + } + + *result = mpf_get_ui(t.data()); + while(digits > 0) + { + *result <<= digits; + digits -= std::numeric_limits::digits; + mpf_mul_2exp(t.data(), t.data(), digits >= 0 ? std::numeric_limits::digits : std::numeric_limits::digits + digits); + unsigned long l = mpf_get_ui(t.data()); + if(digits < 0) + l >>= -digits; + *result |= l; + } +} +#endif // // Native non-member operations: @@ -1289,14 +1351,14 @@ inline void convert_to(long* result, const gmp_rational& val) { double r; convert_to(&r, val); - *result = r; + *result = static_cast(r); } inline void convert_to(unsigned long* result, const gmp_rational& val) { double r; convert_to(&r, val); - *result = r; + *result = static_cast(r); } inline void eval_abs(gmp_rational& result, const gmp_rational& val) @@ -1329,9 +1391,9 @@ namespace std{ // numeric_limits [partial] specializations for the types declared in this header: // template -class numeric_limits > > +class numeric_limits > > { - typedef boost::math::mp_number > number_type; + typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; BOOST_STATIC_CONSTEXPR number_type (min)() noexcept @@ -1421,10 +1483,10 @@ private: { data_initializer() { - std::numeric_limits > >::epsilon(); - std::numeric_limits > >::round_error(); - (std::numeric_limits > >::min)(); - (std::numeric_limits > >::max)(); + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); } void do_nothing()const{} }; @@ -1432,12 +1494,12 @@ private: }; template -const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; +const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; template<> -class numeric_limits > > +class numeric_limits > > { - typedef boost::math::mp_number > number_type; + typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(); } @@ -1474,9 +1536,9 @@ public: }; template<> -class numeric_limits +class numeric_limits { - typedef boost::math::mpz_int number_type; + typedef boost::multiprecision::mpz_int number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; // diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index fc2f2f75..053d45a6 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -21,7 +21,7 @@ #include #include -namespace boost{ namespace math{ +namespace boost{ namespace multiprecision{ template class mp_number @@ -546,31 +546,6 @@ private: divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } -#if 0 - template - void do_assign(const Exp& e, const detail::multiply_and_negate_immediates&) - { - using big_num_default_ops::multiply; - multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - m_backend.negate(); - } - - template - void do_assign(const Exp& e, const detail::divide_and_negate_immediates&) - { - using big_num_default_ops::divide; - divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - m_backend.negate(); - } - - template - void do_assign(const Exp& e, const detail::unary_plus&) - { - typedef typename Exp::left_type left_type; - do_assign(e.left(), typename left_type::tag_type()); - } - -#endif template void do_assign(const Exp& e, const detail::negate&) { @@ -1491,7 +1466,7 @@ struct is_valid_comparison_imp }; template -struct is_valid_comparison : public boost::math::detail::is_valid_comparison_imp::type {}; +struct is_valid_comparison : public boost::multiprecision::detail::is_valid_comparison_imp::type {}; } diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index ad018505..062d926a 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -15,7 +15,7 @@ #include #include -namespace boost{ namespace math{ +namespace boost{ namespace multiprecision{ template struct mpfr_real_backend; @@ -736,10 +736,14 @@ typedef mp_number > mpfr_real_500; typedef mp_number > mpfr_real_1000; typedef mp_number > mpfr_real; +} // namespace boost + +namespace math{ + namespace lanczos{ template -struct lanczos >, Policy> +struct lanczos >, Policy> { typedef typename mpl::if_c< Digits10 <= 36, @@ -771,9 +775,9 @@ namespace std{ // numeric_limits [partial] specializations for the types declared in this header: // template -class numeric_limits > > +class numeric_limits > > { - typedef boost::math::mp_number > number_type; + typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; BOOST_STATIC_CONSTEXPR number_type (min)() noexcept @@ -890,12 +894,12 @@ private: { data_initializer() { - std::numeric_limits > >::epsilon(); - std::numeric_limits > >::round_error(); - (std::numeric_limits > >::min)(); - (std::numeric_limits > >::max)(); - std::numeric_limits > >::infinity(); - std::numeric_limits > >::quiet_NaN(); + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); + std::numeric_limits > >::infinity(); + std::numeric_limits > >::quiet_NaN(); } void do_nothing()const{} }; @@ -903,12 +907,12 @@ private: }; template -const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; +const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; template<> -class numeric_limits > > +class numeric_limits > > { - typedef boost::math::mp_number > number_type; + typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(0); } diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 24b697e7..5e66e5bf 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -187,3 +187,11 @@ run big_number_concept_check.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : big_number_concept_check_mpfr_50 ; +run test_exp.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_exp_mpf50 ; + diff --git a/test/big_number_concept_check.cpp b/test/big_number_concept_check.cpp index 466af22f..ec54755b 100644 --- a/test/big_number_concept_check.cpp +++ b/test/big_number_concept_check.cpp @@ -57,22 +57,22 @@ void foo() { #ifdef TEST_BACKEND - instantiate(boost::math::big_number_real_architype()); + instantiate(boost::multiprecision::big_number_real_architype()); #endif #ifdef TEST_MPF_50 - instantiate(boost::math::mpf_real_50()); + instantiate(boost::multiprecision::mpf_real_50()); #endif #ifdef TEST_MPF - instantiate(boost::math::mpf_real()); + instantiate(boost::multiprecision::mpf_real()); #endif #ifdef TEST_MPFR_50 - instantiate(boost::math::mpfr_real_50()); + instantiate(boost::multiprecision::mpfr_real_50()); #endif #ifdef TEST_MPFR - instantiate(boost::math::mpfr_real()); + instantiate(boost::multiprecision::mpfr_real()); #endif #ifdef TEST_E_FLOAT - instantiate(boost::math::e_float()); + instantiate(boost::multiprecision::e_float()); #endif } @@ -82,19 +82,19 @@ int main() BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPF_50 - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPF - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPFR_50 - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPFR - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_E_FLOAT - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif } diff --git a/test/linpack-benchmark.cpp b/test/linpack-benchmark.cpp index 27fdde3e..1f4d2ab8 100644 --- a/test/linpack-benchmark.cpp +++ b/test/linpack-benchmark.cpp @@ -21,10 +21,10 @@ http://www.netlib.org/f2c/libf2c.zip #ifdef TEST_MPF_100 #include -typedef boost::math::mpf_real_100 real_type; +typedef boost::multiprecision::mpf_real_100 real_type; #elif defined(TEST_MPFR_100) #include -typedef boost::math::mpfr_real_100 real_type; +typedef boost::multiprecision::mpfr_real_100 real_type; #elif defined(TEST_GMPXX) #include typedef mpf_class real_type; @@ -39,7 +39,7 @@ typedef ::efx::e_float real_type; using ef::abs; #elif defined(TEST_E_FLOAT_BN) #include -typedef boost::math::e_float real_type; +typedef boost::multiprecision::e_float real_type; #else typedef double real_type; #endif @@ -111,7 +111,7 @@ extern "C" int MAIN__() #elif defined(TEST_E_FLOAT) std::cout << "Testing boost::ef::e_float" << std::endl; #elif defined(TEST_E_FLOAT_BN) - std::cout << "Testing boost::math::e_float" << std::endl; + std::cout << "Testing boost::multiprecision::e_float" << std::endl; #else std::cout << "Testing double" << std::endl; #endif @@ -1242,7 +1242,7 @@ mp_number >: times for array with leading dimension of1001 279.96 0.84 280.8 2.3813 0.83988 5014.3 -boost::math::ef::e_float: +boost::multiprecision::ef::e_float: ~~~~~~~~~~~~~~~~~~~~~~~~~ norm. resid resid machep x(1) x(n) diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 3e82e749..62405dad 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -74,7 +74,7 @@ template void test_integer_ops(const T&){} template -void test_integer_ops(const boost::mpl::int_&) +void test_integer_ops(const boost::mpl::int_&) { Real a(20); Real b(7); @@ -270,7 +270,7 @@ template void test_real_ops(const T&){} template -void test_real_ops(const boost::mpl::int_&) +void test_real_ops(const boost::mpl::int_&) { #if defined(TEST_MPF) || defined(TEST_MPF_50) || defined(TEST_BACKEND) || defined(TEST_MPFR) BOOST_TEST(abs(Real(2)) == 2); @@ -566,11 +566,11 @@ void test() // // Integer only functions: // - test_integer_ops(typename boost::math::number_category::type()); + test_integer_ops(typename boost::multiprecision::number_category::type()); // // Real number only functions: // - test_real_ops(typename boost::math::number_category::type()); + test_real_ops(typename boost::multiprecision::number_category::type()); // // Test basic arithmetic: // @@ -859,35 +859,35 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF50 - test(); + test(); #endif #ifdef TEST_MPF - boost::math::mpf_real::default_precision(1000); + boost::multiprecision::mpf_real::default_precision(1000); /* - boost::math::mpf_real r; + boost::multiprecision::mpf_real r; r.precision(50); BOOST_TEST(r.precision() >= 50); */ - BOOST_TEST(boost::math::mpf_real::default_precision() == 1000); - test(); + BOOST_TEST(boost::multiprecision::mpf_real::default_precision() == 1000); + test(); #endif #ifdef TEST_MPZ - test(); + test(); #endif #ifdef TEST_MPQ - test(); + test(); #endif #ifdef TEST_E_FLOAT - test(); + test(); #endif #ifdef TEST_MPFR - test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_exp.cpp b/test/test_exp.cpp new file mode 100644 index 00000000..14a3129a --- /dev/null +++ b/test/test_exp.cpp @@ -0,0 +1,129 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif + +template +void test() +{ + static const boost::array data = + {{ + T("1."), + T("9.4774758759621877024211675170518456366884502921505415491512637467314221915954853431757689726613032841249599156149038435317513116309445221664968991934479367736962368912070497862135887440758964938422498610719192114666493107120133053433933470080716434904854804591983841381870449665144170011709399012693158566138960223723364102555657731121349862591746773752353141675856300389702807704522952296232409058995e76"), + T("8.9822548979445237099762393639075561506833309483454509238768979587574644012197081949903511127689329087920328909235374785049128571553031890973238724279779592658729244759890277209350767466719784199679796679076195510817453034019585841414276969807276603422838152196159579020392165208404938697706742432405072185394955217454998873094186010667116964062108348411120353180844989880619261736047981860732797930644e153"), + 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T("9.9491406083653158286834756917422021600764727853686312719802358420566982531788421914469238540915616504216223401740335370367923898274605089490332650511788075886198714135795808528419557141582217964579360685402741569208063074313253490838482414281367060197950065504143914001338572155467333984661503453898847902871372714795379743025547542723839248318892138759596907306100969830936341255021634987471789706941e3309"), + T("9.42927401023380446961314339401657458785389811652244742482194123119943160577946366372207045050095290781679375214307398843926493195734487944624333413228893399732976728321980799677091653454804065271499274601941255651159823827574140068157063214410760869314717732028275496245648005191215048930881016330693755275282258597115402181603925122663256538590166426964332556533036059527784227962722441198371434037e3386"), + T("8.9365716959828116465632229827533775010309573979010794366666818430433566556286774474031057786888009871925254918684981245088107384317036889752292156920146379694165987770273470926340201197874812456173862271880689137375502421735431888891334269040972307308842443051934967463204037988999112477683156448819368015441070611711599827182978835927951062291039453298334013800388495719125476482150507255562932471987e3463"), + T("8.4696142662483591182651710363149061965529671414187214114508986504580419620532836415592194561692587545892671733647852519586965260182156246891106882514113059675737245160959965677478337885852837584798963994305283509311992268344932659689149044725278268851178262071743625689593833327527427790889142934871390124497847187559769333723286181059355730422352609633594972880679988434632727829633392971196615348162e3540"), + T("8.0270564887074008992929481581600294386090831745459505539216873340458312207422342705431057237884163498424349206319209533661302797554406960728685696384646157216820308811030692783501496335637205341645641865876987704911724172887422201095488046489024482854111274279939733922390803256997868575641148291588995771500671739181954270612789001072297006035844811068998273723866529350060897658557177391069889428138e3617"), + T("7.6076234226710136997076519198854581037482480050087592375273646746765716709802670790534160394910843369630438334623933329715061433126854176918572680591852491900095968421410826840041652944667732505393218836407650478812322026068521739096553158504199794298343738853325452463396386800405102937609865179610358195390467842398985491405704400439203254032406556044023342935195219037071893174834506422022272020608e3694"), + T("7.2101067461769422102719046864935900042020946053983858930538783546380741670622477730299778929732944630854151363803543748221329578582604770541719603126349873057195532110292846743563791049380608460124840094825775295226949060515234109528775156283010154878061758953690404860422160965162770534213586973008276804840802176466270909812402590547626695704877606695620372290113893333718784454195491413120278571381e3771"), + T("6.833361275000419432343650592319686694062674227594429857464606108305032877344799885305123090652406787997867592503236607009836687444829395552541403634550659710745653974928907350064693400553697943529341780925791186120102910163514753761188563821153759960369188532092163964559115206212975793696371318151500479047238166891574507004736959512033943570963451048752039151427991562182278434585245918970979972925e3848"), + }}; + + T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"; + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = boost::multiprecision::exp(boost::multiprecision::sqrt((pi * (100 * k)) * (100 * k))); + T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon()); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 1200); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif + return boost::report_errors(); +} + + + diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index 1cd7f695..0bd62a0f 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -138,35 +138,35 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF50 - test(); + test(); #endif #ifdef TEST_MPF - boost::math::mpf_real::default_precision(1000); + boost::multiprecision::mpf_real::default_precision(1000); /* - boost::math::mpf_real r; + boost::multiprecision::mpf_real r; r.precision(50); BOOST_TEST(r.precision() >= 50); */ - BOOST_TEST(boost::math::mpf_real::default_precision() == 1000); - test(); + BOOST_TEST(boost::multiprecision::mpf_real::default_precision() == 1000); + test(); #endif #ifdef TEST_MPZ - test(); + test(); #endif #ifdef TEST_MPQ - test(); + test(); #endif #ifdef TEST_E_FLOAT - test(); + test(); #endif #ifdef TEST_MPFR - test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); + test(); #endif return boost::report_errors(); } From e0309c8492113b36ba46c0d3cf9a75617c5dc6b6 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 3 Oct 2011 17:03:28 +0000 Subject: [PATCH 030/256] More file renames to remove "big_" prefixes. [SVN r74670] --- .../{big_number_architypes.hpp => mp_number_architypes.hpp} | 0 include/boost/multiprecision/detail/default_ops.hpp | 2 +- .../detail/{big_number_base.hpp => mp_number_base.hpp} | 0 test/Jamfile.v2 | 2 +- ...big_number_concept_check.cpp => mp_number_concept_check.cpp} | 2 +- test/test_arithmetic.cpp | 2 +- test/test_exp.cpp | 2 +- test/test_numeric_limits.cpp | 2 +- 8 files changed, 6 insertions(+), 6 deletions(-) rename include/boost/multiprecision/concepts/{big_number_architypes.hpp => mp_number_architypes.hpp} (100%) rename include/boost/multiprecision/detail/{big_number_base.hpp => mp_number_base.hpp} (100%) rename test/{big_number_concept_check.cpp => mp_number_concept_check.cpp} (97%) diff --git a/include/boost/multiprecision/concepts/big_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp similarity index 100% rename from include/boost/multiprecision/concepts/big_number_architypes.hpp rename to include/boost/multiprecision/concepts/mp_number_architypes.hpp diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index da8780e8..58bc9637 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -7,7 +7,7 @@ #define BOOST_MATH_BIG_NUM_DEF_OPS #include -#include +#include #include #include #include diff --git a/include/boost/multiprecision/detail/big_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp similarity index 100% rename from include/boost/multiprecision/detail/big_number_base.hpp rename to include/boost/multiprecision/detail/mp_number_base.hpp diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 5e66e5bf..d36382c6 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -179,7 +179,7 @@ run test_numeric_limits.cpp $(E_FLOAT_SRC) [ check-target-builds ../config//has_e_float : : no ] : test_numeric_limits_e_float ; -run big_number_concept_check.cpp mpfr +run mp_number_concept_check.cpp mpfr : # command line : # input files : # requirements diff --git a/test/big_number_concept_check.cpp b/test/mp_number_concept_check.cpp similarity index 97% rename from test/big_number_concept_check.cpp rename to test/mp_number_concept_check.cpp index ec54755b..635e5de0 100644 --- a/test/big_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -42,7 +42,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_E_FLOAT #include diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 62405dad..d9eebcec 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -29,7 +29,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_E_FLOAT #include diff --git a/test/test_exp.cpp b/test/test_exp.cpp index 14a3129a..5415448a 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_E_FLOAT #include diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index 0bd62a0f..d378becd 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -28,7 +28,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_E_FLOAT #include From b8a60ca6caff5c2ca5779b2f7c65e6c50df1b585 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 3 Oct 2011 17:15:55 +0000 Subject: [PATCH 031/256] Rename "big_number*" to "mp_number*". [SVN r74671] --- .../concepts/mp_number_architypes.hpp | 84 +++++++++---------- .../multiprecision/detail/mp_number_base.hpp | 30 +++---- include/boost/multiprecision/mp_number.hpp | 36 ++++---- test/mp_number_concept_check.cpp | 4 +- test/test_arithmetic.cpp | 2 +- test/test_exp.cpp | 2 +- test/test_numeric_limits.cpp | 2 +- 7 files changed, 80 insertions(+), 80 deletions(-) diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index fbec67b3..032f78f7 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -23,52 +23,52 @@ namespace concepts{ #pragma warning(disable:4244) #endif -struct big_number_backend_real_architype +struct mp_number_backend_real_architype { typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list real_types; - big_number_backend_real_architype() + mp_number_backend_real_architype() { std::cout << "Default construct" << std::endl; } - big_number_backend_real_architype(const big_number_backend_real_architype& o) + mp_number_backend_real_architype(const mp_number_backend_real_architype& o) { std::cout << "Copy construct" << std::endl; m_value = o.m_value; } - big_number_backend_real_architype& operator = (const big_number_backend_real_architype& o) + mp_number_backend_real_architype& operator = (const mp_number_backend_real_architype& o) { m_value = o.m_value; std::cout << "Assignment (" << m_value << ")" << std::endl; return *this; } - big_number_backend_real_architype& operator = (boost::uintmax_t i) + mp_number_backend_real_architype& operator = (boost::uintmax_t i) { m_value = i; std::cout << "UInt Assignment (" << i << ")" << std::endl; return *this; } - big_number_backend_real_architype& operator = (boost::intmax_t i) + mp_number_backend_real_architype& operator = (boost::intmax_t i) { m_value = i; std::cout << "Int Assignment (" << i << ")" << std::endl; return *this; } - big_number_backend_real_architype& operator = (long double d) + mp_number_backend_real_architype& operator = (long double d) { m_value = d; std::cout << "long double Assignment (" << d << ")" << std::endl; return *this; } - big_number_backend_real_architype& operator = (const char* s) + mp_number_backend_real_architype& operator = (const char* s) { m_value = boost::lexical_cast(s); std::cout << "const char* Assignment (" << s << ")" << std::endl; return *this; } - void swap(big_number_backend_real_architype& o) + void swap(mp_number_backend_real_architype& o) { std::cout << "Swapping (" << m_value << " with " << o.m_value << ")" << std::endl; std::swap(m_value, o.m_value); @@ -99,7 +99,7 @@ struct big_number_backend_real_architype std::cout << "Negating (" << m_value << ")" << std::endl; m_value = -m_value; } - int compare(const big_number_backend_real_architype& o)const + int compare(const mp_number_backend_real_architype& o)const { std::cout << "Comparison" << std::endl; return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); @@ -122,151 +122,151 @@ struct big_number_backend_real_architype long double m_value; }; -inline void add(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +inline void add(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& o) { std::cout << "Addition (" << result.m_value << " += " << o.m_value << ")" << std::endl; result.m_value += o.m_value; } -inline void subtract(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +inline void subtract(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& o) { std::cout << "Subtraction (" << result.m_value << " -= " << o.m_value << ")" << std::endl; result.m_value -= o.m_value; } -inline void multiply(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +inline void multiply(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& o) { std::cout << "Multiplication (" << result.m_value << " *= " << o.m_value << ")" << std::endl; result.m_value *= o.m_value; } -inline void divide(big_number_backend_real_architype& result, const big_number_backend_real_architype& o) +inline void divide(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& o) { std::cout << "Division (" << result.m_value << " /= " << o.m_value << ")" << std::endl; result.m_value /= o.m_value; } -inline void convert_to(boost::uintmax_t* result, const big_number_backend_real_architype& val) +inline void convert_to(boost::uintmax_t* result, const mp_number_backend_real_architype& val) { *result = static_cast(val.m_value); } -inline void convert_to(boost::intmax_t* result, const big_number_backend_real_architype& val) +inline void convert_to(boost::intmax_t* result, const mp_number_backend_real_architype& val) { *result = static_cast(val.m_value); } -inline void convert_to(long double* result, big_number_backend_real_architype& val) +inline void convert_to(long double* result, mp_number_backend_real_architype& val) { *result = val.m_value; } -inline void eval_frexp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg, int* exp) +inline void eval_frexp(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg, int* exp) { result = std::frexp(arg.m_value, exp); } -inline void eval_ldexp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg, int exp) +inline void eval_ldexp(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg, int exp) { result = std::ldexp(arg.m_value, exp); } -inline void eval_floor(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_floor(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::floor(arg.m_value); } -inline void eval_ceil(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_ceil(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::ceil(arg.m_value); } -inline void eval_trunc(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_trunc(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = boost::math::trunc(arg.m_value); } -inline void eval_sqrt(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_sqrt(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::sqrt(arg.m_value); } -inline void eval_abs(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_abs(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::abs(arg.m_value); } -inline void eval_fabs(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_fabs(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::fabs(arg.m_value); } -inline int eval_fpclassify(const big_number_backend_real_architype& arg) +inline int eval_fpclassify(const mp_number_backend_real_architype& arg) { return boost::math::fpclassify(arg.m_value); } -inline void eval_pow(big_number_backend_real_architype& result, const big_number_backend_real_architype& b, const big_number_backend_real_architype& e) +inline void eval_pow(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& b, const mp_number_backend_real_architype& e) { result = std::pow(b.m_value, e.m_value); } -inline void eval_pow(big_number_backend_real_architype& result, const big_number_backend_real_architype& b, int e) +inline void eval_pow(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& b, int e) { result = std::pow(b.m_value, e); } -inline void eval_exp(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_exp(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::exp(arg.m_value); } -inline void eval_log(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_log(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::log(arg.m_value); } -inline void eval_sin(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_sin(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::sin(arg.m_value); } -inline void eval_cos(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_cos(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::cos(arg.m_value); } -inline void eval_tan(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_tan(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::tan(arg.m_value); } -inline void eval_asin(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_asin(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::asin(arg.m_value); } -inline void eval_acos(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_acos(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::acos(arg.m_value); } -inline void eval_atan(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_atan(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::atan(arg.m_value); } -inline void eval_sinh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_sinh(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::sinh(arg.m_value); } -inline void eval_cosh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_cosh(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::cosh(arg.m_value); } -inline void eval_tanh(big_number_backend_real_architype& result, const big_number_backend_real_architype& arg) +inline void eval_tanh(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) { result = std::tanh(arg.m_value); } -typedef boost::multiprecision::mp_number big_number_real_architype; +typedef boost::multiprecision::mp_number mp_number_real_architype; }}} // namespaces @@ -277,10 +277,10 @@ namespace std{ #endif template <> -class numeric_limits : public std::numeric_limits +class numeric_limits : public std::numeric_limits { typedef std::numeric_limits base_type; - typedef boost::multiprecision::concepts::big_number_real_architype number_type; + typedef boost::multiprecision::concepts::mp_number_real_architype number_type; public: BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 6b85d7d4..39fd8500 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -137,13 +137,13 @@ struct backend_type > template -struct is_big_number : public mpl::false_{}; +struct is_mp_number : public mpl::false_{}; template -struct is_big_number > : public mpl::true_{}; +struct is_mp_number > : public mpl::true_{}; template -struct is_big_number_exp : public mpl::false_{}; +struct is_mp_number_exp : public mpl::false_{}; template -struct is_big_number_exp > : public mpl::true_{}; +struct is_mp_number_exp > : public mpl::true_{}; template struct combine_expression; @@ -187,25 +187,25 @@ struct unmentionable typedef void (*unmentionable_type)(); template -struct big_number_exp_storage +struct mp_exp_storage { typedef const T& type; }; template -struct big_number_exp_storage +struct mp_exp_storage { typedef T* type; }; template -struct big_number_exp_storage +struct mp_exp_storage { typedef const T* type; }; template -struct big_number_exp_storage > +struct mp_exp_storage > { typedef mp_exp type; }; @@ -233,7 +233,7 @@ struct mp_exp } private: - typename big_number_exp_storage::type arg; + typename mp_exp_storage::type arg; }; template @@ -255,7 +255,7 @@ struct mp_exp } private: - typename big_number_exp_storage::type arg; + typename mp_exp_storage::type arg; }; template @@ -286,8 +286,8 @@ struct mp_exp static const unsigned right_depth = right_type::depth + 1; static const unsigned depth = left_depth > right_depth ? left_depth : right_depth; private: - typename big_number_exp_storage::type arg1; - typename big_number_exp_storage::type arg2; + typename mp_exp_storage::type arg1; + typename mp_exp_storage::type arg2; }; template @@ -326,9 +326,9 @@ struct mp_exp static const unsigned right_depth = right_type::depth + 1; static const unsigned depth = left_depth > right_depth ? (left_depth > middle_depth ? left_depth : middle_depth) : (right_depth > middle_depth ? right_depth : middle_depth); private: - typename big_number_exp_storage::type arg1; - typename big_number_exp_storage::type arg2; - typename big_number_exp_storage::type arg3; + typename mp_exp_storage::type arg1; + typename mp_exp_storage::type arg2; + typename mp_exp_storage::type arg3; }; } // namespace detail diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 053d45a6..e54c85cb 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -1384,37 +1384,37 @@ namespace detail { template -inline int big_number_compare(const mp_number& a, const mp_number& b) +inline int mp_number_compare(const mp_number& a, const mp_number& b) { return a.compare(b); } template -inline int big_number_compare(const mp_number& a, const mp_exp& b) +inline int mp_number_compare(const mp_number& a, const mp_exp& b) { return a.compare(mp_number(b)); } template -inline int big_number_compare(const mp_exp& a, const mp_number& b) +inline int mp_number_compare(const mp_exp& a, const mp_number& b) { return -b.compare(mp_number(a)); } template -inline int big_number_compare(const mp_number& a, const Val b) +inline int mp_number_compare(const mp_number& a, const Val b) { return a.compare(b); } template -inline int big_number_compare(const Val a, const mp_number& b) +inline int mp_number_compare(const Val a, const mp_number& b) { return -b.compare(a); } template -inline int big_number_compare(const mp_exp& a, const mp_exp& b) +inline int mp_number_compare(const mp_exp& a, const mp_exp& b) { typedef typename mp_exp::result_type real1; typedef typename mp_exp::result_type real2; @@ -1422,7 +1422,7 @@ inline int big_number_compare(const mp_exp& a, const mp_exp -inline typename enable_if, int>::type big_number_compare(const mp_exp& a, const Val b) +inline typename enable_if, int>::type mp_number_compare(const mp_exp& a, const Val b) { typedef typename mp_exp::result_type real; real t(a); @@ -1430,7 +1430,7 @@ inline typename enable_if, int>::type big_number_compare(cons } template -inline typename enable_if, int>::type big_number_compare(const Val a, const mp_exp& b) +inline typename enable_if, int>::type mp_number_compare(const Val a, const mp_exp& b) { typedef typename mp_exp::result_type real; return -real(b).compare(a); @@ -1440,12 +1440,12 @@ template struct is_valid_comparison_imp { typedef typename mpl::or_< - is_big_number, - is_big_number_exp + is_mp_number, + is_mp_number_exp >::type is1; typedef typename mpl::or_< - is_big_number, - is_big_number_exp + is_mp_number, + is_mp_number_exp >::type is2; typedef typename mpl::or_< mpl::and_< @@ -1475,42 +1475,42 @@ template inline typename boost::enable_if, bool>::type operator == (const Exp1& a, const Exp2& b) { - return 0 == detail::big_number_compare(a, b); + return 0 == detail::mp_number_compare(a, b); } template inline typename boost::enable_if, bool>::type operator != (const Exp1& a, const Exp2& b) { - return 0 != detail::big_number_compare(a, b); + return 0 != detail::mp_number_compare(a, b); } template inline typename boost::enable_if, bool>::type operator <= (const Exp1& a, const Exp2& b) { - return 0 >= detail::big_number_compare(a, b); + return 0 >= detail::mp_number_compare(a, b); } template inline typename boost::enable_if, bool>::type operator < (const Exp1& a, const Exp2& b) { - return 0 > detail::big_number_compare(a, b); + return 0 > detail::mp_number_compare(a, b); } template inline typename boost::enable_if, bool>::type operator >= (const Exp1& a, const Exp2& b) { - return 0 <= detail::big_number_compare(a, b); + return 0 <= detail::mp_number_compare(a, b); } template inline typename boost::enable_if, bool>::type operator > (const Exp1& a, const Exp2& b) { - return 0 < detail::big_number_compare(a, b); + return 0 < detail::mp_number_compare(a, b); } template diff --git a/test/mp_number_concept_check.cpp b/test/mp_number_concept_check.cpp index 635e5de0..cc814372 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -57,7 +57,7 @@ void foo() { #ifdef TEST_BACKEND - instantiate(boost::multiprecision::big_number_real_architype()); + instantiate(boost::multiprecision::mp_number_real_architype()); #endif #ifdef TEST_MPF_50 instantiate(boost::multiprecision::mpf_real_50()); @@ -79,7 +79,7 @@ void foo() int main() { #ifdef TEST_BACKEND - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPF_50 BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index d9eebcec..2c837f26 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -859,7 +859,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF50 test(); diff --git a/test/test_exp.cpp b/test/test_exp.cpp index 5415448a..592ae720 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -113,7 +113,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF50 test(); diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index d378becd..28c354c9 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -138,7 +138,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF50 test(); From 7be44c1683d0c3bbc6ce03d73921e21c2f6942ca Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 4 Oct 2011 16:46:25 +0000 Subject: [PATCH 032/256] Add log function and tests. [SVN r74700] --- config/Jamfile.v2 | 3 +- .../multiprecision/detail/functions/pow.hpp | 45 +++++ test/Jamfile.v2 | 7 + test/test_log.cpp | 181 ++++++++++++++++++ 4 files changed, 235 insertions(+), 1 deletion(-) create mode 100644 test/test_log.cpp diff --git a/config/Jamfile.v2 b/config/Jamfile.v2 index 832e2936..2aeacdc8 100644 --- a/config/Jamfile.v2 +++ b/config/Jamfile.v2 @@ -32,7 +32,7 @@ obj has_e_float : has_e_float.cpp : $(e_float_path) ; obj has_gmp : has_gmp.cpp : $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; obj has_mpfr : has_mpfr.cpp : - $(mpfr_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; + $(mpfr_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx $(gmp_path) ; explicit has_long_double_support ; explicit has_mpfr_class ; @@ -43,3 +43,4 @@ explicit has_gcc_visibility ; explicit has_e_float ; explicit has_gmp ; explicit has_mpfr ; + diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index de5b2b4e..63f6f223 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -241,3 +241,48 @@ void eval_exp(T& result, const T& x) result = exp_series; } +template +void eval_log(T& result, const T& arg) +{ + // + // We use a variation of http://dlmf.nist.gov/4.45#i + // using frexp to reduce the argument to x * 2^n, + // then let y = x - 1 and compute: + // log(x) = log(2) * n + log1p(1 + y) + // + if(&arg == &result) + { + T temp; + eval_log(temp, arg); + result = temp; + } + + typedef typename boost::multiprecision::detail::canonical::type long_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + + int e; + T t; + eval_frexp(t, arg, &e); + + multiply(result, get_constant_ln2(), long_type(e)); + subtract(t, ui_type(1)); /* -0.5 <= t <= 0 */ + t.negate(); /* 0 <= t <= 0.5 */ + T pow = t; + T lim; + T t2; + multiply(lim, result, std::numeric_limits >::epsilon().backend()); + if(get_sign(lim) < 0) + lim.negate(); + + subtract(result, t); + + ui_type k = 1; + do + { + ++k; + multiply(pow, t); + divide(t2, pow, k); + subtract(result, t2); + }while(lim.compare(t2) <= 0); +} + diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index d36382c6..d3b86aee 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -195,3 +195,10 @@ run test_exp.cpp gmp [ check-target-builds ../config//has_gmp : : no ] : test_exp_mpf50 ; +run test_log.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_log_mpf50 ; diff --git a/test/test_log.cpp b/test/test_log.cpp new file mode 100644 index 00000000..4139a059 --- /dev/null +++ b/test/test_log.cpp @@ -0,0 +1,181 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif + +template +void test() +{ + static const boost::array data = + {{ + T("-2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806"), + T("10.355073440919378699690477472036470469315794905372650461119520557405966250191554948388847794306923706128373152780234988638443954821327953543032075228882306893901540038156503265416950932549208174713640840670002321534598356631953006304821201484830902632165858733357596733427094375150860310219829690440417223992885533566388118595248523193740778052893647271700612136670114224280374211626787106078693643289"), + 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T("19.52500521549816144973266072401605164852396136071234571245810367391072812166019661923143396972741343266046339927362413412251126099193801965681827360699083448218860273549526903661234475357554150017778848244185893299525191263899191588797634058235164494448438674653809951435022502560679429105527325418829543863756825670476364629140951247734867887985343458291386040322597855003211338820555010939867273248"), + T("19.545309958419535630089123088329455125777373731767323301911891787605488456921558805681207304272616222501167615837357366396904683096528060072684210523189673108467018417135186800678628444987751206147451054525963839562634340820804697604369657105969423354842149829173951943549166420900709500398322624130365195674097282456714104812933002700523506427441210494461469512180706693823193924457440917371176532034"), + T("19.565410630120075532420489068555321524954362381908007338302983473268528473151341321768804731192210840056455228388636731122203200610869021021871133154865620432257415783302175345843898977949742849569372169004904667621738405749986270376895267386643049526766451459390277406632576412790748533372863644721976845168460840162066672290292749672668879524315410824251032084115058493720402881895485689493165441193"), + }}; + + T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"; + T tenth = 1; + tenth /= 10; + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = boost::multiprecision::log(tenth + pi * (100 * k) * (100 * k)); + T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon()); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 10); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif + return boost::report_errors(); +} + + + From fa6b1ad9ea9cfbceb9f124256ba4068265b97d5c Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 4 Oct 2011 18:23:26 +0000 Subject: [PATCH 033/256] Add exponent_type as a requirement for floating point backends. Made use of that type in code, and suppressed a few warnings. [SVN r74704] --- .../multiprecision/arithmetic_backend.hpp | 1 + .../concepts/mp_number_architypes.hpp | 1 + .../multiprecision/detail/functions/pow.hpp | 21 ++++++++++++------- include/boost/multiprecision/gmp.hpp | 1 + include/boost/multiprecision/mpfr.hpp | 1 + 5 files changed, 17 insertions(+), 8 deletions(-) diff --git a/include/boost/multiprecision/arithmetic_backend.hpp b/include/boost/multiprecision/arithmetic_backend.hpp index f5429c48..a58a2b6d 100644 --- a/include/boost/multiprecision/arithmetic_backend.hpp +++ b/include/boost/multiprecision/arithmetic_backend.hpp @@ -21,6 +21,7 @@ struct arithmetic_backend typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list real_types; + typedef int exponent_type; arithmetic_backend(){} arithmetic_backend(const arithmetic_backend& o) diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index 032f78f7..92402dbc 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -28,6 +28,7 @@ struct mp_number_backend_real_architype typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list real_types; + typedef int exponent_type; mp_number_backend_real_architype() { diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 63f6f223..44a70c53 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -143,7 +143,10 @@ void eval_exp(T& result, const T& x) eval_exp(temp, x); result = temp; } - typedef typename mpl::front::type ui_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; // Handle special arguments. int type = eval_fpclassify(x); bool isneg = get_sign(x) < 0; @@ -174,7 +177,7 @@ void eval_exp(T& result, const T& x) xx.negate(); // Check the range of the argument. - static const boost::intmax_t maximum_arg_for_exp = std::numeric_limits >::max_exponent == 0 ? std::numeric_limits::max() : std::numeric_limits >::max_exponent; + static const canonical_exp_type maximum_arg_for_exp = std::numeric_limits >::max_exponent == 0 ? std::numeric_limits::max() : std::numeric_limits >::max_exponent; if(xx.compare(maximum_arg_for_exp) >= 0) { @@ -213,13 +216,13 @@ void eval_exp(T& result, const T& x) if(b_scale) { divide(result, xx, get_constant_ln2()); - boost::intmax_t n; + exp_type n; convert_to(&n, result); // The scaling is 2^11 = 2048. - static const long long p2 = static_cast(boost::uint32_t(1u) << 11); + static const si_type p2 = static_cast(si_type(1) << 11); - multiply(exp_series, get_constant_ln2(), n); + multiply(exp_series, get_constant_ln2(), static_cast(n)); subtract(exp_series, xx); divide(exp_series, p2); exp_series.negate(); @@ -257,14 +260,16 @@ void eval_log(T& result, const T& arg) result = temp; } - typedef typename boost::multiprecision::detail::canonical::type long_type; + typedef typename boost::multiprecision::detail::canonical::type si_type; typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - int e; + exp_type e; T t; eval_frexp(t, arg, &e); - multiply(result, get_constant_ln2(), long_type(e)); + multiply(result, get_constant_ln2(), canonical_exp_type(e)); subtract(t, ui_type(1)); /* -0.5 <= t <= 0 */ t.negate(); /* 0 <= t <= 0.5 */ T pow = t; diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index bcaaf1e0..7aab73ab 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -28,6 +28,7 @@ struct gmp_real_imp typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list real_types; + typedef long exponent_type; gmp_real_imp(){} diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 062d926a..b4d6286e 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -30,6 +30,7 @@ struct mpfr_real_imp typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list real_types; + typedef long exponent_type; mpfr_real_imp(){} From d6b9a6e98021fb8554b6664696277f7d27402421 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 5 Oct 2011 11:26:31 +0000 Subject: [PATCH 034/256] Change log to give correct answer for log(1) and to not subtract towards the correct answer when that answer is small. Also improves series convergence. [SVN r74736] --- .../multiprecision/detail/functions/pow.hpp | 26 +++++++++++++++---- test/test_log.cpp | 1 + 2 files changed, 22 insertions(+), 5 deletions(-) diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 44a70c53..85d389ba 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -264,14 +264,24 @@ void eval_log(T& result, const T& arg) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; exp_type e; T t; eval_frexp(t, arg, &e); + bool alternate = false; + + if(t.compare(fp_type(2) / fp_type(3)) <= 0) + { + alternate = true; + eval_ldexp(t, t, 1); + --e; + } multiply(result, get_constant_ln2(), canonical_exp_type(e)); - subtract(t, ui_type(1)); /* -0.5 <= t <= 0 */ - t.negate(); /* 0 <= t <= 0.5 */ + subtract(t, ui_type(1)); /* -0.3 <= t <= 0.3 */ + if(!alternate) + t.negate(); /* 0 <= t <= 0.33333 */ T pow = t; T lim; T t2; @@ -279,7 +289,10 @@ void eval_log(T& result, const T& arg) if(get_sign(lim) < 0) lim.negate(); - subtract(result, t); + if(alternate) + add(result, t); + else + subtract(result, t); ui_type k = 1; do @@ -287,7 +300,10 @@ void eval_log(T& result, const T& arg) ++k; multiply(pow, t); divide(t2, pow, k); - subtract(result, t2); - }while(lim.compare(t2) <= 0); + if(alternate && ((k & 1) != 0)) + add(result, t2); + else + subtract(result, t2); + }while(lim.compare(t2) < 0); } diff --git a/test/test_log.cpp b/test/test_log.cpp index 4139a059..5589a930 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -159,6 +159,7 @@ void test() } std::cout << "Max error was: " << max_err << std::endl; BOOST_TEST(max_err < 10); + BOOST_TEST(log(T(1)) == 0); } From 5f15eaa6793f14c265a49cc742d0b7a994f3da24 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 7 Oct 2011 18:14:34 +0000 Subject: [PATCH 035/256] Added pow, exp, log, sinh, cosh and tanh support. [SVN r74781] --- .../multiprecision/detail/functions/pow.hpp | 292 ++++++++- test/Jamfile.v2 | 80 +++ test/test_cosh.cpp | 137 ++++ test/test_exp.cpp | 12 + test/test_log.cpp | 7 + test/test_pow.cpp | 583 ++++++++++++++++++ test/test_sinh.cpp | 137 ++++ test/test_tanh.cpp | 137 ++++ 8 files changed, 1377 insertions(+), 8 deletions(-) create mode 100644 test/test_cosh.cpp create mode 100644 test/test_pow.cpp create mode 100644 test/test_sinh.cpp create mode 100644 test/test_tanh.cpp diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 85d389ba..4b077f08 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -12,11 +12,6 @@ // This file has no include guards or namespaces - it's expanded inline inside default_ops.hpp // -template -inline void eval_pow(T& result, const T& t, const T& p) -{ -} - namespace detail{ template @@ -103,6 +98,7 @@ void hyp0F0(T& H0F0, const T& x) typedef typename mpl::front::type ui_type; + BOOST_ASSERT(&H0F0 != &x); long tol = std::numeric_limits >::digits; T t; @@ -133,6 +129,58 @@ void hyp0F0(T& H0F0, const T& x) throw std::runtime_error("H0F0 failed to converge"); } +template +void hyp1F0(T& H1F0, const T& a, const T& x) +{ + // Compute the series representation of Hypergeometric1F0 taken from + // http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric1F0/06/01/01/ + // and also see the corresponding section for the power function (i.e. x^a). + // There are no checks on input range or parameter boundaries. + + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; + + BOOST_ASSERT(&H1F0 != &x); + BOOST_ASSERT(&H1F0 != &a); + + T x_pow_n_div_n_fact(x); + T pochham_a (a); + T ap (a); + + multiply(H1F0, pochham_a, x_pow_n_div_n_fact); + add(H1F0, si_type(1)); + + si_type n; + T term, part; + + // Series expansion of hyperg_1f0(a; ; x). + for(n = 2; n < 1000; n++) + { + multiply(x_pow_n_div_n_fact, x); + divide(x_pow_n_div_n_fact, n); + increment(ap); + + multiply(pochham_a, ap); + + multiply(term, pochham_a, x_pow_n_div_n_fact); + + if(n > 20) + { + exp_type e1, e2; + eval_frexp(part, H1F0, &e1); + eval_frexp(part, term, &e2); + if(e1 - e2 >= std::numeric_limits >::digits) + break; + } + + add(H1F0, term); + } + if(n >= 1000) + throw std::runtime_error("H1F0 failed to converge"); +} template void eval_exp(T& result, const T& x) @@ -147,6 +195,8 @@ void eval_exp(T& result, const T& x) typedef typename boost::multiprecision::detail::canonical::type si_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename boost::multiprecision::detail::canonical::type float_type; + // Handle special arguments. int type = eval_fpclassify(x); bool isneg = get_sign(x) < 0; @@ -188,6 +238,34 @@ void eval_exp(T& result, const T& x) result = std::numeric_limits >::has_infinity ? std::numeric_limits >::infinity().backend() : (std::numeric_limits >::max)().backend(); return; } + if(xx.compare(si_type(1)) <= 0) + { + // + // Use series for exp(x) - 1: + // + T lim = std::numeric_limits >::epsilon().backend(); + unsigned k = 2; + exp_series = xx; + result = si_type(1); + if(isneg) + subtract(result, exp_series); + else + add(result, exp_series); + multiply(exp_series, xx); + divide(exp_series, ui_type(k)); + add(result, exp_series); + while(exp_series.compare(lim) > 0) + { + ++k; + multiply(exp_series, xx); + divide(exp_series, ui_type(k)); + if(isneg && (k&1)) + subtract(result, exp_series); + else + add(result, exp_series); + } + return; + } // Check for pure-integer arguments which can be either signed or unsigned. boost::intmax_t ll; @@ -285,15 +363,16 @@ void eval_log(T& result, const T& arg) T pow = t; T lim; T t2; - multiply(lim, result, std::numeric_limits >::epsilon().backend()); - if(get_sign(lim) < 0) - lim.negate(); if(alternate) add(result, t); else subtract(result, t); + multiply(lim, result, std::numeric_limits >::epsilon().backend()); + if(get_sign(lim) < 0) + lim.negate(); + ui_type k = 1; do { @@ -307,3 +386,200 @@ void eval_log(T& result, const T& arg) }while(lim.compare(t2) < 0); } +template +inline void eval_pow(T& result, const T& x, const T& a) +{ + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; + + if((&result == &x) || (&result == &a)) + { + T t; + eval_pow(t, x, a); + result = t; + } + + if(a.compare(si_type(1)) == 0) + { + result = x; + return; + } + + int type = eval_fpclassify(x); + + switch(type) + { + case FP_INFINITE: + result = x; + return; + case FP_ZERO: + result = si_type(1); + return; + case FP_NAN: + result = x; + return; + default: ; + } + + if(get_sign(a) == 0) + { + result = si_type(1); + return; + } + + boost::intmax_t an; + convert_to(&an, a); + const bool bo_a_isint = a.compare(an) == 0; + + if((get_sign(x) < 0) && !bo_a_isint) + { + result = std::numeric_limits >::quiet_NaN().backend(); + } + + T t; + T da(a); + subtract(da, an); + + if(a.compare(si_type(-1)) < 0) + { + t = a; + t.negate(); + eval_pow(da, x, t); + divide(result, si_type(1), da); + return; + } + + subtract(da, a, an); + + if(bo_a_isint) + { + detail::pow_imp(result, x, an, mpl::true_()); + return; + } + + if((get_sign(x) > 0) && (x.compare(fp_type(0.1)) > 0) && (x.compare(fp_type(0.9)) < 0)) + { + if(a.compare(fp_type(1e-5f)) <= 0) + { + // Series expansion for small a. + eval_log(t, x); + multiply(t, a); + hyp0F0(result, t); + return; + } + else + { + // Series expansion for moderately sized x. Note that for large power of a, + // the power of the integer part of a is calculated using the pown function. + if(an) + { + da.negate(); + t = si_type(1); + subtract(t, x); + hyp1F0(result, da, t); + detail::pow_imp(t, x, an, mpl::true_()); + multiply(result, t); + } + else + { + da = a; + da.negate(); + t = si_type(1); + subtract(t, x); + hyp1F0(result, da, t); + } + } + } + else + { + // Series expansion for pow(x, a). Note that for large power of a, the power + // of the integer part of a is calculated using the pown function. + if(an) + { + eval_log(t, x); + multiply(t, da); + eval_exp(result, t); + detail::pow_imp(t, x, an, mpl::true_()); + multiply(result, t); + } + else + { + eval_log(t, x); + multiply(t, a); + eval_exp(result, t); + } + } +} + +namespace detail{ + + template + void sinhcosh(const T& x, T* p_sinh, T* p_cosh) + { + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; + + switch(eval_fpclassify(x)) + { + case FP_NAN: + case FP_INFINITE: + if(p_sinh) + *p_sinh = x; + if(p_cosh) + *p_cosh = x; + return; + case FP_ZERO: + if(p_sinh) + *p_sinh = x; + if(p_cosh) + *p_cosh = ui_type(1); + return; + default: ; + } + + + T e_px; + eval_exp(e_px, x); + T e_mx; + divide(e_mx, ui_type(1), e_px); + + if(p_sinh) + { + subtract(*p_sinh, e_px, e_mx); + divide(*p_sinh, ui_type(2)); + } + if(p_cosh) + { + add(*p_cosh, e_px, e_mx); + divide(*p_cosh, ui_type(2)); + } + } + +} // namespace detail + +template +inline void eval_sinh(T& result, const T& x) +{ + detail::sinhcosh(x, &result, static_cast(0)); +} + +template +inline void eval_cosh(T& result, const T& x) +{ + detail::sinhcosh(x, static_cast(0), &result); +} + +template +inline void eval_tanh(T& result, const T& x) +{ + T c; + detail::sinhcosh(x, &result, &c); + divide(result, c); +} + diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index d3b86aee..3c9242ba 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -202,3 +202,83 @@ run test_log.cpp gmp TEST_MPF50 [ check-target-builds ../config//has_gmp : : no ] : test_log_mpf50 ; + +run test_pow.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_pow_mpf50 ; + +run test_sinh.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_sinh_mpf50 ; + +run test_cosh.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_cosh_mpf50 ; + +run test_tanh.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_tanh_mpf50 ; + +run test_exp.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_exp_mpfr50 ; + +run test_log.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_log_mpfr50 ; + +run test_pow.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_pow_mpfr50 ; + +run test_sinh.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_sinh_mpfr50 ; + +run test_cosh.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_cosh_mpfr50 ; + +run test_tanh.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_tanh_mpfr50 ; diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp new file mode 100644 index 00000000..e2c0b845 --- /dev/null +++ b/test/test_cosh.cpp @@ -0,0 +1,137 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#if defined(TEST_MPFR_50) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif + +template +void test() +{ + static const boost::array data = + {{ + T("1.0560191127459844751259038114395241283965590525302917878166464679729562764239266483419824023679041866569431842053263976225991679105269492268050148624443706785607467750929028856273183654547152707568642275917435773104050171284580773949313906303074811586096214771879801872225500237540725592288167903987152007171391207680034517664218965133028298959753155835975555361514087618679892905973726581183754237665"), + T("6.0577917650974496023981039346694689204850927958941226507775366589415588030232830758139222010716099059155799853188868489737439396141346120898610181630988217093945337280471788812956307352429914669334599644412036010014302812555700905490062030666482387008384856645533100266205122930455496234252478878949675888122615795451076521244771554025667181070733415815608287241160724578541982548132473721865287585003"), + 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T("9.917129372597671132067673866739246238179742417231064062960232866725337575281938597212073697168000155027158148165861617400080837699968785505107579831803685516054837447325150388867488754170677228096524224392410232206238263933144338637103531441623303187445874039234973380151391274490746625993568552049954630793219419614845431626975962881182662815760423226111647056071831411664335144052772436215105801395e786"), + T("2.5869027163543111121878679987081647715187872826677398475096738640583659800068967379551376322170347537454918190603891312949716382621902484616361664158953484778255247083652726854621059785392022847887382779010079407502679229021085320675903109573769331277413372272363218896397965662581357886739691376204316908974081821980432178065394228926767529685562155837452626029223937027004015040825450642409597700449e824"), + T("4.9861251931207080923785686798881789193813879610842675205361210155894774686328710893906543682447029206928934967525495260314937837003448878215156341411477636831113484416124080974502217578408248150338565305116223944900839866528622960352723938548713319425798453345402992146078868053263606234074443024155243450623634720912438841022969909473424559262711669905282193529250216454066716533180418518228387188393e862"), + T("7.1012569014339068241101751233953234216522840280342406520909288232012799547871960723719836516359548198842749536961644100550279020276709043358260853581760590386456213180291689322352732545965831405519844109680619067101311180959399339922706596098526969148981173519865139508665631317310424178378833370605922449094745510812618563813537347841030916512147874232760564378443782164868016244561788356251308121716e901"), + T("7.4730215360486642135431754747074885377840195683583018254892502245011973712084221116813364423492802080799768174534590613188275471080608467087354983850284805514875889145266688973752185071777341375422809910165581997555433091939959406569831183459872344778707098094941193489061532160249775856426569696127193453339548371679229676272663084782830276508737129506676031759345288056484158647796152349867328841634e941"), + T("5.8109375364209112227579654658730977030869454388607076903639465992296616832002964138000947668837140543325908222688655359602408511410663722770167244801973012245657865182739637159804595049180263175014778215232564251739259624759589953677661356104554831551073263668188283861123521688445132164147762321111597028523130093864153999974376790494383016372210442340324038686843345053322425194077414241243050491297e982"), + T("3.33875955701899627718146291382268063073604182131575843695486667154496711979350813988644889979275310892951143249901398447859083674739840084454465850475774696325142148671937407108540250845900941142800157345665761403930889797424808979569550325271558518404559007551625637761142662107757913763221912282957681784053564387104062317729788737215450574233690655931888608424916152893688106181220341997128198692e1024"), + T("1.4174672877823334709610117319768830739080734407353905145632612088824955720198734996604261250019291955883620333545750761619015467840567122066622229379056280064206319780047687015558007624774062399477328822231085767309831266032616053065858739373818651687128093335640388513396191118537181280334430292439188737524362269789272308905723812818882228503013875816702686587035844437102478263525616196832018321602e1067"), + T("4.4466189016791091516801723880812533528438597080549410911235655611382010503145789286158745555771483577943662768773465284793798720178177605712848440200402906836390133865748188969184005230383247111166918721449908133920663776952786683837038180436264738937354101153867171804315769471050303182129269442292354388037298125177941217926845803005587166270803697433886463469168814941555804311717400657004050157245e1110"), + }}; + + T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + const T x = eg + k; + T val = boost::multiprecision::cosh(x * x); + T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon()); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 1200); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif + return boost::report_errors(); +} + + + diff --git a/test/test_exp.cpp b/test/test_exp.cpp index 592ae720..abde8e4c 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -29,6 +29,9 @@ #if defined(TEST_MPF50) #include #endif +#if defined(TEST_MPFR_50) +#include +#endif #ifdef TEST_BACKEND #include #endif @@ -104,6 +107,11 @@ void test() unsigned err = e.template convert_to(); if(err > max_err) max_err = err; + val = boost::multiprecision::exp(-boost::multiprecision::sqrt((pi * (100 * k)) * (100 * k))); + e = ceil(fabs((val - (1/data[k])) / (1/data[k])) / std::numeric_limits::epsilon()); + err = e.template convert_to(); + if(err > max_err) + max_err = err; } std::cout << "Max error was: " << max_err << std::endl; BOOST_TEST(max_err < 1200); @@ -119,6 +127,10 @@ int main() test(); test(); #endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif #ifdef TEST_E_FLOAT test(); #endif diff --git a/test/test_log.cpp b/test/test_log.cpp index 5589a930..6905a19d 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -29,6 +29,9 @@ #if defined(TEST_MPF50) #include #endif +#ifdef TEST_MPFR_50 +#include +#endif #ifdef TEST_BACKEND #include #endif @@ -172,6 +175,10 @@ int main() test(); test(); #endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif #ifdef TEST_E_FLOAT test(); #endif diff --git a/test/test_pow.cpp b/test/test_pow.cpp new file mode 100644 index 00000000..15315716 --- /dev/null +++ b/test/test_pow.cpp @@ -0,0 +1,583 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT +# define TEST_MPFR_50 + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#if defined(TEST_MPFR_50) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif + +template +void test() +{ + static const boost::array, 500> data = + {{ + { static_cast("9.85291419463953934609889984130859375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e4"), static_cast("8.41670862661703722551465034484863281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e2"), 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100644 index 00000000..7f559fec --- /dev/null +++ b/test/test_sinh.cpp @@ -0,0 +1,137 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#if defined(TEST_MPFR_50) 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T("9.917129372597671132067673866739246238179742417231064062960232866725337575281938597212073697168000155027158148165861617400080837699968785505107579831803685516054837447325150388867488754170677228096524224392410232206238263933144338637103531441623303187445874039234973380151391274490746625993568552049954630793219419614845431626975962881182662815760423226111647056071831411664335144052772436215105801395e786"), + T("2.5869027163543111121878679987081647715187872826677398475096738640583659800068967379551376322170347537454918190603891312949716382621902484616361664158953484778255247083652726854621059785392022847887382779010079407502679229021085320675903109573769331277413372272363218896397965662581357886739691376204316908974081821980432178065394228926767529685562155837452626029223937027004015040825450642409597700449e824"), + T("4.9861251931207080923785686798881789193813879610842675205361210155894774686328710893906543682447029206928934967525495260314937837003448878215156341411477636831113484416124080974502217578408248150338565305116223944900839866528622960352723938548713319425798453345402992146078868053263606234074443024155243450623634720912438841022969909473424559262711669905282193529250216454066716533180418518228387188393e862"), + T("7.1012569014339068241101751233953234216522840280342406520909288232012799547871960723719836516359548198842749536961644100550279020276709043358260853581760590386456213180291689322352732545965831405519844109680619067101311180959399339922706596098526969148981173519865139508665631317310424178378833370605922449094745510812618563813537347841030916512147874232760564378443782164868016244561788356251308121716e901"), + T("7.4730215360486642135431754747074885377840195683583018254892502245011973712084221116813364423492802080799768174534590613188275471080608467087354983850284805514875889145266688973752185071777341375422809910165581997555433091939959406569831183459872344778707098094941193489061532160249775856426569696127193453339548371679229676272663084782830276508737129506676031759345288056484158647796152349867328841634e941"), + T("5.8109375364209112227579654658730977030869454388607076903639465992296616832002964138000947668837140543325908222688655359602408511410663722770167244801973012245657865182739637159804595049180263175014778215232564251739259624759589953677661356104554831551073263668188283861123521688445132164147762321111597028523130093864153999974376790494383016372210442340324038686843345053322425194077414241243050491297e982"), + T("3.33875955701899627718146291382268063073604182131575843695486667154496711979350813988644889979275310892951143249901398447859083674739840084454465850475774696325142148671937407108540250845900941142800157345665761403930889797424808979569550325271558518404559007551625637761142662107757913763221912282957681784053564387104062317729788737215450574233690655931888608424916152893688106181220341997128198692e1024"), + T("1.4174672877823334709610117319768830739080734407353905145632612088824955720198734996604261250019291955883620333545750761619015467840567122066622229379056280064206319780047687015558007624774062399477328822231085767309831266032616053065858739373818651687128093335640388513396191118537181280334430292439188737524362269789272308905723812818882228503013875816702686587035844437102478263525616196832018321602e1067"), + T("4.4466189016791091516801723880812533528438597080549410911235655611382010503145789286158745555771483577943662768773465284793798720178177605712848440200402906836390133865748188969184005230383247111166918721449908133920663776952786683837038180436264738937354101153867171804315769471050303182129269442292354388037298125177941217926845803005587166270803697433886463469168814941555804311717400657004050157245e1110"), + }}; + + T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + const T x = eg + k; + T val = boost::multiprecision::sinh(x * x); + T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon()); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 1200); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif + return boost::report_errors(); +} + + + diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp new file mode 100644 index 00000000..a0d3b792 --- /dev/null +++ b/test/test_tanh.cpp @@ -0,0 +1,137 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#if defined(TEST_MPFR_50) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif + +template +void test() +{ + static const boost::array data = + {{ + T("0.32137338579537729992840434899278935725496267444911714908205287462634251052210833615032073534299473485492692600156322137421801432333125051088723502425037485776412801577568405892077585206768190530859883094571475323319480739773193974206966728764224286661945738178210577326172938196062277314761537881936346874075881338768208490193827960565412814349738654540520356903367084438822830345189856017860672463017"), + T("0.98628073997374759901559180515206275902189609982907214282364143439537215491113710345866034807991101303183938339561499559327886956280789743287824488269072297413440935381715378233031399015496124706604318545539544610760151756970229801074280545428642122005982857974921606264103186878499260552388713716032507770319550435738767597150644370033277228635793175246197730488375240713357827246166262087899961098648"), + T("0.99999659728082161113542951278514830809677661658635225532792520501703544628367875293677270218317428676793098034276042396396797568103263882451732810190507733063467333056356770774002596898762991629653041854653269824642873291146068535300466473399592751219449187768646625229500705182676930009096545254478199838990703077597971823456671241141900968900216742636822174010867343154474773040184900973368250708724"), + T("0.9999999999846483268200051609594321550129159997920576480976206867496512752486590660437091205989616108531910897733432934135954788151766561209164605337537937873588006552145390152387235783207736999759875845070169747521389728857476525437483543080651125798739562649414879487621858466223255239845627205850217328574865852922872737234283038190096982410137471391847466112651349436875974689271288261759782261321"), + T("0.9999999999999999987314527242099750648171958211319474558707792311593804963057878814487720997303512134007272111464990650500302215773762906820778949397525329109311974741708703536680512747226155618703318739024344621256722269608969415280035337052044425138281821760268269187377517243951584969175035549994883451471918693502477485385682884154959809285569290940740978684264145737164182111806308430952867505356"), + T("0.9999999999999999999999999980800953069847308586840237590563929855339557065536765765234844240789584487443451033349994294426525006157530320529970966048109743850154174651033567146346966529198814047607015842020039899630884318521543225160212193994911746894335846264878066530266737005606770102869237101848445559941638381625615207320468184414917265299980278164193202897754476112968080358662232635784904263624"), + T("0.9999999999999999999999999999999999999467800140220866754762922747687784133233134010432889959570821554455247528344437918197518545105332713456859236726383195243056599177018396579766073961540714510399202497404647103138524118065391185503678895059096790300665805648569647351935897874460587855127436472608470703384261586158923066272124216158518232588330799027603391275039552776308636189531809031683723259525"), + T("0.9999999999999999999999999999999999999999999999999729795912960133359928587562229512337339217831178574875626619226954752643039860388090399659478676726654102118545764943682017611574275691203710439707807193180604656837503862242700430179591666329131728631752773789406064618682879167351725013888294859467540832310795515139677375807407622028485242969471516812171475098378942187864794497220152019202351747432"), + T("0.9999999999999999999999999999999999999999999999999999999999999997487354938310440650220692519525261552411539996830587326435051159231522052011310872619940247463640019105467860778515384738650636054646551611609757125760437266415865214306396520500343113189907306851418957620080971645943305760132385139924583154317156560414548076370893360020924960120441059315311380109752919823616149973862196846266297710225"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999572050575304159358359221596743379014313563214857593401545331495211888415913558896516895286943572966865708195832339959764445194449615969154689769557903166971249521898883489362426386924297872088925852892350150865941427355319827260914834268754732102528105919811851193667193380541054520023003326858641189063542651960743457613"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998665016733514821204959171836698281165918083005790816030823236096080522860514417075411055633676502699904415882389102672678124683084429720879962355892225321369091298491658349178472270952759208443767848312111069127329160464884932271685986610697222434145553035947750809388321614695213754318979469071722942883"), + T("0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999992372516628147584832950728021842198359205201519966391076994594773600474674435473005118571751514446148292787696117866094991476340344341061706866751156257825144909115117822189019766805825304055482958970512463798453229341693148012213183553546720540880444569824125592343803193018989122964"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999920180539244323143459416025663362517256166793900312667214543096238752838226369161775531456005541374878274529461511286842988937830155704737448202558382612829022464635400289328916240002670783433827234852858267621807568393874737879853500598862298495727481132883728328"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998470116425957155787153557938061034698436461173594805292722874130433614266475136267606498346730583487791266503943659174886554170377537630914770998114573340081594827150737005158607830579000912020838690230498119348251553312722575955142752845289"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999462931048083476382670449719737943481963930626760625326765703815392249622625483433043363664396638162612437367800102332819699131841317348173451308570776544874933173719394861336636728378134900422312720743996219523365098"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996546783689748726752364896615532860288057097437452774779386074906915819380531729493071959232887620213723607155628959529584572083388979892309086717786559916703004365603135284141639480887703759"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999593332381019647939423999969519583099837564321056588766269967853479478603122899456262904869063959564274215899007623362296377022418464303752396325625838280378647335"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999122842714667567128203355585346559126606029196080721845292399104475997315344844970601651757832506169948906646054332493537761143729664"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999965347272050374435790597917065458623422102880662825928396981295898014081371503733411536311258910851858"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999974926240515037403282500845454464621558236030794140169313830052413917"), + T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999667705192725716176070161727364499"), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + T("1."), + }}; + + T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + const T x = eg + k; + T val = boost::multiprecision::tanh(x * x); + T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon()); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 1200); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif + return boost::report_errors(); +} + + + From 8cf2a83683b0909e13a9bceb775f7875ed95042b Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 18 Oct 2011 18:10:20 +0000 Subject: [PATCH 036/256] Add sin/cos/tan/asin functions. [SVN r75053] --- .../multiprecision/detail/default_ops.hpp | 2 + .../detail/functions/constants.hpp | 61 ++ .../multiprecision/detail/functions/pow.hpp | 45 +- .../multiprecision/detail/functions/trig.hpp | 524 ++++++++++++++++++ test/Jamfile.v2 | 49 ++ test/test_asin.cpp | 98 ++++ test/test_cos.cpp | 291 ++++++++++ test/test_sin.cpp | 297 ++++++++++ 8 files changed, 1345 insertions(+), 22 deletions(-) create mode 100644 include/boost/multiprecision/detail/functions/trig.hpp create mode 100644 test/test_asin.cpp create mode 100644 test/test_cos.cpp create mode 100644 test/test_sin.cpp diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 58bc9637..587c99e8 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -363,6 +363,7 @@ inline void eval_fmod(T& result, const T& a, const T& b) T temp; eval_fmod(temp, a, b); result = temp; + return; } T n; divide(result, a, b); @@ -443,6 +444,7 @@ typename enable_if_c::type eval_tanh(); // #include #include +#include } diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp index 60a3bfe8..e1e6a7b2 100644 --- a/include/boost/multiprecision/detail/functions/constants.hpp +++ b/include/boost/multiprecision/detail/functions/constants.hpp @@ -65,6 +65,54 @@ void calc_e(T& result, unsigned digits) divide(result, denom); } +template +void calc_pi(T& result, unsigned digits) +{ + typedef typename mpl::front::type ui_type; + typedef typename mpl::front::type real_type; + + T a; + a = ui_type(1); + T b; + T A(a); + T B; + B = real_type(0.5f); + T D; + D = real_type(0.25f); + + T lim; + lim = ui_type(1); + eval_ldexp(lim, lim, -(int)digits); + + unsigned k = 1; + + do + { + add(result, A, B); + eval_ldexp(result, result, -2); + eval_sqrt(b, B); + add(a, b); + eval_ldexp(a, a, -1); + multiply(A, a, a); + subtract(B, A, result); + eval_ldexp(B, B, 1); + subtract(result, A, B); + bool neg = get_sign(result) < 0; + if(neg) + result.negate(); + if(result.compare(lim) <= 0) + break; + if(neg) + result.negate(); + eval_ldexp(result, result, k - 1); + subtract(D, result); + ++k; + eval_ldexp(lim, lim, 1); + } + while(true); + + divide(result, B, D); +} template struct constant_initializer @@ -114,3 +162,16 @@ const T& get_constant_e() return result; } +template +const T& get_constant_pi() +{ + static T result; + static bool b = false; + if(!b) + calc_pi(result, std::numeric_limits >::digits); + + constant_initializer >::do_nothing(); + + return result; +} + diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 4b077f08..cc6b2489 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -36,6 +36,7 @@ inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) T denom; pow_imp(denom, t, -p, mpl::true_()); divide(result, temp, denom); + return; } switch(p) @@ -106,6 +107,11 @@ void hyp0F0(T& H0F0, const T& x) add(H0F0, x_pow_n_div_n_fact, ui_type(1)); + T lim; + eval_ldexp(lim, H0F0, 1 - tol); + if(get_sign(lim) < 0) + lim.negate(); + ui_type n; // Series expansion of hyperg_0f0(; ; x). @@ -113,17 +119,14 @@ void hyp0F0(T& H0F0, const T& x) { multiply(x_pow_n_div_n_fact, x); divide(x_pow_n_div_n_fact, n); - - if(n > 20) - { - eval_ldexp(t, H0F0, -tol); - if(t.compare(x_pow_n_div_n_fact) >= 0) - { - break; - } - } - add(H0F0, x_pow_n_div_n_fact); + bool neg = get_sign(x_pow_n_div_n_fact); + if(neg) + x_pow_n_div_n_fact.negate(); + if(lim.compare(x_pow_n_div_n_fact) > 0) + break; + if(neg) + x_pow_n_div_n_fact.negate(); } if(n >= 300) throw std::runtime_error("H0F0 failed to converge"); @@ -152,6 +155,10 @@ void hyp1F0(T& H1F0, const T& a, const T& x) multiply(H1F0, pochham_a, x_pow_n_div_n_fact); add(H1F0, si_type(1)); + T lim; + eval_ldexp(lim, H1F0, 1 - std::numeric_limits >::digits); + if(get_sign(lim) < 0) + lim.negate(); si_type n; T term, part; @@ -162,21 +169,13 @@ void hyp1F0(T& H1F0, const T& a, const T& x) multiply(x_pow_n_div_n_fact, x); divide(x_pow_n_div_n_fact, n); increment(ap); - multiply(pochham_a, ap); - multiply(term, pochham_a, x_pow_n_div_n_fact); - - if(n > 20) - { - exp_type e1, e2; - eval_frexp(part, H1F0, &e1); - eval_frexp(part, term, &e2); - if(e1 - e2 >= std::numeric_limits >::digits) - break; - } - add(H1F0, term); + if(get_sign(term) < 0) + term.negate(); + if(lim.compare(term) < 0) + break; } if(n >= 1000) throw std::runtime_error("H1F0 failed to converge"); @@ -190,6 +189,7 @@ void eval_exp(T& result, const T& x) T temp; eval_exp(temp, x); result = temp; + return; } typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename boost::multiprecision::detail::canonical::type si_type; @@ -336,6 +336,7 @@ void eval_log(T& result, const T& arg) T temp; eval_log(temp, arg); result = temp; + return; } typedef typename boost::multiprecision::detail::canonical::type si_type; diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp new file mode 100644 index 00000000..e770e4cd --- /dev/null +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -0,0 +1,524 @@ + +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Distributed under the Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) + +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +// +// This file has no include guards or namespaces - it's expanded inline inside default_ops.hpp +// + +template +void hyp0F1(T& result, const T& b, const T& x) +{ + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; + + // Compute the series representation of Hypergeometric0F1 taken from + // http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric0F1/06/01/01/ + // There are no checks on input range or parameter boundaries. + + T x_pow_n_div_n_fact(x); + T pochham_b (b); + T bp (b); + + divide(result, x_pow_n_div_n_fact, pochham_b); + add(result, ui_type(1)); + + si_type n; + + T tol; + tol = ui_type(1); + eval_ldexp(tol, tol, 1 - std::numeric_limits >::digits); + multiply(tol, result); + if(get_sign(tol) < 0) + tol.negate(); + T term; + + // Series expansion of hyperg_0f1(; b; x). + for(n = 2; n < 300; ++n) + { + multiply(x_pow_n_div_n_fact, x); + divide(x_pow_n_div_n_fact, n); + increment(bp); + multiply(pochham_b, bp); + + divide(term, x_pow_n_div_n_fact, pochham_b); + add(result, term); + + bool neg_term = get_sign(term) < 0; + if(neg_term) + term.negate(); + if(term.compare(tol) <= 0) + break; + } + + if(n >= 300) + throw std::runtime_error("H0F1 Failed to Converge"); +} + + +template +void eval_sin(T& result, const T& x) +{ + if(&result == &x) + { + T temp; + eval_sin(temp, x); + result = temp; + return; + } + + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; + + switch(eval_fpclassify(x)) + { + case FP_INFINITE: + case FP_NAN: + result = std::numeric_limits >::quiet_NaN().backend(); + return; + case FP_ZERO: + result = ui_type(0); + return; + default: ; + } + + // Local copy of the argument + T xx = x; + + // Analyze and prepare the phase of the argument. + // Make a local, positive copy of the argument, xx. + // The argument xx will be reduced to 0 <= xx <= pi/2. + bool b_negate_sin = false; + + if(get_sign(x) < 0) + { + xx.negate(); + b_negate_sin = !b_negate_sin; + } + + T n_pi, t; + // Remove even multiples of pi. + if(xx.compare(get_constant_pi()) > 0) + { + divide(n_pi, xx, get_constant_pi()); + eval_trunc(n_pi, n_pi); + t = ui_type(2); + eval_fmod(t, n_pi, t); + const bool b_n_pi_is_even = get_sign(t) == 0; + multiply(n_pi, get_constant_pi()); + subtract(xx, n_pi); + + // Adjust signs if the multiple of pi is not even. + if(!b_n_pi_is_even) + { + b_negate_sin = !b_negate_sin; + } + } + + // Reduce the argument to 0 <= xx <= pi/2. + eval_ldexp(t, get_constant_pi(), -1); + if(xx.compare(t) > 0) + { + subtract(xx, get_constant_pi(), xx); + } + + subtract(t, xx); + const bool b_zero = get_sign(xx) == 0; + const bool b_pi_half = get_sign(t) == 0; + + // Check if the reduced argument is very close to 0 or pi/2. + const bool b_near_zero = xx.compare(fp_type(1e-1)) < 0; + const bool b_near_pi_half = t.compare(fp_type(1e-1)) < 0;; + + if(b_zero) + { + result = ui_type(0); + } + else if(b_pi_half) + { + result = ui_type(1); + } + else if(b_near_zero) + { + multiply(t, xx, xx); + divide(t, si_type(-4)); + T t2; + t2 = fp_type(1.5); + hyp0F1(result, t2, t); + multiply(result, xx); + } + else if(b_near_pi_half) + { + multiply(t, t); + divide(t, si_type(-4)); + T t2; + t2 = fp_type(0.5); + hyp0F1(result, t2, t); + } + else + { + // Scale to a small argument for an efficient Taylor series, + // implemented as a hypergeometric function. Use a standard + // divide by three identity a certain number of times. + // Here we use division by 3^9 --> (19683 = 3^9). + + static const si_type n_scale = 9; + static const si_type n_three_pow_scale = static_cast(19683L); + + divide(xx, n_three_pow_scale); + + // Now with small arguments, we are ready for a series expansion. + multiply(t, xx, xx); + divide(t, si_type(-4)); + T t2; + t2 = fp_type(1.5); + hyp0F1(result, t2, t); + multiply(result, xx); + + // Convert back using multiple angle identity. + for(boost::int32_t k = static_cast(0); k < n_scale; k++) + { + // Rescale the cosine value using the multiple angle identity. + multiply(t2, result, ui_type(3)); + multiply(t, result, result); + multiply(t, result); + multiply(t, ui_type(4)); + subtract(result, t2, t); + } + } + + if(b_negate_sin) + result.negate(); +} + +template +void eval_cos(T& result, const T& x) +{ + if(&result == &x) + { + T temp; + eval_sin(temp, x); + result = temp; + return; + } + + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; + + switch(eval_fpclassify(x)) + { + case FP_INFINITE: + case FP_NAN: + result = std::numeric_limits >::quiet_NaN().backend(); + return; + case FP_ZERO: + result = ui_type(1); + return; + default: ; + } + + // Local copy of the argument + T xx = x; + + // Analyze and prepare the phase of the argument. + // Make a local, positive copy of the argument, xx. + // The argument xx will be reduced to 0 <= xx <= pi/2. + bool b_negate_cos = false; + + if(get_sign(x) < 0) + { + xx.negate(); + b_negate_cos = !b_negate_cos; + } + + T n_pi, t; + // Remove even multiples of pi. + if(xx.compare(get_constant_pi()) > 0) + { + divide(t, xx, get_constant_pi()); + eval_trunc(n_pi, t); + multiply(t, n_pi, get_constant_pi()); + subtract(xx, t); + + // Adjust signs if the multiple of pi is not even. + t = ui_type(2); + eval_fmod(t, n_pi, t); + const bool b_n_pi_is_even = get_sign(t) == 0; + + if(!b_n_pi_is_even) + { + b_negate_cos = !b_negate_cos; + } + } + + // Reduce the argument to 0 <= xx <= pi/2. + eval_ldexp(t, get_constant_pi(), -1); + int com = xx.compare(t); + if(com > 0) + { + subtract(xx, get_constant_pi(), xx); + b_negate_cos = !b_negate_cos; + } + + const bool b_zero = get_sign(xx) == 0; + const bool b_pi_half = com == 0; + + // Check if the reduced argument is very close to 0 or pi/2. + const bool b_near_zero = xx.compare(fp_type(1e-4)) < 0; + subtract(t, xx); + const bool b_near_pi_half = t.compare(fp_type(1e-4)) < 0; + + if(b_zero) + { + result = si_type(1); + } + else if(b_pi_half) + { + result = si_type(0); + } + else if(b_near_zero) + { + multiply(t, xx, xx); + divide(t, si_type(-4)); + n_pi = fp_type(0.5f); + hyp0F1(result, n_pi, t); + } + else if(b_near_pi_half) + { + T t2(t); + multiply(t, t); + divide(t, si_type(-4)); + n_pi = fp_type(1.5f); + hyp0F1(result, n_pi, t); + multiply(result, t2); + } + else + { + // Scale to a small argument for an efficient Taylor series, + // implemented as a hypergeometric function. Use a standard + // divide by three identity a certain number of times. + // Here we use division by 3^9 --> (19683 = 3^9). + + static const ui_type n_scale = 9; + static const ui_type n_three_pow_scale = 19683; + divide(xx, n_three_pow_scale); + + multiply(t, xx, xx); + divide(t, si_type(-4)); + n_pi = fp_type(0.5f); + + // Now with small arguments, we are ready for a series expansion. + hyp0F1(result, n_pi, t); + + // Convert back using multiple angle identity. + for(ui_type k = 0; k < n_scale; k++) + { + multiply(t, result, result); + multiply(t, result); + multiply(t, ui_type(4)); + multiply(result, si_type(-3)); + add(result, t); + } + } + if(b_negate_cos) + result.negate(); +} + +template +void eval_tan(T& result, const T& x) +{ + T t; + eval_sin(result, x); + eval_cos(t, x); + divide(result, t); +} + +template +void hyp2F1(T& result, const T& a, const T& b, const T& c, const T& x) +{ + // Compute the series representation of hyperg_2f1 taken from + // Abramowitz and Stegun 15.1.1. + // There are no checks on input range or parameter boundaries. + + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; + + T x_pow_n_div_n_fact(x); + T pochham_a (a); + T pochham_b (b); + T pochham_c (c); + T ap (a); + T bp (b); + T cp (c); + + multiply(result, pochham_a, pochham_b); + divide(result, pochham_c); + multiply(result, x_pow_n_div_n_fact); + add(result, ui_type(1)); + + T lim; + eval_ldexp(lim, result, 1 - std::numeric_limits >::digits); + + if(get_sign(lim) < 0) + lim.negate(); + + ui_type n; + T term; + + // Series expansion of hyperg_2f1(a, b; c; x). + for(n = 2; n < 300; ++n) + { + multiply(x_pow_n_div_n_fact, x); + divide(x_pow_n_div_n_fact, n); + + increment(ap); + multiply(pochham_a, ap); + increment(bp); + multiply(pochham_b, bp); + increment(cp); + multiply(pochham_c, cp); + + multiply(term, pochham_a, pochham_b); + divide(term, pochham_c); + multiply(term, x_pow_n_div_n_fact); + add(result, term); + + if(get_sign(term) < 0) + term.negate(); + if(lim.compare(term) >= 0) + break; + } + if(n > 300) + throw std::runtime_error("H2F1 failed to converge."); +} + +template +void eval_asin(T& result, const T& x) +{ + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; + + if(&result == &x) + { + T t(x); + eval_asin(result, t); + return; + } + + switch(eval_fpclassify(x)) + { + case FP_NAN: + case FP_INFINITE: + result = std::numeric_limits >::quiet_NaN().backend(); + return; + case FP_ZERO: + result = ui_type(0); + return; + default: ; + } + + const bool b_neg = get_sign(x) < 0; + + T xx(x); + if(b_neg) + xx.negate(); + + int c = xx.compare(ui_type(1)); + if(c > 0) + { + result = std::numeric_limits >::quiet_NaN().backend(); + return; + } + else if(c == 0) + { + result = get_constant_pi(); + eval_ldexp(result, result, -1); + if(b_neg) + result.negate(); + return; + } + + if(xx.compare(fp_type(1e-4)) < 0) + { + // http://functions.wolfram.com/ElementaryFunctions/ArcSin/26/01/01/ + multiply(xx, xx); + T t1, t2; + t1 = fp_type(0.5f); + t2 = fp_type(1.5f); + hyp2F1(result, t1, t1, t2, xx); + multiply(result, x); + if(b_neg) + result.negate(); + return; + } + else if(xx.compare(fp_type(1 - 1e-4f)) > 0) + { + T dx1; + T t1, t2; + subtract(dx1, ui_type(1), xx); + t1 = fp_type(0.5f); + t2 = fp_type(1.5f); + eval_ldexp(dx1, dx1, -1); + hyp2F1(result, t1, t1, t2, dx1); + eval_ldexp(dx1, dx1, 2); + eval_sqrt(t1, dx1); + multiply(result, t1); + eval_ldexp(t1, get_constant_pi(), -1); + result.negate(); + add(result, t1); + if(b_neg) + result.negate(); + return; + } + + // Get initial estimate using standard math function asin. + double dd; + convert_to(&dd, xx); + + result = fp_type(std::asin(dd)); + + // Newton-Raphson iteration + while(true) + { + T s, c; + eval_sin(s, result); + eval_cos(c, result); + subtract(s, xx); + divide(s, c); + subtract(result, s); + + T lim; + eval_ldexp(lim, result, 1 - std::numeric_limits >::digits); + if(get_sign(s) < 0) + s.negate(); + if(get_sign(lim) < 0) + lim.negate(); + if(lim.compare(s) >= 0) + break; + } + if(b_neg) + result.negate(); +} + + diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 3c9242ba..dbcfbe61 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -282,3 +282,52 @@ run test_tanh.cpp mpfr TEST_MPFR_50 [ check-target-builds ../config//has_mpfr : : no ] : test_tanh_mpfr50 ; + +run test_sin.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_sin_mpf50 ; + +run test_sin.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_sin_mpfr_50 ; + +run test_cos.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_cos_mpf50 ; + +run test_cos.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_cos_mpfr_50 ; + +run test_asin.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_asin_mpf50 ; + +run test_asin.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_asin_mpfr_50 ; + diff --git a/test/test_asin.cpp b/test/test_asin.cpp new file mode 100644 index 00000000..6f1c8768 --- /dev/null +++ b/test/test_asin.cpp @@ -0,0 +1,98 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#if defined(TEST_MPFR_50) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif + +template +void test() +{ + // + // Test with some exact binary values as input - this tests our code + // rather than the test data: + // + static const boost::array, 6> exact_data = + {{ + {{ 0.5, "0.523598775598298873077107230546583814032861566562517636829157432051302734381034833104672470890352844663691347752213717775" }}, + {{ 0.25, "0.252680255142078653485657436993710972252193733096838193633923778740575060481021222411748742228014601605092602909414066566" }}, + {{0.75, "0.848062078981481008052944338998418080073366213263112642860718163570200821228474234349189801731957230300995227265307531834" }}, + {{std::ldexp(1.0, -20), "9.53674316406394560289664793089102218648031077292419572854816420395098616062014311172490017625353237219958438022056661501e-7" }}, + {{ 1 - std::ldexp(1.0, -20), "1.56941525875313420204921285316218397515809899320201864334535204504240776023375739189119474528488143494473216475057072728" }}, + {{ 1, "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064" }}, + }}; + unsigned max_err = 0; + for(unsigned k = 0; k < exact_data.size(); k++) + { + T val = asin(exact_data[k][0]); + T e = (exact_data[k][1] == 0) ? T(ceil(fabs((val - exact_data[k][1]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - exact_data[k][1]) / exact_data[k][1]) / std::numeric_limits::epsilon())); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + val = asin(-exact_data[k][0]); + e = T(ceil(fabs((val + exact_data[k][1]) / exact_data[k][1]) / std::numeric_limits::epsilon())); + err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + BOOST_TEST(asin(T(0)) == 0); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif + return boost::report_errors(); +} + + + diff --git a/test/test_cos.cpp b/test/test_cos.cpp new file mode 100644 index 00000000..419f18b0 --- /dev/null +++ b/test/test_cos.cpp @@ -0,0 +1,291 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#if defined(TEST_MPFR_50) 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T("0.22948154144509182369415746800698328364988547396475691620681392787566104183462052622980774444304368277802870979261579895452333488316470495027443871923297117956210113575448119970237881958246782891025814249305970662163236166516394039705137544157900789683194435211763787511069822409683486532927557658412323180776903688623277362060713475574739265599518489263464320833102602215450190502358534383949241852484"), + T("0.98619528108436834444622772244233500550001863518169392038562682097011946713614830549103565779570404766638555367268020992254689671390965312890416679706192473068433717014095521991774567755994345709131209844512998942709582638991869821050636439257597063856249038092119512871640381123843890013812838185293393263756058350072768448458950380360337889770923256206901689904823829217396801268618019194906772703227"), + T("0.53478241597498682890636923119124507573138434225226478301997338705931821657049944750562391125304256759887391004338167587322019260365925435302391176930331161896818003746464685277508807805130884660314731429722219318699505836398912422599554793162364836595300619860913573673921432325981205409702897337053197706014049687225094538593517626884763534008626048851538197945922313231461994435494917556595912129444"), + T("-0.57175918163121264025616107589630751551161205724757288681494194505248342228571881008866075970817690438186545379919710148119548771419260784258379302863349865022779589406640338106461807885184578720013258862884778613907350162349826641089246855371608494365729193629734711852175384638728815913727055118781471960575965215193534386589450370243853256890375165575818694142504618584610839931680003465519416417686"), + 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T("0.83368761966098380317914918853127190012005517198095141616372457983351189700156411681039093358761555771758536229588242982647239744187242300801829995961871412772468923394414109025642424234703592018655517051393077978860068845984020869413624371103031896740117407710299198562267502869147100200858539656754317575041431701939759759225389946719106478332366708137354276007919533255169664638235639383569564110075"), + T("0.83213248256248718391648282211236200464150938178343837417522635579213705328552770623957486792338755433958256100224720251839082676782210674078979903328623897712870422600430978907177584667709552233768475968506874004560085480509103334782228549116928850495590090914133655583767781543886956699592465303315591578411513564172526903206600594554996369316967222569167592338646796759203865876228192676690576393957"), + 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T("0.98572607094681400469823142383450564975177916157871840422129452719452525174019803417354200370408054482797693621385765351670173144053171524005535725427317409189868483686977845578192854125777358818593005952568285102554187813023457756929121023181880198348203083841375515867843145321766318476866476607321938993078073105088587752971311300418067382395754489252201424628686354714684325074264340586434068083735"), + T("0.2267455177003321384894005667464998092097833850092894238480831378466683827110057043871346060005709235569800215748516185659827893723700508589640891976972716570403665692613477548038629552153079218542242417184271182264022470709072429310981387965885388758575814101891100826647083444934684812292662215448102626341015149572372707444725994248777658076421636637760492982947444020394182326376291158696727384852"), + T("-0.81000689036588888102398287378618104836450574863713892332248232301021899106208419137911694670935600210389307190348154033680700645928539580731142634010602466147128679656911798991740456705453963764056901956423046807435258488930954638670002070774439646670450724500520094586192645160847046520311570082832431061691996839606591067443335185302732221888316818825870721496315105401624866741940813589284275695918"), + T("-0.85447015139344948471094821054366626768019606763269341666053644333072070840260166961763856973284893831954425042860099172316086950440334996806598196522184690224018944138578542327045770832471332376269716674841615467614625539483750018876502303839670098606230317226296309325404589665701938190004997832683948796843166639576625281030300467522347494569768687089899397360725496800596493559470637547748735594697"), + T("0.14782491492260520954264860310453392894688582499520847868449990765772811594316839506757584243129175527745236732059643506743012867347391315093605558463510078020864683057368198129858823908327097108583620570511151521896111105026538667326749527786043478669088587777236123716686756088055458828079103458534402182273835161066708126746360741813126817035007484464329141515901214558732724557437706092450180726378"), + T("0.96902885660223213449832417965462288346382027027907788639786102888188268413128284808786908788351970794814191573322198094839000459295090920127430762740525901384778314480815531039485728089512489227948630012091333107823627672161756650613535363845597750943844039360212709462602480040358932164638277463645635101178868520058961493135889052671922314786442189473233561252419424865659925386520422456933994031412"), + T("0.60313571428133694309325113655636540756247392441681227046917143280974317371916820972719995253248954425492897594051861535050840463205496306256237562726891289696301688567930026444972968333329934552460084325207412884738539384203738886072440013640125030433738691853586812704775040754220545555524237855361445575868855139945713834823411715711428213828850093318644478373792898000948569667301322178250159228606"), + T("-0.50162154214905535006507934761566421365808962336874567677926739022768858180703782104157334491773507690211622144412751863172893119122904872120863946237533655183100979972269651012785895305465091942482860884709266947899655662267052604131701946158941092922207257375120965677001058006645609151579188243577188192831765423148813895489546306047297711022539509473462404019089733447430114238267379980532396311664"), + }}; + + T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + + boost::uintmax_t max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + T val = cos(euler_gamma * ((100 * k) - 5000)); + T e = (data[k] == 0) ? T(ceil(fabs((val - data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon())); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + val = cos(-euler_gamma * ((100 * k) - 5000)); + e = (data[k] == 0) ? T(ceil(fabs((val + data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val + data[k]) / -data[k]) / std::numeric_limits::epsilon())); + err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 5000000000L); + + static const boost::array near_one = + {{ + T("0.001103662615143147017601393734232421549156847219973314118949247990939859507971857976111288683988415478257878902917354105871236439563170045857810738102729287303674642020538722348587741395785016549139854168605590336633274890874911975139498047488076101124170425114828336211817830671418321600962996502656221412102902998671173649312277667706874059520046508702908872747388744526457997404065469953155187340837"), + T("0.0030157041572432190019717764776322147049224887913331212054173669461673516770769148735558540290915754514269097799280330158745508542936966046640795712691698490758472574837678659161855207596563250546269614348515005196657786359646020537231301121492728577410212550350070502426482802490452572415879214994201864402901595309726458026672888041860289772080407882673424767232857435141510615538430445535588448032261"), + T("0.0049277346741750694119109616231402901360500185022482787362616412856233338679208830974124749830793778323997684640684587346403570647040211088376986993615001420565608501262335822815041623056442245053684626079448221530207757672939048030945164948521320401574074802966260975904478775314730002799895049652983052125151436511589335123254582883803928373794668948878049089088843407672795237410750365571990834236348"), + T("0.0068397471757112108044544339281399968563253858411528016363900245610068161564091499398024110635089866212789583403491711476788985949178019078796740862827299289838108117219486357027460681238178010067475221327133396780718266880540272936860185783976937569903778160170225166328920201699827472893824363838439627437187765159770262282930293057633886299749088561182830982345936603553661004526800797082995898813903"), + T("0.008751734671690018552720976028788304981263251327799787402847843531098338033456389098956160956160597460869666211569183483587979772678557230743050583975270977754518475970489741156524119378847305446845331098526962579804361960647344836744631465315238254178161716870409320747176674142306881908614436607977326507761331050644035013756409444911127742401762647885817361924274132830920030936589562922803846509607"), + T("0.010663690172041286306192948782895990881227033104763005629047563262531418373465237876680529005058533981010793759446966868628480908709812402179047774888094761104238131843239037167212206469894485599085717216855637620318723457013401360290343196462723174177342294339229792213396006286331141933952648238459364417067676760977202812721209681621184724443514062993874571816382775241753902032787099435678672474841"), + T("0.012575606686811781116778815864446643746718166744927923785139233710240017201737625088406861185781739628293213436323314376708933534933748436720721568462267317026688561438144113855290140925120435317506169856461386623828941531577425811393721991195661429557079268566156800689149725770186985872449679872155877537432897653904213375816262709009448220490217917537801655330411526526290708967440087145630462068976"), + T("0.014487477226190798137230457835664944872810802211308342685055637400305474021552028493778559102552025380880477103065187688337931713540557562373991431880251553620947836940726544553647739994157300967262941976933375115946629204615918888689039777423610894099269527633757403818072000860056651445780074486612843419789636984117740884711882675016016919064788076097669389652323393864660933705259163296837955978748"), + T("0.016399294800535714798489384358524900105286836154421890562438917862501411947245037986455919696365301666112414890097246479762149456962809638588245466988584093380263545543023411087203351948681559905336010066900667101787138862856447778428938265451537422367650992162004154495705878092019403922006152498705687706013973674800621422751806347308220226407830977673540994341535381202679482907460136241543505771361"), + 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T("0.022134359839997490880406060727014362125793630864951833270601574861700025448109186301755833862830343973100181180995751924514611578149687732808840212399134735559355116816700346196685057916461444889179117142807858883574426062415931319905031345377305247124198345242221848293630112578508459623098934259229893301963120289071135120089672338617200639338087265986570094025605269870532431816151660553037324591448"), + T("0.024045895662035785157706623778569329505432699504171659064296747761761946910295074291838826981712792368282349553905175996858645967280135417577488810651594776626562252686758463813820791031580579721782251705600570838044158357396828391251385978824608388341556751951593319015721256942139947235672567093309227673005475237474351604086627391812539914665025071874865132198040631867741985556198082915821590691115"), + 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T("0.090844401286964974994199780075024285173534240616972938308566124002318176156233343333797652771250228033597767340846476094210813299723066344955542455246897302945908336756464582189829335315055318509171623072382573656172991307091055717376996812421994002305994837615827430425975713541786272473174908117299253875064746541808768776888139494200307162476704515967971265236163183394620211890252072718610942571965"), + T("0.092748373834894294768837248013614869545920040757666771889792264347367335922283987944081370356939214799510822558638935486112190359701790662792925773186897671244831971450474952036618937833706899006048469791213129922302798462311426294239282200248625552430083292818594731518350634587677158329361662244008606299358410273467156168469937529868888478684257396004386633746334360279683178784117372066095688934486"), + T("0.094652007302340089278624856973167138217258137565762699413364163993950641989798336903224059425798872308451866930780842878435503832366316245159154044350517727312654980455290163514021860802028251981954724580292247887851185639950862672925642859475325430465650514258094310141033116303195908372018392349011340787373492402788283020594141795669947097771918542864972570255253465754192708165241608041715996375567"), + T("0.09655529472977379853549858833033074225823562054271495313739665642376685099661084023094270272485976247900824483810911634635819558334630910267353320029261330296977292720266655308513559530586843550229208517388789783011887450865488554143475302590353915732321663418057567573042594801866258948380684000769091353165879953111046260532796891917772727185993569684246844052518121013717183610828519193371796413317"), + }}; + + T half_pi = "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064"; + + max_err = 0; + for(unsigned k = 0; k < near_one.size(); k++) + { + static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + T val = cos(half_pi - (euler_gamma + k) / 523); + T e = (near_one[k] == 0) ? T(ceil(fabs((val - near_one[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - near_one[k]) / near_one[k]) / std::numeric_limits::epsilon())); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 500); + + // + // Test with some exact binary values as input - this tests our code + // rather than the test data: + // + static const boost::array, 7> exact_data = + {{ + {{ 0.5, "0.877582561890372716116281582603829651991645197109744052997610868315950763274213947405794184084682258355478400593109053993" }}, + {{ 0.25, "0.968912421710644784144595449494189199804134190287442831148128124288942561184523327264655202799685025510352709626116202617" }}, + {{0.75, "0.731688868873820886311838753000084543840541276050772482507683220220750082501569499540967562610201174960122884908227300721" }}, + {{std::ldexp(1.0, -20), "0.99999999999954525264911357034690133684385823577463126432241468890539365027135494672267164697779879113636143901797362388" }}, + {{ 2, "-0.416146836547142386997568229500762189766000771075544890755149973781964936124079169074531777860169140367366791365215728559" }}, + {{ 5, "0.283662185463226264466639171513557308334422592252215944930359066586151456767382702286176981668344573238827368717546699737" }}, + {{ 10, "-0.839071529076452452258863947824064834519930165133168546835953731048792586866270768400933712760422138927451054405350243624" }} + }}; + max_err = 0; + for(unsigned k = 0; k < exact_data.size(); k++) + { + T val = cos(exact_data[k][0]); + T e = (exact_data[k][1] == 0) ? T(ceil(fabs((val - exact_data[k][1]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - exact_data[k][1]) / exact_data[k][1]) / std::numeric_limits::epsilon())); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + + BOOST_TEST(cos(T(0)) == 1); + BOOST_TEST(fabs(cos(half_pi)) < std::numeric_limits::epsilon()); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif + return boost::report_errors(); +} + + + diff --git a/test/test_sin.cpp b/test/test_sin.cpp new file mode 100644 index 00000000..f864f216 --- /dev/null +++ b/test/test_sin.cpp @@ -0,0 +1,297 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#if defined(TEST_MPFR_50) 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T("-0.9733130134422248664781076439996325547596041902633251431309613137772871577452457011348386026771902539246123917754369011815275465953253766314483807639106238230199709503923447643159359893490066619470146552346442263259964047308322485032089683425930804181966240839058765435955921596502848477098334939721288492487750073064012585262871240814591890531382462762625592433554435697556163942273461885638661645373"), + T("-0.16558643533491417205585047942945840817444866977186231320483545168338776228411479964576268852405814440921094618356469443677441509984568603636330335278789316351077745488280059266519036588084571034766067428538242876359850813716345435707699637862360396048950400623443566517903264884891653913736982243815926409161441171926621253221896245282532431364608500284511449412428102071793828094632271947929662322388"), + T("0.84498980323075860897972946021725417020274887656496755152613838764676035268791649188464914202966471633575987923264828416390016799882223646789601058107569902148674040269544868920695600748107986559656481124234185704814218734471348170295455557819067840791831040541198080087226424277346298230729678145499808600603861335243905613388932855271426976928024047466289393683437131604292988966125504076029384924023"), + T("0.82042150034016416806875390736702748196355225785028360060677365666061470851725327317484829164156996988612675463903575414696300136809557656769505171924327821177877208936984569326071873868949719900334446867163962763207795935703399610925921076634415348400788763860462929861356452609306026119961919669078311635349472648728526901263549622576885884996291919276608766907523487313088490283878962209939268414829"), + 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T("-0.82202496781424117249008335037366444394838277287311909893953311783617946236226559994208529824007840086283951031540156850110406585677216210109663411850204100009480981960066776312830296812837514885788767571642502602406668355250521717143900938155040050319876970346676468728877434985446025106390443319201723689927608809502112038908318173339375177994594042306023859374748187782138324203679569236625767697521"), + T("-0.84348366891508115788160933441645221250048198837137321279789763092610185698937735368600669544368356295269809174537295606389343383737539420322987993567260099654804618392548221004269952154930593772246006464043499864133979093900482916664339574929175866269202056532433888199203357312856354292159018595451908698245799015703256761432875415473819767251067057623850803832618933566752146583252515995117479236918"), + T("0.16835709980798731779763364790367408966536862842255885422223099514294148991190930841731427782587704016811168224144233724867667772646548196695213703654087451353235456862964457399533377933177974811857965890770102023474800434793450796708363928962489727300887984685066126963778396606401313473669144644834322766129500826515170674439623002622166198644072962305451561242924295496497673865817996583336572441598"), + T("0.97395403906078050869854812754010898778588110998510216999024129038738667688293411233247507547660433481826378554022069634273248636871268889943206657893365085495908990103953837221918076997320773016743323042411543366853067308772133354882422005996025272628299293665330139411017152702226907842064909056524954416279212381635918809975293849765789208374484279614272702262407912547006420026381898882431367705053"), + T("0.58642035909386951523768726695456120016000621264121118748335087467285913667949995440747093529938553592801111543797937432739099086039685347738175389472878030459744416755494430838140051041697426054654163206937572434284771573711696435479889701764370159398277764008561691680023659946126461221466012782190610630337123139316903479632261164136029483310671081582686512548571027968589672841130517258821548718323"), + T("-0.51950049121984044339738214491377557901625353846688754076530639315973808266367537549984077340395292997735469833961726139018356328562746542110713036413300858234570352248446585277165262617881845994831334396201052962253340345385732694479841227791272253515875849614421139763193705915213364104134129815431668002845745090121741132063335533091373430722704456843140034973756911786188684117004466722017726632522"), + T("-0.98901354618029602175090175847463473510249349724827992487552201591187355027688868967642510244298626184812677555619430672681773746616625955520405639182509666726561394718194458471759810888548201804764323767747429110609233156664896859247358618600160567275441201363464883016296014653448896069217108492576553919644561112490398174029484186504656523262450502010870102764110481052688040511085868232105814711948"), + T("-0.24694751481270393816989455015331965599577990782082974819820952118012926923238759680307705708664260650582713915549160371243741339970969856458066110960284501686263922529370992689985210394245398556897269198908375140963677715274995382713675198405319566885196239063678630261988218491689541221423165343153282194748383394932208400962140245741297801785867823531750497892155090643962052920864620306068640533502"), + T("0.79763858366953481259714957489398094215522640329181266031581650731842869736147648450595884906779088504877531298007549709584387968778149220989565106227234119514920955857261247662051707093671536949960734074547532698822613207712655346154633044042812601716529880175764244503721748663711634053406295594334950958339944104852233364538438677862264102037879639671893945361353871735018017912124896762688051071101"), + T("0.86508717968306725270818735916557777730599862881751831435316187689198923993283521790498932671735565487198406771220725516598383731877859238387113868142949869746710189966430151098818077220502499366007854414799684058332411166897077090145203892212195332779437567412064793775991386725873517928401298446944183864288115967332769329141686571538486980106767058872245206155998183801127952563209302584516809804068"), + }}; + + T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + + boost::uintmax_t max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + T val = sin(euler_gamma * ((100 * k) - 5000)); + T e = (data[k] == 0) ? T(ceil(fabs((val - data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon())); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + val = sin(-euler_gamma * ((100 * k) - 5000)); + e = (data[k] == 0) ? T(ceil(fabs((val + data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val + data[k]) / -data[k]) / std::numeric_limits::epsilon())); + err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 5000000000); + + static const boost::array small_data = + {{ + T("0.010890646307437399028563191160252839599929232814970922208664909237494716181484215717644776933044418903207919912063594159099133490979634344811936925144447725948305353257042599564404885434349760121009797816724142318243738364307036155852011004353462651092012819894667485840322627440332163428546845499107471983896711023161969130462687924045508477090891879273259947713367290982391204265694893491531721581439"), + T("0.029754394000520972141380267705677256353702996169858414168445272181777338962866552847084800544086743338130195210005002660881957584567978770485056322086472328896988088721899728258224129935989180857437073412730903070983582129359565450458299328041955729258476583848159389714290107649243089149974776893563078190705561325124542669960182002956940545214147678093802442811362846262655415145897575707676223535749"), + T("0.04860754948595027759689273751438643634234576398271158524070718139962965653841137425728738193533514318422431877217110239554743968609870039776938201724688048349972662394084789924867267405853696017478160702683117974766657840965270625814482422398422216605490620054574252910928068433847115132429726072853170339113804838625536981361490008602432476302086066307320875870985443111858828925332085101376920451257"), + T("0.067443401266329792365583268418977022587089806595860818790246293104463576184436096833111903064801552379988362224633198052490234517656318474005568709048710308123967082103235230201516378834855764348740505470176912466587139988300259624310153055247378188811239571439869254255368050758213303082097176168650573121101094016896349982672715603054645687782535250201448606757920212668324401846105554332382154705308"), + T("0.086255244004175604199645786226683865650130764638142939010554245919172299560583634262067769465886944689883333394099120765964771092069938753689253686543017871063587988437235057514131760587649504670117933814486942187589706655157340717185354058186603027300571692666150552274324933749082047517987509942119060274537912867956274549119040817359639741746006374702951412541338483858389306953539029174581171144916"), + T("0.10503638090893519164596691292161072193010174143933600597680115817738720676321226654184308409972393036413684625874294713490753271261380987552528236660688624108474124469034444076627315674234385578608111398112242272762722849083801773818689342174907858373883192220827687618321085007917387951532673599267211035785307947515638810735621964273183425401191468313574763898720597251843424536611952986478638938787"), + T("0.12378012612096459891996422671239906394195356627713556749926735466337892925173796651675302282473738808218327028589606894825728784823540605065317506645900565980161901287116410208049542818796994171203890952761651470187834173644651508025088970034800067245131759655003164127161058084682831906406941473650395873577925901419536540828468001386512234321890242266327761400155849351025221609783793228816606096155"), + T("0.14247980709161433833827358255114404185333478069639957369769805221957506649654851981837061160249376538785737485777248817812720592537597263252706422066438137522011148566625861552209380620325080441618503257506798981598559897331754555335688284111417797211888381141445522536739542765207936516297907076923899840216864191777039028622886076254231994264908278499537587536902686114072117102531777746791366147472"), + T("0.16112876695857673825462942280040873226725445145336882995544646098546697397681955191516861690559627281570477802647683153249828731761062718487424104325152088763220776831248566486363299448443795266104568555186977695939803420793575204146124697832793773870449082377964029658283741910741804550762511379894890589132658450368609377005630322641674351408014813725947288936865021810537922503050280596331958949813"), + T("0.17972036691564914131189073707203611766536704952071818203835281740755093560444625679032703078557333645546302532200674729781663838075105196332695024246509042831095553050804767663788014113177991938252225120228302734228632787082072480689719322299247090887229731260135165819595797392665106642595359433094386743214852929965104946276195924300495453775467378376551444126292108291215861133471208854009513721707"), + T("0.19824798857606934571352609051549058593435535174283382080060738672122306773474119459815363636791069253463660528114022041674780565798655265640072669329819802234483545444085426470661233958030668844326674768815456315879868376252722369574694411591080512527683145774214215193268992508938562109669843137270238454905091555179756374512457742554641355319960601765568460966738628365652972463731882673979926092423"), + T("0.2167050363285819704223187876642169717474346025766606244643176750460657731203611217470241676182041675112171974414875203007374497968642376196256262296063879827128970901451226217571636202438144440234868076467587220541438440149682254317134405302648426790500751310485432990930185087578150399032543990173811106465656404530116032387260432178319507278340110997943206401370789106214680733463126804159766688178"), + T("0.23508493968539701289801441539326267060915175918342580386836036980227948313782327655061004506711767031388143537081826986030990557707922203603349984851809173788402101756510017046639631528282698404857654444279509591873678208318484036337040837844539190863615310872984455261973647897667843302241773795592355085118273592671348602240382153223466391512738221253451636183066773121830262978729780866153048605159"), + 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T("0.80484791442470288298134387731514331459831415420391927496917008531718727007136925375073869996549995938671025493755987802316807560672754205522916341547950527416285009447065632296220924964603370109747266700136618832767813938243784759073035555035361911772169687111972294262096081393656654067512785827139608367560009298721819281091010743363153063005841441400130721362346287552727162527118465104052539630019"), + T("0.81590174883253870457705586780548750833668862852238889952372206236774966573191832400412494946116015154305873210759963247859431688393192829248700535837612167242633896627292821666890819736549652534738107012873094812825219601489880060491958385552979476621004236099490018887651186347086675381603801017940808290855340870383683075409122477045713172106217670870448929077822708030574128623585863036730829850118"), + }}; + + max_err = 0; + for(unsigned k = 0; k < small_data.size(); k++) + { + static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + T val = sin((euler_gamma + k) / 53); + T e = (small_data[k] == 0) ? T(ceil(fabs((val - small_data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - small_data[k]) / small_data[k]) / std::numeric_limits::epsilon())); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + val = sin(-(euler_gamma + k) / 53); + e = (small_data[k] == 0) ? T(ceil(fabs((val + small_data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val + small_data[k]) / -small_data[k]) / std::numeric_limits::epsilon())); + err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + + + // + // Test with some exact binary values as input - this tests our code + // rather than the test data: + // + static const boost::array, 7> exact_data = + {{ + {{ 0.5, "0.479425538604203000273287935215571388081803367940600675188616613125535000287814832209631274684348269086132091084505717418" }}, + {{ 0.25, "0.247403959254522929596848704849389195893390980386965810676544830494398136043486821690984848527973792338327197752176516138" }}, + {{0.75, "0.681638760023334166733241952779893935338382394659229909213625262151100388887003782753145274849781911981438190343146876189" }}, + {{std::ldexp(1.0, -20), "9.53674316406105439710335272649306549801506698739838753888815787489707114648106832493113326022411646219016312547902694921e-7" }}, + {{ 2, "0.909297426825681695396019865911744842702254971447890268378973011530967301540783544620126688924959380309967896742399486261" }}, + {{ 5, "-0.958924274663138468893154406155993973352461543964601778131672454235102558086559603076995955429532866596530638461663378937" }}, + {{ 10, "-0.544021110889369813404747661851377281683643012916223891574184012616757209640493425707075673894983216158293824238262832286" }} + }}; + max_err = 0; + for(unsigned k = 0; k < exact_data.size(); k++) + { + T val = sin(exact_data[k][0]); + T e = (exact_data[k][1] == 0) ? T(ceil(fabs((val - exact_data[k][1]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - exact_data[k][1]) / exact_data[k][1]) / std::numeric_limits::epsilon())); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + + T half_pi = "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064"; + + BOOST_TEST(sin(T(0)) == 0); + BOOST_TEST(sin(half_pi) == 1); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif + return boost::report_errors(); +} + + + From 636fdc2e5db2ba17f4dd4266e5cf7230e268dded Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 20 Oct 2011 18:16:46 +0000 Subject: [PATCH 037/256] Tidy up the tests with boilerplate relative error calculation. Fix eval_ldexp for mpf_t. Fix power and log calculations. Add acos. Get all the tests passing. [SVN r75070] --- .../multiprecision/detail/functions/pow.hpp | 10 +- .../multiprecision/detail/functions/trig.hpp | 39 +++- include/boost/multiprecision/gmp.hpp | 2 + test/Jamfile.v2 | 16 ++ test/test_acos.cpp | 106 +++++++++ test/test_asin.cpp | 9 +- test/test_cos.cpp | 211 ++++++++--------- test/test_cosh.cpp | 5 +- test/test_exp.cpp | 154 ++++++++----- test/test_log.cpp | 9 +- test/test_pow.cpp | 7 +- test/test_sin.cpp | 213 +++++++++--------- test/test_sinh.cpp | 5 +- test/test_tanh.cpp | 5 +- 14 files changed, 506 insertions(+), 285 deletions(-) create mode 100644 test/test_acos.cpp diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index cc6b2489..a2e75f4c 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -120,7 +120,7 @@ void hyp0F0(T& H0F0, const T& x) multiply(x_pow_n_div_n_fact, x); divide(x_pow_n_div_n_fact, n); add(H0F0, x_pow_n_div_n_fact); - bool neg = get_sign(x_pow_n_div_n_fact); + bool neg = get_sign(x_pow_n_div_n_fact) < 0; if(neg) x_pow_n_div_n_fact.negate(); if(lim.compare(x_pow_n_div_n_fact) > 0) @@ -164,7 +164,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x) T term, part; // Series expansion of hyperg_1f0(a; ; x). - for(n = 2; n < 1000; n++) + for(n = 2; n < std::numeric_limits >::digits + 10; n++) { multiply(x_pow_n_div_n_fact, x); divide(x_pow_n_div_n_fact, n); @@ -174,10 +174,10 @@ void hyp1F0(T& H1F0, const T& a, const T& x) add(H1F0, term); if(get_sign(term) < 0) term.negate(); - if(lim.compare(term) < 0) + if(lim.compare(term) >= 0) break; } - if(n >= 1000) + if(n >= std::numeric_limits >::digits + 10) throw std::runtime_error("H1F0 failed to converge"); } @@ -461,7 +461,7 @@ inline void eval_pow(T& result, const T& x, const T& a) return; } - if((get_sign(x) > 0) && (x.compare(fp_type(0.1)) > 0) && (x.compare(fp_type(0.9)) < 0)) + if((get_sign(x) > 0) && (x.compare(fp_type(0.5)) >= 0) && (x.compare(fp_type(0.9)) < 0)) { if(a.compare(fp_type(1e-5f)) <= 0) { diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index e770e4cd..412d7ed0 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -468,8 +468,6 @@ void eval_asin(T& result, const T& x) t2 = fp_type(1.5f); hyp2F1(result, t1, t1, t2, xx); multiply(result, x); - if(b_neg) - result.negate(); return; } else if(xx.compare(fp_type(1 - 1e-4f)) > 0) @@ -521,4 +519,41 @@ void eval_asin(T& result, const T& x) result.negate(); } +template +inline void eval_acos(T& result, const T& x) +{ + typedef typename boost::multiprecision::detail::canonical::type ui_type; + + switch(eval_fpclassify(x)) + { + case FP_NAN: + case FP_INFINITE: + result = std::numeric_limits >::quiet_NaN().backend(); + return; + case FP_ZERO: + result = get_constant_pi(); + eval_ldexp(result, result, -1); // divide by two. + return; + } + + eval_abs(result, x); + int c = result.compare(ui_type(1)); + + if(c > 0) + { + result = std::numeric_limits >::quiet_NaN().backend(); + return; + } + else if(c == 0) + { + result = ui_type(0); + return; + } + + eval_asin(result, x); + T t; + eval_ldexp(t, get_constant_pi(), -1); + subtract(result, t); + result.negate(); +} diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 7aab73ab..8da15ee7 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -673,6 +673,8 @@ inline void eval_ldexp(gmp_real& result, const gmp_real& val mpf_mul_2exp(result.data(), val.data(), e); else if(e < 0) mpf_div_2exp(result.data(), val.data(), -e); + else + result = val; } template inline void eval_frexp(gmp_real& result, const gmp_real& val, int* e) diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index dbcfbe61..29edef2a 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -331,3 +331,19 @@ run test_asin.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : test_asin_mpfr_50 ; +run test_acos.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF50 + [ check-target-builds ../config//has_gmp : : no ] + : test_acos_mpf50 ; + +run test_acos.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_acos_mpfr_50 ; + diff --git a/test/test_acos.cpp b/test/test_acos.cpp new file mode 100644 index 00000000..eea8e1fc --- /dev/null +++ b/test/test_acos.cpp @@ -0,0 +1,106 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include +#include "test.hpp" + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#if defined(TEST_MPFR_50) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif + +template +void test() +{ + // + // Test with some exact binary values as input - this tests our code + // rather than the test data: + // + static const boost::array, 13> exact_data = + {{ + {{ 0.5, "1.04719755119659774615421446109316762806572313312503527365831486410260546876206966620934494178070568932738269550442743555" }}, + {{ 0.25, "1.31811607165281796574566425464604046984639096659071471685354851741333314266208327690226867044304393238598144034722708676" }}, + {{0.75, "0.722734247813415611178377352641333362025218486424440267626754132583707381914630264964827610939101303690078815991333621490" }}, + {{1 - std::ldexp(1.0, -20), "0.00138106804176241718210883847756746694048570648553426714212025111150044290934710742282266738617709904634187850607042604204" }}, + {{std::ldexp(1.0, -20), "1.57079537312058021283676140197495835299636605165647561806789944133748780804448843729970624018104090863783682329820313127" }}, + {{1, "0" }}, + + {{0, "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332" }}, + + {{ -0.5, "2.09439510239319549230842892218633525613144626625007054731662972820521093752413933241868988356141137865476539100885487110" }}, + {{ -0.25, "1.82347658193697527271697912863346241435077843278439110412139607489448326362412572172576615489907313559616664616605521989" }}, + {{-0.75, "2.41885840577637762728426603063816952217195091295066555334819045972410902437157873366320721440301576429206927052194868516" }}, + {{-1 + std::ldexp(1.0, -20), "3.14021158554803082128053454480193541725668369288957155383282434119631596337686189120521215795593996893580620800721188061" }}, + {{-std::ldexp(1.0, -20), "1.57079728046921302562588198130454453120080334771863020290704515097032859824172056132832858516107615934431126321507917538" }}, + {{-1, "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230665" }}, + }}; + T half_pi = "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064"; + unsigned max_err = 0; + for(unsigned k = 0; k < exact_data.size(); k++) + { + T val = acos(exact_data[k][0]); + T e = relative_error(val, exact_data[k][1]); + unsigned err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + BOOST_TEST(asin(T(0)) == 0); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif + return boost::report_errors(); +} + + + diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 6f1c8768..aff5d824 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -10,6 +10,7 @@ #include #include +#include "test.hpp" #if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 @@ -59,15 +60,19 @@ void test() for(unsigned k = 0; k < exact_data.size(); k++) { T val = asin(exact_data[k][0]); - T e = (exact_data[k][1] == 0) ? T(ceil(fabs((val - exact_data[k][1]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - exact_data[k][1]) / exact_data[k][1]) / std::numeric_limits::epsilon())); + T e = relative_error(val, exact_data[k][1]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; val = asin(-exact_data[k][0]); - e = T(ceil(fabs((val + exact_data[k][1]) / exact_data[k][1]) / std::numeric_limits::epsilon())); + e = relative_error(val, T(-exact_data[k][1])); err = e.template convert_to(); if(err > max_err) + { + std::cout << val << std::endl; + std::cout << -exact_data[k][0] << std::endl; max_err = err; + } } std::cout << "Max error was: " << max_err << std::endl; BOOST_TEST(max_err < 20); diff --git a/test/test_cos.cpp b/test/test_cos.cpp index 419f18b0..1eb36acf 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -10,6 +10,7 @@ #include #include +#include "test.hpp" #if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 @@ -44,107 +45,107 @@ void test() { static const boost::array data = {{ - T("-0.50162154214905535006507934761566421365808962336874567677926739022768858180703782104157334491773507690211622144412751863172893119122904872120863946237533655183100979972269651012785895305465091942482860884709266947899655662267052604131701946158941092922207257375120965677001058006645609151579188243577188192831765423148813895489546306047297711022539509473462404019089733447430114238267379980532396311664"), - T("0.60313571428133694309325113655636540756247392441681227046917143280974317371916820972719995253248954425492897594051861535050840463205496306256237562726891289696301688567930026444972968333329934552460084325207412884738539384203738886072440013640125030433738691853586812704775040754220545555524237855361445575868855139945713834823411715711428213828850093318644478373792898000948569667301322178250159228606"), - T("0.96902885660223213449832417965462288346382027027907788639786102888188268413128284808786908788351970794814191573322198094839000459295090920127430762740525901384778314480815531039485728089512489227948630012091333107823627672161756650613535363845597750943844039360212709462602480040358932164638277463645635101178868520058961493135889052671922314786442189473233561252419424865659925386520422456933994031412"), - T("0.14782491492260520954264860310453392894688582499520847868449990765772811594316839506757584243129175527745236732059643506743012867347391315093605558463510078020864683057368198129858823908327097108583620570511151521896111105026538667326749527786043478669088587777236123716686756088055458828079103458534402182273835161066708126746360741813126817035007484464329141515901214558732724557437706092450180726378"), - T("-0.85447015139344948471094821054366626768019606763269341666053644333072070840260166961763856973284893831954425042860099172316086950440334996806598196522184690224018944138578542327045770832471332376269716674841615467614625539483750018876502303839670098606230317226296309325404589665701938190004997832683948796843166639576625281030300467522347494569768687089899397360725496800596493559470637547748735594697"), - T("-0.81000689036588888102398287378618104836450574863713892332248232301021899106208419137911694670935600210389307190348154033680700645928539580731142634010602466147128679656911798991740456705453963764056901956423046807435258488930954638670002070774439646670450724500520094586192645160847046520311570082832431061691996839606591067443335185302732221888316818825870721496315105401624866741940813589284275695918"), - T("0.2267455177003321384894005667464998092097833850092894238480831378466683827110057043871346060005709235569800215748516185659827893723700508589640891976972716570403665692613477548038629552153079218542242417184271182264022470709072429310981387965885388758575814101891100826647083444934684812292662215448102626341015149572372707444725994248777658076421636637760492982947444020394182326376291158696727384852"), - T("0.98572607094681400469823142383450564975177916157871840422129452719452525174019803417354200370408054482797693621385765351670173144053171524005535725427317409189868483686977845578192854125777358818593005952568285102554187813023457756929121023181880198348203083841375515867843145321766318476866476607321938993078073105088587752971311300418067382395754489252201424628686354714684325074264340586434068083735"), - T("0.53715481965030691887397316962489853948341836449029599646266321884877186476498260019355874856809552188645630606126976563119123530724283602396484950653123503399938294688332329634386257314146589125825636097592371320563696604271190825947497633567945681092924620382686009619110102110209885034787176755762448527267043281608584015012767667899712762371285806841811102653584612955459666723163160014123341963671"), - T("-0.56945144858011886915780505911780725010620323062276283805115420871306570794972703588425077520601752861293077323301792800610549113139402646104081762175534061087117946244152125287975953108704696268847815261917377065241801643783329354778399526877290332215236634903080639679860355847620563822363712579548641527844739938293967364597110377469773489014211951212857101374318452911401420528677259991331090266005"), - T("-0.97845810511310366097345864112668906661089075307983663561178996977421991305045684012227818895513901547325249161241097295038349597373820690088476031256136981855438584632935895625291791741570973153071536443895825053372019222244541345181800559983327493395843212471107951435623879503589116197386166395270332969985628390518342285544128149350904869144760786557644083102040293619728857795557725975446387638082"), - 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"5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; @@ -154,12 +155,12 @@ void test() { static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; T val = cos(euler_gamma * ((100 * k) - 5000)); - T e = (data[k] == 0) ? T(ceil(fabs((val - data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon())); + T e = relative_error(val, data[k]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; val = cos(-euler_gamma * ((100 * k) - 5000)); - e = (data[k] == 0) ? T(ceil(fabs((val + data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val + data[k]) / -data[k]) / std::numeric_limits::epsilon())); + e = relative_error(val, data[k]); err = e.template convert_to(); if(err > max_err) max_err = err; @@ -229,7 +230,7 @@ void test() { static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; T val = cos(half_pi - (euler_gamma + k) / 523); - T e = (near_one[k] == 0) ? T(ceil(fabs((val - near_one[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - near_one[k]) / near_one[k]) / std::numeric_limits::epsilon())); + T e = relative_error(val, near_one[k]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; @@ -255,7 +256,7 @@ void test() for(unsigned k = 0; k < exact_data.size(); k++) { T val = cos(exact_data[k][0]); - T e = (exact_data[k][1] == 0) ? T(ceil(fabs((val - exact_data[k][1]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - exact_data[k][1]) / exact_data[k][1]) / std::numeric_limits::epsilon())); + T e = relative_error(val, exact_data[k][1]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index e2c0b845..38841e62 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -10,6 +10,7 @@ #include #include +#include "test.hpp" #if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 @@ -104,13 +105,13 @@ void test() { const T x = eg + k; T val = boost::multiprecision::cosh(x * x); - T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon()); + T e = relative_error(val, data[k]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; } std::cout << "Max error was: " << max_err << std::endl; - BOOST_TEST(max_err < 1200); + BOOST_TEST(max_err < 2000); } diff --git a/test/test_exp.cpp b/test/test_exp.cpp index abde8e4c..87578245 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -10,6 +10,7 @@ #include #include +#include "test.hpp" #if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 @@ -44,57 +45,57 @@ void test() { static const boost::array data = {{ - T("1."), - T("9.4774758759621877024211675170518456366884502921505415491512637467314221915954853431757689726613032841249599156149038435317513116309445221664968991934479367736962368912070497862135887440758964938422498610719192114666493107120133053433933470080716434904854804591983841381870449665144170011709399012693158566138960223723364102555657731121349862591746773752353141675856300389702807704522952296232409058995e76"), 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T("1.79541977639739687088375911648976940254141946934175300605485966288703931992861387257771264702798405630917098672594899744e2463"), + T("1.70160476180317540861346545791118106171203487587101437710693054174454895160403997508137760007058856854991413121389834429e2540"), + T("1.61269180804119796097157014527479883521656118500417752963675677684343588976915851637637232001139108420659882326614772004e2617"), + T("1.52842477060722969066998464046690349841548269556677423378408183476489015878816585045578141383463708674469365281537792914e2694"), + T("1.44856088916530600122626623629347336702026699647293500058111037526381692645547938577338582002157148103479049071921438452e2771"), + T("1.37287008819265239873777879432333192404914357037749380145412895230166352318128978403808382142784030558123748263528360645e2848"), + T("1.30113431416759441771790128053911040907207490879890145597562380328956450092799014856149474809345424672958343296615764490e2925"), + T("1.23314690739099822369963411660419632130352733806319401863570442920347696015409870236230656305563674376063778482449716744e3002"), + T("1.16871200663155636468514484039368694043851858077879103221831997264419096417014996945143145495038265243932745953706526253e3079"), + T("1.10764398487979357804590117089134596938734185016144401218934115168561552640448889215089150481162977776214124397487013110e3156"), + T("1.04976691458528698318220729857405616816444374000182094405930946710168752954926612218474430081526312018810817657409158490e3233"), + T("9.94914060836531582868347569174220216007647278536863127198023584205669825317884219144692385409156165042162234017403353704e3309"), + T("9.42927401023380446961314339401657458785389811652244742482194123119943160577946366372207045050095290781679375214307398844e3386"), + T("8.93657169598281164656322298275337750103095739790107943666668184304335665562867744740310577868880098719252549186849812451e3463"), + T("8.46961426624835911826517103631490619655296714141872141145089865045804196205328364155921945616925875458926717336478525196e3540"), + T("8.02705648870740089929294815816002943860908317454595055392168733404583122074223427054310572378841634984243492063192095337e3617"), + T("7.60762342267101369970765191988545810374824800500875923752736467467657167098026707905341603949108433696304383346239333297e3694"), + T("7.21010674617694221027190468649359000420209460539838589305387835463807416706224777302997789297329446308541513638035437482e3771"), + T("6.83336127500041943234365059231968669406267422759442985746460610830503287734479988530512309065240678799786759250323660701e3848"), }}; T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"; @@ -102,19 +103,60 @@ void test() unsigned max_err = 0; for(unsigned k = 0; k < data.size(); k++) { - T val = boost::multiprecision::exp(boost::multiprecision::sqrt((pi * (100 * k)) * (100 * k))); - T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon()); + T val = exp(sqrt((pi * (100 * k)) * (100 * k))); + T e = relative_error(val, data[k]); unsigned err = e.template convert_to(); if(err > max_err) + { max_err = err; - val = boost::multiprecision::exp(-boost::multiprecision::sqrt((pi * (100 * k)) * (100 * k))); - e = ceil(fabs((val - (1/data[k])) / (1/data[k])) / std::numeric_limits::epsilon()); + } + val = exp(-sqrt((pi * (100 * k)) * (100 * k))); + e = relative_error(val, T(1/data[k])); err = e.template convert_to(); if(err > max_err) + { max_err = err; + } } std::cout << "Max error was: " << max_err << std::endl; - BOOST_TEST(max_err < 1200); + BOOST_TEST(max_err < 5000); + + static const boost::array, 10> exact_data = + {{ + {{ std::ldexp(1.0, -50), "1.00000000000000088817841970012562676935794497867573073630970950828771105957980924149923657574337470594698012676100224953" }}, + {{ std::ldexp(1.0, -20), "1.00000095367477115374544678824955687428365188553281789775169686343569285229334215539516690752571791280462887427635269562" }}, + {{ std::ldexp(1.0, -10), "1.00097703949241653524284529261160650646585162918174419940186408264916250428896869173656853690882467186075613761065459261" }}, + {{ 0.25, "1.28402541668774148407342056806243645833628086528146308921750729687220776586723800275330641943955356890166283174967968731" }}, + {{ 0.5, "1.64872127070012814684865078781416357165377610071014801157507931164066102119421560863277652005636664300286663775630779700" }}, + {{ 0.75, "2.11700001661267466854536981983709561013449158470240342177913303081098453336401282000279156026661579821888590471901551426" }}, + {{ 10, "22026.4657948067165169579006452842443663535126185567810742354263552252028185707925751991209681645258954515555010924578367" }}, + {{ 10.5, "36315.5026742466377389120269013166179689315579671275857607480190550842856628099187749764427758174866310742771977376827512" }}, + {{ 25, "7.20048993373858725241613514661261579152235338133952787362213864472320593107782569745000325654258093194727871848859163684e10" }}, + {{ 31.25, "3.72994612957188849046766396046821396700589012875701157893019118883826370993674081486706667149871508642909416337810227575e13" }}, + }}; + + max_err = 0; + for(unsigned k = 0; k < exact_data.size(); k++) + { + T val = exp(exact_data[k][0]); + T e = relative_error(val, exact_data[k][1]); + unsigned err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + val = exp(-exact_data[k][0]); + e = relative_error(val, T(1/exact_data[k][1])); + err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 10); + + BOOST_TEST(exp(T(0)) == 1); } diff --git a/test/test_log.cpp b/test/test_log.cpp index 6905a19d..06a1fa90 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -10,6 +10,7 @@ #include #include +#include "test.hpp" #if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 @@ -155,10 +156,16 @@ void test() for(unsigned k = 0; k < data.size(); k++) { T val = boost::multiprecision::log(tenth + pi * (100 * k) * (100 * k)); - T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon()); + T e = relative_error(val, data[k]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; + + val = boost::multiprecision::log(1 / (tenth + pi * (100 * k) * (100 * k))); + e = relative_error(val, T(-data[k])); + err = e.template convert_to(); + if(err > max_err) + max_err = err; } std::cout << "Max error was: " << max_err << std::endl; BOOST_TEST(max_err < 10); diff --git a/test/test_pow.cpp b/test/test_pow.cpp index 15315716..45c81149 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -10,6 +10,7 @@ #include #include +#include "test.hpp" #if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 @@ -550,11 +551,13 @@ void test() unsigned max_err = 0; for(unsigned k = 0; k < data.size(); k++) { - T val = boost::multiprecision::pow(data[k][0], data[k][1]); - T e = ceil(fabs((val - data[k][2]) / data[k][2]) / std::numeric_limits::epsilon()); + T val = pow(data[k][0], data[k][1]); + T e = relative_error(val, data[k][2]); unsigned err = e.template convert_to(); if(err > max_err) + { max_err = err; + } } std::cout << "Max error was: " << max_err << std::endl; } diff --git a/test/test_sin.cpp b/test/test_sin.cpp index f864f216..fcee9188 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -10,6 +10,7 @@ #include #include +#include "test.hpp" #if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 @@ -44,107 +45,107 @@ void test() { static const boost::array data = {{ - 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+T("-9.50882691455803790808811011811129940528171185220498569922200361836899859377942311459807744784166538095896117442350480286e-1"), +T("-8.30804396823694462619418608693397504202900045660409997788297791645107264729830105800672434941805906654953509298579082883e-2"), +T("8.86498500176738212245618093138553877114943127333459437678466772704535139826656179981455385901664422134192971441152486596e-1"), +T("7.70083171278361495868782270594413506070341191348346709317329019377797940394556787220273230008072684372906392335068211595e-1"), +T("-2.89713235318575682157337623325710322388267200178020040738121279630672170355171163891332847251952971324782327373734923025e-1"), +T("-9.94599945986602107902462030221489305674036413322184167100620086215068494963807086265519051279456167270901961176645890910e-1"), +T("-4.81064018790479216363003919039401079745827607566793090566247167201506427394383426836725220489510187378030886775425254046e-1"), +T("6.21793567954698234151923123976248746751871911018984490371928031737872104124834908200003970971778452547150523318639635937e-1"), +T("9.62930462544790791995256817531759605974030310743258985429278608944994805716203043054967792555227147404499205611680348343e-1"), +T("1.24441037037160425420824052419427892644210865386492893504553391973646623439822770473194845274620957661128504291608680469e-1"), +T("-8.66493376243885476034533210550037276824055111358129259572484897399197578809821587005093985112028866251515011805996119334e-1"), +T("-7.95940555954229526911811786010975888490876487056728372525209250018208474961217211282867562886053609351620626802054272020e-1"), +T("2.49669618482792917975718339302754781070461300705127317300546100189317933291972223791458678771914034385073586648459580423e-1"), +T("9.89425045617789945796335206411736550560149597573171983909624851636680028232543261568285131480585113303281176722731984359e-1"), +T("5.17097284014384149171097163430722725596083616428334032893201431916692899725128152827282357887267679461332587145165393473e-1"), +T("-5.88694253013035419947972745515246684318073372460957150709985237608958241550865774225576562359889367149484593966586261944e-1"), +T("-9.73313013442224866478107643999632554759604190263325143130961313777287157745245701134838602677190253924612391775436901182e-1"), +T("-1.65586435334914172055850479429458408174448669771862313204835451683387762284114799645762688524058144409210946183564694437e-1"), +T("8.44989803230758608979729460217254170202748876564967551526138387646760352687916491884649142029664716335759879232648284164e-1"), +T("8.20421500340164168068753907367027481963552257850283600606773656660614708517253273174848291641569969886126754639035754147e-1"), +T("-2.09194241612317592929856274655591551278574667482924447651723415490434554354833563537792618079275726893013991849104465053e-1"), +T("-9.82539107299636472172005507105476251789057582568202763534005396813858490465264145708502581273803767931004018272989858624e-1"), +T("-5.52236319725534543207688775430217404447704139560595336544456138148662731976576062425879410116209671353021251780801885578e-1"), +T("5.54576894095302137473562870411642498454159878739464625116831971740997730359915227524075717328436463081497500485416831879e-1"), +T("9.82012389338213987427432686899213579991770436451929205950504261612336440523069987734051927060071228336651935114247230018e-1"), +T("2.06445480789661722781085666935934466710665000093111315471318244086154187788240397407764949071589419997001126229699279918e-1"), +T("-8.22024967814241172490083350373664443948382772873119098939533117836179462362265599942085298240078400862839510315401568501e-1"), +T("-8.43483668915081157881609334416452212500481988371373212797897630926101856989377353686006695443683562952698091745372956064e-1"), +T("1.68357099807987317797633647903674089665368628422558854222230995142941489911909308417314277825877040168111682241442337249e-1"), +T("9.73954039060780508698548127540108987785881109985102169990241290387386676882934112332475075476604334818263785540220696343e-1"), +T("5.86420359093869515237687266954561200160006212641211187483350874672859136679499954407470935299385535928011115437979374327e-1"), +T("-5.19500491219840443397382144913775579016253538466887540765306393159738082663675375499840773403952929977354698339617261390e-1"), +T("-9.89013546180296021750901758474634735102493497248279924875522015911873550276888689676425102442986261848126775556194306727e-1"), +T("-2.46947514812703938169894550153319655995779907820829748198209521180129269232387596803077057086642606505827139155491603712e-1"), +T("7.97638583669534812597149574893980942155226403291812660315816507318428697361476484505958849067790885048775312980075497096e-1"), +T("8.65087179683067252708187359165577777305998628817518314353161876891989239932835217904989326717355654871984067712207255166e-1"), }}; T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; @@ -154,12 +155,12 @@ void test() { static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; T val = sin(euler_gamma * ((100 * k) - 5000)); - T e = (data[k] == 0) ? T(ceil(fabs((val - data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon())); + T e = relative_error(val, data[k]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; val = sin(-euler_gamma * ((100 * k) - 5000)); - e = (data[k] == 0) ? T(ceil(fabs((val + data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val + data[k]) / -data[k]) / std::numeric_limits::epsilon())); + e = relative_error(val, T(-data[k])); err = e.template convert_to(); if(err > max_err) max_err = err; @@ -227,12 +228,12 @@ void test() { static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; T val = sin((euler_gamma + k) / 53); - T e = (small_data[k] == 0) ? T(ceil(fabs((val - small_data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - small_data[k]) / small_data[k]) / std::numeric_limits::epsilon())); + T e = relative_error(val, small_data[k]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; val = sin(-(euler_gamma + k) / 53); - e = (small_data[k] == 0) ? T(ceil(fabs((val + small_data[k]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val + small_data[k]) / -small_data[k]) / std::numeric_limits::epsilon())); + e = relative_error(val, T(-small_data[k])); err = e.template convert_to(); if(err > max_err) max_err = err; @@ -259,7 +260,7 @@ void test() for(unsigned k = 0; k < exact_data.size(); k++) { T val = sin(exact_data[k][0]); - T e = (exact_data[k][1] == 0) ? T(ceil(fabs((val - exact_data[k][1]) / std::numeric_limits::epsilon()))) : T(ceil(fabs((val - exact_data[k][1]) / exact_data[k][1]) / std::numeric_limits::epsilon())); + T e = relative_error(val, exact_data[k][1]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index 7f559fec..e049b449 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -10,6 +10,7 @@ #include #include +#include "test.hpp" #if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 @@ -104,13 +105,13 @@ void test() { const T x = eg + k; T val = boost::multiprecision::sinh(x * x); - T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon()); + T e = relative_error(val, data[k]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; } std::cout << "Max error was: " << max_err << std::endl; - BOOST_TEST(max_err < 1200); + BOOST_TEST(max_err < 2000); } diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index a0d3b792..547b69a9 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -10,6 +10,7 @@ #include #include +#include "test.hpp" #if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF50 @@ -104,13 +105,13 @@ void test() { const T x = eg + k; T val = boost::multiprecision::tanh(x * x); - T e = ceil(fabs((val - data[k]) / data[k]) / std::numeric_limits::epsilon()); + T e = relative_error(val, data[k]); unsigned err = e.template convert_to(); if(err > max_err) max_err = err; } std::cout << "Max error was: " << max_err << std::endl; - BOOST_TEST(max_err < 1200); + BOOST_TEST(max_err < 10); } From 21a28f3bbe656fcc36bc7d491cfcba6a116cb713 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 20 Oct 2011 18:18:27 +0000 Subject: [PATCH 038/256] Fix eval_ldexp. [SVN r75071] --- include/boost/multiprecision/mpfr.hpp | 2 ++ 1 file changed, 2 insertions(+) diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index b4d6286e..d5941d3f 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -625,6 +625,8 @@ inline void eval_ldexp(mpfr_real_backend& result, const mpfr_real_back mpfr_mul_2exp(result.data(), val.data(), e, GMP_RNDN); else if(e < 0) mpfr_div_2exp(result.data(), val.data(), -e, GMP_RNDN); + else + result = val; } template inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, int* e) From 628c8cd62f856f6f6e92db1b4a906a0bc9505115 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 22 Oct 2011 17:32:01 +0000 Subject: [PATCH 039/256] Added atan2, plus missing file. [SVN r75090] --- .../multiprecision/detail/default_ops.hpp | 9 + .../multiprecision/detail/functions/trig.hpp | 174 ++++++++++++ include/boost/multiprecision/mp_number.hpp | 1 + test/test.hpp | 41 +++ test/test_atan.cpp | 247 ++++++++++++++++++ 5 files changed, 472 insertions(+) create mode 100644 test/test.hpp create mode 100644 test/test_atan.cpp diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 587c99e8..961e03fc 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -398,6 +398,14 @@ inline void eval_round(T& result, const T& a) } } +template +void eval_atan2(T& result, const T& a, const Arithmetic& b) +{ + T x; + x = b; + eval_atan2(result, a, x); +} + // // These have to implemented by the backend, declared here so that our macro generated code compiles OK. // @@ -927,6 +935,7 @@ HETERO_BINARY_OP_FUNCTOR(ldexp, int) HETERO_BINARY_OP_FUNCTOR(frexp, int*) BINARY_OP_FUNCTOR(pow) BINARY_OP_FUNCTOR(fmod) +BINARY_OP_FUNCTOR(atan2) #undef BINARY_OP_FUNCTOR #undef UNARY_OP_FUNCTOR diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index 412d7ed0..a65ffdb6 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -557,3 +557,177 @@ inline void eval_acos(T& result, const T& x) result.negate(); } +template +void eval_atan(T& result, const T& x) +{ + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; + + switch(eval_fpclassify(x)) + { + case FP_NAN: + result = std::numeric_limits >::quiet_NaN().backend(); + return; + case FP_ZERO: + result = ui_type(0); + return; + case FP_INFINITE: + if(get_sign(x) < 0) + { + eval_ldexp(result, get_constant_pi(), -1); + result.negate(); + } + else + eval_ldexp(result, get_constant_pi(), -1); + return; + default: ; + } + + const bool b_neg = get_sign(x) < 0; + + T xx(x); + if(b_neg) + xx.negate(); + + if(xx.compare(fp_type(0.1)) < 0) + { + T t1, t2, t3; + t1 = ui_type(1); + t2 = fp_type(0.5f); + t3 = fp_type(1.5f); + multiply(xx, xx); + xx.negate(); + hyp2F1(result, t1, t2, t3, xx); + multiply(result, x); + return; + } + + if(xx.compare(fp_type(10)) > 0) + { + T t1, t2, t3; + t1 = fp_type(0.5f); + t2 = ui_type(1u); + t3 = fp_type(1.5f); + multiply(xx, xx); + divide(xx, si_type(-1), xx); + hyp2F1(result, t1, t2, t3, xx); + divide(result, x); + if(!b_neg) + result.negate(); + eval_ldexp(t1, get_constant_pi(), -1); + add(result, t1); + if(b_neg) + result.negate(); + return; + } + + + // Get initial estimate using standard math function atan. + fp_type d; + convert_to(&d, xx); + result = fp_type(std::atan(d)); + + // Newton-Raphson iteration + static const boost::int32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; + + T s, c, t; + for(boost::int32_t digits = double_digits10_minus_one; digits <= std::numeric_limits >::digits10; digits *= 2) + { + eval_sin(s, result); + eval_cos(c, result); + multiply(t, xx, c); + subtract(t, s); + multiply(s, t, c); + add(result, s); + } + if(b_neg) + result.negate(); +} + +template +void eval_atan2(T& result, const T& y, const T& x) +{ + typedef typename boost::multiprecision::detail::canonical::type si_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; + typedef typename T::exponent_type exp_type; + typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; + typedef typename mpl::front::type fp_type; + + switch(eval_fpclassify(y)) + { + case FP_NAN: + result = y; + return; + case FP_ZERO: + { + int c = get_sign(x); + if(c < 0) + result = get_constant_pi(); + else if(c >= 0) + result = ui_type(0); // Note we allow atan2(0,0) to be zero, even though it's mathematically undefined + return; + } + case FP_INFINITE: + { + if(eval_fpclassify(x) == FP_INFINITE) + { + result = std::numeric_limits >::quiet_NaN().backend(); + } + else + { + eval_ldexp(result, get_constant_pi(), -1); + if(get_sign(y) < 0) + result.negate(); + } + return; + } + } + + switch(eval_fpclassify(x)) + { + case FP_NAN: + result = x; + return; + case FP_ZERO: + { + eval_ldexp(result, get_constant_pi(), -1); + if(get_sign(x) < 0) + result.negate(); + return; + } + case FP_INFINITE: + if(get_sign(x) > 0) + result = ui_type(0); + else + result = get_constant_pi(); + if(get_sign(y) < 0) + result.negate(); + return; + } + + T xx; + divide(xx, y, x); + if(get_sign(xx) < 0) + xx.negate(); + + eval_atan(result, xx); + + // Determine quadrant (sign) based on signs of x, y + const bool y_neg = get_sign(y) < 0; + const bool x_neg = get_sign(x) < 0; + + if(y_neg != x_neg) + result.negate(); + + if(x_neg) + { + if(y_neg) + subtract(result, get_constant_pi()); + else + add(result, get_constant_pi()); + } +} + diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index e54c85cb..e2b1a6cc 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -28,6 +28,7 @@ class mp_number { typedef mp_number self_type; public: + typedef Backend backend_type; mp_number(){} mp_number(const mp_number& e) : m_backend(e.m_backend){} template diff --git a/test/test.hpp b/test/test.hpp new file mode 100644 index 00000000..657c5737 --- /dev/null +++ b/test/test.hpp @@ -0,0 +1,41 @@ + +#ifndef BOOST_MULTIPRECISION_TEST_HPP +#define BOOST_MULTIPRECISION_TEST_HPP + +template +T relative_error(T a, T b) +{ + T min_val = (std::numeric_limits::min)(); + T max_val = (std::numeric_limits::max)(); + + if((a != 0) && (b != 0)) + { + // TODO: use isfinite: + if(fabs(b) >= max_val) + { + if(fabs(a) >= max_val) + return 0; // one infinity is as good as another! + } + // If the result is denormalised, treat all denorms as equivalent: + if((a < min_val) && (a > 0)) + a = min_val; + else if((a > -min_val) && (a < 0)) + a = -min_val; + if((b < min_val) && (b > 0)) + b = min_val; + else if((b > -min_val) && (b < 0)) + b = -min_val; + return (std::max)(fabs((a-b)/a), fabs((a-b)/b)) / std::numeric_limits::epsilon(); + } + + // Handle special case where one or both are zero: + if(min_val == 0) + return fabs(a-b); + if(fabs(a) < min_val) + a = min_val; + if(fabs(b) < min_val) + b = min_val; + return (std::max)(fabs((a-b)/a), fabs((a-b)/b)) / std::numeric_limits::epsilon(); +} + +#endif diff --git a/test/test_atan.cpp b/test/test_atan.cpp new file mode 100644 index 00000000..db4eb33b --- /dev/null +++ b/test/test_atan.cpp @@ -0,0 +1,247 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include +#include "test.hpp" + +#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_E_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF50) +#include +#endif +#if defined(TEST_MPFR_50) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_E_FLOAT +#include +#endif + +template +T atan2_def(T y, T x) +{ + T t; + t.backend() = boost::multiprecision::big_num_default_ops::get_constant_pi(); + T t2; + if(x) + t2 = atan(y / x); + else + t2 = y.sign() * t / 2; + return t2 + (t / 2) * (1 - x.sign()) * T(y.sign() + 0.5).sign(); +} + +template +struct is_mpfr_type : public boost::mpl::false_ {}; + +template +struct is_mpfr_type > > : public boost::mpl::true_{}; + +template +void test() +{ + static const boost::array data = + {{ + T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999966666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-101"), + 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T("1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017412671057533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730174305227163324106696803963457903970195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138"), + T("1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017412671058533891074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730174305227163324106696803630124570637195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138"), + }}; + + T arg = "1e-100"; + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = atan(arg); + T e = relative_error(val, data[k]); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + val = atan(-arg); + e = relative_error(val, T(-data[k])); + err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + arg *= 10000; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 10); + BOOST_TEST(atan(T(0)) == 0); + + // + // And again, but test all the phases of atan2: + // + arg = "1e-100"; + unsigned err; + for(unsigned k = 0; k < data.size(); k++) + { + T val = atan2(arg, 1); + T e = relative_error(val, atan2_def(arg, T(1))); + err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + val = atan2(-arg, 1); + e = relative_error(val, atan2_def(T(-arg), T(1))); + err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + val = atan2(arg, -1); + e = relative_error(val, atan2_def(arg, T(-1))); + err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + val = atan2(-arg, -1); + e = relative_error(val, atan2_def(T(-arg), T(-1))); + err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + arg *= 10000; + } + // + // special cases: + // + err = relative_error(T(atan2(T(0), T(1))), atan2_def(T(0), T(1))).template convert_to(); + if(err > max_err) + max_err = err; + err = relative_error(T(atan2(T(0), T(-1))), atan2_def(T(0), T(-1))).template convert_to(); + if(err > max_err) + max_err = err; + + T pi; + pi.backend() = boost::multiprecision::big_num_default_ops::get_constant_pi(); + + err = relative_error(T(atan2(T(1), T(0))), T(pi / 2)).template convert_to(); + if(err > max_err) + max_err = err; + if(! is_mpfr_type::value) + { + // MPFR seems to get the sign of this all wrong: + err = relative_error(T(atan2(T(-1), T(0))), T(pi / -2)).template convert_to(); + if(err > max_err) + max_err = err; + } + T mv = (std::numeric_limits::max)(); + err = relative_error(T(atan2(mv, T(1))), T(pi / 2)).template convert_to(); + if(err > max_err) + max_err = err; + err = relative_error(T(atan2(-mv, T(1))), T(pi / -2)).template convert_to(); + if(err > max_err) + max_err = err; + + if(std::numeric_limits::has_infinity) + { + mv = (std::numeric_limits::infinity)(); + err = relative_error(T(atan2(mv, T(1))), T(pi / 2)).template convert_to(); + if(err > max_err) + max_err = err; + err = relative_error(T(atan2(-mv, T(1))), T(pi / -2)).template convert_to(); + if(err > max_err) + max_err = err; + } + + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 40); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_E_FLOAT + test(); +#endif + return boost::report_errors(); +} + + + From c34e9f654f9316f7e25a186299468aeb2bce18f3 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 23 Oct 2011 11:23:13 +0000 Subject: [PATCH 040/256] Big search and replace namespace and class renaming: get rid of last references to "big_number" and "real". [SVN r75093] --- .../concepts/mp_number_architypes.hpp | 84 +++--- .../multiprecision/detail/default_ops.hpp | 16 +- include/boost/multiprecision/gmp.hpp | 212 +++++++-------- include/boost/multiprecision/mp_number.hpp | 124 ++++----- include/boost/multiprecision/mpfr.hpp | 242 +++++++++--------- test/Jamfile.v2 | 47 +++- test/linpack-benchmark.cpp | 10 +- test/mp_number_concept_check.cpp | 26 +- test/test_acos.cpp | 18 +- test/test_arithmetic.cpp | 30 +-- test/test_asin.cpp | 18 +- test/test_atan.cpp | 26 +- test/test_cos.cpp | 18 +- test/test_cosh.cpp | 18 +- test/test_exp.cpp | 18 +- test/test_log.cpp | 18 +- test/test_numeric_limits.cpp | 24 +- test/test_pow.cpp | 18 +- test/test_sin.cpp | 18 +- test/test_sinh.cpp | 18 +- test/test_tanh.cpp | 18 +- 21 files changed, 523 insertions(+), 498 deletions(-) diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index 92402dbc..da417ae1 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -23,53 +23,53 @@ namespace concepts{ #pragma warning(disable:4244) #endif -struct mp_number_backend_real_architype +struct mp_number_backend_float_architype { typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list real_types; typedef int exponent_type; - mp_number_backend_real_architype() + mp_number_backend_float_architype() { std::cout << "Default construct" << std::endl; } - mp_number_backend_real_architype(const mp_number_backend_real_architype& o) + mp_number_backend_float_architype(const mp_number_backend_float_architype& o) { std::cout << "Copy construct" << std::endl; m_value = o.m_value; } - mp_number_backend_real_architype& operator = (const mp_number_backend_real_architype& o) + mp_number_backend_float_architype& operator = (const mp_number_backend_float_architype& o) { m_value = o.m_value; std::cout << "Assignment (" << m_value << ")" << std::endl; return *this; } - mp_number_backend_real_architype& operator = (boost::uintmax_t i) + mp_number_backend_float_architype& operator = (boost::uintmax_t i) { m_value = i; std::cout << "UInt Assignment (" << i << ")" << std::endl; return *this; } - mp_number_backend_real_architype& operator = (boost::intmax_t i) + mp_number_backend_float_architype& operator = (boost::intmax_t i) { m_value = i; std::cout << "Int Assignment (" << i << ")" << std::endl; return *this; } - mp_number_backend_real_architype& operator = (long double d) + mp_number_backend_float_architype& operator = (long double d) { m_value = d; std::cout << "long double Assignment (" << d << ")" << std::endl; return *this; } - mp_number_backend_real_architype& operator = (const char* s) + mp_number_backend_float_architype& operator = (const char* s) { m_value = boost::lexical_cast(s); std::cout << "const char* Assignment (" << s << ")" << std::endl; return *this; } - void swap(mp_number_backend_real_architype& o) + void swap(mp_number_backend_float_architype& o) { std::cout << "Swapping (" << m_value << " with " << o.m_value << ")" << std::endl; std::swap(m_value, o.m_value); @@ -100,7 +100,7 @@ struct mp_number_backend_real_architype std::cout << "Negating (" << m_value << ")" << std::endl; m_value = -m_value; } - int compare(const mp_number_backend_real_architype& o)const + int compare(const mp_number_backend_float_architype& o)const { std::cout << "Comparison" << std::endl; return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); @@ -123,151 +123,151 @@ struct mp_number_backend_real_architype long double m_value; }; -inline void add(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& o) +inline void add(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) { std::cout << "Addition (" << result.m_value << " += " << o.m_value << ")" << std::endl; result.m_value += o.m_value; } -inline void subtract(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& o) +inline void subtract(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) { std::cout << "Subtraction (" << result.m_value << " -= " << o.m_value << ")" << std::endl; result.m_value -= o.m_value; } -inline void multiply(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& o) +inline void multiply(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) { std::cout << "Multiplication (" << result.m_value << " *= " << o.m_value << ")" << std::endl; result.m_value *= o.m_value; } -inline void divide(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& o) +inline void divide(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) { std::cout << "Division (" << result.m_value << " /= " << o.m_value << ")" << std::endl; result.m_value /= o.m_value; } -inline void convert_to(boost::uintmax_t* result, const mp_number_backend_real_architype& val) +inline void convert_to(boost::uintmax_t* result, const mp_number_backend_float_architype& val) { *result = static_cast(val.m_value); } -inline void convert_to(boost::intmax_t* result, const mp_number_backend_real_architype& val) +inline void convert_to(boost::intmax_t* result, const mp_number_backend_float_architype& val) { *result = static_cast(val.m_value); } -inline void convert_to(long double* result, mp_number_backend_real_architype& val) +inline void convert_to(long double* result, mp_number_backend_float_architype& val) { *result = val.m_value; } -inline void eval_frexp(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg, int* exp) +inline void eval_frexp(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg, int* exp) { result = std::frexp(arg.m_value, exp); } -inline void eval_ldexp(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg, int exp) +inline void eval_ldexp(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg, int exp) { result = std::ldexp(arg.m_value, exp); } -inline void eval_floor(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_floor(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::floor(arg.m_value); } -inline void eval_ceil(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_ceil(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::ceil(arg.m_value); } -inline void eval_trunc(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_trunc(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = boost::math::trunc(arg.m_value); } -inline void eval_sqrt(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_sqrt(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::sqrt(arg.m_value); } -inline void eval_abs(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_abs(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::abs(arg.m_value); } -inline void eval_fabs(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_fabs(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::fabs(arg.m_value); } -inline int eval_fpclassify(const mp_number_backend_real_architype& arg) +inline int eval_fpclassify(const mp_number_backend_float_architype& arg) { return boost::math::fpclassify(arg.m_value); } -inline void eval_pow(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& b, const mp_number_backend_real_architype& e) +inline void eval_pow(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& b, const mp_number_backend_float_architype& e) { result = std::pow(b.m_value, e.m_value); } -inline void eval_pow(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& b, int e) +inline void eval_pow(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& b, int e) { result = std::pow(b.m_value, e); } -inline void eval_exp(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_exp(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::exp(arg.m_value); } -inline void eval_log(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_log(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::log(arg.m_value); } -inline void eval_sin(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_sin(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::sin(arg.m_value); } -inline void eval_cos(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_cos(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::cos(arg.m_value); } -inline void eval_tan(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_tan(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::tan(arg.m_value); } -inline void eval_asin(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_asin(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::asin(arg.m_value); } -inline void eval_acos(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_acos(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::acos(arg.m_value); } -inline void eval_atan(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_atan(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::atan(arg.m_value); } -inline void eval_sinh(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_sinh(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::sinh(arg.m_value); } -inline void eval_cosh(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_cosh(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::cosh(arg.m_value); } -inline void eval_tanh(mp_number_backend_real_architype& result, const mp_number_backend_real_architype& arg) +inline void eval_tanh(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::tanh(arg.m_value); } -typedef boost::multiprecision::mp_number mp_number_real_architype; +typedef boost::multiprecision::mp_number mp_number_float_architype; }}} // namespaces @@ -278,10 +278,10 @@ namespace std{ #endif template <> -class numeric_limits : public std::numeric_limits +class numeric_limits : public std::numeric_limits { typedef std::numeric_limits base_type; - typedef boost::multiprecision::concepts::mp_number_real_architype number_type; + typedef boost::multiprecision::concepts::mp_number_float_architype number_type; public: BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 961e03fc..77240092 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -14,7 +14,7 @@ #include #include -namespace boost{ namespace multiprecision{ namespace big_num_default_ops{ +namespace boost{ namespace multiprecision{ namespace default_ops{ // // Default versions of mixed arithmetic, these just construct a temporary @@ -467,7 +467,7 @@ namespace math{ template inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { - using multiprecision::big_num_default_ops::eval_fpclassify; + using multiprecision::default_ops::eval_fpclassify; return eval_fpclassify(arg.backend()); } template @@ -535,7 +535,7 @@ inline typename detail::mp_exp::result_type trunc(const detail: template inline mp_number trunc(const mp_number& v, const Policy& pol) { - using big_num_default_ops::eval_trunc; + using default_ops::eval_trunc; mp_number result; eval_trunc(result.backend(), v.backend()); return result; @@ -603,7 +603,7 @@ inline typename detail::mp_exp::result_result round(const detai template inline mp_number round(const mp_number& v, const Policy& pol) { - using big_num_default_ops::eval_round; + using default_ops::eval_round; mp_number result; eval_round(result.backend(), v.backend()); return result; @@ -670,7 +670,7 @@ struct BOOST_JOIN(func, _funct)\ {\ void operator()(Backend& result, const Backend& arg)const\ {\ - using big_num_default_ops::BOOST_JOIN(eval_,func);\ + using default_ops::BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result, arg);\ }\ };\ @@ -719,13 +719,13 @@ struct BOOST_JOIN(func, _funct)\ {\ void operator()(Backend& result, const Backend& arg, const Backend& a)const\ {\ - using big_num_default_ops:: BOOST_JOIN(eval_,func);\ + using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result, arg, a);\ }\ template \ void operator()(Backend& result, const Backend& arg, const Arithmetic& a)const\ {\ - using big_num_default_ops:: BOOST_JOIN(eval_,func);\ + using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result, arg, a);\ }\ };\ @@ -866,7 +866,7 @@ struct BOOST_JOIN(func, _funct)\ {\ void operator()(Backend& result, Backend const& arg, Arg2 a)const\ {\ - using big_num_default_ops:: BOOST_JOIN(eval_,func);\ + using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result, arg, a);\ }\ };\ diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 8da15ee7..af72d94b 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -18,21 +18,21 @@ namespace boost{ namespace multiprecision{ template -struct gmp_real; +struct gmp_float; namespace detail{ template -struct gmp_real_imp +struct gmp_float_imp { typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list real_types; typedef long exponent_type; - gmp_real_imp(){} + gmp_float_imp(){} - gmp_real_imp(const gmp_real_imp& o) + gmp_float_imp(const gmp_float_imp& o) { // // We have to do an init followed by a set here, otherwise *this may be at @@ -44,25 +44,25 @@ struct gmp_real_imp mpf_set(m_data, o.m_data); } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real_imp(gmp_real_imp&& o) + gmp_float_imp(gmp_float_imp&& o) { m_data[0] = o.m_data[0]; o.m_data[0]._mp_d = 0; } #endif - gmp_real_imp& operator = (const gmp_real_imp& o) + gmp_float_imp& operator = (const gmp_float_imp& o) { mpf_set(m_data, o.m_data); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real_imp& operator = (gmp_real_imp&& o) + gmp_float_imp& operator = (gmp_float_imp&& o) { mpf_swap(m_data, o.m_data); return *this; } #endif - gmp_real_imp& operator = (boost::uintmax_t i) + gmp_float_imp& operator = (boost::uintmax_t i) { boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; @@ -81,7 +81,7 @@ struct gmp_real_imp mpf_clear(t); return *this; } - gmp_real_imp& operator = (boost::intmax_t i) + gmp_float_imp& operator = (boost::intmax_t i) { bool neg = i < 0; *this = static_cast(std::abs(i)); @@ -89,22 +89,22 @@ struct gmp_real_imp mpf_neg(m_data, m_data); return *this; } - gmp_real_imp& operator = (unsigned long i) + gmp_float_imp& operator = (unsigned long i) { mpf_set_ui(m_data, i); return *this; } - gmp_real_imp& operator = (long i) + gmp_float_imp& operator = (long i) { mpf_set_si(m_data, i); return *this; } - gmp_real_imp& operator = (double d) + gmp_float_imp& operator = (double d) { mpf_set_d(m_data, d); return *this; } - gmp_real_imp& operator = (long double a) + gmp_float_imp& operator = (long double a) { using std::frexp; using std::ldexp; @@ -150,12 +150,12 @@ struct gmp_real_imp mpf_div_2exp(m_data, m_data, -e); return *this; } - gmp_real_imp& operator = (const char* s) + gmp_float_imp& operator = (const char* s) { mpf_set_str(m_data, s, 10); return *this; } - void swap(gmp_real_imp& o) + void swap(gmp_float_imp& o) { mpf_swap(m_data, o.m_data); } @@ -195,7 +195,7 @@ struct gmp_real_imp (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); return result; } - ~gmp_real_imp() + ~gmp_float_imp() { if(m_data[0]._mp_d) mpf_clear(m_data); @@ -204,7 +204,7 @@ struct gmp_real_imp { mpf_neg(m_data, m_data); } - int compare(const gmp_real& o)const + int compare(const gmp_float& o)const { return mpf_cmp(m_data, o.m_data); } @@ -219,7 +219,7 @@ struct gmp_real_imp template int compare(V v)const { - gmp_real d; + gmp_float d; d = v; return compare(d); } @@ -237,73 +237,73 @@ protected: } // namespace detail template -struct gmp_real : public detail::gmp_real_imp +struct gmp_float : public detail::gmp_float_imp { - gmp_real() + gmp_float() { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } - gmp_real(const gmp_real& o) : detail::gmp_real_imp(o) {} + gmp_float(const gmp_float& o) : detail::gmp_float_imp(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real(gmp_real&& o) : detail::gmp_real_imp(o) {} + gmp_float(gmp_float&& o) : detail::gmp_float_imp(o) {} #endif - gmp_real& operator=(const gmp_real& o) + gmp_float& operator=(const gmp_float& o) { - *static_cast*>(this) = static_cast const&>(o); + *static_cast*>(this) = static_cast const&>(o); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real& operator=(gmp_real&& o) + gmp_float& operator=(gmp_float&& o) { - *static_cast*>(this) = static_cast&&>(o); + *static_cast*>(this) = static_cast&&>(o); return *this; } #endif template - gmp_real& operator=(const V& v) + gmp_float& operator=(const V& v) { - *static_cast*>(this) = v; + *static_cast*>(this) = v; return *this; } }; template <> -struct gmp_real<0> : public detail::gmp_real_imp<0> +struct gmp_float<0> : public detail::gmp_float_imp<0> { - gmp_real() + gmp_float() { mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); } - gmp_real(unsigned digits10) + gmp_float(unsigned digits10) { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } - gmp_real(const gmp_real& o) : detail::gmp_real_imp<0>(o) {} + gmp_float(const gmp_float& o) : detail::gmp_float_imp<0>(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real(gmp_real&& o) : detail::gmp_real_imp<0>(o) {} + gmp_float(gmp_float&& o) : detail::gmp_float_imp<0>(o) {} #endif - gmp_real(const gmp_real& o, unsigned digits10) + gmp_float(const gmp_float& o, unsigned digits10) { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); *this = o; } - gmp_real& operator=(const gmp_real& o) + gmp_float& operator=(const gmp_float& o) { - *static_cast*>(this) = static_cast const&>(o); + *static_cast*>(this) = static_cast const&>(o); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_real& operator=(gmp_real&& o) + gmp_float& operator=(gmp_float&& o) { - *static_cast*>(this) = static_cast &&>(o); + *static_cast*>(this) = static_cast &&>(o); return *this; } #endif template - gmp_real& operator=(const V& v) + gmp_float& operator=(const V& v) { - *static_cast*>(this) = v; + *static_cast*>(this) = v; return *this; } static unsigned default_precision() @@ -325,47 +325,47 @@ struct gmp_real<0> : public detail::gmp_real_imp<0> }; template -inline void add(gmp_real& result, const gmp_real& o) +inline void add(gmp_float& result, const gmp_float& o) { mpf_add(result.data(), result.data(), o.data()); } template -inline void subtract(gmp_real& result, const gmp_real& o) +inline void subtract(gmp_float& result, const gmp_float& o) { mpf_sub(result.data(), result.data(), o.data()); } template -inline void multiply(gmp_real& result, const gmp_real& o) +inline void multiply(gmp_float& result, const gmp_float& o) { mpf_mul(result.data(), result.data(), o.data()); } template -inline void divide(gmp_real& result, const gmp_real& o) +inline void divide(gmp_float& result, const gmp_float& o) { mpf_div(result.data(), result.data(), o.data()); } template -inline void add(gmp_real& result, unsigned long i) +inline void add(gmp_float& result, unsigned long i) { mpf_add_ui(result.data(), result.data(), i); } template -inline void subtract(gmp_real& result, unsigned long i) +inline void subtract(gmp_float& result, unsigned long i) { mpf_sub_ui(result.data(), result.data(), i); } template -inline void multiply(gmp_real& result, unsigned long i) +inline void multiply(gmp_float& result, unsigned long i) { mpf_mul_ui(result.data(), result.data(), i); } template -inline void divide(gmp_real& result, unsigned long i) +inline void divide(gmp_float& result, unsigned long i) { mpf_div_ui(result.data(), result.data(), i); } template -inline void add(gmp_real& result, long i) +inline void add(gmp_float& result, long i) { if(i > 0) mpf_add_ui(result.data(), result.data(), i); @@ -373,7 +373,7 @@ inline void add(gmp_real& result, long i) mpf_sub_ui(result.data(), result.data(), std::abs(i)); } template -inline void subtract(gmp_real& result, long i) +inline void subtract(gmp_float& result, long i) { if(i > 0) mpf_sub_ui(result.data(), result.data(), i); @@ -381,14 +381,14 @@ inline void subtract(gmp_real& result, long i) mpf_add_ui(result.data(), result.data(), std::abs(i)); } template -inline void multiply(gmp_real& result, long i) +inline void multiply(gmp_float& result, long i) { mpf_mul_ui(result.data(), result.data(), std::abs(i)); if(i < 0) mpf_neg(result.data(), result.data()); } template -inline void divide(gmp_real& result, long i) +inline void divide(gmp_float& result, long i) { mpf_div_ui(result.data(), result.data(), std::abs(i)); if(i < 0) @@ -398,17 +398,17 @@ inline void divide(gmp_real& result, long i) // Specialised 3 arg versions of the basic operators: // template -inline void add(gmp_real& a, const gmp_real& x, const gmp_real& y) +inline void add(gmp_float& a, const gmp_float& x, const gmp_float& y) { mpf_add(a.data(), x.data(), y.data()); } template -inline void add(gmp_real& a, const gmp_real& x, unsigned long y) +inline void add(gmp_float& a, const gmp_float& x, unsigned long y) { mpf_add_ui(a.data(), x.data(), y); } template -inline void add(gmp_real& a, const gmp_real& x, long y) +inline void add(gmp_float& a, const gmp_float& x, long y) { if(y < 0) mpf_sub_ui(a.data(), x.data(), -y); @@ -416,12 +416,12 @@ inline void add(gmp_real& a, const gmp_real& x, long y) mpf_add_ui(a.data(), x.data(), y); } template -inline void add(gmp_real& a, unsigned long x, const gmp_real& y) +inline void add(gmp_float& a, unsigned long x, const gmp_float& y) { mpf_add_ui(a.data(), y.data(), x); } template -inline void add(gmp_real& a, long x, const gmp_real& y) +inline void add(gmp_float& a, long x, const gmp_float& y) { if(x < 0) { @@ -432,17 +432,17 @@ inline void add(gmp_real& a, long x, const gmp_real& y) mpf_add_ui(a.data(), y.data(), x); } template -inline void subtract(gmp_real& a, const gmp_real& x, const gmp_real& y) +inline void subtract(gmp_float& a, const gmp_float& x, const gmp_float& y) { mpf_sub(a.data(), x.data(), y.data()); } template -inline void subtract(gmp_real& a, const gmp_real& x, unsigned long y) +inline void subtract(gmp_float& a, const gmp_float& x, unsigned long y) { mpf_sub_ui(a.data(), x.data(), y); } template -inline void subtract(gmp_real& a, const gmp_real& x, long y) +inline void subtract(gmp_float& a, const gmp_float& x, long y) { if(y < 0) mpf_add_ui(a.data(), x.data(), -y); @@ -450,12 +450,12 @@ inline void subtract(gmp_real& a, const gmp_real& x, long y) mpf_sub_ui(a.data(), x.data(), y); } template -inline void subtract(gmp_real& a, unsigned long x, const gmp_real& y) +inline void subtract(gmp_float& a, unsigned long x, const gmp_float& y) { mpf_ui_sub(a.data(), x, y.data()); } template -inline void subtract(gmp_real& a, long x, const gmp_real& y) +inline void subtract(gmp_float& a, long x, const gmp_float& y) { if(x < 0) { @@ -467,17 +467,17 @@ inline void subtract(gmp_real& a, long x, const gmp_real& y) } template -inline void multiply(gmp_real& a, const gmp_real& x, const gmp_real& y) +inline void multiply(gmp_float& a, const gmp_float& x, const gmp_float& y) { mpf_mul(a.data(), x.data(), y.data()); } template -inline void multiply(gmp_real& a, const gmp_real& x, unsigned long y) +inline void multiply(gmp_float& a, const gmp_float& x, unsigned long y) { mpf_mul_ui(a.data(), x.data(), y); } template -inline void multiply(gmp_real& a, const gmp_real& x, long y) +inline void multiply(gmp_float& a, const gmp_float& x, long y) { if(y < 0) { @@ -488,12 +488,12 @@ inline void multiply(gmp_real& a, const gmp_real& x, long y) mpf_mul_ui(a.data(), x.data(), y); } template -inline void multiply(gmp_real& a, unsigned long x, const gmp_real& y) +inline void multiply(gmp_float& a, unsigned long x, const gmp_float& y) { mpf_mul_ui(a.data(), y.data(), x); } template -inline void multiply(gmp_real& a, long x, const gmp_real& y) +inline void multiply(gmp_float& a, long x, const gmp_float& y) { if(x < 0) { @@ -505,17 +505,17 @@ inline void multiply(gmp_real& a, long x, const gmp_real& y) } template -inline void divide(gmp_real& a, const gmp_real& x, const gmp_real& y) +inline void divide(gmp_float& a, const gmp_float& x, const gmp_float& y) { mpf_div(a.data(), x.data(), y.data()); } template -inline void divide(gmp_real& a, const gmp_real& x, unsigned long y) +inline void divide(gmp_float& a, const gmp_float& x, unsigned long y) { mpf_div_ui(a.data(), x.data(), y); } template -inline void divide(gmp_real& a, const gmp_real& x, long y) +inline void divide(gmp_float& a, const gmp_float& x, long y) { if(y < 0) { @@ -526,12 +526,12 @@ inline void divide(gmp_real& a, const gmp_real& x, long y) mpf_div_ui(a.data(), x.data(), y); } template -inline void divide(gmp_real& a, unsigned long x, const gmp_real& y) +inline void divide(gmp_float& a, unsigned long x, const gmp_float& y) { mpf_ui_div(a.data(), x, y.data()); } template -inline void divide(gmp_real& a, long x, const gmp_real& y) +inline void divide(gmp_float& a, long x, const gmp_float& y) { if(x < 0) { @@ -543,36 +543,36 @@ inline void divide(gmp_real& a, long x, const gmp_real& y) } template -inline bool is_zero(const gmp_real& val) +inline bool is_zero(const gmp_float& val) { return mpf_sgn(val.data()) == 0; } template -inline int get_sign(const gmp_real& val) +inline int get_sign(const gmp_float& val) { return mpf_sgn(val.data()); } template -inline void convert_to(unsigned long* result, const gmp_real& val) +inline void convert_to(unsigned long* result, const gmp_float& val) { *result = mpf_get_ui(val.data()); } template -inline void convert_to(long* result, const gmp_real& val) +inline void convert_to(long* result, const gmp_float& val) { *result = mpf_get_si(val.data()); } template -inline void convert_to(double* result, const gmp_real& val) +inline void convert_to(double* result, const gmp_float& val) { *result = mpf_get_d(val.data()); } #ifdef BOOST_HAS_LONG_LONG template -inline void convert_to(long long* result, const gmp_real& val) +inline void convert_to(long long* result, const gmp_float& val) { - gmp_real t(val); + gmp_float t(val); if(get_sign(t) < 0) t.negate(); @@ -602,9 +602,9 @@ inline void convert_to(long long* result, const gmp_real& val) *result = -*result; } template -inline void convert_to(unsigned long long* result, const gmp_real& val) +inline void convert_to(unsigned long long* result, const gmp_float& val) { - gmp_real t(val); + gmp_float t(val); long digits = std::numeric_limits::digits - std::numeric_limits::digits; @@ -635,39 +635,39 @@ inline void convert_to(unsigned long long* result, const gmp_real& val // Native non-member operations: // template -inline void eval_sqrt(gmp_real& result, const gmp_real& val) +inline void eval_sqrt(gmp_float& result, const gmp_float& val) { mpf_sqrt(result.data(), val.data()); } template -inline void eval_abs(gmp_real& result, const gmp_real& val) +inline void eval_abs(gmp_float& result, const gmp_float& val) { mpf_abs(result.data(), val.data()); } template -inline void eval_fabs(gmp_real& result, const gmp_real& val) +inline void eval_fabs(gmp_float& result, const gmp_float& val) { mpf_abs(result.data(), val.data()); } template -inline void eval_ceil(gmp_real& result, const gmp_real& val) +inline void eval_ceil(gmp_float& result, const gmp_float& val) { mpf_ceil(result.data(), val.data()); } template -inline void eval_floor(gmp_real& result, const gmp_real& val) +inline void eval_floor(gmp_float& result, const gmp_float& val) { mpf_floor(result.data(), val.data()); } template -inline void eval_trunc(gmp_real& result, const gmp_real& val) +inline void eval_trunc(gmp_float& result, const gmp_float& val) { mpf_trunc(result.data(), val.data()); } template -inline void eval_ldexp(gmp_real& result, const gmp_real& val, long e) +inline void eval_ldexp(gmp_float& result, const gmp_float& val, long e) { if(e > 0) mpf_mul_2exp(result.data(), val.data(), e); @@ -677,7 +677,7 @@ inline void eval_ldexp(gmp_real& result, const gmp_real& val result = val; } template -inline void eval_frexp(gmp_real& result, const gmp_real& val, int* e) +inline void eval_frexp(gmp_float& result, const gmp_float& val, int* e) { long v; mpf_get_d_2exp(&v, val.data()); @@ -685,7 +685,7 @@ inline void eval_frexp(gmp_real& result, const gmp_real& val eval_ldexp(result, val, -v); } template -inline void eval_frexp(gmp_real& result, const gmp_real& val, long* e) +inline void eval_frexp(gmp_float& result, const gmp_float& val, long* e) { mpf_get_d_2exp(e, val.data()); eval_ldexp(result, val, -*e); @@ -1208,8 +1208,8 @@ struct gmp_rational using std::frexp; using std::ldexp; using std::floor; - using big_num_default_ops::add; - using big_num_default_ops::subtract; + using default_ops::add; + using default_ops::subtract; if (a == 0) { mpq_set_si(m_data, 0, 1); @@ -1374,11 +1374,11 @@ struct number_category : public mpl::int_{}; template<> struct number_category : public mpl::int_{}; -typedef mp_number > mpf_real_50; -typedef mp_number > mpf_real_100; -typedef mp_number > mpf_real_500; -typedef mp_number > mpf_real_1000; -typedef mp_number > mpf_real; +typedef mp_number > mpf_float_50; +typedef mp_number > mpf_float_100; +typedef mp_number > mpf_float_500; +typedef mp_number > mpf_float_1000; +typedef mp_number > mpf_float; typedef mp_number mpz_int; typedef mp_number mpq_rational; @@ -1394,9 +1394,9 @@ namespace std{ // numeric_limits [partial] specializations for the types declared in this header: // template -class numeric_limits > > +class numeric_limits > > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; BOOST_STATIC_CONSTEXPR number_type (min)() noexcept @@ -1486,10 +1486,10 @@ private: { data_initializer() { - std::numeric_limits > >::epsilon(); - std::numeric_limits > >::round_error(); - (std::numeric_limits > >::min)(); - (std::numeric_limits > >::max)(); + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); } void do_nothing()const{} }; @@ -1497,12 +1497,12 @@ private: }; template -const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; +const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; template<> -class numeric_limits > > +class numeric_limits > > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(); } diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index e2b1a6cc..bb95fd8c 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -111,7 +111,7 @@ public: typename enable_if, mp_number& >::type operator+=(const V& v) { - using big_num_default_ops::add; + using default_ops::add; add(m_backend, canonical_value(v)); return *this; } @@ -142,7 +142,7 @@ public: typename enable_if, mp_number& >::type operator-=(const V& v) { - using big_num_default_ops::subtract; + using default_ops::subtract; subtract(m_backend, canonical_value(v)); return *this; } @@ -175,7 +175,7 @@ public: typename enable_if, mp_number& >::type operator*=(const V& v) { - using big_num_default_ops::multiply; + using default_ops::multiply; multiply(m_backend, canonical_value(v)); return *this; } @@ -207,7 +207,7 @@ public: operator%=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using big_num_default_ops::modulus; + using default_ops::modulus; modulus(m_backend, canonical_value(v)); return *this; } @@ -222,21 +222,21 @@ public: // mp_number& operator++() { - using big_num_default_ops::increment; + using default_ops::increment; increment(m_backend); return *this; } mp_number& operator--() { - using big_num_default_ops::decrement; + using default_ops::decrement; decrement(m_backend); return *this; } mp_number operator++(int) { - using big_num_default_ops::increment; + using default_ops::increment; self_type temp(*this); increment(m_backend); return temp; @@ -244,7 +244,7 @@ public: mp_number operator--(int) { - using big_num_default_ops::decrement; + using default_ops::decrement; self_type temp(*this); decrement(m_backend); return temp; @@ -294,7 +294,7 @@ public: typename enable_if, mp_number& >::type operator/=(const V& v) { - using big_num_default_ops::divide; + using default_ops::divide; divide(m_backend, canonical_value(v)); return *this; } @@ -326,7 +326,7 @@ public: typename enable_if, mp_number& >::type operator&=(const V& v) { - using big_num_default_ops::bitwise_and; + using default_ops::bitwise_and; bitwise_and(m_backend, canonical_value(v)); return *this; } @@ -358,7 +358,7 @@ public: typename enable_if, mp_number& >::type operator|=(const V& v) { - using big_num_default_ops::bitwise_or; + using default_ops::bitwise_or; bitwise_or(m_backend, canonical_value(v)); return *this; } @@ -388,7 +388,7 @@ public: typename enable_if, mp_number& >::type operator^=(const V& v) { - using big_num_default_ops::bitwise_xor; + using default_ops::bitwise_xor; bitwise_xor(m_backend, canonical_value(v)); return *this; } @@ -414,12 +414,12 @@ public: // bool is_zero()const { - using big_num_default_ops::is_zero; + using default_ops::is_zero; return is_zero(m_backend); } int sign()const { - using big_num_default_ops::get_sign; + using default_ops::get_sign; return get_sign(m_backend); } // @@ -432,7 +432,7 @@ public: template T convert_to()const { - using big_num_default_ops::convert_to; + using default_ops::convert_to; T result; convert_to(&result, m_backend); return result; @@ -466,7 +466,7 @@ public: template typename enable_if, int>::type compare(const V& o)const { - using big_num_default_ops::get_sign; + using default_ops::get_sign; if(o == 0) return get_sign(m_backend); return m_backend.compare(canonical_value(o)); @@ -506,14 +506,14 @@ private: template void do_assign(const Exp& e, const detail::add_immediates&) { - using big_num_default_ops::add; + using default_ops::add; add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } /* template void do_assign(const Exp& e, const detail::add_and_negate_immediates&) { - using big_num_default_ops::add; + using default_ops::add; add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); m_backend.negate(); } @@ -521,14 +521,14 @@ private: template void do_assign(const Exp& e, const detail::subtract_immediates&) { - using big_num_default_ops::subtract; + using default_ops::subtract; subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } /* template void do_assign(const Exp& e, const detail::subtract_and_negate_immediates&) { - using big_num_default_ops::subtract; + using default_ops::subtract; subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); m_backend.negate(); } @@ -536,14 +536,14 @@ private: template void do_assign(const Exp& e, const detail::multiply_immediates&) { - using big_num_default_ops::multiply; + using default_ops::multiply; multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template void do_assign(const Exp& e, const detail::divide_immediates&) { - using big_num_default_ops::divide; + using default_ops::divide; divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } @@ -729,7 +729,7 @@ private: void do_assign(const Exp& e, const detail::modulus_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using big_num_default_ops::modulus; + using default_ops::modulus; modulus(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } @@ -774,7 +774,7 @@ private: void do_assign(const Exp& e, const detail::bitwise_and_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - using big_num_default_ops::bitwise_and; + using default_ops::bitwise_and; bitwise_and(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } @@ -819,7 +819,7 @@ private: void do_assign(const Exp& e, const detail::bitwise_or_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - using big_num_default_ops::bitwise_or; + using default_ops::bitwise_or; bitwise_or(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } @@ -864,7 +864,7 @@ private: void do_assign(const Exp& e, const detail::bitwise_xor_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - using big_num_default_ops::bitwise_xor; + using default_ops::bitwise_xor; bitwise_xor(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template @@ -912,7 +912,7 @@ private: template void do_assign(const Exp& e, const detail::bitwise_complement&) { - using big_num_default_ops::complement; + using default_ops::complement; self_type temp(e.left()); complement(m_backend, temp.backend()); } @@ -920,28 +920,28 @@ private: template void do_assign(const Exp& e, const detail::complement_immediates&) { - using big_num_default_ops::complement; + using default_ops::complement; complement(m_backend, canonical_value(e.left().value())); } template void do_assign_right_shift(const Exp& e, const Val& val, const detail::terminal&) { - using big_num_default_ops::right_shift; + using default_ops::right_shift; right_shift(m_backend, canonical_value(e.value()), val); } template void do_assign_left_shift(const Exp& e, const Val& val, const detail::terminal&) { - using big_num_default_ops::left_shift; + using default_ops::left_shift; left_shift(m_backend, canonical_value(e.value()), val); } template void do_assign_right_shift(const Exp& e, const Val& val, const Tag&) { - using big_num_default_ops::right_shift; + using default_ops::right_shift; self_type temp(e); right_shift(m_backend, temp.backend(), val); } @@ -949,7 +949,7 @@ private: template void do_assign_left_shift(const Exp& e, const Val& val, const Tag&) { - using big_num_default_ops::left_shift; + using default_ops::left_shift; self_type temp(e); left_shift(m_backend, temp.backend(), val); } @@ -1014,7 +1014,7 @@ private: template void do_add(const Exp& e, const detail::terminal&) { - using big_num_default_ops::add; + using default_ops::add; add(m_backend, canonical_value(e.value())); } @@ -1053,22 +1053,22 @@ private: template void do_add(const Exp& e, const detail::add_immediates&) { - using big_num_default_ops::add; + using default_ops::add; add(m_backend, canonical_value(e.left().value())); add(m_backend, canonical_value(e.right().value())); } template void do_add(const Exp& e, const detail::subtract_immediates&) { - using big_num_default_ops::add; - using big_num_default_ops::subtract; + using default_ops::add; + using default_ops::subtract; add(m_backend, canonical_value(e.left().value())); subtract(m_backend, canonical_value(e.right().value())); } template void do_subtract(const Exp& e, const detail::terminal&) { - using big_num_default_ops::subtract; + using default_ops::subtract; subtract(m_backend, canonical_value(e.value())); } @@ -1099,15 +1099,15 @@ private: template void do_subtract(const Exp& e, const detail::add_immediates&) { - using big_num_default_ops::subtract; + using default_ops::subtract; subtract(m_backend, canonical_value(e.left().value())); subtract(m_backend, canonical_value(e.right().value())); } template void do_subtract(const Exp& e, const detail::subtract_immediates&) { - using big_num_default_ops::add; - using big_num_default_ops::subtract; + using default_ops::add; + using default_ops::subtract; subtract(m_backend, canonical_value(e.left().value())); add(m_backend, canonical_value(e.right().value())); } @@ -1121,7 +1121,7 @@ private: template void do_multiplies(const Exp& e, const detail::terminal&) { - using big_num_default_ops::multiply; + using default_ops::multiply; multiply(m_backend, canonical_value(e.value())); } @@ -1154,22 +1154,22 @@ private: template void do_multiplies(const Exp& e, const detail::multiply_immediates&) { - using big_num_default_ops::multiply; + using default_ops::multiply; multiply(m_backend, canonical_value(e.left().value())); multiply(m_backend, canonical_value(e.right().value())); } template void do_multiplies(const Exp& e, const detail::divide_immediates&) { - using big_num_default_ops::multiply; - using big_num_default_ops::divide; + using default_ops::multiply; + using default_ops::divide; multiply(m_backend, canonical_value(e.left().value())); divide(m_backend, canonical_value(e.right().value())); } template void do_multiplies(const Exp& e, const unknown&) { - using big_num_default_ops::multiply; + using default_ops::multiply; self_type temp(e); multiply(m_backend, temp.m_backend); } @@ -1177,7 +1177,7 @@ private: template void do_divide(const Exp& e, const detail::terminal&) { - using big_num_default_ops::divide; + using default_ops::divide; divide(m_backend, canonical_value(e.value())); } @@ -1210,15 +1210,15 @@ private: template void do_divides(const Exp& e, const detail::multiply_immediates&) { - using big_num_default_ops::divide; + using default_ops::divide; divide(m_backend, canonical_value(e.left().value())); divide(m_backend, canonical_value(e.right().value())); } template void do_divides(const Exp& e, const detail::divide_immediates&) { - using big_num_default_ops::multiply; - using big_num_default_ops::divide; + using default_ops::multiply; + using default_ops::divide; divide(m_backend, canonical_value(e.left().value())); mutiply(m_backend, canonical_value(e.right().value())); } @@ -1226,7 +1226,7 @@ private: template void do_divide(const Exp& e, const unknown&) { - using big_num_default_ops::multiply; + using default_ops::multiply; self_type temp(e); divide(m_backend, temp.m_backend); } @@ -1235,7 +1235,7 @@ private: void do_modulus(const Exp& e, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using big_num_default_ops::modulus; + using default_ops::modulus; modulus(m_backend, canonical_value(e.value())); } @@ -1243,7 +1243,7 @@ private: void do_modulus(const Exp& e, const Unknown&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using big_num_default_ops::modulus; + using default_ops::modulus; self_type temp(e); modulus(m_backend, canonical_value(temp)); } @@ -1251,7 +1251,7 @@ private: template void do_bitwise_and(const Exp& e, const detail::terminal&) { - using big_num_default_ops::bitwise_and; + using default_ops::bitwise_and; bitwise_and(m_backend, canonical_value(e.value())); } template @@ -1265,7 +1265,7 @@ private: template void do_bitwise_and(const Exp& e, const unknown&) { - using big_num_default_ops::bitwise_and; + using default_ops::bitwise_and; self_type temp(e); bitwise_and(m_backend, temp.m_backend); } @@ -1273,7 +1273,7 @@ private: template void do_bitwise_or(const Exp& e, const detail::terminal&) { - using big_num_default_ops::bitwise_or; + using default_ops::bitwise_or; bitwise_or(m_backend, canonical_value(e.value())); } template @@ -1287,7 +1287,7 @@ private: template void do_bitwise_or(const Exp& e, const unknown&) { - using big_num_default_ops::bitwise_or; + using default_ops::bitwise_or; self_type temp(e); bitwise_or(m_backend, temp.m_backend); } @@ -1295,7 +1295,7 @@ private: template void do_bitwise_xor(const Exp& e, const detail::terminal&) { - using big_num_default_ops::bitwise_xor; + using default_ops::bitwise_xor; bitwise_xor(m_backend, canonical_value(e.value())); } template @@ -1309,7 +1309,7 @@ private: template void do_bitwise_xor(const Exp& e, const unknown&) { - using big_num_default_ops::bitwise_xor; + using default_ops::bitwise_xor; self_type temp(e); bitwise_xor(m_backend, temp.m_backend); } @@ -1323,7 +1323,7 @@ private: template bool contains_self(const Exp& e, mpl::int_<0> const&)const { - return is_really_self(e.value()); + return is_floatly_self(e.value()); } template bool contains_self(const Exp& e, mpl::int_<1> const&)const @@ -1359,7 +1359,7 @@ private: template bool is_self(const Exp& e, mpl::int_<0> const&)const { - return is_really_self(e.value()); + return is_floatly_self(e.value()); } template bool is_self(const Exp& e, mpl::int_ const&)const @@ -1368,8 +1368,8 @@ private: } template - bool is_really_self(const Val&)const { return false; } - bool is_really_self(const self_type& v)const { return &v == this; } + bool is_floatly_self(const Val&)const { return false; } + bool is_floatly_self(const self_type& v)const { return &v == this; } static const Backend& canonical_value(const self_type& v){ return v.m_backend; } //static const Backend& canonical_value(const self_type* v){ return v->m_backend; } diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index d5941d3f..27d6a572 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -18,47 +18,47 @@ namespace boost{ namespace multiprecision{ template -struct mpfr_real_backend; +struct mpfr_float_backend; namespace detail{ long get_default_precision() { return 50; } template -struct mpfr_real_imp +struct mpfr_float_imp { typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list real_types; typedef long exponent_type; - mpfr_real_imp(){} + mpfr_float_imp(){} - mpfr_real_imp(const mpfr_real_imp& o) + mpfr_float_imp(const mpfr_float_imp& o) { mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpfr_set(m_data, o.m_data, GMP_RNDN); } #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_imp(mpfr_real_imp&& o) + mpfr_float_imp(mpfr_float_imp&& o) { m_data[0] = o.m_data[0]; o.m_data[0]._mpfr_d = 0; } #endif - mpfr_real_imp& operator = (const mpfr_real_imp& o) + mpfr_float_imp& operator = (const mpfr_float_imp& o) { mpfr_set(m_data, o.m_data, GMP_RNDN); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_imp& operator = (mpfr_real_imp&& o) + mpfr_float_imp& operator = (mpfr_float_imp&& o) { mpfr_swap(m_data, o.m_data); return *this; } #endif - mpfr_real_imp& operator = (boost::uintmax_t i) + mpfr_float_imp& operator = (boost::uintmax_t i) { boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; @@ -77,7 +77,7 @@ struct mpfr_real_imp mpfr_clear(t); return *this; } - mpfr_real_imp& operator = (boost::intmax_t i) + mpfr_float_imp& operator = (boost::intmax_t i) { bool neg = i < 0; *this = static_cast(std::abs(i)); @@ -85,22 +85,22 @@ struct mpfr_real_imp mpfr_neg(m_data, m_data, GMP_RNDN); return *this; } - mpfr_real_imp& operator = (unsigned long i) + mpfr_float_imp& operator = (unsigned long i) { mpfr_set_ui(m_data, i, GMP_RNDN); return *this; } - mpfr_real_imp& operator = (long i) + mpfr_float_imp& operator = (long i) { mpfr_set_si(m_data, i, GMP_RNDN); return *this; } - mpfr_real_imp& operator = (double d) + mpfr_float_imp& operator = (double d) { mpfr_set_d(m_data, d, GMP_RNDN); return *this; } - mpfr_real_imp& operator = (long double a) + mpfr_float_imp& operator = (long double a) { using std::frexp; using std::ldexp; @@ -146,12 +146,12 @@ struct mpfr_real_imp mpfr_div_2exp(m_data, m_data, -e, GMP_RNDN); return *this; } - mpfr_real_imp& operator = (const char* s) + mpfr_float_imp& operator = (const char* s) { mpfr_set_str(m_data, s, 10, GMP_RNDN); return *this; } - void swap(mpfr_real_imp& o) + void swap(mpfr_float_imp& o) { mpfr_swap(m_data, o.m_data); } @@ -192,7 +192,7 @@ struct mpfr_real_imp mpfr_free_str(ps); return result; } - ~mpfr_real_imp() + ~mpfr_float_imp() { if(m_data[0]._mpfr_d) mpfr_clear(m_data); @@ -201,7 +201,7 @@ struct mpfr_real_imp { mpfr_neg(m_data, m_data, GMP_RNDN); } - int compare(const mpfr_real_backend& o)const + int compare(const mpfr_float_backend& o)const { return mpfr_cmp(m_data, o.m_data); } @@ -216,7 +216,7 @@ struct mpfr_real_imp template int compare(V v)const { - mpfr_real_backend d; + mpfr_float_backend d; d = v; return compare(d); } @@ -234,73 +234,73 @@ protected: } // namespace detail template -struct mpfr_real_backend : public detail::mpfr_real_imp +struct mpfr_float_backend : public detail::mpfr_float_imp { - mpfr_real_backend() + mpfr_float_backend() { mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } - mpfr_real_backend(const mpfr_real_backend& o) : detail::mpfr_real_imp(o) {} + mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_backend(mpfr_real_backend&& o) : detail::mpfr_real_imp(o) {} + mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp(o) {} #endif - mpfr_real_backend& operator=(const mpfr_real_backend& o) + mpfr_float_backend& operator=(const mpfr_float_backend& o) { - *static_cast*>(this) = static_cast const&>(o); + *static_cast*>(this) = static_cast const&>(o); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_backend& operator=(mpfr_real_backend&& o) + mpfr_float_backend& operator=(mpfr_float_backend&& o) { - *static_cast*>(this) = static_cast&&>(o); + *static_cast*>(this) = static_cast&&>(o); return *this; } #endif template - mpfr_real_backend& operator=(const V& v) + mpfr_float_backend& operator=(const V& v) { - *static_cast*>(this) = v; + *static_cast*>(this) = v; return *this; } }; template <> -struct mpfr_real_backend<0> : public detail::mpfr_real_imp<0> +struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> { - mpfr_real_backend() + mpfr_float_backend() { mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); } - mpfr_real_backend(unsigned digits10) + mpfr_float_backend(unsigned digits10) { mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } - mpfr_real_backend(const mpfr_real_backend& o) : detail::mpfr_real_imp<0>(o) {} + mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp<0>(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_backend(mpfr_real_backend&& o) : detail::mpfr_real_imp<0>(o) {} + mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp<0>(o) {} #endif - mpfr_real_backend(const mpfr_real_backend& o, unsigned digits10) + mpfr_float_backend(const mpfr_float_backend& o, unsigned digits10) { mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); *this = o; } - mpfr_real_backend& operator=(const mpfr_real_backend& o) + mpfr_float_backend& operator=(const mpfr_float_backend& o) { - *static_cast*>(this) = static_cast const&>(o); + *static_cast*>(this) = static_cast const&>(o); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_real_backend& operator=(mpfr_real_backend&& o) + mpfr_float_backend& operator=(mpfr_float_backend&& o) { - *static_cast*>(this) = static_cast &&>(o); + *static_cast*>(this) = static_cast &&>(o); return *this; } #endif template - mpfr_real_backend& operator=(const V& v) + mpfr_float_backend& operator=(const V& v) { - *static_cast*>(this) = v; + *static_cast*>(this) = v; return *this; } static unsigned default_precision() @@ -322,47 +322,47 @@ struct mpfr_real_backend<0> : public detail::mpfr_real_imp<0> }; template -inline void add(mpfr_real_backend& result, const mpfr_real_backend& o) +inline void add(mpfr_float_backend& result, const mpfr_float_backend& o) { mpfr_add(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void subtract(mpfr_real_backend& result, const mpfr_real_backend& o) +inline void subtract(mpfr_float_backend& result, const mpfr_float_backend& o) { mpfr_sub(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void multiply(mpfr_real_backend& result, const mpfr_real_backend& o) +inline void multiply(mpfr_float_backend& result, const mpfr_float_backend& o) { mpfr_mul(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void divide(mpfr_real_backend& result, const mpfr_real_backend& o) +inline void divide(mpfr_float_backend& result, const mpfr_float_backend& o) { mpfr_div(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void add(mpfr_real_backend& result, unsigned long i) +inline void add(mpfr_float_backend& result, unsigned long i) { mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void subtract(mpfr_real_backend& result, unsigned long i) +inline void subtract(mpfr_float_backend& result, unsigned long i) { mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void multiply(mpfr_real_backend& result, unsigned long i) +inline void multiply(mpfr_float_backend& result, unsigned long i) { mpfr_mul_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void divide(mpfr_real_backend& result, unsigned long i) +inline void divide(mpfr_float_backend& result, unsigned long i) { mpfr_div_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void add(mpfr_real_backend& result, long i) +inline void add(mpfr_float_backend& result, long i) { if(i > 0) mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); @@ -370,7 +370,7 @@ inline void add(mpfr_real_backend& result, long i) mpfr_sub_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); } template -inline void subtract(mpfr_real_backend& result, long i) +inline void subtract(mpfr_float_backend& result, long i) { if(i > 0) mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); @@ -378,14 +378,14 @@ inline void subtract(mpfr_real_backend& result, long i) mpfr_add_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); } template -inline void multiply(mpfr_real_backend& result, long i) +inline void multiply(mpfr_float_backend& result, long i) { mpfr_mul_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); if(i < 0) mpfr_neg(result.data(), result.data(), GMP_RNDN); } template -inline void divide(mpfr_real_backend& result, long i) +inline void divide(mpfr_float_backend& result, long i) { mpfr_div_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); if(i < 0) @@ -395,17 +395,17 @@ inline void divide(mpfr_real_backend& result, long i) // Specialised 3 arg versions of the basic operators: // template -inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +inline void add(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) { mpfr_add(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +inline void add(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) { mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void add(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +inline void add(mpfr_float_backend& a, const mpfr_float_backend& x, long y) { if(y < 0) mpfr_sub_ui(a.data(), x.data(), -y, GMP_RNDN); @@ -413,12 +413,12 @@ inline void add(mpfr_real_backend& a, const mpfr_real_backend -inline void add(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +inline void add(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) { mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } template -inline void add(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +inline void add(mpfr_float_backend& a, long x, const mpfr_float_backend& y) { if(x < 0) { @@ -429,17 +429,17 @@ inline void add(mpfr_real_backend& a, long x, const mpfr_real_backend< mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } template -inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +inline void subtract(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) { mpfr_sub(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +inline void subtract(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) { mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void subtract(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +inline void subtract(mpfr_float_backend& a, const mpfr_float_backend& x, long y) { if(y < 0) mpfr_add_ui(a.data(), x.data(), -y, GMP_RNDN); @@ -447,12 +447,12 @@ inline void subtract(mpfr_real_backend& a, const mpfr_real_backend -inline void subtract(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +inline void subtract(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) { mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); } template -inline void subtract(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +inline void subtract(mpfr_float_backend& a, long x, const mpfr_float_backend& y) { if(x < 0) { @@ -464,17 +464,17 @@ inline void subtract(mpfr_real_backend& a, long x, const mpfr_real_bac } template -inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +inline void multiply(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) { mpfr_mul(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +inline void multiply(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) { mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void multiply(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +inline void multiply(mpfr_float_backend& a, const mpfr_float_backend& x, long y) { if(y < 0) { @@ -485,12 +485,12 @@ inline void multiply(mpfr_real_backend& a, const mpfr_real_backend -inline void multiply(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +inline void multiply(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) { mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); } template -inline void multiply(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +inline void multiply(mpfr_float_backend& a, long x, const mpfr_float_backend& y) { if(x < 0) { @@ -502,17 +502,17 @@ inline void multiply(mpfr_real_backend& a, long x, const mpfr_real_bac } template -inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, const mpfr_real_backend& y) +inline void divide(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) { mpfr_div(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, unsigned long y) +inline void divide(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) { mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void divide(mpfr_real_backend& a, const mpfr_real_backend& x, long y) +inline void divide(mpfr_float_backend& a, const mpfr_float_backend& x, long y) { if(y < 0) { @@ -523,12 +523,12 @@ inline void divide(mpfr_real_backend& a, const mpfr_real_backend -inline void divide(mpfr_real_backend& a, unsigned long x, const mpfr_real_backend& y) +inline void divide(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) { mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); } template -inline void divide(mpfr_real_backend& a, long x, const mpfr_real_backend& y) +inline void divide(mpfr_float_backend& a, long x, const mpfr_float_backend& y) { if(x < 0) { @@ -540,45 +540,45 @@ inline void divide(mpfr_real_backend& a, long x, const mpfr_real_backe } template -inline bool is_zero(const mpfr_real_backend& val) +inline bool is_zero(const mpfr_float_backend& val) { return 0 != mpfr_zero_p(val.data()); } template -inline int get_sign(const mpfr_real_backend& val) +inline int get_sign(const mpfr_float_backend& val) { return mpfr_sgn(val.data()); } template -inline void convert_to(unsigned long* result, const mpfr_real_backend& val) +inline void convert_to(unsigned long* result, const mpfr_float_backend& val) { *result = mpfr_get_ui(val.data(), GMP_RNDN); } template -inline void convert_to(long* result, const mpfr_real_backend& val) +inline void convert_to(long* result, const mpfr_float_backend& val) { *result = mpfr_get_si(val.data(), GMP_RNDN); } #ifdef _MPFR_H_HAVE_INTMAX_T template -inline void convert_to(boost::uintmax_t* result, const mpfr_real_backend& val) +inline void convert_to(boost::uintmax_t* result, const mpfr_float_backend& val) { *result = mpfr_get_uj(val.data(), GMP_RNDN); } template -inline void convert_to(boost::intmax_t* result, const mpfr_real_backend& val) +inline void convert_to(boost::intmax_t* result, const mpfr_float_backend& val) { *result = mpfr_get_sj(val.data(), GMP_RNDN); } #endif template -inline void convert_to(double* result, const mpfr_real_backend& val) +inline void convert_to(double* result, const mpfr_float_backend& val) { *result = mpfr_get_d(val.data(), GMP_RNDN); } template -inline void convert_to(long double* result, const mpfr_real_backend& val) +inline void convert_to(long double* result, const mpfr_float_backend& val) { *result = mpfr_get_ld(val.data(), GMP_RNDN); } @@ -587,39 +587,39 @@ inline void convert_to(long double* result, const mpfr_real_backend& v // Native non-member operations: // template -inline void eval_sqrt(mpfr_real_backend& result, const mpfr_real_backend& val) +inline void eval_sqrt(mpfr_float_backend& result, const mpfr_float_backend& val) { mpfr_sqrt(result.data(), val.data(), GMP_RNDN); } template -inline void eval_abs(mpfr_real_backend& result, const mpfr_real_backend& val) +inline void eval_abs(mpfr_float_backend& result, const mpfr_float_backend& val) { mpfr_abs(result.data(), val.data(), GMP_RNDN); } template -inline void eval_fabs(mpfr_real_backend& result, const mpfr_real_backend& val) +inline void eval_fabs(mpfr_float_backend& result, const mpfr_float_backend& val) { mpfr_abs(result.data(), val.data(), GMP_RNDN); } template -inline void eval_ceil(mpfr_real_backend& result, const mpfr_real_backend& val) +inline void eval_ceil(mpfr_float_backend& result, const mpfr_float_backend& val) { mpfr_ceil(result.data(), val.data()); } template -inline void eval_floor(mpfr_real_backend& result, const mpfr_real_backend& val) +inline void eval_floor(mpfr_float_backend& result, const mpfr_float_backend& val) { mpfr_floor(result.data(), val.data()); } template -inline void eval_trunc(mpfr_real_backend& result, const mpfr_real_backend& val) +inline void eval_trunc(mpfr_float_backend& result, const mpfr_float_backend& val) { mpfr_trunc(result.data(), val.data()); } template -inline void eval_ldexp(mpfr_real_backend& result, const mpfr_real_backend& val, long e) +inline void eval_ldexp(mpfr_float_backend& result, const mpfr_float_backend& val, long e) { if(e > 0) mpfr_mul_2exp(result.data(), val.data(), e, GMP_RNDN); @@ -629,7 +629,7 @@ inline void eval_ldexp(mpfr_real_backend& result, const mpfr_real_back result = val; } template -inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, int* e) +inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_backend& val, int* e) { long v; mpfr_get_d_2exp(&v, val.data(), GMP_RNDN); @@ -637,107 +637,107 @@ inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_back eval_ldexp(result, val, -v); } template -inline void eval_frexp(mpfr_real_backend& result, const mpfr_real_backend& val, long* e) +inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_backend& val, long* e) { mpfr_get_d_2exp(e, val.data(), GMP_RNDN); return eval_ldexp(result, val, -*e); } template -inline int eval_fpclassify(const mpfr_real_backend& val) +inline int eval_fpclassify(const mpfr_float_backend& val) { return mpfr_inf_p(val.data()) ? FP_INFINITE : mpfr_nan_p(val.data()) ? FP_NAN : mpfr_zero_p(val.data()) ? FP_ZERO : FP_NORMAL; } template -inline void eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const mpfr_real_backend& e) +inline void eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const mpfr_float_backend& e) { mpfr_pow(result.data(), b.data(), e.data(), GMP_RNDN); } template -inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const Integer& e) +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) { mpfr_pow_si(result.data(), b.data(), e, GMP_RNDN); } template -inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_real_backend& result, const mpfr_real_backend& b, const Integer& e) +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) { mpfr_pow_ui(result.data(), b.data(), e, GMP_RNDN); } template -inline void eval_exp(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_exp(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_exp(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_log(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_log(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_log(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_sin(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_sin(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_sin(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_cos(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_cos(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_cos(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_tan(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_tan(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_tan(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_asin(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_asin(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_asin(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_acos(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_acos(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_acos(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_atan(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_atan(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_atan(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_sinh(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_sinh(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_sinh(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_cosh(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_cosh(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_cosh(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_tanh(mpfr_real_backend& result, const mpfr_real_backend& arg) +inline void eval_tanh(mpfr_float_backend& result, const mpfr_float_backend& arg) { mpfr_tanh(result.data(), arg.data(), GMP_RNDN); } -typedef mp_number > mpfr_real_50; -typedef mp_number > mpfr_real_100; -typedef mp_number > mpfr_real_500; -typedef mp_number > mpfr_real_1000; -typedef mp_number > mpfr_real; +typedef mp_number > mpfr_float_50; +typedef mp_number > mpfr_float_100; +typedef mp_number > mpfr_float_500; +typedef mp_number > mpfr_float_1000; +typedef mp_number > mpfr_float; } // namespace boost @@ -746,7 +746,7 @@ namespace math{ namespace lanczos{ template -struct lanczos >, Policy> +struct lanczos >, Policy> { typedef typename mpl::if_c< Digits10 <= 36, @@ -778,9 +778,9 @@ namespace std{ // numeric_limits [partial] specializations for the types declared in this header: // template -class numeric_limits > > +class numeric_limits > > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; BOOST_STATIC_CONSTEXPR number_type (min)() noexcept @@ -897,12 +897,12 @@ private: { data_initializer() { - std::numeric_limits > >::epsilon(); - std::numeric_limits > >::round_error(); - (std::numeric_limits > >::min)(); - (std::numeric_limits > >::max)(); - std::numeric_limits > >::infinity(); - std::numeric_limits > >::quiet_NaN(); + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); + std::numeric_limits > >::infinity(); + std::numeric_limits > >::quiet_NaN(); } void do_nothing()const{} }; @@ -910,12 +910,12 @@ private: }; template -const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; +const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; template<> -class numeric_limits > > +class numeric_limits > > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(0); } diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 29edef2a..b1379fd4 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -63,7 +63,7 @@ run test_arithmetic.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_arithmetic_mpf50 ; @@ -126,7 +126,7 @@ run test_numeric_limits.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_numeric_limits_mpf50 ; @@ -187,11 +187,19 @@ run mp_number_concept_check.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : big_number_concept_check_mpfr_50 ; +run mp_number_concept_check.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : no ] + : big_number_concept_check_mpf50 ; + run test_exp.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_exp_mpf50 ; @@ -199,7 +207,7 @@ run test_log.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_log_mpf50 ; @@ -207,7 +215,7 @@ run test_pow.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_pow_mpf50 ; @@ -215,7 +223,7 @@ run test_sinh.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_sinh_mpf50 ; @@ -223,7 +231,7 @@ run test_cosh.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_cosh_mpf50 ; @@ -231,7 +239,7 @@ run test_tanh.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_tanh_mpf50 ; @@ -287,7 +295,7 @@ run test_sin.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_sin_mpf50 ; @@ -303,7 +311,7 @@ run test_cos.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_cos_mpf50 ; @@ -319,7 +327,7 @@ run test_asin.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_asin_mpf50 ; @@ -335,7 +343,7 @@ run test_acos.cpp gmp : # command line : # input files : # requirements - TEST_MPF50 + TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] : test_acos_mpf50 ; @@ -347,3 +355,18 @@ run test_acos.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : test_acos_mpfr_50 ; +run test_atan.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : no ] + : test_atan_mpf50 ; + +run test_atan.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_atan_mpfr_50 ; diff --git a/test/linpack-benchmark.cpp b/test/linpack-benchmark.cpp index 1f4d2ab8..8798ca6d 100644 --- a/test/linpack-benchmark.cpp +++ b/test/linpack-benchmark.cpp @@ -21,10 +21,10 @@ http://www.netlib.org/f2c/libf2c.zip #ifdef TEST_MPF_100 #include -typedef boost::multiprecision::mpf_real_100 real_type; +typedef boost::multiprecision::mpf_float_100 real_type; #elif defined(TEST_MPFR_100) #include -typedef boost::multiprecision::mpfr_real_100 real_type; +typedef boost::multiprecision::mpfr_float_100 real_type; #elif defined(TEST_GMPXX) #include typedef mpf_class real_type; @@ -99,9 +99,9 @@ int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type extern "C" int MAIN__() { #ifdef TEST_MPF_100 - std::cout << "Testing mp_number >" << std::endl; + std::cout << "Testing mp_number >" << std::endl; #elif defined(TEST_MPFR_100) - std::cout << "Testing mp_number >" << std::endl; + std::cout << "Testing mp_number >" << std::endl; #elif defined(TEST_GMPXX) std::cout << "Testing mpf_class at 100 decimal degits" << std::endl; mpf_set_default_prec(((100 + 1) * 1000L) / 301L); @@ -1229,7 +1229,7 @@ times for array with leading dimension of1001 266.45 0.798 267.24 2.5021 0.79933 4772.2 -mp_number >: +mp_number >: ~~~~~~~~~~~~~~~~~~~~~~~~~~~ norm. resid resid machep x(1) x(n) diff --git a/test/mp_number_concept_check.cpp b/test/mp_number_concept_check.cpp index cc814372..95ff4ffc 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -20,8 +20,8 @@ # pragma warning(disable:4503) // decorated name length exceeded, name was truncated #endif -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) +# define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND # define TEST_MPZ @@ -38,7 +38,7 @@ #endif -#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) +#if defined(TEST_MPF_50) || defined(TEST_MPF) || defined(TEST_MPZ) #include #endif #ifdef TEST_BACKEND @@ -57,19 +57,19 @@ void foo() { #ifdef TEST_BACKEND - instantiate(boost::multiprecision::mp_number_real_architype()); + instantiate(boost::multiprecision::mp_number_float_architype()); #endif #ifdef TEST_MPF_50 - instantiate(boost::multiprecision::mpf_real_50()); + instantiate(boost::multiprecision::mpf_float_50()); #endif #ifdef TEST_MPF - instantiate(boost::multiprecision::mpf_real()); + instantiate(boost::multiprecision::mpf_float()); #endif #ifdef TEST_MPFR_50 - instantiate(boost::multiprecision::mpfr_real_50()); + instantiate(boost::multiprecision::mpfr_float_50()); #endif #ifdef TEST_MPFR - instantiate(boost::multiprecision::mpfr_real()); + instantiate(boost::multiprecision::mpfr_float()); #endif #ifdef TEST_E_FLOAT instantiate(boost::multiprecision::e_float()); @@ -79,19 +79,19 @@ void foo() int main() { #ifdef TEST_BACKEND - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPF_50 - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPF - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPFR_50 - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPFR - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_E_FLOAT BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); diff --git a/test/test_acos.cpp b/test/test_acos.cpp index eea8e1fc..16fca50b 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -27,7 +27,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #if defined(TEST_MPFR_50) @@ -86,15 +86,15 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 2c837f26..86d18619 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -6,8 +6,8 @@ #include #include -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND # define TEST_MPZ @@ -25,7 +25,7 @@ #endif -#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) +#if defined(TEST_MPF_50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) #include #endif #ifdef TEST_BACKEND @@ -267,10 +267,10 @@ void test_integer_ops(const boost::mpl::int_ -void test_real_ops(const T&){} +void test_float_ops(const T&){} template -void test_real_ops(const boost::mpl::int_&) +void test_float_ops(const boost::mpl::int_&) { #if defined(TEST_MPF) || defined(TEST_MPF_50) || defined(TEST_BACKEND) || defined(TEST_MPFR) BOOST_TEST(abs(Real(2)) == 2); @@ -570,7 +570,7 @@ void test() // // Real number only functions: // - test_real_ops(typename boost::multiprecision::number_category::type()); + test_float_ops(typename boost::multiprecision::number_category::type()); // // Test basic arithmetic: // @@ -859,20 +859,20 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); +#ifdef TEST_MPF_50 + test(); #endif #ifdef TEST_MPF - boost::multiprecision::mpf_real::default_precision(1000); + boost::multiprecision::mpf_float::default_precision(1000); /* - boost::multiprecision::mpf_real r; + boost::multiprecision::mpf_float r; r.precision(50); BOOST_TEST(r.precision() >= 50); */ - BOOST_TEST(boost::multiprecision::mpf_real::default_precision() == 1000); - test(); + BOOST_TEST(boost::multiprecision::mpf_float::default_precision() == 1000); + test(); #endif #ifdef TEST_MPZ test(); @@ -884,10 +884,10 @@ int main() test(); #endif #ifdef TEST_MPFR - test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_asin.cpp b/test/test_asin.cpp index aff5d824..60bb3f0c 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -27,7 +27,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #if defined(TEST_MPFR_50) @@ -83,15 +83,15 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); diff --git a/test/test_atan.cpp b/test/test_atan.cpp index db4eb33b..63119ac9 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -27,7 +27,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #if defined(TEST_MPFR_50) @@ -44,7 +44,7 @@ template T atan2_def(T y, T x) { T t; - t.backend() = boost::multiprecision::big_num_default_ops::get_constant_pi(); + t.backend() = boost::multiprecision::default_ops::get_constant_pi(); T t2; if(x) t2 = atan(y / x); @@ -56,8 +56,10 @@ T atan2_def(T y, T x) template struct is_mpfr_type : public boost::mpl::false_ {}; +#ifdef TEST_MPFR_50 template -struct is_mpfr_type > > : public boost::mpl::true_{}; +struct is_mpfr_type > > : public boost::mpl::true_{}; +#endif template void test() @@ -188,7 +190,7 @@ void test() max_err = err; T pi; - pi.backend() = boost::multiprecision::big_num_default_ops::get_constant_pi(); + pi.backend() = boost::multiprecision::default_ops::get_constant_pi(); err = relative_error(T(atan2(T(1), T(0))), T(pi / 2)).template convert_to(); if(err > max_err) @@ -227,15 +229,15 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); diff --git a/test/test_cos.cpp b/test/test_cos.cpp index 1eb36acf..bb9aab89 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -27,7 +27,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #if defined(TEST_MPFR_50) @@ -272,15 +272,15 @@ T("-5.01621542149055350065079347615664213658089623368745676779267390227688581807 int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index 38841e62..c9be8958 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -27,7 +27,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #if defined(TEST_MPFR_50) @@ -118,15 +118,15 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); diff --git a/test/test_exp.cpp b/test/test_exp.cpp index 87578245..ff2bf4d9 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -27,7 +27,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #if defined(TEST_MPFR_50) @@ -163,15 +163,15 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); diff --git a/test/test_log.cpp b/test/test_log.cpp index 06a1fa90..166bfcae 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -27,7 +27,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #ifdef TEST_MPFR_50 @@ -176,15 +176,15 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index 28c354c9..e2075d3b 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -5,8 +5,8 @@ #include -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND # define TEST_MPZ @@ -24,7 +24,7 @@ #endif -#if defined(TEST_MPF50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) +#if defined(TEST_MPF_50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) #include #endif #ifdef TEST_BACKEND @@ -138,20 +138,20 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); +#ifdef TEST_MPF_50 + test(); #endif #ifdef TEST_MPF - boost::multiprecision::mpf_real::default_precision(1000); + boost::multiprecision::mpf_float::default_precision(1000); /* - boost::multiprecision::mpf_real r; + boost::multiprecision::mpf_float r; r.precision(50); BOOST_TEST(r.precision() >= 50); */ - BOOST_TEST(boost::multiprecision::mpf_real::default_precision() == 1000); - test(); + BOOST_TEST(boost::multiprecision::mpf_float::default_precision() == 1000); + test(); #endif #ifdef TEST_MPZ test(); @@ -163,10 +163,10 @@ int main() test(); #endif #ifdef TEST_MPFR - test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_pow.cpp b/test/test_pow.cpp index 45c81149..b681d703 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -28,7 +28,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #if defined(TEST_MPFR_50) @@ -566,15 +566,15 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); diff --git a/test/test_sin.cpp b/test/test_sin.cpp index fcee9188..3843b37d 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -27,7 +27,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #if defined(TEST_MPFR_50) @@ -278,15 +278,15 @@ T("8.650871796830672527081873591655777773059986288175183143531618768919892399328 int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index e049b449..0d33347c 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -27,7 +27,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #if defined(TEST_MPFR_50) @@ -118,15 +118,15 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index 547b69a9..59d67c9f 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -12,8 +12,8 @@ #include #include "test.hpp" -#if !defined(TEST_MPF50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) -# define TEST_MPF50 +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_E_FLOAT @@ -27,7 +27,7 @@ #endif -#if defined(TEST_MPF50) +#if defined(TEST_MPF_50) #include #endif #if defined(TEST_MPFR_50) @@ -118,15 +118,15 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif -#ifdef TEST_MPF50 - test(); - test(); +#ifdef TEST_MPF_50 + test(); + test(); #endif #ifdef TEST_MPFR_50 - test(); - test(); + test(); + test(); #endif #ifdef TEST_E_FLOAT test(); From fc1eb9303f00d9293cab6cfc125ae7a35515ebc6 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 23 Oct 2011 15:49:27 +0000 Subject: [PATCH 041/256] Get the tests passing with gcc on Linux. [SVN r75094] --- include/boost/multiprecision/detail/default_ops.hpp | 10 +--------- include/boost/multiprecision/detail/functions/pow.hpp | 2 -- include/boost/multiprecision/detail/functions/trig.hpp | 8 ++++++++ test/test.hpp | 3 +++ 4 files changed, 12 insertions(+), 11 deletions(-) diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 77240092..dea68ff4 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -398,14 +398,6 @@ inline void eval_round(T& result, const T& a) } } -template -void eval_atan2(T& result, const T& a, const Arithmetic& b) -{ - T x; - x = b; - eval_atan2(result, a, x); -} - // // These have to implemented by the backend, declared here so that our macro generated code compiles OK. // @@ -971,7 +963,7 @@ inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_numb template inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x, const Policy&) { - return boost::multiprecision::sinhc_pi(x); + return boost::math::sinhc_pi(x); } } // namespace math diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index a2e75f4c..7bd0554c 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -285,8 +285,6 @@ void eval_exp(T& result, const T& x) // implemented as a hypergeometric function, |r| is bounded by // ln2 / p2. For small arguments, no scaling is done. - typedef typename mpl::front::type float_type; - const bool b_scale = (xx.compare(float_type(1e-4)) > 0); // Compute the exponential series of the (possibly) scaled argument. diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index a65ffdb6..9a1b2ae7 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -731,3 +731,11 @@ void eval_atan2(T& result, const T& y, const T& x) } } +template +typename disable_if >::type eval_atan2(T& result, const T& a, const Arithmetic& b) +{ + T x; + x = b; + eval_atan2(result, a, x); +} + diff --git a/test/test.hpp b/test/test.hpp index 657c5737..88836794 100644 --- a/test/test.hpp +++ b/test/test.hpp @@ -2,6 +2,9 @@ #ifndef BOOST_MULTIPRECISION_TEST_HPP #define BOOST_MULTIPRECISION_TEST_HPP +#include +#include + template T relative_error(T a, T b) { From 9124ccb4c12991928a24b09cf30085d1271795d4 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 23 Oct 2011 16:03:29 +0000 Subject: [PATCH 042/256] Enable native atan2 for mpfr. [SVN r75095] --- include/boost/multiprecision/mpfr.hpp | 6 ++++++ test/test_atan.cpp | 2 +- 2 files changed, 7 insertions(+), 1 deletion(-) diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 27d6a572..bf478e42 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -715,6 +715,12 @@ inline void eval_atan(mpfr_float_backend& result, const mpfr_float_bac mpfr_atan(result.data(), arg.data(), GMP_RNDN); } +template +inline void eval_atan2(mpfr_float_backend& result, const mpfr_float_backend& arg1, const mpfr_float_backend& arg2) +{ + mpfr_atan2(result.data(), arg1.data(), arg2.data(), GMP_RNDN); +} + template inline void eval_sinh(mpfr_float_backend& result, const mpfr_float_backend& arg) { diff --git a/test/test_atan.cpp b/test/test_atan.cpp index 63119ac9..e572e7af 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -222,7 +222,7 @@ void test() } std::cout << "Max error was: " << max_err << std::endl; - BOOST_TEST(max_err < 40); + BOOST_TEST(max_err < 70); } From b0ac20f3914d8ccfe139b430a73d040b00c01a03 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 27 Oct 2011 12:43:41 +0000 Subject: [PATCH 043/256] Add port of e_float as a backend. [SVN r75129] --- config/Jamfile.v2 | 27 - include/boost/multiprecision/mp_float.hpp | 2461 +++++++++++++++++++++ test/Jamfile.v2 | 51 +- test/test_arithmetic.cpp | 25 +- 4 files changed, 2474 insertions(+), 90 deletions(-) create mode 100644 include/boost/multiprecision/mp_float.hpp diff --git a/config/Jamfile.v2 b/config/Jamfile.v2 index 2aeacdc8..a307db12 100644 --- a/config/Jamfile.v2 +++ b/config/Jamfile.v2 @@ -6,41 +6,14 @@ import modules ; import path ; -local ntl-path = [ modules.peek : NTL_PATH ] ; local gmp_path = [ modules.peek : GMP_PATH ] ; local mpfr_path = [ modules.peek : MPFR_PATH ] ; -local e_float_path = [ modules.peek : BOOST_E_FLOAT_PATH ] ; -if ! $(e_float_path) -{ - e_float_path = ../../../../e_float ; -} - -ECHO $(BOOST_E_FLOAT_PATH) - -obj has_long_double_support : has_long_double_support.cpp ; -obj has_mpfr_class : has_mpfr_class.cpp : - $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; -obj has_mpreal : has_mpreal.cpp : - $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/mpfrc++ ; -obj has_ntl_rr : has_ntl_rr.cpp : $(ntl-path)/include ; -obj has_gmpxx : has_gmpxx.cpp : - $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; -obj has_gcc_visibility : has_gcc_visibility.cpp : - gcc:-fvisibility=hidden gcc:-Werror ; -obj has_e_float : has_e_float.cpp : $(e_float_path) ; obj has_gmp : has_gmp.cpp : $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; obj has_mpfr : has_mpfr.cpp : $(mpfr_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx $(gmp_path) ; -explicit has_long_double_support ; -explicit has_mpfr_class ; -explicit has_mpreal ; -explicit has_ntl_rr ; -explicit has_gmpxx ; -explicit has_gcc_visibility ; -explicit has_e_float ; explicit has_gmp ; explicit has_mpfr ; diff --git a/include/boost/multiprecision/mp_float.hpp b/include/boost/multiprecision/mp_float.hpp new file mode 100644 index 00000000..a07ca1ac --- /dev/null +++ b/include/boost/multiprecision/mp_float.hpp @@ -0,0 +1,2461 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +// + +#ifndef BOOST_MP_EFX_BACKEND_HPP +#define BOOST_MP_EFX_BACKEND_HPP + +#include +#include +#include + +namespace boost{ +namespace multiprecision{ + +template +class mp_float +{ +public: + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + typedef boost::int64_t exponent_type; + + + static const boost::int32_t mp_radix = 10; + static const boost::int32_t mp_float_digits = Digits10; + + static const boost::int32_t mp_float_digits10_setting = Digits10; + static const boost::int32_t mp_float_digits10_limit = boost::integer_traits::const_max; + static const boost::int32_t mp_float_digits10 = ((mp_float_digits10_setting < static_cast(30)) ? static_cast(30) : ((mp_float_digits10_setting > mp_float_digits10_limit) ? mp_float_digits10_limit : mp_float_digits10_setting)); + static const boost::int32_t mp_float_digits10_extra = static_cast(((static_cast(mp_float_digits10) * 15LL) + 50LL) / 100LL); + static const boost::int32_t mp_float_max_digits10 = static_cast(mp_float_digits10 + ((mp_float_digits10_extra < static_cast(5)) ? static_cast(5) : ((mp_float_digits10_extra > static_cast(30)) ? static_cast(30) : mp_float_digits10_extra))); + static const boost::int64_t mp_float_max_exp = static_cast(+9223372036854775795LL); + static const boost::int64_t mp_float_min_exp = static_cast(-9223372036854775795LL); + static const boost::int64_t mp_float_max_exp10 = static_cast(+3063937869882635616LL); // Approx. [mp_float_max_exp / log10(2)], also an even multiple of 8 + static const boost::int64_t mp_float_min_exp10 = static_cast(-3063937869882635616LL); + static const boost::int32_t mp_elem_digits10 = static_cast(8); + +private: + static const boost::int32_t mp_float_digits10_num_base = static_cast((mp_float_max_digits10 / mp_elem_digits10) + (((mp_float_max_digits10 % mp_elem_digits10) != 0) ? 1 : 0)); + static const boost::int32_t mp_elem_number = static_cast(mp_float_digits10_num_base + 2); + static const boost::int32_t mp_elem_mask = static_cast(100000000); + + typedef enum enum_fpclass + { + mp_finite, + mp_inf, + mp_NaN + } + t_fpclass; + + typedef boost::array array_type; + + array_type data; + boost::int64_t exp; + bool neg; + t_fpclass fpclass; + boost::int32_t prec_elem; + + // + // Special values constructor: + // + mp_float(t_fpclass c) : + data(), + exp (static_cast(0)), + neg (false), + fpclass (c), + prec_elem(mp_elem_number) { } + + // + // Static data initializer: + // + struct initializer + { + initializer() + { + mp_float::nan(); + mp_float::inf(); + (mp_float::min)(); + (mp_float::max)(); + mp_float::zero(); + mp_float::one(); + mp_float::two(); + mp_float::double_min(); + mp_float::double_max(); + mp_float::long_double_max(); + mp_float::long_double_min(); + mp_float::long_long_max(); + mp_float::long_long_min(); + mp_float::ulong_long_max(); + mp_float::pow2(0); + } + void do_nothing(){} + }; + + static initializer init; + +public: + // Constructors + mp_float() : + data(), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) { } + + mp_float(const char* s) : + data(), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) + { + *this = s; + } + + template + mp_float(I i, typename enable_if >::type* = 0) : + data(), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) + { + from_unsigned_long_long(i); + } + + template + mp_float(I i, typename enable_if >::type* = 0) : + data(), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) + { + if(i < 0) + { + from_unsigned_long_long(-i); + negate(); + } + else + from_unsigned_long_long(i); + } + + mp_float(const mp_float& f) : + data (f.data), + exp (f.exp), + neg (f.neg), + fpclass (f.fpclass), + prec_elem(f.prec_elem) { } + + template + mp_float(const F val, typename enable_if >::type* = 0): + data(), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) + { + *this = val; + } + + mp_float(const double val, long long exponent); + + // Specific special values. + static const mp_float& nan() + { + static const mp_float val(mp_NaN); + init.do_nothing(); + return val; + } + static const mp_float& inf() + { + static const mp_float val(mp_inf); + init.do_nothing(); + return val; + } + static const mp_float& (max)() + { + init.do_nothing(); + static bool init = false; + static const std::string str_max = std::string("9." + std::string(static_cast(mp_float_max_digits10), static_cast('9'))) + + std::string("e+" + boost::lexical_cast(mp_float_max_exp)); + static mp_float val_max; + if(!init) + { + init = true; + val_max = str_max.c_str(); + } + return val_max; + } + + static const mp_float& (min)() + { + init.do_nothing(); + static bool init = false; + static mp_float val_min; + if(!init) + { + init = true; + val_min = std::string("1.0e" + boost::lexical_cast(mp_float_min_exp)).c_str(); + } + return val_min; + } + static const mp_float& zero() + { + init.do_nothing(); + static mp_float val(static_cast(0u)); + return val; + } + static const mp_float& one() + { + init.do_nothing(); + static mp_float val(static_cast(1u)); + return val; + } + static const mp_float& two() + { + init.do_nothing(); + static mp_float val(static_cast(2u)); + return val; + } + static const mp_float& double_min() + { + init.do_nothing(); + static mp_float val(static_cast((std::numeric_limits::min)())); + return val; + } + static const mp_float& double_max() + { + init.do_nothing(); + static mp_float val(static_cast((std::numeric_limits::max)())); + return val; + } + static const mp_float& long_double_min() + { + init.do_nothing(); + static mp_float val((std::numeric_limits::min)()); + return val; + } + static const mp_float& long_double_max() + { + init.do_nothing(); + static mp_float val((std::numeric_limits::max)()); + return val; + } + static const mp_float& long_long_max() + { + init.do_nothing(); + static mp_float val((std::numeric_limits::max)()); + return val; + } + static const mp_float& long_long_min() + { + init.do_nothing(); + static mp_float val((std::numeric_limits::min)()); + return val; + } + static const mp_float& ulong_long_max() + { + init.do_nothing(); + static mp_float val((std::numeric_limits::max)()); + return val; + } + + // Basic operations. + mp_float& operator= (const mp_float& v) + { + data = v.data; + exp = v.exp; + neg = v.neg; + fpclass = v.fpclass; + prec_elem = v.prec_elem; + return *this; + } + mp_float& operator= (long long v) + { + if(v < 0) + { + from_unsigned_long_long(-v); + negate(); + } + else + from_unsigned_long_long(v); + return *this; + } + mp_float& operator= (unsigned long long v) + { + from_unsigned_long_long(v); + return *this; + } + mp_float& operator= (long double v); + mp_float& operator= (const char* v) + { + rd_string(v); + return *this; + } + + mp_float& operator+=(const mp_float& v); + mp_float& operator-=(const mp_float& v); + mp_float& operator*=(const mp_float& v); + mp_float& operator/=(const mp_float& v); + + mp_float& add_unsigned_long_long(const unsigned long long n) + { + mp_float t; + t.from_unsigned_long_long(n); + return *this += t; + } + mp_float& sub_unsigned_long_long(const unsigned long long n) + { + mp_float t; + t.from_unsigned_long_long(n); + return *this -= t; + } + mp_float& mul_unsigned_long_long(const unsigned long long n); + mp_float& div_unsigned_long_long(const unsigned long long n); + + // Elementary primitives. + mp_float& calculate_inv (void); + mp_float& calculate_sqrt(void); + void negate() + { + if(!iszero()) + neg = !neg; + } + + // Comparison functions + bool isnan (void) const { return (fpclass == mp_NaN); } + bool isinf (void) const { return (fpclass == mp_inf); } + bool isfinite(void) const { return (fpclass == mp_finite); } + + bool iszero (void) const + { + return ((fpclass == mp_finite) && (data[0u] == 0u)); + } + bool isone (void) const; + bool isint (void) const; + bool isneg (void) const { return neg; } + + // Operators pre-increment and pre-decrement + mp_float& operator++(void) + { + return *this += one(); + } + mp_float& operator--(void) + { + return *this -= one(); + } + + std::string str(unsigned digits, bool scientific)const; + + int compare(const mp_float& v)const; + template + int compare(const V& v)const + { + mp_float t; + t = v; + return compare(t); + } + + void swap(mp_float& v) + { + data.swap(v.data); + std::swap(exp, v.exp); + std::swap(neg, v.neg); + std::swap(fpclass, v.fpclass); + std::swap(prec_elem, v.prec_elem); + } + + double extract_double (void) const; + long double extract_long_double (void) const; + signed long long extract_signed_long_long (void) const; + unsigned long long extract_unsigned_long_long(void) const; + void extract_parts (double& mantissa, boost::int64_t& exponent) const; + mp_float extract_integer_part (void) const; + void precision(const boost::int32_t prec_digits) + { + if(prec_digits >= mp_float_digits10) + { + prec_elem = mp_elem_number; + } + else + { + const boost::int32_t elems = static_cast( static_cast( (prec_digits + (mp_elem_digits10 / 2)) / mp_elem_digits10) + + static_cast(((prec_digits % mp_elem_digits10) != 0) ? 1 : 0)); + + prec_elem = (std::min)(mp_elem_number, (std::max)(elems, static_cast(2))); + } + } + static mp_float pow2(long long i); + +private: + static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast(0u)); } + static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast(mp_float::mp_elem_mask - 1)); } + static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast('0')); } + + void from_unsigned_long_long(const unsigned long long u); + + int cmp_data(const array_type& vd) const; + + static void mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p); + static boost::uint32_t mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); + static boost::uint32_t div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); + + bool rd_string(const char* const s); + long long order()const + { + const bool bo_order_is_zero = ((!isfinite()) || (data[0] == static_cast(0u))); + + return (bo_order_is_zero ? static_cast(0) + : static_cast(exp + static_cast(std::log10(static_cast(data[0])) + (std::numeric_limits::epsilon() * 0.9)))); + } +}; + +template +typename mp_float::initializer mp_float::init; + +template +const boost::int32_t mp_float::mp_radix; +template +const boost::int32_t mp_float::mp_float_digits; +template +const boost::int32_t mp_float::mp_float_digits10_setting; +template +const boost::int32_t mp_float::mp_float_digits10_limit; +template +const boost::int32_t mp_float::mp_float_digits10; +template +const boost::int32_t mp_float::mp_float_digits10_extra; +template +const boost::int32_t mp_float::mp_float_max_digits10; +template +const boost::int64_t mp_float::mp_float_max_exp; +template +const boost::int64_t mp_float::mp_float_min_exp; +template +const boost::int64_t mp_float::mp_float_max_exp10; +template +const boost::int64_t mp_float::mp_float_min_exp10; +template +const boost::int32_t mp_float::mp_elem_digits10; +template +const boost::int32_t mp_float::mp_float_digits10_num_base; +template +const boost::int32_t mp_float::mp_elem_number; +template +const boost::int32_t mp_float::mp_elem_mask; + + +template +mp_float& mp_float::operator+=(const mp_float& v) +{ + if(isnan()) + { + return *this; + } + + if(isinf()) + { + if(v.isinf() && (isneg() != v.isneg())) + { + *this = nan(); + } + return *this; + } + + if(iszero()) + { + return operator=(v); + } + + // Get the offset for the add/sub operation. + static const boost::int64_t max_delta_exp = static_cast((mp_elem_number - 1) * mp_elem_digits10); + + const boost::int64_t ofs_exp = static_cast(exp - v.exp); + + // Check if the operation is out of range, requiring special handling. + if(v.iszero() || (ofs_exp > max_delta_exp)) + { + // Result is *this unchanged since v is negligible compared to *this. + return *this; + } + else if(ofs_exp < -max_delta_exp) + { + // Result is *this = v since *this is negligible compared to v. + return operator=(v); + } + + // Do the add/sub operation. + + typename array_type::iterator p_u = data.begin(); + typename array_type::const_iterator p_v = v.data.begin(); + bool b_copy = false; + const boost::int32_t ofs = static_cast(static_cast(ofs_exp) / mp_elem_digits10); + array_type n_data; + + if(neg == v.neg) + { + // Add v to *this, where the data array of either *this or v + // might have to be treated with a positive, negative or zero offset. + // The result is stored in *this. The data are added one element + // at a time, each element with carry. + if(ofs >= static_cast(0)) + { + std::copy(v.data.begin(), v.data.end() - static_cast(ofs), n_data.begin() + static_cast(ofs)); + std::fill(n_data.begin(), n_data.begin() + static_cast(ofs), static_cast(0u)); + p_v = n_data.begin(); + } + else + { + std::copy(data.begin(), data.end() - static_cast(-ofs), n_data.begin() + static_cast(-ofs)); + std::fill(n_data.begin(), n_data.begin() + static_cast(-ofs), static_cast(0u)); + p_u = n_data.begin(); + b_copy = true; + } + + // Addition algorithm + boost::uint32_t carry = static_cast(0u); + + for(boost::int32_t j = static_cast(mp_elem_number - static_cast(1)); j >= static_cast(0); j--) + { + boost::uint32_t t = static_cast(static_cast(p_u[j] + p_v[j]) + carry); + carry = t / static_cast(mp_elem_mask); + p_u[j] = static_cast(t - static_cast(carry * static_cast(mp_elem_mask))); + } + + if(b_copy) + { + data = n_data; + exp = v.exp; + } + + // There needs to be a carry into the element -1 of the array data + if(carry != static_cast(0u)) + { + std::copy_backward(data.begin(), data.end() - static_cast(1u), data.end()); + data[0] = carry; + exp += static_cast(mp_elem_digits10); + } + } + else + { + // Subtract v from *this, where the data array of either *this or v + // might have to be treated with a positive, negative or zero offset. + if((ofs > static_cast(0)) + || ( (ofs == static_cast(0)) + && (cmp_data(v.data) > static_cast(0))) + ) + { + // In this case, |u| > |v| and ofs is positive. + // Copy the data of v, shifted down to a lower value + // into the data array m_n. Set the operand pointer p_v + // to point to the copied, shifted data m_n. + std::copy(v.data.begin(), v.data.end() - static_cast(ofs), n_data.begin() + static_cast(ofs)); + std::fill(n_data.begin(), n_data.begin() + static_cast(ofs), static_cast(0u)); + p_v = n_data.begin(); + } + else + { + if(ofs != static_cast(0)) + { + // In this case, |u| < |v| and ofs is negative. + // Shift the data of u down to a lower value. + std::copy_backward(data.begin(), data.end() - static_cast(-ofs), data.end()); + std::fill(data.begin(), data.begin() + static_cast(-ofs), static_cast(0u)); + } + + // Copy the data of v into the data array n_data. + // Set the u-pointer p_u to point to m_n and the + // operand pointer p_v to point to the shifted + // data m_data. + n_data = v.data; + p_u = n_data.begin(); + p_v = data.begin(); + b_copy = true; + } + + boost::int32_t j; + + // Subtraction algorithm + boost::int32_t borrow = static_cast(0); + + for(j = static_cast(mp_elem_number - static_cast(1)); j >= static_cast(0); j--) + { + boost::int32_t t = static_cast(static_cast( static_cast(p_u[j]) + - static_cast(p_v[j])) - borrow); + + // Underflow? Borrow? + if(t < static_cast(0)) + { + // Yes, underflow and borrow + t += static_cast(mp_elem_mask); + borrow = static_cast(1); + } + else + { + borrow = static_cast(0); + } + + p_u[j] = static_cast(static_cast(t) % static_cast(mp_elem_mask)); + } + + if(b_copy) + { + data = n_data; + exp = v.exp; + neg = v.neg; + } + + // Is it necessary to justify the data? + const typename array_type::const_iterator first_nonzero_elem = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); + + if(first_nonzero_elem != data.begin()) + { + if(first_nonzero_elem == data.end()) + { + // This result of the subtraction is exactly zero. + // Reset the sign and the exponent. + neg = false; + exp = static_cast(0); + } + else + { + // Justify the data + const std::size_t sj = static_cast(std::distance(data.begin(), first_nonzero_elem)); + + std::copy(data.begin() + static_cast(sj), data.end(), data.begin()); + std::fill(data.end() - sj, data.end(), static_cast(0u)); + + exp -= static_cast(sj * static_cast(mp_elem_digits10)); + } + } + } + + // Check for underflow. + if(iszero()) + { + return *this = zero(); + } + + bool overflow = exp >= mp_float_max_exp; + if(exp == mp_float_max_exp) + { + // Check to see if we really truely have an overflow or not... + if(isneg()) + { + mp_float t(*this); + t.negate(); + overflow = t.compare((max)()) > 0; + } + else + { + overflow = compare((max)()) > 0; + } + } + + // Check for overflow. + if(overflow) + { + const bool b_result_is_neg = neg; + + *this = inf(); + if(b_result_is_neg) + negate(); + } + + return *this; +} + +template +mp_float& mp_float::operator-=(const mp_float& v) +{ + // Use *this - v = -(-*this + v). + negate(); + *this += v; + negate(); + return *this; +} + +template +mp_float& mp_float::operator*=(const mp_float& v) +{ + // Evaluate the sign of the result. + const bool b_result_is_neg = (neg != v.neg); + + // Artificially set the sign of the result to be positive. + neg = false; + + // Handle special cases like zero, inf and NaN. + const bool b_u_is_inf = isinf(); + const bool b_v_is_inf = v.isinf(); + const bool b_u_is_zero = iszero(); + const bool b_v_is_zero = v.iszero(); + + if( (isnan() || v.isnan()) + || (b_u_is_inf && b_v_is_zero) + || (b_v_is_inf && b_u_is_zero) + ) + { + *this = nan(); + return *this; + } + + if(b_u_is_inf || b_v_is_inf) + { + *this = inf(); + if(b_result_is_neg) + negate(); + return *this; + } + + if(b_u_is_zero || b_v_is_zero) + { + return *this = zero(); + } + + // Check for overflow or underflow. + const bool u_exp_is_neg = (exp < static_cast(0)); + const bool v_exp_is_neg = (v.exp < static_cast(0)); + + if(u_exp_is_neg == v_exp_is_neg) + { + // Get the unsigned base-10 exponents of *this and v and... + const boost::int64_t u_exp = ((!u_exp_is_neg) ? exp : static_cast( -exp)); + const boost::int64_t v_exp = ((!v_exp_is_neg) ? v.exp : static_cast(-v.exp)); + + // Check the range of the upcoming multiplication. + const bool b_result_is_out_of_range = (v_exp >= static_cast(mp_float_max_exp10 - u_exp)); + + if(b_result_is_out_of_range) + { + if(u_exp_is_neg) + { + *this = zero(); + } + else + { + *this = inf(); + if(b_result_is_neg) + negate(); + } + return *this; + } + } + + // Set the exponent of the result. + exp += v.exp; + + boost::array(mp_elem_number + static_cast(1))> w = {{ 0u }}; + + mul_loop_uv(data.data(), v.data.data(), w.data(), (std::min)(prec_elem, v.prec_elem)); + + // Copy the multiplication data into the result. + // Shift the result and adjust the exponent if necessary. + if(w[static_cast(0u)] != static_cast(0u)) + { + exp += static_cast(mp_elem_digits10); + + std::copy(w.begin(), w.end() - 1u, data.begin()); + } + else + { + std::copy(w.begin() + 1u, w.end(), data.begin()); + } + + // Set the sign of the result. + neg = b_result_is_neg; + + return *this; +} + +template +mp_float& mp_float::operator/=(const mp_float& v) +{ + const bool u_and_v_are_finite_and_identical = ( isfinite() + && (fpclass == v.fpclass) + && (exp == v.exp) + && (cmp_data(v.data) == static_cast(0))); + + if(u_and_v_are_finite_and_identical) + { + *this = one(); + if(neg != v.neg) + negate(); + return *this; + } + else + { + mp_float t(v); + t.calculate_inv(); + return operator*=(t); + } +} + +template +mp_float& mp_float::mul_unsigned_long_long(const unsigned long long n) +{ + // Multiply *this with a constant unsigned long long. + + // Evaluate the sign of the result. + const bool b_neg = neg; + + // Artificially set the sign of the result to be positive. + neg = false; + + // Handle special cases like zero, inf and NaN. + const bool b_u_is_inf = isinf(); + const bool b_n_is_zero = (n == static_cast(0)); + + if(isnan() || (b_u_is_inf && b_n_is_zero)) + { + return (*this = nan()); + } + + if(b_u_is_inf) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + if(iszero() || b_n_is_zero) + { + // Multiplication by zero. + return *this = zero(); + } + + if(n >= static_cast(mp_elem_mask)) + { + neg = b_neg; + mp_float t; + t = n; + return operator*=(t); + } + + if(n == static_cast(1u)) + { + neg = b_neg; + return *this; + } + + // Set up the multiplication loop. + const boost::uint32_t nn = static_cast(n); + const boost::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem); + + // Handle the carry and adjust the exponent. + if(carry != static_cast(0u)) + { + exp += static_cast(mp_elem_digits10); + + // Shift the result of the multiplication one element to the right. + std::copy_backward(data.begin(), + data.begin() + static_cast(prec_elem - static_cast(1)), + data.begin() + static_cast(prec_elem)); + + data.front() = static_cast(carry); + } + + bool overflow = exp >= mp_float_max_exp; + if(exp == mp_float_max_exp) + { + // Check to see if we really truely have an overflow or not... + if(isneg()) + { + mp_float t(*this); + t.negate(); + overflow = t.compare((max)()) > 0; + } + else + { + overflow = compare((max)()) > 0; + } + } + + if(overflow) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + // Set the sign. + neg = b_neg; + + return *this; +} + +template +mp_float& mp_float::div_unsigned_long_long(const unsigned long long n) +{ + // Divide *this by a constant unsigned long long. + + // Evaluate the sign of the result. + const bool b_neg = neg; + + // Artificially set the sign of the result to be positive. + neg = false; + + // Handle special cases like zero, inf and NaN. + if(isnan()) + { + return *this; + } + + if(isinf()) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + if(n == static_cast(0u)) + { + // Divide by 0. + if(iszero()) + { + *this = nan(); + return *this; + } + else + { + *this = inf(); + if(isneg()) + negate(); + return *this; + } + } + + if(iszero()) + { + return *this; + } + + if(n >= static_cast(mp_elem_mask)) + { + neg = b_neg; + mp_float t; + t = n; + return operator/=(t); + } + + const boost::uint32_t nn = static_cast(n); + + if(nn > static_cast(1u)) + { + // Do the division loop. + const boost::uint32_t prev = div_loop_n(data.data(), nn, prec_elem); + + // Determine if one leading zero is in the result data. + if(data[0] == static_cast(0u)) + { + // Adjust the exponent + exp -= static_cast(mp_elem_digits10); + + // Shift result of the division one element to the left. + std::copy(data.begin() + static_cast(1u), + data.begin() + static_cast(prec_elem - static_cast(1)), + data.begin()); + + data[prec_elem - static_cast(1)] = static_cast(static_cast(prev * static_cast(mp_elem_mask)) / nn); + } + } + + // Check for underflow. + if(iszero()) + { + return *this = zero(); + } + + // Set the sign of the result. + neg = b_neg; + + return *this; +} + +template +mp_float& mp_float::calculate_inv() +{ + // Compute the inverse of *this. + const bool b_neg = neg; + + neg = false; + + // Handle special cases like zero, inf and NaN. + if(iszero()) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + if(isnan()) + { + return *this; + } + + if(isinf()) + { + return *this = zero(); + } + + if(isone()) + { + if(b_neg) + negate(); + return *this; + } + + // Save the original *this. + mp_float x(*this); + + // Generate the initial estimate using division. + // Extract the mantissa and exponent for a "manual" + // computation of the estimate. + double dd; + boost::int64_t ne; + x.extract_parts(dd, ne); + + // Do the inverse estimate using double precision estimates of mantissa and exponent. + operator=(mp_float(1.0 / dd, -ne)); + + // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration + // is used. During the iterative steps, the precision of the calculation is limited + // to the minimum required in order to minimize the run-time. + + static const boost::int32_t double_digits10_minus_one = static_cast(static_cast(Digits10) - static_cast(1)); + + for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= static_cast(2)) + { + // Adjust precision of the terms. + precision(static_cast(digits * static_cast(2))); + x.precision(static_cast(digits * static_cast(2))); + + // Next iteration. + mp_float t(*this); + t *= x; + t -= two(); + t.negate(); + *this *= t; + } + + neg = b_neg; + + prec_elem = mp_elem_number; + + return *this; +} + +template +mp_float& mp_float::calculate_sqrt(void) +{ + // Compute the square root of *this. + + if(isneg() || (!isfinite())) + { + *this = nan(); + return *this; + } + + if(iszero() || isone()) + { + return *this; + } + + // Save the original *this. + mp_float x(*this); + + // Generate the initial estimate using division. + // Extract the mantissa and exponent for a "manual" + // computation of the estimate. + double dd; + boost::int64_t ne; + extract_parts(dd, ne); + + // Force the exponent to be an even multiple of two. + if((ne % static_cast(2)) != static_cast(0)) + { + ++ne; + dd /= 10.0; + } + + // Setup the iteration. + // Estimate the square root using simple manipulations. + const double sqd = std::sqrt(dd); + + *this = mp_float(sqd, static_cast(ne / static_cast(2))); + + // Estimate 1.0 / (2.0 * x0) using simple manipulations. + mp_float vi(0.5 / sqd, static_cast(-ne / static_cast(2))); + + // Compute the square root of x. Coupled Newton iteration + // as described in "Pi Unleashed" is used. During the + // iterative steps, the precision of the calculation is + // limited to the minimum required in order to minimize + // the run-time. + // + // Book references: + // http://www.jjj.de/pibook/pibook.html + // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846 + + static const boost::int32_t double_digits10_minus_one = static_cast(static_cast(Digits10) - static_cast(1)); + + for(boost::int32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= static_cast(2)) + { + // Adjust precision of the terms. + precision(static_cast(digits * static_cast(2))); + vi.precision(static_cast(digits * static_cast(2))); + + // Next iteration of vi + mp_float t(*this); + t *= vi; + t.negate(); + t.mul_unsigned_long_long(2); + t += one(); + t *= vi; + vi += t; + + // Next iteration of *this + t = *this; + t *= *this; + t.negate(); + t += x; + t *= vi; + *this += t; + } + + prec_elem = mp_elem_number; + + return *this; +} + +template +int mp_float::cmp_data(const array_type& vd) const +{ + // Compare the data of *this with those of v. + // Return +1 for *this > v + // 0 for *this = v + // -1 for *this < v + + const std::pair mismatch_pair = std::mismatch(data.begin(), data.end(), vd.begin()); + + const bool is_equal = ((mismatch_pair.first == data.end()) && (mismatch_pair.second == vd.end())); + + if(is_equal) + { + return 0; + } + else + { + return ((*mismatch_pair.first > *mismatch_pair.second) ? 1 : -1); + } +} + +template +int mp_float::compare(const mp_float& v) const +{ + // Compare v with *this. + // Return +1 for *this > v + // 0 for *this = v + // -1 for *this < v + + // Handle all non-finite cases. + if((!isfinite()) || (!v.isfinite())) + { + // NaN can never equal NaN. Return an implementation-dependent + // signed result. Also note that comparison of NaN with NaN + // using operators greater-than or less-than is undefined. + if(isnan() || v.isnan()) { return (isnan() ? 1 : -1); } + + if(isinf() && v.isinf()) + { + // Both *this and v are infinite. They are equal if they have the same sign. + // Otherwise, *this is less than v if and only if *this is negative. + return ((neg == v.neg) ? 0 : (neg ? -1 : 1)); + } + + if(isinf()) + { + // *this is infinite, but v is finite. + // So negative infinite *this is less than any finite v. + // Whereas positive infinite *this is greater than any finite v. + return (isneg() ? -1 : 1); + } + else + { + // *this is finite, and v is infinite. + // So any finite *this is greater than negative infinite v. + // Whereas any finite *this is less than positive infinite v. + return (v.neg ? 1 : -1); + } + } + + // And now handle all *finite* cases. + if(iszero()) + { + // The value of *this is zero and v is either zero or non-zero. + return (v.iszero() ? 0 + : (v.neg ? 1 : -1)); + } + else if(v.iszero()) + { + // The value of v is zero and *this is non-zero. + return (neg ? -1 : 1); + } + else + { + // Both *this and v are non-zero. + + if(neg != v.neg) + { + // The signs are different. + return (neg ? -1 : 1); + } + else if(exp != v.exp) + { + // The signs are the same and the exponents are different. + const int val_cmp_exp = ((exp < v.exp) ? 1 : -1); + + return (neg ? val_cmp_exp : -val_cmp_exp); + } + else + { + // The signs are the same and the exponents are the same. + // Compare the data. + const int val_cmp_data = cmp_data(v.data); + + return ((!neg) ? val_cmp_data : -val_cmp_data); + } + } +} + +template +bool mp_float::isone() const +{ + // Check if the value of *this is identically 1 or very close to 1. + + const bool not_negative_and_is_finite = ((!neg) && isfinite()); + + if(not_negative_and_is_finite) + { + if((data[0u] == static_cast(1u)) && (exp == static_cast(0))) + { + const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); + return (it_non_zero == data.end()); + } + else if((data[0u] == static_cast(mp_elem_mask - 1)) && (exp == static_cast(-mp_elem_digits10))) + { + const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate); + return (it_non_nine == data.end()); + } + } + + return false; +} + +template +bool mp_float::isint() const +{ + if(fpclass != mp_finite) { return false; } + + if(iszero()) { return true; } + + if(exp < static_cast(0)) { return false; } // |*this| < 1. + + const typename array_type::size_type offset_decimal_part = static_cast(exp / mp_elem_digits10) + 1u; + + if(offset_decimal_part >= static_cast(mp_elem_number)) + { + // The number is too large to resolve the integer part. + // It considered to be a pure integer. + return true; + } + + typename array_type::const_iterator it_non_zero = std::find_if(data.begin() + offset_decimal_part, data.end(), data_elem_is_non_zero_predicate); + + return (it_non_zero == data.end()); +} + +template +void mp_float::extract_parts(double& mantissa, boost::int64_t& exponent) const +{ + // Extract the approximate parts mantissa and base-10 exponent from the input mp_float value x. + + // Extracts the mantissa and exponent. + exponent = exp; + + boost::uint32_t p10 = static_cast(1u); + boost::uint32_t test = data[0u]; + + for(;;) + { + test /= static_cast(10u); + + if(test == static_cast(0u)) + { + break; + } + + p10 *= static_cast(10u); + ++exponent; + } + + mantissa = static_cast(data[0]) + + (static_cast(data[1]) / static_cast(mp_elem_mask)) + + ((static_cast(data[2]) / static_cast(mp_elem_mask)) / static_cast(mp_elem_mask)); + + mantissa /= static_cast(p10); + + if(neg) { mantissa = -mantissa; } +} + +template +double mp_float::extract_double(void) const +{ + // Returns the double conversion of a mp_float. + + // Check for non-normal mp_float. + if(!isfinite()) + { + if(isnan()) + { + return std::numeric_limits::quiet_NaN(); + } + else + { + return ((!neg) ? std::numeric_limits::infinity() + : -std::numeric_limits::infinity()); + } + } + + mp_float xx(*this); + if(xx.isneg()) + xx.negate(); + + // Check for zero mp_float. + if(iszero() || (xx.compare(double_min()) < 0)) + { + return 0.0; + } + + // Check if mp_float exceeds the maximum of double. + if(xx.compare(double_max()) > 0) + { + return ((!neg) ? std::numeric_limits::infinity() + : -std::numeric_limits::infinity()); + } + + std::stringstream ss; + + ss << str(std::numeric_limits::digits10 + (2 + 1), true); + + double d; + ss >> d; + + return d; +} + +template +long double mp_float::extract_long_double(void) const +{ + // Returns the long double conversion of a mp_float. + + // Check for non-normal mp_float. + if(!isfinite()) + { + if(isnan()) + { + return std::numeric_limits::quiet_NaN(); + } + else + { + return ((!neg) ? std::numeric_limits::infinity() + : -std::numeric_limits::infinity()); + } + } + + mp_float xx(*this); + if(xx.isneg()) + xx.negate(); + + // Check for zero mp_float. + if(iszero() || (xx.compare(long_double_min()) < 0)) + { + return static_cast(0.0); + } + + // Check if mp_float exceeds the maximum of double. + if(xx.compare(long_double_max()) > 0) + { + return ((!neg) ? std::numeric_limits::infinity() + : -std::numeric_limits::infinity()); + } + + std::stringstream ss; + + ss << str(std::numeric_limits::digits10 + (2 + 1), true); + + long double ld; + ss >> ld; + + return ld; +} + +template +signed long long mp_float::extract_signed_long_long(void) const +{ + // Extracts a signed long long from *this. + // If (x > maximum of signed long long) or (x < minimum of signed long long), + // then the maximum or minimum of signed long long is returned accordingly. + + if(exp < static_cast(0)) + { + return static_cast(0); + } + + const bool b_neg = isneg(); + + unsigned long long val; + + if((!b_neg) && (compare(long_long_max()) > 0)) + { + return (std::numeric_limits::max)(); + } + else if(b_neg && (compare(long_long_min()) < 0)) + { + return (std::numeric_limits::min)(); + } + else + { + // Extract the data into an unsigned long long value. + mp_float xn(extract_integer_part()); + if(xn.isneg()) + xn.negate(); + + val = static_cast(xn.data[0]); + + const boost::int32_t imax = (std::min)(static_cast(static_cast(xn.exp) / mp_elem_digits10), static_cast(mp_elem_number - static_cast(1))); + + for(boost::int32_t i = static_cast(1); i <= imax; i++) + { + val *= static_cast(mp_elem_mask); + val += static_cast(xn.data[i]); + } + } + + return ((!b_neg) ? static_cast(val) : static_cast(-static_cast(val))); +} + +template +unsigned long long mp_float::extract_unsigned_long_long(void) const +{ + // Extracts an unsigned long long from *this. + // If x exceeds the maximum of unsigned long long, + // then the maximum of unsigned long long is returned. + // If x is negative, then the unsigned long long cast of + // the signed long long extracted value is returned. + + if(isneg()) + { + return static_cast(extract_signed_long_long()); + } + + if(exp < static_cast(0)) + { + return static_cast(0u); + } + + const mp_float xn(extract_integer_part()); + + unsigned long long val; + + if(xn.compare(ulong_long_max()) > 0) + { + return (std::numeric_limits::max)(); + } + else + { + // Extract the data into an unsigned long long value. + val = static_cast(xn.data[0]); + + const boost::int32_t imax = (std::min)(static_cast(static_cast(xn.exp) / mp_elem_digits10), static_cast(mp_elem_number - static_cast(1))); + + for(boost::int32_t i = static_cast(1); i <= imax; i++) + { + val *= static_cast(mp_elem_mask); + val += static_cast(xn.data[i]); + } + } + + return val; +} + +template +mp_float mp_float::extract_integer_part(void) const +{ + // Compute the signed integer part of x. + + if(!isfinite()) + { + return *this; + } + + if(exp < static_cast(0)) + { + // The absolute value of the number is smaller than 1. + // Thus the integer part is zero. + return zero(); + } + else if(exp >= Digits10 - 1) + { + // The number is too large to resolve the integer part. + // Thus it is already a pure integer part. + return *this; + } + + // Make a local copy. + mp_float x = *this; + + // Clear out the decimal portion + const size_t first_clear = (static_cast(x.exp) / static_cast(mp_elem_digits10)) + 1u; + const size_t last_clear = static_cast(mp_elem_number); + + std::fill(x.data.begin() + first_clear, x.data.begin() + last_clear, static_cast(0u)); + + return x; +} + +template +std::string mp_float::str(std::size_t number_of_digits, bool scientific) const +{ + std::string str; + boost::int64_t my_exp = order(); + if(number_of_digits == 0) + number_of_digits = (std::numeric_limits::max)(); + // Determine the number of elements needed to provide the requested digits from mp_float. + const std::size_t number_of_elements = (std::min)(static_cast((number_of_digits / static_cast(mp_elem_digits10)) + 2u), + static_cast(mp_elem_number)); + + // Extract the remaining digits from mp_float after the decimal point. + str = boost::lexical_cast(data[0]); + + // Extract all of the digits from mp_float, beginning with the first data element. + for(std::size_t i = static_cast(1u); i < number_of_elements; i++) + { + std::stringstream ss; + + ss << std::setw(static_cast(mp_elem_digits10)) + << std::setfill(static_cast('0')) + << data[i]; + + str += ss.str(); + } + + // Cut the output to the size of the precision. + if(str.length() > number_of_digits) + { + // Get the digit after the last needed digit for rounding + const boost::uint32_t round = static_cast(static_cast(str.at(number_of_digits)) - static_cast('0')); + + // Truncate the string + str = str.substr(static_cast(0u), number_of_digits); + + if(round >= static_cast(5u)) + { + std::size_t ix = static_cast(str.length() - 1u); + + // Every trailing 9 must be rounded up + while(ix && (static_cast(str.at(ix)) - static_cast('0') == static_cast(9))) + { + str.at(ix) = static_cast('0'); + --ix; + } + + if(!ix) + { + // There were nothing but trailing nines. + if(static_cast(static_cast(str.at(ix)) - static_cast(0x30)) == static_cast(9)) + { + // Increment up to the next order and adjust exponent. + str.at(ix) = static_cast('1'); + ++my_exp; + } + else + { + // Round up this digit. + ++str.at(ix); + } + } + else + { + // Round up the last digit. + ++str[ix]; + } + } + } + // + // Suppress trailing zeros: + // + std::string::iterator pos = str.end(); + while(pos != str.begin() && *--pos == '0'){} + if(pos != str.end()) + ++pos; + str.erase(pos, str.end()); + if(str.empty()) + str = '0'; + if(!scientific && (str.size() < 20) && (my_exp >= 0) && (my_exp < 20)) + { + if(1 + my_exp > str.size()) + { + // Just pad out the end with zeros: + str.append(static_cast(1 + my_exp - str.size()), '0'); + } + else if(my_exp + 1 != str.size()) + { + // Insert the decimal point: + str.insert(static_cast(my_exp + 1), 1, '.'); + } + } + else + { + // Scientific format: + str.insert(1, 1, '.'); + if(str.size() == 2) + str.append(1, '0'); + str.append(1, 'e'); + str.append(boost::lexical_cast(my_exp)); + } + if(isneg()) + str.insert(0, 1, '-'); + return str; +} + +template +bool mp_float::rd_string(const char* const s) +{ + std::string str(s); + + // Get a possible exponent and remove it. + exp = static_cast(0); + + std::size_t pos; + + if( ((pos = str.find('e')) != std::string::npos) + || ((pos = str.find('E')) != std::string::npos) + ) + { + // Remove the exponent part from the string. + exp = boost::lexical_cast(static_cast(str.c_str() + (pos + 1u))); + str = str.substr(static_cast(0u), pos); + } + + // Get a possible +/- sign and remove it. + neg = false; + + if((pos = str.find(static_cast('-'))) != std::string::npos) + { + neg = true; + str.erase(pos, static_cast(1u)); + } + + if((pos = str.find(static_cast('+'))) != std::string::npos) + { + str.erase(pos, static_cast(1u)); + } + + // Remove leading zeros for all input types. + const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate); + + if(fwd_it_leading_zero != str.begin()) + { + if(fwd_it_leading_zero == str.end()) + { + // The string contains nothing but leading zeros. + // This string represents zero. + operator=(zero()); + return true; + } + else + { + str.erase(str.begin(), fwd_it_leading_zero); + } + } + + // Put the input string into the standard mp_float input form + // aaa.bbbbE+/-n, where aa has 1...mp_elem_digits10, bbbb has an + // even multiple of mp_elem_digits10 which are possibly zero padded + // on the right-end, and n is a signed 32-bit integer which is an + // even multiple of mp_elem_digits10. + + // Find a possible decimal point. + pos = str.find(static_cast('.')); + + if(pos != std::string::npos) + { + // Remove all trailing insignificant zeros. + const std::string::const_reverse_iterator rit_non_zero = std::find_if(str.rbegin(), str.rend(), char_is_nonzero_predicate); + + if(rit_non_zero != str.rbegin()) + { + const std::string::size_type ofs = str.length() - std::distance(str.rbegin(), rit_non_zero); + str.erase(str.begin() + ofs, str.end()); + } + + // Check if the input is identically zero. + if(str == std::string(".")) + { + operator=(zero()); + return true; + } + + // Remove leading significant zeros just after the decimal point + // and adjust the exponent accordingly. + // Note that the while-loop operates only on strings of the form ".000abcd..." + // and peels away the zeros just after the decimal point. + if(str.at(static_cast(0u)) == static_cast('.')) + { + const std::string::iterator it_non_zero = std::find_if(str.begin() + 1u, str.end(), char_is_nonzero_predicate); + + std::size_t delta_exp = static_cast(0u); + + if(str.at(static_cast(1u)) == static_cast('0')) + { + delta_exp = std::distance(str.begin() + 1u, it_non_zero); + } + + // Bring one single digit into the mantissa and adjust exponent accordingly. + str.erase(str.begin(), it_non_zero); + str.insert(static_cast(1u), "."); + exp -= static_cast(delta_exp + 1u); + } + } + else + { + // Input string has no decimal point: Append decimal point. + str.append("."); + } + + // Shift the decimal point such that the exponent is an even multiple of mp_elem_digits10. + std::size_t n_shift = static_cast(0u); + const std::size_t n_exp_rem = static_cast(exp % static_cast(mp_elem_digits10)); + + if((exp % static_cast(mp_elem_digits10)) != static_cast(0)) + { + n_shift = ((exp < static_cast(0)) + ? static_cast(n_exp_rem + static_cast(mp_elem_digits10)) + : static_cast(n_exp_rem)); + } + + // Make sure that there are enough digits for the decimal point shift. + pos = str.find(static_cast('.')); + + std::size_t pos_plus_one = static_cast(pos + 1u); + + if((str.length() - pos_plus_one) < n_shift) + { + const std::size_t sz = static_cast(n_shift - (str.length() - pos_plus_one)); + + str.append(std::string(sz, static_cast('0'))); + } + + // Do the decimal point shift. + if(n_shift != static_cast(0u)) + { + str.insert(static_cast(pos_plus_one + n_shift), "."); + + str.erase(pos, static_cast(1u)); + + exp -= static_cast(n_shift); + } + + // Cut the size of the mantissa to <= mp_elem_digits10. + pos = str.find(static_cast('.')); + pos_plus_one = static_cast(pos + 1u); + + if(pos > static_cast(mp_elem_digits10)) + { + const boost::int32_t n_pos = static_cast(pos); + const boost::int32_t n_rem_is_zero = ((static_cast(n_pos % mp_elem_digits10) == static_cast(0)) ? static_cast(1) : static_cast(0)); + const boost::int32_t n = static_cast(static_cast(n_pos / mp_elem_digits10) - n_rem_is_zero); + + str.insert(static_cast(static_cast(n_pos - static_cast(n * mp_elem_digits10))), "."); + + str.erase(pos_plus_one, static_cast(1u)); + + exp += static_cast(static_cast(n) * static_cast(mp_elem_digits10)); + } + + // Pad the decimal part such that its value is an even + // multiple of mp_elem_digits10. + pos = str.find(static_cast('.')); + pos_plus_one = static_cast(pos + 1u); + + const boost::int32_t n_dec = static_cast(static_cast(str.length() - 1u) - static_cast(pos)); + const boost::int32_t n_rem = static_cast(n_dec % mp_elem_digits10); + boost::int32_t n_cnt = ((n_rem != static_cast(0)) ? static_cast(mp_elem_digits10 - n_rem) + : static_cast(0)); + + if(n_cnt != static_cast(0)) + { + str.append(static_cast(n_cnt), static_cast('0')); + } + + // Truncate decimal part if it is too long. + const std::size_t max_dec = static_cast((mp_elem_number - 1) * mp_elem_digits10); + + if(static_cast(str.length() - pos) > max_dec) + { + str = str.substr(static_cast(0u), + static_cast(pos_plus_one + max_dec)); + } + + // Now the input string has the standard mp_float input form. + // (See the comment above.) + + // Set all the data elements to 0. + std::fill(data.begin(), data.end(), static_cast(0u)); + + // Extract the data. + + // First get the digits to the left of the decimal point... + data[0u] = boost::lexical_cast(str.substr(static_cast(0u), pos)); + + // ...then get the remaining digits to the right of the decimal point. + const std::string::size_type i_end = ((str.length() - pos_plus_one) / static_cast(mp_elem_digits10)); + + for(std::string::size_type i = static_cast(0u); i < i_end; i++) + { + const std::string::const_iterator it = str.begin() + + pos_plus_one + + (i * static_cast(mp_elem_digits10)); + + data[i + 1u] = boost::lexical_cast(std::string(it, it + static_cast(mp_elem_digits10))); + } + + // Check for overflow... + if(exp > mp_float_max_exp) + { + const bool b_result_is_neg = neg; + + *this = inf(); + if(b_result_is_neg) + negate(); + } + + // ...and check for underflow. + if(exp <= mp_float_min_exp) + { + if(exp == mp_float_min_exp) + { + // Check for identity with the minimum value. + mp_float test = *this; + + test.exp = static_cast(0); + + if(test.isone()) + { + *this = zero(); + } + } + else + { + *this = zero(); + } + } + + return true; +} + +template +mp_float::mp_float(const double mantissa, const boost::int64_t exponent) + : data (), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) +{ + // Create an mp_float from mantissa and exponent. + // This ctor does not maintain the full precision of double. + + const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits::min)() * (1.0 + std::numeric_limits::epsilon()))); + + if(mantissa_is_iszero) + { + std::fill(data.begin(), data.end(), static_cast(0u)); + return; + } + + const bool b_neg = (mantissa < 0.0); + + double d = ((!b_neg) ? mantissa : -mantissa); + boost::int64_t e = exponent; + + while(d > 10.0) { d /= 10.0; ++e; } + while(d < 1.0) { d *= 10.0; --e; } + + boost::int32_t shift = static_cast(e % static_cast(mp_elem_digits10)); + + while(static_cast(shift-- % mp_elem_digits10) != static_cast(0)) + { + d *= 10.0; + --e; + } + + exp = e; + neg = b_neg; + + std::fill(data.begin(), data.end(), static_cast(0u)); + + static const boost::int32_t digit_ratio = static_cast(static_cast(std::numeric_limits::digits10) / static_cast(mp_elem_digits10)); + static const boost::int32_t digit_loops = static_cast(digit_ratio + static_cast(2)); + + for(boost::int32_t i = static_cast(0); i < digit_loops; i++) + { + boost::uint32_t n = static_cast(static_cast(d)); + data[i] = static_cast(n); + d -= static_cast(n); + d *= static_cast(mp_elem_mask); + } +} + +template +mp_float& mp_float::operator = (long double a) +{ + // Christopher Kormanyos's original code used a cast to long long here, but that fails + // when long double has more digits than a long long. + using std::frexp; + using std::ldexp; + using std::floor; + + if (a == 0) { + return *this = zero(); + } + + if (a == 1) { + return *this = one(); + } + + if((boost::math::isinf)(a)) + { + return *this = inf(); + } + if((boost::math::isnan)(a)) + return *this = nan(); + + int e; + long double f, term; + *this = zero(); + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + *this *= pow2(shift); + if(term > 0) + add_unsigned_long_long(static_cast(term)); + else + sub_unsigned_long_long(static_cast(-term)); + f -= term; + } + if(e != 0) + *this *= pow2(e); + return *this; +} + +template +void mp_float::from_unsigned_long_long(const unsigned long long u) +{ + std::fill(data.begin(), data.end(), static_cast(0u)); + + exp = static_cast(0); + neg = false; + fpclass = mp_finite; + prec_elem = mp_elem_number; + + std::size_t i =static_cast(0u); + + unsigned long long uu = u; + + boost::uint32_t temp[(std::numeric_limits::digits10 / static_cast(mp_elem_digits10)) + 3] = { static_cast(0u) }; + + while(uu != static_cast(0u)) + { + temp[i] = static_cast(uu % static_cast(mp_elem_mask)); + uu = static_cast(uu / static_cast(mp_elem_mask)); + ++i; + } + + if(i > static_cast(1u)) + { + exp += static_cast((i - 1u) * static_cast(mp_elem_digits10)); + } + + std::reverse(temp, temp + i); + std::copy(temp, temp + (std::min)(i, static_cast(mp_elem_number)), data.begin()); +} + +template +void mp_float::mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p) +{ + boost::uint64_t carry = static_cast(0u); + + for(boost::int32_t j = static_cast(p - 1u); j >= static_cast(0); j--) + { + boost::uint64_t sum = carry; + + for(boost::int32_t i = j; i >= static_cast(0); i--) + { + sum += static_cast(u[i] * static_cast(v[j - i])); + } + + w[j + 1] = static_cast(sum % static_cast(mp_elem_mask)); + carry = static_cast(sum / static_cast(mp_elem_mask)); + } + + w[0u] = static_cast(carry); +} + +template +boost::uint32_t mp_float::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) +{ + boost::uint64_t carry = static_cast(0u); + + // Multiplication loop. + for(boost::int32_t j = p - 1; j >= static_cast(0); j--) + { + const boost::uint64_t t = static_cast(carry + static_cast(u[j] * static_cast(n))); + carry = static_cast(t / static_cast(mp_elem_mask)); + u[j] = static_cast(t - static_cast(static_cast(mp_elem_mask) * static_cast(carry))); + } + + return static_cast(carry); +} + +template +boost::uint32_t mp_float::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) +{ + boost::uint64_t prev = static_cast(0u); + + for(boost::int32_t j = static_cast(0); j < p; j++) + { + const boost::uint64_t t = static_cast(u[j] + static_cast(prev * static_cast(mp_elem_mask))); + u[j] = static_cast(t / n); + prev = static_cast(t - static_cast(n * static_cast(u[j]))); + } + + return static_cast(prev); +} + +template +mp_float mp_float::pow2(const boost::int64_t p) +{ + // Create a static const table of p^2 for -128 < p < +128. + // Note: The size of this table must be odd-numbered and + // symmetric about 0. + init.do_nothing(); + static const boost::array, 255u> p2_data = + {{ + mp_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"), + mp_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"), + mp_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"), + mp_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"), + mp_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"), + mp_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"), + mp_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"), + mp_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"), + mp_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"), + mp_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"), + mp_float("6.018531076210112040799931070577897870431567650673088110124808736145496368408203125000000000000000000e-36"), + mp_float("1.203706215242022408159986214115579574086313530134617622024961747229099273681640625000000000000000000e-35"), + mp_float("2.407412430484044816319972428231159148172627060269235244049923494458198547363281250000000000000000000e-35"), + mp_float("4.814824860968089632639944856462318296345254120538470488099846988916397094726562500000000000000000000e-35"), + mp_float("9.629649721936179265279889712924636592690508241076940976199693977832794189453125000000000000000000000e-35"), + mp_float("1.925929944387235853055977942584927318538101648215388195239938795566558837890625000000000000000000000e-34"), + mp_float("3.851859888774471706111955885169854637076203296430776390479877591133117675781250000000000000000000000e-34"), + mp_float("7.703719777548943412223911770339709274152406592861552780959755182266235351562500000000000000000000000e-34"), + mp_float("1.540743955509788682444782354067941854830481318572310556191951036453247070312500000000000000000000000e-33"), + mp_float("3.081487911019577364889564708135883709660962637144621112383902072906494140625000000000000000000000000e-33"), + mp_float("6.162975822039154729779129416271767419321925274289242224767804145812988281250000000000000000000000000e-33"), + mp_float("1.232595164407830945955825883254353483864385054857848444953560829162597656250000000000000000000000000e-32"), + mp_float("2.465190328815661891911651766508706967728770109715696889907121658325195312500000000000000000000000000e-32"), + mp_float("4.930380657631323783823303533017413935457540219431393779814243316650390625000000000000000000000000000e-32"), + mp_float("9.860761315262647567646607066034827870915080438862787559628486633300781250000000000000000000000000000e-32"), + mp_float("1.972152263052529513529321413206965574183016087772557511925697326660156250000000000000000000000000000e-31"), + 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+ else + { + mp_float t; + default_ops::detail::pow_imp(t, two(), p, mpl::true_()); + return t; + } +} + + +template +inline void add(mp_float& result, const mp_float& o) +{ + result += o; +} +template +inline void subtract(mp_float& result, const mp_float& o) +{ + result -= o; +} +template +inline void multiply(mp_float& result, const mp_float& o) +{ + result *= o; +} +template +inline void divide(mp_float& result, const mp_float& o) +{ + result /= o; +} + +template +inline void add(mp_float& result, const unsigned long long& o) +{ + result.add_unsigned_long_long(o); +} +template +inline void subtract(mp_float& result, const unsigned long long& o) +{ + result.sub_unsigned_long_long(o); +} +template +inline void multiply(mp_float& result, const unsigned long long& o) +{ + result.mul_unsigned_long_long(o); +} +template +inline void divide(mp_float& result, const unsigned long long& o) +{ + result.div_unsigned_long_long(o); +} + +template +inline void add(mp_float& result, long long o) +{ + if(o < 0) + result.sub_unsigned_long_long(-o); + else + result.add_unsigned_long_long(o); +} +template +inline void subtract(mp_float& result, long long o) +{ + if(o < 0) + result.add_unsigned_long_long(-o); + else + result.sub_unsigned_long_long(o); +} +template +inline void multiply(mp_float& result, long long o) +{ + if(o < 0) + { + result.mul_unsigned_long_long(-o); + result.negate(); + } + else + result.mul_unsigned_long_long(o); +} +template +inline void divide(mp_float& result, long long o) +{ + if(o < 0) + { + result.div_unsigned_long_long(-o); + result.negate(); + } + else + result.div_unsigned_long_long(o); +} + +template +inline void convert_to(unsigned long long* result, const mp_float& val) +{ + *result = val.extract_unsigned_long_long(); +} +template +inline void convert_to(long long* result, const mp_float& val) +{ + *result = val.extract_signed_long_long(); +} +template +inline void convert_to(long double* result, mp_float& val) +{ + *result = val.extract_long_double(); +} + + +typedef mp_number > mp_float_50; +typedef mp_number > mp_float_100; + +}} + +#endif + diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index b1379fd4..00078e8e 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -9,12 +9,6 @@ import path ; local ntl-path = [ modules.peek : NTL_PATH ] ; local gmp_path = [ modules.peek : GMP_PATH ] ; local mpfr_path = [ modules.peek : MPFR_PATH ] ; -local e_float_path = [ modules.peek : BOOST_E_FLOAT_PATH ] ; - -if ! $(e_float_path) -{ - e_float_path = ../../../../e_float ; -} project : requirements $(gmp_path) @@ -22,36 +16,15 @@ project : requirements $(gmp_path)/gmpfrxx $(mpfr_path) ../../.. - $(e_float_path) $(gmp_path) $(mpfr_path) $(mpfr_path)/build.vc10/lib/Win32/Debug msvc:static - E_FLOAT_DIGITS10=100 - E_FLOAT_TYPE_EFX ; lib gmp ; lib mpfr ; -E_FLOAT_SRC = [ GLOB $(e_float_path)/libs/e_float/src/e_float : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/e_float/efx : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/constants : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/elementary : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/gamma : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/integer : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/tables : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/functions/zeta : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/generic_functions/constants : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/generic_functions/elementary : *.cpp ] - [ GLOB $(e_float_path)/libs/e_float/src/utility : *.cpp ] - ; - -lib e_float : $(E_FLOAT_SRC) - : - [ check-target-builds ../config//has_e_float : : no ] - ; - run test_arithmetic.cpp : # command line : # input files @@ -59,6 +32,13 @@ run test_arithmetic.cpp TEST_BACKEND : test_arithmetic_backend_concept ; +run test_arithmetic.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_arithmetic_mp_float ; + run test_arithmetic.cpp gmp : # command line : # input files @@ -107,14 +87,6 @@ run test_arithmetic.cpp mpfr gmp [ check-target-builds ../config//has_mpfr : : no ] : test_arithmetic_mpfr_50 ; -run test_arithmetic.cpp $(E_FLOAT_SRC) - : # command line - : # input files - : # requirements - TEST_E_FLOAT - [ check-target-builds ../config//has_e_float : : no ] - : test_arithmetic_e_float ; - run test_numeric_limits.cpp : # command line : # input files @@ -170,15 +142,6 @@ run test_numeric_limits.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : test_numeric_limits_mpfr_50 ; - -run test_numeric_limits.cpp $(E_FLOAT_SRC) - : # command line - : # input files - : # requirements - TEST_E_FLOAT - [ check-target-builds ../config//has_e_float : : no ] - : test_numeric_limits_e_float ; - run mp_number_concept_check.cpp mpfr : # command line : # input files diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 86d18619..dc71ed86 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -6,14 +6,14 @@ #include #include -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND # define TEST_MPZ # define TEST_MPFR # define TEST_MPFR_50 -# define TEST_E_FLOAT +# define TEST_MP_FLOAT # define TEST_MPQ #ifdef _MSC_VER @@ -31,8 +31,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif #if defined(TEST_MPFR) || defined(TEST_MPFR_50) #include @@ -325,16 +325,6 @@ void test_float_ops(const boost::mpl::int_ -struct lexical_cast_target_type -{ - typedef long double type; -}; - -#else - template struct lexical_cast_target_type { @@ -349,8 +339,6 @@ struct lexical_cast_target_type >::type type; }; -#endif - template void test_negative_mixed(boost::mpl::true_ const&) { @@ -483,7 +471,6 @@ void test_mixed() BOOST_TEST(n2 == Real(n2)); BOOST_TEST(n3 == Real(n3)); BOOST_TEST(n4 == Real(n4)); - std::cout << Real(n1).str(0, boost::is_floating_point::value) << std::endl; #if defined(TEST_MPFR) || defined(TEST_MPFR_50) Num tol = 10 * std::numeric_limits::epsilon(); #else @@ -880,8 +867,8 @@ int main() #ifdef TEST_MPQ test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); #endif #ifdef TEST_MPFR test(); From ad66feecbe7b674592620c13742f3ac8ae5e327f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 27 Oct 2011 16:46:46 +0000 Subject: [PATCH 044/256] Add numeric_limits support for mp_float. [SVN r75134] --- include/boost/multiprecision/mp_float.hpp | 65 +++++++++++++++++++++++ test/Jamfile.v2 | 8 +++ test/test_numeric_limits.cpp | 13 ++--- 3 files changed, 80 insertions(+), 6 deletions(-) diff --git a/include/boost/multiprecision/mp_float.hpp b/include/boost/multiprecision/mp_float.hpp index a07ca1ac..0e32e962 100644 --- a/include/boost/multiprecision/mp_float.hpp +++ b/include/boost/multiprecision/mp_float.hpp @@ -95,6 +95,7 @@ private: mp_float::long_long_max(); mp_float::long_long_min(); mp_float::ulong_long_max(); + mp_float::eps(); mp_float::pow2(0); } void do_nothing(){} @@ -269,6 +270,12 @@ public: static mp_float val((std::numeric_limits::max)()); return val; } + static const mp_float& eps() + { + init.do_nothing(); + static mp_float val(1.0, 1 - Digits10); + return val; + } // Basic operations. mp_float& operator= (const mp_float& v) @@ -2451,11 +2458,69 @@ inline void convert_to(long double* result, mp_float& val) *result = val.extract_long_double(); } +// +// Non member function support: +// +template +int eval_fpclassify(const mp_float& x) +{ + if(x.isinf()) + return FP_INFINITE; + if(x.isnan()) + return FP_NAN; + if(x.iszero()) + return FP_ZERO; + return FP_NORMAL; +} + typedef mp_number > mp_float_50; typedef mp_number > mp_float_100; }} +namespace std +{ + template + class numeric_limits > > + { + public: + static const bool is_specialized = true; + static const bool is_signed = true; + static const bool is_integer = false; + static const bool is_exact = false; + static const bool is_bounded = true; + static const bool is_modulo = false; + static const bool is_iec559 = false; + static const int digits = boost::multiprecision::mp_float::mp_float_digits; + static const int digits10 = boost::multiprecision::mp_float::mp_float_digits10; + static const int max_digits10 = boost::multiprecision::mp_float::mp_float_max_digits10; + static const boost::int64_t min_exponent = boost::multiprecision::mp_float::mp_float_min_exp; // Type differs from int. + static const boost::int64_t min_exponent10 = boost::multiprecision::mp_float::mp_float_min_exp10; // Type differs from int. + static const boost::int64_t max_exponent = boost::multiprecision::mp_float::mp_float_max_exp; // Type differs from int. + static const boost::int64_t max_exponent10 = boost::multiprecision::mp_float::mp_float_max_exp10; // Type differs from int. + static const int radix = boost::multiprecision::mp_float::mp_radix; + static const std::float_round_style round_style = std::round_to_nearest; + static const bool has_infinity = true; + static const bool has_quiet_NaN = true; + static const bool has_signaling_NaN = false; + static const std::float_denorm_style has_denorm = std::denorm_absent; + static const bool has_denorm_loss = false; + static const bool traps = false; + static const bool tinyness_before = false; + + static const boost::multiprecision::mp_number > (min) (void) throw() { return (boost::multiprecision::mp_float::min)(); } + static const boost::multiprecision::mp_number > (max) (void) throw() { return (boost::multiprecision::mp_float::max)(); } + static const boost::multiprecision::mp_number > lowest (void) throw() { return boost::multiprecision::mp_float::zero(); } + static const boost::multiprecision::mp_number > epsilon (void) throw() { return boost::multiprecision::mp_float::eps(); } + static const boost::multiprecision::mp_number > round_error (void) throw() { return 0.5L; } + static const boost::multiprecision::mp_number > infinity (void) throw() { return boost::multiprecision::mp_float::inf(); } + static const boost::multiprecision::mp_number > quiet_NaN (void) throw() { return boost::multiprecision::mp_float::nan(); } + static const boost::multiprecision::mp_number > signaling_NaN(void) throw() { return boost::multiprecision::mp_float::zero(); } + static const boost::multiprecision::mp_number > denorm_min (void) throw() { return boost::multiprecision::mp_float::zero(); } + }; +} + + #endif diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 00078e8e..c77d791f 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -142,6 +142,14 @@ run test_numeric_limits.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : test_numeric_limits_mpfr_50 ; +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + [ check-target-builds ../config//has_mpfr : : no ] + : test_numeric_limits_mp_float ; + run mp_number_concept_check.cpp mpfr : # command line : # input files diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index e2075d3b..0dc9e7d0 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -5,14 +5,14 @@ #include -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND # define TEST_MPZ # define TEST_MPFR # define TEST_MPFR_50 -# define TEST_E_FLOAT +# define TEST_MP_FLOAT # define TEST_MPQ #ifdef _MSC_VER @@ -30,8 +30,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif #if defined(TEST_MPFR) || defined(TEST_MPFR_50) #include @@ -159,8 +159,9 @@ int main() #ifdef TEST_MPQ test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif #ifdef TEST_MPFR test(); From 6372f8b6382d29a65a95001dc04ad2cad6efaf49 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 29 Oct 2011 11:57:54 +0000 Subject: [PATCH 045/256] Get mp_float passing all the tests, fix some bugs in acos and atan implementations. [SVN r75166] --- .../multiprecision/detail/default_ops.hpp | 12 +- .../multiprecision/detail/functions/trig.hpp | 7 +- include/boost/multiprecision/gmp.hpp | 28 ++- include/boost/multiprecision/mp_float.hpp | 203 ++++++++++++++++- include/boost/multiprecision/mp_number.hpp | 2 +- test/Jamfile.v2 | 85 +++++++ test/mp_number_concept_check.cpp | 18 +- test/test_acos.cpp | 13 +- test/test_arithmetic.cpp | 6 - test/test_asin.cpp | 13 +- test/test_atan.cpp | 25 +- test/test_cos.cpp | 215 +++++++++--------- test/test_cosh.cpp | 13 +- test/test_exp.cpp | 13 +- test/test_log.cpp | 13 +- test/test_pow.cpp | 13 +- test/test_sin.cpp | 23 +- test/test_sinh.cpp | 13 +- test/test_tanh.cpp | 13 +- 19 files changed, 514 insertions(+), 214 deletions(-) diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index dea68ff4..ed82327c 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -314,7 +314,12 @@ inline void convert_to(R* result, const B& backend) typedef typename calculate_next_larger_type::type next_type; next_type n; convert_to(&n, backend); - *result = static_cast(n); + if(std::numeric_limits::is_specialized && (n > (std::numeric_limits::max)())) + { + *result = (std::numeric_limits::max)(); + } + else + *result = static_cast(n); } template @@ -386,14 +391,15 @@ inline void eval_trunc(T& result, const T& a) template inline void eval_round(T& result, const T& a) { + typedef typename boost::multiprecision::detail::canonical::type fp_type; if(get_sign(a) < 0) { - subtract(result, a, 0.5f); + subtract(result, a, fp_type(0.5f)); eval_ceil(result, result); } else { - add(result, a, 0.5f); + add(result, a, fp_type(0.5f)); eval_floor(result, result); } } diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index 9a1b2ae7..7aca7e53 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -546,7 +546,10 @@ inline void eval_acos(T& result, const T& x) } else if(c == 0) { - result = ui_type(0); + if(get_sign(x) < 0) + result = get_constant_pi(); + else + result = ui_type(0); return; } @@ -694,7 +697,7 @@ void eval_atan2(T& result, const T& y, const T& x) case FP_ZERO: { eval_ldexp(result, get_constant_pi(), -1); - if(get_sign(x) < 0) + if(get_sign(y) < 0) result.negate(); return; } diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index af72d94b..16fa8e71 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -556,12 +556,21 @@ inline int get_sign(const gmp_float& val) template inline void convert_to(unsigned long* result, const gmp_float& val) { - *result = mpf_get_ui(val.data()); + if(0 == mpf_fits_ulong_p(val.data())) + *result = (std::numeric_limits::max)(); + else + *result = mpf_get_ui(val.data()); } template inline void convert_to(long* result, const gmp_float& val) { - *result = mpf_get_si(val.data()); + if(0 == mpf_fits_slong_p(val.data())) + { + *result = (std::numeric_limits::max)(); + *result *= mpf_sgn(val.data()); + } + else + *result = mpf_get_si(val.data()); } template inline void convert_to(double* result, const gmp_float& val) @@ -1122,11 +1131,22 @@ inline int get_sign(const gmp_int& val) } inline void convert_to(unsigned long* result, const gmp_int& val) { - *result = mpz_get_ui(val.data()); + if(0 == mpz_fits_ulong_p(val.data())) + { + *result = (std::numeric_limits::max)(); + } + else + *result = mpz_get_ui(val.data()); } inline void convert_to(long* result, const gmp_int& val) { - *result = mpz_get_si(val.data()); + if(0 == mpz_fits_slong_p(val.data())) + { + *result = (std::numeric_limits::max)(); + *result *= mpz_sgn(val.data()); + } + else + *result = mpz_get_si(val.data()); } inline void convert_to(double* result, const gmp_int& val) { diff --git a/include/boost/multiprecision/mp_float.hpp b/include/boost/multiprecision/mp_float.hpp index 0e32e962..df932965 100644 --- a/include/boost/multiprecision/mp_float.hpp +++ b/include/boost/multiprecision/mp_float.hpp @@ -16,6 +16,11 @@ #include #include +// +// Headers required for Boost.Math integration: +// +#include + namespace boost{ namespace multiprecision{ @@ -88,6 +93,7 @@ private: mp_float::zero(); mp_float::one(); mp_float::two(); + mp_float::half(); mp_float::double_min(); mp_float::double_max(); mp_float::long_double_max(); @@ -228,6 +234,12 @@ public: static mp_float val(static_cast(2u)); return val; } + static const mp_float& half() + { + init.do_nothing(); + static mp_float val(0.5L); + return val; + } static const mp_float& double_min() { init.do_nothing(); @@ -403,6 +415,57 @@ public: } } static mp_float pow2(long long i); + long long order()const + { + const bool bo_order_is_zero = ((!isfinite()) || (data[0] == static_cast(0u))); + // + // Binary search to find the order of the leading term: + // + boost::uint32_t prefix = 0; + + if(data[0] >= 100000UL) + { + if(data[0] >= 10000000UL) + { + if(data[0] >= 100000000UL) + { + if(data[0] >= 1000000000UL) + prefix = 9; + else + prefix = 8; + } + else + prefix = 7; + } + else + { + if(data[0] >= 1000000UL) + prefix = 6; + else + prefix = 5; + } + } + else + { + if(data[0] >= 1000UL) + { + if(data[0] >= 10000UL) + prefix = 4; + else + prefix = 3; + } + else + { + if(data[0] >= 100) + prefix = 2; + else if(data[0] >= 10) + prefix = 1; + } + } + + return (bo_order_is_zero ? static_cast(0) + : static_cast(exp + prefix)); + } private: static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast(0u)); } @@ -418,13 +481,6 @@ private: static boost::uint32_t div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); bool rd_string(const char* const s); - long long order()const - { - const bool bo_order_is_zero = ((!isfinite()) || (data[0] == static_cast(0u))); - - return (bo_order_is_zero ? static_cast(0) - : static_cast(exp + static_cast(std::log10(static_cast(data[0])) + (std::numeric_limits::epsilon() * 0.9)))); - } }; template @@ -2462,7 +2518,7 @@ inline void convert_to(long double* result, mp_float& val) // Non member function support: // template -int eval_fpclassify(const mp_float& x) +inline int eval_fpclassify(const mp_float& x) { if(x.isinf()) return FP_INFINITE; @@ -2473,6 +2529,114 @@ int eval_fpclassify(const mp_float& x) return FP_NORMAL; } +template +inline void eval_abs(mp_float& result, const mp_float& x) +{ + result = x; + if(x.isneg()) + result.negate(); +} + +template +inline void eval_fabs(mp_float& result, const mp_float& x) +{ + result = x; + if(x.isneg()) + result.negate(); +} + +template +inline void eval_sqrt(mp_float& result, const mp_float& x) +{ + result = x; + result.calculate_sqrt(); +} + +template +inline void eval_floor(mp_float& result, const mp_float& x) +{ + result = x; + if(!x.isfinite() || x.isint()) + { + return; + } + + if(x.isneg()) + result -= mp_float::one(); + result = result.extract_integer_part(); +} + +template +inline void eval_ceil(mp_float& result, const mp_float& x) +{ + result = x; + if(!x.isfinite() || x.isint()) + { + return; + } + + if(!x.isneg()) + result += mp_float::one(); + result = result.extract_integer_part(); +} + +template +inline void eval_trunc(mp_float& result, const mp_float& x) +{ + if(!x.isfinite() || x.isint()) + { + result = x; + return; + } + result = x.extract_integer_part(); +} + +template +inline void eval_ldexp(mp_float& result, const mp_float& x, long long e) +{ + result = x; + result *= mp_float::pow2(e); +} + +template +inline void eval_frexp(mp_float& result, const mp_float& x, long long* e) +{ + result = x; + if(result.isneg()) + result.negate(); + + long long t = result.order(); + + if(std::abs(t) > (std::numeric_limits::max)() / 3) + throw std::runtime_error("Exponent is too large to be represented as a power of 2."); + t *= 3; + + result *= mp_float::pow2(-t); + + while(result.compare(mp_float::one()) >= 0) + { + result /= mp_float::two(); + ++t; + } + while(result.compare(mp_float::half()) < 0) + { + result *= mp_float::two(); + --t; + } + *e = t; + if(x.isneg()) + result.negate(); +} + +template +inline void eval_frexp(mp_float& result, const mp_float& x, int* e) +{ + long long t; + eval_frexp(result, x, &t); + if(t > (std::numeric_limits::max)()) + throw std::runtime_error("Exponent is outside the range of an int"); + *e = static_cast(t); +} typedef mp_number > mp_float_50; typedef mp_number > mp_float_100; @@ -2521,6 +2685,29 @@ namespace std }; } +namespace boost{ namespace math{ + +namespace policies{ + +template +struct precision< boost::multiprecision::mp_number >, Policy> +{ + typedef typename Policy::precision_type precision_type; + typedef digits2<((Digits10 + 1) * 1000L) / 301L> digits_2; + typedef typename mpl::if_c< + ((digits_2::value <= precision_type::value) + || (Policy::precision_type::value <= 0)), + // Default case, full precision for RealType: + digits_2, + // User customised precision: + precision_type + >::type type; +}; + +} // namespace policies + +}} // namespaces boost::math + #endif diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index bb95fd8c..b0e2f156 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -45,7 +45,7 @@ public: } template - mp_number(V v, typename enable_if, mpl::not_ > > >::type* dummy1 = 0) + mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* dummy1 = 0) : m_backend(v){} template diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index c77d791f..e2da4d0d 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -166,6 +166,14 @@ run mp_number_concept_check.cpp gmp [ check-target-builds ../config//has_gmp : : no ] : big_number_concept_check_mpf50 ; +run mp_number_concept_check.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + [ check-target-builds ../config//has_gmp : : no ] + : big_number_concept_check_mp_float ; + run test_exp.cpp gmp : # command line : # input files @@ -262,6 +270,55 @@ run test_tanh.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : test_tanh_mpfr50 ; +run test_exp.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_exp_mp_float ; + +run test_log.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_log_mp_float ; + +run test_pow.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_pow_mp_float ; + +run test_sinh.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_sinh_mp_float ; + +run test_cosh.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_cosh_mp_float ; + +run test_tanh.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_tanh_mp_float ; + +run test_sin.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_sin_mp_float ; + run test_sin.cpp gmp : # command line : # input files @@ -278,6 +335,13 @@ run test_sin.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : test_sin_mpfr_50 ; +run test_cos.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_cos_mp_float ; + run test_cos.cpp gmp : # command line : # input files @@ -294,6 +358,13 @@ run test_cos.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : test_cos_mpfr_50 ; +run test_asin.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_asin_mp_float ; + run test_asin.cpp gmp : # command line : # input files @@ -310,6 +381,13 @@ run test_asin.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : test_asin_mpfr_50 ; +run test_acos.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_acos_mp_float ; + run test_acos.cpp gmp : # command line : # input files @@ -334,6 +412,13 @@ run test_atan.cpp gmp [ check-target-builds ../config//has_gmp : : no ] : test_atan_mpf50 ; +run test_atan.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + : test_atan_mp_float ; + run test_atan.cpp mpfr : # command line : # input files diff --git a/test/mp_number_concept_check.cpp b/test/mp_number_concept_check.cpp index 95ff4ffc..99d2c13f 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -5,7 +5,7 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) // -// This tests two things: that e_float meets our +// This tests two things: that mp_float_50 meets our // conceptual requirements, and that we can instantiate // all our distributions and special functions on this type. // @@ -20,14 +20,14 @@ # pragma warning(disable:4503) // decorated name length exceeded, name was truncated #endif -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND # define TEST_MPZ # define TEST_MPFR # define TEST_MPFR_50 -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -44,8 +44,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif #if defined(TEST_MPFR) || defined(TEST_MPFR_50) #include @@ -71,8 +71,8 @@ void foo() #ifdef TEST_MPFR instantiate(boost::multiprecision::mpfr_float()); #endif -#ifdef TEST_E_FLOAT - instantiate(boost::multiprecision::e_float()); +#ifdef TEST_MP_FLOAT + instantiate(boost::multiprecision::mp_float_50()); #endif } @@ -93,8 +93,8 @@ int main() #ifdef TEST_MPFR BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif -#ifdef TEST_E_FLOAT - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#ifdef TEST_MP_FLOAT + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif } diff --git a/test/test_acos.cpp b/test/test_acos.cpp index 16fca50b..f7e350c4 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -96,8 +96,9 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index dc71ed86..aa040478 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -272,7 +272,6 @@ void test_float_ops(const T&){} template void test_float_ops(const boost::mpl::int_&) { -#if defined(TEST_MPF) || defined(TEST_MPF_50) || defined(TEST_BACKEND) || defined(TEST_MPFR) BOOST_TEST(abs(Real(2)) == 2); BOOST_TEST(abs(Real(-2)) == 2); BOOST_TEST(fabs(Real(2)) == 2); @@ -318,11 +317,6 @@ void test_float_ops(const boost::mpl::int_(3.25)); r = pow(v, 25); BOOST_TEST(r == boost::math::pow<25>(Real(3.25))); - /* - r = pow(v, 56); - BOOST_TEST(r == boost::math::pow<56>(Real(3.25))); - */ -#endif } template diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 60bb3f0c..c8c1e810 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -93,8 +93,9 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_atan.cpp b/test/test_atan.cpp index e572e7af..0b07212f 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -195,13 +195,11 @@ void test() err = relative_error(T(atan2(T(1), T(0))), T(pi / 2)).template convert_to(); if(err > max_err) max_err = err; - if(! is_mpfr_type::value) - { - // MPFR seems to get the sign of this all wrong: - err = relative_error(T(atan2(T(-1), T(0))), T(pi / -2)).template convert_to(); - if(err > max_err) - max_err = err; - } + + err = relative_error(T(atan2(T(-1), T(0))), T(pi / -2)).template convert_to(); + if(err > max_err) + max_err = err; + T mv = (std::numeric_limits::max)(); err = relative_error(T(atan2(mv, T(1))), T(pi / 2)).template convert_to(); if(err > max_err) @@ -239,8 +237,9 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_cos.cpp b/test/test_cos.cpp index bb9aab89..2e5dcf48 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -45,107 +45,107 @@ void test() { static const boost::array data = {{ -T("-2.37609908807915949996042688873953402912174184373388399043229539427530802169622688886435380890546981798452174137747437590e-1"), -T("8.03406366226813589517543567844755380935198206635917017883860879215939165740799963435747185200486086864198723786516760875e-1"), -T("8.60219386510802105228997694366289682807721120146423711696179175800635220710279361583231346318224971127450760223168489952e-1"), -T("-1.36768951513839774357595871594675554406872039078811749027554673949684004409484639336417431285061889554892096426752261915e-1"), -T("-9.66210139195431691033548069227792927999642647449593184440815029076272297050360196975341458076547426373476590671462150981e-1"), -T("-6.12007278553856790723803948280976098970972124581361775428331444376106018942231526074915731012122426588769327127413045994e-1"), -T("4.91927698740873688392439262912409276430264703350691359723802294639643655296838880236042651349290074585311025856549893171e-1"), -T("9.93232596718899824059271235487971663771012607519717340071654721877802691370866768064059943491135925674950430467047724563e-1"), -T("2.77789911520199551017947550534057049374212876971194676010301098598339529915403722848373365985645657342475739669568931563e-1"), -T("-7.77955945956221239101360662190442739163791527953499629555756394261998892874934847131138921705713935365505245406994428077e-1"), -T("-8.80676278306736581575818642341143682410874043182925227659938804267878718513212454821032629378618345485453587099696563832e-1"), -T("9.54652155963865007116798560589970996367213754762169439269792747771200843006278637115722685610960738675814993576019945344e-2"), -T("9.54658201427917718824191302196929158303422390793460018465335986921801519149657723689322277773550748806000948225466432438e-1"), -T("6.44358700620889799575033272322899136331490664925359198096632560532437137894857803619177106562399406351419810452110265174e-1"), -T("-4.55304635273050571206400777159475409897339683148730716647371922365967582339285347105376503917296765204188604297021364549e-1"), -T("-9.97202532932553753622481171186283382950122646390227670693679248197349800205205290898290539070732778341271049474946533154e-1"), -T("-3.17489525058325500707686194437148362752290391406825231198381521862930317513649081353670386166519524315810546189268634469e-1"), -T("7.51160186640147504067744846462384089742696250681200524524912647858645140367792164416711871535116761744380912486921554617e-1"), -T("8.99610194168373157174515848193119670768490559799348397680196213249921436405001710937402190319584272526657508442591319630e-1"), -T("-5.39963892484342940823660554048696208293700871414984387094529796385334086703752106515008832585578915389731907422242902573e-2"), -T("-9.41455348900839346761557896365239742769987576963330061702397697388879776230596944312519157729410022380228287314835345969e-1"), 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T("-8.10006890365888881023982873786181048364505748637138923322482323010218991062084191379116946709356002103893071903481540337e-1"), + T("-8.54470151393449484710948210543666267680196067632693416660536443330720708402601669617638569732848938319544250428600991723e-1"), + T("1.47824914922605209542648603104533928946885824995208478684499907657728115943168395067575842431291755277452367320596435067e-1"), + T("9.69028856602232134498324179654622883463820270279077886397861028881882684131282848087869087883519707948141915733221980948e-1"), + T("6.03135714281336943093251136556365407562473924416812270469171432809743173719168209727199952532489544254928975940518615351e-1"), + T("-5.01621542149055350065079347615664213658089623368745676779267390227688581807037821041573344917735076902116221444127518632e-1"), }}; T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; @@ -282,8 +282,9 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index c9be8958..76c4f976 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -128,8 +128,9 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_exp.cpp b/test/test_exp.cpp index ff2bf4d9..8f397d9e 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -173,8 +173,9 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_log.cpp b/test/test_log.cpp index 166bfcae..85c077a9 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -186,8 +186,9 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_pow.cpp b/test/test_pow.cpp index b681d703..38181241 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT # define TEST_MPFR_50 #ifdef _MSC_VER @@ -37,8 +37,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -576,8 +576,9 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_sin.cpp b/test/test_sin.cpp index 3843b37d..03be2a9f 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -246,7 +246,7 @@ T("8.650871796830672527081873591655777773059986288175183143531618768919892399328 // Test with some exact binary values as input - this tests our code // rather than the test data: // - static const boost::array, 7> exact_data = + static const boost::array, 9> exact_data = {{ {{ 0.5, "0.479425538604203000273287935215571388081803367940600675188616613125535000287814832209631274684348269086132091084505717418" }}, {{ 0.25, "0.247403959254522929596848704849389195893390980386965810676544830494398136043486821690984848527973792338327197752176516138" }}, @@ -254,7 +254,9 @@ T("8.650871796830672527081873591655777773059986288175183143531618768919892399328 {{std::ldexp(1.0, -20), "9.53674316406105439710335272649306549801506698739838753888815787489707114648106832493113326022411646219016312547902694921e-7" }}, {{ 2, "0.909297426825681695396019865911744842702254971447890268378973011530967301540783544620126688924959380309967896742399486261" }}, {{ 5, "-0.958924274663138468893154406155993973352461543964601778131672454235102558086559603076995955429532866596530638461663378937" }}, - {{ 10, "-0.544021110889369813404747661851377281683643012916223891574184012616757209640493425707075673894983216158293824238262832286" }} + {{ 10, "-0.544021110889369813404747661851377281683643012916223891574184012616757209640493425707075673894983216158293824238262832286" }}, + {{ 0, 0 }}, + {{ "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064", 1 }} }}; max_err = 0; for(unsigned k = 0; k < exact_data.size(); k++) @@ -267,11 +269,6 @@ T("8.650871796830672527081873591655777773059986288175183143531618768919892399328 } std::cout << "Max error was: " << max_err << std::endl; BOOST_TEST(max_err < 20); - - T half_pi = "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064"; - - BOOST_TEST(sin(T(0)) == 0); - BOOST_TEST(sin(half_pi) == 1); } @@ -288,8 +285,8 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index 0d33347c..bddad689 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -128,8 +128,9 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index 59d67c9f..d226fc95 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_E_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_E_FLOAT +# define TEST_MP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_E_FLOAT -#include +#ifdef TEST_MP_FLOAT +#include #endif template @@ -128,8 +128,9 @@ int main() test(); test(); #endif -#ifdef TEST_E_FLOAT - test(); +#ifdef TEST_MP_FLOAT + test(); + test(); #endif return boost::report_errors(); } From 79d630a0680177a0c71f743fc47ec1cfe03d14e5 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 29 Oct 2011 17:41:31 +0000 Subject: [PATCH 046/256] Fix benchmark to build with new code. [SVN r75169] --- test/linpack-benchmark.cpp | 54 ++++++++++++++++---------------------- 1 file changed, 23 insertions(+), 31 deletions(-) diff --git a/test/linpack-benchmark.cpp b/test/linpack-benchmark.cpp index 8798ca6d..f4829101 100644 --- a/test/linpack-benchmark.cpp +++ b/test/linpack-benchmark.cpp @@ -19,27 +19,21 @@ http://www.netlib.org/f2c/libf2c.zip #include #include -#ifdef TEST_MPF_100 -#include -typedef boost::multiprecision::mpf_float_100 real_type; -#elif defined(TEST_MPFR_100) -#include -typedef boost::multiprecision::mpfr_float_100 real_type; -#elif defined(TEST_GMPXX) +#if defined(TEST_GMPXX) #include typedef mpf_class real_type; #elif defined(TEST_MPFRXX) #include typedef mpfr_class real_type; -#elif defined(TEST_E_FLOAT) -#include -#include -#include -typedef ::efx::e_float real_type; -using ef::abs; -#elif defined(TEST_E_FLOAT_BN) -#include -typedef boost::multiprecision::e_float real_type; +#elif defined(TEST_MP_FLOAT) +#include +typedef boost::multiprecision::mp_float_50 real_type; +#elif defined(TEST_MPFR_50) +#include +typedef boost::multiprecision::mpfr_float_50 real_type; +#elif defined(TEST_MPF_50) +#include +typedef boost::multiprecision::mpf_float_50 real_type; #else typedef double real_type; #endif @@ -98,20 +92,18 @@ int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type extern "C" int MAIN__() { -#ifdef TEST_MPF_100 - std::cout << "Testing mp_number >" << std::endl; -#elif defined(TEST_MPFR_100) - std::cout << "Testing mp_number >" << std::endl; +#ifdef TEST_MPF_50 + std::cout << "Testing mp_number >" << std::endl; +#elif defined(TEST_MPFR_50) + std::cout << "Testing mp_number >" << std::endl; #elif defined(TEST_GMPXX) - std::cout << "Testing mpf_class at 100 decimal degits" << std::endl; - mpf_set_default_prec(((100 + 1) * 1000L) / 301L); + std::cout << "Testing mpf_class at 50 decimal degits" << std::endl; + mpf_set_default_prec(((50 + 1) * 1000L) / 301L); #elif defined(TEST_MPFRXX) - std::cout << "Testing mpfr_class at 100 decimal degits" << std::endl; - mpfr_set_default_prec(((100 + 1) * 1000L) / 301L); -#elif defined(TEST_E_FLOAT) - std::cout << "Testing boost::ef::e_float" << std::endl; -#elif defined(TEST_E_FLOAT_BN) - std::cout << "Testing boost::multiprecision::e_float" << std::endl; + std::cout << "Testing mpfr_class at 50 decimal degits" << std::endl; + mpfr_set_default_prec(((50 + 1) * 1000L) / 301L); +#elif defined(TEST_MP_FLOAT) + std::cout << "Testing mp_number >" << std::endl; #else std::cout << "Testing double" << std::endl; #endif @@ -919,8 +911,8 @@ real_type epslon_(real_type *x) { #if defined(TEST_MPF_100) || defined(TEST_MPFR_100) || defined(TEST_GMPXX) || defined(TEST_MPFRXX) return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); -#elif defined(TEST_E_FLOAT_BN) - return std::pow(10.0, 1-std::numeric_limits::digits10); +#elif defined(TEST_MP_FLOAT_BN) + return std::pow(10.0, 1-std::numeric_limits::digits10); #else return CAST_TO_RT(std::numeric_limits::epsilon()); #endif @@ -1242,7 +1234,7 @@ mp_number >: times for array with leading dimension of1001 279.96 0.84 280.8 2.3813 0.83988 5014.3 -boost::multiprecision::ef::e_float: +boost::multiprecision::ef::mp_float_50: ~~~~~~~~~~~~~~~~~~~~~~~~~ norm. resid resid machep x(1) x(n) From 4061f5275b51c96186d957f62adbbe3fd95ff635 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 30 Oct 2011 18:39:38 +0000 Subject: [PATCH 047/256] Fix Clang failures. [SVN r75180] --- include/boost/multiprecision/mp_number.hpp | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index b0e2f156..3ca21f55 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -129,7 +129,7 @@ public: if(contains_self(e)) { self_type temp(e); - do_subtract(temp, typename self_type::tag_type()); + do_subtract(temp, detail::terminal()); } else { @@ -194,7 +194,7 @@ public: if(contains_self(e)) { self_type temp(e); - do_modulus(temp, typename self_type::tag_type()); + do_modulus(temp, detail::terminal()); } else { @@ -281,7 +281,7 @@ public: if(contains_self(e)) { self_type temp(e); - do_divide(detail::mp_exp(temp), typename self_type::tag_type()); + do_divide(detail::mp_exp(temp), detail::terminal()); } else { @@ -313,7 +313,7 @@ public: if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_bitwise_and(temp, typename self_type::tag_type()); + do_bitwise_and(temp, detail::terminal()); } else { @@ -345,7 +345,7 @@ public: if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_bitwise_or(temp, typename self_type::tag_type()); + do_bitwise_or(temp, detail::terminal()); } else { @@ -375,7 +375,7 @@ public: if(contains_self(e)) { self_type temp(e); - do_bitwise_xor(temp, typename self_type::tag_type()); + do_bitwise_xor(temp, detail::terminal()); } else { From 401af0322a172cc40ef3f1fc1e30a4ed127a22df Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 31 Oct 2011 16:00:21 +0000 Subject: [PATCH 048/256] File rename [SVN r75194] --- doc/Jamfile.v2 | 3 ++- doc/{big_number.qbk => multiprecision.qbk} | 0 2 files changed, 2 insertions(+), 1 deletion(-) rename doc/{big_number.qbk => multiprecision.qbk} (100%) diff --git a/doc/Jamfile.v2 b/doc/Jamfile.v2 index 2f00f026..1a557811 100644 --- a/doc/Jamfile.v2 +++ b/doc/Jamfile.v2 @@ -7,7 +7,7 @@ using quickbook ; path-constant images_location : html ; -xml big_number : big_number.qbk ; +xml big_number : multiprecision.qbk ; boostbook standalone : big_number @@ -65,3 +65,4 @@ boostbook standalone ; install pdf-install : standalone : . PDF ; + diff --git a/doc/big_number.qbk b/doc/multiprecision.qbk similarity index 100% rename from doc/big_number.qbk rename to doc/multiprecision.qbk From 9092a7b1505381abc6ec32696194fae6103edd24 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 31 Oct 2011 16:01:10 +0000 Subject: [PATCH 049/256] Remove old docs. [SVN r75195] --- doc/html/boost_bignumbers/intro.html | 44 -- doc/html/boost_bignumbers/ref.html | 40 -- .../boost_bignumbers/ref/backendconc.html | 38 -- doc/html/boost_bignumbers/ref/bignum.html | 151 ----- doc/html/boost_bignumbers/tut.html | 44 -- doc/html/boost_bignumbers/tut/ints.html | 146 ----- doc/html/boost_bignumbers/tut/reals.html | 158 ----- doc/html/boostbook.css | 588 ------------------ doc/html/images/blank.png | Bin 374 -> 0 bytes doc/html/images/caution.png | Bin 1250 -> 0 bytes doc/html/images/caution.svg | 68 -- doc/html/images/draft.png | Bin 17454 -> 0 bytes doc/html/images/home.png | Bin 358 -> 0 bytes doc/html/images/home.svg | 26 - doc/html/images/important.png | Bin 722 -> 0 bytes doc/html/images/important.svg | 25 - doc/html/images/next.png | Bin 336 -> 0 bytes doc/html/images/next.svg | 19 - doc/html/images/next_disabled.png | Bin 1110 -> 0 bytes doc/html/images/note.png | Bin 490 -> 0 bytes doc/html/images/note.svg | 33 - doc/html/images/prev.png | Bin 334 -> 0 bytes doc/html/images/prev.svg | 19 - doc/html/images/prev_disabled.png | Bin 1109 -> 0 bytes doc/html/images/tip.png | Bin 449 -> 0 bytes doc/html/images/tip.svg | 84 --- doc/html/images/toc-blank.png | Bin 318 -> 0 bytes doc/html/images/toc-minus.png | Bin 259 -> 0 bytes doc/html/images/toc-plus.png | Bin 264 -> 0 bytes doc/html/images/up.png | Bin 370 -> 0 bytes doc/html/images/up.svg | 19 - doc/html/images/up_disabled.png | Bin 1115 -> 0 bytes doc/html/images/warning.png | Bin 1241 -> 0 bytes doc/html/images/warning.svg | 23 - doc/html/index.html | 53 -- 35 files changed, 1578 deletions(-) delete mode 100644 doc/html/boost_bignumbers/intro.html delete mode 100644 doc/html/boost_bignumbers/ref.html delete mode 100644 doc/html/boost_bignumbers/ref/backendconc.html delete mode 100644 doc/html/boost_bignumbers/ref/bignum.html delete mode 100644 doc/html/boost_bignumbers/tut.html delete mode 100644 doc/html/boost_bignumbers/tut/ints.html delete mode 100644 doc/html/boost_bignumbers/tut/reals.html delete mode 100644 doc/html/boostbook.css delete mode 100644 doc/html/images/blank.png delete mode 100644 doc/html/images/caution.png delete mode 100644 doc/html/images/caution.svg delete mode 100644 doc/html/images/draft.png delete mode 100644 doc/html/images/home.png delete mode 100644 doc/html/images/home.svg delete mode 100644 doc/html/images/important.png delete mode 100644 doc/html/images/important.svg delete mode 100644 doc/html/images/next.png delete mode 100644 doc/html/images/next.svg delete mode 100644 doc/html/images/next_disabled.png delete mode 100644 doc/html/images/note.png delete mode 100644 doc/html/images/note.svg delete mode 100644 doc/html/images/prev.png delete mode 100644 doc/html/images/prev.svg delete mode 100644 doc/html/images/prev_disabled.png delete mode 100644 doc/html/images/tip.png delete mode 100644 doc/html/images/tip.svg delete mode 100644 doc/html/images/toc-blank.png delete mode 100644 doc/html/images/toc-minus.png delete mode 100644 doc/html/images/toc-plus.png delete mode 100644 doc/html/images/up.png delete mode 100644 doc/html/images/up.svg delete mode 100644 doc/html/images/up_disabled.png delete mode 100644 doc/html/images/warning.png delete mode 100644 doc/html/images/warning.svg delete mode 100644 doc/html/index.html diff --git a/doc/html/boost_bignumbers/intro.html b/doc/html/boost_bignumbers/intro.html deleted file mode 100644 index ee77f4b1..00000000 --- a/doc/html/boost_bignumbers/intro.html +++ /dev/null @@ -1,44 +0,0 @@ - - - -Introduction - - - - - - - - -
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- The Big Number library comes in two distinct parts: an expression template - enabled front end big_number - that handles all the operator overloading, expression evaluation optimization, - and code reduction, and a selection of backends that implement the actual arithmetic - operations, and need conform only to the reduced interface requirements of - the front end. -

-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

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Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

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- - diff --git a/doc/html/boost_bignumbers/ref/backendconc.html b/doc/html/boost_bignumbers/ref/backendconc.html deleted file mode 100644 index 44dd13af..00000000 --- a/doc/html/boost_bignumbers/ref/backendconc.html +++ /dev/null @@ -1,38 +0,0 @@ - - - -Backend Requirements - - - - - - - -
-
-
-PrevUpHome -
-
-
-

- TODO, big boring job!! -

-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHome -
- - diff --git a/doc/html/boost_bignumbers/ref/bignum.html b/doc/html/boost_bignumbers/ref/bignum.html deleted file mode 100644 index bcf3ef57..00000000 --- a/doc/html/boost_bignumbers/ref/bignum.html +++ /dev/null @@ -1,151 +0,0 @@ - - - -big_number - - - - - - - - -
-
-
-PrevUpHomeNext -
-
-
-
- - Synopsis -
-
namespace boost{ namespace math{
-
-template <class Backend>
-class big_number
-{
-   big_number();
-   big_number(see-below);
-   big_number& operator=(see-below);
-   /* Other number-type operators here */
-   // string conversion:
-   std::string str()const;
-   // precision control:
-   static unsigned default_precision();
-   static void default_precision(unsigned digits10);
-   unsigned precision()const;
-   void precision(unsigned digits10);
-   // Comparison:
-   int compare(const big_number<Backend>& o)const;
-   template <class V>
-   typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
-};
-
-}} // namespaces
-
-
- - Description -
-
big_number();
-big_number(see-below);
-big_number& operator=(see-below);
-
-

- Type big_number is default - constructible, and copy both constructible and assignable from: -

-
    -
  • - Itself. -
    • -
  • - An expression template which is the result of one of the arithmetic operators. -
    • -
  • - Any builtin arithmetic type. -
    • -
  • - A std::string or any type which is convertible - to const char*. -
    • -
-
/* Other number-type operators here */
-
-

- The following arithmetic operations are support for real-numbered types: -

-
    -
  • - Binary +, -, *, /, +, -, *, /, - ==, !, <, >=, <, >. -
    • -
  • - Unary +, -. -
    • -
-

- For integer types the following operators are also supported: -

-

- Binary %, %=. -

-

- (More to follow!!) -

-

- Note that the result of the binary +, -, *, / and % operations is an expression - template of "unmentionable type". -

-
std::string str()const;
-
-

- Returns the number formatted as a string (TODO: enable custom precision). -

-
static unsigned default_precision();
-static void default_precision(unsigned digits10);
-unsigned precision()const;
-void precision(unsigned digits10);
-
-

- These functions are only available if the Backend template parameter supports - runtime changes to precision. They get and set the default precision and - the precision of *this respectively. -

-
int compare(const big_number<Backend>& o)const;
-template <class V>
-typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
-
-

- Returns: -

-
    -
  • - A value less that 0 for *this < other -
    • -
  • - A value greater that 0 for *this > other -
    • -
  • - Zero for *this == other -
    • -
-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHomeNext -
- - diff --git a/doc/html/boost_bignumbers/tut.html b/doc/html/boost_bignumbers/tut.html deleted file mode 100644 index 92e58b08..00000000 --- a/doc/html/boost_bignumbers/tut.html +++ /dev/null @@ -1,44 +0,0 @@ - - - -Tutorial - - - - - - - - -
-
-
-PrevUpHomeNext -
-
-
-
-
Integer Types
-
Real Numbers
-
-

- In order to use this library you need to make two choices: what kind of number - do I want, and which backend do I want to perform the actual arithmetic? -

-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHomeNext -
- - diff --git a/doc/html/boost_bignumbers/tut/ints.html b/doc/html/boost_bignumbers/tut/ints.html deleted file mode 100644 index b2dbce57..00000000 --- a/doc/html/boost_bignumbers/tut/ints.html +++ /dev/null @@ -1,146 +0,0 @@ - - - -Integer Types - - - - - - - - -
-
-
-PrevUpHomeNext -
-
-
-

- The following backends provide integer arithmetic: -

-
-------- - - - - - - - - - - - - - - - - -
-

- Backend Type -

- 		-

- Header -

- 		-

- Radix -

- 		-

- Dependencies -

- 		-

- Pros -

- 		-

- Cons -

-
-

- gmp_int -

- 		-

- boost/math/big_number/gmp.hpp -

- 		-

- 2 -

- 		-

- GMP -

- 		-

- Very fast and efficient backend. -

- 		-

- Dependency on GNU licenced GMP library. -

-
-
- - gmp_int -
-
namespace boost{ namespace math{
-
-class gmp_int;
-
-typedef big_number<gmp_int >         mpz_int;
-
-}} // namespaces
-
-

- The gmp_int backend is used - via the typedef boost::math::mpz_int. It acts as a thin wrapper around - the GMP mpz_t to provide - an integer type that is a drop-in replacement for the native C++ integer - types, but with unlimited precision. -

-
- - Example: -
-
#include <boost/math/big_number/gmp.hpp>
-
-boost::math::mpz_int v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-
-std::cout << i << std::endl; // prints 1000!
-
-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHomeNext -
- - diff --git a/doc/html/boost_bignumbers/tut/reals.html b/doc/html/boost_bignumbers/tut/reals.html deleted file mode 100644 index cd08e445..00000000 --- a/doc/html/boost_bignumbers/tut/reals.html +++ /dev/null @@ -1,158 +0,0 @@ - - - -Real Numbers - - - - - - - - -
-
-
-PrevUpHomeNext -
-
-
-

- The following backends provide real number arithmetic: -

-
-------- - - - - - - - - - - - - - - - - -
-

- Backend Type -

- 		-

- Header -

- 		-

- Radix -

- 		-

- Dependencies -

- 		-

- Pros -

- 		-

- Cons -

-
-

- gmp_real<N> -

- 		-

- boost/math/big_number/gmp.hpp -

- 		-

- 2 -

- 		-

- GMP -

- 		-

- Very fast and efficient backend. -

- 		-

- Dependency on GNU licenced GMP library. -

-
-
- - gmp_real -
-
namespace boost{ namespace math{
-
-template <unsigned Digits10>
-class gmp_real;
-
-typedef big_number<gmp_real<50> >    mpf_real_50;
-typedef big_number<gmp_real<100> >   mpf_real_100;
-typedef big_number<gmp_real<500> >   mpf_real_500;
-typedef big_number<gmp_real<1000> >  mpf_real_1000;
-typedef big_number<gmp_real<0> >     mpf_real;
-
-}} // namespaces
-
-

- The gmp_real backend is used - in conjunction with big_number: - It acts as a thin wrapper around the GMP mpf_t - to provide an real-number type that is a drop-in replacement for the native - C++ floating-point types, but with much greater precision. -

-

- Type gmp_real can be used - at fixed precision by specifying a non-zero Digits10 - template parameter, or at variable precision by setting the template argument - to zero. The typedefs mpf_real_50, mpf_real_100, mpf_real_500, mpf_real_1000 - provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision - respectively. The typedef mpf_real provides a variable precision type whose - precision can be controlled via the big_number's - member functions. -

-
- - example: -
-
#include <boost/math/big_number/gmp.hpp>
-
-boost::math::gmp_real a = 2;
-boost::math::gmp_real::default_precision(1000);
-std::cout << boost::math::gmp_real::default_precision() << std::endl;
-std::cout << sqrt(a) << std::endl; // print root-2
-
-
- - - -
Copyright © 2011 John Maddock

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
-
-PrevUpHomeNext -
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(See accompany- - ing file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -=============================================================================*/ - -/*============================================================================= - Body defaults -=============================================================================*/ - - body - { - margin: 1em; - font-family: sans-serif; - } - -/*============================================================================= - Paragraphs -=============================================================================*/ - - p - { - text-align: left; - font-size: 10pt; - line-height: 1.15; - } - -/*============================================================================= - Program listings -=============================================================================*/ - - /* Code on paragraphs */ - p tt.computeroutput - { - font-size: 9pt; - } - - pre.synopsis - { - font-size: 90%; - margin: 1pc 4% 0pc 4%; - padding: 0.5pc 0.5pc 0.5pc 0.5pc; - } - - .programlisting, - .screen - { - font-size: 9pt; - display: block; - margin: 1pc 4% 0pc 4%; - padding: 0.5pc 0.5pc 0.5pc 0.5pc; - } - - /* Program listings in tables don't get borders */ - td .programlisting, - td .screen - { - margin: 0pc 0pc 0pc 0pc; - padding: 0pc 0pc 0pc 0pc; - } - -/*============================================================================= - Headings -=============================================================================*/ - - h1, h2, h3, h4, h5, h6 - { - text-align: left; - margin: 1em 0em 0.5em 0em; - font-weight: bold; - } - - h1 { font: 140% } - h2 { font: bold 140% } - h3 { font: bold 130% } - h4 { font: bold 120% } - h5 { font: italic 110% } - h6 { font: italic 100% } - - /* Top page titles */ - title, - h1.title, - h2.title - h3.title, - h4.title, - h5.title, - h6.title, - .refentrytitle - { - font-weight: bold; - margin-bottom: 1pc; - } - - h1.title { font-size: 140% } - h2.title { font-size: 140% } - h3.title { 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border: 1px solid #DCDCDC; - } - - div.informaltable table tr th, - div.table table tr th - { - background-color: #F0F0F0; - border: 1px solid #DCDCDC; - } - - .copyright-footer - { - color: #8F8F8F; - } - - /* Misc */ - span.highlight - { - color: #00A000; - } - } - - @media print - { - /* Links */ - a - { - color: black; - } - - a:visited - { - color: black; - } - - .spirit-nav - { - display: none; - } - - /* Program listing */ - pre.synopsis - { - border: 1px solid gray; - } - - .programlisting, - .screen - { - border: 1px solid gray; - } - - td .programlisting, - td .screen - { - border: 0px solid #DCDCDC; - } - - /* Table of contents */ - .toc - { - border: 1px solid gray; - } - - .informaltable table, - .table table - { - border: 1px solid gray; - border-collapse: collapse; - } - - /* Tables */ - div.informaltable table tr td, - div.table table tr td - { - border: 1px solid gray; - } - - div.informaltable table tr th, - div.table table tr th - { - border: 1px solid gray; - } - - 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Next
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-Chapter 1. Boost.BigNumbers

-

-various authors -

-

Copyright © 2011 John Maddock

-
-

- Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

-
-
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-

Table of Contents

-
-
Introduction
-
Tutorial
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-
Integer Types
-
Real Numbers
-
-
Reference
-
-
big_number
-
Backend Requirements
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-
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-
- - - -

Last revised: July 08, 2011 at 18:51:46 +0100

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Next
- - From e97c76f66ffc8f61dcc956f25f783af437436670 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 1 Nov 2011 19:14:08 +0000 Subject: [PATCH 050/256] Add interconversions between GMP types. Updates docs. Add numerator and denominator methods for rational numbers. [SVN r75232] --- doc/Jamfile.v2 | 5 +- doc/multiprecision.qbk | 374 ++++++++++++++++++--- include/boost/multiprecision/gmp.hpp | 288 +++++++++++++++- include/boost/multiprecision/mp_number.hpp | 21 ++ 4 files changed, 633 insertions(+), 55 deletions(-) diff --git a/doc/Jamfile.v2 b/doc/Jamfile.v2 index 1a557811..7cae9abc 100644 --- a/doc/Jamfile.v2 +++ b/doc/Jamfile.v2 @@ -13,12 +13,12 @@ boostbook standalone big_number : # Path for links to Boost: - #boost.root=../../../../.. + #boost.root=http://www.boost.org/doc/libs/release # Some general style settings: table.footnote.number.format=1 footnote.number.format=1 - html.stylesheet=boostbook.css + html.stylesheet=http://www.boost.org/doc/libs/release/doc/src/boostbook.css # HTML options first: # Use graphics not text for navigation: @@ -66,3 +66,4 @@ boostbook standalone install pdf-install : standalone : . PDF ; + diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 4ccfb199..87ebc540 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -5,10 +5,10 @@ http://www.boost.org/LICENSE_1_0.txt). ] -[library Boost.BigNumbers +[library Boost.Multiprecision [quickbook 1.5] [copyright 2011 John Maddock] - [purpose Big Number library] + [purpose Multiprecision Number library] [license Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at @@ -20,7 +20,7 @@ [section:intro Introduction] -The Big Number library comes in two distinct parts: an expression template enabled front end `big_number` +The Multiprecision library comes in two distinct parts: an expression template enabled front end `mp_number` that handles all the operator overloading, expression evaluation optimization, and code reduction, and a selection of backends that implement the actual arithmetic operations, and need conform only to the reduced interface requirements of the front end. @@ -38,27 +38,34 @@ The following backends provide integer arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] -[[`gmp_int`][boost/math/big_number/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] +[[`gmp_int`][boost/multiprecision/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] ] [h4 gmp_int] - namespace boost{ namespace math{ + namespace boost{ namespace multiprecision{ class gmp_int; - typedef big_number mpz_int; + typedef mp_number mpz_int; }} // namespaces -The `gmp_int` backend is used via the typedef `boost::math::mpz_int`. It acts as a thin wrapper around the GMP `mpz_t` +The `gmp_int` backend is used via the typedef `boost::multiprecision::mpz_int`. It acts as a thin wrapper around the GMP `mpz_t` to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. +As well as the usual conversions from arithmetic and string types, type `mpz_int` is copy constructible and asignable from: + +* The GMP native types: `mpf_t`, `mpz_t`, `mpq_t`. +* Instances of `mp_number` that are wrappers around those types: `mp_number >`, `mp_number`. + +It's also possible to access the underlying `mpz_t` via the data() member function of `gmp_int`. + [h5 Example:] - #include + #include - boost::math::mpz_int v = 1; + boost::multiprecision::mpz_int v = 1; // Do some arithmetic: for(unsigned i = 1; i <= 1000; ++i) @@ -66,6 +73,10 @@ to provide an integer type that is a drop-in replacement for the native C++ inte std::cout << i << std::endl; // prints 1000! + // Access the underlying representation: + mpz_t z; + mpz_int(z, v.backend().data()); + [endsect] [section:reals Real Numbers] @@ -74,61 +85,214 @@ The following backends provide real number arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] -[[`gmp_real`][boost/math/big_number/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] +[[`mpf_float`][boost/multiprecision/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] +[[`mpfr_float`][boost/multiprecision/mpfr.hpp][2][GMP and MPFR][Very fast and efficient backend, with it's own standard library implementation.][Dependency on GNU licenced GMP and MPFR libraries.]] +[[`mp_float`][boost/multiprecision/mp_float.hpp][10][None][Header only, all C++ implementation.][Approximately 2x slower than the MPFR or GMP libraries.]] ] -[h4 gmp_real] +[h4 gmp_float] - namespace boost{ namespace math{ + namespace boost{ namespace multiprecision{ template - class gmp_real; + class gmp_float; - typedef big_number > mpf_real_50; - typedef big_number > mpf_real_100; - typedef big_number > mpf_real_500; - typedef big_number > mpf_real_1000; - typedef big_number > mpf_real; + typedef mp_number > mpf_float_50; + typedef mp_number > mpf_float_100; + typedef mp_number > mpf_float_500; + typedef mp_number > mpf_float_1000; + typedef mp_number > mpf_float; }} // namespaces -The `gmp_real` backend is used in conjunction with `big_number`: It acts as a thin wrapper around the GMP `mpf_t` +The `gmp_float` backend is used in conjunction with `mp_number`: It acts as a thin wrapper around the GMP `mpf_t` to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. -Type `gmp_real` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or -at variable precision by setting the template argument to zero. The typedefs mpf_real_50, mpf_real_100, -mpf_real_500, mpf_real_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision -respectively. The typedef mpf_real provides a variable precision type whose precision can be controlled via the -`big_number`'s member functions. +Type `gmp_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or +at variable precision by setting the template argument to zero. The typedefs mpf_float_50, mpf_float_100, +mpf_float_500, mpf_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision +respectively. The typedef mpf_float provides a variable precision type whose precision can be controlled via the +`mp_number`'s member functions. -[h5 example:] +[note This type only provides standard library and numeric_limits support when the precision is fixed at compile time.] - #include +As well as the usual conversions from arithmetic and string types, instances of `mp_number >` are +copy constructible and assignable from: - boost::math::gmp_real a = 2; - boost::math::gmp_real::default_precision(1000); - std::cout << boost::math::gmp_real::default_precision() << std::endl; +* The GMP native types `mpf_t`, `mpz_t`, `mpq_t`. +* The `mp_number` wrappers around those types: `mp_number >`, `mp_number`, `mp_number`. + +It's also possible to access the underlying `mpf_t` via the data() member function of `gmp_float`. + +[h5 GMP example:] + + #include + + // Operations at variable precision and limited standard library support: + boost::multiprecision::gmp_float a = 2; + boost::multiprecision::gmp_float::default_precision(1000); + std::cout << boost::multiprecision::gmp_float::default_precision() << std::endl; std::cout << sqrt(a) << std::endl; // print root-2 + // Operations at fixed precision and full standard library support: + boost::multiprecision::mpf_float_100 b = 2; + std::cout << std::numeric_limits::digits << std::endl; + std::cout << log(b) << std::endl; // print log(2) + + // Access the underlying representation: + mpf_t f; + mpf_init(f, a.backend().data()); + +[h4 mpfr_float] + + namespace boost{ namespace multiprecision{ + + template + class mpfr_float; + + typedef mp_number > mpfr_float_50; + typedef mp_number > mpfr_float_100; + typedef mp_number > mpfr_float_500; + typedef mp_number > mpfr_float_1000; + typedef mp_number > mpfr_float; + + }} // namespaces + +The `mpfr_float` backend is used in conjunction with `mp_number`: It acts as a thin wrapper around the MPFR `mpfr_t` +to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision. + +Type `mpfr_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or +at variable precision by setting the template argument to zero. The typedefs mpfr_float_50, mpfr_float_100, +mpfr_float_500, mpfr_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision +respectively. The typedef mpfr_float provides a variable precision type whose precision can be controlled via the +`mp_number`'s member functions. + +[note This type only provides numeric_limits support when the precision is fixed at compile time.] + +[h5 MPFR example:] + + #include + + // Operations at variable precision and no numeric_limits support: + boost::multiprecision::gmp_float a = 2; + boost::multiprecision::gmp_float::default_precision(1000); + std::cout << boost::multiprecision::gmp_float::default_precision() << std::endl; + std::cout << sqrt(a) << std::endl; // print root-2 + + // Operations at fixed precision and full numeric_limits support: + boost::multiprecision::mpfr_float_100 b = 2; + std::cout << std::numeric_limits::digits << std::endl; + std::cout << log(b) << std::endl; // print log(2) + +[h4 mp_float] + + namespace boost{ namespace multiprecision{ + + template + class mp_float; + + typedef mp_number > mp_float_50; + typedef mp_number > mp_float_100; + + }} // namespaces + +The `mp_float` backend is used in conjunction with `mp_number`: It acts as an entirely C++ (header only and dependency free) +real-number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision. + +Type `mp_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter. +The typedefs mp_float_50 and mp_float_100 provide arithmetic types at 50 and 100 decimal digits precision +respectively. + +There is full standard library and numeric_limits support available for this type. + +[h5 mp_float example:] + + #include + + // Operations at fixed precision and full numeric_limits support: + boost::multiprecision::mp_float_100 b = 2; + std::cout << std::numeric_limits::digits << std::endl; + std::cout << log(b) << std::endl; // print log(2) + +[endsect] + +[section:rational Rational Number Types] + +The following backends provide rational number arithmetic: + +[table +[[Backend Type][Header][Radix][Dependencies][Pros][Cons]] +[[`gmp_rational`][boost/multiprecision/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] +] + +[h4 gmp_rational] + + namespace boost{ namespace multiprecision{ + + class gmp_rational; + + typedef mp_number mpq_rational; + + }} // namespaces + +The `gmp_rational` backend is used via the typedef `boost::multiprecision::mpq_rational`. It acts as a thin wrapper around the GMP `mpq_t` +to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. + +As well as the usual conversions from arithmetic and string types, instances of `mp_number` are copy constructible +and assignable from: + +* The GMP native types: `mpz_t`, `mpq_t`. +* `mp_number`. + +There are also non-member functions: + + mpz_int numerator(const mpq_rational&); + mpz_int denominator(const mpq_rational&); + +Which return the numerator and denominator of the number. + +It's also possible to access the underlying `mpq_t` via the data() member function of `mpq_rational`. + +[h5 Example:] + + #include + + boost::multiprecision::mpq_rational v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + v /= 10; + + std::cout << i << std::endl; // prints 1000! / 10 + std::cout << numerator(i) << std::endl; + std::cout << denominator(i) << std::endl; + + // Access the underlying data: + mpq_t q; + mpq_init(q, i.backend().data()); + [endsect] [endsect] [section:ref Reference] -[section:bignum big_number] +[section:mp_number mp_number] [h4 Synopsis] - namespace boost{ namespace math{ + namespace boost{ namespace multiprecision{ template - class big_number + class mp_number { - big_number(); - big_number(see-below); - big_number& operator=(see-below); + mp_number(); + mp_number(see-below); + mp_number& operator=(see-below); /* Other number-type operators here */ // string conversion: std::string str()const; @@ -138,44 +302,93 @@ respectively. The typedef mpf_real provides a variable precision type whose pre unsigned precision()const; void precision(unsigned digits10); // Comparison: - int compare(const big_number& o)const; + int compare(const mp_number& o)const; template typename enable_if, int>::type compare(const V& o)const; }; + // iostream support: + template + std::ostream& operator << (std::ostream& os, const mp_number& r); + std::ostream& operator << (std::ostream& os, const ``['unmentionable-expression-template-type]``& r); + template + std::istream& operator >> (std::istream& is, mp_number& r); + + // Non-member function standard library support: + ``['unmentionable-expression-template-type]`` abs (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fabs (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sqrt (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` floor (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ceil (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` trunc (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` exp (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cos (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sin (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tan (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` acos (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` asin (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cosh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sinh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tanh (const ``['mp_number-or-expression-template-type]``&); + + ``['unmentionable-expression-template-type]`` ldexp (const ``['mp_number-or-expression-template-type]``&, int); + ``['unmentionable-expression-template-type]`` frexp (const ``['mp_number-or-expression-template-type]``&, int*); + ``['unmentionable-expression-template-type]`` pow (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fmod (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan2 (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); + }} // namespaces + // numeric_limits support: + namespace std{ + + template + struct numeric_limits > + { + /* Usual members here */ + }; + + } + [h4 Description] - big_number(); - big_number(see-below); - big_number& operator=(see-below); + mp_number(); + mp_number(see-below); + mp_number& operator=(see-below); -Type `big_number` is default constructible, and copy both constructible and assignable from: +Type `mp_number` is default constructible, and both copy constructible and assignable from: * Itself. * An expression template which is the result of one of the arithmetic operators. * Any builtin arithmetic type. * A `std::string` or any type which is convertible to `const char*`. +* Any type that the Backend is constructible or assignable from. /* Other number-type operators here */ The following arithmetic operations are support for real-numbered types: -* Binary +, -, *, /, +=, -=, *=, /=, ==, !=, <=, >=, <, >. -* Unary +, -. +* Binary +, -, *, /, +=, -=, *=, /=, ==, !=, <=, >=, <, >, ||, &&, ||=, &&=. +* Unary +, -, ++, --, !. For integer types the following operators are also supported: -Binary %, %=. +Binary %, %=, |, |=, &, &=, ^, ^=, <<, <<=, >>, >>=. -(More to follow!!) +Note that with the exception of the logical operators and unary + the result of applying an operator to +mp_number is an "unmentionable" expression template type. -Note that the result of the binary +, -, *, / and % operations is an expression template of "unmentionable type". +Binary operators, must have at least one argument that is of type `mp_number` or an expression template +derived from `mp_number`. One argument may optionally be of arithmetic type. - std::string str()const; +Note that type `mp_number` (and all expression templates derived from it) may be used in a Boolian context. -Returns the number formatted as a string (TODO: enable custom precision). + std::string str(unsigned precision, bool scientific = true)const; + +Returns the number formatted as a string, with at least /precision/ digits, and in scientific format +if /scientific/ is true. static unsigned default_precision(); static void default_precision(unsigned digits10); @@ -183,9 +396,9 @@ Returns the number formatted as a string (TODO: enable custom precision). void precision(unsigned digits10); These functions are only available if the Backend template parameter supports runtime changes to precision. They get and set -the default precision and the precision of *this respectively. +the default precision and the precision of `*this` respectively. - int compare(const big_number& o)const; + int compare(const mp_number& o)const; template typename enable_if, int>::type compare(const V& other)const; @@ -195,6 +408,69 @@ Returns: * A value greater that 0 for *this > other * Zero for *this == other +[h4 Iostream Support] + + template + std::ostream& operator << (std::ostream& os, const mp_number& r); + template + std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r); + template + inline std::istream& operator >> (std::istream& is, mp_number& r) + +These operators provided formatted input-output operations on `mp_number` types, and expression templates derived from them. + +[h4 Non-member standard library function support] + + ``['unmentionable-expression-template-type]`` abs (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fabs (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sqrt (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` floor (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ceil (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` trunc (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` exp (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cos (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sin (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tan (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` acos (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` asin (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cosh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sinh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tanh (const ``['mp_number-or-expression-template-type]``&); + + ``['unmentionable-expression-template-type]`` ldexp (const ``['mp_number-or-expression-template-type]``&, int); + ``['unmentionable-expression-template-type]`` frexp (const ``['mp_number-or-expression-template-type]``&, int*); + ``['unmentionable-expression-template-type]`` pow (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fmod (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan2 (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); + +These functions all behave exactly as their standard library counterparts do: their argument is either an instance of `mp_number` or +an expression template derived from it; their return value is always an expression template. + +These functions are normally implemented by the Backend type. However, default versions are provided for Backend types that +don't have native support for these functions. Please note however, that this default support requires the precision of the type +to be a compile time constant - this means for example that the GMP MPF Backend will not work with these functions when that type is +used at variable precision. + +Also note that with the exception of `abs` that these functions can only be used with floating point Backend types. + +[h4 std::numeric_limits support] + + namespace std{ + + template + struct numeric_limits > + { + /* Usual members here */ + }; + + } + +Class template `std::numeric_limits` is specialized for all instantiations of `mp_number` whose precision is known at compile time, plus those +types whose precision is unlimited (though it is much less useful in those cases). It is not specialized for types +whose precision can vary at compile time (such as `mpf_float`). + [endsect] [section:backendconc Backend Requirements] diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 16fa8e71..3aaada75 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -236,6 +236,9 @@ protected: } // namespace detail +struct gmp_int; +struct gmp_rational; + template struct gmp_float : public detail::gmp_float_imp { @@ -244,6 +247,37 @@ struct gmp_float : public detail::gmp_float_imp mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } gmp_float(const gmp_float& o) : detail::gmp_float_imp(o) {} + template + gmp_float(const gmp_float& o) + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_set(this->m_data, o.data()); + } + gmp_float(const gmp_int& o) + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_set_z(this->data(), o.data()); + } + gmp_float(const gmp_rational& o) + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_set_q(this->data(), o.data()); + } + gmp_float(mpf_t val) + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_set(this->m_data, val); + } + gmp_float(mpz_t val) + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_set_z(this->m_data, val); + } + gmp_float(mpq_t val) + { + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_set_q(this->m_data, val); + } #ifndef BOOST_NO_RVALUE_REFERENCES gmp_float(gmp_float&& o) : detail::gmp_float_imp(o) {} #endif @@ -259,6 +293,37 @@ struct gmp_float : public detail::gmp_float_imp return *this; } #endif + template + gmp_float& operator=(const gmp_float& o) + { + mpf_set(this->m_data, o.data()); + return *this; + } + gmp_float& operator=(const gmp_int& o) + { + mpf_set_z(this->data(), o.data()); + return *this; + } + gmp_float& operator=(const gmp_rational& o) + { + mpf_set_q(this->data(), o.data()); + return *this; + } + gmp_float& operator=(const mpf_t& val) + { + mpf_set(this->m_data, val); + return *this; + } + gmp_float& operator=(const mpz_t& val) + { + mpf_set_z(this->m_data, val); + return *this; + } + gmp_float& operator=(const mpq_t& val) + { + mpf_set_q(this->m_data, val); + return *this; + } template gmp_float& operator=(const V& v) { @@ -278,14 +343,37 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } + gmp_float(mpf_t val) + { + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_set(this->m_data, val); + } + gmp_float(mpz_t val) + { + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_set_z(this->m_data, val); + } + gmp_float(mpq_t val) + { + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_set_q(this->m_data, val); + } gmp_float(const gmp_float& o) : detail::gmp_float_imp<0>(o) {} + template + gmp_float(const gmp_float& o) + { + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_set(this->m_data, o.data()); + } #ifndef BOOST_NO_RVALUE_REFERENCES gmp_float(gmp_float&& o) : detail::gmp_float_imp<0>(o) {} #endif - gmp_float(const gmp_float& o, unsigned digits10) + gmp_float(const gmp_int& o); + gmp_float(const gmp_rational& o); + gmp_float(const gmp_float& o, unsigned digits10) { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - *this = o; + mpf_set(this->m_data, o.data()); } gmp_float& operator=(const gmp_float& o) @@ -300,6 +388,29 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> return *this; } #endif + template + gmp_float& operator=(const gmp_float& o) + { + mpf_set(this->m_data, o.data()); + return *this; + } + gmp_float& operator=(const gmp_int& o); + gmp_float& operator=(const gmp_rational& o); + gmp_float& operator=(const mpf_t& val) + { + mpf_set(this->m_data, val); + return *this; + } + gmp_float& operator=(const mpz_t& val) + { + mpf_set_z(this->m_data, val); + return *this; + } + gmp_float& operator=(const mpq_t& val) + { + mpf_set_q(this->m_data, val); + return *this; + } template gmp_float& operator=(const V& v) { @@ -702,9 +813,9 @@ inline void eval_frexp(gmp_float& result, const gmp_float& v struct gmp_int { - typedef mpl::list signed_types; + typedef mpl::list signed_types; typedef mpl::list unsigned_types; - typedef mpl::list real_types; + typedef mpl::list real_types; gmp_int() { @@ -714,6 +825,27 @@ struct gmp_int { mpz_init_set(m_data, o.m_data); } + gmp_int(mpf_t val) + { + mpz_init(this->m_data); + mpz_set_f(this->m_data, val); + } + gmp_int(mpz_t val) + { + mpz_init_set(this->m_data, val); + } + gmp_int(mpq_t val) + { + mpz_init(this->m_data); + mpz_set_q(this->m_data, val); + } + template + gmp_int(const gmp_float& o) + { + mpz_init(this->m_data); + mpz_set_f(this->m_data, o.data()); + } + gmp_int(const gmp_rational& o); gmp_int& operator = (const gmp_int& o) { mpz_set(m_data, o.m_data); @@ -812,6 +944,28 @@ struct gmp_int mpz_set_str(m_data, s, 10); return *this; } + gmp_int& operator=(const mpf_t& val) + { + mpz_set_f(this->m_data, val); + return *this; + } + gmp_int& operator=(const mpz_t& val) + { + mpz_set(this->m_data, val); + return *this; + } + gmp_int& operator=(const mpq_t& val) + { + mpz_set_q(this->m_data, val); + return *this; + } + template + gmp_int& operator=(const gmp_float& o) + { + mpz_set_f(this->m_data, o.data()); + return *this; + } + gmp_int& operator=(const gmp_rational& o); void swap(gmp_int& o) { mpz_swap(m_data, o.m_data); @@ -1176,6 +1330,21 @@ struct gmp_rational mpq_init(m_data); mpq_set(m_data, o.m_data); } + gmp_rational(const gmp_int& o) + { + mpq_init(m_data); + mpq_set_z(m_data, o.data()); + } + gmp_rational(mpq_t o) + { + mpq_init(m_data); + mpq_set(m_data, o); + } + gmp_rational(mpz_t o) + { + mpq_init(m_data); + mpq_set_z(m_data, o); + } gmp_rational& operator = (const gmp_rational& o) { mpq_set(m_data, o.m_data); @@ -1276,6 +1445,21 @@ struct gmp_rational mpq_set_str(m_data, s, 10); return *this; } + gmp_rational& operator=(const gmp_int& o) + { + mpq_set_z(m_data, o.data()); + return *this; + } + gmp_rational& operator=(const mpq_t& o) + { + mpq_set(m_data, o); + return *this; + } + gmp_rational& operator=(const mpz_t& o) + { + mpq_set_z(m_data, o); + return *this; + } void swap(gmp_rational& o) { mpq_swap(m_data, o.m_data); @@ -1324,6 +1508,17 @@ protected: mpq_t m_data; }; +inline mp_number numerator(const mp_number& val) +{ + const __mpz_struct* pz = (mpq_numref(val.backend().data())); + return mp_number((mpz_t&)pz); +} +inline mp_number denominator(const mp_number& val) +{ + const __mpz_struct* pz = mpq_denref(val.backend().data()); + return mp_number((mpz_t&)pz); +} + inline void add(gmp_rational& t, const gmp_rational& o) { mpq_add(t.data(), t.data(), o.data()); @@ -1389,6 +1584,41 @@ inline void eval_abs(gmp_rational& result, const gmp_rational& val) mpq_abs(result.data(), val.data()); } +// +// Some member functions that are dependent upon previous code go here: +// +inline gmp_float<0>::gmp_float(const gmp_int& o) +{ + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_set_z(this->data(), o.data()); +} +inline gmp_float<0>::gmp_float(const gmp_rational& o) +{ + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_set_q(this->data(), o.data()); +} +inline gmp_float<0>& gmp_float<0>::operator=(const gmp_int& o) +{ + mpf_set_z(this->data(), o.data()); + return *this; +} +inline gmp_float<0>& gmp_float<0>::operator=(const gmp_rational& o) +{ + mpf_set_q(this->data(), o.data()); + return *this; +} +inline gmp_int::gmp_int(const gmp_rational& o) +{ + mpz_init(this->m_data); + mpz_set_q(this->m_data, o.data()); +} +inline gmp_int& gmp_int::operator=(const gmp_rational& o) +{ + mpz_set_q(this->m_data, o.data()); + return *this; +} + + template<> struct number_category : public mpl::int_{}; template<> @@ -1608,6 +1838,56 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; +template<> +class numeric_limits +{ + typedef boost::multiprecision::mpq_rational number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + // + // Largest and smallest numbers are bounded only by available memory, set + // to zero: + // + BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + { + return number_type(); + } + BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + { + return number_type(); + } + BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return (min)(); } + // Digits are unbounded, use zero for now: + BOOST_STATIC_CONSTEXPR int digits = 0; + BOOST_STATIC_CONSTEXPR int digits10 = 0; + BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = true; + BOOST_STATIC_CONSTEXPR int radix = 2; + BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = false; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + #ifdef BOOST_NO_NOEXCEPT # undef noexcept #endif diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 3ca21f55..5a9aebc2 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -43,6 +43,11 @@ public: m_backend.precision(digits10); m_backend = canonical_value(v); } + template + mp_number(const mp_number& val, typename enable_if >::type* dummy1 = 0) + { + m_backend = val.backend(); + } template mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* dummy1 = 0) @@ -69,6 +74,22 @@ public: return *this; } + template + typename enable_if, mpl::not_, is_same, is_convertible > > >, mp_number& >::type + operator=(const V& v) + { + m_backend = v; + return *this; + } + + template + typename enable_if, mp_number& >::type + operator=(const mp_number& v) + { + m_backend = v.backend(); + return *this; + } + template mp_number(const detail::mp_exp& e) { From 8d23cca8cb01e791792b5f2dea3ba81bb922d235 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 2 Nov 2011 17:15:46 +0000 Subject: [PATCH 051/256] Add mpfr inter-conversions. Fix numerator/denominator for rational types. [SVN r75277] --- include/boost/multiprecision/gmp.hpp | 10 +- include/boost/multiprecision/mpfr.hpp | 169 ++++++++++++++++++++++++++ 2 files changed, 175 insertions(+), 4 deletions(-) diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 3aaada75..c0390c06 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1510,13 +1510,15 @@ protected: inline mp_number numerator(const mp_number& val) { - const __mpz_struct* pz = (mpq_numref(val.backend().data())); - return mp_number((mpz_t&)pz); + mp_number result; + mpz_set(result.backend().data(), (mpq_numref(val.backend().data()))); + return result; } inline mp_number denominator(const mp_number& val) { - const __mpz_struct* pz = mpq_denref(val.backend().data()); - return mp_number((mpz_t&)pz); + mp_number result; + mpz_set(result.backend().data(), (mpq_denref(val.backend().data()))); + return result; } inline void add(gmp_rational& t, const gmp_rational& o) diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index bf478e42..47b20140 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -7,6 +7,7 @@ #define BOOST_MATH_BN_MPFR_HPP #include +#include #include #include #include @@ -244,6 +245,48 @@ struct mpfr_float_backend : public detail::mpfr_float_imp #ifndef BOOST_NO_RVALUE_REFERENCES mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp(o) {} #endif + template + mpfr_float_backend(const mpfr_float_backend& val) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_set(this->m_data, val.data(), GMP_RNDN); + } + template + mpfr_float_backend(const gmp_float& val) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_set_f(this->m_data, val.data(), GMP_RNDN); + } + mpfr_float_backend(const gmp_int& val) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_set_z(this->m_data, val.data(), GMP_RNDN); + } + mpfr_float_backend(const gmp_rational& val) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_set_q(this->m_data, val.data(), GMP_RNDN); + } + mpfr_float_backend(mpfr_t val) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_set(this->m_data, val, GMP_RNDN); + } + mpfr_float_backend(mpf_t val) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_set_f(this->m_data, val, GMP_RNDN); + } + mpfr_float_backend(mpz_t val) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_set_z(this->m_data, val, GMP_RNDN); + } + mpfr_float_backend(mpq_t val) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_set_q(this->m_data, val, GMP_RNDN); + } mpfr_float_backend& operator=(const mpfr_float_backend& o) { *static_cast*>(this) = static_cast const&>(o); @@ -262,6 +305,48 @@ struct mpfr_float_backend : public detail::mpfr_float_imp *static_cast*>(this) = v; return *this; } + mpfr_float_backend& operator=(const mpfr_t& val) + { + mpfr_set(this->m_data, val, GMP_RNDN); + return *this; + } + mpfr_float_backend& operator=(const mpf_t& val) + { + mpfr_set_f(this->m_data, val, GMP_RNDN); + return *this; + } + mpfr_float_backend& operator=(const mpz_t& val) + { + mpfr_set_z(this->m_data, val, GMP_RNDN); + return *this; + } + mpfr_float_backend& operator=(const mpq_t& val) + { + mpfr_set_q(this->m_data, val, GMP_RNDN); + return *this; + } + template + mpfr_float_backend& operator=(const mpfr_float_backend& val) + { + mpfr_set(this->m_data, val.data(), GMP_RNDN); + return *this; + } + template + mpfr_float_backend& operator=(const gmp_float& val) + { + mpfr_set_f(this->m_data, val.data(), GMP_RNDN); + return *this; + } + mpfr_float_backend& operator=(const gmp_int& val) + { + mpfr_set_z(this->m_data, val.data(), GMP_RNDN); + return *this; + } + mpfr_float_backend& operator=(const gmp_rational& val) + { + mpfr_set_q(this->m_data, val.data(), GMP_RNDN); + return *this; + } }; template <> @@ -275,6 +360,26 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> { mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); } + mpfr_float_backend(mpfr_t val) + { + mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_set(this->m_data, val, GMP_RNDN); + } + mpfr_float_backend(mpf_t val) + { + mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_set_f(this->m_data, val, GMP_RNDN); + } + mpfr_float_backend(mpz_t val) + { + mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_set_z(this->m_data, val, GMP_RNDN); + } + mpfr_float_backend(mpq_t val) + { + mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_set_q(this->m_data, val, GMP_RNDN); + } mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp<0>(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp<0>(o) {} @@ -284,6 +389,28 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); *this = o; } + template + mpfr_float_backend(const mpfr_float_backend& val) + { + mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_set(this->m_data, val.data(), GMP_RNDN); + } + template + mpfr_float_backend(const gmp_float& val) + { + mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_set_f(this->m_data, val.data(), GMP_RNDN); + } + mpfr_float_backend(const gmp_int& val) + { + mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_set_z(this->m_data, val.data(), GMP_RNDN); + } + mpfr_float_backend(const gmp_rational& val) + { + mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_set_q(this->m_data, val.data(), GMP_RNDN); + } mpfr_float_backend& operator=(const mpfr_float_backend& o) { @@ -303,6 +430,48 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> *static_cast*>(this) = v; return *this; } + mpfr_float_backend& operator=(const mpfr_t& val) + { + mpfr_set(this->m_data, val, GMP_RNDN); + return *this; + } + mpfr_float_backend& operator=(const mpf_t& val) + { + mpfr_set_f(this->m_data, val, GMP_RNDN); + return *this; + } + mpfr_float_backend& operator=(const mpz_t& val) + { + mpfr_set_z(this->m_data, val, GMP_RNDN); + return *this; + } + mpfr_float_backend& operator=(const mpq_t& val) + { + mpfr_set_q(this->m_data, val, GMP_RNDN); + return *this; + } + template + mpfr_float_backend& operator=(const mpfr_float_backend& val) + { + mpfr_set(this->m_data, val.data(), GMP_RNDN); + return *this; + } + template + mpfr_float_backend& operator=(const gmp_float& val) + { + mpfr_set_f(this->m_data, val.data(), GMP_RNDN); + return *this; + } + mpfr_float_backend& operator=(const gmp_int& val) + { + mpfr_set_z(this->m_data, val.data(), GMP_RNDN); + return *this; + } + mpfr_float_backend& operator=(const gmp_rational& val) + { + mpfr_set_q(this->m_data, val.data(), GMP_RNDN); + return *this; + } static unsigned default_precision() { return get_default_precision(); From 1c6577b5a65caef7d661249f8d6f008d01391bed Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 2 Nov 2011 18:15:00 +0000 Subject: [PATCH 052/256] Add conversion tests and update docs. [SVN r75279] --- doc/multiprecision.qbk | 43 ++++++++--- test/Jamfile.v2 | 13 ++++ test/test_gmp_conversions.cpp | 131 +++++++++++++++++++++++++++++++++ test/test_mpfr_conversions.cpp | 104 ++++++++++++++++++++++++++ 4 files changed, 280 insertions(+), 11 deletions(-) create mode 100644 test/test_gmp_conversions.cpp create mode 100644 test/test_mpfr_conversions.cpp diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 87ebc540..bab92aa3 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -115,7 +115,7 @@ mpf_float_500, mpf_float_1000 provide arithmetic types at 50, 100, 500 and 1000 respectively. The typedef mpf_float provides a variable precision type whose precision can be controlled via the `mp_number`'s member functions. -[note This type only provides standard library and numeric_limits support when the precision is fixed at compile time.] +[note This type only provides standard library and `numeric_limits` support when the precision is fixed at compile time.] As well as the usual conversions from arithmetic and string types, instances of `mp_number >` are copy constructible and assignable from: @@ -149,27 +149,36 @@ It's also possible to access the underlying `mpf_t` via the data() member functi namespace boost{ namespace multiprecision{ template - class mpfr_float; + class mpfr_float_backend; - typedef mp_number > mpfr_float_50; - typedef mp_number > mpfr_float_100; - typedef mp_number > mpfr_float_500; - typedef mp_number > mpfr_float_1000; - typedef mp_number > mpfr_float; + typedef mp_number > mpfr_float_50; + typedef mp_number > mpfr_float_100; + typedef mp_number > mpfr_float_500; + typedef mp_number > mpfr_float_1000; + typedef mp_number > mpfr_float; }} // namespaces -The `mpfr_float` backend is used in conjunction with `mp_number`: It acts as a thin wrapper around the MPFR `mpfr_t` +The `mpfr_float_backend` type is used in conjunction with `mp_number`: It acts as a thin wrapper around the MPFR `mpfr_t` to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. -Type `mpfr_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or +Type `mpfr_float_backend` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or at variable precision by setting the template argument to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision respectively. The typedef mpfr_float provides a variable precision type whose precision can be controlled via the `mp_number`'s member functions. -[note This type only provides numeric_limits support when the precision is fixed at compile time.] +[note This type only provides `numeric_limits` support when the precision is fixed at compile time.] + +As well as the usual conversions from arithmetic and string types, instances of `mp_number >` are +copy constructible and assignable from: + +* The GMP native types `mpf_t`, `mpz_t`, `mpq_t`. +* The MPFR native type `mpfr_t`. +* The `mp_number` wrappers around those types: `mp_number >`, `mp_number >`, `mp_number`, `mp_number`. + +It's also possible to access the underlying `mpf_t` via the data() member function of `gmp_float`. [h5 MPFR example:] @@ -186,6 +195,10 @@ respectively. The typedef mpfr_float provides a variable precision type whose p std::cout << std::numeric_limits::digits << std::endl; std::cout << log(b) << std::endl; // print log(2) + // Access the underlying data: + mpfr_t r; + mpfr_set(r, b.backend().data()); + [h4 mp_float] namespace boost{ namespace multiprecision{ @@ -206,7 +219,7 @@ Type `mp_float` can be used at fixed precision by specifying a non-zero `Digits1 The typedefs mp_float_50 and mp_float_100 provide arithmetic types at 50 and 100 decimal digits precision respectively. -There is full standard library and numeric_limits support available for this type. +There is full standard library and `numeric_limits` support available for this type. [h5 mp_float example:] @@ -305,6 +318,9 @@ It's also possible to access the underlying `mpq_t` via the data() member functi int compare(const mp_number& o)const; template typename enable_if, int>::type compare(const V& o)const; + // Access to the underlying implementation: + Backend& backend(); + const Backend& backend()const; }; // iostream support: @@ -408,6 +424,11 @@ Returns: * A value greater that 0 for *this > other * Zero for *this == other + Backend& backend(); + const Backend& backend()const; + +Returns the underlying backend instance used by *this. + [h4 Iostream Support] template diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index e2da4d0d..889804ca 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -426,3 +426,16 @@ run test_atan.cpp mpfr TEST_MPFR_50 [ check-target-builds ../config//has_mpfr : : no ] : test_atan_mpfr_50 ; + +run test_gmp_conversions.cpp gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : no ] ; + +run test_mpfr_conversions.cpp gmp mpfr + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_mpfr : : no ] ; + diff --git a/test/test_gmp_conversions.cpp b/test/test_gmp_conversions.cpp new file mode 100644 index 00000000..a2e30a7f --- /dev/null +++ b/test/test_gmp_conversions.cpp @@ -0,0 +1,131 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include +#include "test.hpp" + +#include + +int main() +{ + using namespace boost::multiprecision; + // + // Test interconversions between GMP supported backends: + // + mpf_t mpf; + mpz_t mpz; + mpq_t mpq; + mpf_init2(mpf, 100); + mpf_set_ui(mpf, 2u); + mpz_init(mpz); + mpz_set_ui(mpz, 2u); + mpq_init(mpq); + mpq_set_ui(mpq, 2u, 1u); + + BOOST_TEST(mpf_float(mpf) == 2); + BOOST_TEST(mpf_float_50(mpf) == 2); + BOOST_TEST(mpf_float(mpz) == 2); + BOOST_TEST(mpf_float_50(mpz) == 2); + BOOST_TEST(mpf_float(mpq) == 2); + BOOST_TEST(mpf_float_50(mpq) == 2); + + mpf_float f0; + mpf_float_50 f50; + f0 = mpf; + BOOST_TEST(f0 == 2); + f0 = 0; + f0 = mpz; + BOOST_TEST(f0 == 2); + f0 = 0; + f0 = mpq; + BOOST_TEST(f0 == 2); + + f50 = mpf; + BOOST_TEST(f50 == 2); + f50 = 0; + f50 = mpz; + BOOST_TEST(f50 == 2); + f50 = 0; + f50 = mpq; + BOOST_TEST(f50 == 2); + + f50 = 4; + f0 = f50; + BOOST_TEST(f0 == 4); + f0 = 3; + f50 = f0; + BOOST_TEST(f50 == 3); + f50 = 4; + BOOST_TEST(mpf_float(f50) == 4); + BOOST_TEST(mpf_float_50(f0) == 3); + + mpz_int iz(2); + mpq_rational rat(2); + f50 = iz; + BOOST_TEST(f50 == 2); + f0 = iz; + BOOST_TEST(f0 == 2); + BOOST_TEST(mpf_float(iz) == 2); + BOOST_TEST(mpf_float_50(iz) == 2); + BOOST_TEST(mpf_float(rat) == 2); + BOOST_TEST(mpf_float_50(rat) == 2); + + BOOST_TEST(mpz_int(mpf) == 2); + BOOST_TEST(mpz_int(mpz) == 2); + BOOST_TEST(mpz_int(mpq) == 2); + iz = 3; + iz = mpf; + BOOST_TEST(iz == 2); + iz = 3; + iz = mpz; + BOOST_TEST(iz == 2); + iz = 4; + iz = mpq; + BOOST_TEST(iz == 2); + f0 = 2; + f50 = 2; + BOOST_TEST(mpz_int(f0) == 2); + BOOST_TEST(mpz_int(f50) == 2); + rat = 2; + BOOST_TEST(mpz_int(rat) == 2); + iz = 3; + iz = f0; + BOOST_TEST(iz == 2); + iz = 3; + iz = f50; + BOOST_TEST(iz == 2); + iz = 3; + iz = rat; + BOOST_TEST(iz == 2); + + BOOST_TEST(mpq_rational(mpz) == 2); + BOOST_TEST(mpq_rational(mpq) == 2); + BOOST_TEST(mpq_rational(iz) == 2); + rat = 3; + rat = mpz; + BOOST_TEST(rat == 2); + rat = 3; + rat = mpq; + BOOST_TEST(rat == 2); + rat = 3; + rat = iz; + BOOST_TEST(rat == 2); + + iz = numerator(rat); + BOOST_TEST(iz == 2); + iz = denominator(rat); + BOOST_TEST(iz == 1); + + return boost::report_errors(); +} + + + diff --git a/test/test_mpfr_conversions.cpp b/test/test_mpfr_conversions.cpp new file mode 100644 index 00000000..3340697d --- /dev/null +++ b/test/test_mpfr_conversions.cpp @@ -0,0 +1,104 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include +#include "test.hpp" + +#include +#include + +int main() +{ + using namespace boost::multiprecision; + // + // Test interconversions between GMP supported backends: + // + mpf_t mpf; + mpz_t mpz; + mpq_t mpq; + mpfr_t mpfr; + mpf_init2(mpf, 100); + mpf_set_ui(mpf, 2u); + mpz_init(mpz); + mpz_set_ui(mpz, 2u); + mpq_init(mpq); + mpq_set_ui(mpq, 2u, 1u); + mpfr_init(mpfr); + mpfr_set_ui(mpfr, 2u, GMP_RNDN); + + BOOST_TEST(mpfr_float(mpf) == 2); + BOOST_TEST(mpfr_float_50(mpf) == 2); + BOOST_TEST(mpfr_float(mpz) == 2); + BOOST_TEST(mpfr_float_50(mpz) == 2); + BOOST_TEST(mpfr_float(mpq) == 2); + BOOST_TEST(mpfr_float_50(mpq) == 2); + BOOST_TEST(mpfr_float(mpfr) == 2); + BOOST_TEST(mpfr_float_50(mpfr) == 2); + + mpfr_float f0; + mpfr_float_50 f50; + f0 = mpf; + BOOST_TEST(f0 == 2); + f0 = 0; + f0 = mpz; + BOOST_TEST(f0 == 2); + f0 = 0; + f0 = mpq; + BOOST_TEST(f0 == 2); + f0 = mpfr; + BOOST_TEST(f0 == 2); + + f50 = mpf; + BOOST_TEST(f50 == 2); + f50 = 0; + f50 = mpz; + BOOST_TEST(f50 == 2); + f50 = 0; + f50 = mpq; + BOOST_TEST(f50 == 2); + f50 = mpfr; + BOOST_TEST(f50 == 2); + + f50 = 4; + f0 = f50; + BOOST_TEST(f0 == 4); + f0 = 3; + f50 = f0; + BOOST_TEST(f50 == 3); + f50 = 4; + BOOST_TEST(mpfr_float(f50) == 4); + BOOST_TEST(mpfr_float_50(f0) == 3); + + mpz_int iz(2); + mpq_rational rat(2); + mpf_float gf(2); + f50 = 3; + f50 = iz; + BOOST_TEST(f50 == 2); + f50 = 3; + f0 = iz; + BOOST_TEST(f0 == 2); + f50 = 3; + f0 = gf; + BOOST_TEST(f0 == 2); + BOOST_TEST(mpfr_float(iz) == 2); + BOOST_TEST(mpfr_float_50(iz) == 2); + BOOST_TEST(mpfr_float(rat) == 2); + BOOST_TEST(mpfr_float_50(rat) == 2); + BOOST_TEST(mpfr_float(gf) == 2); + BOOST_TEST(mpfr_float_50(gf) == 2); + + + return boost::report_errors(); +} + + + From 6e009f3029dc15fc68594c09a762ce323e51c368 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 3 Nov 2011 11:06:05 +0000 Subject: [PATCH 053/256] Fix gcc warnings and errors. Update docs. [SVN r75284] --- doc/multiprecision.qbk | 76 +- example/gmp_snips.cpp | 88 ++ example/mp_float_snips.cpp | 28 + example/mpfr_snips.cpp | 41 + include/boost/multiprecision/gmp.hpp | 74 +- include/boost/multiprecision/mp_float.hpp | 10 +- include/boost/multiprecision/mpfr.hpp | 2 +- test/Jamfile.v2 | 13 + test/test_cos.cpp | 2 +- test/test_pow.cpp | 1000 ++++++++++----------- test/test_sin.cpp | 2 +- 11 files changed, 731 insertions(+), 605 deletions(-) create mode 100644 example/gmp_snips.cpp create mode 100644 example/mp_float_snips.cpp create mode 100644 example/mpfr_snips.cpp diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index bab92aa3..a585f353 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -18,6 +18,10 @@ [last-revision $Date: 2011-07-08 18:51:46 +0100 (Fri, 08 Jul 2011) $] ] +[import ../example/gmp_snips.cpp] +[import ../example/mpfr_snips.cpp] +[import ../example/mp_float_snips.cpp] + [section:intro Introduction] The Multiprecision library comes in two distinct parts: an expression template enabled front end `mp_number` @@ -63,19 +67,7 @@ It's also possible to access the underlying `mpz_t` via the data() member functi [h5 Example:] - #include - - boost::multiprecision::mpz_int v = 1; - - // Do some arithmetic: - for(unsigned i = 1; i <= 1000; ++i) - v *= i; - - std::cout << i << std::endl; // prints 1000! - - // Access the underlying representation: - mpz_t z; - mpz_int(z, v.backend().data()); +[mpz_eg] [endsect] @@ -127,22 +119,7 @@ It's also possible to access the underlying `mpf_t` via the data() member functi [h5 GMP example:] - #include - - // Operations at variable precision and limited standard library support: - boost::multiprecision::gmp_float a = 2; - boost::multiprecision::gmp_float::default_precision(1000); - std::cout << boost::multiprecision::gmp_float::default_precision() << std::endl; - std::cout << sqrt(a) << std::endl; // print root-2 - - // Operations at fixed precision and full standard library support: - boost::multiprecision::mpf_float_100 b = 2; - std::cout << std::numeric_limits::digits << std::endl; - std::cout << log(b) << std::endl; // print log(2) - - // Access the underlying representation: - mpf_t f; - mpf_init(f, a.backend().data()); +[mpf_eg] [h4 mpfr_float] @@ -182,22 +159,7 @@ It's also possible to access the underlying `mpf_t` via the data() member functi [h5 MPFR example:] - #include - - // Operations at variable precision and no numeric_limits support: - boost::multiprecision::gmp_float a = 2; - boost::multiprecision::gmp_float::default_precision(1000); - std::cout << boost::multiprecision::gmp_float::default_precision() << std::endl; - std::cout << sqrt(a) << std::endl; // print root-2 - - // Operations at fixed precision and full numeric_limits support: - boost::multiprecision::mpfr_float_100 b = 2; - std::cout << std::numeric_limits::digits << std::endl; - std::cout << log(b) << std::endl; // print log(2) - - // Access the underlying data: - mpfr_t r; - mpfr_set(r, b.backend().data()); +[mpfr_eg] [h4 mp_float] @@ -223,12 +185,7 @@ There is full standard library and `numeric_limits` support available for this t [h5 mp_float example:] - #include - - // Operations at fixed precision and full numeric_limits support: - boost::multiprecision::mp_float_100 b = 2; - std::cout << std::numeric_limits::digits << std::endl; - std::cout << log(b) << std::endl; // print log(2) +[mp_float_eg] [endsect] @@ -271,22 +228,7 @@ It's also possible to access the underlying `mpq_t` via the data() member functi [h5 Example:] - #include - - boost::multiprecision::mpq_rational v = 1; - - // Do some arithmetic: - for(unsigned i = 1; i <= 1000; ++i) - v *= i; - v /= 10; - - std::cout << i << std::endl; // prints 1000! / 10 - std::cout << numerator(i) << std::endl; - std::cout << denominator(i) << std::endl; - - // Access the underlying data: - mpq_t q; - mpq_init(q, i.backend().data()); +[mpq_eg] [endsect] diff --git a/example/gmp_snips.cpp b/example/gmp_snips.cpp new file mode 100644 index 00000000..cf763fa2 --- /dev/null +++ b/example/gmp_snips.cpp @@ -0,0 +1,88 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include + +void t1() +{ + //[mpz_eg + //=#include + + using namespace boost::multiprecision; + + mpz_int v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + + std::cout << v << std::endl; // prints 1000! + + // Access the underlying representation: + mpz_t z; + mpz_init(z); + mpz_set(z, v.backend().data()); + //] +} + +void t2() +{ + //[mpf_eg + //=#include + + using namespace boost::multiprecision; + + // Operations at variable precision and limited standard library support: + mpf_float a = 2; + mpf_float::default_precision(1000); + std::cout << mpf_float::default_precision() << std::endl; + std::cout << sqrt(a) << std::endl; // print root-2 + + // Operations at fixed precision and full standard library support: + mpf_float_100 b = 2; + std::cout << std::numeric_limits::digits << std::endl; + std::cout << log(b) << std::endl; // print log(2) + + // Access the underlying representation: + mpf_t f; + mpf_init(f); + mpf_set(f, a.backend().data()); + //] +} + +void t3() +{ + //[mpq_eg + //=#include + + using namespace boost::multiprecision; + + mpq_rational v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + v /= 10; + + std::cout << v << std::endl; // prints 1000! / 10 + std::cout << numerator(v) << std::endl; + std::cout << denominator(v) << std::endl; + + // Access the underlying data: + mpq_t q; + mpq_init(q); + mpq_set(q, v.backend().data()); + //] +} + +int main() +{ + t1(); + t2(); + t3(); + return 0; +} + diff --git a/example/mp_float_snips.cpp b/example/mp_float_snips.cpp new file mode 100644 index 00000000..0b2df0d0 --- /dev/null +++ b/example/mp_float_snips.cpp @@ -0,0 +1,28 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include + +void t1() +{ + //[mp_float_eg + //=#include + + using namespace boost::multiprecision; + + // Operations at fixed precision and full numeric_limits support: + mp_float_100 b = 2; + std::cout << std::numeric_limits::digits << std::endl; + std::cout << log(b) << std::endl; // print log(2) + //] +} + +int main() +{ + t1(); + return 0; +} + diff --git a/example/mpfr_snips.cpp b/example/mpfr_snips.cpp new file mode 100644 index 00000000..3eaf6f31 --- /dev/null +++ b/example/mpfr_snips.cpp @@ -0,0 +1,41 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include + +void t1() +{ + //[mpfr_eg + //=#include + + using namespace boost::multiprecision; + + // Operations at variable precision and no numeric_limits support: + mpfr_float a = 2; + mpfr_float::default_precision(1000); + std::cout << mpfr_float::default_precision() << std::endl; + std::cout << sqrt(a) << std::endl; // print root-2 + + // Operations at fixed precision and full numeric_limits support: + mpfr_float_100 b = 2; + std::cout << std::numeric_limits::digits << std::endl; + std::cout << log(b) << std::endl; // print log(2) + + // Access the underlying data: + mpfr_t r; + mpfr_init(r); + mpfr_set(r, b.backend().data(), GMP_RNDN); + //] +} + +int main() +{ + t1(); + return 0; +} + + + diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index c0390c06..13ac14c3 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -248,21 +248,9 @@ struct gmp_float : public detail::gmp_float_imp } gmp_float(const gmp_float& o) : detail::gmp_float_imp(o) {} template - gmp_float(const gmp_float& o) - { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - mpf_set(this->m_data, o.data()); - } - gmp_float(const gmp_int& o) - { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - mpf_set_z(this->data(), o.data()); - } - gmp_float(const gmp_rational& o) - { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - mpf_set_q(this->data(), o.data()); - } + gmp_float(const gmp_float& o); + gmp_float(const gmp_int& o); + gmp_float(const gmp_rational& o); gmp_float(mpf_t val) { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); @@ -294,21 +282,9 @@ struct gmp_float : public detail::gmp_float_imp } #endif template - gmp_float& operator=(const gmp_float& o) - { - mpf_set(this->m_data, o.data()); - return *this; - } - gmp_float& operator=(const gmp_int& o) - { - mpf_set_z(this->data(), o.data()); - return *this; - } - gmp_float& operator=(const gmp_rational& o) - { - mpf_set_q(this->data(), o.data()); - return *this; - } + gmp_float& operator=(const gmp_float& o); + gmp_float& operator=(const gmp_int& o); + gmp_float& operator=(const gmp_rational& o); gmp_float& operator=(const mpf_t& val) { mpf_set(this->m_data, val); @@ -1589,6 +1565,44 @@ inline void eval_abs(gmp_rational& result, const gmp_rational& val) // // Some member functions that are dependent upon previous code go here: // +template +template +inline gmp_float::gmp_float(const gmp_float& o) +{ + mpf_init2(this->m_data, ((Digits10 + 1) * 1000L) / 301L); + mpf_set(this->m_data, o.data()); +} +template +inline gmp_float::gmp_float(const gmp_int& o) +{ + mpf_init2(this->m_data, ((Digits10 + 1) * 1000L) / 301L); + mpf_set_z(this->data(), o.data()); +} +template +inline gmp_float::gmp_float(const gmp_rational& o) +{ + mpf_init2(this->m_data, ((Digits10 + 1) * 1000L) / 301L); + mpf_set_q(this->data(), o.data()); +} +template +template +inline gmp_float& gmp_float::operator=(const gmp_float& o) +{ + mpf_set(this->m_data, o.data()); + return *this; +} +template +inline gmp_float& gmp_float::operator=(const gmp_int& o) +{ + mpf_set_z(this->data(), o.data()); + return *this; +} +template +inline gmp_float& gmp_float::operator=(const gmp_rational& o) +{ + mpf_set_q(this->data(), o.data()); + return *this; +} inline gmp_float<0>::gmp_float(const gmp_int& o) { mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); diff --git a/include/boost/multiprecision/mp_float.hpp b/include/boost/multiprecision/mp_float.hpp index df932965..e75ed494 100644 --- a/include/boost/multiprecision/mp_float.hpp +++ b/include/boost/multiprecision/mp_float.hpp @@ -1173,19 +1173,19 @@ mp_float& mp_float::calculate_sqrt(void) // http://www.jjj.de/pibook/pibook.html // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846 - static const boost::int32_t double_digits10_minus_one = static_cast(static_cast(Digits10) - static_cast(1)); + static const boost::uint32_t double_digits10_minus_one = static_cast(static_cast(Digits10) - static_cast(1)); - for(boost::int32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= static_cast(2)) + for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= 2u) { // Adjust precision of the terms. - precision(static_cast(digits * static_cast(2))); - vi.precision(static_cast(digits * static_cast(2))); + precision(digits * 2); + vi.precision(digits * 2); // Next iteration of vi mp_float t(*this); t *= vi; t.negate(); - t.mul_unsigned_long_long(2); + t.mul_unsigned_long_long(2u); t += one(); t *= vi; vi += t; diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 47b20140..667f0ea1 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -398,7 +398,7 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> template mpfr_float_backend(const gmp_float& val) { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); mpfr_set_f(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend(const gmp_int& val) diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 889804ca..9ee8b530 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -439,3 +439,16 @@ run test_mpfr_conversions.cpp gmp mpfr : # requirements [ check-target-builds ../config//has_mpfr : : no ] ; +run ../example/gmp_snips.cpp gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : no ] ; + +run ../example/mpfr_snips.cpp mpfr + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_mpfr : : no ] ; + +run ../example/mp_float_snips.cpp ; diff --git a/test/test_cos.cpp b/test/test_cos.cpp index 2e5dcf48..53374292 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -166,7 +166,7 @@ void test() max_err = err; } std::cout << "Max error was: " << max_err << std::endl; - BOOST_TEST(max_err < 5000000000L); + BOOST_TEST(max_err < 5000000000ULL); static const boost::array near_one = {{ diff --git a/test/test_pow.cpp b/test/test_pow.cpp index 38181241..a8ba5495 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -46,506 +46,506 @@ void test() { static const boost::array, 500> data = {{ - { static_cast("9.85291419463953934609889984130859375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e4"), 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5000000000); + BOOST_TEST(max_err < 5000000000uLL); static const boost::array small_data = {{ From fb0acf68724fc5ba306833b04b60bfb6e1a18953 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 5 Nov 2011 18:22:18 +0000 Subject: [PATCH 054/256] Add performance test comparison. Update docs some more. Remove dead code in mp_number.hpp. [SVN r75324] --- doc/multiprecision.qbk | 156 +++++++++- include/boost/multiprecision/mp_number.hpp | 9 - performance/sf_performance.cpp | 321 +++++++++++++++++++++ 3 files changed, 476 insertions(+), 10 deletions(-) create mode 100644 performance/sf_performance.cpp diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index a585f353..2f8dfe1e 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -24,11 +24,165 @@ [section:intro Introduction] -The Multiprecision library comes in two distinct parts: an expression template enabled front end `mp_number` +The Multiprecision library comes in two distinct parts: an expression-template-enabled front end `mp_number` that handles all the operator overloading, expression evaluation optimization, and code reduction, and a selection of backends that implement the actual arithmetic operations, and need conform only to the reduced interface requirements of the front end. +The library is often used by using one of the predfined typedefs: for example if you wanted an arbitrary precision +integer type using GMP as the underlying implementation then you could use: + + #include // Defines the wrappers around the GMP library's types + + boost::multiprecision::mpz_int myint; // Arbitrary precision integer type. + +Alternatively one can compose your own multiprecision type, by combining `mp_number` with one of the +predefined backend types. For example, suppose you wanted a 300 decimal digit floating point type +based on the MPFR library, in this case there's no predefined typedef with that level of precision, +so instead we compose our own: + + #include // Defines the Backend type that wraps MPFR + + namespace mp = boost::multiprecision; // Reduce the typing a bit later... + + typedef mp::mp_number > my_float; + + my_float a, b, c; // These variables have 300 decimal digits precision + +[h4 Expression Templates] + +Class `mp_number` is expression-template-enabled: that means that rather than having a multiplication +operator that looks like this: + + template + mp_number operator * (const mp_number& a, const mp_number& b) + { + mp_number result(a); + result *= b; + return result; + } + +Instead the operator looks more like this: + + template + ``['unmentionable-type]`` operator * (const mp_number& a, const mp_number& b); + +Where the "unmentionable" return type is an implementation detail that, rather than containing the result +of the multiplication, contains instructions on how to compute the result. In effect it's just a pair +of references to the arguments of the function, plus some compile-time information that stores what the operation +is. + +The great advantage of this method is the ['elimination of temporaries]: for example the "naive" implementation +of `operator*` above, requires one temporary for computing the result, and at least another one to return it. It's true +that sometimes this overhead can be reduced by using move-semantics, but it can't be eliminated completely. For example, +lets suppose we're evaluating a polynomial via Horners method, something like this: + + T a[7] = { /* some values */ }; + //.... + y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; + +If type `T` is an `mp_number`, then this expression is evaluated ['without creating a single temporary value], in contrast +if we were using the C++ wrapper that ships with GMP - `mpf_class` - then this expression would result in no less than 11 +temporaries (this is true even though mpf_class does use expression templates to reduce the number of temporaries somewhat). Had +we used an even simpler wrapper around GMP or MPFR like `mpclass` things would have been even worse and no less that 24 temporaries +are created for this simple expression (note - we actually measure the number of memory allocations performed rather than +the number of temporaries directly). + +This library also extends expression template support to standard library functions like `abs` or `sin` with `mp_number` +arguments. This means that an expression such as: + + y = abs(x); + +can be evaluated without a single temporary being calculated. Even expressions like: + + y = sin(x); + +get this treatment, so that variable 'y' is used as "working storage" within the implementation of `sin`, +thus reducing the number of temporaries used by one. Of course, should you write: + + x = sin(x); + +Then we clearly can't use `x` as working storage during the calculation, so then a temporary variable +is created in this case. + +Given the comments above, you might be forgiven for thinking that expression-templates are some kind of universal-panacea: +sadly though, all tricks like this have their downsides. For one thing, expression template libraries +like this one, tend to be slower to compile than their simpler cousins, they're also harder to debug +(should you actually want to step through our code!), and rely on compiler optimizations being turned +on to give really good performance. Also since the return type from expressions involving `mp_number`'s +is an "unmentionable implementation detail", you have to be careful to cast the result of an expression +to the actual number type when passing an expression to a template function. For example given: + + template + void my_proc(const T&); + +Then calling: + + my_proc(a+b); + +Will very likely result in obscure error messages inside the body of `my_proc` - since we've passed it +an expression template type, and not a number type. Instead we probably need: + + my_proc(my_mp_number_type(a+b)); + +Having said that, these situations don't occur that often - or indeed not at all for non-template functions. +In addition all the functions in the Boost.Math library will automatically convert expression-template arguments +to the underlying number type without you having to do anything, so: + + mpfr_float_100 a(20), delta(0.125); + boost::math::gamma_p(a, a + delta); + +Will work just fine, with the `a + delta` expression template argument getting converted to an `mpfr_float_100` +internally by the Boost.Math library. + +One other potential pitfall that's only possible in C++11: you should never store an expression template using: + + auto my_expression = a + b - c; + +Unless you're absolutely sure that the lifetimes of `a`, `b` and `c` will outlive that of `my_expression`. + +And finally.... the performance improvements from an expression template library like this are often not as +dramatic as the reduction in number of temporaries would suggest. For example if we compare this library with +`mpfr_class` and `mpreal`, with all three using the underlying MPFR library at 50 decimal digits precision then +we see the following typical results for polynomial execution: + +[table Evaluation of Order 6 Polynomial. +[[Library][Relative Time][Relative number of memory allocations]] +[[mp_number][1.0 (0.00793s)][1.0 (2996 total)]] +[[mpfr_class][1.2 (0.00931s)][4.3 (12976 total)]] +[[mpreal][1.9 (0.0148s)][9.3 (27947 total)]] +] + +As you can see the execution time increases a lot more slowly than the number of memory allocations. There are +a number of reasons for this: + +* The cost of extended-precision multiplication and division is so great, that the times taken for these tend to +swamp everything else. +* The cost of an in-place multiplication (using `operator*=`) tends to be more than an out-of-place +`operator*` (typically `operator *=` has to create a temporary workspace to carry out the multiplication, where +as `operator*` can use the target variable as workspace). Since the expression templates carry out their +magic by converting out-of-place operators to in-place ones, we necessarily take this hit. Even so the +transformation is more efficient than creating the extra temporary variable, just not by as much as +one would hope. + +We'll conclude this section by providing some more performance comparisons between these three libraries, +again, all are using MPFR to carry out the underlying arithmetic, and all are operating at the same precision +(50 decimal places): + +[table Evaluation of Boost.Math's Bessel function test data +[[Library][Relative Time][Relative Number of Memory Allocations]] +[[mp_number][1.0 (6.21s)][1.0 (2685469)]] +[[mpfr_class][1.04 (6.45s)][1.47 (3946007)]] +[[mpreal][1.53 (9.52s)][4.92 (13222940)]] +] + +[table Evaluation of Boost.Math's Non-Central T distribution test data +[[Library][Relative Time][Relative Number of Memory Allocations]] +[[mp_number][1.0 (269s)][1.0 (139082551)]] +[[mpfr_class][1.04 (278s)][1.81 (252400791)]] +[[mpreal][1.49 (401s)][3.22 (447009280)]] +] + [endsect] [section:tut Tutorial] diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 5a9aebc2..78a0cc74 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -545,15 +545,6 @@ private: using default_ops::subtract; subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } - /* - template - void do_assign(const Exp& e, const detail::subtract_and_negate_immediates&) - { - using default_ops::subtract; - subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - m_backend.negate(); - } - */ template void do_assign(const Exp& e, const detail::multiply_immediates&) { diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp new file mode 100644 index 00000000..04238b9e --- /dev/null +++ b/performance/sf_performance.cpp @@ -0,0 +1,321 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#define BOOST_CHRONO_HEADER_ONLY +#define BOOST_MATH_MAX_ROOT_ITERATION_POLICY 500 + +#include +#include +#include +#include +#include +#include +#include +#include + +template +Real test_bessel(); + +template +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + +template +Real test_bessel() +{ +# define T double +# include "libs/math/test/bessel_i_int_data.ipp" +# include "libs/math/test/bessel_i_data.ipp" + + Real r; + + for(unsigned i = 0; i < bessel_i_int_data.size(); ++i) + { + r += boost::math::cyl_bessel_i(Real(bessel_i_int_data[i][0]), Real(bessel_i_int_data[i][1])); + } + for(unsigned i = 0; i < bessel_i_data.size(); ++i) + { + r += boost::math::cyl_bessel_i(Real(bessel_i_data[i][0]), Real(bessel_i_data[i][1])); + } + +#include "libs/math/test/bessel_j_int_data.ipp" + for(unsigned i = 0; i < bessel_j_int_data.size(); ++i) + { + r += boost::math::cyl_bessel_j(Real(bessel_j_int_data[i][0]), Real(bessel_j_int_data[i][1])); + } + +#include "libs/math/test/bessel_j_data.ipp" + for(unsigned i = 0; i < bessel_j_data.size(); ++i) + { + r += boost::math::cyl_bessel_j(Real(bessel_j_data[i][0]), Real(bessel_j_data[i][1])); + } + +#include "libs/math/test/bessel_j_large_data.ipp" + for(unsigned i = 0; i < bessel_j_large_data.size(); ++i) + { + r += boost::math::cyl_bessel_j(Real(bessel_j_large_data[i][0]), Real(bessel_j_large_data[i][1])); + } + +#include "libs/math/test/sph_bessel_data.ipp" + for(unsigned i = 0; i < sph_bessel_data.size(); ++i) + { + r += boost::math::sph_bessel(static_cast(sph_bessel_data[i][0]), Real(sph_bessel_data[i][1])); + } + + + return r; +} + +template +Real test_polynomial() +{ + static const unsigned t[] = { + 2, 3, 4, 5, 6, 7, 8 }; + Real result = 0; + for(Real k = 2; k < 1000; ++k) + result += boost::math::tools::evaluate_polynomial(t, k); + + return result; +} + +template +Real test_nct() +{ +#define T double +#include "libs/math/test/nct.ipp" + + Real result = 0; + for(unsigned i = 0; i < nct.size(); ++i) + { + try{ + result += quantile(boost::math::non_central_t_distribution(nct[i][0], nct[i][1]), nct[i][3]); + } + catch(const std::exception&) + {} + result += cdf(boost::math::non_central_t_distribution(nct[i][0], nct[i][1]), nct[i][2]); + } + return result; +} + +unsigned allocation_count = 0; + +void *(*alloc_func_ptr) (size_t); +void *(*realloc_func_ptr) (void *, size_t, size_t); +void (*free_func_ptr) (void *, size_t); + +void *alloc_func(size_t n) +{ + ++allocation_count; + return (*alloc_func_ptr)(n); +} + +void free_func(void * p, size_t n) +{ + (*free_func_ptr)(p, n); +} + +void * realloc_func(void * p, size_t old, size_t n) +{ + ++allocation_count; + return (*realloc_func_ptr)(p, old, n); +} + +int main() +{ + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + mp_set_memory_functions(&alloc_func, &realloc_func, &free_func); + + static const unsigned a[] = { + 2, 3, 4, 5, 6, 7, 8 }; + boost::multiprecision::mpfr_float_50 result, x(2); + allocation_count = 0; + result = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; + std::cout << allocation_count << std::endl; + mpfr_class r, x2(2); + allocation_count = 0; + r = (((((a[6] * x2 + a[5]) * x2 + a[4]) * x2 + a[3]) * x2 + a[2]) * x2 + a[1]) * x2 + a[0]; + std::cout << allocation_count << std::endl; + mpfr::mpreal r2, x3(2); + allocation_count = 0; + r2 = (((((a[6] * x3 + a[5]) * x3 + a[4]) * x3 + a[3]) * x3 + a[2]) * x3 + a[1]) * x3 + a[0]; + std::cout << allocation_count << std::endl; + + allocation_count = 0; + result = boost::math::tools::evaluate_polynomial(a, x); + std::cout << allocation_count << std::endl; + allocation_count = 0; + r = boost::math::tools::evaluate_polynomial(a, x2); + std::cout << allocation_count << std::endl; + allocation_count = 0; + r2 = boost::math::tools::evaluate_polynomial(a, x3); + std::cout << allocation_count << std::endl; + + + boost::chrono::duration time; + stopwatch c; + // + // 50 digits first: + // + std::cout << "Testing Bessel Functions....." << std::endl; + mpfr_set_default_prec(50 * 1000L / 301L); + mpfr::mpreal::set_default_prec(50 * 1000L / 301L); + c.reset(); + test_bessel(); + time = c.elapsed(); + std::cout << "Time for mpfr_float_50 = " << time << std::endl; + std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_bessel(); + time = c.elapsed(); + std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl; + std::cout << "Total allocations for mpfr_class (50 digits) = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_bessel(); + time = c.elapsed(); + std::cout << "Time for mpreal (50 digits) = " << time << std::endl; + std::cout << "Total allocations for mpreal (50 digits) = " << allocation_count << std::endl; + allocation_count = 0; + // + // Then 100 digits: + // + mpfr_set_default_prec(100 * 1000L / 301L); + mpfr::mpreal::set_default_prec(100 * 1000L / 301L); + c.reset(); + test_bessel(); + time = c.elapsed(); + std::cout << "Time for mpfr_float_100 = " << time << std::endl; + std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_bessel(); + time = c.elapsed(); + std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl; + std::cout << "Total allocations for mpfr_class (100 digits) = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_bessel(); + time = c.elapsed(); + std::cout << "Time for mpreal (100 digits) = " << time << std::endl; + std::cout << "Total allocations for mpreal (100 digits) = " << allocation_count << std::endl; + allocation_count = 0; + + // + // 50 digits first: + // + c.reset(); + std::cout << "Testing Polynomial Evaluation....." << std::endl; + mpfr_set_default_prec(50 * 1000L / 301L); + mpfr::mpreal::set_default_prec(50 * 1000L / 301L); + c.reset(); + test_polynomial(); + time = c.elapsed(); + std::cout << "Time for mpfr_float_50 = " << time << std::endl; + std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_polynomial(); + time = c.elapsed(); + std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl; + std::cout << "Total allocations for mpfr_class (50 digits) = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_polynomial(); + time = c.elapsed(); + std::cout << "Time for mpreal (50 digits) = " << time << std::endl; + std::cout << "Total allocations for mpreal (50 digits = " << allocation_count << std::endl; + allocation_count = 0; + // + // Then 100 digits: + // + mpfr_set_default_prec(100 * 1000L / 301L); + mpfr::mpreal::set_default_prec(100 * 1000L / 301L); + c.reset(); + test_polynomial(); + time = c.elapsed(); + std::cout << "Time for mpfr_float_100 = " << time << std::endl; + std::cout << "Total allocations for mpfr_float_100 = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_polynomial(); + time = c.elapsed(); + std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl; + std::cout << "Total allocations for mpfr_class (100 digits) = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_polynomial(); + time = c.elapsed(); + std::cout << "Time for mpreal (100 digits) = " << time << std::endl; + std::cout << "Total allocations for mpreal (100 digits) = " << allocation_count << std::endl; + allocation_count = 0; + + // + // 50 digits first: + // + c.reset(); + std::cout << "Testing Non-Central T....." << std::endl; + mpfr_set_default_prec(50 * 1000L / 301L); + mpfr::mpreal::set_default_prec(50 * 1000L / 301L); + c.reset(); + test_nct(); + time = c.elapsed(); + std::cout << "Time for mpfr_float_50 = " << time << std::endl; + std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_nct(); + time = c.elapsed(); + std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl; + std::cout << "Total allocations for mpfr_class (50 digits) = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_nct(); + time = c.elapsed(); + std::cout << "Time for mpreal (50 digits) = " << time << std::endl; + std::cout << "Total allocations for mpreal (50 digits) = " << allocation_count << std::endl; + allocation_count = 0; + // + // Then 100 digits: + // + mpfr_set_default_prec(100 * 1000L / 301L); + mpfr::mpreal::set_default_prec(100 * 1000L / 301L); + c.reset(); + test_nct(); + time = c.elapsed(); + std::cout << "Time for mpfr_float_100 = " << time << std::endl; + std::cout << "Total allocations for mpfr_float_100 = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_nct(); + time = c.elapsed(); + std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl; + std::cout << "Total allocations for mpfr_class (100 digits) = " << allocation_count << std::endl; + allocation_count = 0; + c.reset(); + test_nct(); + time = c.elapsed(); + std::cout << "Time for mpreal (100 digits) = " << time << std::endl; + std::cout << "Total allocations for mpreal (100 digits) = " << allocation_count << std::endl; + allocation_count = 0; +} + From b36be1f5c38b4736300beaa052f97e6cfcbca02b Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 8 Nov 2011 12:50:21 +0000 Subject: [PATCH 055/256] Tighten up and test the architypes. [SVN r75404] --- .../concepts/mp_number_architypes.hpp | 82 +------------------ .../multiprecision/detail/default_ops.hpp | 8 +- test/Jamfile.v2 | 40 ++++++++- test/mp_number_concept_check.cpp | 53 ++++++++---- 4 files changed, 80 insertions(+), 103 deletions(-) diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index da417ae1..accd293d 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -177,94 +177,14 @@ inline void eval_ceil(mp_number_backend_float_architype& result, const mp_number result = std::ceil(arg.m_value); } -inline void eval_trunc(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = boost::math::trunc(arg.m_value); -} - inline void eval_sqrt(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) { result = std::sqrt(arg.m_value); } -inline void eval_abs(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::abs(arg.m_value); -} - -inline void eval_fabs(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::fabs(arg.m_value); -} - inline int eval_fpclassify(const mp_number_backend_float_architype& arg) { - return boost::math::fpclassify(arg.m_value); -} - -inline void eval_pow(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& b, const mp_number_backend_float_architype& e) -{ - result = std::pow(b.m_value, e.m_value); -} - -inline void eval_pow(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& b, int e) -{ - result = std::pow(b.m_value, e); -} - -inline void eval_exp(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::exp(arg.m_value); -} - -inline void eval_log(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::log(arg.m_value); -} - -inline void eval_sin(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::sin(arg.m_value); -} - -inline void eval_cos(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::cos(arg.m_value); -} - -inline void eval_tan(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::tan(arg.m_value); -} - -inline void eval_asin(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::asin(arg.m_value); -} - -inline void eval_acos(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::acos(arg.m_value); -} - -inline void eval_atan(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::atan(arg.m_value); -} - -inline void eval_sinh(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::sinh(arg.m_value); -} - -inline void eval_cosh(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::cosh(arg.m_value); -} - -inline void eval_tanh(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg) -{ - result = std::tanh(arg.m_value); + return (boost::math::fpclassify)(arg.m_value); } typedef boost::multiprecision::mp_number mp_number_float_architype; diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index ed82327c..91bed7f5 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -340,18 +340,18 @@ void eval_abs(T& result, const T& arg) { typedef typename T::signed_types type_list; typedef typename mpl::front::type front; - *result = arg; + result = arg; if(arg.compare(front(0)) < 0) - result->negate(); + result.negate(); } template void eval_fabs(T& result, const T& arg) { typedef typename T::signed_types type_list; typedef typename mpl::front::type front; - *result = arg; + result = arg; if(arg.compare(front(0)) < 0) - result->negate(); + result.negate(); } template diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 9ee8b530..7855a726 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -158,6 +158,38 @@ run mp_number_concept_check.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : big_number_concept_check_mpfr_50 ; +run mp_number_concept_check.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_6 + [ check-target-builds ../config//has_mpfr : : no ] + : big_number_concept_check_mpfr_6 ; + +run mp_number_concept_check.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_15 + [ check-target-builds ../config//has_mpfr : : no ] + : big_number_concept_check_mpfr_15 ; + +run mp_number_concept_check.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_17 + [ check-target-builds ../config//has_mpfr : : no ] + : big_number_concept_check_mpfr_17 ; + +run mp_number_concept_check.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_30 + [ check-target-builds ../config//has_mpfr : : no ] + : big_number_concept_check_mpfr_30 ; + run mp_number_concept_check.cpp gmp : # command line : # input files @@ -171,9 +203,15 @@ run mp_number_concept_check.cpp : # input files : # requirements TEST_MP_FLOAT - [ check-target-builds ../config//has_gmp : : no ] : big_number_concept_check_mp_float ; +run mp_number_concept_check.cpp + : # command line + : # input files + : # requirements + TEST_BACKEND + : big_number_concept_check_backend_concept ; + run test_exp.cpp gmp : # command line : # input files diff --git a/test/mp_number_concept_check.cpp b/test/mp_number_concept_check.cpp index 99d2c13f..35872d75 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -20,13 +20,17 @@ # pragma warning(disable:4503) // decorated name length exceeded, name was truncated #endif -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) # define TEST_MPF_50 -# define TEST_MPF # define TEST_BACKEND # define TEST_MPZ -# define TEST_MPFR # define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 # define TEST_MP_FLOAT #ifdef _MSC_VER @@ -38,7 +42,7 @@ #endif -#if defined(TEST_MPF_50) || defined(TEST_MPF) || defined(TEST_MPZ) +#if defined(TEST_MPF_50) || defined(TEST_MPZ) #include #endif #ifdef TEST_BACKEND @@ -47,7 +51,7 @@ #ifdef TEST_MP_FLOAT #include #endif -#if defined(TEST_MPFR) || defined(TEST_MPFR_50) +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) #include #endif @@ -57,19 +61,25 @@ void foo() { #ifdef TEST_BACKEND - instantiate(boost::multiprecision::mp_number_float_architype()); + instantiate(boost::multiprecision::concepts::mp_number_float_architype()); #endif #ifdef TEST_MPF_50 instantiate(boost::multiprecision::mpf_float_50()); #endif -#ifdef TEST_MPF - instantiate(boost::multiprecision::mpf_float()); -#endif #ifdef TEST_MPFR_50 instantiate(boost::multiprecision::mpfr_float_50()); #endif -#ifdef TEST_MPFR - instantiate(boost::multiprecision::mpfr_float()); +#ifdef TEST_MPFR_6 + instantiate(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_15 + instantiate(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_17 + instantiate(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_30 + instantiate(boost::multiprecision::mp_number >()); #endif #ifdef TEST_MP_FLOAT instantiate(boost::multiprecision::mp_float_50()); @@ -79,19 +89,28 @@ void foo() int main() { #ifdef TEST_BACKEND - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPF_50 BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif -#ifdef TEST_MPF - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); -#endif #ifdef TEST_MPFR_50 BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif -#ifdef TEST_MPFR - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#ifdef TEST_MPFR_6 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); +#endif +#ifdef TEST_MPFR_15 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); +#endif +#ifdef TEST_MPFR_17 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); +#endif +#ifdef TEST_MPFR_30 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); +#endif +#ifdef TEST_MPFR_50 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MP_FLOAT BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); From 0c4dde52eec163ae81d48c7e56e8d7d6fb416e1e Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 9 Nov 2011 17:37:40 +0000 Subject: [PATCH 056/256] Get the rounding functions working and tested, update docs to match. [SVN r75425] --- doc/multiprecision.qbk | 303 +++++++++++-- .../multiprecision/detail/default_ops.hpp | 151 ++++--- .../multiprecision/detail/functions/pow.hpp | 25 ++ include/boost/multiprecision/gmp.hpp | 5 +- include/boost/multiprecision/mp_float.hpp | 9 +- include/boost/multiprecision/mp_number.hpp | 6 + include/boost/multiprecision/mpfr.hpp | 22 + test/Jamfile.v2 | 32 ++ test/test_log.cpp | 13 + test/test_round.cpp | 404 ++++++++++++++++++ 10 files changed, 881 insertions(+), 89 deletions(-) create mode 100644 test/test_round.cpp diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 2f8dfe1e..fdcd45e6 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -402,9 +402,21 @@ It's also possible to access the underlying `mpq_t` via the data() member functi mp_number(); mp_number(see-below); mp_number& operator=(see-below); + /* Other number-type operators here */ + + // Use in Boolean context: + operator ``['convertible-to-bool-type]``()const; + // swap: + void swap(mp_number& other); + // Sign: + bool is_zero()const; + int sign()const; // string conversion: std::string str()const; + // Generic conversion mechanism + template + T convert_to()const; // precision control: static unsigned default_precision(); static void default_precision(unsigned digits10); @@ -419,6 +431,10 @@ It's also possible to access the underlying `mpq_t` via the data() member functi const Backend& backend()const; }; + // Swap: + template + void swap(mp_number& a, mp_number& b); + // iostream support: template std::ostream& operator << (std::ostream& os, const mp_number& r); @@ -427,23 +443,31 @@ It's also possible to access the underlying `mpq_t` via the data() member functi std::istream& operator >> (std::istream& is, mp_number& r); // Non-member function standard library support: - ``['unmentionable-expression-template-type]`` abs (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` fabs (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sqrt (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` floor (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` ceil (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` trunc (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` exp (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` log (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` cos (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sin (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` tan (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` acos (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` asin (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` atan (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` cosh (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sinh (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` tanh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` abs (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fabs (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sqrt (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` floor (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ceil (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` trunc (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` itrunc (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ltrunc (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lltrunc(const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` round (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` iround (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lround (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` llround(const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` exp (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log10 (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cos (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sin (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tan (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` acos (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` asin (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cosh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sinh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tanh (const ``['mp_number-or-expression-template-type]``&); ``['unmentionable-expression-template-type]`` ldexp (const ``['mp_number-or-expression-template-type]``&, int); ``['unmentionable-expression-template-type]`` frexp (const ``['mp_number-or-expression-template-type]``&, int*); @@ -453,6 +477,17 @@ It's also possible to access the underlying `mpq_t` via the data() member functi }} // namespaces + namespace boost{ namespace math{ + + // Boost.Math interoperability functions: + int fpclassify (const ``['mp_number-or-expression-template-type]``&, int); + bool isfinite (const ``['mp_number-or-expression-template-type]``&, int); + bool isnan (const ``['mp_number-or-expression-template-type]``&, int); + bool isinf (const ``['mp_number-or-expression-template-type]``&, int); + bool isnormal (const ``['mp_number-or-expression-template-type]``&, int); + + }} // namespaces + // numeric_limits support: namespace std{ @@ -497,11 +532,37 @@ derived from `mp_number`. One argument may optionally be of arithmetic type. Note that type `mp_number` (and all expression templates derived from it) may be used in a Boolian context. + operator ``['convertible-to-bool-type]``()const; + +Returns an ['unmentionable-type] that is usable in Boolean contexts (this allows `mp_number` to be used in any +Boolean context - if statements, conditional statements, or as an argument to a logical operator - without +type `mp_number` being convertible to type `bool`. + + void swap(mp_number& other); + +Swaps `*this` with `other`. + + bool is_zero()const; + +Returns `true` is `*this` is zero, otherwise `false`. + + int sign()const; + +Returns a value less than zero if `*this` is negative, a value greater than zero if `*this is positive, and zero +if `*this` is zero. + std::string str(unsigned precision, bool scientific = true)const; Returns the number formatted as a string, with at least /precision/ digits, and in scientific format if /scientific/ is true. + template + T convert_to()const; + +Provides a generic conversion mechanism to convert `*this` to type `T`. Type `T` may be any arithmetic type. +Optionally other types may also be supported by specific `Backend` types. + + static unsigned default_precision(); static void default_precision(unsigned digits10); unsigned precision()const; @@ -525,6 +586,13 @@ Returns: Returns the underlying backend instance used by *this. +[h4 swap] + + template + void swap(mp_number& a, mp_number& b); + +Swaps `a` and `b`. + [h4 Iostream Support] template @@ -538,23 +606,31 @@ These operators provided formatted input-output operations on `mp_number` types, [h4 Non-member standard library function support] - ``['unmentionable-expression-template-type]`` abs (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` fabs (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sqrt (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` floor (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` ceil (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` trunc (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` exp (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` log (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` cos (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sin (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` tan (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` acos (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` asin (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` atan (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` cosh (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sinh (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` tanh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` abs (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fabs (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sqrt (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` floor (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ceil (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` trunc (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` itrunc (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ltrunc (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lltrunc(const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` round (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` iround (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lround (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` llround(const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` exp (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log10 (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cos (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sin (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tan (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` acos (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` asin (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cosh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sinh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tanh (const ``['mp_number-or-expression-template-type]``&); ``['unmentionable-expression-template-type]`` ldexp (const ``['mp_number-or-expression-template-type]``&, int); ``['unmentionable-expression-template-type]`` frexp (const ``['mp_number-or-expression-template-type]``&, int*); @@ -572,6 +648,21 @@ used at variable precision. Also note that with the exception of `abs` that these functions can only be used with floating point Backend types. +[h4 Boost.Math Interoperabilty Support] + + namespace boost{ namespace math{ + + int fpclassify (const ``['mp_number-or-expression-template-type]``&, int); + bool isfinite (const ``['mp_number-or-expression-template-type]``&, int); + bool isnan (const ``['mp_number-or-expression-template-type]``&, int); + bool isinf (const ``['mp_number-or-expression-template-type]``&, int); + bool isnormal (const ``['mp_number-or-expression-template-type]``&, int); + + }} // namespaces + +These functions behave exacts as their Boost.Math equivalents. Other Boost.Math functions and templates may also be +specialized or overloaded to ensure interoperability. + [h4 std::numeric_limits support] namespace std{ @@ -592,7 +683,149 @@ whose precision can vary at compile time (such as `mpf_float`). [section:backendconc Backend Requirements] -TODO, big boring job!! +[template super[x]''''''[x]''''''] + +The requirements on the `Backend` template argument to `mp_number` are split up into +compulsary requirements, and optional requirements that are either to improve performance +or provide optional features. + +In the following tables, type B is the `Backend` template arument to `mp_number`, `b` is +a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a variable of Arithmetic type, +`s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`, +`pa` is a variable of type pointer-to-arithmetc-type, `exp` is a variable of type `B::exp_type`, +`pexp` is a variable of type `B::exp_type*`. + +[table Compulsary Requirements on the Backend type. +[[Expression][Return Type][Comments]] +[[`B::signed_types`][`mpl::list`][A list of signed integral types that can be assigned to type B. The types shall be + listed in order of size, smallest first, and shall terminate in the type that is `std::intmax_t`.]] +[[`B::unsigned_types`][`mpl::list`][A list of unsigned integral types that can be assigned to type B. The types shall be + listed in order of size, smallest first, and shall terminate in the type that is `std::uintmax_t`.]] +[[`B::real_types`][`mpl::list`][A list of floating point types that can be assigned to type B.The types shall be + listed in order of size, smallest first, and shall terminate in type `long double`.]] +[[`B::exponent_type`][A signed integral type.][The type of the exponent of type B.]] +[[`B()`][ ][Default constructor.]] +[[`B(cb)`][ ][Copy Constructor.]] +[[`b = b`][`B&`][Assignment operator.]] +[[`b = a`][`B&`][Assignment from an Arithmetic type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`b = s`][`B&`][Assignment from a string.]] +[[`b.swap(b)`][`void`][Swaps the contents of it's arguments.]] +[[`cb.str(ui, bb)`][`std::string`][Returns the string representation of `b` with `ui` digits and in scientific format if `bb` is `true`. + If `ui` is zero, then returns as many digits as are required to reconstruct the original value.]] +[[`b.negate()`][`void`][Negates `b`.]] +[[`cb.compare(cb2)`][`int`][Compares `cb` and `cb2`, returns a value less than zero if `cb < cb2`, a value greater than zero if `cb > cb2` and zero + if `cb == cb2`.]] +[[`cb.compare(a)`][`int`][Compares `cb` and `a`, returns a value less than zero if `cb < a`, a value greater than zero if `cb > a` and zero + if `cb == a`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`add(b, cb)`][`void`][Adds `cb` to `b`.]] +[[`subtract(b, cb)`][`void`][Subtracts `cb` from `b`.]] +[[`multiply(b, cb)`][`void`][Multiplies `b` by `cb`.]] +[[`divide(b, cb)`][`void`][Divides `b` by `cb`.]] +[[`modulus(b, cb)`][`void`][Computes `b %= cb`, only required when `B` is an integer type.]] +[[`bitwise_and(b, cb)`][`void`][Computes `b &= cb`, only required when `B` is an integer type.]] +[[`bitwise_or(b, cb)`][`void`][Computes `b |= cb`, only required when `B` is an integer type.]] +[[`bitwise_xor(b, cb)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type.]] +[[`complement(b, cb)`][`void`][Computes the ones-complement of `cb` and stores the result in `b`, only required when `B` is an integer type.]] +[[`left_shift(b, ui)`][`void`][Computes `b <<= ui`, only required when `B` is an integer type.]] +[[`right_shift(b, ui)`][`void`][Computes `b >>= ui`, only required when `B` is an integer type.]] +[[`convert_to(pa, cb)`][`void`][Converts `cb` to the type of `*pa` and store the result in `*pa`. Type `B` shall support + conversion to at least types `std::intmax_t`, `std::uintmax_t` and `long long`. + Conversion to other arithmetic types can then be synthesised using other operations. + Conversions to other types are entirely optional.]] +[[`eval_frexp(b, cb, pexp)`][`void`][Stores values in `b` and `*pexp` such that the value of `cb` is b * 2[super *pexp], only required when `B` is a floating point type.]] +[[`eval_ldexp(b, cb, exp)`][`void`][Stores a value in `b` that is cb * 2[super exp], only required when `B` is a floating point type.]] +[[`eval_floor(b, cb)`][`void`][Stores the floor of `cb` in `b`, only required when `B` is a floating point type.]] +[[`eval_ceil(b, cb)`][`void`][Stores the ceiling of `cb` in `b`, only required when `B` is a floating point type.]] +[[`eval_sqrt(b, cb)`][`void`][Stores the square root of `cb` in `b`, only required when `B` is a floating point type.]] +] + +[table Optional Requirements on the Backend Type +[[Expression][Returns][Comments]] +[[`add(b, a)`][`void`][Adds `a` to `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`subtract(b, a)`][`void`][Subtracts `a` from `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`multiply(b, a)`][`void`][Multiplies `b` by `a`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`divide(b, a)`][`void`][Divides `b` by `a`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`modulus(b, a)`][`void`][Computes `b %= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`bitwise_and(b, a)`][`void`][Computes `b &= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`bitwise_or(b, a)`][`void`][Computes `b |= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`bitwise_xor(b, a)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`add(b, cb, cb2)`][`void`][Add `cb` to `cb2` and stores the result in `b`.]] +[[`subtract(b, cb, cb2)`][`void`][Subtracts `cb2` from `cb` and stores the result in `b`.]] +[[`multiply(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and stores the result in `b`.]] +[[`divide(b, cb, cb2)`][`void`][Divides `cb` by `cb2` and stores the result in `b`.]] +[[`add(b, cb, a)`][`void`][Add `cb` to `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`subtract(b, cb, a)`][`void`][Subtracts `a` from `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`multiply(b, cb, a)`][`void`][Multiplies `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`divide(b, cb, a)`][`void`][Divides `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`modulus(b, cb, cb2)`][`void`][Computes `cb % cb2` and stores the result in `b`, only required when `B` is an integer type.]] +[[`bitwise_and(b, cb, cb2)`][`void`][Computes `cb & cb2` and stores the result in `b`, only required when `B` is an integer type.]] +[[`bitwise_or(b, cb, cb2)`][`void`][Computes `cb | cb2` and stores the result in `b`, only required when `B` is an integer type.]] +[[`bitwise_xor(b, cb, cb2)`][`void`][Computes `cb ^ cb2` and stores the result in `b`, only required when `B` is an integer type.]] +[[`add(b, a, cb)`][`void`][Add `a` to `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`subtract(b, a, cb)`][`void`][Subtracts `cb` from `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`multiply(b, a, cb)`][`void`][Multiplies `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`divide(b, a, cb)`][`void`][Divides `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`modulus(b, cb, a)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`bitwise_and(b, cb, a)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`bitwise_or(b, cb, a)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`bitwise_xor(b, cb, a)`][`void`][Computes `cb ^ a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`modulus(b, a, cb)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`bitwise_and(b, a, cb)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`bitwise_or(b, a, cb)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`bitwise_xor(b, a, cb)`][`void`][Computes `a ^ cb` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] +[[`left_shift(b, cb, ui)`][`void`][Computes `cb << ui` and stores the result in `b`, only required when `B` is an integer type.]] +[[`right_shift(b, cb, ui)`][`void`][Computes `cb >> ui` and stores the result in `b`, only required when `B` is an integer type.]] +[[`increment(b)`][void][Increments the value of `b` by one.]] +[[`decrement(b)`][void][Decrements the value of `b` by one.]] +[[`is_zero(cb)`][`bool`][Returns `true` if `cb` is zero, otherwise `false`]] +[[`get_sign(cb)`][`int`][Returns a value < zero if `cb` is negative, a value > zero if `cb` is positive, and zero if `cb` is zero.]] +[[`eval_abs(b, cb)`][`void`][Set `b` to the absolute value of `cb`.]] +[[`eval_fabs(b, cb)`][`void`][Set `b` to the absolute value of `cb`.]] +[[`eval_fpclassify(cb)`][`int`][Returns one of the same values returned by `std::fpclassify`. Only required when `B` is an floating point type.]] +[[`eval_trunc(b, cb)`][`void`][Performs the equivalent operation to `std::trunc` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_round(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::round` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_exp(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_log(b, cb)`][`void`][Performs the equivalent operation to `std::log` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_log10(b, cb)`][`void`][Performs the equivalent operation to `std::log10` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_sin(b, cb)`][`void`][Performs the equivalent operation to `std::sin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_cos(b, cb)`][`void`][Performs the equivalent operation to `std::cos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_tan(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_asin(b, cb)`][`void`][Performs the equivalent operation to `std::asin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_acos(b, cb)`][`void`][Performs the equivalent operation to `std::acos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_atan(b, cb)`][`void`][Performs the equivalent operation to `std::atan` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_sinh(b, cb)`][`void`][Performs the equivalent operation to `std::sinh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_cosh(b, cb)`][`void`][Performs the equivalent operation to `std::cosh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_tanh(b, cb)`][`void`][Performs the equivalent operation to `std::tanh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_fmod(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::fmod` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_pow(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::pow` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_atan2(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::atan` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating point type.]] +] [endsect] diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 91bed7f5..775a3b7d 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -382,6 +382,12 @@ inline void eval_fmod(T& result, const T& a, const T& b) template inline void eval_trunc(T& result, const T& a) { + int c = eval_fpclassify(a); + if(c == FP_NAN || c == FP_INFINITE) + { + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number(a), 0, boost::math::policies::policy<>()).backend(); + return; + } if(get_sign(a) < 0) eval_ceil(result, a); else @@ -392,6 +398,12 @@ template inline void eval_round(T& result, const T& a) { typedef typename boost::multiprecision::detail::canonical::type fp_type; + int c = eval_fpclassify(a); + if(c == FP_NAN || c == FP_INFINITE) + { + result = boost::math::policies::raise_rounding_error("boost::multiprecision::round<%1%>(%1%)", 0, mp_number(a), 0, boost::math::policies::policy<>()).backend(); + return; + } if(get_sign(a) < 0) { subtract(result, a, fp_type(0.5f)); @@ -420,31 +432,6 @@ typename enable_if_c::type eval_ldexp(); template typename enable_if_c::type eval_frexp(); // -// TODO: implement default versions of these: -// -template -typename enable_if_c::type eval_exp(); -template -typename enable_if_c::type eval_log(); -template -typename enable_if_c::type eval_sin(); -template -typename enable_if_c::type eval_cos(); -template -typename enable_if_c::type eval_tan(); -template -typename enable_if_c::type eval_asin(); -template -typename enable_if_c::type eval_acos(); -template -typename enable_if_c::type eval_atan(); -template -typename enable_if_c::type eval_sinh(); -template -typename enable_if_c::type eval_cosh(); -template -typename enable_if_c::type eval_tanh(); -// // These functions are implemented in separate files, but expanded inline here, // DO NOT CHANGE THE ORDER OF THESE INCLUDES: // @@ -527,7 +514,7 @@ template inline typename detail::mp_exp::result_type trunc(const detail::mp_exp& v, const Policy& pol) { typedef typename detail::mp_exp::result_type number_type; - return trunc(v, pol); + return trunc(number_type(v), pol); } template @@ -544,58 +531,88 @@ inline int itrunc(const detail::mp_exp& v, const Policy& pol) { typedef typename detail::mp_exp::result_type number_type; number_type r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) + return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, number_type(v), 0, pol).template convert_to(); return r.template convert_to(); } +template +inline int itrunc(const detail::mp_exp& v) +{ + return itrunc(v, boost::math::policies::policy<>()); +} template inline int itrunc(const mp_number& v, const Policy& pol) { mp_number r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } +template +inline int itrunc(const mp_number& v) +{ + return itrunc(v, boost::math::policies::policy<>()); +} template inline long ltrunc(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_result number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) + return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, number_type(v), 0L, pol).template convert_to(); return r.template convert_to(); } +template +inline long ltrunc(const detail::mp_exp& v) +{ + return ltrunc(v, boost::math::policies::policy<>()); +} template inline long ltrunc(const mp_number& v, const Policy& pol) { mp_number r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } +template +inline long ltrunc(const mp_number& v) +{ + return ltrunc(v, boost::math::policies::policy<>()); +} #ifndef BOOST_NO_LONG_LONG template inline long long lltrunc(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_result number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) + return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, number_type(v), 0LL, pol).template convert_to(); return r.template convert_to(); } +template +inline long long lltrunc(const detail::mp_exp& v) +{ + return lltrunc(v, boost::math::policies::policy<>()); +} template inline long long lltrunc(const mp_number& v, const Policy& pol) { mp_number r = trunc(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } +template +inline long long lltrunc(const mp_number& v) +{ + return lltrunc(v, boost::math::policies::policy<>()); +} #endif template -inline typename detail::mp_exp::result_result round(const detail::mp_exp& v, const Policy& pol) +inline typename detail::mp_exp::result_type round(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_result number_type; + typedef typename detail::mp_exp::result_type number_type; return round(static_cast(v), pol); } template @@ -610,55 +627,85 @@ inline mp_number round(const mp_number& v, const Policy& pol) template inline int iround(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_result number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) + return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, number_type(v), 0, pol).template convert_to(); return r.template convert_to(); } +template +inline int iround(const detail::mp_exp& v) +{ + return iround(v, boost::math::policies::policy<>()); +} template inline int iround(const mp_number& v, const Policy& pol) { mp_number r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } +template +inline int iround(const mp_number& v) +{ + return iround(v, boost::math::policies::policy<>()); +} template inline long lround(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_result number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) + return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, number_type(v), 0L, pol).template convert_to(); return r.template convert_to(); } +template +inline long lround(const detail::mp_exp& v) +{ + return lround(v, boost::math::policies::policy<>()); +} template inline long lround(const mp_number& v, const Policy& pol) { mp_number r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } +template +inline long lround(const mp_number& v) +{ + return lround(v, boost::math::policies::policy<>()); +} #ifndef BOOST_NO_LONG_LONG template inline long long llround(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_result number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) - return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) + return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, number_type(v), 0LL, pol).template convert_to(); return r.template convert_to(); } +template +inline long long llround(const detail::mp_exp& v) +{ + return llround(v, boost::math::policies::policy<>()); +} template inline long long llround(const mp_number& v, const Policy& pol) { mp_number r = round(v, pol); - if(fabs(r) > (std::numeric_limits::max)()) + if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } +template +inline long long llround(const mp_number& v) +{ + return llround(v, boost::math::policies::policy<>()); +} #endif #define UNARY_OP_FUNCTOR(func)\ @@ -917,8 +964,10 @@ UNARY_OP_FUNCTOR(sqrt) UNARY_OP_FUNCTOR(floor) UNARY_OP_FUNCTOR(ceil) UNARY_OP_FUNCTOR(trunc) +UNARY_OP_FUNCTOR(round) UNARY_OP_FUNCTOR(exp) UNARY_OP_FUNCTOR(log) +UNARY_OP_FUNCTOR(log10) UNARY_OP_FUNCTOR(cos) UNARY_OP_FUNCTOR(sin) UNARY_OP_FUNCTOR(tan) diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 7bd0554c..fe8ab3ab 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -385,6 +385,31 @@ void eval_log(T& result, const T& arg) }while(lim.compare(t2) < 0); } +template +const T& get_constant_log10() +{ + static T result; + static bool b = false; + if(!b) + { + typedef typename boost::multiprecision::detail::canonical::type ui_type; + T ten; + ten = ui_type(10u); + eval_log(result, ten); + } + + constant_initializer >::do_nothing(); + + return result; +} + +template +void eval_log10(T& result, const T& arg) +{ + eval_log(result, arg); + divide(result, get_constant_log10()); +} + template inline void eval_pow(T& result, const T& x, const T& a) { diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 13ac14c3..ce7413a8 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -679,7 +679,10 @@ inline void convert_to(long long* result, const gmp_float& val) if(!mpf_fits_slong_p(t.data())) { - *result = (std::numeric_limits::max)(); + if(get_sign(val) < 0) + *result = (std::numeric_limits::min)(); + else + *result = (std::numeric_limits::max)(); return; }; diff --git a/include/boost/multiprecision/mp_float.hpp b/include/boost/multiprecision/mp_float.hpp index e75ed494..321364c9 100644 --- a/include/boost/multiprecision/mp_float.hpp +++ b/include/boost/multiprecision/mp_float.hpp @@ -2583,10 +2583,15 @@ inline void eval_ceil(mp_float& result, const mp_float& x) template inline void eval_trunc(mp_float& result, const mp_float& x) { - if(!x.isfinite() || x.isint()) + if(!x.isfinite()) { + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number >(x), 0, boost::math::policies::policy<>()).backend(); + return; + } + else if(x.isint()) + { result = x; - return; + return; } result = x.extract_integer_part(); } diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 78a0cc74..ff11fb42 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -1553,6 +1553,12 @@ inline std::istream& operator >> (std::istream& is, mp_number& r) return is; } +template +inline void swap(mp_number& a, mp_number& b) +{ + a.swap(b); +} + }} // namespaces #endif diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 667f0ea1..8e82ab51 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -785,6 +785,12 @@ inline void eval_floor(mpfr_float_backend& result, const mpfr_float_ba template inline void eval_trunc(mpfr_float_backend& result, const mpfr_float_backend& val) { + int c = eval_fpclassify(val); + if(0 == mpfr_number_p(val.data())) + { + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number >(val), 0, boost::math::policies::policy<>()).backend(); + return; + } mpfr_trunc(result.data(), val.data()); } template @@ -848,6 +854,12 @@ inline void eval_log(mpfr_float_backend& result, const mpfr_float_back mpfr_log(result.data(), arg.data(), GMP_RNDN); } +template +inline void eval_log10(mpfr_float_backend& result, const mpfr_float_backend& arg) +{ + mpfr_log10(result.data(), arg.data(), GMP_RNDN); +} + template inline void eval_sin(mpfr_float_backend& result, const mpfr_float_backend& arg) { @@ -918,6 +930,16 @@ typedef mp_number > mpfr_float; namespace math{ +namespace tools{ + +template <> +inline int digits() +{ + return boost::multiprecision::detail::get_default_precision(); +} + +} + namespace lanczos{ template diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 7855a726..6a85b2f2 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -490,3 +490,35 @@ run ../example/mpfr_snips.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] ; run ../example/mp_float_snips.cpp ; + +run test_round.cpp + : # command line + : # input files + : # requirements + TEST_BACKEND + : test_round_backend_concept ; + +run test_round.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : no ] + : test_round_mpf50 ; + +run test_round.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_round_mpfr_50 ; + +run test_round.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + [ check-target-builds ../config//has_mpfr : : no ] + : test_round_mp_float ; + diff --git a/test/test_log.cpp b/test/test_log.cpp index 85c077a9..8c6e4b19 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -151,6 +151,7 @@ void test() T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"; T tenth = 1; tenth /= 10; + T logten = log(T(10)); unsigned max_err = 0; for(unsigned k = 0; k < data.size(); k++) @@ -166,6 +167,18 @@ void test() err = e.template convert_to(); if(err > max_err) max_err = err; + + val = boost::multiprecision::log10(tenth + pi * (100 * k) * (100 * k)); + e = relative_error(val, T(data[k] / logten)); + err = e.template convert_to(); + if(err > max_err) + max_err = err; + + val = boost::multiprecision::log10(1 / (tenth + pi * (100 * k) * (100 * k))); + e = relative_error(val, T(-data[k] / logten)); + err = e.template convert_to(); + if(err > max_err) + max_err = err; } std::cout << "Max error was: " << max_err << std::endl; BOOST_TEST(max_err < 10); diff --git a/test/test_round.cpp b/test/test_round.cpp new file mode 100644 index 00000000..52734b28 --- /dev/null +++ b/test/test_round.cpp @@ -0,0 +1,404 @@ +// (C) Copyright John Maddock 2007. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include +#include +#include +#include +#include +#include + +#define BOOST_CHECK_THROW(x, EX)\ + try { x; BOOST_ERROR("Expected exception not thrown"); } \ + catch(const EX&){}\ + catch(...){ BOOST_ERROR("Incorrect exception type thrown"); } + + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 +# define TEST_MPFR_50 +# define TEST_BACKEND +# define TEST_MP_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include +#endif +#ifdef TEST_MPFR_50 +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_MP_FLOAT +#include +#endif + +boost::mt19937 rng; + +template +T get_random() +{ + // + // Fill all the bits in T with random values, + // likewise set the exponent to a random value + // that will still fit inside a T, and always + // have a remainder as well as an integer part. + // + int bits = boost::math::tools::digits(); + int shift = 0; + int exponent = rng() % (bits - 4); + T result = 0; + while(bits > 0) + { + result += ldexp(static_cast(rng()), shift); + shift += std::numeric_limits::digits; + bits -= std::numeric_limits::digits; + } + return rng() & 1u ? -ldexp(frexp(result, &bits), exponent) : ldexp(frexp(result, &bits), exponent); +} + +template +void check_within_half(T a, U u) +{ + BOOST_MATH_STD_USING + if(fabs(a-u) > 0.5f) + { + BOOST_ERROR("Rounded result differed by more than 0.5 from the original"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } + if((fabs(a - u) == 0.5f) && (fabs(static_cast(u)) < fabs(a))) + { + BOOST_ERROR("Rounded result was towards zero with boost::round"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } +} + +// +// We may not have an abs overload for long long so provide a fall back: +// +template +inline T safe_abs(T const& v ...) +{ + return v < 0 ? -v : v; +} + +template +void check_trunc_result(T a, U u) +{ + BOOST_MATH_STD_USING + if(fabs(a-u) >= 1) + { + BOOST_ERROR("Rounded result differed by more than 1 from the original"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } + if(abs(a) < safe_abs(u)) + { + BOOST_ERROR("Truncated result had larger absolute value than the original"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } + if(fabs(static_cast(u)) > fabs(a)) + { + BOOST_ERROR("Rounded result was away from zero with boost::trunc"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } +} + +template +void check_modf_result(T a, T fract, U ipart) +{ + BOOST_MATH_STD_USING + if(fract + ipart != a) + { + BOOST_ERROR("Fractional and integer results do not add up to the original value"); + std::cerr << "Values were: " << std::setprecision(35) << " " + << std::left << a << ipart << " " << fract << std::endl; + } + if((boost::math::sign(a) != boost::math::sign(fract)) && boost::math::sign(fract)) + { + BOOST_ERROR("Original and fractional parts have differing signs"); + std::cerr << "Values were: " << std::setprecision(35) << " " + << std::left << a << ipart << " " << fract << std::endl; + } + if((boost::math::sign(a) != boost::math::sign(ipart)) && boost::math::sign(ipart)) + { + BOOST_ERROR("Original and integer parts have differing signs"); + std::cerr << "Values were: " << std::setprecision(35) << " " + << std::left << a << ipart << " " << ipart << std::endl; + } + if(fabs(a-ipart) >= 1) + { + BOOST_ERROR("Rounded result differed by more than 1 from the original"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << ipart << std::endl; + } +} + +template +void test() +{ + BOOST_MATH_STD_USING + + for(int i = 0; i < 1000; ++i) + { + T arg = get_random(); + T r = round(arg); + check_within_half(arg, r); + BOOST_TEST(r == round(arg + 0)); + r = trunc(arg); + check_trunc_result(arg, r); + BOOST_TEST(r == trunc(arg + 0)); + T frac = modf(arg, &r); + check_modf_result(arg, frac, r); + + if(abs(r) < (std::numeric_limits::max)()) + { + int i = iround(arg); + check_within_half(arg, i); + BOOST_TEST(i == iround(arg + 0)); + i = itrunc(arg); + check_trunc_result(arg, i); + BOOST_TEST(i == itrunc(arg + 0)); + r = modf(arg, &i); + check_modf_result(arg, r, i); + } + if(abs(r) < (std::numeric_limits::max)()) + { + long l = lround(arg); + check_within_half(arg, l); + BOOST_TEST(l == lround(arg + 0)); + l = ltrunc(arg); + check_trunc_result(arg, l); + BOOST_TEST(l == ltrunc(arg + 0)); + r = modf(arg, &l); + check_modf_result(arg, r, l); + } + +#ifdef BOOST_HAS_LONG_LONG + if(abs(r) < (std::numeric_limits::max)()) + { + boost::long_long_type ll = llround(arg); + check_within_half(arg, ll); + BOOST_TEST(ll == llround(arg + 0)); + ll = lltrunc(arg); + check_trunc_result(arg, ll); + BOOST_TEST(ll == lltrunc(arg + 0)); + r = modf(arg, &ll); + check_modf_result(arg, r, ll); + } +#endif + } + // + // Test boundary cases: + // + if(std::numeric_limits::digits >= std::numeric_limits::digits) + { + int si = iround(static_cast((std::numeric_limits::max)())); + check_within_half(static_cast((std::numeric_limits::max)()), si); + BOOST_TEST(si == iround(static_cast((std::numeric_limits::max)()) + 0)); + si = iround(static_cast((std::numeric_limits::min)())); + check_within_half(static_cast((std::numeric_limits::min)()), si); + BOOST_TEST(si == iround(static_cast((std::numeric_limits::min)()) + 0)); + si = itrunc(static_cast((std::numeric_limits::max)())); + check_trunc_result(static_cast((std::numeric_limits::max)()), si); + BOOST_TEST(si == itrunc(static_cast((std::numeric_limits::max)()) + 0)); + si = itrunc(static_cast((std::numeric_limits::min)())); + check_trunc_result(static_cast((std::numeric_limits::min)()), si); + BOOST_TEST(si == itrunc(static_cast((std::numeric_limits::min)()) + 0)); + + si = iround(static_cast((std::numeric_limits::max)() - 1)); + check_within_half(static_cast((std::numeric_limits::max)() - 1), si); + si = iround(static_cast((std::numeric_limits::min)() + 1)); + check_within_half(static_cast((std::numeric_limits::min)() + 1), si); + si = itrunc(static_cast((std::numeric_limits::max)() - 1)); + check_trunc_result(static_cast((std::numeric_limits::max)() - 1), si); + si = itrunc(static_cast((std::numeric_limits::min)() + 1)); + check_trunc_result(static_cast((std::numeric_limits::min)() + 1), si); + } + if(std::numeric_limits::digits >= std::numeric_limits::digits) + { + long k = lround(static_cast((std::numeric_limits::max)())); + check_within_half(static_cast((std::numeric_limits::max)()), k); + BOOST_TEST(k == lround(static_cast((std::numeric_limits::max)()) + 0)); + k = lround(static_cast((std::numeric_limits::min)())); + check_within_half(static_cast((std::numeric_limits::min)()), k); + BOOST_TEST(k == lround(static_cast((std::numeric_limits::min)()) + 0)); + k = ltrunc(static_cast((std::numeric_limits::max)())); + check_trunc_result(static_cast((std::numeric_limits::max)()), k); + BOOST_TEST(k == ltrunc(static_cast((std::numeric_limits::max)()) + 0)); + k = ltrunc(static_cast((std::numeric_limits::min)())); + check_trunc_result(static_cast((std::numeric_limits::min)()), k); + BOOST_TEST(k == ltrunc(static_cast((std::numeric_limits::min)()) + 0)); + + k = lround(static_cast((std::numeric_limits::max)() - 1)); + check_within_half(static_cast((std::numeric_limits::max)() - 1), k); + k = lround(static_cast((std::numeric_limits::min)() + 1)); + check_within_half(static_cast((std::numeric_limits::min)() + 1), k); + k = ltrunc(static_cast((std::numeric_limits::max)() - 1)); + check_trunc_result(static_cast((std::numeric_limits::max)() - 1), k); + k = ltrunc(static_cast((std::numeric_limits::min)() + 1)); + check_trunc_result(static_cast((std::numeric_limits::min)() + 1), k); + } +#ifndef BOOST_NO_LONG_LONG + if(std::numeric_limits::digits >= std::numeric_limits::digits) + { + boost::long_long_type j = llround(static_cast((std::numeric_limits::max)())); + check_within_half(static_cast((std::numeric_limits::max)()), j); + BOOST_TEST(j == llround(static_cast((std::numeric_limits::max)()) + 0)); + j = llround(static_cast((std::numeric_limits::min)())); + check_within_half(static_cast((std::numeric_limits::min)()), j); + BOOST_TEST(j == llround(static_cast((std::numeric_limits::min)()) + 0)); + j = lltrunc(static_cast((std::numeric_limits::max)())); + check_trunc_result(static_cast((std::numeric_limits::max)()), j); + BOOST_TEST(j == lltrunc(static_cast((std::numeric_limits::max)()) + 0)); + j = lltrunc(static_cast((std::numeric_limits::min)())); + check_trunc_result(static_cast((std::numeric_limits::min)()), j); + BOOST_TEST(j == lltrunc(static_cast((std::numeric_limits::min)()) + 0)); + + j = llround(static_cast((std::numeric_limits::max)() - 1)); + check_within_half(static_cast((std::numeric_limits::max)() - 1), j); + j = llround(static_cast((std::numeric_limits::min)() + 1)); + check_within_half(static_cast((std::numeric_limits::min)() + 1), j); + j = lltrunc(static_cast((std::numeric_limits::max)() - 1)); + check_trunc_result(static_cast((std::numeric_limits::max)() - 1), j); + j = lltrunc(static_cast((std::numeric_limits::min)() + 1)); + check_trunc_result(static_cast((std::numeric_limits::min)() + 1), j); + } +#endif + // + // Finish off by testing the error handlers: + // + BOOST_CHECK_THROW(static_cast(iround(static_cast(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(iround(static_cast(-1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(lround(static_cast(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(lround(static_cast(-1e20))), boost::math::rounding_error); +#ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast(llround(static_cast(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(llround(static_cast(-1e20))), boost::math::rounding_error); +#endif + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK_THROW(static_cast(round(std::numeric_limits::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(iround(std::numeric_limits::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(iround(-std::numeric_limits::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(lround(std::numeric_limits::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(lround(-std::numeric_limits::infinity())), boost::math::rounding_error); + #ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast(llround(std::numeric_limits::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(llround(-std::numeric_limits::infinity())), boost::math::rounding_error); + #endif + } + if(std::numeric_limits::has_quiet_NaN) + { + BOOST_CHECK_THROW(static_cast(round(std::numeric_limits::quiet_NaN())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(iround(std::numeric_limits::quiet_NaN())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(lround(std::numeric_limits::quiet_NaN())), boost::math::rounding_error); + #ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast(llround(std::numeric_limits::quiet_NaN())), boost::math::rounding_error); + #endif + } + BOOST_CHECK_THROW(static_cast(itrunc(static_cast(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(itrunc(static_cast(-1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(ltrunc(static_cast(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(ltrunc(static_cast(-1e20))), boost::math::rounding_error); +#ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast(lltrunc(static_cast(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(lltrunc(static_cast(-1e20))), boost::math::rounding_error); +#endif + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK_THROW(static_cast(trunc(std::numeric_limits::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(itrunc(std::numeric_limits::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(itrunc(-std::numeric_limits::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(ltrunc(std::numeric_limits::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(ltrunc(-std::numeric_limits::infinity())), boost::math::rounding_error); + #ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast(lltrunc(std::numeric_limits::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(lltrunc(-std::numeric_limits::infinity())), boost::math::rounding_error); + #endif + } + if(std::numeric_limits::has_quiet_NaN) + { + BOOST_CHECK_THROW(static_cast(trunc(std::numeric_limits::quiet_NaN())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(itrunc(std::numeric_limits::quiet_NaN())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(ltrunc(std::numeric_limits::quiet_NaN())), boost::math::rounding_error); + #ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast(lltrunc(std::numeric_limits::quiet_NaN())), boost::math::rounding_error); + #endif + } + if(std::numeric_limits::digits >= std::numeric_limits::digits) + { + BOOST_CHECK_THROW(static_cast(itrunc(static_cast((std::numeric_limits::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(itrunc(static_cast((std::numeric_limits::min)()) - 1)), boost::math::rounding_error); + } + if(std::numeric_limits::digits >= std::numeric_limits::digits) + { + BOOST_CHECK_THROW(static_cast(ltrunc(static_cast((std::numeric_limits::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(ltrunc(static_cast((std::numeric_limits::min)()) - 1)), boost::math::rounding_error); + } +#ifndef BOOST_NO_LONG_LONG + if(std::numeric_limits::digits >= std::numeric_limits::digits) + { + BOOST_CHECK_THROW(static_cast(lltrunc(static_cast((std::numeric_limits::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(lltrunc(static_cast((std::numeric_limits::min)()) - 1)), boost::math::rounding_error); + } +#endif + if(std::numeric_limits::digits >= std::numeric_limits::digits) + { + BOOST_CHECK_THROW(static_cast(iround(static_cast((std::numeric_limits::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(iround(static_cast((std::numeric_limits::min)()) - 1)), boost::math::rounding_error); + } + if(std::numeric_limits::digits >= std::numeric_limits::digits) + { + BOOST_CHECK_THROW(static_cast(lround(static_cast((std::numeric_limits::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(lround(static_cast((std::numeric_limits::min)()) - 1)), boost::math::rounding_error); + } +#ifndef BOOST_NO_LONG_LONG + if(std::numeric_limits::digits >= std::numeric_limits::digits) + { + BOOST_CHECK_THROW(static_cast(llround(static_cast((std::numeric_limits::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast(llround(static_cast((std::numeric_limits::min)()) - 1)), boost::math::rounding_error); + } +#endif +} + +int main() +{ +#ifdef TEST_MPF_50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_MP_FLOAT + test(); + test(); +#endif +#ifdef TEST_BACKEND + test >(); +#endif + return boost::report_errors(); +} + + + + + From 47724a42214cc0beb45ef5bcca1f170856946f98 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 12 Nov 2011 12:15:04 +0000 Subject: [PATCH 057/256] Fixes for bugs in mp_float. Fix constant initialization. Add some instrumentation code. Make mp_exp constructor explicit. Remove some dead code. Note mp_float division has outstanding bugs still!! [SVN r75452] --- .../multiprecision/detail/default_ops.hpp | 10 + .../detail/functions/constants.hpp | 12 + .../multiprecision/detail/functions/pow.hpp | 6 +- .../multiprecision/detail/mp_number_base.hpp | 22 +- include/boost/multiprecision/mp_float.hpp | 24 +- include/boost/multiprecision/mpfr.hpp | 1 - test/Jamfile.v2 | 47 ++- test/test_fpclassify.cpp | 324 ++++++++++++++++++ test/test_round.cpp | 1 - 9 files changed, 417 insertions(+), 30 deletions(-) create mode 100644 test/test_fpclassify.cpp diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 775a3b7d..2e2770fa 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -14,6 +14,16 @@ #include #include +#ifndef INSTRUMENT_BACKEND +#ifndef BOOST_MP_INSTRUMENT +#define INSTRUMENT_BACKEND(x) +#else +#define INSTRUMENT_BACKEND(x)\ + std::cout << BOOST_STRINGIZE(x) << " = " << x.str(0, true) << std::endl; +#endif +#endif + + namespace boost{ namespace multiprecision{ namespace default_ops{ // diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp index e1e6a7b2..1c1c1d06 100644 --- a/include/boost/multiprecision/detail/functions/constants.hpp +++ b/include/boost/multiprecision/detail/functions/constants.hpp @@ -40,7 +40,10 @@ void calc_log2(T& num, unsigned digits) } multiply(denom, ui_type(4)); multiply(num, ui_type(3)); + INSTRUMENT_BACKEND(denom); + INSTRUMENT_BACKEND(num); divide(num, denom); + INSTRUMENT_BACKEND(num); } template @@ -142,7 +145,10 @@ const T& get_constant_ln2() static T result; static bool b = false; if(!b) + { calc_log2(result, std::numeric_limits >::digits); + b = true; + } constant_initializer >::do_nothing(); @@ -155,7 +161,10 @@ const T& get_constant_e() static T result; static bool b = false; if(!b) + { calc_e(result, std::numeric_limits >::digits); + b = true; + } constant_initializer >::do_nothing(); @@ -168,7 +177,10 @@ const T& get_constant_pi() static T result; static bool b = false; if(!b) + { calc_pi(result, std::numeric_limits >::digits); + b = true; + } constant_initializer >::do_nothing(); diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index fe8ab3ab..ad4629d6 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -227,7 +227,7 @@ void eval_exp(T& result, const T& x) xx.negate(); // Check the range of the argument. - static const canonical_exp_type maximum_arg_for_exp = std::numeric_limits >::max_exponent == 0 ? std::numeric_limits::max() : std::numeric_limits >::max_exponent; + static const canonical_exp_type maximum_arg_for_exp = std::numeric_limits >::max_exponent == 0 ? (std::numeric_limits::max)() : std::numeric_limits >::max_exponent; if(xx.compare(maximum_arg_for_exp) >= 0) { @@ -356,6 +356,7 @@ void eval_log(T& result, const T& arg) } multiply(result, get_constant_ln2(), canonical_exp_type(e)); + INSTRUMENT_BACKEND(result); subtract(t, ui_type(1)); /* -0.3 <= t <= 0.3 */ if(!alternate) t.negate(); /* 0 <= t <= 0.33333 */ @@ -371,6 +372,7 @@ void eval_log(T& result, const T& arg) multiply(lim, result, std::numeric_limits >::epsilon().backend()); if(get_sign(lim) < 0) lim.negate(); + INSTRUMENT_BACKEND(lim); ui_type k = 1; do @@ -378,10 +380,12 @@ void eval_log(T& result, const T& arg) ++k; multiply(pow, t); divide(t2, pow, k); + INSTRUMENT_BACKEND(t2); if(alternate && ((k & 1) != 0)) add(result, t2); else subtract(result, t2); + INSTRUMENT_BACKEND(result); }while(lim.compare(t2) < 0); } diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 39fd8500..847ae9b3 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -220,7 +220,7 @@ struct mp_exp mp_exp(const Arg1& a) : arg(a) {} - left_type left()const { return arg; } + left_type left()const { return left_type(arg); } const Arg1& left_ref()const{ return arg; } @@ -243,7 +243,7 @@ struct mp_exp typedef Arg1 result_type; typedef terminal tag_type; - mp_exp(const Arg1& a) : arg(a) {} + explicit mp_exp(const Arg1& a) : arg(a) {} const Arg1& value()const { return arg; } @@ -271,8 +271,8 @@ struct mp_exp mp_exp(const Arg1& a1, const Arg2& a2) : arg1(a1), arg2(a2) {} - left_type left()const { return arg1; } - right_type right()const { return arg2; } + left_type left()const { return left_type(arg1); } + right_type right()const { return right_type(arg2); } const Arg1& left_ref()const{ return arg1; } const Arg2& right_ref()const{ return arg2; } @@ -308,9 +308,9 @@ struct mp_exp mp_exp(const Arg1& a1, const Arg2& a2, const Arg3& a3) : arg1(a1), arg2(a2), arg3(a3) {} - left_type left()const { return arg1; } - middle_type middle()const { return arg2; } - right_type right()const { return arg3; } + left_type left()const { return left_type(arg1); } + middle_type middle()const { return middle_type(arg2); } + right_type right()const { return right_type(arg3); } const Arg1& left_ref()const{ return arg1; } const Arg2& middle_ref()const{ return arg2; } const Arg3& right_ref()const{ return arg3; } @@ -343,13 +343,13 @@ inline const mp_number& operator + (const mp_number& v) { return v; } template inline const detail::mp_exp& operator + (const detail::mp_exp& v) { return v; } template -inline detail::mp_exp > operator - (const mp_number& v) { return v; } +inline detail::mp_exp > operator - (const mp_number& v) { return detail::mp_exp >(v); } template -inline detail::mp_exp > operator - (const detail::mp_exp& v) { return v; } +inline detail::mp_exp > operator - (const detail::mp_exp& v) { return detail::mp_exp >(v); } template -inline detail::mp_exp > operator ~ (const mp_number& v) { return v; } +inline detail::mp_exp > operator ~ (const mp_number& v) { return detail::mp_exp >(v); } template -inline detail::mp_exp > operator ~ (const detail::mp_exp& v) { return v; } +inline detail::mp_exp > operator ~ (const detail::mp_exp& v) { return detail::mp_exp >(v); } // // Then addition: // diff --git a/include/boost/multiprecision/mp_float.hpp b/include/boost/multiprecision/mp_float.hpp index 321364c9..dc7fd375 100644 --- a/include/boost/multiprecision/mp_float.hpp +++ b/include/boost/multiprecision/mp_float.hpp @@ -194,7 +194,7 @@ public: init.do_nothing(); static bool init = false; static const std::string str_max = std::string("9." + std::string(static_cast(mp_float_max_digits10), static_cast('9'))) - + std::string("e+" + boost::lexical_cast(mp_float_max_exp)); + + std::string("e+" + boost::lexical_cast(mp_float_max_exp10)); static mp_float val_max; if(!init) { @@ -212,7 +212,7 @@ public: if(!init) { init = true; - val_min = std::string("1.0e" + boost::lexical_cast(mp_float_min_exp)).c_str(); + val_min = std::string("1.0e" + boost::lexical_cast(mp_float_min_exp10)).c_str(); } return val_min; } @@ -285,7 +285,7 @@ public: static const mp_float& eps() { init.do_nothing(); - static mp_float val(1.0, 1 - Digits10); + static mp_float val(1.0, 1 - (int)Digits10); return val; } @@ -857,6 +857,14 @@ mp_float& mp_float::operator/=(const mp_float& v) } else { + if(iszero()) + { + if(v.isnan() || v.iszero()) + { + return *this = v; + } + return *this; + } mp_float t(v); t.calculate_inv(); return operator*=(t); @@ -1098,7 +1106,7 @@ mp_float& mp_float::calculate_inv() // is used. During the iterative steps, the precision of the calculation is limited // to the minimum required in order to minimize the run-time. - static const boost::int32_t double_digits10_minus_one = static_cast(static_cast(Digits10) - static_cast(1)); + static const boost::int32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= static_cast(2)) { @@ -1908,7 +1916,7 @@ bool mp_float::rd_string(const char* const s) } // Check for overflow... - if(exp > mp_float_max_exp) + if(exp > mp_float_max_exp10) { const bool b_result_is_neg = neg; @@ -1918,9 +1926,9 @@ bool mp_float::rd_string(const char* const s) } // ...and check for underflow. - if(exp <= mp_float_min_exp) + if(exp <= mp_float_min_exp10) { - if(exp == mp_float_min_exp) + if(exp == mp_float_min_exp10) { // Check for identity with the minimum value. mp_float test = *this; @@ -2661,7 +2669,7 @@ namespace std static const bool is_bounded = true; static const bool is_modulo = false; static const bool is_iec559 = false; - static const int digits = boost::multiprecision::mp_float::mp_float_digits; + static const int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); static const int digits10 = boost::multiprecision::mp_float::mp_float_digits10; static const int max_digits10 = boost::multiprecision::mp_float::mp_float_max_digits10; static const boost::int64_t min_exponent = boost::multiprecision::mp_float::mp_float_min_exp; // Type differs from int. diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 8e82ab51..80752d1c 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -785,7 +785,6 @@ inline void eval_floor(mpfr_float_backend& result, const mpfr_float_ba template inline void eval_trunc(mpfr_float_backend& result, const mpfr_float_backend& val) { - int c = eval_fpclassify(val); if(0 == mpfr_number_p(val.data())) { result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number >(val), 0, boost::math::policies::policy<>()).backend(); diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 6a85b2f2..843e64cd 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -156,7 +156,7 @@ run mp_number_concept_check.cpp mpfr : # requirements TEST_MPFR_50 [ check-target-builds ../config//has_mpfr : : no ] - : big_number_concept_check_mpfr_50 ; + : mp_number_concept_check_mpfr_50 ; run mp_number_concept_check.cpp mpfr : # command line @@ -164,7 +164,7 @@ run mp_number_concept_check.cpp mpfr : # requirements TEST_MPFR_6 [ check-target-builds ../config//has_mpfr : : no ] - : big_number_concept_check_mpfr_6 ; + : mp_number_concept_check_mpfr_6 ; run mp_number_concept_check.cpp mpfr : # command line @@ -172,7 +172,7 @@ run mp_number_concept_check.cpp mpfr : # requirements TEST_MPFR_15 [ check-target-builds ../config//has_mpfr : : no ] - : big_number_concept_check_mpfr_15 ; + : mp_number_concept_check_mpfr_15 ; run mp_number_concept_check.cpp mpfr : # command line @@ -180,7 +180,7 @@ run mp_number_concept_check.cpp mpfr : # requirements TEST_MPFR_17 [ check-target-builds ../config//has_mpfr : : no ] - : big_number_concept_check_mpfr_17 ; + : mp_number_concept_check_mpfr_17 ; run mp_number_concept_check.cpp mpfr : # command line @@ -188,7 +188,7 @@ run mp_number_concept_check.cpp mpfr : # requirements TEST_MPFR_30 [ check-target-builds ../config//has_mpfr : : no ] - : big_number_concept_check_mpfr_30 ; + : mp_number_concept_check_mpfr_30 ; run mp_number_concept_check.cpp gmp : # command line @@ -196,21 +196,21 @@ run mp_number_concept_check.cpp gmp : # requirements TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] - : big_number_concept_check_mpf50 ; + : mp_number_concept_check_mpf50 ; run mp_number_concept_check.cpp : # command line : # input files : # requirements TEST_MP_FLOAT - : big_number_concept_check_mp_float ; + : mp_number_concept_check_mp_float ; run mp_number_concept_check.cpp : # command line : # input files : # requirements TEST_BACKEND - : big_number_concept_check_backend_concept ; + : mp_number_concept_check_backend_concept ; run test_exp.cpp gmp : # command line @@ -522,3 +522,34 @@ run test_round.cpp [ check-target-builds ../config//has_mpfr : : no ] : test_round_mp_float ; +run test_fpclassify.cpp + : # command line + : # input files + : # requirements + TEST_BACKEND + : test_fpclassify_backend_concept ; + +run test_fpclassify.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : no ] + : test_fpclassify_mpf50 ; + +run test_fpclassify.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_fpclassify_mpfr_50 ; + +run test_fpclassify.cpp + : # command line + : # input files + : # requirements + TEST_MP_FLOAT + [ check-target-builds ../config//has_mpfr : : no ] + : test_fpclassify_mp_float ; + diff --git a/test/test_fpclassify.cpp b/test/test_fpclassify.cpp new file mode 100644 index 00000000..044f8462 --- /dev/null +++ b/test/test_fpclassify.cpp @@ -0,0 +1,324 @@ +// Copyright John Maddock 2006. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include +#include +#include +#include + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 +# define TEST_MPFR_50 +# define TEST_BACKEND +# define TEST_MP_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include +#endif +#ifdef TEST_MPFR_50 +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_MP_FLOAT +#include +#endif + +#ifdef _MSC_VER +#pragma warning(disable: 4127) // conditional expression is constant +#endif + +#define BOOST_CHECK_EQUAL(x, y)\ + if(x != y)\ + {\ + BOOST_ERROR("Values were not equal.");\ + BOOST_LIGHTWEIGHT_TEST_OSTREAM << x << " != " << y << std::endl;\ + } + +const char* method_name(const boost::math::detail::native_tag&) +{ + return "Native"; +} + +const char* method_name(const boost::math::detail::generic_tag&) +{ + return "Generic (with numeric limits)"; +} + +const char* method_name(const boost::math::detail::generic_tag&) +{ + return "Generic (without numeric limits)"; +} + +const char* method_name(const boost::math::detail::ieee_tag&) +{ + return "IEEE std"; +} + +const char* method_name(const boost::math::detail::ieee_copy_all_bits_tag&) +{ + return "IEEE std, copy all bits"; +} + +const char* method_name(const boost::math::detail::ieee_copy_leading_bits_tag&) +{ + return "IEEE std, copy leading bits"; +} + +template +void test() +{ + typedef typename boost::math::detail::fp_traits::type traits; + typedef typename traits::method method; + + T t = 2; + T u = 2; + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + if(std::numeric_limits::is_specialized) + { + t = (std::numeric_limits::max)(); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + t = (std::numeric_limits::min)(); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + } + if(std::numeric_limits::has_denorm) + { + t = (std::numeric_limits::min)(); + t /= 2; + if(t != 0) + { + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_SUBNORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_SUBNORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + } + t = std::numeric_limits::denorm_min(); + if((t != 0) && (t < (std::numeric_limits::min)())) + { + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_SUBNORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_SUBNORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + } + } + else + { + std::cout << "Denormalised forms not tested" << std::endl; + } + t = 0; + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_ZERO); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_ZERO); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + t /= -u; // create minus zero if it exists + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_ZERO); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_ZERO); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + // infinity: + if(std::numeric_limits::has_infinity) + { + // At least one std::numeric_limits::infinity)() returns zero + // (Compaq true64 cxx), hence the check. + t = (std::numeric_limits::infinity)(); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); +#if !defined(__BORLANDC__) && !(defined(__DECCXX) && !defined(_IEEE_FP)) + // divide by zero on Borland triggers a C++ exception :-( + // divide by zero on Compaq CXX triggers a C style signal :-( + t = 2; + u = 0; + t /= u; + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + t = -2; + t /= u; + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); +#else + std::cout << "Infinities from divide by zero not tested" << std::endl; +#endif + } + else + { + std::cout << "Infinity not tested" << std::endl; + } +#ifndef __BORLANDC__ + // NaN's: + // Note that Borland throws an exception if we even try to obtain a Nan + // by calling std::numeric_limits::quiet_NaN() !!!!!!! + if(std::numeric_limits::has_quiet_NaN) + { + t = std::numeric_limits::quiet_NaN(); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NAN); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NAN); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + } + else + { + std::cout << "Quiet NaN's not tested" << std::endl; + } + if(std::numeric_limits::has_signaling_NaN) + { + t = std::numeric_limits::signaling_NaN(); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NAN); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NAN); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + } + else + { + std::cout << "Signaling NaN's not tested" << std::endl; + } +#endif +} + +int main() +{ + BOOST_MATH_CONTROL_FP; + // start by printing some information: +#ifdef isnan + std::cout << "Platform has isnan macro." << std::endl; +#endif +#ifdef fpclassify + std::cout << "Platform has fpclassify macro." << std::endl; +#endif +#ifdef BOOST_HAS_FPCLASSIFY + std::cout << "Platform has FP_NORMAL macro." << std::endl; +#endif + std::cout << "FP_ZERO: " << (int)FP_ZERO << std::endl; + std::cout << "FP_NORMAL: " << (int)FP_NORMAL << std::endl; + std::cout << "FP_INFINITE: " << (int)FP_INFINITE << std::endl; + std::cout << "FP_NAN: " << (int)FP_NAN << std::endl; + std::cout << "FP_SUBNORMAL: " << (int)FP_SUBNORMAL << std::endl; + +#ifdef TEST_MPF_50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_MP_FLOAT + test(); + test(); +#endif +#ifdef TEST_BACKEND + test >(); +#endif + return boost::report_errors(); +} + diff --git a/test/test_round.cpp b/test/test_round.cpp index 52734b28..31312c2f 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -4,7 +4,6 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) #include -#include #include #include #include From c8eda6845ee1e4d422c4b212cb862b40591cd58f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 12 Nov 2011 13:15:33 +0000 Subject: [PATCH 058/256] Search and replace - rename mp_float cpp_float. [SVN r75453] --- example/mp_float_snips.cpp | 10 +- include/boost/multiprecision/cpp_float.hpp | 2726 ++++++++++++++++++++ include/boost/multiprecision/mp_float.hpp | 986 +++---- test/Jamfile.v2 | 66 +- test/linpack-benchmark.cpp | 16 +- test/mp_number_concept_check.cpp | 18 +- test/test_acos.cpp | 14 +- test/test_arithmetic.cpp | 12 +- test/test_asin.cpp | 14 +- test/test_atan.cpp | 14 +- test/test_cos.cpp | 14 +- test/test_cosh.cpp | 14 +- test/test_exp.cpp | 14 +- test/test_fpclassify.cpp | 14 +- test/test_log.cpp | 18 +- test/test_numeric_limits.cpp | 14 +- test/test_pow.cpp | 14 +- test/test_round.cpp | 14 +- test/test_sin.cpp | 17 +- test/test_sinh.cpp | 14 +- test/test_tanh.cpp | 14 +- 21 files changed, 3386 insertions(+), 651 deletions(-) create mode 100644 include/boost/multiprecision/cpp_float.hpp diff --git a/example/mp_float_snips.cpp b/example/mp_float_snips.cpp index 0b2df0d0..8d3e5c25 100644 --- a/example/mp_float_snips.cpp +++ b/example/mp_float_snips.cpp @@ -3,19 +3,19 @@ // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ -#include +#include #include void t1() { - //[mp_float_eg - //=#include + //[cpp_float_eg + //=#include using namespace boost::multiprecision; // Operations at fixed precision and full numeric_limits support: - mp_float_100 b = 2; - std::cout << std::numeric_limits::digits << std::endl; + cpp_float_100 b = 2; + std::cout << std::numeric_limits::digits << std::endl; std::cout << log(b) << std::endl; // print log(2) //] } diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp new file mode 100644 index 00000000..13c41251 --- /dev/null +++ b/include/boost/multiprecision/cpp_float.hpp @@ -0,0 +1,2726 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +// + +#ifndef BOOST_MP_EFX_BACKEND_HPP +#define BOOST_MP_EFX_BACKEND_HPP + +#include +#include +#include + +// +// Headers required for Boost.Math integration: +// +#include + +namespace boost{ +namespace multiprecision{ + +template +class cpp_float +{ +public: + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list real_types; + typedef boost::int64_t exponent_type; + + + static const boost::int32_t mp_radix = 10; + static const boost::int32_t cpp_float_digits = Digits10; + + static const boost::int32_t cpp_float_digits10_setting = Digits10; + static const boost::int32_t cpp_float_digits10_limit = boost::integer_traits::const_max; + static const boost::int32_t cpp_float_digits10 = ((cpp_float_digits10_setting < static_cast(30)) ? static_cast(30) : ((cpp_float_digits10_setting > cpp_float_digits10_limit) ? cpp_float_digits10_limit : cpp_float_digits10_setting)); + static const boost::int32_t cpp_float_digits10_extra = static_cast(((static_cast(cpp_float_digits10) * 15LL) + 50LL) / 100LL); + static const boost::int32_t cpp_float_max_digits10 = static_cast(cpp_float_digits10 + ((cpp_float_digits10_extra < static_cast(5)) ? static_cast(5) : ((cpp_float_digits10_extra > static_cast(30)) ? static_cast(30) : cpp_float_digits10_extra))); + static const boost::int64_t cpp_float_max_exp = static_cast(+9223372036854775795LL); + static const boost::int64_t cpp_float_min_exp = static_cast(-9223372036854775795LL); + static const boost::int64_t cpp_float_max_exp10 = static_cast(+3063937869882635616LL); // Approx. [cpp_float_max_exp / log10(2)], also an even multiple of 8 + static const boost::int64_t cpp_float_min_exp10 = static_cast(-3063937869882635616LL); + static const boost::int32_t mp_elem_digits10 = static_cast(8); + +private: + static const boost::int32_t cpp_float_digits10_num_base = static_cast((cpp_float_max_digits10 / mp_elem_digits10) + (((cpp_float_max_digits10 % mp_elem_digits10) != 0) ? 1 : 0)); + static const boost::int32_t mp_elem_number = static_cast(cpp_float_digits10_num_base + 2); + static const boost::int32_t mp_elem_mask = static_cast(100000000); + + typedef enum enum_fpclass + { + mp_finite, + mp_inf, + mp_NaN + } + t_fpclass; + + typedef boost::array array_type; + + array_type data; + boost::int64_t exp; + bool neg; + t_fpclass fpclass; + boost::int32_t prec_elem; + + // + // Special values constructor: + // + cpp_float(t_fpclass c) : + data(), + exp (static_cast(0)), + neg (false), + fpclass (c), + prec_elem(mp_elem_number) { } + + // + // Static data initializer: + // + struct initializer + { + initializer() + { + cpp_float::nan(); + cpp_float::inf(); + (cpp_float::min)(); + (cpp_float::max)(); + cpp_float::zero(); + cpp_float::one(); + cpp_float::two(); + cpp_float::half(); + cpp_float::double_min(); + cpp_float::double_max(); + cpp_float::long_double_max(); + cpp_float::long_double_min(); + cpp_float::long_long_max(); + cpp_float::long_long_min(); + cpp_float::ulong_long_max(); + cpp_float::eps(); + cpp_float::pow2(0); + } + void do_nothing(){} + }; + + static initializer init; + +public: + // Constructors + cpp_float() : + data(), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) { } + + cpp_float(const char* s) : + data(), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) + { + *this = s; + } + + template + cpp_float(I i, typename enable_if >::type* = 0) : + data(), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) + { + from_unsigned_long_long(i); + } + + template + cpp_float(I i, typename enable_if >::type* = 0) : + data(), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) + { + if(i < 0) + { + from_unsigned_long_long(-i); + negate(); + } + else + from_unsigned_long_long(i); + } + + cpp_float(const cpp_float& f) : + data (f.data), + exp (f.exp), + neg (f.neg), + fpclass (f.fpclass), + prec_elem(f.prec_elem) { } + + template + cpp_float(const F val, typename enable_if >::type* = 0): + data(), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) + { + *this = val; + } + + cpp_float(const double val, long long exponent); + + // Specific special values. + static const cpp_float& nan() + { + static const cpp_float val(mp_NaN); + init.do_nothing(); + return val; + } + static const cpp_float& inf() + { + static const cpp_float val(mp_inf); + init.do_nothing(); + return val; + } + static const cpp_float& (max)() + { + init.do_nothing(); + static bool init = false; + static const std::string str_max = std::string("9." + std::string(static_cast(cpp_float_max_digits10), static_cast('9'))) + + std::string("e+" + boost::lexical_cast(cpp_float_max_exp10)); + static cpp_float val_max; + if(!init) + { + init = true; + val_max = str_max.c_str(); + } + return val_max; + } + + static const cpp_float& (min)() + { + init.do_nothing(); + static bool init = false; + static cpp_float val_min; + if(!init) + { + init = true; + val_min = std::string("1.0e" + boost::lexical_cast(cpp_float_min_exp10)).c_str(); + } + return val_min; + } + static const cpp_float& zero() + { + init.do_nothing(); + static cpp_float val(static_cast(0u)); + return val; + } + static const cpp_float& one() + { + init.do_nothing(); + static cpp_float val(static_cast(1u)); + return val; + } + static const cpp_float& two() + { + init.do_nothing(); + static cpp_float val(static_cast(2u)); + return val; + } + static const cpp_float& half() + { + init.do_nothing(); + static cpp_float val(0.5L); + return val; + } + static const cpp_float& double_min() + { + init.do_nothing(); + static cpp_float val(static_cast((std::numeric_limits::min)())); + return val; + } + static const cpp_float& double_max() + { + init.do_nothing(); + static cpp_float val(static_cast((std::numeric_limits::max)())); + return val; + } + static const cpp_float& long_double_min() + { + init.do_nothing(); + static cpp_float val((std::numeric_limits::min)()); + return val; + } + static const cpp_float& long_double_max() + { + init.do_nothing(); + static cpp_float val((std::numeric_limits::max)()); + return val; + } + static const cpp_float& long_long_max() + { + init.do_nothing(); + static cpp_float val((std::numeric_limits::max)()); + return val; + } + static const cpp_float& long_long_min() + { + init.do_nothing(); + static cpp_float val((std::numeric_limits::min)()); + return val; + } + static const cpp_float& ulong_long_max() + { + init.do_nothing(); + static cpp_float val((std::numeric_limits::max)()); + return val; + } + static const cpp_float& eps() + { + init.do_nothing(); + static cpp_float val(1.0, 1 - (int)Digits10); + return val; + } + + // Basic operations. + cpp_float& operator= (const cpp_float& v) + { + data = v.data; + exp = v.exp; + neg = v.neg; + fpclass = v.fpclass; + prec_elem = v.prec_elem; + return *this; + } + cpp_float& operator= (long long v) + { + if(v < 0) + { + from_unsigned_long_long(-v); + negate(); + } + else + from_unsigned_long_long(v); + return *this; + } + cpp_float& operator= (unsigned long long v) + { + from_unsigned_long_long(v); + return *this; + } + cpp_float& operator= (long double v); + cpp_float& operator= (const char* v) + { + rd_string(v); + return *this; + } + + cpp_float& operator+=(const cpp_float& v); + cpp_float& operator-=(const cpp_float& v); + cpp_float& operator*=(const cpp_float& v); + cpp_float& operator/=(const cpp_float& v); + + cpp_float& add_unsigned_long_long(const unsigned long long n) + { + cpp_float t; + t.from_unsigned_long_long(n); + return *this += t; + } + cpp_float& sub_unsigned_long_long(const unsigned long long n) + { + cpp_float t; + t.from_unsigned_long_long(n); + return *this -= t; + } + cpp_float& mul_unsigned_long_long(const unsigned long long n); + cpp_float& div_unsigned_long_long(const unsigned long long n); + + // Elementary primitives. + cpp_float& calculate_inv (void); + cpp_float& calculate_sqrt(void); + void negate() + { + if(!iszero()) + neg = !neg; + } + + // Comparison functions + bool isnan (void) const { return (fpclass == mp_NaN); } + bool isinf (void) const { return (fpclass == mp_inf); } + bool isfinite(void) const { return (fpclass == mp_finite); } + + bool iszero (void) const + { + return ((fpclass == mp_finite) && (data[0u] == 0u)); + } + bool isone (void) const; + bool isint (void) const; + bool isneg (void) const { return neg; } + + // Operators pre-increment and pre-decrement + cpp_float& operator++(void) + { + return *this += one(); + } + cpp_float& operator--(void) + { + return *this -= one(); + } + + std::string str(unsigned digits, bool scientific)const; + + int compare(const cpp_float& v)const; + template + int compare(const V& v)const + { + cpp_float t; + t = v; + return compare(t); + } + + void swap(cpp_float& v) + { + data.swap(v.data); + std::swap(exp, v.exp); + std::swap(neg, v.neg); + std::swap(fpclass, v.fpclass); + std::swap(prec_elem, v.prec_elem); + } + + double extract_double (void) const; + long double extract_long_double (void) const; + signed long long extract_signed_long_long (void) const; + unsigned long long extract_unsigned_long_long(void) const; + void extract_parts (double& mantissa, boost::int64_t& exponent) const; + cpp_float extract_integer_part (void) const; + void precision(const boost::int32_t prec_digits) + { + if(prec_digits >= cpp_float_digits10) + { + prec_elem = mp_elem_number; + } + else + { + const boost::int32_t elems = static_cast( static_cast( (prec_digits + (mp_elem_digits10 / 2)) / mp_elem_digits10) + + static_cast(((prec_digits % mp_elem_digits10) != 0) ? 1 : 0)); + + prec_elem = (std::min)(mp_elem_number, (std::max)(elems, static_cast(2))); + } + } + static cpp_float pow2(long long i); + long long order()const + { + const bool bo_order_is_zero = ((!isfinite()) || (data[0] == static_cast(0u))); + // + // Binary search to find the order of the leading term: + // + boost::uint32_t prefix = 0; + + if(data[0] >= 100000UL) + { + if(data[0] >= 10000000UL) + { + if(data[0] >= 100000000UL) + { + if(data[0] >= 1000000000UL) + prefix = 9; + else + prefix = 8; + } + else + prefix = 7; + } + else + { + if(data[0] >= 1000000UL) + prefix = 6; + else + prefix = 5; + } + } + else + { + if(data[0] >= 1000UL) + { + if(data[0] >= 10000UL) + prefix = 4; + else + prefix = 3; + } + else + { + if(data[0] >= 100) + prefix = 2; + else if(data[0] >= 10) + prefix = 1; + } + } + + return (bo_order_is_zero ? static_cast(0) + : static_cast(exp + prefix)); + } + +private: + static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast(0u)); } + static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast(cpp_float::mp_elem_mask - 1)); } + static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast('0')); } + + void from_unsigned_long_long(const unsigned long long u); + + int cmp_data(const array_type& vd) const; + + static void mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p); + static boost::uint32_t mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); + static boost::uint32_t div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); + + bool rd_string(const char* const s); +}; + +template +typename cpp_float::initializer cpp_float::init; + +template +const boost::int32_t cpp_float::mp_radix; +template +const boost::int32_t cpp_float::cpp_float_digits; +template +const boost::int32_t cpp_float::cpp_float_digits10_setting; +template +const boost::int32_t cpp_float::cpp_float_digits10_limit; +template +const boost::int32_t cpp_float::cpp_float_digits10; +template +const boost::int32_t cpp_float::cpp_float_digits10_extra; +template +const boost::int32_t cpp_float::cpp_float_max_digits10; +template +const boost::int64_t cpp_float::cpp_float_max_exp; +template +const boost::int64_t cpp_float::cpp_float_min_exp; +template +const boost::int64_t cpp_float::cpp_float_max_exp10; +template +const boost::int64_t cpp_float::cpp_float_min_exp10; +template +const boost::int32_t cpp_float::mp_elem_digits10; +template +const boost::int32_t cpp_float::cpp_float_digits10_num_base; +template +const boost::int32_t cpp_float::mp_elem_number; +template +const boost::int32_t cpp_float::mp_elem_mask; + + +template +cpp_float& cpp_float::operator+=(const cpp_float& v) +{ + if(isnan()) + { + return *this; + } + + if(isinf()) + { + if(v.isinf() && (isneg() != v.isneg())) + { + *this = nan(); + } + return *this; + } + + if(iszero()) + { + return operator=(v); + } + + // Get the offset for the add/sub operation. + static const boost::int64_t max_delta_exp = static_cast((mp_elem_number - 1) * mp_elem_digits10); + + const boost::int64_t ofs_exp = static_cast(exp - v.exp); + + // Check if the operation is out of range, requiring special handling. + if(v.iszero() || (ofs_exp > max_delta_exp)) + { + // Result is *this unchanged since v is negligible compared to *this. + return *this; + } + else if(ofs_exp < -max_delta_exp) + { + // Result is *this = v since *this is negligible compared to v. + return operator=(v); + } + + // Do the add/sub operation. + + typename array_type::iterator p_u = data.begin(); + typename array_type::const_iterator p_v = v.data.begin(); + bool b_copy = false; + const boost::int32_t ofs = static_cast(static_cast(ofs_exp) / mp_elem_digits10); + array_type n_data; + + if(neg == v.neg) + { + // Add v to *this, where the data array of either *this or v + // might have to be treated with a positive, negative or zero offset. + // The result is stored in *this. The data are added one element + // at a time, each element with carry. + if(ofs >= static_cast(0)) + { + std::copy(v.data.begin(), v.data.end() - static_cast(ofs), n_data.begin() + static_cast(ofs)); + std::fill(n_data.begin(), n_data.begin() + static_cast(ofs), static_cast(0u)); + p_v = n_data.begin(); + } + else + { + std::copy(data.begin(), data.end() - static_cast(-ofs), n_data.begin() + static_cast(-ofs)); + std::fill(n_data.begin(), n_data.begin() + static_cast(-ofs), static_cast(0u)); + p_u = n_data.begin(); + b_copy = true; + } + + // Addition algorithm + boost::uint32_t carry = static_cast(0u); + + for(boost::int32_t j = static_cast(mp_elem_number - static_cast(1)); j >= static_cast(0); j--) + { + boost::uint32_t t = static_cast(static_cast(p_u[j] + p_v[j]) + carry); + carry = t / static_cast(mp_elem_mask); + p_u[j] = static_cast(t - static_cast(carry * static_cast(mp_elem_mask))); + } + + if(b_copy) + { + data = n_data; + exp = v.exp; + } + + // There needs to be a carry into the element -1 of the array data + if(carry != static_cast(0u)) + { + std::copy_backward(data.begin(), data.end() - static_cast(1u), data.end()); + data[0] = carry; + exp += static_cast(mp_elem_digits10); + } + } + else + { + // Subtract v from *this, where the data array of either *this or v + // might have to be treated with a positive, negative or zero offset. + if((ofs > static_cast(0)) + || ( (ofs == static_cast(0)) + && (cmp_data(v.data) > static_cast(0))) + ) + { + // In this case, |u| > |v| and ofs is positive. + // Copy the data of v, shifted down to a lower value + // into the data array m_n. Set the operand pointer p_v + // to point to the copied, shifted data m_n. + std::copy(v.data.begin(), v.data.end() - static_cast(ofs), n_data.begin() + static_cast(ofs)); + std::fill(n_data.begin(), n_data.begin() + static_cast(ofs), static_cast(0u)); + p_v = n_data.begin(); + } + else + { + if(ofs != static_cast(0)) + { + // In this case, |u| < |v| and ofs is negative. + // Shift the data of u down to a lower value. + std::copy_backward(data.begin(), data.end() - static_cast(-ofs), data.end()); + std::fill(data.begin(), data.begin() + static_cast(-ofs), static_cast(0u)); + } + + // Copy the data of v into the data array n_data. + // Set the u-pointer p_u to point to m_n and the + // operand pointer p_v to point to the shifted + // data m_data. + n_data = v.data; + p_u = n_data.begin(); + p_v = data.begin(); + b_copy = true; + } + + boost::int32_t j; + + // Subtraction algorithm + boost::int32_t borrow = static_cast(0); + + for(j = static_cast(mp_elem_number - static_cast(1)); j >= static_cast(0); j--) + { + boost::int32_t t = static_cast(static_cast( static_cast(p_u[j]) + - static_cast(p_v[j])) - borrow); + + // Underflow? Borrow? + if(t < static_cast(0)) + { + // Yes, underflow and borrow + t += static_cast(mp_elem_mask); + borrow = static_cast(1); + } + else + { + borrow = static_cast(0); + } + + p_u[j] = static_cast(static_cast(t) % static_cast(mp_elem_mask)); + } + + if(b_copy) + { + data = n_data; + exp = v.exp; + neg = v.neg; + } + + // Is it necessary to justify the data? + const typename array_type::const_iterator first_nonzero_elem = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); + + if(first_nonzero_elem != data.begin()) + { + if(first_nonzero_elem == data.end()) + { + // This result of the subtraction is exactly zero. + // Reset the sign and the exponent. + neg = false; + exp = static_cast(0); + } + else + { + // Justify the data + const std::size_t sj = static_cast(std::distance(data.begin(), first_nonzero_elem)); + + std::copy(data.begin() + static_cast(sj), data.end(), data.begin()); + std::fill(data.end() - sj, data.end(), static_cast(0u)); + + exp -= static_cast(sj * static_cast(mp_elem_digits10)); + } + } + } + + // Check for underflow. + if(iszero()) + { + return *this = zero(); + } + + bool overflow = exp >= cpp_float_max_exp; + if(exp == cpp_float_max_exp) + { + // Check to see if we really truely have an overflow or not... + if(isneg()) + { + cpp_float t(*this); + t.negate(); + overflow = t.compare((max)()) > 0; + } + else + { + overflow = compare((max)()) > 0; + } + } + + // Check for overflow. + if(overflow) + { + const bool b_result_is_neg = neg; + + *this = inf(); + if(b_result_is_neg) + negate(); + } + + return *this; +} + +template +cpp_float& cpp_float::operator-=(const cpp_float& v) +{ + // Use *this - v = -(-*this + v). + negate(); + *this += v; + negate(); + return *this; +} + +template +cpp_float& cpp_float::operator*=(const cpp_float& v) +{ + // Evaluate the sign of the result. + const bool b_result_is_neg = (neg != v.neg); + + // Artificially set the sign of the result to be positive. + neg = false; + + // Handle special cases like zero, inf and NaN. + const bool b_u_is_inf = isinf(); + const bool b_v_is_inf = v.isinf(); + const bool b_u_is_zero = iszero(); + const bool b_v_is_zero = v.iszero(); + + if( (isnan() || v.isnan()) + || (b_u_is_inf && b_v_is_zero) + || (b_v_is_inf && b_u_is_zero) + ) + { + *this = nan(); + return *this; + } + + if(b_u_is_inf || b_v_is_inf) + { + *this = inf(); + if(b_result_is_neg) + negate(); + return *this; + } + + if(b_u_is_zero || b_v_is_zero) + { + return *this = zero(); + } + + // Check for overflow or underflow. + const bool u_exp_is_neg = (exp < static_cast(0)); + const bool v_exp_is_neg = (v.exp < static_cast(0)); + + if(u_exp_is_neg == v_exp_is_neg) + { + // Get the unsigned base-10 exponents of *this and v and... + const boost::int64_t u_exp = ((!u_exp_is_neg) ? exp : static_cast( -exp)); + const boost::int64_t v_exp = ((!v_exp_is_neg) ? v.exp : static_cast(-v.exp)); + + // Check the range of the upcoming multiplication. + const bool b_result_is_out_of_range = (v_exp >= static_cast(cpp_float_max_exp10 - u_exp)); + + if(b_result_is_out_of_range) + { + if(u_exp_is_neg) + { + *this = zero(); + } + else + { + *this = inf(); + if(b_result_is_neg) + negate(); + } + return *this; + } + } + + // Set the exponent of the result. + exp += v.exp; + + boost::array(mp_elem_number + static_cast(1))> w = {{ 0u }}; + + mul_loop_uv(data.data(), v.data.data(), w.data(), (std::min)(prec_elem, v.prec_elem)); + + // Copy the multiplication data into the result. + // Shift the result and adjust the exponent if necessary. + if(w[static_cast(0u)] != static_cast(0u)) + { + exp += static_cast(mp_elem_digits10); + + std::copy(w.begin(), w.end() - 1u, data.begin()); + } + else + { + std::copy(w.begin() + 1u, w.end(), data.begin()); + } + + // Set the sign of the result. + neg = b_result_is_neg; + + return *this; +} + +template +cpp_float& cpp_float::operator/=(const cpp_float& v) +{ + const bool u_and_v_are_finite_and_identical = ( isfinite() + && (fpclass == v.fpclass) + && (exp == v.exp) + && (cmp_data(v.data) == static_cast(0))); + + if(u_and_v_are_finite_and_identical) + { + *this = one(); + if(neg != v.neg) + negate(); + return *this; + } + else + { + if(iszero()) + { + if(v.isnan() || v.iszero()) + { + return *this = v; + } + return *this; + } + cpp_float t(v); + t.calculate_inv(); + return operator*=(t); + } +} + +template +cpp_float& cpp_float::mul_unsigned_long_long(const unsigned long long n) +{ + // Multiply *this with a constant unsigned long long. + + // Evaluate the sign of the result. + const bool b_neg = neg; + + // Artificially set the sign of the result to be positive. + neg = false; + + // Handle special cases like zero, inf and NaN. + const bool b_u_is_inf = isinf(); + const bool b_n_is_zero = (n == static_cast(0)); + + if(isnan() || (b_u_is_inf && b_n_is_zero)) + { + return (*this = nan()); + } + + if(b_u_is_inf) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + if(iszero() || b_n_is_zero) + { + // Multiplication by zero. + return *this = zero(); + } + + if(n >= static_cast(mp_elem_mask)) + { + neg = b_neg; + cpp_float t; + t = n; + return operator*=(t); + } + + if(n == static_cast(1u)) + { + neg = b_neg; + return *this; + } + + // Set up the multiplication loop. + const boost::uint32_t nn = static_cast(n); + const boost::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem); + + // Handle the carry and adjust the exponent. + if(carry != static_cast(0u)) + { + exp += static_cast(mp_elem_digits10); + + // Shift the result of the multiplication one element to the right. + std::copy_backward(data.begin(), + data.begin() + static_cast(prec_elem - static_cast(1)), + data.begin() + static_cast(prec_elem)); + + data.front() = static_cast(carry); + } + + bool overflow = exp >= cpp_float_max_exp; + if(exp == cpp_float_max_exp) + { + // Check to see if we really truely have an overflow or not... + if(isneg()) + { + cpp_float t(*this); + t.negate(); + overflow = t.compare((max)()) > 0; + } + else + { + overflow = compare((max)()) > 0; + } + } + + if(overflow) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + // Set the sign. + neg = b_neg; + + return *this; +} + +template +cpp_float& cpp_float::div_unsigned_long_long(const unsigned long long n) +{ + // Divide *this by a constant unsigned long long. + + // Evaluate the sign of the result. + const bool b_neg = neg; + + // Artificially set the sign of the result to be positive. + neg = false; + + // Handle special cases like zero, inf and NaN. + if(isnan()) + { + return *this; + } + + if(isinf()) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + if(n == static_cast(0u)) + { + // Divide by 0. + if(iszero()) + { + *this = nan(); + return *this; + } + else + { + *this = inf(); + if(isneg()) + negate(); + return *this; + } + } + + if(iszero()) + { + return *this; + } + + if(n >= static_cast(mp_elem_mask)) + { + neg = b_neg; + cpp_float t; + t = n; + return operator/=(t); + } + + const boost::uint32_t nn = static_cast(n); + + if(nn > static_cast(1u)) + { + // Do the division loop. + const boost::uint32_t prev = div_loop_n(data.data(), nn, prec_elem); + + // Determine if one leading zero is in the result data. + if(data[0] == static_cast(0u)) + { + // Adjust the exponent + exp -= static_cast(mp_elem_digits10); + + // Shift result of the division one element to the left. + std::copy(data.begin() + static_cast(1u), + data.begin() + static_cast(prec_elem - static_cast(1)), + data.begin()); + + data[prec_elem - static_cast(1)] = static_cast(static_cast(prev * static_cast(mp_elem_mask)) / nn); + } + } + + // Check for underflow. + if(iszero()) + { + return *this = zero(); + } + + // Set the sign of the result. + neg = b_neg; + + return *this; +} + +template +cpp_float& cpp_float::calculate_inv() +{ + // Compute the inverse of *this. + const bool b_neg = neg; + + neg = false; + + // Handle special cases like zero, inf and NaN. + if(iszero()) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + if(isnan()) + { + return *this; + } + + if(isinf()) + { + return *this = zero(); + } + + if(isone()) + { + if(b_neg) + negate(); + return *this; + } + + // Save the original *this. + cpp_float x(*this); + + // Generate the initial estimate using division. + // Extract the mantissa and exponent for a "manual" + // computation of the estimate. + double dd; + boost::int64_t ne; + x.extract_parts(dd, ne); + + // Do the inverse estimate using double precision estimates of mantissa and exponent. + operator=(cpp_float(1.0 / dd, -ne)); + + // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration + // is used. During the iterative steps, the precision of the calculation is limited + // to the minimum required in order to minimize the run-time. + + static const boost::int32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; + + for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= static_cast(2)) + { + // Adjust precision of the terms. + precision(static_cast(digits * static_cast(2))); + x.precision(static_cast(digits * static_cast(2))); + + // Next iteration. + cpp_float t(*this); + t *= x; + t -= two(); + t.negate(); + *this *= t; + } + + neg = b_neg; + + prec_elem = mp_elem_number; + + return *this; +} + +template +cpp_float& cpp_float::calculate_sqrt(void) +{ + // Compute the square root of *this. + + if(isneg() || (!isfinite())) + { + *this = nan(); + return *this; + } + + if(iszero() || isone()) + { + return *this; + } + + // Save the original *this. + cpp_float x(*this); + + // Generate the initial estimate using division. + // Extract the mantissa and exponent for a "manual" + // computation of the estimate. + double dd; + boost::int64_t ne; + extract_parts(dd, ne); + + // Force the exponent to be an even multiple of two. + if((ne % static_cast(2)) != static_cast(0)) + { + ++ne; + dd /= 10.0; + } + + // Setup the iteration. + // Estimate the square root using simple manipulations. + const double sqd = std::sqrt(dd); + + *this = cpp_float(sqd, static_cast(ne / static_cast(2))); + + // Estimate 1.0 / (2.0 * x0) using simple manipulations. + cpp_float vi(0.5 / sqd, static_cast(-ne / static_cast(2))); + + // Compute the square root of x. Coupled Newton iteration + // as described in "Pi Unleashed" is used. During the + // iterative steps, the precision of the calculation is + // limited to the minimum required in order to minimize + // the run-time. + // + // Book references: + // http://www.jjj.de/pibook/pibook.html + // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846 + + static const boost::uint32_t double_digits10_minus_one = static_cast(static_cast(Digits10) - static_cast(1)); + + for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= 2u) + { + // Adjust precision of the terms. + precision(digits * 2); + vi.precision(digits * 2); + + // Next iteration of vi + cpp_float t(*this); + t *= vi; + t.negate(); + t.mul_unsigned_long_long(2u); + t += one(); + t *= vi; + vi += t; + + // Next iteration of *this + t = *this; + t *= *this; + t.negate(); + t += x; + t *= vi; + *this += t; + } + + prec_elem = mp_elem_number; + + return *this; +} + +template +int cpp_float::cmp_data(const array_type& vd) const +{ + // Compare the data of *this with those of v. + // Return +1 for *this > v + // 0 for *this = v + // -1 for *this < v + + const std::pair mismatch_pair = std::mismatch(data.begin(), data.end(), vd.begin()); + + const bool is_equal = ((mismatch_pair.first == data.end()) && (mismatch_pair.second == vd.end())); + + if(is_equal) + { + return 0; + } + else + { + return ((*mismatch_pair.first > *mismatch_pair.second) ? 1 : -1); + } +} + +template +int cpp_float::compare(const cpp_float& v) const +{ + // Compare v with *this. + // Return +1 for *this > v + // 0 for *this = v + // -1 for *this < v + + // Handle all non-finite cases. + if((!isfinite()) || (!v.isfinite())) + { + // NaN can never equal NaN. Return an implementation-dependent + // signed result. Also note that comparison of NaN with NaN + // using operators greater-than or less-than is undefined. + if(isnan() || v.isnan()) { return (isnan() ? 1 : -1); } + + if(isinf() && v.isinf()) + { + // Both *this and v are infinite. They are equal if they have the same sign. + // Otherwise, *this is less than v if and only if *this is negative. + return ((neg == v.neg) ? 0 : (neg ? -1 : 1)); + } + + if(isinf()) + { + // *this is infinite, but v is finite. + // So negative infinite *this is less than any finite v. + // Whereas positive infinite *this is greater than any finite v. + return (isneg() ? -1 : 1); + } + else + { + // *this is finite, and v is infinite. + // So any finite *this is greater than negative infinite v. + // Whereas any finite *this is less than positive infinite v. + return (v.neg ? 1 : -1); + } + } + + // And now handle all *finite* cases. + if(iszero()) + { + // The value of *this is zero and v is either zero or non-zero. + return (v.iszero() ? 0 + : (v.neg ? 1 : -1)); + } + else if(v.iszero()) + { + // The value of v is zero and *this is non-zero. + return (neg ? -1 : 1); + } + else + { + // Both *this and v are non-zero. + + if(neg != v.neg) + { + // The signs are different. + return (neg ? -1 : 1); + } + else if(exp != v.exp) + { + // The signs are the same and the exponents are different. + const int val_cmp_exp = ((exp < v.exp) ? 1 : -1); + + return (neg ? val_cmp_exp : -val_cmp_exp); + } + else + { + // The signs are the same and the exponents are the same. + // Compare the data. + const int val_cmp_data = cmp_data(v.data); + + return ((!neg) ? val_cmp_data : -val_cmp_data); + } + } +} + +template +bool cpp_float::isone() const +{ + // Check if the value of *this is identically 1 or very close to 1. + + const bool not_negative_and_is_finite = ((!neg) && isfinite()); + + if(not_negative_and_is_finite) + { + if((data[0u] == static_cast(1u)) && (exp == static_cast(0))) + { + const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); + return (it_non_zero == data.end()); + } + else if((data[0u] == static_cast(mp_elem_mask - 1)) && (exp == static_cast(-mp_elem_digits10))) + { + const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate); + return (it_non_nine == data.end()); + } + } + + return false; +} + +template +bool cpp_float::isint() const +{ + if(fpclass != mp_finite) { return false; } + + if(iszero()) { return true; } + + if(exp < static_cast(0)) { return false; } // |*this| < 1. + + const typename array_type::size_type offset_decimal_part = static_cast(exp / mp_elem_digits10) + 1u; + + if(offset_decimal_part >= static_cast(mp_elem_number)) + { + // The number is too large to resolve the integer part. + // It considered to be a pure integer. + return true; + } + + typename array_type::const_iterator it_non_zero = std::find_if(data.begin() + offset_decimal_part, data.end(), data_elem_is_non_zero_predicate); + + return (it_non_zero == data.end()); +} + +template +void cpp_float::extract_parts(double& mantissa, boost::int64_t& exponent) const +{ + // Extract the approximate parts mantissa and base-10 exponent from the input cpp_float value x. + + // Extracts the mantissa and exponent. + exponent = exp; + + boost::uint32_t p10 = static_cast(1u); + boost::uint32_t test = data[0u]; + + for(;;) + { + test /= static_cast(10u); + + if(test == static_cast(0u)) + { + break; + } + + p10 *= static_cast(10u); + ++exponent; + } + + mantissa = static_cast(data[0]) + + (static_cast(data[1]) / static_cast(mp_elem_mask)) + + ((static_cast(data[2]) / static_cast(mp_elem_mask)) / static_cast(mp_elem_mask)); + + mantissa /= static_cast(p10); + + if(neg) { mantissa = -mantissa; } +} + +template +double cpp_float::extract_double(void) const +{ + // Returns the double conversion of a cpp_float. + + // Check for non-normal cpp_float. + if(!isfinite()) + { + if(isnan()) + { + return std::numeric_limits::quiet_NaN(); + } + else + { + return ((!neg) ? std::numeric_limits::infinity() + : -std::numeric_limits::infinity()); + } + } + + cpp_float xx(*this); + if(xx.isneg()) + xx.negate(); + + // Check for zero cpp_float. + if(iszero() || (xx.compare(double_min()) < 0)) + { + return 0.0; + } + + // Check if cpp_float exceeds the maximum of double. + if(xx.compare(double_max()) > 0) + { + return ((!neg) ? std::numeric_limits::infinity() + : -std::numeric_limits::infinity()); + } + + std::stringstream ss; + + ss << str(std::numeric_limits::digits10 + (2 + 1), true); + + double d; + ss >> d; + + return d; +} + +template +long double cpp_float::extract_long_double(void) const +{ + // Returns the long double conversion of a cpp_float. + + // Check for non-normal cpp_float. + if(!isfinite()) + { + if(isnan()) + { + return std::numeric_limits::quiet_NaN(); + } + else + { + return ((!neg) ? std::numeric_limits::infinity() + : -std::numeric_limits::infinity()); + } + } + + cpp_float xx(*this); + if(xx.isneg()) + xx.negate(); + + // Check for zero cpp_float. + if(iszero() || (xx.compare(long_double_min()) < 0)) + { + return static_cast(0.0); + } + + // Check if cpp_float exceeds the maximum of double. + if(xx.compare(long_double_max()) > 0) + { + return ((!neg) ? std::numeric_limits::infinity() + : -std::numeric_limits::infinity()); + } + + std::stringstream ss; + + ss << str(std::numeric_limits::digits10 + (2 + 1), true); + + long double ld; + ss >> ld; + + return ld; +} + +template +signed long long cpp_float::extract_signed_long_long(void) const +{ + // Extracts a signed long long from *this. + // If (x > maximum of signed long long) or (x < minimum of signed long long), + // then the maximum or minimum of signed long long is returned accordingly. + + if(exp < static_cast(0)) + { + return static_cast(0); + } + + const bool b_neg = isneg(); + + unsigned long long val; + + if((!b_neg) && (compare(long_long_max()) > 0)) + { + return (std::numeric_limits::max)(); + } + else if(b_neg && (compare(long_long_min()) < 0)) + { + return (std::numeric_limits::min)(); + } + else + { + // Extract the data into an unsigned long long value. + cpp_float xn(extract_integer_part()); + if(xn.isneg()) + xn.negate(); + + val = static_cast(xn.data[0]); + + const boost::int32_t imax = (std::min)(static_cast(static_cast(xn.exp) / mp_elem_digits10), static_cast(mp_elem_number - static_cast(1))); + + for(boost::int32_t i = static_cast(1); i <= imax; i++) + { + val *= static_cast(mp_elem_mask); + val += static_cast(xn.data[i]); + } + } + + return ((!b_neg) ? static_cast(val) : static_cast(-static_cast(val))); +} + +template +unsigned long long cpp_float::extract_unsigned_long_long(void) const +{ + // Extracts an unsigned long long from *this. + // If x exceeds the maximum of unsigned long long, + // then the maximum of unsigned long long is returned. + // If x is negative, then the unsigned long long cast of + // the signed long long extracted value is returned. + + if(isneg()) + { + return static_cast(extract_signed_long_long()); + } + + if(exp < static_cast(0)) + { + return static_cast(0u); + } + + const cpp_float xn(extract_integer_part()); + + unsigned long long val; + + if(xn.compare(ulong_long_max()) > 0) + { + return (std::numeric_limits::max)(); + } + else + { + // Extract the data into an unsigned long long value. + val = static_cast(xn.data[0]); + + const boost::int32_t imax = (std::min)(static_cast(static_cast(xn.exp) / mp_elem_digits10), static_cast(mp_elem_number - static_cast(1))); + + for(boost::int32_t i = static_cast(1); i <= imax; i++) + { + val *= static_cast(mp_elem_mask); + val += static_cast(xn.data[i]); + } + } + + return val; +} + +template +cpp_float cpp_float::extract_integer_part(void) const +{ + // Compute the signed integer part of x. + + if(!isfinite()) + { + return *this; + } + + if(exp < static_cast(0)) + { + // The absolute value of the number is smaller than 1. + // Thus the integer part is zero. + return zero(); + } + else if(exp >= Digits10 - 1) + { + // The number is too large to resolve the integer part. + // Thus it is already a pure integer part. + return *this; + } + + // Make a local copy. + cpp_float x = *this; + + // Clear out the decimal portion + const size_t first_clear = (static_cast(x.exp) / static_cast(mp_elem_digits10)) + 1u; + const size_t last_clear = static_cast(mp_elem_number); + + std::fill(x.data.begin() + first_clear, x.data.begin() + last_clear, static_cast(0u)); + + return x; +} + +template +std::string cpp_float::str(std::size_t number_of_digits, bool scientific) const +{ + std::string str; + boost::int64_t my_exp = order(); + if(number_of_digits == 0) + number_of_digits = (std::numeric_limits::max)(); + // Determine the number of elements needed to provide the requested digits from cpp_float. + const std::size_t number_of_elements = (std::min)(static_cast((number_of_digits / static_cast(mp_elem_digits10)) + 2u), + static_cast(mp_elem_number)); + + // Extract the remaining digits from cpp_float after the decimal point. + str = boost::lexical_cast(data[0]); + + // Extract all of the digits from cpp_float, beginning with the first data element. + for(std::size_t i = static_cast(1u); i < number_of_elements; i++) + { + std::stringstream ss; + + ss << std::setw(static_cast(mp_elem_digits10)) + << std::setfill(static_cast('0')) + << data[i]; + + str += ss.str(); + } + + // Cut the output to the size of the precision. + if(str.length() > number_of_digits) + { + // Get the digit after the last needed digit for rounding + const boost::uint32_t round = static_cast(static_cast(str.at(number_of_digits)) - static_cast('0')); + + // Truncate the string + str = str.substr(static_cast(0u), number_of_digits); + + if(round >= static_cast(5u)) + { + std::size_t ix = static_cast(str.length() - 1u); + + // Every trailing 9 must be rounded up + while(ix && (static_cast(str.at(ix)) - static_cast('0') == static_cast(9))) + { + str.at(ix) = static_cast('0'); + --ix; + } + + if(!ix) + { + // There were nothing but trailing nines. + if(static_cast(static_cast(str.at(ix)) - static_cast(0x30)) == static_cast(9)) + { + // Increment up to the next order and adjust exponent. + str.at(ix) = static_cast('1'); + ++my_exp; + } + else + { + // Round up this digit. + ++str.at(ix); + } + } + else + { + // Round up the last digit. + ++str[ix]; + } + } + } + // + // Suppress trailing zeros: + // + std::string::iterator pos = str.end(); + while(pos != str.begin() && *--pos == '0'){} + if(pos != str.end()) + ++pos; + str.erase(pos, str.end()); + if(str.empty()) + str = '0'; + if(!scientific && (str.size() < 20) && (my_exp >= 0) && (my_exp < 20)) + { + if(1 + my_exp > str.size()) + { + // Just pad out the end with zeros: + str.append(static_cast(1 + my_exp - str.size()), '0'); + } + else if(my_exp + 1 != str.size()) + { + // Insert the decimal point: + str.insert(static_cast(my_exp + 1), 1, '.'); + } + } + else + { + // Scientific format: + str.insert(1, 1, '.'); + if(str.size() == 2) + str.append(1, '0'); + str.append(1, 'e'); + str.append(boost::lexical_cast(my_exp)); + } + if(isneg()) + str.insert(0, 1, '-'); + return str; +} + +template +bool cpp_float::rd_string(const char* const s) +{ + std::string str(s); + + // Get a possible exponent and remove it. + exp = static_cast(0); + + std::size_t pos; + + if( ((pos = str.find('e')) != std::string::npos) + || ((pos = str.find('E')) != std::string::npos) + ) + { + // Remove the exponent part from the string. + exp = boost::lexical_cast(static_cast(str.c_str() + (pos + 1u))); + str = str.substr(static_cast(0u), pos); + } + + // Get a possible +/- sign and remove it. + neg = false; + + if((pos = str.find(static_cast('-'))) != std::string::npos) + { + neg = true; + str.erase(pos, static_cast(1u)); + } + + if((pos = str.find(static_cast('+'))) != std::string::npos) + { + str.erase(pos, static_cast(1u)); + } + + // Remove leading zeros for all input types. + const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate); + + if(fwd_it_leading_zero != str.begin()) + { + if(fwd_it_leading_zero == str.end()) + { + // The string contains nothing but leading zeros. + // This string represents zero. + operator=(zero()); + return true; + } + else + { + str.erase(str.begin(), fwd_it_leading_zero); + } + } + + // Put the input string into the standard cpp_float input form + // aaa.bbbbE+/-n, where aa has 1...mp_elem_digits10, bbbb has an + // even multiple of mp_elem_digits10 which are possibly zero padded + // on the right-end, and n is a signed 32-bit integer which is an + // even multiple of mp_elem_digits10. + + // Find a possible decimal point. + pos = str.find(static_cast('.')); + + if(pos != std::string::npos) + { + // Remove all trailing insignificant zeros. + const std::string::const_reverse_iterator rit_non_zero = std::find_if(str.rbegin(), str.rend(), char_is_nonzero_predicate); + + if(rit_non_zero != str.rbegin()) + { + const std::string::size_type ofs = str.length() - std::distance(str.rbegin(), rit_non_zero); + str.erase(str.begin() + ofs, str.end()); + } + + // Check if the input is identically zero. + if(str == std::string(".")) + { + operator=(zero()); + return true; + } + + // Remove leading significant zeros just after the decimal point + // and adjust the exponent accordingly. + // Note that the while-loop operates only on strings of the form ".000abcd..." + // and peels away the zeros just after the decimal point. + if(str.at(static_cast(0u)) == static_cast('.')) + { + const std::string::iterator it_non_zero = std::find_if(str.begin() + 1u, str.end(), char_is_nonzero_predicate); + + std::size_t delta_exp = static_cast(0u); + + if(str.at(static_cast(1u)) == static_cast('0')) + { + delta_exp = std::distance(str.begin() + 1u, it_non_zero); + } + + // Bring one single digit into the mantissa and adjust exponent accordingly. + str.erase(str.begin(), it_non_zero); + str.insert(static_cast(1u), "."); + exp -= static_cast(delta_exp + 1u); + } + } + else + { + // Input string has no decimal point: Append decimal point. + str.append("."); + } + + // Shift the decimal point such that the exponent is an even multiple of mp_elem_digits10. + std::size_t n_shift = static_cast(0u); + const std::size_t n_exp_rem = static_cast(exp % static_cast(mp_elem_digits10)); + + if((exp % static_cast(mp_elem_digits10)) != static_cast(0)) + { + n_shift = ((exp < static_cast(0)) + ? static_cast(n_exp_rem + static_cast(mp_elem_digits10)) + : static_cast(n_exp_rem)); + } + + // Make sure that there are enough digits for the decimal point shift. + pos = str.find(static_cast('.')); + + std::size_t pos_plus_one = static_cast(pos + 1u); + + if((str.length() - pos_plus_one) < n_shift) + { + const std::size_t sz = static_cast(n_shift - (str.length() - pos_plus_one)); + + str.append(std::string(sz, static_cast('0'))); + } + + // Do the decimal point shift. + if(n_shift != static_cast(0u)) + { + str.insert(static_cast(pos_plus_one + n_shift), "."); + + str.erase(pos, static_cast(1u)); + + exp -= static_cast(n_shift); + } + + // Cut the size of the mantissa to <= mp_elem_digits10. + pos = str.find(static_cast('.')); + pos_plus_one = static_cast(pos + 1u); + + if(pos > static_cast(mp_elem_digits10)) + { + const boost::int32_t n_pos = static_cast(pos); + const boost::int32_t n_rem_is_zero = ((static_cast(n_pos % mp_elem_digits10) == static_cast(0)) ? static_cast(1) : static_cast(0)); + const boost::int32_t n = static_cast(static_cast(n_pos / mp_elem_digits10) - n_rem_is_zero); + + str.insert(static_cast(static_cast(n_pos - static_cast(n * mp_elem_digits10))), "."); + + str.erase(pos_plus_one, static_cast(1u)); + + exp += static_cast(static_cast(n) * static_cast(mp_elem_digits10)); + } + + // Pad the decimal part such that its value is an even + // multiple of mp_elem_digits10. + pos = str.find(static_cast('.')); + pos_plus_one = static_cast(pos + 1u); + + const boost::int32_t n_dec = static_cast(static_cast(str.length() - 1u) - static_cast(pos)); + const boost::int32_t n_rem = static_cast(n_dec % mp_elem_digits10); + boost::int32_t n_cnt = ((n_rem != static_cast(0)) ? static_cast(mp_elem_digits10 - n_rem) + : static_cast(0)); + + if(n_cnt != static_cast(0)) + { + str.append(static_cast(n_cnt), static_cast('0')); + } + + // Truncate decimal part if it is too long. + const std::size_t max_dec = static_cast((mp_elem_number - 1) * mp_elem_digits10); + + if(static_cast(str.length() - pos) > max_dec) + { + str = str.substr(static_cast(0u), + static_cast(pos_plus_one + max_dec)); + } + + // Now the input string has the standard cpp_float input form. + // (See the comment above.) + + // Set all the data elements to 0. + std::fill(data.begin(), data.end(), static_cast(0u)); + + // Extract the data. + + // First get the digits to the left of the decimal point... + data[0u] = boost::lexical_cast(str.substr(static_cast(0u), pos)); + + // ...then get the remaining digits to the right of the decimal point. + const std::string::size_type i_end = ((str.length() - pos_plus_one) / static_cast(mp_elem_digits10)); + + for(std::string::size_type i = static_cast(0u); i < i_end; i++) + { + const std::string::const_iterator it = str.begin() + + pos_plus_one + + (i * static_cast(mp_elem_digits10)); + + data[i + 1u] = boost::lexical_cast(std::string(it, it + static_cast(mp_elem_digits10))); + } + + // Check for overflow... + if(exp > cpp_float_max_exp10) + { + const bool b_result_is_neg = neg; + + *this = inf(); + if(b_result_is_neg) + negate(); + } + + // ...and check for underflow. + if(exp <= cpp_float_min_exp10) + { + if(exp == cpp_float_min_exp10) + { + // Check for identity with the minimum value. + cpp_float test = *this; + + test.exp = static_cast(0); + + if(test.isone()) + { + *this = zero(); + } + } + else + { + *this = zero(); + } + } + + return true; +} + +template +cpp_float::cpp_float(const double mantissa, const boost::int64_t exponent) + : data (), + exp (static_cast(0)), + neg (false), + fpclass (mp_finite), + prec_elem(mp_elem_number) +{ + // Create an cpp_float from mantissa and exponent. + // This ctor does not maintain the full precision of double. + + const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits::min)() * (1.0 + std::numeric_limits::epsilon()))); + + if(mantissa_is_iszero) + { + std::fill(data.begin(), data.end(), static_cast(0u)); + return; + } + + const bool b_neg = (mantissa < 0.0); + + double d = ((!b_neg) ? mantissa : -mantissa); + boost::int64_t e = exponent; + + while(d > 10.0) { d /= 10.0; ++e; } + while(d < 1.0) { d *= 10.0; --e; } + + boost::int32_t shift = static_cast(e % static_cast(mp_elem_digits10)); + + while(static_cast(shift-- % mp_elem_digits10) != static_cast(0)) + { + d *= 10.0; + --e; + } + + exp = e; + neg = b_neg; + + std::fill(data.begin(), data.end(), static_cast(0u)); + + static const boost::int32_t digit_ratio = static_cast(static_cast(std::numeric_limits::digits10) / static_cast(mp_elem_digits10)); + static const boost::int32_t digit_loops = static_cast(digit_ratio + static_cast(2)); + + for(boost::int32_t i = static_cast(0); i < digit_loops; i++) + { + boost::uint32_t n = static_cast(static_cast(d)); + data[i] = static_cast(n); + d -= static_cast(n); + d *= static_cast(mp_elem_mask); + } +} + +template +cpp_float& cpp_float::operator = (long double a) +{ + // Christopher Kormanyos's original code used a cast to long long here, but that fails + // when long double has more digits than a long long. + using std::frexp; + using std::ldexp; + using std::floor; + + if (a == 0) { + return *this = zero(); + } + + if (a == 1) { + return *this = one(); + } + + if((boost::math::isinf)(a)) + { + return *this = inf(); + } + if((boost::math::isnan)(a)) + return *this = nan(); + + int e; + long double f, term; + *this = zero(); + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + *this *= pow2(shift); + if(term > 0) + add_unsigned_long_long(static_cast(term)); + else + sub_unsigned_long_long(static_cast(-term)); + f -= term; + } + if(e != 0) + *this *= pow2(e); + return *this; +} + +template +void cpp_float::from_unsigned_long_long(const unsigned long long u) +{ + std::fill(data.begin(), data.end(), static_cast(0u)); + + exp = static_cast(0); + neg = false; + fpclass = mp_finite; + prec_elem = mp_elem_number; + + std::size_t i =static_cast(0u); + + unsigned long long uu = u; + + boost::uint32_t temp[(std::numeric_limits::digits10 / static_cast(mp_elem_digits10)) + 3] = { static_cast(0u) }; + + while(uu != static_cast(0u)) + { + temp[i] = static_cast(uu % static_cast(mp_elem_mask)); + uu = static_cast(uu / static_cast(mp_elem_mask)); + ++i; + } + + if(i > static_cast(1u)) + { + exp += static_cast((i - 1u) * static_cast(mp_elem_digits10)); + } + + std::reverse(temp, temp + i); + std::copy(temp, temp + (std::min)(i, static_cast(mp_elem_number)), data.begin()); +} + +template +void cpp_float::mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p) +{ + boost::uint64_t carry = static_cast(0u); + + for(boost::int32_t j = static_cast(p - 1u); j >= static_cast(0); j--) + { + boost::uint64_t sum = carry; + + for(boost::int32_t i = j; i >= static_cast(0); i--) + { + sum += static_cast(u[i] * static_cast(v[j - i])); + } + + w[j + 1] = static_cast(sum % static_cast(mp_elem_mask)); + carry = static_cast(sum / static_cast(mp_elem_mask)); + } + + w[0u] = static_cast(carry); +} + +template +boost::uint32_t cpp_float::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) +{ + boost::uint64_t carry = static_cast(0u); + + // Multiplication loop. + for(boost::int32_t j = p - 1; j >= static_cast(0); j--) + { + const boost::uint64_t t = static_cast(carry + static_cast(u[j] * static_cast(n))); + carry = static_cast(t / static_cast(mp_elem_mask)); + u[j] = static_cast(t - static_cast(static_cast(mp_elem_mask) * static_cast(carry))); + } + + return static_cast(carry); +} + +template +boost::uint32_t cpp_float::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) +{ + boost::uint64_t prev = static_cast(0u); + + for(boost::int32_t j = static_cast(0); j < p; j++) + { + const boost::uint64_t t = static_cast(u[j] + static_cast(prev * static_cast(mp_elem_mask))); + u[j] = static_cast(t / n); + prev = static_cast(t - static_cast(n * static_cast(u[j]))); + } + + return static_cast(prev); +} + +template +cpp_float cpp_float::pow2(const boost::int64_t p) +{ + // Create a static const table of p^2 for -128 < p < +128. + // Note: The size of this table must be odd-numbered and + // symmetric about 0. + init.do_nothing(); + static const boost::array, 255u> p2_data = + {{ + cpp_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"), + cpp_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"), + cpp_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"), + cpp_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"), + cpp_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"), + cpp_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"), + cpp_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"), + cpp_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"), + cpp_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"), + cpp_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"), + 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cpp_float("1.063382396627932698323045648224275660800000000000000000000000000000000000000000000000000000000000000e37"), + cpp_float("2.126764793255865396646091296448551321600000000000000000000000000000000000000000000000000000000000000e37"), + cpp_float("4.253529586511730793292182592897102643200000000000000000000000000000000000000000000000000000000000000e37"), + cpp_float("8.507059173023461586584365185794205286400000000000000000000000000000000000000000000000000000000000000e37"), + cpp_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38") + }}; + + if((p > static_cast(-128)) && (p < static_cast(+128))) + { + return p2_data[static_cast(p + ((p2_data.size() - 1u) / 2u))]; + } + + // Compute and return 2^p. + if(p < static_cast(0)) + { + return pow2(static_cast(-p)).calculate_inv(); + } + else if(p < static_cast(std::numeric_limits::digits)) + { + const boost::uint64_t p2 = static_cast(static_cast(1uLL) << p); + return cpp_float(p2); + } + else + { + cpp_float t; + default_ops::detail::pow_imp(t, two(), p, mpl::true_()); + return t; + } +} + + +template +inline void add(cpp_float& result, const cpp_float& o) +{ + result += o; +} +template +inline void subtract(cpp_float& result, const cpp_float& o) +{ + result -= o; +} +template +inline void multiply(cpp_float& result, const cpp_float& o) +{ + result *= o; +} +template +inline void divide(cpp_float& result, const cpp_float& o) +{ + result /= o; +} + +template +inline void add(cpp_float& result, const unsigned long long& o) +{ + result.add_unsigned_long_long(o); +} +template +inline void subtract(cpp_float& result, const unsigned long long& o) +{ + result.sub_unsigned_long_long(o); +} +template +inline void multiply(cpp_float& result, const unsigned long long& o) +{ + result.mul_unsigned_long_long(o); +} +template +inline void divide(cpp_float& result, const unsigned long long& o) +{ + result.div_unsigned_long_long(o); +} + +template +inline void add(cpp_float& result, long long o) +{ + if(o < 0) + result.sub_unsigned_long_long(-o); + else + result.add_unsigned_long_long(o); +} +template +inline void subtract(cpp_float& result, long long o) +{ + if(o < 0) + result.add_unsigned_long_long(-o); + else + result.sub_unsigned_long_long(o); +} +template +inline void multiply(cpp_float& result, long long o) +{ + if(o < 0) + { + result.mul_unsigned_long_long(-o); + result.negate(); + } + else + result.mul_unsigned_long_long(o); +} +template +inline void divide(cpp_float& result, long long o) +{ + if(o < 0) + { + result.div_unsigned_long_long(-o); + result.negate(); + } + else + result.div_unsigned_long_long(o); +} + +template +inline void convert_to(unsigned long long* result, const cpp_float& val) +{ + *result = val.extract_unsigned_long_long(); +} +template +inline void convert_to(long long* result, const cpp_float& val) +{ + *result = val.extract_signed_long_long(); +} +template +inline void convert_to(long double* result, cpp_float& val) +{ + *result = val.extract_long_double(); +} + +// +// Non member function support: +// +template +inline int eval_fpclassify(const cpp_float& x) +{ + if(x.isinf()) + return FP_INFINITE; + if(x.isnan()) + return FP_NAN; + if(x.iszero()) + return FP_ZERO; + return FP_NORMAL; +} + +template +inline void eval_abs(cpp_float& result, const cpp_float& x) +{ + result = x; + if(x.isneg()) + result.negate(); +} + +template +inline void eval_fabs(cpp_float& result, const cpp_float& x) +{ + result = x; + if(x.isneg()) + result.negate(); +} + +template +inline void eval_sqrt(cpp_float& result, const cpp_float& x) +{ + result = x; + result.calculate_sqrt(); +} + +template +inline void eval_floor(cpp_float& result, const cpp_float& x) +{ + result = x; + if(!x.isfinite() || x.isint()) + { + return; + } + + if(x.isneg()) + result -= cpp_float::one(); + result = result.extract_integer_part(); +} + +template +inline void eval_ceil(cpp_float& result, const cpp_float& x) +{ + result = x; + if(!x.isfinite() || x.isint()) + { + return; + } + + if(!x.isneg()) + result += cpp_float::one(); + result = result.extract_integer_part(); +} + +template +inline void eval_trunc(cpp_float& result, const cpp_float& x) +{ + if(!x.isfinite()) + { + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number >(x), 0, boost::math::policies::policy<>()).backend(); + return; + } + else if(x.isint()) + { + result = x; + return; + } + result = x.extract_integer_part(); +} + +template +inline void eval_ldexp(cpp_float& result, const cpp_float& x, long long e) +{ + result = x; + result *= cpp_float::pow2(e); +} + +template +inline void eval_frexp(cpp_float& result, const cpp_float& x, long long* e) +{ + result = x; + if(result.isneg()) + result.negate(); + + long long t = result.order(); + + if(std::abs(t) > (std::numeric_limits::max)() / 3) + throw std::runtime_error("Exponent is too large to be represented as a power of 2."); + t *= 3; + + result *= cpp_float::pow2(-t); + + while(result.compare(cpp_float::one()) >= 0) + { + result /= cpp_float::two(); + ++t; + } + while(result.compare(cpp_float::half()) < 0) + { + result *= cpp_float::two(); + --t; + } + *e = t; + if(x.isneg()) + result.negate(); +} + +template +inline void eval_frexp(cpp_float& result, const cpp_float& x, int* e) +{ + long long t; + eval_frexp(result, x, &t); + if(t > (std::numeric_limits::max)()) + throw std::runtime_error("Exponent is outside the range of an int"); + *e = static_cast(t); +} + +typedef mp_number > cpp_float_50; +typedef mp_number > cpp_float_100; + +}} + +namespace std +{ + template + class numeric_limits > > + { + public: + static const bool is_specialized = true; + static const bool is_signed = true; + static const bool is_integer = false; + static const bool is_exact = false; + static const bool is_bounded = true; + static const bool is_modulo = false; + static const bool is_iec559 = false; + static const int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); + static const int digits10 = boost::multiprecision::cpp_float::cpp_float_digits10; + static const int max_digits10 = boost::multiprecision::cpp_float::cpp_float_max_digits10; + static const boost::int64_t min_exponent = boost::multiprecision::cpp_float::cpp_float_min_exp; // Type differs from int. + static const boost::int64_t min_exponent10 = boost::multiprecision::cpp_float::cpp_float_min_exp10; // Type differs from int. + static const boost::int64_t max_exponent = boost::multiprecision::cpp_float::cpp_float_max_exp; // Type differs from int. + static const boost::int64_t max_exponent10 = boost::multiprecision::cpp_float::cpp_float_max_exp10; // Type differs from int. + static const int radix = boost::multiprecision::cpp_float::mp_radix; + static const std::float_round_style round_style = std::round_to_nearest; + static const bool has_infinity = true; + static const bool has_quiet_NaN = true; + static const bool has_signaling_NaN = false; + static const std::float_denorm_style has_denorm = std::denorm_absent; + static const bool has_denorm_loss = false; + static const bool traps = false; + static const bool tinyness_before = false; + + static const boost::multiprecision::mp_number > (min) (void) throw() { return (boost::multiprecision::cpp_float::min)(); } + static const boost::multiprecision::mp_number > (max) (void) throw() { return (boost::multiprecision::cpp_float::max)(); } + static const boost::multiprecision::mp_number > lowest (void) throw() { return boost::multiprecision::cpp_float::zero(); } + static const boost::multiprecision::mp_number > epsilon (void) throw() { return boost::multiprecision::cpp_float::eps(); } + static const boost::multiprecision::mp_number > round_error (void) throw() { return 0.5L; } + static const boost::multiprecision::mp_number > infinity (void) throw() { return boost::multiprecision::cpp_float::inf(); } + static const boost::multiprecision::mp_number > quiet_NaN (void) throw() { return boost::multiprecision::cpp_float::nan(); } + static const boost::multiprecision::mp_number > signaling_NaN(void) throw() { return boost::multiprecision::cpp_float::zero(); } + static const boost::multiprecision::mp_number > denorm_min (void) throw() { return boost::multiprecision::cpp_float::zero(); } + }; +} + +namespace boost{ namespace math{ + +namespace policies{ + +template +struct precision< boost::multiprecision::mp_number >, Policy> +{ + typedef typename Policy::precision_type precision_type; + typedef digits2<((Digits10 + 1) * 1000L) / 301L> digits_2; + typedef typename mpl::if_c< + ((digits_2::value <= precision_type::value) + || (Policy::precision_type::value <= 0)), + // Default case, full precision for RealType: + digits_2, + // User customised precision: + precision_type + >::type type; +}; + +} // namespace policies + +}} // namespaces boost::math + + +#endif + diff --git a/include/boost/multiprecision/mp_float.hpp b/include/boost/multiprecision/mp_float.hpp index dc7fd375..13c41251 100644 --- a/include/boost/multiprecision/mp_float.hpp +++ b/include/boost/multiprecision/mp_float.hpp @@ -25,7 +25,7 @@ namespace boost{ namespace multiprecision{ template -class mp_float +class cpp_float { public: typedef mpl::list signed_types; @@ -35,22 +35,22 @@ public: static const boost::int32_t mp_radix = 10; - static const boost::int32_t mp_float_digits = Digits10; + static const boost::int32_t cpp_float_digits = Digits10; - static const boost::int32_t mp_float_digits10_setting = Digits10; - static const boost::int32_t mp_float_digits10_limit = boost::integer_traits::const_max; - static const boost::int32_t mp_float_digits10 = ((mp_float_digits10_setting < static_cast(30)) ? static_cast(30) : ((mp_float_digits10_setting > mp_float_digits10_limit) ? mp_float_digits10_limit : mp_float_digits10_setting)); - static const boost::int32_t mp_float_digits10_extra = static_cast(((static_cast(mp_float_digits10) * 15LL) + 50LL) / 100LL); - static const boost::int32_t mp_float_max_digits10 = static_cast(mp_float_digits10 + ((mp_float_digits10_extra < static_cast(5)) ? static_cast(5) : ((mp_float_digits10_extra > static_cast(30)) ? static_cast(30) : mp_float_digits10_extra))); - static const boost::int64_t mp_float_max_exp = static_cast(+9223372036854775795LL); - static const boost::int64_t mp_float_min_exp = static_cast(-9223372036854775795LL); - static const boost::int64_t mp_float_max_exp10 = static_cast(+3063937869882635616LL); // Approx. [mp_float_max_exp / log10(2)], also an even multiple of 8 - static const boost::int64_t mp_float_min_exp10 = static_cast(-3063937869882635616LL); + static const boost::int32_t cpp_float_digits10_setting = Digits10; + static const boost::int32_t cpp_float_digits10_limit = boost::integer_traits::const_max; + static const boost::int32_t cpp_float_digits10 = ((cpp_float_digits10_setting < static_cast(30)) ? static_cast(30) : ((cpp_float_digits10_setting > cpp_float_digits10_limit) ? cpp_float_digits10_limit : cpp_float_digits10_setting)); + static const boost::int32_t cpp_float_digits10_extra = static_cast(((static_cast(cpp_float_digits10) * 15LL) + 50LL) / 100LL); + static const boost::int32_t cpp_float_max_digits10 = static_cast(cpp_float_digits10 + ((cpp_float_digits10_extra < static_cast(5)) ? static_cast(5) : ((cpp_float_digits10_extra > static_cast(30)) ? static_cast(30) : cpp_float_digits10_extra))); + static const boost::int64_t cpp_float_max_exp = static_cast(+9223372036854775795LL); + static const boost::int64_t cpp_float_min_exp = static_cast(-9223372036854775795LL); + static const boost::int64_t cpp_float_max_exp10 = static_cast(+3063937869882635616LL); // Approx. [cpp_float_max_exp / log10(2)], also an even multiple of 8 + static const boost::int64_t cpp_float_min_exp10 = static_cast(-3063937869882635616LL); static const boost::int32_t mp_elem_digits10 = static_cast(8); private: - static const boost::int32_t mp_float_digits10_num_base = static_cast((mp_float_max_digits10 / mp_elem_digits10) + (((mp_float_max_digits10 % mp_elem_digits10) != 0) ? 1 : 0)); - static const boost::int32_t mp_elem_number = static_cast(mp_float_digits10_num_base + 2); + static const boost::int32_t cpp_float_digits10_num_base = static_cast((cpp_float_max_digits10 / mp_elem_digits10) + (((cpp_float_max_digits10 % mp_elem_digits10) != 0) ? 1 : 0)); + static const boost::int32_t mp_elem_number = static_cast(cpp_float_digits10_num_base + 2); static const boost::int32_t mp_elem_mask = static_cast(100000000); typedef enum enum_fpclass @@ -72,7 +72,7 @@ private: // // Special values constructor: // - mp_float(t_fpclass c) : + cpp_float(t_fpclass c) : data(), exp (static_cast(0)), neg (false), @@ -86,23 +86,23 @@ private: { initializer() { - mp_float::nan(); - mp_float::inf(); - (mp_float::min)(); - (mp_float::max)(); - mp_float::zero(); - mp_float::one(); - mp_float::two(); - mp_float::half(); - mp_float::double_min(); - mp_float::double_max(); - mp_float::long_double_max(); - mp_float::long_double_min(); - mp_float::long_long_max(); - mp_float::long_long_min(); - mp_float::ulong_long_max(); - mp_float::eps(); - mp_float::pow2(0); + cpp_float::nan(); + cpp_float::inf(); + (cpp_float::min)(); + (cpp_float::max)(); + cpp_float::zero(); + cpp_float::one(); + cpp_float::two(); + cpp_float::half(); + cpp_float::double_min(); + cpp_float::double_max(); + cpp_float::long_double_max(); + cpp_float::long_double_min(); + cpp_float::long_long_max(); + cpp_float::long_long_min(); + cpp_float::ulong_long_max(); + cpp_float::eps(); + cpp_float::pow2(0); } void do_nothing(){} }; @@ -111,14 +111,14 @@ private: public: // Constructors - mp_float() : + cpp_float() : data(), exp (static_cast(0)), neg (false), fpclass (mp_finite), prec_elem(mp_elem_number) { } - mp_float(const char* s) : + cpp_float(const char* s) : data(), exp (static_cast(0)), neg (false), @@ -129,7 +129,7 @@ public: } template - mp_float(I i, typename enable_if >::type* = 0) : + cpp_float(I i, typename enable_if >::type* = 0) : data(), exp (static_cast(0)), neg (false), @@ -140,7 +140,7 @@ public: } template - mp_float(I i, typename enable_if >::type* = 0) : + cpp_float(I i, typename enable_if >::type* = 0) : data(), exp (static_cast(0)), neg (false), @@ -156,7 +156,7 @@ public: from_unsigned_long_long(i); } - mp_float(const mp_float& f) : + cpp_float(const cpp_float& f) : data (f.data), exp (f.exp), neg (f.neg), @@ -164,7 +164,7 @@ public: prec_elem(f.prec_elem) { } template - mp_float(const F val, typename enable_if >::type* = 0): + cpp_float(const F val, typename enable_if >::type* = 0): data(), exp (static_cast(0)), neg (false), @@ -174,28 +174,28 @@ public: *this = val; } - mp_float(const double val, long long exponent); + cpp_float(const double val, long long exponent); // Specific special values. - static const mp_float& nan() + static const cpp_float& nan() { - static const mp_float val(mp_NaN); + static const cpp_float val(mp_NaN); init.do_nothing(); return val; } - static const mp_float& inf() + static const cpp_float& inf() { - static const mp_float val(mp_inf); + static const cpp_float val(mp_inf); init.do_nothing(); return val; } - static const mp_float& (max)() + static const cpp_float& (max)() { init.do_nothing(); static bool init = false; - static const std::string str_max = std::string("9." + std::string(static_cast(mp_float_max_digits10), static_cast('9'))) - + std::string("e+" + boost::lexical_cast(mp_float_max_exp10)); - static mp_float val_max; + static const std::string str_max = std::string("9." + std::string(static_cast(cpp_float_max_digits10), static_cast('9'))) + + std::string("e+" + boost::lexical_cast(cpp_float_max_exp10)); + static cpp_float val_max; if(!init) { init = true; @@ -204,93 +204,93 @@ public: return val_max; } - static const mp_float& (min)() + static const cpp_float& (min)() { init.do_nothing(); static bool init = false; - static mp_float val_min; + static cpp_float val_min; if(!init) { init = true; - val_min = std::string("1.0e" + boost::lexical_cast(mp_float_min_exp10)).c_str(); + val_min = std::string("1.0e" + boost::lexical_cast(cpp_float_min_exp10)).c_str(); } return val_min; } - static const mp_float& zero() + static const cpp_float& zero() { init.do_nothing(); - static mp_float val(static_cast(0u)); + static cpp_float val(static_cast(0u)); return val; } - static const mp_float& one() + static const cpp_float& one() { init.do_nothing(); - static mp_float val(static_cast(1u)); + static cpp_float val(static_cast(1u)); return val; } - static const mp_float& two() + static const cpp_float& two() { init.do_nothing(); - static mp_float val(static_cast(2u)); + static cpp_float val(static_cast(2u)); return val; } - static const mp_float& half() + static const cpp_float& half() { init.do_nothing(); - static mp_float val(0.5L); + static cpp_float val(0.5L); return val; } - static const mp_float& double_min() + static const cpp_float& double_min() { init.do_nothing(); - static mp_float val(static_cast((std::numeric_limits::min)())); + static cpp_float val(static_cast((std::numeric_limits::min)())); return val; } - static const mp_float& double_max() + static const cpp_float& double_max() { init.do_nothing(); - static mp_float val(static_cast((std::numeric_limits::max)())); + static cpp_float val(static_cast((std::numeric_limits::max)())); return val; } - static const mp_float& long_double_min() + static const cpp_float& long_double_min() { init.do_nothing(); - static mp_float val((std::numeric_limits::min)()); + static cpp_float val((std::numeric_limits::min)()); return val; } - static const mp_float& long_double_max() + static const cpp_float& long_double_max() { init.do_nothing(); - static mp_float val((std::numeric_limits::max)()); + static cpp_float val((std::numeric_limits::max)()); return val; } - static const mp_float& long_long_max() + static const cpp_float& long_long_max() { init.do_nothing(); - static mp_float val((std::numeric_limits::max)()); + static cpp_float val((std::numeric_limits::max)()); return val; } - static const mp_float& long_long_min() + static const cpp_float& long_long_min() { init.do_nothing(); - static mp_float val((std::numeric_limits::min)()); + static cpp_float val((std::numeric_limits::min)()); return val; } - static const mp_float& ulong_long_max() + static const cpp_float& ulong_long_max() { init.do_nothing(); - static mp_float val((std::numeric_limits::max)()); + static cpp_float val((std::numeric_limits::max)()); return val; } - static const mp_float& eps() + static const cpp_float& eps() { init.do_nothing(); - static mp_float val(1.0, 1 - (int)Digits10); + static cpp_float val(1.0, 1 - (int)Digits10); return val; } // Basic operations. - mp_float& operator= (const mp_float& v) + cpp_float& operator= (const cpp_float& v) { data = v.data; exp = v.exp; @@ -299,7 +299,7 @@ public: prec_elem = v.prec_elem; return *this; } - mp_float& operator= (long long v) + cpp_float& operator= (long long v) { if(v < 0) { @@ -310,41 +310,41 @@ public: from_unsigned_long_long(v); return *this; } - mp_float& operator= (unsigned long long v) + cpp_float& operator= (unsigned long long v) { from_unsigned_long_long(v); return *this; } - mp_float& operator= (long double v); - mp_float& operator= (const char* v) + cpp_float& operator= (long double v); + cpp_float& operator= (const char* v) { rd_string(v); return *this; } - mp_float& operator+=(const mp_float& v); - mp_float& operator-=(const mp_float& v); - mp_float& operator*=(const mp_float& v); - mp_float& operator/=(const mp_float& v); + cpp_float& operator+=(const cpp_float& v); + cpp_float& operator-=(const cpp_float& v); + cpp_float& operator*=(const cpp_float& v); + cpp_float& operator/=(const cpp_float& v); - mp_float& add_unsigned_long_long(const unsigned long long n) + cpp_float& add_unsigned_long_long(const unsigned long long n) { - mp_float t; + cpp_float t; t.from_unsigned_long_long(n); return *this += t; } - mp_float& sub_unsigned_long_long(const unsigned long long n) + cpp_float& sub_unsigned_long_long(const unsigned long long n) { - mp_float t; + cpp_float t; t.from_unsigned_long_long(n); return *this -= t; } - mp_float& mul_unsigned_long_long(const unsigned long long n); - mp_float& div_unsigned_long_long(const unsigned long long n); + cpp_float& mul_unsigned_long_long(const unsigned long long n); + cpp_float& div_unsigned_long_long(const unsigned long long n); // Elementary primitives. - mp_float& calculate_inv (void); - mp_float& calculate_sqrt(void); + cpp_float& calculate_inv (void); + cpp_float& calculate_sqrt(void); void negate() { if(!iszero()) @@ -365,27 +365,27 @@ public: bool isneg (void) const { return neg; } // Operators pre-increment and pre-decrement - mp_float& operator++(void) + cpp_float& operator++(void) { return *this += one(); } - mp_float& operator--(void) + cpp_float& operator--(void) { return *this -= one(); } std::string str(unsigned digits, bool scientific)const; - int compare(const mp_float& v)const; + int compare(const cpp_float& v)const; template int compare(const V& v)const { - mp_float t; + cpp_float t; t = v; return compare(t); } - void swap(mp_float& v) + void swap(cpp_float& v) { data.swap(v.data); std::swap(exp, v.exp); @@ -399,10 +399,10 @@ public: signed long long extract_signed_long_long (void) const; unsigned long long extract_unsigned_long_long(void) const; void extract_parts (double& mantissa, boost::int64_t& exponent) const; - mp_float extract_integer_part (void) const; + cpp_float extract_integer_part (void) const; void precision(const boost::int32_t prec_digits) { - if(prec_digits >= mp_float_digits10) + if(prec_digits >= cpp_float_digits10) { prec_elem = mp_elem_number; } @@ -414,7 +414,7 @@ public: prec_elem = (std::min)(mp_elem_number, (std::max)(elems, static_cast(2))); } } - static mp_float pow2(long long i); + static cpp_float pow2(long long i); long long order()const { const bool bo_order_is_zero = ((!isfinite()) || (data[0] == static_cast(0u))); @@ -469,7 +469,7 @@ public: private: static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast(0u)); } - static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast(mp_float::mp_elem_mask - 1)); } + static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast(cpp_float::mp_elem_mask - 1)); } static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast('0')); } void from_unsigned_long_long(const unsigned long long u); @@ -484,42 +484,42 @@ private: }; template -typename mp_float::initializer mp_float::init; +typename cpp_float::initializer cpp_float::init; template -const boost::int32_t mp_float::mp_radix; +const boost::int32_t cpp_float::mp_radix; template -const boost::int32_t mp_float::mp_float_digits; +const boost::int32_t cpp_float::cpp_float_digits; template -const boost::int32_t mp_float::mp_float_digits10_setting; +const boost::int32_t cpp_float::cpp_float_digits10_setting; template -const boost::int32_t mp_float::mp_float_digits10_limit; +const boost::int32_t cpp_float::cpp_float_digits10_limit; template -const boost::int32_t mp_float::mp_float_digits10; +const boost::int32_t cpp_float::cpp_float_digits10; template -const boost::int32_t mp_float::mp_float_digits10_extra; +const boost::int32_t cpp_float::cpp_float_digits10_extra; template -const boost::int32_t mp_float::mp_float_max_digits10; +const boost::int32_t cpp_float::cpp_float_max_digits10; template -const boost::int64_t mp_float::mp_float_max_exp; +const boost::int64_t cpp_float::cpp_float_max_exp; template -const boost::int64_t mp_float::mp_float_min_exp; +const boost::int64_t cpp_float::cpp_float_min_exp; template -const boost::int64_t mp_float::mp_float_max_exp10; +const boost::int64_t cpp_float::cpp_float_max_exp10; template -const boost::int64_t mp_float::mp_float_min_exp10; +const boost::int64_t cpp_float::cpp_float_min_exp10; template -const boost::int32_t mp_float::mp_elem_digits10; +const boost::int32_t cpp_float::mp_elem_digits10; template -const boost::int32_t mp_float::mp_float_digits10_num_base; +const boost::int32_t cpp_float::cpp_float_digits10_num_base; template -const boost::int32_t mp_float::mp_elem_number; +const boost::int32_t cpp_float::mp_elem_number; template -const boost::int32_t mp_float::mp_elem_mask; +const boost::int32_t cpp_float::mp_elem_mask; template -mp_float& mp_float::operator+=(const mp_float& v) +cpp_float& cpp_float::operator+=(const cpp_float& v) { if(isnan()) { @@ -709,13 +709,13 @@ mp_float& mp_float::operator+=(const mp_float& v) return *this = zero(); } - bool overflow = exp >= mp_float_max_exp; - if(exp == mp_float_max_exp) + bool overflow = exp >= cpp_float_max_exp; + if(exp == cpp_float_max_exp) { // Check to see if we really truely have an overflow or not... if(isneg()) { - mp_float t(*this); + cpp_float t(*this); t.negate(); overflow = t.compare((max)()) > 0; } @@ -739,7 +739,7 @@ mp_float& mp_float::operator+=(const mp_float& v) } template -mp_float& mp_float::operator-=(const mp_float& v) +cpp_float& cpp_float::operator-=(const cpp_float& v) { // Use *this - v = -(-*this + v). negate(); @@ -749,7 +749,7 @@ mp_float& mp_float::operator-=(const mp_float& v) } template -mp_float& mp_float::operator*=(const mp_float& v) +cpp_float& cpp_float::operator*=(const cpp_float& v) { // Evaluate the sign of the result. const bool b_result_is_neg = (neg != v.neg); @@ -796,7 +796,7 @@ mp_float& mp_float::operator*=(const mp_float& v) const boost::int64_t v_exp = ((!v_exp_is_neg) ? v.exp : static_cast(-v.exp)); // Check the range of the upcoming multiplication. - const bool b_result_is_out_of_range = (v_exp >= static_cast(mp_float_max_exp10 - u_exp)); + const bool b_result_is_out_of_range = (v_exp >= static_cast(cpp_float_max_exp10 - u_exp)); if(b_result_is_out_of_range) { @@ -841,7 +841,7 @@ mp_float& mp_float::operator*=(const mp_float& v) } template -mp_float& mp_float::operator/=(const mp_float& v) +cpp_float& cpp_float::operator/=(const cpp_float& v) { const bool u_and_v_are_finite_and_identical = ( isfinite() && (fpclass == v.fpclass) @@ -865,14 +865,14 @@ mp_float& mp_float::operator/=(const mp_float& v) } return *this; } - mp_float t(v); + cpp_float t(v); t.calculate_inv(); return operator*=(t); } } template -mp_float& mp_float::mul_unsigned_long_long(const unsigned long long n) +cpp_float& cpp_float::mul_unsigned_long_long(const unsigned long long n) { // Multiply *this with a constant unsigned long long. @@ -908,7 +908,7 @@ mp_float& mp_float::mul_unsigned_long_long(const unsigned lo if(n >= static_cast(mp_elem_mask)) { neg = b_neg; - mp_float t; + cpp_float t; t = n; return operator*=(t); } @@ -936,13 +936,13 @@ mp_float& mp_float::mul_unsigned_long_long(const unsigned lo data.front() = static_cast(carry); } - bool overflow = exp >= mp_float_max_exp; - if(exp == mp_float_max_exp) + bool overflow = exp >= cpp_float_max_exp; + if(exp == cpp_float_max_exp) { // Check to see if we really truely have an overflow or not... if(isneg()) { - mp_float t(*this); + cpp_float t(*this); t.negate(); overflow = t.compare((max)()) > 0; } @@ -967,7 +967,7 @@ mp_float& mp_float::mul_unsigned_long_long(const unsigned lo } template -mp_float& mp_float::div_unsigned_long_long(const unsigned long long n) +cpp_float& cpp_float::div_unsigned_long_long(const unsigned long long n) { // Divide *this by a constant unsigned long long. @@ -1016,7 +1016,7 @@ mp_float& mp_float::div_unsigned_long_long(const unsigned lo if(n >= static_cast(mp_elem_mask)) { neg = b_neg; - mp_float t; + cpp_float t; t = n; return operator/=(t); } @@ -1056,7 +1056,7 @@ mp_float& mp_float::div_unsigned_long_long(const unsigned lo } template -mp_float& mp_float::calculate_inv() +cpp_float& cpp_float::calculate_inv() { // Compute the inverse of *this. const bool b_neg = neg; @@ -1090,7 +1090,7 @@ mp_float& mp_float::calculate_inv() } // Save the original *this. - mp_float x(*this); + cpp_float x(*this); // Generate the initial estimate using division. // Extract the mantissa and exponent for a "manual" @@ -1100,7 +1100,7 @@ mp_float& mp_float::calculate_inv() x.extract_parts(dd, ne); // Do the inverse estimate using double precision estimates of mantissa and exponent. - operator=(mp_float(1.0 / dd, -ne)); + operator=(cpp_float(1.0 / dd, -ne)); // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration // is used. During the iterative steps, the precision of the calculation is limited @@ -1115,7 +1115,7 @@ mp_float& mp_float::calculate_inv() x.precision(static_cast(digits * static_cast(2))); // Next iteration. - mp_float t(*this); + cpp_float t(*this); t *= x; t -= two(); t.negate(); @@ -1130,7 +1130,7 @@ mp_float& mp_float::calculate_inv() } template -mp_float& mp_float::calculate_sqrt(void) +cpp_float& cpp_float::calculate_sqrt(void) { // Compute the square root of *this. @@ -1146,7 +1146,7 @@ mp_float& mp_float::calculate_sqrt(void) } // Save the original *this. - mp_float x(*this); + cpp_float x(*this); // Generate the initial estimate using division. // Extract the mantissa and exponent for a "manual" @@ -1166,10 +1166,10 @@ mp_float& mp_float::calculate_sqrt(void) // Estimate the square root using simple manipulations. const double sqd = std::sqrt(dd); - *this = mp_float(sqd, static_cast(ne / static_cast(2))); + *this = cpp_float(sqd, static_cast(ne / static_cast(2))); // Estimate 1.0 / (2.0 * x0) using simple manipulations. - mp_float vi(0.5 / sqd, static_cast(-ne / static_cast(2))); + cpp_float vi(0.5 / sqd, static_cast(-ne / static_cast(2))); // Compute the square root of x. Coupled Newton iteration // as described in "Pi Unleashed" is used. During the @@ -1190,7 +1190,7 @@ mp_float& mp_float::calculate_sqrt(void) vi.precision(digits * 2); // Next iteration of vi - mp_float t(*this); + cpp_float t(*this); t *= vi; t.negate(); t.mul_unsigned_long_long(2u); @@ -1213,7 +1213,7 @@ mp_float& mp_float::calculate_sqrt(void) } template -int mp_float::cmp_data(const array_type& vd) const +int cpp_float::cmp_data(const array_type& vd) const { // Compare the data of *this with those of v. // Return +1 for *this > v @@ -1235,7 +1235,7 @@ int mp_float::cmp_data(const array_type& vd) const } template -int mp_float::compare(const mp_float& v) const +int cpp_float::compare(const cpp_float& v) const { // Compare v with *this. // Return +1 for *this > v @@ -1313,7 +1313,7 @@ int mp_float::compare(const mp_float& v) const } template -bool mp_float::isone() const +bool cpp_float::isone() const { // Check if the value of *this is identically 1 or very close to 1. @@ -1337,7 +1337,7 @@ bool mp_float::isone() const } template -bool mp_float::isint() const +bool cpp_float::isint() const { if(fpclass != mp_finite) { return false; } @@ -1360,9 +1360,9 @@ bool mp_float::isint() const } template -void mp_float::extract_parts(double& mantissa, boost::int64_t& exponent) const +void cpp_float::extract_parts(double& mantissa, boost::int64_t& exponent) const { - // Extract the approximate parts mantissa and base-10 exponent from the input mp_float value x. + // Extract the approximate parts mantissa and base-10 exponent from the input cpp_float value x. // Extracts the mantissa and exponent. exponent = exp; @@ -1393,11 +1393,11 @@ void mp_float::extract_parts(double& mantissa, boost::int64_t& exponen } template -double mp_float::extract_double(void) const +double cpp_float::extract_double(void) const { - // Returns the double conversion of a mp_float. + // Returns the double conversion of a cpp_float. - // Check for non-normal mp_float. + // Check for non-normal cpp_float. if(!isfinite()) { if(isnan()) @@ -1411,17 +1411,17 @@ double mp_float::extract_double(void) const } } - mp_float xx(*this); + cpp_float xx(*this); if(xx.isneg()) xx.negate(); - // Check for zero mp_float. + // Check for zero cpp_float. if(iszero() || (xx.compare(double_min()) < 0)) { return 0.0; } - // Check if mp_float exceeds the maximum of double. + // Check if cpp_float exceeds the maximum of double. if(xx.compare(double_max()) > 0) { return ((!neg) ? std::numeric_limits::infinity() @@ -1439,11 +1439,11 @@ double mp_float::extract_double(void) const } template -long double mp_float::extract_long_double(void) const +long double cpp_float::extract_long_double(void) const { - // Returns the long double conversion of a mp_float. + // Returns the long double conversion of a cpp_float. - // Check for non-normal mp_float. + // Check for non-normal cpp_float. if(!isfinite()) { if(isnan()) @@ -1457,17 +1457,17 @@ long double mp_float::extract_long_double(void) const } } - mp_float xx(*this); + cpp_float xx(*this); if(xx.isneg()) xx.negate(); - // Check for zero mp_float. + // Check for zero cpp_float. if(iszero() || (xx.compare(long_double_min()) < 0)) { return static_cast(0.0); } - // Check if mp_float exceeds the maximum of double. + // Check if cpp_float exceeds the maximum of double. if(xx.compare(long_double_max()) > 0) { return ((!neg) ? std::numeric_limits::infinity() @@ -1485,7 +1485,7 @@ long double mp_float::extract_long_double(void) const } template -signed long long mp_float::extract_signed_long_long(void) const +signed long long cpp_float::extract_signed_long_long(void) const { // Extracts a signed long long from *this. // If (x > maximum of signed long long) or (x < minimum of signed long long), @@ -1511,7 +1511,7 @@ signed long long mp_float::extract_signed_long_long(void) const else { // Extract the data into an unsigned long long value. - mp_float xn(extract_integer_part()); + cpp_float xn(extract_integer_part()); if(xn.isneg()) xn.negate(); @@ -1530,7 +1530,7 @@ signed long long mp_float::extract_signed_long_long(void) const } template -unsigned long long mp_float::extract_unsigned_long_long(void) const +unsigned long long cpp_float::extract_unsigned_long_long(void) const { // Extracts an unsigned long long from *this. // If x exceeds the maximum of unsigned long long, @@ -1548,7 +1548,7 @@ unsigned long long mp_float::extract_unsigned_long_long(void) const return static_cast(0u); } - const mp_float xn(extract_integer_part()); + const cpp_float xn(extract_integer_part()); unsigned long long val; @@ -1574,7 +1574,7 @@ unsigned long long mp_float::extract_unsigned_long_long(void) const } template -mp_float mp_float::extract_integer_part(void) const +cpp_float cpp_float::extract_integer_part(void) const { // Compute the signed integer part of x. @@ -1597,7 +1597,7 @@ mp_float mp_float::extract_integer_part(void) const } // Make a local copy. - mp_float x = *this; + cpp_float x = *this; // Clear out the decimal portion const size_t first_clear = (static_cast(x.exp) / static_cast(mp_elem_digits10)) + 1u; @@ -1609,20 +1609,20 @@ mp_float mp_float::extract_integer_part(void) const } template -std::string mp_float::str(std::size_t number_of_digits, bool scientific) const +std::string cpp_float::str(std::size_t number_of_digits, bool scientific) const { std::string str; boost::int64_t my_exp = order(); if(number_of_digits == 0) number_of_digits = (std::numeric_limits::max)(); - // Determine the number of elements needed to provide the requested digits from mp_float. + // Determine the number of elements needed to provide the requested digits from cpp_float. const std::size_t number_of_elements = (std::min)(static_cast((number_of_digits / static_cast(mp_elem_digits10)) + 2u), static_cast(mp_elem_number)); - // Extract the remaining digits from mp_float after the decimal point. + // Extract the remaining digits from cpp_float after the decimal point. str = boost::lexical_cast(data[0]); - // Extract all of the digits from mp_float, beginning with the first data element. + // Extract all of the digits from cpp_float, beginning with the first data element. for(std::size_t i = static_cast(1u); i < number_of_elements; i++) { std::stringstream ss; @@ -1714,7 +1714,7 @@ std::string mp_float::str(std::size_t number_of_digits, bool scientifi } template -bool mp_float::rd_string(const char* const s) +bool cpp_float::rd_string(const char* const s) { std::string str(s); @@ -1764,7 +1764,7 @@ bool mp_float::rd_string(const char* const s) } } - // Put the input string into the standard mp_float input form + // Put the input string into the standard cpp_float input form // aaa.bbbbE+/-n, where aa has 1...mp_elem_digits10, bbbb has an // even multiple of mp_elem_digits10 which are possibly zero padded // on the right-end, and n is a signed 32-bit integer which is an @@ -1892,7 +1892,7 @@ bool mp_float::rd_string(const char* const s) static_cast(pos_plus_one + max_dec)); } - // Now the input string has the standard mp_float input form. + // Now the input string has the standard cpp_float input form. // (See the comment above.) // Set all the data elements to 0. @@ -1916,7 +1916,7 @@ bool mp_float::rd_string(const char* const s) } // Check for overflow... - if(exp > mp_float_max_exp10) + if(exp > cpp_float_max_exp10) { const bool b_result_is_neg = neg; @@ -1926,12 +1926,12 @@ bool mp_float::rd_string(const char* const s) } // ...and check for underflow. - if(exp <= mp_float_min_exp10) + if(exp <= cpp_float_min_exp10) { - if(exp == mp_float_min_exp10) + if(exp == cpp_float_min_exp10) { // Check for identity with the minimum value. - mp_float test = *this; + cpp_float test = *this; test.exp = static_cast(0); @@ -1950,14 +1950,14 @@ bool mp_float::rd_string(const char* const s) } template -mp_float::mp_float(const double mantissa, const boost::int64_t exponent) +cpp_float::cpp_float(const double mantissa, const boost::int64_t exponent) : data (), exp (static_cast(0)), neg (false), fpclass (mp_finite), prec_elem(mp_elem_number) { - // Create an mp_float from mantissa and exponent. + // Create an cpp_float from mantissa and exponent. // This ctor does not maintain the full precision of double. const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits::min)() * (1.0 + std::numeric_limits::epsilon()))); @@ -2002,7 +2002,7 @@ mp_float::mp_float(const double mantissa, const boost::int64_t exponen } template -mp_float& mp_float::operator = (long double a) +cpp_float& cpp_float::operator = (long double a) { // Christopher Kormanyos's original code used a cast to long long here, but that fails // when long double has more digits than a long long. @@ -2052,7 +2052,7 @@ mp_float& mp_float::operator = (long double a) } template -void mp_float::from_unsigned_long_long(const unsigned long long u) +void cpp_float::from_unsigned_long_long(const unsigned long long u) { std::fill(data.begin(), data.end(), static_cast(0u)); @@ -2084,7 +2084,7 @@ void mp_float::from_unsigned_long_long(const unsigned long long u) } template -void mp_float::mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p) +void cpp_float::mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p) { boost::uint64_t carry = static_cast(0u); @@ -2105,7 +2105,7 @@ void mp_float::mul_loop_uv(const boost::uint32_t* const u, const boost } template -boost::uint32_t mp_float::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) +boost::uint32_t cpp_float::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) { boost::uint64_t carry = static_cast(0u); @@ -2121,7 +2121,7 @@ boost::uint32_t mp_float::mul_loop_n(boost::uint32_t* const u, boost:: } template -boost::uint32_t mp_float::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) +boost::uint32_t cpp_float::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) { boost::uint64_t prev = static_cast(0u); @@ -2136,269 +2136,269 @@ boost::uint32_t mp_float::div_loop_n(boost::uint32_t* const u, boost:: } template -mp_float mp_float::pow2(const boost::int64_t p) +cpp_float cpp_float::pow2(const boost::int64_t p) { // Create a static const table of p^2 for -128 < p < +128. // Note: The size of this table must be odd-numbered and // symmetric about 0. init.do_nothing(); - static const boost::array, 255u> p2_data = + static const boost::array, 255u> p2_data = {{ - mp_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"), - mp_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"), - mp_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"), - mp_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"), - mp_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"), - mp_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"), - mp_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"), - mp_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"), - mp_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"), - mp_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"), - mp_float("6.018531076210112040799931070577897870431567650673088110124808736145496368408203125000000000000000000e-36"), - mp_float("1.203706215242022408159986214115579574086313530134617622024961747229099273681640625000000000000000000e-35"), - mp_float("2.407412430484044816319972428231159148172627060269235244049923494458198547363281250000000000000000000e-35"), - mp_float("4.814824860968089632639944856462318296345254120538470488099846988916397094726562500000000000000000000e-35"), - mp_float("9.629649721936179265279889712924636592690508241076940976199693977832794189453125000000000000000000000e-35"), - mp_float("1.925929944387235853055977942584927318538101648215388195239938795566558837890625000000000000000000000e-34"), - mp_float("3.851859888774471706111955885169854637076203296430776390479877591133117675781250000000000000000000000e-34"), - mp_float("7.703719777548943412223911770339709274152406592861552780959755182266235351562500000000000000000000000e-34"), - mp_float("1.540743955509788682444782354067941854830481318572310556191951036453247070312500000000000000000000000e-33"), - 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cpp_float("8.507059173023461586584365185794205286400000000000000000000000000000000000000000000000000000000000000e37"), + cpp_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38") }}; if((p > static_cast(-128)) && (p < static_cast(+128))) @@ -2414,11 +2414,11 @@ mp_float mp_float::pow2(const boost::int64_t p) else if(p < static_cast(std::numeric_limits::digits)) { const boost::uint64_t p2 = static_cast(static_cast(1uLL) << p); - return mp_float(p2); + return cpp_float(p2); } else { - mp_float t; + cpp_float t; default_ops::detail::pow_imp(t, two(), p, mpl::true_()); return t; } @@ -2426,49 +2426,49 @@ mp_float mp_float::pow2(const boost::int64_t p) template -inline void add(mp_float& result, const mp_float& o) +inline void add(cpp_float& result, const cpp_float& o) { result += o; } template -inline void subtract(mp_float& result, const mp_float& o) +inline void subtract(cpp_float& result, const cpp_float& o) { result -= o; } template -inline void multiply(mp_float& result, const mp_float& o) +inline void multiply(cpp_float& result, const cpp_float& o) { result *= o; } template -inline void divide(mp_float& result, const mp_float& o) +inline void divide(cpp_float& result, const cpp_float& o) { result /= o; } template -inline void add(mp_float& result, const unsigned long long& o) +inline void add(cpp_float& result, const unsigned long long& o) { result.add_unsigned_long_long(o); } template -inline void subtract(mp_float& result, const unsigned long long& o) +inline void subtract(cpp_float& result, const unsigned long long& o) { result.sub_unsigned_long_long(o); } template -inline void multiply(mp_float& result, const unsigned long long& o) +inline void multiply(cpp_float& result, const unsigned long long& o) { result.mul_unsigned_long_long(o); } template -inline void divide(mp_float& result, const unsigned long long& o) +inline void divide(cpp_float& result, const unsigned long long& o) { result.div_unsigned_long_long(o); } template -inline void add(mp_float& result, long long o) +inline void add(cpp_float& result, long long o) { if(o < 0) result.sub_unsigned_long_long(-o); @@ -2476,7 +2476,7 @@ inline void add(mp_float& result, long long o) result.add_unsigned_long_long(o); } template -inline void subtract(mp_float& result, long long o) +inline void subtract(cpp_float& result, long long o) { if(o < 0) result.add_unsigned_long_long(-o); @@ -2484,7 +2484,7 @@ inline void subtract(mp_float& result, long long o) result.sub_unsigned_long_long(o); } template -inline void multiply(mp_float& result, long long o) +inline void multiply(cpp_float& result, long long o) { if(o < 0) { @@ -2495,7 +2495,7 @@ inline void multiply(mp_float& result, long long o) result.mul_unsigned_long_long(o); } template -inline void divide(mp_float& result, long long o) +inline void divide(cpp_float& result, long long o) { if(o < 0) { @@ -2507,17 +2507,17 @@ inline void divide(mp_float& result, long long o) } template -inline void convert_to(unsigned long long* result, const mp_float& val) +inline void convert_to(unsigned long long* result, const cpp_float& val) { *result = val.extract_unsigned_long_long(); } template -inline void convert_to(long long* result, const mp_float& val) +inline void convert_to(long long* result, const cpp_float& val) { *result = val.extract_signed_long_long(); } template -inline void convert_to(long double* result, mp_float& val) +inline void convert_to(long double* result, cpp_float& val) { *result = val.extract_long_double(); } @@ -2526,7 +2526,7 @@ inline void convert_to(long double* result, mp_float& val) // Non member function support: // template -inline int eval_fpclassify(const mp_float& x) +inline int eval_fpclassify(const cpp_float& x) { if(x.isinf()) return FP_INFINITE; @@ -2538,7 +2538,7 @@ inline int eval_fpclassify(const mp_float& x) } template -inline void eval_abs(mp_float& result, const mp_float& x) +inline void eval_abs(cpp_float& result, const cpp_float& x) { result = x; if(x.isneg()) @@ -2546,7 +2546,7 @@ inline void eval_abs(mp_float& result, const mp_float& x) } template -inline void eval_fabs(mp_float& result, const mp_float& x) +inline void eval_fabs(cpp_float& result, const cpp_float& x) { result = x; if(x.isneg()) @@ -2554,14 +2554,14 @@ inline void eval_fabs(mp_float& result, const mp_float& x) } template -inline void eval_sqrt(mp_float& result, const mp_float& x) +inline void eval_sqrt(cpp_float& result, const cpp_float& x) { result = x; result.calculate_sqrt(); } template -inline void eval_floor(mp_float& result, const mp_float& x) +inline void eval_floor(cpp_float& result, const cpp_float& x) { result = x; if(!x.isfinite() || x.isint()) @@ -2570,12 +2570,12 @@ inline void eval_floor(mp_float& result, const mp_float& x) } if(x.isneg()) - result -= mp_float::one(); + result -= cpp_float::one(); result = result.extract_integer_part(); } template -inline void eval_ceil(mp_float& result, const mp_float& x) +inline void eval_ceil(cpp_float& result, const cpp_float& x) { result = x; if(!x.isfinite() || x.isint()) @@ -2584,16 +2584,16 @@ inline void eval_ceil(mp_float& result, const mp_float& x) } if(!x.isneg()) - result += mp_float::one(); + result += cpp_float::one(); result = result.extract_integer_part(); } template -inline void eval_trunc(mp_float& result, const mp_float& x) +inline void eval_trunc(cpp_float& result, const cpp_float& x) { if(!x.isfinite()) { - result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number >(x), 0, boost::math::policies::policy<>()).backend(); + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number >(x), 0, boost::math::policies::policy<>()).backend(); return; } else if(x.isint()) @@ -2605,14 +2605,14 @@ inline void eval_trunc(mp_float& result, const mp_float& x) } template -inline void eval_ldexp(mp_float& result, const mp_float& x, long long e) +inline void eval_ldexp(cpp_float& result, const cpp_float& x, long long e) { result = x; - result *= mp_float::pow2(e); + result *= cpp_float::pow2(e); } template -inline void eval_frexp(mp_float& result, const mp_float& x, long long* e) +inline void eval_frexp(cpp_float& result, const cpp_float& x, long long* e) { result = x; if(result.isneg()) @@ -2624,16 +2624,16 @@ inline void eval_frexp(mp_float& result, const mp_float& x, throw std::runtime_error("Exponent is too large to be represented as a power of 2."); t *= 3; - result *= mp_float::pow2(-t); + result *= cpp_float::pow2(-t); - while(result.compare(mp_float::one()) >= 0) + while(result.compare(cpp_float::one()) >= 0) { - result /= mp_float::two(); + result /= cpp_float::two(); ++t; } - while(result.compare(mp_float::half()) < 0) + while(result.compare(cpp_float::half()) < 0) { - result *= mp_float::two(); + result *= cpp_float::two(); --t; } *e = t; @@ -2642,7 +2642,7 @@ inline void eval_frexp(mp_float& result, const mp_float& x, } template -inline void eval_frexp(mp_float& result, const mp_float& x, int* e) +inline void eval_frexp(cpp_float& result, const cpp_float& x, int* e) { long long t; eval_frexp(result, x, &t); @@ -2651,15 +2651,15 @@ inline void eval_frexp(mp_float& result, const mp_float& x, *e = static_cast(t); } -typedef mp_number > mp_float_50; -typedef mp_number > mp_float_100; +typedef mp_number > cpp_float_50; +typedef mp_number > cpp_float_100; }} namespace std { template - class numeric_limits > > + class numeric_limits > > { public: static const bool is_specialized = true; @@ -2670,13 +2670,13 @@ namespace std static const bool is_modulo = false; static const bool is_iec559 = false; static const int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); - static const int digits10 = boost::multiprecision::mp_float::mp_float_digits10; - static const int max_digits10 = boost::multiprecision::mp_float::mp_float_max_digits10; - static const boost::int64_t min_exponent = boost::multiprecision::mp_float::mp_float_min_exp; // Type differs from int. - static const boost::int64_t min_exponent10 = boost::multiprecision::mp_float::mp_float_min_exp10; // Type differs from int. - static const boost::int64_t max_exponent = boost::multiprecision::mp_float::mp_float_max_exp; // Type differs from int. - static const boost::int64_t max_exponent10 = boost::multiprecision::mp_float::mp_float_max_exp10; // Type differs from int. - static const int radix = boost::multiprecision::mp_float::mp_radix; + static const int digits10 = boost::multiprecision::cpp_float::cpp_float_digits10; + static const int max_digits10 = boost::multiprecision::cpp_float::cpp_float_max_digits10; + static const boost::int64_t min_exponent = boost::multiprecision::cpp_float::cpp_float_min_exp; // Type differs from int. + static const boost::int64_t min_exponent10 = boost::multiprecision::cpp_float::cpp_float_min_exp10; // Type differs from int. + static const boost::int64_t max_exponent = boost::multiprecision::cpp_float::cpp_float_max_exp; // Type differs from int. + static const boost::int64_t max_exponent10 = boost::multiprecision::cpp_float::cpp_float_max_exp10; // Type differs from int. + static const int radix = boost::multiprecision::cpp_float::mp_radix; static const std::float_round_style round_style = std::round_to_nearest; static const bool has_infinity = true; static const bool has_quiet_NaN = true; @@ -2686,15 +2686,15 @@ namespace std static const bool traps = false; static const bool tinyness_before = false; - static const boost::multiprecision::mp_number > (min) (void) throw() { return (boost::multiprecision::mp_float::min)(); } - static const boost::multiprecision::mp_number > (max) (void) throw() { return (boost::multiprecision::mp_float::max)(); } - static const boost::multiprecision::mp_number > lowest (void) throw() { return boost::multiprecision::mp_float::zero(); } - static const boost::multiprecision::mp_number > epsilon (void) throw() { return boost::multiprecision::mp_float::eps(); } - static const boost::multiprecision::mp_number > round_error (void) throw() { return 0.5L; } - static const boost::multiprecision::mp_number > infinity (void) throw() { return boost::multiprecision::mp_float::inf(); } - static const boost::multiprecision::mp_number > quiet_NaN (void) throw() { return boost::multiprecision::mp_float::nan(); } - static const boost::multiprecision::mp_number > signaling_NaN(void) throw() { return boost::multiprecision::mp_float::zero(); } - static const boost::multiprecision::mp_number > denorm_min (void) throw() { return boost::multiprecision::mp_float::zero(); } + static const boost::multiprecision::mp_number > (min) (void) throw() { return (boost::multiprecision::cpp_float::min)(); } + static const boost::multiprecision::mp_number > (max) (void) throw() { return (boost::multiprecision::cpp_float::max)(); } + static const boost::multiprecision::mp_number > lowest (void) throw() { return boost::multiprecision::cpp_float::zero(); } + static const boost::multiprecision::mp_number > epsilon (void) throw() { return boost::multiprecision::cpp_float::eps(); } + static const boost::multiprecision::mp_number > round_error (void) throw() { return 0.5L; } + static const boost::multiprecision::mp_number > infinity (void) throw() { return boost::multiprecision::cpp_float::inf(); } + static const boost::multiprecision::mp_number > quiet_NaN (void) throw() { return boost::multiprecision::cpp_float::nan(); } + static const boost::multiprecision::mp_number > signaling_NaN(void) throw() { return boost::multiprecision::cpp_float::zero(); } + static const boost::multiprecision::mp_number > denorm_min (void) throw() { return boost::multiprecision::cpp_float::zero(); } }; } @@ -2703,7 +2703,7 @@ namespace boost{ namespace math{ namespace policies{ template -struct precision< boost::multiprecision::mp_number >, Policy> +struct precision< boost::multiprecision::mp_number >, Policy> { typedef typename Policy::precision_type precision_type; typedef digits2<((Digits10 + 1) * 1000L) / 301L> digits_2; diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 843e64cd..75fdb952 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -36,8 +36,8 @@ run test_arithmetic.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_arithmetic_mp_float ; + TEST_CPP_FLOAT + : test_arithmetic_cpp_float ; run test_arithmetic.cpp gmp : # command line @@ -146,9 +146,9 @@ run test_numeric_limits.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT + TEST_CPP_FLOAT [ check-target-builds ../config//has_mpfr : : no ] - : test_numeric_limits_mp_float ; + : test_numeric_limits_cpp_float ; run mp_number_concept_check.cpp mpfr : # command line @@ -202,8 +202,8 @@ run mp_number_concept_check.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : mp_number_concept_check_mp_float ; + TEST_CPP_FLOAT + : mp_number_concept_check_cpp_float ; run mp_number_concept_check.cpp : # command line @@ -312,50 +312,50 @@ run test_exp.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_exp_mp_float ; + TEST_CPP_FLOAT + : test_exp_cpp_float ; run test_log.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_log_mp_float ; + TEST_CPP_FLOAT + : test_log_cpp_float ; run test_pow.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_pow_mp_float ; + TEST_CPP_FLOAT + : test_pow_cpp_float ; run test_sinh.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_sinh_mp_float ; + TEST_CPP_FLOAT + : test_sinh_cpp_float ; run test_cosh.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_cosh_mp_float ; + TEST_CPP_FLOAT + : test_cosh_cpp_float ; run test_tanh.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_tanh_mp_float ; + TEST_CPP_FLOAT + : test_tanh_cpp_float ; run test_sin.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_sin_mp_float ; + TEST_CPP_FLOAT + : test_sin_cpp_float ; run test_sin.cpp gmp : # command line @@ -377,8 +377,8 @@ run test_cos.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_cos_mp_float ; + TEST_CPP_FLOAT + : test_cos_cpp_float ; run test_cos.cpp gmp : # command line @@ -400,8 +400,8 @@ run test_asin.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_asin_mp_float ; + TEST_CPP_FLOAT + : test_asin_cpp_float ; run test_asin.cpp gmp : # command line @@ -423,8 +423,8 @@ run test_acos.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_acos_mp_float ; + TEST_CPP_FLOAT + : test_acos_cpp_float ; run test_acos.cpp gmp : # command line @@ -454,8 +454,8 @@ run test_atan.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT - : test_atan_mp_float ; + TEST_CPP_FLOAT + : test_atan_cpp_float ; run test_atan.cpp mpfr : # command line @@ -489,7 +489,7 @@ run ../example/mpfr_snips.cpp mpfr : # requirements [ check-target-builds ../config//has_mpfr : : no ] ; -run ../example/mp_float_snips.cpp ; +run ../example/cpp_float_snips.cpp ; run test_round.cpp : # command line @@ -518,9 +518,9 @@ run test_round.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT + TEST_CPP_FLOAT [ check-target-builds ../config//has_mpfr : : no ] - : test_round_mp_float ; + : test_round_cpp_float ; run test_fpclassify.cpp : # command line @@ -549,7 +549,7 @@ run test_fpclassify.cpp : # command line : # input files : # requirements - TEST_MP_FLOAT + TEST_CPP_FLOAT [ check-target-builds ../config//has_mpfr : : no ] - : test_fpclassify_mp_float ; + : test_fpclassify_cpp_float ; diff --git a/test/linpack-benchmark.cpp b/test/linpack-benchmark.cpp index f4829101..42b1c3a2 100644 --- a/test/linpack-benchmark.cpp +++ b/test/linpack-benchmark.cpp @@ -25,9 +25,9 @@ typedef mpf_class real_type; #elif defined(TEST_MPFRXX) #include typedef mpfr_class real_type; -#elif defined(TEST_MP_FLOAT) -#include -typedef boost::multiprecision::mp_float_50 real_type; +#elif defined(TEST_CPP_FLOAT) +#include +typedef boost::multiprecision::cpp_float_50 real_type; #elif defined(TEST_MPFR_50) #include typedef boost::multiprecision::mpfr_float_50 real_type; @@ -102,8 +102,8 @@ extern "C" int MAIN__() #elif defined(TEST_MPFRXX) std::cout << "Testing mpfr_class at 50 decimal degits" << std::endl; mpfr_set_default_prec(((50 + 1) * 1000L) / 301L); -#elif defined(TEST_MP_FLOAT) - std::cout << "Testing mp_number >" << std::endl; +#elif defined(TEST_CPP_FLOAT) + std::cout << "Testing mp_number >" << std::endl; #else std::cout << "Testing double" << std::endl; #endif @@ -911,8 +911,8 @@ real_type epslon_(real_type *x) { #if defined(TEST_MPF_100) || defined(TEST_MPFR_100) || defined(TEST_GMPXX) || defined(TEST_MPFRXX) return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); -#elif defined(TEST_MP_FLOAT_BN) - return std::pow(10.0, 1-std::numeric_limits::digits10); +#elif defined(TEST_CPP_FLOAT_BN) + return std::pow(10.0, 1-std::numeric_limits::digits10); #else return CAST_TO_RT(std::numeric_limits::epsilon()); #endif @@ -1234,7 +1234,7 @@ mp_number >: times for array with leading dimension of1001 279.96 0.84 280.8 2.3813 0.83988 5014.3 -boost::multiprecision::ef::mp_float_50: +boost::multiprecision::ef::cpp_float_50: ~~~~~~~~~~~~~~~~~~~~~~~~~ norm. resid resid machep x(1) x(n) diff --git a/test/mp_number_concept_check.cpp b/test/mp_number_concept_check.cpp index 35872d75..675aa2b7 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -5,7 +5,7 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) // -// This tests two things: that mp_float_50 meets our +// This tests two things: that cpp_float_50 meets our // conceptual requirements, and that we can instantiate // all our distributions and special functions on this type. // @@ -21,7 +21,7 @@ #endif #if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ - && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)\ && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) # define TEST_MPF_50 # define TEST_BACKEND @@ -31,7 +31,7 @@ # define TEST_MPFR_15 # define TEST_MPFR_17 # define TEST_MPFR_30 -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -48,8 +48,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif #if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) #include @@ -81,8 +81,8 @@ void foo() #ifdef TEST_MPFR_30 instantiate(boost::multiprecision::mp_number >()); #endif -#ifdef TEST_MP_FLOAT - instantiate(boost::multiprecision::mp_float_50()); +#ifdef TEST_CPP_FLOAT + instantiate(boost::multiprecision::cpp_float_50()); #endif } @@ -112,8 +112,8 @@ int main() #ifdef TEST_MPFR_50 BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif -#ifdef TEST_MP_FLOAT - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#ifdef TEST_CPP_FLOAT + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif } diff --git a/test/test_acos.cpp b/test/test_acos.cpp index f7e350c4..c2b1a074 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -96,9 +96,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index aa040478..db49a85b 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -6,14 +6,14 @@ #include #include -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND # define TEST_MPZ # define TEST_MPFR # define TEST_MPFR_50 -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT # define TEST_MPQ #ifdef _MSC_VER @@ -31,8 +31,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif #if defined(TEST_MPFR) || defined(TEST_MPFR_50) #include @@ -861,8 +861,8 @@ int main() #ifdef TEST_MPQ test(); #endif -#ifdef TEST_MP_FLOAT - test(); +#ifdef TEST_CPP_FLOAT + test(); #endif #ifdef TEST_MPFR test(); diff --git a/test/test_asin.cpp b/test/test_asin.cpp index c8c1e810..2813f036 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -93,9 +93,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_atan.cpp b/test/test_atan.cpp index 0b07212f..b1176c6f 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -237,9 +237,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_cos.cpp b/test/test_cos.cpp index 53374292..aacd3ea4 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -282,9 +282,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index 76c4f976..89a002d2 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -128,9 +128,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_exp.cpp b/test/test_exp.cpp index 8f397d9e..a8cc428a 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -173,9 +173,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_fpclassify.cpp b/test/test_fpclassify.cpp index 044f8462..374382a8 100644 --- a/test/test_fpclassify.cpp +++ b/test/test_fpclassify.cpp @@ -10,11 +10,11 @@ #include #include -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 # define TEST_MPFR_50 # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -34,8 +34,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif #ifdef _MSC_VER @@ -312,9 +312,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif #ifdef TEST_BACKEND test >(); diff --git a/test/test_log.cpp b/test/test_log.cpp index 8c6e4b19..49c6d275 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -166,7 +166,11 @@ void test() e = relative_error(val, T(-data[k])); err = e.template convert_to(); if(err > max_err) + { max_err = err; + std::cout << val << std::endl; + std::cout << T(-data[k]) << std::endl; + } val = boost::multiprecision::log10(tenth + pi * (100 * k) * (100 * k)); e = relative_error(val, T(data[k] / logten)); @@ -199,9 +203,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index 0dc9e7d0..ce87c5d6 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -5,14 +5,14 @@ #include -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND # define TEST_MPZ # define TEST_MPFR # define TEST_MPFR_50 -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT # define TEST_MPQ #ifdef _MSC_VER @@ -30,8 +30,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif #if defined(TEST_MPFR) || defined(TEST_MPFR_50) #include @@ -159,9 +159,9 @@ int main() #ifdef TEST_MPQ test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif #ifdef TEST_MPFR test(); diff --git a/test/test_pow.cpp b/test/test_pow.cpp index a8ba5495..096a56c1 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT # define TEST_MPFR_50 #ifdef _MSC_VER @@ -37,8 +37,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -576,9 +576,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_round.cpp b/test/test_round.cpp index 31312c2f..5d0e2923 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -16,11 +16,11 @@ catch(...){ BOOST_ERROR("Incorrect exception type thrown"); } -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 # define TEST_MPFR_50 # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -40,8 +40,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif boost::mt19937 rng; @@ -387,9 +387,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif #ifdef TEST_BACKEND test >(); diff --git a/test/test_sin.cpp b/test/test_sin.cpp index 702e1d06..e5ecbeb6 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -231,7 +231,12 @@ T("8.650871796830672527081873591655777773059986288175183143531618768919892399328 T e = relative_error(val, small_data[k]); unsigned err = e.template convert_to(); if(err > max_err) + { + std::cout << val << std::endl; + std::cout << small_data[k] << std::endl; + std::cout << e << std::endl; max_err = err; + } val = sin(-(euler_gamma + k) / 53); e = relative_error(val, T(-small_data[k])); err = e.template convert_to(); @@ -285,8 +290,8 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); +#ifdef TEST_CPP_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index bddad689..8a626c99 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -128,9 +128,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index d226fc95..9b62aea8 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -12,11 +12,11 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_MP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND -# define TEST_MP_FLOAT +# define TEST_CPP_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,8 +36,8 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_MP_FLOAT -#include +#ifdef TEST_CPP_FLOAT +#include #endif template @@ -128,9 +128,9 @@ int main() test(); test(); #endif -#ifdef TEST_MP_FLOAT - test(); - test(); +#ifdef TEST_CPP_FLOAT + test(); + test(); #endif return boost::report_errors(); } From 0bf6917f18a236133872eef671d61689f21b3561 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 12 Nov 2011 13:16:39 +0000 Subject: [PATCH 059/256] Remove dead file. [SVN r75454] --- include/boost/multiprecision/mp_float.hpp | 2726 --------------------- 1 file changed, 2726 deletions(-) delete mode 100644 include/boost/multiprecision/mp_float.hpp diff --git a/include/boost/multiprecision/mp_float.hpp b/include/boost/multiprecision/mp_float.hpp deleted file mode 100644 index 13c41251..00000000 --- a/include/boost/multiprecision/mp_float.hpp +++ /dev/null @@ -1,2726 +0,0 @@ -/////////////////////////////////////////////////////////////////////////////// -// Copyright Christopher Kormanyos 2002 - 2011. -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -// -// This work is based on an earlier work: -// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", -// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 -// - -#ifndef BOOST_MP_EFX_BACKEND_HPP -#define BOOST_MP_EFX_BACKEND_HPP - -#include -#include -#include - -// -// Headers required for Boost.Math integration: -// -#include - -namespace boost{ -namespace multiprecision{ - -template -class cpp_float -{ -public: - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list real_types; - typedef boost::int64_t exponent_type; - - - static const boost::int32_t mp_radix = 10; - static const boost::int32_t cpp_float_digits = Digits10; - - static const boost::int32_t cpp_float_digits10_setting = Digits10; - static const boost::int32_t cpp_float_digits10_limit = boost::integer_traits::const_max; - static const boost::int32_t cpp_float_digits10 = ((cpp_float_digits10_setting < static_cast(30)) ? static_cast(30) : ((cpp_float_digits10_setting > cpp_float_digits10_limit) ? cpp_float_digits10_limit : cpp_float_digits10_setting)); - static const boost::int32_t cpp_float_digits10_extra = static_cast(((static_cast(cpp_float_digits10) * 15LL) + 50LL) / 100LL); - static const boost::int32_t cpp_float_max_digits10 = static_cast(cpp_float_digits10 + ((cpp_float_digits10_extra < static_cast(5)) ? static_cast(5) : ((cpp_float_digits10_extra > static_cast(30)) ? static_cast(30) : cpp_float_digits10_extra))); - static const boost::int64_t cpp_float_max_exp = static_cast(+9223372036854775795LL); - static const boost::int64_t cpp_float_min_exp = static_cast(-9223372036854775795LL); - static const boost::int64_t cpp_float_max_exp10 = static_cast(+3063937869882635616LL); // Approx. [cpp_float_max_exp / log10(2)], also an even multiple of 8 - static const boost::int64_t cpp_float_min_exp10 = static_cast(-3063937869882635616LL); - static const boost::int32_t mp_elem_digits10 = static_cast(8); - -private: - static const boost::int32_t cpp_float_digits10_num_base = static_cast((cpp_float_max_digits10 / mp_elem_digits10) + (((cpp_float_max_digits10 % mp_elem_digits10) != 0) ? 1 : 0)); - static const boost::int32_t mp_elem_number = static_cast(cpp_float_digits10_num_base + 2); - static const boost::int32_t mp_elem_mask = static_cast(100000000); - - typedef enum enum_fpclass - { - mp_finite, - mp_inf, - mp_NaN - } - t_fpclass; - - typedef boost::array array_type; - - array_type data; - boost::int64_t exp; - bool neg; - t_fpclass fpclass; - boost::int32_t prec_elem; - - // - // Special values constructor: - // - cpp_float(t_fpclass c) : - data(), - exp (static_cast(0)), - neg (false), - fpclass (c), - prec_elem(mp_elem_number) { } - - // - // Static data initializer: - // - struct initializer - { - initializer() - { - cpp_float::nan(); - cpp_float::inf(); - (cpp_float::min)(); - (cpp_float::max)(); - cpp_float::zero(); - cpp_float::one(); - cpp_float::two(); - cpp_float::half(); - cpp_float::double_min(); - cpp_float::double_max(); - cpp_float::long_double_max(); - cpp_float::long_double_min(); - cpp_float::long_long_max(); - cpp_float::long_long_min(); - cpp_float::ulong_long_max(); - cpp_float::eps(); - cpp_float::pow2(0); - } - void do_nothing(){} - }; - - static initializer init; - -public: - // Constructors - cpp_float() : - data(), - exp (static_cast(0)), - neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) { } - - cpp_float(const char* s) : - data(), - exp (static_cast(0)), - neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) - { - *this = s; - } - - template - cpp_float(I i, typename enable_if >::type* = 0) : - data(), - exp (static_cast(0)), - neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) - { - from_unsigned_long_long(i); - } - - template - cpp_float(I i, typename enable_if >::type* = 0) : - data(), - exp (static_cast(0)), - neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) - { - if(i < 0) - { - from_unsigned_long_long(-i); - negate(); - } - else - from_unsigned_long_long(i); - } - - cpp_float(const cpp_float& f) : - data (f.data), - exp (f.exp), - neg (f.neg), - fpclass (f.fpclass), - prec_elem(f.prec_elem) { } - - template - cpp_float(const F val, typename enable_if >::type* = 0): - data(), - exp (static_cast(0)), - neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) - { - *this = val; - } - - cpp_float(const double val, long long exponent); - - // Specific special values. - static const cpp_float& nan() - { - static const cpp_float val(mp_NaN); - init.do_nothing(); - return val; - } - static const cpp_float& inf() - { - static const cpp_float val(mp_inf); - init.do_nothing(); - return val; - } - static const cpp_float& (max)() - { - init.do_nothing(); - static bool init = false; - static const std::string str_max = std::string("9." + std::string(static_cast(cpp_float_max_digits10), static_cast('9'))) - + std::string("e+" + boost::lexical_cast(cpp_float_max_exp10)); - static cpp_float val_max; - if(!init) - { - init = true; - val_max = str_max.c_str(); - } - return val_max; - } - - static const cpp_float& (min)() - { - init.do_nothing(); - static bool init = false; - static cpp_float val_min; - if(!init) - { - init = true; - val_min = std::string("1.0e" + boost::lexical_cast(cpp_float_min_exp10)).c_str(); - } - return val_min; - } - static const cpp_float& zero() - { - init.do_nothing(); - static cpp_float val(static_cast(0u)); - return val; - } - static const cpp_float& one() - { - init.do_nothing(); - static cpp_float val(static_cast(1u)); - return val; - } - static const cpp_float& two() - { - init.do_nothing(); - static cpp_float val(static_cast(2u)); - return val; - } - static const cpp_float& half() - { - init.do_nothing(); - static cpp_float val(0.5L); - return val; - } - static const cpp_float& double_min() - { - init.do_nothing(); - static cpp_float val(static_cast((std::numeric_limits::min)())); - return val; - } - static const cpp_float& double_max() - { - init.do_nothing(); - static cpp_float val(static_cast((std::numeric_limits::max)())); - return val; - } - static const cpp_float& long_double_min() - { - init.do_nothing(); - static cpp_float val((std::numeric_limits::min)()); - return val; - } - static const cpp_float& long_double_max() - { - init.do_nothing(); - static cpp_float val((std::numeric_limits::max)()); - return val; - } - static const cpp_float& long_long_max() - { - init.do_nothing(); - static cpp_float val((std::numeric_limits::max)()); - return val; - } - static const cpp_float& long_long_min() - { - init.do_nothing(); - static cpp_float val((std::numeric_limits::min)()); - return val; - } - static const cpp_float& ulong_long_max() - { - init.do_nothing(); - static cpp_float val((std::numeric_limits::max)()); - return val; - } - static const cpp_float& eps() - { - init.do_nothing(); - static cpp_float val(1.0, 1 - (int)Digits10); - return val; - } - - // Basic operations. - cpp_float& operator= (const cpp_float& v) - { - data = v.data; - exp = v.exp; - neg = v.neg; - fpclass = v.fpclass; - prec_elem = v.prec_elem; - return *this; - } - cpp_float& operator= (long long v) - { - if(v < 0) - { - from_unsigned_long_long(-v); - negate(); - } - else - from_unsigned_long_long(v); - return *this; - } - cpp_float& operator= (unsigned long long v) - { - from_unsigned_long_long(v); - return *this; - } - cpp_float& operator= (long double v); - cpp_float& operator= (const char* v) - { - rd_string(v); - return *this; - } - - cpp_float& operator+=(const cpp_float& v); - cpp_float& operator-=(const cpp_float& v); - cpp_float& operator*=(const cpp_float& v); - cpp_float& operator/=(const cpp_float& v); - - cpp_float& add_unsigned_long_long(const unsigned long long n) - { - cpp_float t; - t.from_unsigned_long_long(n); - return *this += t; - } - cpp_float& sub_unsigned_long_long(const unsigned long long n) - { - cpp_float t; - t.from_unsigned_long_long(n); - return *this -= t; - } - cpp_float& mul_unsigned_long_long(const unsigned long long n); - cpp_float& div_unsigned_long_long(const unsigned long long n); - - // Elementary primitives. - cpp_float& calculate_inv (void); - cpp_float& calculate_sqrt(void); - void negate() - { - if(!iszero()) - neg = !neg; - } - - // Comparison functions - bool isnan (void) const { return (fpclass == mp_NaN); } - bool isinf (void) const { return (fpclass == mp_inf); } - bool isfinite(void) const { return (fpclass == mp_finite); } - - bool iszero (void) const - { - return ((fpclass == mp_finite) && (data[0u] == 0u)); - } - bool isone (void) const; - bool isint (void) const; - bool isneg (void) const { return neg; } - - // Operators pre-increment and pre-decrement - cpp_float& operator++(void) - { - return *this += one(); - } - cpp_float& operator--(void) - { - return *this -= one(); - } - - std::string str(unsigned digits, bool scientific)const; - - int compare(const cpp_float& v)const; - template - int compare(const V& v)const - { - cpp_float t; - t = v; - return compare(t); - } - - void swap(cpp_float& v) - { - data.swap(v.data); - std::swap(exp, v.exp); - std::swap(neg, v.neg); - std::swap(fpclass, v.fpclass); - std::swap(prec_elem, v.prec_elem); - } - - double extract_double (void) const; - long double extract_long_double (void) const; - signed long long extract_signed_long_long (void) const; - unsigned long long extract_unsigned_long_long(void) const; - void extract_parts (double& mantissa, boost::int64_t& exponent) const; - cpp_float extract_integer_part (void) const; - void precision(const boost::int32_t prec_digits) - { - if(prec_digits >= cpp_float_digits10) - { - prec_elem = mp_elem_number; - } - else - { - const boost::int32_t elems = static_cast( static_cast( (prec_digits + (mp_elem_digits10 / 2)) / mp_elem_digits10) - + static_cast(((prec_digits % mp_elem_digits10) != 0) ? 1 : 0)); - - prec_elem = (std::min)(mp_elem_number, (std::max)(elems, static_cast(2))); - } - } - static cpp_float pow2(long long i); - long long order()const - { - const bool bo_order_is_zero = ((!isfinite()) || (data[0] == static_cast(0u))); - // - // Binary search to find the order of the leading term: - // - boost::uint32_t prefix = 0; - - if(data[0] >= 100000UL) - { - if(data[0] >= 10000000UL) - { - if(data[0] >= 100000000UL) - { - if(data[0] >= 1000000000UL) - prefix = 9; - else - prefix = 8; - } - else - prefix = 7; - } - else - { - if(data[0] >= 1000000UL) - prefix = 6; - else - prefix = 5; - } - } - else - { - if(data[0] >= 1000UL) - { - if(data[0] >= 10000UL) - prefix = 4; - else - prefix = 3; - } - else - { - if(data[0] >= 100) - prefix = 2; - else if(data[0] >= 10) - prefix = 1; - } - } - - return (bo_order_is_zero ? static_cast(0) - : static_cast(exp + prefix)); - } - -private: - static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast(0u)); } - static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast(cpp_float::mp_elem_mask - 1)); } - static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast('0')); } - - void from_unsigned_long_long(const unsigned long long u); - - int cmp_data(const array_type& vd) const; - - static void mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p); - static boost::uint32_t mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); - static boost::uint32_t div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); - - bool rd_string(const char* const s); -}; - -template -typename cpp_float::initializer cpp_float::init; - -template -const boost::int32_t cpp_float::mp_radix; -template -const boost::int32_t cpp_float::cpp_float_digits; -template -const boost::int32_t cpp_float::cpp_float_digits10_setting; -template -const boost::int32_t cpp_float::cpp_float_digits10_limit; -template -const boost::int32_t cpp_float::cpp_float_digits10; -template -const boost::int32_t cpp_float::cpp_float_digits10_extra; -template -const boost::int32_t cpp_float::cpp_float_max_digits10; -template -const boost::int64_t cpp_float::cpp_float_max_exp; -template -const boost::int64_t cpp_float::cpp_float_min_exp; -template -const boost::int64_t cpp_float::cpp_float_max_exp10; -template -const boost::int64_t cpp_float::cpp_float_min_exp10; -template -const boost::int32_t cpp_float::mp_elem_digits10; -template -const boost::int32_t cpp_float::cpp_float_digits10_num_base; -template -const boost::int32_t cpp_float::mp_elem_number; -template -const boost::int32_t cpp_float::mp_elem_mask; - - -template -cpp_float& cpp_float::operator+=(const cpp_float& v) -{ - if(isnan()) - { - return *this; - } - - if(isinf()) - { - if(v.isinf() && (isneg() != v.isneg())) - { - *this = nan(); - } - return *this; - } - - if(iszero()) - { - return operator=(v); - } - - // Get the offset for the add/sub operation. - static const boost::int64_t max_delta_exp = static_cast((mp_elem_number - 1) * mp_elem_digits10); - - const boost::int64_t ofs_exp = static_cast(exp - v.exp); - - // Check if the operation is out of range, requiring special handling. - if(v.iszero() || (ofs_exp > max_delta_exp)) - { - // Result is *this unchanged since v is negligible compared to *this. - return *this; - } - else if(ofs_exp < -max_delta_exp) - { - // Result is *this = v since *this is negligible compared to v. - return operator=(v); - } - - // Do the add/sub operation. - - typename array_type::iterator p_u = data.begin(); - typename array_type::const_iterator p_v = v.data.begin(); - bool b_copy = false; - const boost::int32_t ofs = static_cast(static_cast(ofs_exp) / mp_elem_digits10); - array_type n_data; - - if(neg == v.neg) - { - // Add v to *this, where the data array of either *this or v - // might have to be treated with a positive, negative or zero offset. - // The result is stored in *this. The data are added one element - // at a time, each element with carry. - if(ofs >= static_cast(0)) - { - std::copy(v.data.begin(), v.data.end() - static_cast(ofs), n_data.begin() + static_cast(ofs)); - std::fill(n_data.begin(), n_data.begin() + static_cast(ofs), static_cast(0u)); - p_v = n_data.begin(); - } - else - { - std::copy(data.begin(), data.end() - static_cast(-ofs), n_data.begin() + static_cast(-ofs)); - std::fill(n_data.begin(), n_data.begin() + static_cast(-ofs), static_cast(0u)); - p_u = n_data.begin(); - b_copy = true; - } - - // Addition algorithm - boost::uint32_t carry = static_cast(0u); - - for(boost::int32_t j = static_cast(mp_elem_number - static_cast(1)); j >= static_cast(0); j--) - { - boost::uint32_t t = static_cast(static_cast(p_u[j] + p_v[j]) + carry); - carry = t / static_cast(mp_elem_mask); - p_u[j] = static_cast(t - static_cast(carry * static_cast(mp_elem_mask))); - } - - if(b_copy) - { - data = n_data; - exp = v.exp; - } - - // There needs to be a carry into the element -1 of the array data - if(carry != static_cast(0u)) - { - std::copy_backward(data.begin(), data.end() - static_cast(1u), data.end()); - data[0] = carry; - exp += static_cast(mp_elem_digits10); - } - } - else - { - // Subtract v from *this, where the data array of either *this or v - // might have to be treated with a positive, negative or zero offset. - if((ofs > static_cast(0)) - || ( (ofs == static_cast(0)) - && (cmp_data(v.data) > static_cast(0))) - ) - { - // In this case, |u| > |v| and ofs is positive. - // Copy the data of v, shifted down to a lower value - // into the data array m_n. Set the operand pointer p_v - // to point to the copied, shifted data m_n. - std::copy(v.data.begin(), v.data.end() - static_cast(ofs), n_data.begin() + static_cast(ofs)); - std::fill(n_data.begin(), n_data.begin() + static_cast(ofs), static_cast(0u)); - p_v = n_data.begin(); - } - else - { - if(ofs != static_cast(0)) - { - // In this case, |u| < |v| and ofs is negative. - // Shift the data of u down to a lower value. - std::copy_backward(data.begin(), data.end() - static_cast(-ofs), data.end()); - std::fill(data.begin(), data.begin() + static_cast(-ofs), static_cast(0u)); - } - - // Copy the data of v into the data array n_data. - // Set the u-pointer p_u to point to m_n and the - // operand pointer p_v to point to the shifted - // data m_data. - n_data = v.data; - p_u = n_data.begin(); - p_v = data.begin(); - b_copy = true; - } - - boost::int32_t j; - - // Subtraction algorithm - boost::int32_t borrow = static_cast(0); - - for(j = static_cast(mp_elem_number - static_cast(1)); j >= static_cast(0); j--) - { - boost::int32_t t = static_cast(static_cast( static_cast(p_u[j]) - - static_cast(p_v[j])) - borrow); - - // Underflow? Borrow? - if(t < static_cast(0)) - { - // Yes, underflow and borrow - t += static_cast(mp_elem_mask); - borrow = static_cast(1); - } - else - { - borrow = static_cast(0); - } - - p_u[j] = static_cast(static_cast(t) % static_cast(mp_elem_mask)); - } - - if(b_copy) - { - data = n_data; - exp = v.exp; - neg = v.neg; - } - - // Is it necessary to justify the data? - const typename array_type::const_iterator first_nonzero_elem = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); - - if(first_nonzero_elem != data.begin()) - { - if(first_nonzero_elem == data.end()) - { - // This result of the subtraction is exactly zero. - // Reset the sign and the exponent. - neg = false; - exp = static_cast(0); - } - else - { - // Justify the data - const std::size_t sj = static_cast(std::distance(data.begin(), first_nonzero_elem)); - - std::copy(data.begin() + static_cast(sj), data.end(), data.begin()); - std::fill(data.end() - sj, data.end(), static_cast(0u)); - - exp -= static_cast(sj * static_cast(mp_elem_digits10)); - } - } - } - - // Check for underflow. - if(iszero()) - { - return *this = zero(); - } - - bool overflow = exp >= cpp_float_max_exp; - if(exp == cpp_float_max_exp) - { - // Check to see if we really truely have an overflow or not... - if(isneg()) - { - cpp_float t(*this); - t.negate(); - overflow = t.compare((max)()) > 0; - } - else - { - overflow = compare((max)()) > 0; - } - } - - // Check for overflow. - if(overflow) - { - const bool b_result_is_neg = neg; - - *this = inf(); - if(b_result_is_neg) - negate(); - } - - return *this; -} - -template -cpp_float& cpp_float::operator-=(const cpp_float& v) -{ - // Use *this - v = -(-*this + v). - negate(); - *this += v; - negate(); - return *this; -} - -template -cpp_float& cpp_float::operator*=(const cpp_float& v) -{ - // Evaluate the sign of the result. - const bool b_result_is_neg = (neg != v.neg); - - // Artificially set the sign of the result to be positive. - neg = false; - - // Handle special cases like zero, inf and NaN. - const bool b_u_is_inf = isinf(); - const bool b_v_is_inf = v.isinf(); - const bool b_u_is_zero = iszero(); - const bool b_v_is_zero = v.iszero(); - - if( (isnan() || v.isnan()) - || (b_u_is_inf && b_v_is_zero) - || (b_v_is_inf && b_u_is_zero) - ) - { - *this = nan(); - return *this; - } - - if(b_u_is_inf || b_v_is_inf) - { - *this = inf(); - if(b_result_is_neg) - negate(); - return *this; - } - - if(b_u_is_zero || b_v_is_zero) - { - return *this = zero(); - } - - // Check for overflow or underflow. - const bool u_exp_is_neg = (exp < static_cast(0)); - const bool v_exp_is_neg = (v.exp < static_cast(0)); - - if(u_exp_is_neg == v_exp_is_neg) - { - // Get the unsigned base-10 exponents of *this and v and... - const boost::int64_t u_exp = ((!u_exp_is_neg) ? exp : static_cast( -exp)); - const boost::int64_t v_exp = ((!v_exp_is_neg) ? v.exp : static_cast(-v.exp)); - - // Check the range of the upcoming multiplication. - const bool b_result_is_out_of_range = (v_exp >= static_cast(cpp_float_max_exp10 - u_exp)); - - if(b_result_is_out_of_range) - { - if(u_exp_is_neg) - { - *this = zero(); - } - else - { - *this = inf(); - if(b_result_is_neg) - negate(); - } - return *this; - } - } - - // Set the exponent of the result. - exp += v.exp; - - boost::array(mp_elem_number + static_cast(1))> w = {{ 0u }}; - - mul_loop_uv(data.data(), v.data.data(), w.data(), (std::min)(prec_elem, v.prec_elem)); - - // Copy the multiplication data into the result. - // Shift the result and adjust the exponent if necessary. - if(w[static_cast(0u)] != static_cast(0u)) - { - exp += static_cast(mp_elem_digits10); - - std::copy(w.begin(), w.end() - 1u, data.begin()); - } - else - { - std::copy(w.begin() + 1u, w.end(), data.begin()); - } - - // Set the sign of the result. - neg = b_result_is_neg; - - return *this; -} - -template -cpp_float& cpp_float::operator/=(const cpp_float& v) -{ - const bool u_and_v_are_finite_and_identical = ( isfinite() - && (fpclass == v.fpclass) - && (exp == v.exp) - && (cmp_data(v.data) == static_cast(0))); - - if(u_and_v_are_finite_and_identical) - { - *this = one(); - if(neg != v.neg) - negate(); - return *this; - } - else - { - if(iszero()) - { - if(v.isnan() || v.iszero()) - { - return *this = v; - } - return *this; - } - cpp_float t(v); - t.calculate_inv(); - return operator*=(t); - } -} - -template -cpp_float& cpp_float::mul_unsigned_long_long(const unsigned long long n) -{ - // Multiply *this with a constant unsigned long long. - - // Evaluate the sign of the result. - const bool b_neg = neg; - - // Artificially set the sign of the result to be positive. - neg = false; - - // Handle special cases like zero, inf and NaN. - const bool b_u_is_inf = isinf(); - const bool b_n_is_zero = (n == static_cast(0)); - - if(isnan() || (b_u_is_inf && b_n_is_zero)) - { - return (*this = nan()); - } - - if(b_u_is_inf) - { - *this = inf(); - if(b_neg) - negate(); - return *this; - } - - if(iszero() || b_n_is_zero) - { - // Multiplication by zero. - return *this = zero(); - } - - if(n >= static_cast(mp_elem_mask)) - { - neg = b_neg; - cpp_float t; - t = n; - return operator*=(t); - } - - if(n == static_cast(1u)) - { - neg = b_neg; - return *this; - } - - // Set up the multiplication loop. - const boost::uint32_t nn = static_cast(n); - const boost::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem); - - // Handle the carry and adjust the exponent. - if(carry != static_cast(0u)) - { - exp += static_cast(mp_elem_digits10); - - // Shift the result of the multiplication one element to the right. - std::copy_backward(data.begin(), - data.begin() + static_cast(prec_elem - static_cast(1)), - data.begin() + static_cast(prec_elem)); - - data.front() = static_cast(carry); - } - - bool overflow = exp >= cpp_float_max_exp; - if(exp == cpp_float_max_exp) - { - // Check to see if we really truely have an overflow or not... - if(isneg()) - { - cpp_float t(*this); - t.negate(); - overflow = t.compare((max)()) > 0; - } - else - { - overflow = compare((max)()) > 0; - } - } - - if(overflow) - { - *this = inf(); - if(b_neg) - negate(); - return *this; - } - - // Set the sign. - neg = b_neg; - - return *this; -} - -template -cpp_float& cpp_float::div_unsigned_long_long(const unsigned long long n) -{ - // Divide *this by a constant unsigned long long. - - // Evaluate the sign of the result. - const bool b_neg = neg; - - // Artificially set the sign of the result to be positive. - neg = false; - - // Handle special cases like zero, inf and NaN. - if(isnan()) - { - return *this; - } - - if(isinf()) - { - *this = inf(); - if(b_neg) - negate(); - return *this; - } - - if(n == static_cast(0u)) - { - // Divide by 0. - if(iszero()) - { - *this = nan(); - return *this; - } - else - { - *this = inf(); - if(isneg()) - negate(); - return *this; - } - } - - if(iszero()) - { - return *this; - } - - if(n >= static_cast(mp_elem_mask)) - { - neg = b_neg; - cpp_float t; - t = n; - return operator/=(t); - } - - const boost::uint32_t nn = static_cast(n); - - if(nn > static_cast(1u)) - { - // Do the division loop. - const boost::uint32_t prev = div_loop_n(data.data(), nn, prec_elem); - - // Determine if one leading zero is in the result data. - if(data[0] == static_cast(0u)) - { - // Adjust the exponent - exp -= static_cast(mp_elem_digits10); - - // Shift result of the division one element to the left. - std::copy(data.begin() + static_cast(1u), - data.begin() + static_cast(prec_elem - static_cast(1)), - data.begin()); - - data[prec_elem - static_cast(1)] = static_cast(static_cast(prev * static_cast(mp_elem_mask)) / nn); - } - } - - // Check for underflow. - if(iszero()) - { - return *this = zero(); - } - - // Set the sign of the result. - neg = b_neg; - - return *this; -} - -template -cpp_float& cpp_float::calculate_inv() -{ - // Compute the inverse of *this. - const bool b_neg = neg; - - neg = false; - - // Handle special cases like zero, inf and NaN. - if(iszero()) - { - *this = inf(); - if(b_neg) - negate(); - return *this; - } - - if(isnan()) - { - return *this; - } - - if(isinf()) - { - return *this = zero(); - } - - if(isone()) - { - if(b_neg) - negate(); - return *this; - } - - // Save the original *this. - cpp_float x(*this); - - // Generate the initial estimate using division. - // Extract the mantissa and exponent for a "manual" - // computation of the estimate. - double dd; - boost::int64_t ne; - x.extract_parts(dd, ne); - - // Do the inverse estimate using double precision estimates of mantissa and exponent. - operator=(cpp_float(1.0 / dd, -ne)); - - // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration - // is used. During the iterative steps, the precision of the calculation is limited - // to the minimum required in order to minimize the run-time. - - static const boost::int32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; - - for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= static_cast(2)) - { - // Adjust precision of the terms. - precision(static_cast(digits * static_cast(2))); - x.precision(static_cast(digits * static_cast(2))); - - // Next iteration. - cpp_float t(*this); - t *= x; - t -= two(); - t.negate(); - *this *= t; - } - - neg = b_neg; - - prec_elem = mp_elem_number; - - return *this; -} - -template -cpp_float& cpp_float::calculate_sqrt(void) -{ - // Compute the square root of *this. - - if(isneg() || (!isfinite())) - { - *this = nan(); - return *this; - } - - if(iszero() || isone()) - { - return *this; - } - - // Save the original *this. - cpp_float x(*this); - - // Generate the initial estimate using division. - // Extract the mantissa and exponent for a "manual" - // computation of the estimate. - double dd; - boost::int64_t ne; - extract_parts(dd, ne); - - // Force the exponent to be an even multiple of two. - if((ne % static_cast(2)) != static_cast(0)) - { - ++ne; - dd /= 10.0; - } - - // Setup the iteration. - // Estimate the square root using simple manipulations. - const double sqd = std::sqrt(dd); - - *this = cpp_float(sqd, static_cast(ne / static_cast(2))); - - // Estimate 1.0 / (2.0 * x0) using simple manipulations. - cpp_float vi(0.5 / sqd, static_cast(-ne / static_cast(2))); - - // Compute the square root of x. Coupled Newton iteration - // as described in "Pi Unleashed" is used. During the - // iterative steps, the precision of the calculation is - // limited to the minimum required in order to minimize - // the run-time. - // - // Book references: - // http://www.jjj.de/pibook/pibook.html - // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846 - - static const boost::uint32_t double_digits10_minus_one = static_cast(static_cast(Digits10) - static_cast(1)); - - for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= 2u) - { - // Adjust precision of the terms. - precision(digits * 2); - vi.precision(digits * 2); - - // Next iteration of vi - cpp_float t(*this); - t *= vi; - t.negate(); - t.mul_unsigned_long_long(2u); - t += one(); - t *= vi; - vi += t; - - // Next iteration of *this - t = *this; - t *= *this; - t.negate(); - t += x; - t *= vi; - *this += t; - } - - prec_elem = mp_elem_number; - - return *this; -} - -template -int cpp_float::cmp_data(const array_type& vd) const -{ - // Compare the data of *this with those of v. - // Return +1 for *this > v - // 0 for *this = v - // -1 for *this < v - - const std::pair mismatch_pair = std::mismatch(data.begin(), data.end(), vd.begin()); - - const bool is_equal = ((mismatch_pair.first == data.end()) && (mismatch_pair.second == vd.end())); - - if(is_equal) - { - return 0; - } - else - { - return ((*mismatch_pair.first > *mismatch_pair.second) ? 1 : -1); - } -} - -template -int cpp_float::compare(const cpp_float& v) const -{ - // Compare v with *this. - // Return +1 for *this > v - // 0 for *this = v - // -1 for *this < v - - // Handle all non-finite cases. - if((!isfinite()) || (!v.isfinite())) - { - // NaN can never equal NaN. Return an implementation-dependent - // signed result. Also note that comparison of NaN with NaN - // using operators greater-than or less-than is undefined. - if(isnan() || v.isnan()) { return (isnan() ? 1 : -1); } - - if(isinf() && v.isinf()) - { - // Both *this and v are infinite. They are equal if they have the same sign. - // Otherwise, *this is less than v if and only if *this is negative. - return ((neg == v.neg) ? 0 : (neg ? -1 : 1)); - } - - if(isinf()) - { - // *this is infinite, but v is finite. - // So negative infinite *this is less than any finite v. - // Whereas positive infinite *this is greater than any finite v. - return (isneg() ? -1 : 1); - } - else - { - // *this is finite, and v is infinite. - // So any finite *this is greater than negative infinite v. - // Whereas any finite *this is less than positive infinite v. - return (v.neg ? 1 : -1); - } - } - - // And now handle all *finite* cases. - if(iszero()) - { - // The value of *this is zero and v is either zero or non-zero. - return (v.iszero() ? 0 - : (v.neg ? 1 : -1)); - } - else if(v.iszero()) - { - // The value of v is zero and *this is non-zero. - return (neg ? -1 : 1); - } - else - { - // Both *this and v are non-zero. - - if(neg != v.neg) - { - // The signs are different. - return (neg ? -1 : 1); - } - else if(exp != v.exp) - { - // The signs are the same and the exponents are different. - const int val_cmp_exp = ((exp < v.exp) ? 1 : -1); - - return (neg ? val_cmp_exp : -val_cmp_exp); - } - else - { - // The signs are the same and the exponents are the same. - // Compare the data. - const int val_cmp_data = cmp_data(v.data); - - return ((!neg) ? val_cmp_data : -val_cmp_data); - } - } -} - -template -bool cpp_float::isone() const -{ - // Check if the value of *this is identically 1 or very close to 1. - - const bool not_negative_and_is_finite = ((!neg) && isfinite()); - - if(not_negative_and_is_finite) - { - if((data[0u] == static_cast(1u)) && (exp == static_cast(0))) - { - const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); - return (it_non_zero == data.end()); - } - else if((data[0u] == static_cast(mp_elem_mask - 1)) && (exp == static_cast(-mp_elem_digits10))) - { - const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate); - return (it_non_nine == data.end()); - } - } - - return false; -} - -template -bool cpp_float::isint() const -{ - if(fpclass != mp_finite) { return false; } - - if(iszero()) { return true; } - - if(exp < static_cast(0)) { return false; } // |*this| < 1. - - const typename array_type::size_type offset_decimal_part = static_cast(exp / mp_elem_digits10) + 1u; - - if(offset_decimal_part >= static_cast(mp_elem_number)) - { - // The number is too large to resolve the integer part. - // It considered to be a pure integer. - return true; - } - - typename array_type::const_iterator it_non_zero = std::find_if(data.begin() + offset_decimal_part, data.end(), data_elem_is_non_zero_predicate); - - return (it_non_zero == data.end()); -} - -template -void cpp_float::extract_parts(double& mantissa, boost::int64_t& exponent) const -{ - // Extract the approximate parts mantissa and base-10 exponent from the input cpp_float value x. - - // Extracts the mantissa and exponent. - exponent = exp; - - boost::uint32_t p10 = static_cast(1u); - boost::uint32_t test = data[0u]; - - for(;;) - { - test /= static_cast(10u); - - if(test == static_cast(0u)) - { - break; - } - - p10 *= static_cast(10u); - ++exponent; - } - - mantissa = static_cast(data[0]) - + (static_cast(data[1]) / static_cast(mp_elem_mask)) - + ((static_cast(data[2]) / static_cast(mp_elem_mask)) / static_cast(mp_elem_mask)); - - mantissa /= static_cast(p10); - - if(neg) { mantissa = -mantissa; } -} - -template -double cpp_float::extract_double(void) const -{ - // Returns the double conversion of a cpp_float. - - // Check for non-normal cpp_float. - if(!isfinite()) - { - if(isnan()) - { - return std::numeric_limits::quiet_NaN(); - } - else - { - return ((!neg) ? std::numeric_limits::infinity() - : -std::numeric_limits::infinity()); - } - } - - cpp_float xx(*this); - if(xx.isneg()) - xx.negate(); - - // Check for zero cpp_float. - if(iszero() || (xx.compare(double_min()) < 0)) - { - return 0.0; - } - - // Check if cpp_float exceeds the maximum of double. - if(xx.compare(double_max()) > 0) - { - return ((!neg) ? std::numeric_limits::infinity() - : -std::numeric_limits::infinity()); - } - - std::stringstream ss; - - ss << str(std::numeric_limits::digits10 + (2 + 1), true); - - double d; - ss >> d; - - return d; -} - -template -long double cpp_float::extract_long_double(void) const -{ - // Returns the long double conversion of a cpp_float. - - // Check for non-normal cpp_float. - if(!isfinite()) - { - if(isnan()) - { - return std::numeric_limits::quiet_NaN(); - } - else - { - return ((!neg) ? std::numeric_limits::infinity() - : -std::numeric_limits::infinity()); - } - } - - cpp_float xx(*this); - if(xx.isneg()) - xx.negate(); - - // Check for zero cpp_float. - if(iszero() || (xx.compare(long_double_min()) < 0)) - { - return static_cast(0.0); - } - - // Check if cpp_float exceeds the maximum of double. - if(xx.compare(long_double_max()) > 0) - { - return ((!neg) ? std::numeric_limits::infinity() - : -std::numeric_limits::infinity()); - } - - std::stringstream ss; - - ss << str(std::numeric_limits::digits10 + (2 + 1), true); - - long double ld; - ss >> ld; - - return ld; -} - -template -signed long long cpp_float::extract_signed_long_long(void) const -{ - // Extracts a signed long long from *this. - // If (x > maximum of signed long long) or (x < minimum of signed long long), - // then the maximum or minimum of signed long long is returned accordingly. - - if(exp < static_cast(0)) - { - return static_cast(0); - } - - const bool b_neg = isneg(); - - unsigned long long val; - - if((!b_neg) && (compare(long_long_max()) > 0)) - { - return (std::numeric_limits::max)(); - } - else if(b_neg && (compare(long_long_min()) < 0)) - { - return (std::numeric_limits::min)(); - } - else - { - // Extract the data into an unsigned long long value. - cpp_float xn(extract_integer_part()); - if(xn.isneg()) - xn.negate(); - - val = static_cast(xn.data[0]); - - const boost::int32_t imax = (std::min)(static_cast(static_cast(xn.exp) / mp_elem_digits10), static_cast(mp_elem_number - static_cast(1))); - - for(boost::int32_t i = static_cast(1); i <= imax; i++) - { - val *= static_cast(mp_elem_mask); - val += static_cast(xn.data[i]); - } - } - - return ((!b_neg) ? static_cast(val) : static_cast(-static_cast(val))); -} - -template -unsigned long long cpp_float::extract_unsigned_long_long(void) const -{ - // Extracts an unsigned long long from *this. - // If x exceeds the maximum of unsigned long long, - // then the maximum of unsigned long long is returned. - // If x is negative, then the unsigned long long cast of - // the signed long long extracted value is returned. - - if(isneg()) - { - return static_cast(extract_signed_long_long()); - } - - if(exp < static_cast(0)) - { - return static_cast(0u); - } - - const cpp_float xn(extract_integer_part()); - - unsigned long long val; - - if(xn.compare(ulong_long_max()) > 0) - { - return (std::numeric_limits::max)(); - } - else - { - // Extract the data into an unsigned long long value. - val = static_cast(xn.data[0]); - - const boost::int32_t imax = (std::min)(static_cast(static_cast(xn.exp) / mp_elem_digits10), static_cast(mp_elem_number - static_cast(1))); - - for(boost::int32_t i = static_cast(1); i <= imax; i++) - { - val *= static_cast(mp_elem_mask); - val += static_cast(xn.data[i]); - } - } - - return val; -} - -template -cpp_float cpp_float::extract_integer_part(void) const -{ - // Compute the signed integer part of x. - - if(!isfinite()) - { - return *this; - } - - if(exp < static_cast(0)) - { - // The absolute value of the number is smaller than 1. - // Thus the integer part is zero. - return zero(); - } - else if(exp >= Digits10 - 1) - { - // The number is too large to resolve the integer part. - // Thus it is already a pure integer part. - return *this; - } - - // Make a local copy. - cpp_float x = *this; - - // Clear out the decimal portion - const size_t first_clear = (static_cast(x.exp) / static_cast(mp_elem_digits10)) + 1u; - const size_t last_clear = static_cast(mp_elem_number); - - std::fill(x.data.begin() + first_clear, x.data.begin() + last_clear, static_cast(0u)); - - return x; -} - -template -std::string cpp_float::str(std::size_t number_of_digits, bool scientific) const -{ - std::string str; - boost::int64_t my_exp = order(); - if(number_of_digits == 0) - number_of_digits = (std::numeric_limits::max)(); - // Determine the number of elements needed to provide the requested digits from cpp_float. - const std::size_t number_of_elements = (std::min)(static_cast((number_of_digits / static_cast(mp_elem_digits10)) + 2u), - static_cast(mp_elem_number)); - - // Extract the remaining digits from cpp_float after the decimal point. - str = boost::lexical_cast(data[0]); - - // Extract all of the digits from cpp_float, beginning with the first data element. - for(std::size_t i = static_cast(1u); i < number_of_elements; i++) - { - std::stringstream ss; - - ss << std::setw(static_cast(mp_elem_digits10)) - << std::setfill(static_cast('0')) - << data[i]; - - str += ss.str(); - } - - // Cut the output to the size of the precision. - if(str.length() > number_of_digits) - { - // Get the digit after the last needed digit for rounding - const boost::uint32_t round = static_cast(static_cast(str.at(number_of_digits)) - static_cast('0')); - - // Truncate the string - str = str.substr(static_cast(0u), number_of_digits); - - if(round >= static_cast(5u)) - { - std::size_t ix = static_cast(str.length() - 1u); - - // Every trailing 9 must be rounded up - while(ix && (static_cast(str.at(ix)) - static_cast('0') == static_cast(9))) - { - str.at(ix) = static_cast('0'); - --ix; - } - - if(!ix) - { - // There were nothing but trailing nines. - if(static_cast(static_cast(str.at(ix)) - static_cast(0x30)) == static_cast(9)) - { - // Increment up to the next order and adjust exponent. - str.at(ix) = static_cast('1'); - ++my_exp; - } - else - { - // Round up this digit. - ++str.at(ix); - } - } - else - { - // Round up the last digit. - ++str[ix]; - } - } - } - // - // Suppress trailing zeros: - // - std::string::iterator pos = str.end(); - while(pos != str.begin() && *--pos == '0'){} - if(pos != str.end()) - ++pos; - str.erase(pos, str.end()); - if(str.empty()) - str = '0'; - if(!scientific && (str.size() < 20) && (my_exp >= 0) && (my_exp < 20)) - { - if(1 + my_exp > str.size()) - { - // Just pad out the end with zeros: - str.append(static_cast(1 + my_exp - str.size()), '0'); - } - else if(my_exp + 1 != str.size()) - { - // Insert the decimal point: - str.insert(static_cast(my_exp + 1), 1, '.'); - } - } - else - { - // Scientific format: - str.insert(1, 1, '.'); - if(str.size() == 2) - str.append(1, '0'); - str.append(1, 'e'); - str.append(boost::lexical_cast(my_exp)); - } - if(isneg()) - str.insert(0, 1, '-'); - return str; -} - -template -bool cpp_float::rd_string(const char* const s) -{ - std::string str(s); - - // Get a possible exponent and remove it. - exp = static_cast(0); - - std::size_t pos; - - if( ((pos = str.find('e')) != std::string::npos) - || ((pos = str.find('E')) != std::string::npos) - ) - { - // Remove the exponent part from the string. - exp = boost::lexical_cast(static_cast(str.c_str() + (pos + 1u))); - str = str.substr(static_cast(0u), pos); - } - - // Get a possible +/- sign and remove it. - neg = false; - - if((pos = str.find(static_cast('-'))) != std::string::npos) - { - neg = true; - str.erase(pos, static_cast(1u)); - } - - if((pos = str.find(static_cast('+'))) != std::string::npos) - { - str.erase(pos, static_cast(1u)); - } - - // Remove leading zeros for all input types. - const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate); - - if(fwd_it_leading_zero != str.begin()) - { - if(fwd_it_leading_zero == str.end()) - { - // The string contains nothing but leading zeros. - // This string represents zero. - operator=(zero()); - return true; - } - else - { - str.erase(str.begin(), fwd_it_leading_zero); - } - } - - // Put the input string into the standard cpp_float input form - // aaa.bbbbE+/-n, where aa has 1...mp_elem_digits10, bbbb has an - // even multiple of mp_elem_digits10 which are possibly zero padded - // on the right-end, and n is a signed 32-bit integer which is an - // even multiple of mp_elem_digits10. - - // Find a possible decimal point. - pos = str.find(static_cast('.')); - - if(pos != std::string::npos) - { - // Remove all trailing insignificant zeros. - const std::string::const_reverse_iterator rit_non_zero = std::find_if(str.rbegin(), str.rend(), char_is_nonzero_predicate); - - if(rit_non_zero != str.rbegin()) - { - const std::string::size_type ofs = str.length() - std::distance(str.rbegin(), rit_non_zero); - str.erase(str.begin() + ofs, str.end()); - } - - // Check if the input is identically zero. - if(str == std::string(".")) - { - operator=(zero()); - return true; - } - - // Remove leading significant zeros just after the decimal point - // and adjust the exponent accordingly. - // Note that the while-loop operates only on strings of the form ".000abcd..." - // and peels away the zeros just after the decimal point. - if(str.at(static_cast(0u)) == static_cast('.')) - { - const std::string::iterator it_non_zero = std::find_if(str.begin() + 1u, str.end(), char_is_nonzero_predicate); - - std::size_t delta_exp = static_cast(0u); - - if(str.at(static_cast(1u)) == static_cast('0')) - { - delta_exp = std::distance(str.begin() + 1u, it_non_zero); - } - - // Bring one single digit into the mantissa and adjust exponent accordingly. - str.erase(str.begin(), it_non_zero); - str.insert(static_cast(1u), "."); - exp -= static_cast(delta_exp + 1u); - } - } - else - { - // Input string has no decimal point: Append decimal point. - str.append("."); - } - - // Shift the decimal point such that the exponent is an even multiple of mp_elem_digits10. - std::size_t n_shift = static_cast(0u); - const std::size_t n_exp_rem = static_cast(exp % static_cast(mp_elem_digits10)); - - if((exp % static_cast(mp_elem_digits10)) != static_cast(0)) - { - n_shift = ((exp < static_cast(0)) - ? static_cast(n_exp_rem + static_cast(mp_elem_digits10)) - : static_cast(n_exp_rem)); - } - - // Make sure that there are enough digits for the decimal point shift. - pos = str.find(static_cast('.')); - - std::size_t pos_plus_one = static_cast(pos + 1u); - - if((str.length() - pos_plus_one) < n_shift) - { - const std::size_t sz = static_cast(n_shift - (str.length() - pos_plus_one)); - - str.append(std::string(sz, static_cast('0'))); - } - - // Do the decimal point shift. - if(n_shift != static_cast(0u)) - { - str.insert(static_cast(pos_plus_one + n_shift), "."); - - str.erase(pos, static_cast(1u)); - - exp -= static_cast(n_shift); - } - - // Cut the size of the mantissa to <= mp_elem_digits10. - pos = str.find(static_cast('.')); - pos_plus_one = static_cast(pos + 1u); - - if(pos > static_cast(mp_elem_digits10)) - { - const boost::int32_t n_pos = static_cast(pos); - const boost::int32_t n_rem_is_zero = ((static_cast(n_pos % mp_elem_digits10) == static_cast(0)) ? static_cast(1) : static_cast(0)); - const boost::int32_t n = static_cast(static_cast(n_pos / mp_elem_digits10) - n_rem_is_zero); - - str.insert(static_cast(static_cast(n_pos - static_cast(n * mp_elem_digits10))), "."); - - str.erase(pos_plus_one, static_cast(1u)); - - exp += static_cast(static_cast(n) * static_cast(mp_elem_digits10)); - } - - // Pad the decimal part such that its value is an even - // multiple of mp_elem_digits10. - pos = str.find(static_cast('.')); - pos_plus_one = static_cast(pos + 1u); - - const boost::int32_t n_dec = static_cast(static_cast(str.length() - 1u) - static_cast(pos)); - const boost::int32_t n_rem = static_cast(n_dec % mp_elem_digits10); - boost::int32_t n_cnt = ((n_rem != static_cast(0)) ? static_cast(mp_elem_digits10 - n_rem) - : static_cast(0)); - - if(n_cnt != static_cast(0)) - { - str.append(static_cast(n_cnt), static_cast('0')); - } - - // Truncate decimal part if it is too long. - const std::size_t max_dec = static_cast((mp_elem_number - 1) * mp_elem_digits10); - - if(static_cast(str.length() - pos) > max_dec) - { - str = str.substr(static_cast(0u), - static_cast(pos_plus_one + max_dec)); - } - - // Now the input string has the standard cpp_float input form. - // (See the comment above.) - - // Set all the data elements to 0. - std::fill(data.begin(), data.end(), static_cast(0u)); - - // Extract the data. - - // First get the digits to the left of the decimal point... - data[0u] = boost::lexical_cast(str.substr(static_cast(0u), pos)); - - // ...then get the remaining digits to the right of the decimal point. - const std::string::size_type i_end = ((str.length() - pos_plus_one) / static_cast(mp_elem_digits10)); - - for(std::string::size_type i = static_cast(0u); i < i_end; i++) - { - const std::string::const_iterator it = str.begin() - + pos_plus_one - + (i * static_cast(mp_elem_digits10)); - - data[i + 1u] = boost::lexical_cast(std::string(it, it + static_cast(mp_elem_digits10))); - } - - // Check for overflow... - if(exp > cpp_float_max_exp10) - { - const bool b_result_is_neg = neg; - - *this = inf(); - if(b_result_is_neg) - negate(); - } - - // ...and check for underflow. - if(exp <= cpp_float_min_exp10) - { - if(exp == cpp_float_min_exp10) - { - // Check for identity with the minimum value. - cpp_float test = *this; - - test.exp = static_cast(0); - - if(test.isone()) - { - *this = zero(); - } - } - else - { - *this = zero(); - } - } - - return true; -} - -template -cpp_float::cpp_float(const double mantissa, const boost::int64_t exponent) - : data (), - exp (static_cast(0)), - neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) -{ - // Create an cpp_float from mantissa and exponent. - // This ctor does not maintain the full precision of double. - - const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits::min)() * (1.0 + std::numeric_limits::epsilon()))); - - if(mantissa_is_iszero) - { - std::fill(data.begin(), data.end(), static_cast(0u)); - return; - } - - const bool b_neg = (mantissa < 0.0); - - double d = ((!b_neg) ? mantissa : -mantissa); - boost::int64_t e = exponent; - - while(d > 10.0) { d /= 10.0; ++e; } - while(d < 1.0) { d *= 10.0; --e; } - - boost::int32_t shift = static_cast(e % static_cast(mp_elem_digits10)); - - while(static_cast(shift-- % mp_elem_digits10) != static_cast(0)) - { - d *= 10.0; - --e; - } - - exp = e; - neg = b_neg; - - std::fill(data.begin(), data.end(), static_cast(0u)); - - static const boost::int32_t digit_ratio = static_cast(static_cast(std::numeric_limits::digits10) / static_cast(mp_elem_digits10)); - static const boost::int32_t digit_loops = static_cast(digit_ratio + static_cast(2)); - - for(boost::int32_t i = static_cast(0); i < digit_loops; i++) - { - boost::uint32_t n = static_cast(static_cast(d)); - data[i] = static_cast(n); - d -= static_cast(n); - d *= static_cast(mp_elem_mask); - } -} - -template -cpp_float& cpp_float::operator = (long double a) -{ - // Christopher Kormanyos's original code used a cast to long long here, but that fails - // when long double has more digits than a long long. - using std::frexp; - using std::ldexp; - using std::floor; - - if (a == 0) { - return *this = zero(); - } - - if (a == 1) { - return *this = one(); - } - - if((boost::math::isinf)(a)) - { - return *this = inf(); - } - if((boost::math::isnan)(a)) - return *this = nan(); - - int e; - long double f, term; - *this = zero(); - - f = frexp(a, &e); - - static const int shift = std::numeric_limits::digits - 1; - - while(f) - { - // extract int sized bits from f: - f = ldexp(f, shift); - term = floor(f); - e -= shift; - *this *= pow2(shift); - if(term > 0) - add_unsigned_long_long(static_cast(term)); - else - sub_unsigned_long_long(static_cast(-term)); - f -= term; - } - if(e != 0) - *this *= pow2(e); - return *this; -} - -template -void cpp_float::from_unsigned_long_long(const unsigned long long u) -{ - std::fill(data.begin(), data.end(), static_cast(0u)); - - exp = static_cast(0); - neg = false; - fpclass = mp_finite; - prec_elem = mp_elem_number; - - std::size_t i =static_cast(0u); - - unsigned long long uu = u; - - boost::uint32_t temp[(std::numeric_limits::digits10 / static_cast(mp_elem_digits10)) + 3] = { static_cast(0u) }; - - while(uu != static_cast(0u)) - { - temp[i] = static_cast(uu % static_cast(mp_elem_mask)); - uu = static_cast(uu / static_cast(mp_elem_mask)); - ++i; - } - - if(i > static_cast(1u)) - { - exp += static_cast((i - 1u) * static_cast(mp_elem_digits10)); - } - - std::reverse(temp, temp + i); - std::copy(temp, temp + (std::min)(i, static_cast(mp_elem_number)), data.begin()); -} - -template -void cpp_float::mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p) -{ - boost::uint64_t carry = static_cast(0u); - - for(boost::int32_t j = static_cast(p - 1u); j >= static_cast(0); j--) - { - boost::uint64_t sum = carry; - - for(boost::int32_t i = j; i >= static_cast(0); i--) - { - sum += static_cast(u[i] * static_cast(v[j - i])); - } - - w[j + 1] = static_cast(sum % static_cast(mp_elem_mask)); - carry = static_cast(sum / static_cast(mp_elem_mask)); - } - - w[0u] = static_cast(carry); -} - -template -boost::uint32_t cpp_float::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) -{ - boost::uint64_t carry = static_cast(0u); - - // Multiplication loop. - for(boost::int32_t j = p - 1; j >= static_cast(0); j--) - { - const boost::uint64_t t = static_cast(carry + static_cast(u[j] * static_cast(n))); - carry = static_cast(t / static_cast(mp_elem_mask)); - u[j] = static_cast(t - static_cast(static_cast(mp_elem_mask) * static_cast(carry))); - } - - return static_cast(carry); -} - -template -boost::uint32_t cpp_float::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) -{ - boost::uint64_t prev = static_cast(0u); - - for(boost::int32_t j = static_cast(0); j < p; j++) - { - const boost::uint64_t t = static_cast(u[j] + static_cast(prev * static_cast(mp_elem_mask))); - u[j] = static_cast(t / n); - prev = static_cast(t - static_cast(n * static_cast(u[j]))); - } - - return static_cast(prev); -} - -template -cpp_float cpp_float::pow2(const boost::int64_t p) -{ - // Create a static const table of p^2 for -128 < p < +128. - // Note: The size of this table must be odd-numbered and - // symmetric about 0. - init.do_nothing(); - static const boost::array, 255u> p2_data = - {{ - cpp_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"), - cpp_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"), - cpp_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"), - cpp_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"), - cpp_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"), - cpp_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"), - cpp_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"), - cpp_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"), - cpp_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"), - cpp_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"), - 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cpp_float("8.507059173023461586584365185794205286400000000000000000000000000000000000000000000000000000000000000e37"), - cpp_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38") - }}; - - if((p > static_cast(-128)) && (p < static_cast(+128))) - { - return p2_data[static_cast(p + ((p2_data.size() - 1u) / 2u))]; - } - - // Compute and return 2^p. - if(p < static_cast(0)) - { - return pow2(static_cast(-p)).calculate_inv(); - } - else if(p < static_cast(std::numeric_limits::digits)) - { - const boost::uint64_t p2 = static_cast(static_cast(1uLL) << p); - return cpp_float(p2); - } - else - { - cpp_float t; - default_ops::detail::pow_imp(t, two(), p, mpl::true_()); - return t; - } -} - - -template -inline void add(cpp_float& result, const cpp_float& o) -{ - result += o; -} -template -inline void subtract(cpp_float& result, const cpp_float& o) -{ - result -= o; -} -template -inline void multiply(cpp_float& result, const cpp_float& o) -{ - result *= o; -} -template -inline void divide(cpp_float& result, const cpp_float& o) -{ - result /= o; -} - -template -inline void add(cpp_float& result, const unsigned long long& o) -{ - result.add_unsigned_long_long(o); -} -template -inline void subtract(cpp_float& result, const unsigned long long& o) -{ - result.sub_unsigned_long_long(o); -} -template -inline void multiply(cpp_float& result, const unsigned long long& o) -{ - result.mul_unsigned_long_long(o); -} -template -inline void divide(cpp_float& result, const unsigned long long& o) -{ - result.div_unsigned_long_long(o); -} - -template -inline void add(cpp_float& result, long long o) -{ - if(o < 0) - result.sub_unsigned_long_long(-o); - else - result.add_unsigned_long_long(o); -} -template -inline void subtract(cpp_float& result, long long o) -{ - if(o < 0) - result.add_unsigned_long_long(-o); - else - result.sub_unsigned_long_long(o); -} -template -inline void multiply(cpp_float& result, long long o) -{ - if(o < 0) - { - result.mul_unsigned_long_long(-o); - result.negate(); - } - else - result.mul_unsigned_long_long(o); -} -template -inline void divide(cpp_float& result, long long o) -{ - if(o < 0) - { - result.div_unsigned_long_long(-o); - result.negate(); - } - else - result.div_unsigned_long_long(o); -} - -template -inline void convert_to(unsigned long long* result, const cpp_float& val) -{ - *result = val.extract_unsigned_long_long(); -} -template -inline void convert_to(long long* result, const cpp_float& val) -{ - *result = val.extract_signed_long_long(); -} -template -inline void convert_to(long double* result, cpp_float& val) -{ - *result = val.extract_long_double(); -} - -// -// Non member function support: -// -template -inline int eval_fpclassify(const cpp_float& x) -{ - if(x.isinf()) - return FP_INFINITE; - if(x.isnan()) - return FP_NAN; - if(x.iszero()) - return FP_ZERO; - return FP_NORMAL; -} - -template -inline void eval_abs(cpp_float& result, const cpp_float& x) -{ - result = x; - if(x.isneg()) - result.negate(); -} - -template -inline void eval_fabs(cpp_float& result, const cpp_float& x) -{ - result = x; - if(x.isneg()) - result.negate(); -} - -template -inline void eval_sqrt(cpp_float& result, const cpp_float& x) -{ - result = x; - result.calculate_sqrt(); -} - -template -inline void eval_floor(cpp_float& result, const cpp_float& x) -{ - result = x; - if(!x.isfinite() || x.isint()) - { - return; - } - - if(x.isneg()) - result -= cpp_float::one(); - result = result.extract_integer_part(); -} - -template -inline void eval_ceil(cpp_float& result, const cpp_float& x) -{ - result = x; - if(!x.isfinite() || x.isint()) - { - return; - } - - if(!x.isneg()) - result += cpp_float::one(); - result = result.extract_integer_part(); -} - -template -inline void eval_trunc(cpp_float& result, const cpp_float& x) -{ - if(!x.isfinite()) - { - result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number >(x), 0, boost::math::policies::policy<>()).backend(); - return; - } - else if(x.isint()) - { - result = x; - return; - } - result = x.extract_integer_part(); -} - -template -inline void eval_ldexp(cpp_float& result, const cpp_float& x, long long e) -{ - result = x; - result *= cpp_float::pow2(e); -} - -template -inline void eval_frexp(cpp_float& result, const cpp_float& x, long long* e) -{ - result = x; - if(result.isneg()) - result.negate(); - - long long t = result.order(); - - if(std::abs(t) > (std::numeric_limits::max)() / 3) - throw std::runtime_error("Exponent is too large to be represented as a power of 2."); - t *= 3; - - result *= cpp_float::pow2(-t); - - while(result.compare(cpp_float::one()) >= 0) - { - result /= cpp_float::two(); - ++t; - } - while(result.compare(cpp_float::half()) < 0) - { - result *= cpp_float::two(); - --t; - } - *e = t; - if(x.isneg()) - result.negate(); -} - -template -inline void eval_frexp(cpp_float& result, const cpp_float& x, int* e) -{ - long long t; - eval_frexp(result, x, &t); - if(t > (std::numeric_limits::max)()) - throw std::runtime_error("Exponent is outside the range of an int"); - *e = static_cast(t); -} - -typedef mp_number > cpp_float_50; -typedef mp_number > cpp_float_100; - -}} - -namespace std -{ - template - class numeric_limits > > - { - public: - static const bool is_specialized = true; - static const bool is_signed = true; - static const bool is_integer = false; - static const bool is_exact = false; - static const bool is_bounded = true; - static const bool is_modulo = false; - static const bool is_iec559 = false; - static const int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); - static const int digits10 = boost::multiprecision::cpp_float::cpp_float_digits10; - static const int max_digits10 = boost::multiprecision::cpp_float::cpp_float_max_digits10; - static const boost::int64_t min_exponent = boost::multiprecision::cpp_float::cpp_float_min_exp; // Type differs from int. - static const boost::int64_t min_exponent10 = boost::multiprecision::cpp_float::cpp_float_min_exp10; // Type differs from int. - static const boost::int64_t max_exponent = boost::multiprecision::cpp_float::cpp_float_max_exp; // Type differs from int. - static const boost::int64_t max_exponent10 = boost::multiprecision::cpp_float::cpp_float_max_exp10; // Type differs from int. - static const int radix = boost::multiprecision::cpp_float::mp_radix; - static const std::float_round_style round_style = std::round_to_nearest; - static const bool has_infinity = true; - static const bool has_quiet_NaN = true; - static const bool has_signaling_NaN = false; - static const std::float_denorm_style has_denorm = std::denorm_absent; - static const bool has_denorm_loss = false; - static const bool traps = false; - static const bool tinyness_before = false; - - static const boost::multiprecision::mp_number > (min) (void) throw() { return (boost::multiprecision::cpp_float::min)(); } - static const boost::multiprecision::mp_number > (max) (void) throw() { return (boost::multiprecision::cpp_float::max)(); } - static const boost::multiprecision::mp_number > lowest (void) throw() { return boost::multiprecision::cpp_float::zero(); } - static const boost::multiprecision::mp_number > epsilon (void) throw() { return boost::multiprecision::cpp_float::eps(); } - static const boost::multiprecision::mp_number > round_error (void) throw() { return 0.5L; } - static const boost::multiprecision::mp_number > infinity (void) throw() { return boost::multiprecision::cpp_float::inf(); } - static const boost::multiprecision::mp_number > quiet_NaN (void) throw() { return boost::multiprecision::cpp_float::nan(); } - static const boost::multiprecision::mp_number > signaling_NaN(void) throw() { return boost::multiprecision::cpp_float::zero(); } - static const boost::multiprecision::mp_number > denorm_min (void) throw() { return boost::multiprecision::cpp_float::zero(); } - }; -} - -namespace boost{ namespace math{ - -namespace policies{ - -template -struct precision< boost::multiprecision::mp_number >, Policy> -{ - typedef typename Policy::precision_type precision_type; - typedef digits2<((Digits10 + 1) * 1000L) / 301L> digits_2; - typedef typename mpl::if_c< - ((digits_2::value <= precision_type::value) - || (Policy::precision_type::value <= 0)), - // Default case, full precision for RealType: - digits_2, - // User customised precision: - precision_type - >::type type; -}; - -} // namespace policies - -}} // namespaces boost::math - - -#endif - From 40d1b2f1dd90e0ff52ca27f98ce603badc3efd0c Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 13 Nov 2011 17:36:39 +0000 Subject: [PATCH 060/256] Add sqrt tests. Fix remaining cpp_float failures. [SVN r75478] --- include/boost/multiprecision/cpp_float.hpp | 12 +- .../multiprecision/detail/functions/trig.hpp | 13 ++ test/Jamfile.v2 | 3 +- test/test_asin.cpp | 2 - test/test_log.cpp | 2 - test/test_sin.cpp | 3 - test/test_sqrt.cpp | 190 ++++++++++++++++++ 7 files changed, 213 insertions(+), 12 deletions(-) create mode 100644 test/test_sqrt.cpp diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 13c41251..17bf1c90 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -850,9 +850,13 @@ cpp_float& cpp_float::operator/=(const cpp_float& if(u_and_v_are_finite_and_identical) { - *this = one(); if(neg != v.neg) + { + *this = one(); negate(); + } + else + *this = one(); return *this; } else @@ -1108,7 +1112,7 @@ cpp_float& cpp_float::calculate_inv() static const boost::int32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; - for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= static_cast(2)) + for(boost::uint32_t digits = double_digits10_minus_one; digits <= cpp_float_max_digits10; digits *= static_cast(2)) { // Adjust precision of the terms. precision(static_cast(digits * static_cast(2))); @@ -1181,9 +1185,9 @@ cpp_float& cpp_float::calculate_sqrt(void) // http://www.jjj.de/pibook/pibook.html // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846 - static const boost::uint32_t double_digits10_minus_one = static_cast(static_cast(Digits10) - static_cast(1)); + static const boost::uint32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; - for(boost::uint32_t digits = double_digits10_minus_one; digits <= Digits10; digits *= 2u) + for(boost::uint32_t digits = double_digits10_minus_one; digits <= cpp_float_max_digits10; digits *= 2u) { // Adjust precision of the terms. precision(digits * 2); diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index 7aca7e53..cf2b8dd2 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -653,6 +653,19 @@ void eval_atan(T& result, const T& x) template void eval_atan2(T& result, const T& y, const T& x) { + if(&result == &y) + { + T temp(y); + eval_atan2(result, temp, x); + return; + } + else if(&result == &x) + { + T temp(x); + eval_atan2(result, y, temp); + return; + } + typedef typename boost::multiprecision::detail::canonical::type si_type; typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 75fdb952..83de9b40 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -489,7 +489,7 @@ run ../example/mpfr_snips.cpp mpfr : # requirements [ check-target-builds ../config//has_mpfr : : no ] ; -run ../example/cpp_float_snips.cpp ; +run ../example/mp_float_snips.cpp ; run test_round.cpp : # command line @@ -553,3 +553,4 @@ run test_fpclassify.cpp [ check-target-builds ../config//has_mpfr : : no ] : test_fpclassify_cpp_float ; + diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 2813f036..834e6bf1 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -69,8 +69,6 @@ void test() err = e.template convert_to(); if(err > max_err) { - std::cout << val << std::endl; - std::cout << -exact_data[k][0] << std::endl; max_err = err; } } diff --git a/test/test_log.cpp b/test/test_log.cpp index 49c6d275..ff7b8b5a 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -168,8 +168,6 @@ void test() if(err > max_err) { max_err = err; - std::cout << val << std::endl; - std::cout << T(-data[k]) << std::endl; } val = boost::multiprecision::log10(tenth + pi * (100 * k) * (100 * k)); diff --git a/test/test_sin.cpp b/test/test_sin.cpp index e5ecbeb6..d320ac1d 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -232,9 +232,6 @@ T("8.650871796830672527081873591655777773059986288175183143531618768919892399328 unsigned err = e.template convert_to(); if(err > max_err) { - std::cout << val << std::endl; - std::cout << small_data[k] << std::endl; - std::cout << e << std::endl; max_err = err; } val = sin(-(euler_gamma + k) / 53); diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp new file mode 100644 index 00000000..f3cfad43 --- /dev/null +++ b/test/test_sqrt.cpp @@ -0,0 +1,190 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include +#include +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_CPP_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include +#endif +#if defined(TEST_MPFR_50) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_CPP_FLOAT +#include +#endif + +template +void test() +{ + static const boost::array data = + {{ + T("0"), + T("1.7724538509055160272981674833411451827975494561223871282138077898529112845910321813749506567385446654162268236242825706662361528657244226025250937096027870684620376986531051228499251730289508262289320953792679628001746390153514797205167001901852340185854469744949126403139217755259062164054193325009063984076137334774751534336679897893658518364087954511651617387600590673934317913328098548462481849021"), + T("2.506628274631000502415765284811045253006986740609938316629923576342293654607841974946595838378057266116009972665203879644866323618126736180957855655966147931913435480458123731137327804313019938802647150234465504898425802329413862779668683613033675823844181156078490095600041375150275291651461225843861864920699060926664091188015739697252377702538748247848633488642597506589513095738763427251926880402"), + T("3.0699801238394654654386548746677945821221293132529234536092078633942877416889511494096190816646754176075937074244926190270345429405099416216417975877667492169521054332143197658279274969526803993603118331066475990710709664118358901594985707262626428113026982211562266383695623138538180531502756293265592878111781185072888638355377253555018107077854544789544383440520575813285321747411416665951698336554"), + 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T("17.724538509055160272981674833411451827975494561223871282138077898529112845910321813749506567385446654162268236242825706662361528657244226025250937096027870684620376986531051228499251730289508262289320953792679628001746390153514797205167001901852340185854469744949126403139217755259062164054193325009063984076137334774751534336679897893658518364087954511651617387600590673934317913328098548462481849021"), + }}; + + T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"; + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = sqrt(pi * k); + T e = relative_error(val, data[k]); + unsigned err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF_50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_CPP_FLOAT + test(); + test(); +#endif + return boost::report_errors(); +} + + + From b85306e0761c3b7ec57548046e8808be9bf6e0b7 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 14 Nov 2011 12:19:17 +0000 Subject: [PATCH 061/256] Fix remaining cpp_float bugs. Fix use of expression templates in conditional expressions. [SVN r75485] --- include/boost/multiprecision/cpp_float.hpp | 14 +++++- .../multiprecision/detail/mp_number_base.hpp | 44 ++++++++++++------- test/test_round.cpp | 2 +- 3 files changed, 43 insertions(+), 17 deletions(-) diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 17bf1c90..19e704c4 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -1112,7 +1112,7 @@ cpp_float& cpp_float::calculate_inv() static const boost::int32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; - for(boost::uint32_t digits = double_digits10_minus_one; digits <= cpp_float_max_digits10; digits *= static_cast(2)) + for(boost::int32_t digits = double_digits10_minus_one; digits <= cpp_float_max_digits10; digits *= static_cast(2)) { // Adjust precision of the terms. precision(static_cast(digits * static_cast(2))); @@ -2655,6 +2655,18 @@ inline void eval_frexp(cpp_float& result, const cpp_float& x *e = static_cast(t); } +template +inline bool is_zero(const cpp_float& val) +{ + return val.iszero(); +} +template +inline int get_sign(const cpp_float& val) +{ + return val.iszero() ? 0 : val.isneg() ? -1 : 1; +} + + typedef mp_number > cpp_float_50; typedef mp_number > cpp_float_100; diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 847ae9b3..e85328b1 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -218,7 +218,7 @@ struct mp_exp typedef typename left_type::result_type result_type; typedef tag tag_type; - mp_exp(const Arg1& a) : arg(a) {} + explicit mp_exp(const Arg1& a) : arg(a) {} left_type left()const { return left_type(arg); } @@ -504,7 +504,8 @@ template inline detail::mp_exp, typename detail::mp_exp::left_type > > operator - (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref()); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); } template inline detail::mp_exp, mp_number > @@ -516,7 +517,8 @@ template inline detail::mp_exp, mp_number > > operator - (const detail::mp_exp >& a, const mp_number& b) { - return detail::mp_exp, mp_number >(b, a.left_ref()); + return detail::mp_exp, mp_number > >( + detail::mp_exp, mp_number >(b, a.left_ref())); } template inline typename enable_if, detail::mp_exp, V > > >::type @@ -588,37 +590,43 @@ template inline detail::mp_exp, typename detail::mp_exp::left_type > > operator * (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, typename detail::mp_exp::left_type > (a, b.left_ref()); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type > (a, b.left_ref())); } template inline detail::mp_exp, typename detail::mp_exp::left_type > > operator * (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref()); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); } template inline detail::mp_exp, mp_number > > operator * (const mp_number& a, const detail::mp_exp >& b) { - return detail::mp_exp, mp_number >(a, b.left_ref()); + return detail::mp_exp, mp_number > >( + detail::mp_exp, mp_number >(a, b.left_ref())); } template inline detail::mp_exp, mp_number > > operator * (const detail::mp_exp >& a, const mp_number& b) { - return detail::mp_exp, mp_number >(b, a.left_ref()); + return detail::mp_exp, mp_number > >( + detail::mp_exp, mp_number >(b, a.left_ref())); } template inline typename enable_if, detail::mp_exp, V > > >::type operator * (const detail::mp_exp >& a, const V& b) { - return detail::mp_exp, V >(a.left_ref(), b); + return detail::mp_exp, V > > ( + detail::mp_exp, V >(a.left_ref(), b)); } template inline typename enable_if, detail::mp_exp, V > > >::type operator * (const V& a, const detail::mp_exp >& b) { - return detail::mp_exp, V >(b.left_ref(), a); + return detail::mp_exp, V > >( + detail::mp_exp, V >(b.left_ref(), a)); } // // Division: @@ -678,37 +686,43 @@ template inline detail::mp_exp, typename detail::mp_exp::left_type > > operator / (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref())); } template inline detail::mp_exp::left_type, mp_number > > operator / (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp::left_type, mp_number >(a.left_ref(), b); + return detail::mp_exp::left_type, mp_number > >( + detail::mp_exp::left_type, mp_number >(a.left_ref(), b)); } template inline detail::mp_exp, mp_number > > operator / (const mp_number& a, const detail::mp_exp >& b) { - return detail::mp_exp, mp_number >(a, b.left_ref()); + return detail::mp_exp, mp_number > >( + detail::mp_exp, mp_number >(a, b.left_ref())); } template inline detail::mp_exp, mp_number > > operator / (const detail::mp_exp >& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a.left_ref(), b); + return detail::mp_exp, mp_number > >( + detail::mp_exp, mp_number >(a.left_ref(), b)); } template inline typename enable_if, detail::mp_exp, V > > >::type operator / (const detail::mp_exp >& a, const V& b) { - return detail::mp_exp, V>(a.left_ref(), b); + return detail::mp_exp, V > >( + detail::mp_exp, V>(a.left_ref(), b)); } template inline typename enable_if, detail::mp_exp > > >::type operator / (const V& a, const detail::mp_exp >& b) { - return detail::mp_exp >(a, b.left_ref()); + return detail::mp_exp > >( + detail::mp_exp >(a, b.left_ref())); } // // Modulus: diff --git a/test/test_round.cpp b/test/test_round.cpp index 5d0e2923..6e56437f 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -65,7 +65,7 @@ T get_random() shift += std::numeric_limits::digits; bits -= std::numeric_limits::digits; } - return rng() & 1u ? -ldexp(frexp(result, &bits), exponent) : ldexp(frexp(result, &bits), exponent); + return rng() & 1u ? T(-ldexp(frexp(result, &bits), exponent)) : T(ldexp(frexp(result, &bits), exponent)); } template From f5eb2f330bace5e2f716eda3659d700f8971c781 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 14 Nov 2011 12:41:15 +0000 Subject: [PATCH 062/256] Update docs, rename remaining occurrences of mp_float. [SVN r75487] --- doc/html/boost_multiprecision/intro.html | 476 ++++ doc/html/boost_multiprecision/ref.html | 40 + .../boost_multiprecision/ref/backendconc.html | 2024 +++++++++++++++++ .../boost_multiprecision/ref/mp_number.html | 411 ++++ doc/html/boost_multiprecision/tut.html | 45 + doc/html/boost_multiprecision/tut/ints.html | 177 ++ .../boost_multiprecision/tut/rational.html | 188 ++ doc/html/boost_multiprecision/tut/reals.html | 420 ++++ doc/html/index.html | 54 + doc/multiprecision.qbk | 24 +- ...mp_float_snips.cpp => cpp_float_snips.cpp} | 0 11 files changed, 3847 insertions(+), 12 deletions(-) create mode 100644 doc/html/boost_multiprecision/intro.html create mode 100644 doc/html/boost_multiprecision/ref.html create mode 100644 doc/html/boost_multiprecision/ref/backendconc.html create mode 100644 doc/html/boost_multiprecision/ref/mp_number.html create mode 100644 doc/html/boost_multiprecision/tut.html create mode 100644 doc/html/boost_multiprecision/tut/ints.html create mode 100644 doc/html/boost_multiprecision/tut/rational.html create mode 100644 doc/html/boost_multiprecision/tut/reals.html create mode 100644 doc/html/index.html rename example/{mp_float_snips.cpp => cpp_float_snips.cpp} (100%) diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html new file mode 100644 index 00000000..6a2d9aaf --- /dev/null +++ b/doc/html/boost_multiprecision/intro.html @@ -0,0 +1,476 @@ + + + +Introduction + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+

+ The Multiprecision library comes in two distinct parts: an expression-template-enabled + front end mp_number that handles + all the operator overloading, expression evaluation optimization, and code + reduction, and a selection of backends that implement the actual arithmetic + operations, and need conform only to the reduced interface requirements of + the front end. +

+

+ The library is often used by using one of the predfined typedefs: for example + if you wanted an arbitrary precision integer type using GMP as the underlying + implementation then you could use: +

+
#include <boost/multiprecision/gmp.hpp>  // Defines the wrappers around the GMP library's types
+
+boost::multiprecision::mpz_int myint;    // Arbitrary precision integer type.
+
+

+ Alternatively one can compose your own multiprecision type, by combining mp_number with one of the predefined backend + types. For example, suppose you wanted a 300 decimal digit floating point type + based on the MPFR library, in this case there's no predefined typedef with + that level of precision, so instead we compose our own: +

+
#include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
+
+namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
+
+typedef mp::mp_number<mp::mpfr_float_backend<300> >  my_float;
+
+my_float a, b, c; // These variables have 300 decimal digits precision
+
+
+ + Expression + Templates +
+

+ Class mp_number is expression-template-enabled: + that means that rather than having a multiplication operator that looks like + this: +

+
template <class Backend>
+mp_number<Backend> operator * (const mp_number<Backend>& a, const mp_number<Backend>& b)
+{
+   mp_number<Backend> result(a);
+   result *= b;
+   return result;
+}
+
+

+ Instead the operator looks more like this: +

+
template <class Backend>
+unmentionable-type operator * (const mp_number<Backend>& a, const mp_number<Backend>& b);
+
+

+ Where the "unmentionable" return type is an implementation detail + that, rather than containing the result of the multiplication, contains instructions + on how to compute the result. In effect it's just a pair of references to the + arguments of the function, plus some compile-time information that stores what + the operation is. +

+

+ The great advantage of this method is the elimination of temporaries: + for example the "naive" implementation of operator* above, requires one temporary for computing + the result, and at least another one to return it. It's true that sometimes + this overhead can be reduced by using move-semantics, but it can't be eliminated + completely. For example, lets suppose we're evaluating a polynomial via Horners + method, something like this: +

+
T a[7] = { /* some values */ };
+//....
+y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0];
+
+

+ If type T is an mp_number, then this expression is evaluated + without creating a single temporary value, in contrast + if we were using the C++ wrapper that ships with GMP - mpf_class + - then this expression would result in no less than 11 temporaries (this is + true even though mpf_class does use expression templates to reduce the number + of temporaries somewhat). Had we used an even simpler wrapper around GMP or + MPFR like mpclass things would + have been even worse and no less that 24 temporaries are created for this simple + expression (note - we actually measure the number of memory allocations performed + rather than the number of temporaries directly). +

+

+ This library also extends expression template support to standard library functions + like abs or sin + with mp_number arguments. This + means that an expression such as: +

+
y = abs(x);
+
+

+ can be evaluated without a single temporary being calculated. Even expressions + like: +

+
y = sin(x);
+
+

+ get this treatment, so that variable 'y' is used as "working storage" + within the implementation of sin, + thus reducing the number of temporaries used by one. Of course, should you + write: +

+
x = sin(x);
+
+

+ Then we clearly can't use x + as working storage during the calculation, so then a temporary variable is + created in this case. +

+

+ Given the comments above, you might be forgiven for thinking that expression-templates + are some kind of universal-panacea: sadly though, all tricks like this have + their downsides. For one thing, expression template libraries like this one, + tend to be slower to compile than their simpler cousins, they're also harder + to debug (should you actually want to step through our code!), and rely on + compiler optimizations being turned on to give really good performance. Also + since the return type from expressions involving mp_number's + is an "unmentionable implementation detail", you have to be careful + to cast the result of an expression to the actual number type when passing + an expression to a template function. For example given: +

+
template <class T>
+void my_proc(const T&);
+
+

+ Then calling: +

+
my_proc(a+b);
+
+

+ Will very likely result in obscure error messages inside the body of my_proc - since we've passed it an expression + template type, and not a number type. Instead we probably need: +

+
my_proc(my_mp_number_type(a+b));
+
+

+ Having said that, these situations don't occur that often - or indeed not at + all for non-template functions. In addition all the functions in the Boost.Math + library will automatically convert expression-template arguments to the underlying + number type without you having to do anything, so: +

+
mpfr_float_100 a(20), delta(0.125);
+boost::math::gamma_p(a, a + delta);
+
+

+ Will work just fine, with the a + delta expression + template argument getting converted to an mpfr_float_100 + internally by the Boost.Math library. +

+

+ One other potential pitfall that's only possible in C++11: you should never + store an expression template using: +

+
auto my_expression = a + b - c;
+
+

+ Unless you're absolutely sure that the lifetimes of a, + b and c + will outlive that of my_expression. +

+

+ And finally.... the performance improvements from an expression template library + like this are often not as dramatic as the reduction in number of temporaries + would suggest. For example if we compare this library with mpfr_class + and mpreal, with all three + using the underlying MPFR library at 50 decimal digits precision then we see + the following typical results for polynomial execution: +

+
+

Table 1.1. Evaluation of Order 6 Polynomial.

+
+++++ + + + + + + + + + + + + + + + + + + + + + + +
+

+ Library +

+ 		+

+ Relative Time +

+ 		+

+ Relative number of memory allocations +

+
+

+ mp_number +

+ 		+

+ 1.0 (0.00793s) +

+ 		+

+ 1.0 (2996 total) +

+
+

+ mpfr_class +

+ 		+

+ 1.2 (0.00931s) +

+ 		+

+ 4.3 (12976 total) +

+
+

+ mpreal +

+ 		+

+ 1.9 (0.0148s) +

+ 		+

+ 9.3 (27947 total) +

+
+
+

+ As you can see the execution time increases a lot more slowly than the number + of memory allocations. There are a number of reasons for this: +

+
    +
  • + The cost of extended-precision multiplication and division is so great, + that the times taken for these tend to swamp everything else. +
    • +
  • + The cost of an in-place multiplication (using operator*=) tends to be more than an out-of-place + operator* + (typically operator *= + has to create a temporary workspace to carry out the multiplication, where + as operator* + can use the target variable as workspace). Since the expression templates + carry out their magic by converting out-of-place operators to in-place + ones, we necessarily take this hit. Even so the transformation is more + efficient than creating the extra temporary variable, just not by as much + as one would hope. +
    • +
+

+ We'll conclude this section by providing some more performance comparisons + between these three libraries, again, all are using MPFR to carry out the underlying + arithmetic, and all are operating at the same precision (50 decimal places): +

+
+

Table 1.2. Evaluation of Boost.Math's Bessel function test data

+
+++++ + + + + + + + + + + + + + + + + + + + + + + +
+

+ Library +

+ 		+

+ Relative Time +

+ 		+

+ Relative Number of Memory Allocations +

+
+

+ mp_number +

+ 		+

+ 1.0 (6.21s) +

+ 		+

+ 1.0 (2685469) +

+
+

+ mpfr_class +

+ 		+

+ 1.04 (6.45s) +

+ 		+

+ 1.47 (3946007) +

+
+

+ mpreal +

+ 		+

+ 1.53 (9.52s) +

+ 		+

+ 4.92 (13222940) +

+
+
+
+

Table 1.3. Evaluation of Boost.Math's Non-Central T distribution test data

+
+++++ + + + + + + + + + + + + + + + + + + + + + + +
+

+ Library +

+ 		+

+ Relative Time +

+ 		+

+ Relative Number of Memory Allocations +

+
+

+ mp_number +

+ 		+

+ 1.0 (269s) +

+ 		+

+ 1.0 (139082551) +

+
+

+ mpfr_class +

+ 		+

+ 1.04 (278s) +

+ 		+

+ 1.81 (252400791) +

+
+

+ mpreal +

+ 		+

+ 1.49 (401s) +

+ 		+

+ 3.22 (447009280) +

+
+
+
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html new file mode 100644 index 00000000..5bff5c01 --- /dev/null +++ b/doc/html/boost_multiprecision/ref.html @@ -0,0 +1,40 @@ + + + +Reference + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+
+
mp_number
+
Backend Requirements
+
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html new file mode 100644 index 00000000..a15e98a4 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -0,0 +1,2024 @@ + + + +Backend Requirements + + + + + + + +
+
+
+PrevUpHome +
+
+
+

+ The requirements on the Backend + template argument to mp_number + are split up into compulsary requirements, and optional requirements that + are either to improve performance or provide optional features. +

+

+ In the following tables, type B is the Backend + template arument to mp_number, + b is a variable of B, cb and cb2 + are constant variables of type B, a + is a variable of Arithmetic type, s + is a variable of type const char*, ui is a variable of type unsigned, bb + is a variable of type bool, + pa is a variable of type + pointer-to-arithmetc-type, exp + is a variable of type B::exp_type, pexp + is a variable of type B::exp_type*. +

+
+

Table 1.4. Compulsary Requirements on the Backend type.

+
+++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+

+ Expression +

+ 		+

+ Return Type +

+ 		+

+ Comments +

+
+

+ B::signed_types +

+ 		+

+ mpl::list<type-list> +

+ 		+

+ A list of signed integral types that can be assigned to type B. + The types shall be listed in order of size, smallest first, and + shall terminate in the type that is std::intmax_t. +

+
+

+ B::unsigned_types +

+ 		+

+ mpl::list<type-list> +

+ 		+

+ A list of unsigned integral types that can be assigned to type + B. The types shall be listed in order of size, smallest first, + and shall terminate in the type that is std::uintmax_t. +

+
+

+ B::real_types +

+ 		+

+ mpl::list<type-list> +

+ 		+

+ A list of floating point types that can be assigned to type B.The + types shall be listed in order of size, smallest first, and shall + terminate in type long double. +

+
+

+ B::exponent_type +

+ 		+

+ A signed integral type. +

+ 		+

+ The type of the exponent of type B. +

+
+

+ B() +

+ 		+ +

+ Default constructor. +

+
+

+ B(cb) +

+ 		+ +

+ Copy Constructor. +

+
+

+ b = + b +

+ 		+

+ B& +

+ 		+

+ Assignment operator. +

+
+

+ b = + a +

+ 		+

+ B& +

+ 		+

+ Assignment from an Arithmetic type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ b = + s +

+ 		+

+ B& +

+ 		+

+ Assignment from a string. +

+
+

+ b.swap(b) +

+ 		+

+ void +

+ 		+

+ Swaps the contents of it's arguments. +

+
+

+ cb.str(ui, + bb) +

+ 		+

+ std::string +

+ 		+

+ Returns the string representation of b + with ui digits + and in scientific format if bb + is true. If ui is zero, then returns as many + digits as are required to reconstruct the original value. +

+
+

+ b.negate() +

+ 		+

+ void +

+ 		+

+ Negates b. +

+
+

+ cb.compare(cb2) +

+ 		+

+ int +

+ 		+

+ Compares cb and + cb2, returns a + value less than zero if cb + < cb2, + a value greater than zero if cb + > cb2 + and zero if cb == cb2. +

+
+

+ cb.compare(a) +

+ 		+

+ int +

+ 		+

+ Compares cb and + a, returns a value + less than zero if cb + < a, + a value greater than zero if cb + > a + and zero if cb == a. + The type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ add(b, + cb) +

+ 		+

+ void +

+ 		+

+ Adds cb to b. +

+
+

+ subtract(b, + cb) +

+ 		+

+ void +

+ 		+

+ Subtracts cb from + b. +

+
+

+ multiply(b, + cb) +

+ 		+

+ void +

+ 		+

+ Multiplies b by + cb. +

+
+

+ divide(b, + cb) +

+ 		+

+ void +

+ 		+

+ Divides b by cb. +

+
+

+ modulus(b, + cb) +

+ 		+

+ void +

+ 		+

+ Computes b %= + cb, only required when + B is an integer + type. +

+
+

+ bitwise_and(b, + cb) +

+ 		+

+ void +

+ 		+

+ Computes b &= + cb, only required when + B is an integer + type. +

+
+

+ bitwise_or(b, + cb) +

+ 		+

+ void +

+ 		+

+ Computes b |= + cb, only required when + B is an integer + type. +

+
+

+ bitwise_xor(b, + cb) +

+ 		+

+ void +

+ 		+

+ Computes b ^= + cb, only required when + B is an integer + type. +

+
+

+ complement(b, + cb) +

+ 		+

+ void +

+ 		+

+ Computes the ones-complement of cb + and stores the result in b, + only required when B + is an integer type. +

+
+

+ left_shift(b, + ui) +

+ 		+

+ void +

+ 		+

+ Computes b <<= + ui, only required when + B is an integer + type. +

+
+

+ right_shift(b, + ui) +

+ 		+

+ void +

+ 		+

+ Computes b >>= + ui, only required when + B is an integer + type. +

+
+

+ convert_to(pa, + cb) +

+ 		+

+ void +

+ 		+

+ Converts cb to + the type of *pa + and store the result in *pa. Type B + shall support conversion to at least types std::intmax_t, + std::uintmax_t and long + long. Conversion to other + arithmetic types can then be synthesised using other operations. + Conversions to other types are entirely optional. +

+
+

+ eval_frexp(b, + cb, + pexp) +

+ 		+

+ void +

+ 		+

+ Stores values in b + and *pexp + such that the value of cb + is b * 2*pexp, only required when B + is a floating point type. +

+
+

+ eval_ldexp(b, + cb, + exp) +

+ 		+

+ void +

+ 		+

+ Stores a value in b + that is cb * 2exp, only required when B + is a floating point type. +

+
+

+ eval_floor(b, + cb) +

+ 		+

+ void +

+ 		+

+ Stores the floor of cb + in b, only required + when B is a floating + point type. +

+
+

+ eval_ceil(b, + cb) +

+ 		+

+ void +

+ 		+

+ Stores the ceiling of cb + in b, only required + when B is a floating + point type. +

+
+

+ eval_sqrt(b, + cb) +

+ 		+

+ void +

+ 		+

+ Stores the square root of cb + in b, only required + when B is a floating + point type. +

+
+
+
+

Table 1.5. Optional Requirements on the Backend Type

+
+++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+

+ Expression +

+ 		+

+ Returns +

+ 		+

+ Comments +

+
+

+ add(b, + a) +

+ 		+

+ void +

+ 		+

+ Adds a to b. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::real_types. +

+
+

+ subtract(b, + a) +

+ 		+

+ void +

+ 		+

+ Subtracts a from + b. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ multiply(b, + a) +

+ 		+

+ void +

+ 		+

+ Multiplies b by + a. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ divide(b, + a) +

+ 		+

+ void +

+ 		+

+ Divides b by a. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::real_types. +

+
+

+ modulus(b, + a) +

+ 		+

+ void +

+ 		+

+ Computes b %= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ bitwise_and(b, + a) +

+ 		+

+ void +

+ 		+

+ Computes b &= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ bitwise_or(b, + a) +

+ 		+

+ void +

+ 		+

+ Computes b |= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ bitwise_xor(b, + a) +

+ 		+

+ void +

+ 		+

+ Computes b ^= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ add(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Add cb to cb2 and stores the result in + b. +

+
+

+ subtract(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Subtracts cb2 from + cb and stores the + result in b. +

+
+

+ multiply(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Multiplies cb by + cb2 and stores + the result in b. +

+
+

+ divide(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Divides cb by + cb2 and stores + the result in b. +

+
+

+ add(b, + cb, + a) +

+ 		+

+ void +

+ 		+

+ Add cb to a and stores the result in b. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::real_types. +

+
+

+ subtract(b, + cb, + a) +

+ 		+

+ void +

+ 		+

+ Subtracts a from + cb and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ multiply(b, + cb, + a) +

+ 		+

+ void +

+ 		+

+ Multiplies cb by + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ divide(b, + cb, + a) +

+ 		+

+ void +

+ 		+

+ Divides cb by + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ modulus(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Computes cb % + cb2 and stores the result + in b, only required + when B is an integer + type. +

+
+

+ bitwise_and(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Computes cb & + cb2 and stores the result + in b, only required + when B is an integer + type. +

+
+

+ bitwise_or(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Computes cb | + cb2 and stores the result + in b, only required + when B is an integer + type. +

+
+

+ bitwise_xor(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Computes cb ^ + cb2 and stores the result + in b, only required + when B is an integer + type. +

+
+

+ add(b, + a, + cb) +

+ 		+

+ void +

+ 		+

+ Add a to cb and stores the result in + b. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ subtract(b, + a, + cb) +

+ 		+

+ void +

+ 		+

+ Subtracts cb from + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ multiply(b, + a, + cb) +

+ 		+

+ void +

+ 		+

+ Multiplies a by + cb and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ divide(b, + a, + cb) +

+ 		+

+ void +

+ 		+

+ Divides a by cb and stores the result in + b. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ modulus(b, + cb, + a) +

+ 		+

+ void +

+ 		+

+ Computes cb % + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ bitwise_and(b, + cb, + a) +

+ 		+

+ void +

+ 		+

+ Computes cb & + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ bitwise_or(b, + cb, + a) +

+ 		+

+ void +

+ 		+

+ Computes cb | + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ bitwise_xor(b, + cb, + a) +

+ 		+

+ void +

+ 		+

+ Computes cb ^ + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ modulus(b, + a, + cb) +

+ 		+

+ void +

+ 		+

+ Computes cb % + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ bitwise_and(b, + a, + cb) +

+ 		+

+ void +

+ 		+

+ Computes cb & + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ bitwise_or(b, + a, + cb) +

+ 		+

+ void +

+ 		+

+ Computes cb | + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ bitwise_xor(b, + a, + cb) +

+ 		+

+ void +

+ 		+

+ Computes a ^ + cb and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::real_types. +

+
+

+ left_shift(b, + cb, + ui) +

+ 		+

+ void +

+ 		+

+ Computes cb << + ui and stores the result + in b, only required + when B is an integer + type. +

+
+

+ right_shift(b, + cb, + ui) +

+ 		+

+ void +

+ 		+

+ Computes cb >> + ui and stores the result + in b, only required + when B is an integer + type. +

+
+

+ increment(b) +

+ 		+

+ void +

+ 		+

+ Increments the value of b + by one. +

+
+

+ decrement(b) +

+ 		+

+ void +

+ 		+

+ Decrements the value of b + by one. +

+
+

+ is_zero(cb) +

+ 		+

+ bool +

+ 		+

+ Returns true if cb is zero, otherwise false +

+
+

+ get_sign(cb) +

+ 		+

+ int +

+ 		+

+ Returns a value < zero if cb + is negative, a value > zero if cb + is positive, and zero if cb + is zero. +

+
+

+ eval_abs(b, + cb) +

+ 		+

+ void +

+ 		+

+ Set b to the absolute + value of cb. +

+
+

+ eval_fabs(b, + cb) +

+ 		+

+ void +

+ 		+

+ Set b to the absolute + value of cb. +

+
+

+ eval_fpclassify(cb) +

+ 		+

+ int +

+ 		+

+ Returns one of the same values returned by std::fpclassify. + Only required when B + is an floating point type. +

+
+

+ eval_trunc(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::trunc + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_round(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::round + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_exp(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::exp + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_log(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::log + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_log10(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::log10 + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_sin(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::sin + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_cos(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::cos + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_tan(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::exp + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_asin(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::asin + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_acos(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::acos + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_atan(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::atan + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_sinh(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::sinh + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_cosh(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::cosh + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_tanh(b, + cb) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::tanh + on argument cb + and stores the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_fmod(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::fmod + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_pow(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::pow + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating point type. +

+
+

+ eval_atan2(b, + cb, + cb2) +

+ 		+

+ void +

+ 		+

+ Performs the equivalent operation to std::atan + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating point type. +

+
+
+
+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHome +
+ + diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html new file mode 100644 index 00000000..613feeaa --- /dev/null +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -0,0 +1,411 @@ + + + +mp_number + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+
+ + Synopsis +
+
namespace boost{ namespace multiprecision{
+
+template <class Backend>
+class mp_number
+{
+   mp_number();
+   mp_number(see-below);
+   mp_number& operator=(see-below);
+
+   /* Other number-type operators here */
+
+   // Use in Boolean context:
+   operator convertible-to-bool-type()const;
+   // swap:
+   void swap(mp_number& other);
+   // Sign:
+   bool is_zero()const;
+   int sign()const;
+   // string conversion:
+   std::string str()const;
+   // Generic conversion mechanism
+   template <class T>
+   T convert_to()const;
+   // precision control:
+   static unsigned default_precision();
+   static void default_precision(unsigned digits10);
+   unsigned precision()const;
+   void precision(unsigned digits10);
+   // Comparison:
+   int compare(const mp_number<Backend>& o)const;
+   template <class V>
+   typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
+   // Access to the underlying implementation:
+   Backend& backend();
+   const Backend& backend()const;
+};
+
+// Swap:
+template <class Backend>
+void swap(mp_number<Backend>& a, mp_number<Backend>& b);
+
+// iostream support:
+template <class Backend>
+std::ostream& operator << (std::ostream& os, const mp_number<Backend>& r);
+std::ostream& operator << (std::ostream& os, const unmentionable-expression-template-type& r);
+template <class Backend>
+std::istream& operator >> (std::istream& is, mp_number<Backend>& r);
+
+// Non-member function standard library support:
+unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
+
+unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
+unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
+unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+
+}} // namespaces
+
+namespace boost{ namespace math{
+
+// Boost.Math interoperability functions:
+int                                              fpclassify     (const mp_number-or-expression-template-type&, int);
+bool                                             isfinite       (const mp_number-or-expression-template-type&, int);
+bool                                             isnan          (const mp_number-or-expression-template-type&, int);
+bool                                             isinf          (const mp_number-or-expression-template-type&, int);
+bool                                             isnormal       (const mp_number-or-expression-template-type&, int);
+
+}} // namespaces
+
+// numeric_limits support:
+namespace std{
+
+template <class Backend>
+struct numeric_limits<boost::multiprecision<Backend> >
+{
+   /* Usual members here */
+};
+
+}
+
+
+ + Description +
+
mp_number();
+mp_number(see-below);
+mp_number& operator=(see-below);
+
+

+ Type mp_number is default + constructible, and both copy constructible and assignable from: +

+
    +
  • + Itself. +
    • +
  • + An expression template which is the result of one of the arithmetic operators. +
    • +
  • + Any builtin arithmetic type. +
    • +
  • + A std::string or any type which is convertible + to const char*. +
    • +
  • + Any type that the Backend is constructible or assignable from. +
    • +
+
/* Other number-type operators here */
+
+

+ The following arithmetic operations are support for real-numbered types: +

+
    +
  • + Binary +, -, *, /, +, -, *, /, + ==, !, <, >, <, >, ||, &&, + ||, &&=. +
    • +
  • + Unary +, -, ++, --, !. +
    • +
+

+ For integer types the following operators are also supported: +

+

+ Binary %, %, |, |, &, &, ^, ^, + <<, <<, >>, >>. +

+

+ Note that with the exception of the logical operators and unary + the result + of applying an operator to mp_number is an "unmentionable" expression + template type. +

+

+ Binary operators, must have at least one argument that is of type mp_number or an expression template derived + from mp_number. One argument + may optionally be of arithmetic type. +

+

+ Note that type mp_number + (and all expression templates derived from it) may be used in a Boolian context. +

+
operator convertible-to-bool-type()const;
+
+

+ Returns an unmentionable-type that is usable in Boolean + contexts (this allows mp_number + to be used in any Boolean context - if statements, conditional statements, + or as an argument to a logical operator - without type mp_number + being convertible to type bool. +

+
void swap(mp_number& other);
+
+

+ Swaps *this + with other. +

+
bool is_zero()const;
+
+

+ Returns true is *this is zero, + otherwise false. +

+
int sign()const;
+
+

+ Returns a value less than zero if *this is negative, a value greater than zero + if *this + is positive, and zero if *this + is zero. +

+
std::string str(unsigned precision, bool scientific = true)const;
+
+

+ Returns the number formatted as a string, with at least precision + digits, and in scientific format if scientific is true. +

+
template <class T>
+T convert_to()const;
+
+

+ Provides a generic conversion mechanism to convert *this to type T. + Type T may be any arithmetic + type. Optionally other types may also be supported by specific Backend types. +

+
static unsigned default_precision();
+static void default_precision(unsigned digits10);
+unsigned precision()const;
+void precision(unsigned digits10);
+
+

+ These functions are only available if the Backend template parameter supports + runtime changes to precision. They get and set the default precision and + the precision of *this + respectively. +

+
int compare(const mp_number<Backend>& o)const;
+template <class V>
+typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
+
+

+ Returns: +

+
    +
  • + A value less that 0 for *this < other +
    • +
  • + A value greater that 0 for *this > other +
    • +
  • + Zero for *this == other +
    • +
+
Backend& backend();
+const Backend& backend()const;
+
+

+ Returns the underlying backend instance used by *this. +

+
+ + swap +
+
template <class Backend>
+void swap(mp_number<Backend>& a, mp_number<Backend>& b);
+
+

+ Swaps a and b. +

+
+ + Iostream + Support +
+
template <class Backend>
+std::ostream& operator << (std::ostream& os, const mp_number<Backend>& r);
+template <class Backend>
+std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r);
+template <class Backend>
+inline std::istream& operator >> (std::istream& is, mp_number<Backend>& r)
+
+

+ These operators provided formatted input-output operations on mp_number types, and expression templates + derived from them. +

+
+ + Non-member + standard library function support +
+
unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
+
+unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
+unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
+unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+
+

+ These functions all behave exactly as their standard library counterparts + do: their argument is either an instance of mp_number + or an expression template derived from it; their return value is always an + expression template. +

+

+ These functions are normally implemented by the Backend type. However, default + versions are provided for Backend types that don't have native support for + these functions. Please note however, that this default support requires + the precision of the type to be a compile time constant - this means for + example that the GMP MPF Backend will not work with these functions when + that type is used at variable precision. +

+

+ Also note that with the exception of abs + that these functions can only be used with floating point Backend types. +

+
+ + Boost.Math + Interoperabilty Support +
+
namespace boost{ namespace math{
+
+int                                              fpclassify     (const mp_number-or-expression-template-type&, int);
+bool                                             isfinite       (const mp_number-or-expression-template-type&, int);
+bool                                             isnan          (const mp_number-or-expression-template-type&, int);
+bool                                             isinf          (const mp_number-or-expression-template-type&, int);
+bool                                             isnormal       (const mp_number-or-expression-template-type&, int);
+
+}} // namespaces
+
+

+ These functions behave exacts as their Boost.Math equivalents. Other Boost.Math + functions and templates may also be specialized or overloaded to ensure interoperability. +

+
+ + std::numeric_limits + support +
+
namespace std{
+
+template <class Backend>
+struct numeric_limits<boost::multiprecision<Backend> >
+{
+   /* Usual members here */
+};
+
+}
+
+

+ Class template std::numeric_limits is specialized for all instantiations + of mp_number whose precision + is known at compile time, plus those types whose precision is unlimited (though + it is much less useful in those cases). It is not specialized for types whose + precision can vary at compile time (such as mpf_float). +

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html new file mode 100644 index 00000000..d6d8a0bb --- /dev/null +++ b/doc/html/boost_multiprecision/tut.html @@ -0,0 +1,45 @@ + + + +Tutorial + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+
+
Integer Types
+
Real Numbers
+
Rational Number Types
+
+

+ In order to use this library you need to make two choices: what kind of number + do I want, and which backend do I want to perform the actual arithmetic? +

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html new file mode 100644 index 00000000..bccd2e4f --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints.html @@ -0,0 +1,177 @@ + + + +Integer Types + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+

+ The following backends provide integer arithmetic: +

+
++++++++ + + + + + + + + + + + + + + + + +
+

+ Backend Type +

+ 		+

+ Header +

+ 		+

+ Radix +

+ 		+

+ Dependencies +

+ 		+

+ Pros +

+ 		+

+ Cons +

+
+

+ gmp_int +

+ 		+

+ boost/multiprecision/gmp.hpp +

+ 		+

+ 2 +

+ 		+

+ GMP +

+ 		+

+ Very fast and efficient backend. +

+ 		+

+ Dependency on GNU licenced GMP library. +

+
+
+ + gmp_int +
+
namespace boost{ namespace multiprecision{
+
+class gmp_int;
+
+typedef mp_number<gmp_int >         mpz_int;
+
+}} // namespaces
+
+

+ The gmp_int backend is used + via the typedef boost::multiprecision::mpz_int. It acts as a thin wrapper around + the GMP mpz_t to provide + an integer type that is a drop-in replacement for the native C++ integer + types, but with unlimited precision. +

+

+ As well as the usual conversions from arithmetic and string types, type + mpz_int is copy constructible + and asignable from: +

+
    +
  • + The GMP native types: mpf_t, + mpz_t, mpq_t. +
    • +
  • + Instances of mp_number<T> that are wrappers around those types: + mp_number<gmp_float<N> >, mp_number<gmp_rational>. +
    • +
+

+ It's also possible to access the underlying mpz_t + via the data() member function of gmp_int. +

+
+ + Example: +
+

+ +

+
#include <boost/multiprecision/gmp.hpp>
+
+using namespace boost::multiprecision;
+
+mpz_int v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 1000!
+
+// Access the underlying representation:
+mpz_t z;
+mpz_init(z);
+mpz_set(z, v.backend().data());
+
+

+

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html new file mode 100644 index 00000000..4f5308d5 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -0,0 +1,188 @@ + + + +Rational Number Types + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+

+ The following backends provide rational number arithmetic: +

+
++++++++ + + + + + + + + + + + + + + + + +
+

+ Backend Type +

+ 		+

+ Header +

+ 		+

+ Radix +

+ 		+

+ Dependencies +

+ 		+

+ Pros +

+ 		+

+ Cons +

+
+

+ gmp_rational +

+ 		+

+ boost/multiprecision/gmp.hpp +

+ 		+

+ 2 +

+ 		+

+ GMP +

+ 		+

+ Very fast and efficient backend. +

+ 		+

+ Dependency on GNU licenced GMP library. +

+
+
+ + gmp_rational +
+
namespace boost{ namespace multiprecision{
+
+class gmp_rational;
+
+typedef mp_number<gmp_rational >         mpq_rational;
+
+}} // namespaces
+
+

+ The gmp_rational backend + is used via the typedef boost::multiprecision::mpq_rational. + It acts as a thin wrapper around the GMP mpq_t + to provide a rational number type that is a drop-in replacement for the native + C++ number types, but with unlimited precision. +

+

+ As well as the usual conversions from arithmetic and string types, instances + of mp_number<gmp_rational> + are copy constructible and assignable from: +

+
    +
  • + The GMP native types: mpz_t, + mpq_t. +
    • +
  • + mp_number<gmp_int>. +
    • +
+

+ There are also non-member functions: +

+
mpz_int numerator(const mpq_rational&);
+mpz_int denominator(const mpq_rational&);
+
+

+ Which return the numerator and denominator of the number. +

+

+ It's also possible to access the underlying mpq_t + via the data() member function of mpq_rational. +

+
+ + Example: +
+

+ +

+
#include <boost/multiprecision/gmp.hpp>
+
+using namespace boost::multiprecision;
+
+mpq_rational v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+v /= 10;
+
+std::cout << v << std::endl; // prints 1000! / 10
+std::cout << numerator(v) << std::endl;
+std::cout << denominator(v) << std::endl;
+
+// Access the underlying data:
+mpq_t q;
+mpq_init(q);
+mpq_set(q, v.backend().data());
+
+

+

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_multiprecision/tut/reals.html b/doc/html/boost_multiprecision/tut/reals.html new file mode 100644 index 00000000..a5df3c35 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/reals.html @@ -0,0 +1,420 @@ + + + +Real Numbers + + + + + + + + +
+
+
+PrevUpHomeNext +
+
+
+

+ The following backends provide real number arithmetic: +

+
++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+

+ Backend Type +

+ 		+

+ Header +

+ 		+

+ Radix +

+ 		+

+ Dependencies +

+ 		+

+ Pros +

+ 		+

+ Cons +

+
+

+ mpf_float<N> +

+ 		+

+ boost/multiprecision/gmp.hpp +

+ 		+

+ 2 +

+ 		+

+ GMP +

+ 		+

+ Very fast and efficient backend. +

+ 		+

+ Dependency on GNU licenced GMP library. +

+
+

+ mpfr_float<N> +

+ 		+

+ boost/multiprecision/mpfr.hpp +

+ 		+

+ 2 +

+ 		+

+ GMP and MPFR +

+ 		+

+ Very fast and efficient backend, with it's own standard library + implementation. +

+ 		+

+ Dependency on GNU licenced GMP and MPFR libraries. +

+
+

+ cpp_float<N> +

+ 		+

+ boost/multiprecision/cpp_float.hpp +

+ 		+

+ 10 +

+ 		+

+ None +

+ 		+

+ Header only, all C++ implementation. +

+ 		+

+ Approximately 2x slower than the MPFR or GMP libraries. +

+
+
+ + gmp_float +
+
namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class gmp_float;
+
+typedef mp_number<gmp_float<50> >    mpf_float_50;
+typedef mp_number<gmp_float<100> >   mpf_float_100;
+typedef mp_number<gmp_float<500> >   mpf_float_500;
+typedef mp_number<gmp_float<1000> >  mpf_float_1000;
+typedef mp_number<gmp_float<0> >     mpf_float;
+
+}} // namespaces
+
+

+ The gmp_float backend is + used in conjunction with mp_number: + It acts as a thin wrapper around the GMP mpf_t + to provide an real-number type that is a drop-in replacement for the native + C++ floating-point types, but with much greater precision. +

+

+ Type gmp_float can be used + at fixed precision by specifying a non-zero Digits10 + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpf_float provides a variable precision type whose + precision can be controlled via the mp_number's + member functions. +

+
+ + + + + +
[Note]Note

+ This type only provides standard library and numeric_limits + support when the precision is fixed at compile time. +

+

+ As well as the usual conversions from arithmetic and string types, instances + of mp_number<mpf_float<N> > are copy constructible and assignable + from: +

+
    +
  • + The GMP native types mpf_t, + mpz_t, mpq_t. +
    • +
  • + The mp_number wrappers + around those types: mp_number<mpf_float<M> >, + mp_number<gmp_int>, + mp_number<gmp_rational>. +
    • +
+

+ It's also possible to access the underlying mpf_t + via the data() member function of gmp_float. +

+
+ + GMP example: +
+

+ +

+
#include <boost/multiprecision/gmp.hpp>
+
+using namespace boost::multiprecision;
+
+// Operations at variable precision and limited standard library support:
+mpf_float a = 2;
+mpf_float::default_precision(1000);
+std::cout << mpf_float::default_precision() << std::endl;
+std::cout << sqrt(a) << std::endl; // print root-2
+
+// Operations at fixed precision and full standard library support:
+mpf_float_100 b = 2;
+std::cout << std::numeric_limits<mpf_float_100>::digits << std::endl;
+std::cout << log(b) << std::endl; // print log(2)
+
+// Access the underlying representation:
+mpf_t f;
+mpf_init(f);
+mpf_set(f, a.backend().data());
+
+

+

+
+ + mpfr_float +
+
namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class mpfr_float_backend;
+
+typedef mp_number<mpfr_float_backend<50> >    mpfr_float_50;
+typedef mp_number<mpfr_float_backend<100> >   mpfr_float_100;
+typedef mp_number<mpfr_float_backend<500> >   mpfr_float_500;
+typedef mp_number<mpfr_float_backend<1000> >  mpfr_float_1000;
+typedef mp_number<mpfr_float_backend<0> >     mpfr_float;
+
+}} // namespaces
+
+

+ The mpfr_float_backend type + is used in conjunction with mp_number: + It acts as a thin wrapper around the MPFR mpfr_t + to provide an real-number type that is a drop-in replacement for the native + C++ floating-point types, but with much greater precision. +

+

+ Type mpfr_float_backend can + be used at fixed precision by specifying a non-zero Digits10 + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpfr_float provides a variable precision type whose + precision can be controlled via the mp_number's + member functions. +

+
+ + + + + +
[Note]Note

+ This type only provides numeric_limits + support when the precision is fixed at compile time. +

+

+ As well as the usual conversions from arithmetic and string types, instances + of mp_number<mpfr_float_backend<N> > are copy constructible and assignable + from: +

+
    +
  • + The GMP native types mpf_t, + mpz_t, mpq_t. +
    • +
  • + The MPFR native type mpfr_t. +
    • +
  • + The mp_number wrappers + around those types: mp_number<mpfr_float_backend<M> >, + mp_number<mpf_float<M> >, mp_number<gmp_int>, mp_number<gmp_rational>. +
    • +
+

+ It's also possible to access the underlying mpf_t + via the data() member function of gmp_float. +

+
+ + MPFR example: +
+

+ +

+
#include <boost/multiprecision/mpfr.hpp>
+
+using namespace boost::multiprecision;
+
+// Operations at variable precision and no numeric_limits support:
+mpfr_float a = 2;
+mpfr_float::default_precision(1000);
+std::cout << mpfr_float::default_precision() << std::endl;
+std::cout << sqrt(a) << std::endl; // print root-2
+
+// Operations at fixed precision and full numeric_limits support:
+mpfr_float_100 b = 2;
+std::cout << std::numeric_limits<mpfr_float_100>::digits << std::endl;
+std::cout << log(b) << std::endl; // print log(2)
+
+// Access the underlying data:
+mpfr_t r;
+mpfr_init(r);
+mpfr_set(r, b.backend().data(), GMP_RNDN);
+
+

+

+
+ + cpp_float +
+
namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class cpp_float;
+
+typedef mp_number<cpp_float<50> > cpp_float_50;
+typedef mp_number<cpp_float<100> > cpp_float_100;
+
+}} // namespaces
+
+

+ The cpp_float backend is + used in conjunction with mp_number: + It acts as an entirely C++ (header only and dependency free) real-number + type that is a drop-in replacement for the native C++ floating-point types, + but with much greater precision. +

+

+ Type cpp_float can be used + at fixed precision by specifying a non-zero Digits10 + template parameter. The typedefs cpp_float_50 and cpp_float_100 provide arithmetic + types at 50 and 100 decimal digits precision respectively. +

+

+ There is full standard library and numeric_limits + support available for this type. +

+
+ + cpp_float + example: +
+

+ +

+
#include <boost/multiprecision/cpp_float.hpp>
+
+using namespace boost::multiprecision;
+
+// Operations at fixed precision and full numeric_limits support:
+cpp_float_100 b = 2;
+std::cout << std::numeric_limits<cpp_float_100>::digits << std::endl;
+std::cout << log(b) << std::endl; // print log(2)
+
+

+

+
+ + + +
Copyright © 2011 John Maddock

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/index.html b/doc/html/index.html new file mode 100644 index 00000000..1b43772d --- /dev/null +++ b/doc/html/index.html @@ -0,0 +1,54 @@ + + + +Chapter 1. Boost.Multiprecision + + + + + + +
+
+
Next
+
+
+

+Chapter 1. Boost.Multiprecision

+

+various authors +

+

Copyright © 2011 John Maddock

+
+

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+

Table of Contents

+
+
Introduction
+
Tutorial
+
+
Integer Types
+
Real Numbers
+
Rational Number Types
+
+
Reference
+
+
mp_number
+
Backend Requirements
+
+
+
+
+ + + +

Last revised: July 08, 2011 at 18:51:46 +0100

+
+
Next
+ + diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index fdcd45e6..2e5e7b9e 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -20,7 +20,7 @@ [import ../example/gmp_snips.cpp] [import ../example/mpfr_snips.cpp] -[import ../example/mp_float_snips.cpp] +[import ../example/cpp_float_snips.cpp] [section:intro Introduction] @@ -233,7 +233,7 @@ The following backends provide real number arithmetic: [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] [[`mpf_float`][boost/multiprecision/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] [[`mpfr_float`][boost/multiprecision/mpfr.hpp][2][GMP and MPFR][Very fast and efficient backend, with it's own standard library implementation.][Dependency on GNU licenced GMP and MPFR libraries.]] -[[`mp_float`][boost/multiprecision/mp_float.hpp][10][None][Header only, all C++ implementation.][Approximately 2x slower than the MPFR or GMP libraries.]] +[[`cpp_float`][boost/multiprecision/cpp_float.hpp][10][None][Header only, all C++ implementation.][Approximately 2x slower than the MPFR or GMP libraries.]] ] [h4 gmp_float] @@ -315,31 +315,31 @@ It's also possible to access the underlying `mpf_t` via the data() member functi [mpfr_eg] -[h4 mp_float] +[h4 cpp_float] namespace boost{ namespace multiprecision{ template - class mp_float; + class cpp_float; - typedef mp_number > mp_float_50; - typedef mp_number > mp_float_100; + typedef mp_number > cpp_float_50; + typedef mp_number > cpp_float_100; }} // namespaces -The `mp_float` backend is used in conjunction with `mp_number`: It acts as an entirely C++ (header only and dependency free) +The `cpp_float` backend is used in conjunction with `mp_number`: It acts as an entirely C++ (header only and dependency free) real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. -Type `mp_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter. -The typedefs mp_float_50 and mp_float_100 provide arithmetic types at 50 and 100 decimal digits precision +Type `cpp_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter. +The typedefs cpp_float_50 and cpp_float_100 provide arithmetic types at 50 and 100 decimal digits precision respectively. There is full standard library and `numeric_limits` support available for this type. -[h5 mp_float example:] +[h5 cpp_float example:] -[mp_float_eg] +[cpp_float_eg] [endsect] @@ -548,7 +548,7 @@ Returns `true` is `*this` is zero, otherwise `false`. int sign()const; -Returns a value less than zero if `*this` is negative, a value greater than zero if `*this is positive, and zero +Returns a value less than zero if `*this` is negative, a value greater than zero if `*this` is positive, and zero if `*this` is zero. std::string str(unsigned precision, bool scientific = true)const; diff --git a/example/mp_float_snips.cpp b/example/cpp_float_snips.cpp similarity index 100% rename from example/mp_float_snips.cpp rename to example/cpp_float_snips.cpp From 0c413f735247963d8f8746750c616581402d62a0 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 14 Nov 2011 13:39:10 +0000 Subject: [PATCH 063/256] Change real_types to float_types. [SVN r75489] --- .../boost_multiprecision/ref/backendconc.html | 54 +++++++++---------- doc/html/index.html | 2 +- doc/multiprecision.qbk | 54 +++++++++---------- .../multiprecision/arithmetic_backend.hpp | 2 +- .../concepts/mp_number_architypes.hpp | 2 +- include/boost/multiprecision/cpp_float.hpp | 2 +- .../multiprecision/detail/default_ops.hpp | 2 +- .../detail/functions/constants.hpp | 4 +- .../multiprecision/detail/functions/pow.hpp | 8 +-- .../multiprecision/detail/functions/trig.hpp | 14 ++--- .../multiprecision/detail/mp_number_base.hpp | 2 +- include/boost/multiprecision/gmp.hpp | 6 +-- include/boost/multiprecision/mpfr.hpp | 2 +- test/Jamfile.v2 | 2 +- 14 files changed, 78 insertions(+), 78 deletions(-) diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index a15e98a4..765eb817 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -104,7 +104,7 @@

- B::real_types + B::float_types

@@ -199,7 +199,7 @@

Assignment from an Arithmetic type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -322,7 +322,7 @@ and zero if cb == a. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -724,7 +724,7 @@

Adds a to b. The type of a shall be listed in one of the type lists B::signed_types, B::unsigned_types - or B::real_types. + or B::float_types.

@@ -746,7 +746,7 @@ b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -768,7 +768,7 @@ a. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -788,7 +788,7 @@

Divides b by a. The type of a shall be listed in one of the type lists B::signed_types, B::unsigned_types - or B::real_types. + or B::float_types.

@@ -811,7 +811,7 @@ B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -834,7 +834,7 @@ B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -857,7 +857,7 @@ B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -880,7 +880,7 @@ B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -984,7 +984,7 @@

Add cb to a and stores the result in b. The type of a shall be listed in one of the type lists B::signed_types, B::unsigned_types - or B::real_types. + or B::float_types.

@@ -1008,7 +1008,7 @@ result in b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1032,7 +1032,7 @@ result in b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1056,7 +1056,7 @@ result in b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1171,7 +1171,7 @@ b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1195,7 +1195,7 @@ result in b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1219,7 +1219,7 @@ result in b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1242,7 +1242,7 @@ b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1267,7 +1267,7 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1292,7 +1292,7 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1317,7 +1317,7 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1342,7 +1342,7 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1367,7 +1367,7 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1392,7 +1392,7 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1417,7 +1417,7 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

@@ -1442,7 +1442,7 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::real_types. + B::unsigned_types or B::float_types.

diff --git a/doc/html/index.html b/doc/html/index.html index 1b43772d..2f877f6c 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -20,7 +20,7 @@

Copyright © 2011 John Maddock

-

+

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 2e5e7b9e..1d539382 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -701,14 +701,14 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia listed in order of size, smallest first, and shall terminate in the type that is `std::intmax_t`.]] [[`B::unsigned_types`][`mpl::list`][A list of unsigned integral types that can be assigned to type B. The types shall be listed in order of size, smallest first, and shall terminate in the type that is `std::uintmax_t`.]] -[[`B::real_types`][`mpl::list`][A list of floating point types that can be assigned to type B.The types shall be +[[`B::float_types`][`mpl::list`][A list of floating point types that can be assigned to type B.The types shall be listed in order of size, smallest first, and shall terminate in type `long double`.]] [[`B::exponent_type`][A signed integral type.][The type of the exponent of type B.]] [[`B()`][ ][Default constructor.]] [[`B(cb)`][ ][Copy Constructor.]] [[`b = b`][`B&`][Assignment operator.]] [[`b = a`][`B&`][Assignment from an Arithmetic type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`b = s`][`B&`][Assignment from a string.]] [[`b.swap(b)`][`void`][Swaps the contents of it's arguments.]] [[`cb.str(ui, bb)`][`std::string`][Returns the string representation of `b` with `ui` digits and in scientific format if `bb` is `true`. @@ -718,7 +718,7 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia if `cb == cb2`.]] [[`cb.compare(a)`][`int`][Compares `cb` and `a`, returns a value less than zero if `cb < a`, a value greater than zero if `cb > a` and zero if `cb == a`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`add(b, cb)`][`void`][Adds `cb` to `b`.]] [[`subtract(b, cb)`][`void`][Subtracts `cb` from `b`.]] [[`multiply(b, cb)`][`void`][Multiplies `b` by `cb`.]] @@ -744,61 +744,61 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia [table Optional Requirements on the Backend Type [[Expression][Returns][Comments]] [[`add(b, a)`][`void`][Adds `a` to `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`subtract(b, a)`][`void`][Subtracts `a` from `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`multiply(b, a)`][`void`][Multiplies `b` by `a`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`divide(b, a)`][`void`][Divides `b` by `a`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`modulus(b, a)`][`void`][Computes `b %= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`bitwise_and(b, a)`][`void`][Computes `b &= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`bitwise_or(b, a)`][`void`][Computes `b |= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`bitwise_xor(b, a)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`add(b, cb, cb2)`][`void`][Add `cb` to `cb2` and stores the result in `b`.]] [[`subtract(b, cb, cb2)`][`void`][Subtracts `cb2` from `cb` and stores the result in `b`.]] [[`multiply(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and stores the result in `b`.]] [[`divide(b, cb, cb2)`][`void`][Divides `cb` by `cb2` and stores the result in `b`.]] [[`add(b, cb, a)`][`void`][Add `cb` to `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`subtract(b, cb, a)`][`void`][Subtracts `a` from `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`multiply(b, cb, a)`][`void`][Multiplies `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`divide(b, cb, a)`][`void`][Divides `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`modulus(b, cb, cb2)`][`void`][Computes `cb % cb2` and stores the result in `b`, only required when `B` is an integer type.]] [[`bitwise_and(b, cb, cb2)`][`void`][Computes `cb & cb2` and stores the result in `b`, only required when `B` is an integer type.]] [[`bitwise_or(b, cb, cb2)`][`void`][Computes `cb | cb2` and stores the result in `b`, only required when `B` is an integer type.]] [[`bitwise_xor(b, cb, cb2)`][`void`][Computes `cb ^ cb2` and stores the result in `b`, only required when `B` is an integer type.]] [[`add(b, a, cb)`][`void`][Add `a` to `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`subtract(b, a, cb)`][`void`][Subtracts `cb` from `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`multiply(b, a, cb)`][`void`][Multiplies `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`divide(b, a, cb)`][`void`][Divides `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`modulus(b, cb, a)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`bitwise_and(b, cb, a)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`bitwise_or(b, cb, a)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`bitwise_xor(b, cb, a)`][`void`][Computes `cb ^ a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`modulus(b, a, cb)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`bitwise_and(b, a, cb)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`bitwise_or(b, a, cb)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`bitwise_xor(b, a, cb)`][`void`][Computes `a ^ cb` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::real_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`left_shift(b, cb, ui)`][`void`][Computes `cb << ui` and stores the result in `b`, only required when `B` is an integer type.]] [[`right_shift(b, cb, ui)`][`void`][Computes `cb >> ui` and stores the result in `b`, only required when `B` is an integer type.]] [[`increment(b)`][void][Increments the value of `b` by one.]] diff --git a/include/boost/multiprecision/arithmetic_backend.hpp b/include/boost/multiprecision/arithmetic_backend.hpp index a58a2b6d..25f173ad 100644 --- a/include/boost/multiprecision/arithmetic_backend.hpp +++ b/include/boost/multiprecision/arithmetic_backend.hpp @@ -20,7 +20,7 @@ struct arithmetic_backend { typedef mpl::list signed_types; typedef mpl::list unsigned_types; - typedef mpl::list real_types; + typedef mpl::list float_types; typedef int exponent_type; arithmetic_backend(){} diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index accd293d..a51f93b7 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -27,7 +27,7 @@ struct mp_number_backend_float_architype { typedef mpl::list signed_types; typedef mpl::list unsigned_types; - typedef mpl::list real_types; + typedef mpl::list float_types; typedef int exponent_type; mp_number_backend_float_architype() diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 19e704c4..ab5b5432 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -30,7 +30,7 @@ class cpp_float public: typedef mpl::list signed_types; typedef mpl::list unsigned_types; - typedef mpl::list real_types; + typedef mpl::list float_types; typedef boost::int64_t exponent_type; diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 2e2770fa..917a99e2 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -303,7 +303,7 @@ struct calculate_next_larger_type typename mpl::if_< is_unsigned, typename B::unsigned_types, - typename B::real_types + typename B::float_types >::type >::type list_type; typedef typename has_enough_bits::digits>::template type pred_type; diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp index 1c1c1d06..56bb4716 100644 --- a/include/boost/multiprecision/detail/functions/constants.hpp +++ b/include/boost/multiprecision/detail/functions/constants.hpp @@ -50,7 +50,7 @@ template void calc_e(T& result, unsigned digits) { typedef typename mpl::front::type ui_type; - typedef typename mpl::front::type real_type; + typedef typename mpl::front::type real_type; T lim; lim = ui_type(1); eval_ldexp(lim, lim, digits); @@ -72,7 +72,7 @@ template void calc_pi(T& result, unsigned digits) { typedef typename mpl::front::type ui_type; - typedef typename mpl::front::type real_type; + typedef typename mpl::front::type real_type; T a; a = ui_type(1); diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index ad4629d6..f4e98eaf 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -144,7 +144,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; BOOST_ASSERT(&H1F0 != &x); BOOST_ASSERT(&H1F0 != &a); @@ -341,7 +341,7 @@ void eval_log(T& result, const T& arg) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; exp_type e; T t; @@ -421,7 +421,7 @@ inline void eval_pow(T& result, const T& x, const T& a) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; if((&result == &x) || (&result == &a)) { @@ -551,7 +551,7 @@ namespace detail{ typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; switch(eval_fpclassify(x)) { diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index cf2b8dd2..d6119eaf 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -19,7 +19,7 @@ void hyp0F1(T& result, const T& b, const T& x) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; // Compute the series representation of Hypergeometric0F1 taken from // http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric0F1/06/01/01/ @@ -80,7 +80,7 @@ void eval_sin(T& result, const T& x) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; switch(eval_fpclassify(x)) { @@ -218,7 +218,7 @@ void eval_cos(T& result, const T& x) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; switch(eval_fpclassify(x)) { @@ -359,7 +359,7 @@ void hyp2F1(T& result, const T& a, const T& b, const T& c, const T& x) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; T x_pow_n_div_n_fact(x); T pochham_a (a); @@ -417,7 +417,7 @@ void eval_asin(T& result, const T& x) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; if(&result == &x) { @@ -567,7 +567,7 @@ void eval_atan(T& result, const T& x) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; switch(eval_fpclassify(x)) { @@ -670,7 +670,7 @@ void eval_atan2(T& result, const T& y, const T& x) typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; typedef typename boost::multiprecision::detail::canonical::type canonical_exp_type; - typedef typename mpl::front::type fp_type; + typedef typename mpl::front::type fp_type; switch(eval_fpclassify(y)) { diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index e85328b1..6a7f0ff1 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -58,7 +58,7 @@ struct canonical_imp > { typedef typename has_enough_bits::digits>::template type pred_type; typedef typename mpl::find_if< - typename Backend::real_types, + typename Backend::float_types, pred_type >::type iter_type; typedef typename mpl::deref::type type; diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index ce7413a8..f5260057 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -27,7 +27,7 @@ struct gmp_float_imp { typedef mpl::list signed_types; typedef mpl::list unsigned_types; - typedef mpl::list real_types; + typedef mpl::list float_types; typedef long exponent_type; gmp_float_imp(){} @@ -794,7 +794,7 @@ struct gmp_int { typedef mpl::list signed_types; typedef mpl::list unsigned_types; - typedef mpl::list real_types; + typedef mpl::list float_types; gmp_int() { @@ -1298,7 +1298,7 @@ struct gmp_rational { typedef mpl::list signed_types; typedef mpl::list unsigned_types; - typedef mpl::list real_types; + typedef mpl::list float_types; gmp_rational() { diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 80752d1c..e37e5082 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -30,7 +30,7 @@ struct mpfr_float_imp { typedef mpl::list signed_types; typedef mpl::list unsigned_types; - typedef mpl::list real_types; + typedef mpl::list float_types; typedef long exponent_type; mpfr_float_imp(){} diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 83de9b40..3bd9ac01 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -489,7 +489,7 @@ run ../example/mpfr_snips.cpp mpfr : # requirements [ check-target-builds ../config//has_mpfr : : no ] ; -run ../example/mp_float_snips.cpp ; +run ../example/cpp_float_snips.cpp ; run test_round.cpp : # command line From bf4c85c584926bd385e6ed7b4209f2d8d8db6b33 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 15 Nov 2011 12:16:49 +0000 Subject: [PATCH 064/256] Minor editorial corrections. [SVN r75494] --- doc/multiprecision.qbk | 136 +++++++++++++++++++++-------------------- 1 file changed, 70 insertions(+), 66 deletions(-) diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 1d539382..48117bfd 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -15,7 +15,7 @@ [@http://www.boost.org/LICENSE_1_0.txt]) ] [authors [authors, various]] - [last-revision $Date: 2011-07-08 18:51:46 +0100 (Fri, 08 Jul 2011) $] + [/last-revision $Date: 2011-07-08 18:51:46 +0100 (Fri, 08 Jul 2011) $] ] [import ../example/gmp_snips.cpp] @@ -24,21 +24,23 @@ [section:intro Introduction] -The Multiprecision library comes in two distinct parts: an expression-template-enabled front end `mp_number` -that handles all the operator overloading, expression evaluation optimization, and code reduction, and -a selection of backends that implement the actual arithmetic operations, and need conform only to the +The Multiprecision library comes in two distinct parts: + +* An expression-template-enabled front end `mp_number` +that handles all the operator overloading, expression evaluation optimization, and code reduction. +* A selection of backends that implement the actual arithmetic operations, and need conform only to the reduced interface requirements of the front end. -The library is often used by using one of the predfined typedefs: for example if you wanted an arbitrary precision +The library is often used by using one of the predefined typedefs: for example if you wanted an arbitrary precision integer type using GMP as the underlying implementation then you could use: #include // Defines the wrappers around the GMP library's types boost::multiprecision::mpz_int myint; // Arbitrary precision integer type. -Alternatively one can compose your own multiprecision type, by combining `mp_number` with one of the -predefined backend types. For example, suppose you wanted a 300 decimal digit floating point type -based on the MPFR library, in this case there's no predefined typedef with that level of precision, +Alternatively, you can compose your own multiprecision type, by combining `mp_number` with one of the +predefined backend types. For example, suppose you wanted a 300 decimal digit floating-point type +based on the MPFR library. In this case, there's no predefined typedef with that level of precision, so instead we compose our own: #include // Defines the Backend type that wraps MPFR @@ -81,9 +83,9 @@ lets suppose we're evaluating a polynomial via Horners method, something like th //.... y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; -If type `T` is an `mp_number`, then this expression is evaluated ['without creating a single temporary value], in contrast +If type `T` is an `mp_number`, then this expression is evaluated ['without creating a single temporary value]. In contrast, if we were using the C++ wrapper that ships with GMP - `mpf_class` - then this expression would result in no less than 11 -temporaries (this is true even though mpf_class does use expression templates to reduce the number of temporaries somewhat). Had +temporaries (this is true even though `mpf_class` does use expression templates to reduce the number of temporaries somewhat). Had we used an even simpler wrapper around GMP or MPFR like `mpclass` things would have been even worse and no less that 24 temporaries are created for this simple expression (note - we actually measure the number of memory allocations performed rather than the number of temporaries directly). @@ -109,9 +111,9 @@ Given the comments above, you might be forgiven for thinking that expression-tem sadly though, all tricks like this have their downsides. For one thing, expression template libraries like this one, tend to be slower to compile than their simpler cousins, they're also harder to debug (should you actually want to step through our code!), and rely on compiler optimizations being turned -on to give really good performance. Also since the return type from expressions involving `mp_number`'s +on to give really good performance. Also, since the return type from expressions involving `mp_number`'s is an "unmentionable implementation detail", you have to be careful to cast the result of an expression -to the actual number type when passing an expression to a template function. For example given: +to the actual number type when passing an expression to a template function. For example, given: template void my_proc(const T&); @@ -126,7 +128,7 @@ an expression template type, and not a number type. Instead we probably need: my_proc(my_mp_number_type(a+b)); Having said that, these situations don't occur that often - or indeed not at all for non-template functions. -In addition all the functions in the Boost.Math library will automatically convert expression-template arguments +In addition, all the functions in the Boost.Math library will automatically convert expression-template arguments to the underlying number type without you having to do anything, so: mpfr_float_100 a(20), delta(0.125); @@ -139,9 +141,9 @@ One other potential pitfall that's only possible in C++11: you should never stor auto my_expression = a + b - c; -Unless you're absolutely sure that the lifetimes of `a`, `b` and `c` will outlive that of `my_expression`. +unless you're absolutely sure that the lifetimes of `a`, `b` and `c` will outlive that of `my_expression`. -And finally.... the performance improvements from an expression template library like this are often not as +And finally... the performance improvements from an expression template library like this are often not as dramatic as the reduction in number of temporaries would suggest. For example if we compare this library with `mpfr_class` and `mpreal`, with all three using the underlying MPFR library at 50 decimal digits precision then we see the following typical results for polynomial execution: @@ -153,7 +155,7 @@ we see the following typical results for polynomial execution: [[mpreal][1.9 (0.0148s)][9.3 (27947 total)]] ] -As you can see the execution time increases a lot more slowly than the number of memory allocations. There are +As you can see, the execution time increases a lot more slowly than the number of memory allocations. There are a number of reasons for this: * The cost of extended-precision multiplication and division is so great, that the times taken for these tend to @@ -167,7 +169,7 @@ one would hope. We'll conclude this section by providing some more performance comparisons between these three libraries, again, all are using MPFR to carry out the underlying arithmetic, and all are operating at the same precision -(50 decimal places): +(50 decimal digits): [table Evaluation of Boost.Math's Bessel function test data [[Library][Relative Time][Relative Number of Memory Allocations]] @@ -212,12 +214,12 @@ The following backends provide integer arithmetic: The `gmp_int` backend is used via the typedef `boost::multiprecision::mpz_int`. It acts as a thin wrapper around the GMP `mpz_t` to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. -As well as the usual conversions from arithmetic and string types, type `mpz_int` is copy constructible and asignable from: +As well as the usual conversions from arithmetic and string types, type `mpz_int` is copy constructible and assignable from: * The GMP native types: `mpf_t`, `mpz_t`, `mpq_t`. * Instances of `mp_number` that are wrappers around those types: `mp_number >`, `mp_number`. -It's also possible to access the underlying `mpz_t` via the data() member function of `gmp_int`. +It's also possible to access the underlying `mpz_t` via the `data()` member function of `gmp_int`. [h5 Example:] @@ -232,8 +234,8 @@ The following backends provide real number arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] [[`mpf_float`][boost/multiprecision/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] -[[`mpfr_float`][boost/multiprecision/mpfr.hpp][2][GMP and MPFR][Very fast and efficient backend, with it's own standard library implementation.][Dependency on GNU licenced GMP and MPFR libraries.]] -[[`cpp_float`][boost/multiprecision/cpp_float.hpp][10][None][Header only, all C++ implementation.][Approximately 2x slower than the MPFR or GMP libraries.]] +[[`mpfr_float`][boost/multiprecision/mpfr.hpp][2][GMP and MPFR][Very fast and efficient backend, with its own standard library implementation.][Dependency on GNU licenced GMP and MPFR libraries.]] +[[`cpp_float`][boost/multiprecision/cpp_float.hpp][10][None][Header only, all C++ implementation. Boost licence.][Approximately 2x slower than the MPFR or GMP libraries.]] ] [h4 gmp_float] @@ -251,7 +253,7 @@ The following backends provide real number arithmetic: }} // namespaces -The `gmp_float` backend is used in conjunction with `mp_number`: It acts as a thin wrapper around the GMP `mpf_t` +The `gmp_float` backend is used in conjunction with `mp_number` : it acts as a thin wrapper around the GMP `mpf_t` to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. @@ -269,7 +271,7 @@ copy constructible and assignable from: * The GMP native types `mpf_t`, `mpz_t`, `mpq_t`. * The `mp_number` wrappers around those types: `mp_number >`, `mp_number`, `mp_number`. -It's also possible to access the underlying `mpf_t` via the data() member function of `gmp_float`. +It's also possible to access the underlying `mpf_t` via the `data()` member function of `gmp_float`. [h5 GMP example:] @@ -376,9 +378,9 @@ There are also non-member functions: mpz_int numerator(const mpq_rational&); mpz_int denominator(const mpq_rational&); -Which return the numerator and denominator of the number. +which return the numerator and denominator of the number. -It's also possible to access the underlying `mpq_t` via the data() member function of `mpq_rational`. +It's also possible to access the underlying `mpq_t` via the `data()` member function of `mpq_rational`. [h5 Example:] @@ -530,7 +532,7 @@ mp_number is an "unmentionable" expression template type. Binary operators, must have at least one argument that is of type `mp_number` or an expression template derived from `mp_number`. One argument may optionally be of arithmetic type. -Note that type `mp_number` (and all expression templates derived from it) may be used in a Boolian context. +Note that type `mp_number` (and all expression templates derived from it) may be used in a Boolean context. operator ``['convertible-to-bool-type]``()const; @@ -577,14 +579,14 @@ the default precision and the precision of `*this` respectively. Returns: -* A value less that 0 for *this < other -* A value greater that 0 for *this > other -* Zero for *this == other +* A value less that 0 for `*this < other` +* A value greater that 0 for `*this > other` +* Zero for `*this == other` Backend& backend(); const Backend& backend()const; -Returns the underlying backend instance used by *this. +Returns the underlying backend instance used by `*this`. [h4 swap] @@ -646,21 +648,23 @@ don't have native support for these functions. Please note however, that this d to be a compile time constant - this means for example that the GMP MPF Backend will not work with these functions when that type is used at variable precision. -Also note that with the exception of `abs` that these functions can only be used with floating point Backend types. +Also note that with the exception of `abs` that these functions can only be used with floating-point Backend types. -[h4 Boost.Math Interoperabilty Support] +[h4 Boost.Math Interoperability Support] namespace boost{ namespace math{ - int fpclassify (const ``['mp_number-or-expression-template-type]``&, int); - bool isfinite (const ``['mp_number-or-expression-template-type]``&, int); - bool isnan (const ``['mp_number-or-expression-template-type]``&, int); - bool isinf (const ``['mp_number-or-expression-template-type]``&, int); - bool isnormal (const ``['mp_number-or-expression-template-type]``&, int); + int fpclassify (const ``['mp_number-or-expression-template-type]``&, int); + bool isfinite (const ``['mp_number-or-expression-template-type]``&, int); + bool isnan (const ``['mp_number-or-expression-template-type]``&, int); + bool isinf (const ``['mp_number-or-expression-template-type]``&, int); + bool isnormal (const ``['mp_number-or-expression-template-type]``&, int); }} // namespaces -These functions behave exacts as their Boost.Math equivalents. Other Boost.Math functions and templates may also be +These floating-point classification functions behave exactly as their Boost.Math equivalents. + +Other Boost.Math functions and templates may also be specialized or overloaded to ensure interoperability. [h4 std::numeric_limits support] @@ -686,22 +690,22 @@ whose precision can vary at compile time (such as `mpf_float`). [template super[x]''''''[x]''''''] The requirements on the `Backend` template argument to `mp_number` are split up into -compulsary requirements, and optional requirements that are either to improve performance +compulsory requirements, and optional requirements that are either to improve performance or provide optional features. In the following tables, type B is the `Backend` template arument to `mp_number`, `b` is a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a variable of Arithmetic type, `s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`, -`pa` is a variable of type pointer-to-arithmetc-type, `exp` is a variable of type `B::exp_type`, +`pa` is a variable of type pointer-to-arithmetic-type, `exp` is a variable of type `B::exp_type`, `pexp` is a variable of type `B::exp_type*`. -[table Compulsary Requirements on the Backend type. +[table Compulsory Requirements on the Backend type. [[Expression][Return Type][Comments]] [[`B::signed_types`][`mpl::list`][A list of signed integral types that can be assigned to type B. The types shall be listed in order of size, smallest first, and shall terminate in the type that is `std::intmax_t`.]] [[`B::unsigned_types`][`mpl::list`][A list of unsigned integral types that can be assigned to type B. The types shall be listed in order of size, smallest first, and shall terminate in the type that is `std::uintmax_t`.]] -[[`B::float_types`][`mpl::list`][A list of floating point types that can be assigned to type B.The types shall be +[[`B::float_types`][`mpl::list`][A list of floating-point types that can be assigned to type B.The types shall be listed in order of size, smallest first, and shall terminate in type `long double`.]] [[`B::exponent_type`][A signed integral type.][The type of the exponent of type B.]] [[`B()`][ ][Default constructor.]] @@ -710,7 +714,7 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia [[`b = a`][`B&`][Assignment from an Arithmetic type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`b = s`][`B&`][Assignment from a string.]] -[[`b.swap(b)`][`void`][Swaps the contents of it's arguments.]] +[[`b.swap(b)`][`void`][Swaps the contents of its arguments.]] [[`cb.str(ui, bb)`][`std::string`][Returns the string representation of `b` with `ui` digits and in scientific format if `bb` is `true`. If `ui` is zero, then returns as many digits as are required to reconstruct the original value.]] [[`b.negate()`][`void`][Negates `b`.]] @@ -734,11 +738,11 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia conversion to at least types `std::intmax_t`, `std::uintmax_t` and `long long`. Conversion to other arithmetic types can then be synthesised using other operations. Conversions to other types are entirely optional.]] -[[`eval_frexp(b, cb, pexp)`][`void`][Stores values in `b` and `*pexp` such that the value of `cb` is b * 2[super *pexp], only required when `B` is a floating point type.]] -[[`eval_ldexp(b, cb, exp)`][`void`][Stores a value in `b` that is cb * 2[super exp], only required when `B` is a floating point type.]] -[[`eval_floor(b, cb)`][`void`][Stores the floor of `cb` in `b`, only required when `B` is a floating point type.]] -[[`eval_ceil(b, cb)`][`void`][Stores the ceiling of `cb` in `b`, only required when `B` is a floating point type.]] -[[`eval_sqrt(b, cb)`][`void`][Stores the square root of `cb` in `b`, only required when `B` is a floating point type.]] +[[`eval_frexp(b, cb, pexp)`][`void`][Stores values in `b` and `*pexp` such that the value of `cb` is b * 2[super *pexp], only required when `B` is a floating-point type.]] +[[`eval_ldexp(b, cb, exp)`][`void`][Stores a value in `b` that is cb * 2[super exp], only required when `B` is a floating-point type.]] +[[`eval_floor(b, cb)`][`void`][Stores the floor of `cb` in `b`, only required when `B` is a floating-point type.]] +[[`eval_ceil(b, cb)`][`void`][Stores the ceiling of `cb` in `b`, only required when `B` is a floating-point type.]] +[[`eval_sqrt(b, cb)`][`void`][Stores the square root of `cb` in `b`, only required when `B` is a floating-point type.]] ] [table Optional Requirements on the Backend Type @@ -807,24 +811,24 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia [[`get_sign(cb)`][`int`][Returns a value < zero if `cb` is negative, a value > zero if `cb` is positive, and zero if `cb` is zero.]] [[`eval_abs(b, cb)`][`void`][Set `b` to the absolute value of `cb`.]] [[`eval_fabs(b, cb)`][`void`][Set `b` to the absolute value of `cb`.]] -[[`eval_fpclassify(cb)`][`int`][Returns one of the same values returned by `std::fpclassify`. Only required when `B` is an floating point type.]] -[[`eval_trunc(b, cb)`][`void`][Performs the equivalent operation to `std::trunc` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_round(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::round` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_exp(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_log(b, cb)`][`void`][Performs the equivalent operation to `std::log` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_log10(b, cb)`][`void`][Performs the equivalent operation to `std::log10` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_sin(b, cb)`][`void`][Performs the equivalent operation to `std::sin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_cos(b, cb)`][`void`][Performs the equivalent operation to `std::cos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_tan(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_asin(b, cb)`][`void`][Performs the equivalent operation to `std::asin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_acos(b, cb)`][`void`][Performs the equivalent operation to `std::acos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_atan(b, cb)`][`void`][Performs the equivalent operation to `std::atan` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_sinh(b, cb)`][`void`][Performs the equivalent operation to `std::sinh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_cosh(b, cb)`][`void`][Performs the equivalent operation to `std::cosh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_tanh(b, cb)`][`void`][Performs the equivalent operation to `std::tanh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_fmod(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::fmod` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_pow(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::pow` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating point type.]] -[[`eval_atan2(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::atan` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating point type.]] +[[`eval_fpclassify(cb)`][`int`][Returns one of the same values returned by `std::fpclassify`. Only required when `B` is an floating-point type.]] +[[`eval_trunc(b, cb)`][`void`][Performs the equivalent operation to `std::trunc` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_round(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::round` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_exp(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_log(b, cb)`][`void`][Performs the equivalent operation to `std::log` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_log10(b, cb)`][`void`][Performs the equivalent operation to `std::log10` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_sin(b, cb)`][`void`][Performs the equivalent operation to `std::sin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_cos(b, cb)`][`void`][Performs the equivalent operation to `std::cos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_tan(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_asin(b, cb)`][`void`][Performs the equivalent operation to `std::asin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_acos(b, cb)`][`void`][Performs the equivalent operation to `std::acos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_atan(b, cb)`][`void`][Performs the equivalent operation to `std::atan` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_sinh(b, cb)`][`void`][Performs the equivalent operation to `std::sinh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_cosh(b, cb)`][`void`][Performs the equivalent operation to `std::cosh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_tanh(b, cb)`][`void`][Performs the equivalent operation to `std::tanh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_fmod(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::fmod` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_pow(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::pow` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_atan2(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::atan` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] ] [endsect] From 050ae32c4438bbb00b0b4b2ab4aae00e552f94cb Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 16 Nov 2011 09:40:05 +0000 Subject: [PATCH 065/256] Add initial libtommath support. Fix use of noexcept. Remove dead files. [SVN r75505] --- config/Jamfile.v2 | 5 +- config/has_e_float.cpp | 17 - config/has_gcc_visibility.cpp | 13 - config/has_long_double_support.cpp | 10 - config/has_mpfr_class.cpp | 14 - config/has_mpreal.cpp | 14 - config/has_ntl_rr.cpp | 12 - config/{has_gmpxx.cpp => has_tommath.cpp} | 4 +- .../multiprecision/arithmetic_backend.hpp | 22 +- .../concepts/mp_number_architypes.hpp | 22 +- .../multiprecision/detail/mp_number_base.hpp | 6 + include/boost/multiprecision/e_float.hpp | 80 ---- include/boost/multiprecision/gmp.hpp | 83 ++-- include/boost/multiprecision/mpfr.hpp | 42 +- include/boost/multiprecision/tommath.hpp | 411 ++++++++++++++++++ test/Jamfile.v2 | 29 ++ test/test_arithmetic.cpp | 24 +- test/test_numeric_limits.cpp | 9 +- 18 files changed, 564 insertions(+), 253 deletions(-) delete mode 100644 config/has_e_float.cpp delete mode 100644 config/has_gcc_visibility.cpp delete mode 100644 config/has_long_double_support.cpp delete mode 100644 config/has_mpfr_class.cpp delete mode 100644 config/has_mpreal.cpp delete mode 100644 config/has_ntl_rr.cpp rename config/{has_gmpxx.cpp => has_tommath.cpp} (78%) delete mode 100644 include/boost/multiprecision/e_float.hpp create mode 100644 include/boost/multiprecision/tommath.hpp diff --git a/config/Jamfile.v2 b/config/Jamfile.v2 index a307db12..91f9cbb3 100644 --- a/config/Jamfile.v2 +++ b/config/Jamfile.v2 @@ -8,12 +8,15 @@ import path ; local gmp_path = [ modules.peek : GMP_PATH ] ; local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local tommath_path = [ modules.peek : TOMMATH_PATH ] ; obj has_gmp : has_gmp.cpp : $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx ; obj has_mpfr : has_mpfr.cpp : $(mpfr_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx $(gmp_path) ; +obj has_tommath : has_tommath.cpp : + $(tommath_path) ; explicit has_gmp ; explicit has_mpfr ; - +explicit has_tommath ; diff --git a/config/has_e_float.cpp b/config/has_e_float.cpp deleted file mode 100644 index 8cadc5c6..00000000 --- a/config/has_e_float.cpp +++ /dev/null @@ -1,17 +0,0 @@ -// Copyright John Maddock 2011. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - - -#ifdef _MSC_VER -# pragma warning (disable : 4100) // unreferenced formal parameter -#endif - -#define E_FLOAT_TYPE_EFX - -#include -#include -#include - - diff --git a/config/has_gcc_visibility.cpp b/config/has_gcc_visibility.cpp deleted file mode 100644 index 6c7d6f91..00000000 --- a/config/has_gcc_visibility.cpp +++ /dev/null @@ -1,13 +0,0 @@ -// Copyright John Maddock 20010. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef __GNUC__ -# error "This is a GCC specific test case". -#endif - -int main() -{ - return 0; -} diff --git a/config/has_long_double_support.cpp b/config/has_long_double_support.cpp deleted file mode 100644 index d314cf38..00000000 --- a/config/has_long_double_support.cpp +++ /dev/null @@ -1,10 +0,0 @@ -// Copyright John Maddock 2008. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#include - -#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS -#error "long double support is not supported by Boost.Math on this Plaform: the long double version of the TR1 library will not be built." -#endif diff --git a/config/has_mpfr_class.cpp b/config/has_mpfr_class.cpp deleted file mode 100644 index 8eb3c7b2..00000000 --- a/config/has_mpfr_class.cpp +++ /dev/null @@ -1,14 +0,0 @@ -// Copyright John Maddock 2008. -// Copyright Paul A. Britow 2009 -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifdef _MSC_VER -# pragma warning (disable : 4127) // conditional expression is constant -# pragma warning (disable : 4800) // 'int' : forcing value to bool 'true' or 'false' (performance warning) -# pragma warning (disable : 4512) // assignment operator could not be generated -#endif - -#include - diff --git a/config/has_mpreal.cpp b/config/has_mpreal.cpp deleted file mode 100644 index 8ee8897d..00000000 --- a/config/has_mpreal.cpp +++ /dev/null @@ -1,14 +0,0 @@ -// Copyright John Maddock 2008. -// Copyright Paul A. Britow 2009 -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifdef _MSC_VER -# pragma warning (disable : 4127) // conditional expression is constant -# pragma warning (disable : 4800) // 'int' : forcing value to bool 'true' or 'false' (performance warning) -# pragma warning (disable : 4512) // assignment operator could not be generated -#endif - -#include - diff --git a/config/has_ntl_rr.cpp b/config/has_ntl_rr.cpp deleted file mode 100644 index f3844217..00000000 --- a/config/has_ntl_rr.cpp +++ /dev/null @@ -1,12 +0,0 @@ -// Copyright John Maddock 2008. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - - -#ifdef _MSC_VER -# pragma warning (disable : 4100) // unreferenced formal parameter -#endif - -#include - diff --git a/config/has_gmpxx.cpp b/config/has_tommath.cpp similarity index 78% rename from config/has_gmpxx.cpp rename to config/has_tommath.cpp index edf62d8c..8d230043 100644 --- a/config/has_gmpxx.cpp +++ b/config/has_tommath.cpp @@ -1,7 +1,7 @@ -// Copyright John Maddock 2008. +// Copyright John Maddock 2011. // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -#include +#include diff --git a/include/boost/multiprecision/arithmetic_backend.hpp b/include/boost/multiprecision/arithmetic_backend.hpp index 25f173ad..88098dab 100644 --- a/include/boost/multiprecision/arithmetic_backend.hpp +++ b/include/boost/multiprecision/arithmetic_backend.hpp @@ -119,7 +119,7 @@ inline void divide(arithmetic_backend& result, const arithmetic_back namespace std{ #ifdef BOOST_NO_NOEXCEPT -# define noexcept +# define BOOST_MP_NOEXCEPT #endif template @@ -128,19 +128,19 @@ class numeric_limits base_type; typedef boost::multiprecision::mp_number > number_type; public: - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return -(max)(); } - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return base_type::epsilon(); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return epsilon() / 2; } - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return base_type::infinity(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return base_type::quiet_NaN(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return base_type::signaling_NaN(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return base_type::denorm_min(); } + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } }; #ifdef BOOST_NO_NOEXCEPT -# undef noexcept +# undef BOOST_MP_NOEXCEPT #endif } diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index a51f93b7..18a4b85c 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -194,7 +194,7 @@ typedef boost::multiprecision::mp_number mp_n namespace std{ #ifdef BOOST_NO_NOEXCEPT -# define noexcept +# define BOOST_MP_NOEXCEPT #endif template <> @@ -203,19 +203,19 @@ class numeric_limits typedef std::numeric_limits base_type; typedef boost::multiprecision::concepts::mp_number_float_architype number_type; public: - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return (base_type::min)(); } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return (base_type::max)(); } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return -(max)(); } - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return base_type::epsilon(); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return epsilon() / 2; } - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return base_type::infinity(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return base_type::quiet_NaN(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return base_type::signaling_NaN(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return base_type::denorm_min(); } + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } }; #ifdef BOOST_NO_NOEXCEPT -# undef noexcept +# undef BOOST_MP_NOEXCEPT #endif } diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 6a7f0ff1..ca9cc5e9 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -10,6 +10,12 @@ #include #include +#ifdef BOOST_NO_NOEXCEPT +#define BOOST_MP_NOEXCEPT +#else +#define BOOST_MP_NOEXCEPT noexcept +#endif + namespace boost{ namespace multiprecision{ template diff --git a/include/boost/multiprecision/e_float.hpp b/include/boost/multiprecision/e_float.hpp deleted file mode 100644 index 68931334..00000000 --- a/include/boost/multiprecision/e_float.hpp +++ /dev/null @@ -1,80 +0,0 @@ -/////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ - -#ifndef BOOST_MATH_EFX_BACKEND_HPP -#define BOOST_MATH_EFX_BACKEND_HPP - -#include -#include -#include -#include -#include - -namespace boost{ -namespace multiprecision{ - -typedef mp_number > e_float; - -template<> -inline void arithmetic_backend::negate() -{ - m_value.negate(); -} -template<> -inline std::string arithmetic_backend::str(unsigned digits, bool scientific)const -{ - std::fstream os; - os << std::setprecision(digits ? digits : efx::e_float::ef_digits + 5); - if(scientific) - os << std::scientific; - std::string result; - this->data().wr_string(result, os); - return result; -} - -inline void eval_abs(arithmetic_backend& result, const arithmetic_backend& arg) -{ - result.data() = ef::fabs(arg.data()); -} - -inline void eval_fabs(arithmetic_backend& result, const arithmetic_backend& arg) -{ - result.data() = ef::fabs(arg.data()); -} - -inline bool is_zero(const arithmetic_backend& val) -{ - return val.data().iszero(); -} -inline int get_sign(const arithmetic_backend& val) -{ - return val.data().isneg() ? -1 : val.data().iszero() ? 0 : 1; -} - -inline void convert_to(boost::uintmax_t* result, const arithmetic_backend& val) -{ - *result = val.data().extract_unsigned_long_long(); -} -inline void convert_to(boost::intmax_t* result, const arithmetic_backend& val) -{ - *result = val.data().extract_signed_long_long(); -} -inline void convert_to(double* result, const arithmetic_backend& val) -{ - *result = val.data().extract_double(); -} -inline void convert_to(long double* result, const arithmetic_backend& val) -{ - *result = val.data().extract_long_double(); -} -inline int eval_fpclassify(const arithmetic_backend& val) -{ - return val.data().isinf() ? FP_INFINITE : val.data().isnan() ? FP_NAN : val.data().iszero() ? FP_ZERO : FP_NORMAL; -} - - -}} // namespaces - -#endif diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index f5260057..80153bed 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1656,7 +1656,7 @@ typedef mp_number mpq_rational; namespace std{ #ifdef BOOST_NO_NOEXCEPT -# define noexcept +# define BOOST_MP_NOEXCEPT #endif // @@ -1668,7 +1668,7 @@ class numeric_limits > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1680,7 +1680,7 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1692,7 +1692,7 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } @@ -1704,7 +1704,7 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1717,7 +1717,7 @@ public: return value.second; } // What value should this be???? - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { // returns epsilon/2 initializer.do_nothing(); @@ -1739,10 +1739,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = true; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -1774,9 +1774,9 @@ class numeric_limits > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int digits = 0; BOOST_STATIC_CONSTEXPR int digits10 = 0; BOOST_STATIC_CONSTEXPR int max_digits10 = 0; @@ -1784,8 +1784,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 0; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -1795,10 +1795,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -1817,25 +1817,24 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return (min)(); } - // Digits are unbounded, use zero for now: - BOOST_STATIC_CONSTEXPR int digits = 0; - BOOST_STATIC_CONSTEXPR int digits10 = 0; - BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + BOOST_STATIC_CONSTEXPR int digits = INT_MAX; + BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L; + BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; BOOST_STATIC_CONSTEXPR bool is_signed = true; BOOST_STATIC_CONSTEXPR bool is_integer = true; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -1845,10 +1844,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -1867,15 +1866,15 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return (min)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } // Digits are unbounded, use zero for now: BOOST_STATIC_CONSTEXPR int digits = 0; BOOST_STATIC_CONSTEXPR int digits10 = 0; @@ -1884,8 +1883,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -1895,10 +1894,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -1908,7 +1907,7 @@ public: }; #ifdef BOOST_NO_NOEXCEPT -# undef noexcept +# undef BOOST_MP_NOEXCEPT #endif } // namespace std diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index e37e5082..08ef8a92 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -967,7 +967,7 @@ struct lanczos > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -991,7 +991,7 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1003,7 +1003,7 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } @@ -1015,7 +1015,7 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1028,7 +1028,7 @@ public: return value.second; } // What value should this be???? - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { // returns epsilon/2 initializer.do_nothing(); @@ -1050,7 +1050,7 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { // returns epsilon/2 initializer.do_nothing(); @@ -1063,7 +1063,7 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { // returns epsilon/2 initializer.do_nothing(); @@ -1076,11 +1076,11 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = true; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -1114,9 +1114,9 @@ class numeric_limits > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; - BOOST_STATIC_CONSTEXPR number_type (min)() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type (max)() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type lowest() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR int digits = 0; BOOST_STATIC_CONSTEXPR int digits10 = 0; BOOST_STATIC_CONSTEXPR int max_digits10 = 0; @@ -1124,8 +1124,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 0; - BOOST_STATIC_CONSTEXPR number_type epsilon() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type round_error() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -1135,10 +1135,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() noexcept { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() noexcept { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -1147,8 +1147,8 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -#ifdef noexcept -#undef noexcept +#ifdef BOOST_MP_NOEXCEPT +#undef BOOST_MP_NOEXCEPT #endif } // namespace std diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp new file mode 100644 index 00000000..90448520 --- /dev/null +++ b/include/boost/multiprecision/tommath.hpp @@ -0,0 +1,411 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_MP_TOMMATH_BACKEND_HPP +#define BOOST_MATH_MP_TOMMATH_BACKEND_HPP + +#include +#include +#include +#include +#include +#include +#include +#include +#include + +namespace boost{ namespace multiprecision{ + +struct tommath_int +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list float_types; + + tommath_int() + { + mp_init(&m_data); + } + tommath_int(const tommath_int& o) + { + mp_init_copy(&m_data, const_cast<::mp_int*>(&o.m_data)); + } + tommath_int& operator = (const tommath_int& o) + { + mp_copy(const_cast<::mp_int*>(&o.m_data), &m_data); + return *this; + } + tommath_int& operator = (boost::uintmax_t i) + { + boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned shift = 0; + ::mp_int t; + mp_init(&t); + mp_zero(&m_data); + while(i) + { + mp_set_int(&t, static_cast(i & mask)); + if(shift) + mp_mul_2d(&t, shift, &t); + mp_add(&m_data, &t, &m_data); + shift += std::numeric_limits::digits; + i >>= std::numeric_limits::digits; + } + mp_clear(&t); + return *this; + } + tommath_int& operator = (boost::intmax_t i) + { + bool neg = i < 0; + *this = static_cast(std::abs(i)); + if(neg) + mp_neg(&m_data, &m_data); + return *this; + } + tommath_int& operator = (unsigned long i) + { + mp_set_int(&m_data, i); + return *this; + } + tommath_int& operator = (long i) + { + bool neg = i < 0; + *this = static_cast(std::abs(i)); + if(neg) + mp_neg(&m_data, &m_data); + return *this; + } + tommath_int& operator = (long double a) + { + using std::frexp; + using std::ldexp; + using std::floor; + + if (a == 0) { + mp_set_int(&m_data, 0); + return *this; + } + + if (a == 1) { + mp_set_int(&m_data, 1); + return *this; + } + + BOOST_ASSERT(!(boost::math::isinf)(a)); + BOOST_ASSERT(!(boost::math::isnan)(a)); + + int e; + long double f, term; + mp_init_set_int(&m_data, 0u); + ::mp_int t; + mp_init(&t); + + f = frexp(a, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + mp_mul_2d(&m_data, shift, &m_data); + if(term > 0) + { + mp_set_int(&t, static_cast(term)); + mp_add(&m_data, &t, &m_data); + } + else + { + mp_set_int(&t, static_cast(-term)); + mp_sub(&m_data, &t, &m_data); + } + f -= term; + } + if(e > 0) + mp_mul_2d(&m_data, e, &m_data); + else if(e < 0) + { + tommath_int t2; + mp_div_2d(&m_data, -e, &m_data, &t2.data()); + } + return *this; + } + tommath_int& operator = (const char* s) + { + mp_read_radix(&m_data, s, 10); + return *this; + } + std::string str(unsigned /*digits*/, bool /*scientific*/)const + { + int s; + mp_radix_size(const_cast<::mp_int*>(&m_data), 10, &s); + boost::scoped_array a(new char[s+1]); + mp_toradix_n(const_cast<::mp_int*>(&m_data), a.get(), 10, s+1); + return a.get(); + } + ~tommath_int() + { + mp_clear(&m_data); + } + void negate() + { + mp_neg(&m_data, &m_data); + } + int compare(const tommath_int& o)const + { + return mp_cmp(const_cast<::mp_int*>(&m_data), const_cast<::mp_int*>(&o.m_data)); + } + template + int compare(V v)const + { + tommath_int d; + tommath_int t(*this); + mp_shrink(&t.data()); + d = v; + return t.compare(d); + } + mp_int& data() { return m_data; } + const mp_int& data()const { return m_data; } + void swap(tommath_int& o) + { + mp_exch(&m_data, &o.data()); + } +protected: + mp_int m_data; +}; + +int get_sign(const tommath_int& val); + +inline void add(tommath_int& t, const tommath_int& o) +{ + mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); +} +inline void subtract(tommath_int& t, const tommath_int& o) +{ + mp_sub(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); +} +inline void multiply(tommath_int& t, const tommath_int& o) +{ + mp_mul(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); +} +inline void divide(tommath_int& t, const tommath_int& o) +{ + tommath_int temp; + mp_div(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data(), &temp.data()); +} +inline void modulus(tommath_int& t, const tommath_int& o) +{ + bool neg = get_sign(t) < 0; + bool neg2 = get_sign(o) < 0; + mp_mod(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); + if(neg != neg2) + { + t.negate(); + mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); + t.negate(); + } +} +template +inline void left_shift(tommath_int& t, UI i) +{ + mp_mul_2d(&t.data(), static_cast(i), &t.data()); +} +template +inline void right_shift(tommath_int& t, UI i) +{ + tommath_int d; + mp_div_2d(&t.data(), static_cast(i), &t.data(), &d.data()); +} +template +inline void left_shift(tommath_int& t, const tommath_int& v, UI i) +{ + mp_mul_2d(const_cast<::mp_int*>(&v.data()), static_cast(i), &t.data()); +} +template +inline void right_shift(tommath_int& t, const tommath_int& v, UI i) +{ + tommath_int d; + mp_div_2d(const_cast<::mp_int*>(&v.data()), static_cast(i), &t.data(), &d.data()); +} + +inline void bitwise_and(tommath_int& result, const tommath_int& v) +{ + mp_and(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data()); +} + +inline void bitwise_or(tommath_int& result, const tommath_int& v) +{ + mp_or(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data()); +} + +inline void bitwise_xor(tommath_int& result, const tommath_int& v) +{ + mp_xor(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data()); +} + +inline void add(tommath_int& t, const tommath_int& p, const tommath_int& o) +{ + mp_add(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data()); +} +inline void subtract(tommath_int& t, const tommath_int& p, const tommath_int& o) +{ + mp_sub(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data()); +} +inline void multiply(tommath_int& t, const tommath_int& p, const tommath_int& o) +{ + mp_mul(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data()); +} +inline void divide(tommath_int& t, const tommath_int& p, const tommath_int& o) +{ + tommath_int d; + mp_div(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data(), &d.data()); +} +inline void modulus(tommath_int& t, const tommath_int& p, const tommath_int& o) +{ + bool neg = get_sign(p) < 0; + bool neg2 = get_sign(o) < 0; + mp_mod(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data()); + if(neg != neg2) + { + t.negate(); + mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); + t.negate(); + } +} + +inline void bitwise_and(tommath_int& result, const tommath_int& u, const tommath_int& v) +{ + mp_and(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data()); +} + +inline void bitwise_or(tommath_int& result, const tommath_int& u, const tommath_int& v) +{ + mp_or(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data()); +} + +inline void bitwise_xor(tommath_int& result, const tommath_int& u, const tommath_int& v) +{ + mp_xor(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data()); +} + +inline void complement(tommath_int& result, const tommath_int& u) +{ + result = u; + for(int i = 0; i < result.data().used; ++i) + { + result.data().dp[i] = MP_MASK & ~(result.data().dp[i]); + } + // + // We now need to pad out the left of the value with 1's to round up to a whole number of + // CHAR_BIT * sizeof(mp_digit) units. Otherwise we'll end up with a very strange number of + // bits set! + // + unsigned shift = result.data().used * DIGIT_BIT; // How many bits we're actually using + // How many bits we actually need, reduced by one to account for a mythical sign bit: + unsigned padding = result.data().used * std::numeric_limits::digits - shift - 1; + while(padding >= std::numeric_limits::digits) + padding -= std::numeric_limits::digits; + + // Create a mask providing the extra bits we need and add to result: + tommath_int mask; + mask = static_cast((1u << padding) - 1); + left_shift(mask, shift); + add(result, mask); +} + +inline bool is_zero(const tommath_int& val) +{ + return mp_iszero(&val.data()); +} +inline int get_sign(const tommath_int& val) +{ + return mp_iszero(&val.data()) ? 0 : SIGN(&val.data()) ? -1 : 1; +} +template +inline void convert_to(A* result, const tommath_int& val) +{ + *result = boost::lexical_cast(val.str(0, false)); +} +inline void convert_to(char* result, const tommath_int& val) +{ + *result = static_cast(boost::lexical_cast(val.str(0, false))); +} +inline void convert_to(unsigned char* result, const tommath_int& val) +{ + *result = static_cast(boost::lexical_cast(val.str(0, false))); +} +inline void convert_to(signed char* result, const tommath_int& val) +{ + *result = static_cast(boost::lexical_cast(val.str(0, false))); +} +inline void eval_abs(tommath_int& result, const tommath_int& val) +{ + mp_abs(const_cast<::mp_int*>(&val.data()), &result.data()); +} + + +template<> +struct number_category : public mpl::int_{}; + +typedef mp_number mp_int; + +}} // namespaces + +namespace std{ + +template<> +class numeric_limits +{ + typedef boost::multiprecision::mp_int number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + // + // Largest and smallest numbers are bounded only by available memory, set + // to zero: + // + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT + { + return number_type(); + } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT + { + return number_type(); + } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + BOOST_STATIC_CONSTEXPR int digits = INT_MAX; + BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L; + BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = true; + BOOST_STATIC_CONSTEXPR bool is_exact = true; + BOOST_STATIC_CONSTEXPR int radix = 2; + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = false; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + +} + +#endif diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 3bd9ac01..a076a565 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -9,22 +9,35 @@ import path ; local ntl-path = [ modules.peek : NTL_PATH ] ; local gmp_path = [ modules.peek : GMP_PATH ] ; local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local tommath_path = [ modules.peek : TOMMATH_PATH ] ; project : requirements $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx $(mpfr_path) + $(tommath_path) ../../.. $(gmp_path) $(mpfr_path) $(mpfr_path)/build.vc10/lib/Win32/Debug + $(tommath_path) msvc:static ; lib gmp ; lib mpfr ; +if $(tommath_path) +{ + TOMMATH = [ GLOB $(tommath_path) : *.c ] ; +} +else +{ + lib tommath ; + TOMMATH = tommath ; +} + run test_arithmetic.cpp : # command line : # input files @@ -87,6 +100,14 @@ run test_arithmetic.cpp mpfr gmp [ check-target-builds ../config//has_mpfr : : no ] : test_arithmetic_mpfr_50 ; +run test_arithmetic.cpp $(TOMMATH) + : # command line + : # input files + : # requirements + TEST_TOMMATH + [ check-target-builds ../config//has_tommath : : no ] + : test_arithmetic_tommath ; + run test_numeric_limits.cpp : # command line : # input files @@ -150,6 +171,14 @@ run test_numeric_limits.cpp [ check-target-builds ../config//has_mpfr : : no ] : test_numeric_limits_cpp_float ; +run test_numeric_limits.cpp $(TOMMATH) + : # command line + : # input files + : # requirements + TEST_TOMMATH + [ check-target-builds ../config//has_tommath : : no ] + : test_numeric_limits_tommath ; + run mp_number_concept_check.cpp mpfr : # command line : # input files diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index db49a85b..a39dc351 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -6,7 +6,7 @@ #include #include -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && !defined(TEST_TOMMATH) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND @@ -15,6 +15,7 @@ # define TEST_MPFR_50 # define TEST_CPP_FLOAT # define TEST_MPQ +# define TEST_TOMMATH #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -37,6 +38,9 @@ #if defined(TEST_MPFR) || defined(TEST_MPFR_50) #include #endif +#ifdef TEST_TOMMATH +#include +#endif #define BOOST_TEST_THROW(x, EX)\ try { x; BOOST_ERROR("Expected exception not thrown"); } \ @@ -70,6 +74,14 @@ template bool isfloat(T){ return false; } << " tolerance = " << tol << std::endl;\ } +template +struct is_twos_complement_integer : public boost::mpl::true_ {}; + +#ifdef TEST_TOMMATH +template <> +struct is_twos_complement_integer : public boost::mpl::false_ {}; +#endif + template void test_integer_ops(const T&){} @@ -180,6 +192,7 @@ void test_integer_ops(const boost::mpl::int_::value ? ~0 : (std::numeric_limits::max)(); a = i; b = j; c = a; @@ -248,11 +261,11 @@ void test_integer_ops(const boost::mpl::int_(); +#endif +#ifdef TEST_TOMMATH + test(); #endif return boost::report_errors(); } diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index ce87c5d6..ea18665c 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -5,7 +5,7 @@ #include -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && !defined(TEST_TOMMATH) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND @@ -14,6 +14,7 @@ # define TEST_MPFR_50 # define TEST_CPP_FLOAT # define TEST_MPQ +# define TEST_TOMMATH #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -36,6 +37,9 @@ #if defined(TEST_MPFR) || defined(TEST_MPFR_50) #include #endif +#ifdef TEST_TOMMATH +#include +#endif #define PRINT(x)\ std::cout << BOOST_STRINGIZE(x) << " = " << std::numeric_limits::x << std::endl; @@ -168,6 +172,9 @@ int main() #endif #ifdef TEST_MPFR_50 test(); +#endif +#ifdef TEST_TOMMATH + test(); #endif return boost::report_errors(); } From b653174c77628b25cc37506b94016bbcabee6f89 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 16 Nov 2011 17:36:40 +0000 Subject: [PATCH 066/256] Add enhanced testing support. Remove throw statements for BOOST_THROW_EXCEPTION. Remove throw() qualifiers: they're a dis-optimization. [SVN r75511] --- include/boost/multiprecision/cpp_float.hpp | 22 +- .../multiprecision/detail/functions/pow.hpp | 4 +- .../multiprecision/detail/functions/trig.hpp | 4 +- test/Jamfile.v2 | 1 + test/test.hpp | 193 ++++++++++++++++++ test/test_fpclassify.cpp | 9 +- test/test_round.cpp | 7 +- test/test_test.cpp | 85 ++++++++ 8 files changed, 296 insertions(+), 29 deletions(-) create mode 100644 test/test_test.cpp diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index ab5b5432..28db0a82 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -2625,7 +2625,7 @@ inline void eval_frexp(cpp_float& result, const cpp_float& x long long t = result.order(); if(std::abs(t) > (std::numeric_limits::max)() / 3) - throw std::runtime_error("Exponent is too large to be represented as a power of 2."); + BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2.")); t *= 3; result *= cpp_float::pow2(-t); @@ -2651,7 +2651,7 @@ inline void eval_frexp(cpp_float& result, const cpp_float& x long long t; eval_frexp(result, x, &t); if(t > (std::numeric_limits::max)()) - throw std::runtime_error("Exponent is outside the range of an int"); + BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is outside the range of an int")); *e = static_cast(t); } @@ -2702,15 +2702,15 @@ namespace std static const bool traps = false; static const bool tinyness_before = false; - static const boost::multiprecision::mp_number > (min) (void) throw() { return (boost::multiprecision::cpp_float::min)(); } - static const boost::multiprecision::mp_number > (max) (void) throw() { return (boost::multiprecision::cpp_float::max)(); } - static const boost::multiprecision::mp_number > lowest (void) throw() { return boost::multiprecision::cpp_float::zero(); } - static const boost::multiprecision::mp_number > epsilon (void) throw() { return boost::multiprecision::cpp_float::eps(); } - static const boost::multiprecision::mp_number > round_error (void) throw() { return 0.5L; } - static const boost::multiprecision::mp_number > infinity (void) throw() { return boost::multiprecision::cpp_float::inf(); } - static const boost::multiprecision::mp_number > quiet_NaN (void) throw() { return boost::multiprecision::cpp_float::nan(); } - static const boost::multiprecision::mp_number > signaling_NaN(void) throw() { return boost::multiprecision::cpp_float::zero(); } - static const boost::multiprecision::mp_number > denorm_min (void) throw() { return boost::multiprecision::cpp_float::zero(); } + static const boost::multiprecision::mp_number > (min) (void) { return (boost::multiprecision::cpp_float::min)(); } + static const boost::multiprecision::mp_number > (max) (void) { return (boost::multiprecision::cpp_float::max)(); } + static const boost::multiprecision::mp_number > lowest (void) { return boost::multiprecision::cpp_float::zero(); } + static const boost::multiprecision::mp_number > epsilon (void) { return boost::multiprecision::cpp_float::eps(); } + static const boost::multiprecision::mp_number > round_error (void) { return 0.5L; } + static const boost::multiprecision::mp_number > infinity (void) { return boost::multiprecision::cpp_float::inf(); } + static const boost::multiprecision::mp_number > quiet_NaN (void) { return boost::multiprecision::cpp_float::nan(); } + static const boost::multiprecision::mp_number > signaling_NaN(void) { return boost::multiprecision::cpp_float::zero(); } + static const boost::multiprecision::mp_number > denorm_min (void) { return boost::multiprecision::cpp_float::zero(); } }; } diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index f4e98eaf..323325c2 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -129,7 +129,7 @@ void hyp0F0(T& H0F0, const T& x) x_pow_n_div_n_fact.negate(); } if(n >= 300) - throw std::runtime_error("H0F0 failed to converge"); + BOOST_THROW_EXCEPTION(std::runtime_error("H0F0 failed to converge")); } template @@ -178,7 +178,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x) break; } if(n >= std::numeric_limits >::digits + 10) - throw std::runtime_error("H1F0 failed to converge"); + BOOST_THROW_EXCEPTION(std::runtime_error("H1F0 failed to converge")); } template diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index d6119eaf..930dadcb 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -61,7 +61,7 @@ void hyp0F1(T& result, const T& b, const T& x) } if(n >= 300) - throw std::runtime_error("H0F1 Failed to Converge"); + BOOST_THROW_EXCEPTION(std::runtime_error("H0F1 Failed to Converge")); } @@ -407,7 +407,7 @@ void hyp2F1(T& result, const T& a, const T& b, const T& c, const T& x) break; } if(n > 300) - throw std::runtime_error("H2F1 failed to converge."); + BOOST_THROW_EXCEPTION(std::runtime_error("H2F1 failed to converge.")); } template diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index a076a565..975e7a0e 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -583,3 +583,4 @@ run test_fpclassify.cpp : test_fpclassify_cpp_float ; +run test_test.cpp ; \ No newline at end of file diff --git a/test/test.hpp b/test/test.hpp index 88836794..7999c896 100644 --- a/test/test.hpp +++ b/test/test.hpp @@ -5,6 +5,10 @@ #include #include +#include +#include +#include + template T relative_error(T a, T b) { @@ -41,4 +45,193 @@ T relative_error(T a, T b) return (std::max)(fabs((a-b)/a), fabs((a-b)/b)) / std::numeric_limits::epsilon(); } +enum +{ + warn_on_fail, + error_on_fail, + abort_on_fail +}; + +template +inline T epsilon_of(const T&) +{ + BOOST_STATIC_ASSERT(std::numeric_limits::is_specialized); + return std::numeric_limits::epsilon(); +} + +template +inline int digits_of(const T&) +{ + return std::numeric_limits::is_specialized ? std::numeric_limits::digits10 + 2 : std::numeric_limits::digits10 + 2; +} + +inline std::ostream& report_where(const char* file, int line, const char* function) +{ + if(function) + BOOST_LIGHTWEIGHT_TEST_OSTREAM << "In function: "<< function << std::endl; + BOOST_LIGHTWEIGHT_TEST_OSTREAM << file << ":" << line; + return BOOST_LIGHTWEIGHT_TEST_OSTREAM; +} + +#define BOOST_MP_REPORT_WHERE report_where(__FILE__, __LINE__, BOOST_CURRENT_FUNCTION) + +inline void report_severity(int severity) +{ + if(severity == error_on_fail) + ++boost::detail::test_errors(); + else if(severity == abort_on_fail) + { + ++boost::detail::test_errors(); + abort(); + } +} + +#define BOOST_MP_REPORT_SEVERITY(severity) report_severity(severity) + +template +void report_unexpected_exception(const E& e, int severity, const char* file, int line, const char* function) +{ + report_where(file, line, function) << " Unexpected exception of type " << typeid(e).name() << std::endl; + BOOST_LIGHTWEIGHT_TEST_OSTREAM << "Errot message was: " << e.what() << std::endl; + BOOST_MP_REPORT_SEVERITY(severity); +} + +#define BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) catch(const std::exception& e) { report_unexpected_exception(e, severity, __FILE__, __LINE__, BOOST_CURRENT_FUNCTION); } + + +#define BOOST_CHECK_IMP(x, severity)\ + try{ if(x){}else{\ + BOOST_MP_REPORT_WHERE << " Failed predicate: " << BOOST_STRINGIZE(x) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_CHECK(x) BOOST_CHECK_IMP(x, error_on_fail) +#define BOOST_WARN(x) BOOST_CHECK_IMP(x, warn_on_fail) +#define BOOST_REQUIRE(x) BOOST_CHECK_IMP(x, abort_on_fail) + +#define BOOST_CLOSE_IMP(x, y, tol, severity)\ + try{ if(relative_error(x, y) > tol){\ + BOOST_MP_REPORT_WHERE << " Failed check for closeness: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3)\ + << "Relative error was: " << relative_error(x, y) << "eps\n"\ + << "Tolerance was: " << tol << "eps" << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_EQUAL_IMP(x, y, severity)\ + try{ if(x != y){\ + BOOST_MP_REPORT_WHERE << " Failed check for equality: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_NE_IMP(x, y, severity)\ + try{ if(!(x != y)){\ + BOOST_MP_REPORT_WHERE << " Failed check for non-equality: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_LT_IMP(x, y, severity)\ + try{ if(!(x < y)){\ + BOOST_MP_REPORT_WHERE << " Failed check for less than: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_GT_IMP(x, y, severity)\ + try{ if(!(x > y)){\ + BOOST_MP_REPORT_WHERE << " Failed check for greater than: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_LE_IMP(x, y, severity)\ + try{ if(!(x <= y)){\ + BOOST_MP_REPORT_WHERE << " Failed check for less-than-equal-to: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_GE_IMP(x, y, severity)\ + try{ if(!(x >= y)){\ + BOOST_MP_REPORT_WHERE << " Failed check for greater-than-equal-to \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_MT_CHECK_THROW_IMP(x, E, severity)\ + try{ \ + x;\ + BOOST_MP_REPORT_WHERE << " Expected exception not thrown in expression " << BOOST_STRINGIZE(x) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + catch(const E&){}\ + BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_CHECK_CLOSE(x, y, tol) BOOST_CLOSE_IMP(x, y, ((tol / (100 * epsilon_of(x)))), error_on_fail) +#define BOOST_WARN_CLOSE(x, y, tol) BOOST_CLOSE_IMP(x, y, (tol / (100 * epsilon_of(x))), warn_on_fail) +#define BOOST_REQUIRE_CLOSE(x, y, tol) BOOST_CLOSE_IMP(x, y, (tol / (100 * epsilon_of(x))), abort_on_fail) + +#define BOOST_CHECK_CLOSE_FRACTION(x, y, tol) BOOST_CLOSE_IMP(x, y, ((tol / (epsilon_of(x)))), error_on_fail) +#define BOOST_WARN_CLOSE_FRACTION(x, y, tol) BOOST_CLOSE_IMP(x, y, (tol / (epsilon_of(x))), warn_on_fail) +#define BOOST_REQUIRE_CLOSE_FRACTION(x, y, tol) BOOST_CLOSE_IMP(x, y, (tol / (epsilon_of(x))), abort_on_fail) + +#define BOOST_CHECK_EQUAL(x, y) BOOST_EQUAL_IMP(x, y, error_on_fail) +#define BOOST_WARN_EQUAL(x, y) BOOST_EQUAL_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_EQUAL(x, y) BOOST_EQUAL_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_NE(x, y) BOOST_NE_IMP(x, y, error_on_fail) +#define BOOST_WARN_NE(x, y) BOOST_NE_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_NE(x, y) BOOST_NE_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_LT(x, y) BOOST_LT_IMP(x, y, error_on_fail) +#define BOOST_WARN_LT(x, y) BOOST_LT_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_LT(x, y) BOOST_LT_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_GT(x, y) BOOST_GT_IMP(x, y, error_on_fail) +#define BOOST_WARN_GT(x, y) BOOST_GT_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_GT(x, y) BOOST_GT_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_LE(x, y) BOOST_LE_IMP(x, y, error_on_fail) +#define BOOST_WARN_LE(x, y) BOOST_LE_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_LE(x, y) BOOST_LE_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_GE(x, y) BOOST_GE_IMP(x, y, error_on_fail) +#define BOOST_WARN_GE(x, y) BOOST_GE_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_GE(x, y) BOOST_GE_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_THROW(x, E) BOOST_MT_CHECK_THROW_IMP(x, E, error_on_fail) +#define BOOST_WARN_THROW(x, E) BOOST_MT_CHECK_THROW_IMP(x, E, warn_on_fail) +#define BOOST_REQUIRE_THROW(x, E) BOOST_MT_CHECK_THROW_IMP(x, E, abort_on_fail) + #endif diff --git a/test/test_fpclassify.cpp b/test/test_fpclassify.cpp index 374382a8..e3e28825 100644 --- a/test/test_fpclassify.cpp +++ b/test/test_fpclassify.cpp @@ -8,7 +8,7 @@ #include #include #include -#include +#include "test.hpp" #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 @@ -42,13 +42,6 @@ #pragma warning(disable: 4127) // conditional expression is constant #endif -#define BOOST_CHECK_EQUAL(x, y)\ - if(x != y)\ - {\ - BOOST_ERROR("Values were not equal.");\ - BOOST_LIGHTWEIGHT_TEST_OSTREAM << x << " != " << y << std::endl;\ - } - const char* method_name(const boost::math::detail::native_tag&) { return "Native"; diff --git a/test/test_round.cpp b/test/test_round.cpp index 6e56437f..4be856b1 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -9,12 +9,7 @@ #include #include #include - -#define BOOST_CHECK_THROW(x, EX)\ - try { x; BOOST_ERROR("Expected exception not thrown"); } \ - catch(const EX&){}\ - catch(...){ BOOST_ERROR("Incorrect exception type thrown"); } - +#include "test.hpp" #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) # define TEST_MPF_50 diff --git a/test/test_test.cpp b/test/test_test.cpp new file mode 100644 index 00000000..3d0b207d --- /dev/null +++ b/test/test_test.cpp @@ -0,0 +1,85 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "test.hpp" +#include + +void proc_that_throws() +{ + throw std::runtime_error(""); +} + +int main() +{ + boost::multiprecision::cpp_float_50 a1(1), a2(1), b(3), c(-2); + + BOOST_WARN(a1); + BOOST_WARN(a1 == b); + BOOST_CHECK(a1); + BOOST_CHECK(a1 == b); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + boost::multiprecision::cpp_float_50 a_tol = a1 + a1 * 100 * std::numeric_limits::epsilon(); + boost::multiprecision::cpp_float_50 tol = 100 * std::numeric_limits::epsilon(); + + BOOST_CHECK_CLOSE(a1, a_tol, tol * 102); // Passes + BOOST_WARN_CLOSE(a1, a_tol, tol * 98); // fails + BOOST_CHECK_CLOSE(a1, a_tol, tol * 98); // fails + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_CLOSE_FRACTION(a1, a_tol, tol * 1.02); // Passes + BOOST_WARN_CLOSE_FRACTION(a1, a_tol, tol * 0.98); // fails + BOOST_CHECK_CLOSE_FRACTION(a1, a_tol, tol * 0.98); // fails + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_EQUAL(a1, a2); + BOOST_WARN_EQUAL(a1, b); + BOOST_CHECK_EQUAL(a1, b); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_NE(a1, b); + BOOST_WARN_NE(a1, a2); + BOOST_CHECK_NE(a1, a2); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_GT(a1, c); + BOOST_WARN_GT(a1, a2); + BOOST_CHECK_GT(a1, a2); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_LT(a1, b); + BOOST_WARN_LT(a1, a2); + BOOST_CHECK_LT(a1, a2); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_GE(a1, a2); + BOOST_CHECK_GE(a1, c); + BOOST_WARN_GE(a1, b); + BOOST_CHECK_GE(a1, b); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_LE(a1, a2); + BOOST_CHECK_LE(a1, b); + BOOST_WARN_LE(a1, c); + BOOST_CHECK_LE(a1, c); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_THROW(proc_that_throws(), std::runtime_error); + BOOST_CHECK_THROW(a1+b+c, std::runtime_error); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + return boost::report_errors(); +} + From cd31fbde7ae3d646004429fde98fbc95cf4c3a07 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 17 Nov 2011 18:08:51 +0000 Subject: [PATCH 067/256] Fix operator>> for mp_number. Add template inter-conversions on cpp_float. Adjust precision of test reporting. [SVN r75520] --- include/boost/multiprecision/cpp_float.hpp | 26 ++++++++++++++++++++++ include/boost/multiprecision/mp_number.hpp | 4 +++- test/test.hpp | 2 +- 3 files changed, 30 insertions(+), 2 deletions(-) diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 28db0a82..19e5d588 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -163,6 +163,18 @@ public: fpclass (f.fpclass), prec_elem(f.prec_elem) { } + template + cpp_float(const cpp_float& f) : + exp (f.exp), + neg (f.neg), + fpclass (static_cast(static_cast(f.fpclass))), + prec_elem(mp_elem_number) + { + // TODO: this doesn't round! + std::copy_n(f.data.begin(), std::min(f.prec_elem, prec_elem), data.begin()); + precision(std::min(f.prec_elem, prec_elem)); + } + template cpp_float(const F val, typename enable_if >::type* = 0): data(), @@ -299,6 +311,16 @@ public: prec_elem = v.prec_elem; return *this; } + template + cpp_float& operator=(const cpp_float& f) + { + exp = f.exp; + neg = f.neg; + fpclass = static_cast(static_cast(f.fpclass)); + std::copy_n(f.data.begin(), std::min(f.prec_elem, prec_elem), data.begin()); + precision(std::min(f.prec_elem, prec_elem)); + return *this; + } cpp_float& operator= (long long v) { if(v < 0) @@ -481,6 +503,10 @@ private: static boost::uint32_t div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); bool rd_string(const char* const s); + + template + friend class cpp_float; + }; template diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index ff11fb42..6c92093b 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -1529,7 +1529,9 @@ inline typename boost::enable_if, bool>: template inline std::ostream& operator << (std::ostream& os, const mp_number& r) { - return os << r.str(static_cast(os.precision(), os.flags() & os.scientific)); + unsigned d = os.precision(); + bool b = os.flags() & os.scientific; + return os << r.str(d, b); } namespace detail{ diff --git a/test/test.hpp b/test/test.hpp index 7999c896..d44af84f 100644 --- a/test/test.hpp +++ b/test/test.hpp @@ -116,7 +116,7 @@ void report_unexpected_exception(const E& e, int severity, const char* file, int << std::setprecision(digits_of(x)) << std::scientific\ << "Value of LHS was: " << x << "\n"\ << "Value of RHS was: " << y << "\n"\ - << std::setprecision(3)\ + << std::setprecision(5) << std::fixed\ << "Relative error was: " << relative_error(x, y) << "eps\n"\ << "Tolerance was: " << tol << "eps" << std::endl;\ BOOST_MP_REPORT_SEVERITY(severity);\ From ecead4525a8ab5a5bab55ea9ef4de839c51c77eb Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 21 Nov 2011 09:52:32 +0000 Subject: [PATCH 068/256] Suppress MSVC warnings in tests. Add support for std::ios_base::fmtflags in string formatting. Fix the errors that result from above change! [SVN r75586] --- .../multiprecision/arithmetic_backend.hpp | 16 +- .../concepts/mp_number_architypes.hpp | 17 +- include/boost/multiprecision/cpp_float.hpp | 42 +++-- .../multiprecision/detail/default_ops.hpp | 4 +- .../detail/functions/constants.hpp | 6 +- .../multiprecision/detail/functions/pow.hpp | 8 +- .../multiprecision/detail/functions/trig.hpp | 8 +- .../multiprecision/detail/mp_number_base.hpp | 8 + include/boost/multiprecision/gmp.hpp | 87 ++++++++--- include/boost/multiprecision/mp_number.hpp | 34 ++-- include/boost/multiprecision/mpfr.hpp | 49 +++--- include/boost/multiprecision/tommath.hpp | 145 ++++++++++++------ test/mp_number_concept_check.cpp | 2 +- test/test.hpp | 1 + test/test_acos.cpp | 4 + test/test_arithmetic.cpp | 22 ++- test/test_asin.cpp | 4 + test/test_atan.cpp | 4 + test/test_cos.cpp | 4 + test/test_cosh.cpp | 4 + test/test_exp.cpp | 4 + test/test_fpclassify.cpp | 4 + test/test_gmp_conversions.cpp | 4 + test/test_log.cpp | 4 + test/test_mpfr_conversions.cpp | 4 + test/test_numeric_limits.cpp | 4 + test/test_pow.cpp | 4 + test/test_round.cpp | 4 + test/test_sin.cpp | 4 + test/test_sinh.cpp | 4 + test/test_sqrt.cpp | 4 + test/test_tanh.cpp | 4 + test/test_test.cpp | 4 + 33 files changed, 361 insertions(+), 160 deletions(-) diff --git a/include/boost/multiprecision/arithmetic_backend.hpp b/include/boost/multiprecision/arithmetic_backend.hpp index 88098dab..b213c819 100644 --- a/include/boost/multiprecision/arithmetic_backend.hpp +++ b/include/boost/multiprecision/arithmetic_backend.hpp @@ -8,6 +8,7 @@ #include #include +#include #include #include #include @@ -62,9 +63,12 @@ struct arithmetic_backend { std::swap(m_value, o.m_value); } - std::string str(unsigned digits, bool scientific)const + std::string str(std::streamsize digits, std::ios_base::fmtflags f)const { - return boost::lexical_cast(m_value); + std::stringstream ss; + ss.flags(f); + ss << std::setprecision(digits) << m_data; + return ss.str(); } void negate() { @@ -118,10 +122,6 @@ inline void divide(arithmetic_backend& result, const arithmetic_back namespace std{ -#ifdef BOOST_NO_NOEXCEPT -# define BOOST_MP_NOEXCEPT -#endif - template class numeric_limits > > : public std::numeric_limits { @@ -139,10 +139,6 @@ public: BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } }; -#ifdef BOOST_NO_NOEXCEPT -# undef BOOST_MP_NOEXCEPT -#endif - } #endif diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index 18a4b85c..d8380e93 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -74,20 +74,19 @@ struct mp_number_backend_float_architype std::cout << "Swapping (" << m_value << " with " << o.m_value << ")" << std::endl; std::swap(m_value, o.m_value); } - std::string str(unsigned digits, bool scientific)const + std::string str(std::streamsize digits, std::ios_base::fmtflags f)const { std::stringstream ss; - if(scientific) - ss.setf(ss.scientific); + ss.flags(f); if(digits) ss.precision(digits); else ss.precision(std::numeric_limits::digits10 + 2); boost::intmax_t i = m_value; boost::uintmax_t u = m_value; - if(!scientific && m_value == i) + if(!(f & std::ios_base::scientific) && m_value == i) ss << i; - else if(!scientific && m_value == u) + else if(!(f & std::ios_base::scientific) && m_value == u) ss << u; else ss << m_value; @@ -193,10 +192,6 @@ typedef boost::multiprecision::mp_number mp_n namespace std{ -#ifdef BOOST_NO_NOEXCEPT -# define BOOST_MP_NOEXCEPT -#endif - template <> class numeric_limits : public std::numeric_limits { @@ -214,10 +209,6 @@ public: BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } }; -#ifdef BOOST_NO_NOEXCEPT -# undef BOOST_MP_NOEXCEPT -#endif - } #ifdef BOOST_MSVC diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 19e5d588..38b527c1 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -171,7 +171,7 @@ public: prec_elem(mp_elem_number) { // TODO: this doesn't round! - std::copy_n(f.data.begin(), std::min(f.prec_elem, prec_elem), data.begin()); + std::copy(f.data.begin(), f.data.begin() + std::min(f.prec_elem, prec_elem), data.begin()); precision(std::min(f.prec_elem, prec_elem)); } @@ -317,7 +317,7 @@ public: exp = f.exp; neg = f.neg; fpclass = static_cast(static_cast(f.fpclass)); - std::copy_n(f.data.begin(), std::min(f.prec_elem, prec_elem), data.begin()); + std::copy(f.data.begin(), f.data.begin() + std::min(f.prec_elem, prec_elem), data.begin()); precision(std::min(f.prec_elem, prec_elem)); return *this; } @@ -396,7 +396,7 @@ public: return *this -= one(); } - std::string str(unsigned digits, bool scientific)const; + std::string str(std::streamsize digits, std::ios_base::fmtflags f)const; int compare(const cpp_float& v)const; template @@ -1460,7 +1460,7 @@ double cpp_float::extract_double(void) const std::stringstream ss; - ss << str(std::numeric_limits::digits10 + (2 + 1), true); + ss << str(std::numeric_limits::digits10 + (2 + 1), std::ios_base::scientific); double d; ss >> d; @@ -1506,7 +1506,7 @@ long double cpp_float::extract_long_double(void) const std::stringstream ss; - ss << str(std::numeric_limits::digits10 + (2 + 1), true); + ss << str(std::numeric_limits::digits10 + (2 + 1), std::ios_base::scientific); long double ld; ss >> ld; @@ -1639,8 +1639,12 @@ cpp_float cpp_float::extract_integer_part(void) const } template -std::string cpp_float::str(std::size_t number_of_digits, bool scientific) const +std::string cpp_float::str(std::streamsize number_of_digits, std::ios_base::fmtflags f) const { + bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; + bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; + bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; + std::string str; boost::int64_t my_exp = order(); if(number_of_digits == 0) @@ -1665,13 +1669,13 @@ std::string cpp_float::str(std::size_t number_of_digits, bool scientif } // Cut the output to the size of the precision. - if(str.length() > number_of_digits) + if(str.length() > static_cast(number_of_digits)) { // Get the digit after the last needed digit for rounding - const boost::uint32_t round = static_cast(static_cast(str.at(number_of_digits)) - static_cast('0')); + const boost::uint32_t round = static_cast(static_cast(str[static_cast(number_of_digits)]) - static_cast('0')); // Truncate the string - str = str.substr(static_cast(0u), number_of_digits); + str.erase(static_cast(number_of_digits)); if(round >= static_cast(5u)) { @@ -1716,18 +1720,30 @@ std::string cpp_float::str(std::size_t number_of_digits, bool scientif str.erase(pos, str.end()); if(str.empty()) str = '0'; - if(!scientific && (str.size() < 20) && (my_exp >= 0) && (my_exp < 20)) + if(fixed || (!scientific && (str.size() < 20) && (my_exp >= -3) && (my_exp < 20))) { if(1 + my_exp > str.size()) { // Just pad out the end with zeros: str.append(static_cast(1 + my_exp - str.size()), '0'); + if(showpoint) + str.append(".0"); } else if(my_exp + 1 != str.size()) { - // Insert the decimal point: - str.insert(static_cast(my_exp + 1), 1, '.'); + if(my_exp < 0) + { + str.insert(0, static_cast(-1-my_exp), '0'); + str.insert(0, "0."); + } + else + { + // Insert the decimal point: + str.insert(static_cast(my_exp + 1), 1, '.'); + } } + else if(showpoint) + str += ".0"; } else { @@ -2711,7 +2727,7 @@ namespace std static const bool is_bounded = true; static const bool is_modulo = false; static const bool is_iec559 = false; - static const int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); + static const int digits = Digits10; static const int digits10 = boost::multiprecision::cpp_float::cpp_float_digits10; static const int max_digits10 = boost::multiprecision::cpp_float::cpp_float_max_digits10; static const boost::int64_t min_exponent = boost::multiprecision::cpp_float::cpp_float_min_exp; // Type differs from int. diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 917a99e2..e6b18a7a 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -19,7 +19,7 @@ #define INSTRUMENT_BACKEND(x) #else #define INSTRUMENT_BACKEND(x)\ - std::cout << BOOST_STRINGIZE(x) << " = " << x.str(0, true) << std::endl; + std::cout << BOOST_STRINGIZE(x) << " = " << x.str(0, std::ios_base::scientific) << std::endl; #endif #endif @@ -339,7 +339,7 @@ inline void convert_to(terminal* result, const B& backend) // We ran out of types to try for the convertion, try // a lexical_cast and hope for the best: // - result->value = boost::lexical_cast(backend.str(0, false)); + result->value = boost::lexical_cast(backend.str(0, std::ios_base::fmtflags(0))); } // diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp index 56bb4716..d8fc9966 100644 --- a/include/boost/multiprecision/detail/functions/constants.hpp +++ b/include/boost/multiprecision/detail/functions/constants.hpp @@ -146,7 +146,7 @@ const T& get_constant_ln2() static bool b = false; if(!b) { - calc_log2(result, std::numeric_limits >::digits); + calc_log2(result, boost::multiprecision::detail::digits2 >::value); b = true; } @@ -162,7 +162,7 @@ const T& get_constant_e() static bool b = false; if(!b) { - calc_e(result, std::numeric_limits >::digits); + calc_e(result, boost::multiprecision::detail::digits2 >::value); b = true; } @@ -178,7 +178,7 @@ const T& get_constant_pi() static bool b = false; if(!b) { - calc_pi(result, std::numeric_limits >::digits); + calc_pi(result, boost::multiprecision::detail::digits2 >::value); b = true; } diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 323325c2..3883d938 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -100,7 +100,7 @@ void hyp0F0(T& H0F0, const T& x) typedef typename mpl::front::type ui_type; BOOST_ASSERT(&H0F0 != &x); - long tol = std::numeric_limits >::digits; + long tol = boost::multiprecision::detail::digits2 >::value; T t; T x_pow_n_div_n_fact(x); @@ -156,7 +156,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x) multiply(H1F0, pochham_a, x_pow_n_div_n_fact); add(H1F0, si_type(1)); T lim; - eval_ldexp(lim, H1F0, 1 - std::numeric_limits >::digits); + eval_ldexp(lim, H1F0, 1 - boost::multiprecision::detail::digits2 >::value); if(get_sign(lim) < 0) lim.negate(); @@ -164,7 +164,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x) T term, part; // Series expansion of hyperg_1f0(a; ; x). - for(n = 2; n < std::numeric_limits >::digits + 10; n++) + for(n = 2; n < boost::multiprecision::detail::digits2 >::value + 10; n++) { multiply(x_pow_n_div_n_fact, x); divide(x_pow_n_div_n_fact, n); @@ -177,7 +177,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x) if(lim.compare(term) >= 0) break; } - if(n >= std::numeric_limits >::digits + 10) + if(n >= boost::multiprecision::detail::digits2 >::value + 10) BOOST_THROW_EXCEPTION(std::runtime_error("H1F0 failed to converge")); } diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index 930dadcb..d466b84c 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -36,7 +36,7 @@ void hyp0F1(T& result, const T& b, const T& x) T tol; tol = ui_type(1); - eval_ldexp(tol, tol, 1 - std::numeric_limits >::digits); + eval_ldexp(tol, tol, 1 - boost::multiprecision::detail::digits2 >::value); multiply(tol, result); if(get_sign(tol) < 0) tol.negate(); @@ -375,7 +375,7 @@ void hyp2F1(T& result, const T& a, const T& b, const T& c, const T& x) add(result, ui_type(1)); T lim; - eval_ldexp(lim, result, 1 - std::numeric_limits >::digits); + eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value); if(get_sign(lim) < 0) lim.negate(); @@ -507,7 +507,7 @@ void eval_asin(T& result, const T& x) subtract(result, s); T lim; - eval_ldexp(lim, result, 1 - std::numeric_limits >::digits); + eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value); if(get_sign(s) < 0) s.negate(); if(get_sign(lim) < 0) @@ -751,7 +751,7 @@ template typename disable_if >::type eval_atan2(T& result, const T& a, const Arithmetic& b) { T x; - x = b; + x = static_cast::type>(b); eval_atan2(result, a, x); } diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index ca9cc5e9..e4c9a619 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -337,6 +337,14 @@ private: typename mp_exp_storage::type arg3; }; +template +struct digits2 +{ + BOOST_STATIC_ASSERT(std::numeric_limits::is_specialized); + BOOST_STATIC_ASSERT((std::numeric_limits::radix == 2) || (std::numeric_limits::radix == 10)); + static const long value = std::numeric_limits::radix == 10 ? (((std::numeric_limits::digits + 1) * 1000L) / 301L) : std::numeric_limits::digits; +}; + } // namespace detail // diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 80153bed..56ade6a2 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -159,30 +159,48 @@ struct gmp_float_imp { mpf_swap(m_data, o.m_data); } - std::string str(unsigned digits, bool scientific)const + std::string str(std::streamsize digits, std::ios_base::fmtflags f)const { + bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; + bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; + bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; + std::string result; mp_exp_t e; void *(*alloc_func_ptr) (size_t); void *(*realloc_func_ptr) (void *, size_t, size_t); void (*free_func_ptr) (void *, size_t); - const char* ps = mpf_get_str (0, &e, 10, digits, m_data); + const char* ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); std::ptrdiff_t sl = std::strlen(ps); if(sl == 0) return "0"; if(*ps == '-') --sl; // number of digits excluding sign. - if(!scientific - && (sl <= std::numeric_limits::digits10 + 1) - && (e >= sl) - && (sl <= std::numeric_limits::digits10 + 1)) + result = ps; + if(fixed || (!scientific && (e > -4) && (e <= std::numeric_limits::digits10 + 2))) { - result = ps; - result.append(e-sl, '0'); + if(1 + e >= sl) + { + result.append(e - sl, '0'); + if(showpoint) + result.append(".0"); + } + else + { + if(e <= 0) + { + result.insert(0, -e, '0'); + result.insert(0, "0."); + } + else + { + // Insert the decimal point: + result.insert(e, 1, '.'); + } + } } else { - result = ps; if(ps[0] == '-') result.insert(2, 1, '.'); else @@ -920,7 +938,26 @@ struct gmp_int } gmp_int& operator = (const char* s) { - mpz_set_str(m_data, s, 10); + std::size_t n = s ? std::strlen(s) : 0; + int radix = 10; + if(n && (*s == '0')) + { + if((n > 1) && ((s[1] == 'x') || (s[1] == 'X'))) + { + radix = 16; + s +=2; + n -= 2; + } + else + { + radix = 8; + n -= 1; + } + } + if(n) + mpz_set_str(m_data, s, radix); + else + mpz_set_ui(m_data, 0); return *this; } gmp_int& operator=(const mpf_t& val) @@ -949,15 +986,30 @@ struct gmp_int { mpz_swap(m_data, o.m_data); } - std::string str(unsigned /*digits*/, bool /*scientific*/)const + std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const { + int base = 10; + if((f & std::ios_base::oct) == std::ios_base::oct) + base = 8; + else if((f & std::ios_base::hex) == std::ios_base::hex) + base = 16; void *(*alloc_func_ptr) (size_t); void *(*realloc_func_ptr) (void *, size_t, size_t); void (*free_func_ptr) (void *, size_t); - const char* ps = mpz_get_str (0, 10, m_data); + const char* ps = mpz_get_str (0, base, m_data); std::string s = ps; mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); + + if((base != 10) && (f & std::ios_base::showbase)) + { + int pos = s[0] == '-' ? 1 : 0; + const char* pp = base == 8 ? "0" : "0x"; + s.insert(pos, pp); + } + if((f & std::ios_base::showpos) && (s[0] != '-')) + s.insert(0, 1, '+'); + return s; } ~gmp_int() @@ -1443,8 +1495,9 @@ struct gmp_rational { mpq_swap(m_data, o.m_data); } - std::string str(unsigned /*digits*/, bool /*scientific*/)const + std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const { + // TODO make a better job of this including handling of f!! void *(*alloc_func_ptr) (size_t); void *(*realloc_func_ptr) (void *, size_t, size_t); void (*free_func_ptr) (void *, size_t); @@ -1655,10 +1708,6 @@ typedef mp_number mpq_rational; namespace std{ -#ifdef BOOST_NO_NOEXCEPT -# define BOOST_MP_NOEXCEPT -#endif - // // numeric_limits [partial] specializations for the types declared in this header: // @@ -1906,10 +1955,6 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -#ifdef BOOST_NO_NOEXCEPT -# undef BOOST_MP_NOEXCEPT -#endif - } // namespace std #endif diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 6c92093b..71aa1fc6 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -446,9 +446,9 @@ public: // // String conversion functions: // - std::string str(unsigned digits = 0, bool scientific = true)const + std::string str(std::streamsize digits = 0, std::ios_base::fmtflags f = std::ios_base::fmtflags(0))const { - return m_backend.str(digits, scientific); + return m_backend.str(digits, f); } template T convert_to()const @@ -981,7 +981,7 @@ private: template void do_assign_function_1(const F& f, const Exp& val, const detail::terminal&) { - f(m_backend, canonical_value(val.value())); + f(m_backend, function_arg_value(val.value())); } template void do_assign_function_1(const F& f, const Exp& val, const Tag&) @@ -1001,19 +1001,19 @@ private: template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const detail::terminal&) { - f(m_backend, canonical_value(val1.value()), canonical_value(val2.value())); + f(m_backend, function_arg_value(val1.value()), function_arg_value(val2.value())); } template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const detail::terminal&) { self_type temp1(val1); - f(m_backend, temp1.backend(), canonical_value(val2.value())); + f(m_backend, temp1.backend(), function_arg_value(val2.value())); } template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const Tag2&) { self_type temp2(val2); - f(m_backend, canonical_value(val1.value()), temp2.backend()); + f(m_backend, function_arg_value(val1.value()), temp2.backend()); } template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const Tag2&) @@ -1384,12 +1384,13 @@ private: bool is_floatly_self(const self_type& v)const { return &v == this; } static const Backend& canonical_value(const self_type& v){ return v.m_backend; } - //static const Backend& canonical_value(const self_type* v){ return v->m_backend; } - //static const Backend& canonical_value(self_type* v){ return v->m_backend; } - //static const Backend& canonical_value(self_type& v){ return v.m_backend; } template static typename detail::canonical::type canonical_value(const V& v){ return v; } static typename detail::canonical::type canonical_value(const std::string& v){ return v.c_str(); } + + static const Backend& function_arg_value(const self_type& v) { return v.backend(); } + template + static const V& function_arg_value(const V& v) { return v; } Backend m_backend; }; @@ -1529,9 +1530,18 @@ inline typename boost::enable_if, bool>: template inline std::ostream& operator << (std::ostream& os, const mp_number& r) { - unsigned d = os.precision(); - bool b = os.flags() & os.scientific; - return os << r.str(d, b); + std::streamsize d = os.precision(); + std::string s = r.str(d, os.flags()); + std::streamsize ss = os.width(); + if(ss > static_cast(s.size())) + { + char fill = os.fill(); + if((os.flags() & std::ios_base::left) == std::ios_base::left) + s.append(static_cast(ss - s.size()), fill); + else + s.insert(0, static_cast(ss - s.size()), fill); + } + return os << s; } namespace detail{ diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 08ef8a92..1eae2c7d 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -156,32 +156,51 @@ struct mpfr_float_imp { mpfr_swap(m_data, o.m_data); } - std::string str(unsigned digits, bool scientific)const + std::string str(std::streamsize digits, std::ios_base::fmtflags f)const { + bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; + bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; + bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; + std::string result; mp_exp_t e; - char* ps = mpfr_get_str (0, &e, 10, digits, m_data, GMP_RNDN); + char* ps = mpfr_get_str (0, &e, 10, static_cast(digits), m_data, GMP_RNDN); std::ptrdiff_t sl = std::strlen(ps); - unsigned chars = sl; + int chars = sl; if(sl == 0) return "0"; while(ps[chars-1] == '0') --chars; + ps[chars] = 0; if(*ps == '-') --chars; // number of digits excluding sign. if(chars == 0) - return "0"; - if(!scientific - && (chars <= std::numeric_limits::digits10 + 1) - && (e >= (int)chars) - && (chars <= std::numeric_limits::digits10 + 1)) + return scientific ? "0.0e0" : showpoint ? "0.0" : "0"; + result = ps; + if(fixed || (!scientific && (e > -4) && (e <= std::numeric_limits::digits10 + 2))) { - result.assign(ps, (*ps == '-' ? chars+1 : chars)); - result.append(e-chars, '0'); + if(e >= chars) + { + result.append(e - chars, '0'); + if(showpoint) + result.append(".0"); + } + else + { + if(e <= 0) + { + result.insert(0, -e, '0'); + result.insert(0, "0."); + } + else + { + // Insert the decimal point: + result.insert(e, 1, '.'); + } + } } else { - result = ps; if(ps[0] == '-') result.insert(2, 1, '.'); else @@ -966,10 +985,6 @@ struct lanczos signed_types; @@ -26,15 +38,15 @@ struct tommath_int tommath_int() { - mp_init(&m_data); + detail::check_tommath_result(mp_init(&m_data)); } tommath_int(const tommath_int& o) { - mp_init_copy(&m_data, const_cast<::mp_int*>(&o.m_data)); + detail::check_tommath_result(mp_init_copy(&m_data, const_cast<::mp_int*>(&o.m_data))); } tommath_int& operator = (const tommath_int& o) { - mp_copy(const_cast<::mp_int*>(&o.m_data), &m_data); + detail::check_tommath_result(mp_copy(const_cast<::mp_int*>(&o.m_data), &m_data)); return *this; } tommath_int& operator = (boost::uintmax_t i) @@ -42,14 +54,14 @@ struct tommath_int boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; ::mp_int t; - mp_init(&t); + detail::check_tommath_result(mp_init(&t)); mp_zero(&m_data); while(i) { - mp_set_int(&t, static_cast(i & mask)); + detail::check_tommath_result(mp_set_int(&t, static_cast(i & mask))); if(shift) - mp_mul_2d(&t, shift, &t); - mp_add(&m_data, &t, &m_data); + detail::check_tommath_result(mp_mul_2d(&t, shift, &t)); + detail::check_tommath_result((mp_add(&m_data, &t, &m_data))); shift += std::numeric_limits::digits; i >>= std::numeric_limits::digits; } @@ -61,12 +73,12 @@ struct tommath_int bool neg = i < 0; *this = static_cast(std::abs(i)); if(neg) - mp_neg(&m_data, &m_data); + detail::check_tommath_result(mp_neg(&m_data, &m_data)); return *this; } tommath_int& operator = (unsigned long i) { - mp_set_int(&m_data, i); + detail::check_tommath_result((mp_set_int(&m_data, i))); return *this; } tommath_int& operator = (long i) @@ -74,7 +86,7 @@ struct tommath_int bool neg = i < 0; *this = static_cast(std::abs(i)); if(neg) - mp_neg(&m_data, &m_data); + detail::check_tommath_result(mp_neg(&m_data, &m_data)); return *this; } tommath_int& operator = (long double a) @@ -84,12 +96,12 @@ struct tommath_int using std::floor; if (a == 0) { - mp_set_int(&m_data, 0); + detail::check_tommath_result(mp_set_int(&m_data, 0)); return *this; } if (a == 1) { - mp_set_int(&m_data, 1); + detail::check_tommath_result(mp_set_int(&m_data, 1)); return *this; } @@ -98,9 +110,9 @@ struct tommath_int int e; long double f, term; - mp_init_set_int(&m_data, 0u); + detail::check_tommath_result(mp_init_set_int(&m_data, 0u)); ::mp_int t; - mp_init(&t); + detail::check_tommath_result(mp_init(&t)); f = frexp(a, &e); @@ -112,40 +124,73 @@ struct tommath_int f = ldexp(f, shift); term = floor(f); e -= shift; - mp_mul_2d(&m_data, shift, &m_data); + detail::check_tommath_result(mp_mul_2d(&m_data, shift, &m_data)); if(term > 0) { - mp_set_int(&t, static_cast(term)); - mp_add(&m_data, &t, &m_data); + detail::check_tommath_result(mp_set_int(&t, static_cast(term))); + detail::check_tommath_result(mp_add(&m_data, &t, &m_data)); } else { - mp_set_int(&t, static_cast(-term)); - mp_sub(&m_data, &t, &m_data); + detail::check_tommath_result(mp_set_int(&t, static_cast(-term))); + detail::check_tommath_result(mp_sub(&m_data, &t, &m_data)); } f -= term; } if(e > 0) - mp_mul_2d(&m_data, e, &m_data); + detail::check_tommath_result(mp_mul_2d(&m_data, e, &m_data)); else if(e < 0) { tommath_int t2; - mp_div_2d(&m_data, -e, &m_data, &t2.data()); + detail::check_tommath_result(mp_div_2d(&m_data, -e, &m_data, &t2.data())); } return *this; } tommath_int& operator = (const char* s) { - mp_read_radix(&m_data, s, 10); + std::size_t n = s ? std::strlen(s) : 0; + int radix = 10; + if(n && (*s == '0')) + { + if((n > 1) && ((s[1] == 'x') || (s[1] == 'X'))) + { + radix = 16; + s +=2; + n -= 2; + } + else + { + radix = 8; + n -= 1; + } + } + if(n) + detail::check_tommath_result(mp_read_radix(&m_data, s, 10)); + else + detail::check_tommath_result(mp_set_int(&m_data, 0)); return *this; } - std::string str(unsigned /*digits*/, bool /*scientific*/)const + std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const { + int base = 10; + if((f & std::ios_base::oct) == std::ios_base::oct) + base = 8; + else if((f & std::ios_base::hex) == std::ios_base::hex) + base = 16; int s; - mp_radix_size(const_cast<::mp_int*>(&m_data), 10, &s); + detail::check_tommath_result(mp_radix_size(const_cast<::mp_int*>(&m_data), 10, &s)); boost::scoped_array a(new char[s+1]); - mp_toradix_n(const_cast<::mp_int*>(&m_data), a.get(), 10, s+1); - return a.get(); + detail::check_tommath_result(mp_toradix_n(const_cast<::mp_int*>(&m_data), a.get(), base, s+1)); + std::string result = a.get(); + if((base != 10) && (f & std::ios_base::showbase)) + { + int pos = result[0] == '-' ? 1 : 0; + const char* pp = base == 8 ? "0" : "0x"; + result.insert(pos, pp); + } + if((f & std::ios_base::showpos) && (result[0] != '-')) + result.insert(0, 1, '+'); + return result; } ~tommath_int() { @@ -164,7 +209,7 @@ struct tommath_int { tommath_int d; tommath_int t(*this); - mp_shrink(&t.data()); + detail::check_tommath_result(mp_shrink(&t.data())); d = v; return t.compare(d); } @@ -182,114 +227,114 @@ int get_sign(const tommath_int& val); inline void add(tommath_int& t, const tommath_int& o) { - mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); + detail::check_tommath_result(mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); } inline void subtract(tommath_int& t, const tommath_int& o) { - mp_sub(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); + detail::check_tommath_result(mp_sub(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); } inline void multiply(tommath_int& t, const tommath_int& o) { - mp_mul(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); + detail::check_tommath_result(mp_mul(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); } inline void divide(tommath_int& t, const tommath_int& o) { tommath_int temp; - mp_div(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data(), &temp.data()); + detail::check_tommath_result(mp_div(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data(), &temp.data())); } inline void modulus(tommath_int& t, const tommath_int& o) { bool neg = get_sign(t) < 0; bool neg2 = get_sign(o) < 0; - mp_mod(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); + detail::check_tommath_result(mp_mod(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); if(neg != neg2) { t.negate(); - mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); + detail::check_tommath_result(mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); t.negate(); } } template inline void left_shift(tommath_int& t, UI i) { - mp_mul_2d(&t.data(), static_cast(i), &t.data()); + detail::check_tommath_result(mp_mul_2d(&t.data(), static_cast(i), &t.data())); } template inline void right_shift(tommath_int& t, UI i) { tommath_int d; - mp_div_2d(&t.data(), static_cast(i), &t.data(), &d.data()); + detail::check_tommath_result(mp_div_2d(&t.data(), static_cast(i), &t.data(), &d.data())); } template inline void left_shift(tommath_int& t, const tommath_int& v, UI i) { - mp_mul_2d(const_cast<::mp_int*>(&v.data()), static_cast(i), &t.data()); + detail::check_tommath_result(mp_mul_2d(const_cast<::mp_int*>(&v.data()), static_cast(i), &t.data())); } template inline void right_shift(tommath_int& t, const tommath_int& v, UI i) { tommath_int d; - mp_div_2d(const_cast<::mp_int*>(&v.data()), static_cast(i), &t.data(), &d.data()); + detail::check_tommath_result(mp_div_2d(const_cast<::mp_int*>(&v.data()), static_cast(i), &t.data(), &d.data())); } inline void bitwise_and(tommath_int& result, const tommath_int& v) { - mp_and(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data()); + detail::check_tommath_result(mp_and(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data())); } inline void bitwise_or(tommath_int& result, const tommath_int& v) { - mp_or(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data()); + detail::check_tommath_result(mp_or(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data())); } inline void bitwise_xor(tommath_int& result, const tommath_int& v) { - mp_xor(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data()); + detail::check_tommath_result(mp_xor(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data())); } inline void add(tommath_int& t, const tommath_int& p, const tommath_int& o) { - mp_add(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data()); + detail::check_tommath_result(mp_add(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data())); } inline void subtract(tommath_int& t, const tommath_int& p, const tommath_int& o) { - mp_sub(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data()); + detail::check_tommath_result(mp_sub(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data())); } inline void multiply(tommath_int& t, const tommath_int& p, const tommath_int& o) { - mp_mul(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data()); + detail::check_tommath_result(mp_mul(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data())); } inline void divide(tommath_int& t, const tommath_int& p, const tommath_int& o) { tommath_int d; - mp_div(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data(), &d.data()); + detail::check_tommath_result(mp_div(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data(), &d.data())); } inline void modulus(tommath_int& t, const tommath_int& p, const tommath_int& o) { bool neg = get_sign(p) < 0; bool neg2 = get_sign(o) < 0; - mp_mod(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data()); + detail::check_tommath_result(mp_mod(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data())); if(neg != neg2) { t.negate(); - mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data()); + detail::check_tommath_result(mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); t.negate(); } } inline void bitwise_and(tommath_int& result, const tommath_int& u, const tommath_int& v) { - mp_and(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data()); + detail::check_tommath_result(mp_and(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data())); } inline void bitwise_or(tommath_int& result, const tommath_int& u, const tommath_int& v) { - mp_or(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data()); + detail::check_tommath_result(mp_or(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data())); } inline void bitwise_xor(tommath_int& result, const tommath_int& u, const tommath_int& v) { - mp_xor(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data()); + detail::check_tommath_result(mp_xor(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data())); } inline void complement(tommath_int& result, const tommath_int& u) @@ -344,7 +389,7 @@ inline void convert_to(signed char* result, const tommath_int& val) } inline void eval_abs(tommath_int& result, const tommath_int& val) { - mp_abs(const_cast<::mp_int*>(&val.data()), &result.data()); + detail::check_tommath_result(mp_abs(const_cast<::mp_int*>(&val.data()), &result.data())); } diff --git a/test/mp_number_concept_check.cpp b/test/mp_number_concept_check.cpp index 675aa2b7..c5787b1e 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -1,4 +1,3 @@ - // Copyright John Maddock 2011. // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file @@ -13,6 +12,7 @@ #define BOOST_MATH_INSTANTIATE_MINIMUM #ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS # pragma warning(disable:4800) # pragma warning(disable:4512) # pragma warning(disable:4127) diff --git a/test/test.hpp b/test/test.hpp index d44af84f..b4d21e1c 100644 --- a/test/test.hpp +++ b/test/test.hpp @@ -4,6 +4,7 @@ #include #include +#include #include #include diff --git a/test/test_acos.cpp b/test/test_acos.cpp index c2b1a074..2528378e 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index a39dc351..b6ae1a92 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -3,6 +3,10 @@ // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include @@ -382,10 +386,11 @@ void test_negative_mixed(boost::mpl::true_ const&) #else Num tol = 0; #endif - BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), tol); - BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), 0); - BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), 0); - BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), 0); + std::ios_base::fmtflags f = boost::is_floating_point::value ? std::ios_base::scientific : std::ios_base::fmtflags(0); + BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, f)), tol); + BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, f)), 0); + BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, f)), 0); + BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, f)), 0); // Assignment: Real r(0); BOOST_TEST(r != n1); @@ -483,10 +488,11 @@ void test_mixed() #else Num tol = 0; #endif - BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, boost::is_floating_point::value)), tol); - BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, boost::is_floating_point::value)), 0); - BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, boost::is_floating_point::value)), 0); - BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, boost::is_floating_point::value)), 0); + std::ios_base::fmtflags f = boost::is_floating_point::value ? std::ios_base::scientific : std::ios_base::fmtflags(0); + BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, f)), tol); + BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, f)), 0); + BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, f)), 0); + BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, f)), 0); // Assignment: Real r(0); BOOST_TEST(r != n1); diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 834e6bf1..21015134 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_atan.cpp b/test/test_atan.cpp index b1176c6f..afa589d6 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_cos.cpp b/test/test_cos.cpp index aacd3ea4..4ea8b163 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index 89a002d2..7100e4f7 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_exp.cpp b/test/test_exp.cpp index a8cc428a..9582cb58 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_fpclassify.cpp b/test/test_fpclassify.cpp index e3e28825..5e02c661 100644 --- a/test/test_fpclassify.cpp +++ b/test/test_fpclassify.cpp @@ -4,6 +4,10 @@ // Boost Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include diff --git a/test/test_gmp_conversions.cpp b/test/test_gmp_conversions.cpp index a2e30a7f..fad3d97d 100644 --- a/test/test_gmp_conversions.cpp +++ b/test/test_gmp_conversions.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_log.cpp b/test/test_log.cpp index ff7b8b5a..e965e6d0 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_mpfr_conversions.cpp b/test/test_mpfr_conversions.cpp index 3340697d..cd11e638 100644 --- a/test/test_mpfr_conversions.cpp +++ b/test/test_mpfr_conversions.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index ea18665c..489f1047 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -3,6 +3,10 @@ // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && !defined(TEST_TOMMATH) diff --git a/test/test_pow.cpp b/test/test_pow.cpp index 096a56c1..680db5de 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_round.cpp b/test/test_round.cpp index 4be856b1..c921073e 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -3,6 +3,10 @@ // Boost Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include diff --git a/test/test_sin.cpp b/test/test_sin.cpp index d320ac1d..d8747218 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index 8a626c99..a12ce09d 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp index f3cfad43..adc27efc 100644 --- a/test/test_sqrt.cpp +++ b/test/test_sqrt.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index 9b62aea8..96bf4574 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -8,6 +8,10 @@ // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include #include #include "test.hpp" diff --git a/test/test_test.cpp b/test/test_test.cpp index 3d0b207d..f01c073e 100644 --- a/test/test_test.cpp +++ b/test/test_test.cpp @@ -3,6 +3,10 @@ // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include "test.hpp" #include From 60525e3a9b940ccc75c9b12d5832f6ae9d30f730 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 21 Nov 2011 19:20:35 +0000 Subject: [PATCH 069/256] Fix showpos support. [SVN r75597] --- include/boost/multiprecision/cpp_float.hpp | 3 +++ include/boost/multiprecision/gmp.hpp | 8 ++++++++ include/boost/multiprecision/mpfr.hpp | 8 ++++++++ 3 files changed, 19 insertions(+) diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 38b527c1..51b0eb95 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -1644,6 +1644,7 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_ bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; + bool shopos = (f & std::ios_base::showpos) == std::ios_base::showpos; std::string str; boost::int64_t my_exp = order(); @@ -1756,6 +1757,8 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_ } if(isneg()) str.insert(0, 1, '-'); + else if(shopos) + str.insert(0, 1, '+'); return str; } diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 56ade6a2..7faa4b58 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -164,6 +164,7 @@ struct gmp_float_imp bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; + bool showpos = (f & std::ios_base::showpos) == std::ios_base::showpos; std::string result; mp_exp_t e; @@ -173,7 +174,12 @@ struct gmp_float_imp const char* ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); std::ptrdiff_t sl = std::strlen(ps); if(sl == 0) + { + result = scientific ? "0.0e0" : showpoint ? "0.0" : "0"; + if(showpos) + result.insert(0, 1, '+'); return "0"; + } if(*ps == '-') --sl; // number of digits excluding sign. result = ps; @@ -209,6 +215,8 @@ struct gmp_float_imp if(e) result += "e" + lexical_cast(e); } + if(shopos && (str[0] != '-')) + str.insert(0, 1, '+'); mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); return result; diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 1eae2c7d..22c2f3f9 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -161,6 +161,7 @@ struct mpfr_float_imp bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; + bool showpos = (f & std::ios_base::showpos) == std::ios_base::showpos; std::string result; mp_exp_t e; @@ -168,7 +169,12 @@ struct mpfr_float_imp std::ptrdiff_t sl = std::strlen(ps); int chars = sl; if(sl == 0) + { + result = scientific ? "0.0e0" : showpoint ? "0.0" : "0"; + if(showpos) + result.insert(0, 1, '+'); return "0"; + } while(ps[chars-1] == '0') --chars; ps[chars] = 0; @@ -209,6 +215,8 @@ struct mpfr_float_imp if(e) result += "e" + lexical_cast(e); } + if(shopos && (str[0] != '-')) + str.insert(0, 1, '+'); mpfr_free_str(ps); return result; } From 40123e7170713d33945b472dfeaf73d485af67e7 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 22 Nov 2011 09:51:58 +0000 Subject: [PATCH 070/256] Change number formatting when std::ios_base::fixed is set to print the requested number of digits, padding with zeros as required. [SVN r75602] --- include/boost/multiprecision/cpp_float.hpp | 8 ++++++ include/boost/multiprecision/gmp.hpp | 27 ++++++++++++------ include/boost/multiprecision/mpfr.hpp | 32 +++++++++++++--------- 3 files changed, 45 insertions(+), 22 deletions(-) diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 51b0eb95..41ad3005 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -1755,6 +1755,14 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_ str.append(1, 'e'); str.append(boost::lexical_cast(my_exp)); } + if(showpoint || scientific) + { + std::streamsize chars = str.size() - 1; + BOOST_ASSERT(str.find('.') != std::string::npos); // there must be a decimal point!! + chars = number_of_digits - chars; + if(chars > 0) + str.append(chars, '0'); + } if(isneg()) str.insert(0, 1, '-'); else if(shopos) diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 7faa4b58..150782cb 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -173,17 +173,14 @@ struct gmp_float_imp void (*free_func_ptr) (void *, size_t); const char* ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); std::ptrdiff_t sl = std::strlen(ps); + if(ps && *ps == '-') + --sl; // number of digits excluding sign. + result = ps; if(sl == 0) { result = scientific ? "0.0e0" : showpoint ? "0.0" : "0"; - if(showpos) - result.insert(0, 1, '+'); - return "0"; } - if(*ps == '-') - --sl; // number of digits excluding sign. - result = ps; - if(fixed || (!scientific && (e > -4) && (e <= std::numeric_limits::digits10 + 2))) + else if(fixed || (!scientific && (e > -4) && (e <= std::numeric_limits::digits10 + 2))) { if(1 + e >= sl) { @@ -215,8 +212,20 @@ struct gmp_float_imp if(e) result += "e" + lexical_cast(e); } - if(shopos && (str[0] != '-')) - str.insert(0, 1, '+'); + if(showpoint || scientific) + { + // Pad out end with zeros as required to give required precision. + std::streamsize chars = result.size() - 1; + BOOST_ASSERT(result.find('.') != std::string::npos); // there must be a decimal point!! + BOOST_ASSERT(result.size()); // Better not be a null string by this point!! + if(result[0] == '-') + --chars; + chars = digits - chars; + if(chars > 0) + result.append(static_cast(chars), '0'); + } + if(showpos && (result[0] != '-')) + result.insert(0, 1, '+'); mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); return result; diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 22c2f3f9..2fbae2c8 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -168,21 +168,15 @@ struct mpfr_float_imp char* ps = mpfr_get_str (0, &e, 10, static_cast(digits), m_data, GMP_RNDN); std::ptrdiff_t sl = std::strlen(ps); int chars = sl; - if(sl == 0) - { - result = scientific ? "0.0e0" : showpoint ? "0.0" : "0"; - if(showpos) - result.insert(0, 1, '+'); - return "0"; - } - while(ps[chars-1] == '0') + while(chars && (ps[chars-1] == '0')) --chars; ps[chars] = 0; - if(*ps == '-') + if(chars && (*ps == '-')) --chars; // number of digits excluding sign. if(chars == 0) - return scientific ? "0.0e0" : showpoint ? "0.0" : "0"; - result = ps; + result = "0"; + else + result = ps; if(fixed || (!scientific && (e > -4) && (e <= std::numeric_limits::digits10 + 2))) { if(e >= chars) @@ -215,8 +209,20 @@ struct mpfr_float_imp if(e) result += "e" + lexical_cast(e); } - if(shopos && (str[0] != '-')) - str.insert(0, 1, '+'); + if(showpoint || scientific) + { + // Pad out end with zeros as required to give required precision. + std::streamsize chars = result.size() - 1; + BOOST_ASSERT(result.find('.') != std::string::npos); // there must be a decimal point!! + BOOST_ASSERT(result.size()); // Better not be a null string by this point!! + if(result[0] == '-') + --chars; + chars = digits - chars; + if(chars > 0) + result.append(static_cast(chars), '0'); + } + if(showpos && (result[0] != '-')) + result.insert(0, 1, '+'); mpfr_free_str(ps); return result; } From b3048e4ad2c0ec9b68ccd3fd06a6fda17194d6f9 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 22 Nov 2011 10:07:24 +0000 Subject: [PATCH 071/256] Fix bug in previous formatting code. [SVN r75603] --- include/boost/multiprecision/cpp_float.hpp | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 41ad3005..7a33dfa9 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -1755,13 +1755,13 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_ str.append(1, 'e'); str.append(boost::lexical_cast(my_exp)); } - if(showpoint || scientific) + if((showpoint || scientific) && (number_of_digits != (std::numeric_limits::max)())) { std::streamsize chars = str.size() - 1; BOOST_ASSERT(str.find('.') != std::string::npos); // there must be a decimal point!! chars = number_of_digits - chars; if(chars > 0) - str.append(chars, '0'); + str.append(static_cast(chars), '0'); } if(isneg()) str.insert(0, 1, '-'); From a448d536d0497760f2e53abfb6e3e589be6a6354 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 23 Nov 2011 10:14:41 +0000 Subject: [PATCH 072/256] Re-factor and fix (again) floating point formatting. [SVN r75637] --- include/boost/multiprecision/cpp_float.hpp | 66 ++------------- .../multiprecision/detail/mp_number_base.hpp | 81 +++++++++++++++++++ include/boost/multiprecision/gmp.hpp | 72 ++++------------- include/boost/multiprecision/mpfr.hpp | 77 +++++------------- 4 files changed, 122 insertions(+), 174 deletions(-) diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 7a33dfa9..8bf78bd1 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -1641,15 +1641,14 @@ cpp_float cpp_float::extract_integer_part(void) const template std::string cpp_float::str(std::streamsize number_of_digits, std::ios_base::fmtflags f) const { - bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; - bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; - bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; - bool shopos = (f & std::ios_base::showpos) == std::ios_base::showpos; - std::string str; boost::int64_t my_exp = order(); if(number_of_digits == 0) - number_of_digits = (std::numeric_limits::max)(); + number_of_digits = cpp_float_max_digits10; + if(f & std::ios_base::fixed) + number_of_digits += my_exp + 1; + else if(f & std::ios_base::scientific) + ++number_of_digits; // Determine the number of elements needed to provide the requested digits from cpp_float. const std::size_t number_of_elements = (std::min)(static_cast((number_of_digits / static_cast(mp_elem_digits10)) + 2u), static_cast(mp_elem_number)); @@ -1711,62 +1710,9 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_ } } } - // - // Suppress trailing zeros: - // - std::string::iterator pos = str.end(); - while(pos != str.begin() && *--pos == '0'){} - if(pos != str.end()) - ++pos; - str.erase(pos, str.end()); - if(str.empty()) - str = '0'; - if(fixed || (!scientific && (str.size() < 20) && (my_exp >= -3) && (my_exp < 20))) - { - if(1 + my_exp > str.size()) - { - // Just pad out the end with zeros: - str.append(static_cast(1 + my_exp - str.size()), '0'); - if(showpoint) - str.append(".0"); - } - else if(my_exp + 1 != str.size()) - { - if(my_exp < 0) - { - str.insert(0, static_cast(-1-my_exp), '0'); - str.insert(0, "0."); - } - else - { - // Insert the decimal point: - str.insert(static_cast(my_exp + 1), 1, '.'); - } - } - else if(showpoint) - str += ".0"; - } - else - { - // Scientific format: - str.insert(1, 1, '.'); - if(str.size() == 2) - str.append(1, '0'); - str.append(1, 'e'); - str.append(boost::lexical_cast(my_exp)); - } - if((showpoint || scientific) && (number_of_digits != (std::numeric_limits::max)())) - { - std::streamsize chars = str.size() - 1; - BOOST_ASSERT(str.find('.') != std::string::npos); // there must be a decimal point!! - chars = number_of_digits - chars; - if(chars > 0) - str.append(static_cast(chars), '0'); - } if(isneg()) str.insert(0, 1, '-'); - else if(shopos) - str.insert(0, 1, '+'); + boost::multiprecision::detail::format_float_string(str, my_exp, number_of_digits, f); return str; } diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index e4c9a619..d059ba17 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -345,6 +345,87 @@ struct digits2 static const long value = std::numeric_limits::radix == 10 ? (((std::numeric_limits::digits + 1) * 1000L) / 301L) : std::numeric_limits::digits; }; +template +void format_float_string(S& str, long long my_exp, std::streamsize digits, std::ios_base::fmtflags f) +{ + bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; + bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; + bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; + bool showpos = (f & std::ios_base::showpos) == std::ios_base::showpos; + + if(!fixed && !scientific) + { + // + // Suppress trailing zeros: + // + std::string::iterator pos = str.end(); + while(pos != str.begin() && *--pos == '0'){} + if(pos != str.end()) + ++pos; + str.erase(pos, str.end()); + if(str.empty()) + str = '0'; + } + else + { + // + // Pad out the end with zero's if we need to: + // + std::streamsize chars = str.size(); + if(chars && str[0] == '-') + --chars; + chars = digits - chars; + if(chars > 0) + { + str.append(static_cast(chars), '0'); + } + } + + if(fixed || (!scientific && (str.size() < 20) && (my_exp >= -3) && (my_exp < 20))) + { + if(1 + my_exp > str.size()) + { + // Just pad out the end with zeros: + str.append(static_cast(1 + my_exp - str.size()), '0'); + if(showpoint) + str.append(".0"); + } + else if(my_exp + 1 != str.size()) + { + if(my_exp < 0) + { + str.insert(0, static_cast(-1-my_exp), '0'); + str.insert(0, "0."); + } + else + { + // Insert the decimal point: + str.insert(static_cast(my_exp + 1), 1, '.'); + } + } + else if(showpoint) + str += ".0"; + } + else + { + // Scientific format: + str.insert(1, 1, '.'); + if(str.size() == 2) + str.append(1, '0'); + str.append(1, 'e'); + S e = boost::lexical_cast(std::abs(my_exp)); + if(e.size() < 3) + e.insert(0, 3-e.size(), '0'); + if(my_exp < 0) + e.insert(0, 1, '-'); + else + e.insert(0, 1, '+'); + str.append(e); + } + if(showpos && (str[0] != '-')) + str.insert(0, 1, '+'); +} + } // namespace detail // diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 150782cb..5184375a 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -163,71 +163,29 @@ struct gmp_float_imp { bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; - bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; - bool showpos = (f & std::ios_base::showpos) == std::ios_base::showpos; + + if(scientific) + ++digits; std::string result; mp_exp_t e; void *(*alloc_func_ptr) (size_t); void *(*realloc_func_ptr) (void *, size_t, size_t); void (*free_func_ptr) (void *, size_t); - const char* ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); - std::ptrdiff_t sl = std::strlen(ps); - if(ps && *ps == '-') - --sl; // number of digits excluding sign. - result = ps; - if(sl == 0) - { - result = scientific ? "0.0e0" : showpoint ? "0.0" : "0"; - } - else if(fixed || (!scientific && (e > -4) && (e <= std::numeric_limits::digits10 + 2))) - { - if(1 + e >= sl) - { - result.append(e - sl, '0'); - if(showpoint) - result.append(".0"); - } - else - { - if(e <= 0) - { - result.insert(0, -e, '0'); - result.insert(0, "0."); - } - else - { - // Insert the decimal point: - result.insert(e, 1, '.'); - } - } - } - else - { - if(ps[0] == '-') - result.insert(2, 1, '.'); - else - result.insert(1, 1, '.'); - --e; - if(e) - result += "e" + lexical_cast(e); - } - if(showpoint || scientific) - { - // Pad out end with zeros as required to give required precision. - std::streamsize chars = result.size() - 1; - BOOST_ASSERT(result.find('.') != std::string::npos); // there must be a decimal point!! - BOOST_ASSERT(result.size()); // Better not be a null string by this point!! - if(result[0] == '-') - --chars; - chars = digits - chars; - if(chars > 0) - result.append(static_cast(chars), '0'); - } - if(showpos && (result[0] != '-')) - result.insert(0, 1, '+'); mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + const char* ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); + --e; // To match with what our formatter expects. + if(fixed && e != -1) + { + // Oops we actually need a different number of digits to what we asked for: + (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); + digits += e + 1; + ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); + --e; // To match with what our formatter expects. + } + result = ps; (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); + boost::multiprecision::detail::format_float_string(result, e, digits, f); return result; } ~gmp_float_imp() diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 2fbae2c8..7e162839 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -160,70 +160,33 @@ struct mpfr_float_imp { bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; - bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; - bool showpos = (f & std::ios_base::showpos) == std::ios_base::showpos; + + if(scientific) + ++digits; std::string result; mp_exp_t e; - char* ps = mpfr_get_str (0, &e, 10, static_cast(digits), m_data, GMP_RNDN); - std::ptrdiff_t sl = std::strlen(ps); - int chars = sl; - while(chars && (ps[chars-1] == '0')) - --chars; - ps[chars] = 0; - if(chars && (*ps == '-')) - --chars; // number of digits excluding sign. - if(chars == 0) + if(mpfr_zero_p(m_data)) + { + e = 0; result = "0"; + } else + { + char* ps = mpfr_get_str (0, &e, 10, static_cast(digits), m_data, GMP_RNDN); + --e; // To match with what our formatter expects. + if(fixed && e != -1) + { + // Oops we actually need a different number of digits to what we asked for: + mpfr_free_str(ps); + digits += e + 1; + ps = ps = mpfr_get_str (0, &e, 10, static_cast(digits), m_data, GMP_RNDN); + --e; // To match with what our formatter expects. + } result = ps; - if(fixed || (!scientific && (e > -4) && (e <= std::numeric_limits::digits10 + 2))) - { - if(e >= chars) - { - result.append(e - chars, '0'); - if(showpoint) - result.append(".0"); - } - else - { - if(e <= 0) - { - result.insert(0, -e, '0'); - result.insert(0, "0."); - } - else - { - // Insert the decimal point: - result.insert(e, 1, '.'); - } - } + mpfr_free_str(ps); } - else - { - if(ps[0] == '-') - result.insert(2, 1, '.'); - else - result.insert(1, 1, '.'); - --e; - if(e) - result += "e" + lexical_cast(e); - } - if(showpoint || scientific) - { - // Pad out end with zeros as required to give required precision. - std::streamsize chars = result.size() - 1; - BOOST_ASSERT(result.find('.') != std::string::npos); // there must be a decimal point!! - BOOST_ASSERT(result.size()); // Better not be a null string by this point!! - if(result[0] == '-') - --chars; - chars = digits - chars; - if(chars > 0) - result.append(static_cast(chars), '0'); - } - if(showpos && (result[0] != '-')) - result.insert(0, 1, '+'); - mpfr_free_str(ps); + boost::multiprecision::detail::format_float_string(result, e, digits, f); return result; } ~mpfr_float_imp() From a82c12c4472e8fe1cfc8d68b9b11a8806ba3ceab Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 24 Nov 2011 17:27:17 +0000 Subject: [PATCH 073/256] Mostly fix IO failures. [SVN r75644] --- include/boost/multiprecision/cpp_float.hpp | 79 ++++++++++++------- .../multiprecision/detail/mp_number_base.hpp | 37 ++++++--- include/boost/multiprecision/gmp.hpp | 31 +++++--- include/boost/multiprecision/mpfr.hpp | 2 + 4 files changed, 97 insertions(+), 52 deletions(-) diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 8bf78bd1..b1a6b1f5 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -1646,7 +1646,9 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_ if(number_of_digits == 0) number_of_digits = cpp_float_max_digits10; if(f & std::ios_base::fixed) + { number_of_digits += my_exp + 1; + } else if(f & std::ios_base::scientific) ++number_of_digits; // Determine the number of elements needed to provide the requested digits from cpp_float. @@ -1667,47 +1669,64 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_ str += ss.str(); } - - // Cut the output to the size of the precision. - if(str.length() > static_cast(number_of_digits)) + if(number_of_digits == 0) { - // Get the digit after the last needed digit for rounding - const boost::uint32_t round = static_cast(static_cast(str[static_cast(number_of_digits)]) - static_cast('0')); - - // Truncate the string - str.erase(static_cast(number_of_digits)); - - if(round >= static_cast(5u)) + // We only get here if the output format is "fixed" and we just need to + // round the first digit. + str.insert(0, 1, '0'); + ++number_of_digits; + } + if(number_of_digits < 0) + { + str = "0"; + if(isneg()) + str.insert(0, 1, '-'); + boost::multiprecision::detail::format_float_string(str, 0, number_of_digits - my_exp - 1, f); + return str; + } + else + { + // Cut the output to the size of the precision. + if(str.length() > static_cast(number_of_digits)) { - std::size_t ix = static_cast(str.length() - 1u); + // Get the digit after the last needed digit for rounding + const boost::uint32_t round = static_cast(static_cast(str[static_cast(number_of_digits)]) - static_cast('0')); - // Every trailing 9 must be rounded up - while(ix && (static_cast(str.at(ix)) - static_cast('0') == static_cast(9))) - { - str.at(ix) = static_cast('0'); - --ix; - } + // Truncate the string + str.erase(static_cast(number_of_digits)); - if(!ix) + if(round >= static_cast(5u)) { - // There were nothing but trailing nines. - if(static_cast(static_cast(str.at(ix)) - static_cast(0x30)) == static_cast(9)) + std::size_t ix = static_cast(str.length() - 1u); + + // Every trailing 9 must be rounded up + while(ix && (static_cast(str.at(ix)) - static_cast('0') == static_cast(9))) { - // Increment up to the next order and adjust exponent. - str.at(ix) = static_cast('1'); - ++my_exp; + str.at(ix) = static_cast('0'); + --ix; + } + + if(!ix) + { + // There were nothing but trailing nines. + if(static_cast(static_cast(str.at(ix)) - static_cast(0x30)) == static_cast(9)) + { + // Increment up to the next order and adjust exponent. + str.at(ix) = static_cast('1'); + ++my_exp; + } + else + { + // Round up this digit. + ++str.at(ix); + } } else { - // Round up this digit. - ++str.at(ix); + // Round up the last digit. + ++str[ix]; } } - else - { - // Round up the last digit. - ++str[ix]; - } } } if(isneg()) diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index d059ba17..8376405f 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -9,6 +9,7 @@ #include #include #include +#include #ifdef BOOST_NO_NOEXCEPT #define BOOST_MP_NOEXCEPT @@ -345,6 +346,14 @@ struct digits2 static const long value = std::numeric_limits::radix == 10 ? (((std::numeric_limits::digits + 1) * 1000L) / 301L) : std::numeric_limits::digits; }; +#ifndef BOOST_MP_MIN_EXPONENT_DIGITS +#ifdef _MSC_VER +# define BOOST_MP_MIN_EXPONENT_DIGITS 3 +#else +# define BOOST_MP_MIN_EXPONENT_DIGITS 2 +#endif +#endif + template void format_float_string(S& str, long long my_exp, std::streamsize digits, std::ios_base::fmtflags f) { @@ -353,7 +362,12 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std:: bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; bool showpos = (f & std::ios_base::showpos) == std::ios_base::showpos; - if(!fixed && !scientific) + bool neg = str.size() && (str[0] == '-'); + + if(neg) + str.erase(0, 1); + + if(!fixed && !scientific && !showpoint) { // // Suppress trailing zeros: @@ -372,8 +386,6 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std:: // Pad out the end with zero's if we need to: // std::streamsize chars = str.size(); - if(chars && str[0] == '-') - --chars; chars = digits - chars; if(chars > 0) { @@ -381,14 +393,14 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std:: } } - if(fixed || (!scientific && (str.size() < 20) && (my_exp >= -3) && (my_exp < 20))) + if(fixed || (!scientific && (my_exp >= -4) && (my_exp < digits))) { if(1 + my_exp > str.size()) { // Just pad out the end with zeros: str.append(static_cast(1 + my_exp - str.size()), '0'); if(showpoint) - str.append(".0"); + str.append("."); } else if(my_exp + 1 != str.size()) { @@ -404,25 +416,26 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std:: } } else if(showpoint) - str += ".0"; + str += "."; } else { // Scientific format: - str.insert(1, 1, '.'); - if(str.size() == 2) - str.append(1, '0'); + if(showpoint || (str.size() > 1)) + str.insert(1, 1, '.'); str.append(1, 'e'); S e = boost::lexical_cast(std::abs(my_exp)); - if(e.size() < 3) - e.insert(0, 3-e.size(), '0'); + if(e.size() < BOOST_MP_MIN_EXPONENT_DIGITS) + e.insert(0, BOOST_MP_MIN_EXPONENT_DIGITS-e.size(), '0'); if(my_exp < 0) e.insert(0, 1, '-'); else e.insert(0, 1, '+'); str.append(e); } - if(showpos && (str[0] != '-')) + if(neg) + str.insert(0, 1, '-'); + else if(showpos) str.insert(0, 1, '+'); } diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 5184375a..bec26f6b 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -173,18 +173,29 @@ struct gmp_float_imp void *(*realloc_func_ptr) (void *, size_t, size_t); void (*free_func_ptr) (void *, size_t); mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); - const char* ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); - --e; // To match with what our formatter expects. - if(fixed && e != -1) + + if(mpf_sgn(m_data) == 0) { - // Oops we actually need a different number of digits to what we asked for: - (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); - digits += e + 1; - ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); - --e; // To match with what our formatter expects. + e = 0; + result = "0"; + if(fixed) + ++digits; + } + else + { + const char* ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); + --e; // To match with what our formatter expects. + if(fixed && e != -1) + { + // Oops we actually need a different number of digits to what we asked for: + (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); + digits += e + 1; + ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); + --e; // To match with what our formatter expects. + } + result = ps; + (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); } - result = ps; - (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); boost::multiprecision::detail::format_float_string(result, e, digits, f); return result; } diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 7e162839..b030957b 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -170,6 +170,8 @@ struct mpfr_float_imp { e = 0; result = "0"; + if(fixed) + ++digits; } else { From ffc6bcedc9ecae0c40bcc7c600063bdee6cbe725 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 28 Nov 2011 09:13:12 +0000 Subject: [PATCH 074/256] Fix float IO and add test. [SVN r75707] --- include/boost/multiprecision/cpp_float.hpp | 54 +++++- .../multiprecision/detail/mp_number_base.hpp | 59 +++++- include/boost/multiprecision/gmp.hpp | 67 ++++++- include/boost/multiprecision/mpfr.hpp | 71 ++++++- test/Jamfile.v2 | 27 ++- test/test_float_io.cpp | 181 ++++++++++++++++++ 6 files changed, 430 insertions(+), 29 deletions(-) create mode 100644 test/test_float_io.cpp diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index b1a6b1f5..8e4bdb16 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -1642,6 +1642,7 @@ template std::string cpp_float::str(std::streamsize number_of_digits, std::ios_base::fmtflags f) const { std::string str; + std::streamsize org_digits(number_of_digits); boost::int64_t my_exp = order(); if(number_of_digits == 0) number_of_digits = cpp_float_max_digits10; @@ -1669,19 +1670,21 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_ str += ss.str(); } + bool have_leading_zeros = false; if(number_of_digits == 0) { // We only get here if the output format is "fixed" and we just need to - // round the first digit. - str.insert(0, 1, '0'); - ++number_of_digits; + // round the first non-zero digit. + number_of_digits -= my_exp + 1; // reset to original value + str.insert(0, std::string::size_type(number_of_digits), '0'); + have_leading_zeros = true; } if(number_of_digits < 0) { str = "0"; if(isneg()) str.insert(0, 1, '-'); - boost::multiprecision::detail::format_float_string(str, 0, number_of_digits - my_exp - 1, f); + boost::multiprecision::detail::format_float_string(str, 0, number_of_digits - my_exp - 1, f, this->iszero()); return str; } else @@ -1692,10 +1695,37 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_ // Get the digit after the last needed digit for rounding const boost::uint32_t round = static_cast(static_cast(str[static_cast(number_of_digits)]) - static_cast('0')); + bool need_round_up = round >= 5u; + + if(round == 5u) + { + const boost::uint32_t ix = static_cast(static_cast(str[static_cast(number_of_digits - 1)]) - static_cast('0')); + if((ix & 1u) == 0) + { + // We have an even digit followed by a 5, so we might not actually need to round up + // if all the remaining digits are zero: + if(str.find_first_not_of('0', static_cast(number_of_digits + 1)) == std::string::npos) + { + bool all_zeros = true; + // No none-zero trailing digits in the string, now check whatever parts we didn't convert to the string: + for(std::size_t i = number_of_elements; i < data.size(); i++) + { + if(data[i]) + { + all_zeros = false; + break; + } + } + if(all_zeros) + need_round_up = false; // tie break - round to even. + } + } + } + // Truncate the string str.erase(static_cast(number_of_digits)); - if(round >= static_cast(5u)) + if(need_round_up) { std::size_t ix = static_cast(str.length() - 1u); @@ -1729,9 +1759,21 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_ } } } + if(have_leading_zeros) + { + // We need to take the zeros back out again, and correct the exponent + // if we rounded up: + if(str[std::string::size_type(number_of_digits - 1)] != '0') + { + ++my_exp; + str.erase(0, std::string::size_type(number_of_digits - 1)); + } + else + str.erase(0, std::string::size_type(number_of_digits)); + } if(isneg()) str.insert(0, 1, '-'); - boost::multiprecision::detail::format_float_string(str, my_exp, number_of_digits, f); + boost::multiprecision::detail::format_float_string(str, my_exp, org_digits, f, this->iszero()); return str; } diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 8376405f..fb2cb147 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -348,15 +348,16 @@ struct digits2 #ifndef BOOST_MP_MIN_EXPONENT_DIGITS #ifdef _MSC_VER -# define BOOST_MP_MIN_EXPONENT_DIGITS 3 +# define BOOST_MP_MIN_EXPONENT_DIGITS 2 #else # define BOOST_MP_MIN_EXPONENT_DIGITS 2 #endif #endif template -void format_float_string(S& str, long long my_exp, std::streamsize digits, std::ios_base::fmtflags f) +void format_float_string(S& str, long long my_exp, std::streamsize digits, std::ios_base::fmtflags f, bool iszero) { + typedef typename S::size_type size_type; bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; @@ -367,6 +368,39 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std:: if(neg) str.erase(0, 1); + if(digits == 0) + { + digits = (std::max)(str.size(), size_type(16)); + } + + if(iszero || str.empty() || (str.find_first_not_of('0') == S::npos)) + { + // We will be printing zero, even though the value might not + // actually be zero (it just may have been rounded to zero). + str = "0"; + if(scientific || fixed) + { + str.append(1, '.'); + str.append(size_type(digits), '0'); + if(scientific) + str.append("e+00"); + } + else + { + if(showpoint) + { + str.append(1, '.'); + if(digits > 1) + str.append(size_type(digits - 1), '0'); + } + } + if(neg) + str.insert(0, 1, '-'); + else if(showpos) + str.insert(0, 1, '+'); + return; + } + if(!fixed && !scientific && !showpoint) { // @@ -380,13 +414,15 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std:: if(str.empty()) str = '0'; } - else + else if(!fixed || (my_exp >= 0)) { // // Pad out the end with zero's if we need to: // std::streamsize chars = str.size(); chars = digits - chars; + if(scientific) + ++chars; if(chars > 0) { str.append(static_cast(chars), '0'); @@ -399,14 +435,14 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std:: { // Just pad out the end with zeros: str.append(static_cast(1 + my_exp - str.size()), '0'); - if(showpoint) + if(showpoint || fixed) str.append("."); } - else if(my_exp + 1 != str.size()) + else if(my_exp + 1 < str.size()) { if(my_exp < 0) { - str.insert(0, static_cast(-1-my_exp), '0'); + str.insert(0, static_cast(-1 - my_exp), '0'); str.insert(0, "0."); } else @@ -415,8 +451,17 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std:: str.insert(static_cast(my_exp + 1), 1, '.'); } } - else if(showpoint) + else if(showpoint || fixed) // we have exactly the digits we require to left of the point str += "."; + + if(fixed) + { + // We may need to add trailing zeros: + std::streamsize l = str.find('.') + 1; + l = digits - (str.size() - l); + if(l > 0) + str.append(size_type(l), '0'); + } } else { diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index bec26f6b..e5d5fcc9 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -163,8 +163,9 @@ struct gmp_float_imp { bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; + std::streamsize org_digits(digits); - if(scientific) + if(scientific && digits) ++digits; std::string result; @@ -178,25 +179,79 @@ struct gmp_float_imp { e = 0; result = "0"; - if(fixed) + if(fixed && digits) ++digits; } else { - const char* ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); + char* ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); --e; // To match with what our formatter expects. if(fixed && e != -1) { // Oops we actually need a different number of digits to what we asked for: (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); digits += e + 1; - ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); - --e; // To match with what our formatter expects. + if(digits == 0) + { + // We need to get *all* the digits and then possibly round up, + // we end up with either "0" or "1" as the result. + ps = mpf_get_str (0, &e, 10, 0, m_data); + --e; + unsigned offset = *ps == '-' ? 1 : 0; + if(ps[offset] > '5') + { + ++e; + ps[offset] = '1'; + ps[offset + 1] = 0; + } + else if(ps[offset] == '5') + { + unsigned i = offset + 1; + bool round_up = false; + while(ps[i] != 0) + { + if(ps[i] != '0') + { + round_up = true; + break; + } + } + if(round_up) + { + ++e; + ps[offset] = '1'; + ps[offset + 1] = 0; + } + else + { + ps[offset] = '0'; + ps[offset + 1] = 0; + } + } + else + { + ps[offset] = '0'; + ps[offset + 1] = 0; + } + } + else if(digits > 0) + { + ps = mpf_get_str (0, &e, 10, static_cast(digits), m_data); + --e; // To match with what our formatter expects. + } + else + { + ps = mpf_get_str (0, &e, 10, 1, m_data); + --e; + unsigned offset = *ps == '-' ? 1 : 0; + ps[offset] = '0'; + ps[offset + 1] = 0; + } } result = ps; (*free_func_ptr)((void*)ps, std::strlen(ps) + 1); } - boost::multiprecision::detail::format_float_string(result, e, digits, f); + boost::multiprecision::detail::format_float_string(result, e, org_digits, f, mpf_sgn(m_data) == 0); return result; } ~gmp_float_imp() diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index b030957b..9afdc01a 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -161,7 +161,9 @@ struct mpfr_float_imp bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; - if(scientific) + std::streamsize org_digits(digits); + + if(scientific && digits) ++digits; std::string result; @@ -170,8 +172,6 @@ struct mpfr_float_imp { e = 0; result = "0"; - if(fixed) - ++digits; } else { @@ -182,13 +182,68 @@ struct mpfr_float_imp // Oops we actually need a different number of digits to what we asked for: mpfr_free_str(ps); digits += e + 1; - ps = ps = mpfr_get_str (0, &e, 10, static_cast(digits), m_data, GMP_RNDN); - --e; // To match with what our formatter expects. + if(digits == 0) + { + // We need to get *all* the digits and then possibly round up, + // we end up with either "0" or "1" as the result. + ps = mpfr_get_str (0, &e, 10, 0, m_data, GMP_RNDN); + --e; + unsigned offset = *ps == '-' ? 1 : 0; + if(ps[offset] > '5') + { + ++e; + ps[offset] = '1'; + ps[offset + 1] = 0; + } + else if(ps[offset] == '5') + { + unsigned i = offset + 1; + bool round_up = false; + while(ps[i] != 0) + { + if(ps[i] != '0') + { + round_up = true; + break; + } + } + if(round_up) + { + ++e; + ps[offset] = '1'; + ps[offset + 1] = 0; + } + else + { + ps[offset] = '0'; + ps[offset + 1] = 0; + } + } + else + { + ps[offset] = '0'; + ps[offset + 1] = 0; + } + } + else if(digits > 0) + { + ps = mpfr_get_str (0, &e, 10, static_cast(digits), m_data, GMP_RNDN); + --e; // To match with what our formatter expects. + } + else + { + ps = mpfr_get_str (0, &e, 10, 1, m_data, GMP_RNDN); + --e; + unsigned offset = *ps == '-' ? 1 : 0; + ps[offset] = '0'; + ps[offset + 1] = 0; + } } - result = ps; - mpfr_free_str(ps); + result = ps ? ps : "0"; + if(ps) + mpfr_free_str(ps); } - boost::multiprecision::detail::format_float_string(result, e, digits, f); + boost::multiprecision::detail::format_float_string(result, e, org_digits, f, 0 != mpfr_zero_p(m_data)); return result; } ~mpfr_float_imp() diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 975e7a0e..d707576b 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -579,8 +579,31 @@ run test_fpclassify.cpp : # input files : # requirements TEST_CPP_FLOAT - [ check-target-builds ../config//has_mpfr : : no ] : test_fpclassify_cpp_float ; -run test_test.cpp ; \ No newline at end of file +run test_test.cpp ; + +run test_float_io.cpp + : # command line + : # input files + : # requirements + TEST_CPP_FLOAT + : test_float_io_cpp_float ; + +run test_float_io.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : no ] + : test_float_io_mpf ; + +run test_float_io.cpp mpfr gmp + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_float_io_mpfr ; + diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp new file mode 100644 index 00000000..944c1721 --- /dev/null +++ b/test/test_float_io.cpp @@ -0,0 +1,181 @@ +// Copyright John Maddock 2011. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#if !defined(TEST_MPF_50) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50) +# define TEST_MPF_50 +# define TEST_CPP_FLOAT +# define TEST_MPFR_50 + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include +#endif +#if defined(TEST_MPFR_50) +#include +#endif +#ifdef TEST_CPP_FLOAT +#include +#endif + +#include +#include +#include +#include + +#if defined(TEST_MPF_50) +template +bool is_mpf(const boost::multiprecision::mp_number >&) +{ return true; } +#endif +template +bool is_mpf(const T&) { return false; } + +bool is_bankers_rounding_error(const std::string& s, const char* expect) +{ + // This check isn't foolproof: that would require *much* more sofisticated code!!! + std::string::size_type l = std::strlen(expect); + if(l != s.size()) + return false; + std::string::size_type len = s.find('e'); + if(len == std::string::npos) + len = l - 1; + else + --len; + if(s.compare(0, len, expect, len)) + return false; + if(s[len] != expect[len] + 1) + return false; + return true; +} + +void print_flags(std::ios_base::fmtflags f) +{ + std::cout << "Formatting flags were: "; + if(f & std::ios_base::scientific) + std::cout << "scientific "; + if(f & std::ios_base::fixed) + std::cout << "fixed "; + if(f & std::ios_base::showpoint) + std::cout << "showpoint "; + if(f & std::ios_base::showpos) + std::cout << "showpos "; + std::cout << std::endl; +} + + +template +void test() +{ + typedef T mp_t; + boost::array f = + {{ + std::ios_base::fmtflags(0), std::ios_base::showpoint, std::ios_base::showpos, std::ios_base::scientific, std::ios_base::scientific|std::ios_base::showpos, + std::ios_base::scientific|std::ios_base::showpoint, std::ios_base::fixed, std::ios_base::fixed|std::ios_base::showpoint, + std::ios_base::fixed|std::ios_base::showpos + }}; + + boost::array, 40> string_data = {{ +#include "libs/multiprecision/string_data.ipp" + }}; + + double num = 123456789.0; + double denom = 1; + double val = num; + for(unsigned j = 0; j < 40; ++j) + { + unsigned col = 0; + for(unsigned prec = 1; prec < 14; ++prec) + { + for(unsigned i = 0; i < f.size(); ++i, ++col) + { + std::stringstream ss; + ss.precision(prec); + ss.flags(f[i]); + ss << mp_t(val); + const char* expect = string_data[j][col]; + if(ss.str() != expect) + { + if(is_mpf(mp_t()) && is_bankers_rounding_error(ss.str(), expect)) + { + std::cout << "Ignoring bankers-rounding error with GMP mp_f.\n"; + } + else + { + std::cout << std::setprecision(20) << "Testing value " << val << std::endl; + print_flags(f[i]); + std::cout << "Precision is: " << prec << std::endl; + std::cout << "Got: " << ss.str() << std::endl; + std::cout << "Expected: " << expect << std::endl; + ++boost::detail::test_errors(); + mp_t(val).str(prec, f[i]); // for debugging + } + } + } + } + num = -num; + if(j & 1) + denom *= 8; + val = num / denom; + } + + boost::array zeros = + {{ "0", "0.", "+0", "0.0e+00", "+0.0e+00", "0.0e+00", "0.0", "0.0", "+0.0", "0", "0.0", "+0", "0.00e+00", "+0.00e+00", "0.00e+00", "0.00", "0.00", "+0.00", "0", "0.00", "+0", "0.000e+00", "+0.000e+00", "0.000e+00", "0.000", "0.000", "+0.000", "0", "0.000", "+0", "0.0000e+00", "+0.0000e+00", "0.0000e+00", "0.0000", "0.0000", "+0.0000", "0", "0.0000", "+0", "0.00000e+00", "+0.00000e+00", "0.00000e+00", "0.00000", "0.00000", "+0.00000", "0", "0.00000", "+0", "0.000000e+00", "+0.000000e+00", "0.000000e+00", "0.000000", "0.000000", "+0.000000", "0", "0.000000", "+0", "0.0000000e+00", "+0.0000000e+00", "0.0000000e+00", "0.0000000", "0.0000000", "+0.0000000", "0", "0.0000000", "+0", "0.00000000e+00", "+0.00000000e+00", "0.00000000e+00", "0.00000000", "0.00000000", "+0.00000000", "0", "0.00000000", "+0", "0.000000000e+00", "+0.000000000e+00", "0.000000000e+00", "0.000000000", "0.000000000", "+0.000000000", "0", "0.000000000", "+0", "0.0000000000e+00", "+0.0000000000e+00", "0.0000000000e+00", "0.0000000000", "0.0000000000", "+0.0000000000", "0", "0.0000000000", "+0", "0.00000000000e+00", "+0.00000000000e+00", "0.00000000000e+00", "0.00000000000", "0.00000000000", "+0.00000000000", "0", "0.00000000000", "+0", "0.000000000000e+00", "+0.000000000000e+00", "0.000000000000e+00", "0.000000000000", "0.000000000000", "+0.000000000000", "0", "0.000000000000", "+0", "0.0000000000000e+00", "+0.0000000000000e+00", "0.0000000000000e+00", "0.0000000000000", "0.0000000000000", "+0.0000000000000" }}; + + unsigned col = 0; + val = 0; + for(unsigned prec = 1; prec < 14; ++prec) + { + for(unsigned i = 0; i < f.size(); ++i, ++col) + { + std::stringstream ss; + ss.precision(prec); + ss.flags(f[i]); + ss << mp_t(val); + const char* expect = zeros[col]; + if(ss.str() != expect) + { + std::cout << std::setprecision(20) << "Testing value " << val << std::endl; + print_flags(f[i]); + std::cout << "Precision is: " << prec << std::endl; + std::cout << "Got: " << ss.str() << std::endl; + std::cout << "Expected: " << expect << std::endl; + ++boost::detail::test_errors(); + mp_t(val).str(prec, f[i]); // for debugging + } + } + } +} + +int main() +{ +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_CPP_FLOAT + test(); + test(); +#endif +#ifdef TEST_MPF_50 + test(); + test(); +#endif + return boost::report_errors(); +} + From 7143af0191252363c64bce436e076847283cfd32 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 28 Nov 2011 16:28:31 +0000 Subject: [PATCH 075/256] Fix IO of infinities and NaN's. Add IO round trip test and adjust max_digits10 accordingly. [SVN r75714] --- include/boost/multiprecision/cpp_float.hpp | 55 ++++++++++-- include/boost/multiprecision/gmp.hpp | 4 +- include/boost/multiprecision/mpfr.hpp | 17 +++- test/test.hpp | 2 +- test/test_float_io.cpp | 98 +++++++++++++++++++++- 5 files changed, 164 insertions(+), 12 deletions(-) diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 8e4bdb16..c432a13f 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -53,6 +53,11 @@ private: static const boost::int32_t mp_elem_number = static_cast(cpp_float_digits10_num_base + 2); static const boost::int32_t mp_elem_mask = static_cast(100000000); +public: + static const boost::int32_t cpp_float_total_digits10 = mp_elem_number * mp_elem_digits10; + +private: + typedef enum enum_fpclass { mp_finite, @@ -1641,6 +1646,20 @@ cpp_float cpp_float::extract_integer_part(void) const template std::string cpp_float::str(std::streamsize number_of_digits, std::ios_base::fmtflags f) const { + if(this->isinf()) + { + if(this->isneg()) + return "-inf"; + else if(f & std::ios_base::showpos) + return "+inf"; + else + return "inf"; + } + else if(this->isnan()) + { + return "nan"; + } + std::string str; std::streamsize org_digits(number_of_digits); boost::int64_t my_exp = order(); @@ -1799,16 +1818,38 @@ bool cpp_float::rd_string(const char* const s) // Get a possible +/- sign and remove it. neg = false; - if((pos = str.find(static_cast('-'))) != std::string::npos) + if(str.size()) { - neg = true; - str.erase(pos, static_cast(1u)); + if(str[0] == '-') + { + neg = true; + str.erase(0, 1); + } + else if(str[0] == '+') + { + str.erase(0, 1); + } + } + // + // Special cases for infinities and NaN's: + // + if((str == "inf") || (str == "INF") || (str == "infinity") || (str == "INFINITY")) + { + if(neg) + { + *this = this->inf(); + this->negate(); + } + else + *this = this->inf(); + return true; + } + if((str.size() >= 3) && ((str.substr(0, 3) == "nan") || (str.substr(0, 3) == "NAN"))) + { + *this = this->nan(); + return true; } - if((pos = str.find(static_cast('+'))) != std::string::npos) - { - str.erase(pos, static_cast(1u)); - } // Remove leading zeros for all input types. const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate); diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index e5d5fcc9..b6467a50 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1788,8 +1788,8 @@ public: } BOOST_STATIC_CONSTEXPR int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); BOOST_STATIC_CONSTEXPR int digits10 = Digits10; - // Is this really correct??? - BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 1; + // Have to allow for a possible extra limb inside the gmp data structure: + BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 2 + ((GMP_LIMB_BITS * 301L) / 1000L); BOOST_STATIC_CONSTEXPR bool is_signed = true; BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 9afdc01a..ea5023ef 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -168,6 +168,21 @@ struct mpfr_float_imp std::string result; mp_exp_t e; + if(mpfr_inf_p(m_data)) + { + if(mpfr_sgn(m_data) < 0) + result = "-inf"; + else if(f & std::ios_base::showpos) + result = "+inf"; + else + result = "inf"; + return result; + } + if(mpfr_nan_p(m_data)) + { + result = "nan"; + return result; + } if(mpfr_zero_p(m_data)) { e = 0; @@ -1059,7 +1074,7 @@ public: BOOST_STATIC_CONSTEXPR int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); BOOST_STATIC_CONSTEXPR int digits10 = Digits10; // Is this really correct??? - BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 1; + BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 2; BOOST_STATIC_CONSTEXPR bool is_signed = true; BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; diff --git a/test/test.hpp b/test/test.hpp index b4d21e1c..de2224f5 100644 --- a/test/test.hpp +++ b/test/test.hpp @@ -63,7 +63,7 @@ inline T epsilon_of(const T&) template inline int digits_of(const T&) { - return std::numeric_limits::is_specialized ? std::numeric_limits::digits10 + 2 : std::numeric_limits::digits10 + 2; + return std::numeric_limits::is_specialized ? std::numeric_limits::max_digits10 + 2 : std::numeric_limits::max_digits10 + 2; } inline std::ostream& report_where(const char* file, int line, const char* function) diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp index 944c1721..bd512991 100644 --- a/test/test_float_io.cpp +++ b/test/test_float_io.cpp @@ -33,7 +33,9 @@ #include #endif -#include +#include +#include +#include "test.hpp" #include #include #include @@ -160,6 +162,85 @@ void test() } } } + + if(std::numeric_limits::has_infinity) + { + T val = std::numeric_limits::infinity(); + BOOST_CHECK_EQUAL(val.str(), "inf"); + BOOST_CHECK_EQUAL(val.str(0, std::ios_base::showpos), "+inf"); + val = -val; + BOOST_CHECK_EQUAL(val.str(), "-inf"); + BOOST_CHECK_EQUAL(val.str(0, std::ios_base::showpos), "-inf"); + + val = "inf"; + BOOST_CHECK_EQUAL(val, std::numeric_limits::infinity()); + val = "+inf"; + BOOST_CHECK_EQUAL(val, std::numeric_limits::infinity()); + val = "-inf"; + BOOST_CHECK_EQUAL(val, -std::numeric_limits::infinity()); + } + if(std::numeric_limits::has_quiet_NaN) + { + T val = std::numeric_limits::quiet_NaN(); + BOOST_CHECK_EQUAL(val.str(), "nan"); + val = "nan"; + BOOST_CHECK(boost::math::isnan(val)); + } +} + +template +T generate_random() +{ + static boost::random::mt19937 gen; + T val = gen(); + T prev_val = -1; + while(val != prev_val) + { + val *= (gen.max)(); + prev_val = val; + val += gen(); + } + int e; + val = frexp(val, &e); + + typedef typename T::backend_type::exponent_type e_type; + static boost::random::uniform_int_distribution ui(0, std::numeric_limits::max_exponent - 10); + return ldexp(val, ui(gen)); +} + +template +void do_round_trip(const T& val, std::ios_base::fmtflags f) +{ + std::stringstream ss; + ss << std::setprecision(std::numeric_limits::max_digits10); + ss.flags(f); + ss << val; + T new_val = ss.str(); + BOOST_CHECK_EQUAL(new_val, val); + new_val = val.str(0, f); + BOOST_CHECK_EQUAL(new_val, val); +} + +template +void do_round_trip(const T& val) +{ + do_round_trip(val, std::ios_base::fmtflags(0)); + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::scientific)); + if((fabs(val) > 1) && (fabs(val) < 1e100)) + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::fixed)); +} + +template +void test_round_trip() +{ + for(unsigned i = 0; i < 1000; ++i) + { + T val = generate_random(); + do_round_trip(val); + do_round_trip(T(-val)); + do_round_trip(T(1/val)); + do_round_trip(T(-1/val)); + } } int main() @@ -167,14 +248,29 @@ int main() #ifdef TEST_MPFR_50 test(); test(); + + test_round_trip(); + test_round_trip(); #endif #ifdef TEST_CPP_FLOAT test(); test(); + + /* + // cpp_float has extra guard digits that messes this up: + test_round_trip(); + test_round_trip(); + */ #endif #ifdef TEST_MPF_50 test(); test(); + /* + // I can't get this to work with mpf_t - mpf_str appears + // not to actually print enough decimal digits: + test_round_trip(); + test_round_trip(); + */ #endif return boost::report_errors(); } From 4a9845ac7e87e42d16026e759616efd9513e8a2f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 28 Nov 2011 19:24:20 +0000 Subject: [PATCH 076/256] Fix and test integer formatted output. [SVN r75716] --- include/boost/multiprecision/gmp.hpp | 5 + include/boost/multiprecision/tommath.hpp | 70 +++++++------- test/Jamfile.v2 | 15 +++ test/test.hpp | 2 +- test/test_int_io.cpp | 112 +++++++++++++++++++++++ 5 files changed, 171 insertions(+), 33 deletions(-) create mode 100644 test/test_int_io.cpp diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index b6467a50..4e678fd1 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1034,6 +1034,11 @@ struct gmp_int base = 8; else if((f & std::ios_base::hex) == std::ios_base::hex) base = 16; + // + // sanity check, bases 8 and 16 are only available for positive numbers: + // + if((base != 10) && (mpz_sgn(m_data) < 0)) + BOOST_THROW_EXCEPTION(std::runtime_error("Formatted output in bases 8 or 16 is only available for positive numbers")); void *(*alloc_func_ptr) (size_t); void *(*realloc_func_ptr) (void *, size_t, size_t); void (*free_func_ptr) (void *, size_t); diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index f55c485e..b0b9067e 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -42,11 +42,11 @@ struct tommath_int } tommath_int(const tommath_int& o) { - detail::check_tommath_result(mp_init_copy(&m_data, const_cast<::mp_int*>(&o.m_data))); + detail::check_tommath_result(mp_init_copy(&m_data, const_cast< ::mp_int*>(&o.m_data))); } tommath_int& operator = (const tommath_int& o) { - detail::check_tommath_result(mp_copy(const_cast<::mp_int*>(&o.m_data), &m_data)); + detail::check_tommath_result(mp_copy(const_cast< ::mp_int*>(&o.m_data), &m_data)); return *this; } tommath_int& operator = (boost::uintmax_t i) @@ -162,10 +162,11 @@ struct tommath_int { radix = 8; n -= 1; + s += 1; } } if(n) - detail::check_tommath_result(mp_read_radix(&m_data, s, 10)); + detail::check_tommath_result(mp_read_radix(&m_data, s, radix)); else detail::check_tommath_result(mp_set_int(&m_data, 0)); return *this; @@ -177,10 +178,15 @@ struct tommath_int base = 8; else if((f & std::ios_base::hex) == std::ios_base::hex) base = 16; + // + // sanity check, bases 8 and 16 are only available for positive numbers: + // + if((base != 10) && m_data.sign) + BOOST_THROW_EXCEPTION(std::runtime_error("Formatted output in bases 8 or 16 is only available for positive numbers")); int s; - detail::check_tommath_result(mp_radix_size(const_cast<::mp_int*>(&m_data), 10, &s)); + detail::check_tommath_result(mp_radix_size(const_cast< ::mp_int*>(&m_data), base, &s)); boost::scoped_array a(new char[s+1]); - detail::check_tommath_result(mp_toradix_n(const_cast<::mp_int*>(&m_data), a.get(), base, s+1)); + detail::check_tommath_result(mp_toradix_n(const_cast< ::mp_int*>(&m_data), a.get(), base, s+1)); std::string result = a.get(); if((base != 10) && (f & std::ios_base::showbase)) { @@ -202,7 +208,7 @@ struct tommath_int } int compare(const tommath_int& o)const { - return mp_cmp(const_cast<::mp_int*>(&m_data), const_cast<::mp_int*>(&o.m_data)); + return mp_cmp(const_cast< ::mp_int*>(&m_data), const_cast< ::mp_int*>(&o.m_data)); } template int compare(V v)const @@ -227,30 +233,30 @@ int get_sign(const tommath_int& val); inline void add(tommath_int& t, const tommath_int& o) { - detail::check_tommath_result(mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); + detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); } inline void subtract(tommath_int& t, const tommath_int& o) { - detail::check_tommath_result(mp_sub(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); + detail::check_tommath_result(mp_sub(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); } inline void multiply(tommath_int& t, const tommath_int& o) { - detail::check_tommath_result(mp_mul(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); + detail::check_tommath_result(mp_mul(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); } inline void divide(tommath_int& t, const tommath_int& o) { tommath_int temp; - detail::check_tommath_result(mp_div(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data(), &temp.data())); + detail::check_tommath_result(mp_div(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data(), &temp.data())); } inline void modulus(tommath_int& t, const tommath_int& o) { bool neg = get_sign(t) < 0; bool neg2 = get_sign(o) < 0; - detail::check_tommath_result(mp_mod(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); + detail::check_tommath_result(mp_mod(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); if(neg != neg2) { t.negate(); - detail::check_tommath_result(mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); + detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); t.negate(); } } @@ -268,73 +274,73 @@ inline void right_shift(tommath_int& t, UI i) template inline void left_shift(tommath_int& t, const tommath_int& v, UI i) { - detail::check_tommath_result(mp_mul_2d(const_cast<::mp_int*>(&v.data()), static_cast(i), &t.data())); + detail::check_tommath_result(mp_mul_2d(const_cast< ::mp_int*>(&v.data()), static_cast(i), &t.data())); } template inline void right_shift(tommath_int& t, const tommath_int& v, UI i) { tommath_int d; - detail::check_tommath_result(mp_div_2d(const_cast<::mp_int*>(&v.data()), static_cast(i), &t.data(), &d.data())); + detail::check_tommath_result(mp_div_2d(const_cast< ::mp_int*>(&v.data()), static_cast(i), &t.data(), &d.data())); } inline void bitwise_and(tommath_int& result, const tommath_int& v) { - detail::check_tommath_result(mp_and(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data())); + detail::check_tommath_result(mp_and(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data())); } inline void bitwise_or(tommath_int& result, const tommath_int& v) { - detail::check_tommath_result(mp_or(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data())); + detail::check_tommath_result(mp_or(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data())); } inline void bitwise_xor(tommath_int& result, const tommath_int& v) { - detail::check_tommath_result(mp_xor(&result.data(), const_cast<::mp_int*>(&v.data()), &result.data())); + detail::check_tommath_result(mp_xor(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data())); } inline void add(tommath_int& t, const tommath_int& p, const tommath_int& o) { - detail::check_tommath_result(mp_add(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data())); + detail::check_tommath_result(mp_add(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data())); } inline void subtract(tommath_int& t, const tommath_int& p, const tommath_int& o) { - detail::check_tommath_result(mp_sub(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data())); + detail::check_tommath_result(mp_sub(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data())); } inline void multiply(tommath_int& t, const tommath_int& p, const tommath_int& o) { - detail::check_tommath_result(mp_mul(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data())); + detail::check_tommath_result(mp_mul(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data())); } inline void divide(tommath_int& t, const tommath_int& p, const tommath_int& o) { tommath_int d; - detail::check_tommath_result(mp_div(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data(), &d.data())); + detail::check_tommath_result(mp_div(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data(), &d.data())); } inline void modulus(tommath_int& t, const tommath_int& p, const tommath_int& o) { bool neg = get_sign(p) < 0; bool neg2 = get_sign(o) < 0; - detail::check_tommath_result(mp_mod(const_cast<::mp_int*>(&p.data()), const_cast<::mp_int*>(&o.data()), &t.data())); + detail::check_tommath_result(mp_mod(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data())); if(neg != neg2) { t.negate(); - detail::check_tommath_result(mp_add(&t.data(), const_cast<::mp_int*>(&o.data()), &t.data())); + detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); t.negate(); } } inline void bitwise_and(tommath_int& result, const tommath_int& u, const tommath_int& v) { - detail::check_tommath_result(mp_and(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data())); + detail::check_tommath_result(mp_and(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data())); } inline void bitwise_or(tommath_int& result, const tommath_int& u, const tommath_int& v) { - detail::check_tommath_result(mp_or(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data())); + detail::check_tommath_result(mp_or(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data())); } inline void bitwise_xor(tommath_int& result, const tommath_int& u, const tommath_int& v) { - detail::check_tommath_result(mp_xor(const_cast<::mp_int*>(&u.data()), const_cast<::mp_int*>(&v.data()), &result.data())); + detail::check_tommath_result(mp_xor(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data())); } inline void complement(tommath_int& result, const tommath_int& u) @@ -351,7 +357,7 @@ inline void complement(tommath_int& result, const tommath_int& u) // unsigned shift = result.data().used * DIGIT_BIT; // How many bits we're actually using // How many bits we actually need, reduced by one to account for a mythical sign bit: - unsigned padding = result.data().used * std::numeric_limits::digits - shift - 1; + int padding = result.data().used * std::numeric_limits::digits - shift - 1; while(padding >= std::numeric_limits::digits) padding -= std::numeric_limits::digits; @@ -373,23 +379,23 @@ inline int get_sign(const tommath_int& val) template inline void convert_to(A* result, const tommath_int& val) { - *result = boost::lexical_cast(val.str(0, false)); + *result = boost::lexical_cast(val.str(0, std::ios_base::fmtflags(0))); } inline void convert_to(char* result, const tommath_int& val) { - *result = static_cast(boost::lexical_cast(val.str(0, false))); + *result = static_cast(boost::lexical_cast(val.str(0, std::ios_base::fmtflags(0)))); } inline void convert_to(unsigned char* result, const tommath_int& val) { - *result = static_cast(boost::lexical_cast(val.str(0, false))); + *result = static_cast(boost::lexical_cast(val.str(0, std::ios_base::fmtflags(0)))); } inline void convert_to(signed char* result, const tommath_int& val) { - *result = static_cast(boost::lexical_cast(val.str(0, false))); + *result = static_cast(boost::lexical_cast(val.str(0, std::ios_base::fmtflags(0)))); } inline void eval_abs(tommath_int& result, const tommath_int& val) { - detail::check_tommath_result(mp_abs(const_cast<::mp_int*>(&val.data()), &result.data())); + detail::check_tommath_result(mp_abs(const_cast< ::mp_int*>(&val.data()), &result.data())); } diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index d707576b..3a2c300e 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -607,3 +607,18 @@ run test_float_io.cpp mpfr gmp [ check-target-builds ../config//has_mpfr : : no ] : test_float_io_mpfr ; +run test_int_io.cpp $(TOMMATH) + : # command line + : # input files + : # requirements + TEST_TOMMATH + [ check-target-builds ../config//has_tommath : : no ] + : test_int_io_tommath ; + +run test_int_io.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPZ + [ check-target-builds ../config//has_gmp : : no ] + : test_int_io_mpz ; diff --git a/test/test.hpp b/test/test.hpp index de2224f5..b4d21e1c 100644 --- a/test/test.hpp +++ b/test/test.hpp @@ -63,7 +63,7 @@ inline T epsilon_of(const T&) template inline int digits_of(const T&) { - return std::numeric_limits::is_specialized ? std::numeric_limits::max_digits10 + 2 : std::numeric_limits::max_digits10 + 2; + return std::numeric_limits::is_specialized ? std::numeric_limits::digits10 + 2 : std::numeric_limits::digits10 + 2; } inline std::ostream& report_where(const char* file, int line, const char* function) diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp new file mode 100644 index 00000000..35963444 --- /dev/null +++ b/test/test_int_io.cpp @@ -0,0 +1,112 @@ +// Copyright John Maddock 2011. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) +# define TEST_TOMMATH +# define TEST_MPZ + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPZ) +#include +#endif +#if defined(TEST_TOMMATH) +#include +#endif + +#include +#include +#include +#include "test.hpp" +#include +#include + +template +T generate_random() +{ + static boost::random::uniform_int_distribution ui(0, 20); + static boost::random::mt19937 gen; + T val = gen(); + unsigned lim = ui(gen); + for(unsigned i = 0; i < lim; ++i) + { + val *= (gen.max)(); + val += gen(); + } + return val; +} + +template +void do_round_trip(const T& val, std::ios_base::fmtflags f) +{ + std::stringstream ss; + ss << std::setprecision(std::numeric_limits::max_digits10); + ss.flags(f); + ss << val; + T new_val = ss.str(); + BOOST_CHECK_EQUAL(new_val, val); + new_val = val.str(0, f); + BOOST_CHECK_EQUAL(new_val, val); +} + +template +void do_round_trip(const T& val) +{ + do_round_trip(val, std::ios_base::fmtflags(0)); + if(val >= 0) + { + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::showbase|std::ios_base::hex)); + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::showbase|std::ios_base::oct)); + } +} + +template +void test_round_trip() +{ + for(unsigned i = 0; i < 1000; ++i) + { + T val = generate_random(); + do_round_trip(val); + do_round_trip(T(-val)); + } + + BOOST_CHECK_EQUAL(T(1002).str(), "1002"); + BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::showpos), "+1002"); + BOOST_CHECK_EQUAL(T(-1002).str(), "-1002"); + BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::oct), "1752"); + BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::oct|std::ios_base::showbase), "01752"); + BOOST_CHECK_EQUAL(boost::to_lower_copy(T(1002).str(0, std::ios_base::hex)), "3ea"); + BOOST_CHECK_EQUAL(boost::to_lower_copy(T(1002).str(0, std::ios_base::hex|std::ios_base::showbase)), "0x3ea"); + BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::dec), "1002"); + BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::dec|std::ios_base::showbase), "1002"); + + BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::oct), std::runtime_error); + BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::hex), std::runtime_error); +} + +int main() +{ +#ifdef TEST_MPZ + test_round_trip(); +#endif +#ifdef TEST_TOMMATH + test_round_trip(); +#endif + return boost::report_errors(); +} + From d76492ddaa2e11551593057bf842655e653b6549 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 29 Nov 2011 12:27:40 +0000 Subject: [PATCH 077/256] Suppress some GCC warnings. [SVN r75723] --- include/boost/multiprecision/cpp_float.hpp | 2 +- test/test_acos.cpp | 1 - test/test_cos.cpp | 2 -- test/test_sin.cpp | 2 -- 4 files changed, 1 insertion(+), 6 deletions(-) diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index c432a13f..01af3e30 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -1218,7 +1218,7 @@ cpp_float& cpp_float::calculate_sqrt(void) static const boost::uint32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; - for(boost::uint32_t digits = double_digits10_minus_one; digits <= cpp_float_max_digits10; digits *= 2u) + for(boost::int32_t digits = double_digits10_minus_one; digits <= cpp_float_max_digits10; digits *= 2u) { // Adjust precision of the terms. precision(digits * 2); diff --git a/test/test_acos.cpp b/test/test_acos.cpp index 2528378e..317790ec 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -69,7 +69,6 @@ void test() {{-std::ldexp(1.0, -20), "1.57079728046921302562588198130454453120080334771863020290704515097032859824172056132832858516107615934431126321507917538" }}, {{-1, "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230665" }}, }}; - T half_pi = "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064"; unsigned max_err = 0; for(unsigned k = 0; k < exact_data.size(); k++) { diff --git a/test/test_cos.cpp b/test/test_cos.cpp index 4ea8b163..7bd0059f 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -152,8 +152,6 @@ void test() T("-5.01621542149055350065079347615664213658089623368745676779267390227688581807037821041573344917735076902116221444127518632e-1"), }}; - T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; - boost::uintmax_t max_err = 0; for(unsigned k = 0; k < data.size(); k++) { diff --git a/test/test_sin.cpp b/test/test_sin.cpp index d8747218..d5c0a850 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -152,8 +152,6 @@ T("7.976385836695348125971495748939809421552264032918126603158165073184286973614 T("8.65087179683067252708187359165577777305998628817518314353161876891989239932835217904989326717355654871984067712207255166e-1"), }}; - T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; - boost::uintmax_t max_err = 0; for(unsigned k = 0; k < data.size(); k++) { From fdcc1a5034620a2e07987680441217b6befc13e5 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 30 Nov 2011 12:08:59 +0000 Subject: [PATCH 078/256] Document libtommath support, add error checking to tommath bitwise operators. [SVN r75746] --- doc/html/boost_multiprecision/intro.html | 64 ++--- .../boost_multiprecision/ref/backendconc.html | 86 ++++--- .../boost_multiprecision/ref/mp_number.html | 228 +++++++++++++----- doc/html/boost_multiprecision/tut/ints.html | 153 +++++++++++- .../boost_multiprecision/tut/rational.html | 18 +- doc/html/boost_multiprecision/tut/reals.html | 52 ++-- doc/html/index.html | 4 +- doc/multiprecision.qbk | 151 ++++++++++-- include/boost/multiprecision/tommath.hpp | 24 +- test/Jamfile.v2 | 36 +-- test/test_arithmetic.cpp | 26 +- 11 files changed, 637 insertions(+), 205 deletions(-) diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index 6a2d9aaf..04fc3f7e 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -20,15 +20,22 @@ Introduction

- The Multiprecision library comes in two distinct parts: an expression-template-enabled - front end mp_number that handles - all the operator overloading, expression evaluation optimization, and code - reduction, and a selection of backends that implement the actual arithmetic - operations, and need conform only to the reduced interface requirements of - the front end. + The Multiprecision library comes in two distinct parts:

+
    +
  • + An expression-template-enabled front end mp_number + that handles all the operator overloading, expression evaluation optimization, + and code reduction. +
    • +
  • + A selection of backends that implement the actual arithmetic operations, + and need conform only to the reduced interface requirements of the front + end. +
    • +

- The library is often used by using one of the predfined typedefs: for example + The library is often used by using one of the predefined typedefs: for example if you wanted an arbitrary precision integer type using GMP as the underlying implementation then you could use:

@@ -37,10 +44,11 @@ boost::multiprecision::mpz_int myint; // Arbitrary precision integer type.

- Alternatively one can compose your own multiprecision type, by combining mp_number with one of the predefined backend - types. For example, suppose you wanted a 300 decimal digit floating point type - based on the MPFR library, in this case there's no predefined typedef with - that level of precision, so instead we compose our own: + Alternatively, you can compose your own multiprecision type, by combining + mp_number with one of the predefined + backend types. For example, suppose you wanted a 300 decimal digit floating-point + type based on the MPFR library. In this case, there's no predefined typedef + with that level of precision, so instead we compose our own: 

#include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
 
@@ -50,9 +58,9 @@
 
 my_float a, b, c; // These variables have 300 decimal digits precision
-
- - Expression +
+ + Expression Templates

@@ -95,15 +103,15 @@

If type T is an mp_number, then this expression is evaluated - without creating a single temporary value, in contrast + without creating a single temporary value. In contrast, if we were using the C++ wrapper that ships with GMP - mpf_class - then this expression would result in no less than 11 temporaries (this is - true even though mpf_class does use expression templates to reduce the number - of temporaries somewhat). Had we used an even simpler wrapper around GMP or - MPFR like mpclass things would - have been even worse and no less that 24 temporaries are created for this simple - expression (note - we actually measure the number of memory allocations performed - rather than the number of temporaries directly). + true even though mpf_class + does use expression templates to reduce the number of temporaries somewhat). + Had we used an even simpler wrapper around GMP or MPFR like mpclass + things would have been even worse and no less that 24 temporaries are created + for this simple expression (note - we actually measure the number of memory + allocations performed rather than the number of temporaries directly).

This library also extends expression template support to standard library functions @@ -138,11 +146,11 @@ their downsides. For one thing, expression template libraries like this one, tend to be slower to compile than their simpler cousins, they're also harder to debug (should you actually want to step through our code!), and rely on - compiler optimizations being turned on to give really good performance. Also + compiler optimizations being turned on to give really good performance. Also, since the return type from expressions involving mp_number's is an "unmentionable implementation detail", you have to be careful to cast the result of an expression to the actual number type when passing - an expression to a template function. For example given: + an expression to a template function. For example, given: 

template <class T>
 void my_proc(const T&);
@@ -160,7 +168,7 @@

Having said that, these situations don't occur that often - or indeed not at - all for non-template functions. In addition all the functions in the Boost.Math + all for non-template functions. In addition, all the functions in the Boost.Math library will automatically convert expression-template arguments to the underlying number type without you having to do anything, so:

@@ -179,12 +187,12 @@ 
auto my_expression = a + b - c;

- Unless you're absolutely sure that the lifetimes of a, + unless you're absolutely sure that the lifetimes of a, b and c will outlive that of my_expression.

- And finally.... the performance improvements from an expression template library + And finally... the performance improvements from an expression template library like this are often not as dramatic as the reduction in number of temporaries would suggest. For example if we compare this library with mpfr_class and mpreal, with all three @@ -272,7 +280,7 @@

- As you can see the execution time increases a lot more slowly than the number + As you can see, the execution time increases a lot more slowly than the number of memory allocations. There are a number of reasons for this:

    @@ -296,7 +304,7 @@

    We'll conclude this section by providing some more performance comparisons between these three libraries, again, all are using MPFR to carry out the underlying - arithmetic, and all are operating at the same precision (50 decimal places): + arithmetic, and all are operating at the same precision (50 decimal digits):

    Table 1.2. Evaluation of Boost.Math's Bessel function test data

    diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index 765eb817..99d7d865 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -21,7 +21,7 @@

    The requirements on the Backend template argument to mp_number - are split up into compulsary requirements, and optional requirements that + are split up into compulsory requirements, and optional requirements that are either to improve performance or provide optional features.

    @@ -33,13 +33,13 @@ is a variable of type const char*, ui is a variable of type unsigned, bb is a variable of type bool, pa is a variable of type - pointer-to-arithmetc-type, exp + pointer-to-arithmetic-type, exp is a variable of type B::exp_type, pexp is a variable of type B::exp_type*.

    -

    Table 1.4. Compulsary Requirements on the Backend type.

    -
    +

    Table 1.4. Compulsory Requirements on the Backend type.

    +
    @@ -114,7 +114,7 @@ @@ -591,7 +591,7 @@ and *pexp such that the value of cb is b * 2*pexp, only required when B - is a floating point type. + is a floating-point type.

    @@ -612,7 +612,7 @@

    Stores a value in b that is cb * 2exp, only required when B - is a floating point type. + is a floating-point type.

    @@ -632,8 +632,8 @@

    Stores the floor of cb in b, only required - when B is a floating - point type. + when B is a floating-point + type.

    @@ -653,8 +653,8 @@

    Stores the ceiling of cb in b, only required - when B is a floating - point type. + when B is a floating-point + type.

    @@ -674,8 +674,30 @@

    Stores the square root of cb in b, only required - when B is a floating - point type. + when B is a floating-point + type. +

    + + + + + + @@ -1618,7 +1640,7 @@

    Returns one of the same values returned by std::fpclassify. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1640,7 +1662,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1663,7 +1685,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1685,7 +1707,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1707,7 +1729,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1729,7 +1751,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1751,7 +1773,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1773,7 +1795,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1795,7 +1817,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1817,7 +1839,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1839,7 +1861,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1861,7 +1883,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1883,7 +1905,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1905,7 +1927,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1927,7 +1949,7 @@ on argument cb and stores the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1951,7 +1973,7 @@ and cb2, and store the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1975,7 +1997,7 @@ and cb2, and store the result in b. Only required when B - is an floating point type. + is an floating-point type.

    @@ -1999,7 +2021,7 @@ and cb2, and store the result in b. Only required when B - is an floating point type. + is an floating-point type.

    diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html index 613feeaa..727527eb 100644 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -19,9 +19,9 @@
    -
    - - Synopsis +
    + + Synopsis 
    namespace boost{ namespace multiprecision{
 
@@ -32,7 +32,22 @@
    mp_number(see-below);
    mp_number& operator=(see-below);
 
-   /* Other number-type operators here */
+   // Member operators
+   mp_number& operator+=(const see-below&);
+   mp_number& operator-=(const see-below&);
+   mp_number& operator*=(const see-below&);
+   mp_number& operator/=(const see-below&);
+   mp_number& operator++();
+   mp_number& operator--();
+   mp_number  operator++(int);
+   mp_number  operator--(int);
+
+   mp_number& operator%=(const see-below&);
+   mp_number& operator&=(const see-below&);
+   mp_number& operator|=(const see-below&);
+   mp_number& operator^=(const see-below&);
+   mp_number& operator<<=(const integer-type&);
+   mp_number& operator>>=(const integer-type&);
 
    // Use in Boolean context:
    operator convertible-to-bool-type()const;
@@ -60,6 +75,26 @@
    const Backend& backend()const;
 };
 
+// Non member operators:
+unmentionable-expression-template-type operator+(const see-below&, const see-below&);
+unmentionable-expression-template-type operator-(const see-below&, const see-below&);
+unmentionable-expression-template-type operator*(const see-below&, const see-below&);
+unmentionable-expression-template-type operator/(const see-below&, const see-below&);
+// Integer only operations:
+unmentionable-expression-template-type operator%(const see-below&, const see-below&);
+unmentionable-expression-template-type operator&(const see-below&, const see-below&);
+unmentionable-expression-template-type operator|(const see-below&, const see-below&);
+unmentionable-expression-template-type operator^(const see-below&, const see-below&);
+unmentionable-expression-template-type operator<<(const see-below&, const integer-type&);
+unmentionable-expression-template-type operator>>(const see-below&, const integer-type&);
+// Comparison operators:
+bool operator==(const see-below&, const see-below&);
+bool operator!=(const see-below&, const see-below&);
+bool operator< (const see-below&, const see-below&);
+bool operator> (const see-below&, const see-below&);
+bool operator<=(const see-below&, const see-below&);
+bool operator>=(const see-below&, const see-below&);
+
 // Swap:
 template <class Backend>
 void swap(mp_number<Backend>& a, mp_number<Backend>& b);
@@ -128,9 +163,9 @@
 
 }
    -
    - - Description +
    + + Description 
    mp_number();
 mp_number(see-below);
@@ -158,41 +193,43 @@
             Any type that the Backend is constructible or assignable from.
           
 
-
    /* Other number-type operators here */
+
    mp_number& operator+=(const see-below&);
+mp_number& operator-=(const see-below&);
+mp_number& operator*=(const see-below&);
+mp_number& operator/=(const see-below&);
+mp_number& operator++();
+mp_number& operator--();
+mp_number  operator++(int);
+mp_number  operator--(int);
+// Integer only operations:
+mp_number& operator%=(const see-below&);
+mp_number& operator&=(const see-below&);
+mp_number& operator|=(const see-below&);
+mp_number& operator^=(const see-below&);
+mp_number& operator<<=(const integer-type&);
+mp_number& operator>>=(const integer-type&);
 
    
 
    
-        The following arithmetic operations are support for real-numbered types:
+        These operators all take their usual arithmetic meanings.
+      
    
+
    
+        The arguments to these operators is either:
       
    
 
      
 
    • 
-            Binary +, -, *, /, +, -, *, /,
-            ==, !, <, >, <, >, ||, &&,
-            ||, &&=.
+            Another mp_number<Backend>.
           
      • 
 
    • 
-            Unary +, -, ++, --, !.
+            A builtin arithmetic type.
+          
      • 
+
    • 
+            An expression template derived from mp_number<Backend>.
           
      • 
 
    
 
    
-        For integer types the following operators are also supported:
-      
    
-
    
-        Binary %, %, |, |, &, &, ^, ^,
-        <<, <<, >>, >>.
-      
    
-
    
-        Note that with the exception of the logical operators and unary + the result
-        of applying an operator to mp_number is an "unmentionable" expression
-        template type.
-      
    
-
    
-        Binary operators, must have at least one argument that is of type mp_number or an expression template derived
-        from mp_number. One argument
-        may optionally be of arithmetic type.
-      
    
-
    
-        Note that type mp_number
-        (and all expression templates derived from it) may be used in a Boolian context.
+        For the left and right shift operations, the argument must be a builtin integer
+        type with a positive value (negative values result in a std::runtime_error
+        being thrown).
       
    
 
    operator convertible-to-bool-type()const;
 
    
@@ -203,6 +240,12 @@
         or as an argument to a logical operator - without type mp_number
         being convertible to type bool.
       
    
+
    
+        This operator also enables the use of mp_number
+        with any of the following operators: !,
+        ||, &&
+        and ?:.
+      
    
 
    void swap(mp_number& other);
 
    
 
    
@@ -257,24 +300,80 @@
       
    
 
      
 
    • 
-            A value less that 0 for *this < other
+            A value less that 0 for *this < other
           
      • 
 
    • 
-            A value greater that 0 for *this > other
+            A value greater that 0 for *this > other
           
      • 
 
    • 
-            Zero for *this == other
+            Zero for *this
+            == other
           
      • 
 
    
 
    Backend& backend();
 const Backend& backend()const;
 
    
 
    
-        Returns the underlying backend instance used by *this.
+        Returns the underlying backend instance used by *this.
       
    
-
    
-
-        swap
+
    
+
+        Non-member
+        operators
+      
    
+
    // Non member operators:
+unmentionable-expression-template-type operator+(const see-below&, const see-below&);
+unmentionable-expression-template-type operator-(const see-below&, const see-below&);
+unmentionable-expression-template-type operator*(const see-below&, const see-below&);
+unmentionable-expression-template-type operator/(const see-below&, const see-below&);
+// Integer only operations:
+unmentionable-expression-template-type operator%(const see-below&, const see-below&);
+unmentionable-expression-template-type operator&(const see-below&, const see-below&);
+unmentionable-expression-template-type operator|(const see-below&, const see-below&);
+unmentionable-expression-template-type operator^(const see-below&, const see-below&);
+unmentionable-expression-template-type operator<<(const see-below&, const integer-type&);
+unmentionable-expression-template-type operator>>(const see-below&, const integer-type&);
+// Comparison operators:
+bool operator==(const see-below&, const see-below&);
+bool operator!=(const see-below&, const see-below&);
+bool operator< (const see-below&, const see-below&);
+bool operator> (const see-below&, const see-below&);
+bool operator<=(const see-below&, const see-below&);
+bool operator>=(const see-below&, const see-below&);
+
    
+
    
+        These operators all take their usual arithmetic meanings.
+      
    
+
    
+        The arguments to these functions must contain at least one of the following:
+      
    
+
      
+
    • 
+            An mp_number.
+          
      • 
+
    • 
+            An expression template type derived from mp_number.
+          
      • 
+
    
+
    
+        In addition, one of the two arguments may be a builtin arithmetic type.
+      
    
+
    
+        With the exception of the comparison operators (which always evaluate their
+        arguments and return a bool
+        result), these operators return an "unmentionable" expression template
+        type which defers evaluation of the operator until the result is actually
+        required.
+      
    
+
    
+        Finally note that the second argument to the left and right shift operations
+        must be a builtin integer type, and that the argument must be positive (negative
+        arguments result in a std::runtime_error
+        being thrown).
+      
    
+
    
+
+        swap
       
    
 
    template <class Backend>
 void swap(mp_number<Backend>& a, mp_number<Backend>& b);
@@ -282,9 +381,9 @@
 
    
         Swaps a and b.
       
    
-
    
-
-        Iostream
+
    
+
+        Iostream
         Support
       
    
 
    template <class Backend>
@@ -298,9 +397,14 @@
         These operators provided formatted input-output operations on mp_number types, and expression templates
         derived from them.
       
    
-
    
-
-        Non-member
+
    
+        It's down to the backend type to actually implement string conversion. However,
+        the backends provided with this library support all of the iostream formatting
+        flags, field width and precision settings.
+      
    
+
    
+
+        Non-member
         standard library function support
       
    
 
    unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
@@ -351,30 +455,34 @@
       
    
 
    
         Also note that with the exception of abs
-        that these functions can only be used with floating point Backend types.
+        that these functions can only be used with floating-point Backend types.
       
    
-
    
-
-        Boost.Math
-        Interoperabilty Support
+
    
+
+        Boost.Math
+        Interoperability Support
       
    
 
    namespace boost{ namespace math{
 
-int                                              fpclassify     (const mp_number-or-expression-template-type&, int);
-bool                                             isfinite       (const mp_number-or-expression-template-type&, int);
-bool                                             isnan          (const mp_number-or-expression-template-type&, int);
-bool                                             isinf          (const mp_number-or-expression-template-type&, int);
-bool                                             isnormal       (const mp_number-or-expression-template-type&, int);
+int  fpclassify     (const mp_number-or-expression-template-type&, int);
+bool isfinite       (const mp_number-or-expression-template-type&, int);
+bool isnan          (const mp_number-or-expression-template-type&, int);
+bool isinf          (const mp_number-or-expression-template-type&, int);
+bool isnormal       (const mp_number-or-expression-template-type&, int);
 
 }} // namespaces
 
    
 
    
-        These functions behave exacts as their Boost.Math equivalents. Other Boost.Math
-        functions and templates may also be specialized or overloaded to ensure interoperability.
+        These floating-point classification functions behave exactly as their Boost.Math
+        equivalents.
       
    
-
    
-
-        std::numeric_limits
+
    
+        Other Boost.Math functions and templates may also be specialized or overloaded
+        to ensure interoperability.
+      
    
+
    
+
+        std::numeric_limits
         support
       
    
 
    namespace std{
diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html
index bccd2e4f..814eac46 100644
--- a/doc/html/boost_multiprecision/tut/ints.html
+++ b/doc/html/boost_multiprecision/tut/ints.html
@@ -63,7 +63,8 @@
                 
    
               
 
-
    + + - + + + + + + + + + +

    - A list of floating point types that can be assigned to type B.The + A list of floating-point types that can be assigned to type B.The types shall be listed in order of size, smallest first, and shall terminate in type long double.

    @@ -234,7 +234,7 @@

    - Swaps the contents of it's arguments. + Swaps the contents of its arguments.

    +

    + boost::multiprecision::number_category<B>::type +

    +     		+

    + mpl::int_<N> +

    +     		+

    + N is one of the + values number_kind_integer, + number_kind_floating_point, + number_kind_rational + or number_kind_fixed_point. + Defaults to number_kind_floating_point.

    gmp_int @@ -94,11 +95,44 @@ Dependency on GNU licenced GMP library.

    +

    + mp_int +

    +     		+

    + boost/multiprecision/tommath.hpp +

    +     		+

    + 2 +

    +     		+

    + libtommath +

    +     		+

    + Public domain backend with no licence restrictions. +

    +     		+

    + Slower than GMP. +

    +
    -
    - - gmp_int +
    + + gmp_int 
    namespace boost{ namespace multiprecision{
 
@@ -118,7 +152,7 @@
 
    
         As well as the usual conversions from arithmetic and string types, type
         mpz_int is copy constructible
-        and asignable from:
+        and assignable from:
       
    
 
      
 
    • 
@@ -132,14 +166,26 @@
 
    
 
    
         It's also possible to access the underlying mpz_t
-        via the data() member function of gmp_int.
+        via the data()
+        member function of gmp_int.
       
    
-
    
-
-        Example:
+
    
+
+
+
+
+
+
    [Note]Note
    
+          Formatted IO for this type does not support octal or hexadecimal notation
+          for negative values, as a result performing formatted output on this type
+          when the argument is negative and either of the flags std::ios_base::oct
+          or std::ios_base::hex are set, will result in a std::runtime_error will be thrown.
+        
    
+
    
+
+        Example:
       
    
 
    
-        
 
    
 
    #include <boost/multiprecision/gmp.hpp>
 
@@ -157,6 +203,91 @@
 mpz_t z;
 mpz_init(z);
 mpz_set(z, v.backend().data());
+
    
+
    
+      
    
+
    
+
+        mp_int
+      
    
+
    namespace boost{ namespace multiprecision{
+
+class tommath_int;
+
+typedef mp_number<tommath_int >         mp_int;
+
+}} // namespaces
+
    
+
    
+        The tommath_int backend is
+        used via the typedef boost::multiprecision::mp_int.
+        It acts as a thin wrapper around the libtommath mp_int
+        to provide an integer type that is a drop-in replacement for the native C++
+        integer types, but with unlimited precision.
+      
    
+
    
+
+
+
+
+
+
    [Caution]Caution
    
+          Although mp_int is mostly
+          a drop in replacement for the builtin integer types, it should be noted
+          that it is a rather strange beast as it's a signed type that is not a 2's
+          complement type. As a result the bitwise operations |
+          & ^
+          will throw a std::runtime_error exception if either of
+          the arguments is negative. Similarly the complement operator~ is deliberately not implemented for this
+          type.
+        
    
+
    
+
+
+
+
+
+
    [Note]Note
    
+          Formatted IO for this type does not support octal or hexadecimal notation
+          for negative values, as a result performing formatted output on this type
+          when the argument is negative and either of the flags std::ios_base::oct
+          or std::ios_base::hex are set, will result in a std::runtime_error will be thrown.
+        
    
+
    
+
+        Example:
+      
    
+
    
+
    
+
    #include <boost/multiprecision/tommath.hpp>
+
+boost::multiprecision::mp_int v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 1000!
+std::cout << std::hex << v << std::endl; // prints 1000! in hex format
+
+try{
+   std::cout << std::hex << -v << std::endl; // Ooops! can't print a negative value in hex format!
+}
+catch(const std::runtime_error& e)
+{
+   std::cout << e.what() << std::endl;
+}
+
+try{
+   // v is not a 2's complement type, bitwise operations are only supported
+   // on positive values:
+   v = -v & 2;
+}
+catch(const std::runtime_error& e)
+{
+   std::cout << e.what() << std::endl;
+}
+
 
    
 
    
       
    
diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html
index 4f5308d5..957ea0ee 100644
--- a/doc/html/boost_multiprecision/tut/rational.html
+++ b/doc/html/boost_multiprecision/tut/rational.html
@@ -96,9 +96,9 @@
    -
    - - gmp_rational +
    + + gmp_rational 
    namespace boost{ namespace multiprecision{
 
@@ -136,18 +136,18 @@
 mpz_int denominator(const mpq_rational&);

    - Which return the numerator and denominator of the number. + which return the numerator and denominator of the number.

    It's also possible to access the underlying mpq_t - via the data() member function of mpq_rational. + via the data() + member function of mpq_rational.

    -
    - - Example: +
    + + Example:

    - 

    #include <boost/multiprecision/gmp.hpp>
 
diff --git a/doc/html/boost_multiprecision/tut/reals.html b/doc/html/boost_multiprecision/tut/reals.html
index a5df3c35..429cf67d 100644
--- a/doc/html/boost_multiprecision/tut/reals.html
+++ b/doc/html/boost_multiprecision/tut/reals.html
@@ -119,7 +119,7 @@
               
 
                 
    
-                  Very fast and efficient backend, with it's own standard library
+                  Very fast and efficient backend, with its own standard library
                   implementation.
                 
    
               
@@ -152,7 +152,7 @@
               
 
                 
    
-                  Header only, all C++ implementation.
+                  Header only, all C++ implementation. Boost licence.
                 
    
               
 
@@ -163,9 +163,9 @@
    -
    - - gmp_float +
    + + gmp_float 
    namespace boost{ namespace multiprecision{
 
@@ -182,8 +182,8 @@

    The gmp_float backend is - used in conjunction with mp_number: - It acts as a thin wrapper around the GMP mpf_t + used in conjunction with mp_number + : it acts as a thin wrapper around the GMP mpf_t to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision.

    @@ -226,14 +226,15 @@

It's also possible to access the underlying mpf_t - via the data() member function of gmp_float. + via the data() + member function of gmp_float.

-
- - GMP example: +
+ + GMP + example:

- 

#include <boost/multiprecision/gmp.hpp>
 
@@ -257,9 +258,9 @@

-
- - mpfr_float +
+ + mpfr_float 
namespace boost{ namespace multiprecision{
 
@@ -324,12 +325,12 @@
         It's also possible to access the underlying mpf_t
         via the data() member function of gmp_float.
       

-

-
-        MPFR example:
+

+
+        MPFR
+        example:
       

 

-        
 

 
#include <boost/multiprecision/mpfr.hpp>
 
@@ -353,9 +354,9 @@
 

 

       

-

-
-        cpp_float
+

+
+        cpp_float
       

 
namespace boost{ namespace multiprecision{
 
@@ -384,13 +385,12 @@
         There is full standard library and numeric_limits
         support available for this type.
       

-

-
-        cpp_float
+

+
+        cpp_float
         example:
       

 

-        
 

 
#include <boost/multiprecision/cpp_float.hpp>
 
diff --git a/doc/html/index.html b/doc/html/index.html
index 2f877f6c..78af59a2 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -20,7 +20,7 @@
 

 
Copyright © 2011 John Maddock

 

-

+

         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       

@@ -45,7 +45,7 @@
 

 

 
-
+
Last revised: July 08, 2011 at 18:51:46 +0100
Last revised: November 29, 2011 at 19:27:45 GMT

 

 

 

diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk
index 48117bfd..e29dd22b 100644
--- a/doc/multiprecision.qbk
+++ b/doc/multiprecision.qbk
@@ -21,6 +21,7 @@
 [import ../example/gmp_snips.cpp]
 [import ../example/mpfr_snips.cpp]
 [import ../example/cpp_float_snips.cpp]
+[import ../example/tommath_snips.cpp]
 
 [section:intro Introduction]
 
@@ -199,6 +200,7 @@ The following backends provide integer arithmetic:
 [table
 [[Backend Type][Header][Radix][Dependencies][Pros][Cons]]
 [[`gmp_int`][boost/multiprecision/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]]
+[[`mp_int`][boost/multiprecision/tommath.hpp][2][libtommath][Public domain backend with no licence restrictions.][Slower than GMP.]]
 ]
 
 [h4 gmp_int]
@@ -221,10 +223,40 @@ As well as the usual conversions from arithmetic and string types, type `mpz_int
 
 It's also possible to access the underlying `mpz_t` via the `data()` member function of `gmp_int`.
 
+[note Formatted IO for this type does not support octal or hexadecimal notation for negative values, 
+as a result performing formatted output on this type when the argument is negative and either of the flags
+`std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown.]
+
 [h5 Example:]
 
 [mpz_eg]
 
+[h4 mp_int]
+
+   namespace boost{ namespace multiprecision{
+
+   class tommath_int;
+
+   typedef mp_number         mp_int;
+
+   }} // namespaces
+
+The `tommath_int` backend is used via the typedef `boost::multiprecision::mp_int`.  It acts as a thin wrapper around the libtommath `mp_int`
+to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision.
+
+[caution Although `mp_int` is mostly a drop in replacement for the builtin integer types, it should be noted that it is a
+rather strange beast as it's a signed type that is not a 2's complement type.  As a result the bitwise operations
+`| & ^` will throw a `std::runtime_error` exception if either of the arguments is negative.  Similarly the complement
+operator`~` is deliberately not implemented for this type.]
+
+[note Formatted IO for this type does not support octal or hexadecimal notation for negative values, 
+as a result performing formatted output on this type when the argument is negative and either of the flags
+`std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown.]
+
+[h5 Example:]
+
+[tommath_eg]
+
 [endsect]
 
 [section:reals Real Numbers]
@@ -405,7 +437,22 @@ It's also possible to access the underlying `mpq_t` via the `data()` member func
       mp_number(see-below);
       mp_number& operator=(see-below);
 
-      /* Other number-type operators here */
+      // Member operators
+      mp_number& operator+=(const ``['see-below]``&);
+      mp_number& operator-=(const ``['see-below]``&);
+      mp_number& operator*=(const ``['see-below]``&);
+      mp_number& operator/=(const ``['see-below]``&);
+      mp_number& operator++();
+      mp_number& operator--();
+      mp_number  operator++(int);
+      mp_number  operator--(int);
+
+      mp_number& operator%=(const ``['see-below]``&);
+      mp_number& operator&=(const ``['see-below]``&);
+      mp_number& operator|=(const ``['see-below]``&);
+      mp_number& operator^=(const ``['see-below]``&);
+      mp_number& operator<<=(const ``['integer-type]``&);
+      mp_number& operator>>=(const ``['integer-type]``&);
 
       // Use in Boolean context:
       operator ``['convertible-to-bool-type]``()const;
@@ -433,6 +480,26 @@ It's also possible to access the underlying `mpq_t` via the `data()` member func
       const Backend& backend()const;
    };
 
+   // Non member operators:
+   ``['unmentionable-expression-template-type]`` operator+(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator-(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator*(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator/(const ``['see-below]``&, const ``['see-below]``&);
+   // Integer only operations:
+   ``['unmentionable-expression-template-type]`` operator%(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator&(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator|(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator^(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator<<(const ``['see-below]``&, const ``['integer-type]``&);
+   ``['unmentionable-expression-template-type]`` operator>>(const ``['see-below]``&, const ``['integer-type]``&);
+   // Comparison operators:
+   bool operator==(const ``['see-below]``&, const ``['see-below]``&);
+   bool operator!=(const ``['see-below]``&, const ``['see-below]``&);
+   bool operator< (const ``['see-below]``&, const ``['see-below]``&);
+   bool operator> (const ``['see-below]``&, const ``['see-below]``&);
+   bool operator<=(const ``['see-below]``&, const ``['see-below]``&);
+   bool operator>=(const ``['see-below]``&, const ``['see-below]``&);
+
    // Swap:
    template 
    void swap(mp_number& a, mp_number& b);
@@ -515,24 +582,32 @@ Type `mp_number` is default constructible, and both copy constructible and assig
 * A `std::string` or any type which is convertible to `const char*`.
 * Any type that the Backend is constructible or assignable from.
 
-      /* Other number-type operators here */
+      mp_number& operator+=(const ``['see-below]``&);
+      mp_number& operator-=(const ``['see-below]``&);
+      mp_number& operator*=(const ``['see-below]``&);
+      mp_number& operator/=(const ``['see-below]``&);
+      mp_number& operator++();
+      mp_number& operator--();
+      mp_number  operator++(int);
+      mp_number  operator--(int);
+      // Integer only operations:
+      mp_number& operator%=(const ``['see-below]``&);
+      mp_number& operator&=(const ``['see-below]``&);
+      mp_number& operator|=(const ``['see-below]``&);
+      mp_number& operator^=(const ``['see-below]``&);
+      mp_number& operator<<=(const ``['integer-type]``&);
+      mp_number& operator>>=(const ``['integer-type]``&);
 
-The following arithmetic operations are support for real-numbered types:
+These operators all take their usual arithmetic meanings.
 
-* Binary +, -, *, /, +=, -=, *=, /=, ==, !=, <=, >=, <, >, ||, &&, ||=, &&=.
-* Unary +, -, ++, --, !.
+The arguments to these operators is either:
 
-For integer types the following operators are also supported:
+* Another `mp_number`.
+* A builtin arithmetic type.
+* An expression template derived from `mp_number`.
 
-Binary %, %=, |, |=, &, &=, ^, ^=, <<, <<=, >>, >>=.
-
-Note that with the exception of the logical operators and unary + the result of applying an operator to
-mp_number is an "unmentionable" expression template type.
-
-Binary operators, must have at least one argument that is of type `mp_number` or an expression template
-derived from `mp_number`.  One argument may optionally be of arithmetic type.
-
-Note that type `mp_number` (and all expression templates derived from it) may be used in a Boolean context.
+For the left and right shift operations, the argument must be a builtin
+integer type with a positive value (negative values result in a `std::runtime_error` being thrown).
 
       operator ``['convertible-to-bool-type]``()const;
 
@@ -540,6 +615,9 @@ Returns an ['unmentionable-type] that is usable in Boolean contexts (this allows
 Boolean context - if statements, conditional statements, or as an argument to a logical operator - without
 type `mp_number` being convertible to type `bool`.
 
+This operator also enables the use of `mp_number` with any of the following operators:
+`!`, `||`, `&&` and `?:`.
+
       void swap(mp_number& other);
 
 Swaps `*this` with `other`.
@@ -588,6 +666,44 @@ Returns:
 
 Returns the underlying backend instance used by `*this`.
 
+[h4 Non-member operators]
+
+   // Non member operators:
+   ``['unmentionable-expression-template-type]`` operator+(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator-(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator*(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator/(const ``['see-below]``&, const ``['see-below]``&);
+   // Integer only operations:
+   ``['unmentionable-expression-template-type]`` operator%(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator&(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator|(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator^(const ``['see-below]``&, const ``['see-below]``&);
+   ``['unmentionable-expression-template-type]`` operator<<(const ``['see-below]``&, const ``['integer-type]``&);
+   ``['unmentionable-expression-template-type]`` operator>>(const ``['see-below]``&, const ``['integer-type]``&);
+   // Comparison operators:
+   bool operator==(const ``['see-below]``&, const ``['see-below]``&);
+   bool operator!=(const ``['see-below]``&, const ``['see-below]``&);
+   bool operator< (const ``['see-below]``&, const ``['see-below]``&);
+   bool operator> (const ``['see-below]``&, const ``['see-below]``&);
+   bool operator<=(const ``['see-below]``&, const ``['see-below]``&);
+   bool operator>=(const ``['see-below]``&, const ``['see-below]``&);
+
+These operators all take their usual arithmetic meanings.
+
+The arguments to these functions must contain at least one of the following:
+
+* An `mp_number`.
+* An expression template type derived from `mp_number`.
+
+In addition, one of the two arguments may be a builtin arithmetic type.
+
+With the exception of the comparison operators (which always evaluate their arguments and return a `bool` result),
+these operators return an "unmentionable" expression template type which defers evaluation of the operator
+until the result is actually required.
+
+Finally note that the second argument to the left and right shift operations must be a builtin integer type, 
+and that the argument must be positive (negative arguments result in a `std::runtime_error` being thrown).
+
 [h4 swap]
 
    template 
@@ -606,6 +722,9 @@ Swaps `a` and `b`.
 
 These operators provided formatted input-output operations on `mp_number` types, and expression templates derived from them.
 
+It's down to the backend type to actually implement string conversion.  However, the backends provided with
+this library support all of the iostream formatting flags, field width and precision settings.
+
 [h4 Non-member standard library function support]
 
    ``['unmentionable-expression-template-type]``    abs    (const ``['mp_number-or-expression-template-type]``&);
@@ -743,6 +862,8 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia
 [[`eval_floor(b, cb)`][`void`][Stores the floor of `cb` in `b`, only required when `B` is a floating-point type.]]
 [[`eval_ceil(b, cb)`][`void`][Stores the ceiling of `cb` in `b`, only required when `B` is a floating-point type.]]
 [[`eval_sqrt(b, cb)`][`void`][Stores the square root of `cb` in `b`, only required when `B` is a floating-point type.]]
+[[`boost::multiprecision::number_category::type`][`mpl::int_`][`N` is one of the values `number_kind_integer`, `number_kind_floating_point`, `number_kind_rational` or `number_kind_fixed_point`.
+                                                Defaults to `number_kind_floating_point`.]]
 ]
 
 [table Optional Requirements on the Backend Type
diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp
index b0b9067e..bd3ba689 100644
--- a/include/boost/multiprecision/tommath.hpp
+++ b/include/boost/multiprecision/tommath.hpp
@@ -229,6 +229,10 @@ protected:
    mp_int m_data;
 };
 
+#define BOOST_MP_TOMMATH_BIT_OP_CHECK(x)\
+   if(SIGN(&x.data()))\
+      BOOST_THROW_EXCEPTION(std::runtime_error("Bitwise operations on libtommath negative valued integers are disabled as they produce unpredictable results"))
+
 int get_sign(const tommath_int& val);
 
 inline void add(tommath_int& t, const tommath_int& o)
@@ -285,16 +289,22 @@ inline void right_shift(tommath_int& t, const tommath_int& v, UI i)
 
 inline void bitwise_and(tommath_int& result, const tommath_int& v)
 {
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(result);
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
    detail::check_tommath_result(mp_and(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data()));
 }
 
 inline void bitwise_or(tommath_int& result, const tommath_int& v)
 {
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(result);
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
    detail::check_tommath_result(mp_or(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data()));
 }
 
 inline void bitwise_xor(tommath_int& result, const tommath_int& v)
 {
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(result);
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
    detail::check_tommath_result(mp_xor(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data()));
 }
 
@@ -330,21 +340,31 @@ inline void modulus(tommath_int& t, const tommath_int& p, const tommath_int& o)
 
 inline void bitwise_and(tommath_int& result, const tommath_int& u, const tommath_int& v)
 {
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(u);
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
    detail::check_tommath_result(mp_and(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data()));
 }
 
 inline void bitwise_or(tommath_int& result, const tommath_int& u, const tommath_int& v)
 {
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(u);
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
    detail::check_tommath_result(mp_or(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data()));
 }
 
 inline void bitwise_xor(tommath_int& result, const tommath_int& u, const tommath_int& v)
 {
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(u);
+   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
    detail::check_tommath_result(mp_xor(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data()));
 }
-
+/*
 inline void complement(tommath_int& result, const tommath_int& u)
 {
+   //
+   // Although this code works, it doesn't really do what the user might expect....
+   // and it's hard to see how it ever could.  Disabled for now:
+   //
    result = u;
    for(int i = 0; i < result.data().used; ++i)
    {
@@ -367,7 +387,7 @@ inline void complement(tommath_int& result, const tommath_int& u)
    left_shift(mask, shift);
    add(result, mask);
 }
-
+*/
 inline bool is_zero(const tommath_int& val)
 {
    return mp_iszero(&val.data());
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 3a2c300e..018e0802 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -506,20 +506,6 @@ run test_mpfr_conversions.cpp gmp mpfr
         : # requirements
          [ check-target-builds ../config//has_mpfr : : no ] ;
 
-run ../example/gmp_snips.cpp gmp
-        : # command line
-        : # input files
-        : # requirements
-         [ check-target-builds ../config//has_gmp : : no ] ;
-
-run ../example/mpfr_snips.cpp mpfr
-        : # command line
-        : # input files
-        : # requirements
-         [ check-target-builds ../config//has_mpfr : : no ] ;
-
-run ../example/cpp_float_snips.cpp ;
-
 run test_round.cpp
         : # command line
         : # input files
@@ -622,3 +608,25 @@ run test_int_io.cpp gmp
 	      TEST_MPZ
          [ check-target-builds ../config//has_gmp : : no ]
         : test_int_io_mpz ;
+
+run ../example/gmp_snips.cpp gmp
+        : # command line
+        : # input files
+        : # requirements
+         [ check-target-builds ../config//has_gmp : : no ] ;
+
+run ../example/mpfr_snips.cpp mpfr
+        : # command line
+        : # input files
+        : # requirements
+         [ check-target-builds ../config//has_mpfr : : no ] ;
+
+run ../example/cpp_float_snips.cpp ;
+
+run ../example/tommath_snips.cpp $(TOMMATH)
+        : # command line
+        : # input files
+        : # requirements
+         [ check-target-builds ../config//has_tommath : : no ] ;
+
+
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index b6ae1a92..1a7b5bc7 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -86,6 +86,24 @@ template <>
 struct is_twos_complement_integer : public boost::mpl::false_ {};
 #endif
 
+template 
+void test_complement(Real a, Real b, Real c, const boost::mpl::true_&)
+{
+   int i = 1020304;
+   int j = 56789123;
+   int sign_mask = ~0;
+   BOOST_TEST(~a == (~i & sign_mask));
+   c = a & ~b;
+   BOOST_TEST(c == (i & (~j & sign_mask)));
+   c = ~(a | b);
+   BOOST_TEST(c == (~(i | j) & sign_mask));
+}
+
+template 
+void test_complement(Real, Real, Real, const boost::mpl::false_&)
+{
+}
+
 template 
 void test_integer_ops(const T&){}
 
@@ -196,7 +214,6 @@ void test_integer_ops(const boost::mpl::int_::value ? ~0 : (std::numeric_limits::max)();
    a = i;
    b = j;
    c = a;
@@ -219,6 +236,8 @@ void test_integer_ops(const boost::mpl::int_(a, b, c, typename is_twos_complement_integer::type());
+
    a = i;
    b = j;
    c = a;
@@ -265,11 +284,6 @@ void test_integer_ops(const boost::mpl::int_
Date: Wed, 30 Nov 2011 12:16:52 +0000
Subject: [PATCH 079/256] Add roadmap and TODO list.

[SVN r75747]
---
 doc/html/boost_multiprecision/map.html        | 40 +++++++++++++
 doc/html/boost_multiprecision/map/hist.html   | 34 +++++++++++
 doc/html/boost_multiprecision/map/todo.html   | 57 +++++++++++++++++++
 .../boost_multiprecision/ref/backendconc.html |  5 +-
 doc/html/index.html                           |  7 ++-
 doc/multiprecision.qbk                        | 19 +++++++
 6 files changed, 159 insertions(+), 3 deletions(-)
 create mode 100644 doc/html/boost_multiprecision/map.html
 create mode 100644 doc/html/boost_multiprecision/map/hist.html
 create mode 100644 doc/html/boost_multiprecision/map/todo.html

diff --git a/doc/html/boost_multiprecision/map.html b/doc/html/boost_multiprecision/map.html
new file mode 100644
index 00000000..0f9be0ff
--- /dev/null
+++ b/doc/html/boost_multiprecision/map.html
@@ -0,0 +1,40 @@
+
+
+
+Roadmap
+
+
+
+
+
+
+
+
+

+

+

+PrevUpHomeNext
+

+

+

+

+
History

+
TODO

+

+

+
+
+
+
Copyright © 2011 John Maddock

+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      

+

+

+

+PrevUpHomeNext
+

+
+
diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html
new file mode 100644
index 00000000..2403eb82
--- /dev/null
+++ b/doc/html/boost_multiprecision/map/hist.html
@@ -0,0 +1,34 @@
+
+
+
+History
+
+
+
+
+
+
+
+
+

+

+

+PrevUpHomeNext
+

+

+
+
+
+
Copyright © 2011 John Maddock

+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      

+

+

+

+PrevUpHomeNext
+

+
+
diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html
new file mode 100644
index 00000000..977961ff
--- /dev/null
+++ b/doc/html/boost_multiprecision/map/todo.html
@@ -0,0 +1,57 @@
+
+
+
+TODO
+
+
+
+
+
+
+
+

+

+

+PrevUpHome
+

+

+

+TODO
+

+

+        More a list of what could be done, rather than what
+        should be done (which may be a much smaller list!).
+      

+
    
+
  • 
+            Adapt Boost.Math special function tests for this library: will make a
+            very good test of arithmetic and std lib support.
+          
    • 
+
  • 
+            Add an adapter backend for complex number types.
+          
    • 
+
  • 
+            Add an adapter backend for rational types.
+          
    • 
+
  • 
+            Test integer types with Boost.Rational.
+          
    • 
+
  • 
+            Adapt libtommath code to make an all C++ fixed precision integer type.
+          
    • 
+

+

+
+
+
+
Copyright © 2011 John Maddock

+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      

+

+

+

+PrevUpHome
+

+
+
diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html
index 99d7d865..fdb54705 100644
--- a/doc/html/boost_multiprecision/ref/backendconc.html
+++ b/doc/html/boost_multiprecision/ref/backendconc.html
@@ -7,12 +7,13 @@
 
 
 
+
 
 
 

 

 

-PrevUpHome
+PrevUpHomeNext
 

 

 

@@ -2040,7 +2041,7 @@
 
 

 

-PrevUpHome
+PrevUpHomeNext
 

 
 
diff --git a/doc/html/index.html b/doc/html/index.html
index 78af59a2..9abc8978 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -41,11 +41,16 @@
 
mp_number

 
Backend Requirements

 
+
Roadmap

+

+
History

+
TODO

+

 
 

 

 
-
+
Last revised: November 29, 2011 at 19:27:45 GMT
Last revised: November 30, 2011 at 12:15:51 GMT

 

 

 

diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk
index e29dd22b..d074fe83 100644
--- a/doc/multiprecision.qbk
+++ b/doc/multiprecision.qbk
@@ -956,3 +956,22 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia
 
 [endsect]
 
+[section:map Roadmap]
+
+[section:hist History]
+
+[endsect]
+
+[section:todo TODO]
+
+More a list of what ['could] be done, rather than what ['should] be done (which may be a much smaller list!).
+
+* Adapt Boost.Math special function tests for this library: will make a very good test of arithmetic and std lib support.
+* Add an adapter backend for complex number types.
+* Add an adapter backend for rational types.
+* Test integer types with Boost.Rational.
+* Adapt libtommath code to make an all C++ fixed precision integer type.
+
+[endsect]
+
+[endsect]
\ No newline at end of file

From 018ac8cd6cc486dc1c8a784f44d1eca242af7534 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Tue, 6 Dec 2011 19:03:41 +0000
Subject: [PATCH 080/256] Begin adding tests taken from Boost.Math and fix the
 issues they flag up.

[SVN r75832]
---
 include/boost/multiprecision/cpp_float.hpp    |  63 +++++++--
 .../detail/functions/constants.hpp            |   2 +-
 .../multiprecision/detail/functions/pow.hpp   |  66 +++++++--
 .../multiprecision/detail/functions/trig.hpp  |  15 +-
 test/Jamfile.v2                               |  29 ++++
 test/math/log1p_expm1_test.cpp                | 131 +++++++++++++++++
 test/math/powm1_sqrtp1m1_test.cpp             | 132 ++++++++++++++++++
 test/math/test_bessel_i.cpp                   | 107 ++++++++++++++
 test/math/test_bessel_j.cpp                   | 129 +++++++++++++++++
 test/math/test_bessel_k.cpp                   | 115 +++++++++++++++
 test/math/test_bessel_y.cpp                   | 121 ++++++++++++++++
 test/math/test_beta.cpp                       | 128 +++++++++++++++++
 test/math/test_binomial_coeff.cpp             | 107 ++++++++++++++
 test/math/test_carlson.cpp                    | 108 ++++++++++++++
 test/test_atan.cpp                            |   2 +-
 test/test_cos.cpp                             |  15 +-
 test/test_cosh.cpp                            |   5 +
 test/test_numeric_limits.cpp                  |  29 +++-
 test/test_sinh.cpp                            |  81 +++++++++++
 test/test_tanh.cpp                            |   2 +-
 20 files changed, 1357 insertions(+), 30 deletions(-)
 create mode 100644 test/math/log1p_expm1_test.cpp
 create mode 100644 test/math/powm1_sqrtp1m1_test.cpp
 create mode 100644 test/math/test_bessel_i.cpp
 create mode 100644 test/math/test_bessel_j.cpp
 create mode 100644 test/math/test_bessel_k.cpp
 create mode 100644 test/math/test_bessel_y.cpp
 create mode 100644 test/math/test_beta.cpp
 create mode 100644 test/math/test_binomial_coeff.cpp
 create mode 100644 test/math/test_carlson.cpp

diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp
index 01af3e30..8c2f0411 100644
--- a/include/boost/multiprecision/cpp_float.hpp
+++ b/include/boost/multiprecision/cpp_float.hpp
@@ -42,12 +42,15 @@ public:
    static const boost::int32_t cpp_float_digits10         = ((cpp_float_digits10_setting < static_cast(30)) ? static_cast(30) : ((cpp_float_digits10_setting > cpp_float_digits10_limit) ? cpp_float_digits10_limit : cpp_float_digits10_setting));
    static const boost::int32_t cpp_float_digits10_extra   = static_cast(((static_cast(cpp_float_digits10) * 15LL) + 50LL) / 100LL);
    static const boost::int32_t cpp_float_max_digits10     = static_cast(cpp_float_digits10 + ((cpp_float_digits10_extra < static_cast(5)) ? static_cast(5) : ((cpp_float_digits10_extra > static_cast(30)) ? static_cast(30) : cpp_float_digits10_extra)));
-   static const boost::int64_t cpp_float_max_exp   = static_cast(+9223372036854775795LL);
-   static const boost::int64_t cpp_float_min_exp   = static_cast(-9223372036854775795LL);
-   static const boost::int64_t cpp_float_max_exp10 = static_cast(+3063937869882635616LL); // Approx. [cpp_float_max_exp / log10(2)], also an even multiple of 8
-   static const boost::int64_t cpp_float_min_exp10 = static_cast(-3063937869882635616LL);
+   static const boost::int64_t cpp_float_max_exp10 = 2776234983093287512;
+   static const boost::int64_t cpp_float_min_exp10 = -2776234983093287512;
+   static const boost::int64_t cpp_float_max_exp   = (cpp_float_max_exp10 / 301LL) * 1000LL;
+   static const boost::int64_t cpp_float_min_exp   = (cpp_float_min_exp10 / 301LL) * 1000LL;
    static const boost::int32_t mp_elem_digits10   = static_cast(8);
 
+   BOOST_STATIC_ASSERT(0 == cpp_float_max_exp10 % mp_elem_digits10);
+   BOOST_STATIC_ASSERT(cpp_float_max_exp10 == -cpp_float_min_exp10);
+
 private:
    static const boost::int32_t cpp_float_digits10_num_base = static_cast((cpp_float_max_digits10 / mp_elem_digits10) + (((cpp_float_max_digits10 % mp_elem_digits10) != 0) ? 1 : 0));
    static const boost::int32_t mp_elem_number       = static_cast(cpp_float_digits10_num_base + 2);
@@ -740,8 +743,8 @@ cpp_float& cpp_float::operator+=(const cpp_float&
       return *this = zero();
    }
 
-   bool overflow = exp >= cpp_float_max_exp;
-   if(exp == cpp_float_max_exp)
+   bool overflow = exp >= cpp_float_max_exp10;
+   if(exp == cpp_float_max_exp10)
    {
       // Check to see if we really truely have an overflow or not...
       if(isneg())
@@ -971,8 +974,8 @@ cpp_float& cpp_float::mul_unsigned_long_long(const unsigned
       data.front() = static_cast(carry);
    }
 
-   bool overflow = exp >= cpp_float_max_exp;
-   if(exp == cpp_float_max_exp)
+   bool overflow = exp >= cpp_float_max_exp10;
+   if(exp == cpp_float_max_exp10)
    {
       // Check to see if we really truely have an overflow or not...
       if(isneg())
@@ -2723,14 +2726,52 @@ inline void eval_frexp(cpp_float& result, const cpp_float& x
    if(result.isneg())
       result.negate();
 
+   if(result.iszero())
+   {
+      *e = 0;
+      return;
+   }
+
    long long t = result.order();
 
-   if(std::abs(t) > (std::numeric_limits::max)() / 3)
-      BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2."));
-   t *= 3;
+   if(std::abs(t) < ((std::numeric_limits::max)() / 1000))
+   {
+      t *= 1000;
+      t /= 301;
+   }
+   else
+   {
+      t /= 301;
+      t *= 1000;
+   }
 
    result *= cpp_float::pow2(-t);
 
+   if(result.iszero() || result.isinf() || result.isnan())
+   {
+      // pow2 overflowed, slip the calculation up:
+      result = x;
+      if(result.isneg())
+         result.negate();
+      t /= 2;
+      result *= cpp_float::pow2(-t);
+   }
+
+   if(std::abs(result.order()) > 5)
+   {
+      // If our first estimate doesn't get close enough then try recursion until we do:
+      long long e2;
+      cpp_float r2;
+      eval_frexp(r2, result, &e2);
+      // overflow prtection:
+      if((t > 0) && (e2 > 0) && (t > (std::numeric_limits::max)() - e2))
+         BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2."));
+      if((t < 0) && (e2 < 0) && (t < (std::numeric_limits::min)() - e2))
+         BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2."));
+      t += e2;
+      result = r2;
+   }
+
    while(result.compare(cpp_float::one()) >= 0)
    {
       result /= cpp_float::two();
diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp
index d8fc9966..dab1e2c3 100644
--- a/include/boost/multiprecision/detail/functions/constants.hpp
+++ b/include/boost/multiprecision/detail/functions/constants.hpp
@@ -178,7 +178,7 @@ const T& get_constant_pi()
    static bool b = false;
    if(!b)
    {
-      calc_pi(result, boost::multiprecision::detail::digits2 >::value);
+      calc_pi(result, boost::multiprecision::detail::digits2 >::value + 10);
       b = true;
    }
 
diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp
index 3883d938..91b1a084 100644
--- a/include/boost/multiprecision/detail/functions/pow.hpp
+++ b/include/boost/multiprecision/detail/functions/pow.hpp
@@ -544,6 +544,33 @@ inline void eval_pow(T& result, const T& x, const T& a)
 
 namespace detail{
 
+   template 
+   void small_sinh_series(T x, T& result)
+   {
+      typedef typename boost::multiprecision::detail::canonical::type ui_type;
+      bool neg = get_sign(x) < 0;
+      if(neg)
+         x.negate();
+      T p(x);
+      T mult(x);
+      multiply(mult, x);
+      result = x;
+      ui_type k = 1;
+
+      T lim(x);
+      eval_ldexp(lim, lim, 1 - boost::multiprecision::detail::digits2 >::value);
+
+      do
+      {
+         multiply(p, mult);
+         divide(p, ++k);
+         divide(p, ++k);
+         add(result, p);
+      }while(p.compare(lim) >= 0);
+      if(neg)
+         result.negate();
+   }
+
    template 
    void sinhcosh(const T& x, T* p_sinh, T* p_cosh)
    {
@@ -571,21 +598,36 @@ namespace detail{
       default: ;
       }
 
+      T e_px, e_mx;
 
-      T e_px;
-      eval_exp(e_px, x);
-      T e_mx;
-      divide(e_mx, ui_type(1), e_px);
+      bool small_sinh = get_sign(x) < 0 ? e_px.compare(fp_type(-0.5)) > 0 : e_px.compare(fp_type(0.5)) < 0;
 
-      if(p_sinh) 
-      { 
-         subtract(*p_sinh, e_px, e_mx);
-         divide(*p_sinh, ui_type(2));
+      if(p_cosh || !small_sinh)
+      {
+         eval_exp(e_px, x);
+         divide(e_mx, ui_type(1), e_px);
+
+         if(p_sinh) 
+         { 
+            if(small_sinh)
+            {
+               small_sinh_series(x, *p_sinh);
+            }
+            else
+            {
+               subtract(*p_sinh, e_px, e_mx);
+               divide(*p_sinh, ui_type(2));
+            }
+         }
+         if(p_cosh) 
+         { 
+            add(*p_cosh, e_px, e_mx);
+            divide(*p_cosh, ui_type(2)); 
+         }
       }
-      if(p_cosh) 
-      { 
-         add(*p_cosh, e_px, e_mx);
-         divide(*p_cosh, ui_type(2)); 
+      else
+      {
+         small_sinh_series(x, *p_sinh);
       }
    }
 
diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp
index d466b84c..17a7f353 100644
--- a/include/boost/multiprecision/detail/functions/trig.hpp
+++ b/include/boost/multiprecision/detail/functions/trig.hpp
@@ -120,6 +120,9 @@ void eval_sin(T& result, const T& x)
       multiply(n_pi, get_constant_pi());
       subtract(xx, n_pi);
 
+      BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific));
+      BOOST_MATH_INSTRUMENT_CODE(n_pi.str(0, std::ios_base::scientific));
+
       // Adjust signs if the multiple of pi is not even.
       if(!b_n_pi_is_even)
       {
@@ -132,6 +135,7 @@ void eval_sin(T& result, const T& x)
    if(xx.compare(t) > 0)
    {
       subtract(xx, get_constant_pi(), xx);
+      BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific));
    }
 
    subtract(t, xx);
@@ -157,6 +161,7 @@ void eval_sin(T& result, const T& x)
       T t2;
       t2 = fp_type(1.5);
       hyp0F1(result, t2, t);
+      BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific));
       multiply(result, xx);
    }
    else if(b_near_pi_half)
@@ -166,6 +171,7 @@ void eval_sin(T& result, const T& x)
       T t2;
       t2 = fp_type(0.5);
       hyp0F1(result, t2, t);
+      BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific));
    }
    else
    {
@@ -185,6 +191,7 @@ void eval_sin(T& result, const T& x)
       T t2;
       t2 = fp_type(1.5);
       hyp0F1(result, t2, t);
+      BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific));
       multiply(result, xx);
 
       // Convert back using multiple angle identity.
@@ -243,7 +250,6 @@ void eval_cos(T& result, const T& x)
    if(get_sign(x) < 0)
    {
       xx.negate();
-      b_negate_cos = !b_negate_cos;
    }
 
    T n_pi, t;
@@ -252,8 +258,11 @@ void eval_cos(T& result, const T& x)
    {
       divide(t, xx, get_constant_pi());
       eval_trunc(n_pi, t);
+      BOOST_MATH_INSTRUMENT_CODE(n_pi.str(0, std::ios_base::scientific));
       multiply(t, n_pi, get_constant_pi());
+      BOOST_MATH_INSTRUMENT_CODE(t.str(0, std::ios_base::scientific));
       subtract(xx, t);
+      BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific));
 
       // Adjust signs if the multiple of pi is not even.
       t = ui_type(2);
@@ -273,6 +282,7 @@ void eval_cos(T& result, const T& x)
    {
       subtract(xx, get_constant_pi(), xx);
       b_negate_cos = !b_negate_cos;
+      BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific));
    }
 
    const bool b_zero    = get_sign(xx) == 0;
@@ -297,6 +307,7 @@ void eval_cos(T& result, const T& x)
       divide(t, si_type(-4));
       n_pi = fp_type(0.5f);
       hyp0F1(result, n_pi, t);
+      BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific));
    }
    else if(b_near_pi_half)
    {
@@ -306,6 +317,7 @@ void eval_cos(T& result, const T& x)
       n_pi = fp_type(1.5f);
       hyp0F1(result, n_pi, t);
       multiply(result, t2);
+      BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific));
    }
    else
    {
@@ -324,6 +336,7 @@ void eval_cos(T& result, const T& x)
 
       // Now with small arguments, we are ready for a series expansion.
       hyp0F1(result, n_pi, t);
+      BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific));
 
       // Convert back using multiple angle identity.
       for(ui_type k = 0; k < n_scale; k++)
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 018e0802..6269b724 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -630,3 +630,32 @@ run ../example/tommath_snips.cpp $(TOMMATH)
          [ check-target-builds ../config//has_tommath : : no ] ;
 
 
+for local source in [ glob math/*.cpp ]
+{
+   run $(source) mpfr gmp /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
+        : # command line
+        : # input files
+        : # requirements
+         [ check-target-builds ../config//has_mpfr : : no ] 
+         TEST_MPFR_50
+         speed
+         BOOST_ALL_NO_LIB
+        : $(source:B)_mpfr ;
+   run $(source) gmp /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
+        : # command line
+        : # input files
+        : # requirements
+         [ check-target-builds ../config//has_gmp : : no ] 
+         speed
+         TEST_MPF_50
+         BOOST_ALL_NO_LIB
+        : $(source:B)_mpf ;
+   run $(source) /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
+        : # command line
+        : # input files
+        : # requirements
+         TEST_CPP_FLOAT
+         BOOST_ALL_NO_LIB
+         speed
+        : $(source:B)_cpp_float ;
+}
diff --git a/test/math/log1p_expm1_test.cpp b/test/math/log1p_expm1_test.cpp
new file mode 100644
index 00000000..0006ac18
--- /dev/null
+++ b/test/math/log1p_expm1_test.cpp
@@ -0,0 +1,131 @@
+///////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2002 - 2011.
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#include 
+#include 
+#include 
+#include 
+
+#define SC_(x) BOOST_STRINGIZE(x)
+
+#include "libs/math/test/log1p_expm1_test.hpp"
+
+//
+// DESCRIPTION:
+// ~~~~~~~~~~~~
+//
+// This file tests the functions log1p and expm1.  The accuracy tests
+// use values generated with NTL::RR at 1000-bit precision
+// and our generic versions of these functions.
+//
+// Note that when this file is first run on a new platform many of
+// these tests will fail: the default accuracy is 1 epsilon which
+// is too tight for most platforms.  In this situation you will 
+// need to cast a human eye over the error rates reported and make
+// a judgement as to whether they are acceptable.  Either way please
+// report the results to the Boost mailing list.  Acceptable rates of
+// error are marked up below as a series of regular expressions that
+// identify the compiler/stdlib/platform/data-type/test-data/test-function
+// along with the maximum expected peek and RMS mean errors for that
+// test.
+//
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+
+   //
+   // Catch all cases come last:
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*",                          // test function
+      8,                             // Max Peek error
+      5);                            // Max mean error
+
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test(mp_number >(), "mp_number >");
+   test(mp_number >(), "mp_number >");
+   test(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test(mp_number >(), "mp_number >");
+   test(mp_number >(), "mp_number >");
+   test(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test(mp_number >(), "mp_number >");
+   test(mp_number >(), "mp_number >");
+   test(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/math/powm1_sqrtp1m1_test.cpp b/test/math/powm1_sqrtp1m1_test.cpp
new file mode 100644
index 00000000..0e419958
--- /dev/null
+++ b/test/math/powm1_sqrtp1m1_test.cpp
@@ -0,0 +1,132 @@
+///////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2002 - 2011.
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#include 
+#include 
+#include 
+#include 
+
+#define SC_(x) BOOST_STRINGIZE(x)
+
+#include "libs/math/test/powm1_sqrtp1m1_test.hpp"
+
+//
+// DESCRIPTION:
+// ~~~~~~~~~~~~
+//
+// This file tests the functions log1p and expm1.  The accuracy tests
+// use values generated with NTL::RR at 1000-bit precision
+// and our generic versions of these functions.
+//
+// Note that when this file is first run on a new platform many of
+// these tests will fail: the default accuracy is 1 epsilon which
+// is too tight for most platforms.  In this situation you will 
+// need to cast a human eye over the error rates reported and make
+// a judgement as to whether they are acceptable.  Either way please
+// report the results to the Boost mailing list.  Acceptable rates of
+// error are marked up below as a series of regular expressions that
+// identify the compiler/stdlib/platform/data-type/test-data/test-function
+// along with the maximum expected peek and RMS mean errors for that
+// test.
+//
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+
+   //
+   // Catch all cases come last:
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*",                          // test function
+      15,                             // Max Peek error
+      5);                            // Max mean error
+
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // We test two different precisions:
+   // 18 decimal digits triggers Boost.Math's 64-bit long double support.
+   // 30 decimal digits triggers Boost.Math's 128-bit long double support.
+   // 35 decimal digits triggers true arbitrary precision support.
+   //
+#ifdef TEST_MPF_50
+   // We have accuracy issues with gmp_float<18> - maybe in std::exp??  Disabled for now.
+   //test_powm1_sqrtp1m1(mp_number >(), "mp_number >");
+   test_powm1_sqrtp1m1(mp_number >(), "mp_number >");
+   test_powm1_sqrtp1m1(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_powm1_sqrtp1m1(mp_number >(), "mp_number >");
+   test_powm1_sqrtp1m1(mp_number >(), "mp_number >");
+   test_powm1_sqrtp1m1(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_powm1_sqrtp1m1(mp_number >(), "mp_number >");
+   test_powm1_sqrtp1m1(mp_number >(), "mp_number >");
+   test_powm1_sqrtp1m1(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/math/test_bessel_i.cpp b/test/math/test_bessel_i.cpp
new file mode 100644
index 00000000..b514e24a
--- /dev/null
+++ b/test/math/test_bessel_i.cpp
@@ -0,0 +1,107 @@
+///////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2002 - 2011.
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+
+#include "libs/math/test/test_bessel_i.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+
+   //
+   // Catch all cases come last:
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*",                          // test function
+      250,                           // Max Peek error
+      100);                          // Max mean error
+
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   // We have accuracy issues with gmp_float<18> - maybe in std::exp??  Disabled for now.
+   //test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/math/test_bessel_j.cpp b/test/math/test_bessel_j.cpp
new file mode 100644
index 00000000..c6115e33
--- /dev/null
+++ b/test/math/test_bessel_j.cpp
@@ -0,0 +1,129 @@
+///////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2002 - 2011.
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+
+#include "libs/math/test/test_bessel_j.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                  // test type(s)
+      ".*J0.*Tricky.*",              // test data group
+      ".*", 400000000, 400000000);   // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                  // test type(s)
+      ".*J1.*Tricky.*",              // test data group
+      ".*", 5000000, 5000000);       // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                  // test type(s)
+      ".*JN.*Integer.*",              // test data group
+      ".*", 40000, 10000);       // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                  // test type(s)
+      ".*(JN|j).*|.*Tricky.*",       // test data group
+      ".*", 4000, 700);               // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                  // test type(s)
+      ".*",                          // test data group
+      ".*", 40, 20);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   // We have accuracy issues with gmp_float<18> - maybe in std::exp??  Disabled for now.
+   //test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/math/test_bessel_k.cpp b/test/math/test_bessel_k.cpp
new file mode 100644
index 00000000..95d5c387
--- /dev/null
+++ b/test/math/test_bessel_k.cpp
@@ -0,0 +1,115 @@
+///////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2002 - 2011.
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+
+#include "libs/math/test/test_bessel_k.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp.*",                     // test type(s)
+      ".*",                          // test data group
+      ".*", 2000, 1500);                // test function
+
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*large.*",                   // test data group
+      ".*", 80, 50);                 // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 50, 15);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   // We have accuracy issues with gmp_float<18> - maybe in std::exp??  Disabled for now.
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp
new file mode 100644
index 00000000..d0295a2e
--- /dev/null
+++ b/test/math/test_bessel_y.cpp
@@ -0,0 +1,121 @@
+///////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2002 - 2011.
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+
+#include "libs/math/test/test_bessel_y.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*(Y[nv]|y).*Random.*",       // test data group
+      ".*", 70000, 4000);             // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*Y0.*",                      // test data group
+      ".*", 800, 400);               // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*Yn.*",                      // test data group
+      ".*", 1700, 600);               // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                         // test type(s)
+      ".*",                          // test data group
+      ".*", 80, 40);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   // We have accuracy issues with gmp_float<18> - our argument reduction in std::sin isn't accurate enough:
+   //test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+   test_bessel(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/math/test_beta.cpp b/test/math/test_beta.cpp
new file mode 100644
index 00000000..83849258
--- /dev/null
+++ b/test/math/test_beta.cpp
@@ -0,0 +1,128 @@
+///////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2002 - 2011.
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+
+#include "libs/math/test/test_beta.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp.*",                     // test type(s)
+      "Beta Function: Medium.*",     // test data group
+      "boost::math::beta", 2200, 1000); // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp.*",                     // test type(s)
+      "Beta Function: Divergent.*",  // test data group
+      "boost::math::beta", 2200, 1000);   // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      "Beta Function: Small.*",      // test data group
+      "boost::math::beta", 8, 5);    // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      "Beta Function: Medium.*",     // test data group
+      "boost::math::beta", 160, 35); // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      "Beta Function: Divergent.*",  // test data group
+      "boost::math::beta", 30, 6);   // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   // We have accuracy issues with gmp_float<18> - our argument reduction in std::sin isn't accurate enough:
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/math/test_binomial_coeff.cpp b/test/math/test_binomial_coeff.cpp
new file mode 100644
index 00000000..aa7f3eaa
--- /dev/null
+++ b/test/math/test_binomial_coeff.cpp
@@ -0,0 +1,107 @@
+///////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2002 - 2011.
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+
+#include "libs/math/test/test_binomial_coeff.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp.*",                     // test type(s)
+      ".*",                          // test data group
+      ".*", 3000, 200);              // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 100, 20);                // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   // We have accuracy issues with gmp_float<18> - our argument reduction in std::sin isn't accurate enough:
+   test_binomial(mp_number >(), "mp_number >");
+   test_binomial(mp_number >(), "mp_number >");
+   test_binomial(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_binomial(mp_number >(), "mp_number >");
+   test_binomial(mp_number >(), "mp_number >");
+   test_binomial(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_binomial(mp_number >(), "mp_number >");
+   test_binomial(mp_number >(), "mp_number >");
+   test_binomial(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/math/test_carlson.cpp b/test/math/test_carlson.cpp
new file mode 100644
index 00000000..fce96091
--- /dev/null
+++ b/test/math/test_carlson.cpp
@@ -0,0 +1,108 @@
+///////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2002 - 2011.
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// This work is based on an earlier work:
+// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
+// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_carlson.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*RJ.*",                      // test data group
+      ".*", 2700, 250);              // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 40, 20);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   // We have accuracy issues with gmp_float<18> - our argument reduction in std::sin isn't accurate enough:
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/test_atan.cpp b/test/test_atan.cpp
index afa589d6..2c0bf6ee 100644
--- a/test/test_atan.cpp
+++ b/test/test_atan.cpp
@@ -224,7 +224,7 @@ void test()
    }
    
    std::cout << "Max error was: " << max_err << std::endl;
-   BOOST_TEST(max_err < 70);
+   BOOST_TEST(max_err < 2000);
 }
 
 
diff --git a/test/test_cos.cpp b/test/test_cos.cpp
index 7bd0059f..1ce8baaa 100644
--- a/test/test_cos.cpp
+++ b/test/test_cos.cpp
@@ -236,6 +236,11 @@ void test()
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
+      val = cos(-half_pi + (euler_gamma + k) / 523);
+      e = relative_error(val, near_one[k]);
+      err = e.template convert_to();
+      if(err > max_err)
+         max_err = err;
    }
    std::cout << "Max error was: " << max_err << std::endl;
    BOOST_TEST(max_err < 500);
@@ -244,7 +249,7 @@ void test()
    // Test with some exact binary values as input - this tests our code
    // rather than the test data:
    //
-   static const boost::array, 7> exact_data =
+   static const boost::array, 8> exact_data =
    {{
       {{ 0.5, "0.877582561890372716116281582603829651991645197109744052997610868315950763274213947405794184084682258355478400593109053993" }},
       {{ 0.25, "0.968912421710644784144595449494189199804134190287442831148128124288942561184523327264655202799685025510352709626116202617" }},
@@ -252,7 +257,8 @@ void test()
       {{std::ldexp(1.0, -20), "0.99999999999954525264911357034690133684385823577463126432241468890539365027135494672267164697779879113636143901797362388" }},
       {{ 2, "-0.416146836547142386997568229500762189766000771075544890755149973781964936124079169074531777860169140367366791365215728559" }},
       {{ 5, "0.283662185463226264466639171513557308334422592252215944930359066586151456767382702286176981668344573238827368717546699737" }},
-      {{ 10, "-0.839071529076452452258863947824064834519930165133168546835953731048792586866270768400933712760422138927451054405350243624" }}
+      {{ 10, "-0.839071529076452452258863947824064834519930165133168546835953731048792586866270768400933712760422138927451054405350243624" }},
+      {{ 8.5, "-0.60201190268482361534842652295699870029606776360435523539636606145572515876770619546025351418378467287262574566665150299" }}
    }};
    max_err = 0;
    for(unsigned k = 0; k < exact_data.size(); k++)
@@ -262,6 +268,11 @@ void test()
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
+      val = cos(-exact_data[k][0]);
+      e = relative_error(val, exact_data[k][1]);
+      err = e.template convert_to();
+      if(err > max_err)
+         max_err = err;
    }
    std::cout << "Max error was: " << max_err << std::endl;
    BOOST_TEST(max_err < 20);
diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp
index 7100e4f7..b4dc8601 100644
--- a/test/test_cosh.cpp
+++ b/test/test_cosh.cpp
@@ -113,6 +113,11 @@ void test()
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
+      val = boost::multiprecision::cosh(-x * x);
+      e = relative_error(val, data[k]);
+      err = e.template convert_to();
+      if(err > max_err)
+         max_err = err;
    }
    std::cout << "Max error was: " << max_err << std::endl;
    BOOST_TEST(max_err < 2000);
diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp
index 489f1047..bb8db580 100644
--- a/test/test_numeric_limits.cpp
+++ b/test/test_numeric_limits.cpp
@@ -7,7 +7,7 @@
 #  define _SCL_SECURE_NO_WARNINGS
 #endif
 
-#include 
+#include "test.hpp"
 
 #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && !defined(TEST_TOMMATH)
 #  define TEST_MPF_50
@@ -48,6 +48,25 @@
 #define PRINT(x)\
    std::cout << BOOST_STRINGIZE(x) << " = " << std::numeric_limits::x << std::endl;
 
+template 
+void test_fp(const boost::mpl::int_&)
+{
+   Number minv, maxv;
+   minv = (std::numeric_limits::min)();
+   maxv = (std::numeric_limits::max)();
+   BOOST_CHECK(boost::math::isnormal(minv));
+   BOOST_CHECK(boost::math::isnormal(maxv));
+   BOOST_CHECK(boost::math::isnormal(log(minv)));
+   BOOST_CHECK(boost::math::isnormal(log(maxv)));
+   BOOST_CHECK(boost::math::isnormal(sqrt(minv)));
+   BOOST_CHECK(boost::math::isnormal(sqrt(maxv)));
+}
+
+template 
+void test_fp(const T&)
+{
+}
+
 template 
 void test()
 {
@@ -140,6 +159,14 @@ void test()
    BOOST_TEST((boost::math::isnormal)(n));
    BOOST_TEST(!(boost::math::isinf)(n));
    BOOST_TEST(!(boost::math::isnan)(n));
+
+   typedef typename boost::mpl::if_c<
+      std::numeric_limits::is_specialized,
+      typename boost::multiprecision::number_category::type,
+      boost::mpl::int_<500> // not a number type
+   >::type fp_test_type;
+
+   test_fp(fp_test_type());
 }
 
 
diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp
index a12ce09d..04dc679b 100644
--- a/test/test_sinh.cpp
+++ b/test/test_sinh.cpp
@@ -113,7 +113,88 @@ void test()
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
+      val = boost::multiprecision::sinh(-x * x);
+      e = relative_error(val, T(-data[k]));
+      err = e.template convert_to();
+      if(err > max_err)
+         max_err = err;
    }
+
+   boost::array small_values = 
+   {{
+      "8.223167319358299807036616344469138485821440027829633696917375433348917938654659351596020080036406671343718039863220496616e-01",
+      "2.526123168081683079141251505420579055197542874276608074880949653019810769068593790606537020961198741487692473633089323967e-01",
+      "8.342981744595282037256218647969712476322487890550784823763249893556153270975172951404094950587944959561849750490537201329e-02",
+      "2.778135016068299789938671680845480653984976507019542653788637161116587306168290886761259072846829249121589698206609261524e-02",
+      "9.259391565199916442789400306996794489540862711193761818262415211084389468754315525525896238827358889826875006042447587516e-03",
+      "3.086424653287772358219607529932097884435043040527155440187640095572710676452654803730003577747633690318001961509535020849e-03",
+      "1.028806765851002064810061084014826478832745077469708149635730407866217436751337520417458090265791086156438275231514030381e-03",
+      "3.429355348425226988441198390119109217716503769838753365112550442738406326637684639052252898314646892490045395290022292013e-04",
+      "1.143118429558603374406653541544292690548937361618336125287018361332072426474632105217297150810234138626767253281422813482e-04",
+      "3.810394757818873406266877296641684693312194735341898368873067089928172619067423751257049691985638480762032673977695116880e-05",
+      "1.270131585666421832817527834137477593266387525701388601975733237436369505733715799310429349744168792375082834509467436523e-05",
+      "4.233771952120219947940459634636576539101577724347428305072378100562649548884420218224692461748739725090626754420296122389e-06",
+      "1.411257317369659013704209000288436132710449162963127340562961271337242582661013580874165903770246169179192268836124421074e-06",
+      "4.704191057897475365825409916786898392364235667906752767514580467152163619657508910797742266406961516358439252434955007668e-07",
+      "1.568063685965773714045928492719360014894368531987759414833778466374819836545157375950693756664550256136222396871173634254e-07",
+      "5.226878953219226673524993193392503058475862017726848548717100658392470633650387274004511940515056405069137033934323251644e-08",
+      "1.742292984406408185991240874995689487745140228031202510923711784729440494088066989430128101759261047316736074663327672115e-08",
+      "5.807643281354693692124967044009687283114597355717062156493618245876910131607338183944830908381903728560328284173507220743e-09",
+      "1.935881093784897887701686451485601671131342930785061493703969418728524594573922282309665275558709040519461560600768780392e-09",
+      "6.452936979282992955422916851920785543106383715381924626175995859924351552325880931187614903984801793287071578640505194508e-10",
+      "2.150978993094330985008279519046512957825521218238790792201835497215534851989750722105234826300738623838446309250309905466e-10",
+      "7.169929976981103283311786261663531258230547972690500493476881079295129579131280734024784107219045379345460886663104148486e-11",
+      "2.389976658993701094435441884684454421835327948893136184573938864819002944442339456827931472237274353903634036758669394620e-11",
+      "7.966588863312336981450798799860506345287566898810744342680146925029151178981033890759916168189916177504592939240995619757e-12",
+      "2.655529621104112327150241298135440075805848488054800577703768668100658036999584228451100239039042920681377381394421710121e-12",
+      "8.851765403680374423834128412864530361591097252230621965426275532533242581680245794741067906285298655116802944992368126680e-13",
+      "2.950588467893458141278042461784956914687338675140497707333871358819185395356569206661450997145748756956497959702280685427e-13",
+      "9.835294892978193804260141412430145318398649753331401112621871794012928366988233744354238387090649589382104704221708773516e-14",
+      "3.278431630992731268086713799445120869198593899364655036314007566906378666339665297288092596796135684816883503781385164489e-14",
+      "1.092810543664243756028904599641030626636532928735904320784337625844108091213506619051042206148385975354700234586478575025e-14",
+      "3.642701812214145853429681998738987398752764686754626492252324567456938623579239392678142797020213493844816454129960310753e-15",
+      "1.214233937404715284476560666243942169089106312534317920490462975351305354471020532764015606315872085933262687299655265697e-15",
+      "4.047446458015717614921868887478923169619805517194433471908835726595116905187672132801369948377551282604828733616045843751e-16",
+      "1.349148819338572538307289629159608313551890152969010184597042496758528297346351553643241208769191557898925543369605617734e-16",
+      "4.497162731128575127690965430532015584807024576774799020494128293451281927637267192489558050090835454302448780391749096414e-17",
+      "1.499054243709525042563655143510671412452985626833998379862387948592418229228808284088934491020852037924756758483008288052e-17",
+      "4.996847479031750141878850478368904541825005460277179305602161748681654262243578435201096986093377131577325573917436618470e-18",
+      "1.665615826343916713959616826122968174447164290616980189746184851537351248309665330601503343215376981550822569162631313560e-18",
+      "5.552052754479722379865389420409893912541965834349657578615232567585047309856390957625702896178052275806406957076143469634e-19",
+      "1.850684251493240793288463140136631304096139902769381795814754672989850701401641374814254071564872119933498619234778448524e-19",
+      "6.168947504977469310961543800455437680289164351695283493312025632359317744715643192414807145394613572397590534364339391526e-20",
+      "2.056315834992489770320514600151812560095228784236601072113743484455321300338926430301421880927367590178440922006775473367e-20",
+      "6.854386116641632567735048667172708533650333231531203539518552950777817440179277823487619201513258000884052637516041835420e-21",
+      "2.284795372213877522578349555724236177883428507451482660054557452824460619777642844796449091646418601791047308814504431261e-21",
+      "7.615984574046258408594498519080787259611422468149787192854095139994568043598766360557598146279482678180281335390895949036e-22",
+      "2.538661524682086136198166173026929086537140604567639372655275057673980680372673609490963070062819520295998328327889923353e-22",
+      "8.462205082273620453993887243423096955123801934429554813185698344472203995997708879527322555715697860578416576045982358004e-23",
+      "2.820735027424540151331295747807698985041267308484077168753311108116374235508697904826049959781116012127075951788533527897e-23",
+      "9.402450091415133837770985826025663283470891027171945709804152456669015193736201020401750153196590359525341207466344738924e-24",
+      "3.134150030471711279256995275341887761156963675682933328476437810109959425395050019306074135780459168092270327572635795510e-24",   
+   }};
+
+   max_err = 0;
+   T v = 0.75;
+   for(unsigned k = 0; k < small_values.size(); ++k)
+   {
+      T val = boost::multiprecision::sinh(v);
+      T e = relative_error(val, small_values[k]);
+      unsigned err = e.template convert_to();
+      if(err > max_err)
+      {
+         max_err = err;
+      }
+      val = boost::multiprecision::sinh(-v);
+      e = relative_error(val, T(-small_values[k]));
+      err = e.template convert_to();
+      if(err > max_err)
+      {
+         max_err = err;
+      }
+      v /= 3;
+   }
+
    std::cout << "Max error was: " << max_err << std::endl;
    BOOST_TEST(max_err < 2000);
 }
diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp
index 96bf4574..4e5ca6c8 100644
--- a/test/test_tanh.cpp
+++ b/test/test_tanh.cpp
@@ -115,7 +115,7 @@ void test()
          max_err = err;
    }
    std::cout << "Max error was: " << max_err << std::endl;
-   BOOST_TEST(max_err < 10);
+   BOOST_TEST(max_err < 100);
 }
 
 

From 6e3ab5380b647855f8044ff08f77378da711d0bc Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Tue, 20 Dec 2011 16:19:55 +0000
Subject: [PATCH 081/256] Add tests for Boost.Math special functions, and fix
 whatever errors came up in running those tests. Add workaround for compilers
 that don't have a std::abs(long long).

[SVN r76079]
---
 include/boost/multiprecision/cpp_float.hpp    |   8 +-
 .../multiprecision/detail/mp_number_base.hpp  |  11 +-
 include/boost/multiprecision/gmp.hpp          |   9 +-
 include/boost/multiprecision/mpfr.hpp         |   3 +-
 include/boost/multiprecision/tommath.hpp      |   3 +-
 test/Jamfile.v2                               |   3 +
 test/math/log1p_expm1_test.cpp                |  18 +++
 test/math/powm1_sqrtp1m1_test.cpp             |   9 ++
 test/math/test_bessel_i.cpp                   |   4 +-
 test/math/test_bessel_j.cpp                   |   2 +-
 test/math/test_bessel_k.cpp                   |   8 ++
 test/math/test_bessel_y.cpp                   |  14 ++
 test/math/test_binomial_coeff.cpp             |  10 +-
 test/math/test_carlson.cpp                    |   5 -
 test/math/test_cbrt.cpp                       |  95 +++++++++++++
 test/math/test_digamma.cpp                    | 100 ++++++++++++++
 test/math/test_ellint_1.cpp                   |  93 +++++++++++++
 test/math/test_ellint_2.cpp                   |  93 +++++++++++++
 test/math/test_ellint_3.cpp                   | 107 +++++++++++++++
 test/math/test_erf.cpp                        | 114 ++++++++++++++++
 test/math/test_expint.cpp                     | 114 ++++++++++++++++
 test/math/test_gamma.cpp                      | 128 ++++++++++++++++++
 test/math/test_hermite.cpp                    |  93 +++++++++++++
 test/math/test_ibeta.cpp                      | 117 ++++++++++++++++
 test/math/test_ibeta_2.cpp                    | 124 +++++++++++++++++
 test/math/test_ibeta_3.cpp                    | 110 +++++++++++++++
 test/math/test_ibeta_4.cpp                    | 117 ++++++++++++++++
 test/math/test_ibeta_inv_1.cpp                |  96 +++++++++++++
 test/math/test_ibeta_inv_ab_4.cpp             |  96 +++++++++++++
 test/math/test_igamma.cpp                     | 100 ++++++++++++++
 test/math/test_igamma_inv.cpp                 | 108 +++++++++++++++
 test/math/test_igamma_inva.cpp                |  94 +++++++++++++
 test/math/test_laguerre.cpp                   |  93 +++++++++++++
 test/math/test_legendre.cpp                   |  93 +++++++++++++
 test/math/test_tgamma_ratio.cpp               | 100 ++++++++++++++
 test/math/test_zeta.cpp                       | 100 ++++++++++++++
 36 files changed, 2373 insertions(+), 19 deletions(-)
 create mode 100644 test/math/test_cbrt.cpp
 create mode 100644 test/math/test_digamma.cpp
 create mode 100644 test/math/test_ellint_1.cpp
 create mode 100644 test/math/test_ellint_2.cpp
 create mode 100644 test/math/test_ellint_3.cpp
 create mode 100644 test/math/test_erf.cpp
 create mode 100644 test/math/test_expint.cpp
 create mode 100644 test/math/test_gamma.cpp
 create mode 100644 test/math/test_hermite.cpp
 create mode 100644 test/math/test_ibeta.cpp
 create mode 100644 test/math/test_ibeta_2.cpp
 create mode 100644 test/math/test_ibeta_3.cpp
 create mode 100644 test/math/test_ibeta_4.cpp
 create mode 100644 test/math/test_ibeta_inv_1.cpp
 create mode 100644 test/math/test_ibeta_inv_ab_4.cpp
 create mode 100644 test/math/test_igamma.cpp
 create mode 100644 test/math/test_igamma_inv.cpp
 create mode 100644 test/math/test_igamma_inva.cpp
 create mode 100644 test/math/test_laguerre.cpp
 create mode 100644 test/math/test_legendre.cpp
 create mode 100644 test/math/test_tgamma_ratio.cpp
 create mode 100644 test/math/test_zeta.cpp

diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp
index 8c2f0411..037672eb 100644
--- a/include/boost/multiprecision/cpp_float.hpp
+++ b/include/boost/multiprecision/cpp_float.hpp
@@ -2733,8 +2733,8 @@ inline void eval_frexp(cpp_float& result, const cpp_float& x
    }
 
    long long t = result.order();
-
-   if(std::abs(t) < ((std::numeric_limits::max)() / 1000))
+   BOOST_MP_USING_ABS
+   if(abs(t) < ((std::numeric_limits::max)() / 1000))
    {
       t *= 1000;
       t /= 301;
@@ -2756,8 +2756,8 @@ inline void eval_frexp(cpp_float& result, const cpp_float& x
       t /= 2;
       result *= cpp_float::pow2(-t);
    }
-
-   if(std::abs(result.order()) > 5)
+   BOOST_MP_USING_ABS
+   if(abs(result.order()) > 5)
    {
       // If our first estimate doesn't get close enough then try recursion until we do:
       long long e2;
diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp
index fb2cb147..b0eb1611 100644
--- a/include/boost/multiprecision/detail/mp_number_base.hpp
+++ b/include/boost/multiprecision/detail/mp_number_base.hpp
@@ -28,6 +28,14 @@ namespace detail{
 template
 struct mp_exp;
 
+template 
+typename boost::enable_if, T>::type abs(const T& t)
+{
+   return t < 0 ? -t : t;
+}
+
+#define BOOST_MP_USING_ABS using std::abs; using boost::multiprecision::detail::abs;
+
 template 
 struct has_enough_bits
 {
@@ -465,11 +473,12 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std::
    }
    else
    {
+      BOOST_MP_USING_ABS
       // Scientific format:
       if(showpoint || (str.size() > 1))
          str.insert(1, 1, '.');
       str.append(1, 'e');
-      S e = boost::lexical_cast(std::abs(my_exp));
+      S e = boost::lexical_cast(abs(my_exp));
       if(e.size() < BOOST_MP_MIN_EXPONENT_DIGITS)
          e.insert(0, BOOST_MP_MIN_EXPONENT_DIGITS-e.size(), '0');
       if(my_exp < 0)
diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp
index 4e678fd1..5a966277 100644
--- a/include/boost/multiprecision/gmp.hpp
+++ b/include/boost/multiprecision/gmp.hpp
@@ -83,8 +83,9 @@ struct gmp_float_imp
    }
    gmp_float_imp& operator = (boost::intmax_t i)
    {
+      BOOST_MP_USING_ABS
       bool neg = i < 0;
-      *this = static_cast(std::abs(i));
+      *this = static_cast(abs(i));
       if(neg)
          mpf_neg(m_data, m_data);
       return *this;
@@ -910,8 +911,9 @@ struct gmp_int
    }
    gmp_int& operator = (boost::intmax_t i)
    {
+      BOOST_MP_USING_ABS
       bool neg = i < 0;
-      *this = static_cast(std::abs(i));
+      *this = static_cast(abs(i));
       if(neg)
          mpz_neg(m_data, m_data);
       return *this;
@@ -1448,8 +1450,9 @@ struct gmp_rational
    }
    gmp_rational& operator = (boost::intmax_t i)
    {
+      BOOST_MP_USING_ABS
       bool neg = i < 0;
-      *this = static_cast(std::abs(i));
+      *this = static_cast(abs(i));
       if(neg)
          mpq_neg(m_data, m_data);
       return *this;
diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp
index ea5023ef..3129171e 100644
--- a/include/boost/multiprecision/mpfr.hpp
+++ b/include/boost/multiprecision/mpfr.hpp
@@ -80,8 +80,9 @@ struct mpfr_float_imp
    }
    mpfr_float_imp& operator = (boost::intmax_t i)
    {
+      BOOST_MP_USING_ABS
       bool neg = i < 0;
-      *this = static_cast(std::abs(i));
+      *this = static_cast(abs(i));
       if(neg)
          mpfr_neg(m_data, m_data, GMP_RNDN);
       return *this;
diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp
index bd3ba689..19f5a4ed 100644
--- a/include/boost/multiprecision/tommath.hpp
+++ b/include/boost/multiprecision/tommath.hpp
@@ -70,8 +70,9 @@ struct tommath_int
    }
    tommath_int& operator = (boost::intmax_t i)
    {
+      BOOST_MP_USING_ABS
       bool neg = i < 0;
-      *this = static_cast(std::abs(i));
+      *this = static_cast(abs(i));
       if(neg)
          detail::check_tommath_result(mp_neg(&m_data, &m_data));
       return *this;
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 6269b724..1f3c0ea7 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -640,6 +640,7 @@ for local source in [ glob math/*.cpp ]
          TEST_MPFR_50
          speed
          BOOST_ALL_NO_LIB
+         msvc:-bigobj
         : $(source:B)_mpfr ;
    run $(source) gmp /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
         : # command line
@@ -649,6 +650,7 @@ for local source in [ glob math/*.cpp ]
          speed
          TEST_MPF_50
          BOOST_ALL_NO_LIB
+         msvc:-bigobj
         : $(source:B)_mpf ;
    run $(source) /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
         : # command line
@@ -657,5 +659,6 @@ for local source in [ glob math/*.cpp ]
          TEST_CPP_FLOAT
          BOOST_ALL_NO_LIB
          speed
+         msvc:-bigobj
         : $(source:B)_cpp_float ;
 }
diff --git a/test/math/log1p_expm1_test.cpp b/test/math/log1p_expm1_test.cpp
index 0006ac18..10653fc9 100644
--- a/test/math/log1p_expm1_test.cpp
+++ b/test/math/log1p_expm1_test.cpp
@@ -80,6 +80,24 @@ void expected_results()
    //
    // Catch all cases come last:
    //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp_float<18>.*",           // test type(s)
+      ".*",                          // test data group
+      ".*",                          // test function
+      500,                           // Max Peek error
+      100);                          // Max mean error
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*mpfr_float_backend<18>.*",  // test type(s)
+      ".*",                          // test data group
+      ".*",                          // test function
+      500,                           // Max Peek error
+      100);                          // Max mean error
    add_expected_result(
       ".*",                          // compiler
       ".*",                          // stdlib
diff --git a/test/math/powm1_sqrtp1m1_test.cpp b/test/math/powm1_sqrtp1m1_test.cpp
index 0e419958..8c44e8f4 100644
--- a/test/math/powm1_sqrtp1m1_test.cpp
+++ b/test/math/powm1_sqrtp1m1_test.cpp
@@ -80,6 +80,15 @@ void expected_results()
    //
    // Catch all cases come last:
    //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*mpfr_float_backend<18>.*",  // test type(s)
+      ".*",                          // test data group
+      ".*",                          // test function
+      300,                           // Max Peek error
+      50);                           // Max mean error
    add_expected_result(
       ".*",                          // compiler
       ".*",                          // stdlib
diff --git a/test/math/test_bessel_i.cpp b/test/math/test_bessel_i.cpp
index b514e24a..168563e2 100644
--- a/test/math/test_bessel_i.cpp
+++ b/test/math/test_bessel_i.cpp
@@ -62,8 +62,8 @@ void expected_results()
       ".*",                          // test type(s)
       ".*",                          // test data group
       ".*",                          // test function
-      250,                           // Max Peek error
-      100);                          // Max mean error
+      300,                           // Max Peek error
+      200);                          // Max mean error
 
    //
    // Finish off by printing out the compiler/stdlib/platform names,
diff --git a/test/math/test_bessel_j.cpp b/test/math/test_bessel_j.cpp
index c6115e33..b2e6b936 100644
--- a/test/math/test_bessel_j.cpp
+++ b/test/math/test_bessel_j.cpp
@@ -65,7 +65,7 @@ void expected_results()
       ".*",                          // platform
       ".*",                  // test type(s)
       ".*J1.*Tricky.*",              // test data group
-      ".*", 5000000, 5000000);       // test function
+      ".*", 10000000, 5000000);       // test function
    add_expected_result(
       ".*",                          // compiler
       ".*",                          // stdlib
diff --git a/test/math/test_bessel_k.cpp b/test/math/test_bessel_k.cpp
index 95d5c387..1432a4e3 100644
--- a/test/math/test_bessel_k.cpp
+++ b/test/math/test_bessel_k.cpp
@@ -13,6 +13,7 @@
 #endif
 
 #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_SMALL_CONSTANT(x) x
 
 #if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
 #  define TEST_MPF_50
@@ -59,6 +60,13 @@ void expected_results()
       ".*",                          // test data group
       ".*", 2000, 1500);                // test function
 
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*mpfr_float_backend<18>.*",  // test type(s)
+      ".*",                          // test data group
+      ".*", 3000, 1000);             // test function
    add_expected_result(
       ".*",                          // compiler
       ".*",                          // stdlib
diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp
index d0295a2e..e224865a 100644
--- a/test/math/test_bessel_y.cpp
+++ b/test/math/test_bessel_y.cpp
@@ -58,6 +58,13 @@ void expected_results()
       ".*",                          // test type(s)
       ".*(Y[nv]|y).*Random.*",       // test data group
       ".*", 70000, 4000);             // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*mpfr_float_backend<18>.*",  // test type(s)
+      ".*Y0.*",                      // test data group
+      ".*", 3000, 2000);             // test function
    add_expected_result(
       ".*",                          // compiler
       ".*",                          // stdlib
@@ -72,6 +79,13 @@ void expected_results()
       ".*",                          // test type(s)
       ".*Yn.*",                      // test data group
       ".*", 1700, 600);               // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*mpfr_float_backend<18>.*",  // test type(s)
+      ".*",                          // test data group
+      ".*", 10000, 4000);            // test function
    add_expected_result(
       ".*",                          // compiler
       ".*",                          // stdlib
diff --git a/test/math/test_binomial_coeff.cpp b/test/math/test_binomial_coeff.cpp
index aa7f3eaa..6272d647 100644
--- a/test/math/test_binomial_coeff.cpp
+++ b/test/math/test_binomial_coeff.cpp
@@ -57,7 +57,14 @@ void expected_results()
       ".*",                          // platform
       ".*gmp.*",                     // test type(s)
       ".*",                          // test data group
-      ".*", 3000, 200);              // test function
+      ".*", 3000, 1500);             // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*mpfr_float_backend<18>.*",  // test type(s)
+      ".*",                          // test data group
+      ".*", 500, 100);               // test function
    add_expected_result(
       ".*",                          // compiler
       ".*",                          // stdlib
@@ -105,3 +112,4 @@ int test_main(int, char* [])
 
 
 
+
diff --git a/test/math/test_carlson.cpp b/test/math/test_carlson.cpp
index fce96091..b698bd0c 100644
--- a/test/math/test_carlson.cpp
+++ b/test/math/test_carlson.cpp
@@ -1,12 +1,7 @@
 ///////////////////////////////////////////////////////////////
-//  Copyright Christopher Kormanyos 2002 - 2011.
 //  Copyright 2011 John Maddock. Distributed under the Boost
 //  Software License, Version 1.0. (See accompanying file
 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
-//
-// This work is based on an earlier work:
-// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
-// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
 
 #ifdef _MSC_VER
 #  define _SCL_SECURE_NO_WARNINGS
diff --git a/test/math/test_cbrt.cpp b/test/math/test_cbrt.cpp
new file mode 100644
index 00000000..5c3b6906
--- /dev/null
+++ b/test/math/test_cbrt.cpp
@@ -0,0 +1,95 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_cbrt.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 5, 3);                   // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_cbrt(mp_number >(), "mp_number >");
+   test_cbrt(mp_number >(), "mp_number >");
+   test_cbrt(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_cbrt(mp_number >(), "mp_number >");
+   test_cbrt(mp_number >(), "mp_number >");
+   test_cbrt(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_cbrt(mp_number >(), "mp_number >");
+   test_cbrt(mp_number >(), "mp_number >");
+   test_cbrt(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/math/test_digamma.cpp b/test/math/test_digamma.cpp
new file mode 100644
index 00000000..1098ae6e
--- /dev/null
+++ b/test/math/test_digamma.cpp
@@ -0,0 +1,100 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_digamma.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*Negative.*",                // test data group
+      ".*", 350, 40);                // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 80, 30);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_digamma(mp_number >(), "mp_number >");
+   test_digamma(mp_number >(), "mp_number >");
+   test_digamma(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_digamma(mp_number >(), "mp_number >");
+   test_digamma(mp_number >(), "mp_number >");
+   test_digamma(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_digamma(mp_number >(), "mp_number >");
+   test_digamma(mp_number >(), "mp_number >");
+   test_digamma(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_ellint_1.cpp b/test/math/test_ellint_1.cpp
new file mode 100644
index 00000000..a9b88450
--- /dev/null
+++ b/test/math/test_ellint_1.cpp
@@ -0,0 +1,93 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_ellint_1.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 40, 20);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_ellint_2.cpp b/test/math/test_ellint_2.cpp
new file mode 100644
index 00000000..4accc451
--- /dev/null
+++ b/test/math/test_ellint_2.cpp
@@ -0,0 +1,93 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_ellint_2.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 60, 30);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_ellint_3.cpp b/test/math/test_ellint_3.cpp
new file mode 100644
index 00000000..880d4743
--- /dev/null
+++ b/test/math/test_ellint_3.cpp
@@ -0,0 +1,107 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_ellint_3.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp_float<18>.*",           // test type(s)
+      ".*",                          // test data group
+      ".*", 3000, 500);              // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*Large.*",                   // test data group
+      ".*", 75, 40);                 // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 60, 30);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+   test_spots(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_erf.cpp b/test/math/test_erf.cpp
new file mode 100644
index 00000000..f056d2bd
--- /dev/null
+++ b/test/math/test_erf.cpp
@@ -0,0 +1,114 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_erf.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp_float<18>.*",           // test type(s)
+      "Erf Function:.*",             // test data group
+      "boost::math::erfc?", 2200, 1500);// test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp_float<18>.*",           // test type(s)
+      "Inverse Erf.*",               // test data group
+      "boost::math::erfc?_inv", 2200, 1500);  // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      "Erf Function:.*",             // test data group
+      "boost::math::erfc?", 300, 200); // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      "Inverse Erf.*",               // test data group
+      "boost::math::erfc?_inv", 35, 20);  // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_erf(mp_number >(), "mp_number >");
+   test_erf(mp_number >(), "mp_number >");
+   test_erf(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_erf(mp_number >(), "mp_number >");
+   test_erf(mp_number >(), "mp_number >");
+   test_erf(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_erf(mp_number >(), "mp_number >");
+   test_erf(mp_number >(), "mp_number >");
+   test_erf(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_expint.cpp b/test/math/test_expint.cpp
new file mode 100644
index 00000000..4f19cb0c
--- /dev/null
+++ b/test/math/test_expint.cpp
@@ -0,0 +1,114 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_expint.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp_float<18>.*",             // test type(s)
+      ".*",                          // test data group
+      ".*", 2500, 1500);             // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*mpfr_float_backend<18>.*",  // test type(s)
+      ".*",                          // test data group
+      ".*", 1000, 500);              // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp_float.*",               // test type(s)
+      ".*",                          // test data group
+      ".*", 250, 100);               // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 250, 50);                // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_expint(mp_number >(), "mp_number >");
+   test_expint(mp_number >(), "mp_number >");
+   test_expint(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_expint(mp_number >(), "mp_number >");
+   test_expint(mp_number >(), "mp_number >");
+   test_expint(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_expint(mp_number >(), "mp_number >");
+   test_expint(mp_number >(), "mp_number >");
+   test_expint(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_gamma.cpp b/test/math/test_gamma.cpp
new file mode 100644
index 00000000..9e6528e5
--- /dev/null
+++ b/test/math/test_gamma.cpp
@@ -0,0 +1,128 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_gamma.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp_float<18>.*",           // test type(s)
+      ".*",                          // test data group
+      "boost::math::tgamma", 4000, 2500);  // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      "factorials",                  // test data group
+      "boost::math::tgamma", 70, 25);  // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      "factorials",                  // test data group
+      "boost::math::lgamma", 80, 40);  // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      "near.*",                      // test data group
+      "boost::math::tgamma", 80, 60);  // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      "near.*",                      // test data group
+      "boost::math::lgamma", 10000000, 10000000);  // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      "tgamma1pm1.*",                // test data group
+      "boost::math::tgamma1pm1", 1000, 150);  // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_hermite.cpp b/test/math/test_hermite.cpp
new file mode 100644
index 00000000..bd776eb4
--- /dev/null
+++ b/test/math/test_hermite.cpp
@@ -0,0 +1,93 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_hermite.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      "boost::math::hermite", 10, 5);  // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_hermite(mp_number >(), "mp_number >");
+   test_hermite(mp_number >(), "mp_number >");
+   test_hermite(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_hermite(mp_number >(), "mp_number >");
+   test_hermite(mp_number >(), "mp_number >");
+   test_hermite(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_hermite(mp_number >(), "mp_number >");
+   test_hermite(mp_number >(), "mp_number >");
+   test_hermite(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_ibeta.cpp b/test/math/test_ibeta.cpp
new file mode 100644
index 00000000..4cf95bb1
--- /dev/null
+++ b/test/math/test_ibeta.cpp
@@ -0,0 +1,117 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_SMALL_CONSTANT(x) x
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#define TEST_DATA 1
+
+#include "libs/math/test/test_ibeta.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*gmp_float<18>.*",              // test type(s)
+      "(?i).*small.*",                  // test data group
+      ".*", 3000, 1000);                // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*small.*",                  // test data group
+      ".*", 90, 25);  // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*medium.*",                 // test data group
+      ".*", 150, 50);  // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*large.*",                  // test data group
+      ".*", 5000, 500);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_ibeta_2.cpp b/test/math/test_ibeta_2.cpp
new file mode 100644
index 00000000..a149c837
--- /dev/null
+++ b/test/math/test_ibeta_2.cpp
@@ -0,0 +1,124 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_SMALL_CONSTANT(x) x
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#define TEST_DATA 2
+
+#include "libs/math/test/test_ibeta.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*gmp_float<18>.*",              // test type(s)
+      "(?i).*medium.*",                 // test data group
+      ".*", 4000, 1000);                // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*mpfr_float_backend<18>.*",     // test type(s)
+      "(?i).*medium.*",                 // test data group
+      ".*", 20000, 1000);               // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*small.*",                  // test data group
+      ".*", 90, 25);  // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*medium.*",                 // test data group
+      ".*", 200, 50);  // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*large.*",                  // test data group
+      ".*", 5000, 500);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_ibeta_3.cpp b/test/math/test_ibeta_3.cpp
new file mode 100644
index 00000000..6f42b026
--- /dev/null
+++ b/test/math/test_ibeta_3.cpp
@@ -0,0 +1,110 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_SMALL_CONSTANT(x) x
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#define TEST_DATA 3
+
+#include "libs/math/test/test_ibeta.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*small.*",                  // test data group
+      ".*", 90, 25);  // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*medium.*",                 // test data group
+      ".*", 200, 50);  // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*large.*",                  // test data group
+      ".*", 6000000, 500000);           // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_ibeta_4.cpp b/test/math/test_ibeta_4.cpp
new file mode 100644
index 00000000..d5c665bd
--- /dev/null
+++ b/test/math/test_ibeta_4.cpp
@@ -0,0 +1,117 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_SMALL_CONSTANT(x) x
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#define TEST_DATA 4
+
+#include "libs/math/test/test_ibeta.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*small.*",                  // test data group
+      ".*", 4000, 1000);                // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*small.*",                  // test data group
+      ".*", 90, 25);  // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*medium.*",                 // test data group
+      ".*", 200, 50);  // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      ".*",                             // test type(s)
+      "(?i).*large.*",                  // test data group
+      ".*", 5000, 500);                 // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_ibeta_inv_1.cpp b/test/math/test_ibeta_inv_1.cpp
new file mode 100644
index 00000000..2b3b616d
--- /dev/null
+++ b/test/math/test_ibeta_inv_1.cpp
@@ -0,0 +1,96 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_SMALL_CONSTANT(x) x
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#define TEST_DATA 4
+
+#include "libs/math/test/test_ibeta_inv.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 1000000, 100000);        // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   //test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_ibeta_inv_ab_4.cpp b/test/math/test_ibeta_inv_ab_4.cpp
new file mode 100644
index 00000000..4ff6dbca
--- /dev/null
+++ b/test/math/test_ibeta_inv_ab_4.cpp
@@ -0,0 +1,96 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#define TEST_DATA 4
+#define FULL_TEST
+
+#include "libs/math/test/test_ibeta_inv_ab.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 1000, 100);              // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   //test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+   test_beta(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_igamma.cpp b/test/math/test_igamma.cpp
new file mode 100644
index 00000000..ee60a91b
--- /dev/null
+++ b/test/math/test_igamma.cpp
@@ -0,0 +1,100 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_SMALL_CONSTANT(x) x
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+
+#include "libs/math/test/test_igamma.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*large.*",                   // test data group
+      ".*", 20000000L, 1000000L);    // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 7000, 2000);             // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_igamma_inv.cpp b/test/math/test_igamma_inv.cpp
new file mode 100644
index 00000000..44c5a718
--- /dev/null
+++ b/test/math/test_igamma_inv.cpp
@@ -0,0 +1,108 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_SMALL_CONSTANT(x) x
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_igamma_inv.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp_float<18>.*",           // test type(s)
+      ".*small.*",                   // test data group
+      ".*", 2000000000L, 300000000L);    // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*small.*",                   // test data group
+      ".*", 10000000L, 2000000L);    // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 7000, 2000);             // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_igamma_inva.cpp b/test/math/test_igamma_inva.cpp
new file mode 100644
index 00000000..7cca029c
--- /dev/null
+++ b/test/math/test_igamma_inva.cpp
@@ -0,0 +1,94 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+#define BOOST_MATH_SMALL_CONSTANT(x) x
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_igamma_inva.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 7000, 2000);             // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+   test_gamma(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_laguerre.cpp b/test/math/test_laguerre.cpp
new file mode 100644
index 00000000..da304c5d
--- /dev/null
+++ b/test/math/test_laguerre.cpp
@@ -0,0 +1,93 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_laguerre.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 7000, 500);             // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_laguerre(mp_number >(), "mp_number >");
+   test_laguerre(mp_number >(), "mp_number >");
+   test_laguerre(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_laguerre(mp_number >(), "mp_number >");
+   test_laguerre(mp_number >(), "mp_number >");
+   test_laguerre(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_laguerre(mp_number >(), "mp_number >");
+   test_laguerre(mp_number >(), "mp_number >");
+   test_laguerre(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_legendre.cpp b/test/math/test_legendre.cpp
new file mode 100644
index 00000000..2c0a6787
--- /dev/null
+++ b/test/math/test_legendre.cpp
@@ -0,0 +1,93 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_legendre.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 5000, 500);              // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_legendre_p(mp_number >(), "mp_number >");
+   test_legendre_p(mp_number >(), "mp_number >");
+   test_legendre_p(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_legendre_p(mp_number >(), "mp_number >");
+   test_legendre_p(mp_number >(), "mp_number >");
+   test_legendre_p(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_legendre_p(mp_number >(), "mp_number >");
+   test_legendre_p(mp_number >(), "mp_number >");
+   test_legendre_p(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_tgamma_ratio.cpp b/test/math/test_tgamma_ratio.cpp
new file mode 100644
index 00000000..71d45a79
--- /dev/null
+++ b/test/math/test_tgamma_ratio.cpp
@@ -0,0 +1,100 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_tgamma_ratio.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*gmp_float<18>.*",           // test type(s)
+      ".*",                          // test data group
+      ".*", 4000, 2000);             // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 1000, 200);             // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_tgamma_ratio(mp_number >(), "mp_number >");
+   test_tgamma_ratio(mp_number >(), "mp_number >");
+   test_tgamma_ratio(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_tgamma_ratio(mp_number >(), "mp_number >");
+   test_tgamma_ratio(mp_number >(), "mp_number >");
+   test_tgamma_ratio(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_tgamma_ratio(mp_number >(), "mp_number >");
+   test_tgamma_ratio(mp_number >(), "mp_number >");
+   test_tgamma_ratio(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+
diff --git a/test/math/test_zeta.cpp b/test/math/test_zeta.cpp
new file mode 100644
index 00000000..b4503eb1
--- /dev/null
+++ b/test/math/test_zeta.cpp
@@ -0,0 +1,100 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR_50)
+#  define TEST_MPF_50
+#  define TEST_MPFR_50
+#  define TEST_CPP_FLOAT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF_50)
+#include 
+#endif
+#if defined(TEST_MPFR_50)
+#include 
+#endif
+#ifdef TEST_BACKEND
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+
+#define SC_(x) T(BOOST_STRINGIZE(x))
+#define TEST_UDT
+
+#include "libs/math/test/test_zeta.hpp"
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*Random values less than 1", // test data group
+      ".*", 5000, 2000);             // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 1000, 200);              // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+
+int test_main(int, char* [])
+{
+   using namespace boost::multiprecision;
+   expected_results();
+   //
+   // Test at:
+   // 18 decimal digits: tests 80-bit long double approximations
+   // 30 decimal digits: tests 128-bit long double approximations
+   // 35 decimal digits: tests arbitrary precision code
+   //
+#ifdef TEST_MPF_50
+   test_zeta(mp_number >(), "mp_number >");
+   test_zeta(mp_number >(), "mp_number >");
+   test_zeta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_MPFR_50
+   test_zeta(mp_number >(), "mp_number >");
+   test_zeta(mp_number >(), "mp_number >");
+   test_zeta(mp_number >(), "mp_number >");
+#endif
+#ifdef TEST_CPP_FLOAT
+   test_zeta(mp_number >(), "mp_number >");
+   test_zeta(mp_number >(), "mp_number >");
+   test_zeta(mp_number >(), "mp_number >");
+#endif
+   return 0;
+}
+

From 3327eb6b8b8691a70eadf46cc7e36b2109245bc6 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Tue, 20 Dec 2011 16:46:54 +0000
Subject: [PATCH 082/256] Fix some MSVC warnings.

[SVN r76082]
---
 include/boost/multiprecision/cpp_float.hpp             | 6 +++---
 include/boost/multiprecision/detail/mp_number_base.hpp | 6 +++---
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp
index 037672eb..84811b12 100644
--- a/include/boost/multiprecision/cpp_float.hpp
+++ b/include/boost/multiprecision/cpp_float.hpp
@@ -404,7 +404,7 @@ public:
       return *this -= one();
    }
 
-   std::string str(std::streamsize digits, std::ios_base::fmtflags f)const;
+   std::string str(boost::intmax_t digits, std::ios_base::fmtflags f)const;
 
    int compare(const cpp_float& v)const;
    template 
@@ -1647,7 +1647,7 @@ cpp_float cpp_float::extract_integer_part(void) const
 }
 
 template 
-std::string cpp_float::str(std::streamsize number_of_digits, std::ios_base::fmtflags f) const
+std::string cpp_float::str(boost::intmax_t number_of_digits, std::ios_base::fmtflags f) const
 {
    if(this->isinf())
    {
@@ -1664,7 +1664,7 @@ std::string cpp_float::str(std::streamsize number_of_digits, std::ios_
    }
 
    std::string str;
-   std::streamsize org_digits(number_of_digits);
+   boost::intmax_t org_digits(number_of_digits);
    boost::int64_t my_exp = order();
    if(number_of_digits == 0)
       number_of_digits = cpp_float_max_digits10;
diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp
index b0eb1611..781f8f71 100644
--- a/include/boost/multiprecision/detail/mp_number_base.hpp
+++ b/include/boost/multiprecision/detail/mp_number_base.hpp
@@ -363,7 +363,7 @@ struct digits2
 #endif
 
 template 
-void format_float_string(S& str, long long my_exp, std::streamsize digits, std::ios_base::fmtflags f, bool iszero)
+void format_float_string(S& str, boost::intmax_t my_exp, boost::intmax_t digits, std::ios_base::fmtflags f, bool iszero)
 {
    typedef typename S::size_type size_type;
    bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific;
@@ -427,7 +427,7 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std::
       //
       // Pad out the end with zero's if we need to:
       //
-      std::streamsize chars = str.size();
+      boost::intmax_t chars = str.size();
       chars = digits - chars;
       if(scientific)
          ++chars;
@@ -465,7 +465,7 @@ void format_float_string(S& str, long long my_exp, std::streamsize digits, std::
       if(fixed)
       {
          // We may need to add trailing zeros:
-         std::streamsize l = str.find('.') + 1;
+         boost::intmax_t l = str.find('.') + 1;
          l = digits - (str.size() - l);
          if(l > 0)
             str.append(size_type(l), '0');

From ebe14443af47cca1fb3ac3db36d8bb367af092b3 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 22 Dec 2011 11:52:51 +0000
Subject: [PATCH 083/256] Update TODO list.

[SVN r76103]
---
 doc/html/boost_multiprecision/map/todo.html | 3 +--
 doc/html/index.html                         | 2 +-
 doc/multiprecision.qbk                      | 2 +-
 3 files changed, 3 insertions(+), 4 deletions(-)

diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html
index 977961ff..7d07e878 100644
--- a/doc/html/boost_multiprecision/map/todo.html
+++ b/doc/html/boost_multiprecision/map/todo.html
@@ -24,8 +24,7 @@
       

 
    
 
  • 
-            Adapt Boost.Math special function tests for this library: will make a
-            very good test of arithmetic and std lib support.
+            Add backend support for libdecNumber.
           
    • 
 
  • 
             Add an adapter backend for complex number types.
diff --git a/doc/html/index.html b/doc/html/index.html
index 9abc8978..a404ace7 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -50,7 +50,7 @@
 

 

 
-
+
Last revised: November 30, 2011 at 12:15:51 GMT
Last revised: December 22, 2011 at 11:51:46 GMT

 

 

 

diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk
index d074fe83..5e717788 100644
--- a/doc/multiprecision.qbk
+++ b/doc/multiprecision.qbk
@@ -966,7 +966,7 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia
 
 More a list of what ['could] be done, rather than what ['should] be done (which may be a much smaller list!).
 
-* Adapt Boost.Math special function tests for this library: will make a very good test of arithmetic and std lib support.
+* Add backend support for libdecNumber.
 * Add an adapter backend for complex number types.
 * Add an adapter backend for rational types.
 * Test integer types with Boost.Rational.

From a2dc3b968cf9c344520a7d3a07f126d6644bcd7c Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Fri, 23 Dec 2011 17:13:29 +0000
Subject: [PATCH 084/256] Fix remaining Boost.Rational support issues and add
 rational number IO test.

[SVN r76121]
---
 include/boost/multiprecision/mp_number.hpp |  42 +++-
 test/Jamfile.v2                            | 228 ++++++++++++---------
 test/test_arithmetic.cpp                   |  49 ++++-
 test/test_float_io.cpp                     |   2 +-
 test/test_rational_io.cpp                  | 131 ++++++++++++
 5 files changed, 350 insertions(+), 102 deletions(-)
 create mode 100644 test/test_rational_io.cpp

diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp
index 71aa1fc6..2d638b2c 100644
--- a/include/boost/multiprecision/mp_number.hpp
+++ b/include/boost/multiprecision/mp_number.hpp
@@ -1571,6 +1571,46 @@ inline void swap(mp_number& a, mp_number& b)
    a.swap(b);
 }
 
-}} // namespaces
+}  // namespace multipreciion
+
+template 
+class rational;
+
+template 
+inline std::istream& operator >> (std::istream& is, rational >& r)
+{
+   std::string s1;
+   multiprecision::mp_number v1, v2;
+   char c;
+   bool have_hex = false;
+
+   while((EOF != (c = is.peek())) && (c == 'x' || c == 'X' || c == '-' || c == '+' || (c >= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F'))))
+   {
+      if(c == 'x' || c == 'X')
+         have_hex = true;
+      s1.append(1, c);
+      is.get();
+   }
+   v1 = s1;
+   s1.erase();
+   if(c == '/')
+   {
+      is.get();
+      while((EOF != (c = is.peek())) && (c == 'x' || c == 'X' || c == '-' || c == '+' || (c >= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F'))))
+      {
+         if(c == 'x' || c == 'X')
+            have_hex = true;
+         s1.append(1, c);
+         is.get();
+      }
+      v2 = s1;
+   }
+   else
+      v2 = 1;
+   r.assign(v1, v2);
+   return is;
+}
+
+} // namespaces
 
 #endif
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 1f3c0ea7..0c36ed4a 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -25,6 +25,10 @@ project : requirements
    msvc:static
    ;
 
+local disable-specfun = [ MATCH (--disable-specfun) : [ modules.peek : ARGV ] ] ;
+local disable-concepts = [ MATCH (--disable-concepts) : [ modules.peek : ARGV ] ] ;
+
+
 lib gmp ;
 lib mpfr ;
 
@@ -76,6 +80,14 @@ run test_arithmetic.cpp gmp
          [ check-target-builds ../config//has_gmp : : no ]
         : test_arithmetic_mpz ;
 
+run test_arithmetic.cpp gmp
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_MPZ_BOOST_RATIONAL
+         [ check-target-builds ../config//has_gmp : : no ]
+        : test_arithmetic_mpz_br ;
+
 run test_arithmetic.cpp gmp
         : # command line
         : # input files
@@ -108,6 +120,14 @@ run test_arithmetic.cpp $(TOMMATH)
          [ check-target-builds ../config//has_tommath : : no ]
         : test_arithmetic_tommath ;
 
+run test_arithmetic.cpp $(TOMMATH)
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_TOMMATH_BOOST_RATIONAL
+         [ check-target-builds ../config//has_tommath : : no ]
+        : test_arithmetic_tommath_br ;
+
 run test_numeric_limits.cpp
         : # command line
         : # input files
@@ -179,68 +199,6 @@ run test_numeric_limits.cpp $(TOMMATH)
          [ check-target-builds ../config//has_tommath : : no ]
         : test_numeric_limits_tommath ;
 
-run mp_number_concept_check.cpp  mpfr
-        : # command line
-        : # input files
-        : # requirements
-	      TEST_MPFR_50
-         [ check-target-builds ../config//has_mpfr : : no ]
-        : mp_number_concept_check_mpfr_50 ;
-
-run mp_number_concept_check.cpp  mpfr
-        : # command line
-        : # input files
-        : # requirements
-	      TEST_MPFR_6
-         [ check-target-builds ../config//has_mpfr : : no ]
-        : mp_number_concept_check_mpfr_6 ;
-
-run mp_number_concept_check.cpp  mpfr
-        : # command line
-        : # input files
-        : # requirements
-	      TEST_MPFR_15
-         [ check-target-builds ../config//has_mpfr : : no ]
-        : mp_number_concept_check_mpfr_15 ;
-
-run mp_number_concept_check.cpp  mpfr
-        : # command line
-        : # input files
-        : # requirements
-	      TEST_MPFR_17
-         [ check-target-builds ../config//has_mpfr : : no ]
-        : mp_number_concept_check_mpfr_17 ;
-
-run mp_number_concept_check.cpp  mpfr
-        : # command line
-        : # input files
-        : # requirements
-	      TEST_MPFR_30
-         [ check-target-builds ../config//has_mpfr : : no ]
-        : mp_number_concept_check_mpfr_30 ;
-
-run mp_number_concept_check.cpp  gmp
-        : # command line
-        : # input files
-        : # requirements
-	      TEST_MPF_50
-         [ check-target-builds ../config//has_gmp : : no ]
-        : mp_number_concept_check_mpf50 ;
-
-run mp_number_concept_check.cpp
-        : # command line
-        : # input files
-        : # requirements
-	      TEST_CPP_FLOAT
-        : mp_number_concept_check_cpp_float ;
-
-run mp_number_concept_check.cpp
-        : # command line
-        : # input files
-        : # requirements
-	      TEST_BACKEND
-        : mp_number_concept_check_backend_concept ;
-
 run test_exp.cpp gmp
         : # command line
         : # input files
@@ -609,6 +567,22 @@ run test_int_io.cpp gmp
          [ check-target-builds ../config//has_gmp : : no ]
         : test_int_io_mpz ;
 
+run test_rational_io.cpp $(TOMMATH)
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_TOMMATH
+         [ check-target-builds ../config//has_tommath : : no ]
+        : test_rational_io_tommath ;
+
+run test_rational_io.cpp gmp
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_MPQ
+         [ check-target-builds ../config//has_gmp : : no ]
+        : test_rational_io_mpz ;
+
 run ../example/gmp_snips.cpp gmp
         : # command line
         : # input files
@@ -630,35 +604,105 @@ run ../example/tommath_snips.cpp $(TOMMATH)
          [ check-target-builds ../config//has_tommath : : no ] ;
 
 
-for local source in [ glob math/*.cpp ]
+if ! $(disable-specfun)
 {
-   run $(source) mpfr gmp /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
-        : # command line
-        : # input files
-        : # requirements
-         [ check-target-builds ../config//has_mpfr : : no ] 
-         TEST_MPFR_50
-         speed
-         BOOST_ALL_NO_LIB
-         msvc:-bigobj
-        : $(source:B)_mpfr ;
-   run $(source) gmp /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
-        : # command line
-        : # input files
-        : # requirements
-         [ check-target-builds ../config//has_gmp : : no ] 
-         speed
-         TEST_MPF_50
-         BOOST_ALL_NO_LIB
-         msvc:-bigobj
-        : $(source:B)_mpf ;
-   run $(source) /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
-        : # command line
-        : # input files
-        : # requirements
-         TEST_CPP_FLOAT
-         BOOST_ALL_NO_LIB
-         speed
-         msvc:-bigobj
-        : $(source:B)_cpp_float ;
+
+   for local source in [ glob math/*.cpp ]
+   {
+      run $(source) mpfr gmp /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
+           : # command line
+           : # input files
+           : # requirements
+            [ check-target-builds ../config//has_mpfr : : no ] 
+            TEST_MPFR_50
+            speed
+            BOOST_ALL_NO_LIB
+            msvc:-bigobj
+           : $(source:B)_mpfr ;
+      run $(source) gmp /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
+           : # command line
+           : # input files
+           : # requirements
+            [ check-target-builds ../config//has_gmp : : no ] 
+            speed
+            TEST_MPF_50
+            BOOST_ALL_NO_LIB
+            msvc:-bigobj
+           : $(source:B)_mpf ;
+      run $(source) /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static
+           : # command line
+           : # input files
+           : # requirements
+            TEST_CPP_FLOAT
+            BOOST_ALL_NO_LIB
+            speed
+            msvc:-bigobj
+           : $(source:B)_cpp_float ;
+   }
+}
+
+if ! $(disable-concepts)
+{
+   run mp_number_concept_check.cpp  mpfr
+           : # command line
+           : # input files
+           : # requirements
+	         TEST_MPFR_50
+            [ check-target-builds ../config//has_mpfr : : no ]
+           : mp_number_concept_check_mpfr_50 ;
+
+   run mp_number_concept_check.cpp  mpfr
+           : # command line
+           : # input files
+           : # requirements
+	         TEST_MPFR_6
+            [ check-target-builds ../config//has_mpfr : : no ]
+           : mp_number_concept_check_mpfr_6 ;
+
+   run mp_number_concept_check.cpp  mpfr
+           : # command line
+           : # input files
+           : # requirements
+	         TEST_MPFR_15
+            [ check-target-builds ../config//has_mpfr : : no ]
+           : mp_number_concept_check_mpfr_15 ;
+
+   run mp_number_concept_check.cpp  mpfr
+           : # command line
+           : # input files
+           : # requirements
+	         TEST_MPFR_17
+            [ check-target-builds ../config//has_mpfr : : no ]
+           : mp_number_concept_check_mpfr_17 ;
+
+   run mp_number_concept_check.cpp  mpfr
+           : # command line
+           : # input files
+           : # requirements
+	         TEST_MPFR_30
+            [ check-target-builds ../config//has_mpfr : : no ]
+           : mp_number_concept_check_mpfr_30 ;
+
+   run mp_number_concept_check.cpp  gmp
+           : # command line
+           : # input files
+           : # requirements
+	         TEST_MPF_50
+            [ check-target-builds ../config//has_gmp : : no ]
+           : mp_number_concept_check_mpf50 ;
+
+   run mp_number_concept_check.cpp
+           : # command line
+           : # input files
+           : # requirements
+	         TEST_CPP_FLOAT
+           : mp_number_concept_check_cpp_float ;
+
+   run mp_number_concept_check.cpp
+           : # command line
+           : # input files
+           : # requirements
+	         TEST_BACKEND
+           : mp_number_concept_check_backend_concept ;
+
 }
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index 1a7b5bc7..6c5fabf1 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -10,7 +10,9 @@
 #include 
 #include 
 
-#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && !defined(TEST_TOMMATH)
+#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \
+   !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) \
+   && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)
 #  define TEST_MPF_50
 #  define TEST_MPF
 #  define TEST_BACKEND
@@ -30,7 +32,7 @@
 
 #endif
 
-#if defined(TEST_MPF_50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ)
+#if defined(TEST_MPF_50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) || defined(TEST_MPZ_BOOST_RATIONAL)
 #include 
 #endif
 #ifdef TEST_BACKEND
@@ -42,8 +44,27 @@
 #if defined(TEST_MPFR) || defined(TEST_MPFR_50)
 #include 
 #endif
-#ifdef TEST_TOMMATH
+#if defined(TEST_TOMMATH) || defined(TEST_TOMMATH_BOOST_RATIONAL)
 #include 
+#endif
+#if defined(TEST_TOMMATH_BOOST_RATIONAL) || defined(TEST_MPZ_BOOST_RATIONAL)
+#include 
+
+#define NO_MIXED_OPS
+
+namespace boost{ namespace multiprecision{
+
+#ifdef TEST_TOMMATH_BOOST_RATIONAL
+template<>
+struct number_category > : public mpl::int_ {};
+#endif
+#ifdef TEST_MPZ_BOOST_RATIONAL
+template<>
+struct number_category > : public mpl::int_ {};
+#endif
+
+}}
+
 #endif
 
 #define BOOST_TEST_THROW(x, EX)\
@@ -637,7 +658,9 @@ void test()
    BOOST_TEST(ac == 64 * 2);
    ac = a;
    ac = b - ac * a;
+#ifndef NO_MIXED_OPS
    BOOST_TEST(ac == 0);
+#endif
    ac = a;
    ac = b * (ac + a);
    BOOST_TEST(ac == 64 * (16));
@@ -655,7 +678,9 @@ void test()
    BOOST_TEST(ac == 8 - 64);
    ac = a;
    ac = a - ac;
+#ifndef NO_MIXED_OPS
    BOOST_TEST(ac == 0);
+#endif
    ac = a;
    ac += a + b;
    BOOST_TEST(ac == 80);
@@ -681,7 +706,9 @@ void test()
    BOOST_TEST(ac == 16);
    ac = a;
    ac += -a;
+#ifndef NO_MIXED_OPS
    BOOST_TEST(ac == 0);
+#endif
    ac = a;
    ac += b - a;
    BOOST_TEST(ac == 8 + 64-8);
@@ -691,7 +718,9 @@ void test()
    ac = a;
    ac = a;
    ac -= +a;
+#ifndef NO_MIXED_OPS
    BOOST_TEST(ac == 0);
+#endif
    ac = a;
    ac -= -a;
    BOOST_TEST(ac == 16);
@@ -805,6 +834,7 @@ void test()
    BOOST_TEST((72 < b+a) == false);
    BOOST_TEST((72 >= b+a) == true);
    BOOST_TEST((72 > b+a) == false);
+#ifndef NO_MIXED_OPS
    //
    // Test sign and zero functions, plus use in boolian context:
    //
@@ -817,6 +847,8 @@ void test()
    a = 0;
    BOOST_TEST(a.sign() == 0);
    BOOST_TEST(a.is_zero());
+#endif
+   a = 0;
    if(a)
    {
       BOOST_ERROR("Unexpected non-zero result");
@@ -880,11 +912,6 @@ int main()
 #endif
 #ifdef TEST_MPF
    boost::multiprecision::mpf_float::default_precision(1000);
-   /*
-   boost::multiprecision::mpf_float r;
-   r.precision(50);
-   BOOST_TEST(r.precision() >= 50);
-   */
    BOOST_TEST(boost::multiprecision::mpf_float::default_precision() == 1000);
    test();
 #endif
@@ -905,6 +932,12 @@ int main()
 #endif
 #ifdef TEST_TOMMATH
    test();
+#endif
+#ifdef TEST_TOMMATH_BOOST_RATIONAL
+   test >();
+#endif
+#ifdef TEST_MPZ_BOOST_RATIONAL
+   test >();
 #endif
    return boost::report_errors();
 }
diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp
index bd512991..59afe975 100644
--- a/test/test_float_io.cpp
+++ b/test/test_float_io.cpp
@@ -50,7 +50,7 @@ bool is_mpf(const T&) { return false; }
 
 bool is_bankers_rounding_error(const std::string& s, const char* expect)
 {
-   // This check isn't foolproof: that would require *much* more sofisticated code!!!
+   // This check isn't foolproof: that would require *much* more sophisticated code!!!
    std::string::size_type l = std::strlen(expect);
    if(l != s.size())
       return false;
diff --git a/test/test_rational_io.cpp b/test/test_rational_io.cpp
new file mode 100644
index 00000000..66246c0f
--- /dev/null
+++ b/test/test_rational_io.cpp
@@ -0,0 +1,131 @@
+// Copyright John Maddock 2011.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#if !defined(TEST_MPQ) && !defined(TEST_TOMMATH)
+#  define TEST_MPQ
+#  define TEST_TOMMATH
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPQ)
+#include 
+#endif
+#if defined(TEST_TOMMATH)
+#include 
+#endif
+
+#include 
+#include 
+#include 
+#include 
+#include "test.hpp"
+#include 
+#include 
+
+template 
+T generate_random()
+{
+   static boost::random::uniform_int_distribution ui(0, 20);
+   static boost::random::mt19937 gen;
+   T val = gen();
+   unsigned lim = ui(gen);
+   for(unsigned i = 0; i < lim; ++i)
+   {
+      val *= (gen.max)();
+      val += gen();
+   }
+   T denom = gen();
+   lim = ui(gen);
+   for(unsigned i = 0; i < lim; ++i)
+   {
+      denom *= (gen.max)();
+      denom += gen();
+   }
+   return val / denom;
+}
+
+template 
+void do_round_trip(const T& val, std::ios_base::fmtflags f, const boost::mpl::true_&)
+{
+   std::stringstream ss;
+   ss << std::setprecision(std::numeric_limits::max_digits10);
+   ss.flags(f);
+   ss << val;
+   T new_val = ss.str();
+   BOOST_CHECK_EQUAL(new_val, val);
+   new_val = val.str(0, f);
+   BOOST_CHECK_EQUAL(new_val, val);
+}
+
+template 
+void do_round_trip(const T& val, std::ios_base::fmtflags f, const boost::mpl::false_&)
+{
+   std::stringstream ss;
+   ss << std::setprecision(std::numeric_limits::max_digits10);
+   ss.flags(f);
+   ss << val;
+   T new_val;
+   ss >> new_val;
+   BOOST_CHECK_EQUAL(new_val, val);
+}
+
+template 
+struct is_mp_number : public boost::mpl::false_{};
+template 
+struct is_mp_number > : public boost::mpl::true_{};
+
+template 
+void do_round_trip(const T& val, std::ios_base::fmtflags f)
+{
+   do_round_trip(val, f, is_mp_number());
+}
+
+template 
+void do_round_trip(const T& val)
+{
+   do_round_trip(val, std::ios_base::fmtflags(0));
+   if(val >= 0)
+   {
+      do_round_trip(val, std::ios_base::fmtflags(std::ios_base::showbase|std::ios_base::hex));
+      do_round_trip(val, std::ios_base::fmtflags(std::ios_base::showbase|std::ios_base::oct));
+   }
+}
+
+template 
+void test_round_trip()
+{
+   for(unsigned i = 0; i < 1000; ++i)
+   {
+      T val = generate_random();
+      do_round_trip(val);
+      do_round_trip(T(-val));
+   }
+}
+
+int main()
+{
+#ifdef TEST_MPQ
+   test_round_trip();
+   test_round_trip >();
+#endif
+#ifdef TEST_TOMMATH
+   test_round_trip >();
+#endif
+   return boost::report_errors();
+}
+

From b9ea00966fbc9d61954e0d6d65adbdaf0584f011 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Sat, 24 Dec 2011 10:07:32 +0000
Subject: [PATCH 085/256] Fix modulus operations for negative numbers that
 should yield zero results (and update tests to match). Fix boost::rational
 comparison operator support. Fix GCC failures in test_rational_io.cpp. Add
 adapter for rational types.

[SVN r76128]
---
 include/boost/multiprecision/gmp.hpp          |  12 +-
 include/boost/multiprecision/mp_number.hpp    |  24 +++
 .../boost/multiprecision/rational_adapter.hpp | 161 ++++++++++++++++++
 include/boost/multiprecision/tommath.hpp      |  12 +-
 test/test_arithmetic.cpp                      |  22 ++-
 test/test_rational_io.cpp                     |   6 +-
 6 files changed, 217 insertions(+), 20 deletions(-)
 create mode 100644 include/boost/multiprecision/rational_adapter.hpp

diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp
index 5a966277..be5c3b3d 100644
--- a/include/boost/multiprecision/gmp.hpp
+++ b/include/boost/multiprecision/gmp.hpp
@@ -1114,7 +1114,7 @@ inline void modulus(gmp_int& t, const gmp_int& o)
    bool neg = mpz_sgn(t.data()) < 0;
    bool neg2 = mpz_sgn(o.data()) < 0;
    mpz_mod(t.data(), t.data(), o.data());
-   if(neg)
+   if(neg && mpz_sgn(t.data()) != 0)
    {
       if(!neg2)
          t.negate();
@@ -1139,7 +1139,7 @@ inline void modulus(gmp_int& t, unsigned long i)
 {
    bool neg = mpz_sgn(t.data()) < 0;
    mpz_mod_ui(t.data(), t.data(), i);
-   if(neg)
+   if(neg && mpz_sgn(t.data()) != 0)
    {
       t.negate();
       mpz_add_ui(t.data(), t.data(), i);
@@ -1175,7 +1175,7 @@ inline void modulus(gmp_int& t, long i)
    bool neg = mpz_sgn(t.data()) < 0;
    bool neg2 = i < 0;
    mpz_mod_ui(t.data(), t.data(), std::abs(i));
-   if(neg)
+   if(neg && mpz_sgn(t.data()) != 0)
    {
       if(!neg2)
       {
@@ -1252,7 +1252,7 @@ inline void modulus(gmp_int& t, const gmp_int& p, const gmp_int& o)
    bool neg = mpz_sgn(p.data()) < 0;
    bool neg2 = mpz_sgn(o.data()) < 0;
    mpz_mod(t.data(), p.data(), o.data());
-   if(neg)
+   if(neg && mpz_sgn(t.data()) != 0)
    {
       if(!neg2)
          t.negate();
@@ -1277,7 +1277,7 @@ inline void modulus(gmp_int& t, const gmp_int& p, unsigned long i)
 {
    bool neg = mpz_sgn(p.data()) < 0;
    mpz_mod_ui(t.data(), p.data(), i);
-   if(neg)
+   if(neg && mpz_sgn(t.data()) != 0)
    {
       t.negate();
       mpz_add_ui(t.data(), t.data(), i);
@@ -1313,7 +1313,7 @@ inline void modulus(gmp_int& t, const gmp_int& p, long i)
    bool neg = mpz_sgn(p.data()) < 0;
    bool neg2 = i < 0;
    mpz_mod_ui(t.data(), p.data(), std::abs(i));
-   if(neg)
+   if(neg && mpz_sgn(t.data()) != 0)
    {
       if(!neg2)
       {
diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp
index 2d638b2c..a04eba59 100644
--- a/include/boost/multiprecision/mp_number.hpp
+++ b/include/boost/multiprecision/mp_number.hpp
@@ -1611,6 +1611,30 @@ inline std::istream& operator >> (std::istream& is, rational
+typename enable_if, bool>::type operator == (const rational >& a, const Arithmetic& b)
+{
+   return a == multiprecision::mp_number(b);
+}
+
+template 
+typename enable_if, bool>::type operator == (const Arithmetic& b, const rational >& a)
+{
+   return a == multiprecision::mp_number(b);
+}
+
+template 
+typename enable_if, bool>::type operator != (const rational >& a, const Arithmetic& b)
+{
+   return a != multiprecision::mp_number(b);
+}
+
+template 
+typename enable_if, bool>::type operator != (const Arithmetic& b, const rational >& a)
+{
+   return a != multiprecision::mp_number(b);
+}
+
 } // namespaces
 
 #endif
diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp
new file mode 100644
index 00000000..074c136e
--- /dev/null
+++ b/include/boost/multiprecision/rational_adapter.hpp
@@ -0,0 +1,161 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifndef BOOST_MATH_RATIONAL_ADAPTER_HPP
+#define BOOST_MATH_RATIONAL_ADAPTER_HPP
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+
+namespace boost{
+namespace multiprecision{
+
+template 
+struct rational_adapter
+{
+   typedef mp_number                integer_type;
+   typedef boost::rational        rational_type;
+
+   typedef typename IntBackend::signed_types    signed_types;
+   typedef typename IntBackend::unsigned_types  unsigned_types;
+   typedef typename IntBackend::float_types     float_types;
+
+   rational_adapter(){}
+   rational_adapter(const rational_adapter& o)
+   {
+      m_value = o.m_value;
+   }
+   rational_adapter(const IntBackend& o) : m_value(o) {}
+#ifndef BOOST_NO_RVALUE_REFERENCES
+   rational_adapter(rational_adapter&& o) : m_value(o.m_value) {}
+   rational_adapter(IntBackend&& o) : m_value(o) {}
+#endif
+   rational_adapter& operator = (const rational_adapter& o)
+   {
+      m_value = o.m_value;
+      return *this;
+   }
+   template 
+   typename enable_if, rational_adapter&>::type operator = (Arithmetic i)
+   {
+      m_value = i;
+      return *this;
+   }
+   rational_adapter& operator = (const char* s)
+   {
+      m_value = s;
+      return *this;
+   }
+   void swap(rational_adapter& o)
+   {
+      std::swap(m_value, o.m_value);
+   }
+   std::string str(std::streamsize digits, std::ios_base::fmtflags f)const
+   {
+      //
+      // We format the string ourselves so we can match what GMP's mpq type does:
+      //
+      std::string result = data().numerator().str(digits, f);
+      if(data().denominator() != 1)
+      {
+         result.append(1, ',');
+         result.append(data().denominator().str(digits, f));
+      }
+      return result;
+   }
+   void negate()
+   {
+      m_value = -m_value;
+   }
+   int compare(const rational_adapter& o)const
+   {
+      return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0);
+   }
+   template 
+   typename enable_if, int>::type compare(Arithmatic i)const
+   {
+      return m_value > i ? 1 : (m_value < i ? -1 : 0);
+   }
+   rational_type& data() { return m_value; }
+   const rational_type& data()const { return m_value; }
+private:
+   rational_type m_value;
+};
+
+template 
+inline void add(rational_adapter& result, const rational_adapter& o)
+{
+   result.data() += o.data();
+}
+template 
+inline void subtract(rational_adapter& result, const rational_adapter& o)
+{
+   result.data() -= o.data();
+}
+template 
+inline void multiply(rational_adapter& result, const rational_adapter& o)
+{
+   result.data() *= o.data();
+}
+template 
+inline void divide(rational_adapter& result, const rational_adapter& o)
+{
+   result.data() /= o.data();
+}
+
+template 
+inline void convert_to(R* result, const rational_adapter& backend)
+{
+   *result = backend.data().numerator().template convert_to();
+   *result /= backend.data().denominator().template convert_to();
+}
+
+template 
+inline bool is_zero(const rational_adapter& val)
+{
+   return is_zero(val.data().numerator().backend());
+}
+template 
+inline int get_sign(const rational_adapter& val)
+{
+   return get_sign(val.data().numerator().backend());
+}
+
+
+template
+struct number_category > : public mpl::int_{};
+
+}} // namespaces
+
+
+namespace std{
+
+template 
+class numeric_limits > > : public std::numeric_limits
+{
+   typedef std::numeric_limits base_type;
+   typedef boost::multiprecision::mp_number > number_type;
+public:
+   BOOST_STATIC_CONSTEXPR bool is_integer = false;
+   BOOST_STATIC_CONSTEXPR bool is_exact = true;
+   BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); }
+   BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); }
+   BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); }
+   BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); }
+   BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; }
+   BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); }
+   BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); }
+   BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); }
+   BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); }
+};
+
+}
+
+#endif
diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp
index 19f5a4ed..fbe834cb 100644
--- a/include/boost/multiprecision/tommath.hpp
+++ b/include/boost/multiprecision/tommath.hpp
@@ -258,12 +258,16 @@ inline void modulus(tommath_int& t, const tommath_int& o)
    bool neg = get_sign(t) < 0;
    bool neg2 = get_sign(o) < 0;
    detail::check_tommath_result(mp_mod(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
-   if(neg != neg2)
+   if((neg != neg2) && (get_sign(t) != 0))
    {
       t.negate();
       detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
       t.negate();
    }
+   else if(neg && (t.compare(o) == 0))
+   {
+      mp_zero(&t.data());
+   }
 }
 template 
 inline void left_shift(tommath_int& t, UI i)
@@ -331,12 +335,16 @@ inline void modulus(tommath_int& t, const tommath_int& p, const tommath_int& o)
    bool neg = get_sign(p) < 0;
    bool neg2 = get_sign(o) < 0;
    detail::check_tommath_result(mp_mod(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data()));
-   if(neg != neg2)
+   if((neg != neg2) && (get_sign(t) != 0))
    {
       t.negate();
       detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
       t.negate();
    }
+   else if(neg  && (t.compare(o) == 0))
+   {
+      mp_zero(&t.data());
+   }
 }
 
 inline void bitwise_and(tommath_int& result, const tommath_int& u, const tommath_int& v)
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index 6c5fabf1..0419cf82 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -34,6 +34,7 @@
 
 #if defined(TEST_MPF_50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) || defined(TEST_MPZ_BOOST_RATIONAL)
 #include 
+#include 
 #endif
 #ifdef TEST_BACKEND
 #include 
@@ -46,6 +47,7 @@
 #endif
 #if defined(TEST_TOMMATH) || defined(TEST_TOMMATH_BOOST_RATIONAL)
 #include 
+#include 
 #endif
 #if defined(TEST_TOMMATH_BOOST_RATIONAL) || defined(TEST_MPZ_BOOST_RATIONAL)
 #include 
@@ -133,7 +135,7 @@ void test_integer_ops(const boost::mpl::int_();
+   test > >();
 #endif
 #ifdef TEST_MPQ
    test();
@@ -932,6 +935,7 @@ int main()
 #endif
 #ifdef TEST_TOMMATH
    test();
+   test > >();
 #endif
 #ifdef TEST_TOMMATH_BOOST_RATIONAL
    test >();
diff --git a/test/test_rational_io.cpp b/test/test_rational_io.cpp
index 66246c0f..b8fcacd9 100644
--- a/test/test_rational_io.cpp
+++ b/test/test_rational_io.cpp
@@ -42,14 +42,14 @@ T generate_random()
 {
    static boost::random::uniform_int_distribution ui(0, 20);
    static boost::random::mt19937 gen;
-   T val = gen();
+   T val = T(gen());
    unsigned lim = ui(gen);
    for(unsigned i = 0; i < lim; ++i)
    {
       val *= (gen.max)();
       val += gen();
    }
-   T denom = gen();
+   T denom = T(gen());
    lim = ui(gen);
    for(unsigned i = 0; i < lim; ++i)
    {
@@ -76,7 +76,7 @@ template 
 void do_round_trip(const T& val, std::ios_base::fmtflags f, const boost::mpl::false_&)
 {
    std::stringstream ss;
-   ss << std::setprecision(std::numeric_limits::max_digits10);
+   ss << std::setprecision(std::numeric_limits::digits10 + 4);
    ss.flags(f);
    ss << val;
    T new_val;

From c32e35aaced570cb553071e320753135b718d10e Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Sat, 24 Dec 2011 11:59:25 +0000
Subject: [PATCH 086/256] Fix File IO and string conversion for
 rational_adapter, and update tests accordingly.

[SVN r76129]
---
 .../boost/multiprecision/rational_adapter.hpp | 32 +++++++++++++++++--
 test/test_rational_io.cpp                     |  3 ++
 2 files changed, 33 insertions(+), 2 deletions(-)

diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp
index 074c136e..64a34de9 100644
--- a/include/boost/multiprecision/rational_adapter.hpp
+++ b/include/boost/multiprecision/rational_adapter.hpp
@@ -50,7 +50,35 @@ struct rational_adapter
    }
    rational_adapter& operator = (const char* s)
    {
-      m_value = s;
+      std::string s1;
+      multiprecision::mp_number v1, v2;
+      char c;
+      bool have_hex = false;
+
+      while((0 != (c = *s)) && (c == 'x' || c == 'X' || c == '-' || c == '+' || (c >= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F'))))
+      {
+         if(c == 'x' || c == 'X')
+            have_hex = true;
+         s1.append(1, c);
+         ++s;
+      }
+      v1 = s1;
+      s1.erase();
+      if(c == '/')
+      {
+         ++s;
+         while((0 != (c = *s)) && (c == 'x' || c == 'X' || c == '-' || c == '+' || (c >= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F'))))
+         {
+            if(c == 'x' || c == 'X')
+               have_hex = true;
+            s1.append(1, c);
+            ++s;
+         }
+         v2 = s1;
+      }
+      else
+         v2 = 1;
+      data().assign(v1, v2);
       return *this;
    }
    void swap(rational_adapter& o)
@@ -65,7 +93,7 @@ struct rational_adapter
       std::string result = data().numerator().str(digits, f);
       if(data().denominator() != 1)
       {
-         result.append(1, ',');
+         result.append(1, '/');
          result.append(data().denominator().str(digits, f));
       }
       return result;
diff --git a/test/test_rational_io.cpp b/test/test_rational_io.cpp
index b8fcacd9..583b891e 100644
--- a/test/test_rational_io.cpp
+++ b/test/test_rational_io.cpp
@@ -33,6 +33,7 @@
 #include 
 #include 
 #include 
+#include 
 #include "test.hpp"
 #include 
 #include 
@@ -122,9 +123,11 @@ int main()
 #ifdef TEST_MPQ
    test_round_trip();
    test_round_trip >();
+   test_round_trip > >();
 #endif
 #ifdef TEST_TOMMATH
    test_round_trip >();
+   test_round_trip > >();
 #endif
    return boost::report_errors();
 }

From d7578f242cf85006a0ad9e6ffffc38b2d58d23ad Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Sat, 24 Dec 2011 13:13:16 +0000
Subject: [PATCH 087/256] Add numerator/denominator accessor functions to
 rational_adapter.hpp. Define predefined rational number type for libtommath.
 Add rational number specific tests to test_arithmetic.cpp. Document
 rational_adapter and related stuff, regenerate docs.

[SVN r76130]
---
 doc/html/boost_multiprecision/intro.html      |   2 -
 doc/html/boost_multiprecision/map.html        |   2 -
 doc/html/boost_multiprecision/map/hist.html   |   2 -
 doc/html/boost_multiprecision/map/todo.html   |   2 -
 doc/html/boost_multiprecision/ref.html        |   2 -
 .../boost_multiprecision/ref/backendconc.html |   2 -
 .../boost_multiprecision/ref/mp_number.html   |   2 -
 doc/html/boost_multiprecision/tut.html        |   2 -
 doc/html/boost_multiprecision/tut/ints.html   |   2 -
 .../boost_multiprecision/tut/rational.html    | 203 +++++++++++++++++-
 doc/html/boost_multiprecision/tut/reals.html  |   2 -
 doc/html/index.html                           |   4 +-
 doc/multiprecision.qbk                        |  59 +++++
 example/tommath_snips.cpp                     |  70 ++++++
 .../boost/multiprecision/rational_adapter.hpp |  10 +
 include/boost/multiprecision/tommath.hpp      |   5 +-
 test/test_arithmetic.cpp                      |  12 ++
 test/test_rational_io.cpp                     |   2 +-
 18 files changed, 356 insertions(+), 29 deletions(-)
 create mode 100644 example/tommath_snips.cpp

diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html
index 04fc3f7e..90451449 100644
--- a/doc/html/boost_multiprecision/intro.html
+++ b/doc/html/boost_multiprecision/intro.html
@@ -10,8 +10,6 @@
 
 
 
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diff --git a/doc/html/boost_multiprecision/map.html b/doc/html/boost_multiprecision/map.html
index 0f9be0ff..0587898f 100644
--- a/doc/html/boost_multiprecision/map.html
+++ b/doc/html/boost_multiprecision/map.html
@@ -10,8 +10,6 @@
 
 
 
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diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html
index 2403eb82..4701f08a 100644
--- a/doc/html/boost_multiprecision/map/hist.html
+++ b/doc/html/boost_multiprecision/map/hist.html
@@ -10,8 +10,6 @@
 
 
 
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diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html
index 7d07e878..0f7290bb 100644
--- a/doc/html/boost_multiprecision/map/todo.html
+++ b/doc/html/boost_multiprecision/map/todo.html
@@ -9,8 +9,6 @@
 
 
 
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-

 

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diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html
index 5bff5c01..4634199e 100644
--- a/doc/html/boost_multiprecision/ref.html
+++ b/doc/html/boost_multiprecision/ref.html
@@ -10,8 +10,6 @@
 
 
 
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-

 

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diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html
index fdb54705..c6e86a15 100644
--- a/doc/html/boost_multiprecision/ref/backendconc.html
+++ b/doc/html/boost_multiprecision/ref/backendconc.html
@@ -10,8 +10,6 @@
 
 
 
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diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html
index 727527eb..be7d53ba 100644
--- a/doc/html/boost_multiprecision/ref/mp_number.html
+++ b/doc/html/boost_multiprecision/ref/mp_number.html
@@ -10,8 +10,6 @@
 
 
 
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diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html
index d6d8a0bb..4c86cbe3 100644
--- a/doc/html/boost_multiprecision/tut.html
+++ b/doc/html/boost_multiprecision/tut.html
@@ -10,8 +10,6 @@
 
 
 
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diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html
index 814eac46..c1612d16 100644
--- a/doc/html/boost_multiprecision/tut/ints.html
+++ b/doc/html/boost_multiprecision/tut/ints.html
@@ -10,8 +10,6 @@
 
 
 
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diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html
index 957ea0ee..8fe67803 100644
--- a/doc/html/boost_multiprecision/tut/rational.html
+++ b/doc/html/boost_multiprecision/tut/rational.html
@@ -10,8 +10,6 @@
 
 
 
-

-

 

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@@ -63,7 +61,8 @@
                 

               
 
-
+
+
 
                 

                   gmp_rational
@@ -94,7 +93,107 @@
                   Dependency on GNU licenced GMP library.
                 

               
-
+
+
+
+                

+                  tommath_rational
+                

+              
+
+                

+                  boost/multiprecision/tommath.hpp
+                

+              
+
+                

+                  2
+                

+              
+
+                

+                  libtommath
+                

+              
+
+                

+                  All C/C++ implementation that's Boost Software Licence compatible.
+                

+              
+
+                

+                  Slower than GMP.
+                

+              
+
+
+
+                

+                  rational_adapter
+                

+              
+
+                

+                  boost/multiprecision/rational_adapter.hpp
+                

+              
+
+                

+                  N/A
+                

+              
+
+                

+                  none
+                

+              
+
+                

+                  All C++ adapter that allows any inetger backend type to be used
+                  as a rational type.
+                

+              
+
+                

+                  Requires an underlying integer backend type.
+                

+              
+
+
+
+                

+                  boost::rational
+                

+              
+
+                

+                  boost/rational.hpp
+                

+              
+
+                

+                  N/A
+                

+              
+
+                

+                  None
+                

+              
+
+                

+                  A C++ rational number type that can used with any mp_number integer type.
+                

+              
+
+                

+                  The expression templates used by mp_number
+                  end up being "hidden" inside boost::rational:
+                  performance may well suffer as a result.
+                

+              
+
+
 

 

 
@@ -171,6 +270,102 @@
 

 

       

+

+
+        tommath_rational
+      

+
namespace boost{ namespace multiprecision{
+
+typedef rational_adpater<tommath_int>        tommath_rational;
+typedef mp_number<tommath_rational >         mp_rational;
+
+}} // namespaces
+

+

+        The tommath_rational backend
+        is used via the typedef boost::multiprecision::mp_rational.
+        It acts as a thin wrapper around boost::rational<mp_int> to provide a rational number type that
+        is a drop-in replacement for the native C++ number types, but with unlimited
+        precision.
+      

+

+        The advantage of using this type rather than boost::rational<mp_int> directly, is that it is expression-template
+        enabled, greatly reducing the number of temporaries created in complex expressions.
+      

+

+        There are also non-member functions:
+      

+
mp_int numerator(const mp_rational&);
+mp_int denominator(const mp_rational&);
+

+

+        which return the numerator and denominator of the number.
+      

+

+
+        Example:
+      

+

+

+
#include <boost/multiprecision/tommath.hpp>
+
+using namespace boost::multiprecision;
+
+mp_rational v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+v /= 10;
+
+std::cout << v << std::endl; // prints 1000! / 10
+std::cout << numerator(v) << std::endl;
+std::cout << denominator(v) << std::endl;
+
+

+

+      

+

+
+        Use With
+        Boost.Rational
+      

+

+        All of the inetger types in this library can be used as template arguments
+        to boost::rational<IntType>.
+      

+

+        Note that using the library in this way largely negates the effect of the
+        expression templates in mp_number.
+      

+

+
+        rational_adapter
+      

+
namespace boost{ namespace multiprecision{
+
+template <class IntBackend>
+class rational_adpater;
+
+}}
+

+

+        The class template rational_adapter
+        is a backend for mp_number
+        which converts any existing integer backend into a rational-number backend.
+      

+

+        So for example, given an integer backend type MyIntegerBackend,
+        the use would be something like:
+      

+
typedef mp_number<MyIntegerBackend>                    MyInt;
+typedef mp_number<rational_adapter<MyIntegerBackend> > MyRational;
+
+MyRational r = 2;
+r /= 3;
+MyInt i = numerator(r);
+assert(i == 2);
+

 
 
diff --git a/doc/html/boost_multiprecision/tut/reals.html b/doc/html/boost_multiprecision/tut/reals.html
index 429cf67d..5fd1090c 100644
--- a/doc/html/boost_multiprecision/tut/reals.html
+++ b/doc/html/boost_multiprecision/tut/reals.html
@@ -10,8 +10,6 @@
 
-

 
 
 

-

 

 PrevUpHomeNext
 

diff --git a/doc/html/index.html b/doc/html/index.html
index a404ace7..67cdb54d 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -8,8 +8,6 @@
 
 
 
-

-

 
Next

 

 

@@ -50,7 +48,7 @@
 

 

 
-
+
Last revised: December 22, 2011 at 11:51:46 GMT
Last revised: December 24, 2011 at 13:09:42 GMT

 

 

 

diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk
index 5e717788..9ed0f3ce 100644
--- a/doc/multiprecision.qbk
+++ b/doc/multiprecision.qbk
@@ -384,6 +384,9 @@ The following backends provide rational number arithmetic:
 [table
 [[Backend Type][Header][Radix][Dependencies][Pros][Cons]]
 [[`gmp_rational`][boost/multiprecision/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]]
+[[`tommath_rational`][boost/multiprecision/tommath.hpp][2][libtommath][All C/C++ implementation that's Boost Software Licence compatible.][Slower than GMP.]]
+[[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any inetger backend type to be used as a rational type.][Requires an underlying integer backend type.]]
+[[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `mp_number` integer type.][The expression templates used by `mp_number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]]
 ]
 
 [h4 gmp_rational]
@@ -418,6 +421,62 @@ It's also possible to access the underlying `mpq_t` via the `data()` member func
 
 [mpq_eg]
 
+[h4 tommath_rational]
+
+   namespace boost{ namespace multiprecision{
+
+   typedef rational_adpater        tommath_rational;
+   typedef mp_number         mp_rational;
+
+   }} // namespaces
+
+The `tommath_rational` backend is used via the typedef `boost::multiprecision::mp_rational`.  It acts as a thin wrapper around 
+`boost::rational`
+to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision.
+
+The advantage of using this type rather than `boost::rational` directly, is that it is expression-template enabled,
+greatly reducing the number of temporaries created in complex expressions.
+
+There are also non-member functions:
+
+   mp_int numerator(const mp_rational&);
+   mp_int denominator(const mp_rational&);
+
+which return the numerator and denominator of the number.
+
+[h5 Example:]
+
+[mp_rat_eg]
+
+[h4 Use With Boost.Rational]
+
+All of the inetger types in this library can be used as template arguments to `boost::rational`.
+
+Note that using the library in this way largely negates the effect of the expression templates in `mp_number`.
+
+[h4 rational_adapter]
+
+   namespace boost{ namespace multiprecision{
+
+   template  
+   class rational_adpater;
+
+   }}
+
+The class template `rational_adapter` is a backend for `mp_number` which converts any existing integer backend
+into a rational-number backend.
+
+So for example, given an integer backend type `MyIntegerBackend`, the use would be something like:
+
+   typedef mp_number                    MyInt;
+   typedef mp_number > MyRational;
+
+   MyRational r = 2;
+   r /= 3;
+   MyInt i = numerator(r);
+   assert(i == 2);
+
+
 [endsect]
 
 [endsect]
diff --git a/example/tommath_snips.cpp b/example/tommath_snips.cpp
new file mode 100644
index 00000000..793aa5f6
--- /dev/null
+++ b/example/tommath_snips.cpp
@@ -0,0 +1,70 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#include 
+#include 
+
+void t1()
+{
+   //[tommath_eg
+   //=#include 
+
+   boost::multiprecision::mp_int v = 1;
+
+   // Do some arithmetic:
+   for(unsigned i = 1; i <= 1000; ++i)
+      v *= i;
+
+   std::cout << v << std::endl; // prints 1000!
+   std::cout << std::hex << v << std::endl; // prints 1000! in hex format
+
+   try{
+      std::cout << std::hex << -v << std::endl; // Ooops! can't print a negative value in hex format!
+   }
+   catch(const std::runtime_error& e)
+   {
+      std::cout << e.what() << std::endl;
+   }
+
+   try{
+      // v is not a 2's complement type, bitwise operations are only supported
+      // on positive values:
+      v = -v & 2;
+   }
+   catch(const std::runtime_error& e)
+   {
+      std::cout << e.what() << std::endl;
+   }
+
+   //]
+}
+
+void t3()
+{
+   //[mp_rat_eg
+   //=#include 
+
+   using namespace boost::multiprecision;
+
+   mp_rational v = 1;
+
+   // Do some arithmetic:
+   for(unsigned i = 1; i <= 1000; ++i)
+      v *= i;
+   v /= 10;
+
+   std::cout << v << std::endl; // prints 1000! / 10
+   std::cout << numerator(v) << std::endl;
+   std::cout << denominator(v) << std::endl;
+
+   //]
+}
+
+int main()
+{
+   t1();
+   return 0;
+}
+
diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp
index 64a34de9..e417653d 100644
--- a/include/boost/multiprecision/rational_adapter.hpp
+++ b/include/boost/multiprecision/rational_adapter.hpp
@@ -156,6 +156,16 @@ inline int get_sign(const rational_adapter& val)
    return get_sign(val.data().numerator().backend());
 }
 
+template 
+inline mp_number numerator(const mp_number >& val)
+{
+   return val.backend().data().numerator();
+}
+template 
+inline mp_number denominator(const mp_number >& val)
+{
+   return val.backend().data().denominator();
+}
 
 template
 struct number_category > : public mpl::int_{};
diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp
index fbe834cb..95e035b4 100644
--- a/include/boost/multiprecision/tommath.hpp
+++ b/include/boost/multiprecision/tommath.hpp
@@ -7,6 +7,7 @@
 #define BOOST_MATH_MP_TOMMATH_BACKEND_HPP
 
 #include 
+#include 
 #include 
 #include 
 #include 
@@ -431,7 +432,9 @@ inline void eval_abs(tommath_int& result, const tommath_int& val)
 template<>
 struct number_category : public mpl::int_{};
 
-typedef mp_number         mp_int;
+typedef mp_number                     mp_int;
+typedef rational_adapter               tommath_rational;
+typedef mp_number                 mp_rational;
 
 }}  // namespaces
 
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index 0419cf82..fba084b3 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -130,6 +130,18 @@ void test_complement(Real, Real, Real, const boost::mpl::false_&)
 template 
 void test_integer_ops(const T&){}
 
+template 
+void test_integer_ops(const boost::mpl::int_&)
+{
+   Real a(2);
+   a /= 3;
+   BOOST_TEST(numerator(a) == 2);
+   BOOST_TEST(denominator(a) == 3);
+   Real b(4);
+   b /= 6;
+   BOOST_TEST(a == b);
+}
+
 template 
 void test_integer_ops(const boost::mpl::int_&)
 {
diff --git a/test/test_rational_io.cpp b/test/test_rational_io.cpp
index 583b891e..7b1d4290 100644
--- a/test/test_rational_io.cpp
+++ b/test/test_rational_io.cpp
@@ -127,7 +127,7 @@ int main()
 #endif
 #ifdef TEST_TOMMATH
    test_round_trip >();
-   test_round_trip > >();
+   test_round_trip();
 #endif
    return boost::report_errors();
 }

From 5ada2d816973ddfcbfaf097f6a90383110de99ea Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Sat, 24 Dec 2011 13:14:17 +0000
Subject: [PATCH 088/256] Correct TODO list and regenerate docs.

[SVN r76131]
---
 doc/html/boost_multiprecision/map/todo.html | 6 ------
 doc/html/index.html                         | 2 +-
 doc/multiprecision.qbk                      | 2 --
 3 files changed, 1 insertion(+), 9 deletions(-)

diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html
index 0f7290bb..fadf395e 100644
--- a/doc/html/boost_multiprecision/map/todo.html
+++ b/doc/html/boost_multiprecision/map/todo.html
@@ -27,12 +27,6 @@
 
  • 
             Add an adapter backend for complex number types.
           
    • 
-
  • 
-            Add an adapter backend for rational types.
-          
    • 
-
  • 
-            Test integer types with Boost.Rational.
-          
    • 
 
  • 
             Adapt libtommath code to make an all C++ fixed precision integer type.
           
    • 
diff --git a/doc/html/index.html b/doc/html/index.html
index 67cdb54d..35e62118 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -48,7 +48,7 @@
 
    
 
 
-
+
    Last revised: December 24, 2011 at 13:09:42 GMT
    Last revised: December 24, 2011 at 13:13:53 GMT
    		
 
    		
 
    
 
    
diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk
index 9ed0f3ce..b2107616 100644
--- a/doc/multiprecision.qbk
+++ b/doc/multiprecision.qbk
@@ -1027,8 +1027,6 @@ More a list of what ['could] be done, rather than what ['should] be done (which
 
 * Add backend support for libdecNumber.
 * Add an adapter backend for complex number types.
-* Add an adapter backend for rational types.
-* Test integer types with Boost.Rational.
 * Adapt libtommath code to make an all C++ fixed precision integer type.
 
 [endsect]

From 30310e4a528d389ab546efe58249d462c7606b0c Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Fri, 30 Dec 2011 18:21:08 +0000
Subject: [PATCH 089/256] Another Boost.Rational fix. Add tentative version of
 a fixed width, bit-packed 2's complement integer type.

[SVN r76234]
---
 include/boost/multiprecision/mp_number.hpp    |  12 +
 .../boost/multiprecision/packed_cpp_int.hpp   | 888 ++++++++++++++++++
 test/Jamfile.v2                               |  28 +
 test/test_arithmetic.cpp                      | 236 +++--
 test/test_int_io.cpp                          |  36 +-
 5 files changed, 1107 insertions(+), 93 deletions(-)
 create mode 100644 include/boost/multiprecision/packed_cpp_int.hpp

diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp
index a04eba59..2c8b9d4d 100644
--- a/include/boost/multiprecision/mp_number.hpp
+++ b/include/boost/multiprecision/mp_number.hpp
@@ -1635,6 +1635,18 @@ typename enable_if, bool>::type operator != (co
    return a != multiprecision::mp_number(b);
 }
 
+template 
+inline multiprecision::mp_number numerator(const rational >& a)
+{
+   return a.numerator();
+}
+
+template 
+inline multiprecision::mp_number denominator(const rational >& a)
+{
+   return a.denominator();
+}
+
 } // namespaces
 
 #endif
diff --git a/include/boost/multiprecision/packed_cpp_int.hpp b/include/boost/multiprecision/packed_cpp_int.hpp
new file mode 100644
index 00000000..1c8e7af6
--- /dev/null
+++ b/include/boost/multiprecision/packed_cpp_int.hpp
@@ -0,0 +1,888 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifndef BOOST_MATH_RATIONAL_ADAPTER_HPP
+#define BOOST_MATH_RATIONAL_ADAPTER_HPP
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+
+namespace boost{
+namespace multiprecision{
+
+template 
+struct packed_cpp_int
+{
+   typedef mpl::list      signed_types;
+   typedef mpl::list    unsigned_types;
+   typedef mpl::list                          float_types;
+
+   typedef boost::uint32_t   limb_type;
+   BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT);
+   BOOST_STATIC_CONSTANT(unsigned, limb_count = Bits / limb_bits + (Bits % limb_bits ? 1 : 0));
+   BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u));
+   BOOST_STATIC_CONSTANT(limb_type, upper_limb_mask = (Bits % limb_bits ? (1 << (Bits % limb_bits)) - 1 : max_limb_value));
+   BOOST_STATIC_CONSTANT(limb_type, upper_limb_not_mask = ~upper_limb_mask);
+   BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1 << ((Bits % limb_bits ? Bits % limb_bits : limb_bits) - 1));
+   typedef boost::array data_type;
+
+   packed_cpp_int(){}
+   packed_cpp_int(const packed_cpp_int& o)
+   {
+      m_value = o.m_value;
+   }
+#ifndef BOOST_NO_RVALUE_REFERENCES
+   packed_cpp_int(packed_cpp_int&& o) : m_value(o.m_value) {}
+#endif
+   packed_cpp_int& operator = (const packed_cpp_int& o)
+   {
+      m_value = o.m_value;
+      return *this;
+   }
+   packed_cpp_int& operator = (boost::uint32_t i)
+   {
+      m_value[limb_count - 1] = i;
+      for(int j = limb_count - 2; j >= 0; --j)
+         m_value[j] = 0;
+      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      return *this;
+   }
+   packed_cpp_int& operator = (boost::int32_t i)
+   {
+      m_value[limb_count - 1] = i;
+      // sign extend:
+      for(int j = limb_count - 2; j >= 0; --j)
+         m_value[j] = i < 0 ? max_limb_value : 0;
+      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      return *this;
+   }
+   packed_cpp_int& operator = (boost::uintmax_t i)
+   {
+      BOOST_STATIC_ASSERT(sizeof(i) % sizeof(limb_type) == 0);
+      boost::uintmax_t mask = max_limb_value;
+      unsigned shift = 0;
+      for(int j = limb_count - 1; j >= static_cast(limb_count) - static_cast(sizeof(boost::intmax_t) / sizeof(limb_type)); --j)
+      {
+         m_value[j] = static_cast((i & mask) >> shift);
+         mask <<= limb_bits;
+         shift += limb_bits;
+      }
+      for(int j = static_cast(limb_count) - static_cast(sizeof(boost::intmax_t) / sizeof(limb_type)) - 1; j >= 0; --j)
+         m_value[j] = 0;
+      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      return *this;
+   }
+   packed_cpp_int& operator = (boost::intmax_t i)
+   {
+      BOOST_STATIC_ASSERT(sizeof(i) % sizeof(limb_type) == 0);
+      boost::uintmax_t mask = max_limb_value;
+      unsigned shift = 0;
+      for(int j = limb_count - 1; j >= static_cast(limb_count) - static_cast(sizeof(boost::intmax_t) / sizeof(limb_type)); --j)
+      {
+         m_value[j] = static_cast((i & mask) >> shift);
+         mask <<= limb_bits;
+         shift += limb_bits;
+      }
+      for(int j = static_cast(limb_count) - static_cast(sizeof(boost::intmax_t) / sizeof(limb_type)) - 1; j >= 0; --j)
+         m_value[j] = i < 0 ? max_limb_value : 0;
+      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      return *this;
+   }
+   packed_cpp_int& operator = (long double a)
+   {
+      BOOST_STATIC_ASSERT(Bits >= std::numeric_limits::digits);
+      using std::frexp;
+      using std::ldexp;
+      using std::floor;
+
+      if (a == 0) {
+         return *this = static_cast(0u);
+      }
+
+      if (a == 1) {
+         return *this = static_cast(1u);
+      }
+
+      BOOST_ASSERT(!(boost::math::isinf)(a));
+      BOOST_ASSERT(!(boost::math::isnan)(a));
+
+      int e;
+      long double f, term;
+      *this = static_cast(0u);
+
+      f = frexp(a, &e);
+
+      static const boost::uint32_t shift = std::numeric_limits::digits;
+
+      while(f)
+      {
+         // extract int sized bits from f:
+         f = ldexp(f, shift);
+         term = floor(f);
+         e -= shift;
+         left_shift(*this, shift);
+         if(term > 0)
+            add(*this, static_cast(term));
+         else
+            subtract(*this, static_cast(-term));
+         f -= term;
+      }
+      if(e > 0)
+         left_shift(*this, e);
+      else if(e < 0)
+         right_shift(*this, -e);
+      data()[0] &= packed_cpp_int::upper_limb_mask;
+      return *this;
+   }
+   packed_cpp_int& operator = (const char* s)
+   {
+      std::size_t n = s ? std::strlen(s) : 0;
+      *this = static_cast(0u);
+      unsigned radix = 10;
+      bool isneg = false;
+      if(n && (*s == '-'))
+      {
+         --n;
+         ++s;
+         isneg = true;
+      }
+      if(n && (*s == '0'))
+      {
+         if((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
+         {
+            radix = 16;
+            s +=2;
+            n -= 2;
+         }
+         else
+         {
+            radix = 8;
+            n -= 1;
+         }
+      }
+      if(n)
+      {
+         if(radix == 8 || radix == 16)
+         {
+            unsigned shift = radix == 8 ? 3 : 4;
+            boost::uint32_t val = max_limb_value;
+            while(*s)
+            {
+               left_shift(*this, shift);
+               if(*s >= '0' && *s <= '9')
+                  val = *s - '0';
+               else if(*s >= 'a' && *s <= 'f')
+                  val = 10 + *s - 'a';
+               else if(*s >= 'A' && *s <= 'F')
+                  val = 10 + *s - 'A';
+               else
+                  val = max_limb_value;
+               if(val > radix)
+               {
+                  m_value[0] &= packed_cpp_int::upper_limb_mask;
+                  return *this; // TODO raise an exception here?
+               }
+               m_value[limb_count - 1] |= val;
+               ++s;
+            }
+         }
+         else
+         {
+            // Base 10:
+            while(*s)
+            {
+               // TODO: this implementation is brain dead, Fix Me!
+               multiply(*this, static_cast(10));
+               boost::uint32_t val;
+               if(*s >= '0' && *s <= '9')
+                  val = *s - '0';
+               else
+                  return *this; // TODO raise an exception here?
+               add(*this, val);
+               ++s;
+            }
+         }
+      }
+      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      if(isneg)
+         negate();
+      return *this;
+   }
+   void swap(packed_cpp_int& o)
+   {
+      std::swap(m_value, o.m_value);
+   }
+   std::string str(std::streamsize digits, std::ios_base::fmtflags f)const
+   {
+      int base = 10;
+      if((f & std::ios_base::oct) == std::ios_base::oct)
+         base = 8;
+      else if((f & std::ios_base::hex) == std::ios_base::hex)
+         base = 16;
+      std::string result;
+
+      if(base == 8 || base == 16)
+      {
+         boost::uint32_t shift = base == 8 ? 3 : 4;
+         boost::uint32_t mask = static_cast((1u << shift) - 1);
+         packed_cpp_int t(*this);
+         for(unsigned i = 0; i < Bits / shift; ++i)
+         {
+            char c = '0' + (t.data()[limb_count-1] & mask);
+            if(c > '9')
+               c += 'A' - '9' - 1;
+            result.insert(0, 1, c);
+            right_shift(t, shift);
+         }
+         if(Bits % shift)
+         {
+            mask = static_cast((1u << (Bits % shift)) - 1);
+            char c = '0' + (t.data()[limb_count-1] & mask);
+            if(c > '9')
+               c += 'A' - '9';
+            result.insert(0, 1, c);
+         }
+         //
+         // Get rid of leading zeros:
+         //
+         std::string::size_type n = result.find_first_not_of('0');
+         if(!result.empty() && (n == std::string::npos))
+            n = result.size() - 1;
+         result.erase(0, n);
+         if(f & std::ios_base::showbase)
+         {
+            const char* pp = base == 8 ? "0" : "0x";
+            result.insert(0, pp);
+         }
+      }
+      else
+      {
+         packed_cpp_int t(*this);
+         packed_cpp_int ten, r;
+         ten = boost::uint32_t(1000000000);
+         bool neg = false;
+         if(Signed && (t.data()[0] & sign_bit_mask))
+         {
+            t.negate();
+            neg = true;
+         }
+         if(limb_count == 1)
+         {
+            result = boost::lexical_cast(t.data()[0]);
+         }
+         else
+         {
+            while(get_sign(t) != 0)
+            {
+               packed_cpp_int t2;
+               divide_unsigned_helper(t2, t, ten, r);
+               t = t2;
+               boost::uint32_t v = r.data()[limb_count - 1];
+               for(unsigned i = 0; i < 9; ++i)
+               {
+                  char c = '0' + v % 10;
+                  v /= 10;
+                  result.insert(0, 1, c);
+               }
+            }
+         }
+         unsigned n = result.find_first_not_of('0');
+         result.erase(0, n);
+         if(result.empty())
+            result = "0";
+         if(neg)
+            result.insert(0, 1, '-');
+         else if(f & std::ios_base::showpos)
+            result.insert(0, 1, '+');
+      }
+      return result;
+   }
+   void negate()
+   {
+      using default_ops::increment;
+      // complement and add 1:
+      complement(*this, *this);
+      increment(*this);
+   }
+   int compare(const packed_cpp_int& o)const
+   {
+      int result = 0;
+      if(Signed && ((m_value[0] & sign_bit_mask) != (o.data()[0] & sign_bit_mask)))
+      {
+         return m_value[0] & sign_bit_mask ? -1 : 1;
+      }
+      for(data_type::size_type i = 0; i < limb_count; ++i)
+      {
+         if(m_value[i] != o.data()[i])
+         {
+            result = (m_value[i] < o.data()[i]) ? -1 : 1;
+            break;
+         }
+      }
+      return Signed && (m_value[0] & sign_bit_mask) ? -result : result ;
+   }
+   template 
+   typename enable_if, int>::type compare(Arithmatic i)const
+   {
+      // braindead version:
+      packed_cpp_int t;
+      t = i;
+      return compare(t);
+   }
+   data_type& data() { return m_value; }
+   const data_type& data()const { return m_value; }
+private:
+   data_type m_value;
+};
+
+template 
+inline void add(packed_cpp_int& result, const packed_cpp_int& o)
+{
+   // Addition using modular arithmatic.
+   // Nothing fancy, just let uintmax_t take the strain:
+   boost::uintmax_t carry = 0;
+   for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
+   {
+      boost::uintmax_t v = static_cast(result.data()[i]) + static_cast(o.data()[i]) + carry;
+      result.data()[i] = static_cast::limb_type>(v);
+      carry = v > packed_cpp_int::max_limb_value ? 1 : 0;
+   }
+   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+}
+template 
+inline void add(packed_cpp_int& result, const boost::uint32_t& o)
+{
+   // Addition using modular arithmatic.
+   // Nothing fancy, just let uintmax_t take the strain:
+   boost::uintmax_t carry = o;
+   for(int i = packed_cpp_int::limb_count - 1; carry && i >= 0; --i)
+   {
+      boost::uintmax_t v = static_cast(result.data()[i]) + carry;
+      result.data()[i] = static_cast::limb_type>(v);
+      carry = v > packed_cpp_int::max_limb_value ? 1 : 0;
+   }
+   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+}
+template 
+inline void add(packed_cpp_int& result, const boost::int32_t& o)
+{
+   if(o < 0)
+      subtract(result, static_cast(-o));
+   else if(o > 0)
+      add(result, static_cast(o));
+}
+template 
+inline void subtract(packed_cpp_int& result, const boost::uint32_t& o)
+{
+   if(o)
+   {
+      packed_cpp_int t;
+      t.data()[packed_cpp_int::limb_count - 1] = ~o + 1;
+      for(int i = packed_cpp_int::limb_count - 2; i >= 0; --i)
+      {
+         t.data()[i] = packed_cpp_int::max_limb_value;
+      }
+      add(result, t);
+   }
+}
+template 
+inline void subtract(packed_cpp_int& result, const boost::int32_t& o)
+{
+   if(o)
+   {
+      if(o < 0)
+         add(result, static_cast(-o));
+      else
+         subtract(result, static_cast(o));
+   }
+}
+template 
+inline void increment(packed_cpp_int& result)
+{
+   static const boost::uint32_t one = 1;
+   add(result, one);
+}
+template 
+inline void decrement(packed_cpp_int& result)
+{
+   static const boost::uint32_t one = 1;
+   subtract(result, one);
+}
+template 
+inline void subtract(packed_cpp_int& result, const packed_cpp_int& o)
+{
+   // Negate and add:
+   packed_cpp_int t(o);
+   t.negate();
+   add(result, t);
+}
+template 
+inline void multiply(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
+{
+   // Very simple long multiplication, only usable for small numbers of limb_type's
+   // but that's the typical use case for this type anyway:
+   if(&result == &a)
+   {
+      packed_cpp_int t(a);
+      multiply(result, t, b);
+      return;
+   }
+   if(&result == &b)
+   {
+      packed_cpp_int t(b);
+      multiply(result, a, t);
+      return;
+   }
+   boost::uintmax_t carry = 0;
+   for(unsigned i = 0; i < packed_cpp_int::limb_count; ++i)
+      result.data()[i] = 0;
+   for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
+   {
+      for(int j = packed_cpp_int::limb_count - 1; j >= static_cast(packed_cpp_int::limb_count) - i - 1; --j)
+      {
+         boost::uintmax_t v = static_cast(a.data()[i]) * static_cast(b.data()[j]) + carry;
+         v += result.data()[i + j + 1 - packed_cpp_int::limb_count];
+         result.data()[i + j + 1 - packed_cpp_int::limb_count] = static_cast::limb_type>(v);
+         carry = v >> sizeof(packed_cpp_int::limb_type) * CHAR_BIT;
+      }
+      carry = 0;
+   }
+   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+}
+template 
+inline void multiply(packed_cpp_int& result, const packed_cpp_int& a)
+{
+   // There is no in-place multiply:
+   packed_cpp_int b(result);
+   multiply(result, b, a);
+}
+template 
+inline void multiply(packed_cpp_int& result, const boost::uint32_t& a)
+{
+   boost::uintmax_t carry = 0;
+   for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
+   {
+      boost::uintmax_t v = static_cast(result.data()[i]) * static_cast(a) + carry;
+      result.data()[i] = static_cast::limb_type>(v);
+      carry = v >> sizeof(packed_cpp_int::limb_type) * CHAR_BIT;
+   }
+   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+}
+template 
+inline void multiply(packed_cpp_int& result, const boost::int32_t& a)
+{
+   if(a > 0)
+      multiply(result, static_cast(a));
+   else
+   {
+      multiply(result, static_cast(-a));
+      result.negate();
+   }
+}
+
+template 
+boost::uint32_t bitcount(const packed_cpp_int& a)
+{
+   // returns the location of the MSB in a:
+   boost::uint32_t i = 0;
+   for(; (i < packed_cpp_int::limb_count) && (a.data()[i] == 0); ++i){}
+   boost::uint32_t count = (packed_cpp_int::limb_count - i) * packed_cpp_int::limb_bits;
+   if(!count)
+      return count; // no bits are set, value is zero
+   boost::uint32_t mask = static_cast(1u) << (packed_cpp_int::limb_bits - 1);
+   while((a.data()[i] & mask) == 0)
+   {
+      --count;
+      mask >>= 1;
+   }
+   return count;
+}
+
+template 
+void divide_unsigned_helper(packed_cpp_int& result, const packed_cpp_int& x, const packed_cpp_int& y, packed_cpp_int& r)
+{
+   if((&result == &x) || (&r == &x))
+   {
+      packed_cpp_int t(x);
+      divide_unsigned_helper(result, t, y, r);
+      return;
+   }
+   if((&result == &y) || (&r == &y))
+   {
+      packed_cpp_int t(y);
+      divide_unsigned_helper(result, x, t, r);
+      return;
+   }
+
+
+   using default_ops::subtract;
+
+
+   if (is_zero(y))
+   {
+      volatile int i = 0;
+      i /= i;
+      return;
+   }
+
+   if (is_zero(x))
+   {
+      r = y;
+      result = x;
+      return;
+   }
+
+   if(&result == &r)
+   {
+      packed_cpp_int rem;
+      divide_unsigned_helper(result, x, y, rem);
+      r = rem;
+      return;
+   }
+
+   r = x;
+   result = static_cast(0u);
+   if(x.compare(y) < 0)
+   {
+      return; // We already have the answer: zero.
+   }
+
+   boost::uint32_t n = bitcount(x) - bitcount(y);
+
+   if(n == 0)
+   {
+      // result is exactly 1:
+      result = static_cast(1u);
+      subtract(r, y);
+      return;
+   }
+
+   // Together mask_index and mask give us the bit we may be about to set in the result:
+   boost::uint32_t mask_index = packed_cpp_int::limb_count - 1 - n / packed_cpp_int::limb_bits;
+   boost::uint32_t mask = static_cast(1u) << n % packed_cpp_int::limb_bits;
+   packed_cpp_int t(y);
+   left_shift(t, n);
+   while(mask_index < packed_cpp_int::limb_count)
+   {
+      int comp = r.compare(t);
+      if(comp >= 0)
+      {
+         result.data()[mask_index] |= mask;
+         subtract(r, t);
+         if(comp == 0)
+            break; // no remainder left - we have an exact result!
+      }
+      right_shift(t, 1u);
+      if(0 == (mask >>= 1))
+      {
+         ++mask_index;
+         mask = static_cast(1u) << (packed_cpp_int::limb_bits - 1);
+      }
+   }
+   BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed
+}
+
+template 
+inline void divide(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
+{
+   packed_cpp_int r;
+   if(Signed && (a.data()[0] & packed_cpp_int::sign_bit_mask))
+   {
+      if(Signed && (b.data()[0] & packed_cpp_int::sign_bit_mask))
+      {
+         packed_cpp_int t1(a), t2(b);
+         t1.negate();
+         t2.negate();
+         divide_unsigned_helper(result, t1, t2, r);
+      }
+      else
+      {
+         packed_cpp_int t(a);
+         t.negate();
+         divide_unsigned_helper(result, t, b, r);
+         result.negate();
+      }
+   }
+   else if(Signed && (b.data()[0] & packed_cpp_int::sign_bit_mask))
+   {
+      packed_cpp_int t(b);
+      t.negate();
+      divide_unsigned_helper(result, a, t, r);
+      result.negate();
+   }
+   else
+   {
+      divide_unsigned_helper(result, a, b, r);
+   }
+}
+template 
+inline void divide(packed_cpp_int& result, const packed_cpp_int& b)
+{
+   // There is no in place divide:
+   packed_cpp_int a(result);
+   divide(result, a, b);
+}
+template 
+inline void modulus(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
+{
+   packed_cpp_int r;
+   if(Signed && (a.data()[0] & packed_cpp_int::sign_bit_mask))
+   {
+      if(Signed && (b.data()[0] & packed_cpp_int::sign_bit_mask))
+      {
+         packed_cpp_int t1(a), t2(b);
+         t1.negate();
+         t2.negate();
+         divide_unsigned_helper(r, t1, t2, result);
+         result.negate();
+      }
+      else
+      {
+         packed_cpp_int t(a);
+         t.negate();
+         divide_unsigned_helper(r, t, b, result);
+         result.negate();
+      }
+   }
+   else if(Signed && (b.data()[0] & packed_cpp_int::sign_bit_mask))
+   {
+      packed_cpp_int t(b);
+      t.negate();
+      divide_unsigned_helper(r, a, t, result);
+   }
+   else
+   {
+      divide_unsigned_helper(r, a, b, result);
+   }
+}
+template 
+inline void modulus(packed_cpp_int& result, const packed_cpp_int& b)
+{
+   // There is no in place divide:
+   packed_cpp_int a(result);
+   modulus(result, a, b);
+}
+
+template 
+inline void bitwise_and(packed_cpp_int& result, const packed_cpp_int& o)
+{
+   for(packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+      result.data()[i] &= o.data()[i];
+}
+template 
+inline void bitwise_or(packed_cpp_int& result, const packed_cpp_int& o)
+{
+   for(packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+      result.data()[i] |= o.data()[i];
+}
+template 
+inline void bitwise_xor(packed_cpp_int& result, const packed_cpp_int& o)
+{
+   for(packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+      result.data()[i] ^= o.data()[i];
+   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+}
+template 
+inline void complement(packed_cpp_int& result, const packed_cpp_int& o)
+{
+   for(packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+      result.data()[i] = ~o.data()[i];
+   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+}
+template 
+inline void left_shift(packed_cpp_int& result, boost::uintmax_t s)
+{
+   if(s >= Bits)
+   {
+      result = static_cast(0);
+      return;
+   }
+   boost::uint32_t offset = static_cast(s / packed_cpp_int::limb_bits);
+   boost::uint32_t shift  = static_cast(s % packed_cpp_int::limb_bits);
+   unsigned i = 0;
+   if(shift)
+   {
+      // This code only works when shift is non-zero, otherwise we invoke undefined behaviour!
+      for(; i + offset + 1 < packed_cpp_int::limb_count; ++i)
+      {
+         result.data()[i] = result.data()[i+offset] << shift;
+         result.data()[i] |= result.data()[i+offset+1] >> (packed_cpp_int::limb_bits - shift);
+      }
+      result.data()[i] = result.data()[i+offset] << shift;
+      ++i;
+      for(; i < packed_cpp_int::limb_count; ++i)
+         result.data()[i] = 0;
+   }
+   else
+   {
+      for(; i + offset < packed_cpp_int::limb_count; ++i)
+         result.data()[i] = result.data()[i+offset];
+      for(; i < packed_cpp_int::limb_count; ++i)
+         result.data()[i] = 0;
+   }
+   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+}
+template 
+inline void right_shift(packed_cpp_int& result, boost::uintmax_t s)
+{
+   boost::uint32_t fill = (Signed && (result.data()[0] & packed_cpp_int::sign_bit_mask)) ? packed_cpp_int::max_limb_value : 0u;
+   if(s >= Bits)
+   {
+      for(unsigned i = 0; i < packed_cpp_int::limb_count; ++i)
+         result.data()[i] = fill;
+      return;
+   }
+   boost::uint32_t offset = static_cast(s / packed_cpp_int::limb_bits);
+   boost::uint32_t shift  = static_cast(s % packed_cpp_int::limb_bits);
+   int i = packed_cpp_int::limb_count - 1;
+   if(shift)
+   {
+      // This code only works for non-zero shift, otherwise we invoke undefined behaviour!
+      if(fill && (Bits % packed_cpp_int::limb_bits))
+      {
+         // We need to sign extend the leftmost bits, otherwise we may shift zeros into the result:
+         result.data()[0] |= fill << (Bits % packed_cpp_int::limb_bits);
+      }
+      for(; i - offset > 0; --i)
+      {
+         result.data()[i] = result.data()[i-offset] >> shift;
+         result.data()[i] |= result.data()[i-offset-1] << (packed_cpp_int::limb_bits - shift);
+      }
+      result.data()[i] = result.data()[i+offset] >> shift;
+      result.data()[i] |= fill << (packed_cpp_int::limb_bits - shift);
+      --i;
+      for(; i >= 0; --i)
+         result.data()[i] = fill;
+   }
+   else
+   {
+      for(; i - offset > 0; --i)
+         result.data()[i] = result.data()[i - offset];
+      for(; i >= 0; --i)
+         result.data()[i] = fill;
+   }
+   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+}
+
+template 
+inline typename enable_if, void>::type convert_to(R* result, const packed_cpp_int& backend)
+{
+   unsigned shift = (packed_cpp_int::limb_count - 1) * packed_cpp_int::limb_bits;
+   *result = 0;
+   for(unsigned i = 0; i < packed_cpp_int::limb_count; ++i)
+   {
+      *result += static_cast(backend.data()[i]) << shift;
+      shift -= packed_cpp_int::limb_bits;
+   }
+}
+
+template 
+inline typename enable_if, void>::type convert_to(R* result, const packed_cpp_int& backend)
+{
+   unsigned shift = (packed_cpp_int::limb_count - 1) * packed_cpp_int::limb_bits;
+   *result = 0;
+   for(unsigned i = 0; i < packed_cpp_int::limb_count; ++i)
+   {
+      *result += static_cast(std::ldexp(static_cast(backend.data()[i]), shift));
+      shift -= packed_cpp_int::limb_bits;
+   }
+}
+
+template 
+inline bool is_zero(const packed_cpp_int& val)
+{
+   for(typename packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+   {
+      if(val.data()[i])
+         return false;
+   }
+   return true;
+}
+template 
+inline int get_sign(const packed_cpp_int& val)
+{
+   return is_zero(val) ? 0 : 1;
+}
+template 
+inline int get_sign(const packed_cpp_int& val)
+{
+   return is_zero(val) ? 0 : val.data()[0] & packed_cpp_int::sign_bit_mask ? -1 : 1;
+}
+
+template 
+struct number_category > : public mpl::int_{};
+
+typedef mp_number > mp_uint64_t;
+typedef mp_number > mp_uint128_t;
+typedef mp_number > mp_uint256_t;
+typedef mp_number > mp_uint512_t;
+
+typedef mp_number > mp_int64_t;
+typedef mp_number > mp_int128_t;
+typedef mp_number > mp_int256_t;
+typedef mp_number > mp_int512_t;
+
+}} // namespaces
+
+
+namespace std{
+
+template 
+class numeric_limits > >
+{
+   typedef boost::multiprecision::mp_number > number_type;
+public:
+   BOOST_STATIC_CONSTEXPR bool is_specialized = true;
+   //
+   // Largest and smallest numbers are bounded only by available memory, set
+   // to zero:
+   //
+   BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT
+   { 
+      return number_type();
+   }
+   BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT 
+   { 
+      return number_type();
+   }
+   BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); }
+   BOOST_STATIC_CONSTEXPR int digits = Bits;
+   BOOST_STATIC_CONSTEXPR int digits10 = (digits * 301L) / 1000;
+   BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2;
+   BOOST_STATIC_CONSTEXPR bool is_signed = Signed;
+   BOOST_STATIC_CONSTEXPR bool is_integer = true;
+   BOOST_STATIC_CONSTEXPR bool is_exact = true;
+   BOOST_STATIC_CONSTEXPR int radix = 2;
+   BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); }
+   BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); }
+   BOOST_STATIC_CONSTEXPR int min_exponent = 0;
+   BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
+   BOOST_STATIC_CONSTEXPR int max_exponent = 0;
+   BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
+   BOOST_STATIC_CONSTEXPR bool has_infinity = false;
+   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
+   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
+   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
+   BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
+   BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); }
+   BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); }
+   BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); }
+   BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); }
+   BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
+   BOOST_STATIC_CONSTEXPR bool is_bounded = true;
+   BOOST_STATIC_CONSTEXPR bool is_modulo = true;
+   BOOST_STATIC_CONSTEXPR bool traps = false;
+   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
+   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
+};
+
+}
+
+#endif
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 0c36ed4a..3f028183 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -128,6 +128,20 @@ run test_arithmetic.cpp $(TOMMATH)
          [ check-target-builds ../config//has_tommath : : no ]
         : test_arithmetic_tommath_br ;
 
+run test_arithmetic.cpp
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_PACKED_INT1
+        : test_arithmetic_packed_int1 ;
+
+run test_arithmetic.cpp
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_PACKED_INT2
+        : test_arithmetic_packed_int2 ;
+
 run test_numeric_limits.cpp
         : # command line
         : # input files
@@ -567,6 +581,20 @@ run test_int_io.cpp gmp
          [ check-target-builds ../config//has_gmp : : no ]
         : test_int_io_mpz ;
 
+run test_int_io.cpp
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_PACKED_INT1
+        : test_int_io_packed_int1 ;
+
+run test_int_io.cpp
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_PACKED_INT2
+        : test_int_io_packed_int2 ;
+
 run test_rational_io.cpp $(TOMMATH)
         : # command line
         : # input files
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index fba084b3..5339152a 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -12,7 +12,8 @@
 
 #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \
    !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) \
-   && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)
+   && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\
+   && !defined(TEST_PACKED_INT1) && !defined(TEST_PACKED_INT2)
 #  define TEST_MPF_50
 #  define TEST_MPF
 #  define TEST_BACKEND
@@ -22,6 +23,8 @@
 #  define TEST_CPP_FLOAT
 #  define TEST_MPQ
 #  define TEST_TOMMATH
+#  define TEST_PACKED_INT1
+#  define TEST_PACKED_INT2
 
 #ifdef _MSC_VER
 #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
@@ -49,6 +52,9 @@
 #include 
 #include 
 #endif
+#if defined(TEST_PACKED_INT1) || defined(TEST_PACKED_INT2)
+#include 
+#endif
 #if defined(TEST_TOMMATH_BOOST_RATIONAL) || defined(TEST_MPZ_BOOST_RATIONAL)
 #include 
 
@@ -151,70 +157,79 @@ void test_integer_ops(const boost::mpl::int_::is_signed)
+   {
+      BOOST_TEST(-a % c == 0);
+      BOOST_TEST(-a % b == -20 % 7);
+      BOOST_TEST(-a % -b == -20 % -7);
+      BOOST_TEST(a % -b == 20 % -7);
+      BOOST_TEST(-a % 7 == -20 % 7);
+      BOOST_TEST(-a % -7 == -20 % -7);
+      BOOST_TEST(a % -7 == 20 % -7);
+      BOOST_TEST(-a % 7u == -20 % 7);
+      BOOST_TEST(-a % a == 0);
+      BOOST_TEST(-a % 5 == 0);
+      BOOST_TEST(-a % -5 == 0);
+      BOOST_TEST(a % -5 == 0);
 
-   b = -b;
-   BOOST_TEST(a % b == 20 % -7);
-   a = -a;
-   BOOST_TEST(a % b == -20 % -7);
-   BOOST_TEST(a % -7 == -20 % -7);
-   b = 7;
-   BOOST_TEST(a % b == -20 % 7);
-   BOOST_TEST(a % 7 == -20 % 7);
-   BOOST_TEST(a % 7u == -20 % 7);
+      b = -b;
+      BOOST_TEST(a % b == 20 % -7);
+      a = -a;
+      BOOST_TEST(a % b == -20 % -7);
+      BOOST_TEST(a % -7 == -20 % -7);
+      b = 7;
+      BOOST_TEST(a % b == -20 % 7);
+      BOOST_TEST(a % 7 == -20 % 7);
+      BOOST_TEST(a % 7u == -20 % 7);
 
-   a = 20;
-   a %= b;
-   BOOST_TEST(a == 20 % 7);
-   a = -20;
-   a %= b;
-   BOOST_TEST(a == -20 % 7);
-   a = 20;
-   a %= -b;
-   BOOST_TEST(a == 20 % -7);
-   a = -20;
-   a %= -b;
-   BOOST_TEST(a == -20 % -7);
+      a = 20;
+      a %= b;
+      BOOST_TEST(a == 20 % 7);
+      a = -20;
+      a %= b;
+      BOOST_TEST(a == -20 % 7);
+      a = 20;
+      a %= -b;
+      BOOST_TEST(a == 20 % -7);
+      a = -20;
+      a %= -b;
+      BOOST_TEST(a == -20 % -7);
+   }
 
    a = 20;
    a %= 7;
    BOOST_TEST(a == 20 % 7);
-   a = -20;
-   a %= 7;
-   BOOST_TEST(a == -20 % 7);
-   a = 20;
-   a %= -7;
-   BOOST_TEST(a == 20 % -7);
-   a = -20;
-   a %= -7;
-   BOOST_TEST(a == -20 % -7);
+   if(std::numeric_limits::is_signed)
+   {
+      a = -20;
+      a %= 7;
+      BOOST_TEST(a == -20 % 7);
+      a = 20;
+      a %= -7;
+      BOOST_TEST(a == 20 % -7);
+      a = -20;
+      a %= -7;
+      BOOST_TEST(a == -20 % -7);
+   }
 #ifndef BOOST_NO_LONG_LONG
    a = 20;
    a %= 7uLL;
    BOOST_TEST(a == 20 % 7);
-   a = -20;
-   a %= 7uLL;
-   BOOST_TEST(a == -20 % 7);
-   a = 20;
-   a %= -7LL;
-   BOOST_TEST(a == 20 % -7);
-   a = -20;
-   a %= -7LL;
-   BOOST_TEST(a == -20 % -7);
+   if(std::numeric_limits::is_signed)
+   {
+      a = -20;
+      a %= 7uLL;
+      BOOST_TEST(a == -20 % 7);
+      a = 20;
+      a %= -7LL;
+      BOOST_TEST(a == 20 % -7);
+      a = -20;
+      a %= -7LL;
+      BOOST_TEST(a == -20 % -7);
+   }
 #endif
    a = 20;
    BOOST_TEST(++a == 21);
@@ -330,14 +345,17 @@ void test_integer_ops(const boost::mpl::int_::is_signed)
+   {
+      a = -20;
+      BOOST_TEST(abs(a) == 20);
+      BOOST_TEST(abs(-a) == 20);
+      BOOST_TEST(abs(+a) == 20);
+      a = 20;
+      BOOST_TEST(abs(a) == 20);
+      BOOST_TEST(abs(-a) == 20);
+      BOOST_TEST(abs(+a) == 20);
+   }
 }
 
 template 
@@ -410,6 +428,8 @@ struct lexical_cast_target_type
 template 
 void test_negative_mixed(boost::mpl::true_ const&)
 {
+   if(std::numeric_limits::is_specialized && !std::numeric_limits::is_signed)
+      return;
    typedef typename lexical_cast_target_type::type target_type;
    std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name()  << " and " << typeid(Num).name() << std::endl;
    Num n1 = -static_cast(1uLL << (std::numeric_limits::digits - 1));
@@ -649,7 +669,10 @@ void test()
    BOOST_TEST(a == 8);
    Real ac(a);
    BOOST_TEST(ac == a);
-   BOOST_TEST(-a == -8);
+   if(std::numeric_limits::is_signed)
+   {
+      BOOST_TEST(-a == -8);
+   }
    ac = a * c;
    BOOST_TEST(ac == 8*500L);
    ac = 8*500L;
@@ -693,9 +716,12 @@ void test()
    ac = a;
    ac = a + ac;
    BOOST_TEST(ac == 16);
-   ac = a;
-   ac = ac - b;
-   BOOST_TEST(ac == 8 - 64);
+   if(std::numeric_limits::is_signed)
+   {
+      ac = a;
+      ac = ac - b;
+      BOOST_TEST(ac == 8 - 64);
+   }
    ac = a;
    ac = a - ac;
    BOOST_TEST(ac == 0);
@@ -705,16 +731,22 @@ void test()
    ac = a;
    ac += b + a;
    BOOST_TEST(ac == 80);
-   ac = a;
-   ac -= a + b;
-   BOOST_TEST(ac == -64);
-   ac = a;
-   ac -= b - a;
-   BOOST_TEST(ac == 16 - 64);
+   if(std::numeric_limits::is_signed)
+   {
+      ac = a;
+      ac -= a + b;
+      BOOST_TEST(ac == -64);
+      ac = a;
+      ac -= b - a;
+      BOOST_TEST(ac == 16 - 64);
+   }
    ac = +a;
    BOOST_TEST(ac == 8);
-   ac = -a;
-   BOOST_TEST(ac == -8);
+   if(std::numeric_limits::is_signed)
+   {
+      ac = -a;
+      BOOST_TEST(ac == -8);
+   }
    ac = 8;
    ac = a * ac;
    BOOST_TEST(ac == 8*8);
@@ -736,8 +768,11 @@ void test()
    ac -= +a;
    BOOST_TEST(ac == 0);
    ac = a;
-   ac -= -a;
-   BOOST_TEST(ac == 16);
+   if(std::numeric_limits::is_signed)
+   {
+      ac -= -a;
+      BOOST_TEST(ac == 16);
+   }
    ac = a;
    ac -= c - b;
    BOOST_TEST(ac == 8 - (500-64));
@@ -768,9 +803,12 @@ void test()
    ac = b;
    ac /= +a;
    BOOST_TEST(ac == 8);
-   ac = b;
-   ac /= -a;
-   BOOST_TEST(ac == -8);
+   if(std::numeric_limits::is_signed)
+   {
+      ac = b;
+      ac /= -a;
+      BOOST_TEST(ac == -8);
+   }
    ac = b;
    ac /= b / a;
    BOOST_TEST(ac == 64 / (64/8));
@@ -788,14 +826,17 @@ void test()
    BOOST_TEST(ac == 72);
    ac = +a + +b;
    BOOST_TEST(ac == 72);
-   ac = a + -b;
-   BOOST_TEST(ac == 8 - 64);
-   ac = -a + b;
-   BOOST_TEST(ac == -8+64);
-   ac = -a + -b;
-   BOOST_TEST(ac == -72);
-   ac = a + - + -b; // lots of unary operators!!
-   BOOST_TEST(ac == 72);
+   if(std::numeric_limits::is_signed)
+   {
+      ac = a + -b;
+      BOOST_TEST(ac == 8 - 64);
+      ac = -a + b;
+      BOOST_TEST(ac == -8+64);
+      ac = -a + -b;
+      BOOST_TEST(ac == -72);
+      ac = a + - + -b; // lots of unary operators!!
+      BOOST_TEST(ac == 72);
+   }
    ac = a;
    ac = b / ac;
    BOOST_TEST(ac == b / a);
@@ -855,9 +896,12 @@ void test()
    a = 20;
    BOOST_TEST(a.sign() > 0);
    BOOST_TEST(!a.is_zero());
-   a = -20;
-   BOOST_TEST(a.sign() < 0);
-   BOOST_TEST(!a.is_zero());
+   if(std::numeric_limits::is_signed)
+   {
+      a = -20;
+      BOOST_TEST(a.sign() < 0);
+      BOOST_TEST(!a.is_zero());
+   }
    a = 0;
    BOOST_TEST(a.sign() == 0);
    BOOST_TEST(a.is_zero());
@@ -954,6 +998,22 @@ int main()
 #endif
 #ifdef TEST_MPZ_BOOST_RATIONAL
    test >();
+#endif
+#ifdef TEST_PACKED_INT1
+   test();
+   test();
+   test();
+   test > >();
+#endif
+#ifdef TEST_PACKED_INT2
+   //
+   // Can't test 64-bit signed ints - they don't have enough bits
+   // to interoperate with uint64_t without loss:
+   //
+   //test();
+   test();
+   test();
+   test > >();
 #endif
    return boost::report_errors();
 }
diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp
index 35963444..93a33fb3 100644
--- a/test/test_int_io.cpp
+++ b/test/test_int_io.cpp
@@ -9,9 +9,11 @@
 #  define _SCL_SECURE_NO_WARNINGS
 #endif
 
-#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH)
+#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) && !defined(TEST_PACKED_INT1) && !defined(TEST_PACKED_INT2)
 #  define TEST_TOMMATH
 #  define TEST_MPZ
+#  define TEST_PACKED_INT1
+#  define TEST_PACKED_INT2
 
 #ifdef _MSC_VER
 #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
@@ -28,6 +30,9 @@
 #if defined(TEST_TOMMATH)
 #include 
 #endif
+#if defined(TEST_PACKED_INT1) || defined(TEST_PACKED_INT2)
+#include 
+#endif
 
 #include 
 #include 
@@ -82,12 +87,16 @@ void test_round_trip()
    {
       T val = generate_random();
       do_round_trip(val);
-      do_round_trip(T(-val));
+      if(std::numeric_limits::is_signed)
+         do_round_trip(T(-val));
    }
 
    BOOST_CHECK_EQUAL(T(1002).str(), "1002");
    BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::showpos), "+1002");
-   BOOST_CHECK_EQUAL(T(-1002).str(), "-1002");
+   if(std::numeric_limits::is_signed)
+   {
+      BOOST_CHECK_EQUAL(T(-1002).str(), "-1002");
+   }
    BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::oct), "1752");
    BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::oct|std::ios_base::showbase), "01752");
    BOOST_CHECK_EQUAL(boost::to_lower_copy(T(1002).str(0, std::ios_base::hex)), "3ea");
@@ -95,8 +104,11 @@ void test_round_trip()
    BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::dec), "1002");
    BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::dec|std::ios_base::showbase), "1002");
 
-   BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::oct), std::runtime_error);
-   BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::hex), std::runtime_error);
+   if(std::numeric_limits::is_signed && !std::numeric_limits::is_modulo)
+   {
+      BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::oct), std::runtime_error);
+      BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::hex), std::runtime_error);
+   }
 }
 
 int main()
@@ -106,6 +118,20 @@ int main()
 #endif
 #ifdef TEST_TOMMATH
    test_round_trip();
+#endif
+#ifdef TEST_PACKED_INT1
+   test_round_trip();
+   test_round_trip();
+   test_round_trip();
+   test_round_trip > >();
+   test_round_trip > >();
+#endif
+#ifdef TEST_PACKED_INT2
+   test_round_trip();
+   test_round_trip();
+   test_round_trip();
+   test_round_trip > >();
+   test_round_trip > >();
 #endif
    return boost::report_errors();
 }

From 9a1f7c14a5687ab23127765cab7956948d4b3dfe Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Sun, 1 Jan 2012 11:37:46 +0000
Subject: [PATCH 090/256] Update special functions performance test and add
 generic lanczos support to floating point types.

[SVN r76252]
---
 include/boost/multiprecision/cpp_float.hpp    |  1 +
 .../multiprecision/detail/big_lanczos.hpp     | 46 ++++++++++++
 include/boost/multiprecision/gmp.hpp          |  1 +
 include/boost/multiprecision/mpfr.hpp         | 25 +------
 performance/sf_performance-msvc-10.log        | 69 ++++++++++++++++++
 performance/sf_performance.cpp                | 73 +++++++++++++++++++
 6 files changed, 191 insertions(+), 24 deletions(-)
 create mode 100644 include/boost/multiprecision/detail/big_lanczos.hpp
 create mode 100644 performance/sf_performance-msvc-10.log

diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp
index 84811b12..968e29c1 100644
--- a/include/boost/multiprecision/cpp_float.hpp
+++ b/include/boost/multiprecision/cpp_float.hpp
@@ -15,6 +15,7 @@
 #include 
 #include 
 #include 
+#include 
 
 //
 // Headers required for Boost.Math integration:
diff --git a/include/boost/multiprecision/detail/big_lanczos.hpp b/include/boost/multiprecision/detail/big_lanczos.hpp
new file mode 100644
index 00000000..a3dd8cb2
--- /dev/null
+++ b/include/boost/multiprecision/detail/big_lanczos.hpp
@@ -0,0 +1,46 @@
+
+//  Copyright (c) 2011 John Maddock
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MP_BIG_LANCZOS
+#define BOOST_MP_BIG_LANCZOS
+
+#include 
+
+namespace boost{ namespace math{
+
+namespace lanczos{
+
+template 
+struct lanczos;
+
+template
+struct lanczos, Policy>
+{
+   typedef typename boost::math::policies::precision, Policy>::type precision_type;
+   typedef typename mpl::if_c<
+      precision_type::value <= 73,
+      lanczos13UDT,
+      typename mpl::if_c<
+         precision_type::value <= 122,
+         lanczos22UDT,
+         typename mpl::if_c<
+            precision_type::value <= 172,
+            lanczos31UDT,
+            typename mpl::if_c<
+               precision_type::value <= 372,
+               lanczos61UDT,
+               undefined_lanczos
+            >::type
+         >::type
+      >::type
+   >::type type;
+};
+
+} // namespace lanczos
+
+}} // namespaces
+
+#endif
diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp
index be5c3b3d..b5d71181 100644
--- a/include/boost/multiprecision/gmp.hpp
+++ b/include/boost/multiprecision/gmp.hpp
@@ -7,6 +7,7 @@
 #define BOOST_MATH_ER_GMP_BACKEND_HPP
 
 #include 
+#include 
 #include 
 #include 
 #include 
diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp
index 3129171e..c0c497ce 100644
--- a/include/boost/multiprecision/mpfr.hpp
+++ b/include/boost/multiprecision/mpfr.hpp
@@ -11,7 +11,7 @@
 #include 
 #include 
 #include 
-#include 
+#include 
 #include 
 #include 
 #include 
@@ -1008,29 +1008,6 @@ inline int digits()
 
 }
 
-namespace lanczos{
-
-template
-struct lanczos >, Policy>
-{
-   typedef typename mpl::if_c<
-      Digits10 <= 36,
-      lanczos22UDT,
-      typename mpl::if_c<
-         Digits10 <= 50,
-         lanczos31UDT,
-         typename mpl::if_c<
-            Digits10 <= 110,
-            lanczos61UDT,
-            undefined_lanczos
-         >::type
-      >::type
-   >::type type;
-};
-
-} // namespace lanczos
-
-
 }}  // namespaces
 
 namespace std{
diff --git a/performance/sf_performance-msvc-10.log b/performance/sf_performance-msvc-10.log
new file mode 100644
index 00000000..82722d81
--- /dev/null
+++ b/performance/sf_performance-msvc-10.log
@@ -0,0 +1,69 @@
+0
+11
+24
+3
+13
+27
+Testing Bessel Functions.....
+Time for mpfr_float_50 = 6.2742 seconds
+Total allocations for mpfr_float_50 = 2684348
+Time for mpf_float_50 = 11.2255 seconds
+Total allocations for mpf_float_50 = 2601366
+Time for cpp_float_50 = 19.5712 seconds
+Total allocations for cpp_float_50 = 0
+Time for mpfr_class (50 digits) = 6.11757 seconds
+Total allocations for mpfr_class (50 digits) = 3946031
+Time for mpreal (50 digits) = 9.38756 seconds
+Total allocations for mpreal (50 digits) = 13223017
+Time for mpfr_float_100 = 9.61944 seconds
+Total allocations for mpfr_float_50 = 3671485
+Time for mpf_float_100 = 8.29211 seconds
+Total allocations for mpf_float_100 = 3593669
+Time for cpp_float_100 = 20.4485 seconds
+Total allocations for cpp_float_100 = 0
+Time for mpfr_class (100 digits) = 9.88427 seconds
+Total allocations for mpfr_class (100 digits) = 5447348
+Time for mpreal (100 digits) = 13.7811 seconds
+Total allocations for mpreal (100 digits) = 16671065
+Testing Polynomial Evaluation.....
+Time for mpfr_float_50 = 0.00839464 seconds
+Total allocations for mpfr_float_50 = 2996
+Time for mpf_float_50 = 0.0042138 seconds
+Total allocations for mpf_float_50 = 2996
+Time for cpp_float_50 = 0.0046054 seconds
+Total allocations for cpp_float_50 = 0
+Time for mpfr_class (50 digits) = 0.00990538 seconds
+Total allocations for mpfr_class (50 digits) = 12976
+Time for mpreal (50 digits) = 0.0152955 seconds
+Total allocations for mpreal (50 digits = 27947
+Time for mpfr_float_100 = 0.00957098 seconds
+Total allocations for mpfr_float_100 = 2996
+Time for mpf_float_100 = 0.00418726 seconds
+Total allocations for mpf_float_100 = 2996
+Time for cpp_float_100 = 0.0090742 seconds
+Total allocations for cpp_float_100 = 0
+Time for mpfr_class (100 digits) = 0.011094 seconds
+Total allocations for mpfr_class (100 digits) = 12976
+Time for mpreal (100 digits) = 0.0172028 seconds
+Total allocations for mpreal (100 digits) = 27947
+Testing Non-Central T.....
+Time for mpfr_float_50 = 260.324 seconds
+Total allocations for mpfr_float_50 = 139149049
+Time for mpf_float_50 = 201.95 seconds
+Total allocations for mpf_float_50 = 134600354
+Time for cpp_float_50 = 340.292 seconds
+Total allocations for cpp_float_50 = 0
+Time for mpfr_class (50 digits) = 269.03 seconds
+Total allocations for mpfr_class (50 digits) = 252401115
+Time for mpreal (50 digits) = 350.758 seconds
+Total allocations for mpreal (50 digits) = 447009420
+Time for mpfr_float_100 = 519.421 seconds
+Total allocations for mpfr_float_100 = 220400854
+Time for mpf_float_100 = 404.593 seconds
+Total allocations for mpf_float_100 = 212307349
+Time for cpp_float_100 = 1118.91 seconds
+Total allocations for cpp_float_100 = 0
+Time for mpfr_class (100 digits) = 541.35 seconds
+Total allocations for mpfr_class (100 digits) = 407154781
+Time for mpreal (100 digits) = 677.265 seconds
+Total allocations for mpreal (100 digits) = 724581024
diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp
index 04238b9e..5b2d0fbf 100644
--- a/performance/sf_performance.cpp
+++ b/performance/sf_performance.cpp
@@ -9,6 +9,8 @@
 #include 
 #include 
 #include 
+#include 
+#include 
 #include 
 #include 
 #include 
@@ -43,6 +45,7 @@ template 
 Real test_bessel()
 {
 #  define T double
+#  define SC_(x) x
 #  include "libs/math/test/bessel_i_int_data.ipp"
 #  include "libs/math/test/bessel_i_data.ipp"
 
@@ -184,6 +187,16 @@ int main()
    std::cout << "Time for mpfr_float_50 = " << time << std::endl;
    std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl;
    allocation_count = 0;
+   test_bessel();
+   time = c.elapsed();
+   std::cout << "Time for mpf_float_50 = " << time << std::endl;
+   std::cout << "Total allocations for mpf_float_50 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   test_bessel();
+   time = c.elapsed();
+   std::cout << "Time for cpp_float_50 = " << time << std::endl;
+   std::cout << "Total allocations for cpp_float_50 = " << allocation_count << std::endl;
+   allocation_count = 0;
    c.reset();
    test_bessel();
    time = c.elapsed();
@@ -208,6 +221,18 @@ int main()
    std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl;
    allocation_count = 0;
    c.reset();
+   test_bessel();
+   time = c.elapsed();
+   std::cout << "Time for mpf_float_100 = " << time << std::endl;
+   std::cout << "Total allocations for mpf_float_100 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   c.reset();
+   test_bessel();
+   time = c.elapsed();
+   std::cout << "Time for cpp_float_100 = " << time << std::endl;
+   std::cout << "Total allocations for cpp_float_100 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   c.reset();
    test_bessel();
    time = c.elapsed();
    std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl;
@@ -234,6 +259,18 @@ int main()
    std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl;
    allocation_count = 0;
    c.reset();
+   test_polynomial();
+   time = c.elapsed();
+   std::cout << "Time for mpf_float_50 = " << time << std::endl;
+   std::cout << "Total allocations for mpf_float_50 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   c.reset();
+   test_polynomial();
+   time = c.elapsed();
+   std::cout << "Time for cpp_float_50 = " << time << std::endl;
+   std::cout << "Total allocations for cpp_float_50 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   c.reset();
    test_polynomial();
    time = c.elapsed();
    std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl;
@@ -257,6 +294,18 @@ int main()
    std::cout << "Total allocations for mpfr_float_100 = " << allocation_count << std::endl;
    allocation_count = 0;
    c.reset();
+   test_polynomial();
+   time = c.elapsed();
+   std::cout << "Time for mpf_float_100 = " << time << std::endl;
+   std::cout << "Total allocations for mpf_float_100 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   c.reset();
+   test_polynomial();
+   time = c.elapsed();
+   std::cout << "Time for cpp_float_100 = " << time << std::endl;
+   std::cout << "Total allocations for cpp_float_100 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   c.reset();
    test_polynomial();
    time = c.elapsed();
    std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl;
@@ -283,6 +332,18 @@ int main()
    std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl;
    allocation_count = 0;
    c.reset();
+   test_nct();
+   time = c.elapsed();
+   std::cout << "Time for mpf_float_50 = " << time << std::endl;
+   std::cout << "Total allocations for mpf_float_50 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   c.reset();
+   test_nct();
+   time = c.elapsed();
+   std::cout << "Time for cpp_float_50 = " << time << std::endl;
+   std::cout << "Total allocations for cpp_float_50 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   c.reset();
    test_nct();
    time = c.elapsed();
    std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl;
@@ -306,6 +367,18 @@ int main()
    std::cout << "Total allocations for mpfr_float_100 = " << allocation_count << std::endl;
    allocation_count = 0;
    c.reset();
+   test_nct();
+   time = c.elapsed();
+   std::cout << "Time for mpf_float_100 = " << time << std::endl;
+   std::cout << "Total allocations for mpf_float_100 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   c.reset();
+   test_nct();
+   time = c.elapsed();
+   std::cout << "Time for cpp_float_100 = " << time << std::endl;
+   std::cout << "Total allocations for cpp_float_100 = " << allocation_count << std::endl;
+   allocation_count = 0;
+   c.reset();
    test_nct();
    time = c.elapsed();
    std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl;

From b607dc2c470574bae1fff58c32657d1a50b7c695 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Sun, 1 Jan 2012 11:46:48 +0000
Subject: [PATCH 091/256] Move file.

[SVN r76253]
---
 {test => performance}/linpack-benchmark.cpp | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename {test => performance}/linpack-benchmark.cpp (100%)

diff --git a/test/linpack-benchmark.cpp b/performance/linpack-benchmark.cpp
similarity index 100%
rename from test/linpack-benchmark.cpp
rename to performance/linpack-benchmark.cpp

From 8dec0e4db6de2577617d56d59a8b0267443c71eb Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Mon, 2 Jan 2012 17:45:49 +0000
Subject: [PATCH 092/256] Add initial performance test program for testing
 basic arithmetic. Fix header include on packed_cpp_int.hpp and add
 numeric_limits min/max values.

[SVN r76279]
---
 .../boost/multiprecision/packed_cpp_int.hpp   |  50 ++-
 performance/performance_test.cpp              | 347 ++++++++++++++++++
 2 files changed, 386 insertions(+), 11 deletions(-)
 create mode 100644 performance/performance_test.cpp

diff --git a/include/boost/multiprecision/packed_cpp_int.hpp b/include/boost/multiprecision/packed_cpp_int.hpp
index 1c8e7af6..3e0510e8 100644
--- a/include/boost/multiprecision/packed_cpp_int.hpp
+++ b/include/boost/multiprecision/packed_cpp_int.hpp
@@ -3,8 +3,8 @@
 //  Software License, Version 1.0. (See accompanying file
 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
 
-#ifndef BOOST_MATH_RATIONAL_ADAPTER_HPP
-#define BOOST_MATH_RATIONAL_ADAPTER_HPP
+#ifndef BOOST_MP_PACKED_INT_HPP
+#define BOOST_MP_PACKED_INT_HPP
 
 #include 
 #include 
@@ -838,6 +838,17 @@ template 
 class numeric_limits > >
 {
    typedef boost::multiprecision::mp_number > number_type;
+
+   struct initializer
+   {
+      initializer()
+      {
+         (std::numeric_limits > >::min)();
+         (std::numeric_limits > >::max)();
+      }
+      void do_nothing()const{}
+   };
+   static const initializer init;
 public:
    BOOST_STATIC_CONSTEXPR bool is_specialized = true;
    //
@@ -845,12 +856,26 @@ public:
    // to zero:
    //
    BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT
-   { 
-      return number_type();
+   {
+      static bool init = false;
+      static number_type val;
+      if(!init)
+      {
+         init = true;
+         val = Signed ? number_type(1) << Bits - 1 : 0;
+      }
+      return val;
    }
    BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT 
    { 
-      return number_type();
+      static bool init = false;
+      static number_type val;
+      if(!init)
+      {
+         init = true;
+         val = Signed ? number_type(~(number_type(1) << Bits - 1)) : number_type(~number_type(0));
+      }
+      return val;
    }
    BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); }
    BOOST_STATIC_CONSTEXPR int digits = Bits;
@@ -860,8 +885,8 @@ public:
    BOOST_STATIC_CONSTEXPR bool is_integer = true;
    BOOST_STATIC_CONSTEXPR bool is_exact = true;
    BOOST_STATIC_CONSTEXPR int radix = 2;
-   BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); }
-   BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); }
+   BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return 0; }
+   BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return 0; }
    BOOST_STATIC_CONSTEXPR int min_exponent = 0;
    BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
    BOOST_STATIC_CONSTEXPR int max_exponent = 0;
@@ -871,10 +896,10 @@ public:
    BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
    BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
    BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
-   BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); }
-   BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); }
-   BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); }
-   BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); }
+   BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return 0; }
+   BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return 0; }
+   BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return 0; }
+   BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return 0; }
    BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
    BOOST_STATIC_CONSTEXPR bool is_bounded = true;
    BOOST_STATIC_CONSTEXPR bool is_modulo = true;
@@ -883,6 +908,9 @@ public:
    BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
 };
 
+template 
+typename numeric_limits > >::initializer
+   typename numeric_limits > >::init;
 }
 
 #endif
diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp
new file mode 100644
index 00000000..b02ac616
--- /dev/null
+++ b/performance/performance_test.cpp
@@ -0,0 +1,347 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2011 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#define BOOST_CHRONO_HEADER_ONLY
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#if !defined(TEST_MPF) && !defined(TEST_MPZ) && \
+   !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPQ) \
+   && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\
+   && !defined(TEST_PACKED_INT)
+#  define TEST_MPF
+#  define TEST_MPZ
+#  define TEST_MPFR
+#  define TEST_CPP_FLOAT
+#  define TEST_MPQ
+#  define TEST_TOMMATH
+#  define TEST_PACKED_INT
+
+#ifdef _MSC_VER
+#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
+#endif
+#ifdef __GNUC__
+#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
+#endif
+
+#endif
+
+#if defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) || defined(TEST_MPZ_BOOST_RATIONAL)
+#include 
+#include 
+#endif
+#ifdef TEST_CPP_FLOAT
+#include 
+#endif
+#if defined(TEST_MPFR)
+#include 
+#endif
+#if defined(TEST_TOMMATH) || defined(TEST_TOMMATH_BOOST_RATIONAL)
+#include 
+#include 
+#endif
+#if defined(TEST_PACKED_INT)
+#include 
+#endif
+
+#include 
+#include 
+#include 
+#include 
+
+template 
+struct stopwatch
+{
+   typedef typename Clock::duration duration;
+   stopwatch()
+   {
+      m_start = Clock::now();
+   }
+   duration elapsed()
+   {
+      return Clock::now() - m_start;
+   }
+   void reset()
+   {
+      m_start = Clock::now();
+   }
+
+private:
+   typename Clock::time_point m_start;
+};
+
+unsigned bits_wanted; // for integer types
+
+template 
+struct tester
+{
+   tester()
+   {
+      a.assign(500, 0);
+      for(int i = 0; i < 500; ++i)
+      {
+         b.push_back(generate_random());
+         c.push_back(generate_random());
+         small.push_back(gen());
+      }
+   }
+   double test_add()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] + c[i];
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_subtract()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] - c[i];
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_multiply()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] * c[i];
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_divide()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] / c[i] + b[i] / small[i];
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_str()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < b.size(); ++i)
+         a[i] = b[i].str();
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   //
+   // The following tests only work for ineteger types:
+   //
+   double test_mod()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] % c[i] + b[i] % small[i];
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_or()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] | c[i];
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_and()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] & c[i];
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_xor()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] ^ c[i];
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_complement()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = ~b[i];
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_left_shift()
+   {
+      int shift = std::numeric_limits::is_bounded ? std::numeric_limits::digits : bits_wanted;
+      shift /= 2;
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] << shift;
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_right_shift()
+   {
+      int shift = std::numeric_limits::is_bounded ? std::numeric_limits::digits : bits_wanted;
+      shift /= 2;
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] >> shift;
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+private:
+   T generate_random()
+   {
+      return generate_random(boost::mpl::int_());
+   }
+   T generate_random(const boost::mpl::int_&)
+   {
+      T val = gen();
+      T prev_val = -1;
+      while(val != prev_val)
+      {
+         val *= (gen.max)();
+         prev_val = val;
+         val += gen();
+      }
+      int e;
+      val = frexp(val, &e);
+
+      typedef typename T::backend_type::exponent_type e_type;
+      static boost::random::uniform_int_distribution ui(0, std::numeric_limits::max_exponent - 10);
+      return ldexp(val, ui(gen));
+   }
+   T generate_random(const boost::mpl::int_&)
+   {
+      typedef boost::random::mt19937::result_type random_type;
+
+      T max_val;
+      unsigned digits;
+      if(std::numeric_limits::is_bounded)
+      {
+         max_val = (std::numeric_limits::max)();
+         digits = std::numeric_limits::digits;
+      }
+      else
+      {
+         max_val = T(1) << bits_wanted;
+         digits = bits_wanted;
+      }
+
+      unsigned bits_per_r_val = std::numeric_limits::digits - 1;
+      while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val;
+
+      unsigned terms_needed = digits / bits_per_r_val + 1;
+
+      T val = 0;
+      for(unsigned i = 0; i < terms_needed; ++i)
+      {
+         val *= (gen.max)();
+         val += gen();
+      }
+      val %= max_val;
+      return val;
+   }
+   std::vector a, b, c, small;
+   static boost::random::mt19937 gen;
+};
+
+template 
+boost::random::mt19937 tester::gen;
+
+template 
+void test_int_ops(tester& t, const char* type, unsigned precision, const boost::mpl::int_&)
+{
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "%" << t.test_mod() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "|" << t.test_or() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "&" << t.test_and() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "^" << t.test_xor() << std::endl;
+   //std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "~" << t.test_complement() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "<<" << t.test_left_shift() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << ">>" << t.test_right_shift() << std::endl;
+}
+template 
+void test_int_ops(tester& t, const char* type, unsigned precision, const U&)
+{
+}
+
+template 
+void test(const char* type, unsigned precision)
+{
+   bits_wanted = precision;
+   tester::value> t;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "+" << t.test_add() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "-" << t.test_subtract() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "*" << t.test_multiply() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "/" << t.test_divide() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "str" << t.test_str() << std::endl;
+
+   test_int_ops(t, type, precision, typename boost::multiprecision::number_category::type());
+}
+
+
+int main()
+{
+#ifdef TEST_MPF
+   test("gmp_float", 50);
+   test("gmp_float", 100);
+   test("gmp_float", 500);
+#endif
+#ifdef TEST_MPZ
+   test("gmp_int", 64);
+   test("gmp_int", 128);
+   test("gmp_int", 256);
+   test("gmp_int", 512);
+   test("gmp_int", 1024);
+#endif
+#ifdef TEST_TOMMATH
+   test("tommath_int", 64);
+   test("tommath_int", 128);
+   test("tommath_int", 256);
+   test("tommath_int", 512);
+   test("tommath_int", 1024);
+#endif
+#ifdef TEST_PACKED_INT
+   test("mp_int64_t", 64);
+   test("mp_int128_t", 128);
+   test("mp_int256_t", 256);
+   test("mp_int512_t", 512);
+   test > >("mp_int1024_t", 1024);
+#endif
+#ifdef TEST_CPP_FLOAT
+   test("cpp_float", 50);
+   test("cpp_float", 100);
+   test > >("cpp_float", 500);
+#endif
+#ifdef TEST_MPFR
+   test("mpfr_float", 50);
+   test("mpfr_float", 100);
+   test("mpfr_float", 500);
+#endif
+   return 0;
+}
+

From 99707d8925720d5f47baadae62f87a3d0b7aded2 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Tue, 10 Jan 2012 13:20:29 +0000
Subject: [PATCH 093/256] Switch to faster division code and add better test
 case for packed int's.

[SVN r76398]
---
 .../boost/multiprecision/packed_cpp_int.hpp   | 166 +++++++++++++++++-
 test/Jamfile.v2                               |   8 +
 test/packed_int_test.cpp                      | 151 ++++++++++++++++
 3 files changed, 324 insertions(+), 1 deletion(-)
 create mode 100644 test/packed_int_test.cpp

diff --git a/include/boost/multiprecision/packed_cpp_int.hpp b/include/boost/multiprecision/packed_cpp_int.hpp
index 3e0510e8..62082f70 100644
--- a/include/boost/multiprecision/packed_cpp_int.hpp
+++ b/include/boost/multiprecision/packed_cpp_int.hpp
@@ -504,7 +504,7 @@ boost::uint32_t bitcount(const packed_cpp_int& a)
    }
    return count;
 }
-
+/*
 template 
 void divide_unsigned_helper(packed_cpp_int& result, const packed_cpp_int& x, const packed_cpp_int& y, packed_cpp_int& r)
 {
@@ -588,6 +588,170 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
    }
    BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed
 }
+*/
+template 
+void divide_unsigned_helper(packed_cpp_int& result, const packed_cpp_int& x, const packed_cpp_int& y, packed_cpp_int& r)
+{
+   if((&result == &x) || (&r == &x))
+   {
+      packed_cpp_int t(x);
+      divide_unsigned_helper(result, t, y, r);
+      return;
+   }
+   if((&result == &y) || (&r == &y))
+   {
+      packed_cpp_int t(y);
+      divide_unsigned_helper(result, x, t, r);
+      return;
+   }
+
+
+   using default_ops::subtract;
+
+
+   if (is_zero(y))
+   {
+      volatile int i = 0;
+      i /= i;
+      return;
+   }
+
+   if (is_zero(x))
+   {
+      r = y;
+      result = x;
+      return;
+   }
+
+   if(&result == &r)
+   {
+      packed_cpp_int rem;
+      divide_unsigned_helper(result, x, y, rem);
+      r = rem;
+      return;
+   }
+
+   r = x;
+   result = static_cast(0u);
+   if(x.compare(y) < 0)
+   {
+      return; // We already have the answer: zero.
+   }
+
+   //
+   // Find the most significant words of numerator and denominator.
+   // Note that this code can't run past the end of the array because
+   // we know already that neither are all zero:
+   //
+   boost::uint32_t r_order = 0;
+   while(r.data()[r_order] == 0)
+      ++r_order;
+   boost::uint32_t y_order = 0;
+   while(y.data()[y_order] == 0)
+      ++y_order;
+
+   packed_cpp_int t;
+   bool r_neg = false;
+
+   //
+   // See if we can short-circuit long division, and use basic arithmetic instead:
+   //
+   if(r_order == packed_cpp_int::limb_count - 1)
+   {
+      result = r.data()[packed_cpp_int::limb_count - 1] / y.data()[packed_cpp_int::limb_count - 1];
+      r = x.data()[packed_cpp_int::limb_count - 1] % y.data()[packed_cpp_int::limb_count - 1];
+      return;
+   }
+   else if(r_order == packed_cpp_int::limb_count - 2)
+   {
+      unsigned long long a, b;
+      a = (static_cast(r.data()[r_order]) << packed_cpp_int::limb_bits) | r.data()[r_order + 1];
+      b = y_order < packed_cpp_int::limb_count - 1 ? 
+         (static_cast(y.data()[y_order]) << packed_cpp_int::limb_bits) | y.data()[y_order + 1] 
+         : y.data()[y_order];
+      result = a / b;
+      r = a % b;
+      return;
+   }
+
+   do
+   {
+      //
+      // Update r_order, this can't run past the end as r must be non-zero at this point:
+      //
+      while(r.data()[r_order] == 0)
+         ++r_order;
+      //
+      // Calculate our best guess for how many times y divides into r:
+      //
+      boost::uint32_t guess;
+      if((r.data()[r_order] <= y.data()[y_order]) && (r_order < packed_cpp_int::limb_count - 1))
+      {
+         unsigned long long a, b, v;
+         a = (static_cast(r.data()[r_order]) << packed_cpp_int::limb_bits) | r.data()[r_order + 1];
+         b = y.data()[y_order];
+         v = a / b;
+         if(v > packed_cpp_int::max_limb_value)
+            guess = 1;
+         else
+         {
+            guess = static_cast(v);
+            ++r_order;
+         }
+      }
+      else
+      {
+         guess = r.data()[r_order] / y.data()[y_order];
+      }
+      //
+      // Update result:
+      //
+      boost::uint32_t shift = y_order - r_order;
+      t = boost::uint32_t(0);
+      t.data()[packed_cpp_int::limb_count - 1 - shift] = guess;
+      if(r_neg)
+         subtract(result, t);
+      else
+         add(result, t);
+      //
+      // Calculate guess * y, we use a fused mutiply-shift O(N) for this
+      // rather than a full O(N^2) multiply:
+      //
+      boost::uintmax_t carry = 0;
+      for(unsigned i = packed_cpp_int::limb_count - 1; i > packed_cpp_int::limb_count - shift - 1; --i)
+         t.data()[i] = 0;
+      for(int i = packed_cpp_int::limb_count - 1; i >= static_cast(shift); --i)
+      {
+         boost::uintmax_t v = static_cast(y.data()[i]) * static_cast(guess) + carry;
+         t.data()[i - shift] = static_cast::limb_type>(v);
+         carry = v >> sizeof(packed_cpp_int::limb_type) * CHAR_BIT;
+      }
+      t.data()[0] &= packed_cpp_int::upper_limb_mask;
+       //
+      // Update r:
+      //
+      subtract(r, t);
+      if(r.data()[0] & packed_cpp_int::sign_bit_mask)
+      {
+         r.negate();
+         r_neg = !r_neg;
+      }
+   }
+   while(r.compare(y) > 0);
+
+   //
+   // We now just have to normalise the result:
+   //
+   if(r_neg)
+   {
+      // We have one too many in the result:
+      decrement(result);
+      r.negate();
+      add(r, y);
+   }
+
+   BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed
+}
 
 template 
 inline void divide(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 3f028183..9fed404a 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -595,6 +595,14 @@ run test_int_io.cpp
 	      TEST_PACKED_INT2
         : test_int_io_packed_int2 ;
 
+run packed_int_test.cpp gmp
+        : # command line
+        : # input files
+        : # requirements
+         [ check-target-builds ../config//has_gmp : : no ]
+         release  # otherwise runtime is too slow!!
+        : packed_int_test.cpp ;
+
 run test_rational_io.cpp $(TOMMATH)
         : # command line
         : # input files
diff --git a/test/packed_int_test.cpp b/test/packed_int_test.cpp
new file mode 100644
index 00000000..68314b9f
--- /dev/null
+++ b/test/packed_int_test.cpp
@@ -0,0 +1,151 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+//
+// Compare arithmetic results using packed_cpp_int to GMP results.
+//
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#define BOOST_CHRONO_HEADER_ONLY
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include "test.hpp"
+
+template 
+struct stopwatch
+{
+   typedef typename Clock::duration duration;
+   stopwatch()
+   {
+      m_start = Clock::now();
+   }
+   duration elapsed()
+   {
+      return Clock::now() - m_start;
+   }
+   void reset()
+   {
+      m_start = Clock::now();
+   }
+
+private:
+   typename Clock::time_point m_start;
+};
+
+template 
+T generate_random(unsigned bits_wanted)
+{
+   static boost::random::mt19937 gen;
+   typedef boost::random::mt19937::result_type random_type;
+
+   T max_val;
+   unsigned digits;
+   if(std::numeric_limits::is_bounded && (bits_wanted == std::numeric_limits::digits))
+   {
+      max_val = (std::numeric_limits::max)();
+      digits = std::numeric_limits::digits;
+   }
+   else
+   {
+      max_val = T(1) << bits_wanted;
+      digits = bits_wanted;
+   }
+
+   unsigned bits_per_r_val = std::numeric_limits::digits - 1;
+   while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val;
+
+   unsigned terms_needed = digits / bits_per_r_val + 1;
+
+   T val = 0;
+   for(unsigned i = 0; i < terms_needed; ++i)
+   {
+      val *= (gen.max)();
+      val += gen();
+   }
+   val %= max_val;
+   return val;
+}
+
+int main()
+{
+   using namespace boost::multiprecision;
+   typedef mp_number > packed_type;
+   stopwatch w;
+   unsigned last_error_count = 0;
+   for(int i = 0; i < 1000; ++i)
+   {
+      mpz_int a = generate_random(1000);
+      mpz_int b = generate_random(512);
+      mpz_int c = generate_random(256);
+      mpz_int d = generate_random(32);
+
+      packed_type a1 = a.str();
+      packed_type b1 = b.str();
+      packed_type c1 = c.str();
+      packed_type d1 = d.str();
+
+      BOOST_CHECK_EQUAL(a.str(), a1.str());
+      BOOST_CHECK_EQUAL(b.str(), b1.str());
+      BOOST_CHECK_EQUAL(c.str(), c1.str());
+      BOOST_CHECK_EQUAL(d.str(), d1.str());
+      BOOST_CHECK_EQUAL(mpz_int(a+b).str(), packed_type(a1 + b1).str());
+      BOOST_CHECK_EQUAL(mpz_int(a-b).str(), packed_type(a1 - b1).str());
+      BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)+b).str(), packed_type(packed_type(-a1) + b1).str());
+      BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)-b).str(), packed_type(packed_type(-a1) - b1).str());
+      BOOST_CHECK_EQUAL(mpz_int(c * d).str(), packed_type(c1 * d1).str());
+      BOOST_CHECK_EQUAL(mpz_int(b * c).str(), packed_type(b1 * c1).str());
+      BOOST_CHECK_EQUAL(mpz_int(a / b).str(), packed_type(a1 / b1).str());
+      BOOST_CHECK_EQUAL(mpz_int(a / d).str(), packed_type(a1 / d1).str());
+      BOOST_CHECK_EQUAL(mpz_int(a % b).str(), packed_type(a1 % b1).str());
+      BOOST_CHECK_EQUAL(mpz_int(a % d).str(), packed_type(a1 % d1).str());
+
+      if(last_error_count != boost::detail::test_errors())
+      {
+         last_error_count = boost::detail::test_errors();
+         std::cout << std::hex << std::showbase;
+
+         std::cout << "a    = " << a << std::endl;
+         std::cout << "a1   = " << a1 << std::endl;
+         std::cout << "b    = " << b << std::endl;
+         std::cout << "b1   = " << b1 << std::endl;
+         std::cout << "c    = " << c << std::endl;
+         std::cout << "c1   = " << c1 << std::endl;
+         std::cout << "d    = " << d << std::endl;
+         std::cout << "d1   = " << d1 << std::endl;
+         std::cout << "a + b   = " << a+b << std::endl;
+         std::cout << "a1 + b1 = " << a1+b1 << std::endl;
+         std::cout << "a - b   = " << a-b << std::endl;
+         std::cout << "a1 - b1 = " << a1-b1 << std::endl;
+         std::cout << "-a + b   = " << mpz_int(-a)+b << std::endl;
+         std::cout << "-a1 + b1 = " << packed_type(-a1)+b1 << std::endl;
+         std::cout << "-a - b   = " << mpz_int(-a)-b << std::endl;
+         std::cout << "-a1 - b1 = " << packed_type(-a1)-b1 << std::endl;
+         std::cout << "c*d    = " << c*d << std::endl;
+         std::cout << "c1*d1  = " << c1*d1 << std::endl;
+         std::cout << "b*c    = " << b*c << std::endl;
+         std::cout << "b1*c1  = " << b1*c1 << std::endl;
+         std::cout << "a/b    = " << a/b << std::endl;
+         std::cout << "a1/b1  = " << a1/b1 << std::endl;
+         std::cout << "a/d    = " << a/d << std::endl;
+         std::cout << "a1/d1  = " << a1/d1 << std::endl;
+         std::cout << "a%b    = " << a%b << std::endl;
+         std::cout << "a1%b1  = " << a1%b1 << std::endl;
+         std::cout << "a%d    = " << a%d << std::endl;
+         std::cout << "a1%d1  = " << a1%d1 << std::endl;
+      }
+   }
+   std::cout << w.elapsed() << std::endl;
+   return boost::report_errors();
+}
+
+
+

From 8c28b89dfcb52a6a6c82d7b58057f1df73f72797 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Wed, 11 Jan 2012 11:53:49 +0000
Subject: [PATCH 094/256] Fix GCC failures and generally improve performance of
 packed_cpp_int.

[SVN r76409]
---
 .../boost/multiprecision/packed_cpp_int.hpp   | 105 +++++++++++-------
 performance/performance_test.cpp              |  22 ++++
 test/Jamfile.v2                               |   4 +-
 test/packed_int_test.cpp                      |  26 -----
 test/test_float_io.cpp                        |   4 +
 test/test_int_io.cpp                          |   4 +
 test/test_rational_io.cpp                     |   4 +
 7 files changed, 100 insertions(+), 69 deletions(-)

diff --git a/include/boost/multiprecision/packed_cpp_int.hpp b/include/boost/multiprecision/packed_cpp_int.hpp
index 62082f70..6dbc8657 100644
--- a/include/boost/multiprecision/packed_cpp_int.hpp
+++ b/include/boost/multiprecision/packed_cpp_int.hpp
@@ -97,7 +97,7 @@ struct packed_cpp_int
    }
    packed_cpp_int& operator = (long double a)
    {
-      BOOST_STATIC_ASSERT(Bits >= std::numeric_limits::digits);
+      BOOST_STATIC_ASSERT(Bits >= (unsigned)std::numeric_limits::digits);
       using std::frexp;
       using std::ldexp;
       using std::floor;
@@ -306,10 +306,14 @@ struct packed_cpp_int
    }
    void negate()
    {
-      using default_ops::increment;
-      // complement and add 1:
-      complement(*this, *this);
-      increment(*this);
+      boost::uintmax_t carry = 1;
+      for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
+      {
+         carry += static_cast(~m_value[i]);
+         m_value[i] = static_cast(carry);
+         carry >>= limb_bits;
+      }
+      m_value[0] &= packed_cpp_int::upper_limb_mask;
    }
    int compare(const packed_cpp_int& o)const
    {
@@ -318,7 +322,7 @@ struct packed_cpp_int
       {
          return m_value[0] & sign_bit_mask ? -1 : 1;
       }
-      for(data_type::size_type i = 0; i < limb_count; ++i)
+      for(typename data_type::size_type i = 0; i < limb_count; ++i)
       {
          if(m_value[i] != o.data()[i])
          {
@@ -344,15 +348,20 @@ private:
 
 template 
 inline void add(packed_cpp_int& result, const packed_cpp_int& o)
+{
+   add(result, result, o);
+}
+template 
+inline void add(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
 {
    // Addition using modular arithmatic.
    // Nothing fancy, just let uintmax_t take the strain:
    boost::uintmax_t carry = 0;
    for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
    {
-      boost::uintmax_t v = static_cast(result.data()[i]) + static_cast(o.data()[i]) + carry;
-      result.data()[i] = static_cast::limb_type>(v);
-      carry = v > packed_cpp_int::max_limb_value ? 1 : 0;
+      carry += static_cast(a.data()[i]) + static_cast(b.data()[i]);
+      result.data()[i] = static_cast::limb_type>(carry);
+      carry >>= packed_cpp_int::limb_bits;
    }
    result.data()[0] &= packed_cpp_int::upper_limb_mask;
 }
@@ -364,9 +373,9 @@ inline void add(packed_cpp_int& result, const boost::uint32_t& o)
    boost::uintmax_t carry = o;
    for(int i = packed_cpp_int::limb_count - 1; carry && i >= 0; --i)
    {
-      boost::uintmax_t v = static_cast(result.data()[i]) + carry;
-      result.data()[i] = static_cast::limb_type>(v);
-      carry = v > packed_cpp_int::max_limb_value ? 1 : 0;
+      carry += static_cast(result.data()[i]);
+      result.data()[i] = static_cast::limb_type>(carry);
+      carry >>= packed_cpp_int::limb_bits;
    }
    result.data()[0] &= packed_cpp_int::upper_limb_mask;
 }
@@ -381,16 +390,19 @@ inline void add(packed_cpp_int& result, const boost::int32_t& o)
 template 
 inline void subtract(packed_cpp_int& result, const boost::uint32_t& o)
 {
-   if(o)
+   // Subtract using modular arithmatic.
+   // This is the same code as for addition, with the twist that we negate o "on the fly":
+   boost::uintmax_t carry = static_cast(result.data()[packed_cpp_int::limb_count - 1]) 
+      + 1uLL + static_cast(~o);
+   result.data()[packed_cpp_int::limb_count - 1] = static_cast::limb_type>(carry);
+   carry >>= packed_cpp_int::limb_bits;
+   for(int i = packed_cpp_int::limb_count - 2; i >= 0; --i)
    {
-      packed_cpp_int t;
-      t.data()[packed_cpp_int::limb_count - 1] = ~o + 1;
-      for(int i = packed_cpp_int::limb_count - 2; i >= 0; --i)
-      {
-         t.data()[i] = packed_cpp_int::max_limb_value;
-      }
-      add(result, t);
+      carry += static_cast(result.data()[i]) + 0xFFFFFFFF;
+      result.data()[i] = static_cast::limb_type>(carry);
+      carry >>= packed_cpp_int::limb_bits;
    }
+   result.data()[0] &= packed_cpp_int::upper_limb_mask;
 }
 template 
 inline void subtract(packed_cpp_int& result, const boost::int32_t& o)
@@ -418,10 +430,21 @@ inline void decrement(packed_cpp_int& result)
 template 
 inline void subtract(packed_cpp_int& result, const packed_cpp_int& o)
 {
-   // Negate and add:
-   packed_cpp_int t(o);
-   t.negate();
-   add(result, t);
+   subtract(result, result, o);
+}
+template 
+inline void subtract(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
+{
+   // Subtract using modular arithmatic.
+   // This is the same code as for addition, with the twist that we negate b "on the fly":
+   boost::uintmax_t carry = 1;
+   for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
+   {
+      carry += static_cast(a.data()[i]) + static_cast(~b.data()[i]);
+      result.data()[i] = static_cast::limb_type>(carry);
+      carry >>= packed_cpp_int::limb_bits;
+   }
+   result.data()[0] &= packed_cpp_int::upper_limb_mask;
 }
 template 
 inline void multiply(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
@@ -447,10 +470,10 @@ inline void multiply(packed_cpp_int& result, const packed_cpp_int<
    {
       for(int j = packed_cpp_int::limb_count - 1; j >= static_cast(packed_cpp_int::limb_count) - i - 1; --j)
       {
-         boost::uintmax_t v = static_cast(a.data()[i]) * static_cast(b.data()[j]) + carry;
-         v += result.data()[i + j + 1 - packed_cpp_int::limb_count];
-         result.data()[i + j + 1 - packed_cpp_int::limb_count] = static_cast::limb_type>(v);
-         carry = v >> sizeof(packed_cpp_int::limb_type) * CHAR_BIT;
+         carry += static_cast(a.data()[i]) * static_cast(b.data()[j]);
+         carry += result.data()[i + j + 1 - packed_cpp_int::limb_count];
+         result.data()[i + j + 1 - packed_cpp_int::limb_count] = static_cast::limb_type>(carry);
+         carry >>= packed_cpp_int::limb_bits;
       }
       carry = 0;
    }
@@ -469,9 +492,9 @@ inline void multiply(packed_cpp_int& result, const boost::uint32_t
    boost::uintmax_t carry = 0;
    for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
    {
-      boost::uintmax_t v = static_cast(result.data()[i]) * static_cast(a) + carry;
-      result.data()[i] = static_cast::limb_type>(v);
-      carry = v >> sizeof(packed_cpp_int::limb_type) * CHAR_BIT;
+      carry += static_cast(result.data()[i]) * static_cast(a);
+      result.data()[i] = static_cast::limb_type>(carry);
+      carry >>= packed_cpp_int::limb_bits;
    }
    result.data()[0] &= packed_cpp_int::upper_limb_mask;
 }
@@ -487,6 +510,7 @@ inline void multiply(packed_cpp_int& result, const boost::int32_t&
    }
 }
 
+/*
 template 
 boost::uint32_t bitcount(const packed_cpp_int& a)
 {
@@ -504,7 +528,6 @@ boost::uint32_t bitcount(const packed_cpp_int& a)
    }
    return count;
 }
-/*
 template 
 void divide_unsigned_helper(packed_cpp_int& result, const packed_cpp_int& x, const packed_cpp_int& y, packed_cpp_int& r)
 {
@@ -722,9 +745,9 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
          t.data()[i] = 0;
       for(int i = packed_cpp_int::limb_count - 1; i >= static_cast(shift); --i)
       {
-         boost::uintmax_t v = static_cast(y.data()[i]) * static_cast(guess) + carry;
-         t.data()[i - shift] = static_cast::limb_type>(v);
-         carry = v >> sizeof(packed_cpp_int::limb_type) * CHAR_BIT;
+         carry += static_cast(y.data()[i]) * static_cast(guess);
+         t.data()[i - shift] = static_cast::limb_type>(carry);
+         carry >>= packed_cpp_int::limb_bits;
       }
       t.data()[0] &= packed_cpp_int::upper_limb_mask;
        //
@@ -837,26 +860,26 @@ inline void modulus(packed_cpp_int& result, const packed_cpp_int
 inline void bitwise_and(packed_cpp_int& result, const packed_cpp_int& o)
 {
-   for(packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(typename packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
       result.data()[i] &= o.data()[i];
 }
 template 
 inline void bitwise_or(packed_cpp_int& result, const packed_cpp_int& o)
 {
-   for(packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(typename packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
       result.data()[i] |= o.data()[i];
 }
 template 
 inline void bitwise_xor(packed_cpp_int& result, const packed_cpp_int& o)
 {
-   for(packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(typename packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
       result.data()[i] ^= o.data()[i];
    result.data()[0] &= packed_cpp_int::upper_limb_mask;
 }
 template 
 inline void complement(packed_cpp_int& result, const packed_cpp_int& o)
 {
-   for(packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(typename packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
       result.data()[i] = ~o.data()[i];
    result.data()[0] &= packed_cpp_int::upper_limb_mask;
 }
@@ -1073,8 +1096,8 @@ public:
 };
 
 template 
-typename numeric_limits > >::initializer
-   typename numeric_limits > >::init;
+typename numeric_limits > >::initializer const
+   numeric_limits > >::init;
 }
 
 #endif
diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp
index b02ac616..1d53c89c 100644
--- a/performance/performance_test.cpp
+++ b/performance/performance_test.cpp
@@ -109,6 +109,26 @@ struct tester
       }
       return boost::chrono::duration_cast >(w.elapsed()).count();
    }
+   double test_add_int()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] + 1;
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
+   double test_subtract_int()
+   {
+      stopwatch w;
+      for(unsigned i = 0; i < 1000; ++i)
+      {
+         for(unsigned i = 0; i < b.size(); ++i)
+            a[i] = b[i] - 1;
+      }
+      return boost::chrono::duration_cast >(w.elapsed()).count();
+   }
    double test_multiply()
    {
       stopwatch w;
@@ -296,6 +316,8 @@ void test(const char* type, unsigned precision)
    tester::value> t;
    std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "+" << t.test_add() << std::endl;
    std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "-" << t.test_subtract() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "+ (int)" << t.test_add_int() << std::endl;
+   std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "- (int)" << t.test_subtract_int() << std::endl;
    std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "*" << t.test_multiply() << std::endl;
    std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "/" << t.test_divide() << std::endl;
    std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "str" << t.test_str() << std::endl;
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 9fed404a..b3f0be1c 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -600,8 +600,8 @@ run packed_int_test.cpp gmp
         : # input files
         : # requirements
          [ check-target-builds ../config//has_gmp : : no ]
-         release  # otherwise runtime is too slow!!
-        : packed_int_test.cpp ;
+         release  # otherwise runtime is too slow!! 
+         ;
 
 run test_rational_io.cpp $(TOMMATH)
         : # command line
diff --git a/test/packed_int_test.cpp b/test/packed_int_test.cpp
index 68314b9f..f895c142 100644
--- a/test/packed_int_test.cpp
+++ b/test/packed_int_test.cpp
@@ -11,36 +11,12 @@
 #  define _SCL_SECURE_NO_WARNINGS
 #endif
 
-#define BOOST_CHRONO_HEADER_ONLY
-
 #include 
 #include 
 #include 
 #include 
-#include 
 #include "test.hpp"
 
-template 
-struct stopwatch
-{
-   typedef typename Clock::duration duration;
-   stopwatch()
-   {
-      m_start = Clock::now();
-   }
-   duration elapsed()
-   {
-      return Clock::now() - m_start;
-   }
-   void reset()
-   {
-      m_start = Clock::now();
-   }
-
-private:
-   typename Clock::time_point m_start;
-};
-
 template 
 T generate_random(unsigned bits_wanted)
 {
@@ -79,7 +55,6 @@ int main()
 {
    using namespace boost::multiprecision;
    typedef mp_number > packed_type;
-   stopwatch w;
    unsigned last_error_count = 0;
    for(int i = 0; i < 1000; ++i)
    {
@@ -143,7 +118,6 @@ int main()
          std::cout << "a1%d1  = " << a1%d1 << std::endl;
       }
    }
-   std::cout << w.elapsed() << std::endl;
    return boost::report_errors();
 }
 
diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp
index 59afe975..fb098b31 100644
--- a/test/test_float_io.cpp
+++ b/test/test_float_io.cpp
@@ -212,7 +212,11 @@ template 
 void do_round_trip(const T& val, std::ios_base::fmtflags f)
 {
    std::stringstream ss;
+#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST
    ss << std::setprecision(std::numeric_limits::max_digits10);
+#else
+   ss << std::setprecision(std::numeric_limits::digits10 + 5);
+#endif
    ss.flags(f);
    ss << val;
    T new_val = ss.str();
diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp
index 93a33fb3..ffd7d063 100644
--- a/test/test_int_io.cpp
+++ b/test/test_int_io.cpp
@@ -60,7 +60,11 @@ template 
 void do_round_trip(const T& val, std::ios_base::fmtflags f)
 {
    std::stringstream ss;
+#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST
    ss << std::setprecision(std::numeric_limits::max_digits10);
+#else
+   ss << std::setprecision(std::numeric_limits::digits10 + 5);
+#endif
    ss.flags(f);
    ss << val;
    T new_val = ss.str();
diff --git a/test/test_rational_io.cpp b/test/test_rational_io.cpp
index 7b1d4290..05c037c7 100644
--- a/test/test_rational_io.cpp
+++ b/test/test_rational_io.cpp
@@ -64,7 +64,11 @@ template 
 void do_round_trip(const T& val, std::ios_base::fmtflags f, const boost::mpl::true_&)
 {
    std::stringstream ss;
+#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST
    ss << std::setprecision(std::numeric_limits::max_digits10);
+#else
+   ss << std::setprecision(std::numeric_limits::digits10 + 5);
+#endif
    ss.flags(f);
    ss << val;
    T new_val = ss.str();

From 44d5a3e3942b65167dae35a0c918dfcb3ce41257 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Wed, 11 Jan 2012 19:09:49 +0000
Subject: [PATCH 095/256] Change tests for faster compile times.

[SVN r76412]
---
 test/Jamfile.v2    |    4 +-
 test/test_atan.cpp |  108 ++---
 test/test_cos.cpp  |  316 +++++++-------
 test/test_cosh.cpp |  108 ++---
 test/test_exp.cpp  |  108 ++---
 test/test_log.cpp  |  212 +++++-----
 test/test_pow.cpp  | 1006 ++++++++++++++++++++++----------------------
 test/test_sin.cpp  |  316 +++++++-------
 test/test_sinh.cpp |  114 ++---
 test/test_sqrt.cpp |  206 ++++-----
 test/test_tanh.cpp |  106 ++---
 11 files changed, 1302 insertions(+), 1302 deletions(-)

diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index b3f0be1c..c06d453b 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -25,7 +25,7 @@ project : requirements
    msvc:static
    ;
 
-local disable-specfun = [ MATCH (--disable-specfun) : [ modules.peek : ARGV ] ] ;
+local enable-specfun = [ MATCH (--enable-specfun) : [ modules.peek : ARGV ] ] ;
 local disable-concepts = [ MATCH (--disable-concepts) : [ modules.peek : ARGV ] ] ;
 
 
@@ -640,7 +640,7 @@ run ../example/tommath_snips.cpp $(TOMMATH)
          [ check-target-builds ../config//has_tommath : : no ] ;
 
 
-if ! $(disable-specfun)
+if $(enable-specfun)
 {
 
    for local source in [ glob math/*.cpp ]
diff --git a/test/test_atan.cpp b/test/test_atan.cpp
index 2c0bf6ee..7dadf291 100644
--- a/test/test_atan.cpp
+++ b/test/test_atan.cpp
@@ -68,59 +68,59 @@ struct is_mpfr_type
 void test()
 {
-   static const boost::array data =
+   static const boost::array data =
    {{
-      T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999966666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-101"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666668666666666666667e-97"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666686666666666666666666666666666667e-93"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999966666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666866666666666666666666666666666666666666666666667e-89"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666668666666666666666666666666666666666666666666666666666666666666667e-85"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666686666666666666666666666666666666666666666666666666666666666666666666666666666667e-81"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999966666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-77"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666668666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-73"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666686666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-69"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999966666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666665238095238095238e-65"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666668666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666665238095238095238095238095238095238095238e-61"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666686666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666665238095238095238095238095238095238095238095238095238095238095238e-57"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999966666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666665238095238095238095238095238095238095238095238095238095238095238095238095238095238095238e-53"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666668666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666665238095238095238095238095238095238095238095238095238095238095238095238095238095238095238095238096349206349206349e-49"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999666666666666666666666666666666666666666666666666666666666666666666666666666666666666666686666666666666666666666666666666666666666666666666666666666666666666666666666666666666665238095238095238095238095238095238095238095238095238095238095238095238095238095238095238206349206349206349206349206349206349206349206349e-45"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999999999999999999966666666666666666666666666666666666666666666666666666666666666666666666666666666866666666666666666666666666666666666666666666666666666666666666666666666666666665238095238095238095238095238095238095238095238095238095238095238095238095238095249206349206349206349206349206349206349206349206349206349206349206349206349206349e-41"),
-         T("9.99999999999999999999999999999999999999999999999999999999999999999999999666666666666666666666666666666666666666666666666666666666666666666666666866666666666666666666666666666666666666666666666666666666666666666666666523809523809523809523809523809523809523809523809523809523809523809523809634920634920634920634920634920634920634920634920634920634920634920634920544011544011544011544011544011544011544e-37"),
-         T("9.999999999999999999999999999999999999999999999999999999999999999666666666666666666666666666666666666666666666666666666666666666686666666666666666666666666666666666666666666666666666666666666665238095238095238095238095238095238095238095238095238095238095238206349206349206349206349206349206349206349206349206349206349206340115440115440115440115440115440115440115440115440115440115440116209346209346209e-33"),
-         T("9.999999999999999999999999999999999999999999999999999999966666666666666666666666666666666666666666666666666666666866666666666666666666666666666666666666666666666666666665238095238095238095238095238095238095238095238095238095249206349206349206349206349206349206349206349206349206349115440115440115440115440115440115440115440115440115440116209346209346209346209346209346209346209346209346209346202679543e-29"),
-         T("9.99999999999999999999999999999999999999999999999666666666666666666666666666666666666666666666666866666666666666666666666666666666666666666666666523809523809523809523809523809523809523809523809634920634920634920634920634920634920634920634920544011544011544011544011544011544011544011544011620934620934620934620934620934620934620934620934554267954267954267954267954267954267954267954268013091483679719e-25"),
-         T("9.999999999999999999999999999999999999999666666666666666666666666666666666666666686666666666666666666666666666666666666665238095238095238095238095238095238095238206349206349206349206349206349206349206340115440115440115440115440115440115440116209346209346209346209346209346209346209279542679542679542679542679542679542679548561895620719150130914836797189738366208428128459088211410192834341441152586663e-21"),
-         T("9.999999999999999999999999999999966666666666666666666666666666666866666666666666666666666666666665238095238095238095238095238095249206349206349206349206349206349115440115440115440115440115440116209346209346209346209346209346202679542679542679542679542679542738366208954444248561895620719149604599047323505527839893164970569113274066834438351466215243304983108499463325146458811824271509689681318218133e-17"),
-         T("9.999999999999999999999996666666666666666666666668666666666666666666666665238095238095238095238096349206349206349206349205440115440115440115440116209346209346209346209345542679542679542679542680130914836797189738366208428128459088211410192834817631628777139613052925311641589740930163598087002528653948764327011735444703713649735994600714288656350334489593033695272837185114343249547095046272603174268e-13"),
-         T("9.999999999999999666666666666666686666666666666665238095238095238206349206349206340115440115440116209346209346209279542679542679548561895620719149604599047323505575458940784018179051162265592202726621494746410579611835097095566286199717626418813764642659343446728207455753397291482030056516178836684094391777365260695851470017381944166954115569576329193296454393446430574957840819236721213626802085619e-9"),
-         T("0.00009999999966666666866666665238095249206349115440116209346202679542738366208428128463850116128619335776637836253560167434464812879197215298894881707269927081030999737549925482008672363799937606915962379247584324159094536421375755997513179578610677454920512897850953612762990732913046921088456079984429888220262137400213929962691532176198436788640624698990926490105259050461938357510947570244880435664081"),
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+         "0.78539816339744830961566084581987572104929234984377645524373614807695410157155224965700870633552926699553702162832057666177346115238764555793133985203212027936257102567548463027638991115573723873259549110720274391648336153211891205844669579131780047728641214173086508715261358166205334840181506228531843114675165157889704372038023024070731352292884109197314759000283263263720511663034603673798537790236",
+         "1.5706963267952299525626550249873704896065212085331517483940102693584808194810202180293789115097723406333076648941055516492022741759833189628737308869915412879148320539754700057326930986734751013960313584219296445913757777000240665569182597868494941800236191544832206381775972559949762275927455637707925634113006817837919481411335451596526426779712759369563859151046126747697908496855825977735219514481",
+         "1.5707963167948966192313220249730847754318980330208862438222342009158129649367552929648110725556184185509578339104318071142673796252326115673007840833450909541260947278453938016119958041324233151995987794877839930865561434524027270213271053829179745357590596408023867275770197075707094053216000680544580256094089113804288267449089904640326828789035666143699659867092108718279796583028512542392495421779",
+         "1.5707963267938966192313216916397514424319180330208862438208054294872415364764378326474936031472490101815502336217205184029120016698547471043186681600526965471042074304163483259318452680435202095109230279463923963492870040904012032740805456738144599352893425202988524603439218707929425378295371082108281620406379082813613862672159901100496534463976107550806601465567059619048829495421806391510160463001",
+         "1.5707963267948965192313216916397514420985846996878862438208056294872415364764378306473507460043918673244073765899887723711659699238229101634817272120007484952330785592874771970616254211570733230640365810600043257395046296021443620234312981206088055277773974880349347475097997796620171523611445056144296707974573126845590321623615288317089359131170138395627805178532322154433252386274406088878525130896",
+         "1.5707963267948966192213216916397514420985846996875529104874726294872415364764378326473507460043918673044073765899744866568802556381086244491974416088261453206299039561128740224575416159622681282588417758651991386266175167241223840014532761425201608391327088433455208280958809539778973505942839152244275827508237604782514078980809178018719474972957865632271450490908284680846718670522639450168825443945",
+         "1.5707963267948966192313206916397514420985846996875529104874722961539082034764378326473507460043918673244073765899744866566802556381086244491960130373975738920584753846844454510289702985019506679413814584048816783091570881436029034819727566620006803196521893628268096302936831517800951527920861130266253182819592915368594665061395258604800061112367475630116742454513973110064559653064241192080164878504",
+         "1.5707963267948966192313216915397514420985846996875529104874722961539082031431044993143507460043918673244073765899744866568802556381086244491940130373975738920584753846843025938861131556448078107985386012620245354520143421118568717359410106302546485736203322199696666822417350998320432047401380610785733702300121487566396862863593060802602258914565277827918940256045031718123167711672299800138772937113",
+         "1.5707963267948966192313216916397414420985846996875529104874722961539082031431044993140174126710588673244073765899744866568802556381086244491960130373975738920584553846843025938861131556448078107985243155477388211663000563975725860216552963445403628593347290453664920790671319252288686015654237753642876559442969539514448810915541112750654206966513329776061797398902251498342947931452519580358553156893",
+         "1.5707963267948966192313216916397514410985846996875529104874722961539082031431044993140174126710585339910740435899744866568802556381086244491960130373975738920584753846843025938861129556448078107985243155477388211663000563975711574502267249159689342879063004739379206504957033538002971729941063150468273384839794936339845636311255398464939921252227615490256602593707446303537753126257714385553358352607",
+         "1.5707963267948966192313216916397514420984846996875529104874722961539082031431044993140174126710585339910740432566411533238802556381086244491960130373975738920584753846843025938861131556448078107985243135477388211663000563975711574502267249159689342879061576167950635076385604966574543158512491721896844813411223507768417064883795081004622460934767298029939142275136017732109181697686285814124786923127",
+         "1.5707963267948966192313216916397514420985846896875529104874722961539082031431044993140174126710585339910740432566411533235469223047756244491960130373975738920584753846843025938861131556448078107985243155477388211663000563775711574502267249159689342879061576167950635076385604966574400301369634579039701956268380650625559922026652223861765318077624440887081999419104271700363149951654539782378755175984",
+         "1.5707963267948966192313216916397514420985846996865529104874722961539082031431044993140174126710585339910740432566411533235469223047752911158626800373975738920584753846843025938861131556448078107985243155477388211663000563975711574502267249157689342879061576167950635076385604966574400301369634579039701956268366364911274207740937938147481032363338726601367713704818557414648864237368825496664469462809",
+         "1.5707963267948966192313216916397514420985846996875528104874722961539082031431044993140174126710585339910740432566411533235469223047752911158626797040642405590584753846843025938861131556448078107985243155477388211663000563975711574502267249159689342879061576167930635076385604966574400301369634579039701956268366364911274207740937938147479603791910155172796285133390128843220292808797396925235898034238",
+         "1.5707963267948966192313216916397514420985846996875529104774722961539082031431044993140174126710585339910740432566411533235469223047752911158626797040642405587251420513513025938861131556448078107985243155477388211663000563975711574502267249159689342879061576167950635076385604966574200301369634579039701956268366364911274207740937938147479603791910155172796285133389985986077435665940254068093055177095",
+         "1.570796326794896619231321691639751442098584699687552910487471296153908203143104499314017412671058533991074043256641153323546922304775291115862679704064240558725142051350969260552780155644807810798524315547738821166300056397571157450226724915968934287906157616795063507638560496657440030136963457903969995626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138",
+         "1.570796326794896619231321691639751442098584699687552910487472296053908203143104499314017412671058533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477798524315547738821166300056397571157450226724915968934287906157616795063507638560496657440030136963457903970195626836636491127418774093793814747960379191015517279628513338998598607743566594025406809304089138",
+         "1.570796326794896619231321691639751442098584699687552910487472296153898203143104499314017412671058533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214738821166300056397571157450226724915968934287906157616795063507638560496657440030136963457903970195626836636491127420774093793814747960359191015517279628513338998598607743566594025406809304089138",
+         "1.570796326794896619231321691639751442098584699687552910487472296153908202143104499314017412671058533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832967056397571157450226724915968934287906157616795063507638560496657440030136963457903970195626836636491127420774093793814747960379191015517279628513138998598607743566594025406809304089138",
+         "1.570796326794896619231321691639751442098584699687552910487472296153908203143004499314017412671058533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824450226724915968934287906157616795063507638560496657440030136963457903970195626836636491127420774093793814747960379191015517279628513338998598607743566592025406809304089138",
+         "1.570796326794896619231321691639751442098584699687552910487472296153908203143104489314017412671058533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582968934287906157616795063507638560496657440030136963457903970195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138",
+         "1.570796326794896619231321691639751442098584699687552910487472296153908203143104499313017412671058533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954573157616795063507638560496657440030136963457903970195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138",
+         "1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017312671058533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730507638560496657440030136963457903970195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138",
+         "1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017412661058533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730174305227163657440030136963457903970195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138",
+         "1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017412671057533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730174305227163324106696803963457903970195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138",
+         "1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017412671058533891074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730174305227163324106696803630124570637195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138",
    }};
 
    T arg = "1e-100";
@@ -129,12 +129,12 @@ void test()
    for(unsigned k = 0; k < data.size(); k++)
    {
       T val = atan(arg);
-      T e = relative_error(val, data[k]);
+      T e = relative_error(val, T(data[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
       val = atan(-arg);
-      e = relative_error(val, T(-data[k]));
+      e = relative_error(val, T(-T(data[k])));
       err = e.template convert_to();
       if(err > max_err)
       {
diff --git a/test/test_cos.cpp b/test/test_cos.cpp
index 1ce8baaa..1bc55918 100644
--- a/test/test_cos.cpp
+++ b/test/test_cos.cpp
@@ -47,109 +47,109 @@
 template 
 void test()
 {
-   static const boost::array data =
+   static const boost::array data =
    {{
-         T("-2.37609908807915949996042688873953402912174184373388399043229539427530802169622688886435380890546981798452174137747437590e-1"),
-         T("8.03406366226813589517543567844755380935198206635917017883860879215939165740799963435747185200486086864198723786516760875e-1"),
-         T("8.60219386510802105228997694366289682807721120146423711696179175800635220710279361583231346318224971127450760223168489952e-1"),
-         T("-1.36768951513839774357595871594675554406872039078811749027554673949684004409484639336417431285061889554892096426752261915e-1"),
-         T("-9.66210139195431691033548069227792927999642647449593184440815029076272297050360196975341458076547426373476590671462150981e-1"),
-         T("-6.12007278553856790723803948280976098970972124581361775428331444376106018942231526074915731012122426588769327127413045994e-1"),
-         T("4.91927698740873688392439262912409276430264703350691359723802294639643655296838880236042651349290074585311025856549893171e-1"),
-         T("9.93232596718899824059271235487971663771012607519717340071654721877802691370866768064059943491135925674950430467047724563e-1"),
-         T("2.77789911520199551017947550534057049374212876971194676010301098598339529915403722848373365985645657342475739669568931563e-1"),
-         T("-7.77955945956221239101360662190442739163791527953499629555756394261998892874934847131138921705713935365505245406994428077e-1"),
-         T("-8.80676278306736581575818642341143682410874043182925227659938804267878718513212454821032629378618345485453587099696563832e-1"),
-         T("9.54652155963865007116798560589970996367213754762169439269792747771200843006278637115722685610960738675814993576019945344e-2"),
-         T("9.54658201427917718824191302196929158303422390793460018465335986921801519149657723689322277773550748806000948225466432438e-1"),
-         T("6.44358700620889799575033272322899136331490664925359198096632560532437137894857803619177106562399406351419810452110265174e-1"),
-         T("-4.55304635273050571206400777159475409897339683148730716647371922365967582339285347105376503917296765204188604297021364549e-1"),
-         T("-9.97202532932553753622481171186283382950122646390227670693679248197349800205205290898290539070732778341271049474946533154e-1"),
-         T("-3.17489525058325500707686194437148362752290391406825231198381521862930317513649081353670386166519524315810546189268634469e-1"),
-         T("7.51160186640147504067744846462384089742696250681200524524912647858645140367792164416711871535116761744380912486921554617e-1"),
-         T("8.99610194168373157174515848193119670768490559799348397680196213249921436405001710937402190319584272526657508442591319630e-1"),
-         T("-5.39963892484342940823660554048696208293700871414984387094529796385334086703752106515008832585578915389731907422242902573e-2"),
-         T("-9.41455348900839346761557896365239742769987576963330061702397697388879776230596944312519157729410022380228287314835345969e-1"),
-         T("-6.75595816763857390859268297670835380459024839344154743310231115864242050771191159334664874097564054770066166961642073448e-1"),
-         T("4.17894201894880415042381733708896725748531223743344790054523182948440843948904650988733732381978194392219295696279423635e-1"),
-         T("9.99447981389824371458566861195586395552622718284098766856978062347139060489410032781030191080200904443096549587568037683e-1"),
-         T("3.56640095868759075150409032448421838265699043643228482503057299699740924345262819242042067863780263400092250418388628640e-1"),
-         T("-7.23065426868134142613141384486526262450487633432466529798821958977732347646832059032382447792655111641456570392189752211e-1"),
-         T("-9.16988391192434436877664999042786024703848714036221388727578305299843547352325574309860356272561772723624753484063972217e-1"),
-         T("1.24341855683226931265962750806821531283439413068694552738675989282017066737438591268502070364982899342633928417210588531e-2"),
-         T("9.26624413643579136646620112107410908114766812511471130116341925013001661546817531064974089666536893346764523464250445838e-1"),
-         T("7.05664607841658050248613256866289182754229289446384595719719495272020558391145537620968819401219414243210529013148958366e-1"),
-         T("-3.79761093422301890838671114556341706055562482358183402807224298533060188038450560241345615647754569347252101282386222173e-1"),
-         T("-9.99965058979463689113370264378210962384824970050865061898892508056811665771886385589295806419278045318841717598003331419e-1"),
-         T("-3.95173919871548266286836251448043149039940610894391718791244019288314418437411707835924620250473697245151743147215758686e-1"),
-         T("6.93720251624319621941983929806434090162802383400620564454074825718151625795576680427510026452063593762417421561201654156e-1"),
-         T("9.32780816819880202610269817418700102084277332259524791943833699964920012022753227823298655560837271746316929623378078695e-1"),
-         T("2.91495208658083070508005579692813621670878962971611104453227900103973434149303469066898102622556226584993895360896300290e-2"),
-         T("-9.10191043170480685360743788297835112117551819731152897291272407935139876953384666161532187572493791297095784055525159185e-1"),
-         T("-7.34513075127503122343910106816656237074878218180284276449954797048122379869002663646507706411949095015624141821039453971e-1"),
-         T("3.40971254411713599427147477626159847871020791931107106418841144080445813896332252160005593096670674809345703079384115052e-1"),
-         T("9.98752871506016936810666998588493462933191829230756181478046320353377054175122206889047094521687205093218701141334147081e-1"),
-         T("4.33024359542714849537532946954507232835434973891665238942502273464321666207117525270650546741831354943253652514490075246e-1"),
-         T("-6.63175408268187738636594884921931867786416057472876635147295424128144233911929585327601381618059327766986981109409782838e-1"),
-         T("-9.46960160806563725719808910991708075372282242401645009270517113290439792088443109178772446465191984149998211903724560065e-1"),
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+         "-4.99188570507651271652464431008309802023236218596632956064119419694573621896525872847587264755853127438644874992889777436e-1",
+         "6.05374785886620830935500306718810628353011877048386199574451402773468315797082901705593423724389976967865835641164117478e-1",
+         "9.68331080574540181354402420018944004334504868848934676984951546671476956051983469715128604348963016773169794077158289730e-1",
+         "1.45045093347669933436797325432376656017480150281100519869038554695618054318368975927557872948037203212941966706926758604e-1",
+         "-8.55926631706799584065153976496431313099942493164544290051315786450857575707615522517293656706329757352795226750189755758e-1",
+         "-8.08355785820466703104647317116964786017731181599256098405978700298563758509572188640629418770593008092680980412866065299e-1",
+         "2.29481541445091823694157468006983283649885473964756916206813927875661041834620526229807744443043682778028709792615798955e-1",
+         "9.86195281084368344446227722442335005500018635181693920385626820970119467136148305491035657795704047666385553672680209923e-1",
+         "5.34782415974986828906369231191245075731384342252264783019973387059318216570499447505623911253042567598873910043381675873e-1",
+         "-5.71759181631212640256161075896307515511612057247572886814941945052483422285718810088660759708176904381865453799197101481e-1",
+         "-9.77874107069129472007009478090869879295520839405452365411822873037906082086100232576241983901051327761231156641104065497e-1",
+         "-1.86056181372276495846711248156316208757691570931906856005697361080864028851991674077024223201008430626166447144444086146e-1",
+         "8.33687619660983803179149188531271900120055171980951416163724579833511897001564116810390933587615557717585362295882429826e-1",
+         "8.32132482562487183916482822112362004641509381783438374175226355792137053285527706239574867923387554339582561002247202518e-1",
+         "-1.88816490768820368180947188938258919466912959009058295775702554895970560887437777994365295452696990115940651570073217522e-1",
+         "-9.78458105113103660973458641126689066610890753079836635611789969774219913050456840122278188955139015473252491612410972950e-1",
+         "-5.69451448580118869157805059117807250106203230622762838051154208713065707949727035884250775206017528612930773233017928006e-1",
+         "5.37154819650306918873973169624898539483418364490295996462663218848771864764982600193558748568095521886456306061269765631e-1",
+         "9.85726070946814004698231423834505649751779161578718404221294527194525251740198034173542003704080544827976936213857653517e-1",
+         "2.26745517700332138489400566746499809209783385009289423848083137846668382711005704387134606000570923556980021574851618566e-1",
+         "-8.10006890365888881023982873786181048364505748637138923322482323010218991062084191379116946709356002103893071903481540337e-1",
+         "-8.54470151393449484710948210543666267680196067632693416660536443330720708402601669617638569732848938319544250428600991723e-1",
+         "1.47824914922605209542648603104533928946885824995208478684499907657728115943168395067575842431291755277452367320596435067e-1",
+         "9.69028856602232134498324179654622883463820270279077886397861028881882684131282848087869087883519707948141915733221980948e-1",
+         "6.03135714281336943093251136556365407562473924416812270469171432809743173719168209727199952532489544254928975940518615351e-1",
+         "-5.01621542149055350065079347615664213658089623368745676779267390227688581807037821041573344917735076902116221444127518632e-1",
    }};
 
    boost::uintmax_t max_err = 0;
@@ -157,12 +157,12 @@ void test()
    {
       static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1";
       T val = cos(euler_gamma * ((100 * k) - 5000));
-      T e = relative_error(val, data[k]);
+      T e = relative_error(val, T(data[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
       val = cos(-euler_gamma * ((100 * k) - 5000));
-      e = relative_error(val, data[k]);
+      e = relative_error(val, T(data[k]));
       err = e.template convert_to();
       if(err > max_err)
          max_err = err;
@@ -170,59 +170,59 @@ void test()
    std::cout << "Max error was: " << max_err << std::endl;
    BOOST_TEST(max_err < 5000000000ULL);
 
-   static const boost::array near_one =
+   static const boost::array near_one =
    {{
-      T("0.001103662615143147017601393734232421549156847219973314118949247990939859507971857976111288683988415478257878902917354105871236439563170045857810738102729287303674642020538722348587741395785016549139854168605590336633274890874911975139498047488076101124170425114828336211817830671418321600962996502656221412102902998671173649312277667706874059520046508702908872747388744526457997404065469953155187340837"),
-         T("0.0030157041572432190019717764776322147049224887913331212054173669461673516770769148735558540290915754514269097799280330158745508542936966046640795712691698490758472574837678659161855207596563250546269614348515005196657786359646020537231301121492728577410212550350070502426482802490452572415879214994201864402901595309726458026672888041860289772080407882673424767232857435141510615538430445535588448032261"),
-         T("0.0049277346741750694119109616231402901360500185022482787362616412856233338679208830974124749830793778323997684640684587346403570647040211088376986993615001420565608501262335822815041623056442245053684626079448221530207757672939048030945164948521320401574074802966260975904478775314730002799895049652983052125151436511589335123254582883803928373794668948878049089088843407672795237410750365571990834236348"),
-         T("0.0068397471757112108044544339281399968563253858411528016363900245610068161564091499398024110635089866212789583403491711476788985949178019078796740862827299289838108117219486357027460681238178010067475221327133396780718266880540272936860185783976937569903778160170225166328920201699827472893824363838439627437187765159770262282930293057633886299749088561182830982345936603553661004526800797082995898813903"),
-         T("0.008751734671690018552720976028788304981263251327799787402847843531098338033456389098956160956160597460869666211569183483587979772678557230743050583975270977754518475970489741156524119378847305446845331098526962579804361960647344836744631465315238254178161716870409320747176674142306881908614436607977326507761331050644035013756409444911127742401762647885817361924274132830920030936589562922803846509607"),
-         T("0.010663690172041286306192948782895990881227033104763005629047563262531418373465237876680529005058533981010793759446966868628480908709812402179047774888094761104238131843239037167212206469894485599085717216855637620318723457013401360290343196462723174177342294339229792213396006286331141933952648238459364417067676760977202812721209681621184724443514062993874571816382775241753902032787099435678672474841"),
-         T("0.012575606686811781116778815864446643746718166744927923785139233710240017201737625088406861185781739628293213436323314376708933534933748436720721568462267317026688561438144113855290140925120435317506169856461386623828941531577425811393721991195661429557079268566156800689149725770186985872449679872155877537432897653904213375816262709009448220490217917537801655330411526526290708967440087145630462068976"),
-         T("0.014487477226190798137230457835664944872810802211308342685055637400305474021552028493778559102552025380880477103065187688337931713540557562373991431880251553620947836940726544553647739994157300967262941976933375115946629204615918888689039777423610894099269527633757403818072000860056651445780074486612843419789636984117740884711882675016016919064788076097669389652323393864660933705259163296837955978748"),
-         T("0.016399294800535714798489384358524900105286836154421890562438917862501411947245037986455919696365301666112414890097246479762149456962809638588245466988584093380263545543023411087203351948681559905336010066900667101787138862856447778428938265451537422367650992162004154495705878092019403922006152498705687706013973674800621422751806347308220226407830977673540994341535381202679482907460136241543505771361"),
-         T("0.018311052420397544372537858201001145083914223029622271478159852925692124442640247100336262041440360412392318902558295108452513123454103504516607498763863728284797202978975409264141138861738184468257576157204552383675442780049333490201800526935793000727771598103735596829143729912656158790924063286176336412427525710457367751437348230246446466833498557166002214984255422115833828533909144072330080184872"),
-         T("0.020222743096546488827333191237246591760639730704704148795009602627175281013458865557238240830203973690492882935553111519759474835556686812553430134442713057622274348510526931333124437928482001301214776111358848026164688447150395879262705323533149853785508106018564787140458587165768350143018847840661371060583295055600185059031740386698369796694993301139380463919242175430688496936048982929502368583755"),
-         T("0.022134359839997490880406060727014362125793630864951833270601574861700025448109186301755833862830343973100181180995751924514611578149687732808840212399134735559355116816700346196685057916461444889179117142807858883574426062415931319905031345377305247124198345242221848293630112578508459623098934259229893301963120289071135120089672338617200639338087265986570094025605269870532431816151660553037324591448"),
-         T("0.024045895662035785157706623778569329505432699504171659064296747761761946910295074291838826981712792368282349553905175996858645967280135417577488810651594776626562252686758463813820791031580579721782251705600570838044158357396828391251385978824608388341556751951593319015721256942139947235672567093309227673005475237474351604086627391812539914665025071874865132198040631867741985556198082915821590691115"),
-         T("0.025957343574242448364285479040344211549214421772336408904791690210449825580868841229728937909141136116652894475476991471494524501035809956288247010861464302066154254736425460468024350571584780489213056428098560686376999562953811729945811217829999284678155635497607933780499844559793793320393174691097636750027421158473345884329284455326733063073401001936304522649050748641723222539485352644237494855455"),
-         T("0.027868696588519948373400137317728007608587427701668964330844960393232962659347088604492706251530487148805683505883152882204177723404307465324383408418716579280515871949790204586171885981761699066301009410176801635003961167315448162116236938093263170474354430610732127054993766008385425707409224417795873645410443727472246508894027549288331903202127478347028519320691939639175445464091747341289465807076"),
-         T("0.029779947717117692140641616959423088975059158964671307393654571763491553590582559015283533532986018614029995854278748039155177088839414450454409571267110720713374288363670804692289394770804051182510495900322915294613479146430103948686457060129295537542317247965142780968717375277053102667416124807987527429828758851341378395347636356414345553353015296944031211364374602764176767114282660874356057979248"),
-         T("0.03169108997265757234968007548831539092664261419258315028339932724609641378752993073240305448323210275610250474048387518003293691429670190316839718892647475151605557113852966925288722557261748981001717642661075734993748510506277165730472207647763678204813714194082852502621623007244214605646094787730992510318924772328958129857640953691466395972638014259980360897599169526022683004620965496473543834477"),
-         T("0.033602116368159512696233026049065446239504816931754722314316906991719894135599777826750609185018647633748023602662568553364455253741994701511752478506175671449029859193583332380924298164350627023797218098539441228986492601142199774579432202424360114528105854714450548265654769162069979862894518829365029262734944196495563243510942310738160350648115273816371164862001848102516957052031698646996790510953"),
-         T("0.035513019917067011716864665791693591701266221069066142988726516832036728613300457006403299601385922973285573124147669717618486570986860008564309641657943172757912451506572783449830586163814477502720341010870119231030511664725149033496023356743601581035789746158436049009960920433265660001864258067191594425969638702851317416487965304378219676062220223886417078628342731900948906319081697480745936074075"),
-         T("0.037423793633272685069230163289099410548201460485083250584815890545695501760634737348027106921155349564805321222282824709072582234185849564440670000847571561359324629877368620222775856068569278590582843550096096627510109210574429458414697641703261368397349100700647508781941466979105505468662952228018391181441110331804231754679360190526351574820397399161022517352576803713854137820941977691824804918229"),
-         T("0.039334430531143806170384413477273936914540782490679532559795199052084263353981243128408259086619593938946158294175465792633584421592350011455198124846778194417281005620258982615227234871780679327289232072858751285307955384102986030326321993554199425677956531006546270705693578070953933490084008156062047268010604414954653769711129551190023978078265436680151306319349753427763894284339669614362603225399"),
-         T("0.041244923625547845099780771389235760645292527949481044094490883777921290140650504322516472637184803214130714431279474404434513167088543202171922178874118967991301744186858054508473413647148744260057423931033177973119110921967581379650616945061418716237102199971097086754171168500651650526166023618723542873290120298640370217463634503988257867984189842393302366909916756244585593509804376197012137137735"),
-         T("0.043155265931878005673591620105503250213648422568500347993529171942176855000247082147052189275394127432389966427668413127665366489709229602926384588361071126297040547180622989395253518259197742053810419372452372506534313264090033740095357809571640645325965973975968081307185286025492280541542290934505383760407808393490207181258819590768103829347539943429968533891105456889889207923129412409325200337396"),
-         T("0.045065450466078760596989313842010956972889269629840996618541471076456145341576346037140737554087089598232657340541865108389258265511462307708855932308284610805209084413460614598570062354088931179587984702006847566162492414964136182928014974554852612762940578089297583097434972291633301329615187665009664697057933900728259220674217919826618275818024987757805509580781060051826778978395144370327934582031"),
-         T("0.046975470244671384601033063916347240271496301008030038885300525267985292259051299166038486168462131096926077920611254966322965395673221324506213593415263189667393727124978454125104192236004303056348320706091018781990803164595039969574510002737990997634364247271320535459089400357647302806652831431190979518269432197656547265417669309719787317687585776029758282182901563328846367691507505917911626458378"),
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-         T("0.050794987604154532871523976044438688478988546522275702591135165295075684834775069782087540212155311599924632216878717363279038406203747968637573994688146329296755023729170505930935028107359530042909822369245609091696704070694133386183688825674952803613566914142157159664703170379754943610785780639205752343103591085978554489192416588288410803225066825839880971435465232206429722600557780654218330146221"),
-         T("0.052704471221201384879102044313723519214541830844294339002006150295000261803629777930668202713875629368914012613840180174156598399096984605842000917709330893871365961242812860633022132663435078869433262371062200555333508565564704972551921154864927879748108180002977668648111714062992755985320189721615088748697314805428967770533095416911693326757965362169171309026356339280576158225848771071227224373815"),
-         T("0.054613762155003812122160305957618147686113745063989650607179163157398820817715079449268802189362998719256947035541552524839497119721884536865240705017403409053301625152685151644761334409897199810093505097528650897729279062117617766845257388412635800174656504897022571125534403010151970450307624961920347280823962725005822339087173498538012712497715370388872960900453285934131578336748483622553313648565"),
-         T("0.056522853425350019441850338124226420404372628229474954730316461224029279793449121148941830155705856364290655296696008865349058650396297667951745639266344993911111272076019522476315254920931469406381088740392436352997178777214659473302034620137440843681809428909274912969436139312159105442160243076856936138443854294531618433726198293972487505166088883354213979143973990964298454127970039847456893860203"),
-         T("0.058431738052758164976379864942430396555977098734986011309321413104802080798824039565461521608355122102022725461220269967251619843394860641070621951433765763369761658916816880868188275032453137184211673934079277285593935159478757148621410070196500221526968060556586710920750728824112282461003224923995158937905479480579208549847478185757177039153501786271361921802927586114942206193581554801605680183774"),
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+         "0.054613762155003812122160305957618147686113745063989650607179163157398820817715079449268802189362998719256947035541552524839497119721884536865240705017403409053301625152685151644761334409897199810093505097528650897729279062117617766845257388412635800174656504897022571125534403010151970450307624961920347280823962725005822339087173498538012712497715370388872960900453285934131578336748483622553313648565",
+         "0.056522853425350019441850338124226420404372628229474954730316461224029279793449121148941830155705856364290655296696008865349058650396297667951745639266344993911111272076019522476315254920931469406381088740392436352997178777214659473302034620137440843681809428909274912969436139312159105442160243076856936138443854294531618433726198293972487505166088883354213979143973990964298454127970039847456893860203",
+         "0.058431738052758164976379864942430396555977098734986011309321413104802080798824039565461521608355122102022725461220269967251619843394860641070621951433765763369761658916816880868188275032453137184211673934079277285593935159478757148621410070196500221526968060556586710920750728824112282461003224923995158937905479480579208549847478185757177039153501786271361921802927586114942206193581554801605680183774",
+         "0.060340409058501876576879058406717550375449897922866349024612531373677724965692896763451690034750214807393086060232183962741893455630800282528706094634312497867863194252914455062127544671909424505367559503649890477570116767021509485710626043408265846213906257952113003324887350087083283630715857354116849013376841533857321740197047217435805280085872071354373524395263864933170034771001607559366437835689",
+         "0.06224885946463576546133123915706193746686049729742751789281333411875145041642253752249398319274836506892916659694331849766284472811963607782488993959669913942440995816339529777656740297867471191540909520680122909159182411803441391065468297111274482089347737322313334144161837035757661055283810143238846811496286086926075008068489724098160672664550444107807861952850135669761489736449089327971794824585",
+         "0.064157082294020937013292141108273585068933185681722806586173136512969086561151000586083228827704474922133659368208499428517560937267711287558275856325851735527047525549135602809953924346232393575354505341516408877034795144989051337120442048812961016500803766780090428411925756071299228254760633032932651170483895163866111455935100454818941073761804284777739005007991141161823471943803047351369535073521",
+         "0.066065070570350498632132342303164932774411476452581548988386145454309844170784631219900687545375669726062411278210148833761887075889382631711319762066717518842787273543143969874177059386003262516941215168234997245420735913778365997498382320917159517052861653706668051150014889560865161606396037665048820655743861710636504450723955435275019348223982732095398949832565423361714391500479155224225613768011",
+         "0.067972817318175064541548243754498015429928588516517183822313264446879635682093113384264993280408482780193047687370305892309106748875519486540879020142902362307237689684697063792225838111742241714789823601251998299331254097504567214769822096812914869886418586879378868131071702869283011709161582762527864014863950459121468893761825841337802563429112718615110803469902519051203360473993644451463303576859",
+         "0.069880315562928257463098098362562671709183706398122146969098129179472379455539984270317889382725678551314678030902515782188203802362460214070192378666311369730755912670660970378408284876465192356340335277225457776091515934608751710356445501169982098020701963512215973413220903547301855847279762573955110834619967590588317288171580291576756417265600792610005176888567344924086299458709493921684370833814",
+         "0.071787558330952207061531053207739391124226218288071373402959685303573894071937999096931283415397385296306228484128726125223568292760110763075739612174182840148193517540379302896938375357744754831885570482299802985278525692833941172622048860945698352794727105726197891701070706523197225463566498764869186174536278875440544967870368440256565084805804998877012238900798874720340885805165811704445925369809",
+         "0.07369453864952304506868897057861922170414313661538863465614770246556638808351254050794164760581857499175318127117745597595046399453737415234966090460819383278338184265518294393589316067434296307320873514873375534499000895507092920123162793722742278902956263178675873980121089525814840115300730124457959632013360479776554262210801798434607194598511786777350540581826836696200671400628870250659962729555",
+         "0.075601249546876396992772935963040077834759122887264324876826746597298507042570795315940378957369646666545616927930046677179646722187557860442506025110541968257406052679604681892086517951648112201767029044637142334937786145563391280677987040697732028896674786378870229133792190093646530752257521390201161387698590619925316803401938362974478273195688740273778224688121208296858072701246429755713258468481",
+         "0.077507684052232870319778844857360483087988665809157375994805235390695227945273826842335916971262245322463861698987988491433092759415620685754813456247989287157909601376742141647886684380473379403067343977633347655683745871434202230624968375294472571053679501320680048739346844244553807193670436672857163839591129928936603341033670518982144557944158002407590669543043048232580344768659176122645763500513",
+         "0.079413835195823539113919284592789131508074280056913456617148863190077260584186476150168101766032692499585019572300009477107342325731806003539645749720998260074894005503243715777788187754550286488316966320623707403846973934258796072434720381188302956748572794547906591019552569722211941807674118070825610462581312695693650893380241875873254675082431417454526920871842555422162216221640850141209989864308",
+         "0.081319696008915424923862092389736899811819511475112310887916890436246797704730704673729056088324784096921353721791055102563812592375189346816348952621603248827528923433998597558478366712658235656924601774921095079356565867874041683517103417362062033545480747089630436317004907748679995334911923789802669273406449877710501792905734235548100216242648355048174292232350538531258791292074224222773259366265",
+         "0.083225259523836973901629476483826882570495097409722948211156651871411915926347698443317606324912095013846386144848076019334983060323996364575622231284156371311209803383868297666027142776492604713451401116304951916037351315288808149328656282592946622481248077426878390562084748274992526750980236994304445617883874613002677387890383751048690275480465558930319669630406765794141303531112767626885032234711",
+         "0.085130518774003530041015433371012162123590338565297712899451572274044870858132401685294989726432756808251618198809497117031428754224182463768189333992610411750324249283786647605964593556580841488686189374310703328490638378071341189999989736919850819640255203388192531225871093915262442913255553964348789674386732423763999398384843950222967487918049677831350991752153610543052586794779289758903475438463",
+         "0.087035466793942804442393380943589773874807384137701777807755858606555806090045313793349743667697666495784828540247587627381581545620918795107877715086227932192756144780086856515641298195558204484728115519445514732755572178929839231921546119143469647706999890259163924570037168105911942268212237224359201159897493303064534985539474450028748960081579369980283792804593122976296597796047722827878891322393",
+         "0.088940096619320340510800454481897179643787714504988904779549430422905882044782054375828906100456879992313640144934242418129400679706865644316664458061953684856607341811667576418163339843372041295322709797007871604740491453013916791024918954258557372755707588171502529270934617054742841996068375532958173787119651672031238405892943090742861150287144368470297356054911834742041692715934237148148936307154",
+         "0.090844401286964974994199780075024285173534240616972938308566124002318176156233343333797652771250228033597767340846476094210813299723066344955542455246897302945908336756464582189829335315055318509171623072382573656172991307091055717376996812421994002305994837615827430425975713541786272473174908117299253875064746541808768776888139494200307162476704515967971265236163183394620211890252072718610942571965",
+         "0.092748373834894294768837248013614869545920040757666771889792264347367335922283987944081370356939214799510822558638935486112190359701790662792925773186897671244831971450474952036618937833706899006048469791213129922302798462311426294239282200248625552430083292818594731518350634587677158329361662244008606299358410273467156168469937529868888478684257396004386633746334360279683178784117372066095688934486",
+         "0.094652007302340089278624856973167138217258137565762699413364163993950641989798336903224059425798872308451866930780842878435503832366316245159154044350517727312654980455290163514021860802028251981954724580292247887851185639950862672925642859475325430465650514258094310141033116303195908372018392349011340787373492402788283020594141795669947097771918542864972570255253465754192708165241608041715996375567",
+         "0.09655529472977379853549858833033074225823562054271495313739665642376685099661084023094270272485976247900824483810911634635819558334630910267353320029261330296977292720266655308513559530586843550229208517388789783011887450865488554143475302590353915732321663418057567573042594801866258948380684000769091353165879953111046260532796891917772727185993569684246844052518121013717183610828519193371796413317",
    }};
 
    T half_pi = "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064";
@@ -232,12 +232,12 @@ void test()
    {
       static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1";
       T val = cos(half_pi - (euler_gamma + k) / 523);
-      T e = relative_error(val, near_one[k]);
+      T e = relative_error(val, T(near_one[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
       val = cos(-half_pi + (euler_gamma + k) / 523);
-      e = relative_error(val, near_one[k]);
+      e = relative_error(val, T(near_one[k]));
       err = e.template convert_to();
       if(err > max_err)
          max_err = err;
diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp
index b4dc8601..a107e4ce 100644
--- a/test/test_cosh.cpp
+++ b/test/test_cosh.cpp
@@ -47,59 +47,59 @@
 template 
 void test()
 {
-   static const boost::array data =
+   static const boost::array data =
    {{
-           T("1.0560191127459844751259038114395241283965590525302917878166464679729562764239266483419824023679041866569431842053263976225991679105269492268050148624443706785607467750929028856273183654547152707568642275917435773104050171284580773949313906303074811586096214771879801872225500237540725592288167903987152007171391207680034517664218965133028298959753155835975555361514087618679892905973726581183754237665"),
-           T("6.0577917650974496023981039346694689204850927958941226507775366589415588030232830758139222010716099059155799853188868489737439396141346120898610181630988217093945337280471788812956307352429914669334599644412036010014302812555700905490062030666482387008384856645533100266205122930455496234252478878949675888122615795451076521244771554025667181070733415815608287241160724578541982548132473721865287585003"),
-           T("383.32956577005424506758441449272199796616394738942294350035763341369127219359132618750028176886177362785452836065735889720098699937365992620246167965376788963171659530350198190156275836547285437366012371175910490835823389352716981464503672749829183569550509561579181434088407652213421105693358960196044447948190823567291153397039759820680087749250557665869797605969680417240900163183563482342795870741"),
-           T("180470.88335034971169904627554690213669106779370247753503772451628313223853228134148123711258586005038324156900626143047383382773083164188515409766952843294484598668304799186411411329575367546332731190431166613267871177008493921416649792646568096789971466064344922873643120446759328638447781504932928745974584136039698220604099816877847080168890581112550484205291341188894903342677757367415636409890558"),
-           T("6.2781497954189513287619297175142770025826052476955600323495790530946900406209789437212923381830889846578651793922971071825731424267985994598149826652782605981764572599129753631344305259620294513472869937699509893247230674850025066547664563263958672029867981296029855675095947587305949634130736118694040608573981560192569935477462121110619100122692626135788198431038121227062383110684489973794745342204e8"),
-           T("1.613783114750852113223226710244634574082654363427931747177970610142560035434819323665197978270795707611590961019502906079030261920109649748962125930850198625621792763842224096823299250338750953491004408731082880660125641628213970297576817341593254767125933119462446651783267917469179893016103516988279473907996009458208097272806046395206212403180775656514566222835047724943633607736647735739948551096e13"),
-           T("3.0651210048650948869531196671342477415226643123350617715268971834881834615138925908518703584506447138436613632341330640449725016173384960626760387649747643297918807083363913015806893683786389067836005832038060734248371426886808175554210317756018846109627572546314172492701544345965940408777570519312837860014177872754358662463423939942202520475422342889660750666147940146262635303938752019875745307992e18"),
-           T("4.3016893602106215864771434464025735547192956887050537014696231526954713331351791376069506688795159316625154458115179050297716224800318064110052445970764898870599885508391064218065806885129697936678362276766771902589638957537168339190488273555753876162633237990462617955892238424402124353124736879474651977422350856642986446591941163073842974714357745162365700428610167249762162775568692443158879770006e24"),
-           T("4.4608685929681360001024935791890661655506049487122331222491789277138083092507844933483858468341107613657448783043064935174812965310544903547535217357996429824403225005261842368679242972243707736489629610256554995236901040773902962370130989883960298987808008001651650799892267761089302132749037069497452309074389846493140222931714618697738906019885122076310868220596765753447232222740129365498326869428e31"),
-           T("3.4181315955816806472569357441100390029536003312981931954091744304974491527743601285017456624487264929971022746516079644284683284072159616291298593217459064246713801084801182706805865477209408120733740982340972570739267039630582468876075574706187115643861449939429503730606743466086010115127464706315791765264572070452800816054590653675962889901898843712936126341807733200610910325052666512334161414655e39"),
-           T("1.935294628272790810141453021278524976364077691905248015888165919062516673344977091262644262832934899971824373171672037249361491844419302323587942915162859665992916625636813244576210109931852761921719987632855596663907494303248513195744818730879742963301327852160193919379798462926667740594397712731448572837824802330973561570848397758210619453310032286208701226098998940360395267237151018055781640126e48"),
-           T("8.0964449511890098565841496436016431651692307764702784234901741408135381374668439020986470675941110923614446905696411023621632714191313583360826598468217983223558130595633054971338824192327248896500337050246640453410159732184419096917171044075711156867804851018388576371530520943696439917673720450911725466781235347212700849702742625663288687644090935756560022610000629006347244369388824818661974220426e57"),
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+           "5.8109375364209112227579654658730977030869454388607076903639465992296616832002964138000947668837140543325908222688655359602408511410663722770167244801973012245657865182739637159804595049180263175014778215232564251739259624759589953677661356104554831551073263668188283861123521688445132164147762321111597028523130093864153999974376790494383016372210442340324038686843345053322425194077414241243050491297e982",
+           "3.33875955701899627718146291382268063073604182131575843695486667154496711979350813988644889979275310892951143249901398447859083674739840084454465850475774696325142148671937407108540250845900941142800157345665761403930889797424808979569550325271558518404559007551625637761142662107757913763221912282957681784053564387104062317729788737215450574233690655931888608424916152893688106181220341997128198692e1024",
+           "1.4174672877823334709610117319768830739080734407353905145632612088824955720198734996604261250019291955883620333545750761619015467840567122066622229379056280064206319780047687015558007624774062399477328822231085767309831266032616053065858739373818651687128093335640388513396191118537181280334430292439188737524362269789272308905723812818882228503013875816702686587035844437102478263525616196832018321602e1067",
+           "4.4466189016791091516801723880812533528438597080549410911235655611382010503145789286158745555771483577943662768773465284793798720178177605712848440200402906836390133865748188969184005230383247111166918721449908133920663776952786683837038180436264738937354101153867171804315769471050303182129269442292354388037298125177941217926845803005587166270803697433886463469168814941555804311717400657004050157245e1110",
    }};
 
    T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1";
@@ -109,12 +109,12 @@ void test()
    {
       const T x = eg + k;
       T val = boost::multiprecision::cosh(x * x);
-      T e = relative_error(val, data[k]);
+      T e = relative_error(val, T(data[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
       val = boost::multiprecision::cosh(-x * x);
-      e = relative_error(val, data[k]);
+      e = relative_error(val, T(data[k]));
       err = e.template convert_to();
       if(err > max_err)
          max_err = err;
diff --git a/test/test_exp.cpp b/test/test_exp.cpp
index 9582cb58..cd677c24 100644
--- a/test/test_exp.cpp
+++ b/test/test_exp.cpp
@@ -47,59 +47,59 @@
 template 
 void test()
 {
-   static const boost::array data =
+   static const boost::array data =
    {{
-      T("1.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
-      T("9.47747587596218770242116751705184563668845029215054154915126374673142219159548534317576897266130328412495991561490384353e76"),
-      T("8.98225489794452370997623936390755615068333094834545092387689795875746440121970819499035111276893290879203289092353747850e153"),
-      T("8.51291041070124257524798251795398355552294928156627848633073113916721592074889256105483993631579761345100284245144410506e230"),
-      T("8.06809030516483860484254925989129017112482132468761563276276594763374886826841745433660192438855214332469192411759402790e307"),
-      T("7.64651312322841630493169711336894888932951818957138997327518186691187347879142222644283389432604713409023263917264358401e384"),
-      T("7.24696436606255985380192585665173794455118215150711210905481870053193336336731228464367470327868286988180495111406609690e461"),
-      T("6.86829299533155197480610865771404565313986987801060270120621935139741577246731459024227828759564450034267891072352816870e538"),
-      T("6.50940811722948585242669672360741252715012399316164518226061001845519670701239429603657927628755169479689062519606799624e615"),
-      T("6.16927583978348964454665652571294215251327375137123272041877979478545511090085756858225302357977159539777447847855503405e692"),
-      T("5.84691629437043896753869572004324228849833391140408095171257918435296982661233664069534601413835876272500275725690968474e769"),
-      T("5.54140081286660645835370762406928689330724181979654545550204201113926269281603301564114980528619942840737770415885783439e846"),
-      T("5.25184925229805200184933663459660562493261505058724212670923083643709964294855282715531768162298567379648573804433968486e923"),
-      T("4.97742745928448409225535325233998957076879979440190164347796593390995994951755710667491911026476108957070504003155645761e1000"),
-      T("4.71734486697204622371883518659702954552385115723942808636490157561056417525827884479573988899517566587636669779645610803e1077"),
-      T("4.47085221753216236037602345430121605512330975424643767098987010800161616413051148037751552110081034066081309007796182114e1154"),
-      T("4.23723940366531198300986713567588008777043812458400705569721660157434941774066620870256745107265536124077734836797938268e1231"),
-      T("4.01583342289144005397455901781647949754375366066998182220342540048111140676724909947493787596336610499122085983712119281e1308"),
-      T("3.80599643873362813900306284477369187319506389058898599816705625750135796510808933786432614186155972485637939057212164098e1385"),
-      T("3.60712394320959592074309301816510372687695286650188776957291994751966018917404878612237961367128638199290387601511358836e1462"),
-      T("3.41864301533745457066062991907289263038319874930395315315257927161138360206596116102724713069518697248463965164712972907e1539"),
-      T("3.24001067063873569456703204286462007769933831045558617578289414699244767403736057931834775727420762410328297596596814910e1616"),
-      T("3.07071229688386868087623659761166306563170839771162347830514606977592027644137144160294469813988158463967740978461420862e1693"),
-      T("2.91026017157373047094077218552378456052150304677863670611408570458991015300131731261787644801415538043027268185097710615e1770"),
-      T("2.75819205688636078700279174380111581147323147951670302427494196210176478494486073721584055059489736040565979466551070179e1847"),
-      T("2.61406986804110104534167739704643351039975992759905579635058824027507742375380077276380178376470686987855503581867681046e1924"),
-      T("2.47747841124391945459619002346303925269640785743990333362087223895627681769816204236257960940497519376881830373722711456e2001"),
-      T("2.34802418757813746316913800667907927718925648696508255347624141597281474683823345136640610924639820192825966082309575303e2078"),
-      T("2.22533425939475124828943430510333464605535146852848680647615867629953075390889821397228584866395924176189346073006180260e2155"),
-      T("2.10905517593659363154553947631071808925462553114068144748077359132255993441363479041540672158497404660986163617828972963e2232"),
-      T("1.99885195510122536266653916064141606295420554580140619900425370702471778604391774578696867899999534265169574306808906810e2309"),
-      T("1.89440711840917173277691572886942144916664047407963356271198286654087884646102070148271284410118233470318337745546895603e2386"),
-      T("1.79541977639739687088375911648976940254141946934175300605485966288703931992861387257771264702798405630917098672594899744e2463"),
-      T("1.70160476180317540861346545791118106171203487587101437710693054174454895160403997508137760007058856854991413121389834429e2540"),
-      T("1.61269180804119796097157014527479883521656118500417752963675677684343588976915851637637232001139108420659882326614772004e2617"),
-      T("1.52842477060722969066998464046690349841548269556677423378408183476489015878816585045578141383463708674469365281537792914e2694"),
-      T("1.44856088916530600122626623629347336702026699647293500058111037526381692645547938577338582002157148103479049071921438452e2771"),
-      T("1.37287008819265239873777879432333192404914357037749380145412895230166352318128978403808382142784030558123748263528360645e2848"),
-      T("1.30113431416759441771790128053911040907207490879890145597562380328956450092799014856149474809345424672958343296615764490e2925"),
-      T("1.23314690739099822369963411660419632130352733806319401863570442920347696015409870236230656305563674376063778482449716744e3002"),
-      T("1.16871200663155636468514484039368694043851858077879103221831997264419096417014996945143145495038265243932745953706526253e3079"),
-      T("1.10764398487979357804590117089134596938734185016144401218934115168561552640448889215089150481162977776214124397487013110e3156"),
-      T("1.04976691458528698318220729857405616816444374000182094405930946710168752954926612218474430081526312018810817657409158490e3233"),
-      T("9.94914060836531582868347569174220216007647278536863127198023584205669825317884219144692385409156165042162234017403353704e3309"),
-      T("9.42927401023380446961314339401657458785389811652244742482194123119943160577946366372207045050095290781679375214307398844e3386"),
-      T("8.93657169598281164656322298275337750103095739790107943666668184304335665562867744740310577868880098719252549186849812451e3463"),
-      T("8.46961426624835911826517103631490619655296714141872141145089865045804196205328364155921945616925875458926717336478525196e3540"),
-      T("8.02705648870740089929294815816002943860908317454595055392168733404583122074223427054310572378841634984243492063192095337e3617"),
-      T("7.60762342267101369970765191988545810374824800500875923752736467467657167098026707905341603949108433696304383346239333297e3694"),
-      T("7.21010674617694221027190468649359000420209460539838589305387835463807416706224777302997789297329446308541513638035437482e3771"),
-      T("6.83336127500041943234365059231968669406267422759442985746460610830503287734479988530512309065240678799786759250323660701e3848"),
+      "1.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "9.47747587596218770242116751705184563668845029215054154915126374673142219159548534317576897266130328412495991561490384353e76",
+      "8.98225489794452370997623936390755615068333094834545092387689795875746440121970819499035111276893290879203289092353747850e153",
+      "8.51291041070124257524798251795398355552294928156627848633073113916721592074889256105483993631579761345100284245144410506e230",
+      "8.06809030516483860484254925989129017112482132468761563276276594763374886826841745433660192438855214332469192411759402790e307",
+      "7.64651312322841630493169711336894888932951818957138997327518186691187347879142222644283389432604713409023263917264358401e384",
+      "7.24696436606255985380192585665173794455118215150711210905481870053193336336731228464367470327868286988180495111406609690e461",
+      "6.86829299533155197480610865771404565313986987801060270120621935139741577246731459024227828759564450034267891072352816870e538",
+      "6.50940811722948585242669672360741252715012399316164518226061001845519670701239429603657927628755169479689062519606799624e615",
+      "6.16927583978348964454665652571294215251327375137123272041877979478545511090085756858225302357977159539777447847855503405e692",
+      "5.84691629437043896753869572004324228849833391140408095171257918435296982661233664069534601413835876272500275725690968474e769",
+      "5.54140081286660645835370762406928689330724181979654545550204201113926269281603301564114980528619942840737770415885783439e846",
+      "5.25184925229805200184933663459660562493261505058724212670923083643709964294855282715531768162298567379648573804433968486e923",
+      "4.97742745928448409225535325233998957076879979440190164347796593390995994951755710667491911026476108957070504003155645761e1000",
+      "4.71734486697204622371883518659702954552385115723942808636490157561056417525827884479573988899517566587636669779645610803e1077",
+      "4.47085221753216236037602345430121605512330975424643767098987010800161616413051148037751552110081034066081309007796182114e1154",
+      "4.23723940366531198300986713567588008777043812458400705569721660157434941774066620870256745107265536124077734836797938268e1231",
+      "4.01583342289144005397455901781647949754375366066998182220342540048111140676724909947493787596336610499122085983712119281e1308",
+      "3.80599643873362813900306284477369187319506389058898599816705625750135796510808933786432614186155972485637939057212164098e1385",
+      "3.60712394320959592074309301816510372687695286650188776957291994751966018917404878612237961367128638199290387601511358836e1462",
+      "3.41864301533745457066062991907289263038319874930395315315257927161138360206596116102724713069518697248463965164712972907e1539",
+      "3.24001067063873569456703204286462007769933831045558617578289414699244767403736057931834775727420762410328297596596814910e1616",
+      "3.07071229688386868087623659761166306563170839771162347830514606977592027644137144160294469813988158463967740978461420862e1693",
+      "2.91026017157373047094077218552378456052150304677863670611408570458991015300131731261787644801415538043027268185097710615e1770",
+      "2.75819205688636078700279174380111581147323147951670302427494196210176478494486073721584055059489736040565979466551070179e1847",
+      "2.61406986804110104534167739704643351039975992759905579635058824027507742375380077276380178376470686987855503581867681046e1924",
+      "2.47747841124391945459619002346303925269640785743990333362087223895627681769816204236257960940497519376881830373722711456e2001",
+      "2.34802418757813746316913800667907927718925648696508255347624141597281474683823345136640610924639820192825966082309575303e2078",
+      "2.22533425939475124828943430510333464605535146852848680647615867629953075390889821397228584866395924176189346073006180260e2155",
+      "2.10905517593659363154553947631071808925462553114068144748077359132255993441363479041540672158497404660986163617828972963e2232",
+      "1.99885195510122536266653916064141606295420554580140619900425370702471778604391774578696867899999534265169574306808906810e2309",
+      "1.89440711840917173277691572886942144916664047407963356271198286654087884646102070148271284410118233470318337745546895603e2386",
+      "1.79541977639739687088375911648976940254141946934175300605485966288703931992861387257771264702798405630917098672594899744e2463",
+      "1.70160476180317540861346545791118106171203487587101437710693054174454895160403997508137760007058856854991413121389834429e2540",
+      "1.61269180804119796097157014527479883521656118500417752963675677684343588976915851637637232001139108420659882326614772004e2617",
+      "1.52842477060722969066998464046690349841548269556677423378408183476489015878816585045578141383463708674469365281537792914e2694",
+      "1.44856088916530600122626623629347336702026699647293500058111037526381692645547938577338582002157148103479049071921438452e2771",
+      "1.37287008819265239873777879432333192404914357037749380145412895230166352318128978403808382142784030558123748263528360645e2848",
+      "1.30113431416759441771790128053911040907207490879890145597562380328956450092799014856149474809345424672958343296615764490e2925",
+      "1.23314690739099822369963411660419632130352733806319401863570442920347696015409870236230656305563674376063778482449716744e3002",
+      "1.16871200663155636468514484039368694043851858077879103221831997264419096417014996945143145495038265243932745953706526253e3079",
+      "1.10764398487979357804590117089134596938734185016144401218934115168561552640448889215089150481162977776214124397487013110e3156",
+      "1.04976691458528698318220729857405616816444374000182094405930946710168752954926612218474430081526312018810817657409158490e3233",
+      "9.94914060836531582868347569174220216007647278536863127198023584205669825317884219144692385409156165042162234017403353704e3309",
+      "9.42927401023380446961314339401657458785389811652244742482194123119943160577946366372207045050095290781679375214307398844e3386",
+      "8.93657169598281164656322298275337750103095739790107943666668184304335665562867744740310577868880098719252549186849812451e3463",
+      "8.46961426624835911826517103631490619655296714141872141145089865045804196205328364155921945616925875458926717336478525196e3540",
+      "8.02705648870740089929294815816002943860908317454595055392168733404583122074223427054310572378841634984243492063192095337e3617",
+      "7.60762342267101369970765191988545810374824800500875923752736467467657167098026707905341603949108433696304383346239333297e3694",
+      "7.21010674617694221027190468649359000420209460539838589305387835463807416706224777302997789297329446308541513638035437482e3771",
+      "6.83336127500041943234365059231968669406267422759442985746460610830503287734479988530512309065240678799786759250323660701e3848",
    }};
 
    T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609";
@@ -108,14 +108,14 @@ void test()
    for(unsigned k = 0; k < data.size(); k++)
    {
       T val = exp(sqrt((pi * (100 * k)) * (100 * k)));
-      T e = relative_error(val, data[k]);
+      T e = relative_error(val, T(data[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
       {
          max_err = err;
       }
       val = exp(-sqrt((pi * (100 * k)) * (100 * k)));
-      e = relative_error(val, T(1/data[k]));
+      e = relative_error(val, T(1/T(data[k])));
       err = e.template convert_to();
       if(err > max_err)
       {
diff --git a/test/test_log.cpp b/test/test_log.cpp
index e965e6d0..f7b3e2d0 100644
--- a/test/test_log.cpp
+++ b/test/test_log.cpp
@@ -47,109 +47,109 @@
 template 
 void test()
 {
-   static const boost::array data =
+   static const boost::array data =
    {{
-           T("-2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806"),
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+         "18.963200444815204167404888798469665227431788358892299847438551435971105813566329353339851076750530262901184430318825907802984559086828099838800823075902608236275943927671387049630228757166718632225359114181378374769186216486342164672374303171089906235756037703334480067642792992542669516647312965086899057259968955796081732571906843773036664256360263051447703790357359429377002031207739864979999279347",
+         "18.990046485464088033353325238570094871523592746407402454864447659438418650897352188003827603659585905257296788261872980663015351591030286798753545075312871886708540373690732957230479307213846083134185408782477823043603415914158563765104431367119681516469558190435321626296408405773925785846797696565762444462069369032104851518168840362055319574446706630124442642806832354006488607879109906061011225994",
+         "19.016536938949335590921908878972071081608578803308502271146163132935001206102423418117835863551157682291011036313549071538079474102791095379250735204641651869626255407971202952320707788423726057706822543117840676308428340234652209177652929619836857962138281947043694787969753375808877555756525156889419987622193160096718082756877689454214937644538436622120458515758071395625444960838247998451767464267",
+         "19.042681102069820040323211057777714109150558076228575985448688497208727928412122242888431932498284067180966108960090928128416538326586163291672353531766027111567123306015724614143020205136706498507055346813817986209642505418179828757157587146552894936306186818734849750397304488535715134906592464324381660408650130874094490704788761416060096501351661608424222204094369103147551037672603814369634649173",
+         "19.068487911727958175697030382906549671323284692477975980792892280404995909757933182996822232452584791269433004172376138676679805214029937405307084300414313959313789831600985178255638111559270519906326622715617717964168412002699242926437873012736620082535900009120622005729068876661407020205549742970102634687260159098231611555026386636952356914915597529253373429394903680674472796958663494038067669179",
+         "19.093965963269656159901801532857652686731313095114787279282350143184060615248880952958892345276101741792959203039945279273255821413683057071718873479055914318955623580559627285483449590741119271240498698177664589148961791164562328382134513604070535948997556425774535241433839196056647337630745324677877037589790564832932809741759428622931327986353687891898499439791429917840804474313864245639140963876",
+         "19.119123527670705331793258647026174473061813878914781070641605073424527485626683566355878191198143709838509389044950724156590593262994411423265514055870555330957166471517671117689943118929441254707396532385048466111853801352620946858612646592880180562600210076019427990165200479741063391057955342589569972650353707736819649707138135073772494722116787681314798945037658461538374603477221825614061123586",
+         "19.143968567655614969812922707872905228504499895574401195919290684664632292543319151929670686365568982588326143748358606442800755409560708661213139514248609009613770051771501624762852458893105259920477327438788243371302722213272226600736522283567127277667156871770413468147870394343816746792945999572244176333552811712447483231232773171106511438260175071145300046115843401710072061507331123043607901766",
+         "19.168508752827482780609154136923082745746771414212427034681109262302000645968087085215520638009496537393752178754873475983837687377025695010556483691979309217953419255985001727184619660158435191823702770674175581797631578786818852604111682506864006199186805540809913091091561814668081471402749434233431033452441548505582706019452955567976154397574205270457372773342241946969622998755580434262211071558",
+         "19.192751473880834042563713562225153433521577940186973776803866639536641104273721851582869330116346851241224039623128541122821371810756925681002641212419779923811384320279466454221232217629041792882431116499214977303106306157966687858071257893713340199820635963233697984370035461108601863346164084264967404520613456100656965925875472210769471793070984755357524002396981276686789870757739219539841324669",
+         "19.216703855963329593992083348877341510356872855419154524286060224198192164950344042194924570763041352943159776496534086655621090662648765929073480563926604513272233491262353914647091955902924297702861031248271549558718609763974479507490837350364617085882753391176792131259310397149374028556893735115741447201974608383790314541221313482249282941830681505989160209022143487123591182161037084387107577471",
+         "19.240372771246783136336288622974117018573581443774444767997147210768023102387819846722491865244820295698055584478151667485670300985795814036287612086238394489310685917822308982062485897587424683040075624404469719368214374255580054164790522993745386564072906888203344350441788631572056395846260169628655731587443716443908470481602481327796867951175756539602824534024677208143458306390998693538144276002",
+         "19.263764850762979509196317705761686108092922892356892210254799469999751475179529646750512177469718303426094538082717842694993912366018532429385996195100165328675330327321101942399890523238950583083919577089467043577581159099371618262297126999910295820866611740582812686480215151994304295620401944519281853807987442610790122820927006439539980791908595120476521299636624843377591628005484740938263373595",
+         "19.286886495555294522450851525927489255646333848651043717882790718796769943763203547772413744395083720600670009266257171342692898145198064660758379840502214228374875168690401725272168814130387964227940171355345107459707413634435078254467165459318134413588306046635342334572072865760417877208230914828250259039270224031775041480686581149991980042698893384296012208438178584526032640636530664689171174514",
+         "19.309743887193036513569909003754932688390195189494409126081957694707453295769725463252527373922995550848707616892717734716346726926003376949988744940329952938435722400261306789658518736487435455592323288866363564460056999876237001095092480820045715217327131479089102764865100373961878408215166685028270522348153253852064527393390794401890890932406298166622224431486187051653736399833197687524233000392",
+         "19.332342997691718269365647851051829244300572144237799985690236148794296859647334840581772744190077146167636205171422529047782401411481872480699008041273574144705390909628455554205882856537701103044535844002047328262877230706418721410147702147287802942241134713881576962004492246225067150128745210304021219616585555420191917418786300056829952680702638022710700076784220324428140020802898115083347702904",
+         "19.354689598879088211883278917315015191222443867565368209411861608347893184500809153071123456883339348988675265028178228103174790923741638364554293709103213239495123865898742141584076941660965692453426480770865774436380303703020587851939728834028918714275983773159730132531253761589283704592841895713231304417993106469276962707965968679020792759185611101812841427933459395519877074670185732532077876915",
+         "19.376789271243668798743209719830951710660724013826759987563467708214368337563307069810449676142525612003499201086112645501159094078378318648014400550345870757023544381773094826620272453238529286555419097429861755219673554476395943490245768513403194721941361801918811127988057063915654267554707302094460700078255016831241731287084620030531370389406858605301314913503432729894455360413554796057743624785",
+         "19.398647412299738536733101983020344760416543000933452586938357216391679714568872063480206587627849607725892049860100424409512218327903976557192129920072602449053963631370720893361294311430877864798057636106390383386608343478253049758287190639090148001663846660919016228401517981946486814580501445191763231914170223651871543954569563229752867364010807484149328122287932691728836607206296504503654291916",
+         "19.420269244500125639443026886412358511499173347101740173789245348545649777799992933455717128782979425999232096035698012165274922488616903998818326535687811364645463339885951676665882203155018792792505473796600843314336576346118972683035247786115152970665197263535031125663311669153219106967873840911780618890220192918885584791820817380351857621444438732170662912318105800373867459654881916254806601924",
+         "19.441659822725832764853886827062860938003360575287073851586808019473777348197590834815623551815029267586554639358825375063360984210103069003729612683914916394217674289812465439813541316938870999354861402160375582810342455043995730819816948505547453029096197833928688735935982538915244747599958654970407704104602569366784225221531104839626781845870092648147888203880688567605208831444945817857785153427",
+         "19.462824041379362514202453738329145059871795167945778128620896576209292571177865023083134487492542931078517939464890630420523665550799939651548618906955780515811541533057671943504991862669514142328738958049297858093270685582461594213632344682911288013670395835728596839923778216755784200501989248577166652556656745561631320914185098036550279972269808563352717494278133064808018424486494613581670904697",
+         "19.483766641106643718481178395114340475919752681994355643610181441860832131581914604665304968112958314746911243491535376957183544987386808635080341126118126364286470448001964590403332961518317007864293940732767763315935539659300785943459751426720740528037173390794501709108627539732588206226415399674048608843262175783293190807110169521287571898125826758063922707869247389042070537305271065057452360137",
+         "19.504492215170652185153425611551614568097792837031617515988255748353971463776213613651972980845739009653411602074763823583486335276886222365741099356087975815479321535979397651959714956358141934399110351847826398926624666313434326948757230737160647513320407575743953348133831681915668076630219831345596329489041495050445409516995558844346940248424949708046529076568535423815692145534030368195098701895",
+         "19.52500521549816144973266072401605164852396136071234571245810367391072812166019661923143396972741343266046339927362413412251126099193801965681827360699083448218860273549526903661234475357554150017778848244185893299525191263899191588797634058235164494448438674653809951435022502560679429105527325418829543863756825670476364629140951247734867887985343458291386040322597855003211338820555010939867273248",
+         "19.545309958419535630089123088329455125777373731767323301911891787605488456921558805681207304272616222501167615837357366396904683096528060072684210523189673108467018417135186800678628444987751206147451054525963839562634340820804697604369657105969423354842149829173951943549166420900709500398322624130365195674097282456714104812933002700523506427441210494461469512180706693823193924457440917371176532034",
+         "19.565410630120075532420489068555321524954362381908007338302983473268528473151341321768804731192210840056455228388636731122203200610869021021871133154865620432257415783302175345843898977949742849569372169004904667621738405749986270376895267386643049526766451459390277406632576412790748533372863644721976845168460840162066672290292749672668879524315410824251032084115058493720402881895485689493165441193",
    }};
 
    T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609";
@@ -161,13 +161,13 @@ void test()
    for(unsigned k = 0; k < data.size(); k++)
    {
       T val = boost::multiprecision::log(tenth + pi * (100 * k) * (100 * k));
-      T e = relative_error(val, data[k]);
+      T e = relative_error(val, T(data[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
 
       val = boost::multiprecision::log(1 / (tenth + pi * (100 * k) * (100 * k)));
-      e = relative_error(val, T(-data[k]));
+      e = relative_error(val, T(-T(data[k])));
       err = e.template convert_to();
       if(err > max_err)
       {
@@ -175,13 +175,13 @@ void test()
       }
 
       val = boost::multiprecision::log10(tenth + pi * (100 * k) * (100 * k));
-      e = relative_error(val, T(data[k] / logten));
+      e = relative_error(val, T(T(data[k]) / logten));
       err = e.template convert_to();
       if(err > max_err)
          max_err = err;
 
       val = boost::multiprecision::log10(1 / (tenth + pi * (100 * k) * (100 * k)));
-      e = relative_error(val, T(-data[k] / logten));
+      e = relative_error(val, T(-T(data[k]) / logten));
       err = e.template convert_to();
       if(err > max_err)
          max_err = err;
diff --git a/test/test_pow.cpp b/test/test_pow.cpp
index 680db5de..69811e57 100644
--- a/test/test_pow.cpp
+++ b/test/test_pow.cpp
@@ -48,515 +48,515 @@
 template 
 void test()
 {
-   static const boost::array, 500> data =
+   static const boost::array, 500> data =
    {{
-      {{ static_cast("9.85291419463953934609889984130859375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e4"), static_cast("8.41670862661703722551465034484863281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e2"), static_cast("8.66781019918879108354226292713799369912745098619466567318041467361236175866573114777000418440761829061824953361563557580935951901405814080757565313129904800947783606850513184296612628910656615168927761935861462770335134108408073175949783551491164949747086136599355880600420490275164555515512645668845e4202") }},
-      {{ static_cast("1.65291435510970359246130101382732391357421875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e1"), static_cast("4.93652894786225093781695250072516500949859619140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2"), static_cast("1.14852190138491736562279120519668390081141778746743826681517181158751264571350304943298501284647564489716027476004029804110782430201351750715968215799574772058637701195873519618784612525011353325208230847515250406858209757415407239793739704829281917272032288615255140733409015874140869835291148547238") }},
-      {{ static_cast("2.95673953882856110908505797851830720901489257812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), static_cast("5.30915509717990971694234758615493774414062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e2"), static_cast("9.16137091634529046709182958669115589757019722367818747705232600776240821857227718551873067599347313641575272826830417174591636547915061517391300131065931465784194067711359196329143298499263726513131614582697830908424187934868152998838921216586737465291051289708299364409624364999366486746226077050764e249") }},
-      {{ static_cast("6.08581487679821513288314083212071636808104813098907470703125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-5"), static_cast("7.65778516457987279864028096199035644531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e2"), static_cast("5.27056224622668410282266686919173718609676411389459024877282902746284033954589536288634973757568176464096389580016576960309487231057438455595655805167665817497028295657665023126747065443986739792258870082022889306909488139458069146748438042701949551909468708242176394539901613782225328586614222105675e-3229") }},
-      {{ static_cast("2.72264614486854572561469467473216354846954345703125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1"), static_cast("4.86954434555903360043460637029966164845973253250122070312500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-4"), static_cast("9.99366682241962146368589809577120011723198308450433185299366732500677873637460155970547267099719914327909694930518383012498797681761846242526638144261306834523078708261122471803832490341687603813336927181436827534082878781252668704774445437548691251936499670077735883150461534069270846997649139259014e-1") }},
-      {{ static_cast("1.15866069758449596882599053060403093695640563964843750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1"), static_cast("4.91253262757665787319183436920866370201110839843750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1"), static_cast("3.46868982488456565751167443881314840659743514173491612010770748877346398177489343237604160804413931931718223750314831998907846386274396179552445359933868165880372381338724806279781831953896898649659594755834925976964179275873971118494605322798850925802574178528777014182338769959249415096934378557388e-1") }},
-      {{ static_cast("4.72825938314130529761314392089843750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e5"), static_cast("1.22893132739781236750786774791777133941650390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e1"), static_cast("5.47245157077269889091085696140795527282280334677569169487973419233796250189843816560261965111196061138868370890204338231535198008079068304184762140493830719955323588998399173073261634891767823614143691840392792367527470000847416054709559319143615840412839768396194451923527439592939735228732869467965e69") }},
-      {{ static_cast("1.29556572255334176588803529739379882812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e4"), static_cast("1.81521083299418428680382930906489491462707519531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), static_cast("2.91729899451736210436889587963352494969987265352294254442114149825297350300933403119961677078224257818567229354512108221647637427508041941647518586565006416113534560289731038664091154857692367872604020422463457596747145816854139701847749519264660326361171185139298113322096978245544144264234481020815e7") }},
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    }};
 
    unsigned max_err = 0;
    for(unsigned k = 0; k < data.size(); k++)
    {
-      T val = pow(data[k][0], data[k][1]);
-      T e = relative_error(val, data[k][2]);
+      T val = pow(T(data[k][0]), T(data[k][1]));
+      T e = relative_error(val, T(data[k][2]));
       unsigned err = e.template convert_to();
       if(err > max_err)
       {
diff --git a/test/test_sin.cpp b/test/test_sin.cpp
index d5c0a850..49d91ec3 100644
--- a/test/test_sin.cpp
+++ b/test/test_sin.cpp
@@ -47,109 +47,109 @@
 template 
 void test()
 {
-   static const boost::array data =
+   static const boost::array data =
    {{
-T("-9.71360659712083391437631022096936715962104815777147739346439739644168480837178969413799829610404829247283169084501281105e-1"),
-T("-5.95431113317256105006804890684659010940293672390817519158205264611725147142085353698349092164137652363446368483953564682e-1"),
-T("5.09924118934356013545988500545586843463766955556781588535384546070893806324487181574368899833574915659357543038822935347e-1"),
-T("9.90602974910637417521410554344955057938063175873799034495811832851567842600306335485818201417146475654562543760051881571e-1"),
-T("2.57755634110962773819397192502372718147953063328591480930319110437537556577887190430547163274290595074462686853519200826e-1"),
-T("-7.90852129665907861812449876176102241731921451584589870529143390612597378289323905030142878920134443274067663564142249906e-1"),
-T("-8.70636054394434218558219672958497111094237434037462776135170928197514857325641761722162169311905082223410873872693125021e-1"),
-T("1.16142192225871586802402588799179588339908282696987123538816621894316618250692422106879105583060486278819650782761165055e-1"),
-T("9.60641850565339311654365605083646127348817546384991780755200411966145627086231307074524787693440076802209868233548778731e-1"),
-T("6.28318825240308217440049590303028869715272770671179428040549526344092598897275498972932981684079339892035243316790587027e-1"),
-T("-4.73718579778960595001132927360485548840577209745936881040433718918629103032639945353908537818475936329314134212199346978e-1"),
-T("-9.95432766494621395340223548609251497842694553405493731879049259799325119533316838972006879914623359183523219011870805961e-1"),
-T("-2.97704078652633309130390182393607392013126109733352620573058826659738026681661456497779386104992235762190242017128767206e-1"),
-T("7.64723391125286889782047394187107836056829439952009227196240883193721606229047061163517791688110517783506991004016374431e-1"),
-T("8.90335717074674250432504838435892622513509178529392798127561987551398090841490265311069534613651712468228001675091153605e-1"),
-T("-7.47469618974513669394515485690188234127771130501791709462887130373371023385813212165673231177548426835629029005547008861e-2"),
-T("-9.48261778982069330544079494960981900232314056127899219497335245577354566418258722147558010380033694835705634428764954401e-1"),
-T("-6.60119969404606610211922488494059074732492583049845598285779387022002845776084527598443564095143849120847643366330179739e-1"),
-T("4.36693827009658961576344650626557410722590226545637608661764593658572210930294024902150766064738444736422263939746970132e-1"),
-T("9.98541130824430070642243744636010968399851408459030982248969144276197147611376115185206245742327729890090526273555800490e-1"),
-T("3.37137695943362070360548307779555944485385294617304662646987679063953108310365389494460188124285214040163147170304540339e-1"),
-T("-7.37272196933518190054375156317136276073182897209685319124536092629865074949247291797880288692223977281455156619510259042e-1"),
-T("-9.08495699506960201290293288218820500948312195353635174830883006841931398581001427066173033535720385301624330783999899511e-1"),
-T("3.32224697427099307204044509056982627738295866011152619834749776109067529453431741767996787924292629814505731320175556430e-2"),
-T("9.34241854135599266375493853147210486293657026766576383005045752264274587199837314096798394557243705656211732557069413970e-1"),
-T("6.90779551281016826784976005137338585011513089446563025258584317423906941741640583083551185645679047405447557105684226754e-1"),
-T("-3.98913888475082839741071010629509607776766095858433376450534753556286110518195743624946499527251336022805096741714382999e-1"),
-T("-9.99922692526403520897313527841668431397204867244750030781062964701898557028332255650446046614062333174844253917288331438e-1"),
-T("-3.75988292423704532504216998833472116186771022412627192871974303806891208635376610998425108046077306043945435504842144332e-1"),
-T("7.08546019140379445669962535829318394094758212505515423960726677977484727061149949358051741627739138448760095710063342839e-1"),
-T("9.25084597170819667485373176055260044057716794391569156042799693611964098948722923916237050181882167134906470192542857299e-1"),
-T("8.35947487571472125423673177137150279693224632368449469153892167972732129345714981936363891382927399742266512920038864004e-3"),
-T("-9.18606321039298722214219289469027246078943851192917449117591801249272620492502932760495762195965214412326830491755901723e-1"),
-T("-7.20244550473164405555518647469765134103488938825118543602681358279149452868549672550326500728323814331193184035259160414e-1"),
-T("3.60444097985855629825697367385029316833790934188475151408740160657889784929257301330229580694580194294034115152177674537e-1"),
-T("9.99575062430677992414643463029115424067356090568060307410717467085018957489304987413609313388961297483138454662118061646e-1"),
-T("4.14188682766963304833862149212585018360876819555612195218295874225032162838027842720351664698295767693697842043579048219e-1"),
-T("-6.78594534657286312316409269272929566493548786915986771929001823358451551885758307761400157853363173388867780400090112946e-1"),
-T("-9.40073722462713282312837596921874850901167502371739429501407718251639587081137893231736511487958940802467918593519005653e-1"),
-T("-4.99269632411748222821310824324558181913141458235676771744322439351386139493233963671531219603373207564905654915871172017e-2"),
-T("9.01382218619061521491363679812206948759377256420255657634443270431495336446996377562469573885297156497163691224107230524e-1"),
-T("7.48464012406957686684753003872919309910943477238245908909177973105841950470333390670719219379167068809799710776770734833e-1"),
-T("-3.21350982331168500558883709193541886146178412146971245706190880193067020283050714591560922441331235332970961845050217575e-1"),
-T("-9.97498841702838239659412520756556451623238132913559678626409839807628110807613195403956929948379909495726426243705794281e-1"),
-T("-4.51672806064485973599605876288778011355969815150135195358334589946828629430271875346142404286368814526016297993583170592e-1"),
-T("6.47469539349743367777844577149239337681085253251300560380374646379682072633705733561446355539618404778987844138766238618e-1"),
-T("9.53437154306238691456130012770111782377503876017231780889420296856266641153714110120975772709549811845909173386912105405e-1"),
-T("9.14081116365893107669584386407698218216480671014671832303147213716318806206478591012619084058741626713939006968851852873e-2"),
-T("-8.82599332954202005638662236444958997569939600897565089251125658458817750203393016337212996488633688567918453254294067039e-1"),
-T("-7.75389136447631492669594511701990356678047393586968390929688701894781023967621486245394406725747074772996680491766725244e-1"),
-T("0"),
-T("9.21877670451674413245307018032333288624288893879527153976730741889055419244554390143014969580425598422296522787223865492e-1"),
-T("7.14420247379307162288182477560228852605155250738051326022559557923361829606843109334201812861061126243914893718333771523e-1"),
-T("-3.68229061503980158220203193441625324286779814470455045264018328963975686564161509474566417124652588774892207244798533238e-1"),
-T("-9.99783810945210864429782835782052003838999970584938136857974918523615732378678641269300999292060748749245257644847852880e-1"),
-T("-4.06565491434208630299086167510578859920684132980243005899494321151205958987020300473732138517681916554185382528057861016e-1"),
-T("6.84710967469127345624707128760638003100107237269026812211460044517359789036617753689648451870956943571853410785082804567e-1"),
-T("9.37190534692875414284475879207349713030454322911019395907169592096165438597133651606167760904128838721803617281109050826e-1"),
-T("4.15761692057244148543310701200534576325308397337003695681679007540324069366547327722258885686349619359915993749152386902e-2"),
-T("-9.04970579658619470380865991258110513843850446973806499697900678159194774744593408797468966041695053471205276923200577190e-1"),
-T("-7.42894062146919717307486895770712177633720181625852464705801879158549930143011385755502810839808877188169347497140463278e-1"),
-T("3.29255843672460745277513964057060067396377984587222455665841087186879420769340447084849343957766905952270152874052907066e-1"),
-T("9.98054859318969984153930327705164465077718593220578997216979734167429154849012382322757855259404199572095265136279871773e-1"),
-T("4.44198837297768694342150710437773511448850303134514239359160353596186338967438818161771076138440975975069051604632938785e-1"),
-T("-6.53817599431343721060913145888825198919543068369083977787231740776950274433927919565042681494795499030972133972973154991e-1"),
-T("-9.50882691455803790808811011811129940528171185220498569922200361836899859377942311459807744784166538095896117442350480286e-1"),
-T("-8.30804396823694462619418608693397504202900045660409997788297791645107264729830105800672434941805906654953509298579082883e-2"),
-T("8.86498500176738212245618093138553877114943127333459437678466772704535139826656179981455385901664422134192971441152486596e-1"),
-T("7.70083171278361495868782270594413506070341191348346709317329019377797940394556787220273230008072684372906392335068211595e-1"),
-T("-2.89713235318575682157337623325710322388267200178020040738121279630672170355171163891332847251952971324782327373734923025e-1"),
-T("-9.94599945986602107902462030221489305674036413322184167100620086215068494963807086265519051279456167270901961176645890910e-1"),
-T("-4.81064018790479216363003919039401079745827607566793090566247167201506427394383426836725220489510187378030886775425254046e-1"),
-T("6.21793567954698234151923123976248746751871911018984490371928031737872104124834908200003970971778452547150523318639635937e-1"),
-T("9.62930462544790791995256817531759605974030310743258985429278608944994805716203043054967792555227147404499205611680348343e-1"),
-T("1.24441037037160425420824052419427892644210865386492893504553391973646623439822770473194845274620957661128504291608680469e-1"),
-T("-8.66493376243885476034533210550037276824055111358129259572484897399197578809821587005093985112028866251515011805996119334e-1"),
-T("-7.95940555954229526911811786010975888490876487056728372525209250018208474961217211282867562886053609351620626802054272020e-1"),
-T("2.49669618482792917975718339302754781070461300705127317300546100189317933291972223791458678771914034385073586648459580423e-1"),
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+      "-2.46947514812703938169894550153319655995779907820829748198209521180129269232387596803077057086642606505827139155491603712e-1",
+      "7.97638583669534812597149574893980942155226403291812660315816507318428697361476484505958849067790885048775312980075497096e-1",
+      "8.65087179683067252708187359165577777305998628817518314353161876891989239932835217904989326717355654871984067712207255166e-1",
    }};
 
    boost::uintmax_t max_err = 0;
@@ -157,12 +157,12 @@ T("8.650871796830672527081873591655777773059986288175183143531618768919892399328
    {
       static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1";
       T val = sin(euler_gamma * ((100 * k) - 5000));
-      T e = relative_error(val, data[k]);
+      T e = relative_error(val, T(data[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
       val = sin(-euler_gamma * ((100 * k) - 5000));
-      e = relative_error(val, T(-data[k]));
+      e = relative_error(val, T(-T(data[k])));
       err = e.template convert_to();
       if(err > max_err)
          max_err = err;
@@ -170,59 +170,59 @@ T("8.650871796830672527081873591655777773059986288175183143531618768919892399328
    std::cout << "Max error was: " << max_err << std::endl;
    BOOST_TEST(max_err < 5000000000uLL);
 
-   static const boost::array small_data =
+   static const boost::array small_data =
    {{
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+         "0.65107817188809080279752785471799265973958362274943758073000075578938519480042543196041314945170036193559782763524413154927612489597355144799562963417455961310886431794132437757357185377007718709790504976900339191552944965308823754898079933186431693664015814010551367365293786806527034958873669211570906132849013497458819941168651227792824572805777219160376304646562062564773441718051418178414899683019",
+         "0.6652823904315739978766556052897347198651017349760138699519597733553278561013395851136458951983261597283585391502588949649092379467069209284755289821255744166256794329589771465045421874634188329764638118238723545310838064785644468083837991172367935880462068347034222894524074808990476036821633127927532229213401486467496527893691588255513769781016943243185567913995336109327864083859254466073492381187",
+         "0.67924977641755138662041086036801948989088186294785002709809874961811116536667286127777672928127306388394020078452402417993836722984523906631302047812425809759286220237826357465064765092612104224837992075711035615650942777454297235908308024053950635657488001916036801234116581671119069849133344664024677517075723660642709275823456343659009540444032487248071553674961012055521740306092600444870718199652",
+         "0.69297535762401272778114932738244728669670875114228232862389083194872888693112134130021641463393969624412179768291914405554577080353247136859984307940401373940521815913274464950964347624918449081645304540343160683388727015489772202472645406318288749244334156857814927405528763108558137488794292057315715995191324964500528600378291562277858608403425720078390497455476055579003286296442406491998525563297",
+         "0.70645424790855122905182233963742667718470686911515869065744744473731249895412640632516625097411541437953942564566468313798077366853928608154168668667806938130662439220702019172328936889436324187304262248463334787504456805683070026006307765178787997020889111556678907849442591478755800698808480163225125777511828352357189284217101098738405458071150544253514248561787426067001460586251699075230390564367",
+         "0.71968164894777168289159927814596788937422432901416956306230349431557362414856173295064125294878325237342190029914430775648665560145040598898117000971783978541799092281781000633902779626437866517288284324732827083065703448279654800632624171861777710582293639879819116932680545313562525074940809403693475624332169458744562386580074420532959714281903926902622613852892104465683714186704831143197300465955",
+         "0.73265285194543608674851404628602868786755398311878599262050209465658337331457767882450516660833910207846986678480603058221329185506983962144302950162737505562091432645466997334653618075359372680522922578429510783107155224742867979206003853893418268095936450823867623873015528453108944563276576646508412198497923383466470895808777876544429706485835161864475122029711660543090876323595451165397047981956",
+         "0.74536323930873866831066285008063416514858255428941319323031554151661731879818806472410911187787504167842137286019020264008471692607030872105020489874402631524823767448432915438225335869622093354538021006314536198469136634364850042715775621307965524560308901397550829610851125072518884822515926626213581949190024268711827023522012804341871590177804438418738255381261594827085100659777173578154500251787",
+         "0.75780828629211358196731753685850074775187628883294491833833279769413437275246840580617185041212744084038976069700142887035937511309419495512390089087847775651833369173386038513330257480188204696687136231267595399438343156895032682495327740328291738325217778497473260463740600852973600297913238958828132336080624048815574113414592522918778477418427876829087439774857073733879539765547872800792711360592",
+         "0.76998356260799010064124325420889481428942836988785464918451704687709959533402569414853910266075223008145347866420469852220997470992987183595134711278161994827010482478666523199914707457365681979989417199177427808129308850228595726632468139527316915481709465938257650120793934685421343443942356060396291075752713480402305699120964704579260218579751719693291565685728074939857101460901984240449471777639",
+         "0.78188473400392189344901888012886357289691591193533323711550248487573232160560048524966536928562079994581390209192526509899176077393862245482807165569409036943146775931090958041945317489351020506180957959482939768275851398130892970557450783138983566392455270904228057175489097967314871299150832712632639718878702471658606369540854496281803565819545728647765960328269135853132407415684491934581417388002",
+         "0.79350756380552895006859336306152006552993066088382163294295016384877329185292344719536879395060919553184640006473875955257330264813115929942877156894433233876161573894628944452740080653935089289153173836334040374431360850336851424574668632837338016740333716530963434291489645017931035529052587483629111178971917421121398732580060101294617212337648611654041575132820234403350225337355214099696493406567",
+         "0.80484791442470288298134387731514331459831415420391927496917008531718727007136925375073869996549995938671025493755987802316807560672754205522916341547950527416285009447065632296220924964603370109747266700136618832767813938243784759073035555035361911772169687111972294262096081393656654067512785827139608367560009298721819281091010743363153063005841441400130721362346287552727162527118465104052539630019",
+         "0.81590174883253870457705586780548750833668862852238889952372206236774966573191832400412494946116015154305873210759963247859431688393192829248700535837612167242633896627292821666890819736549652534738107012873094812825219601489880060491958385552979476621004236099490018887651186347086675381603801017940808290855340870383683075409122477045713172106217670870448929077822708030574128623585863036730829850118",
    }};
 
    max_err = 0;
@@ -230,14 +230,14 @@ T("8.650871796830672527081873591655777773059986288175183143531618768919892399328
    {
       static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1";
       T val = sin((euler_gamma + k) / 53);
-      T e = relative_error(val, small_data[k]);
+      T e = relative_error(val, T(small_data[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
       {
          max_err = err;
       }
       val = sin(-(euler_gamma + k) / 53);
-      e = relative_error(val, T(-small_data[k]));
+      e = relative_error(val, T(-T(small_data[k])));
       err = e.template convert_to();
       if(err > max_err)
          max_err = err;
diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp
index 04dc679b..cae2e70e 100644
--- a/test/test_sinh.cpp
+++ b/test/test_sinh.cpp
@@ -47,59 +47,59 @@
 template 
 void test()
 {
-   static const boost::array data =
+   static const boost::array data =
    {{
-      T("0.33937643772780730649735035088117439284797964277099188367427256402032493952288848579083622213428182842627923924487560393743204013166230906610274533504451302298480596207257724471359936027198954417317381228420986152562253196896619001418292769103034561794393400788635610424360775622370491149170501475453034747306600304507650361914904138327962144190354572359428689767990353722392457982930942617983634601752"),
-      T("5.9746833446871871874685235810964396457491766537010251792063372398172074828151074989468673672535421045923659313715467371148678693662985453590831122722616951299822923837410906027605763677066945998696776562438704017846907508677186762421899376364636371743116519071733413775650991880222096045615827530741679305666041641331859757012015389431793705875600863391408448065773828563483223117178640044499399723744"),
-      T("383.32826140718915582837967448860824902040431804683461630967288341613741467095168380744762629948507973653220772087887989292128183196493611623766470283358542341824134250511562240487252437079958429586344329111208041197054162309164204144237855212391474938076935722386012246677813568519769393617755607372817372398764101401294149353978426057544810680225593132066193858006901125069663362991172745649465725272"),
-      T("180470.88334757918167934673473709881208559849920820465419382707969109187448281704429118605409224039018180517847684905660962429505828088398660499158213746722168139372781263849989865384042531846290813274318773753295025006473736660333640052386121946183935053629928496714560749082485275242374067168149435272169334475060524974384307351757201698786200303374802146857634893509516262245925287553380389076772488"),
-      T("6.2781497954189513207977998975338639259302378413658035459603622432839117790845430762753614618299222131433987986511235061633658516824123179660244932375967566163895461895213509376427850290780942550513918615228886566287592461085762554208269169000672149592375451149457664991726947185145469263932975075681560662428417041932848357447220175607720561540370653825438750168143857523868718856189519864027430308779e8"),
-      T("1.6137831147508521132232267071463247985636947830692243664921522457394294988129666666745854084767325882717254318322908201512400243137564101564235450151960593110176457803621675408660678871179456625850704076654060872094257085919134755925910859520026379969099492921728083639989029675808598278170215911879751320574053132699172028082102336989338403081942130794464992491330850160862146024982135931859868176809e13"),
-      T("3.065121004865094886953119667134247741359538615435533822684602797608029400610449009335078883525336625519599034934744634528257351124420564267197918749480389135525897886434344884370577475363556341414615470556433033106705280531443046669163916446454890662947185057748542735928453570069226294801221403438864013368364219717148075652123561545773399076318560221173734215703610924057158101731263882232550297741e18"),
-      T("4.3016893602106215864771434464025735547192956887049374680649926707919814241961779812200280749930256501997849507695395125441756421661413154730888574483309057229943886742437071251707738990393977398403536175642762242808350076543018009682725019125106175929448866428526984370017465117236484653179596869643117790492866002064306593104169410537341890174831622159415936125041593936992634719906123727028419057537e24"),
-      T("4.4608685929681360001024935791890661655506049487122331222491789265929503651540405036031990380918459104583255735620288691363060079360758406339887417913286769718423759522832754263499878135869223253358698774066131403822428286318351390574838877307934317251880890827523325360658275060099119902102399714992704146743744108968362755624325107486994088414126705458507082103811086372240878942983212662081104875997e31"),
-      T("3.4181315955816806472569357441100390029536003312981931954091744304974491527743599822230006760631204302243855667216955365986192324833652299336285826148922073950348547795494738267861098328516497599288314822606511466743212319770180141969147554023326883651348621187276823849839283609071336923316655316828855943689100621619083822127788284160652232283630351386798636794979234576432977468152969056493038423561e39"),
-      T("1.9352946282727908101414530212785249763640776919052480158881659190625166733449770912626442628329346416132299268886589920690636914906717492301836773331460154604580407945460359957380672599434023197425489039882987443681919056322268437224184910074985583829184831034293865504101338027818555871946080687710035062238789949143319550108801094190098446234092310048150477274502060870736716324117412815209633124145e48"),
-      T("8.0964449511890098565841496436016431651692307764702784234901741408135381374668439020986470675941110923614446905696410406066640351065195237123718468440597743167713019447544827353458477844468727834630038609140168354634397475741840053079910210908251252223665806813131724262334693137656218010287981601097259534068903471812189212459231851835393208367369054618963204727992168556204168791513644815218096463093e57"),
-      T("2.5028257092625174549175008952222569141816383637904981644379473858250736896174216539673733521627607209322019413420937570273676341726636306931304501320694017061891400181233108050930610234076339285157392030024769366663118692571469493256243952018705693924919037621083041696227375589264811876761430035546270312014570431860268644276406457398485042029556392894799022733858611415899182421526634018060028309384e68"),
-      T("5.7168370213792649967466315312864179662895170192695050789061362839510836418124645968032989149068311018994324517420345278843446068634292140996241291031113395887824145000873531937856827299256489358571593850210528248202703396455363364446996158929674989959483681393263782486430231288067231095140919741928337466492665857902913114664767450432510739209971738097074002526312039248809036478310948111740897528204e79"),
-      T("9.6487261169670031207955841899729386502708125098394777808615183927342163909284025992243201020435915122698808649711566042372911206942311277943247994427354130507790526857797833309691667375441761513692598664419973302444660838882173718713387158013802112502169254860961105745895124415352002289485483908952674562396552790441656755711709645516914188860464353624992313010889765422981069429049436524222321550149e91"),
-      T("1.2032977660238608232537005158851668311089986235965463249220377778638489972355974848209035082333822309902237165042868213438627625544096344578102199846440476859557339736747791529782018329078191477783605471526120462726353510147373798347292650122930289404816748193194907382572774906323766342758092979989633448828636445074016110331338699464788279882402189027828261039788079556739180915346692779065476431369e105"),
-      T("1.1088306081278288754492401130897590262404571813281460605683836139669281218442501421935533170636990866165181664561596333701204545493730707210930818738817252706131805203538144119244917164949716209095542194899833868499263375700313934257155600824601418042452138211549248837967344874095248283887929145923103153332810091693393888809653081365270947112297406471162377655179657693898463736926911943490619163092e119"),
-      T("7.5499880591625965663868042832675300901799245732418501707646792135512053284835138294796976048691668315442427834949618514094329533376442442492757936744857569785450769927581802961191319878260712808001736830227501518832554201816224207300614310712430470538022948957433004823102746037654096845266998518623332118892916505020627868405618942429551700207476696585635930562973459491424179233918050890206232214765e133"),
-      T("3.798536358006797624025033016530070695826982685154937173246022092345982280900791849578041210970037835270398289956157015064696375146357207576854029748413680946201805214954504282866534528711715039215051307866373994662368105368505465037259587291440042344663580680646178313958620437868058550744621854406871361710599007951099013146571208384054250556080476992977623024059268095813712424244902009427293468485e149"),
-      T("1.4121319341572581270215359848706630542776633675711529687593487346259283960708095601494823112486631023721124235640943167173029348028743563902367757599140008654691320430919753414890689949599421028277624880392344132646738394546195638261279687543208503932172926275294218429086816560213399180179494004109164546844899632385177835442946174653663068675983237955855108059376913611877439522917217336109804190399e166"),
-      T("3.8790307719997974510664339744260233373881096199933152202662556556779783775106563986911859526413282055258612522499767709123313205863879946518297779104337686883587019222829967005608205535314284003183828513113021722123872387036435113517356676447376715595408179555267871947671679098986651665719279348025058713817796876795915844151719103197410787508530261619841035613531487094949084263218956635085585632719e183"),
-      T("7.8733605373835840397434523264038598405672829925651165847065668324385430746087633348848905637835428739401439679896923081980364912472282573695612463537585283007941057172128277340402716645674443632827653710173742423648839359547777694778576675604645880219833375227941998426325886558435214355022240854563558864080627758653439429917072753785194675103766900514602432580639079224631229479607396935864512990879e201"),
-      T("1.1808262995038900942517891457926200063018079695348469762725520377876370005771518954251015338402886097689762895044056273430051256244413916763438966705458118354189107806216991150264176024521937328179762640422127608560103802431672144866013216405157197709788484197720057702118788168789816074560208078260433548283881535909071116553897893659656781376448427981358955547508806938614921874867135186509274509121e221"),
-      T("1.3085817499987842655130548827168955655838432140245228169691892267707778790498773914833199368916114043966197329562444577848635313938483757629541576533880917215885485474416704968999200090496252044959849927443732134176975867869986011315975625868009065373046224716063168977788103866885720471095547385342868632018951910603936835789387464412366605713487321530237148912677199033012777178113821791621549557963e241"),
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+      "4.9861251931207080923785686798881789193813879610842675205361210155894774686328710893906543682447029206928934967525495260314937837003448878215156341411477636831113484416124080974502217578408248150338565305116223944900839866528622960352723938548713319425798453345402992146078868053263606234074443024155243450623634720912438841022969909473424559262711669905282193529250216454066716533180418518228387188393e862",
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+      "7.4730215360486642135431754747074885377840195683583018254892502245011973712084221116813364423492802080799768174534590613188275471080608467087354983850284805514875889145266688973752185071777341375422809910165581997555433091939959406569831183459872344778707098094941193489061532160249775856426569696127193453339548371679229676272663084782830276508737129506676031759345288056484158647796152349867328841634e941",
+      "5.8109375364209112227579654658730977030869454388607076903639465992296616832002964138000947668837140543325908222688655359602408511410663722770167244801973012245657865182739637159804595049180263175014778215232564251739259624759589953677661356104554831551073263668188283861123521688445132164147762321111597028523130093864153999974376790494383016372210442340324038686843345053322425194077414241243050491297e982",
+      "3.33875955701899627718146291382268063073604182131575843695486667154496711979350813988644889979275310892951143249901398447859083674739840084454465850475774696325142148671937407108540250845900941142800157345665761403930889797424808979569550325271558518404559007551625637761142662107757913763221912282957681784053564387104062317729788737215450574233690655931888608424916152893688106181220341997128198692e1024",
+      "1.4174672877823334709610117319768830739080734407353905145632612088824955720198734996604261250019291955883620333545750761619015467840567122066622229379056280064206319780047687015558007624774062399477328822231085767309831266032616053065858739373818651687128093335640388513396191118537181280334430292439188737524362269789272308905723812818882228503013875816702686587035844437102478263525616196832018321602e1067",
+      "4.4466189016791091516801723880812533528438597080549410911235655611382010503145789286158745555771483577943662768773465284793798720178177605712848440200402906836390133865748188969184005230383247111166918721449908133920663776952786683837038180436264738937354101153867171804315769471050303182129269442292354388037298125177941217926845803005587166270803697433886463469168814941555804311717400657004050157245e1110",
    }};
 
    T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1";
@@ -109,18 +109,18 @@ void test()
    {
       const T x = eg + k;
       T val = boost::multiprecision::sinh(x * x);
-      T e = relative_error(val, data[k]);
+      T e = relative_error(val, T(data[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;
       val = boost::multiprecision::sinh(-x * x);
-      e = relative_error(val, T(-data[k]));
+      e = relative_error(val, T(-T(data[k])));
       err = e.template convert_to();
       if(err > max_err)
          max_err = err;
    }
 
-   boost::array small_values = 
+   boost::array small_values = 
    {{
       "8.223167319358299807036616344469138485821440027829633696917375433348917938654659351596020080036406671343718039863220496616e-01",
       "2.526123168081683079141251505420579055197542874276608074880949653019810769068593790606537020961198741487692473633089323967e-01",
@@ -179,14 +179,14 @@ void test()
    for(unsigned k = 0; k < small_values.size(); ++k)
    {
       T val = boost::multiprecision::sinh(v);
-      T e = relative_error(val, small_values[k]);
+      T e = relative_error(val, T(small_values[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
       {
          max_err = err;
       }
       val = boost::multiprecision::sinh(-v);
-      e = relative_error(val, T(-small_values[k]));
+      e = relative_error(val, T(-T(small_values[k])));
       err = e.template convert_to();
       if(err > max_err)
       {
diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp
index adc27efc..e8b76c54 100644
--- a/test/test_sqrt.cpp
+++ b/test/test_sqrt.cpp
@@ -47,109 +47,109 @@
 template 
 void test()
 {
-   static const boost::array data =
+   static const boost::array data =
    {{
-           T("0"),
-           T("1.7724538509055160272981674833411451827975494561223871282138077898529112845910321813749506567385446654162268236242825706662361528657244226025250937096027870684620376986531051228499251730289508262289320953792679628001746390153514797205167001901852340185854469744949126403139217755259062164054193325009063984076137334774751534336679897893658518364087954511651617387600590673934317913328098548462481849021"),
-           T("2.506628274631000502415765284811045253006986740609938316629923576342293654607841974946595838378057266116009972665203879644866323618126736180957855655966147931913435480458123731137327804313019938802647150234465504898425802329413862779668683613033675823844181156078490095600041375150275291651461225843861864920699060926664091188015739697252377702538748247848633488642597506589513095738763427251926880402"),
-           T("3.0699801238394654654386548746677945821221293132529234536092078633942877416889511494096190816646754176075937074244926190270345429405099416216417975877667492169521054332143197658279274969526803993603118331066475990710709664118358901594985707262626428113026982211562266383695623138538180531502756293265592878111781185072888638355377253555018107077854544789544383440520575813285321747411416665951698336554"),
-           T("3.5449077018110320545963349666822903655950989122447742564276155797058225691820643627499013134770893308324536472485651413324723057314488452050501874192055741369240753973062102456998503460579016524578641907585359256003492780307029594410334003803704680371708939489898252806278435510518124328108386650018127968152274669549503068673359795787317036728175909023303234775201181347868635826656197096924963698041"),
-           T("3.9633272976060110133450287651201830315223597563961947927072580621967387180265716572287741878596340312327405647932953536228865576823564748759947646553751734998345995939694212511640273087471173966245241872854466233365203399138209787201764302154653389399844478265349330231414848625437655715466042970013389483751348124861944502103329498799507208968519689075130370544887031405163197191213743249921794351351"),
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+           "15.753914422567924620983011231186756248927500048298297966046797894473026288195693602724718689673345950533773458261077009361447048732755177208182393190558955000510862906901264875534878251422852119708834699869325135138115458649625715331447841946651213506247785763655954618727631238085210998597640478337632316374699558747521521322958958007061686783767533791960628390158818930229551073161600125867700021792",
+           "15.85330919042404405338011506048073212608943902558477917082903224878695487210628662891509675143853612493096225917318141449154623072942589950397905862150069399933839837587768500465610923498846958649809674914178649334608135965528391488070572086186135575993779130613973209256593945017506228618641718800535579350053924994477780084133179951980288358740787563005214821795481256206527887648549729996871774054",
+           "15.952084658149644245683507350070306645177945105101484153924270108676201561319289632374555910646901988746041412618543135996125375791519803422725843386425083616158339287877946105649326557260557436060388858413411665201571751138163317484650301711667106167269022770454213762825295979733155947648773992508157585668523601297276380903011908104292666527679159060486455648840531606540886121995288693616233664118",
+           "16.050252259524242304765819675794450638017457570575983927825323032144525082963948191096147193145311656453873849743947855717510860973988659112083956949050053482287530484973632648820968563125979705559716208799062595086459726936476696439381910220384322311324311842667158228425675297979222265812106596748979173989790155646435957100594433524698909367347330792212795303074381195611252785521380020853492164213",
+           "16.147823080773235880405791115635997557864326968336419500556329380232598367900898497414264871456444239647173004031647690209887509450260015358377350981847404025422287378732373648981765201137038640626625054151148020200007297959878815562787393121096595035600314225225829183114125474497018547223659528472930900422571056329570935652356761026639723378971526771480442539666833071774260326796995470405776697508",
+           "16.244807875180999875501121715806898107481293878037690793428836596906771575458065188122883764864387960703385536810260167663245388411090356221198720241639510406887891671012502982802097814197179053506077944546781492021156361482371793971423102721583613594407654464704630769172660190680210371421155562677809881516769741092121847876124182917158329121447444811423396067108583211752995130120466339417213690103",
+           "16.341217076923383960696369420161248669121212808135654273983491452937095658109553619994922766756319666975188172033084786774938321749356282450853819283481043653079525140374828081598688868309044496356854434283025399835051607515358702243412387084009896448573365043827048092425743953483386894323518311923913690941609208424884900176315736258863356896904842838787088633319141807219561302676306271570497938951",
+           "16.437060814169977953327247404361277316133609673377048855107248395882567096603010277067169202635116275806042691595212970108586780272931810640625169517986388546454661584514822804714353912243137592516024763283438958227839402433048048710441109095172462035564435115216917054500940736255985371596025417460999236751644500293733791545234403402763313780467186900924301219121627362814381042265364554244922063244",
+           "16.532348921502715844688082576333627653976665425427208876480987568125771090198651469125133728158959771903048097921398391233385160724013876315451069276292964513405939027110844786864417344898464954584607502706435338641340198705784007825954758491636479758251565454590803621730664169376188515867591916106130400067381048724859197544495864321744604824010272768413212368063633927635680949445491291877351894002",
+           "16.627090951693919358811327574245345505772490789347183724819005227768402181270609385967456291735846450867894473133567131236111152863521170798185176128190539042865125306336585771487343846002698226533251590813449657459827132440585220359867286748933370108772977365669225547985182074953209927803366884415741125333825698418900521403979162491994853083311352577067312818794931106189069819989170801482405536514",
+           "16.721296186883706959605742705233010783899326523984270864686085184270332637146646055028529386107385333643018392715062510774480808240365813021854787737722340862660933836784188253900670608552564136025173808090739064412712504259523027988063714336820233104689334204836546487559659633964043151984340548060532718923362128881432934135325567300871046043987974739750202594174747157312786841203825015000569906569",
+           "16.814973649193786097933847301606402681562971325632349794875060180956850132955663923009153012573756121825144011723368897136662622661949455269993484003323635485583818294689986393593513505114877524833927851543136113228167938420410768779051463092595000942849953376285816848692899746766156718610029919169840578968793144831181110694079933876981901697748511259778526616029120021849351522400364185613786904682",
+           "16.908132110811980070323724133825443669074486306220411933324368366059977522675356589320971338976776616316134235802112798127138113465084701628640560443298729802233609863856357626793535493930184649436981665533778324622620988007501131586355391858595913504065552289654660238871963950906549509361444433014511210945609775277269846879360970012281095853461600076871591771412527553822562541374853347368516919083",
+           "17.00078010357939362811213388133714288679743748928643153663650451825307495746227127079152413843479206992933536382011926203019216433130463160332871953682367444656008183382791141675614213387139286651404042270148438772631374392794365954621449715918679411346821231311323476100996185815327842728964327386825980705399348021964722656926231691638306207473227031037077068888418792782089031054095068740132333953",
+           "17.092925928109873230856890966518170609049635890295121605225309418908275818470576879572890960685410581830840991105430126130887790543881945170122581670877506416385845881122034595711744339948691879348516227414909772352427723381307136312192527194398703992339257139025461873121242339773525646882099071218455368070360012094043767404721710936020967834426862977103157516068354293085070758241766981055235066209",
+           "17.184577662469350439927855242766012175901435587217348622500720382402437284043691040754973131531272064166131201551424433897942349835349079351126685371244284352588634150544638769966985677717022600144009093735325965072805119643341927076098445506587163233137151789343227901578709257933753169161253949701854384420333694583107005741557086141652266134114205529376278344127778702038153204605578398292401917015",
+           "17.275743170440754085190445015394979038018668745865422068491523038650327582540706316060451728873454611950564439169497072829566902102398394981985975990083088007962977970505915486567012863555181572053681584109963952561485141768953808491468086742419682163408958624144213019203883451244657001188829080210013359418255598633772348738641653443346826322446562330527464133013054079541191939171126793437194110759",
+           "17.366430109398423824712351054979098428930613474829102247429095866488836926871097486002790757634772330314712617641418478706058891283246904611170260177746489064263225115406081681716133431691882356650113682077003571633473268618161370540232547230765011660610678347706101216301120462332270486556205728312463947537274846803558500731691464611989523847617789541328126476219681754040672802158483643453738827221",
+           "17.456645937814341319169222501542608627403113623558293524363238531385820187770170403648403252074964213113377845095534227202560251082915822197277767058606166170134732818652676480521208063952545598229201593834632528912430284433244772566961770292191780850052527418760053662080114781916361358783723872887199722599102508052518044253446686455582486241466233995573362181026486277618737441990128524043149017597",
+           "17.546397922417003516910356993677316771048907184269568216409465034396055582254893824626170868646400862812069808656427157514064265326887153266704989591763035523394048363206866117961294630191139571618530051641258534288980616305897039457680785291235730766909268092549430669200289626051927041560228580907033054444893426486648638316110177880766643917771237734940434420498182546126591670171343990763488162814",
+           "17.635693145022384705163262633691212915995304763116023125519426321471973674534505657400633405294778370478985112465094235780644028343844807586537417764875542174488900481208823741517400211272188843356948118444398002656002506943982233003640824565969970560720816740945971824478145915185970128692068679139758731692468366100636144656973628038665916994346324396985373751630840364738989989994328896453907404578",
+           "17.724538509055160272981674833411451827975494561223871282138077898529112845910321813749506567385446654162268236242825706662361528657244226025250937096027870684620376986531051228499251730289508262289320953792679628001746390153514797205167001901852340185854469744949126403139217755259062164054193325009063984076137334774751534336679897893658518364087954511651617387600590673934317913328098548462481849021",
    }};
 
    T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609";
@@ -158,7 +158,7 @@ void test()
    for(unsigned k = 0; k < data.size(); k++)
    {
       T val = sqrt(pi * k);
-      T e = relative_error(val, data[k]);
+      T e = relative_error(val, T(data[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
       {
diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp
index 4e5ca6c8..7b2b3412 100644
--- a/test/test_tanh.cpp
+++ b/test/test_tanh.cpp
@@ -47,59 +47,59 @@
 template 
 void test()
 {
-   static const boost::array data =
+   static const boost::array data =
    {{
-           T("0.32137338579537729992840434899278935725496267444911714908205287462634251052210833615032073534299473485492692600156322137421801432333125051088723502425037485776412801577568405892077585206768190530859883094571475323319480739773193974206966728764224286661945738178210577326172938196062277314761537881936346874075881338768208490193827960565412814349738654540520356903367084438822830345189856017860672463017"),
-           T("0.98628073997374759901559180515206275902189609982907214282364143439537215491113710345866034807991101303183938339561499559327886956280789743287824488269072297413440935381715378233031399015496124706604318545539544610760151756970229801074280545428642122005982857974921606264103186878499260552388713716032507770319550435738767597150644370033277228635793175246197730488375240713357827246166262087899961098648"),
-           T("0.99999659728082161113542951278514830809677661658635225532792520501703544628367875293677270218317428676793098034276042396396797568103263882451732810190507733063467333056356770774002596898762991629653041854653269824642873291146068535300466473399592751219449187768646625229500705182676930009096545254478199838990703077597971823456671241141900968900216742636822174010867343154474773040184900973368250708724"),
-           T("0.9999999999846483268200051609594321550129159997920576480976206867496512752486590660437091205989616108531910897733432934135954788151766561209164605337537937873588006552145390152387235783207736999759875845070169747521389728857476525437483543080651125798739562649414879487621858466223255239845627205850217328574865852922872737234283038190096982410137471391847466112651349436875974689271288261759782261321"),
-           T("0.9999999999999999987314527242099750648171958211319474558707792311593804963057878814487720997303512134007272111464990650500302215773762906820778949397525329109311974741708703536680512747226155618703318739024344621256722269608969415280035337052044425138281821760268269187377517243951584969175035549994883451471918693502477485385682884154959809285569290940740978684264145737164182111806308430952867505356"),
-           T("0.9999999999999999999999999980800953069847308586840237590563929855339557065536765765234844240789584487443451033349994294426525006157530320529970966048109743850154174651033567146346966529198814047607015842020039899630884318521543225160212193994911746894335846264878066530266737005606770102869237101848445559941638381625615207320468184414917265299980278164193202897754476112968080358662232635784904263624"),
-           T("0.9999999999999999999999999999999999999467800140220866754762922747687784133233134010432889959570821554455247528344437918197518545105332713456859236726383195243056599177018396579766073961540714510399202497404647103138524118065391185503678895059096790300665805648569647351935897874460587855127436472608470703384261586158923066272124216158518232588330799027603391275039552776308636189531809031683723259525"),
-           T("0.9999999999999999999999999999999999999999999999999729795912960133359928587562229512337339217831178574875626619226954752643039860388090399659478676726654102118545764943682017611574275691203710439707807193180604656837503862242700430179591666329131728631752773789406064618682879167351725013888294859467540832310795515139677375807407622028485242969471516812171475098378942187864794497220152019202351747432"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999997487354938310440650220692519525261552411539996830587326435051159231522052011310872619940247463640019105467860778515384738650636054646551611609757125760437266415865214306396520500343113189907306851418957620080971645943305760132385139924583154317156560414548076370893360020924960120441059315311380109752919823616149973862196846266297710225"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999572050575304159358359221596743379014313563214857593401545331495211888415913558896516895286943572966865708195832339959764445194449615969154689769557903166971249521898883489362426386924297872088925852892350150865941427355319827260914834268754732102528105919811851193667193380541054520023003326858641189063542651960743457613"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998665016733514821204959171836698281165918083005790816030823236096080522860514417075411055633676502699904415882389102672678124683084429720879962355892225321369091298491658349178472270952759208443767848312111069127329160464884932271685986610697222434145553035947750809388321614695213754318979469071722942883"),
-           T("0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999992372516628147584832950728021842198359205201519966391076994594773600474674435473005118571751514446148292787696117866094991476340344341061706866751156257825144909115117822189019766805825304055482958970512463798453229341693148012213183553546720540880444569824125592343803193018989122964"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999920180539244323143459416025663362517256166793900312667214543096238752838226369161775531456005541374878274529461511286842988937830155704737448202558382612829022464635400289328916240002670783433827234852858267621807568393874737879853500598862298495727481132883728328"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998470116425957155787153557938061034698436461173594805292722874130433614266475136267606498346730583487791266503943659174886554170377537630914770998114573340081594827150737005158607830579000912020838690230498119348251553312722575955142752845289"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999462931048083476382670449719737943481963930626760625326765703815392249622625483433043363664396638162612437367800102332819699131841317348173451308570776544874933173719394861336636728378134900422312720743996219523365098"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996546783689748726752364896615532860288057097437452774779386074906915819380531729493071959232887620213723607155628959529584572083388979892309086717786559916703004365603135284141639480887703759"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999593332381019647939423999969519583099837564321056588766269967853479478603122899456262904869063959564274215899007623362296377022418464303752396325625838280378647335"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999122842714667567128203355585346559126606029196080721845292399104475997315344844970601651757832506169948906646054332493537761143729664"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999965347272050374435790597917065458623422102880662825928396981295898014081371503733411536311258910851858"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999974926240515037403282500845454464621558236030794140169313830052413917"),
-           T("0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999667705192725716176070161727364499"),
-           T("1."),
-           T("1."),
-           T("1."),
-           T("1."),
-           T("1."),
-           T("1."),
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-           T("1."),
-           T("1."),
-           T("1."),
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-           T("1."),
-           T("1."),
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-           T("1."),
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-           T("1."),
-           T("1."),
-           T("1."),
+         "0.32137338579537729992840434899278935725496267444911714908205287462634251052210833615032073534299473485492692600156322137421801432333125051088723502425037485776412801577568405892077585206768190530859883094571475323319480739773193974206966728764224286661945738178210577326172938196062277314761537881936346874075881338768208490193827960565412814349738654540520356903367084438822830345189856017860672463017",
+         "0.98628073997374759901559180515206275902189609982907214282364143439537215491113710345866034807991101303183938339561499559327886956280789743287824488269072297413440935381715378233031399015496124706604318545539544610760151756970229801074280545428642122005982857974921606264103186878499260552388713716032507770319550435738767597150644370033277228635793175246197730488375240713357827246166262087899961098648",
+         "0.99999659728082161113542951278514830809677661658635225532792520501703544628367875293677270218317428676793098034276042396396797568103263882451732810190507733063467333056356770774002596898762991629653041854653269824642873291146068535300466473399592751219449187768646625229500705182676930009096545254478199838990703077597971823456671241141900968900216742636822174010867343154474773040184900973368250708724",
+         "0.9999999999846483268200051609594321550129159997920576480976206867496512752486590660437091205989616108531910897733432934135954788151766561209164605337537937873588006552145390152387235783207736999759875845070169747521389728857476525437483543080651125798739562649414879487621858466223255239845627205850217328574865852922872737234283038190096982410137471391847466112651349436875974689271288261759782261321",
+         "0.9999999999999999987314527242099750648171958211319474558707792311593804963057878814487720997303512134007272111464990650500302215773762906820778949397525329109311974741708703536680512747226155618703318739024344621256722269608969415280035337052044425138281821760268269187377517243951584969175035549994883451471918693502477485385682884154959809285569290940740978684264145737164182111806308430952867505356",
+         "0.9999999999999999999999999980800953069847308586840237590563929855339557065536765765234844240789584487443451033349994294426525006157530320529970966048109743850154174651033567146346966529198814047607015842020039899630884318521543225160212193994911746894335846264878066530266737005606770102869237101848445559941638381625615207320468184414917265299980278164193202897754476112968080358662232635784904263624",
+         "0.9999999999999999999999999999999999999467800140220866754762922747687784133233134010432889959570821554455247528344437918197518545105332713456859236726383195243056599177018396579766073961540714510399202497404647103138524118065391185503678895059096790300665805648569647351935897874460587855127436472608470703384261586158923066272124216158518232588330799027603391275039552776308636189531809031683723259525",
+         "0.9999999999999999999999999999999999999999999999999729795912960133359928587562229512337339217831178574875626619226954752643039860388090399659478676726654102118545764943682017611574275691203710439707807193180604656837503862242700430179591666329131728631752773789406064618682879167351725013888294859467540832310795515139677375807407622028485242969471516812171475098378942187864794497220152019202351747432",
+         "0.9999999999999999999999999999999999999999999999999999999999999997487354938310440650220692519525261552411539996830587326435051159231522052011310872619940247463640019105467860778515384738650636054646551611609757125760437266415865214306396520500343113189907306851418957620080971645943305760132385139924583154317156560414548076370893360020924960120441059315311380109752919823616149973862196846266297710225",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999572050575304159358359221596743379014313563214857593401545331495211888415913558896516895286943572966865708195832339959764445194449615969154689769557903166971249521898883489362426386924297872088925852892350150865941427355319827260914834268754732102528105919811851193667193380541054520023003326858641189063542651960743457613",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998665016733514821204959171836698281165918083005790816030823236096080522860514417075411055633676502699904415882389102672678124683084429720879962355892225321369091298491658349178472270952759208443767848312111069127329160464884932271685986610697222434145553035947750809388321614695213754318979469071722942883",
+         "0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999992372516628147584832950728021842198359205201519966391076994594773600474674435473005118571751514446148292787696117866094991476340344341061706866751156257825144909115117822189019766805825304055482958970512463798453229341693148012213183553546720540880444569824125592343803193018989122964",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999920180539244323143459416025663362517256166793900312667214543096238752838226369161775531456005541374878274529461511286842988937830155704737448202558382612829022464635400289328916240002670783433827234852858267621807568393874737879853500598862298495727481132883728328",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998470116425957155787153557938061034698436461173594805292722874130433614266475136267606498346730583487791266503943659174886554170377537630914770998114573340081594827150737005158607830579000912020838690230498119348251553312722575955142752845289",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999462931048083476382670449719737943481963930626760625326765703815392249622625483433043363664396638162612437367800102332819699131841317348173451308570776544874933173719394861336636728378134900422312720743996219523365098",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996546783689748726752364896615532860288057097437452774779386074906915819380531729493071959232887620213723607155628959529584572083388979892309086717786559916703004365603135284141639480887703759",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999593332381019647939423999969519583099837564321056588766269967853479478603122899456262904869063959564274215899007623362296377022418464303752396325625838280378647335",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999122842714667567128203355585346559126606029196080721845292399104475997315344844970601651757832506169948906646054332493537761143729664",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999965347272050374435790597917065458623422102880662825928396981295898014081371503733411536311258910851858",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999974926240515037403282500845454464621558236030794140169313830052413917",
+         "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999667705192725716176070161727364499",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
+         "1.",
    }};
 
    T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1";
@@ -109,7 +109,7 @@ void test()
    {
       const T x = eg + k;
       T val = boost::multiprecision::tanh(x * x);
-      T e = relative_error(val, data[k]);
+      T e = relative_error(val, T(data[k]));
       unsigned err = e.template convert_to();
       if(err > max_err)
          max_err = err;

From db83a1c4add6f8124a4113d46a54564bd3766044 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 12 Jan 2012 11:55:09 +0000
Subject: [PATCH 096/256] Tentative rename of packed_cpp_int to fixed_int.

[SVN r76428]
---
 .../boost/multiprecision/packed_cpp_int.hpp   | 399 +++++++++---------
 performance/performance_test.cpp              |  12 +-
 test/Jamfile.v2                               |  18 +-
 test/packed_int_test.cpp                      |   6 +-
 test/test_arithmetic.cpp                      |  18 +-
 test/test_int_io.cpp                          |  22 +-
 6 files changed, 249 insertions(+), 226 deletions(-)

diff --git a/include/boost/multiprecision/packed_cpp_int.hpp b/include/boost/multiprecision/packed_cpp_int.hpp
index 6dbc8657..0bbc2fa7 100644
--- a/include/boost/multiprecision/packed_cpp_int.hpp
+++ b/include/boost/multiprecision/packed_cpp_int.hpp
@@ -18,7 +18,7 @@ namespace boost{
 namespace multiprecision{
 
 template 
-struct packed_cpp_int
+struct fixed_int
 {
    typedef mpl::list      signed_types;
    typedef mpl::list    unsigned_types;
@@ -33,37 +33,37 @@ struct packed_cpp_int
    BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1 << ((Bits % limb_bits ? Bits % limb_bits : limb_bits) - 1));
    typedef boost::array data_type;
 
-   packed_cpp_int(){}
-   packed_cpp_int(const packed_cpp_int& o)
+   fixed_int(){}
+   fixed_int(const fixed_int& o)
    {
       m_value = o.m_value;
    }
 #ifndef BOOST_NO_RVALUE_REFERENCES
-   packed_cpp_int(packed_cpp_int&& o) : m_value(o.m_value) {}
+   fixed_int(fixed_int&& o) : m_value(o.m_value) {}
 #endif
-   packed_cpp_int& operator = (const packed_cpp_int& o)
+   fixed_int& operator = (const fixed_int& o)
    {
       m_value = o.m_value;
       return *this;
    }
-   packed_cpp_int& operator = (boost::uint32_t i)
+   fixed_int& operator = (boost::uint32_t i)
    {
       m_value[limb_count - 1] = i;
       for(int j = limb_count - 2; j >= 0; --j)
          m_value[j] = 0;
-      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      m_value[0] &= fixed_int::upper_limb_mask;
       return *this;
    }
-   packed_cpp_int& operator = (boost::int32_t i)
+   fixed_int& operator = (boost::int32_t i)
    {
       m_value[limb_count - 1] = i;
       // sign extend:
       for(int j = limb_count - 2; j >= 0; --j)
          m_value[j] = i < 0 ? max_limb_value : 0;
-      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      m_value[0] &= fixed_int::upper_limb_mask;
       return *this;
    }
-   packed_cpp_int& operator = (boost::uintmax_t i)
+   fixed_int& operator = (boost::uintmax_t i)
    {
       BOOST_STATIC_ASSERT(sizeof(i) % sizeof(limb_type) == 0);
       boost::uintmax_t mask = max_limb_value;
@@ -76,10 +76,10 @@ struct packed_cpp_int
       }
       for(int j = static_cast(limb_count) - static_cast(sizeof(boost::intmax_t) / sizeof(limb_type)) - 1; j >= 0; --j)
          m_value[j] = 0;
-      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      m_value[0] &= fixed_int::upper_limb_mask;
       return *this;
    }
-   packed_cpp_int& operator = (boost::intmax_t i)
+   fixed_int& operator = (boost::intmax_t i)
    {
       BOOST_STATIC_ASSERT(sizeof(i) % sizeof(limb_type) == 0);
       boost::uintmax_t mask = max_limb_value;
@@ -92,10 +92,10 @@ struct packed_cpp_int
       }
       for(int j = static_cast(limb_count) - static_cast(sizeof(boost::intmax_t) / sizeof(limb_type)) - 1; j >= 0; --j)
          m_value[j] = i < 0 ? max_limb_value : 0;
-      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      m_value[0] &= fixed_int::upper_limb_mask;
       return *this;
    }
-   packed_cpp_int& operator = (long double a)
+   fixed_int& operator = (long double a)
    {
       BOOST_STATIC_ASSERT(Bits >= (unsigned)std::numeric_limits::digits);
       using std::frexp;
@@ -138,10 +138,10 @@ struct packed_cpp_int
          left_shift(*this, e);
       else if(e < 0)
          right_shift(*this, -e);
-      data()[0] &= packed_cpp_int::upper_limb_mask;
+      data()[0] &= fixed_int::upper_limb_mask;
       return *this;
    }
-   packed_cpp_int& operator = (const char* s)
+   fixed_int& operator = (const char* s)
    {
       std::size_t n = s ? std::strlen(s) : 0;
       *this = static_cast(0u);
@@ -186,7 +186,7 @@ struct packed_cpp_int
                   val = max_limb_value;
                if(val > radix)
                {
-                  m_value[0] &= packed_cpp_int::upper_limb_mask;
+                  m_value[0] &= fixed_int::upper_limb_mask;
                   return *this; // TODO raise an exception here?
                }
                m_value[limb_count - 1] |= val;
@@ -210,12 +210,12 @@ struct packed_cpp_int
             }
          }
       }
-      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      m_value[0] &= fixed_int::upper_limb_mask;
       if(isneg)
          negate();
       return *this;
    }
-   void swap(packed_cpp_int& o)
+   void swap(fixed_int& o)
    {
       std::swap(m_value, o.m_value);
    }
@@ -232,7 +232,7 @@ struct packed_cpp_int
       {
          boost::uint32_t shift = base == 8 ? 3 : 4;
          boost::uint32_t mask = static_cast((1u << shift) - 1);
-         packed_cpp_int t(*this);
+         fixed_int t(*this);
          for(unsigned i = 0; i < Bits / shift; ++i)
          {
             char c = '0' + (t.data()[limb_count-1] & mask);
@@ -264,8 +264,8 @@ struct packed_cpp_int
       }
       else
       {
-         packed_cpp_int t(*this);
-         packed_cpp_int ten, r;
+         fixed_int t(*this);
+         fixed_int ten, r;
          ten = boost::uint32_t(1000000000);
          bool neg = false;
          if(Signed && (t.data()[0] & sign_bit_mask))
@@ -281,7 +281,7 @@ struct packed_cpp_int
          {
             while(get_sign(t) != 0)
             {
-               packed_cpp_int t2;
+               fixed_int t2;
                divide_unsigned_helper(t2, t, ten, r);
                t = t2;
                boost::uint32_t v = r.data()[limb_count - 1];
@@ -307,15 +307,15 @@ struct packed_cpp_int
    void negate()
    {
       boost::uintmax_t carry = 1;
-      for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
+      for(int i = fixed_int::limb_count - 1; i >= 0; --i)
       {
          carry += static_cast(~m_value[i]);
          m_value[i] = static_cast(carry);
          carry >>= limb_bits;
       }
-      m_value[0] &= packed_cpp_int::upper_limb_mask;
+      m_value[0] &= fixed_int::upper_limb_mask;
    }
-   int compare(const packed_cpp_int& o)const
+   int compare(const fixed_int& o)const
    {
       int result = 0;
       if(Signed && ((m_value[0] & sign_bit_mask) != (o.data()[0] & sign_bit_mask)))
@@ -336,7 +336,7 @@ struct packed_cpp_int
    typename enable_if, int>::type compare(Arithmatic i)const
    {
       // braindead version:
-      packed_cpp_int t;
+      fixed_int t;
       t = i;
       return compare(t);
    }
@@ -347,40 +347,40 @@ private:
 };
 
 template 
-inline void add(packed_cpp_int& result, const packed_cpp_int& o)
+inline void add(fixed_int& result, const fixed_int& o)
 {
    add(result, result, o);
 }
 template 
-inline void add(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
+inline void add(fixed_int& result, const fixed_int& a, const fixed_int& b)
 {
    // Addition using modular arithmatic.
    // Nothing fancy, just let uintmax_t take the strain:
    boost::uintmax_t carry = 0;
-   for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
+   for(int i = fixed_int::limb_count - 1; i >= 0; --i)
    {
       carry += static_cast(a.data()[i]) + static_cast(b.data()[i]);
-      result.data()[i] = static_cast::limb_type>(carry);
-      carry >>= packed_cpp_int::limb_bits;
+      result.data()[i] = static_cast::limb_type>(carry);
+      carry >>= fixed_int::limb_bits;
    }
-   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+   result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void add(packed_cpp_int& result, const boost::uint32_t& o)
+inline void add(fixed_int& result, const boost::uint32_t& o)
 {
    // Addition using modular arithmatic.
    // Nothing fancy, just let uintmax_t take the strain:
    boost::uintmax_t carry = o;
-   for(int i = packed_cpp_int::limb_count - 1; carry && i >= 0; --i)
+   for(int i = fixed_int::limb_count - 1; carry && i >= 0; --i)
    {
       carry += static_cast(result.data()[i]);
-      result.data()[i] = static_cast::limb_type>(carry);
-      carry >>= packed_cpp_int::limb_bits;
+      result.data()[i] = static_cast::limb_type>(carry);
+      carry >>= fixed_int::limb_bits;
    }
-   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+   result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void add(packed_cpp_int& result, const boost::int32_t& o)
+inline void add(fixed_int& result, const boost::int32_t& o)
 {
    if(o < 0)
       subtract(result, static_cast(-o));
@@ -388,24 +388,24 @@ inline void add(packed_cpp_int& result, const boost::int32_t& o)
       add(result, static_cast(o));
 }
 template 
-inline void subtract(packed_cpp_int& result, const boost::uint32_t& o)
+inline void subtract(fixed_int& result, const boost::uint32_t& o)
 {
    // Subtract using modular arithmatic.
    // This is the same code as for addition, with the twist that we negate o "on the fly":
-   boost::uintmax_t carry = static_cast(result.data()[packed_cpp_int::limb_count - 1]) 
+   boost::uintmax_t carry = static_cast(result.data()[fixed_int::limb_count - 1]) 
       + 1uLL + static_cast(~o);
-   result.data()[packed_cpp_int::limb_count - 1] = static_cast::limb_type>(carry);
-   carry >>= packed_cpp_int::limb_bits;
-   for(int i = packed_cpp_int::limb_count - 2; i >= 0; --i)
+   result.data()[fixed_int::limb_count - 1] = static_cast::limb_type>(carry);
+   carry >>= fixed_int::limb_bits;
+   for(int i = fixed_int::limb_count - 2; i >= 0; --i)
    {
       carry += static_cast(result.data()[i]) + 0xFFFFFFFF;
-      result.data()[i] = static_cast::limb_type>(carry);
-      carry >>= packed_cpp_int::limb_bits;
+      result.data()[i] = static_cast::limb_type>(carry);
+      carry >>= fixed_int::limb_bits;
    }
-   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+   result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void subtract(packed_cpp_int& result, const boost::int32_t& o)
+inline void subtract(fixed_int& result, const boost::int32_t& o)
 {
    if(o)
    {
@@ -416,90 +416,90 @@ inline void subtract(packed_cpp_int& result, const boost::int32_t&
    }
 }
 template 
-inline void increment(packed_cpp_int& result)
+inline void increment(fixed_int& result)
 {
    static const boost::uint32_t one = 1;
    add(result, one);
 }
 template 
-inline void decrement(packed_cpp_int& result)
+inline void decrement(fixed_int& result)
 {
    static const boost::uint32_t one = 1;
    subtract(result, one);
 }
 template 
-inline void subtract(packed_cpp_int& result, const packed_cpp_int& o)
+inline void subtract(fixed_int& result, const fixed_int& o)
 {
    subtract(result, result, o);
 }
 template 
-inline void subtract(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
+inline void subtract(fixed_int& result, const fixed_int& a, const fixed_int& b)
 {
    // Subtract using modular arithmatic.
    // This is the same code as for addition, with the twist that we negate b "on the fly":
    boost::uintmax_t carry = 1;
-   for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
+   for(int i = fixed_int::limb_count - 1; i >= 0; --i)
    {
       carry += static_cast(a.data()[i]) + static_cast(~b.data()[i]);
-      result.data()[i] = static_cast::limb_type>(carry);
-      carry >>= packed_cpp_int::limb_bits;
+      result.data()[i] = static_cast::limb_type>(carry);
+      carry >>= fixed_int::limb_bits;
    }
-   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+   result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void multiply(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
+inline void multiply(fixed_int& result, const fixed_int& a, const fixed_int& b)
 {
    // Very simple long multiplication, only usable for small numbers of limb_type's
    // but that's the typical use case for this type anyway:
    if(&result == &a)
    {
-      packed_cpp_int t(a);
+      fixed_int t(a);
       multiply(result, t, b);
       return;
    }
    if(&result == &b)
    {
-      packed_cpp_int t(b);
+      fixed_int t(b);
       multiply(result, a, t);
       return;
    }
    boost::uintmax_t carry = 0;
-   for(unsigned i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(unsigned i = 0; i < fixed_int::limb_count; ++i)
       result.data()[i] = 0;
-   for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
+   for(int i = fixed_int::limb_count - 1; i >= 0; --i)
    {
-      for(int j = packed_cpp_int::limb_count - 1; j >= static_cast(packed_cpp_int::limb_count) - i - 1; --j)
+      for(int j = fixed_int::limb_count - 1; j >= static_cast(fixed_int::limb_count) - i - 1; --j)
       {
          carry += static_cast(a.data()[i]) * static_cast(b.data()[j]);
-         carry += result.data()[i + j + 1 - packed_cpp_int::limb_count];
-         result.data()[i + j + 1 - packed_cpp_int::limb_count] = static_cast::limb_type>(carry);
-         carry >>= packed_cpp_int::limb_bits;
+         carry += result.data()[i + j + 1 - fixed_int::limb_count];
+         result.data()[i + j + 1 - fixed_int::limb_count] = static_cast::limb_type>(carry);
+         carry >>= fixed_int::limb_bits;
       }
       carry = 0;
    }
-   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+   result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void multiply(packed_cpp_int& result, const packed_cpp_int& a)
+inline void multiply(fixed_int& result, const fixed_int& a)
 {
    // There is no in-place multiply:
-   packed_cpp_int b(result);
+   fixed_int b(result);
    multiply(result, b, a);
 }
 template 
-inline void multiply(packed_cpp_int& result, const boost::uint32_t& a)
+inline void multiply(fixed_int& result, const boost::uint32_t& a)
 {
    boost::uintmax_t carry = 0;
-   for(int i = packed_cpp_int::limb_count - 1; i >= 0; --i)
+   for(int i = fixed_int::limb_count - 1; i >= 0; --i)
    {
       carry += static_cast(result.data()[i]) * static_cast(a);
-      result.data()[i] = static_cast::limb_type>(carry);
-      carry >>= packed_cpp_int::limb_bits;
+      result.data()[i] = static_cast::limb_type>(carry);
+      carry >>= fixed_int::limb_bits;
    }
-   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+   result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void multiply(packed_cpp_int& result, const boost::int32_t& a)
+inline void multiply(fixed_int& result, const boost::int32_t& a)
 {
    if(a > 0)
       multiply(result, static_cast(a));
@@ -512,15 +512,15 @@ inline void multiply(packed_cpp_int& result, const boost::int32_t&
 
 /*
 template 
-boost::uint32_t bitcount(const packed_cpp_int& a)
+boost::uint32_t bitcount(const fixed_int& a)
 {
    // returns the location of the MSB in a:
    boost::uint32_t i = 0;
-   for(; (i < packed_cpp_int::limb_count) && (a.data()[i] == 0); ++i){}
-   boost::uint32_t count = (packed_cpp_int::limb_count - i) * packed_cpp_int::limb_bits;
+   for(; (i < fixed_int::limb_count) && (a.data()[i] == 0); ++i){}
+   boost::uint32_t count = (fixed_int::limb_count - i) * fixed_int::limb_bits;
    if(!count)
       return count; // no bits are set, value is zero
-   boost::uint32_t mask = static_cast(1u) << (packed_cpp_int::limb_bits - 1);
+   boost::uint32_t mask = static_cast(1u) << (fixed_int::limb_bits - 1);
    while((a.data()[i] & mask) == 0)
    {
       --count;
@@ -529,17 +529,17 @@ boost::uint32_t bitcount(const packed_cpp_int& a)
    return count;
 }
 template 
-void divide_unsigned_helper(packed_cpp_int& result, const packed_cpp_int& x, const packed_cpp_int& y, packed_cpp_int& r)
+void divide_unsigned_helper(fixed_int& result, const fixed_int& x, const fixed_int& y, fixed_int& r)
 {
    if((&result == &x) || (&r == &x))
    {
-      packed_cpp_int t(x);
+      fixed_int t(x);
       divide_unsigned_helper(result, t, y, r);
       return;
    }
    if((&result == &y) || (&r == &y))
    {
-      packed_cpp_int t(y);
+      fixed_int t(y);
       divide_unsigned_helper(result, x, t, r);
       return;
    }
@@ -564,7 +564,7 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
 
    if(&result == &r)
    {
-      packed_cpp_int rem;
+      fixed_int rem;
       divide_unsigned_helper(result, x, y, rem);
       r = rem;
       return;
@@ -588,11 +588,11 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
    }
 
    // Together mask_index and mask give us the bit we may be about to set in the result:
-   boost::uint32_t mask_index = packed_cpp_int::limb_count - 1 - n / packed_cpp_int::limb_bits;
-   boost::uint32_t mask = static_cast(1u) << n % packed_cpp_int::limb_bits;
-   packed_cpp_int t(y);
+   boost::uint32_t mask_index = fixed_int::limb_count - 1 - n / fixed_int::limb_bits;
+   boost::uint32_t mask = static_cast(1u) << n % fixed_int::limb_bits;
+   fixed_int t(y);
    left_shift(t, n);
-   while(mask_index < packed_cpp_int::limb_count)
+   while(mask_index < fixed_int::limb_count)
    {
       int comp = r.compare(t);
       if(comp >= 0)
@@ -606,28 +606,46 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
       if(0 == (mask >>= 1))
       {
          ++mask_index;
-         mask = static_cast(1u) << (packed_cpp_int::limb_bits - 1);
+         mask = static_cast(1u) << (fixed_int::limb_bits - 1);
       }
    }
    BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed
 }
 */
 template 
-void divide_unsigned_helper(packed_cpp_int& result, const packed_cpp_int& x, const packed_cpp_int& y, packed_cpp_int& r)
+void divide_unsigned_helper(fixed_int& result, const fixed_int& x, const fixed_int& y, fixed_int& r)
 {
    if((&result == &x) || (&r == &x))
    {
-      packed_cpp_int t(x);
+      fixed_int t(x);
       divide_unsigned_helper(result, t, y, r);
       return;
    }
    if((&result == &y) || (&r == &y))
    {
-      packed_cpp_int t(y);
+      fixed_int t(y);
       divide_unsigned_helper(result, x, t, r);
       return;
    }
 
+   /*
+    Very simple, fairly braindead long division.
+    Start by setting the remainder equal to x, and the
+    result equal to 0.  Then in each loop we calculate our
+    "best guess" for how many times y divides into r,
+    add our guess to the result, and subtract guess*y
+    from the remainder r.  One wrinckle is that the remainder
+    may go negative, in which case we subtract the current guess
+    from the result rather than adding.  The value of the guess
+    is determined by dividing the most-significant-limb of the
+    current remainder by the most-significant-limb of y.
+
+    Note that there are more efficient algorithms than this
+    available, in particular see Knuth Vol 2.  However for small
+    numbers of limbs this generally outperforms the alternatives
+    and avoids the normalisation step which would require extra storage.
+    */
+
 
    using default_ops::subtract;
 
@@ -648,7 +666,7 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
 
    if(&result == &r)
    {
-      packed_cpp_int rem;
+      fixed_int rem;
       divide_unsigned_helper(result, x, y, rem);
       r = rem;
       return;
@@ -673,24 +691,24 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
    while(y.data()[y_order] == 0)
       ++y_order;
 
-   packed_cpp_int t;
+   fixed_int t;
    bool r_neg = false;
 
    //
    // See if we can short-circuit long division, and use basic arithmetic instead:
    //
-   if(r_order == packed_cpp_int::limb_count - 1)
+   if(r_order == fixed_int::limb_count - 1)
    {
-      result = r.data()[packed_cpp_int::limb_count - 1] / y.data()[packed_cpp_int::limb_count - 1];
-      r = x.data()[packed_cpp_int::limb_count - 1] % y.data()[packed_cpp_int::limb_count - 1];
+      result = r.data()[fixed_int::limb_count - 1] / y.data()[fixed_int::limb_count - 1];
+      r = x.data()[fixed_int::limb_count - 1] % y.data()[fixed_int::limb_count - 1];
       return;
    }
-   else if(r_order == packed_cpp_int::limb_count - 2)
+   else if(r_order == fixed_int::limb_count - 2)
    {
       unsigned long long a, b;
-      a = (static_cast(r.data()[r_order]) << packed_cpp_int::limb_bits) | r.data()[r_order + 1];
-      b = y_order < packed_cpp_int::limb_count - 1 ? 
-         (static_cast(y.data()[y_order]) << packed_cpp_int::limb_bits) | y.data()[y_order + 1] 
+      a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1];
+      b = y_order < fixed_int::limb_count - 1 ? 
+         (static_cast(y.data()[y_order]) << fixed_int::limb_bits) | y.data()[y_order + 1] 
          : y.data()[y_order];
       result = a / b;
       r = a % b;
@@ -708,13 +726,13 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
       // Calculate our best guess for how many times y divides into r:
       //
       boost::uint32_t guess;
-      if((r.data()[r_order] <= y.data()[y_order]) && (r_order < packed_cpp_int::limb_count - 1))
+      if((r.data()[r_order] <= y.data()[y_order]) && (r_order < fixed_int::limb_count - 1))
       {
          unsigned long long a, b, v;
-         a = (static_cast(r.data()[r_order]) << packed_cpp_int::limb_bits) | r.data()[r_order + 1];
+         a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1];
          b = y.data()[y_order];
          v = a / b;
-         if(v > packed_cpp_int::max_limb_value)
+         if(v > fixed_int::max_limb_value)
             guess = 1;
          else
          {
@@ -724,14 +742,19 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
       }
       else
       {
-         guess = r.data()[r_order] / y.data()[y_order];
+         unsigned long long a, b, v;
+         a = (r_order < fixed_int::limb_count - 1) ? (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1] : r.data()[r_order];
+         b = (y_order < fixed_int::limb_count - 1) ? (static_cast(y.data()[y_order]) << fixed_int::limb_bits) | y.data()[y_order + 1] : (static_cast(y.data()[y_order])  << fixed_int::limb_bits);
+         v = a / b;
+         guess = static_cast::limb_type>(v);
+         //guess = r.data()[r_order] / y.data()[y_order];
       }
       //
       // Update result:
       //
       boost::uint32_t shift = y_order - r_order;
       t = boost::uint32_t(0);
-      t.data()[packed_cpp_int::limb_count - 1 - shift] = guess;
+      t.data()[fixed_int::limb_count - 1 - shift] = guess;
       if(r_neg)
          subtract(result, t);
       else
@@ -741,20 +764,20 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
       // rather than a full O(N^2) multiply:
       //
       boost::uintmax_t carry = 0;
-      for(unsigned i = packed_cpp_int::limb_count - 1; i > packed_cpp_int::limb_count - shift - 1; --i)
+      for(unsigned i = fixed_int::limb_count - 1; i > fixed_int::limb_count - shift - 1; --i)
          t.data()[i] = 0;
-      for(int i = packed_cpp_int::limb_count - 1; i >= static_cast(shift); --i)
+      for(int i = fixed_int::limb_count - 1; i >= static_cast(shift); --i)
       {
          carry += static_cast(y.data()[i]) * static_cast(guess);
-         t.data()[i - shift] = static_cast::limb_type>(carry);
-         carry >>= packed_cpp_int::limb_bits;
+         t.data()[i - shift] = static_cast::limb_type>(carry);
+         carry >>= fixed_int::limb_bits;
       }
-      t.data()[0] &= packed_cpp_int::upper_limb_mask;
+      t.data()[0] &= fixed_int::upper_limb_mask;
        //
       // Update r:
       //
       subtract(r, t);
-      if(r.data()[0] & packed_cpp_int::sign_bit_mask)
+      if(r.data()[0] & fixed_int::sign_bit_mask)
       {
          r.negate();
          r_neg = !r_neg;
@@ -777,29 +800,29 @@ void divide_unsigned_helper(packed_cpp_int& result, const packed_c
 }
 
 template 
-inline void divide(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
+inline void divide(fixed_int& result, const fixed_int& a, const fixed_int& b)
 {
-   packed_cpp_int r;
-   if(Signed && (a.data()[0] & packed_cpp_int::sign_bit_mask))
+   fixed_int r;
+   if(Signed && (a.data()[0] & fixed_int::sign_bit_mask))
    {
-      if(Signed && (b.data()[0] & packed_cpp_int::sign_bit_mask))
+      if(Signed && (b.data()[0] & fixed_int::sign_bit_mask))
       {
-         packed_cpp_int t1(a), t2(b);
+         fixed_int t1(a), t2(b);
          t1.negate();
          t2.negate();
          divide_unsigned_helper(result, t1, t2, r);
       }
       else
       {
-         packed_cpp_int t(a);
+         fixed_int t(a);
          t.negate();
          divide_unsigned_helper(result, t, b, r);
          result.negate();
       }
    }
-   else if(Signed && (b.data()[0] & packed_cpp_int::sign_bit_mask))
+   else if(Signed && (b.data()[0] & fixed_int::sign_bit_mask))
    {
-      packed_cpp_int t(b);
+      fixed_int t(b);
       t.negate();
       divide_unsigned_helper(result, a, t, r);
       result.negate();
@@ -810,21 +833,21 @@ inline void divide(packed_cpp_int& result, const packed_cpp_int
-inline void divide(packed_cpp_int& result, const packed_cpp_int& b)
+inline void divide(fixed_int& result, const fixed_int& b)
 {
    // There is no in place divide:
-   packed_cpp_int a(result);
+   fixed_int a(result);
    divide(result, a, b);
 }
 template 
-inline void modulus(packed_cpp_int& result, const packed_cpp_int& a, const packed_cpp_int& b)
+inline void modulus(fixed_int& result, const fixed_int& a, const fixed_int& b)
 {
-   packed_cpp_int r;
-   if(Signed && (a.data()[0] & packed_cpp_int::sign_bit_mask))
+   fixed_int r;
+   if(Signed && (a.data()[0] & fixed_int::sign_bit_mask))
    {
-      if(Signed && (b.data()[0] & packed_cpp_int::sign_bit_mask))
+      if(Signed && (b.data()[0] & fixed_int::sign_bit_mask))
       {
-         packed_cpp_int t1(a), t2(b);
+         fixed_int t1(a), t2(b);
          t1.negate();
          t2.negate();
          divide_unsigned_helper(r, t1, t2, result);
@@ -832,15 +855,15 @@ inline void modulus(packed_cpp_int& result, const packed_cpp_int t(a);
+         fixed_int t(a);
          t.negate();
          divide_unsigned_helper(r, t, b, result);
          result.negate();
       }
    }
-   else if(Signed && (b.data()[0] & packed_cpp_int::sign_bit_mask))
+   else if(Signed && (b.data()[0] & fixed_int::sign_bit_mask))
    {
-      packed_cpp_int t(b);
+      fixed_int t(b);
       t.negate();
       divide_unsigned_helper(r, a, t, result);
    }
@@ -850,100 +873,100 @@ inline void modulus(packed_cpp_int& result, const packed_cpp_int
-inline void modulus(packed_cpp_int& result, const packed_cpp_int& b)
+inline void modulus(fixed_int& result, const fixed_int& b)
 {
    // There is no in place divide:
-   packed_cpp_int a(result);
+   fixed_int a(result);
    modulus(result, a, b);
 }
 
 template 
-inline void bitwise_and(packed_cpp_int& result, const packed_cpp_int& o)
+inline void bitwise_and(fixed_int& result, const fixed_int& o)
 {
-   for(typename packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i)
       result.data()[i] &= o.data()[i];
 }
 template 
-inline void bitwise_or(packed_cpp_int& result, const packed_cpp_int& o)
+inline void bitwise_or(fixed_int& result, const fixed_int& o)
 {
-   for(typename packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i)
       result.data()[i] |= o.data()[i];
 }
 template 
-inline void bitwise_xor(packed_cpp_int& result, const packed_cpp_int& o)
+inline void bitwise_xor(fixed_int& result, const fixed_int& o)
 {
-   for(typename packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i)
       result.data()[i] ^= o.data()[i];
-   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+   result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void complement(packed_cpp_int& result, const packed_cpp_int& o)
+inline void complement(fixed_int& result, const fixed_int& o)
 {
-   for(typename packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i)
       result.data()[i] = ~o.data()[i];
-   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+   result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void left_shift(packed_cpp_int& result, boost::uintmax_t s)
+inline void left_shift(fixed_int& result, boost::uintmax_t s)
 {
    if(s >= Bits)
    {
       result = static_cast(0);
       return;
    }
-   boost::uint32_t offset = static_cast(s / packed_cpp_int::limb_bits);
-   boost::uint32_t shift  = static_cast(s % packed_cpp_int::limb_bits);
+   boost::uint32_t offset = static_cast(s / fixed_int::limb_bits);
+   boost::uint32_t shift  = static_cast(s % fixed_int::limb_bits);
    unsigned i = 0;
    if(shift)
    {
       // This code only works when shift is non-zero, otherwise we invoke undefined behaviour!
-      for(; i + offset + 1 < packed_cpp_int::limb_count; ++i)
+      for(; i + offset + 1 < fixed_int::limb_count; ++i)
       {
          result.data()[i] = result.data()[i+offset] << shift;
-         result.data()[i] |= result.data()[i+offset+1] >> (packed_cpp_int::limb_bits - shift);
+         result.data()[i] |= result.data()[i+offset+1] >> (fixed_int::limb_bits - shift);
       }
       result.data()[i] = result.data()[i+offset] << shift;
       ++i;
-      for(; i < packed_cpp_int::limb_count; ++i)
+      for(; i < fixed_int::limb_count; ++i)
          result.data()[i] = 0;
    }
    else
    {
-      for(; i + offset < packed_cpp_int::limb_count; ++i)
+      for(; i + offset < fixed_int::limb_count; ++i)
          result.data()[i] = result.data()[i+offset];
-      for(; i < packed_cpp_int::limb_count; ++i)
+      for(; i < fixed_int::limb_count; ++i)
          result.data()[i] = 0;
    }
-   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+   result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void right_shift(packed_cpp_int& result, boost::uintmax_t s)
+inline void right_shift(fixed_int& result, boost::uintmax_t s)
 {
-   boost::uint32_t fill = (Signed && (result.data()[0] & packed_cpp_int::sign_bit_mask)) ? packed_cpp_int::max_limb_value : 0u;
+   boost::uint32_t fill = (Signed && (result.data()[0] & fixed_int::sign_bit_mask)) ? fixed_int::max_limb_value : 0u;
    if(s >= Bits)
    {
-      for(unsigned i = 0; i < packed_cpp_int::limb_count; ++i)
+      for(unsigned i = 0; i < fixed_int::limb_count; ++i)
          result.data()[i] = fill;
       return;
    }
-   boost::uint32_t offset = static_cast(s / packed_cpp_int::limb_bits);
-   boost::uint32_t shift  = static_cast(s % packed_cpp_int::limb_bits);
-   int i = packed_cpp_int::limb_count - 1;
+   boost::uint32_t offset = static_cast(s / fixed_int::limb_bits);
+   boost::uint32_t shift  = static_cast(s % fixed_int::limb_bits);
+   int i = fixed_int::limb_count - 1;
    if(shift)
    {
       // This code only works for non-zero shift, otherwise we invoke undefined behaviour!
-      if(fill && (Bits % packed_cpp_int::limb_bits))
+      if(fill && (Bits % fixed_int::limb_bits))
       {
          // We need to sign extend the leftmost bits, otherwise we may shift zeros into the result:
-         result.data()[0] |= fill << (Bits % packed_cpp_int::limb_bits);
+         result.data()[0] |= fill << (Bits % fixed_int::limb_bits);
       }
       for(; i - offset > 0; --i)
       {
          result.data()[i] = result.data()[i-offset] >> shift;
-         result.data()[i] |= result.data()[i-offset-1] << (packed_cpp_int::limb_bits - shift);
+         result.data()[i] |= result.data()[i-offset-1] << (fixed_int::limb_bits - shift);
       }
       result.data()[i] = result.data()[i+offset] >> shift;
-      result.data()[i] |= fill << (packed_cpp_int::limb_bits - shift);
+      result.data()[i] |= fill << (fixed_int::limb_bits - shift);
       --i;
       for(; i >= 0; --i)
          result.data()[i] = fill;
@@ -955,37 +978,37 @@ inline void right_shift(packed_cpp_int& result, boost::uintmax_t s
       for(; i >= 0; --i)
          result.data()[i] = fill;
    }
-   result.data()[0] &= packed_cpp_int::upper_limb_mask;
+   result.data()[0] &= fixed_int::upper_limb_mask;
 }
 
 template 
-inline typename enable_if, void>::type convert_to(R* result, const packed_cpp_int& backend)
+inline typename enable_if, void>::type convert_to(R* result, const fixed_int& backend)
 {
-   unsigned shift = (packed_cpp_int::limb_count - 1) * packed_cpp_int::limb_bits;
+   unsigned shift = (fixed_int::limb_count - 1) * fixed_int::limb_bits;
    *result = 0;
-   for(unsigned i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(unsigned i = 0; i < fixed_int::limb_count; ++i)
    {
       *result += static_cast(backend.data()[i]) << shift;
-      shift -= packed_cpp_int::limb_bits;
+      shift -= fixed_int::limb_bits;
    }
 }
 
 template 
-inline typename enable_if, void>::type convert_to(R* result, const packed_cpp_int& backend)
+inline typename enable_if, void>::type convert_to(R* result, const fixed_int& backend)
 {
-   unsigned shift = (packed_cpp_int::limb_count - 1) * packed_cpp_int::limb_bits;
+   unsigned shift = (fixed_int::limb_count - 1) * fixed_int::limb_bits;
    *result = 0;
-   for(unsigned i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(unsigned i = 0; i < fixed_int::limb_count; ++i)
    {
       *result += static_cast(std::ldexp(static_cast(backend.data()[i]), shift));
-      shift -= packed_cpp_int::limb_bits;
+      shift -= fixed_int::limb_bits;
    }
 }
 
 template 
-inline bool is_zero(const packed_cpp_int& val)
+inline bool is_zero(const fixed_int& val)
 {
-   for(typename packed_cpp_int::data_type::size_type i = 0; i < packed_cpp_int::limb_count; ++i)
+   for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i)
    {
       if(val.data()[i])
          return false;
@@ -993,28 +1016,28 @@ inline bool is_zero(const packed_cpp_int& val)
    return true;
 }
 template 
-inline int get_sign(const packed_cpp_int& val)
+inline int get_sign(const fixed_int& val)
 {
    return is_zero(val) ? 0 : 1;
 }
 template 
-inline int get_sign(const packed_cpp_int& val)
+inline int get_sign(const fixed_int& val)
 {
-   return is_zero(val) ? 0 : val.data()[0] & packed_cpp_int::sign_bit_mask ? -1 : 1;
+   return is_zero(val) ? 0 : val.data()[0] & fixed_int::sign_bit_mask ? -1 : 1;
 }
 
 template 
-struct number_category > : public mpl::int_{};
+struct number_category > : public mpl::int_{};
 
-typedef mp_number > mp_uint64_t;
-typedef mp_number > mp_uint128_t;
-typedef mp_number > mp_uint256_t;
-typedef mp_number > mp_uint512_t;
+typedef mp_number > mp_uint64_t;
+typedef mp_number > mp_uint128_t;
+typedef mp_number > mp_uint256_t;
+typedef mp_number > mp_uint512_t;
 
-typedef mp_number > mp_int64_t;
-typedef mp_number > mp_int128_t;
-typedef mp_number > mp_int256_t;
-typedef mp_number > mp_int512_t;
+typedef mp_number > mp_int64_t;
+typedef mp_number > mp_int128_t;
+typedef mp_number > mp_int256_t;
+typedef mp_number > mp_int512_t;
 
 }} // namespaces
 
@@ -1022,16 +1045,16 @@ typedef mp_number > mp_int512_t;
 namespace std{
 
 template 
-class numeric_limits > >
+class numeric_limits > >
 {
-   typedef boost::multiprecision::mp_number > number_type;
+   typedef boost::multiprecision::mp_number > number_type;
 
    struct initializer
    {
       initializer()
       {
-         (std::numeric_limits > >::min)();
-         (std::numeric_limits > >::max)();
+         (std::numeric_limits > >::min)();
+         (std::numeric_limits > >::max)();
       }
       void do_nothing()const{}
    };
@@ -1096,8 +1119,8 @@ public:
 };
 
 template 
-typename numeric_limits > >::initializer const
-   numeric_limits > >::init;
+typename numeric_limits > >::initializer const
+   numeric_limits > >::init;
 }
 
 #endif
diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp
index 1d53c89c..1eecb5d7 100644
--- a/performance/performance_test.cpp
+++ b/performance/performance_test.cpp
@@ -12,14 +12,14 @@
 #if !defined(TEST_MPF) && !defined(TEST_MPZ) && \
    !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPQ) \
    && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\
-   && !defined(TEST_PACKED_INT)
+   && !defined(TEST_FIXED_INT)
 #  define TEST_MPF
 #  define TEST_MPZ
 #  define TEST_MPFR
 #  define TEST_CPP_FLOAT
 #  define TEST_MPQ
 #  define TEST_TOMMATH
-#  define TEST_PACKED_INT
+#  define TEST_FIXED_INT
 
 #ifdef _MSC_VER
 #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
@@ -44,8 +44,8 @@
 #include 
 #include 
 #endif
-#if defined(TEST_PACKED_INT)
-#include 
+#if defined(TEST_FIXED_INT)
+#include 
 #endif
 
 #include 
@@ -347,12 +347,12 @@ int main()
    test("tommath_int", 512);
    test("tommath_int", 1024);
 #endif
-#ifdef TEST_PACKED_INT
+#ifdef TEST_FIXED_INT
    test("mp_int64_t", 64);
    test("mp_int128_t", 128);
    test("mp_int256_t", 256);
    test("mp_int512_t", 512);
-   test > >("mp_int1024_t", 1024);
+   test > >("mp_int1024_t", 1024);
 #endif
 #ifdef TEST_CPP_FLOAT
    test("cpp_float", 50);
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index c06d453b..c74c7f1f 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -132,15 +132,15 @@ run test_arithmetic.cpp
         : # command line
         : # input files
         : # requirements
-	      TEST_PACKED_INT1
-        : test_arithmetic_packed_int1 ;
+	      TEST_FIXED_INT1
+        : test_arithmetic_fixed_int1 ;
 
 run test_arithmetic.cpp
         : # command line
         : # input files
         : # requirements
-	      TEST_PACKED_INT2
-        : test_arithmetic_packed_int2 ;
+	      TEST_FIXED_INT2
+        : test_arithmetic_fixed_int2 ;
 
 run test_numeric_limits.cpp
         : # command line
@@ -585,17 +585,17 @@ run test_int_io.cpp
         : # command line
         : # input files
         : # requirements
-	      TEST_PACKED_INT1
-        : test_int_io_packed_int1 ;
+	      TEST_FIXED_INT1
+        : test_int_io_fixed_int1 ;
 
 run test_int_io.cpp
         : # command line
         : # input files
         : # requirements
-	      TEST_PACKED_INT2
-        : test_int_io_packed_int2 ;
+	      TEST_FIXED_INT2
+        : test_int_io_fixed_int2 ;
 
-run packed_int_test.cpp gmp
+run fixed_int_test.cpp gmp
         : # command line
         : # input files
         : # requirements
diff --git a/test/packed_int_test.cpp b/test/packed_int_test.cpp
index f895c142..02bed7cb 100644
--- a/test/packed_int_test.cpp
+++ b/test/packed_int_test.cpp
@@ -4,7 +4,7 @@
 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
 
 //
-// Compare arithmetic results using packed_cpp_int to GMP results.
+// Compare arithmetic results using fixed_int to GMP results.
 //
 
 #ifdef _MSC_VER
@@ -12,7 +12,7 @@
 #endif
 
 #include 
-#include 
+#include 
 #include 
 #include 
 #include "test.hpp"
@@ -54,7 +54,7 @@ T generate_random(unsigned bits_wanted)
 int main()
 {
    using namespace boost::multiprecision;
-   typedef mp_number > packed_type;
+   typedef mp_number > packed_type;
    unsigned last_error_count = 0;
    for(int i = 0; i < 1000; ++i)
    {
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index 5339152a..e4fd33ae 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -13,7 +13,7 @@
 #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \
    !defined(TEST_CPP_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) \
    && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\
-   && !defined(TEST_PACKED_INT1) && !defined(TEST_PACKED_INT2)
+   && !defined(TEST_FIXED_INT1) && !defined(TEST_FIXED_INT2)
 #  define TEST_MPF_50
 #  define TEST_MPF
 #  define TEST_BACKEND
@@ -23,8 +23,8 @@
 #  define TEST_CPP_FLOAT
 #  define TEST_MPQ
 #  define TEST_TOMMATH
-#  define TEST_PACKED_INT1
-#  define TEST_PACKED_INT2
+#  define TEST_FIXED_INT1
+#  define TEST_FIXED_INT2
 
 #ifdef _MSC_VER
 #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
@@ -52,8 +52,8 @@
 #include 
 #include 
 #endif
-#if defined(TEST_PACKED_INT1) || defined(TEST_PACKED_INT2)
-#include 
+#if defined(TEST_FIXED_INT1) || defined(TEST_FIXED_INT2)
+#include 
 #endif
 #if defined(TEST_TOMMATH_BOOST_RATIONAL) || defined(TEST_MPZ_BOOST_RATIONAL)
 #include 
@@ -999,13 +999,13 @@ int main()
 #ifdef TEST_MPZ_BOOST_RATIONAL
    test >();
 #endif
-#ifdef TEST_PACKED_INT1
+#ifdef TEST_FIXED_INT1
    test();
    test();
    test();
-   test > >();
+   test > >();
 #endif
-#ifdef TEST_PACKED_INT2
+#ifdef TEST_FIXED_INT2
    //
    // Can't test 64-bit signed ints - they don't have enough bits
    // to interoperate with uint64_t without loss:
@@ -1013,7 +1013,7 @@ int main()
    //test();
    test();
    test();
-   test > >();
+   test > >();
 #endif
    return boost::report_errors();
 }
diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp
index ffd7d063..d091521d 100644
--- a/test/test_int_io.cpp
+++ b/test/test_int_io.cpp
@@ -9,11 +9,11 @@
 #  define _SCL_SECURE_NO_WARNINGS
 #endif
 
-#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) && !defined(TEST_PACKED_INT1) && !defined(TEST_PACKED_INT2)
+#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) && !defined(TEST_FIXED_INT1) && !defined(TEST_FIXED_INT2)
 #  define TEST_TOMMATH
 #  define TEST_MPZ
-#  define TEST_PACKED_INT1
-#  define TEST_PACKED_INT2
+#  define TEST_FIXED_INT1
+#  define TEST_FIXED_INT2
 
 #ifdef _MSC_VER
 #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
@@ -30,8 +30,8 @@
 #if defined(TEST_TOMMATH)
 #include 
 #endif
-#if defined(TEST_PACKED_INT1) || defined(TEST_PACKED_INT2)
-#include 
+#if defined(TEST_FIXED_INT1) || defined(TEST_FIXED_INT2)
+#include 
 #endif
 
 #include 
@@ -123,19 +123,19 @@ int main()
 #ifdef TEST_TOMMATH
    test_round_trip();
 #endif
-#ifdef TEST_PACKED_INT1
+#ifdef TEST_FIXED_INT1
    test_round_trip();
    test_round_trip();
    test_round_trip();
-   test_round_trip > >();
-   test_round_trip > >();
+   test_round_trip > >();
+   test_round_trip > >();
 #endif
-#ifdef TEST_PACKED_INT2
+#ifdef TEST_FIXED_INT2
    test_round_trip();
    test_round_trip();
    test_round_trip();
-   test_round_trip > >();
-   test_round_trip > >();
+   test_round_trip > >();
+   test_round_trip > >();
 #endif
    return boost::report_errors();
 }

From 036dc2bacc516253e17136b0d37c1f9d4c3eb136 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 12 Jan 2012 12:06:27 +0000
Subject: [PATCH 097/256] Rename files.

[SVN r76429]
---
 .../boost/multiprecision/{packed_cpp_int.hpp => fixed_int.hpp}  | 0
 test/Jamfile.v2                                                 | 2 +-
 test/{packed_int_test.cpp => test_fixed_int.cpp}                | 0
 3 files changed, 1 insertion(+), 1 deletion(-)
 rename include/boost/multiprecision/{packed_cpp_int.hpp => fixed_int.hpp} (100%)
 rename test/{packed_int_test.cpp => test_fixed_int.cpp} (100%)

diff --git a/include/boost/multiprecision/packed_cpp_int.hpp b/include/boost/multiprecision/fixed_int.hpp
similarity index 100%
rename from include/boost/multiprecision/packed_cpp_int.hpp
rename to include/boost/multiprecision/fixed_int.hpp
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index c74c7f1f..04133118 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -595,7 +595,7 @@ run test_int_io.cpp
 	      TEST_FIXED_INT2
         : test_int_io_fixed_int2 ;
 
-run fixed_int_test.cpp gmp
+run test_fixed_int.cpp gmp
         : # command line
         : # input files
         : # requirements
diff --git a/test/packed_int_test.cpp b/test/test_fixed_int.cpp
similarity index 100%
rename from test/packed_int_test.cpp
rename to test/test_fixed_int.cpp

From e5c5802d9f2c32ec3231be3c71c0a72ac72cbdc4 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 12 Jan 2012 12:29:52 +0000
Subject: [PATCH 098/256] Tidy up type usage.

[SVN r76431]
---
 include/boost/multiprecision/fixed_int.hpp | 189 +++++++++++----------
 1 file changed, 97 insertions(+), 92 deletions(-)

diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp
index 0bbc2fa7..4a4f8643 100644
--- a/include/boost/multiprecision/fixed_int.hpp
+++ b/include/boost/multiprecision/fixed_int.hpp
@@ -17,14 +17,19 @@
 namespace boost{
 namespace multiprecision{
 
+typedef boost::uint32_t limb_type;
+typedef boost::int32_t signed_limb_type;
+typedef boost::uint64_t double_limb_type;
+typedef boost::int64_t signed_double_limb_type;
+
 template 
 struct fixed_int
 {
-   typedef mpl::list      signed_types;
-   typedef mpl::list    unsigned_types;
+   typedef mpl::list      signed_types;
+   typedef mpl::list    unsigned_types;
    typedef mpl::list                          float_types;
 
-   typedef boost::uint32_t   limb_type;
+   typedef limb_type   limb_type;
    BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT);
    BOOST_STATIC_CONSTANT(unsigned, limb_count = Bits / limb_bits + (Bits % limb_bits ? 1 : 0));
    BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u));
@@ -46,7 +51,7 @@ struct fixed_int
       m_value = o.m_value;
       return *this;
    }
-   fixed_int& operator = (boost::uint32_t i)
+   fixed_int& operator = (limb_type i)
    {
       m_value[limb_count - 1] = i;
       for(int j = limb_count - 2; j >= 0; --j)
@@ -54,7 +59,7 @@ struct fixed_int
       m_value[0] &= fixed_int::upper_limb_mask;
       return *this;
    }
-   fixed_int& operator = (boost::int32_t i)
+   fixed_int& operator = (signed_limb_type i)
    {
       m_value[limb_count - 1] = i;
       // sign extend:
@@ -63,34 +68,34 @@ struct fixed_int
       m_value[0] &= fixed_int::upper_limb_mask;
       return *this;
    }
-   fixed_int& operator = (boost::uintmax_t i)
+   fixed_int& operator = (double_limb_type i)
    {
       BOOST_STATIC_ASSERT(sizeof(i) % sizeof(limb_type) == 0);
-      boost::uintmax_t mask = max_limb_value;
+      double_limb_type mask = max_limb_value;
       unsigned shift = 0;
-      for(int j = limb_count - 1; j >= static_cast(limb_count) - static_cast(sizeof(boost::intmax_t) / sizeof(limb_type)); --j)
+      for(int j = limb_count - 1; j >= static_cast(limb_count) - static_cast(sizeof(signed_double_limb_type) / sizeof(limb_type)); --j)
       {
          m_value[j] = static_cast((i & mask) >> shift);
          mask <<= limb_bits;
          shift += limb_bits;
       }
-      for(int j = static_cast(limb_count) - static_cast(sizeof(boost::intmax_t) / sizeof(limb_type)) - 1; j >= 0; --j)
+      for(int j = static_cast(limb_count) - static_cast(sizeof(signed_double_limb_type) / sizeof(limb_type)) - 1; j >= 0; --j)
          m_value[j] = 0;
       m_value[0] &= fixed_int::upper_limb_mask;
       return *this;
    }
-   fixed_int& operator = (boost::intmax_t i)
+   fixed_int& operator = (signed_double_limb_type i)
    {
       BOOST_STATIC_ASSERT(sizeof(i) % sizeof(limb_type) == 0);
-      boost::uintmax_t mask = max_limb_value;
+      double_limb_type mask = max_limb_value;
       unsigned shift = 0;
-      for(int j = limb_count - 1; j >= static_cast(limb_count) - static_cast(sizeof(boost::intmax_t) / sizeof(limb_type)); --j)
+      for(int j = limb_count - 1; j >= static_cast(limb_count) - static_cast(sizeof(signed_double_limb_type) / sizeof(limb_type)); --j)
       {
          m_value[j] = static_cast((i & mask) >> shift);
          mask <<= limb_bits;
          shift += limb_bits;
       }
-      for(int j = static_cast(limb_count) - static_cast(sizeof(boost::intmax_t) / sizeof(limb_type)) - 1; j >= 0; --j)
+      for(int j = static_cast(limb_count) - static_cast(sizeof(signed_double_limb_type) / sizeof(limb_type)) - 1; j >= 0; --j)
          m_value[j] = i < 0 ? max_limb_value : 0;
       m_value[0] &= fixed_int::upper_limb_mask;
       return *this;
@@ -103,11 +108,11 @@ struct fixed_int
       using std::floor;
 
       if (a == 0) {
-         return *this = static_cast(0u);
+         return *this = static_cast(0u);
       }
 
       if (a == 1) {
-         return *this = static_cast(1u);
+         return *this = static_cast(1u);
       }
 
       BOOST_ASSERT(!(boost::math::isinf)(a));
@@ -115,11 +120,11 @@ struct fixed_int
 
       int e;
       long double f, term;
-      *this = static_cast(0u);
+      *this = static_cast(0u);
 
       f = frexp(a, &e);
 
-      static const boost::uint32_t shift = std::numeric_limits::digits;
+      static const limb_type shift = std::numeric_limits::digits;
 
       while(f)
       {
@@ -129,9 +134,9 @@ struct fixed_int
          e -= shift;
          left_shift(*this, shift);
          if(term > 0)
-            add(*this, static_cast(term));
+            add(*this, static_cast(term));
          else
-            subtract(*this, static_cast(-term));
+            subtract(*this, static_cast(-term));
          f -= term;
       }
       if(e > 0)
@@ -144,7 +149,7 @@ struct fixed_int
    fixed_int& operator = (const char* s)
    {
       std::size_t n = s ? std::strlen(s) : 0;
-      *this = static_cast(0u);
+      *this = static_cast(0u);
       unsigned radix = 10;
       bool isneg = false;
       if(n && (*s == '-'))
@@ -172,7 +177,7 @@ struct fixed_int
          if(radix == 8 || radix == 16)
          {
             unsigned shift = radix == 8 ? 3 : 4;
-            boost::uint32_t val = max_limb_value;
+            limb_type val = max_limb_value;
             while(*s)
             {
                left_shift(*this, shift);
@@ -199,8 +204,8 @@ struct fixed_int
             while(*s)
             {
                // TODO: this implementation is brain dead, Fix Me!
-               multiply(*this, static_cast(10));
-               boost::uint32_t val;
+               multiply(*this, static_cast(10));
+               limb_type val;
                if(*s >= '0' && *s <= '9')
                   val = *s - '0';
                else
@@ -230,8 +235,8 @@ struct fixed_int
 
       if(base == 8 || base == 16)
       {
-         boost::uint32_t shift = base == 8 ? 3 : 4;
-         boost::uint32_t mask = static_cast((1u << shift) - 1);
+         limb_type shift = base == 8 ? 3 : 4;
+         limb_type mask = static_cast((1u << shift) - 1);
          fixed_int t(*this);
          for(unsigned i = 0; i < Bits / shift; ++i)
          {
@@ -243,7 +248,7 @@ struct fixed_int
          }
          if(Bits % shift)
          {
-            mask = static_cast((1u << (Bits % shift)) - 1);
+            mask = static_cast((1u << (Bits % shift)) - 1);
             char c = '0' + (t.data()[limb_count-1] & mask);
             if(c > '9')
                c += 'A' - '9';
@@ -266,7 +271,7 @@ struct fixed_int
       {
          fixed_int t(*this);
          fixed_int ten, r;
-         ten = boost::uint32_t(1000000000);
+         ten = limb_type(1000000000);
          bool neg = false;
          if(Signed && (t.data()[0] & sign_bit_mask))
          {
@@ -284,7 +289,7 @@ struct fixed_int
                fixed_int t2;
                divide_unsigned_helper(t2, t, ten, r);
                t = t2;
-               boost::uint32_t v = r.data()[limb_count - 1];
+               limb_type v = r.data()[limb_count - 1];
                for(unsigned i = 0; i < 9; ++i)
                {
                   char c = '0' + v % 10;
@@ -306,10 +311,10 @@ struct fixed_int
    }
    void negate()
    {
-      boost::uintmax_t carry = 1;
+      double_limb_type carry = 1;
       for(int i = fixed_int::limb_count - 1; i >= 0; --i)
       {
-         carry += static_cast(~m_value[i]);
+         carry += static_cast(~m_value[i]);
          m_value[i] = static_cast(carry);
          carry >>= limb_bits;
       }
@@ -356,75 +361,75 @@ inline void add(fixed_int& result, const fixed_int&
 {
    // Addition using modular arithmatic.
    // Nothing fancy, just let uintmax_t take the strain:
-   boost::uintmax_t carry = 0;
+   double_limb_type carry = 0;
    for(int i = fixed_int::limb_count - 1; i >= 0; --i)
    {
-      carry += static_cast(a.data()[i]) + static_cast(b.data()[i]);
+      carry += static_cast(a.data()[i]) + static_cast(b.data()[i]);
       result.data()[i] = static_cast::limb_type>(carry);
       carry >>= fixed_int::limb_bits;
    }
    result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void add(fixed_int& result, const boost::uint32_t& o)
+inline void add(fixed_int& result, const limb_type& o)
 {
    // Addition using modular arithmatic.
    // Nothing fancy, just let uintmax_t take the strain:
-   boost::uintmax_t carry = o;
+   double_limb_type carry = o;
    for(int i = fixed_int::limb_count - 1; carry && i >= 0; --i)
    {
-      carry += static_cast(result.data()[i]);
+      carry += static_cast(result.data()[i]);
       result.data()[i] = static_cast::limb_type>(carry);
       carry >>= fixed_int::limb_bits;
    }
    result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void add(fixed_int& result, const boost::int32_t& o)
+inline void add(fixed_int& result, const signed_limb_type& o)
 {
    if(o < 0)
-      subtract(result, static_cast(-o));
+      subtract(result, static_cast(-o));
    else if(o > 0)
-      add(result, static_cast(o));
+      add(result, static_cast(o));
 }
 template 
-inline void subtract(fixed_int& result, const boost::uint32_t& o)
+inline void subtract(fixed_int& result, const limb_type& o)
 {
    // Subtract using modular arithmatic.
    // This is the same code as for addition, with the twist that we negate o "on the fly":
-   boost::uintmax_t carry = static_cast(result.data()[fixed_int::limb_count - 1]) 
-      + 1uLL + static_cast(~o);
+   double_limb_type carry = static_cast(result.data()[fixed_int::limb_count - 1]) 
+      + 1uLL + static_cast(~o);
    result.data()[fixed_int::limb_count - 1] = static_cast::limb_type>(carry);
    carry >>= fixed_int::limb_bits;
    for(int i = fixed_int::limb_count - 2; i >= 0; --i)
    {
-      carry += static_cast(result.data()[i]) + 0xFFFFFFFF;
+      carry += static_cast(result.data()[i]) + 0xFFFFFFFF;
       result.data()[i] = static_cast::limb_type>(carry);
       carry >>= fixed_int::limb_bits;
    }
    result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void subtract(fixed_int& result, const boost::int32_t& o)
+inline void subtract(fixed_int& result, const signed_limb_type& o)
 {
    if(o)
    {
       if(o < 0)
-         add(result, static_cast(-o));
+         add(result, static_cast(-o));
       else
-         subtract(result, static_cast(o));
+         subtract(result, static_cast(o));
    }
 }
 template 
 inline void increment(fixed_int& result)
 {
-   static const boost::uint32_t one = 1;
+   static const limb_type one = 1;
    add(result, one);
 }
 template 
 inline void decrement(fixed_int& result)
 {
-   static const boost::uint32_t one = 1;
+   static const limb_type one = 1;
    subtract(result, one);
 }
 template 
@@ -437,10 +442,10 @@ inline void subtract(fixed_int& result, const fixed_int::limb_count - 1; i >= 0; --i)
    {
-      carry += static_cast(a.data()[i]) + static_cast(~b.data()[i]);
+      carry += static_cast(a.data()[i]) + static_cast(~b.data()[i]);
       result.data()[i] = static_cast::limb_type>(carry);
       carry >>= fixed_int::limb_bits;
    }
@@ -463,14 +468,14 @@ inline void multiply(fixed_int& result, const fixed_int::limb_count; ++i)
       result.data()[i] = 0;
    for(int i = fixed_int::limb_count - 1; i >= 0; --i)
    {
       for(int j = fixed_int::limb_count - 1; j >= static_cast(fixed_int::limb_count) - i - 1; --j)
       {
-         carry += static_cast(a.data()[i]) * static_cast(b.data()[j]);
+         carry += static_cast(a.data()[i]) * static_cast(b.data()[j]);
          carry += result.data()[i + j + 1 - fixed_int::limb_count];
          result.data()[i + j + 1 - fixed_int::limb_count] = static_cast::limb_type>(carry);
          carry >>= fixed_int::limb_bits;
@@ -487,40 +492,40 @@ inline void multiply(fixed_int& result, const fixed_int
-inline void multiply(fixed_int& result, const boost::uint32_t& a)
+inline void multiply(fixed_int& result, const limb_type& a)
 {
-   boost::uintmax_t carry = 0;
+   double_limb_type carry = 0;
    for(int i = fixed_int::limb_count - 1; i >= 0; --i)
    {
-      carry += static_cast(result.data()[i]) * static_cast(a);
+      carry += static_cast(result.data()[i]) * static_cast(a);
       result.data()[i] = static_cast::limb_type>(carry);
       carry >>= fixed_int::limb_bits;
    }
    result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void multiply(fixed_int& result, const boost::int32_t& a)
+inline void multiply(fixed_int& result, const signed_limb_type& a)
 {
    if(a > 0)
-      multiply(result, static_cast(a));
+      multiply(result, static_cast(a));
    else
    {
-      multiply(result, static_cast(-a));
+      multiply(result, static_cast(-a));
       result.negate();
    }
 }
 
 /*
 template 
-boost::uint32_t bitcount(const fixed_int& a)
+limb_type bitcount(const fixed_int& a)
 {
    // returns the location of the MSB in a:
-   boost::uint32_t i = 0;
+   limb_type i = 0;
    for(; (i < fixed_int::limb_count) && (a.data()[i] == 0); ++i){}
-   boost::uint32_t count = (fixed_int::limb_count - i) * fixed_int::limb_bits;
+   limb_type count = (fixed_int::limb_count - i) * fixed_int::limb_bits;
    if(!count)
       return count; // no bits are set, value is zero
-   boost::uint32_t mask = static_cast(1u) << (fixed_int::limb_bits - 1);
+   limb_type mask = static_cast(1u) << (fixed_int::limb_bits - 1);
    while((a.data()[i] & mask) == 0)
    {
       --count;
@@ -571,25 +576,25 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int(0u);
+   result = static_cast(0u);
    if(x.compare(y) < 0)
    {
       return; // We already have the answer: zero.
    }
 
-   boost::uint32_t n = bitcount(x) - bitcount(y);
+   limb_type n = bitcount(x) - bitcount(y);
 
    if(n == 0)
    {
       // result is exactly 1:
-      result = static_cast(1u);
+      result = static_cast(1u);
       subtract(r, y);
       return;
    }
 
    // Together mask_index and mask give us the bit we may be about to set in the result:
-   boost::uint32_t mask_index = fixed_int::limb_count - 1 - n / fixed_int::limb_bits;
-   boost::uint32_t mask = static_cast(1u) << n % fixed_int::limb_bits;
+   limb_type mask_index = fixed_int::limb_count - 1 - n / fixed_int::limb_bits;
+   limb_type mask = static_cast(1u) << n % fixed_int::limb_bits;
    fixed_int t(y);
    left_shift(t, n);
    while(mask_index < fixed_int::limb_count)
@@ -606,7 +611,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int>= 1))
       {
          ++mask_index;
-         mask = static_cast(1u) << (fixed_int::limb_bits - 1);
+         mask = static_cast(1u) << (fixed_int::limb_bits - 1);
       }
    }
    BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed
@@ -673,7 +678,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int(0u);
+   result = static_cast(0u);
    if(x.compare(y) < 0)
    {
       return; // We already have the answer: zero.
@@ -684,10 +689,10 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int& result, const fixed_int::limb_count - 2)
    {
-      unsigned long long a, b;
-      a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1];
+      double_limb_type a, b;
+      a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1];
       b = y_order < fixed_int::limb_count - 1 ? 
-         (static_cast(y.data()[y_order]) << fixed_int::limb_bits) | y.data()[y_order + 1] 
+         (static_cast(y.data()[y_order]) << fixed_int::limb_bits) | y.data()[y_order + 1] 
          : y.data()[y_order];
       result = a / b;
       r = a % b;
@@ -725,26 +730,26 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1))
       {
-         unsigned long long a, b, v;
-         a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1];
+         double_limb_type a, b, v;
+         a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1];
          b = y.data()[y_order];
          v = a / b;
          if(v > fixed_int::max_limb_value)
             guess = 1;
          else
          {
-            guess = static_cast(v);
+            guess = static_cast(v);
             ++r_order;
          }
       }
       else
       {
-         unsigned long long a, b, v;
-         a = (r_order < fixed_int::limb_count - 1) ? (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1] : r.data()[r_order];
-         b = (y_order < fixed_int::limb_count - 1) ? (static_cast(y.data()[y_order]) << fixed_int::limb_bits) | y.data()[y_order + 1] : (static_cast(y.data()[y_order])  << fixed_int::limb_bits);
+         double_limb_type a, b, v;
+         a = (r_order < fixed_int::limb_count - 1) ? (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1] : r.data()[r_order];
+         b = (y_order < fixed_int::limb_count - 1) ? (static_cast(y.data()[y_order]) << fixed_int::limb_bits) | y.data()[y_order + 1] : (static_cast(y.data()[y_order])  << fixed_int::limb_bits);
          v = a / b;
          guess = static_cast::limb_type>(v);
          //guess = r.data()[r_order] / y.data()[y_order];
@@ -752,8 +757,8 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1 - shift] = guess;
       if(r_neg)
          subtract(result, t);
@@ -763,12 +768,12 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1; i > fixed_int::limb_count - shift - 1; --i)
          t.data()[i] = 0;
       for(int i = fixed_int::limb_count - 1; i >= static_cast(shift); --i)
       {
-         carry += static_cast(y.data()[i]) * static_cast(guess);
+         carry += static_cast(y.data()[i]) * static_cast(guess);
          t.data()[i - shift] = static_cast::limb_type>(carry);
          carry >>= fixed_int::limb_bits;
       }
@@ -907,15 +912,15 @@ inline void complement(fixed_int& result, const fixed_int::upper_limb_mask;
 }
 template 
-inline void left_shift(fixed_int& result, boost::uintmax_t s)
+inline void left_shift(fixed_int& result, double_limb_type s)
 {
    if(s >= Bits)
    {
-      result = static_cast(0);
+      result = static_cast(0);
       return;
    }
-   boost::uint32_t offset = static_cast(s / fixed_int::limb_bits);
-   boost::uint32_t shift  = static_cast(s % fixed_int::limb_bits);
+   limb_type offset = static_cast(s / fixed_int::limb_bits);
+   limb_type shift  = static_cast(s % fixed_int::limb_bits);
    unsigned i = 0;
    if(shift)
    {
@@ -940,17 +945,17 @@ inline void left_shift(fixed_int& result, boost::uintmax_t s)
    result.data()[0] &= fixed_int::upper_limb_mask;
 }
 template 
-inline void right_shift(fixed_int& result, boost::uintmax_t s)
+inline void right_shift(fixed_int& result, double_limb_type s)
 {
-   boost::uint32_t fill = (Signed && (result.data()[0] & fixed_int::sign_bit_mask)) ? fixed_int::max_limb_value : 0u;
+   limb_type fill = (Signed && (result.data()[0] & fixed_int::sign_bit_mask)) ? fixed_int::max_limb_value : 0u;
    if(s >= Bits)
    {
       for(unsigned i = 0; i < fixed_int::limb_count; ++i)
          result.data()[i] = fill;
       return;
    }
-   boost::uint32_t offset = static_cast(s / fixed_int::limb_bits);
-   boost::uint32_t shift  = static_cast(s % fixed_int::limb_bits);
+   limb_type offset = static_cast(s / fixed_int::limb_bits);
+   limb_type shift  = static_cast(s % fixed_int::limb_bits);
    int i = fixed_int::limb_count - 1;
    if(shift)
    {

From a97c3bd8962fd43f78d8b395a5d01447513ce1d6 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 12 Jan 2012 13:56:22 +0000
Subject: [PATCH 099/256] Update docs to include fixed_int.hpp. Remove 64-bit
 versions of fixed_int typedefs - better to use boost::int64_t instead.

[SVN r76433]
---
 doc/html/boost_multiprecision/intro.html      |  2 +-
 doc/html/boost_multiprecision/map.html        |  2 +-
 doc/html/boost_multiprecision/map/hist.html   |  2 +-
 doc/html/boost_multiprecision/map/todo.html   |  2 +-
 doc/html/boost_multiprecision/ref.html        |  2 +-
 .../boost_multiprecision/ref/backendconc.html |  2 +-
 .../boost_multiprecision/ref/mp_number.html   |  2 +-
 doc/html/boost_multiprecision/tut.html        |  2 +-
 doc/html/boost_multiprecision/tut/ints.html   | 87 ++++++++++++++++++-
 .../boost_multiprecision/tut/rational.html    |  2 +-
 doc/html/boost_multiprecision/tut/reals.html  |  2 +-
 doc/html/index.html                           |  2 +-
 doc/multiprecision.qbk                        | 29 +++++++
 example/fixed_int_snips.cpp                   | 34 ++++++++
 include/boost/multiprecision/fixed_int.hpp    |  2 -
 performance/performance_test.cpp              |  2 +-
 test/test_arithmetic.cpp                      |  2 +-
 test/test_int_io.cpp                          |  4 +-
 18 files changed, 164 insertions(+), 18 deletions(-)
 create mode 100644 example/fixed_int_snips.cpp

diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html
index 90451449..fadcea1c 100644
--- a/doc/html/boost_multiprecision/intro.html
+++ b/doc/html/boost_multiprecision/intro.html
@@ -13,7 +13,7 @@
 
    
 PrevUpHomeNext
 
    
-
    
+
    
 
    
diff --git a/doc/html/boost_multiprecision/map.html b/doc/html/boost_multiprecision/map.html
index 0587898f..d528688d 100644
--- a/doc/html/boost_multiprecision/map.html
+++ b/doc/html/boost_multiprecision/map.html
@@ -13,7 +13,7 @@
 
    
 PrevUpHomeNext
 
    
-
    
+
    
 
    
diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html
index 4701f08a..8c480119 100644
--- a/doc/html/boost_multiprecision/map/hist.html
+++ b/doc/html/boost_multiprecision/map/hist.html
@@ -13,7 +13,7 @@
 
    
 PrevUpHomeNext
 
    
-
    
+
    
 
diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html
index fadf395e..b780d2da 100644
--- a/doc/html/boost_multiprecision/map/todo.html
+++ b/doc/html/boost_multiprecision/map/todo.html
@@ -12,7 +12,7 @@
 
    
 PrevUpHome
 
    
-
    
+
    
 
    
diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html
index 4634199e..d909f999 100644
--- a/doc/html/boost_multiprecision/ref.html
+++ b/doc/html/boost_multiprecision/ref.html
@@ -13,7 +13,7 @@
 
    
 PrevUpHomeNext
 
    
-
    
+
    
 
    
diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html
index c6e86a15..3d7a2998 100644
--- a/doc/html/boost_multiprecision/ref/backendconc.html
+++ b/doc/html/boost_multiprecision/ref/backendconc.html
@@ -13,7 +13,7 @@
 
    
 PrevUpHomeNext
 
    
-
    
+
    
 
    
diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html
index be7d53ba..af55cb6a 100644
--- a/doc/html/boost_multiprecision/ref/mp_number.html
+++ b/doc/html/boost_multiprecision/ref/mp_number.html
@@ -13,7 +13,7 @@
 
    
 PrevUpHomeNext
 
    
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+
    
 
    
diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html
index 4c86cbe3..896c5a8d 100644
--- a/doc/html/boost_multiprecision/tut.html
+++ b/doc/html/boost_multiprecision/tut.html
@@ -13,7 +13,7 @@
 
    
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+
    
 
    
diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html
index c1612d16..6439bd4b 100644
--- a/doc/html/boost_multiprecision/tut/ints.html
+++ b/doc/html/boost_multiprecision/tut/ints.html
@@ -13,7 +13,7 @@
 
    
 PrevUpHomeNext
 
    
-
    
+
    
 
    
@@ -126,6 +126,38 @@
                 
    
               
 
    
+
+
+
+
+
+
+
+
    
+                
    
+                  fixed_int
+                
    
+                  		
+                
    
+                  boost/multiprecision/fixed_int.hpp
+                
    
+                  		
+                
    
+                  2
+                
    
+                  		
+                
    
+                  None
+                
    
+                  		
+                
    
+                  Boost licenced fixed precision modular arithmetic integer.
+                
    
+                  		
+                
    
+                  Slower than GMP.
+                
    
+              
    
     
 
    
 
    
@@ -286,6 +318,59 @@
    std::cout << e.what() << std::endl;
 }
 
+
    +

    +

    +
    + + fixed_int +
    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits, bool Signed>
+class fixed_int;
+
+typedef mp_number<fixed_int<128, false> > mp_uint128_t;
+typedef mp_number<fixed_int<256, false> > mp_uint256_t;
+typedef mp_number<fixed_int<512, false> > mp_uint512_t;
+
+typedef mp_number<fixed_int<128, true> > mp_int128_t;
+typedef mp_number<fixed_int<256, true> > mp_int256_t;
+typedef mp_number<fixed_int<512, true> > mp_int512_t;
+
+}} // namespaces
+
    +

    + The fixed_int backend is + used via one of the typedefs boost::multiprecision::mp_uint128_t, + boost::multiprecision::mp_uint256_t, boost::multiprecision::mp_uint512_t, + boost::multiprecision::mp_int128_t, boost::multiprecision::mp_int256_t + or boost::multiprecision::mp_int512_t. It provides both signed and + unsigned integer types with a fixed precision and modular arithmetic with + a 2's complement representation for negative values. In other words it's + designed to work just like a typical built in integer type, but with larger + precision. +

    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/fixed_int.hpp>
+
+using namespace boost::multiprecision;
+
+mp_int128_t v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 20; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 20!
+v = -v;
+std::cout << std::hex << v << std::endl; // prints 2's complement representation
+

    diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 8fe67803..ff68aa78 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -13,7 +13,7 @@
    PrevUpHomeNext
    -
    +
    diff --git a/doc/html/boost_multiprecision/tut/reals.html b/doc/html/boost_multiprecision/tut/reals.html index 5fd1090c..9451d5f0 100644 --- a/doc/html/boost_multiprecision/tut/reals.html +++ b/doc/html/boost_multiprecision/tut/reals.html @@ -13,7 +13,7 @@
    PrevUpHomeNext
    -
    +
    diff --git a/doc/html/index.html b/doc/html/index.html index 35e62118..5bccd937 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -48,7 +48,7 @@
    - +

    Last revised: December 24, 2011 at 13:13:53 GMT

    Last revised: January 12, 2012 at 13:44:32 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index b2107616..290e8f42 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -22,6 +22,7 @@ [import ../example/mpfr_snips.cpp] [import ../example/cpp_float_snips.cpp] [import ../example/tommath_snips.cpp] +[import ../example/fixed_int_snips.cpp] [section:intro Introduction] @@ -201,6 +202,7 @@ The following backends provide integer arithmetic: [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] [[`gmp_int`][boost/multiprecision/gmp.hpp][2][GMP][Very fast and efficient backend.][Dependency on GNU licenced GMP library.]] [[`mp_int`][boost/multiprecision/tommath.hpp][2][libtommath][Public domain backend with no licence restrictions.][Slower than GMP.]] +[[`fixed_int`][boost/multiprecision/fixed_int.hpp][2][None][Boost licenced fixed precision modular arithmetic integer.][Slower than GMP.]] ] [h4 gmp_int] @@ -257,6 +259,33 @@ as a result performing formatted output on this type when the argument is negati [tommath_eg] +[h4 fixed_int] + + namespace boost{ namespace multiprecision{ + + template + class fixed_int; + + typedef mp_number > mp_uint128_t; + typedef mp_number > mp_uint256_t; + typedef mp_number > mp_uint512_t; + + typedef mp_number > mp_int128_t; + typedef mp_number > mp_int256_t; + typedef mp_number > mp_int512_t; + + }} // namespaces + +The `fixed_int` backend is used via one of the typedefs `boost::multiprecision::mp_uint128_t`, `boost::multiprecision::mp_uint256_t`, +`boost::multiprecision::mp_uint512_t`, `boost::multiprecision::mp_int128_t`, `boost::multiprecision::mp_int256_t` +or `boost::multiprecision::mp_int512_t`. It provides both signed and unsigned integer types with a fixed precision +and modular arithmetic with a 2's complement representation for negative values. In other words it's designed to work just +like a typical built in integer type, but with larger precision. + +[h5 Example:] + +[fixed_int_eg] + [endsect] [section:reals Real Numbers] diff --git a/example/fixed_int_snips.cpp b/example/fixed_int_snips.cpp new file mode 100644 index 00000000..e076b60f --- /dev/null +++ b/example/fixed_int_snips.cpp @@ -0,0 +1,34 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include + +void t1() +{ + //[fixed_int_eg + //=#include + + using namespace boost::multiprecision; + + mp_int128_t v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 20; ++i) + v *= i; + + std::cout << v << std::endl; // prints 20! + v = -v; + std::cout << std::hex << v << std::endl; // prints 2's complement representation + + //] +} + +int main() +{ + t1(); + return 0; +} + diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index 4a4f8643..a99f8570 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -1034,12 +1034,10 @@ inline int get_sign(const fixed_int& val) template struct number_category > : public mpl::int_{}; -typedef mp_number > mp_uint64_t; typedef mp_number > mp_uint128_t; typedef mp_number > mp_uint256_t; typedef mp_number > mp_uint512_t; -typedef mp_number > mp_int64_t; typedef mp_number > mp_int128_t; typedef mp_number > mp_int256_t; typedef mp_number > mp_int512_t; diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index 1eecb5d7..ee1eb0ea 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -348,7 +348,7 @@ int main() test("tommath_int", 1024); #endif #ifdef TEST_FIXED_INT - test("mp_int64_t", 64); + test > >("mp_int64_t", 64); test("mp_int128_t", 128); test("mp_int256_t", 256); test("mp_int512_t", 512); diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index e4fd33ae..282baac6 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -1000,7 +1000,7 @@ int main() test >(); #endif #ifdef TEST_FIXED_INT1 - test(); + test > >(); test(); test(); test > >(); diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp index d091521d..1078ac8e 100644 --- a/test/test_int_io.cpp +++ b/test/test_int_io.cpp @@ -124,14 +124,14 @@ int main() test_round_trip(); #endif #ifdef TEST_FIXED_INT1 - test_round_trip(); + test_round_trip > >(); test_round_trip(); test_round_trip(); test_round_trip > >(); test_round_trip > >(); #endif #ifdef TEST_FIXED_INT2 - test_round_trip(); + test_round_trip > >(); test_round_trip(); test_round_trip(); test_round_trip > >(); From a7d480c438af23d20fc8f8a467434414e745eb72 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 12 Jan 2012 17:03:27 +0000 Subject: [PATCH 100/256] Optimize increment and decrement. [SVN r76434] --- include/boost/multiprecision/fixed_int.hpp | 14 ++++++++++++-- 1 file changed, 12 insertions(+), 2 deletions(-) diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index a99f8570..c5eebfa4 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -424,13 +424,19 @@ template inline void increment(fixed_int& result) { static const limb_type one = 1; - add(result, one); + if(result.data().elems[fixed_int::limb_count - 1] < fixed_int::max_limb_value) + ++result.data().elems[fixed_int::limb_count - 1]; + else + add(result, one); } template inline void decrement(fixed_int& result) { static const limb_type one = 1; - subtract(result, one); + if(result.data().elems[fixed_int::limb_count - 1]) + --result.data().elems[fixed_int::limb_count - 1]; + else + subtract(result, one); } template inline void subtract(fixed_int& result, const fixed_int& o) @@ -720,6 +726,8 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int last_r; + //bool last_neg; do { // @@ -731,6 +739,8 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1)) { double_limb_type a, b, v; From c98f15f30d5ba968fef823d27223ac845d21c986 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 14 Jan 2012 13:24:52 +0000 Subject: [PATCH 101/256] Update docs with performance results. Add component based initialization of rationals. [SVN r76486] --- doc/html/boost_multiprecision/map.html | 6 +- doc/html/boost_multiprecision/map/todo.html | 3 - doc/html/boost_multiprecision/perf.html | 41 + .../perf/float_performance.html | 757 +++++++ .../perf/integer_performance.html | 1909 +++++++++++++++++ .../boost_multiprecision/perf/realworld.html | 276 +++ .../boost_multiprecision/ref/backendconc.html | 83 +- .../boost_multiprecision/ref/mp_number.html | 58 +- .../boost_multiprecision/tut/rational.html | 6 + doc/html/index.html | 10 +- doc/multiprecision.qbk | 234 +- example/gmp_snips.cpp | 3 + example/tommath_snips.cpp | 3 + .../multiprecision/detail/default_ops.hpp | 15 + .../multiprecision/detail/mp_number_base.hpp | 7 + include/boost/multiprecision/gmp.hpp | 23 + include/boost/multiprecision/mp_number.hpp | 42 + .../boost/multiprecision/rational_adapter.hpp | 21 +- performance/performance_test-msvc-10.log | 447 ++++ performance/performance_test.cpp | 219 +- performance/sf_performance-msvc-10.log | 60 +- 21 files changed, 4155 insertions(+), 68 deletions(-) create mode 100644 doc/html/boost_multiprecision/perf.html create mode 100644 doc/html/boost_multiprecision/perf/float_performance.html create mode 100644 doc/html/boost_multiprecision/perf/integer_performance.html create mode 100644 doc/html/boost_multiprecision/perf/realworld.html create mode 100644 performance/performance_test-msvc-10.log diff --git a/doc/html/boost_multiprecision/map.html b/doc/html/boost_multiprecision/map.html index d528688d..891900e9 100644 --- a/doc/html/boost_multiprecision/map.html +++ b/doc/html/boost_multiprecision/map.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -32,7 +32,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index b780d2da..3f92de36 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -27,9 +27,6 @@
  • Add an adapter backend for complex number types.
    • -
  • - Adapt libtommath code to make an all C++ fixed precision integer type. -

    • diff --git a/doc/html/boost_multiprecision/perf.html b/doc/html/boost_multiprecision/perf.html new file mode 100644 index 00000000..e62c527a --- /dev/null +++ b/doc/html/boost_multiprecision/perf.html @@ -0,0 +1,41 @@ + + + +Performance Comparison + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    Real World Tests
    +
    Float Algorithm + Perfomance
    +
    Integer + Algorithm Perfomance
    +
    +
    +
    + + +
    Copyright © 2011 John Maddock

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html new file mode 100644 index 00000000..c746b939 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/float_performance.html @@ -0,0 +1,757 @@ + + + +Float Algorithm Perfomance + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticsm, and real-world + peformance may vary widely depending upon the specifics of the program. In + each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on + 32-bit Windows Vista machine. +

    +
    +

    Table 1.8. Operator *

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_float +

    +     		+

    + 1.0826 (0.287216s) +

    +     		+

    + 1.48086 (0.586363s) +

    +     		+

    + 1.57545 (5.05269s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.265302s) +

    +     		+

    + 1 (0.395962s) +

    +     		+

    + 1 (3.20714s) +

    +
    +

    + mpfr_float +

    +     		+

    + 1.24249 (0.329636s) +

    +     		+

    + 1.15432 (0.457067s) +

    +     		+

    + 1.16182 (3.72612s) +

    +
    +
    +
    +

    Table 1.9. Operator +

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_float +

    +     		+

    + 1 (0.0242151s) +

    +     		+

    + 1 (0.029252s) +

    +     		+

    + 1 (0.0584099s) +

    +
    +

    + gmp_float +

    +     		+

    + 4.55194 (0.110226s) +

    +     		+

    + 3.67516 (0.107506s) +

    +     		+

    + 2.42489 (0.141638s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.45362 (0.0594147s) +

    +     		+

    + 2.18552 (0.0639309s) +

    +     		+

    + 1.32099 (0.0771588s) +

    +
    +
    +
    +

    Table 1.10. Operator +(int)

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_float +

    +     		+

    + 1.51995 (0.0484155s) +

    +     		+

    + 1.78781 (0.0611055s) +

    +     		+

    + 1.8309 (0.104123s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.0318533s) +

    +     		+

    + 1 (0.0341789s) +

    +     		+

    + 1 (0.0568699s) +

    +
    +

    + mpfr_float +

    +     		+

    + 3.39055 (0.108s) +

    +     		+

    + 3.30142 (0.112839s) +

    +     		+

    + 2.05293 (0.11675s) +

    +
    +
    +
    +

    Table 1.11. Operator -

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_float +

    +     		+

    + 1 (0.0261498s) +

    +     		+

    + 1 (0.030946s) +

    +     		+

    + 1 (0.0606388s) +

    +
    +

    + gmp_float +

    +     		+

    + 4.48753 (0.117348s) +

    +     		+

    + 3.75823 (0.116302s) +

    +     		+

    + 2.4823 (0.150524s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.96057 (0.0774183s) +

    +     		+

    + 2.61897 (0.0810465s) +

    +     		+

    + 1.56236 (0.0947396s) +

    +
    +
    +
    +

    Table 1.12. Operator -(int)

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_float +

    +     		+

    + 1 (0.0567601s) +

    +     		+

    + 1 (0.0626685s) +

    +     		+

    + 1 (0.111692s) +

    +
    +

    + gmp_float +

    +     		+

    + 2.27932 (0.129374s) +

    +     		+

    + 2.04821 (0.128358s) +

    +     		+

    + 1.48297 (0.165635s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.43199 (0.13804s) +

    +     		+

    + 2.32131 (0.145473s) +

    +     		+

    + 1.38152 (0.154304s) +

    +
    +
    +
    +

    Table 1.13. Operator /

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_float +

    +     		+

    + 3.2662 (3.98153s) +

    +     		+

    + 5.07021 (8.11948s) +

    +     		+

    + 6.78872 (53.6099s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (1.21901s) +

    +     		+

    + 1 (1.60141s) +

    +     		+

    + 1 (7.89691s) +

    +
    +

    + mpfr_float +

    +     		+

    + 1.33238 (1.62419s) +

    +     		+

    + 1.39529 (2.23443s) +

    +     		+

    + 1.70882 (13.4944s) +

    +
    +
    +
    +

    Table 1.14. Operator str

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_float +

    +     		+

    + 1.46076 (0.0192656s) +

    +     		+

    + 1.59438 (0.0320398s) +

    +     		+

    + 1 (0.134302s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.0131888s) +

    +     		+

    + 1 (0.0200954s) +

    +     		+

    + 1.01007 (0.135655s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.19174 (0.0289065s) +

    +     		+

    + 1.86101 (0.0373977s) +

    +     		+

    + 1.15842 (0.155578s) +

    +
    +
    +
    +
    + + + +
    Copyright © 2011 John Maddock

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html new file mode 100644 index 00000000..fdd2c062 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/integer_performance.html @@ -0,0 +1,1909 @@ + + + +Integer Algorithm Perfomance + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticsm, and real-world + peformance may vary widely depending upon the specifics of the program. In + each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on + 32-bit Windows Vista machine. +

    +
    +

    Table 1.15. Operator +

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.0031173s) +

    +     		+

    + 1 (0.00696555s) +

    +     		+

    + 1 (0.0163707s) +

    +     		+

    + 1 (0.0314806s) +

    +     		+

    + 1 (0.0596158s) +

    +
    +

    + gmp_int +

    +     		+

    + 12.7096 (0.0396194s) +

    +     		+

    + 5.89178 (0.0410395s) +

    +     		+

    + 2.66402 (0.0436119s) +

    +     		+

    + 1.59356 (0.0501664s) +

    +     		+

    + 1.11155 (0.0662662s) +

    +
    +

    + tommath_int +

    +     		+

    + 6.14357 (0.0191513s) +

    +     		+

    + 3.16177 (0.0220235s) +

    +     		+

    + 1.85441 (0.030358s) +

    +     		+

    + 1.45895 (0.0459287s) +

    +     		+

    + 1.26576 (0.0754591s) +

    +
    +
    +
    +

    Table 1.16. Operator +(int)

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00329336s) +

    +     		+

    + 1 (0.00370718s) +

    +     		+

    + 1 (0.00995385s) +

    +     		+

    + 1 (0.0117467s) +

    +     		+

    + 1 (0.0233483s) +

    +
    +

    + gmp_int +

    +     		+

    + 9.56378 (0.031497s) +

    +     		+

    + 8.0588 (0.0298754s) +

    +     		+

    + 4.15824 (0.0413905s) +

    +     		+

    + 5.47974 (0.0643691s) +

    +     		+

    + 4.46265 (0.104195s) +

    +
    +

    + tommath_int +

    +     		+

    + 76.2624 (0.25116s) +

    +     		+

    + 71.3973 (0.264682s) +

    +     		+

    + 28.0238 (0.278945s) +

    +     		+

    + 25.9035 (0.304282s) +

    +     		+

    + 13.1635 (0.307346s) +

    +
    +
    +
    +

    Table 1.17. Operator -

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00359417s) +

    +     		+

    + 1 (0.00721041s) +

    +     		+

    + 1 (0.0168213s) +

    +     		+

    + 1 (0.0323563s) +

    +     		+

    + 1 (0.061385s) +

    +
    +

    + gmp_int +

    +     		+

    + 10.6794 (0.0383836s) +

    +     		+

    + 5.65517 (0.0407761s) +

    +     		+

    + 2.63634 (0.0443466s) +

    +     		+

    + 1.59979 (0.0517632s) +

    +     		+

    + 1.13379 (0.0695978s) +

    +
    +

    + tommath_int +

    +     		+

    + 6.43615 (0.0231326s) +

    +     		+

    + 3.6161 (0.0260736s) +

    +     		+

    + 2.2585 (0.0379908s) +

    +     		+

    + 1.52006 (0.0491835s) +

    +     		+

    + 1.24231 (0.0762591s) +

    +
    +
    +
    +

    Table 1.18. Operator -(int)

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00353606s) +

    +     		+

    + 1 (0.00577573s) +

    +     		+

    + 1 (0.0155184s) +

    +     		+

    + 1 (0.029385s) +

    +     		+

    + 1 (0.0586271s) +

    +
    +

    + gmp_int +

    +     		+

    + 9.04434 (0.0319814s) +

    +     		+

    + 5.12393 (0.0295945s) +

    +     		+

    + 2.50743 (0.0389112s) +

    +     		+

    + 2.01898 (0.0593277s) +

    +     		+

    + 1.68381 (0.098717s) +

    +
    +

    + tommath_int +

    +     		+

    + 60.2486 (0.213043s) +

    +     		+

    + 38.3032 (0.221229s) +

    +     		+

    + 15.8792 (0.24642s) +

    +     		+

    + 8.71166 (0.255992s) +

    +     		+

    + 4.85236 (0.28448s) +

    +
    +
    +
    +

    Table 1.19. Operator *

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.0175309s) +

    +     		+

    + 1 (0.0388232s) +

    +     		+

    + 1 (0.123609s) +

    +     		+

    + 1 (0.427489s) +

    +     		+

    + 1 (1.46312s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.93263 (0.0514117s) +

    +     		+

    + 1.70358 (0.0661383s) +

    +     		+

    + 1.01811 (0.125848s) +

    +     		+

    + 1.20692 (0.515943s) +

    +     		+

    + 1.03248 (1.51064s) +

    +
    +

    + tommath_int +

    +     		+

    + 3.82476 (0.0670515s) +

    +     		+

    + 2.87425 (0.111587s) +

    +     		+

    + 2.74339 (0.339108s) +

    +     		+

    + 2.26768 (0.969408s) +

    +     		+

    + 2.1233 (3.10664s) +

    +
    +
    +
    +

    Table 1.20. Operator /

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.0973696s) +

    +     		+

    + 1 (0.260936s) +

    +     		+

    + 1 (0.845628s) +

    +     		+

    + 2.4597 (2.51371s) +

    +     		+

    + 6.21836 (7.93136s) +

    +
    +

    + gmp_int +

    +     		+

    + 7.66851 (0.74668s) +

    +     		+

    + 3.17732 (0.829077s) +

    +     		+

    + 1.05006 (0.887961s) +

    +     		+

    + 1 (1.02196s) +

    +     		+

    + 1 (1.27547s) +

    +
    +

    + tommath_int +

    +     		+

    + 18.3945 (1.79107s) +

    +     		+

    + 8.11201 (2.11671s) +

    +     		+

    + 3.49119 (2.95225s) +

    +     		+

    + 4.55727 (4.65733s) +

    +     		+

    + 9.06813 (11.5662s) +

    +
    +
    +
    +

    Table 1.21. Operator %

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.098458s) +

    +     		+

    + 1 (0.269155s) +

    +     		+

    + 1.10039 (0.849272s) +

    +     		+

    + 2.92096 (2.55909s) +

    +     		+

    + 7.47157 (7.99106s) +

    +
    +

    + gmp_int +

    +     		+

    + 6.63934 (0.653697s) +

    +     		+

    + 2.6753 (0.72007s) +

    +     		+

    + 1 (0.771794s) +

    +     		+

    + 1 (0.87611s) +

    +     		+

    + 1 (1.06953s) +

    +
    +

    + tommath_int +

    +     		+

    + 18.5522 (1.82661s) +

    +     		+

    + 8.00831 (2.15548s) +

    +     		+

    + 3.89737 (3.00797s) +

    +     		+

    + 5.38078 (4.71416s) +

    +     		+

    + 10.7885 (11.5386s) +

    +
    +
    +
    +

    Table 1.22. Operator <<

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.0120907s) +

    +     		+

    + 1 (0.0129147s) +

    +     		+

    + 1 (0.0214412s) +

    +     		+

    + 1 (0.0249208s) +

    +     		+

    + 1 (0.0341293s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.93756 (0.0234265s) +

    +     		+

    + 1.97785 (0.0255433s) +

    +     		+

    + 1.43607 (0.0307911s) +

    +     		+

    + 1.815 (0.0452311s) +

    +     		+

    + 2.00167 (0.0683156s) +

    +
    +

    + tommath_int +

    +     		+

    + 3.42859 (0.0414542s) +

    +     		+

    + 3.04951 (0.0393836s) +

    +     		+

    + 3.04202 (0.0652246s) +

    +     		+

    + 3.81169 (0.0949903s) +

    +     		+

    + 4.93896 (0.168563s) +

    +
    +
    +
    +

    Table 1.23. Operator >>

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.0064833s) +

    +     		+

    + 1 (0.00772857s) +

    +     		+

    + 1 (0.0186871s) +

    +     		+

    + 1 (0.0218303s) +

    +     		+

    + 1 (0.0326372s) +

    +
    +

    + gmp_int +

    +     		+

    + 4.212 (0.0273077s) +

    +     		+

    + 3.72696 (0.0288041s) +

    +     		+

    + 1.55046 (0.0289735s) +

    +     		+

    + 1.51403 (0.0330518s) +

    +     		+

    + 1.13695 (0.037107s) +

    +
    +

    + tommath_int +

    +     		+

    + 33.9418 (0.220055s) +

    +     		+

    + 29.104 (0.224932s) +

    +     		+

    + 13.8407 (0.258642s) +

    +     		+

    + 13.1488 (0.287043s) +

    +     		+

    + 15.1741 (0.495242s) +

    +
    +
    +
    +

    Table 1.24. Operator &

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.0028732s) +

    +     		+

    + 1 (0.00552933s) +

    +     		+

    + 1 (0.0125148s) +

    +     		+

    + 1 (0.020299s) +

    +     		+

    + 1 (0.034856s) +

    +
    +

    + gmp_int +

    +     		+

    + 16.3018 (0.0468383s) +

    +     		+

    + 9.51109 (0.05259s) +

    +     		+

    + 5.20026 (0.0650802s) +

    +     		+

    + 4.46545 (0.0906443s) +

    +     		+

    + 3.99377 (0.139207s) +

    +
    +

    + tommath_int +

    +     		+

    + 42.221 (0.121309s) +

    +     		+

    + 22.2471 (0.123011s) +

    +     		+

    + 11.3587 (0.142151s) +

    +     		+

    + 7.3475 (0.149147s) +

    +     		+

    + 11.4043 (0.397507s) +

    +
    +
    +
    +

    Table 1.25. Operator ^

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00287983s) +

    +     		+

    + 1 (0.00543128s) +

    +     		+

    + 1 (0.0125726s) +

    +     		+

    + 1 (0.019987s) +

    +     		+

    + 1 (0.034697s) +

    +
    +

    + gmp_int +

    +     		+

    + 14.938 (0.0430189s) +

    +     		+

    + 9.00973 (0.0489344s) +

    +     		+

    + 4.83803 (0.0608267s) +

    +     		+

    + 4.33359 (0.0866154s) +

    +     		+

    + 3.89518 (0.135151s) +

    +
    +

    + tommath_int +

    +     		+

    + 41.6898 (0.12006s) +

    +     		+

    + 22.4393 (0.121874s) +

    +     		+

    + 10.7513 (0.135172s) +

    +     		+

    + 7.2632 (0.145169s) +

    +     		+

    + 11.5765 (0.401671s) +

    +
    +
    +
    +

    Table 1.26. Operator |

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00314803s) +

    +     		+

    + 1 (0.00548233s) +

    +     		+

    + 1 (0.0125434s) +

    +     		+

    + 1 (0.0198161s) +

    +     		+

    + 1 (0.034957s) +

    +
    +

    + gmp_int +

    +     		+

    + 13.0622 (0.0411201s) +

    +     		+

    + 8.63936 (0.0473638s) +

    +     		+

    + 4.6932 (0.0588688s) +

    +     		+

    + 4.25792 (0.0843755s) +

    +     		+

    + 3.78236 (0.13222s) +

    +
    +

    + tommath_int +

    +     		+

    + 38.5896 (0.121481s) +

    +     		+

    + 22.3609 (0.12259s) +

    +     		+

    + 10.9015 (0.136742s) +

    +     		+

    + 7.68521 (0.152291s) +

    +     		+

    + 11.6322 (0.406628s) +

    +
    +
    +
    +

    Table 1.27. Operator str

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1.03557 (0.00143356s) +

    +     		+

    + 1.39844 (0.00290281s) +

    +     		+

    + 3.14081 (0.0099558s) +

    +     		+

    + 6.28067 (0.0372769s) +

    +     		+

    + 13.2101 (0.188878s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (0.00138432s) +

    +     		+

    + 1 (0.00207575s) +

    +     		+

    + 1 (0.00316982s) +

    +     		+

    + 1 (0.00593518s) +

    +     		+

    + 1 (0.014298s) +

    +
    +

    + tommath_int +

    +     		+

    + 5.31194 (0.00735345s) +

    +     		+

    + 7.90724 (0.0164135s) +

    +     		+

    + 15.8581 (0.0502673s) +

    +     		+

    + 19.7526 (0.117235s) +

    +     		+

    + 26.6031 (0.380373s) +

    +
    +
    +
    +
    + + + +
    Copyright © 2011 John Maddock

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html new file mode 100644 index 00000000..9762e244 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/realworld.html @@ -0,0 +1,276 @@ + + + +Real World Tests + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + These tests test the total time taken to execute all of Boost.Math's test + cases for these functions. In each case the best performing library gets + a relative score of 1, with the total execution time given in brackets. The + first three libraries listed are the various floating point types provided + by this library, while for comparison, two popular C++ frontends to MPFR + (mpfr_class and mpreal) are also shown. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on + 32-bit Windows Vista machine. +

    +
    +

    Table 1.6. Bessel Function Performance

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +
    +

    + mpfr_float +

    +     		+

    + 1.0 (6.472s) +

    +     		+

    + 1.193 (10.154s) +

    +
    +

    + mpf_float +

    +     		+

    + 1.801 (11.662s) +

    +     		+

    + 1.0(8.511s) +

    +
    +

    + cpp_float +

    +     		+

    + 3.13 (20.285s) +

    +     		+

    + 2.46 (21.019s) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.001 (6.480s) +

    +     		+

    + 1.15(9.805s) +

    +
    +

    + mpreal +

    +     		+

    + 1.542 (9.981s) +

    +     		+

    + 1.61 (13.702s) +

    +
    +
    +
    +

    Table 1.7. Non-Central T Distribution Performance

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +
    +

    + mpfr_float +

    +     		+

    + 1.308 (258.09s) +

    +     		+

    + 1.30 (516.74s) +

    +
    +

    + mpf_float +

    +     		+

    + 1.0 (197.30s) +

    +     		+

    + 1.0(397.30s) +

    +
    +

    + cpp_float +

    +     		+

    + 1.695 (334.50s) +

    +     		+

    + 2.68 (1064.53s) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.35 (266.39s) +

    +     		+

    + 1.323 (525.74s) +

    +
    +

    + mpreal +

    +     		+

    + 1.75 (346.64s) +

    +     		+

    + 1.635 (649.94s) +

    +
    +
    +
    +
    + + + +
    Copyright © 2011 John Maddock

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index 3d7a2998..95fe4403 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -7,11 +7,11 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -34,7 +34,9 @@ pa is a variable of type pointer-to-arithmetic-type, exp is a variable of type B::exp_type, pexp - is a variable of type B::exp_type*. + is a variable of type B::exp_type*, + B2 is another type that meets these requirements, b2 is a variable of type + B2.

    Table 1.4. Compulsory Requirements on the Backend type.

    @@ -730,6 +732,79 @@ + +

    + B(b2) +

    + + +

    + B +

    + + +

    + Copy constructor from a different backend type. +

    + + + + +

    + b = + b2 +

    + + +

    + b& +

    + + +

    + Assignment operator from a different backend type. +

    + + + + +

    + assign_components(b, a, a) +

    + + +

    + void +

    + + +

    + Assigns to b the + two components in the following arguments. Only applies to rational + and complex number types. +

    + + + + +

    + assign_components(b, b2, b2) +

    + + +

    + void +

    + + +

    + Assigns to b the + two components in the following arguments. Only applies to rational + and complex number types. +

    + + +

    add(b, @@ -2039,7 +2114,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html index af55cb6a..87f856a8 100644 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -137,6 +137,16 @@ unmentionable-expression-template-type fmod (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&); unmentionable-expression-template-type atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&); +// Traits support: +template <class T> +struct component_type; +template <class T> +struct number_category; + +// Rational number support: +typename component_type<mp_number-or-expression-template-type>::type numerator (const mp_number-or-expression-template-type&); +typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&); + }} // namespaces namespace boost{ namespace math{ @@ -191,6 +201,16 @@ Any type that the Backend is constructible or assignable from.
    +

    + In addition, if the type has multiple components (for example rational or + complex number types), then there is a two argument constructor: +

    +
    mp_number(arg1, arg2);
+
    +

    + Where the two args must either be arithmetic types, or types that are convertible + to the two components of this. + 

    mp_number& operator+=(const see-below&);
 mp_number& operator-=(const see-below&);
 mp_number& operator*=(const see-below&);
@@ -457,6 +477,42 @@
       
    
 
    
 
+        Traits
+        Class Support
+      
    
+
    template <class T>
+struct component_type;
+
    
+
    
+        If this is a type with mutiple components (for example rational or complex
+        types), then this trait has a single member type
+        that is the type of those components.
+      
    
+
    template <class T>
+struct number_category;
+
    
+
    
+        A traits class that inherits from mpl::int_<N>
+        where N is one of the enumerated
+        values number_kind_integer,
+        number_kind_floating_point,
+        number_kind_rational or
+        number_kind_fixed_point.
+      
    
+
    
+
+        Rational
+        Number Functions
+      
    
+
    typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
+typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
+
    
+
    
+        These functions return the numerator and denominator of a rational number
+        respectively.
+      
    
+
    
+
         Boost.Math
         Interoperability Support
       
    
@@ -479,7 +535,7 @@
         to ensure interoperability.
       
    
 
    
-
+
         std::numeric_limits
         support
       
    
diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html
index ff68aa78..184beae4 100644
--- a/doc/html/boost_multiprecision/tut/rational.html
+++ b/doc/html/boost_multiprecision/tut/rational.html
@@ -263,6 +263,9 @@
 std::cout << numerator(v) << std::endl;
 std::cout << denominator(v) << std::endl;
 
+mpq_rational w(2, 3);  // component wise constructor
+std::cout << w << std::endl; // prints 2/3
+
 // Access the underlying data:
 mpq_t q;
 mpq_init(q);
@@ -322,6 +325,9 @@
 std::cout << numerator(v) << std::endl;
 std::cout << denominator(v) << std::endl;
 
+mp_rational w(2, 3); // Component wise constructor
+std::cout << w << std::endl; // prints 2/3
+

    diff --git a/doc/html/index.html b/doc/html/index.html index 5bccd937..f35eb4ab 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -39,6 +39,14 @@
    mp_number
    Backend Requirements
    +
    Performance Comparison
    +
    +
    Real World Tests
    +
    Float Algorithm + Perfomance
    +
    Integer + Algorithm Perfomance
    +
    Roadmap
    History
    @@ -48,7 +56,7 @@

    - +

    Last revised: January 12, 2012 at 13:44:32 GMT

    Last revised: January 14, 2012 at 13:20:36 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 290e8f42..ccd74dd4 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -632,6 +632,16 @@ So for example, given an integer backend type `MyIntegerBackend`, the use would ``['unmentionable-expression-template-type]`` fmod (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); ``['unmentionable-expression-template-type]`` atan2 (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); + // Traits support: + template + struct component_type; + template + struct number_category; + + // Rational number support: + typename component_type<``['mp_number-or-expression-template-type]``>::type numerator (const ``['mp_number-or-expression-template-type]``&); + typename component_type<``['mp_number-or-expression-template-type]``>::type denominator(const ``['mp_number-or-expression-template-type]``&); + }} // namespaces namespace boost{ namespace math{ @@ -670,6 +680,13 @@ Type `mp_number` is default constructible, and both copy constructible and assig * A `std::string` or any type which is convertible to `const char*`. * Any type that the Backend is constructible or assignable from. +In addition, if the type has multiple components (for example rational or complex number types), then there is a +two argument constructor: + + mp_number(arg1, arg2); + +Where the two args must either be arithmetic types, or types that are convertible to the two components of `this`. + mp_number& operator+=(const ``['see-below]``&); mp_number& operator-=(const ``['see-below]``&); mp_number& operator*=(const ``['see-below]``&); @@ -857,6 +874,27 @@ used at variable precision. Also note that with the exception of `abs` that these functions can only be used with floating-point Backend types. +[h4 Traits Class Support] + + template + struct component_type; + +If this is a type with mutiple components (for example rational or complex types), then this trait has a single member +`type` that is the type of those components. + + template + struct number_category; + +A traits class that inherits from `mpl::int_` where `N` is one of the enumerated values `number_kind_integer`, `number_kind_floating_point`, +`number_kind_rational` or `number_kind_fixed_point`. + +[h4 Rational Number Functions] + + typename component_type<``['mp_number-or-expression-template-type]``>::type numerator (const ``['mp_number-or-expression-template-type]``&); + typename component_type<``['mp_number-or-expression-template-type]``>::type denominator(const ``['mp_number-or-expression-template-type]``&); + +These functions return the numerator and denominator of a rational number respectively. + [h4 Boost.Math Interoperability Support] namespace boost{ namespace math{ @@ -904,7 +942,8 @@ In the following tables, type B is the `Backend` template arument to `mp_number` a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a variable of Arithmetic type, `s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`, `pa` is a variable of type pointer-to-arithmetic-type, `exp` is a variable of type `B::exp_type`, -`pexp` is a variable of type `B::exp_type*`. +`pexp` is a variable of type `B::exp_type*`, B2 is another type that meets these requirements, b2 is a variable +of type B2. [table Compulsory Requirements on the Backend type. [[Expression][Return Type][Comments]] @@ -956,6 +995,12 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia [table Optional Requirements on the Backend Type [[Expression][Returns][Comments]] +[[`B(b2)`][`B`][Copy constructor from a different backend type.]] +[[`b = b2`][`b&`][Assignment operator from a different backend type.]] +[[`assign_components(b, a, a)`][`void`][Assigns to `b` the two components in the following arguments. + Only applies to rational and complex number types.]] +[[`assign_components(b, b2, b2)`][`void`][Assigns to `b` the two components in the following arguments. + Only applies to rational and complex number types.]] [[`add(b, a)`][`void`][Adds `a` to `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] [[`subtract(b, a)`][`void`][Subtracts `a` from `b`. The type of `a` shall be listed in one of the type lists @@ -1044,6 +1089,192 @@ a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a varia [endsect] +[section:perf Performance Comparison] + +[section:realworld Real World Tests] + +These tests test the total time taken to execute all of Boost.Math's test cases for these functions. +In each case the best performing library gets a relative score of 1, with the total execution time +given in brackets. The first three libraries listed are the various floating point types provided +by this library, while for comparison, two popular C++ frontends to MPFR (mpfr_class and mpreal) +are also shown. + +Test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on 32-bit +Windows Vista machine. + +[table Bessel Function Performance +[[Library][50 Decimal Digits][100 Decimal Digits]] +[[mpfr_float][[*1.0] (6.472s)][1.193 (10.154s)]] +[[mpf_float][1.801 (11.662s)][[*1.0](8.511s)]] +[[cpp_float][3.13 (20.285s)][2.46 (21.019s)]] +[[mpfr_class][1.001 (6.480s)][1.15(9.805s)]] +[[mpreal][1.542 (9.981s)][1.61 (13.702s)]] +] + +[table Non-Central T Distribution Performance +[[Library][50 Decimal Digits][100 Decimal Digits]] +[[mpfr_float][1.308 (258.09s)][1.30 (516.74s)]] +[[mpf_float][[*1.0] (197.30s)][[*1.0](397.30s)]] +[[cpp_float][1.695 (334.50s)][2.68 (1064.53s)]] +[[mpfr_class][1.35 (266.39s)][1.323 (525.74s)]] +[[mpreal][1.75 (346.64s)][1.635 (649.94s)]] +] + +[endsect] + +[section:float_performance Float Algorithm Perfomance] + +Note that these tests are carefully designed to test performance of the underlying algorithms +and not memory allocation or variable copying. As usual, performance results should be taken +with a healthy dose of scepticsm, and real-world peformance may vary widely depending upon the +specifics of the program. In each table relative times are given first, with the best performer +given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 +operations. + +Test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on 32-bit +Windows Vista machine. + +[table Operator * +[[Backend][50 Decimal Digits][100 Decimal Digits][500 Decimal Digits]] +[[cpp_float][1.0826 (0.287216s)][1.48086 (0.586363s)][1.57545 (5.05269s)]] +[[gmp_float][[*1] (0.265302s)][[*1] (0.395962s)][[*1] (3.20714s)]] +[[mpfr_float][1.24249 (0.329636s)][1.15432 (0.457067s)][1.16182 (3.72612s)]] +] +[table Operator + +[[Backend][50 Decimal Digits][100 Decimal Digits][500 Decimal Digits]] +[[cpp_float][[*1] (0.0242151s)][[*1] (0.029252s)][[*1] (0.0584099s)]] +[[gmp_float][4.55194 (0.110226s)][3.67516 (0.107506s)][2.42489 (0.141638s)]] +[[mpfr_float][2.45362 (0.0594147s)][2.18552 (0.0639309s)][1.32099 (0.0771588s)]] +] +[table Operator +(int) +[[Backend][50 Decimal Digits][100 Decimal Digits][500 Decimal Digits]] +[[cpp_float][1.51995 (0.0484155s)][1.78781 (0.0611055s)][1.8309 (0.104123s)]] +[[gmp_float][[*1] (0.0318533s)][[*1] (0.0341789s)][[*1] (0.0568699s)]] +[[mpfr_float][3.39055 (0.108s)][3.30142 (0.112839s)][2.05293 (0.11675s)]] +] +[table Operator - +[[Backend][50 Decimal Digits][100 Decimal Digits][500 Decimal Digits]] +[[cpp_float][[*1] (0.0261498s)][[*1] (0.030946s)][[*1] (0.0606388s)]] +[[gmp_float][4.48753 (0.117348s)][3.75823 (0.116302s)][2.4823 (0.150524s)]] +[[mpfr_float][2.96057 (0.0774183s)][2.61897 (0.0810465s)][1.56236 (0.0947396s)]] +] +[table Operator -(int) +[[Backend][50 Decimal Digits][100 Decimal Digits][500 Decimal Digits]] +[[cpp_float][[*1] (0.0567601s)][[*1] (0.0626685s)][[*1] (0.111692s)]] +[[gmp_float][2.27932 (0.129374s)][2.04821 (0.128358s)][1.48297 (0.165635s)]] +[[mpfr_float][2.43199 (0.13804s)][2.32131 (0.145473s)][1.38152 (0.154304s)]] +] +[table Operator / +[[Backend][50 Decimal Digits][100 Decimal Digits][500 Decimal Digits]] +[[cpp_float][3.2662 (3.98153s)][5.07021 (8.11948s)][6.78872 (53.6099s)]] +[[gmp_float][[*1] (1.21901s)][[*1] (1.60141s)][[*1] (7.89691s)]] +[[mpfr_float][1.33238 (1.62419s)][1.39529 (2.23443s)][1.70882 (13.4944s)]] +] +[table Operator str +[[Backend][50 Decimal Digits][100 Decimal Digits][500 Decimal Digits]] +[[cpp_float][1.46076 (0.0192656s)][1.59438 (0.0320398s)][[*1] (0.134302s)]] +[[gmp_float][[*1] (0.0131888s)][[*1] (0.0200954s)][1.01007 (0.135655s)]] +[[mpfr_float][2.19174 (0.0289065s)][1.86101 (0.0373977s)][1.15842 (0.155578s)]] +] +[endsect] + +[section:integer_performance Integer Algorithm Perfomance] + +Note that these tests are carefully designed to test performance of the underlying algorithms +and not memory allocation or variable copying. As usual, performance results should be taken +with a healthy dose of scepticsm, and real-world peformance may vary widely depending upon the +specifics of the program. In each table relative times are given first, with the best performer +given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 +operations. + +Test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on 32-bit +Windows Vista machine. + +[table Operator + +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0031173s)][[*1] (0.00696555s)][[*1] (0.0163707s)][[*1] (0.0314806s)][[*1] (0.0596158s)]] +[[gmp_int][12.7096 (0.0396194s)][5.89178 (0.0410395s)][2.66402 (0.0436119s)][1.59356 (0.0501664s)][1.11155 (0.0662662s)]] +[[tommath_int][6.14357 (0.0191513s)][3.16177 (0.0220235s)][1.85441 (0.030358s)][1.45895 (0.0459287s)][1.26576 (0.0754591s)]] +] +[table Operator +(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00329336s)][[*1] (0.00370718s)][[*1] (0.00995385s)][[*1] (0.0117467s)][[*1] (0.0233483s)]] +[[gmp_int][9.56378 (0.031497s)][8.0588 (0.0298754s)][4.15824 (0.0413905s)][5.47974 (0.0643691s)][4.46265 (0.104195s)]] +[[tommath_int][76.2624 (0.25116s)][71.3973 (0.264682s)][28.0238 (0.278945s)][25.9035 (0.304282s)][13.1635 (0.307346s)]] +] +[table Operator - +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00359417s)][[*1] (0.00721041s)][[*1] (0.0168213s)][[*1] (0.0323563s)][[*1] (0.061385s)]] +[[gmp_int][10.6794 (0.0383836s)][5.65517 (0.0407761s)][2.63634 (0.0443466s)][1.59979 (0.0517632s)][1.13379 (0.0695978s)]] +[[tommath_int][6.43615 (0.0231326s)][3.6161 (0.0260736s)][2.2585 (0.0379908s)][1.52006 (0.0491835s)][1.24231 (0.0762591s)]] +] +[table Operator -(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00353606s)][[*1] (0.00577573s)][[*1] (0.0155184s)][[*1] (0.029385s)][[*1] (0.0586271s)]] +[[gmp_int][9.04434 (0.0319814s)][5.12393 (0.0295945s)][2.50743 (0.0389112s)][2.01898 (0.0593277s)][1.68381 (0.098717s)]] +[[tommath_int][60.2486 (0.213043s)][38.3032 (0.221229s)][15.8792 (0.24642s)][8.71166 (0.255992s)][4.85236 (0.28448s)]] +] +[table Operator * +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0175309s)][[*1] (0.0388232s)][[*1] (0.123609s)][[*1] (0.427489s)][[*1] (1.46312s)]] +[[gmp_int][2.93263 (0.0514117s)][1.70358 (0.0661383s)][1.01811 (0.125848s)][1.20692 (0.515943s)][1.03248 (1.51064s)]] +[[tommath_int][3.82476 (0.0670515s)][2.87425 (0.111587s)][2.74339 (0.339108s)][2.26768 (0.969408s)][2.1233 (3.10664s)]] +] +[table Operator / +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0973696s)][[*1] (0.260936s)][[*1] (0.845628s)][2.4597 (2.51371s)][6.21836 (7.93136s)]] +[[gmp_int][7.66851 (0.74668s)][3.17732 (0.829077s)][1.05006 (0.887961s)][[*1] (1.02196s)][[*1] (1.27547s)]] +[[tommath_int][18.3945 (1.79107s)][8.11201 (2.11671s)][3.49119 (2.95225s)][4.55727 (4.65733s)][9.06813 (11.5662s)]] +] +[table Operator % +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.098458s)][[*1] (0.269155s)][1.10039 (0.849272s)][2.92096 (2.55909s)][7.47157 (7.99106s)]] +[[gmp_int][6.63934 (0.653697s)][2.6753 (0.72007s)][[*1] (0.771794s)][[*1] (0.87611s)][[*1] (1.06953s)]] +[[tommath_int][18.5522 (1.82661s)][8.00831 (2.15548s)][3.89737 (3.00797s)][5.38078 (4.71416s)][10.7885 (11.5386s)]] +] +[table Operator << +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0120907s)][[*1] (0.0129147s)][[*1] (0.0214412s)][[*1] (0.0249208s)][[*1] (0.0341293s)]] +[[gmp_int][1.93756 (0.0234265s)][1.97785 (0.0255433s)][1.43607 (0.0307911s)][1.815 (0.0452311s)][2.00167 (0.0683156s)]] +[[tommath_int][3.42859 (0.0414542s)][3.04951 (0.0393836s)][3.04202 (0.0652246s)][3.81169 (0.0949903s)][4.93896 (0.168563s)]] +] +[table Operator >> +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0064833s)][[*1] (0.00772857s)][[*1] (0.0186871s)][[*1] (0.0218303s)][[*1] (0.0326372s)]] +[[gmp_int][4.212 (0.0273077s)][3.72696 (0.0288041s)][1.55046 (0.0289735s)][1.51403 (0.0330518s)][1.13695 (0.037107s)]] +[[tommath_int][33.9418 (0.220055s)][29.104 (0.224932s)][13.8407 (0.258642s)][13.1488 (0.287043s)][15.1741 (0.495242s)]] +] +[table Operator & +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0028732s)][[*1] (0.00552933s)][[*1] (0.0125148s)][[*1] (0.020299s)][[*1] (0.034856s)]] +[[gmp_int][16.3018 (0.0468383s)][9.51109 (0.05259s)][5.20026 (0.0650802s)][4.46545 (0.0906443s)][3.99377 (0.139207s)]] +[[tommath_int][42.221 (0.121309s)][22.2471 (0.123011s)][11.3587 (0.142151s)][7.3475 (0.149147s)][11.4043 (0.397507s)]] +] +[table Operator ^ +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00287983s)][[*1] (0.00543128s)][[*1] (0.0125726s)][[*1] (0.019987s)][[*1] (0.034697s)]] +[[gmp_int][14.938 (0.0430189s)][9.00973 (0.0489344s)][4.83803 (0.0608267s)][4.33359 (0.0866154s)][3.89518 (0.135151s)]] +[[tommath_int][41.6898 (0.12006s)][22.4393 (0.121874s)][10.7513 (0.135172s)][7.2632 (0.145169s)][11.5765 (0.401671s)]] +] +[table Operator | +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00314803s)][[*1] (0.00548233s)][[*1] (0.0125434s)][[*1] (0.0198161s)][[*1] (0.034957s)]] +[[gmp_int][13.0622 (0.0411201s)][8.63936 (0.0473638s)][4.6932 (0.0588688s)][4.25792 (0.0843755s)][3.78236 (0.13222s)]] +[[tommath_int][38.5896 (0.121481s)][22.3609 (0.12259s)][10.9015 (0.136742s)][7.68521 (0.152291s)][11.6322 (0.406628s)]] +] +[table Operator str +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][1.03557 (0.00143356s)][1.39844 (0.00290281s)][3.14081 (0.0099558s)][6.28067 (0.0372769s)][13.2101 (0.188878s)]] +[[gmp_int][[*1] (0.00138432s)][[*1] (0.00207575s)][[*1] (0.00316982s)][[*1] (0.00593518s)][[*1] (0.014298s)]] +[[tommath_int][5.31194 (0.00735345s)][7.90724 (0.0164135s)][15.8581 (0.0502673s)][19.7526 (0.117235s)][26.6031 (0.380373s)]] +] +[endsect] + +[endsect] + [section:map Roadmap] [section:hist History] @@ -1056,7 +1287,6 @@ More a list of what ['could] be done, rather than what ['should] be done (which * Add backend support for libdecNumber. * Add an adapter backend for complex number types. -* Adapt libtommath code to make an all C++ fixed precision integer type. [endsect] diff --git a/example/gmp_snips.cpp b/example/gmp_snips.cpp index cf763fa2..511a2894 100644 --- a/example/gmp_snips.cpp +++ b/example/gmp_snips.cpp @@ -71,6 +71,9 @@ void t3() std::cout << numerator(v) << std::endl; std::cout << denominator(v) << std::endl; + mpq_rational w(2, 3); // component wise constructor + std::cout << w << std::endl; // prints 2/3 + // Access the underlying data: mpq_t q; mpq_init(q); diff --git a/example/tommath_snips.cpp b/example/tommath_snips.cpp index 793aa5f6..92fbaeed 100644 --- a/example/tommath_snips.cpp +++ b/example/tommath_snips.cpp @@ -59,6 +59,9 @@ void t3() std::cout << numerator(v) << std::endl; std::cout << denominator(v) << std::endl; + mp_rational w(2, 3); // Component wise constructor + std::cout << w << std::endl; // prints 2/3 + //] } diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index e6b18a7a..1ed7aacf 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -277,6 +277,21 @@ inline int get_sign(const T& val) return val.compare(static_cast(0)); } +template +inline void assign_components_imp(T& result, const V& v1, const V& v2, const mpl::int_&) +{ + result = v1; + T t; + t = v2; + divide(result, t); +} + +template +inline void assign_components(T& result, const V& v1, const V& v2) +{ + return assign_components_imp(result, v1, v2, typename number_category::type()); +} + template struct has_enough_bits { diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 781f8f71..6d183709 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -1139,6 +1139,13 @@ struct number_category > : public number_category{}; template struct number_category > : public number_category::result_type>{}; +template +struct component_type; +template +struct component_type > : public component_type{}; +template +struct component_type > : public component_type::result_type>{}; + }} // namespaces namespace boost{ namespace math{ namespace tools{ diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index b5d71181..90cf2fb7 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1603,6 +1603,12 @@ inline mp_number denominator(const mp_number& val) return result; } +template <> +struct component_type > +{ + typedef mp_number type; +}; + inline void add(gmp_rational& t, const gmp_rational& o) { mpq_add(t.data(), t.data(), o.data()); @@ -1668,6 +1674,23 @@ inline void eval_abs(gmp_rational& result, const gmp_rational& val) mpq_abs(result.data(), val.data()); } +inline void assign_components(gmp_rational& result, unsigned long v1, unsigned long v2) +{ + mpq_set_ui(result.data(), v1, v2); + mpq_canonicalize(result.data()); +} +inline void assign_components(gmp_rational& result, long v1, long v2) +{ + mpq_set_si(result.data(), v1, v2); + mpq_canonicalize(result.data()); +} +inline void assign_components(gmp_rational& result, gmp_int const& v1, gmp_int const& v2) +{ + mpz_set(mpq_numref(result.data()), v1.data()); + mpz_set(mpq_denref(result.data()), v2.data()); + mpq_canonicalize(result.data()); +} + // // Some member functions that are dependent upon previous code go here: // diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 2c8b9d4d..bb48f629 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -37,17 +37,35 @@ public: m_backend = canonical_value(v); } mp_number(const mp_number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} + /* + // + // This conflicts with component based initialization (for rational and complex types) + // which is arguably more useful. Disabled for now. + // template mp_number(V v, unsigned digits10, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) { m_backend.precision(digits10); m_backend = canonical_value(v); } + */ template mp_number(const mp_number& val, typename enable_if >::type* dummy1 = 0) { m_backend = val.backend(); } + template + mp_number(V v1, V v2, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) + { + using default_ops::assign_components; + assign_components(m_backend, canonical_value(v1), canonical_value(v2)); + } + template + mp_number(const mp_number& v1, const mp_number& v2, typename enable_if >::type* dummy1 = 0) + { + using default_ops::assign_components; + assign_components(m_backend, v1.backend(), v2.backend()); + } template mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* dummy1 = 0) @@ -322,6 +340,7 @@ public: mp_number& operator&=(const self_type& e) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); do_bitwise_and(detail::mp_exp(e), detail::terminal()); return *this; } @@ -329,6 +348,7 @@ public: template mp_number& operator&=(const detail::mp_exp& e) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); // Create a temporary if the RHS references *this, but not // if we're just doing an x &= x; if(contains_self(e) && !is_self(e)) @@ -347,6 +367,7 @@ public: typename enable_if, mp_number& >::type operator&=(const V& v) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); using default_ops::bitwise_and; bitwise_and(m_backend, canonical_value(v)); return *this; @@ -354,6 +375,7 @@ public: mp_number& operator|=(const self_type& e) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); do_bitwise_or(detail::mp_exp(e), detail::terminal()); return *this; } @@ -361,6 +383,7 @@ public: template mp_number& operator|=(const detail::mp_exp& e) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); // Create a temporary if the RHS references *this, but not // if we're just doing an x |= x; if(contains_self(e) && !is_self(e)) @@ -379,6 +402,7 @@ public: typename enable_if, mp_number& >::type operator|=(const V& v) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); using default_ops::bitwise_or; bitwise_or(m_backend, canonical_value(v)); return *this; @@ -386,6 +410,7 @@ public: mp_number& operator^=(const self_type& e) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); do_bitwise_xor(detail::mp_exp(e), detail::terminal()); return *this; } @@ -393,6 +418,7 @@ public: template mp_number& operator^=(const detail::mp_exp& e) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); if(contains_self(e)) { self_type temp(e); @@ -409,6 +435,7 @@ public: typename enable_if, mp_number& >::type operator^=(const V& v) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); using default_ops::bitwise_xor; bitwise_xor(m_backend, canonical_value(v)); return *this; @@ -924,6 +951,7 @@ private: template void do_assign(const Exp& e, const detail::bitwise_complement&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ~ operation is only valid for integer types"); using default_ops::complement; self_type temp(e.left()); complement(m_backend, temp.backend()); @@ -932,6 +960,7 @@ private: template void do_assign(const Exp& e, const detail::complement_immediates&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ~ operation is only valid for integer types"); using default_ops::complement; complement(m_backend, canonical_value(e.left().value())); } @@ -939,6 +968,7 @@ private: template void do_assign_right_shift(const Exp& e, const Val& val, const detail::terminal&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right shift operation is only valid for integer types"); using default_ops::right_shift; right_shift(m_backend, canonical_value(e.value()), val); } @@ -946,6 +976,7 @@ private: template void do_assign_left_shift(const Exp& e, const Val& val, const detail::terminal&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left shift operation is only valid for integer types"); using default_ops::left_shift; left_shift(m_backend, canonical_value(e.value()), val); } @@ -953,6 +984,7 @@ private: template void do_assign_right_shift(const Exp& e, const Val& val, const Tag&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right shift operation is only valid for integer types"); using default_ops::right_shift; self_type temp(e); right_shift(m_backend, temp.backend(), val); @@ -961,6 +993,7 @@ private: template void do_assign_left_shift(const Exp& e, const Val& val, const Tag&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left shift operation is only valid for integer types"); using default_ops::left_shift; self_type temp(e); left_shift(m_backend, temp.backend(), val); @@ -1263,12 +1296,14 @@ private: template void do_bitwise_and(const Exp& e, const detail::terminal&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); using default_ops::bitwise_and; bitwise_and(m_backend, canonical_value(e.value())); } template void do_bitwise_and(const Exp& e, const detail::bitwise_and&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_bitwise_and(e.left(), typename left_type::tag_type()); @@ -1277,6 +1312,7 @@ private: template void do_bitwise_and(const Exp& e, const unknown&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); using default_ops::bitwise_and; self_type temp(e); bitwise_and(m_backend, temp.m_backend); @@ -1285,12 +1321,14 @@ private: template void do_bitwise_or(const Exp& e, const detail::terminal&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); using default_ops::bitwise_or; bitwise_or(m_backend, canonical_value(e.value())); } template void do_bitwise_or(const Exp& e, const detail::bitwise_or&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_bitwise_or(e.left(), typename left_type::tag_type()); @@ -1299,6 +1337,7 @@ private: template void do_bitwise_or(const Exp& e, const unknown&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); using default_ops::bitwise_or; self_type temp(e); bitwise_or(m_backend, temp.m_backend); @@ -1307,12 +1346,14 @@ private: template void do_bitwise_xor(const Exp& e, const detail::terminal&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); using default_ops::bitwise_xor; bitwise_xor(m_backend, canonical_value(e.value())); } template void do_bitwise_xor(const Exp& e, const detail::bitwise_xor&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_bitwise_xor(e.left(), typename left_type::tag_type()); @@ -1321,6 +1362,7 @@ private: template void do_bitwise_xor(const Exp& e, const unknown&) { + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); using default_ops::bitwise_xor; self_type temp(e); bitwise_xor(m_backend, temp.m_backend); diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index e417653d..cc0e786b 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -42,6 +42,11 @@ struct rational_adapter m_value = o.m_value; return *this; } + rational_adapter& operator = (const IntBackend& o) + { + m_value = o; + return *this; + } template typename enable_if, rational_adapter&>::type operator = (Arithmetic i) { @@ -167,18 +172,30 @@ inline mp_number denominator(const mp_number +inline void assign_components(rational_adapter& result, const V& v1, const V& v2) +{ + result.data().assign(v1, v2); +} + template struct number_category > : public mpl::int_{}; +template +struct component_type > +{ + typedef mp_number type; +}; + }} // namespaces namespace std{ template -class numeric_limits > > : public std::numeric_limits +class numeric_limits > > : public std::numeric_limits > { - typedef std::numeric_limits base_type; + typedef std::numeric_limits > base_type; typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_integer = false; diff --git a/performance/performance_test-msvc-10.log b/performance/performance_test-msvc-10.log new file mode 100644 index 00000000..d6ed1e17 --- /dev/null +++ b/performance/performance_test-msvc-10.log @@ -0,0 +1,447 @@ +gmp_float 50 + 0.110226 +gmp_float 50 - 0.117348 +gmp_float 50 +(int)0.0318533 +gmp_float 50 -(int)0.129374 +gmp_float 50 * 0.265302 +gmp_float 50 / 1.21901 +gmp_float 50 str 0.0131888 +gmp_float 100 + 0.107506 +gmp_float 100 - 0.116302 +gmp_float 100 +(int)0.0341789 +gmp_float 100 -(int)0.128358 +gmp_float 100 * 0.395962 +gmp_float 100 / 1.60141 +gmp_float 100 str 0.0200954 +gmp_float 500 + 0.141638 +gmp_float 500 - 0.150524 +gmp_float 500 +(int)0.0568699 +gmp_float 500 -(int)0.165635 +gmp_float 500 * 3.20714 +gmp_float 500 / 7.89691 +gmp_float 500 str 0.135655 +gmp_int 64 + 0.0396194 +gmp_int 64 - 0.0383836 +gmp_int 64 +(int)0.031497 +gmp_int 64 -(int)0.0319814 +gmp_int 64 * 0.0514117 +gmp_int 64 / 0.74668 +gmp_int 64 str 0.00138432 +gmp_int 64 % 0.653697 +gmp_int 64 | 0.0411201 +gmp_int 64 & 0.0468383 +gmp_int 64 ^ 0.0430189 +gmp_int 64 << 0.0234265 +gmp_int 64 >> 0.0273077 +gmp_int 128 + 0.0410395 +gmp_int 128 - 0.0407761 +gmp_int 128 +(int)0.0298754 +gmp_int 128 -(int)0.0295945 +gmp_int 128 * 0.0661383 +gmp_int 128 / 0.829077 +gmp_int 128 str 0.00207575 +gmp_int 128 % 0.72007 +gmp_int 128 | 0.0473638 +gmp_int 128 & 0.05259 +gmp_int 128 ^ 0.0489344 +gmp_int 128 << 0.0255433 +gmp_int 128 >> 0.0288041 +gmp_int 256 + 0.0436119 +gmp_int 256 - 0.0443466 +gmp_int 256 +(int)0.0413905 +gmp_int 256 -(int)0.0389112 +gmp_int 256 * 0.125848 +gmp_int 256 / 0.887961 +gmp_int 256 str 0.00316982 +gmp_int 256 % 0.771794 +gmp_int 256 | 0.0588688 +gmp_int 256 & 0.0650802 +gmp_int 256 ^ 0.0608267 +gmp_int 256 << 0.0307911 +gmp_int 256 >> 0.0289735 +gmp_int 512 + 0.0501664 +gmp_int 512 - 0.0517632 +gmp_int 512 +(int)0.0643691 +gmp_int 512 -(int)0.0593277 +gmp_int 512 * 0.515943 +gmp_int 512 / 1.02196 +gmp_int 512 str 0.00593518 +gmp_int 512 % 0.87611 +gmp_int 512 | 0.0843755 +gmp_int 512 & 0.0906443 +gmp_int 512 ^ 0.0866154 +gmp_int 512 << 0.0452311 +gmp_int 512 >> 0.0330518 +gmp_int 1024 + 0.0662662 +gmp_int 1024 - 0.0695978 +gmp_int 1024 +(int)0.104195 +gmp_int 1024 -(int)0.098717 +gmp_int 1024 * 1.51064 +gmp_int 1024 / 1.27547 +gmp_int 1024 str 0.014298 +gmp_int 1024 % 1.06953 +gmp_int 1024 | 0.13222 +gmp_int 1024 & 0.139207 +gmp_int 1024 ^ 0.135151 +gmp_int 1024 << 0.0683156 +gmp_int 1024 >> 0.037107 +mpq_rational 64 + 1.47058 +mpq_rational 64 - 1.47214 +mpq_rational 64 +(int)0.654198 +mpq_rational 64 -(int)0.646626 +mpq_rational 64 * 2.63854 +mpq_rational 64 / 9.24093 +mpq_rational 64 str 0.00265152 +mpq_rational 128 + 3.18485 +mpq_rational 128 - 3.1691 +mpq_rational 128 +(int)0.66159 +mpq_rational 128 -(int)0.657712 +mpq_rational 128 * 5.8426 +mpq_rational 128 / 14.6415 +mpq_rational 128 str 0.00372512 +mpq_rational 256 + 6.67422 +mpq_rational 256 - 6.67532 +mpq_rational 256 +(int)0.705687 +mpq_rational 256 -(int)0.704919 +mpq_rational 256 * 12.6093 +mpq_rational 256 / 26.2341 +mpq_rational 256 str 0.00573139 +mpq_rational 512 + 15.5117 +mpq_rational 512 - 15.6279 +mpq_rational 512 +(int)0.817714 +mpq_rational 512 -(int)0.818141 +mpq_rational 512 * 28.654 +mpq_rational 512 / 52.808 +mpq_rational 512 str 0.011966 +mpq_rational 1024 + 37.688 +mpq_rational 1024 - 37.6616 +mpq_rational 1024 +(int)0.925526 +mpq_rational 1024 -(int)0.935657 +mpq_rational 1024 * 68.7938 +mpq_rational 1024 / 119.722 +mpq_rational 1024 str 0.0288116 +tommath_int 64 + 0.0191513 +tommath_int 64 - 0.0231326 +tommath_int 64 +(int)0.25116 +tommath_int 64 -(int)0.213043 +tommath_int 64 * 0.0670515 +tommath_int 64 / 1.79107 +tommath_int 64 str 0.00735345 +tommath_int 64 % 1.82661 +tommath_int 64 | 0.121481 +tommath_int 64 & 0.121309 +tommath_int 64 ^ 0.12006 +tommath_int 64 << 0.0414542 +tommath_int 64 >> 0.220055 +tommath_int 128 + 0.0220235 +tommath_int 128 - 0.0260736 +tommath_int 128 +(int)0.264682 +tommath_int 128 -(int)0.221229 +tommath_int 128 * 0.111587 +tommath_int 128 / 2.11671 +tommath_int 128 str 0.0164135 +tommath_int 128 % 2.15548 +tommath_int 128 | 0.12259 +tommath_int 128 & 0.123011 +tommath_int 128 ^ 0.121874 +tommath_int 128 << 0.0393836 +tommath_int 128 >> 0.224932 +tommath_int 256 + 0.030358 +tommath_int 256 - 0.0379908 +tommath_int 256 +(int)0.278945 +tommath_int 256 -(int)0.24642 +tommath_int 256 * 0.339108 +tommath_int 256 / 2.95225 +tommath_int 256 str 0.0502673 +tommath_int 256 % 3.00797 +tommath_int 256 | 0.136742 +tommath_int 256 & 0.142151 +tommath_int 256 ^ 0.135172 +tommath_int 256 << 0.0652246 +tommath_int 256 >> 0.258642 +tommath_int 512 + 0.0459287 +tommath_int 512 - 0.0491835 +tommath_int 512 +(int)0.304282 +tommath_int 512 -(int)0.255992 +tommath_int 512 * 0.969408 +tommath_int 512 / 4.65733 +tommath_int 512 str 0.117235 +tommath_int 512 % 4.71416 +tommath_int 512 | 0.152291 +tommath_int 512 & 0.149147 +tommath_int 512 ^ 0.145169 +tommath_int 512 << 0.0949903 +tommath_int 512 >> 0.287043 +tommath_int 1024 + 0.0754591 +tommath_int 1024 - 0.0762591 +tommath_int 1024 +(int)0.307346 +tommath_int 1024 -(int)0.28448 +tommath_int 1024 * 3.10664 +tommath_int 1024 / 11.5662 +tommath_int 1024 str 0.380373 +tommath_int 1024 % 11.5386 +tommath_int 1024 | 0.406628 +tommath_int 1024 & 0.397507 +tommath_int 1024 ^ 0.401671 +tommath_int 1024 << 0.168563 +tommath_int 1024 >> 0.495242 +fixed_int 64 + 0.0031173 +fixed_int 64 - 0.00359417 +fixed_int 64 +(int)0.00329336 +fixed_int 64 -(int)0.00353606 +fixed_int 64 * 0.0175309 +fixed_int 64 / 0.0973696 +fixed_int 64 str 0.00143356 +fixed_int 64 % 0.098458 +fixed_int 64 | 0.00314803 +fixed_int 64 & 0.0028732 +fixed_int 64 ^ 0.00287983 +fixed_int 64 << 0.0120907 +fixed_int 64 >> 0.0064833 +fixed_int 128 + 0.00696555 +fixed_int 128 - 0.00721041 +fixed_int 128 +(int)0.00370718 +fixed_int 128 -(int)0.00577573 +fixed_int 128 * 0.0388232 +fixed_int 128 / 0.260936 +fixed_int 128 str 0.00290281 +fixed_int 128 % 0.269155 +fixed_int 128 | 0.00548233 +fixed_int 128 & 0.00552933 +fixed_int 128 ^ 0.00543128 +fixed_int 128 << 0.0129147 +fixed_int 128 >> 0.00772857 +fixed_int 256 + 0.0163707 +fixed_int 256 - 0.0168213 +fixed_int 256 +(int)0.00995385 +fixed_int 256 -(int)0.0155184 +fixed_int 256 * 0.123609 +fixed_int 256 / 0.845628 +fixed_int 256 str 0.0099558 +fixed_int 256 % 0.849272 +fixed_int 256 | 0.0125434 +fixed_int 256 & 0.0125148 +fixed_int 256 ^ 0.0125726 +fixed_int 256 << 0.0214412 +fixed_int 256 >> 0.0186871 +fixed_int 512 + 0.0314806 +fixed_int 512 - 0.0323563 +fixed_int 512 +(int)0.0117467 +fixed_int 512 -(int)0.029385 +fixed_int 512 * 0.427489 +fixed_int 512 / 2.51371 +fixed_int 512 str 0.0372769 +fixed_int 512 % 2.55909 +fixed_int 512 | 0.0198161 +fixed_int 512 & 0.020299 +fixed_int 512 ^ 0.019987 +fixed_int 512 << 0.0249208 +fixed_int 512 >> 0.0218303 +fixed_int 1024 + 0.0596158 +fixed_int 1024 - 0.061385 +fixed_int 1024 +(int)0.0233483 +fixed_int 1024 -(int)0.0586271 +fixed_int 1024 * 1.46312 +fixed_int 1024 / 7.93136 +fixed_int 1024 str 0.188878 +fixed_int 1024 % 7.99106 +fixed_int 1024 | 0.034957 +fixed_int 1024 & 0.034856 +fixed_int 1024 ^ 0.034697 +fixed_int 1024 << 0.0341293 +fixed_int 1024 >> 0.0326372 +cpp_float 50 + 0.0242151 +cpp_float 50 - 0.0261498 +cpp_float 50 +(int)0.0484155 +cpp_float 50 -(int)0.0567601 +cpp_float 50 * 0.287216 +cpp_float 50 / 3.98153 +cpp_float 50 str 0.0192656 +cpp_float 100 + 0.029252 +cpp_float 100 - 0.030946 +cpp_float 100 +(int)0.0611055 +cpp_float 100 -(int)0.0626685 +cpp_float 100 * 0.586363 +cpp_float 100 / 8.11948 +cpp_float 100 str 0.0320398 +cpp_float 500 + 0.0584099 +cpp_float 500 - 0.0606388 +cpp_float 500 +(int)0.104123 +cpp_float 500 -(int)0.111692 +cpp_float 500 * 5.05269 +cpp_float 500 / 53.6099 +cpp_float 500 str 0.134302 +mpfr_float 50 + 0.0594147 +mpfr_float 50 - 0.0774183 +mpfr_float 50 +(int)0.108 +mpfr_float 50 -(int)0.13804 +mpfr_float 50 * 0.329636 +mpfr_float 50 / 1.62419 +mpfr_float 50 str 0.0289065 +mpfr_float 100 + 0.0639309 +mpfr_float 100 - 0.0810465 +mpfr_float 100 +(int)0.112839 +mpfr_float 100 -(int)0.145473 +mpfr_float 100 * 0.457067 +mpfr_float 100 / 2.23443 +mpfr_float 100 str 0.0373977 +mpfr_float 500 + 0.0771588 +mpfr_float 500 - 0.0947396 +mpfr_float 500 +(int)0.11675 +mpfr_float 500 -(int)0.154304 +mpfr_float 500 * 3.72612 +mpfr_float 500 / 13.4944 +mpfr_float 500 str 0.155578 +[section:float_performance Float Type Perfomance] +[table Operator * +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][1.0826 (0.287216s)][1.48086 (0.586363s)][1.57545 (5.05269s)]] +[[gmp_float][[*1] (0.265302s)][[*1] (0.395962s)][[*1] (3.20714s)]] +[[mpfr_float][1.24249 (0.329636s)][1.15432 (0.457067s)][1.16182 (3.72612s)]] +] +[table Operator + +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][[*1] (0.0242151s)][[*1] (0.029252s)][[*1] (0.0584099s)]] +[[gmp_float][4.55194 (0.110226s)][3.67516 (0.107506s)][2.42489 (0.141638s)]] +[[mpfr_float][2.45362 (0.0594147s)][2.18552 (0.0639309s)][1.32099 (0.0771588s)]] +] +[table Operator +(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][1.51995 (0.0484155s)][1.78781 (0.0611055s)][1.8309 (0.104123s)]] +[[gmp_float][[*1] (0.0318533s)][[*1] (0.0341789s)][[*1] (0.0568699s)]] +[[mpfr_float][3.39055 (0.108s)][3.30142 (0.112839s)][2.05293 (0.11675s)]] +] +[table Operator - +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][[*1] (0.0261498s)][[*1] (0.030946s)][[*1] (0.0606388s)]] +[[gmp_float][4.48753 (0.117348s)][3.75823 (0.116302s)][2.4823 (0.150524s)]] +[[mpfr_float][2.96057 (0.0774183s)][2.61897 (0.0810465s)][1.56236 (0.0947396s)]] +] +[table Operator -(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][[*1] (0.0567601s)][[*1] (0.0626685s)][[*1] (0.111692s)]] +[[gmp_float][2.27932 (0.129374s)][2.04821 (0.128358s)][1.48297 (0.165635s)]] +[[mpfr_float][2.43199 (0.13804s)][2.32131 (0.145473s)][1.38152 (0.154304s)]] +] +[table Operator / +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][3.2662 (3.98153s)][5.07021 (8.11948s)][6.78872 (53.6099s)]] +[[gmp_float][[*1] (1.21901s)][[*1] (1.60141s)][[*1] (7.89691s)]] +[[mpfr_float][1.33238 (1.62419s)][1.39529 (2.23443s)][1.70882 (13.4944s)]] +] +[table Operator str +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][1.46076 (0.0192656s)][1.59438 (0.0320398s)][[*1] (0.134302s)]] +[[gmp_float][[*1] (0.0131888s)][[*1] (0.0200954s)][1.01007 (0.135655s)]] +[[mpfr_float][2.19174 (0.0289065s)][1.86101 (0.0373977s)][1.15842 (0.155578s)]] +] +[endsect] +[section:integer_performance Integer Type Perfomance] +[table Operator % +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.098458s)][[*1] (0.269155s)][1.10039 (0.849272s)][2.92096 (2.55909s)][7.47157 (7.99106s)]] +[[gmp_int][6.63934 (0.653697s)][2.6753 (0.72007s)][[*1] (0.771794s)][[*1] (0.87611s)][[*1] (1.06953s)]] +[[tommath_int][18.5522 (1.82661s)][8.00831 (2.15548s)][3.89737 (3.00797s)][5.38078 (4.71416s)][10.7885 (11.5386s)]] +] +[table Operator & +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0028732s)][[*1] (0.00552933s)][[*1] (0.0125148s)][[*1] (0.020299s)][[*1] (0.034856s)]] +[[gmp_int][16.3018 (0.0468383s)][9.51109 (0.05259s)][5.20026 (0.0650802s)][4.46545 (0.0906443s)][3.99377 (0.139207s)]] +[[tommath_int][42.221 (0.121309s)][22.2471 (0.123011s)][11.3587 (0.142151s)][7.3475 (0.149147s)][11.4043 (0.397507s)]] +] +[table Operator * +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0175309s)][[*1] (0.0388232s)][[*1] (0.123609s)][[*1] (0.427489s)][[*1] (1.46312s)]] +[[gmp_int][2.93263 (0.0514117s)][1.70358 (0.0661383s)][1.01811 (0.125848s)][1.20692 (0.515943s)][1.03248 (1.51064s)]] +[[tommath_int][3.82476 (0.0670515s)][2.87425 (0.111587s)][2.74339 (0.339108s)][2.26768 (0.969408s)][2.1233 (3.10664s)]] +] +[table Operator + +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0031173s)][[*1] (0.00696555s)][[*1] (0.0163707s)][[*1] (0.0314806s)][[*1] (0.0596158s)]] +[[gmp_int][12.7096 (0.0396194s)][5.89178 (0.0410395s)][2.66402 (0.0436119s)][1.59356 (0.0501664s)][1.11155 (0.0662662s)]] +[[tommath_int][6.14357 (0.0191513s)][3.16177 (0.0220235s)][1.85441 (0.030358s)][1.45895 (0.0459287s)][1.26576 (0.0754591s)]] +] +[table Operator +(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00329336s)][[*1] (0.00370718s)][[*1] (0.00995385s)][[*1] (0.0117467s)][[*1] (0.0233483s)]] +[[gmp_int][9.56378 (0.031497s)][8.0588 (0.0298754s)][4.15824 (0.0413905s)][5.47974 (0.0643691s)][4.46265 (0.104195s)]] +[[tommath_int][76.2624 (0.25116s)][71.3973 (0.264682s)][28.0238 (0.278945s)][25.9035 (0.304282s)][13.1635 (0.307346s)]] +] +[table Operator - +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00359417s)][[*1] (0.00721041s)][[*1] (0.0168213s)][[*1] (0.0323563s)][[*1] (0.061385s)]] +[[gmp_int][10.6794 (0.0383836s)][5.65517 (0.0407761s)][2.63634 (0.0443466s)][1.59979 (0.0517632s)][1.13379 (0.0695978s)]] +[[tommath_int][6.43615 (0.0231326s)][3.6161 (0.0260736s)][2.2585 (0.0379908s)][1.52006 (0.0491835s)][1.24231 (0.0762591s)]] +] +[table Operator -(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00353606s)][[*1] (0.00577573s)][[*1] (0.0155184s)][[*1] (0.029385s)][[*1] (0.0586271s)]] +[[gmp_int][9.04434 (0.0319814s)][5.12393 (0.0295945s)][2.50743 (0.0389112s)][2.01898 (0.0593277s)][1.68381 (0.098717s)]] +[[tommath_int][60.2486 (0.213043s)][38.3032 (0.221229s)][15.8792 (0.24642s)][8.71166 (0.255992s)][4.85236 (0.28448s)]] +] +[table Operator / +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0973696s)][[*1] (0.260936s)][[*1] (0.845628s)][2.4597 (2.51371s)][6.21836 (7.93136s)]] +[[gmp_int][7.66851 (0.74668s)][3.17732 (0.829077s)][1.05006 (0.887961s)][[*1] (1.02196s)][[*1] (1.27547s)]] +[[tommath_int][18.3945 (1.79107s)][8.11201 (2.11671s)][3.49119 (2.95225s)][4.55727 (4.65733s)][9.06813 (11.5662s)]] +] +[table Operator << +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0120907s)][[*1] (0.0129147s)][[*1] (0.0214412s)][[*1] (0.0249208s)][[*1] (0.0341293s)]] +[[gmp_int][1.93756 (0.0234265s)][1.97785 (0.0255433s)][1.43607 (0.0307911s)][1.815 (0.0452311s)][2.00167 (0.0683156s)]] +[[tommath_int][3.42859 (0.0414542s)][3.04951 (0.0393836s)][3.04202 (0.0652246s)][3.81169 (0.0949903s)][4.93896 (0.168563s)]] +] +[table Operator >> +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0064833s)][[*1] (0.00772857s)][[*1] (0.0186871s)][[*1] (0.0218303s)][[*1] (0.0326372s)]] +[[gmp_int][4.212 (0.0273077s)][3.72696 (0.0288041s)][1.55046 (0.0289735s)][1.51403 (0.0330518s)][1.13695 (0.037107s)]] +[[tommath_int][33.9418 (0.220055s)][29.104 (0.224932s)][13.8407 (0.258642s)][13.1488 (0.287043s)][15.1741 (0.495242s)]] +] +[table Operator ^ +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00287983s)][[*1] (0.00543128s)][[*1] (0.0125726s)][[*1] (0.019987s)][[*1] (0.034697s)]] +[[gmp_int][14.938 (0.0430189s)][9.00973 (0.0489344s)][4.83803 (0.0608267s)][4.33359 (0.0866154s)][3.89518 (0.135151s)]] +[[tommath_int][41.6898 (0.12006s)][22.4393 (0.121874s)][10.7513 (0.135172s)][7.2632 (0.145169s)][11.5765 (0.401671s)]] +] +[table Operator str +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][1.03557 (0.00143356s)][1.39844 (0.00290281s)][3.14081 (0.0099558s)][6.28067 (0.0372769s)][13.2101 (0.188878s)]] +[[gmp_int][[*1] (0.00138432s)][[*1] (0.00207575s)][[*1] (0.00316982s)][[*1] (0.00593518s)][[*1] (0.014298s)]] +[[tommath_int][5.31194 (0.00735345s)][7.90724 (0.0164135s)][15.8581 (0.0502673s)][19.7526 (0.117235s)][26.6031 (0.380373s)]] +] +[table Operator | +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00314803s)][[*1] (0.00548233s)][[*1] (0.0125434s)][[*1] (0.0198161s)][[*1] (0.034957s)]] +[[gmp_int][13.0622 (0.0411201s)][8.63936 (0.0473638s)][4.6932 (0.0588688s)][4.25792 (0.0843755s)][3.78236 (0.13222s)]] +[[tommath_int][38.5896 (0.121481s)][22.3609 (0.12259s)][10.9015 (0.136742s)][7.68521 (0.152291s)][11.6322 (0.406628s)]] +] +[endsect] +[section:rational_performance Rational Type Perfomance] +[table Operator * +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (2.63854s)][[*1] (5.8426s)][[*1] (12.6093s)][[*1] (28.654s)][[*1] (68.7938s)]] +] +[table Operator + +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (1.47058s)][[*1] (3.18485s)][[*1] (6.67422s)][[*1] (15.5117s)][[*1] (37.688s)]] +] +[table Operator +(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.654198s)][[*1] (0.66159s)][[*1] (0.705687s)][[*1] (0.817714s)][[*1] (0.925526s)]] +] +[table Operator - +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (1.47214s)][[*1] (3.1691s)][[*1] (6.67532s)][[*1] (15.6279s)][[*1] (37.6616s)]] +] +[table Operator -(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.646626s)][[*1] (0.657712s)][[*1] (0.704919s)][[*1] (0.818141s)][[*1] (0.935657s)]] +] +[table Operator / +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (9.24093s)][[*1] (14.6415s)][[*1] (26.2341s)][[*1] (52.808s)][[*1] (119.722s)]] +] +[table Operator str +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.00265152s)][[*1] (0.00372512s)][[*1] (0.00573139s)][[*1] (0.011966s)][[*1] (0.0288116s)]] +] +[endsect] diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index ee1eb0ea..f151ec8d 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -50,6 +50,12 @@ #include #include +#include +#include +#include +#include +#include +#include #include #include @@ -134,8 +140,8 @@ struct tester stopwatch w; for(unsigned i = 0; i < 1000; ++i) { - for(unsigned i = 0; i < b.size(); ++i) - a[i] = b[i] * c[i]; + for(unsigned k = 0; k < b.size(); ++k) + a[k] = b[k] * c[k]; } return boost::chrono::duration_cast >(w.elapsed()).count(); } @@ -253,7 +259,7 @@ private: typedef typename T::backend_type::exponent_type e_type; static boost::random::uniform_int_distribution ui(0, std::numeric_limits::max_exponent - 10); - return ldexp(val, ui(gen)); + return ldexp(val, static_cast(ui(gen))); } T generate_random(const boost::mpl::int_&) { @@ -286,6 +292,47 @@ private: val %= max_val; return val; } + T generate_random(const boost::mpl::int_&) + { + typedef boost::random::mt19937::result_type random_type; + typedef typename boost::multiprecision::component_type::type IntType; + + IntType max_val; + unsigned digits; + if(std::numeric_limits::is_bounded) + { + max_val = (std::numeric_limits::max)(); + digits = std::numeric_limits::digits; + } + else + { + max_val = IntType(1) << bits_wanted; + digits = bits_wanted; + } + + unsigned bits_per_r_val = std::numeric_limits::digits - 1; + while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val; + + unsigned terms_needed = digits / bits_per_r_val + 1; + + IntType val = 0; + IntType denom = 0; + for(unsigned i = 0; i < terms_needed; ++i) + { + val *= (gen.max)(); + val += gen(); + } + for(unsigned i = 0; i < terms_needed; ++i) + { + denom *= (gen.max)(); + denom += gen(); + } + if(denom == 0) + denom = 1; + val %= max_val; + denom %= max_val; + return T(val, denom); + } std::vector a, b, c, small; static boost::random::mt19937 gen; }; @@ -293,16 +340,46 @@ private: template boost::random::mt19937 tester::gen; +const char* category_name(const boost::mpl::int_&) +{ + return "integer"; +} +const char* category_name(const boost::mpl::int_&) +{ + return "float"; +} +const char* category_name(const boost::mpl::int_&) +{ + return "rational"; +} + +// +// Keys in order are: +// Category +// Operator +// Type +// Precision +// Time +// +std::map > > > result_table; + +void report_result(const char* cat, const char* type, const char* op, unsigned precision, double time) +{ + std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << op << time << std::endl; + result_table[cat][op][type][precision] = time; +} + template void test_int_ops(tester& t, const char* type, unsigned precision, const boost::mpl::int_&) { - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "%" << t.test_mod() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "|" << t.test_or() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "&" << t.test_and() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "^" << t.test_xor() << std::endl; - //std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "~" << t.test_complement() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "<<" << t.test_left_shift() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << ">>" << t.test_right_shift() << std::endl; + const char* cat = "integer"; + report_result(cat, type, "%", precision, t.test_mod()); + report_result(cat, type, "|", precision, t.test_or()); + report_result(cat, type, "&", precision, t.test_and()); + report_result(cat, type, "^", precision, t.test_xor()); + //report_result(cat, type, "~", precision, t.test_complement()); + report_result(cat, type, "<<", precision, t.test_left_shift()); + report_result(cat, type, ">>", precision, t.test_right_shift()); } template void test_int_ops(tester& t, const char* type, unsigned precision, const U&) @@ -314,17 +391,98 @@ void test(const char* type, unsigned precision) { bits_wanted = precision; tester::value> t; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "+" << t.test_add() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "-" << t.test_subtract() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "+ (int)" << t.test_add_int() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "- (int)" << t.test_subtract_int() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "*" << t.test_multiply() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "/" << t.test_divide() << std::endl; - std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(5) << "str" << t.test_str() << std::endl; + const char* cat = category_name(typename boost::multiprecision::number_category::type()); + // + // call t.test_multiply() first so that the destination operands are + // forced to perform whatever memory allocation may be needed. That way + // we measure only algorithm performance, and not memory allocation effects. + // + t.test_multiply(); + // + // Now the actual tests: + // + report_result(cat, type, "+", precision, t.test_add()); + report_result(cat, type, "-", precision, t.test_subtract()); + report_result(cat, type, "+(int)", precision, t.test_add_int()); + report_result(cat, type, "-(int)", precision, t.test_subtract_int()); + report_result(cat, type, "*", precision, t.test_multiply()); + report_result(cat, type, "/", precision, t.test_divide()); + report_result(cat, type, "str", precision, t.test_str()); test_int_ops(t, type, precision, typename boost::multiprecision::number_category::type()); } +void quickbook_results() +{ + // + // Keys in order are: + // Category + // Operator + // Type + // Precision + // Time + // + typedef std::map > > >::const_iterator category_iterator; + typedef std::map > >::const_iterator operator_iterator; + typedef std::map >::const_iterator type_iterator; + typedef std::map::const_iterator precision_iterator; + + for(category_iterator i = result_table.begin(); i != result_table.end(); ++i) + { + std::string cat = i->first; + cat[0] = std::toupper(cat[0]); + std::cout << "[section:" << i->first << "_performance " << cat << " Type Perfomance]" << std::endl; + + for(operator_iterator j = i->second.begin(); j != i->second.end(); ++j) + { + std::string op = j->first; + std::cout << "[table Operator " << op << std::endl; + std::cout << "[[Backend]"; + + for(precision_iterator k = j->second.begin()->second.begin(); k != j->second.begin()->second.end(); ++k) + { + std::cout << "[" << k->first << " Bits]"; + } + std::cout << "]\n"; + + std::vector best_times(j->second.begin()->second.size(), (std::numeric_limits::max)()); + for(unsigned m = 0; m < j->second.begin()->second.size(); ++m) + { + for(type_iterator k = j->second.begin(); k != j->second.end(); ++k) + { + precision_iterator l = k->second.begin(); + std::advance(l, m); + if(best_times[m] > l->second) + best_times[m] = l->second; + } + } + + for(type_iterator k = j->second.begin(); k != j->second.end(); ++k) + { + std::cout << "[[" << k->first << "]"; + + unsigned m = 0; + for(precision_iterator l = k->second.begin(); l != k->second.end(); ++l) + { + double rel_time = l->second / best_times[m]; + if(rel_time == 1) + std::cout << "[[*" << rel_time << "]"; + else + std::cout << "[" << rel_time; + std::cout << " (" << l->second << "s)]"; + ++m; + } + + std::cout << "]\n"; + } + + std::cout << "]\n"; + } + + std::cout << "[endsect]" << std::endl; + } +} + int main() { @@ -339,6 +497,12 @@ int main() test("gmp_int", 256); test("gmp_int", 512); test("gmp_int", 1024); + + test("mpq_rational", 64); + test("mpq_rational", 128); + test("mpq_rational", 256); + test("mpq_rational", 512); + test("mpq_rational", 1024); #endif #ifdef TEST_TOMMATH test("tommath_int", 64); @@ -346,13 +510,23 @@ int main() test("tommath_int", 256); test("tommath_int", 512); test("tommath_int", 1024); + /* + // + // These are actually too slow to test!!! + // + test("mp_rational", 64); + test("mp_rational", 128); + test("mp_rational", 256); + test("mp_rational", 512); + test("mp_rational", 1024); + */ #endif #ifdef TEST_FIXED_INT - test > >("mp_int64_t", 64); - test("mp_int128_t", 128); - test("mp_int256_t", 256); - test("mp_int512_t", 512); - test > >("mp_int1024_t", 1024); + test > >("fixed_int", 64); + test("fixed_int", 128); + test("fixed_int", 256); + test("fixed_int", 512); + test > >("fixed_int", 1024); #endif #ifdef TEST_CPP_FLOAT test("cpp_float", 50); @@ -364,6 +538,7 @@ int main() test("mpfr_float", 100); test("mpfr_float", 500); #endif + quickbook_results(); return 0; } diff --git a/performance/sf_performance-msvc-10.log b/performance/sf_performance-msvc-10.log index 82722d81..9dc8de7b 100644 --- a/performance/sf_performance-msvc-10.log +++ b/performance/sf_performance-msvc-10.log @@ -5,65 +5,65 @@ 13 27 Testing Bessel Functions..... -Time for mpfr_float_50 = 6.2742 seconds +Time for mpfr_float_50 = 6.47208 seconds Total allocations for mpfr_float_50 = 2684348 -Time for mpf_float_50 = 11.2255 seconds +Time for mpf_float_50 = 11.6627 seconds Total allocations for mpf_float_50 = 2601366 -Time for cpp_float_50 = 19.5712 seconds +Time for cpp_float_50 = 20.2855 seconds Total allocations for cpp_float_50 = 0 -Time for mpfr_class (50 digits) = 6.11757 seconds +Time for mpfr_class (50 digits) = 6.48063 seconds Total allocations for mpfr_class (50 digits) = 3946031 -Time for mpreal (50 digits) = 9.38756 seconds +Time for mpreal (50 digits) = 9.98151 seconds Total allocations for mpreal (50 digits) = 13223017 -Time for mpfr_float_100 = 9.61944 seconds +Time for mpfr_float_100 = 10.154 seconds Total allocations for mpfr_float_50 = 3671485 -Time for mpf_float_100 = 8.29211 seconds +Time for mpf_float_100 = 8.51179 seconds Total allocations for mpf_float_100 = 3593669 -Time for cpp_float_100 = 20.4485 seconds +Time for cpp_float_100 = 21.0198 seconds Total allocations for cpp_float_100 = 0 -Time for mpfr_class (100 digits) = 9.88427 seconds +Time for mpfr_class (100 digits) = 9.80571 seconds Total allocations for mpfr_class (100 digits) = 5447348 -Time for mpreal (100 digits) = 13.7811 seconds +Time for mpreal (100 digits) = 13.7021 seconds Total allocations for mpreal (100 digits) = 16671065 Testing Polynomial Evaluation..... -Time for mpfr_float_50 = 0.00839464 seconds +Time for mpfr_float_50 = 0.00823841 seconds Total allocations for mpfr_float_50 = 2996 -Time for mpf_float_50 = 0.0042138 seconds +Time for mpf_float_50 = 0.00401608 seconds Total allocations for mpf_float_50 = 2996 -Time for cpp_float_50 = 0.0046054 seconds +Time for cpp_float_50 = 0.00492116 seconds Total allocations for cpp_float_50 = 0 -Time for mpfr_class (50 digits) = 0.00990538 seconds +Time for mpfr_class (50 digits) = 0.00935629 seconds Total allocations for mpfr_class (50 digits) = 12976 -Time for mpreal (50 digits) = 0.0152955 seconds +Time for mpreal (50 digits) = 0.0148374 seconds Total allocations for mpreal (50 digits = 27947 -Time for mpfr_float_100 = 0.00957098 seconds +Time for mpfr_float_100 = 0.00948452 seconds Total allocations for mpfr_float_100 = 2996 -Time for mpf_float_100 = 0.00418726 seconds +Time for mpf_float_100 = 0.00390071 seconds Total allocations for mpf_float_100 = 2996 -Time for cpp_float_100 = 0.0090742 seconds +Time for cpp_float_100 = 0.00893563 seconds Total allocations for cpp_float_100 = 0 -Time for mpfr_class (100 digits) = 0.011094 seconds +Time for mpfr_class (100 digits) = 0.0106166 seconds Total allocations for mpfr_class (100 digits) = 12976 -Time for mpreal (100 digits) = 0.0172028 seconds +Time for mpreal (100 digits) = 0.0162364 seconds Total allocations for mpreal (100 digits) = 27947 Testing Non-Central T..... -Time for mpfr_float_50 = 260.324 seconds +Time for mpfr_float_50 = 258.087 seconds Total allocations for mpfr_float_50 = 139149049 -Time for mpf_float_50 = 201.95 seconds +Time for mpf_float_50 = 197.303 seconds Total allocations for mpf_float_50 = 134600354 -Time for cpp_float_50 = 340.292 seconds +Time for cpp_float_50 = 334.503 seconds Total allocations for cpp_float_50 = 0 -Time for mpfr_class (50 digits) = 269.03 seconds +Time for mpfr_class (50 digits) = 266.389 seconds Total allocations for mpfr_class (50 digits) = 252401115 -Time for mpreal (50 digits) = 350.758 seconds +Time for mpreal (50 digits) = 346.641 seconds Total allocations for mpreal (50 digits) = 447009420 -Time for mpfr_float_100 = 519.421 seconds +Time for mpfr_float_100 = 516.741 seconds Total allocations for mpfr_float_100 = 220400854 -Time for mpf_float_100 = 404.593 seconds +Time for mpf_float_100 = 397.302 seconds Total allocations for mpf_float_100 = 212307349 -Time for cpp_float_100 = 1118.91 seconds +Time for cpp_float_100 = 1064.53 seconds Total allocations for cpp_float_100 = 0 -Time for mpfr_class (100 digits) = 541.35 seconds +Time for mpfr_class (100 digits) = 525.74 seconds Total allocations for mpfr_class (100 digits) = 407154781 -Time for mpreal (100 digits) = 677.265 seconds +Time for mpreal (100 digits) = 649.941 seconds Total allocations for mpreal (100 digits) = 724581024 From 66b67a1c095acd485ee75e4ded68822f9664ab98 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 16 Jan 2012 18:26:50 +0000 Subject: [PATCH 102/256] Refactor SF tests for much faster compile times. [SVN r76545] --- test/Jamfile.v2 | 3 +++ test/math/test_bessel_i.cpp | 3 ++- test/math/test_bessel_j.cpp | 3 ++- test/math/test_bessel_k.cpp | 3 ++- test/math/test_bessel_y.cpp | 3 ++- test/math/test_beta.cpp | 3 ++- test/math/test_binomial_coeff.cpp | 3 ++- test/math/test_carlson.cpp | 6 +++++- test/math/test_cbrt.cpp | 3 ++- test/math/test_digamma.cpp | 3 ++- test/math/test_ellint_1.cpp | 3 ++- test/math/test_ellint_2.cpp | 3 ++- test/math/test_ellint_3.cpp | 3 ++- test/math/test_erf.cpp | 3 ++- test/math/test_expint.cpp | 3 ++- test/math/test_gamma.cpp | 3 ++- test/math/test_hermite.cpp | 3 ++- test/math/test_ibeta.cpp | 3 ++- test/math/test_ibeta_2.cpp | 3 ++- test/math/test_ibeta_3.cpp | 3 ++- test/math/test_ibeta_4.cpp | 3 ++- test/math/test_ibeta_inv_1.cpp | 3 ++- test/math/test_ibeta_inv_ab_4.cpp | 3 ++- test/math/test_igamma.cpp | 3 ++- test/math/test_igamma_inv.cpp | 3 ++- test/math/test_igamma_inva.cpp | 3 ++- test/math/test_laguerre.cpp | 3 ++- test/math/test_legendre.cpp | 3 ++- test/math/test_tgamma_ratio.cpp | 3 ++- test/math/test_zeta.cpp | 3 ++- 30 files changed, 64 insertions(+), 29 deletions(-) diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 04133118..3e547c5b 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -654,6 +654,7 @@ if $(enable-specfun) speed BOOST_ALL_NO_LIB msvc:-bigobj + release : $(source:B)_mpfr ; run $(source) gmp /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static : # command line @@ -664,6 +665,7 @@ if $(enable-specfun) TEST_MPF_50 BOOST_ALL_NO_LIB msvc:-bigobj + release : $(source:B)_mpf ; run $(source) /boost/test//boost_test_exec_monitor/static /boost/regex//boost_regex/static : # command line @@ -673,6 +675,7 @@ if $(enable-specfun) BOOST_ALL_NO_LIB speed msvc:-bigobj + release : $(source:B)_cpp_float ; } } diff --git a/test/math/test_bessel_i.cpp b/test/math/test_bessel_i.cpp index 168563e2..d210de6a 100644 --- a/test/math/test_bessel_i.cpp +++ b/test/math/test_bessel_i.cpp @@ -41,8 +41,9 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) +#include #include "libs/math/test/test_bessel_i.hpp" void expected_results() diff --git a/test/math/test_bessel_j.cpp b/test/math/test_bessel_j.cpp index b2e6b936..5be8f196 100644 --- a/test/math/test_bessel_j.cpp +++ b/test/math/test_bessel_j.cpp @@ -41,8 +41,9 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) +#include #include "libs/math/test/test_bessel_j.hpp" void expected_results() diff --git a/test/math/test_bessel_k.cpp b/test/math/test_bessel_k.cpp index 1432a4e3..f1adb73a 100644 --- a/test/math/test_bessel_k.cpp +++ b/test/math/test_bessel_k.cpp @@ -42,8 +42,9 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) +#include #include "libs/math/test/test_bessel_k.hpp" void expected_results() diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp index e224865a..7dde570a 100644 --- a/test/math/test_bessel_y.cpp +++ b/test/math/test_bessel_y.cpp @@ -41,8 +41,9 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) +#include #include "libs/math/test/test_bessel_y.hpp" void expected_results() diff --git a/test/math/test_beta.cpp b/test/math/test_beta.cpp index 83849258..cfd8848d 100644 --- a/test/math/test_beta.cpp +++ b/test/math/test_beta.cpp @@ -41,8 +41,9 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) +#include #include "libs/math/test/test_beta.hpp" void expected_results() diff --git a/test/math/test_binomial_coeff.cpp b/test/math/test_binomial_coeff.cpp index 6272d647..67923858 100644 --- a/test/math/test_binomial_coeff.cpp +++ b/test/math/test_binomial_coeff.cpp @@ -41,8 +41,9 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) +#include #include "libs/math/test/test_binomial_coeff.hpp" void expected_results() diff --git a/test/math/test_carlson.cpp b/test/math/test_carlson.cpp index b698bd0c..353380ed 100644 --- a/test/math/test_carlson.cpp +++ b/test/math/test_carlson.cpp @@ -36,9 +36,13 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include +#include +#include +#include #include "libs/math/test/test_carlson.hpp" void expected_results() diff --git a/test/math/test_cbrt.cpp b/test/math/test_cbrt.cpp index 5c3b6906..7c21cd3e 100644 --- a/test/math/test_cbrt.cpp +++ b/test/math/test_cbrt.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_cbrt.hpp" void expected_results() diff --git a/test/math/test_digamma.cpp b/test/math/test_digamma.cpp index 1098ae6e..6aae7dd8 100644 --- a/test/math/test_digamma.cpp +++ b/test/math/test_digamma.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_digamma.hpp" void expected_results() diff --git a/test/math/test_ellint_1.cpp b/test/math/test_ellint_1.cpp index a9b88450..b5ce8e4d 100644 --- a/test/math/test_ellint_1.cpp +++ b/test/math/test_ellint_1.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_ellint_1.hpp" void expected_results() diff --git a/test/math/test_ellint_2.cpp b/test/math/test_ellint_2.cpp index 4accc451..67300ff5 100644 --- a/test/math/test_ellint_2.cpp +++ b/test/math/test_ellint_2.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_ellint_2.hpp" void expected_results() diff --git a/test/math/test_ellint_3.cpp b/test/math/test_ellint_3.cpp index 880d4743..feffa5ed 100644 --- a/test/math/test_ellint_3.cpp +++ b/test/math/test_ellint_3.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_ellint_3.hpp" void expected_results() diff --git a/test/math/test_erf.cpp b/test/math/test_erf.cpp index f056d2bd..878b70c6 100644 --- a/test/math/test_erf.cpp +++ b/test/math/test_erf.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_erf.hpp" void expected_results() diff --git a/test/math/test_expint.cpp b/test/math/test_expint.cpp index 4f19cb0c..8758fca2 100644 --- a/test/math/test_expint.cpp +++ b/test/math/test_expint.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_expint.hpp" void expected_results() diff --git a/test/math/test_gamma.cpp b/test/math/test_gamma.cpp index 9e6528e5..65ae04bd 100644 --- a/test/math/test_gamma.cpp +++ b/test/math/test_gamma.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_gamma.hpp" void expected_results() diff --git a/test/math/test_hermite.cpp b/test/math/test_hermite.cpp index bd776eb4..82fafd9b 100644 --- a/test/math/test_hermite.cpp +++ b/test/math/test_hermite.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_hermite.hpp" void expected_results() diff --git a/test/math/test_ibeta.cpp b/test/math/test_ibeta.cpp index 4cf95bb1..a3da2063 100644 --- a/test/math/test_ibeta.cpp +++ b/test/math/test_ibeta.cpp @@ -37,11 +37,12 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT #define TEST_DATA 1 +#include #include "libs/math/test/test_ibeta.hpp" void expected_results() diff --git a/test/math/test_ibeta_2.cpp b/test/math/test_ibeta_2.cpp index a149c837..21f9b840 100644 --- a/test/math/test_ibeta_2.cpp +++ b/test/math/test_ibeta_2.cpp @@ -37,11 +37,12 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT #define TEST_DATA 2 +#include #include "libs/math/test/test_ibeta.hpp" void expected_results() diff --git a/test/math/test_ibeta_3.cpp b/test/math/test_ibeta_3.cpp index 6f42b026..89181669 100644 --- a/test/math/test_ibeta_3.cpp +++ b/test/math/test_ibeta_3.cpp @@ -37,11 +37,12 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT #define TEST_DATA 3 +#include #include "libs/math/test/test_ibeta.hpp" void expected_results() diff --git a/test/math/test_ibeta_4.cpp b/test/math/test_ibeta_4.cpp index d5c665bd..5d0783c7 100644 --- a/test/math/test_ibeta_4.cpp +++ b/test/math/test_ibeta_4.cpp @@ -37,11 +37,12 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT #define TEST_DATA 4 +#include #include "libs/math/test/test_ibeta.hpp" void expected_results() diff --git a/test/math/test_ibeta_inv_1.cpp b/test/math/test_ibeta_inv_1.cpp index 2b3b616d..8171686a 100644 --- a/test/math/test_ibeta_inv_1.cpp +++ b/test/math/test_ibeta_inv_1.cpp @@ -37,11 +37,12 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT #define TEST_DATA 4 +#include #include "libs/math/test/test_ibeta_inv.hpp" void expected_results() diff --git a/test/math/test_ibeta_inv_ab_4.cpp b/test/math/test_ibeta_inv_ab_4.cpp index 4ff6dbca..6caba045 100644 --- a/test/math/test_ibeta_inv_ab_4.cpp +++ b/test/math/test_ibeta_inv_ab_4.cpp @@ -36,12 +36,13 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT #define TEST_DATA 4 #define FULL_TEST +#include #include "libs/math/test/test_ibeta_inv_ab.hpp" void expected_results() diff --git a/test/math/test_igamma.cpp b/test/math/test_igamma.cpp index ee60a91b..6f9da83c 100644 --- a/test/math/test_igamma.cpp +++ b/test/math/test_igamma.cpp @@ -37,8 +37,9 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) +#include #include "libs/math/test/test_igamma.hpp" void expected_results() diff --git a/test/math/test_igamma_inv.cpp b/test/math/test_igamma_inv.cpp index 44c5a718..2b530a9f 100644 --- a/test/math/test_igamma_inv.cpp +++ b/test/math/test_igamma_inv.cpp @@ -37,9 +37,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_igamma_inv.hpp" void expected_results() diff --git a/test/math/test_igamma_inva.cpp b/test/math/test_igamma_inva.cpp index 7cca029c..2f6dfe5e 100644 --- a/test/math/test_igamma_inva.cpp +++ b/test/math/test_igamma_inva.cpp @@ -37,9 +37,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_igamma_inva.hpp" void expected_results() diff --git a/test/math/test_laguerre.cpp b/test/math/test_laguerre.cpp index da304c5d..32890c32 100644 --- a/test/math/test_laguerre.cpp +++ b/test/math/test_laguerre.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_laguerre.hpp" void expected_results() diff --git a/test/math/test_legendre.cpp b/test/math/test_legendre.cpp index 2c0a6787..1311d4f7 100644 --- a/test/math/test_legendre.cpp +++ b/test/math/test_legendre.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_legendre.hpp" void expected_results() diff --git a/test/math/test_tgamma_ratio.cpp b/test/math/test_tgamma_ratio.cpp index 71d45a79..8e5d8629 100644 --- a/test/math/test_tgamma_ratio.cpp +++ b/test/math/test_tgamma_ratio.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_tgamma_ratio.hpp" void expected_results() diff --git a/test/math/test_zeta.cpp b/test/math/test_zeta.cpp index b4503eb1..78800950 100644 --- a/test/math/test_zeta.cpp +++ b/test/math/test_zeta.cpp @@ -36,9 +36,10 @@ #include #endif -#define SC_(x) T(BOOST_STRINGIZE(x)) +#define SC_(x) BOOST_STRINGIZE(x) #define TEST_UDT +#include #include "libs/math/test/test_zeta.hpp" void expected_results() From ca5a793b3dcf2c373cce7b9718a9c8b04319dde1 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 17 Jan 2012 13:06:33 +0000 Subject: [PATCH 103/256] Rejig intmax_t and long long usage to be much more consistent. [SVN r76550] --- .../multiprecision/arithmetic_backend.hpp | 8 +++---- .../concepts/mp_number_architypes.hpp | 16 ++++++------- include/boost/multiprecision/cpp_float.hpp | 6 ++--- include/boost/multiprecision/fixed_int.hpp | 23 +++++++++--------- include/boost/multiprecision/gmp.hpp | 24 +++++++++---------- include/boost/multiprecision/mpfr.hpp | 10 ++++---- include/boost/multiprecision/tommath.hpp | 8 +++---- 7 files changed, 47 insertions(+), 48 deletions(-) diff --git a/include/boost/multiprecision/arithmetic_backend.hpp b/include/boost/multiprecision/arithmetic_backend.hpp index b213c819..8225bd0e 100644 --- a/include/boost/multiprecision/arithmetic_backend.hpp +++ b/include/boost/multiprecision/arithmetic_backend.hpp @@ -39,12 +39,12 @@ struct arithmetic_backend m_value = o.m_value; return *this; } - arithmetic_backend& operator = (boost::uintmax_t i) + arithmetic_backend& operator = (unsigned long long i) { m_value = i; return *this; } - arithmetic_backend& operator = (boost::intmax_t i) + arithmetic_backend& operator = (long long i) { m_value = i; return *this; @@ -78,11 +78,11 @@ struct arithmetic_backend { return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); } - int compare(boost::intmax_t i)const + int compare(long long i)const { return m_value > i ? 1 : (m_value < i ? -1 : 0); } - int compare(boost::uintmax_t i)const + int compare(unsigned long long i)const { return m_value > i ? 1 : (m_value < i ? -1 : 0); } diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index d8380e93..bfa941be 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -45,13 +45,13 @@ struct mp_number_backend_float_architype std::cout << "Assignment (" << m_value << ")" << std::endl; return *this; } - mp_number_backend_float_architype& operator = (boost::uintmax_t i) + mp_number_backend_float_architype& operator = (unsigned long long i) { m_value = i; std::cout << "UInt Assignment (" << i << ")" << std::endl; return *this; } - mp_number_backend_float_architype& operator = (boost::intmax_t i) + mp_number_backend_float_architype& operator = (long long i) { m_value = i; std::cout << "Int Assignment (" << i << ")" << std::endl; @@ -104,12 +104,12 @@ struct mp_number_backend_float_architype std::cout << "Comparison" << std::endl; return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); } - int compare(boost::intmax_t i)const + int compare(long long i)const { std::cout << "Comparison with int" << std::endl; return m_value > i ? 1 : (m_value < i ? -1 : 0); } - int compare(boost::uintmax_t i)const + int compare(unsigned long long i)const { std::cout << "Comparison with unsigned" << std::endl; return m_value > i ? 1 : (m_value < i ? -1 : 0); @@ -143,13 +143,13 @@ inline void divide(mp_number_backend_float_architype& result, const mp_number_ba result.m_value /= o.m_value; } -inline void convert_to(boost::uintmax_t* result, const mp_number_backend_float_architype& val) +inline void convert_to(unsigned long long* result, const mp_number_backend_float_architype& val) { - *result = static_cast(val.m_value); + *result = static_cast(val.m_value); } -inline void convert_to(boost::intmax_t* result, const mp_number_backend_float_architype& val) +inline void convert_to(long long* result, const mp_number_backend_float_architype& val) { - *result = static_cast(val.m_value); + *result = static_cast(val.m_value); } inline void convert_to(long double* result, mp_number_backend_float_architype& val) { diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 968e29c1..12cde7b4 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -1815,7 +1815,7 @@ bool cpp_float::rd_string(const char* const s) ) { // Remove the exponent part from the string. - exp = boost::lexical_cast(static_cast(str.c_str() + (pos + 1u))); + exp = boost::lexical_cast(static_cast(str.c_str() + (pos + 1u))); str = str.substr(static_cast(0u), pos); } @@ -2059,7 +2059,7 @@ bool cpp_float::rd_string(const char* const s) } template -cpp_float::cpp_float(const double mantissa, const boost::int64_t exponent) +cpp_float::cpp_float(const double mantissa, const long long exponent) : data (), exp (static_cast(0)), neg (false), @@ -2245,7 +2245,7 @@ boost::uint32_t cpp_float::div_loop_n(boost::uint32_t* const u, boost: } template -cpp_float cpp_float::pow2(const boost::int64_t p) +cpp_float cpp_float::pow2(const long long p) { // Create a static const table of p^2 for -128 < p < +128. // Note: The size of this table must be odd-numbered and diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index c5eebfa4..7dda8ff5 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -26,10 +26,9 @@ template struct fixed_int { typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list float_types; + typedef mpl::list unsigned_types; + typedef mpl::list float_types; - typedef limb_type limb_type; BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT); BOOST_STATIC_CONSTANT(unsigned, limb_count = Bits / limb_bits + (Bits % limb_bits ? 1 : 0)); BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u)); @@ -365,7 +364,7 @@ inline void add(fixed_int& result, const fixed_int& for(int i = fixed_int::limb_count - 1; i >= 0; --i) { carry += static_cast(a.data()[i]) + static_cast(b.data()[i]); - result.data()[i] = static_cast::limb_type>(carry); + result.data()[i] = static_cast(carry); carry >>= fixed_int::limb_bits; } result.data()[0] &= fixed_int::upper_limb_mask; @@ -379,7 +378,7 @@ inline void add(fixed_int& result, const limb_type& o) for(int i = fixed_int::limb_count - 1; carry && i >= 0; --i) { carry += static_cast(result.data()[i]); - result.data()[i] = static_cast::limb_type>(carry); + result.data()[i] = static_cast(carry); carry >>= fixed_int::limb_bits; } result.data()[0] &= fixed_int::upper_limb_mask; @@ -399,12 +398,12 @@ inline void subtract(fixed_int& result, const limb_type& o) // This is the same code as for addition, with the twist that we negate o "on the fly": double_limb_type carry = static_cast(result.data()[fixed_int::limb_count - 1]) + 1uLL + static_cast(~o); - result.data()[fixed_int::limb_count - 1] = static_cast::limb_type>(carry); + result.data()[fixed_int::limb_count - 1] = static_cast(carry); carry >>= fixed_int::limb_bits; for(int i = fixed_int::limb_count - 2; i >= 0; --i) { carry += static_cast(result.data()[i]) + 0xFFFFFFFF; - result.data()[i] = static_cast::limb_type>(carry); + result.data()[i] = static_cast(carry); carry >>= fixed_int::limb_bits; } result.data()[0] &= fixed_int::upper_limb_mask; @@ -452,7 +451,7 @@ inline void subtract(fixed_int& result, const fixed_int::limb_count - 1; i >= 0; --i) { carry += static_cast(a.data()[i]) + static_cast(~b.data()[i]); - result.data()[i] = static_cast::limb_type>(carry); + result.data()[i] = static_cast(carry); carry >>= fixed_int::limb_bits; } result.data()[0] &= fixed_int::upper_limb_mask; @@ -483,7 +482,7 @@ inline void multiply(fixed_int& result, const fixed_int(a.data()[i]) * static_cast(b.data()[j]); carry += result.data()[i + j + 1 - fixed_int::limb_count]; - result.data()[i + j + 1 - fixed_int::limb_count] = static_cast::limb_type>(carry); + result.data()[i + j + 1 - fixed_int::limb_count] = static_cast(carry); carry >>= fixed_int::limb_bits; } carry = 0; @@ -504,7 +503,7 @@ inline void multiply(fixed_int& result, const limb_type& a) for(int i = fixed_int::limb_count - 1; i >= 0; --i) { carry += static_cast(result.data()[i]) * static_cast(a); - result.data()[i] = static_cast::limb_type>(carry); + result.data()[i] = static_cast(carry); carry >>= fixed_int::limb_bits; } result.data()[0] &= fixed_int::upper_limb_mask; @@ -761,7 +760,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1) ? (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1] : r.data()[r_order]; b = (y_order < fixed_int::limb_count - 1) ? (static_cast(y.data()[y_order]) << fixed_int::limb_bits) | y.data()[y_order + 1] : (static_cast(y.data()[y_order]) << fixed_int::limb_bits); v = a / b; - guess = static_cast::limb_type>(v); + guess = static_cast(v); //guess = r.data()[r_order] / y.data()[y_order]; } // @@ -784,7 +783,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1; i >= static_cast(shift); --i) { carry += static_cast(y.data()[i]) * static_cast(guess); - t.data()[i - shift] = static_cast::limb_type>(carry); + t.data()[i - shift] = static_cast(carry); carry >>= fixed_int::limb_bits; } t.data()[0] &= fixed_int::upper_limb_mask; diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 90cf2fb7..d4bdb350 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -63,9 +63,9 @@ struct gmp_float_imp return *this; } #endif - gmp_float_imp& operator = (boost::uintmax_t i) + gmp_float_imp& operator = (unsigned long long i) { - boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpf_t t; mpf_init2(t, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); @@ -82,11 +82,11 @@ struct gmp_float_imp mpf_clear(t); return *this; } - gmp_float_imp& operator = (boost::intmax_t i) + gmp_float_imp& operator = (long long i) { BOOST_MP_USING_ABS bool neg = i < 0; - *this = static_cast(abs(i)); + *this = static_cast(abs(i)); if(neg) mpf_neg(m_data, m_data); return *this; @@ -891,9 +891,9 @@ struct gmp_int mpz_set(m_data, o.m_data); return *this; } - gmp_int& operator = (boost::uintmax_t i) + gmp_int& operator = (unsigned long long i) { - boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpz_t t; mpz_init(m_data); @@ -910,11 +910,11 @@ struct gmp_int mpz_clear(t); return *this; } - gmp_int& operator = (boost::intmax_t i) + gmp_int& operator = (long long i) { BOOST_MP_USING_ABS bool neg = i < 0; - *this = static_cast(abs(i)); + *this = static_cast(abs(i)); if(neg) mpz_neg(m_data, m_data); return *this; @@ -1430,9 +1430,9 @@ struct gmp_rational mpq_set(m_data, o.m_data); return *this; } - gmp_rational& operator = (boost::uintmax_t i) + gmp_rational& operator = (unsigned long long i) { - boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpq_t t; mpq_init(m_data); @@ -1449,11 +1449,11 @@ struct gmp_rational mpq_clear(t); return *this; } - gmp_rational& operator = (boost::intmax_t i) + gmp_rational& operator = (long long i) { BOOST_MP_USING_ABS bool neg = i < 0; - *this = static_cast(abs(i)); + *this = static_cast(abs(i)); if(neg) mpq_neg(m_data, m_data); return *this; diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index c0c497ce..74b9a614 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -59,12 +59,12 @@ struct mpfr_float_imp return *this; } #endif - mpfr_float_imp& operator = (boost::uintmax_t i) + mpfr_float_imp& operator = (unsigned long long i) { - boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpfr_t t; - mpfr_init2(t, (std::max)(static_cast(std::numeric_limits::digits), static_cast(((digits10 + 1) * 1000L) / 301L))); + mpfr_init2(t, (std::max)(static_cast(std::numeric_limits::digits), static_cast(((digits10 + 1) * 1000L) / 301L))); mpfr_set_ui(m_data, 0, GMP_RNDN); while(i) { @@ -78,11 +78,11 @@ struct mpfr_float_imp mpfr_clear(t); return *this; } - mpfr_float_imp& operator = (boost::intmax_t i) + mpfr_float_imp& operator = (long long i) { BOOST_MP_USING_ABS bool neg = i < 0; - *this = static_cast(abs(i)); + *this = static_cast(abs(i)); if(neg) mpfr_neg(m_data, m_data, GMP_RNDN); return *this; diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 95e035b4..86ecea9e 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -50,9 +50,9 @@ struct tommath_int detail::check_tommath_result(mp_copy(const_cast< ::mp_int*>(&o.m_data), &m_data)); return *this; } - tommath_int& operator = (boost::uintmax_t i) + tommath_int& operator = (unsigned long long i) { - boost::uintmax_t mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; ::mp_int t; detail::check_tommath_result(mp_init(&t)); @@ -69,11 +69,11 @@ struct tommath_int mp_clear(&t); return *this; } - tommath_int& operator = (boost::intmax_t i) + tommath_int& operator = (long long i) { BOOST_MP_USING_ABS bool neg = i < 0; - *this = static_cast(abs(i)); + *this = static_cast(abs(i)); if(neg) detail::check_tommath_result(mp_neg(&m_data, &m_data)); return *this; From 3c13b7a4d1f1793ce1b1c5d79a39e53792360b08 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 18 Jan 2012 12:16:20 +0000 Subject: [PATCH 104/256] Add missing file. Fix some inconsistent uses of long long and intmax_t. [SVN r76573] --- include/boost/multiprecision/cpp_float.hpp | 2 +- .../multiprecision/detail/functions/pow.hpp | 4 +- test/string_data.ipp | 40 +++++++++++++++++++ test/test_float_io.cpp | 2 +- 4 files changed, 44 insertions(+), 4 deletions(-) create mode 100644 test/string_data.ipp diff --git a/include/boost/multiprecision/cpp_float.hpp b/include/boost/multiprecision/cpp_float.hpp index 12cde7b4..ce78f659 100644 --- a/include/boost/multiprecision/cpp_float.hpp +++ b/include/boost/multiprecision/cpp_float.hpp @@ -32,7 +32,7 @@ public: typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list float_types; - typedef boost::int64_t exponent_type; + typedef long long exponent_type; static const boost::int32_t mp_radix = 10; diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 91b1a084..444f7f64 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -268,7 +268,7 @@ void eval_exp(T& result, const T& x) } // Check for pure-integer arguments which can be either signed or unsigned. - boost::intmax_t ll; + long long ll; eval_trunc(exp_series, x); convert_to(&ll, exp_series); if(x.compare(ll) == 0) @@ -458,7 +458,7 @@ inline void eval_pow(T& result, const T& x, const T& a) return; } - boost::intmax_t an; + long long an; convert_to(&an, a); const bool bo_a_isint = a.compare(an) == 0; diff --git a/test/string_data.ipp b/test/string_data.ipp new file mode 100644 index 00000000..824940ad --- /dev/null +++ b/test/string_data.ipp @@ -0,0 +1,40 @@ + {{ "1e+08", "1.e+08", "+1e+08", "1.2e+08", "+1.2e+08", "1.2e+08", "123456789.0", "123456789.0", "+123456789.0", "1.2e+08", "1.2e+08", "+1.2e+08", "1.23e+08", "+1.23e+08", "1.23e+08", "123456789.00", "123456789.00", "+123456789.00", "1.23e+08", "1.23e+08", "+1.23e+08", "1.235e+08", "+1.235e+08", "1.235e+08", "123456789.000", 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"-8.56653560588e-10", "-8.566535605881e-10", "-8.566535605881e-10", "-8.566535605881e-10", "-0.000000000857", "-0.000000000857", "-0.000000000857", "-8.566535605881e-10", "-8.566535605881e-10", "-8.566535605881e-10", "-8.5665356058806e-10", "-8.5665356058806e-10", "-8.5665356058806e-10", "-0.0000000008567", "-0.0000000008567", "-0.0000000008567", }}, diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp index fb098b31..1141375a 100644 --- a/test/test_float_io.cpp +++ b/test/test_float_io.cpp @@ -93,7 +93,7 @@ void test() }}; boost::array, 40> string_data = {{ -#include "libs/multiprecision/string_data.ipp" +#include "libs/multiprecision/libs/string_data.ipp" }}; double num = 123456789.0; From a53f46637ef0a9cfc2110507c8d15f7ab971010c Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 20 Jan 2012 17:15:22 +0000 Subject: [PATCH 105/256] Fix Linux 64 failures [SVN r76593] --- .../multiprecision/detail/mp_number_base.hpp | 4 ++-- include/boost/multiprecision/fixed_int.hpp | 10 +++++----- include/boost/multiprecision/gmp.hpp | 9 +++++++-- include/boost/multiprecision/mpfr.hpp | 4 ++-- include/boost/multiprecision/tommath.hpp | 17 +++++++++++------ test/test_float_io.cpp | 2 +- 6 files changed, 28 insertions(+), 18 deletions(-) diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 6d183709..4178c8f4 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -439,14 +439,14 @@ void format_float_string(S& str, boost::intmax_t my_exp, boost::intmax_t digits, if(fixed || (!scientific && (my_exp >= -4) && (my_exp < digits))) { - if(1 + my_exp > str.size()) + if(1 + my_exp > static_cast(str.size())) { // Just pad out the end with zeros: str.append(static_cast(1 + my_exp - str.size()), '0'); if(showpoint || fixed) str.append("."); } - else if(my_exp + 1 < str.size()) + else if(my_exp + 1 < static_cast(str.size())) { if(my_exp < 0) { diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index 7dda8ff5..9c9a47d7 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -34,7 +34,7 @@ struct fixed_int BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u)); BOOST_STATIC_CONSTANT(limb_type, upper_limb_mask = (Bits % limb_bits ? (1 << (Bits % limb_bits)) - 1 : max_limb_value)); BOOST_STATIC_CONSTANT(limb_type, upper_limb_not_mask = ~upper_limb_mask); - BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1 << ((Bits % limb_bits ? Bits % limb_bits : limb_bits) - 1)); + BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << ((Bits % limb_bits ? Bits % limb_bits : limb_bits) - 1)); typedef boost::array data_type; fixed_int(){} @@ -53,7 +53,7 @@ struct fixed_int fixed_int& operator = (limb_type i) { m_value[limb_count - 1] = i; - for(int j = limb_count - 2; j >= 0; --j) + for(int j = static_cast(limb_count) - 2; j >= 0; --j) m_value[j] = 0; m_value[0] &= fixed_int::upper_limb_mask; return *this; @@ -62,7 +62,7 @@ struct fixed_int { m_value[limb_count - 1] = i; // sign extend: - for(int j = limb_count - 2; j >= 0; --j) + for(int j = static_cast(limb_count) - 2; j >= 0; --j) m_value[j] = i < 0 ? max_limb_value : 0; m_value[0] &= fixed_int::upper_limb_mask; return *this; @@ -400,7 +400,7 @@ inline void subtract(fixed_int& result, const limb_type& o) + 1uLL + static_cast(~o); result.data()[fixed_int::limb_count - 1] = static_cast(carry); carry >>= fixed_int::limb_bits; - for(int i = fixed_int::limb_count - 2; i >= 0; --i) + for(int i = static_cast(fixed_int::limb_count) - 2; i >= 0; --i) { carry += static_cast(result.data()[i]) + 0xFFFFFFFF; result.data()[i] = static_cast(carry); @@ -713,7 +713,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1] % y.data()[fixed_int::limb_count - 1]; return; } - else if(r_order == fixed_int::limb_count - 2) + else if(r_order == static_cast(fixed_int::limb_count) - 2) { double_limb_type a, b; a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1]; diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index d4bdb350..d246b07b 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1790,6 +1790,11 @@ class numeric_limits > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; + // + // min and max values chosen so as to not cause segfaults when calling + // mpf_get_str on 64-bit Linux builds. Possibly we could use larger + // exponent values elsewhere. + // BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { initializer.do_nothing(); @@ -1798,7 +1803,7 @@ public: { value.first = true; value.second = 1; - mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), LONG_MAX); + mpf_div_2exp(value.second.backend().data(), value.second.backend().data(), (std::numeric_limits::max)() / 64 + 1); } return value.second; } @@ -1810,7 +1815,7 @@ public: { value.first = true; value.second = 1; - mpf_mul_2exp(value.second.backend().data(), value.second.backend().data(), LONG_MAX - 1); + mpf_mul_2exp(value.second.backend().data(), value.second.backend().data(), (std::numeric_limits::max)() / 64 + 1); } return value.second; } diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 74b9a614..aed383e2 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -800,12 +800,12 @@ inline void convert_to(long* result, const mpfr_float_backend& val) } #ifdef _MPFR_H_HAVE_INTMAX_T template -inline void convert_to(boost::uintmax_t* result, const mpfr_float_backend& val) +inline void convert_to(unsigned long long* result, const mpfr_float_backend& val) { *result = mpfr_get_uj(val.data(), GMP_RNDN); } template -inline void convert_to(boost::intmax_t* result, const mpfr_float_backend& val) +inline void convert_to(long long* result, const mpfr_float_backend& val) { *result = mpfr_get_sj(val.data(), GMP_RNDN); } diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 86ecea9e..41757e32 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -33,9 +33,9 @@ inline void check_tommath_result(unsigned v) struct tommath_int { - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list float_types; + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list float_types; tommath_int() { @@ -78,15 +78,20 @@ struct tommath_int detail::check_tommath_result(mp_neg(&m_data, &m_data)); return *this; } - tommath_int& operator = (unsigned long i) + // + // Note that although mp_set_int takes an unsigned long as an argument + // it only sets the first 32-bits to the result, and ignores the rest. + // So use uint32_t as the largest type to pass to this function. + // + tommath_int& operator = (boost::uint32_t i) { detail::check_tommath_result((mp_set_int(&m_data, i))); return *this; } - tommath_int& operator = (long i) + tommath_int& operator = (boost::int32_t i) { bool neg = i < 0; - *this = static_cast(std::abs(i)); + *this = static_cast(std::abs(i)); if(neg) detail::check_tommath_result(mp_neg(&m_data, &m_data)); return *this; diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp index 1141375a..17c0e02b 100644 --- a/test/test_float_io.cpp +++ b/test/test_float_io.cpp @@ -93,7 +93,7 @@ void test() }}; boost::array, 40> string_data = {{ -#include "libs/multiprecision/libs/string_data.ipp" +#include "libs/multiprecision/test/string_data.ipp" }}; double num = 123456789.0; From a7d4ab19fbacc059eda70632a89959ea1ba6c48f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 21 Jan 2012 13:12:56 +0000 Subject: [PATCH 106/256] Tweak division and string conversion routines for better performance - sadly we're still way behind GMP on these (though better than libtommath). [SVN r76609] --- include/boost/multiprecision/fixed_int.hpp | 121 +++++++++++++++------ 1 file changed, 88 insertions(+), 33 deletions(-) diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index 9c9a47d7..6cf8c308 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -21,6 +21,16 @@ typedef boost::uint32_t limb_type; typedef boost::int32_t signed_limb_type; typedef boost::uint64_t double_limb_type; typedef boost::int64_t signed_double_limb_type; +static const limb_type max_block_10 = 1000000000; +static const limb_type digits_per_block_10 = 9; + +inline limb_type block_multiplier(int count) +{ + static const limb_type values[digits_per_block_10] + = { 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 }; + BOOST_ASSERT(count < digits_per_block_10); + return values[count]; +} template struct fixed_int @@ -176,41 +186,65 @@ struct fixed_int if(radix == 8 || radix == 16) { unsigned shift = radix == 8 ? 3 : 4; - limb_type val = max_limb_value; + unsigned block_count = limb_bits / shift; + unsigned block_shift = shift * block_count; + limb_type val, block; while(*s) { - left_shift(*this, shift); - if(*s >= '0' && *s <= '9') - val = *s - '0'; - else if(*s >= 'a' && *s <= 'f') - val = 10 + *s - 'a'; - else if(*s >= 'A' && *s <= 'F') - val = 10 + *s - 'A'; - else - val = max_limb_value; - if(val > radix) + block = 0; + for(unsigned i = 0; (i < block_count); ++i) { - m_value[0] &= fixed_int::upper_limb_mask; - return *this; // TODO raise an exception here? + if(*s >= '0' && *s <= '9') + val = *s - '0'; + else if(*s >= 'a' && *s <= 'f') + val = 10 + *s - 'a'; + else if(*s >= 'A' && *s <= 'F') + val = 10 + *s - 'A'; + else + val = max_limb_value; + if(val > radix) + { + m_value[0] &= fixed_int::upper_limb_mask; + BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string.")); + } + block <<= shift; + block |= val; + if(!*++s) + { + // final shift is different: + block_shift = (i + 1) * shift; + break; + } } - m_value[limb_count - 1] |= val; - ++s; + left_shift(*this, block_shift); + m_value[limb_count - 1] |= block; } } else { - // Base 10: + // Base 10, we extract blocks of size 10^9 at a time, that way + // the number of multiplications is kept to a minimum: + limb_type block_mult = max_block_10; while(*s) { - // TODO: this implementation is brain dead, Fix Me! - multiply(*this, static_cast(10)); - limb_type val; - if(*s >= '0' && *s <= '9') - val = *s - '0'; - else - return *this; // TODO raise an exception here? - add(*this, val); - ++s; + limb_type block = 0; + for(unsigned i = 0; i < digits_per_block_10; ++i) + { + limb_type val; + if(*s >= '0' && *s <= '9') + val = *s - '0'; + else + BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected character encountered in input.")); + block *= 10; + block += val; + if(!*++s) + { + block_mult = block_multiplier(i); + break; + } + } + multiply(*this, block_mult); + add(*this, block); } } } @@ -237,12 +271,14 @@ struct fixed_int limb_type shift = base == 8 ? 3 : 4; limb_type mask = static_cast((1u << shift) - 1); fixed_int t(*this); + result.assign(Bits / shift + (Bits % shift ? 1 : 0), '0'); + int pos = result.size() - 1; for(unsigned i = 0; i < Bits / shift; ++i) { char c = '0' + (t.data()[limb_count-1] & mask); if(c > '9') c += 'A' - '9' - 1; - result.insert(0, 1, c); + result[pos--] = c; right_shift(t, shift); } if(Bits % shift) @@ -251,7 +287,7 @@ struct fixed_int char c = '0' + (t.data()[limb_count-1] & mask); if(c > '9') c += 'A' - '9'; - result.insert(0, 1, c); + result[pos] = c; } // // Get rid of leading zeros: @@ -268,9 +304,11 @@ struct fixed_int } else { + result.assign(Bits / 3 + 1, '0'); + int pos = result.size() - 1; fixed_int t(*this); fixed_int ten, r; - ten = limb_type(1000000000); + ten = limb_type(max_block_10); bool neg = false; if(Signed && (t.data()[0] & sign_bit_mask)) { @@ -289,11 +327,13 @@ struct fixed_int divide_unsigned_helper(t2, t, ten, r); t = t2; limb_type v = r.data()[limb_count - 1]; - for(unsigned i = 0; i < 9; ++i) + for(unsigned i = 0; i < digits_per_block_10; ++i) { char c = '0' + v % 10; v /= 10; - result.insert(0, 1, c); + result[pos] = c; + if(pos-- == 0) + break; } } } @@ -767,12 +807,27 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1 - shift] = guess; + //t = limb_type(0); + //t.data()[fixed_int::limb_count - 1 - shift] = guess; if(r_neg) - subtract(result, t); + { + if(result.data()[fixed_int::limb_count - 1 - shift] > guess) + result.data()[fixed_int::limb_count - 1 - shift] -= guess; + else + { + t = limb_type(0); + t.data()[fixed_int::limb_count - 1 - shift] = guess; + subtract(result, t); + } + } + else if(fixed_int::max_limb_value - result.data()[fixed_int::limb_count - 1 - shift] > guess) + result.data()[fixed_int::limb_count - 1 - shift] += guess; else + { + t = limb_type(0); + t.data()[fixed_int::limb_count - 1 - shift] = guess; add(result, t); + } // // Calculate guess * y, we use a fused mutiply-shift O(N) for this // rather than a full O(N^2) multiply: From 4b844fc60cb86d2ef9f217a50624dd87103b69ea Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 22 Jan 2012 19:12:37 +0000 Subject: [PATCH 107/256] Improve performance of fixed_int divide and string conversion. Add mixed integer ops to fixed_int. Improve fixed_int test cases. Add improved default forwarding functions that preserve arithmetic type arguments. Fix some operator overloads. Update performance tests. [SVN r76639] --- .../multiprecision/detail/default_ops.hpp | 33 ++ .../multiprecision/detail/mp_number_base.hpp | 4 +- include/boost/multiprecision/fixed_int.hpp | 358 ++++++++++++++++-- performance/Jamfile.v2 | 106 ++++++ performance/performance_test.cpp | 75 +++- performance/sf_performance.cpp | 119 +++++- test/Jamfile.v2 | 2 +- test/test_fixed_int.cpp | 37 ++ 8 files changed, 683 insertions(+), 51 deletions(-) create mode 100644 performance/Jamfile.v2 diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 1ed7aacf..25010500 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -131,6 +131,12 @@ inline void add(T& t, const U& u, const V& v) add(t, v); } } +template +inline typename disable_if >::type add(T& t, const U& a, const T& b) +{ + return add(t, b, a); +} + template inline void subtract(T& t, const U& u, const V& v) { @@ -147,6 +153,13 @@ inline void subtract(T& t, const U& u, const V& v) subtract(t, v); } } +template +inline typename disable_if >::type subtract(T& t, const U& a, const T& b) +{ + subtract(t, b, a); + t.negate(); +} + template inline void multiply(T& t, const U& u, const V& v) { @@ -160,6 +173,11 @@ inline void multiply(T& t, const U& u, const V& v) multiply(t, v); } } +template +inline typename disable_if >::type multiply(T& t, const U& a, const T& b) +{ + multiply(t, b, a); +} template inline void divide(T& t, const U& u, const V& v) { @@ -207,6 +225,11 @@ inline void bitwise_and(T& t, const U& u, const V& v) bitwise_and(t, v); } } +template +inline typename disable_if >::type bitwise_and(T& t, const U& a, const T& b) +{ + bitwise_and(t, b, a); +} template inline void bitwise_or(T& t, const U& u, const V& v) @@ -221,6 +244,11 @@ inline void bitwise_or(T& t, const U& u, const V& v) bitwise_or(t, v); } } +template +inline typename disable_if >::type bitwise_or(T& t, const U& a, const T& b) +{ + bitwise_or(t, b, a); +} template inline void bitwise_xor(T& t, const U& u, const V& v) @@ -235,6 +263,11 @@ inline void bitwise_xor(T& t, const U& u, const V& v) bitwise_xor(t, v); } } +template +inline typename disable_if >::type bitwise_xor(T& t, const U& a, const T& b) +{ + bitwise_xor(t, b, a); +} template inline void increment(T& val) diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 4178c8f4..870adace 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -591,7 +591,7 @@ inline detail::mp_exp, mp_number > return detail::mp_exp, mp_number >(b, a.left_ref()); } template -inline typename enable_if, detail::mp_exp, V > >::type +inline typename enable_if, detail::mp_exp > >::type operator + (const detail::mp_exp >& a, const V& b) { return detail::mp_exp >(b, a.left_ref()); @@ -686,7 +686,7 @@ template inline typename enable_if, detail::mp_exp, V > > >::type operator - (const detail::mp_exp >& a, const V& b) { - return detail::mp_exp >(b, a.left_ref()); + return detail::mp_exp, V > >(detail::mp_exp, V >(a.left_ref(), b)); } template inline typename enable_if, detail::mp_exp > >::type diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index 6cf8c308..449c90d2 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -307,8 +307,7 @@ struct fixed_int result.assign(Bits / 3 + 1, '0'); int pos = result.size() - 1; fixed_int t(*this); - fixed_int ten, r; - ten = limb_type(max_block_10); + fixed_int r; bool neg = false; if(Signed && (t.data()[0] & sign_bit_mask)) { @@ -324,7 +323,7 @@ struct fixed_int while(get_sign(t) != 0) { fixed_int t2; - divide_unsigned_helper(t2, t, ten, r); + divide_unsigned_helper(t2, t, max_block_10, r); t = t2; limb_type v = r.data()[limb_count - 1]; for(unsigned i = 0; i < digits_per_block_10; ++i) @@ -440,7 +439,7 @@ inline void subtract(fixed_int& result, const limb_type& o) + 1uLL + static_cast(~o); result.data()[fixed_int::limb_count - 1] = static_cast(carry); carry >>= fixed_int::limb_bits; - for(int i = static_cast(fixed_int::limb_count) - 2; i >= 0; --i) + for(int i = static_cast(fixed_int::limb_count) - 2; (carry != 1) && (i >= 0); --i) { carry += static_cast(result.data()[i]) + 0xFFFFFFFF; result.data()[i] = static_cast(carry); @@ -684,7 +683,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int& result, const fixed_int rem; @@ -722,25 +706,50 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int(0u); - if(x.compare(y) < 0) - { - return; // We already have the answer: zero. - } - // // Find the most significant words of numerator and denominator. - // Note that this code can't run past the end of the array because - // we know already that neither are all zero: // - limb_type r_order = 0; - while(r.data()[r_order] == 0) - ++r_order; limb_type y_order = 0; - while(y.data()[y_order] == 0) + while((y.data()[y_order] == 0) && (y_order < fixed_int::limb_count)) ++y_order; + if(y_order >= fixed_int::limb_count - 1) + { + // + // Only a single non-zero limb in the denominator, in this case + // we can use a specialized divide-by-single-limb routine which is + // much faster. This also handles division by zero: + // + divide_unsigned_helper(result, x, y.data()[y_order], r); + return; + } + + limb_type r_order = 0; + while((x.data()[r_order] == 0) && (r_order < fixed_int::limb_count)) + ++r_order; + if(r_order == fixed_int::limb_count) + { + // x is zero, so is the result: + r = y; + result = x; + return; + } + + r = x; + result = static_cast(0u); + // + // Check if the remainder is already less than the divisor, if so + // we already have the result. Note we try and avoid a full compare + // if we can: + // + if(r_order >= y_order) + { + if((r_order > y_order) || (r.compare(y) < 0)) + { + return; + } + } + fixed_int t; bool r_neg = false; @@ -765,8 +774,6 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int last_r; - //bool last_neg; do { // @@ -778,8 +785,6 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1)) { double_limb_type a, b, v; @@ -794,15 +799,19 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1) + { + guess = r.data()[r_order] / y.data()[y_order]; + } else { double_limb_type a, b, v; - a = (r_order < fixed_int::limb_count - 1) ? (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1] : r.data()[r_order]; + a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1]; b = (y_order < fixed_int::limb_count - 1) ? (static_cast(y.data()[y_order]) << fixed_int::limb_bits) | y.data()[y_order + 1] : (static_cast(y.data()[y_order]) << fixed_int::limb_bits); v = a / b; guess = static_cast(v); - //guess = r.data()[r_order] / y.data()[y_order]; } + BOOST_ASSERT(guess); // If the guess ever gets to zero we go on forever.... // // Update result: // @@ -842,7 +851,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int>= fixed_int::limb_bits; } t.data()[0] &= fixed_int::upper_limb_mask; - // + // // Update r: // subtract(r, t); @@ -852,7 +861,9 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int 0); + // Termination condition is really just a check that r > y, but with two common + // short-circuit cases handled first: + while((r_order < y_order) || (r.data()[r_order] > y.data()[y_order]) || (r.compare(y) > 0)); // // We now just have to normalise the result: @@ -868,6 +879,110 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int +void divide_unsigned_helper(fixed_int& result, const fixed_int& x, limb_type y, fixed_int& r) +{ + if((&result == &x) || (&r == &x)) + { + fixed_int t(x); + divide_unsigned_helper(result, t, y, r); + return; + } + + if(&result == &r) + { + fixed_int rem; + divide_unsigned_helper(result, x, y, rem); + r = rem; + return; + } + + // As above, but simplified for integer divisor: + + using default_ops::subtract; + + if(y == 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Integer Division by zero.")); + } + // + // Find the most significant word of numerator. + // + limb_type r_order = 0; + while((x.data()[r_order] == 0) && (r_order < fixed_int::limb_count)) + ++r_order; + + // + // Set remainder and result to their initial values: + // + r = x; + result = static_cast(0u); + + if(r_order == fixed_int::limb_count) + { + // All the limbs in x are zero, so is the result: + return; + } + // + // check for x < y, try to do this without actually having to + // do a full comparison: + // + if((r_order == fixed_int::limb_count - 1) && (r.data()[r_order] < y)) + { + return; + } + + // + // See if we can short-circuit long division, and use basic arithmetic instead: + // + if(r_order == fixed_int::limb_count - 1) + { + result = r.data()[fixed_int::limb_count - 1] / y; + r = x.data()[fixed_int::limb_count - 1] % y; + return; + } + else if(r_order == static_cast(fixed_int::limb_count) - 2) + { + double_limb_type a; + a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1]; + result = a / y; + r = a % y; + return; + } + + do + { + // + // Update r_order, this can't run past the end as r must be non-zero at this point: + // + while(r.data()[r_order] == 0) + ++r_order; + // + // Calculate our best guess for how many times y divides into r: + // + if((r.data()[r_order] < y) && (r_order < fixed_int::limb_count - 1)) + { + double_limb_type a, b; + a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1]; + b = a % y; + r.data()[r_order] = 0; + ++r_order; + r.data()[r_order] = static_cast(b); + result.data()[r_order] = static_cast(a / y); + } + else + { + result.data()[r_order] = r.data()[r_order] / y; + r.data()[r_order] %= y; + } + } + // Termination condition is really just a check that r > y, but with two common + // short-circuit cases handled first: + while((r_order < fixed_int::limb_count - 1) || (r.data()[r_order] > y)); + + BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed +} + template inline void divide(fixed_int& result, const fixed_int& a, const fixed_int& b) { @@ -902,6 +1017,52 @@ inline void divide(fixed_int& result, const fixed_int +inline void divide(fixed_int& result, const fixed_int& a, limb_type& b) +{ + fixed_int r; + if(Signed && (a.data()[0] & fixed_int::sign_bit_mask)) + { + fixed_int t(a); + t.negate(); + divide_unsigned_helper(result, t, b, r); + result.negate(); + } + else + { + divide_unsigned_helper(result, a, b, r); + } +} +template +inline void divide(fixed_int& result, const fixed_int& a, signed_limb_type& b) +{ + fixed_int r; + if(Signed && (a.data()[0] & fixed_int::sign_bit_mask)) + { + if(b < 0) + { + fixed_int t(a); + t.negate(); + divide_unsigned_helper(result, t, static_cast(-b), r); + } + else + { + fixed_int t(a); + t.negate(); + divide_unsigned_helper(result, t, b, r); + result.negate(); + } + } + else if(b < 0) + { + divide_unsigned_helper(result, a, static_cast(-b), r); + result.negate(); + } + else + { + divide_unsigned_helper(result, a, static_cast(b), r); + } +} +template inline void divide(fixed_int& result, const fixed_int& b) { // There is no in place divide: @@ -909,6 +1070,20 @@ inline void divide(fixed_int& result, const fixed_int +inline void divide(fixed_int& result, limb_type b) +{ + // There is no in place divide: + fixed_int a(result); + divide(result, a, b); +} +template +inline void divide(fixed_int& result, signed_limb_type b) +{ + // There is no in place divide: + fixed_int a(result); + divide(result, a, b); +} +template inline void modulus(fixed_int& result, const fixed_int& a, const fixed_int& b) { fixed_int r; @@ -942,12 +1117,72 @@ inline void modulus(fixed_int& result, const fixed_int +inline void modulus(fixed_int& result, const fixed_int& a, limb_type b) +{ + fixed_int r; + if(Signed && (a.data()[0] & fixed_int::sign_bit_mask)) + { + fixed_int t(a); + t.negate(); + divide_unsigned_helper(r, t, b, result); + result.negate(); + } + else + { + divide_unsigned_helper(r, a, b, result); + } +} +template +inline void modulus(fixed_int& result, const fixed_int& a, signed_limb_type b) +{ + fixed_int r; + if(Signed && (a.data()[0] & fixed_int::sign_bit_mask)) + { + if(b < 0) + { + fixed_int t1(a); + t1.negate(); + divide_unsigned_helper(r, t1, static_cast(-b), result); + result.negate(); + } + else + { + fixed_int t(a); + t.negate(); + divide_unsigned_helper(r, t, b, result); + result.negate(); + } + } + else if(b < 0) + { + divide_unsigned_helper(r, a, static_cast(-b), result); + } + else + { + divide_unsigned_helper(r, a, static_cast(b), result); + } +} +template inline void modulus(fixed_int& result, const fixed_int& b) { // There is no in place divide: fixed_int a(result); modulus(result, a, b); } +template +inline void modulus(fixed_int& result, limb_type b) +{ + // There is no in place divide: + fixed_int a(result); + modulus(result, a, b); +} +template +inline void modulus(fixed_int& result, signed_limb_type b) +{ + // There is no in place divide: + fixed_int a(result); + modulus(result, a, b); +} template inline void bitwise_and(fixed_int& result, const fixed_int& o) @@ -956,12 +1191,40 @@ inline void bitwise_and(fixed_int& result, const fixed_int +inline void bitwise_and(fixed_int& result, limb_type o) +{ + result.data()[fixed_int::limb_count - 1] &= o; + for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count - 1; ++i) + result.data()[i] = 0; +} +template +inline void bitwise_and(fixed_int& result, signed_limb_type o) +{ + result.data()[fixed_int::limb_count - 1] &= o; + limb_type mask = o < 0 ? fixed_int::max_limb_value : 0; + for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count - 1; ++i) + result.data()[i] &= mask; +} +template inline void bitwise_or(fixed_int& result, const fixed_int& o) { for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i) result.data()[i] |= o.data()[i]; } template +inline void bitwise_or(fixed_int& result, limb_type o) +{ + result.data()[fixed_int::limb_count - 1] |= o; +} +template +inline void bitwise_or(fixed_int& result, signed_limb_type o) +{ + result.data()[fixed_int::limb_count - 1] |= o; + limb_type mask = o < 0 ? fixed_int::max_limb_value : 0; + for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count - 1; ++i) + result.data()[i] |= mask; +} +template inline void bitwise_xor(fixed_int& result, const fixed_int& o) { for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i) @@ -969,6 +1232,19 @@ inline void bitwise_xor(fixed_int& result, const fixed_int::upper_limb_mask; } template +inline void bitwise_xor(fixed_int& result, limb_type o) +{ + result.data()[fixed_int::limb_count - 1] ^= o; +} +template +inline void bitwise_xor(fixed_int& result, signed_limb_type o) +{ + result.data()[fixed_int::limb_count - 1] ^= o; + limb_type mask = o < 0 ? fixed_int::max_limb_value : 0; + for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count - 1; ++i) + result.data()[i] ^= mask; +} +template inline void complement(fixed_int& result, const fixed_int& o) { for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i) diff --git a/performance/Jamfile.v2 b/performance/Jamfile.v2 new file mode 100644 index 00000000..d141a9af --- /dev/null +++ b/performance/Jamfile.v2 @@ -0,0 +1,106 @@ +# copyright John Maddock 2012 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + +import modules ; +import path ; + +local ntl-path = [ modules.peek : NTL_PATH ] ; +local gmp_path = [ modules.peek : GMP_PATH ] ; +local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local tommath_path = [ modules.peek : TOMMATH_PATH ] ; + +project : requirements + $(gmp_path) + $(gmp_path)/mpfr + $(gmp_path)/gmpfrxx + $(mpfr_path) + $(tommath_path) + ../../.. + $(gmp_path) + $(mpfr_path) + $(mpfr_path)/build.vc10/lib/Win32/Debug + $(tommath_path) + static + BOOST_ALL_NO_LIB + off + ; + + +lib gmp ; +lib mpfr ; + +if $(tommath_path) +{ + TOMMATH = [ GLOB $(tommath_path) : *.c ] ; +} +else +{ + lib tommath ; + TOMMATH = tommath ; +} + +exe performance_test : performance_test.cpp /boost/system//boost_system + : release + [ check-target-builds ../config//has_gmp : TEST_MPF TEST_MPZ gmp : ] + [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr : ] + [ check-target-builds ../config//has_tommath : TEST_TOMMATH $(TOMMATH) : ] + TEST_CPP_FLOAT + TEST_FIXED_INT + ; + +exe sf_performance : sf_performance.cpp + : release + [ check-target-builds ../config//has_gmp : TEST_MPF TEST_MPZ gmp : ] + [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr : ] + TEST_CPP_FLOAT + msvc:-bigobj + ; + +obj obj_linpack_benchmark_mpfr : linpack-benchmark.cpp + : release + [ check-target-builds ../config//has_mpfr : : no ] + TEST_MPFR_50 + ; + +obj obj_linpack_benchmark_mpf : linpack-benchmark.cpp + : release + [ check-target-builds ../config//has_gmp : : no ] + TEST_MPF_50 + ; + +obj obj_linpack_benchmark_cpp_float : linpack-benchmark.cpp + : release + TEST_CPP_FLOAT + ; + +obj obj_linpack_benchmark_double : linpack-benchmark.cpp + : release + ; + +obj obj_f2c : f2c.c : release ; + +exe linpack_benchmark_mpfr : obj_linpack_benchmark_mpfr mpfr obj_f2c + : release + [ check-target-builds ../config//has_mpfr : : no ] + TEST_MPFR_50 + ; + +exe linpack_benchmark_mpf : obj_linpack_benchmark_mpf gmp obj_f2c + : release + [ check-target-builds ../config//has_gmp : : no ] + TEST_MPF_50 + ; + +exe linpack_benchmark_cpp_float : obj_linpack_benchmark_cpp_float obj_f2c + : release + TEST_CPP_FLOAT + ; + +exe linpack_benchmark_double : obj_linpack_benchmark_double obj_f2c + : release + ; + +install . : performance_test sf_performance linpack_benchmark_double linpack_benchmark_cpp_float linpack_benchmark_mpf linpack_benchmark_mpfr ; + diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index f151ec8d..a365ee82 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -145,6 +145,16 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } + double test_multiply_int() + { + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] * 3; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } double test_divide() { stopwatch w; @@ -155,6 +165,16 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } + double test_divide_int() + { + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] / 3; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } double test_str() { stopwatch w; @@ -163,7 +183,7 @@ struct tester return boost::chrono::duration_cast >(w.elapsed()).count(); } // - // The following tests only work for ineteger types: + // The following tests only work for integer types: // double test_mod() { @@ -175,6 +195,16 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } + double test_mod_int() + { + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] % 254; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } double test_or() { stopwatch w; @@ -185,6 +215,16 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } + double test_or_int() + { + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] | 234; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } double test_and() { stopwatch w; @@ -195,6 +235,16 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } + double test_and_int() + { + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] & 234; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } double test_xor() { stopwatch w; @@ -205,6 +255,16 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } + double test_xor_int() + { + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] ^ 234; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } double test_complement() { stopwatch w; @@ -380,6 +440,11 @@ void test_int_ops(tester& t, const char* type, unsigned precision, co //report_result(cat, type, "~", precision, t.test_complement()); report_result(cat, type, "<<", precision, t.test_left_shift()); report_result(cat, type, ">>", precision, t.test_right_shift()); + // integer ops: + report_result(cat, type, "%(int)", precision, t.test_mod_int()); + report_result(cat, type, "|(int)", precision, t.test_or_int()); + report_result(cat, type, "&(int)", precision, t.test_and_int()); + report_result(cat, type, "^(int)", precision, t.test_xor_int()); } template void test_int_ops(tester& t, const char* type, unsigned precision, const U&) @@ -403,12 +468,14 @@ void test(const char* type, unsigned precision) // report_result(cat, type, "+", precision, t.test_add()); report_result(cat, type, "-", precision, t.test_subtract()); - report_result(cat, type, "+(int)", precision, t.test_add_int()); - report_result(cat, type, "-(int)", precision, t.test_subtract_int()); report_result(cat, type, "*", precision, t.test_multiply()); report_result(cat, type, "/", precision, t.test_divide()); report_result(cat, type, "str", precision, t.test_str()); - + // integer ops: + report_result(cat, type, "+(int)", precision, t.test_add_int()); + report_result(cat, type, "-(int)", precision, t.test_subtract_int()); + report_result(cat, type, "*(int)", precision, t.test_multiply_int()); + report_result(cat, type, "/(int)", precision, t.test_divide_int()); test_int_ops(t, type, precision, typename boost::multiprecision::number_category::type()); } diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index 5b2d0fbf..750f668d 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -6,14 +6,31 @@ #define BOOST_CHRONO_HEADER_ONLY #define BOOST_MATH_MAX_ROOT_ITERATION_POLICY 500 +#if !defined(TEST_MPFR) && !defined(TEST_MP_REAL) && !defined(TEST_MPF) +# define TEST_MPFR +# define TEST_MPF +# define TEST_MPF +# define TEST_CPP_FLOAT +# define TEST_MPFR_CLASS +#endif + +#ifdef TEST_MPFR #include -#include #include +#endif +#ifdef TEST_MP_REAL +#include +#endif +#ifdef TEST_MPF #include +#endif +#ifdef TEST_CPP_FLOAT #include +#endif #include #include #include +#include #include #include @@ -149,29 +166,40 @@ int main() static const unsigned a[] = { 2, 3, 4, 5, 6, 7, 8 }; +#ifdef TEST_MPFR boost::multiprecision::mpfr_float_50 result, x(2); allocation_count = 0; result = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; std::cout << allocation_count << std::endl; +#endif +#ifdef TEST_MPFR_CLASS mpfr_class r, x2(2); allocation_count = 0; r = (((((a[6] * x2 + a[5]) * x2 + a[4]) * x2 + a[3]) * x2 + a[2]) * x2 + a[1]) * x2 + a[0]; std::cout << allocation_count << std::endl; +#endif +#ifdef TEST_MPREAL mpfr::mpreal r2, x3(2); allocation_count = 0; r2 = (((((a[6] * x3 + a[5]) * x3 + a[4]) * x3 + a[3]) * x3 + a[2]) * x3 + a[1]) * x3 + a[0]; std::cout << allocation_count << std::endl; +#endif allocation_count = 0; +#ifdef TEST_MPFR result = boost::math::tools::evaluate_polynomial(a, x); std::cout << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPFR_CLASS r = boost::math::tools::evaluate_polynomial(a, x2); std::cout << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPREAL r2 = boost::math::tools::evaluate_polynomial(a, x3); std::cout << allocation_count << std::endl; - +#endif boost::chrono::duration time; stopwatch c; @@ -179,216 +207,301 @@ int main() // 50 digits first: // std::cout << "Testing Bessel Functions....." << std::endl; +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) mpfr_set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL mpfr::mpreal::set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPFR c.reset(); test_bessel(); time = c.elapsed(); std::cout << "Time for mpfr_float_50 = " << time << std::endl; std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPF + c.reset(); test_bessel(); time = c.elapsed(); std::cout << "Time for mpf_float_50 = " << time << std::endl; std::cout << "Total allocations for mpf_float_50 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_CPP_FLOAT + c.reset(); test_bessel(); time = c.elapsed(); std::cout << "Time for cpp_float_50 = " << time << std::endl; std::cout << "Total allocations for cpp_float_50 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPFR_CLASS c.reset(); test_bessel(); time = c.elapsed(); std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl; std::cout << "Total allocations for mpfr_class (50 digits) = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MP_REAL c.reset(); test_bessel(); time = c.elapsed(); std::cout << "Time for mpreal (50 digits) = " << time << std::endl; std::cout << "Total allocations for mpreal (50 digits) = " << allocation_count << std::endl; allocation_count = 0; +#endif // // Then 100 digits: // +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) mpfr_set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL mpfr::mpreal::set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPFR c.reset(); test_bessel(); time = c.elapsed(); std::cout << "Time for mpfr_float_100 = " << time << std::endl; std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPF c.reset(); test_bessel(); time = c.elapsed(); std::cout << "Time for mpf_float_100 = " << time << std::endl; std::cout << "Total allocations for mpf_float_100 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_CPP_FLOAT c.reset(); test_bessel(); time = c.elapsed(); std::cout << "Time for cpp_float_100 = " << time << std::endl; std::cout << "Total allocations for cpp_float_100 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPFR_CLASS c.reset(); test_bessel(); time = c.elapsed(); std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl; std::cout << "Total allocations for mpfr_class (100 digits) = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPREAL c.reset(); test_bessel(); time = c.elapsed(); std::cout << "Time for mpreal (100 digits) = " << time << std::endl; std::cout << "Total allocations for mpreal (100 digits) = " << allocation_count << std::endl; allocation_count = 0; +#endif // // 50 digits first: // c.reset(); std::cout << "Testing Polynomial Evaluation....." << std::endl; +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) mpfr_set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL mpfr::mpreal::set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPFR c.reset(); test_polynomial(); time = c.elapsed(); std::cout << "Time for mpfr_float_50 = " << time << std::endl; std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPF c.reset(); test_polynomial(); time = c.elapsed(); std::cout << "Time for mpf_float_50 = " << time << std::endl; std::cout << "Total allocations for mpf_float_50 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_CPP_FLOAT c.reset(); test_polynomial(); time = c.elapsed(); std::cout << "Time for cpp_float_50 = " << time << std::endl; std::cout << "Total allocations for cpp_float_50 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPFR_CLASS c.reset(); test_polynomial(); time = c.elapsed(); std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl; std::cout << "Total allocations for mpfr_class (50 digits) = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPREAL c.reset(); test_polynomial(); time = c.elapsed(); std::cout << "Time for mpreal (50 digits) = " << time << std::endl; std::cout << "Total allocations for mpreal (50 digits = " << allocation_count << std::endl; allocation_count = 0; +#endif // // Then 100 digits: // +#ifdef TEST_MPFR_CLASS mpfr_set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL mpfr::mpreal::set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPFR c.reset(); test_polynomial(); time = c.elapsed(); std::cout << "Time for mpfr_float_100 = " << time << std::endl; std::cout << "Total allocations for mpfr_float_100 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPF c.reset(); test_polynomial(); time = c.elapsed(); std::cout << "Time for mpf_float_100 = " << time << std::endl; std::cout << "Total allocations for mpf_float_100 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_CPP_FLOAT c.reset(); test_polynomial(); time = c.elapsed(); std::cout << "Time for cpp_float_100 = " << time << std::endl; std::cout << "Total allocations for cpp_float_100 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPFR_CLASS c.reset(); test_polynomial(); time = c.elapsed(); std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl; std::cout << "Total allocations for mpfr_class (100 digits) = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPREAL c.reset(); test_polynomial(); time = c.elapsed(); std::cout << "Time for mpreal (100 digits) = " << time << std::endl; std::cout << "Total allocations for mpreal (100 digits) = " << allocation_count << std::endl; allocation_count = 0; - +#endif // // 50 digits first: // c.reset(); std::cout << "Testing Non-Central T....." << std::endl; +#ifdef TEST_MPFR_CLASS mpfr_set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL mpfr::mpreal::set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPFR c.reset(); test_nct(); time = c.elapsed(); std::cout << "Time for mpfr_float_50 = " << time << std::endl; std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPF c.reset(); test_nct(); time = c.elapsed(); std::cout << "Time for mpf_float_50 = " << time << std::endl; std::cout << "Total allocations for mpf_float_50 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_CPP_FLOAT c.reset(); test_nct(); time = c.elapsed(); std::cout << "Time for cpp_float_50 = " << time << std::endl; std::cout << "Total allocations for cpp_float_50 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPFR_CLASS c.reset(); test_nct(); time = c.elapsed(); std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl; std::cout << "Total allocations for mpfr_class (50 digits) = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MP_REAL c.reset(); test_nct(); time = c.elapsed(); std::cout << "Time for mpreal (50 digits) = " << time << std::endl; std::cout << "Total allocations for mpreal (50 digits) = " << allocation_count << std::endl; allocation_count = 0; +#endif // // Then 100 digits: // +#ifdef TEST_MPFR_CLASS mpfr_set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL mpfr::mpreal::set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPFR c.reset(); test_nct(); time = c.elapsed(); std::cout << "Time for mpfr_float_100 = " << time << std::endl; std::cout << "Total allocations for mpfr_float_100 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPF c.reset(); test_nct(); time = c.elapsed(); std::cout << "Time for mpf_float_100 = " << time << std::endl; std::cout << "Total allocations for mpf_float_100 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_CPP_FLOAT c.reset(); test_nct(); time = c.elapsed(); std::cout << "Time for cpp_float_100 = " << time << std::endl; std::cout << "Total allocations for cpp_float_100 = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPFR_CLASS c.reset(); test_nct(); time = c.elapsed(); std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl; std::cout << "Total allocations for mpfr_class (100 digits) = " << allocation_count << std::endl; allocation_count = 0; +#endif +#ifdef TEST_MPREAL c.reset(); test_nct(); time = c.elapsed(); std::cout << "Time for mpreal (100 digits) = " << time << std::endl; std::cout << "Total allocations for mpreal (100 digits) = " << allocation_count << std::endl; allocation_count = 0; +#endif } diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 3e547c5b..336d1cb9 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -1,4 +1,4 @@ -# copyright John Maddock 2008 +# copyright John Maddock 2011 # Distributed under the Boost Software License, Version 1.0. # (See accompanying file LICENSE_1_0.txt or copy at # http://www.boost.org/LICENSE_1_0.txt. diff --git a/test/test_fixed_int.cpp b/test/test_fixed_int.cpp index 02bed7cb..cbf2458e 100644 --- a/test/test_fixed_int.cpp +++ b/test/test_fixed_int.cpp @@ -63,6 +63,8 @@ int main() mpz_int c = generate_random(256); mpz_int d = generate_random(32); + int si = d.convert_to(); + packed_type a1 = a.str(); packed_type b1 = b.str(); packed_type c1 = c.str(); @@ -77,11 +79,46 @@ int main() BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)+b).str(), packed_type(packed_type(-a1) + b1).str()); BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)-b).str(), packed_type(packed_type(-a1) - b1).str()); BOOST_CHECK_EQUAL(mpz_int(c * d).str(), packed_type(c1 * d1).str()); + BOOST_CHECK_EQUAL(mpz_int(c * -d).str(), packed_type(c1 * -d1).str()); + BOOST_CHECK_EQUAL(mpz_int(-c * d).str(), packed_type(-c1 * d1).str()); BOOST_CHECK_EQUAL(mpz_int(b * c).str(), packed_type(b1 * c1).str()); BOOST_CHECK_EQUAL(mpz_int(a / b).str(), packed_type(a1 / b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / -b).str(), packed_type(a1 / -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / b).str(), packed_type(-a1 / b1).str()); BOOST_CHECK_EQUAL(mpz_int(a / d).str(), packed_type(a1 / d1).str()); BOOST_CHECK_EQUAL(mpz_int(a % b).str(), packed_type(a1 % b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % -b).str(), packed_type(a1 % -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % b).str(), packed_type(-a1 % b1).str()); BOOST_CHECK_EQUAL(mpz_int(a % d).str(), packed_type(a1 % d1).str()); + // bitwise ops: + BOOST_CHECK_EQUAL(mpz_int(a|b).str(), packed_type(a1 | b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a&b).str(), packed_type(a1 & b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a^b).str(), packed_type(a1 ^ b1).str()); + // Now check operations involving integers: + BOOST_CHECK_EQUAL(mpz_int(a + si).str(), packed_type(a1 + si).str()); + BOOST_CHECK_EQUAL(mpz_int(a + -si).str(), packed_type(a1 + -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a + si).str(), packed_type(-a1 + si).str()); + BOOST_CHECK_EQUAL(mpz_int(si + a).str(), packed_type(si + a1).str()); + BOOST_CHECK_EQUAL(mpz_int(a - si).str(), packed_type(a1 - si).str()); + BOOST_CHECK_EQUAL(mpz_int(a - -si).str(), packed_type(a1 - -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a - si).str(), packed_type(-a1 - si).str()); + BOOST_CHECK_EQUAL(mpz_int(si - a).str(), packed_type(si - a1).str()); + BOOST_CHECK_EQUAL(mpz_int(b * si).str(), packed_type(b1 * si).str()); + BOOST_CHECK_EQUAL(mpz_int(b * -si).str(), packed_type(b1 * -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-b * si).str(), packed_type(-b1 * si).str()); + BOOST_CHECK_EQUAL(mpz_int(si * b).str(), packed_type(si * b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / si).str(), packed_type(a1 / si).str()); + BOOST_CHECK_EQUAL(mpz_int(a / -si).str(), packed_type(a1 / -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / si).str(), packed_type(-a1 / si).str()); + BOOST_CHECK_EQUAL(mpz_int(a % si).str(), packed_type(a1 % si).str()); + BOOST_CHECK_EQUAL(mpz_int(a % -si).str(), packed_type(a1 % -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % si).str(), packed_type(-a1 % si).str()); + BOOST_CHECK_EQUAL(mpz_int(a|si).str(), packed_type(a1 | si).str()); + BOOST_CHECK_EQUAL(mpz_int(a&si).str(), packed_type(a1 & si).str()); + BOOST_CHECK_EQUAL(mpz_int(a^si).str(), packed_type(a1 ^ si).str()); + BOOST_CHECK_EQUAL(mpz_int(si|a).str(), packed_type(si|a1).str()); + BOOST_CHECK_EQUAL(mpz_int(si&a).str(), packed_type(si&a1).str()); + BOOST_CHECK_EQUAL(mpz_int(si^a).str(), packed_type(si^a1).str()); if(last_error_count != boost::detail::test_errors()) { From 57612b470388079ee9f9f2b11c376d8ed67ea4c2 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 23 Jan 2012 11:23:54 +0000 Subject: [PATCH 108/256] Fix performance Jamfile. [SVN r76649] --- performance/Jamfile.v2 | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/performance/Jamfile.v2 b/performance/Jamfile.v2 index d141a9af..f7b81703 100644 --- a/performance/Jamfile.v2 +++ b/performance/Jamfile.v2 @@ -50,7 +50,7 @@ exe performance_test : performance_test.cpp /boost/system//boost_system TEST_FIXED_INT ; -exe sf_performance : sf_performance.cpp +exe sf_performance : sf_performance.cpp /boost/system//boost_system : release [ check-target-builds ../config//has_gmp : TEST_MPF TEST_MPZ gmp : ] [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr : ] @@ -79,26 +79,26 @@ obj obj_linpack_benchmark_double : linpack-benchmark.cpp : release ; -obj obj_f2c : f2c.c : release ; +lib f2c ; -exe linpack_benchmark_mpfr : obj_linpack_benchmark_mpfr mpfr obj_f2c +exe linpack_benchmark_mpfr : obj_linpack_benchmark_mpfr mpfr f2c : release [ check-target-builds ../config//has_mpfr : : no ] TEST_MPFR_50 ; -exe linpack_benchmark_mpf : obj_linpack_benchmark_mpf gmp obj_f2c +exe linpack_benchmark_mpf : obj_linpack_benchmark_mpf gmp f2c : release [ check-target-builds ../config//has_gmp : : no ] TEST_MPF_50 ; -exe linpack_benchmark_cpp_float : obj_linpack_benchmark_cpp_float obj_f2c +exe linpack_benchmark_cpp_float : obj_linpack_benchmark_cpp_float f2c : release TEST_CPP_FLOAT ; -exe linpack_benchmark_double : obj_linpack_benchmark_double obj_f2c +exe linpack_benchmark_double : obj_linpack_benchmark_double f2c : release ; From fc280b359e6046587d6110183466938a8d600b0e Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 23 Jan 2012 17:07:35 +0000 Subject: [PATCH 109/256] Linux performance results and fixes. [SVN r76652] --- performance/Jamfile.v2 | 5 +- performance/performance_test-gcc-linux.log | 621 +++++++++++++++++++ performance/performance_test-intel-linux.log | 507 +++++++++++++++ performance/sf_performance.cpp | 4 +- 4 files changed, 1135 insertions(+), 2 deletions(-) create mode 100644 performance/performance_test-gcc-linux.log create mode 100644 performance/performance_test-intel-linux.log diff --git a/performance/Jamfile.v2 b/performance/Jamfile.v2 index f7b81703..9ab22e91 100644 --- a/performance/Jamfile.v2 +++ b/performance/Jamfile.v2 @@ -12,6 +12,9 @@ local mpfr_path = [ modules.peek : MPFR_PATH ] ; local tommath_path = [ modules.peek : TOMMATH_PATH ] ; project : requirements + freebsd:"-lrt" + linux:"-lrt" + pgi:"-lrt" $(gmp_path) $(gmp_path)/mpfr $(gmp_path)/gmpfrxx @@ -81,7 +84,7 @@ obj obj_linpack_benchmark_double : linpack-benchmark.cpp lib f2c ; -exe linpack_benchmark_mpfr : obj_linpack_benchmark_mpfr mpfr f2c +exe linpack_benchmark_mpfr : obj_linpack_benchmark_mpfr mpfr f2c gmp : release [ check-target-builds ../config//has_mpfr : : no ] TEST_MPFR_50 diff --git a/performance/performance_test-gcc-linux.log b/performance/performance_test-gcc-linux.log new file mode 100644 index 00000000..8ef6ee7b --- /dev/null +++ b/performance/performance_test-gcc-linux.log @@ -0,0 +1,621 @@ +gmp_float 50 + 0.0172634 +gmp_float 50 - 0.0190593 +gmp_float 50 * 0.0496313 +gmp_float 50 / 0.270376 +gmp_float 50 str 0.00338283 +gmp_float 50 +(int)0.0107627 +gmp_float 50 -(int)0.0189185 +gmp_float 50 *(int)0.0161546 +gmp_float 50 /(int)0.0751156 +gmp_float 100 + 0.0189236 +gmp_float 100 - 0.0210418 +gmp_float 100 * 0.0892922 +gmp_float 100 / 0.376385 +gmp_float 100 str 0.00695061 +gmp_float 100 +(int)0.0120513 +gmp_float 100 -(int)0.0198354 +gmp_float 100 *(int)0.0195997 +gmp_float 100 /(int)0.0947924 +gmp_float 500 + 0.0301919 +gmp_float 500 - 0.0323239 +gmp_float 500 * 0.870235 +gmp_float 500 / 1.42311 +gmp_float 500 str 0.0313911 +gmp_float 500 +(int)0.0179283 +gmp_float 500 -(int)0.0258331 +gmp_float 500 *(int)0.0407228 +gmp_float 500 /(int)0.231398 +gmp_int 64 + 0.0169318 +gmp_int 64 - 0.0173731 +gmp_int 64 * 0.0113175 +gmp_int 64 / 0.169581 +gmp_int 64 str 0.000400819 +gmp_int 64 +(int)0.00684333 +gmp_int 64 -(int)0.00707918 +gmp_int 64 *(int)0.00855311 +gmp_int 64 /(int)0.0451154 +gmp_int 64 % 0.157075 +gmp_int 64 | 0.00932794 +gmp_int 64 & 0.00932918 +gmp_int 64 ^ 0.00974691 +gmp_int 64 << 0.00891992 +gmp_int 64 >> 0.00890735 +gmp_int 64 %(int)0.0278521 +gmp_int 64 |(int)0.0381401 +gmp_int 64 &(int)0.039882 +gmp_int 64 ^(int)0.0387007 +gmp_int 128 + 0.0187076 +gmp_int 128 - 0.0183551 +gmp_int 128 * 0.0156906 +gmp_int 128 / 0.191252 +gmp_int 128 str 0.000364851 +gmp_int 128 +(int)0.0102801 +gmp_int 128 -(int)0.00860256 +gmp_int 128 *(int)0.0114853 +gmp_int 128 /(int)0.0523559 +gmp_int 128 % 0.15528 +gmp_int 128 | 0.0103394 +gmp_int 128 & 0.0110643 +gmp_int 128 ^ 0.0109019 +gmp_int 128 << 0.00971087 +gmp_int 128 >> 0.00747274 +gmp_int 128 %(int)0.0344314 +gmp_int 128 |(int)0.0397332 +gmp_int 128 &(int)0.0413597 +gmp_int 128 ^(int)0.0404831 +gmp_int 256 + 0.022606 +gmp_int 256 - 0.0247961 +gmp_int 256 * 0.0417861 +gmp_int 256 / 0.234977 +gmp_int 256 str 0.00059847 +gmp_int 256 +(int)0.0109994 +gmp_int 256 -(int)0.0115691 +gmp_int 256 *(int)0.0135361 +gmp_int 256 /(int)0.0654383 +gmp_int 256 % 0.186922 +gmp_int 256 | 0.0128787 +gmp_int 256 & 0.0126536 +gmp_int 256 ^ 0.0133999 +gmp_int 256 << 0.01177 +gmp_int 256 >> 0.00803845 +gmp_int 256 %(int)0.0470174 +gmp_int 256 |(int)0.0405797 +gmp_int 256 &(int)0.0422895 +gmp_int 256 ^(int)0.0411956 +gmp_int 512 + 0.0277407 +gmp_int 512 - 0.0314653 +gmp_int 512 * 0.09803 +gmp_int 512 / 0.267598 +gmp_int 512 str 0.00121866 +gmp_int 512 +(int)0.0135739 +gmp_int 512 -(int)0.0143368 +gmp_int 512 *(int)0.0181278 +gmp_int 512 /(int)0.0892225 +gmp_int 512 % 0.217246 +gmp_int 512 | 0.0173872 +gmp_int 512 & 0.016516 +gmp_int 512 ^ 0.0185213 +gmp_int 512 << 0.0143127 +gmp_int 512 >> 0.00949988 +gmp_int 512 %(int)0.0599828 +gmp_int 512 |(int)0.0437876 +gmp_int 512 &(int)0.0454139 +gmp_int 512 ^(int)0.0443687 +gmp_int 1024 + 0.0398652 +gmp_int 1024 - 0.0416822 +gmp_int 1024 * 0.316471 +gmp_int 1024 / 0.352869 +gmp_int 1024 str 0.00278974 +gmp_int 1024 +(int)0.0188639 +gmp_int 1024 -(int)0.0194421 +gmp_int 1024 *(int)0.0265822 +gmp_int 1024 /(int)0.140502 +gmp_int 1024 % 0.281408 +gmp_int 1024 | 0.0243975 +gmp_int 1024 & 0.0233641 +gmp_int 1024 ^ 0.0248742 +gmp_int 1024 << 0.0205595 +gmp_int 1024 >> 0.012374 +gmp_int 1024 %(int)0.075892 +gmp_int 1024 |(int)0.0475998 +gmp_int 1024 &(int)0.0492285 +gmp_int 1024 ^(int)0.0488719 +mpq_rational 64 + 0.248703 +mpq_rational 64 - 0.248085 +mpq_rational 64 * 0.415269 +mpq_rational 64 / 1.34308 +mpq_rational 64 str 0.000573396 +mpq_rational 64 +(int)0.287841 +mpq_rational 64 -(int)0.28346 +mpq_rational 64 *(int)0.310676 +mpq_rational 64 /(int)0.311221 +mpq_rational 128 + 0.525318 +mpq_rational 128 - 0.53016 +mpq_rational 128 * 0.933404 +mpq_rational 128 / 2.63133 +mpq_rational 128 str 0.000723346 +mpq_rational 128 +(int)0.144307 +mpq_rational 128 -(int)0.14385 +mpq_rational 128 *(int)0.172035 +mpq_rational 128 /(int)0.175494 +mpq_rational 256 + 2.26207 +mpq_rational 256 - 2.26907 +mpq_rational 256 * 4.28222 +mpq_rational 256 / 8.12755 +mpq_rational 256 str 0.00120085 +mpq_rational 256 +(int)0.162372 +mpq_rational 256 -(int)0.160533 +mpq_rational 256 *(int)0.192923 +mpq_rational 256 /(int)0.197356 +mpq_rational 512 + 5.07193 +mpq_rational 512 - 5.07942 +mpq_rational 512 * 9.65569 +mpq_rational 512 / 16.8657 +mpq_rational 512 str 0.00233842 +mpq_rational 512 +(int)0.197738 +mpq_rational 512 -(int)0.198744 +mpq_rational 512 *(int)0.240048 +mpq_rational 512 /(int)0.250338 +mpq_rational 1024 + 11.2925 +mpq_rational 1024 - 11.3536 +mpq_rational 1024 * 21.0382 +mpq_rational 1024 / 35.6477 +mpq_rational 1024 str 0.00549707 +mpq_rational 1024 +(int)0.269222 +mpq_rational 1024 -(int)0.267056 +mpq_rational 1024 *(int)0.324096 +mpq_rational 1024 /(int)0.338966 +tommath_int 64 + 0.0159939 +tommath_int 64 - 0.0250036 +tommath_int 64 * 0.0363444 +tommath_int 64 / 0.977073 +tommath_int 64 str 0.00445496 +tommath_int 64 +(int)0.164295 +tommath_int 64 -(int)0.162629 +tommath_int 64 *(int)0.179095 +tommath_int 64 /(int)0.842398 +tommath_int 64 % 0.977861 +tommath_int 64 | 0.0691489 +tommath_int 64 & 0.073788 +tommath_int 64 ^ 0.0709205 +tommath_int 64 << 0.0193922 +tommath_int 64 >> 0.124706 +tommath_int 64 %(int)0.727338 +tommath_int 64 |(int)0.239311 +tommath_int 64 &(int)0.217949 +tommath_int 64 ^(int)0.239579 +tommath_int 128 + 0.0164327 +tommath_int 128 - 0.0232398 +tommath_int 128 * 0.0548361 +tommath_int 128 / 1.08958 +tommath_int 128 str 0.00876306 +tommath_int 128 +(int)0.165193 +tommath_int 128 -(int)0.165879 +tommath_int 128 *(int)0.183198 +tommath_int 128 /(int)0.912304 +tommath_int 128 % 1.08174 +tommath_int 128 | 0.0704018 +tommath_int 128 & 0.0720242 +tommath_int 128 ^ 0.0707622 +tommath_int 128 << 0.0307909 +tommath_int 128 >> 0.135357 +tommath_int 128 %(int)0.838173 +tommath_int 128 |(int)0.239724 +tommath_int 128 &(int)0.216927 +tommath_int 128 ^(int)0.241914 +tommath_int 256 + 0.0186154 +tommath_int 256 - 0.0251722 +tommath_int 256 * 0.0904396 +tommath_int 256 / 1.35539 +tommath_int 256 str 0.0211627 +tommath_int 256 +(int)0.171325 +tommath_int 256 -(int)0.171589 +tommath_int 256 *(int)0.195625 +tommath_int 256 /(int)1.16415 +tommath_int 256 % 1.30947 +tommath_int 256 | 0.0732898 +tommath_int 256 & 0.0736961 +tommath_int 256 ^ 0.0734515 +tommath_int 256 << 0.038933 +tommath_int 256 >> 0.138079 +tommath_int 256 %(int)1.18164 +tommath_int 256 |(int)0.243102 +tommath_int 256 &(int)0.223836 +tommath_int 256 ^(int)0.245577 +tommath_int 512 + 0.0235136 +tommath_int 512 - 0.0288817 +tommath_int 512 * 0.192319 +tommath_int 512 / 1.91905 +tommath_int 512 str 0.0619139 +tommath_int 512 +(int)0.168344 +tommath_int 512 -(int)0.165763 +tommath_int 512 *(int)0.213072 +tommath_int 512 /(int)1.6709 +tommath_int 512 % 1.91623 +tommath_int 512 | 0.0782698 +tommath_int 512 & 0.0785497 +tommath_int 512 ^ 0.0787174 +tommath_int 512 << 0.0445723 +tommath_int 512 >> 0.148176 +tommath_int 512 %(int)1.724 +tommath_int 512 |(int)0.247972 +tommath_int 512 &(int)0.227986 +tommath_int 512 ^(int)0.245992 +tommath_int 1024 + 0.0353819 +tommath_int 1024 - 0.0411398 +tommath_int 1024 * 0.548938 +tommath_int 1024 / 3.19059 +tommath_int 1024 str 0.186976 +tommath_int 1024 +(int)0.179688 +tommath_int 1024 -(int)0.177946 +tommath_int 1024 *(int)0.257986 +tommath_int 1024 /(int)2.90617 +tommath_int 1024 % 3.17595 +tommath_int 1024 | 0.0928142 +tommath_int 1024 & 0.0989265 +tommath_int 1024 ^ 0.096274 +tommath_int 1024 << 0.0663455 +tommath_int 1024 >> 0.164607 +tommath_int 1024 %(int)2.83798 +tommath_int 1024 |(int)0.256182 +tommath_int 1024 &(int)0.241025 +tommath_int 1024 ^(int)0.258545 +fixed_int 64 + 0.00139124 +fixed_int 64 - 0.00164434 +fixed_int 64 * 0.00699488 +fixed_int 64 / 0.0516797 +fixed_int 64 str 0.000232222 +fixed_int 64 +(int)0.002316 +fixed_int 64 -(int)0.00191233 +fixed_int 64 *(int)0.00233361 +fixed_int 64 /(int)0.0232935 +fixed_int 64 % 0.0534904 +fixed_int 64 | 0.00176279 +fixed_int 64 & 0.00177991 +fixed_int 64 ^ 0.00173416 +fixed_int 64 << 0.000672222 +fixed_int 64 >> 0.000779919 +fixed_int 64 %(int)0.022105 +fixed_int 64 |(int)0.00108065 +fixed_int 64 &(int)0.00120958 +fixed_int 64 ^(int)0.00107863 +fixed_int 128 + 0.00260327 +fixed_int 128 - 0.00292914 +fixed_int 128 * 0.017405 +fixed_int 128 / 0.10547 +fixed_int 128 str 0.000458298 +fixed_int 128 +(int)0.00202532 +fixed_int 128 -(int)0.00163065 +fixed_int 128 *(int)0.0029341 +fixed_int 128 /(int)0.086585 +fixed_int 128 % 0.104705 +fixed_int 128 | 0.00262583 +fixed_int 128 & 0.00263365 +fixed_int 128 ^ 0.00261842 +fixed_int 128 << 0.00180218 +fixed_int 128 >> 0.00195989 +fixed_int 128 %(int)0.076707 +fixed_int 128 |(int)0.00127991 +fixed_int 128 &(int)0.00221857 +fixed_int 128 ^(int)0.00129423 +fixed_int 256 + 0.00544189 +fixed_int 256 - 0.00594733 +fixed_int 256 * 0.0716955 +fixed_int 256 / 0.18658 +fixed_int 256 str 0.0011329 +fixed_int 256 +(int)0.00239115 +fixed_int 256 -(int)0.00196589 +fixed_int 256 *(int)0.00536465 +fixed_int 256 /(int)0.177415 +fixed_int 256 % 0.18577 +fixed_int 256 | 0.00654441 +fixed_int 256 & 0.00658456 +fixed_int 256 ^ 0.00653302 +fixed_int 256 << 0.00366541 +fixed_int 256 >> 0.00345938 +fixed_int 256 %(int)0.146564 +fixed_int 256 |(int)0.00179758 +fixed_int 256 &(int)0.00406972 +fixed_int 256 ^(int)0.00174107 +fixed_int 512 + 0.0119663 +fixed_int 512 - 0.0122849 +fixed_int 512 * 0.250144 +fixed_int 512 / 0.362685 +fixed_int 512 str 0.00353655 +fixed_int 512 +(int)0.00525298 +fixed_int 512 -(int)0.0054428 +fixed_int 512 *(int)0.0104665 +fixed_int 512 /(int)0.35372 +fixed_int 512 % 0.364137 +fixed_int 512 | 0.0133848 +fixed_int 512 & 0.0134244 +fixed_int 512 ^ 0.0133775 +fixed_int 512 << 0.0111573 +fixed_int 512 >> 0.0104619 +fixed_int 512 %(int)0.293131 +fixed_int 512 |(int)0.00511566 +fixed_int 512 &(int)0.00944583 +fixed_int 512 ^(int)0.00520143 +fixed_int 1024 + 0.0265669 +fixed_int 1024 - 0.0305353 +fixed_int 1024 * 0.792037 +fixed_int 1024 / 0.758868 +fixed_int 1024 str 0.0137457 +fixed_int 1024 +(int)0.0101279 +fixed_int 1024 -(int)0.00950205 +fixed_int 1024 *(int)0.026544 +fixed_int 1024 /(int)0.709808 +fixed_int 1024 % 0.760095 +fixed_int 1024 | 0.0258782 +fixed_int 1024 & 0.0244113 +fixed_int 1024 ^ 0.0258119 +fixed_int 1024 << 0.0193046 +fixed_int 1024 >> 0.0195598 +fixed_int 1024 %(int)0.591454 +fixed_int 1024 |(int)0.010103 +fixed_int 1024 &(int)0.0249342 +fixed_int 1024 ^(int)0.0100668 +cpp_float 50 + 0.0135692 +cpp_float 50 - 0.014813 +cpp_float 50 * 0.121949 +cpp_float 50 / 1.86438 +cpp_float 50 str 0.00921786 +cpp_float 50 +(int)0.0231423 +cpp_float 50 -(int)0.0245803 +cpp_float 50 *(int)0.036823 +cpp_float 50 /(int)0.200073 +cpp_float 100 + 0.0194008 +cpp_float 100 - 0.0179391 +cpp_float 100 * 0.237444 +cpp_float 100 / 3.67594 +cpp_float 100 str 0.0156382 +cpp_float 100 +(int)0.032027 +cpp_float 100 -(int)0.0355546 +cpp_float 100 *(int)0.0596723 +cpp_float 100 /(int)0.341129 +cpp_float 500 + 0.0431376 +cpp_float 500 - 0.0441081 +cpp_float 500 * 2.11624 +cpp_float 500 / 25.3672 +cpp_float 500 str 0.0619948 +cpp_float 500 +(int)0.0717688 +cpp_float 500 -(int)0.0737847 +cpp_float 500 *(int)0.240091 +cpp_float 500 /(int)1.39098 +mpfr_float 50 + 0.018534 +mpfr_float 50 - 0.0219753 +mpfr_float 50 * 0.0573856 +mpfr_float 50 / 0.318134 +mpfr_float 50 str 0.00683453 +mpfr_float 50 +(int)0.0267235 +mpfr_float 50 -(int)0.0449984 +mpfr_float 50 *(int)0.0345749 +mpfr_float 50 /(int)0.0856313 +mpfr_float 100 + 0.0203895 +mpfr_float 100 - 0.023673 +mpfr_float 100 * 0.0922367 +mpfr_float 100 / 0.455272 +mpfr_float 100 str 0.00688747 +mpfr_float 100 +(int)0.0280739 +mpfr_float 100 -(int)0.048047 +mpfr_float 100 *(int)0.039831 +mpfr_float 100 /(int)0.107712 +mpfr_float 500 + 0.032386 +mpfr_float 500 - 0.0362805 +mpfr_float 500 * 0.853213 +mpfr_float 500 / 2.82089 +mpfr_float 500 str 0.0336548 +mpfr_float 500 +(int)0.0383341 +mpfr_float 500 -(int)0.0587852 +mpfr_float 500 *(int)0.0845355 +mpfr_float 500 /(int)0.252175 +[section:float_performance Float Type Perfomance] +[table Operator * +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][2.45709 (0.121949s)][2.65918 (0.237444s)][2.48032 (2.11624s)]] +[[gmp_float][[*1] (0.0496313s)][[*1] (0.0892922s)][1.01995 (0.870235s)]] +[[mpfr_float][1.15624 (0.0573856s)][1.03298 (0.0922367s)][[*1] (0.853213s)]] +] +[table Operator *(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][2.27942 (0.036823s)][3.04455 (0.0596723s)][5.89573 (0.240091s)]] +[[gmp_float][[*1] (0.0161546s)][[*1] (0.0195997s)][[*1] (0.0407228s)]] +[[mpfr_float][2.14025 (0.0345749s)][2.03222 (0.039831s)][2.07588 (0.0845355s)]] +] +[table Operator + +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][[*1] (0.0135692s)][1.02522 (0.0194008s)][1.42878 (0.0431376s)]] +[[gmp_float][1.27225 (0.0172634s)][[*1] (0.0189236s)][[*1] (0.0301919s)]] +[[mpfr_float][1.36589 (0.018534s)][1.07746 (0.0203895s)][1.07267 (0.032386s)]] +] +[table Operator +(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][2.15023 (0.0231423s)][2.65755 (0.032027s)][4.0031 (0.0717688s)]] +[[gmp_float][[*1] (0.0107627s)][[*1] (0.0120513s)][[*1] (0.0179283s)]] +[[mpfr_float][2.48298 (0.0267235s)][2.32953 (0.0280739s)][2.13819 (0.0383341s)]] +] +[table Operator - +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][[*1] (0.014813s)][[*1] (0.0179391s)][1.36457 (0.0441081s)]] +[[gmp_float][1.28666 (0.0190593s)][1.17296 (0.0210418s)][[*1] (0.0323239s)]] +[[mpfr_float][1.48351 (0.0219753s)][1.31963 (0.023673s)][1.12241 (0.0362805s)]] +] +[table Operator -(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][1.29928 (0.0245803s)][1.79248 (0.0355546s)][2.85621 (0.0737847s)]] +[[gmp_float][[*1] (0.0189185s)][[*1] (0.0198354s)][[*1] (0.0258331s)]] +[[mpfr_float][2.37854 (0.0449984s)][2.42229 (0.048047s)][2.27558 (0.0587852s)]] +] +[table Operator / +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][6.89549 (1.86438s)][9.76642 (3.67594s)][17.8252 (25.3672s)]] +[[gmp_float][[*1] (0.270376s)][[*1] (0.376385s)][[*1] (1.42311s)]] +[[mpfr_float][1.17664 (0.318134s)][1.20959 (0.455272s)][1.9822 (2.82089s)]] +] +[table Operator /(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][2.66353 (0.200073s)][3.59869 (0.341129s)][6.01121 (1.39098s)]] +[[gmp_float][[*1] (0.0751156s)][[*1] (0.0947924s)][[*1] (0.231398s)]] +[[mpfr_float][1.13999 (0.0856313s)][1.1363 (0.107712s)][1.08979 (0.252175s)]] +] +[table Operator str +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][2.72489 (0.00921786s)][2.27053 (0.0156382s)][1.97491 (0.0619948s)]] +[[gmp_float][[*1] (0.00338283s)][1.00917 (0.00695061s)][[*1] (0.0313911s)]] +[[mpfr_float][2.02036 (0.00683453s)][[*1] (0.00688747s)][1.07211 (0.0336548s)]] +] +[endsect] +[section:integer_performance Integer Type Perfomance] +[table Operator % +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0534904s)][[*1] (0.104705s)][[*1] (0.18577s)][1.67615 (0.364137s)][2.70105 (0.760095s)]] +[[gmp_int][2.93651 (0.157075s)][1.48303 (0.15528s)][1.0062 (0.186922s)][[*1] (0.217246s)][[*1] (0.281408s)]] +[[tommath_int][18.2811 (0.977861s)][10.3314 (1.08174s)][7.04886 (1.30947s)][8.82054 (1.91623s)][11.2859 (3.17595s)]] +] +[table Operator %(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.022105s)][2.22782 (0.076707s)][3.11723 (0.146564s)][4.88691 (0.293131s)][7.79337 (0.591454s)]] +[[gmp_int][1.25999 (0.0278521s)][[*1] (0.0344314s)][[*1] (0.0470174s)][[*1] (0.0599828s)][[*1] (0.075892s)]] +[[tommath_int][32.9037 (0.727338s)][24.3433 (0.838173s)][25.1319 (1.18164s)][28.7415 (1.724s)][37.3949 (2.83798s)]] +] +[table Operator & +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00177991s)][[*1] (0.00263365s)][[*1] (0.00658456s)][[*1] (0.0134244s)][1.04482 (0.0244113s)]] +[[gmp_int][5.24139 (0.00932918s)][4.20114 (0.0110643s)][1.9217 (0.0126536s)][1.2303 (0.016516s)][[*1] (0.0233641s)]] +[[tommath_int][41.4562 (0.073788s)][27.3477 (0.0720242s)][11.1923 (0.0736961s)][5.85126 (0.0785497s)][4.23413 (0.0989265s)]] +] +[table Operator &(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00120958s)][[*1] (0.00221857s)][[*1] (0.00406972s)][[*1] (0.00944583s)][[*1] (0.0249342s)]] +[[gmp_int][32.9717 (0.039882s)][18.6425 (0.0413597s)][10.3913 (0.0422895s)][4.80782 (0.0454139s)][1.97433 (0.0492285s)]] +[[tommath_int][180.185 (0.217949s)][97.7774 (0.216927s)][55.0003 (0.223836s)][24.1362 (0.227986s)][9.6664 (0.241025s)]] +] +[table Operator * +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00699488s)][1.10926 (0.017405s)][1.71577 (0.0716955s)][2.55171 (0.250144s)][2.50272 (0.792037s)]] +[[gmp_int][1.61797 (0.0113175s)][[*1] (0.0156906s)][[*1] (0.0417861s)][[*1] (0.09803s)][[*1] (0.316471s)]] +[[tommath_int][5.19586 (0.0363444s)][3.49483 (0.0548361s)][2.16435 (0.0904396s)][1.96183 (0.192319s)][1.73456 (0.548938s)]] +] +[table Operator *(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00233361s)][[*1] (0.0029341s)][[*1] (0.00536465s)][[*1] (0.0104665s)][[*1] (0.026544s)]] +[[gmp_int][3.66519 (0.00855311s)][3.9144 (0.0114853s)][2.52321 (0.0135361s)][1.73199 (0.0181278s)][1.00144 (0.0265822s)]] +[[tommath_int][76.7461 (0.179095s)][62.4375 (0.183198s)][36.4656 (0.195625s)][20.3576 (0.213072s)][9.71918 (0.257986s)]] +] +[table Operator + +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00139124s)][[*1] (0.00260327s)][[*1] (0.00544189s)][[*1] (0.0119663s)][[*1] (0.0265669s)]] +[[gmp_int][12.1703 (0.0169318s)][7.18621 (0.0187076s)][4.15407 (0.022606s)][2.31823 (0.0277407s)][1.50056 (0.0398652s)]] +[[tommath_int][11.4962 (0.0159939s)][6.31236 (0.0164327s)][3.42075 (0.0186154s)][1.96498 (0.0235136s)][1.33181 (0.0353819s)]] +] +[table Operator +(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.002316s)][[*1] (0.00202532s)][[*1] (0.00239115s)][[*1] (0.00525298s)][[*1] (0.0101279s)]] +[[gmp_int][2.9548 (0.00684333s)][5.07577 (0.0102801s)][4.60003 (0.0109994s)][2.58403 (0.0135739s)][1.86257 (0.0188639s)]] +[[tommath_int][70.9391 (0.164295s)][81.5638 (0.165193s)][71.6493 (0.171325s)][32.0474 (0.168344s)][17.7419 (0.179688s)]] +] +[table Operator - +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00164434s)][[*1] (0.00292914s)][[*1] (0.00594733s)][[*1] (0.0122849s)][[*1] (0.0305353s)]] +[[gmp_int][10.5654 (0.0173731s)][6.26638 (0.0183551s)][4.16928 (0.0247961s)][2.56129 (0.0314653s)][1.36505 (0.0416822s)]] +[[tommath_int][15.2058 (0.0250036s)][7.934 (0.0232398s)][4.23252 (0.0251722s)][2.35098 (0.0288817s)][1.34729 (0.0411398s)]] +] +[table Operator -(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00191233s)][[*1] (0.00163065s)][[*1] (0.00196589s)][[*1] (0.0054428s)][[*1] (0.00950205s)]] +[[gmp_int][3.70187 (0.00707918s)][5.27553 (0.00860256s)][5.88489 (0.0115691s)][2.63409 (0.0143368s)][2.04609 (0.0194421s)]] +[[tommath_int][85.0424 (0.162629s)][101.726 (0.165879s)][87.2831 (0.171589s)][30.4554 (0.165763s)][18.7271 (0.177946s)]] +] +[table Operator / +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0516797s)][[*1] (0.10547s)][[*1] (0.18658s)][1.35534 (0.362685s)][2.15056 (0.758868s)]] +[[gmp_int][3.28139 (0.169581s)][1.81332 (0.191252s)][1.25939 (0.234977s)][[*1] (0.267598s)][[*1] (0.352869s)]] +[[tommath_int][18.9063 (0.977073s)][10.3307 (1.08958s)][7.26443 (1.35539s)][7.17138 (1.91905s)][9.04185 (3.19059s)]] +] +[table Operator /(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0232935s)][1.65378 (0.086585s)][2.71117 (0.177415s)][3.96447 (0.35372s)][5.05194 (0.709808s)]] +[[gmp_int][1.93682 (0.0451154s)][[*1] (0.0523559s)][[*1] (0.0654383s)][[*1] (0.0892225s)][[*1] (0.140502s)]] +[[tommath_int][36.1645 (0.842398s)][17.4251 (0.912304s)][17.7901 (1.16415s)][18.7273 (1.6709s)][20.6842 (2.90617s)]] +] +[table Operator << +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.000672222s)][[*1] (0.00180218s)][[*1] (0.00366541s)][[*1] (0.0111573s)][[*1] (0.0193046s)]] +[[gmp_int][13.2693 (0.00891992s)][5.38839 (0.00971087s)][3.2111 (0.01177s)][1.28281 (0.0143127s)][1.06501 (0.0205595s)]] +[[tommath_int][28.8479 (0.0193922s)][17.0853 (0.0307909s)][10.6217 (0.038933s)][3.99491 (0.0445723s)][3.43678 (0.0663455s)]] +] +[table Operator >> +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.000779919s)][[*1] (0.00195989s)][[*1] (0.00345938s)][1.10127 (0.0104619s)][1.58072 (0.0195598s)]] +[[gmp_int][11.4209 (0.00890735s)][3.81284 (0.00747274s)][2.32367 (0.00803845s)][[*1] (0.00949988s)][[*1] (0.012374s)]] +[[tommath_int][159.896 (0.124706s)][69.0639 (0.135357s)][39.9143 (0.138079s)][15.5977 (0.148176s)][13.3026 (0.164607s)]] +] +[table Operator ^ +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00173416s)][[*1] (0.00261842s)][[*1] (0.00653302s)][[*1] (0.0133775s)][1.0377 (0.0258119s)]] +[[gmp_int][5.62054 (0.00974691s)][4.16356 (0.0109019s)][2.0511 (0.0133999s)][1.38452 (0.0185213s)][[*1] (0.0248742s)]] +[[tommath_int][40.8962 (0.0709205s)][27.0248 (0.0707622s)][11.2431 (0.0734515s)][5.88433 (0.0787174s)][3.87044 (0.096274s)]] +] +[table Operator ^(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00107863s)][[*1] (0.00129423s)][[*1] (0.00174107s)][[*1] (0.00520143s)][[*1] (0.0100668s)]] +[[gmp_int][35.8795 (0.0387007s)][31.2797 (0.0404831s)][23.661 (0.0411956s)][8.5301 (0.0443687s)][4.85477 (0.0488719s)]] +[[tommath_int][222.114 (0.239579s)][186.918 (0.241914s)][141.049 (0.245577s)][47.2931 (0.245992s)][25.683 (0.258545s)]] +] +[table Operator str +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.000232222s)][1.25612 (0.000458298s)][1.89299 (0.0011329s)][2.90199 (0.00353655s)][4.92723 (0.0137457s)]] +[[gmp_int][1.72602 (0.000400819s)][[*1] (0.000364851s)][[*1] (0.00059847s)][[*1] (0.00121866s)][[*1] (0.00278974s)]] +[[tommath_int][19.1841 (0.00445496s)][24.0182 (0.00876306s)][35.3614 (0.0211627s)][50.8048 (0.0619139s)][67.0227 (0.186976s)]] +] +[table Operator | +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00176279s)][[*1] (0.00262583s)][[*1] (0.00654441s)][[*1] (0.0133848s)][1.06069 (0.0258782s)]] +[[gmp_int][5.29157 (0.00932794s)][3.93757 (0.0103394s)][1.96789 (0.0128787s)][1.29902 (0.0173872s)][[*1] (0.0243975s)]] +[[tommath_int][39.2269 (0.0691489s)][26.8113 (0.0704018s)][11.1988 (0.0732898s)][5.84766 (0.0782698s)][3.80426 (0.0928142s)]] +] +[table Operator |(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00108065s)][[*1] (0.00127991s)][[*1] (0.00179758s)][[*1] (0.00511566s)][[*1] (0.010103s)]] +[[gmp_int][35.2935 (0.0381401s)][31.0437 (0.0397332s)][22.5747 (0.0405797s)][8.55952 (0.0437876s)][4.71147 (0.0475998s)]] +[[tommath_int][221.45 (0.239311s)][187.298 (0.239724s)][135.239 (0.243102s)][48.473 (0.247972s)][25.3571 (0.256182s)]] +] +[endsect] +[section:rational_performance Rational Type Perfomance] +[table Operator * +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.415269s)][[*1] (0.933404s)][[*1] (4.28222s)][[*1] (9.65569s)][[*1] (21.0382s)]] +] +[table Operator *(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.310676s)][[*1] (0.172035s)][[*1] (0.192923s)][[*1] (0.240048s)][[*1] (0.324096s)]] +] +[table Operator + +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.248703s)][[*1] (0.525318s)][[*1] (2.26207s)][[*1] (5.07193s)][[*1] (11.2925s)]] +] +[table Operator +(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.287841s)][[*1] (0.144307s)][[*1] (0.162372s)][[*1] (0.197738s)][[*1] (0.269222s)]] +] +[table Operator - +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.248085s)][[*1] (0.53016s)][[*1] (2.26907s)][[*1] (5.07942s)][[*1] (11.3536s)]] +] +[table Operator -(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.28346s)][[*1] (0.14385s)][[*1] (0.160533s)][[*1] (0.198744s)][[*1] (0.267056s)]] +] +[table Operator / +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (1.34308s)][[*1] (2.63133s)][[*1] (8.12755s)][[*1] (16.8657s)][[*1] (35.6477s)]] +] +[table Operator /(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.311221s)][[*1] (0.175494s)][[*1] (0.197356s)][[*1] (0.250338s)][[*1] (0.338966s)]] +] +[table Operator str +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.000573396s)][[*1] (0.000723346s)][[*1] (0.00120085s)][[*1] (0.00233842s)][[*1] (0.00549707s)]] +] +[endsect] diff --git a/performance/performance_test-intel-linux.log b/performance/performance_test-intel-linux.log new file mode 100644 index 00000000..cacc4056 --- /dev/null +++ b/performance/performance_test-intel-linux.log @@ -0,0 +1,507 @@ +gmp_float 50 + 0.0180644 +gmp_float 50 - 0.0194673 +gmp_float 50 * 0.0505578 +gmp_float 50 / 0.278179 +gmp_float 50 str 0.00357972 +gmp_float 50 +(int)0.0115205 +gmp_float 50 -(int)0.0197263 +gmp_float 50 *(int)0.0165976 +gmp_float 50 /(int)0.0758893 +gmp_float 100 + 0.019475 +gmp_float 100 - 0.0218422 +gmp_float 100 * 0.090686 +gmp_float 100 / 0.378055 +gmp_float 100 str 0.00557522 +gmp_float 100 +(int)0.0127856 +gmp_float 100 -(int)0.0205184 +gmp_float 100 *(int)0.0200577 +gmp_float 100 /(int)0.0948556 +gmp_float 500 + 0.0317241 +gmp_float 500 - 0.0335304 +gmp_float 500 * 0.947017 +gmp_float 500 / 1.5881 +gmp_float 500 str 0.0313793 +gmp_float 500 +(int)0.0187639 +gmp_float 500 -(int)0.0265882 +gmp_float 500 *(int)0.0415067 +gmp_float 500 /(int)0.232493 +gmp_int 64 + 0.0167521 +gmp_int 64 - 0.0188881 +gmp_int 64 * 0.011645 +gmp_int 64 / 0.1697 +gmp_int 64 str 0.000336635 +gmp_int 64 +(int)0.00723269 +gmp_int 64 -(int)0.00741945 +gmp_int 64 *(int)0.0120496 +gmp_int 64 /(int)0.0501068 +gmp_int 64 % 0.16582 +gmp_int 64 | 0.0115873 +gmp_int 64 & 0.0125951 +gmp_int 64 ^ 0.0129732 +gmp_int 64 << 0.00969083 +gmp_int 64 >> 0.0130601 +gmp_int 64 %(int)0.034786 +gmp_int 64 |(int)0.0424747 +gmp_int 64 &(int)0.0441868 +gmp_int 64 ^(int)0.0442481 +gmp_int 128 + 0.0192114 +gmp_int 128 - 0.0219479 +gmp_int 128 * 0.0182506 +gmp_int 128 / 0.196561 +gmp_int 128 str 0.00232097 +gmp_int 128 +(int)0.00871277 +gmp_int 128 -(int)0.0130434 +gmp_int 128 *(int)0.0127078 +gmp_int 128 /(int)0.0568248 +gmp_int 128 % 0.164977 +gmp_int 128 | 0.0134681 +gmp_int 128 & 0.01436 +gmp_int 128 ^ 0.0140653 +gmp_int 128 << 0.0131179 +gmp_int 128 >> 0.0107065 +gmp_int 128 %(int)0.0405959 +gmp_int 128 |(int)0.0440289 +gmp_int 128 &(int)0.0453998 +gmp_int 128 ^(int)0.0468496 +gmp_int 256 + 0.0230482 +gmp_int 256 - 0.0289896 +gmp_int 256 * 0.0476911 +gmp_int 256 / 0.240552 +gmp_int 256 str 0.000971703 +gmp_int 256 +(int)0.0145101 +gmp_int 256 -(int)0.0148337 +gmp_int 256 *(int)0.0170638 +gmp_int 256 /(int)0.0686065 +gmp_int 256 % 0.197103 +gmp_int 256 | 0.0159192 +gmp_int 256 & 0.015575 +gmp_int 256 ^ 0.0166751 +gmp_int 256 << 0.0148945 +gmp_int 256 >> 0.0111136 +gmp_int 256 %(int)0.0516333 +gmp_int 256 |(int)0.0474723 +gmp_int 256 &(int)0.0466442 +gmp_int 256 ^(int)0.0465869 +gmp_int 512 + 0.028268 +gmp_int 512 - 0.0352221 +gmp_int 512 * 0.103105 +gmp_int 512 / 0.281226 +gmp_int 512 str 0.00167382 +gmp_int 512 +(int)0.0170154 +gmp_int 512 -(int)0.0179625 +gmp_int 512 *(int)0.021358 +gmp_int 512 /(int)0.0950571 +gmp_int 512 % 0.230214 +gmp_int 512 | 0.0208511 +gmp_int 512 & 0.019777 +gmp_int 512 ^ 0.025011 +gmp_int 512 << 0.0182795 +gmp_int 512 >> 0.0121814 +gmp_int 512 %(int)0.0651899 +gmp_int 512 |(int)0.0493584 +gmp_int 512 &(int)0.0498514 +gmp_int 512 ^(int)0.049668 +gmp_int 1024 + 0.0408966 +gmp_int 1024 - 0.0463151 +gmp_int 1024 * 0.326898 +gmp_int 1024 / 0.36922 +gmp_int 1024 str 0.00297363 +gmp_int 1024 +(int)0.0197647 +gmp_int 1024 -(int)0.0199956 +gmp_int 1024 *(int)0.0300116 +gmp_int 1024 /(int)0.144581 +gmp_int 1024 % 0.302132 +gmp_int 1024 | 0.0284821 +gmp_int 1024 & 0.0266602 +gmp_int 1024 ^ 0.0299441 +gmp_int 1024 << 0.0247868 +gmp_int 1024 >> 0.0162548 +gmp_int 1024 %(int)0.0799406 +gmp_int 1024 |(int)0.0525727 +gmp_int 1024 &(int)0.0539474 +gmp_int 1024 ^(int)0.0539722 +mpq_rational 64 + 0.254473 +mpq_rational 64 - 0.260331 +mpq_rational 64 * 0.426868 +mpq_rational 64 / 1.50105 +mpq_rational 64 str 0.000927423 +mpq_rational 64 +(int)0.309729 +mpq_rational 64 -(int)0.306598 +mpq_rational 64 *(int)0.344178 +mpq_rational 64 /(int)0.32842 +mpq_rational 128 + 0.542374 +mpq_rational 128 - 0.545764 +mpq_rational 128 * 0.968054 +mpq_rational 128 / 2.78757 +mpq_rational 128 str 0.00111655 +mpq_rational 128 +(int)0.154116 +mpq_rational 128 -(int)0.151187 +mpq_rational 128 *(int)0.179899 +mpq_rational 128 /(int)0.184167 +mpq_rational 256 + 2.34795 +mpq_rational 256 - 2.3565 +mpq_rational 256 * 4.39195 +mpq_rational 256 / 8.9203 +mpq_rational 256 str 0.00175742 +mpq_rational 256 +(int)0.177483 +mpq_rational 256 -(int)0.16783 +mpq_rational 256 *(int)0.200539 +mpq_rational 256 /(int)0.206129 +mpq_rational 512 + 5.10523 +mpq_rational 512 - 5.08802 +mpq_rational 512 * 9.6344 +mpq_rational 512 / 16.8502 +mpq_rational 512 str 0.00246714 +mpq_rational 512 +(int)0.212807 +mpq_rational 512 -(int)0.212048 +mpq_rational 512 *(int)0.254142 +mpq_rational 512 /(int)0.262442 +mpq_rational 1024 + 11.2331 +mpq_rational 1024 - 11.2446 +mpq_rational 1024 * 20.9879 +mpq_rational 1024 / 35.6472 +mpq_rational 1024 str 0.00550783 +mpq_rational 1024 +(int)0.27756 +mpq_rational 1024 -(int)0.271845 +mpq_rational 1024 *(int)0.328602 +mpq_rational 1024 /(int)0.350883 +fixed_int 64 + 0.00207163 +fixed_int 64 - 0.00216403 +fixed_int 64 * 0.00392745 +fixed_int 64 / 0.0556903 +fixed_int 64 str 0.000302762 +fixed_int 64 +(int)0.00358307 +fixed_int 64 -(int)0.00354668 +fixed_int 64 *(int)0.00294381 +fixed_int 64 /(int)0.0169012 +fixed_int 64 % 0.054413 +fixed_int 64 | 0.00257616 +fixed_int 64 & 0.00259593 +fixed_int 64 ^ 0.00256688 +fixed_int 64 << 0.00115455 +fixed_int 64 >> 0.00147407 +fixed_int 64 %(int)0.0243407 +fixed_int 64 |(int)0.00208078 +fixed_int 64 &(int)0.00209559 +fixed_int 64 ^(int)0.00202777 +fixed_int 128 + 0.00326026 +fixed_int 128 - 0.00372498 +fixed_int 128 * 0.0104772 +fixed_int 128 / 0.105756 +fixed_int 128 str 0.000500691 +fixed_int 128 +(int)0.00359962 +fixed_int 128 -(int)0.00360689 +fixed_int 128 *(int)0.00422148 +fixed_int 128 /(int)0.0634475 +fixed_int 128 % 0.106105 +fixed_int 128 | 0.00363433 +fixed_int 128 & 0.00361924 +fixed_int 128 ^ 0.00361813 +fixed_int 128 << 0.00632357 +fixed_int 128 >> 0.00238745 +fixed_int 128 %(int)0.0811764 +fixed_int 128 |(int)0.00190869 +fixed_int 128 &(int)0.00245967 +fixed_int 128 ^(int)0.00237775 +fixed_int 256 + 0.00834722 +fixed_int 256 - 0.00653903 +fixed_int 256 * 0.0324122 +fixed_int 256 / 0.198305 +fixed_int 256 str 0.00111683 +fixed_int 256 +(int)0.00405163 +fixed_int 256 -(int)0.00385712 +fixed_int 256 *(int)0.00849409 +fixed_int 256 /(int)0.127666 +fixed_int 256 % 0.19685 +fixed_int 256 | 0.0108232 +fixed_int 256 & 0.0108415 +fixed_int 256 ^ 0.0108455 +fixed_int 256 << 0.00826823 +fixed_int 256 >> 0.00854822 +fixed_int 256 %(int)0.15306 +fixed_int 256 |(int)0.00275195 +fixed_int 256 &(int)0.00419648 +fixed_int 256 ^(int)0.0027653 +fixed_int 512 + 0.0128543 +fixed_int 512 - 0.0120433 +fixed_int 512 * 0.201059 +fixed_int 512 / 0.385977 +fixed_int 512 str 0.00286314 +fixed_int 512 +(int)0.00694047 +fixed_int 512 -(int)0.00681002 +fixed_int 512 *(int)0.015882 +fixed_int 512 /(int)0.244657 +fixed_int 512 % 0.385184 +fixed_int 512 | 0.0131341 +fixed_int 512 & 0.013122 +fixed_int 512 ^ 0.013116 +fixed_int 512 << 0.0150546 +fixed_int 512 >> 0.0134889 +fixed_int 512 %(int)0.303051 +fixed_int 512 |(int)0.00618124 +fixed_int 512 &(int)0.00836021 +fixed_int 512 ^(int)0.00608555 +fixed_int 1024 + 0.0330379 +fixed_int 1024 - 0.0311489 +fixed_int 1024 * 0.701951 +fixed_int 1024 / 0.708393 +fixed_int 1024 str 0.00872206 +fixed_int 1024 +(int)0.0116939 +fixed_int 1024 -(int)0.0116182 +fixed_int 1024 *(int)0.0346698 +fixed_int 1024 /(int)0.692818 +fixed_int 1024 % 0.711308 +fixed_int 1024 | 0.0176472 +fixed_int 1024 & 0.0176585 +fixed_int 1024 ^ 0.0177043 +fixed_int 1024 << 0.0242721 +fixed_int 1024 >> 0.0248274 +fixed_int 1024 %(int)0.584615 +fixed_int 1024 |(int)0.0107899 +fixed_int 1024 &(int)0.0166854 +fixed_int 1024 ^(int)0.0108555 +cpp_float 50 + 0.0142302 +cpp_float 50 - 0.0153931 +cpp_float 50 * 0.137722 +cpp_float 50 / 2.0214 +cpp_float 50 str 0.00924301 +cpp_float 50 +(int)0.0240351 +cpp_float 50 -(int)0.0252498 +cpp_float 50 *(int)0.0387713 +cpp_float 50 /(int)0.199003 +cpp_float 100 + 0.0178132 +cpp_float 100 - 0.0189367 +cpp_float 100 * 0.293407 +cpp_float 100 / 4.24891 +cpp_float 100 str 0.0160219 +cpp_float 100 +(int)0.0334828 +cpp_float 100 -(int)0.0326407 +cpp_float 100 *(int)0.063236 +cpp_float 100 /(int)0.341837 +cpp_float 500 + 0.044608 +cpp_float 500 - 0.0457737 +cpp_float 500 * 2.88591 +cpp_float 500 / 31.8072 +cpp_float 500 str 0.0639606 +cpp_float 500 +(int)0.0947227 +cpp_float 500 -(int)0.0966926 +cpp_float 500 *(int)0.224258 +cpp_float 500 /(int)1.39765 +mpfr_float 50 + 0.0194724 +mpfr_float 50 - 0.0228715 +mpfr_float 50 * 0.0587051 +mpfr_float 50 / 0.319258 +mpfr_float 50 str 0.00735177 +mpfr_float 50 +(int)0.0285879 +mpfr_float 50 -(int)0.0468028 +mpfr_float 50 *(int)0.03626 +mpfr_float 50 /(int)0.0889091 +mpfr_float 100 + 0.0211419 +mpfr_float 100 - 0.0251794 +mpfr_float 100 * 0.0946069 +mpfr_float 100 / 0.464237 +mpfr_float 100 str 0.00743083 +mpfr_float 100 +(int)0.0302544 +mpfr_float 100 -(int)0.0478439 +mpfr_float 100 *(int)0.0407275 +mpfr_float 100 /(int)0.109517 +mpfr_float 500 + 0.0338 +mpfr_float 500 - 0.037242 +mpfr_float 500 * 0.852196 +mpfr_float 500 / 2.80673 +mpfr_float 500 str 0.0339866 +mpfr_float 500 +(int)0.0427411 +mpfr_float 500 -(int)0.060913 +mpfr_float 500 *(int)0.0814603 +mpfr_float 500 /(int)0.254409 +[section:float_performance Float Type Perfomance] +[table Operator * +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][2.72405 (0.137722s)][3.23542 (0.293407s)][3.38644 (2.88591s)]] +[[gmp_float][[*1] (0.0505578s)][[*1] (0.090686s)][1.11127 (0.947017s)]] +[[mpfr_float][1.16115 (0.0587051s)][1.04324 (0.0946069s)][[*1] (0.852196s)]] +] +[table Operator *(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][2.33595 (0.0387713s)][3.1527 (0.063236s)][5.40294 (0.224258s)]] +[[gmp_float][[*1] (0.0165976s)][[*1] (0.0200577s)][[*1] (0.0415067s)]] +[[mpfr_float][2.18465 (0.03626s)][2.03052 (0.0407275s)][1.96258 (0.0814603s)]] +] +[table Operator + +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][[*1] (0.0142302s)][[*1] (0.0178132s)][1.40612 (0.044608s)]] +[[gmp_float][1.26944 (0.0180644s)][1.09329 (0.019475s)][[*1] (0.0317241s)]] +[[mpfr_float][1.36838 (0.0194724s)][1.18686 (0.0211419s)][1.06543 (0.0338s)]] +] +[table Operator +(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][2.08629 (0.0240351s)][2.61878 (0.0334828s)][5.04813 (0.0947227s)]] +[[gmp_float][[*1] (0.0115205s)][[*1] (0.0127856s)][[*1] (0.0187639s)]] +[[mpfr_float][2.48148 (0.0285879s)][2.36628 (0.0302544s)][2.27784 (0.0427411s)]] +] +[table Operator - +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][[*1] (0.0153931s)][[*1] (0.0189367s)][1.36514 (0.0457737s)]] +[[gmp_float][1.26468 (0.0194673s)][1.15343 (0.0218422s)][[*1] (0.0335304s)]] +[[mpfr_float][1.48583 (0.0228715s)][1.32966 (0.0251794s)][1.11069 (0.037242s)]] +] +[table Operator -(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][1.28001 (0.0252498s)][1.5908 (0.0326407s)][3.63667 (0.0966926s)]] +[[gmp_float][[*1] (0.0197263s)][[*1] (0.0205184s)][[*1] (0.0265882s)]] +[[mpfr_float][2.37262 (0.0468028s)][2.33176 (0.0478439s)][2.29098 (0.060913s)]] +] +[table Operator / +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][7.26654 (2.0214s)][11.2389 (4.24891s)][20.0284 (31.8072s)]] +[[gmp_float][[*1] (0.278179s)][[*1] (0.378055s)][[*1] (1.5881s)]] +[[mpfr_float][1.14767 (0.319258s)][1.22796 (0.464237s)][1.76735 (2.80673s)]] +] +[table Operator /(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][2.62228 (0.199003s)][3.60376 (0.341837s)][6.01157 (1.39765s)]] +[[gmp_float][[*1] (0.0758893s)][[*1] (0.0948556s)][[*1] (0.232493s)]] +[[mpfr_float][1.17156 (0.0889091s)][1.15457 (0.109517s)][1.09427 (0.254409s)]] +] +[table Operator str +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_float][2.58205 (0.00924301s)][2.87378 (0.0160219s)][2.03831 (0.0639606s)]] +[[gmp_float][[*1] (0.00357972s)][[*1] (0.00557522s)][[*1] (0.0313793s)]] +[[mpfr_float][2.05373 (0.00735177s)][1.33283 (0.00743083s)][1.08309 (0.0339866s)]] +] +[endsect] +[section:integer_performance Integer Type Perfomance] +[table Operator % +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.054413s)][[*1] (0.106105s)][[*1] (0.19685s)][1.67316 (0.385184s)][2.3543 (0.711308s)]] +[[gmp_int][3.04743 (0.16582s)][1.55485 (0.164977s)][1.00128 (0.197103s)][[*1] (0.230214s)][[*1] (0.302132s)]] +] +[table Operator %(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0243407s)][1.99962 (0.0811764s)][2.96437 (0.15306s)][4.64875 (0.303051s)][7.31311 (0.584615s)]] +[[gmp_int][1.42913 (0.034786s)][[*1] (0.0405959s)][[*1] (0.0516333s)][[*1] (0.0651899s)][[*1] (0.0799406s)]] +] +[table Operator & +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00259593s)][[*1] (0.00361924s)][[*1] (0.0108415s)][[*1] (0.013122s)][[*1] (0.0176585s)]] +[[gmp_int][4.85187 (0.0125951s)][3.96768 (0.01436s)][1.43661 (0.015575s)][1.50716 (0.019777s)][1.50977 (0.0266602s)]] +] +[table Operator &(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00209559s)][[*1] (0.00245967s)][[*1] (0.00419648s)][[*1] (0.00836021s)][[*1] (0.0166854s)]] +[[gmp_int][21.0856 (0.0441868s)][18.4577 (0.0453998s)][11.1151 (0.0466442s)][5.96293 (0.0498514s)][3.23322 (0.0539474s)]] +] +[table Operator * +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00392745s)][[*1] (0.0104772s)][[*1] (0.0324122s)][1.95004 (0.201059s)][2.14731 (0.701951s)]] +[[gmp_int][2.96502 (0.011645s)][1.74194 (0.0182506s)][1.4714 (0.0476911s)][[*1] (0.103105s)][[*1] (0.326898s)]] +] +[table Operator *(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00294381s)][[*1] (0.00422148s)][[*1] (0.00849409s)][[*1] (0.015882s)][1.15522 (0.0346698s)]] +[[gmp_int][4.09319 (0.0120496s)][3.01026 (0.0127078s)][2.0089 (0.0170638s)][1.34479 (0.021358s)][[*1] (0.0300116s)]] +] +[table Operator + +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00207163s)][[*1] (0.00326026s)][[*1] (0.00834722s)][[*1] (0.0128543s)][[*1] (0.0330379s)]] +[[gmp_int][8.08642 (0.0167521s)][5.89259 (0.0192114s)][2.76118 (0.0230482s)][2.19911 (0.028268s)][1.23787 (0.0408966s)]] +] +[table Operator +(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00358307s)][[*1] (0.00359962s)][[*1] (0.00405163s)][[*1] (0.00694047s)][[*1] (0.0116939s)]] +[[gmp_int][2.01857 (0.00723269s)][2.42047 (0.00871277s)][3.5813 (0.0145101s)][2.45162 (0.0170154s)][1.69017 (0.0197647s)]] +] +[table Operator - +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00216403s)][[*1] (0.00372498s)][[*1] (0.00653903s)][[*1] (0.0120433s)][[*1] (0.0311489s)]] +[[gmp_int][8.72818 (0.0188881s)][5.89208 (0.0219479s)][4.43331 (0.0289896s)][2.92463 (0.0352221s)][1.48689 (0.0463151s)]] +] +[table Operator -(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00354668s)][[*1] (0.00360689s)][[*1] (0.00385712s)][[*1] (0.00681002s)][[*1] (0.0116182s)]] +[[gmp_int][2.09194 (0.00741945s)][3.61625 (0.0130434s)][3.8458 (0.0148337s)][2.63767 (0.0179625s)][1.72107 (0.0199956s)]] +] +[table Operator / +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0556903s)][[*1] (0.105756s)][[*1] (0.198305s)][1.37248 (0.385977s)][1.91862 (0.708393s)]] +[[gmp_int][3.04721 (0.1697s)][1.85862 (0.196561s)][1.21304 (0.240552s)][[*1] (0.281226s)][[*1] (0.36922s)]] +] +[table Operator /(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.0169012s)][1.11654 (0.0634475s)][1.86084 (0.127666s)][2.57379 (0.244657s)][4.79191 (0.692818s)]] +[[gmp_int][2.96468 (0.0501068s)][[*1] (0.0568248s)][[*1] (0.0686065s)][[*1] (0.0950571s)][[*1] (0.144581s)]] +] +[table Operator << +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00115455s)][[*1] (0.00632357s)][[*1] (0.00826823s)][[*1] (0.0150546s)][[*1] (0.0242721s)]] +[[gmp_int][8.39362 (0.00969083s)][2.07445 (0.0131179s)][1.80141 (0.0148945s)][1.21421 (0.0182795s)][1.02121 (0.0247868s)]] +] +[table Operator >> +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00147407s)][[*1] (0.00238745s)][[*1] (0.00854822s)][1.10734 (0.0134889s)][1.52739 (0.0248274s)]] +[[gmp_int][8.85991 (0.0130601s)][4.4845 (0.0107065s)][1.30011 (0.0111136s)][[*1] (0.0121814s)][[*1] (0.0162548s)]] +] +[table Operator ^ +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00256688s)][[*1] (0.00361813s)][[*1] (0.0108455s)][[*1] (0.013116s)][[*1] (0.0177043s)]] +[[gmp_int][5.05409 (0.0129732s)][3.88746 (0.0140653s)][1.53751 (0.0166751s)][1.90691 (0.025011s)][1.69135 (0.0299441s)]] +] +[table Operator ^(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00202777s)][[*1] (0.00237775s)][[*1] (0.0027653s)][[*1] (0.00608555s)][[*1] (0.0108555s)]] +[[gmp_int][21.821 (0.0442481s)][19.7034 (0.0468496s)][16.847 (0.0465869s)][8.16164 (0.049668s)][4.97188 (0.0539722s)]] +] +[table Operator str +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.000302762s)][[*1] (0.000500691s)][1.14936 (0.00111683s)][1.71055 (0.00286314s)][2.93313 (0.00872206s)]] +[[gmp_int][1.11188 (0.000336635s)][4.63553 (0.00232097s)][[*1] (0.000971703s)][[*1] (0.00167382s)][[*1] (0.00297363s)]] +] +[table Operator | +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00257616s)][[*1] (0.00363433s)][[*1] (0.0108232s)][[*1] (0.0131341s)][[*1] (0.0176472s)]] +[[gmp_int][4.49789 (0.0115873s)][3.7058 (0.0134681s)][1.47085 (0.0159192s)][1.58756 (0.0208511s)][1.61398 (0.0284821s)]] +] +[table Operator |(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[fixed_int][[*1] (0.00208078s)][[*1] (0.00190869s)][[*1] (0.00275195s)][[*1] (0.00618124s)][[*1] (0.0107899s)]] +[[gmp_int][20.4129 (0.0424747s)][23.0676 (0.0440289s)][17.2504 (0.0474723s)][7.98521 (0.0493584s)][4.87243 (0.0525727s)]] +] +[endsect] +[section:rational_performance Rational Type Perfomance] +[table Operator * +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.426868s)][[*1] (0.968054s)][[*1] (4.39195s)][[*1] (9.6344s)][[*1] (20.9879s)]] +] +[table Operator *(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.344178s)][[*1] (0.179899s)][[*1] (0.200539s)][[*1] (0.254142s)][[*1] (0.328602s)]] +] +[table Operator + +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.254473s)][[*1] (0.542374s)][[*1] (2.34795s)][[*1] (5.10523s)][[*1] (11.2331s)]] +] +[table Operator +(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.309729s)][[*1] (0.154116s)][[*1] (0.177483s)][[*1] (0.212807s)][[*1] (0.27756s)]] +] +[table Operator - +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.260331s)][[*1] (0.545764s)][[*1] (2.3565s)][[*1] (5.08802s)][[*1] (11.2446s)]] +] +[table Operator -(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.306598s)][[*1] (0.151187s)][[*1] (0.16783s)][[*1] (0.212048s)][[*1] (0.271845s)]] +] +[table Operator / +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (1.50105s)][[*1] (2.78757s)][[*1] (8.9203s)][[*1] (16.8502s)][[*1] (35.6472s)]] +] +[table Operator /(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.32842s)][[*1] (0.184167s)][[*1] (0.206129s)][[*1] (0.262442s)][[*1] (0.350883s)]] +] +[table Operator str +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[mpq_rational][[*1] (0.000927423s)][[*1] (0.00111655s)][[*1] (0.00175742s)][[*1] (0.00246714s)][[*1] (0.00550783s)]] +] +[endsect] diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index 750f668d..8dff3baa 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -14,8 +14,10 @@ # define TEST_MPFR_CLASS #endif -#ifdef TEST_MPFR +#ifdef TEST_MPFR_CLASS #include +#endif +#ifdef TEST_MPFR #include #endif #ifdef TEST_MP_REAL From 4472a37b0e3676e69c2826c1f7b571853bfab6bb Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 23 Jan 2012 19:01:43 +0000 Subject: [PATCH 110/256] Update docs with latest performance results. [SVN r76653] --- doc/html/boost_multiprecision/intro.html | 45 +- .../perf/float_performance.html | 532 ++-- .../perf/integer_performance.html | 2299 ++++++++++++----- .../boost_multiprecision/perf/realworld.html | 17 +- .../boost_multiprecision/ref/mp_number.html | 4 +- doc/html/boost_multiprecision/tut/ints.html | 139 +- .../boost_multiprecision/tut/rational.html | 62 +- doc/html/boost_multiprecision/tut/reals.html | 127 +- doc/html/index.html | 2 +- doc/multiprecision.qbk | 377 ++- performance/performance_test-msvc-10.log | 894 ++++--- 11 files changed, 3023 insertions(+), 1475 deletions(-) diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index fadcea1c..59d5fc82 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -33,9 +33,9 @@

    - The library is often used by using one of the predefined typedefs: for example - if you wanted an arbitrary precision integer type using GMP as the underlying - implementation then you could use: + The library is often used via one of the predefined typedefs: for example if + you wanted an arbitrary precision integer type using GMP + as the underlying implementation then you could use: 

    #include <boost/multiprecision/gmp.hpp>  // Defines the wrappers around the GMP library's types
 
@@ -45,8 +45,9 @@
       Alternatively, you can compose your own multiprecision type, by combining
       mp_number with one of the predefined
       backend types. For example, suppose you wanted a 300 decimal digit floating-point
-      type based on the MPFR library. In this case, there's no predefined typedef
-      with that level of precision, so instead we compose our own:
+      type based on the MPFR library. In
+      this case, there's no predefined typedef with that level of precision, so instead
+      we compose our own:
     
    
 
    #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
 
@@ -102,11 +103,13 @@
 
    
       If type T is an mp_number, then this expression is evaluated
       without creating a single temporary value. In contrast,
-      if we were using the C++ wrapper that ships with GMP - mpf_class
+      if we were using the C++ wrapper that ships with GMP
+      - mpfr_class
       - then this expression would result in no less than 11 temporaries (this is
-      true even though mpf_class
+      true even though mpfr_class
       does use expression templates to reduce the number of temporaries somewhat).
-      Had we used an even simpler wrapper around GMP or MPFR like mpclass
+      Had we used an even simpler wrapper around GMP
+      or MPFR like mpclass
       things would have been even worse and no less that 24 temporaries are created
       for this simple expression (note - we actually measure the number of memory
       allocations performed rather than the number of temporaries directly).
@@ -192,10 +195,11 @@
 
    
       And finally... the performance improvements from an expression template library
       like this are often not as dramatic as the reduction in number of temporaries
-      would suggest. For example if we compare this library with mpfr_class
-      and mpreal, with all three
-      using the underlying MPFR library at 50 decimal digits precision then we see
-      the following typical results for polynomial execution:
+      would suggest. For example if we compare this library with mpfr_class
+      and mpreal, with
+      all three using the underlying MPFR
+      library at 50 decimal digits precision then we see the following typical results
+      for polynomial execution:
     
    
 
    
 
    Table 1.1. Evaluation of Order 6 Polynomial.
    
@@ -243,7 +247,7 @@
 
 
               
    
-                mpfr_class
+                mpfr_class
               
    
             
 
@@ -260,7 +264,7 @@
 
 
               
    
-                mpreal
+                mpreal
               
    
             
 
@@ -301,8 +305,9 @@
 
    
 
    
       We'll conclude this section by providing some more performance comparisons
-      between these three libraries, again, all are using MPFR to carry out the underlying
-      arithmetic, and all are operating at the same precision (50 decimal digits):
+      between these three libraries, again, all are using MPFR
+      to carry out the underlying arithmetic, and all are operating at the same precision
+      (50 decimal digits):
     
    
 
    
 
    Table 1.2. Evaluation of Boost.Math's Bessel function test data
    
@@ -350,7 +355,7 @@
 
 
               
    
-                mpfr_class
+                mpfr_class
               
    
             
 
@@ -367,7 +372,7 @@
 
 
               
    
-                mpreal
+                mpreal
               
    
             
 
@@ -430,7 +435,7 @@
 
 
               
    
-                mpfr_class
+                mpfr_class
               
    
             
 
@@ -447,7 +452,7 @@
 
 
               
    
-                mpreal
+                mpreal
               
    
             
 
diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html
index c746b939..0483f675 100644
--- a/doc/html/boost_multiprecision/perf/float_performance.html
+++ b/doc/html/boost_multiprecision/perf/float_performance.html
@@ -29,112 +29,11 @@
       
    
 
    
         Test code was compiled with Microsoft Visual Studio 2010 with all optimisations
-        turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on
-        32-bit Windows Vista machine.
+        turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0.
+        The tests were run on 32-bit Windows Vista machine.
       
    
 
    
-
    Table 1.8. Operator *
    
-
    
------
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
    





    
-                
    
-                  Backend
-                
    
-                  		
-                
    
-                  50 Decimal Digits
-                
    
-                  		
-                
    
-                  100 Decimal Digits
-                
    
-                  		
-                
    
-                  500 Decimal Digits
-                
    
-              
    
-                
    
-                  cpp_float
-                
    
-                  		
-                
    
-                  1.0826 (0.287216s)
-                
    
-                  		
-                
    
-                  1.48086 (0.586363s)
-                
    
-                  		
-                
    
-                  1.57545 (5.05269s)
-                
    
-              
    
-                
    
-                  gmp_float
-                
    
-                  		
-                
    
-                  1 (0.265302s)
-                
    
-                  		
-                
    
-                  1 (0.395962s)
-                
    
-                  		
-                
    
-                  1 (3.20714s)
-                
    
-              
    
-                
    
-                  mpfr_float
-                
    
-                  		
-                
    
-                  1.24249 (0.329636s)
-                
    
-                  		
-                
    
-                  1.15432 (0.457067s)
-                
    
-                  		
-                
    
-                  1.16182 (3.72612s)
-                
    
-              
    
-
    
-
    
-
    Table 1.9. Operator +
    
+
    Table 1.8. Operator +
    
 
    @@ -173,17 +72,17 @@
               
@@ -195,17 +94,17 @@
               
@@ -217,17 +116,17 @@
               
@@ -235,7 +134,7 @@
 
    
 
 

 
    
                 
    
-                  1 (0.0242151s)
+                  1 (0.02382s)
                 
    
                   		
 
                 
    
-                  1 (0.029252s)
+                  1 (0.0294619s)
                 
    
                   		
 
                 
    
-                  1 (0.0584099s)
+                  1 (0.058466s)
                 
    
                   		
 
    
 
    
                 
    
-                  4.55194 (0.110226s)
+                  4.55086 (0.108402s)
                 
    
                   		
 
                 
    
-                  3.67516 (0.107506s)
+                  3.86443 (0.113853s)
                 
    
                   		
 
                 
    
-                  2.42489 (0.141638s)
+                  2.6241 (0.15342s)
                 
    
                   		
 
    
 
    
                 
    
-                  2.45362 (0.0594147s)
+                  2.52036 (0.060035s)
                 
    
                   		
 
                 
    
-                  2.18552 (0.0639309s)
+                  2.1833 (0.0643242s)
                 
    
                   		
 
                 
    
-                  1.32099 (0.0771588s)
+                  1.37736 (0.0805287s)
                 
    
                   		
 
    
 
    
 
    
-
    Table 1.10. Operator +(int)
    
+
    Table 1.9. Operator +(int)
    
 
    @@ -274,17 +173,17 @@
               
@@ -296,17 +195,17 @@
               
@@ -318,17 +217,17 @@
               
@@ -336,7 +235,7 @@
 
    
 
 

 
    
                 
    
-                  1.51995 (0.0484155s)
+                  1.56759 (0.0527023s)
                 
    
                   		
 
                 
    
-                  1.78781 (0.0611055s)
+                  1.74629 (0.0618102s)
                 
    
                   		
 
                 
    
-                  1.8309 (0.104123s)
+                  1.68077 (0.105927s)
                 
    
                   		
 
    
 
    
                 
    
-                  1 (0.0318533s)
+                  1 (0.0336201s)
                 
    
                   		
 
                 
    
-                  1 (0.0341789s)
+                  1 (0.0353951s)
                 
    
                   		
 
                 
    
-                  1 (0.0568699s)
+                  1 (0.0630232s)
                 
    
                   		
 
    
 
    
                 
    
-                  3.39055 (0.108s)
+                  3.14875 (0.105861s)
                 
    
                   		
 
                 
    
-                  3.30142 (0.112839s)
+                  3.15499 (0.111671s)
                 
    
                   		
 
                 
    
-                  2.05293 (0.11675s)
+                  1.92831 (0.121528s)
                 
    
                   		
 
    
 
    
 
    
-
    Table 1.11. Operator -
    
+
    Table 1.10. Operator -
    
 
    @@ -375,17 +274,17 @@
               
@@ -397,17 +296,17 @@
               
@@ -419,17 +318,17 @@
               
@@ -437,7 +336,7 @@
 
    
 
 

 
    
                 
    
-                  1 (0.0261498s)
+                  1 (0.0265783s)
                 
    
                   		
 
                 
    
-                  1 (0.030946s)
+                  1 (0.031465s)
                 
    
                   		
 
                 
    
-                  1 (0.0606388s)
+                  1 (0.0619405s)
                 
    
                   		
 
    
 
    
                 
    
-                  4.48753 (0.117348s)
+                  4.66954 (0.124108s)
                 
    
                   		
 
                 
    
-                  3.75823 (0.116302s)
+                  3.72645 (0.117253s)
                 
    
                   		
 
                 
    
-                  2.4823 (0.150524s)
+                  2.67536 (0.165713s)
                 
    
                   		
 
    
 
    
                 
    
-                  2.96057 (0.0774183s)
+                  2.7909 (0.0741774s)
                 
    
                   		
 
                 
    
-                  2.61897 (0.0810465s)
+                  2.48557 (0.0782083s)
                 
    
                   		
 
                 
    
-                  1.56236 (0.0947396s)
+                  1.50944 (0.0934957s)
                 
    
                   		
 
    
 
    
 
    
-
    Table 1.12. Operator -(int)
    
+
    Table 1.11. Operator -(int)
    
 
    @@ -476,17 +375,17 @@
               
@@ -498,17 +397,17 @@
               
@@ -520,17 +419,17 @@
               
@@ -538,7 +437,209 @@
 
    
 
 

 
    
                 
    
-                  1 (0.0567601s)
+                  1 (0.0577674s)
                 
    
                   		
 
                 
    
-                  1 (0.0626685s)
+                  1 (0.0633795s)
                 
    
                   		
 
                 
    
-                  1 (0.111692s)
+                  1 (0.11146s)
                 
    
                   		
 
    
 
    
                 
    
-                  2.27932 (0.129374s)
+                  2.31811 (0.133911s)
                 
    
                   		
 
                 
    
-                  2.04821 (0.128358s)
+                  2.07251 (0.131355s)
                 
    
                   		
 
                 
    
-                  1.48297 (0.165635s)
+                  1.67161 (0.186319s)
                 
    
                   		
 
    
 
    
                 
    
-                  2.43199 (0.13804s)
+                  2.45081 (0.141577s)
                 
    
                   		
 
                 
    
-                  2.32131 (0.145473s)
+                  2.29174 (0.145249s)
                 
    
                   		
 
                 
    
-                  1.38152 (0.154304s)
+                  1.395 (0.155487s)
                 
    
                   		
 
    
 
    
 
    
-
    Table 1.13. Operator /
    
+
    Table 1.12. Operator *
    
+
    
++++++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    





    
+                
    
+                  Backend
+                
    
+                  		
+                
    
+                  50 Decimal Digits
+                
    
+                  		
+                
    
+                  100 Decimal Digits
+                
    
+                  		
+                
    
+                  500 Decimal Digits
+                
    
+              
    
+                
    
+                  cpp_float
+                
    
+                  		
+                
    
+                  1.07276 (0.287898s)
+                
    
+                  		
+                
    
+                  1.47724 (0.584569s)
+                
    
+                  		
+                
    
+                  1.55145 (5.09969s)
+                
    
+              
    
+                
    
+                  gmp_float
+                
    
+                  		
+                
    
+                  1 (0.268372s)
+                
    
+                  		
+                
    
+                  1 (0.395718s)
+                
    
+                  		
+                
    
+                  1 (3.28705s)
+                
    
+              
    
+                
    
+                  mpfr_float
+                
    
+                  		
+                
    
+                  1.27302 (0.341642s)
+                
    
+                  		
+                
    
+                  1.17649 (0.465557s)
+                
    
+                  		
+                
    
+                  1.14029 (3.7482s)
+                
    
+              
    
+
    
+
    
+
    Table 1.13. Operator *(int)
    
+
    
++++++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    





    
+                
    
+                  Backend
+                
    
+                  		
+                
    
+                  50 Decimal Digits
+                
    
+                  		
+                
    
+                  100 Decimal Digits
+                
    
+                  		
+                
    
+                  500 Decimal Digits
+                
    
+              
    
+                
    
+                  cpp_float
+                
    
+                  		
+                
    
+                  2.89945 (0.11959s)
+                
    
+                  		
+                
    
+                  4.56335 (0.197945s)
+                
    
+                  		
+                
    
+                  9.03602 (0.742044s)
+                
    
+              
    
+                
    
+                  gmp_float
+                
    
+                  		
+                
    
+                  1 (0.0412457s)
+                
    
+                  		
+                
    
+                  1 (0.0433772s)
+                
    
+                  		
+                
    
+                  1 (0.0821206s)
+                
    
+              
    
+                
    
+                  mpfr_float
+                
    
+                  		
+                
    
+                  3.6951 (0.152407s)
+                
    
+                  		
+                
    
+                  3.71977 (0.161353s)
+                
    
+                  		
+                
    
+                  3.30958 (0.271785s)
+                
    
+              
    
+
    
+
    
+
    Table 1.14. Operator /
    
 
    @@ -577,17 +678,17 @@
               
@@ -599,17 +700,17 @@
               
@@ -621,17 +722,17 @@
               
@@ -639,7 +740,108 @@
 
    
 
 

 
    
                 
    
-                  3.2662 (3.98153s)
+                  3.24327 (4.00108s)
                 
    
                   		
 
                 
    
-                  5.07021 (8.11948s)
+                  5.00532 (8.12985s)
                 
    
                   		
 
                 
    
-                  6.78872 (53.6099s)
+                  6.79566 (54.2796s)
                 
    
                   		
 
    
 
    
                 
    
-                  1 (1.21901s)
+                  1 (1.23366s)
                 
    
                   		
 
                 
    
-                  1 (1.60141s)
+                  1 (1.62424s)
                 
    
                   		
 
                 
    
-                  1 (7.89691s)
+                  1 (7.9874s)
                 
    
                   		
 
    
 
    
                 
    
-                  1.33238 (1.62419s)
+                  1.32521 (1.63486s)
                 
    
                   		
 
                 
    
-                  1.39529 (2.23443s)
+                  1.38967 (2.25716s)
                 
    
                   		
 
                 
    
-                  1.70882 (13.4944s)
+                  1.72413 (13.7713s)
                 
    
                   		
 
    
 
    
 
    
-
    Table 1.14. Operator str
    
+
    Table 1.15. Operator /(int)
    
+
    
++++++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    





    
+                
    
+                  Backend
+                
    
+                  		
+                
    
+                  50 Decimal Digits
+                
    
+                  		
+                
    
+                  100 Decimal Digits
+                
    
+                  		
+                
    
+                  500 Decimal Digits
+                
    
+              
    
+                
    
+                  cpp_float
+                
    
+                  		
+                
    
+                  1.45093 (0.253675s)
+                
    
+                  		
+                
    
+                  1.83306 (0.419569s)
+                
    
+                  		
+                
    
+                  2.3644 (1.64187s)
+                
    
+              
    
+                
    
+                  gmp_float
+                
    
+                  		
+                
    
+                  1 (0.174836s)
+                
    
+                  		
+                
    
+                  1 (0.22889s)
+                
    
+                  		
+                
    
+                  1 (0.694411s)
+                
    
+              
    
+                
    
+                  mpfr_float
+                
    
+                  		
+                
    
+                  1.16731 (0.204088s)
+                
    
+                  		
+                
    
+                  1.13211 (0.259127s)
+                
    
+                  		
+                
    
+                  1.02031 (0.708513s)
+                
    
+              
    
+
    
+
    
+
    Table 1.16. Operator str
    
 
    @@ -678,17 +880,17 @@
               
@@ -700,17 +902,17 @@
               
@@ -722,24 +924,26 @@
               
    
 
 

 
    
                 
    
-                  1.46076 (0.0192656s)
+                  1.4585 (0.0188303s)
                 
    
                   		
 
                 
    
-                  1.59438 (0.0320398s)
+                  1.55515 (0.03172s)
                 
    
                   		
 
                 
    
-                  1 (0.134302s)
+                  1 (0.131962s)
                 
    
                   		
 
    
 
    
                 
    
-                  1 (0.0131888s)
+                  1 (0.0129107s)
                 
    
                   		
 
                 
    
-                  1 (0.0200954s)
+                  1 (0.0203967s)
                 
    
                   		
 
                 
    
-                  1.01007 (0.135655s)
+                  1.04632 (0.138075s)
                 
    
                   		
 
    
 
    
                 
    
-                  2.19174 (0.0289065s)
+                  2.19015 (0.0282764s)
                 
    
                   		
 
                 
    
-                  1.86101 (0.0373977s)
+                  1.84679 (0.0376683s)
                 
    
                   		
 
                 
    
-                  1.15842 (0.155578s)
+                  1.20295 (0.158743s)
                 
    
                   		
 
    
     
 
    
 
    
-
    
+
    
+        ]
+      
    
 
    
 
diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html
index fdd2c062..4cca438f 100644
--- a/doc/html/boost_multiprecision/perf/integer_performance.html
+++ b/doc/html/boost_multiprecision/perf/integer_performance.html
@@ -29,11 +29,16 @@
       
    
         Test code was compiled with Microsoft Visual Studio 2010 with all optimisations
-        turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on
-        32-bit Windows Vista machine.
+        turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0.
+        The tests were run on 32-bit Windows Vista machine.
+      
    
+
    
+        Note that Linux x64 tests showed significantly worse performance for fixed_int division than on Win32 (or possibly
+        GMP behaves much better in that case).
+        Otherwise the results are much the same.
       
    
-
    Table 1.15. Operator +
    
+
    Table 1.17. Operator +
    
 
    
 
 
 
    @@ -84,27 +89,27 @@
               
@@ -116,27 +121,27 @@
               
@@ -148,27 +153,27 @@
               
@@ -176,7 +181,7 @@
 
    
 
 

 
    
                 
    
-                  1 (0.0031173s)
+                  1 (0.0031291s)
                 
    
                   		
 
                 
    
-                  1 (0.00696555s)
+                  1 (0.00703043s)
                 
    
                   		
 
                 
    
-                  1 (0.0163707s)
+                  1 (0.0163669s)
                 
    
                   		
 
                 
    
-                  1 (0.0314806s)
+                  1 (0.0326567s)
                 
    
                   		
 
                 
    
-                  1 (0.0596158s)
+                  1 (0.0603087s)
                 
    
                   		
 
    
 
    
                 
    
-                  12.7096 (0.0396194s)
+                  12.4866 (0.0390717s)
                 
    
                   		
 
                 
    
-                  5.89178 (0.0410395s)
+                  6.01034 (0.0422553s)
                 
    
                   		
 
                 
    
-                  2.66402 (0.0436119s)
+                  2.65628 (0.0434751s)
                 
    
                   		
 
                 
    
-                  1.59356 (0.0501664s)
+                  1.54295 (0.0503875s)
                 
    
                   		
 
                 
    
-                  1.11155 (0.0662662s)
+                  1.16477 (0.0702458s)
                 
    
                   		
 
    
 
    
                 
    
-                  6.14357 (0.0191513s)
+                  6.03111 (0.018872s)
                 
    
                   		
 
                 
    
-                  3.16177 (0.0220235s)
+                  3.08173 (0.0216659s)
                 
    
                   		
 
                 
    
-                  1.85441 (0.030358s)
+                  1.84243 (0.0301548s)
                 
    
                   		
 
                 
    
-                  1.45895 (0.0459287s)
+                  1.30199 (0.0425188s)
                 
    
                   		
 
                 
    
-                  1.26576 (0.0754591s)
+                  1.18909 (0.0717123s)

    -

    Table 1.16. Operator +(int)

    +

    Table 1.18. Operator +(int)

    @@ -227,27 +232,27 @@ @@ -259,27 +264,27 @@ @@ -291,27 +296,27 @@ @@ -319,7 +324,7 @@

    - 1 (0.00329336s) + 1 (0.00335294s)

    - 1 (0.00370718s) + 1 (0.00376116s)

    - 1 (0.00995385s) + 1 (0.00985174s)

    - 1 (0.0117467s) + 1 (0.0119345s)

    - 1 (0.0233483s) + 1 (0.0170918s)

    - 9.56378 (0.031497s) + 9.47407 (0.031766s)

    - 8.0588 (0.0298754s) + 8.44794 (0.0317741s)

    - 4.15824 (0.0413905s) + 4.23857 (0.0417573s)

    - 5.47974 (0.0643691s) + 5.40856 (0.0645488s)

    - 4.46265 (0.104195s) + 6.31314 (0.107903s)

    - 76.2624 (0.25116s) + 67.0025 (0.224655s)

    - 71.3973 (0.264682s) + 60.4203 (0.22725s)

    - 28.0238 (0.278945s) + 25.1834 (0.2481s)

    - 25.9035 (0.304282s) + 23.2996 (0.27807s)

    - 13.1635 (0.307346s) + 17.1743 (0.293538s)


    -

    Table 1.17. Operator -

    +

    Table 1.19. Operator -

    @@ -370,27 +375,27 @@ @@ -402,27 +407,27 @@ @@ -434,27 +439,27 @@ @@ -462,7 +467,7 @@

    - 1 (0.00359417s) + 1 (0.00339191s)

    - 1 (0.00721041s) + 1 (0.0073172s)

    - 1 (0.0168213s) + 1 (0.0166428s)

    - 1 (0.0323563s) + 1 (0.0349375s)

    - 1 (0.061385s) + 1 (0.0600083s)

    - 10.6794 (0.0383836s) + 12.5182 (0.0424608s)

    - 5.65517 (0.0407761s) + 5.57936 (0.0408253s)

    - 2.63634 (0.0443466s) + 2.78496 (0.0463496s)

    - 1.59979 (0.0517632s) + 1.48373 (0.051838s)

    - 1.13379 (0.0695978s) + 1.29928 (0.0779673s)

    - 6.43615 (0.0231326s) + 7.00782 (0.0237699s)

    - 3.6161 (0.0260736s) + 3.69919 (0.0270677s)

    - 2.2585 (0.0379908s) + 2.29645 (0.0382195s)

    - 1.52006 (0.0491835s) + 1.39777 (0.0488346s)

    - 1.24231 (0.0762591s) + 1.28243 (0.0769566s)


    -

    Table 1.18. Operator -(int)

    +

    Table 1.20. Operator -(int)

    @@ -513,27 +518,27 @@ @@ -545,27 +550,27 @@ @@ -577,27 +582,27 @@ @@ -605,7 +610,7 @@

    - 1 (0.00353606s) + 1 (0.00250933s)

    - 1 (0.00577573s) + 1 (0.00358055s)

    - 1 (0.0155184s) + 1 (0.0103282s)

    - 1 (0.029385s) + 1 (0.0119127s)

    - 1 (0.0586271s) + 1 (0.0176089s)

    - 9.04434 (0.0319814s) + 12.093 (0.0303454s)

    - 5.12393 (0.0295945s) + 8.50898 (0.0304669s)

    - 2.50743 (0.0389112s) + 3.9284 (0.0405733s)

    - 2.01898 (0.0593277s) + 5.03037 (0.0599252s)

    - 1.68381 (0.098717s) + 5.96617 (0.105058s)

    - 60.2486 (0.213043s) + 80.8477 (0.202873s)

    - 38.3032 (0.221229s) + 57.8371 (0.207089s)

    - 15.8792 (0.24642s) + 21.3372 (0.220375s)

    - 8.71166 (0.255992s) + 23.526 (0.280258s)

    - 4.85236 (0.28448s) + 14.793 (0.260488s)


    -

    Table 1.19. Operator *

    +

    Table 1.21. Operator *

    @@ -656,27 +661,27 @@ @@ -688,27 +693,27 @@ @@ -720,27 +725,27 @@ @@ -748,7 +753,150 @@

    - 1 (0.0175309s) + 1 (0.0223481s)

    - 1 (0.0388232s) + 1 (0.0375288s)

    - 1 (0.123609s) + 1 (0.120353s)

    - 1 (0.427489s) + 1 (0.439147s)

    - 1 (1.46312s) + 1 (1.46969s)

    - 2.93263 (0.0514117s) + 2.50746 (0.0560369s)

    - 1.70358 (0.0661383s) + 1.76676 (0.0663044s)

    - 1.01811 (0.125848s) + 1.06052 (0.127636s)

    - 1.20692 (0.515943s) + 1.22558 (0.53821s)

    - 1.03248 (1.51064s) + 1.03538 (1.52168s)

    - 3.82476 (0.0670515s) + 3.00028 (0.0670506s)

    - 2.87425 (0.111587s) + 2.97696 (0.111722s)

    - 2.74339 (0.339108s) + 2.86257 (0.34452s)

    - 2.26768 (0.969408s) + 2.26661 (0.995374s)

    - 2.1233 (3.10664s) + 2.12926 (3.12935s)


    -

    Table 1.20. Operator /

    +

    Table 1.22. Operator *(int)

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00444316s) +

    +     		+

    + 1 (0.0135739s) +

    +     		+

    + 1 (0.0192615s) +

    +     		+

    + 1 (0.0328339s) +

    +     		+

    + 1.18198 (0.0567364s) +

    +
    +

    + gmp_int +

    +     		+

    + 4.57776 (0.0203397s) +

    +     		+

    + 1.79901 (0.0244196s) +

    +     		+

    + 1.32814 (0.025582s) +

    +     		+

    + 1.01453 (0.033311s) +

    +     		+

    + 1 (0.048001s) +

    +
    +

    + tommath_int +

    +     		+

    + 53.8709 (0.239357s) +

    +     		+

    + 18.3773 (0.249452s) +

    +     		+

    + 14.2088 (0.273682s) +

    +     		+

    + 14.0907 (0.462652s) +

    +     		+

    + 9.10761 (0.437175s) +

    +
    +
    +
    +

    Table 1.23. Operator /

    @@ -799,27 +947,27 @@ @@ -831,27 +979,27 @@ @@ -863,27 +1011,27 @@ @@ -891,7 +1039,150 @@

    - 1 (0.0973696s) + 1 (0.0991632s)

    - 1 (0.260936s) + 1 (0.172328s)

    - 1 (0.845628s) + 1 (0.309492s)

    - 2.4597 (2.51371s) + 1 (0.573815s)

    - 6.21836 (7.93136s) + 1 (1.06356s)

    - 7.66851 (0.74668s) + 7.81859 (0.775316s)

    - 3.17732 (0.829077s) + 5.11069 (0.880715s)

    - 1.05006 (0.887961s) + 2.93514 (0.908404s)

    - 1 (1.02196s) + 1.80497 (1.03572s)

    - 1 (1.27547s) + 1.21878 (1.29625s)

    - 18.3945 (1.79107s) + 18.0766 (1.79253s)

    - 8.11201 (2.11671s) + 12.3939 (2.13582s)

    - 3.49119 (2.95225s) + 9.80438 (3.03438s)

    - 4.55727 (4.65733s) + 8.74047 (5.01541s)

    - 9.06813 (11.5662s) + 10.8288 (11.517s)


    -

    Table 1.21. Operator %

    +

    Table 1.24. Operator /(int)

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1.04098 (0.0443082s) +

    +     		+

    + 1.61317 (0.110308s) +

    +     		+

    + 2.18324 (0.229148s) +

    +     		+

    + 2.36331 (0.442167s) +

    +     		+

    + 2.45159 (0.866172s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (0.042564s) +

    +     		+

    + 1 (0.06838s) +

    +     		+

    + 1 (0.104957s) +

    +     		+

    + 1 (0.187096s) +

    +     		+

    + 1 (0.35331s) +

    +
    +

    + tommath_int +

    +     		+

    + 32.4072 (1.37938s) +

    +     		+

    + 23.7471 (1.62383s) +

    +     		+

    + 22.1907 (2.32908s) +

    +     		+

    + 19.9054 (3.72421s) +

    +     		+

    + 24.2219 (8.55783s) +

    +
    +
    +
    +

    Table 1.25. Operator %

    @@ -942,27 +1233,27 @@ @@ -974,27 +1265,27 @@ @@ -1006,27 +1297,27 @@ @@ -1034,8 +1325,8 @@

    - 1 (0.098458s) + 1 (0.0946529s)

    - 1 (0.269155s) + 1 (0.170561s)

    - 1.10039 (0.849272s) + 1 (0.328458s)

    - 2.92096 (2.55909s) + 1 (0.575884s)

    - 7.47157 (7.99106s) + 1 (1.05006s)

    - 6.63934 (0.653697s) + 7.77525 (0.73595s)

    - 2.6753 (0.72007s) + 4.39387 (0.749422s)

    - 1 (0.771794s) + 2.35075 (0.772122s)

    - 1 (0.87611s) + 1.51922 (0.874894s)

    - 1 (1.06953s) + 1.02263 (1.07382s)

    - 18.5522 (1.82661s) + 27.1503 (2.56986s)

    - 8.00831 (2.15548s) + 12.8743 (2.19585s)

    - 3.89737 (3.00797s) + 9.43965 (3.10053s)

    - 5.38078 (4.71416s) + 8.24936 (4.75068s)

    - 10.7885 (11.5386s) + 10.9719 (11.5211s)


    -

    Table 1.22. Operator <<

    -
    +

    Table 1.26. Operator %(int)

    +
    @@ -1085,27 +1376,27 @@ @@ -1117,27 +1408,27 @@ @@ -1149,599 +1440,27 @@ - - -

    - 1 (0.0120907s) + 1.25034 (0.0425984s)

    - 1 (0.0129147s) + 1.91617 (0.106226s)

    - 1 (0.0214412s) + 2.02166 (0.195577s)

    - 1 (0.0249208s) + 2.14437 (0.387067s)

    - 1 (0.0341293s) + 2.23514 (0.776075s)

    - 1.93756 (0.0234265s) + 1 (0.0340695s)

    - 1.97785 (0.0255433s) + 1 (0.0554367s)

    - 1.43607 (0.0307911s) + 1 (0.0967406s)

    - 1.815 (0.0452311s) + 1 (0.180504s)

    - 2.00167 (0.0683156s) + 1 (0.347216s)

    - 3.42859 (0.0414542s) + 42.8781 (1.46083s)

    - 3.04951 (0.0393836s) + 29.879 (1.65639s)

    - 3.04202 (0.0652246s) + 23.4323 (2.26685s)

    - 3.81169 (0.0949903s) + 19.932 (3.5978s)

    - 4.93896 (0.168563s) -

    -
    -
    -
    -

    Table 1.23. Operator >>

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 64 Bits -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - fixed_int -

    -     		-

    - 1 (0.0064833s) -

    -     		-

    - 1 (0.00772857s) -

    -     		-

    - 1 (0.0186871s) -

    -     		-

    - 1 (0.0218303s) -

    -     		-

    - 1 (0.0326372s) -

    -
    -

    - gmp_int -

    -     		-

    - 4.212 (0.0273077s) -

    -     		-

    - 3.72696 (0.0288041s) -

    -     		-

    - 1.55046 (0.0289735s) -

    -     		-

    - 1.51403 (0.0330518s) -

    -     		-

    - 1.13695 (0.037107s) -

    -
    -

    - tommath_int -

    -     		-

    - 33.9418 (0.220055s) -

    -     		-

    - 29.104 (0.224932s) -

    -     		-

    - 13.8407 (0.258642s) -

    -     		-

    - 13.1488 (0.287043s) -

    -     		-

    - 15.1741 (0.495242s) -

    -
    -
    -
    -

    Table 1.24. Operator &

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 64 Bits -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - fixed_int -

    -     		-

    - 1 (0.0028732s) -

    -     		-

    - 1 (0.00552933s) -

    -     		-

    - 1 (0.0125148s) -

    -     		-

    - 1 (0.020299s) -

    -     		-

    - 1 (0.034856s) -

    -
    -

    - gmp_int -

    -     		-

    - 16.3018 (0.0468383s) -

    -     		-

    - 9.51109 (0.05259s) -

    -     		-

    - 5.20026 (0.0650802s) -

    -     		-

    - 4.46545 (0.0906443s) -

    -     		-

    - 3.99377 (0.139207s) -

    -
    -

    - tommath_int -

    -     		-

    - 42.221 (0.121309s) -

    -     		-

    - 22.2471 (0.123011s) -

    -     		-

    - 11.3587 (0.142151s) -

    -     		-

    - 7.3475 (0.149147s) -

    -     		-

    - 11.4043 (0.397507s) -

    -
    -
    -
    -

    Table 1.25. Operator ^

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 64 Bits -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - fixed_int -

    -     		-

    - 1 (0.00287983s) -

    -     		-

    - 1 (0.00543128s) -

    -     		-

    - 1 (0.0125726s) -

    -     		-

    - 1 (0.019987s) -

    -     		-

    - 1 (0.034697s) -

    -
    -

    - gmp_int -

    -     		-

    - 14.938 (0.0430189s) -

    -     		-

    - 9.00973 (0.0489344s) -

    -     		-

    - 4.83803 (0.0608267s) -

    -     		-

    - 4.33359 (0.0866154s) -

    -     		-

    - 3.89518 (0.135151s) -

    -
    -

    - tommath_int -

    -     		-

    - 41.6898 (0.12006s) -

    -     		-

    - 22.4393 (0.121874s) -

    -     		-

    - 10.7513 (0.135172s) -

    -     		-

    - 7.2632 (0.145169s) -

    -     		-

    - 11.5765 (0.401671s) -

    -
    -
    -
    -

    Table 1.26. Operator |

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - @@ -1800,27 +1519,27 @@ @@ -1832,27 +1551,27 @@ @@ -1864,27 +1583,1171 @@ + + +
    -

    - Backend -

    -     		-

    - 64 Bits -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - fixed_int -

    -     		-

    - 1 (0.00314803s) -

    -     		-

    - 1 (0.00548233s) -

    -     		-

    - 1 (0.0125434s) -

    -     		-

    - 1 (0.0198161s) -

    -     		-

    - 1 (0.034957s) -

    -
    -

    - gmp_int -

    -     		-

    - 13.0622 (0.0411201s) -

    -     		-

    - 8.63936 (0.0473638s) -

    -     		-

    - 4.6932 (0.0588688s) -

    -     		-

    - 4.25792 (0.0843755s) -

    -     		-

    - 3.78236 (0.13222s) -

    -
    -

    - tommath_int -

    -     		-

    - 38.5896 (0.121481s) -

    -     		-

    - 22.3609 (0.12259s) -

    -     		-

    - 10.9015 (0.136742s) -

    -     		-

    - 7.68521 (0.152291s) -

    -     		-

    - 11.6322 (0.406628s) + 25.0046 (8.682s)

    - 1.03557 (0.00143356s) + 1 (0.000465841s)

    - 1.39844 (0.00290281s) + 1 (0.00102073s)

    - 3.14081 (0.0099558s) + 1 (0.00207212s)

    - 6.28067 (0.0372769s) + 1.02618 (0.0062017s)

    - 13.2101 (0.188878s) + 1.32649 (0.0190043s)

    - 1 (0.00138432s) + 2.83823 (0.00132216s)

    - 1 (0.00207575s) + 2.17537 (0.00222046s)

    - 1 (0.00316982s) + 1.46978 (0.00304557s)

    - 1 (0.00593518s) + 1 (0.00604351s)

    - 1 (0.014298s) + 1 (0.0143268s)

    - 5.31194 (0.00735345s) + 15.76 (0.00734164s)

    - 7.90724 (0.0164135s) + 15.9879 (0.0163193s)

    - 15.8581 (0.0502673s) + 21.7337 (0.0450349s)

    - 19.7526 (0.117235s) + 19.7183 (0.119168s)

    - 26.6031 (0.380373s) + 26.3445 (0.377431s) +

    +
    +
    +
    +

    Table 1.28. Operator <<

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.0119095s) +

    +     		+

    + 1 (0.0131746s) +

    +     		+

    + 1 (0.0213483s) +

    +     		+

    + 1 (0.0247552s) +

    +     		+

    + 1 (0.0339579s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.9355 (0.0230509s) +

    +     		+

    + 1.94257 (0.0255925s) +

    +     		+

    + 1.49684 (0.031955s) +

    +     		+

    + 1.79202 (0.0443618s) +

    +     		+

    + 2.0846 (0.0707887s) +

    +
    +

    + tommath_int +

    +     		+

    + 2.64273 (0.0314737s) +

    +     		+

    + 2.95612 (0.0389456s) +

    +     		+

    + 3.05842 (0.065292s) +

    +     		+

    + 3.79496 (0.0939451s) +

    +     		+

    + 4.82142 (0.163725s) +

    +
    +
    +
    +

    Table 1.29. Operator >>

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.006361s) +

    +     		+

    + 1 (0.00880189s) +

    +     		+

    + 1 (0.0180295s) +

    +     		+

    + 1 (0.0220786s) +

    +     		+

    + 1 (0.0325312s) +

    +
    +

    + gmp_int +

    +     		+

    + 4.26889 (0.0271544s) +

    +     		+

    + 3.14669 (0.0276968s) +

    +     		+

    + 1.74396 (0.0314426s) +

    +     		+

    + 1.45928 (0.0322188s) +

    +     		+

    + 1.24596 (0.0405327s) +

    +
    +

    + tommath_int +

    +     		+

    + 39.4379 (0.250865s) +

    +     		+

    + 28.6225 (0.251932s) +

    +     		+

    + 16.4543 (0.296661s) +

    +     		+

    + 14.2167 (0.313884s) +

    +     		+

    + 15.5842 (0.506974s) +

    +
    +
    +
    +

    Table 1.30. Operator &

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00298048s) +

    +     		+

    + 1 (0.00546222s) +

    +     		+

    + 1 (0.0127546s) +

    +     		+

    + 1 (0.01985s) +

    +     		+

    + 1 (0.0349286s) +

    +
    +

    + gmp_int +

    +     		+

    + 16.0105 (0.0477189s) +

    +     		+

    + 9.67027 (0.0528211s) +

    +     		+

    + 5.12678 (0.0653902s) +

    +     		+

    + 4.62316 (0.0917698s) +

    +     		+

    + 4.00837 (0.140007s) +

    +
    +

    + tommath_int +

    +     		+

    + 43.6665 (0.130147s) +

    +     		+

    + 23.8003 (0.130002s) +

    +     		+

    + 11.4242 (0.145711s) +

    +     		+

    + 7.83416 (0.155508s) +

    +     		+

    + 9.50103 (0.331858s) +

    +
    +
    +
    +

    Table 1.31. Operator &(int)

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00222291s) +

    +     		+

    + 1 (0.0035522s) +

    +     		+

    + 1 (0.0110247s) +

    +     		+

    + 1 (0.0154281s) +

    +     		+

    + 1 (0.0275044s) +

    +
    +

    + gmp_int +

    +     		+

    + 70.8538 (0.157502s) +

    +     		+

    + 42.1478 (0.149717s) +

    +     		+

    + 13.9023 (0.153268s) +

    +     		+

    + 10.3271 (0.159328s) +

    +     		+

    + 6.0529 (0.166481s) +

    +
    +

    + tommath_int +

    +     		+

    + 154.134 (0.342626s) +

    +     		+

    + 93.2035 (0.331077s) +

    +     		+

    + 31.9151 (0.351853s) +

    +     		+

    + 23.6515 (0.364899s) +

    +     		+

    + 22.0042 (0.605213s) +

    +
    +
    +
    +

    Table 1.32. Operator ^

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00307714s) +

    +     		+

    + 1 (0.00538197s) +

    +     		+

    + 1 (0.0127717s) +

    +     		+

    + 1 (0.0198304s) +

    +     		+

    + 1 (0.0345822s) +

    +
    +

    + gmp_int +

    +     		+

    + 13.9543 (0.0429392s) +

    +     		+

    + 9.92785 (0.0534314s) +

    +     		+

    + 4.80398 (0.0613552s) +

    +     		+

    + 4.35864 (0.0864335s) +

    +     		+

    + 3.887 (0.134421s) +

    +
    +

    + tommath_int +

    +     		+

    + 41.5958 (0.127996s) +

    +     		+

    + 24.2396 (0.130457s) +

    +     		+

    + 11.3666 (0.145171s) +

    +     		+

    + 8.01016 (0.158845s) +

    +     		+

    + 9.84853 (0.340584s) +

    +
    +
    +
    +

    Table 1.33. Operator ^(int)

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00236664s) +

    +     		+

    + 1 (0.0035339s) +

    +     		+

    + 1 (0.0100442s) +

    +     		+

    + 1 (0.0155814s) +

    +     		+

    + 1 (0.0293253s) +

    +
    +

    + gmp_int +

    +     		+

    + 61.4272 (0.145376s) +

    +     		+

    + 41.6319 (0.147123s) +

    +     		+

    + 14.9744 (0.150405s) +

    +     		+

    + 9.64857 (0.150338s) +

    +     		+

    + 5.46649 (0.160306s) +

    +
    +

    + tommath_int +

    +     		+

    + 145.509 (0.344367s) +

    +     		+

    + 93.9055 (0.331853s) +

    +     		+

    + 35.0456 (0.352003s) +

    +     		+

    + 22.7371 (0.354275s) +

    +     		+

    + 19.1373 (0.561207s) +

    +
    +
    +
    +

    Table 1.34. Operator |

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00295261s) +

    +     		+

    + 1 (0.00560832s) +

    +     		+

    + 1 (0.0127056s) +

    +     		+

    + 1 (0.0200759s) +

    +     		+

    + 1 (0.034651s) +

    +
    +

    + gmp_int +

    +     		+

    + 14.1091 (0.0416586s) +

    +     		+

    + 8.52475 (0.0478096s) +

    +     		+

    + 4.74593 (0.0602998s) +

    +     		+

    + 4.19694 (0.0842575s) +

    +     		+

    + 3.85525 (0.133588s) +

    +
    +

    + tommath_int +

    +     		+

    + 44.8889 (0.132539s) +

    +     		+

    + 25.2503 (0.141612s) +

    +     		+

    + 11.0488 (0.140382s) +

    +     		+

    + 7.39273 (0.148416s) +

    +     		+

    + 9.75809 (0.338127s) +

    +
    +
    +
    +

    Table 1.35. Operator |(int)

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html index 9762e244..b1186c41 100644 --- a/doc/html/boost_multiprecision/perf/realworld.html +++ b/doc/html/boost_multiprecision/perf/realworld.html @@ -22,13 +22,14 @@ cases for these functions. In each case the best performing library gets a relative score of 1, with the total execution time given in brackets. The first three libraries listed are the various floating point types provided - by this library, while for comparison, two popular C++ frontends to MPFR - (mpfr_class and mpreal) are also shown. + by this library, while for comparison, two popular C++ frontends to MPFR ( mpfr_class + and mpreal) are + also shown.

    Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on - 32-bit Windows Vista machine. + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. + The tests were run on 32-bit Windows Vista machine.

    Table 1.6. Bessel Function Performance

    @@ -110,7 +111,7 @@
    @@ -122,7 +123,7 @@ @@ -154,7 +155,7 @@ @@ -175,9 +176,9 @@

    The gmp_int backend is used via the typedef boost::multiprecision::mpz_int. It acts as a thin wrapper around - the GMP mpz_t to provide - an integer type that is a drop-in replacement for the native C++ integer - types, but with unlimited precision. + the GMP mpz_t + to provide an integer type that is a drop-in replacement for the native C++ + integer types, but with unlimited precision.

    As well as the usual conversions from arithmetic and string types, type @@ -186,8 +187,8 @@

    • - The GMP native types: mpf_t, - mpz_t, mpq_t. + The GMP native types: mpf_t, mpz_t, + mpq_t.
    • Instances of mp_number<T> that are wrappers around those types: @@ -199,18 +200,36 @@ via the data() member function of gmp_int.

      -
    +

    + Backend +

    +     		+

    + 64 Bits +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + fixed_int +

    +     		+

    + 1 (0.00244005s) +

    +     		+

    + 1 (0.0040142s) +

    +     		+

    + 1 (0.00983777s) +

    +     		+

    + 1 (0.0155223s) +

    +     		+

    + 1 (0.0293444s) +

    +
    +

    + gmp_int +

    +     		+

    + 64.6148 (0.157663s) +

    +     		+

    + 34.5827 (0.138822s) +

    +     		+

    + 14.2764 (0.140448s) +

    +     		+

    + 10.3248 (0.160264s) +

    +     		+

    + 5.33565 (0.156572s) +

    +
    +

    + tommath_int +

    +     		+

    + 137.825 (0.3363s) +

    +     		+

    + 81.1074 (0.325581s) +

    +     		+

    + 34.8737 (0.343079s) +

    +     		+

    + 22.3727 (0.347276s) +

    +     		+

    + 18.912 (0.554963s)

    - mpfr_class + mpfr_class

    		@@ -127,7 +128,7 @@

    - mpreal + mpreal

    		@@ -224,7 +225,7 @@

    - mpfr_class + mpfr_class

    		@@ -241,7 +242,7 @@

    - mpreal + mpreal

    		diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html index 87f856a8..f039c147 100644 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -468,8 +468,8 @@ versions are provided for Backend types that don't have native support for these functions. Please note however, that this default support requires the precision of the type to be a compile time constant - this means for - example that the GMP MPF Backend will not work with these functions when - that type is used at variable precision. + example that the GMP MPF Backend will + not work with these functions when that type is used at variable precision.

    Also note that with the exception of abs diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html index 6439bd4b..c59d3f9a 100644 --- a/doc/html/boost_multiprecision/tut/ints.html +++ b/doc/html/boost_multiprecision/tut/ints.html @@ -80,7 +80,7 @@

    - GMP + GMP

    		@@ -90,7 +90,8 @@

    - Dependency on GNU licenced GMP library. + Dependency on GNU licenced GMP + library.

    - Slower than GMP. + Slower than GMP.

    - Slower than GMP. + Slower than GMP.

    - - - - - -
    [Note]Note

    - Formatted IO for this type does not support octal or hexadecimal notation - for negative values, as a result performing formatted output on this type - when the argument is negative and either of the flags std::ios_base::oct - or std::ios_base::hex are set, will result in a std::runtime_error will be thrown. -

    +

    + Things you should know when using this type: +

    +
      +
    • + No changes are made to the GMP library's global settings - so you can + safely mix this type with existing code that uses GMP. +
      • +
    • + Default constructed gmp_int's + have the value zero (this is GMP's default behavior). +
      • +
    • + Formatted IO for this type does not support octal or hexadecimal notation + for negative values, as a result performing formatted output on this + type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex + are set, will result in a std::runtime_error + will be thrown. +
      • +
    • + Division by zero is handled by the GMP + library - it will trigger a division by zero signal. +
      • +
    • + Although this type is a wrapper around GMP + it will work equally well with MPIR. + Indeed use of MPIR is recomended + on Win32. +
      • +
    Example: @@ -255,34 +274,34 @@ to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision.

    -
    - - - - - -
    [Caution]Caution

    - Although mp_int is mostly - a drop in replacement for the builtin integer types, it should be noted - that it is a rather strange beast as it's a signed type that is not a 2's - complement type. As a result the bitwise operations | - & ^ - will throw a std::runtime_error exception if either of - the arguments is negative. Similarly the complement operator~ is deliberately not implemented for this - type. -

    -
    - - - - - -
    [Note]Note

    - Formatted IO for this type does not support octal or hexadecimal notation - for negative values, as a result performing formatted output on this type - when the argument is negative and either of the flags std::ios_base::oct - or std::ios_base::hex are set, will result in a std::runtime_error will be thrown. -

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed objects have the value zero (this is libtommath's + default behavior). +
      • +
    • + Although mp_int is mostly + a drop in replacement for the builtin integer types, it should be noted + that it is a rather strange beast as it's a signed type that is not a + 2's complement type. As a result the bitwise operations | & ^ will throw a std::runtime_error + exception if either of the arguments is negative. Similarly the complement + operator~ is deliberately + not implemented for this type. +
      • +
    • + Formatted IO for this type does not support octal or hexadecimal notation + for negative values, as a result performing formatted output on this + type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex + are set, will result in a std::runtime_error + will be thrown. +
      • +
    • + Division by zero will result in a hardware signal being raised by libtommath. +
      • +
    Example: @@ -351,6 +370,28 @@ designed to work just like a typical built in integer type, but with larger precision.

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed fixed_int's + have indeterminate value - just like normal built in integers. +
      • +
    • + Division by zero results in a std::runtime_error + being thrown. +
      • +
    • + Construction from a string that contains invalid non-numeric characters + results in a std::runtime_error being thrown. +
      • +
    • + Since the precision of fixed_int + is necessarily limited, care should be taken to avoid numeric overflow + when using this type unless you actually want modulo-arithmetic behavior. +
      • +
    Example: diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 184beae4..13d4cbb0 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -80,7 +80,7 @@

    - GMP + GMP

    @@ -90,7 +90,8 @@

    - Dependency on GNU licenced GMP library. + Dependency on GNU licenced GMP + library.

    @@ -122,7 +123,7 @@

    - Slower than GMP. + Slower than GMP.

    @@ -210,9 +211,10 @@

    The gmp_rational backend is used via the typedef boost::multiprecision::mpq_rational. - It acts as a thin wrapper around the GMP mpq_t - to provide a rational number type that is a drop-in replacement for the native - C++ number types, but with unlimited precision. + It acts as a thin wrapper around the GMP + mpq_t to provide a rational + number type that is a drop-in replacement for the native C++ number types, + but with unlimited precision.

    As well as the usual conversions from arithmetic and string types, instances @@ -221,8 +223,7 @@

    - +

    Last revised: January 23, 2012 at 18:58:32 GMT

    Last revised: February 15, 2012 at 18:08:37 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index c484f28b..3c18dd73 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -20,7 +20,7 @@ [import ../example/gmp_snips.cpp] [import ../example/mpfr_snips.cpp] -[import ../example/cpp_float_snips.cpp] +[import ../example/cpp_dec_float_snips.cpp] [import ../example/tommath_snips.cpp] [import ../example/fixed_int_snips.cpp] @@ -434,8 +434,8 @@ Things you should know when using this type: template class cpp_dec_float; - typedef mp_number > cpp_float_50; - typedef mp_number > cpp_float_100; + typedef mp_number > cpp_dec_float_50; + typedef mp_number > cpp_dec_float_100; }} // namespaces @@ -444,7 +444,7 @@ real-number type that is a drop-in replacement for the native C++ floating-point much greater precision. Type `cpp_dec_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter. -The typedefs cpp_float_50 and cpp_float_100 provide arithmetic types at 50 and 100 decimal digits precision +The typedefs cpp_dec_float_50 and cpp_dec_float_100 provide arithmetic types at 50 and 100 decimal digits precision respectively. There is full standard library and `numeric_limits` support available for this type. @@ -460,7 +460,7 @@ Normally these should not be visible to the user. [h5 cpp_dec_float example:] -[cpp_float_eg] +[cpp_dec_float_eg] [endsect] diff --git a/example/cpp_float_snips.cpp b/example/cpp_dec_float_snips.cpp similarity index 82% rename from example/cpp_float_snips.cpp rename to example/cpp_dec_float_snips.cpp index c16b78c3..7794c5fe 100644 --- a/example/cpp_float_snips.cpp +++ b/example/cpp_dec_float_snips.cpp @@ -8,14 +8,14 @@ void t1() { - //[cpp_float_eg + //[cpp_dec_float_eg //=#include using namespace boost::multiprecision; // Operations at fixed precision and full numeric_limits support: - cpp_float_100 b = 2; - std::cout << std::numeric_limits::digits << std::endl; + cpp_dec_float_100 b = 2; + std::cout << std::numeric_limits::digits << std::endl; std::cout << log(b) << std::endl; // print log(2) //] } diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index b4c85dae..dfe947ae 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -36,29 +36,29 @@ public: static const boost::int32_t mp_radix = 10; - static const boost::int32_t cpp_float_digits = Digits10; + static const boost::int32_t cpp_dec_float_digits = Digits10; - static const boost::int32_t cpp_float_digits10_setting = Digits10; - static const boost::int32_t cpp_float_digits10_limit = boost::integer_traits::const_max; - static const boost::int32_t cpp_float_digits10 = ((cpp_float_digits10_setting < static_cast(30)) ? static_cast(30) : ((cpp_float_digits10_setting > cpp_float_digits10_limit) ? cpp_float_digits10_limit : cpp_float_digits10_setting)); - static const boost::int32_t cpp_float_digits10_extra = static_cast(((static_cast(cpp_float_digits10) * 15LL) + 50LL) / 100LL); - static const boost::int32_t cpp_float_max_digits10 = static_cast(cpp_float_digits10 + ((cpp_float_digits10_extra < static_cast(5)) ? static_cast(5) : ((cpp_float_digits10_extra > static_cast(30)) ? static_cast(30) : cpp_float_digits10_extra))); - static const boost::int64_t cpp_float_max_exp10 = 2776234983093287512; - static const boost::int64_t cpp_float_min_exp10 = -2776234983093287512; - static const boost::int64_t cpp_float_max_exp = (cpp_float_max_exp10 / 301LL) * 1000LL; - static const boost::int64_t cpp_float_min_exp = (cpp_float_min_exp10 / 301LL) * 1000LL; + static const boost::int32_t cpp_dec_float_digits10_setting = Digits10; + static const boost::int32_t cpp_dec_float_digits10_limit = boost::integer_traits::const_max; + static const boost::int32_t cpp_dec_float_digits10 = ((cpp_dec_float_digits10_setting < static_cast(30)) ? static_cast(30) : ((cpp_dec_float_digits10_setting > cpp_dec_float_digits10_limit) ? cpp_dec_float_digits10_limit : cpp_dec_float_digits10_setting)); + static const boost::int32_t cpp_dec_float_digits10_extra = static_cast(((static_cast(cpp_dec_float_digits10) * 15LL) + 50LL) / 100LL); + static const boost::int32_t cpp_dec_float_max_digits10 = static_cast(cpp_dec_float_digits10 + ((cpp_dec_float_digits10_extra < static_cast(5)) ? static_cast(5) : ((cpp_dec_float_digits10_extra > static_cast(30)) ? static_cast(30) : cpp_dec_float_digits10_extra))); + static const boost::int64_t cpp_dec_float_max_exp10 = 2776234983093287512; + static const boost::int64_t cpp_dec_float_min_exp10 = -2776234983093287512; + static const boost::int64_t cpp_dec_float_max_exp = (cpp_dec_float_max_exp10 / 301LL) * 1000LL; + static const boost::int64_t cpp_dec_float_min_exp = (cpp_dec_float_min_exp10 / 301LL) * 1000LL; static const boost::int32_t mp_elem_digits10 = static_cast(8); - BOOST_STATIC_ASSERT(0 == cpp_float_max_exp10 % mp_elem_digits10); - BOOST_STATIC_ASSERT(cpp_float_max_exp10 == -cpp_float_min_exp10); + BOOST_STATIC_ASSERT(0 == cpp_dec_float_max_exp10 % mp_elem_digits10); + BOOST_STATIC_ASSERT(cpp_dec_float_max_exp10 == -cpp_dec_float_min_exp10); private: - static const boost::int32_t cpp_float_digits10_num_base = static_cast((cpp_float_max_digits10 / mp_elem_digits10) + (((cpp_float_max_digits10 % mp_elem_digits10) != 0) ? 1 : 0)); - static const boost::int32_t mp_elem_number = static_cast(cpp_float_digits10_num_base + 2); + static const boost::int32_t cpp_dec_float_digits10_num_base = static_cast((cpp_dec_float_max_digits10 / mp_elem_digits10) + (((cpp_dec_float_max_digits10 % mp_elem_digits10) != 0) ? 1 : 0)); + static const boost::int32_t mp_elem_number = static_cast(cpp_dec_float_digits10_num_base + 2); static const boost::int32_t mp_elem_mask = static_cast(100000000); public: - static const boost::int32_t cpp_float_total_digits10 = mp_elem_number * mp_elem_digits10; + static const boost::int32_t cpp_dec_float_total_digits10 = mp_elem_number * mp_elem_digits10; private: @@ -214,8 +214,8 @@ public: { init.do_nothing(); static bool init = false; - static const std::string str_max = std::string("9." + std::string(static_cast(cpp_float_max_digits10), static_cast('9'))) - + std::string("e+" + boost::lexical_cast(cpp_float_max_exp10)); + static const std::string str_max = std::string("9." + std::string(static_cast(cpp_dec_float_max_digits10), static_cast('9'))) + + std::string("e+" + boost::lexical_cast(cpp_dec_float_max_exp10)); static cpp_dec_float val_max; if(!init) { @@ -233,7 +233,7 @@ public: if(!init) { init = true; - val_min = std::string("1.0e" + boost::lexical_cast(cpp_float_min_exp10)).c_str(); + val_min = std::string("1.0e" + boost::lexical_cast(cpp_dec_float_min_exp10)).c_str(); } return val_min; } @@ -433,7 +433,7 @@ public: cpp_dec_float extract_integer_part (void) const; void precision(const boost::int32_t prec_digits) { - if(prec_digits >= cpp_float_digits10) + if(prec_digits >= cpp_dec_float_digits10) { prec_elem = mp_elem_number; } @@ -524,29 +524,29 @@ typename cpp_dec_float::initializer cpp_dec_float::init; template const boost::int32_t cpp_dec_float::mp_radix; template -const boost::int32_t cpp_dec_float::cpp_float_digits; +const boost::int32_t cpp_dec_float::cpp_dec_float_digits; template -const boost::int32_t cpp_dec_float::cpp_float_digits10_setting; +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_setting; template -const boost::int32_t cpp_dec_float::cpp_float_digits10_limit; +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_limit; template -const boost::int32_t cpp_dec_float::cpp_float_digits10; +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10; template -const boost::int32_t cpp_dec_float::cpp_float_digits10_extra; +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_extra; template -const boost::int32_t cpp_dec_float::cpp_float_max_digits10; +const boost::int32_t cpp_dec_float::cpp_dec_float_max_digits10; template -const boost::int64_t cpp_dec_float::cpp_float_max_exp; +const boost::int64_t cpp_dec_float::cpp_dec_float_max_exp; template -const boost::int64_t cpp_dec_float::cpp_float_min_exp; +const boost::int64_t cpp_dec_float::cpp_dec_float_min_exp; template -const boost::int64_t cpp_dec_float::cpp_float_max_exp10; +const boost::int64_t cpp_dec_float::cpp_dec_float_max_exp10; template -const boost::int64_t cpp_dec_float::cpp_float_min_exp10; +const boost::int64_t cpp_dec_float::cpp_dec_float_min_exp10; template const boost::int32_t cpp_dec_float::mp_elem_digits10; template -const boost::int32_t cpp_dec_float::cpp_float_digits10_num_base; +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_num_base; template const boost::int32_t cpp_dec_float::mp_elem_number; template @@ -744,8 +744,8 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float return *this = zero(); } - bool overflow = exp >= cpp_float_max_exp10; - if(exp == cpp_float_max_exp10) + bool overflow = exp >= cpp_dec_float_max_exp10; + if(exp == cpp_dec_float_max_exp10) { // Check to see if we really truely have an overflow or not... if(isneg()) @@ -831,7 +831,7 @@ cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float const boost::int64_t v_exp = ((!v_exp_is_neg) ? v.exp : static_cast(-v.exp)); // Check the range of the upcoming multiplication. - const bool b_result_is_out_of_range = (v_exp >= static_cast(cpp_float_max_exp10 - u_exp)); + const bool b_result_is_out_of_range = (v_exp >= static_cast(cpp_dec_float_max_exp10 - u_exp)); if(b_result_is_out_of_range) { @@ -975,8 +975,8 @@ cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const u data.front() = static_cast(carry); } - bool overflow = exp >= cpp_float_max_exp10; - if(exp == cpp_float_max_exp10) + bool overflow = exp >= cpp_dec_float_max_exp10; + if(exp == cpp_dec_float_max_exp10) { // Check to see if we really truely have an overflow or not... if(isneg()) @@ -1147,7 +1147,7 @@ cpp_dec_float& cpp_dec_float::calculate_inv() static const boost::int32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; - for(boost::int32_t digits = double_digits10_minus_one; digits <= cpp_float_max_digits10; digits *= static_cast(2)) + for(boost::int32_t digits = double_digits10_minus_one; digits <= cpp_dec_float_max_digits10; digits *= static_cast(2)) { // Adjust precision of the terms. precision(static_cast(digits * static_cast(2))); @@ -1222,7 +1222,7 @@ cpp_dec_float& cpp_dec_float::calculate_sqrt(void) static const boost::uint32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; - for(boost::int32_t digits = double_digits10_minus_one; digits <= cpp_float_max_digits10; digits *= 2u) + for(boost::int32_t digits = double_digits10_minus_one; digits <= cpp_dec_float_max_digits10; digits *= 2u) { // Adjust precision of the terms. precision(digits * 2); @@ -1668,7 +1668,7 @@ std::string cpp_dec_float::str(boost::intmax_t number_of_digits, std:: boost::intmax_t org_digits(number_of_digits); boost::int64_t my_exp = order(); if(number_of_digits == 0) - number_of_digits = cpp_float_max_digits10; + number_of_digits = cpp_dec_float_max_digits10; if(f & std::ios_base::fixed) { number_of_digits += my_exp + 1; @@ -2025,7 +2025,7 @@ bool cpp_dec_float::rd_string(const char* const s) } // Check for overflow... - if(exp > cpp_float_max_exp10) + if(exp > cpp_dec_float_max_exp10) { const bool b_result_is_neg = neg; @@ -2035,9 +2035,9 @@ bool cpp_dec_float::rd_string(const char* const s) } // ...and check for underflow. - if(exp <= cpp_float_min_exp10) + if(exp <= cpp_dec_float_min_exp10) { - if(exp == cpp_float_min_exp10) + if(exp == cpp_dec_float_min_exp10) { // Check for identity with the minimum value. cpp_dec_float test = *this; @@ -2810,8 +2810,8 @@ inline int get_sign(const cpp_dec_float& val) } -typedef mp_number > cpp_float_50; -typedef mp_number > cpp_float_100; +typedef mp_number > cpp_dec_float_50; +typedef mp_number > cpp_dec_float_100; }} @@ -2829,12 +2829,12 @@ namespace std static const bool is_modulo = false; static const bool is_iec559 = false; static const int digits = Digits10; - static const int digits10 = boost::multiprecision::cpp_dec_float::cpp_float_digits10; - static const int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_float_max_digits10; - static const boost::int64_t min_exponent = boost::multiprecision::cpp_dec_float::cpp_float_min_exp; // Type differs from int. - static const boost::int64_t min_exponent10 = boost::multiprecision::cpp_dec_float::cpp_float_min_exp10; // Type differs from int. - static const boost::int64_t max_exponent = boost::multiprecision::cpp_dec_float::cpp_float_max_exp; // Type differs from int. - static const boost::int64_t max_exponent10 = boost::multiprecision::cpp_dec_float::cpp_float_max_exp10; // Type differs from int. + static const int digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; + static const int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_digits10; + static const boost::int64_t min_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp; // Type differs from int. + static const boost::int64_t min_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp10; // Type differs from int. + static const boost::int64_t max_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp; // Type differs from int. + static const boost::int64_t max_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp10; // Type differs from int. static const int radix = boost::multiprecision::cpp_dec_float::mp_radix; static const std::float_round_style round_style = std::round_to_nearest; static const bool has_infinity = true; diff --git a/performance/linpack-benchmark.cpp b/performance/linpack-benchmark.cpp index fea8a598..8db9b096 100644 --- a/performance/linpack-benchmark.cpp +++ b/performance/linpack-benchmark.cpp @@ -27,7 +27,7 @@ typedef mpf_class real_type; typedef mpfr_class real_type; #elif defined(TEST_CPP_DEC_FLOAT) #include -typedef boost::multiprecision::cpp_float_50 real_type; +typedef boost::multiprecision::cpp_dec_float_50 real_type; #elif defined(TEST_MPFR_50) #include typedef boost::multiprecision::mpfr_float_50 real_type; @@ -912,7 +912,7 @@ real_type epslon_(real_type *x) #if defined(TEST_MPF_100) || defined(TEST_MPFR_100) || defined(TEST_GMPXX) || defined(TEST_MPFRXX) return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); #elif defined(TEST_CPP_DEC_FLOAT_BN) - return std::pow(10.0, 1-std::numeric_limits::digits10); + return std::pow(10.0, 1-std::numeric_limits::digits10); #else return CAST_TO_RT(std::numeric_limits::epsilon()); #endif @@ -1234,7 +1234,7 @@ mp_number >: times for array with leading dimension of1001 279.96 0.84 280.8 2.3813 0.83988 5014.3 -boost::multiprecision::ef::cpp_float_50: +boost::multiprecision::ef::cpp_dec_float_50: ~~~~~~~~~~~~~~~~~~~~~~~~~ norm. resid resid machep x(1) x(n) diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index 734fb8bd..c98059f9 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -609,8 +609,8 @@ int main() test > >("fixed_int", 1024); #endif #ifdef TEST_CPP_DEC_FLOAT - test("cpp_dec_float", 50); - test("cpp_dec_float", 100); + test("cpp_dec_float", 50); + test("cpp_dec_float", 100); test > >("cpp_dec_float", 500); #endif #ifdef TEST_MPFR diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index cd2ea692..195b991c 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -233,10 +233,10 @@ int main() #endif #ifdef TEST_CPP_DEC_FLOAT c.reset(); - test_bessel(); + test_bessel(); time = c.elapsed(); - std::cout << "Time for cpp_float_50 = " << time << std::endl; - std::cout << "Total allocations for cpp_float_50 = " << allocation_count << std::endl; + std::cout << "Time for cpp_dec_float_50 = " << time << std::endl; + std::cout << "Total allocations for cpp_dec_float_50 = " << allocation_count << std::endl; allocation_count = 0; #endif #ifdef TEST_MPFR_CLASS @@ -282,10 +282,10 @@ int main() #endif #ifdef TEST_CPP_DEC_FLOAT c.reset(); - test_bessel(); + test_bessel(); time = c.elapsed(); - std::cout << "Time for cpp_float_100 = " << time << std::endl; - std::cout << "Total allocations for cpp_float_100 = " << allocation_count << std::endl; + std::cout << "Time for cpp_dec_float_100 = " << time << std::endl; + std::cout << "Total allocations for cpp_dec_float_100 = " << allocation_count << std::endl; allocation_count = 0; #endif #ifdef TEST_MPFR_CLASS @@ -334,10 +334,10 @@ int main() #endif #ifdef TEST_CPP_DEC_FLOAT c.reset(); - test_polynomial(); + test_polynomial(); time = c.elapsed(); - std::cout << "Time for cpp_float_50 = " << time << std::endl; - std::cout << "Total allocations for cpp_float_50 = " << allocation_count << std::endl; + std::cout << "Time for cpp_dec_float_50 = " << time << std::endl; + std::cout << "Total allocations for cpp_dec_float_50 = " << allocation_count << std::endl; allocation_count = 0; #endif #ifdef TEST_MPFR_CLASS @@ -383,10 +383,10 @@ int main() #endif #ifdef TEST_CPP_DEC_FLOAT c.reset(); - test_polynomial(); + test_polynomial(); time = c.elapsed(); - std::cout << "Time for cpp_float_100 = " << time << std::endl; - std::cout << "Total allocations for cpp_float_100 = " << allocation_count << std::endl; + std::cout << "Time for cpp_dec_float_100 = " << time << std::endl; + std::cout << "Total allocations for cpp_dec_float_100 = " << allocation_count << std::endl; allocation_count = 0; #endif #ifdef TEST_MPFR_CLASS @@ -434,10 +434,10 @@ int main() #endif #ifdef TEST_CPP_DEC_FLOAT c.reset(); - test_nct(); + test_nct(); time = c.elapsed(); - std::cout << "Time for cpp_float_50 = " << time << std::endl; - std::cout << "Total allocations for cpp_float_50 = " << allocation_count << std::endl; + std::cout << "Time for cpp_dec_float_50 = " << time << std::endl; + std::cout << "Total allocations for cpp_dec_float_50 = " << allocation_count << std::endl; allocation_count = 0; #endif #ifdef TEST_MPFR_CLASS @@ -483,10 +483,10 @@ int main() #endif #ifdef TEST_CPP_DEC_FLOAT c.reset(); - test_nct(); + test_nct(); time = c.elapsed(); - std::cout << "Time for cpp_float_100 = " << time << std::endl; - std::cout << "Total allocations for cpp_float_100 = " << allocation_count << std::endl; + std::cout << "Time for cpp_dec_float_100 = " << time << std::endl; + std::cout << "Total allocations for cpp_dec_float_100 = " << allocation_count << std::endl; allocation_count = 0; #endif #ifdef TEST_MPFR_CLASS diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 2026ad79..9b7d1c23 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -54,7 +54,7 @@ run test_arithmetic.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_arithmetic_cpp_float ; + : test_arithmetic_cpp_dec_float ; run test_arithmetic.cpp gmp : # command line @@ -203,7 +203,7 @@ run test_numeric_limits.cpp : # requirements TEST_CPP_DEC_FLOAT [ check-target-builds ../config//has_mpfr : : no ] - : test_numeric_limits_cpp_float ; + : test_numeric_limits_cpp_dec_float ; run test_numeric_limits.cpp $(TOMMATH) : # command line @@ -314,49 +314,49 @@ run test_exp.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_exp_cpp_float ; + : test_exp_cpp_dec_float ; run test_log.cpp : # command line : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_log_cpp_float ; + : test_log_cpp_dec_float ; run test_pow.cpp : # command line : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_pow_cpp_float ; + : test_pow_cpp_dec_float ; run test_sinh.cpp : # command line : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_sinh_cpp_float ; + : test_sinh_cpp_dec_float ; run test_cosh.cpp : # command line : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_cosh_cpp_float ; + : test_cosh_cpp_dec_float ; run test_tanh.cpp : # command line : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_tanh_cpp_float ; + : test_tanh_cpp_dec_float ; run test_sin.cpp : # command line : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_sin_cpp_float ; + : test_sin_cpp_dec_float ; run test_sin.cpp gmp : # command line @@ -379,7 +379,7 @@ run test_cos.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_cos_cpp_float ; + : test_cos_cpp_dec_float ; run test_cos.cpp gmp : # command line @@ -402,7 +402,7 @@ run test_asin.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_asin_cpp_float ; + : test_asin_cpp_dec_float ; run test_asin.cpp gmp : # command line @@ -425,7 +425,7 @@ run test_acos.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_acos_cpp_float ; + : test_acos_cpp_dec_float ; run test_acos.cpp gmp : # command line @@ -456,7 +456,7 @@ run test_atan.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_atan_cpp_float ; + : test_atan_cpp_dec_float ; run test_atan.cpp mpfr : # command line @@ -507,7 +507,7 @@ run test_round.cpp : # requirements TEST_CPP_DEC_FLOAT [ check-target-builds ../config//has_mpfr : : no ] - : test_round_cpp_float ; + : test_round_cpp_dec_float ; run test_fpclassify.cpp : # command line @@ -537,7 +537,7 @@ run test_fpclassify.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_fpclassify_cpp_float ; + : test_fpclassify_cpp_dec_float ; run test_test.cpp ; @@ -547,7 +547,7 @@ run test_float_io.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - : test_float_io_cpp_float ; + : test_float_io_cpp_dec_float ; run test_float_io.cpp gmp : # command line @@ -631,7 +631,7 @@ run ../example/mpfr_snips.cpp mpfr : # requirements [ check-target-builds ../config//has_mpfr : : no ] ; -run ../example/cpp_float_snips.cpp ; +run ../example/cpp_dec_float_snips.cpp ; run ../example/tommath_snips.cpp $(TOMMATH) : # command line @@ -676,7 +676,7 @@ if $(enable-specfun) speed msvc:-bigobj release - : $(source:B)_cpp_float ; + : $(source:B)_cpp_dec_float ; } } @@ -735,7 +735,7 @@ if ! $(disable-concepts) : # input files : # requirements TEST_CPP_DEC_FLOAT - : mp_number_concept_check_cpp_float ; + : mp_number_concept_check_cpp_dec_float ; run mp_number_concept_check.cpp : # command line diff --git a/test/math/test_beta.cpp b/test/math/test_beta.cpp index c339969d..f2983d8e 100644 --- a/test/math/test_beta.cpp +++ b/test/math/test_beta.cpp @@ -58,7 +58,7 @@ void expected_results() ".*", // platform ".*gmp.*", // test type(s) "Beta Function: Medium.*", // test data group - "boost::math::beta", 2200, 1000); // test function + "boost::math::beta", 2300, 1000); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/mp_number_concept_check.cpp b/test/mp_number_concept_check.cpp index 120c6285..15d56a27 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -4,7 +4,7 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) // -// This tests two things: that cpp_float_50 meets our +// This tests two things: that cpp_dec_float_50 meets our // conceptual requirements, and that we can instantiate // all our distributions and special functions on this type. // @@ -82,7 +82,7 @@ void foo() instantiate(boost::multiprecision::mp_number >()); #endif #ifdef TEST_CPP_DEC_FLOAT - instantiate(boost::multiprecision::cpp_float_50()); + instantiate(boost::multiprecision::cpp_dec_float_50()); #endif } @@ -113,7 +113,7 @@ int main() BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_CPP_DEC_FLOAT - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif } diff --git a/test/test_acos.cpp b/test/test_acos.cpp index b9141907..de5957c1 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -100,8 +100,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 9d5fb9b7..14d3da67 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -1003,7 +1003,7 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); + test(); #endif #ifdef TEST_MPFR test(); diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 0e27b21c..ac6b4541 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -96,8 +96,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_atan.cpp b/test/test_atan.cpp index 33eed7b7..ae0886d0 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -242,8 +242,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_cos.cpp b/test/test_cos.cpp index 5bdc516c..81138810 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -296,8 +296,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index 97c4b945..ef6b372c 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -138,8 +138,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_exp.cpp b/test/test_exp.cpp index a39fa411..34a19a35 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -178,8 +178,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp index 936a9b21..caeb2c02 100644 --- a/test/test_float_io.cpp +++ b/test/test_float_io.cpp @@ -257,13 +257,13 @@ int main() test_round_trip(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); /* // cpp_dec_float has extra guard digits that messes this up: - test_round_trip(); - test_round_trip(); + test_round_trip(); + test_round_trip(); */ #endif #ifdef TEST_MPF_50 diff --git a/test/test_fpclassify.cpp b/test/test_fpclassify.cpp index a1cdb99e..732a2069 100644 --- a/test/test_fpclassify.cpp +++ b/test/test_fpclassify.cpp @@ -310,8 +310,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif #ifdef TEST_BACKEND test >(); diff --git a/test/test_log.cpp b/test/test_log.cpp index c1f5c52c..a8a743d3 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -206,8 +206,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index 32d126d2..6cc53374 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -195,8 +195,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif #ifdef TEST_MPFR test(); diff --git a/test/test_pow.cpp b/test/test_pow.cpp index a56483ba..3c909653 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -581,8 +581,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_round.cpp b/test/test_round.cpp index 593a3335..4efa024a 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -387,8 +387,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif #ifdef TEST_BACKEND test >(); diff --git a/test/test_sin.cpp b/test/test_sin.cpp index b17edda4..23470635 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -290,7 +290,7 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index 4dd8b8ad..cfa84bdb 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -214,8 +214,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp index a1fd03fa..ec801267 100644 --- a/test/test_sqrt.cpp +++ b/test/test_sqrt.cpp @@ -184,8 +184,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index b80ae9a9..71a05174 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -133,8 +133,8 @@ int main() test(); #endif #ifdef TEST_CPP_DEC_FLOAT - test(); - test(); + test(); + test(); #endif return boost::report_errors(); } diff --git a/test/test_test.cpp b/test/test_test.cpp index e62a9c57..68a277f4 100644 --- a/test/test_test.cpp +++ b/test/test_test.cpp @@ -17,7 +17,7 @@ void proc_that_throws() int main() { - boost::multiprecision::cpp_float_50 a1(1), a2(1), b(3), c(-2); + boost::multiprecision::cpp_dec_float_50 a1(1), a2(1), b(3), c(-2); BOOST_WARN(a1); BOOST_WARN(a1 == b); @@ -26,8 +26,8 @@ int main() BOOST_CHECK(boost::detail::test_errors() == 1); --boost::detail::test_errors(); - boost::multiprecision::cpp_float_50 a_tol = a1 + a1 * 100 * std::numeric_limits::epsilon(); - boost::multiprecision::cpp_float_50 tol = 100 * std::numeric_limits::epsilon(); + boost::multiprecision::cpp_dec_float_50 a_tol = a1 + a1 * 100 * std::numeric_limits::epsilon(); + boost::multiprecision::cpp_dec_float_50 tol = 100 * std::numeric_limits::epsilon(); BOOST_CHECK_CLOSE(a1, a_tol, tol * 102); // Passes BOOST_WARN_CLOSE(a1, a_tol, tol * 98); // fails From 1b73913249b34ad999bfa65c7af7a40073935422 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 21 Feb 2012 18:19:02 +0000 Subject: [PATCH 114/256] Fix some C++0x errors. [SVN r77088] --- include/boost/multiprecision/gmp.hpp | 54 ++++++++++++------------ include/boost/multiprecision/tommath.hpp | 18 ++++---- 2 files changed, 36 insertions(+), 36 deletions(-) diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 4311e5b0..b5e6c8d0 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1926,9 +1926,9 @@ class numeric_limits > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type (min)() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type (max)() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type lowest() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int digits = 0; BOOST_STATIC_CONSTEXPR int digits10 = 0; BOOST_STATIC_CONSTEXPR int max_digits10 = 0; @@ -1936,8 +1936,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 0; - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -1947,10 +1947,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -1969,15 +1969,15 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT + static number_type (min)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT + static number_type (max)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } BOOST_STATIC_CONSTEXPR int digits = INT_MAX; BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L; BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; @@ -1985,8 +1985,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = true; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -1996,10 +1996,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -2018,15 +2018,15 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT + static number_type (min)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT + static number_type (max)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } // Digits are unbounded, use zero for now: BOOST_STATIC_CONSTEXPR int digits = 0; BOOST_STATIC_CONSTEXPR int digits10 = 0; @@ -2035,8 +2035,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -2046,10 +2046,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 41eeaf76..1f697a5e 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -463,15 +463,15 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT + static number_type (min)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT + static number_type (max)() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } BOOST_STATIC_CONSTEXPR int digits = INT_MAX; BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L; BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; @@ -479,8 +479,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = true; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -490,10 +490,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; From eb631b8291bd36dd50f8651c0a577e502874234a Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 27 Feb 2012 17:10:46 +0000 Subject: [PATCH 115/256] Fix some multiple initializations of mpz_t. [SVN r77128] --- include/boost/multiprecision/gmp.hpp | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index b5e6c8d0..308607c7 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -896,8 +896,8 @@ struct gmp_int unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpz_t t; - mpz_init(m_data); - mpz_init(t); + mpz_set_ui(m_data, 0); + mpz_init_set_ui(t, 0); while(i) { mpz_set_ui(t, static_cast(i & mask)); @@ -955,7 +955,7 @@ struct gmp_int int e; long double f, term; - mpz_init_set_ui(m_data, 0u); + mpz_set_ui(m_data, 0u); f = frexp(a, &e); From fda499be4378add9aa4a763f7ac3c1be3df21742 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 29 Feb 2012 10:42:23 +0000 Subject: [PATCH 116/256] Fix memory leaks / bugs in mpq_t and tommath support. [SVN r77140] --- include/boost/multiprecision/gmp.hpp | 4 ++-- include/boost/multiprecision/tommath.hpp | 3 ++- 2 files changed, 4 insertions(+), 3 deletions(-) diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 308607c7..648d60c5 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1460,7 +1460,7 @@ struct gmp_rational unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpq_t t; - mpq_init(m_data); + mpq_set_ui(m_data, 0, 1); mpq_init(t); while(i) { @@ -1521,7 +1521,7 @@ struct gmp_rational int e; long double f, term; - mpq_init(m_data); + mpq_set_ui(m_data, 0, 1); mpq_set_ui(m_data, 0u, 1); gmp_rational t; diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 1f697a5e..683d5e5b 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -117,7 +117,7 @@ struct tommath_int int e; long double f, term; - detail::check_tommath_result(mp_init_set_int(&m_data, 0u)); + detail::check_tommath_result(mp_set_int(&m_data, 0u)); ::mp_int t; detail::check_tommath_result(mp_init(&t)); @@ -151,6 +151,7 @@ struct tommath_int tommath_int t2; detail::check_tommath_result(mp_div_2d(&m_data, -e, &m_data, &t2.data())); } + mp_clear(&t); return *this; } tommath_int& operator = (const char* s) From bea370732635d76c824c10b7ef664a233e82cd28 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 29 Feb 2012 13:05:51 +0000 Subject: [PATCH 117/256] Add initial version of an arbitrary precision integer type. Hook up some more fixed_int tests. [SVN r77141] --- include/boost/multiprecision/cpp_int.hpp | 1915 ++++++++++++++++++++ include/boost/multiprecision/fixed_int.hpp | 2 +- performance/performance_test.cpp | 13 +- test/Jamfile.v2 | 37 +- test/test_arithmetic.cpp | 18 +- test/test_cpp_int.cpp | 179 ++ test/test_numeric_limits.cpp | 21 +- 7 files changed, 2179 insertions(+), 6 deletions(-) create mode 100644 include/boost/multiprecision/cpp_int.hpp create mode 100644 test/test_cpp_int.cpp diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp new file mode 100644 index 00000000..6ffe9f8a --- /dev/null +++ b/include/boost/multiprecision/cpp_int.hpp @@ -0,0 +1,1915 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_CPP_INT_HPP +#define BOOST_MP_CPP_INT_HPP + +#include +#include +#include +#include +#include +#include +#include +#include +#include + +namespace boost{ +namespace multiprecision{ + + /* +typedef boost::uint32_t limb_type; +typedef boost::int32_t signed_limb_type; +typedef boost::uint64_t double_limb_type; +typedef boost::int64_t signed_double_limb_type; +static const limb_type max_block_10 = 1000000000; +static const limb_type digits_per_block_10 = 9; + +inline limb_type block_multiplier(int count) +{ + static const limb_type values[digits_per_block_10] + = { 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 }; + BOOST_ASSERT(count < digits_per_block_10); + return values[count]; +} +*/ +template +inline void minmax(const T& a, const T& b, T& aa, T& bb) +{ + if(a < b) + { + aa = a; + bb = b; + } + else + { + aa = b; + bb = a; + } +} + +template > +struct cpp_int_backend : private Allocator::template rebind::other +{ + typedef typename Allocator::template rebind::other allocator_type; + typedef typename allocator_type::pointer limb_pointer; + typedef typename allocator_type::const_pointer const_limb_pointer; + +private: + struct limb_data + { + unsigned capacity; + limb_pointer data; + }; + +public: + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list float_types; + + BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT); + BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u)); + BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << (limb_bits - 1)); + BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = InternalLimbs ? InternalLimbs : sizeof(limb_data) / sizeof(limb_type)); + +private: + + union data_type + { + limb_data ld; + limb_type la[internal_limb_count]; + }; + + data_type m_data; + unsigned m_limbs; + bool m_sign, m_internal; + +public: + + // + // Helper functions for getting at our internal data, and manipulating storage: + // + allocator_type& allocator(){ return *this; } + const allocator_type& allocator()const{ return *this; } + unsigned size()const { return m_limbs; } + limb_pointer limbs() { return m_internal ? m_data.la : m_data.ld.data; } + const_limb_pointer limbs()const { return m_internal ? m_data.la : m_data.ld.data; } + unsigned capacity()const { return m_internal ? internal_limb_count : m_data.ld.capacity; } + bool sign()const { return m_sign; } + void sign(bool b) + { + m_sign = b; + // Check for zero value: + if(m_sign && (m_limbs == 1)) + { + if(limbs()[0] == 0) + m_sign = false; + } + } + void resize(unsigned new_size) + { + unsigned cap = capacity(); + if(new_size > cap) + { + cap = (std::max)(cap * 4, new_size); + limb_pointer pl = allocator().allocate(cap); + std::memcpy(pl, limbs(), size() * sizeof(limb_type)); + if(!m_internal) + allocator().deallocate(limbs(), capacity()); + else + m_internal = false; + m_limbs = new_size; + m_data.ld.capacity = cap; + m_data.ld.data = pl; + } + else + { + m_limbs = new_size; + } + } + + cpp_int_backend() : m_limbs(1), m_internal(true), m_sign(false) + { + *limbs() = 0; + } + cpp_int_backend(const cpp_int_backend& o) : m_limbs(0), m_internal(true) + { + resize(o.size()); + std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + m_sign = o.m_sign; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + cpp_int_backend(cpp_int_backend&& o) : m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) + { + if(m_internal) + { + std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + } + else + { + data.ld = o.data.ld; + o.m_limbs = 0; + o.m_internal = true; + } + } +#endif + ~cpp_int_backend() + { + if(!m_internal) + allocator().deallocate(limbs(), capacity()); + } + cpp_int_backend& operator = (const cpp_int_backend& o) + { + if(this != &o) + { + m_limbs = 0; + resize(o.size()); + std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + m_sign = o.m_sign; + } + return *this; + } + cpp_int_backend& operator = (limb_type i) + { + m_limbs = 1; + *limbs() = i; + m_sign = false; + return *this; + } + cpp_int_backend& operator = (signed_limb_type i) + { + m_limbs = 1; + *limbs() = static_cast(std::abs(i)); + m_sign = i < 0; + return *this; + } + cpp_int_backend& operator = (double_limb_type i) + { + BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type)); + BOOST_STATIC_ASSERT(internal_limb_count >= 2); + limb_pointer p = limbs(); + *p = static_cast(i); + p[1] = static_cast(i >> limb_bits); + m_limbs = p[1] ? 2 : 1; + m_sign = false; + return *this; + } + cpp_int_backend& operator = (signed_double_limb_type i) + { + BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type)); + BOOST_STATIC_ASSERT(internal_limb_count >= 2); + if(i < 0) + { + m_sign = true; + i = -i; + } + else + m_sign = false; + limb_pointer p = limbs(); + *p = static_cast(i); + p[1] = static_cast(i >> limb_bits); + m_limbs = p[1] ? 2 : 1; + return *this; + } + + cpp_int_backend& operator = (long double a) + { + using default_ops::add; + using default_ops::subtract; + using std::frexp; + using std::ldexp; + using std::floor; + + if (a == 0) { + return *this = static_cast(0u); + } + + if (a == 1) { + return *this = static_cast(1u); + } + + BOOST_ASSERT(!(boost::math::isinf)(a)); + BOOST_ASSERT(!(boost::math::isnan)(a)); + + int e; + long double f, term; + *this = static_cast(0u); + + f = frexp(a, &e); + + static const limb_type shift = std::numeric_limits::digits; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + left_shift(*this, shift); + if(term > 0) + add(*this, static_cast(term)); + else + subtract(*this, static_cast(-term)); + f -= term; + } + if(e > 0) + left_shift(*this, e); + else if(e < 0) + right_shift(*this, -e); + return *this; + } + cpp_int_backend& operator = (const char* s) + { + using default_ops::multiply; + using default_ops::add; + std::size_t n = s ? std::strlen(s) : 0; + *this = static_cast(0u); + unsigned radix = 10; + bool isneg = false; + if(n && (*s == '-')) + { + --n; + ++s; + isneg = true; + } + if(n && (*s == '0')) + { + if((n > 1) && ((s[1] == 'x') || (s[1] == 'X'))) + { + radix = 16; + s +=2; + n -= 2; + } + else + { + radix = 8; + n -= 1; + } + } + if(n) + { + if(radix == 8 || radix == 16) + { + unsigned shift = radix == 8 ? 3 : 4; + unsigned block_count = limb_bits / shift; + unsigned block_shift = shift * block_count; + limb_type val, block; + while(*s) + { + block = 0; + for(unsigned i = 0; (i < block_count); ++i) + { + if(*s >= '0' && *s <= '9') + val = *s - '0'; + else if(*s >= 'a' && *s <= 'f') + val = 10 + *s - 'a'; + else if(*s >= 'A' && *s <= 'F') + val = 10 + *s - 'A'; + else + val = max_limb_value; + if(val > radix) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string.")); + } + block <<= shift; + block |= val; + if(!*++s) + { + // final shift is different: + block_shift = (i + 1) * shift; + break; + } + } + left_shift(*this, block_shift); + limbs()[0] |= block; + } + } + else + { + // Base 10, we extract blocks of size 10^9 at a time, that way + // the number of multiplications is kept to a minimum: + limb_type block_mult = max_block_10; + while(*s) + { + limb_type block = 0; + for(unsigned i = 0; i < digits_per_block_10; ++i) + { + limb_type val; + if(*s >= '0' && *s <= '9') + val = *s - '0'; + else + BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected character encountered in input.")); + block *= 10; + block += val; + if(!*++s) + { + block_mult = block_multiplier(i); + break; + } + } + multiply(*this, block_mult); + add(*this, block); + } + } + } + if(isneg) + negate(); + return *this; + } + void swap(cpp_int_backend& o) + { + std::swap(m_data, o.m_data); + std::swap(m_sign, o.m_sign); + std::swap(m_internal, o.m_internal); + std::swap(m_limbs, o.m_limbs); + } + std::string str(std::streamsize digits, std::ios_base::fmtflags f)const + { + int base = 10; + if((f & std::ios_base::oct) == std::ios_base::oct) + base = 8; + else if((f & std::ios_base::hex) == std::ios_base::hex) + base = 16; + std::string result; + + unsigned Bits = size() * limb_bits; + + if(base == 8 || base == 16) + { + limb_type shift = base == 8 ? 3 : 4; + limb_type mask = static_cast((1u << shift) - 1); + cpp_int_backend t(*this); + result.assign(Bits / shift + (Bits % shift ? 1 : 0), '0'); + int pos = result.size() - 1; + for(unsigned i = 0; i < Bits / shift; ++i) + { + char c = '0' + (t.limbs()[0] & mask); + if(c > '9') + c += 'A' - '9' - 1; + result[pos--] = c; + right_shift(t, shift); + } + if(Bits % shift) + { + mask = static_cast((1u << (Bits % shift)) - 1); + char c = '0' + (t.limbs()[0] & mask); + if(c > '9') + c += 'A' - '9'; + result[pos] = c; + } + // + // Get rid of leading zeros: + // + std::string::size_type n = result.find_first_not_of('0'); + if(!result.empty() && (n == std::string::npos)) + n = result.size() - 1; + result.erase(0, n); + if(f & std::ios_base::showbase) + { + const char* pp = base == 8 ? "0" : "0x"; + result.insert(0, pp); + } + } + else + { + result.assign(Bits / 3 + 1, '0'); + int pos = result.size() - 1; + cpp_int_backend t(*this); + cpp_int_backend r; + bool neg = false; + if(t.sign()) + { + t.negate(); + neg = true; + } + if(size() == 1) + { + result = boost::lexical_cast(t.limbs()[0]); + } + else + { + cpp_int_backend block10; + block10 = max_block_10; + while(get_sign(t) != 0) + { + cpp_int_backend t2; + divide_unsigned_helper(t2, t, block10, r); + t = t2; + limb_type v = r.limbs()[0]; + for(unsigned i = 0; i < digits_per_block_10; ++i) + { + char c = '0' + v % 10; + v /= 10; + result[pos] = c; + if(pos-- == 0) + break; + } + } + } + unsigned n = result.find_first_not_of('0'); + result.erase(0, n); + if(result.empty()) + result = "0"; + if(neg) + result.insert(0, 1, '-'); + else if(f & std::ios_base::showpos) + result.insert(0, 1, '+'); + } + return result; + } + void negate() + { + m_sign = !m_sign; + // Check for zero value: + if(m_sign && (m_limbs == 1)) + { + if(limbs()[0] == 0) + m_sign = false; + } + } + bool isneg()const + { + return m_sign; + } + int compare(const cpp_int_backend& o)const + { + if(m_sign != o.m_sign) + return m_sign ? -1 : 1; + int result = 0; + // Only do the compare if the same sign: + result = compare_unsigned(o); + + if(m_sign) + result = -result; + return result; + } + int compare_unsigned(const cpp_int_backend& o)const + { + if(m_limbs != o.m_limbs) + { + return m_limbs > o.m_limbs ? 1 : -1; + } + const_limb_pointer pa = limbs(); + const_limb_pointer pb = o.limbs(); + for(int i = m_limbs - 1; i >= 0; --i) + { + if(pa[i] != pb[i]) + return pa[i] > pb[i] ? 1 : -1; + } + return 0; + } + template + typename enable_if, int>::type compare(Arithmatic i)const + { + // braindead version: + cpp_int_backend t; + t = i; + return compare(t); + } +}; + +template +const unsigned cpp_int_backend::limb_bits; +template +const limb_type cpp_int_backend::max_limb_value; +template +const limb_type cpp_int_backend::sign_bit_mask; +template +const unsigned cpp_int_backend::internal_limb_count; + + +template +inline void add(cpp_int_backend& result, const cpp_int_backend& o) +{ + add(result, result, o); +} +template +inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +{ + using std::swap; + + // Nothing fancy, just let uintmax_t take the strain: + double_limb_type carry = 0; + unsigned m, x; + minmax(a.size(), b.size(), m, x); + if(x == 1) + { + bool s = a.sign(); + result = static_cast(*a.limbs()) + static_cast(*b.limbs()); + result.sign(s); + return; + } + result.resize(x); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr_end = pr + m; + + if(a.size() < b.size()) + swap(pa, pb); + + // First where a and b overlap: + while(pr != pr_end) + { + carry += static_cast(*pa) + static_cast(*pb); + *pr = static_cast(carry); + carry >>= cpp_int_backend::limb_bits; + ++pr, ++pa, ++pb; + } + pr_end += x - m; + // Now where only a has digits: + while(pr != pr_end) + { + if(!carry) + { + if(pa != pr) + std::memcpy(pr, pa, (pr_end - pr) * sizeof(limb_type)); + break; + } + carry += static_cast(*pa); + *pr = static_cast(carry); + carry >>= cpp_int_backend::limb_bits; + ++pr, ++pa; + } + if(carry) + { + result.resize(x + 1); + // We overflowed, need to add one more limb: + result.limbs()[x] = static_cast(carry); + } + result.sign(a.sign()); +} +template +inline void add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +{ + if(a.sign() != b.sign()) + { + subtract_unsigned(result, a, b); + return; + } + add_unsigned(result, a, b); +} + +template +inline void add_unsigned(cpp_int_backend& result, const limb_type& o) +{ + // Addition using modular arithmatic. + // Nothing fancy, just let uintmax_t take the strain: + double_limb_type carry = o; + typename cpp_int_backend::limb_pointer pr = result.limbs(); + for(unsigned i = 0; carry && (i < result.size()); ++i) + { + carry += static_cast(pr[i]); + pr[i] = static_cast(carry); + carry >>= cpp_int_backend::limb_bits; + } +} +template +inline void add(cpp_int_backend& result, const limb_type& o) +{ + if(result.sign()) + { + subtract_unsigned(result, o); + } + else + add_unsigned(result, o); +} +template +inline void add(cpp_int_backend& result, const signed_limb_type& o) +{ + if(o < 0) + subtract(result, static_cast(-o)); + else if(o > 0) + add(result, static_cast(o)); +} + +template +inline void subtract_unsigned(cpp_int_backend& result, const limb_type& o) +{ + // Subtract one limb. + // Nothing fancy, just let uintmax_t take the strain: + BOOST_STATIC_CONSTANT(double_limb_type, borrow = static_cast(cpp_int_backend::max_limb_value) + 1); + typename cpp_int_backend::limb_pointer p = result.limbs(); + if(*p > o) + { + *p -= o; + } + else if(result.size() == 1) + { + *p = o - *p; + result.negate(); + } + else + { + *p = static_cast((borrow + *p) - o); + ++p; + while(!*p) + { + *p = cpp_int_backend::max_limb_value; + ++p; + } + --*p; + if(!result.limbs()[result.size() - 1]) + result.resize(result.size() - 1); + } +} +template +inline void subtract(cpp_int_backend& result, const limb_type& o) +{ + if(result.sign()) + add_unsigned(result, o); + else + subtract_unsigned(result, o); +} +template +inline void subtract(cpp_int_backend& result, const signed_limb_type& o) +{ + if(o) + { + if(o < 0) + add(result, static_cast(-o)); + else + subtract(result, static_cast(o)); + } +} +template +inline void increment(cpp_int_backend& result) +{ + static const limb_type one = 1; + if(!result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) + ++result.limbs()[0]; + else if(result.sign() && result.limbs()[0]) + --result.limbs()[0]; + else + add(result, one); +} +template +inline void decrement(cpp_int_backend& result) +{ + static const limb_type one = 1; + if(!result.sign() && result.limbs()[0]) + --result.limbs()[0]; + else if(result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) + ++result.limbs()[0]; + else + subtract(result, one); +} +template +inline void subtract(cpp_int_backend& result, const cpp_int_backend& o) +{ + subtract(result, result, o); +} +template +inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +{ + using std::swap; + + // Nothing fancy, just let uintmax_t take the strain: + double_limb_type borrow = 0; + unsigned m, x; + minmax(a.size(), b.size(), m, x); + // + // special cases for small limb counts: + // + if(x == 1) + { + bool s = a.sign(); + limb_type al = *a.limbs(); + limb_type bl = *b.limbs(); + if(bl > al) + { + std::swap(al, bl); + s = !s; + } + result = al - bl; + result.sign(s); + return; + }/* + else if(m == 1) + { + if(b.size() == 1) + { + result = a; + subtract_unsigned(result, *b.limbs()); + } + else + { + result = b; + subtract_unsigned(result, *a.limbs()); + result.negate(); + } + return; + }*/ + result.resize(x); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + bool swapped = false; + int c = a.compare_unsigned(b); + if(c < 0) + { + swap(pa, pb); + swapped = true; + } + else if(c == 0) + { + result = 0; + return; + } + + unsigned i = 0; + BOOST_STATIC_CONSTANT(double_limb_type, borrow_value = static_cast(cpp_int_backend::max_limb_value) + 1); + // First where a and b overlap: + while(i < m) + { + borrow += pb[i]; + borrow = (borrow_value + static_cast(pa[i])) - borrow; + pr[i] = static_cast(borrow); + borrow = borrow & borrow_value ? 0 : 1; + ++i; + } + // Now where only a has digits, only as long as we've borrowed: + while(borrow && (i < x)) + { + borrow = (borrow_value + static_cast(pa[i])) - borrow; + pr[i] = static_cast(borrow); + borrow = borrow & borrow_value ? 0 : 1; + ++i; + } + // Any remaining digits are the same as those in pa: + if((x != i) && (pa != pr)) + std::memcpy(pr + i, pa + i, (x - i) * sizeof(limb_type)); + BOOST_ASSERT(0 == borrow); + + // + // We may have lost digits, if so update limb usage count: + // + i = result.size() - 1; + while(!pr[i] && i) + { + --i; + } + result.resize(i + 1); + result.sign(a.sign()); + if(swapped) + result.negate(); +} +template +inline void subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +{ + if(a.sign() != b.sign()) + { + add_unsigned(result, a, b); + return; + } + subtract_unsigned(result, a, b); +} +template +inline void multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +{ + // Very simple long multiplication, only usable for small numbers of limb_type's + // but that's the typical use case for this type anyway: + // + // Special cases first: + // + unsigned as = a.size(); + unsigned bs = b.size(); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + if(as == 1) + { + bool s = b.sign() != a.sign(); + if(bs == 1) + { + result = static_cast(*pa) * static_cast(*pb); + } + else + { + limb_type l = *pa; + result = b; + multiply(result, l); + } + result.sign(s); + return; + } + if(bs == 1) + { + limb_type l = *pb; + bool s = b.sign() != a.sign(); + result = a; + multiply(result, l); + result.sign(s); + return; + } + + if(&result == &a) + { + cpp_int_backend t(a); + multiply(result, t, b); + return; + } + if(&result == &b) + { + cpp_int_backend t(b); + multiply(result, a, t); + return; + } + + result.resize(as + bs); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + + double_limb_type carry = 0; + std::memset(pr, 0, (as + bs) * sizeof(limb_type)); + for(unsigned i = 0; i < as; ++i) + { + for(unsigned j = 0; j < bs; ++j) + { + carry += static_cast(pa[i]) * static_cast(pb[j]); + carry += pr[i + j]; + pr[i + j] = static_cast(carry); + carry >>= cpp_int_backend::limb_bits; + } + pr[i + bs] = static_cast(carry); + carry = 0; + } + // + // We may not have filled all the digits, if so update limb usage count: + // + unsigned i = result.size() - 1; + while(!pr[i] && i) + { + --i; + } + result.resize(i + 1); + // + // Set the sign of the result: + // + result.sign(a.sign() != b.sign()); +} +template +inline void multiply(cpp_int_backend& result, const cpp_int_backend& a) +{ + multiply(result, result, a); +} +template +inline void multiply(cpp_int_backend& result, cpp_int_backend& a, const limb_type& val) +{ + if(!val) + { + result = 0; + return; + } + double_limb_type carry = 0; + typename cpp_int_backend::limb_pointer p = result.limbs(); + typename cpp_int_backend::limb_pointer pe = result.limbs() + result.size(); + typename cpp_int_backend::limb_pointer pa = a.limbs(); + while(p != pe) + { + carry += static_cast(*pa * static_cast(val)); + *p = static_cast(carry); + carry >>= cpp_int_backend::limb_bits; + ++p, ++pa; + } + if(carry) + { + result.resize(result.size() + 1); + result.limbs()[result.size() - 1] = static_cast(carry); + } +} +template +inline void multiply(cpp_int_backend& result, const limb_type& val) +{ + multiply(result, result, val); +} +template +inline void multiply(cpp_int_backend& result, cpp_int_backend& a, const signed_limb_type& val) +{ + if(val > 0) + multiply(result, a, static_cast(val)); + else + { + multiply(result, a, static_cast(-val)); + result.negate(); + } +} +template +inline void multiply(cpp_int_backend& result, const signed_limb_type& val) +{ + multiply(result, result, val); +} +template +void divide_unsigned_helper(cpp_int_backend& result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) +{ + if((&result == &x) || (&r == &x)) + { + cpp_int_backend t(x); + divide_unsigned_helper(result, t, y, r); + return; + } + if((&result == &y) || (&r == &y)) + { + cpp_int_backend t(y); + divide_unsigned_helper(result, x, t, r); + return; + } + + /* + Very simple, fairly braindead long division. + Start by setting the remainder equal to x, and the + result equal to 0. Then in each loop we calculate our + "best guess" for how many times y divides into r, + add our guess to the result, and subtract guess*y + from the remainder r. One wrinkle is that the remainder + may go negative, in which case we subtract the current guess + from the result rather than adding. The value of the guess + is determined by dividing the most-significant-limb of the + current remainder by the most-significant-limb of y. + + Note that there are more efficient algorithms than this + available, in particular see Knuth Vol 2. However for small + numbers of limbs this generally outperforms the alternatives + and avoids the normalisation step which would require extra storage. + */ + + + using default_ops::subtract; + + if(&result == &r) + { + cpp_int_backend rem; + divide_unsigned_helper(result, x, y, rem); + r = rem; + return; + } + + // + // Find the most significant words of numerator and denominator. + // + limb_type y_order = y.size() - 1; + + if(y_order == 0) + { + // + // Only a single non-zero limb in the denominator, in this case + // we can use a specialized divide-by-single-limb routine which is + // much faster. This also handles division by zero: + // + divide_unsigned_helper(result, x, y.limbs()[y_order], r); + return; + } + + typename cpp_int_backend::const_limb_pointer px = x.limbs(); + typename cpp_int_backend::const_limb_pointer py = y.limbs(); + + limb_type r_order = x.size() - 1; + if((r_order == 0) && (*px == 0)) + { + // x is zero, so is the result: + r = y; + result = x; + return; + } + + r = x; + r.sign(false); + result = static_cast(0u); + // + // Check if the remainder is already less than the divisor, if so + // we already have the result. Note we try and avoid a full compare + // if we can: + // + if(r_order <= y_order) + { + if((r_order < y_order) || (r.compare(y) < 0)) + { + return; + } + } + + cpp_int_backend t; + bool r_neg = false; + + // + // See if we can short-circuit long division, and use basic arithmetic instead: + // + if(r_order == 0) + { + result = px[0] / py[0]; + r = px[0] % py[0]; + return; + } + else if(r_order == 1) + { + double_limb_type a, b; + a = (static_cast(px[1]) << cpp_int_backend::limb_bits) | px[0]; + b = y_order > 1 ? + (static_cast(py[1]) << cpp_int_backend::limb_bits) | py[0] + : py[0]; + result = a / b; + r = a % b; + return; + } + // + // prepare result: + // + result.resize(1 + r_order - y_order); + typename cpp_int_backend::const_limb_pointer prem = r.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + for(unsigned i = 1; i < 1 + r_order - y_order; ++i) + pr[i] = 0; + bool first_pass = true; + + do + { + // + // Update r_order, this can't run past the end as r must be non-zero at this point: + // + r_order = r.size() - 1; + // + // Calculate our best guess for how many times y divides into r: + // + limb_type guess; + if((prem[r_order] <= py[y_order]) && (r_order > 0)) + { + double_limb_type a, b, v; + a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; + b = py[y_order]; + v = a / b; + if(v > cpp_int_backend::max_limb_value) + guess = 1; + else + { + guess = static_cast(v); + --r_order; + } + } + else if(r_order == 0) + { + guess = prem[0] / py[y_order]; + } + else + { + double_limb_type a, b, v; + a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; + b = (y_order > 0) ? (static_cast(py[y_order]) << cpp_int_backend::limb_bits) | py[y_order - 1] : (static_cast(py[y_order]) << cpp_int_backend::limb_bits); + v = a / b; + guess = static_cast(v); + } + BOOST_ASSERT(guess); // If the guess ever gets to zero we go on forever.... + // + // Update result: + // + limb_type shift = r_order - y_order; + if(r_neg) + { + if(pr[shift] > guess) + pr[shift] -= guess; + else + { + t.resize(shift + 1); + t.limbs()[shift] = guess; + for(unsigned i = 0; i < shift; ++i) + t.limbs()[i] = 0; + subtract(result, t); + } + } + else if(cpp_int_backend::max_limb_value - pr[shift] > guess) + pr[shift] += guess; + else + { + t.resize(shift + 1); + t.limbs()[shift] = guess; + for(unsigned i = 0; i < shift; ++i) + t.limbs()[i] = 0; + add(result, t); + } + // + // Calculate guess * y, we use a fused mutiply-shift O(N) for this + // rather than a full O(N^2) multiply: + // + double_limb_type carry = 0; + t.resize(y.size() + shift + 1); + typename cpp_int_backend::limb_pointer pt = t.limbs(); + for(unsigned i = 0; i < shift; ++i) + pt[i] = 0; + for(unsigned i = 0; i < y.size(); ++i) + { + carry += static_cast(py[i]) * static_cast(guess); + pt[i + shift] = static_cast(carry); + carry >>= cpp_int_backend::limb_bits; + } + if(carry) + { + pt[t.size() - 1] = static_cast(carry); + } + else + { + t.resize(t.size() - 1); + } + // + // Update r: + // + subtract(r, t); + if(r.isneg()) + { + r.negate(); + r_neg = !r_neg; + } + // + // First time through we need to strip any leading zero, otherwise + // the termination condition goes belly-up: + // + if(first_pass) + { + first_pass = false; + while(pr[result.size() - 1] == 0) + result.resize(result.size() - 1); + } + } + // Termination condition is really just a check that r > y, but with two common + // short-circuit cases handled first: + while((r_order > y_order) || (prem[r_order] > py[y_order]) || (r.compare_unsigned(y) > 0)); + + // + // We now just have to normalise the result: + // + if(r_neg) + { + // We have one too many in the result: + decrement(result); + r.negate(); + if(y.sign()) + subtract(r, y); + else + add(r, y); + } + + BOOST_ASSERT(r.compare_unsigned(y) < 0); // remainder must be less than the divisor or our code has failed +} + +template +void divide_unsigned_helper(cpp_int_backend& result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) +{ + if((&result == &x) || (&r == &x)) + { + cpp_int_backend t(x); + divide_unsigned_helper(result, t, y, r); + return; + } + + if(&result == &r) + { + cpp_int_backend rem; + divide_unsigned_helper(result, x, y, rem); + r = rem; + return; + } + + // As above, but simplified for integer divisor: + + using default_ops::subtract; + + if(y == 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Integer Division by zero.")); + } + // + // Find the most significant word of numerator. + // + limb_type r_order = x.size() - 1; + + // + // Set remainder and result to their initial values: + // + r = x; + r.sign(false); + typename cpp_int_backend::limb_pointer pr = r.limbs(); + + if((r_order == 0) && (*pr == 0)) + { + // All the limbs in x are zero, so is the result: + return; + } + // + // check for x < y, try to do this without actually having to + // do a full comparison: + // + if((r_order == 0) && (*pr < y)) + { + result = static_cast(0u); + return; + } + + // + // See if we can short-circuit long division, and use basic arithmetic instead: + // + if(r_order == 0) + { + result = *pr / y; + result.sign(x.sign()); + r.sign(x.sign()); + *pr %= y; + return; + } + else if(r_order == 1) + { + double_limb_type a; + a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[0]; + result = a / y; + result.sign(x.sign()); + r = a % y; + r.sign(x.sign()); + return; + } + + result.resize(r_order + 1); + typename cpp_int_backend::limb_pointer pres = result.limbs(); + pres[r_order] = 0; // just in case we don't set the most significant limb below. + + do + { + // + // Calculate our best guess for how many times y divides into r: + // + if((pr[r_order] < y) && r_order) + { + double_limb_type a, b; + a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[r_order - 1]; + b = a % y; + r.resize(r.size() - 1); + --r_order; + pr[r_order] = static_cast(b); + pres[r_order] = static_cast(a / y); + } + else + { + pres[r_order] = pr[r_order] / y; + pr[r_order] %= y; + } + } + // Termination condition is really just a check that r > y, but with two common + // short-circuit cases handled first: + while(r_order || (pr[r_order] > y)); + + if(pres[result.size() - 1] == 0) + result.resize(result.size() - 1); + + result.sign(x.sign()); + r.sign(x.sign()); + + BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed +} + +template +inline void divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +{ + cpp_int_backend r; + divide_unsigned_helper(result, a, b, r); + result.sign(a.sign() != b.sign()); +} +template +inline void divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) +{ + cpp_int_backend r; + divide_unsigned_helper(result, a, b, r); +} +template +inline void divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) +{ + cpp_int_backend r; + divide_unsigned_helper(result, a, std::abs(b), r); + if(b < 0) + result.negate(); +} +template +inline void divide(cpp_int_backend& result, const cpp_int_backend& b) +{ + // There is no in place divide: + cpp_int_backend a(result); + divide(result, a, b); +} +template +inline void divide(cpp_int_backend& result, limb_type b) +{ + // There is no in place divide: + cpp_int_backend a(result); + divide(result, a, b); +} +template +inline void divide(cpp_int_backend& result, signed_limb_type b) +{ + // There is no in place divide: + cpp_int_backend a(result); + divide(result, a, b); +} +template +inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +{ + cpp_int_backend r; + divide_unsigned_helper(r, a, b, result); + result.sign(a.sign()); +} +template +inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) +{ + cpp_int_backend r; + divide_unsigned_helper(r, a, b, result); +} +template +inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) +{ + cpp_int_backend r; + divide_unsigned_helper(r, a, static_cast(std::abs(b)), result); +} +template +inline void modulus(cpp_int_backend& result, const cpp_int_backend& b) +{ + // There is no in place divide: + cpp_int_backend a(result); + modulus(result, a, b); +} +template +inline void modulus(cpp_int_backend& result, limb_type b) +{ + // There is no in place divide: + cpp_int_backend a(result); + modulus(result, a, b); +} +template +inline void modulus(cpp_int_backend& result, signed_limb_type b) +{ + // There is no in place divide: + cpp_int_backend a(result); + modulus(result, a, b); +} +template +void bitwise_op(cpp_int_backend& result, const cpp_int_backend& o, Op op) +{ + // + // There are 4 cases: + // * Both positive. + // * result negative, o positive. + // * o negative, result positive. + // * Both negative. + // + // When one arg is negative we convert to 2's complement form "on the fly", + // and then convert back to signed-magnitude form at the end. + // + // First figure out how big the result needs to be and set up some data: + // + unsigned rs = result.size(); + unsigned os = o.size(); + unsigned m, x; + minmax(rs, os, m, x); + result.resize(x); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::const_limb_pointer po = o.limbs(); + for(unsigned i = rs; i < x; ++i) + pr[i] = 0; + + limb_type next_limb = 0; + + if(!result.sign()) + { + if(!o.sign()) + { + for(unsigned i = 0; i < os; ++i) + pr[i] = op(pr[i], po[i]); + for(unsigned i = os; i < x; ++i) + pr[i] = op(pr[i], limb_type(0)); + } + else + { + // "o" is negative: + double_limb_type carry = 1; + for(unsigned i = 0; i < os; ++i) + { + carry += static_cast(~po[i]); + pr[i] = op(pr[i], static_cast(carry)); + carry >>= cpp_int_backend::limb_bits; + } + for(unsigned i = os; i < x; ++i) + { + carry += static_cast(~limb_type(0)); + pr[i] = op(pr[i], static_cast(carry)); + carry >>= cpp_int_backend::limb_bits; + } + // Set the overflow into the "extra" limb: + carry += static_cast(~limb_type(0)); + next_limb = op(limb_type(0), static_cast(carry)); + } + } + else + { + if(!o.sign()) + { + // "result" is negative: + double_limb_type carry = 1; + for(unsigned i = 0; i < os; ++i) + { + carry += static_cast(~pr[i]); + pr[i] = op(static_cast(carry), po[i]); + carry >>= cpp_int_backend::limb_bits; + } + for(unsigned i = os; i < x; ++i) + { + carry += static_cast(~pr[i]); + pr[i] = op(static_cast(carry), limb_type(0)); + carry >>= cpp_int_backend::limb_bits; + } + // Set the overflow into the "extra" limb: + carry += static_cast(~limb_type(0)); + next_limb = op(static_cast(carry), limb_type(0)); + } + else + { + // both are negative: + double_limb_type r_carry = 1; + double_limb_type o_carry = 1; + for(unsigned i = 0; i < os; ++i) + { + r_carry += static_cast(~pr[i]); + o_carry += static_cast(~po[i]); + pr[i] = op(static_cast(r_carry), static_cast(o_carry)); + r_carry >>= cpp_int_backend::limb_bits; + o_carry >>= cpp_int_backend::limb_bits; + } + for(unsigned i = os; i < x; ++i) + { + r_carry += static_cast(~pr[i]); + o_carry += static_cast(~limb_type(0)); + pr[i] = op(static_cast(r_carry), static_cast(o_carry)); + r_carry >>= cpp_int_backend::limb_bits; + o_carry >>= cpp_int_backend::limb_bits; + } + // Set the overflow into the "extra" limb: + r_carry += static_cast(~limb_type(0)); + o_carry += static_cast(~limb_type(0)); + next_limb = op(static_cast(r_carry), static_cast(o_carry)); + } + } + // + // See if the result is negative or not: + // + if(static_cast(next_limb) < 0) + { + result.sign(true); + double_limb_type carry = 1; + for(unsigned i = 0; i < x; ++i) + { + carry += static_cast(~pr[i]); + pr[i] = static_cast(carry); + carry >>= cpp_int_backend::limb_bits; + } + } + else + result.sign(false); + // + // Strip leading zeros: + // + while(result.limbs()[result.size()-1] == 0) + result.resize(result.size()-1); +} + +struct bit_and{ limb_type operator()(limb_type a, limb_type b)const{ return a & b; } }; +struct bit_or{ limb_type operator()(limb_type a, limb_type b)const{ return a | b; } }; +struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const{ return a ^ b; } }; + +template +inline void bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) +{ + bitwise_op(result, o, bit_and()); +} +#if 0 +template +inline void bitwise_and(cpp_int_backend& result, limb_type o) +{ + result.data()[cpp_int_backend::limb_count - 1] &= o; + for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) + result.data()[i] = 0; +} +template +inline void bitwise_and(cpp_int_backend& result, signed_limb_type o) +{ + result.data()[cpp_int_backend::limb_count - 1] &= o; + limb_type mask = o < 0 ? cpp_int_backend::max_limb_value : 0; + for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) + result.data()[i] &= mask; +} +template +inline void bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) +{ + for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count; ++i) + result.data()[i] |= o.data()[i]; +} +template +inline void bitwise_or(cpp_int_backend& result, limb_type o) +{ + result.data()[cpp_int_backend::limb_count - 1] |= o; +} +#endif +template +inline void bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) +{ + bitwise_op(result, o, bit_or()); +} +template +inline void bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) +{ + bitwise_op(result, o, bit_xor()); +} +#if 0 +template +inline void bitwise_xor(cpp_int_backend& result, limb_type o) +{ + result.data()[cpp_int_backend::limb_count - 1] ^= o; +} +template +inline void bitwise_xor(cpp_int_backend& result, signed_limb_type o) +{ + result.data()[cpp_int_backend::limb_count - 1] ^= o; + limb_type mask = o < 0 ? cpp_int_backend::max_limb_value : 0; + for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) + result.data()[i] ^= mask; +} +#endif +template +inline void complement(cpp_int_backend& result, const cpp_int_backend& o) +{ + // Increment and negate: + result = o; + increment(result); + result.negate(); +} +template +inline void left_shift(cpp_int_backend& result, double_limb_type s) +{ + if(!s) + return; + + limb_type offset = static_cast(s / cpp_int_backend::limb_bits); + limb_type shift = static_cast(s % cpp_int_backend::limb_bits); + + unsigned ors = result.size(); + if((ors == 1) && (!*result.limbs())) + return; // shifting zero yields zero. + unsigned rs = ors; + if(shift && (result.limbs()[rs - 1] >> (cpp_int_backend::limb_bits - shift))) + ++rs; // Most significant limb will overflow when shifted + rs += offset; + result.resize(rs); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + + unsigned i = 0; + if(shift) + { + // This code only works when shift is non-zero, otherwise we invoke undefined behaviour! + i = 0; + if(rs > ors) + { + pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift); + --rs; + } + else + { + pr[rs - 1 - i] = pr[ors - 1 - i] << shift; + if(ors > 1) + pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); + ++i; + } + for(; ors > 1 + i; ++i) + { + pr[rs - 1 - i] = pr[ors - 1 - i] << shift; + pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); + } + if(ors >= 1 + i) + { + pr[rs - 1 - i] = pr[ors - 1 - i] << shift; + ++i; + } + for(; i < rs; ++i) + pr[rs - 1 - i] = 0; + } + else + { + for(; i < ors; ++i) + pr[rs - 1 - i] = pr[ors - 1 - i]; + for(; i < rs; ++i) + pr[rs - 1 - i] = 0; + } +} +template +inline void right_shift(cpp_int_backend& result, double_limb_type s) +{ + if(!s) + return; + + limb_type offset = static_cast(s / cpp_int_backend::limb_bits); + limb_type shift = static_cast(s % cpp_int_backend::limb_bits); + unsigned ors = result.size(); + unsigned rs = ors; + if(offset >= rs) + { + result = limb_type(0); + return; + } + rs -= offset; + typename cpp_int_backend::limb_pointer pr = result.limbs(); + if((pr[ors - 1] >> shift) == 0) + --rs; + if(rs == 0) + { + result = limb_type(0); + return; + } + unsigned i = 0; + if(shift) + { + // This code only works for non-zero shift, otherwise we invoke undefined behaviour! + for(; i + offset + 1 < ors; ++i) + { + pr[i] = pr[i + offset] >> shift; + pr[i] |= pr[i + offset + 1] << (cpp_int_backend::limb_bits - shift); + } + pr[i] = pr[i + offset] >> shift; + } + else + { + for(; i < rs; ++i) + pr[i] = pr[i + offset]; + } + result.resize(rs); +} + +template +inline Integer negate_integer(Integer i, const mpl::true_&) +{ + return -i; +} +template +inline Integer negate_integer(Integer i, const mpl::false_&) +{ + return ~--i; +} + +template +inline typename enable_if, void>::type convert_to(R* result, const cpp_int_backend& backend) +{ + *result = static_cast(backend.limbs()[0]); + unsigned shift = cpp_int_backend::limb_bits; + for(unsigned i = 1; i < backend.size(); ++i) + { + *result += static_cast(backend.limbs()[i]) << shift; + shift += cpp_int_backend::limb_bits; + if(shift > std::numeric_limits::digits) + break; + } + if(backend.sign()) + { + *result = negate_integer(*result, mpl::bool_::is_signed>()); + } +} + +template +inline typename enable_if, void>::type convert_to(R* result, const cpp_int_backend& backend) +{ + typename cpp_int_backend::const_limb_pointer p = backend.limbs(); + unsigned shift = cpp_int_backend::limb_bits; + *result = static_cast(*p); + for(unsigned i = 1; i < backend.size(); ++i) + { + *result += static_cast(std::ldexp(static_cast(p[i]), shift)); + shift += cpp_int_backend::limb_bits; + } + if(backend.sign()) + *result = -*result; +} + +template +inline bool is_zero(const cpp_int_backend& val) +{ + return (val.size() == 1) && (val.limbs()[0] == 0); +} +template +inline int get_sign(const cpp_int_backend& val) +{ + return is_zero(val) ? 0 : val.sign() ? -1 : 1; +} + +namespace detail{ +// +// Get the location of the least-significant-bit: +// +template +inline unsigned get_lsb(const cpp_int_backend& a) +{ + BOOST_ASSERT(get_sign(a) != 0); + + unsigned result = 0; + // + // Find the index of the least significant limb that is non-zero: + // + unsigned index = 0; + while(!a.limbs()[index] && (index < a.size())) + ++index; + // + // Find the index of the least significant bit within that limb: + // + limb_type l = a.limbs()[index]; + while(!(l & 1u)) + { + l >>= 1; + ++result; + } + + return result + index * cpp_int_backend::limb_bits; +} + +} + +template +inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +{ + int shift; + + cpp_int_backend u(a), v(b); + + int s = get_sign(u); + + /* GCD(0,x) := x */ + if(s < 0) + { + u.negate(); + } + else if(s == 0) + { + result = v; + return; + } + s = get_sign(v); + if(s < 0) + { + v.negate(); + } + else if(s == 0) + { + result = u; + return; + } + + /* Let shift := lg K, where K is the greatest power of 2 + dividing both u and v. */ + + unsigned us = detail::get_lsb(u); + unsigned vs = detail::get_lsb(v); + shift = (std::min)(us, vs); + right_shift(u, us); + right_shift(v, vs); + + do + { + /* Now u and v are both odd, so diff(u, v) is even. + Let u = min(u, v), v = diff(u, v)/2. */ + if(u.compare(v) > 0) + u.swap(v); + subtract(v, u); + // Termination condition tries not to do a full compare if possible: + if(!v.limbs()[0] && is_zero(v)) + break; + vs = detail::get_lsb(v); + right_shift(v, vs); + BOOST_ASSERT((v.limbs()[0] & 1)); + BOOST_ASSERT((u.limbs()[0] & 1)); + } + while(true); + + result = u; + left_shift(result, shift); +} + +template +inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +{ + cpp_int_backend t; + eval_gcd(t, a, b); + + if(is_zero(t)) + { + result = 0; + } + else + { + divide(result, a, t); + multiply(result, b); + } + if(get_sign(result) < 0) + result.negate(); +} + +template +struct number_category > : public mpl::int_{}; + +typedef mp_number > cpp_int; +typedef rational_adapter > cpp_rational_backend; +typedef mp_number cpp_rational; + +}} // namespaces + + +namespace std{ + +template +class numeric_limits > > +{ + typedef boost::multiprecision::mp_number > number_type; + +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + // + // Largest and smallest numbers are bounded only by available memory, set + // to zero: + // + static number_type (min)() BOOST_MP_NOEXCEPT + { + return number_type(0); + } + static number_type (max)() BOOST_MP_NOEXCEPT + { + return number_type(0); + } + static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + BOOST_STATIC_CONSTEXPR int digits = 0; + BOOST_STATIC_CONSTEXPR int digits10 = 0; + BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = true; + BOOST_STATIC_CONSTEXPR bool is_exact = true; + BOOST_STATIC_CONSTEXPR int radix = 2; + static number_type epsilon() BOOST_MP_NOEXCEPT { return 0; } + static number_type round_error() BOOST_MP_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + static number_type infinity() BOOST_MP_NOEXCEPT { return 0; } + static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return 0; } + static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return 0; } + static number_type denorm_min() BOOST_MP_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = false; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + +} + +#endif diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index a8b99318..5ea5be09 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -1559,7 +1559,7 @@ public: if(!init) { init = true; - val = Signed ? number_type(1) << Bits - 1 : 0; + val = Signed ? number_type(number_type(1) << (Bits - 1)) : 0; } return val; } diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index c98059f9..72ef2938 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -12,7 +12,7 @@ #if !defined(TEST_MPF) && !defined(TEST_MPZ) && \ !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPQ) \ && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\ - && !defined(TEST_FIXED_INT) + && !defined(TEST_FIXED_INT) && !defined(TEST_CPP_INT) # define TEST_MPF # define TEST_MPZ # define TEST_MPQ @@ -21,6 +21,7 @@ # define TEST_MPQ # define TEST_TOMMATH # define TEST_FIXED_INT +# define TEST_CPP_INT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -48,6 +49,9 @@ #if defined(TEST_FIXED_INT) #include #endif +#if defined(TEST_CPP_INT) +#include +#endif #include #include @@ -577,6 +581,13 @@ int main() test("gmp_int", 512); test("gmp_int", 1024); #endif +#ifdef TEST_CPP_INT + test("cpp_int", 64); + test("cpp_int", 128); + test("cpp_int", 256); + test("cpp_int", 512); + test("cpp_int", 1024); +#endif #ifdef TEST_MPQ test("mpq_rational", 64); test("mpq_rational", 128); diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 9b7d1c23..47dc5082 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -142,6 +142,20 @@ run test_arithmetic.cpp TEST_FIXED_INT2 : test_arithmetic_fixed_int2 ; +run test_arithmetic.cpp + : # command line + : # input files + : # requirements + TEST_CPP_INT + : test_arithmetic_fixed_cpp_int ; + +run test_arithmetic.cpp + : # command line + : # input files + : # requirements + TEST_CPP_INT_BR + : test_arithmetic_cpp_int_br ; + run test_numeric_limits.cpp : # command line : # input files @@ -202,7 +216,6 @@ run test_numeric_limits.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - [ check-target-builds ../config//has_mpfr : : no ] : test_numeric_limits_cpp_dec_float ; run test_numeric_limits.cpp $(TOMMATH) @@ -213,6 +226,20 @@ run test_numeric_limits.cpp $(TOMMATH) [ check-target-builds ../config//has_tommath : : no ] : test_numeric_limits_tommath ; +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + TEST_CPP_INT + : test_numeric_limits_cpp_int ; + +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + TEST_FIXED_INT + : test_numeric_limits_fixed_int ; + run test_exp.cpp gmp : # command line : # input files @@ -603,6 +630,14 @@ run test_fixed_int.cpp gmp release # otherwise runtime is too slow!! ; +run test_cpp_int.cpp gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : no ] + release # otherwise runtime is too slow!! + ; + run test_rational_io.cpp $(TOMMATH) : # command line : # input files diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 14d3da67..eb2a7de0 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -7,6 +7,10 @@ # define _SCL_SECURE_NO_WARNINGS #endif +#ifdef TEST_VLD +#include +#endif + #include #include #include @@ -14,7 +18,7 @@ #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \ !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) \ && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\ - && !defined(TEST_FIXED_INT1) && !defined(TEST_FIXED_INT2) + && !defined(TEST_FIXED_INT1) && !defined(TEST_FIXED_INT2) && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_BR) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND @@ -26,6 +30,8 @@ # define TEST_TOMMATH # define TEST_FIXED_INT1 # define TEST_FIXED_INT2 +# define TEST_CPP_INT +# define TEST_CPP_INT_BR #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -56,6 +62,9 @@ #if defined(TEST_FIXED_INT1) || defined(TEST_FIXED_INT2) #include #endif +#if defined(TEST_CPP_INT) || defined(TEST_CPP_INT_BR) +#include +#endif #if defined(TEST_TOMMATH_BOOST_RATIONAL) || defined(TEST_MPZ_BOOST_RATIONAL) #include @@ -364,7 +373,6 @@ void test_integer_ops(const boost::mpl::int_(); test(); test > >(); +#endif +#ifdef TEST_CPP_INT + test(); +#endif +#ifdef TEST_CPP_INT_BR + test(); #endif return boost::report_errors(); } diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp new file mode 100644 index 00000000..ee6bcde2 --- /dev/null +++ b/test/test_cpp_int.cpp @@ -0,0 +1,179 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include +#include +#include +#include +#include "test.hpp" + +template +T generate_random(unsigned bits_wanted) +{ + static boost::random::mt19937 gen; + typedef boost::random::mt19937::result_type random_type; + + T max_val; + unsigned digits; + if(std::numeric_limits::is_bounded && (bits_wanted == std::numeric_limits::digits)) + { + max_val = (std::numeric_limits::max)(); + digits = std::numeric_limits::digits; + } + else + { + max_val = T(1) << bits_wanted; + digits = bits_wanted; + } + + unsigned bits_per_r_val = std::numeric_limits::digits - 1; + while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val; + + unsigned terms_needed = digits / bits_per_r_val + 1; + + T val = 0; + for(unsigned i = 0; i < terms_needed; ++i) + { + val *= (gen.max)(); + val += gen(); + } + val %= max_val; + return val; +} + +int main() +{ + using namespace boost::multiprecision; + typedef cpp_int packed_type; + unsigned last_error_count = 0; + for(int i = 0; i < 1000; ++i) + { + mpz_int a = generate_random(1000); + mpz_int b = generate_random(512); + mpz_int c = generate_random(256); + mpz_int d = generate_random(32); + + int si = d.convert_to(); + + packed_type a1 = a.str(); + packed_type b1 = b.str(); + packed_type c1 = c.str(); + packed_type d1 = d.str(); + + BOOST_CHECK_EQUAL(a.str(), a1.str()); + BOOST_CHECK_EQUAL(b.str(), b1.str()); + BOOST_CHECK_EQUAL(c.str(), c1.str()); + BOOST_CHECK_EQUAL(d.str(), d1.str()); + BOOST_CHECK_EQUAL(mpz_int(a+b).str(), packed_type(a1 + b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a-b).str(), packed_type(a1 - b1).str()); + BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)+b).str(), packed_type(packed_type(-a1) + b1).str()); + BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)-b).str(), packed_type(packed_type(-a1) - b1).str()); + BOOST_CHECK_EQUAL(mpz_int(c * d).str(), packed_type(c1 * d1).str()); + BOOST_CHECK_EQUAL(mpz_int(c * -d).str(), packed_type(c1 * -d1).str()); + BOOST_CHECK_EQUAL(mpz_int(-c * d).str(), packed_type(-c1 * d1).str()); + BOOST_CHECK_EQUAL(mpz_int(b * c).str(), packed_type(b1 * c1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / b).str(), packed_type(a1 / b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / -b).str(), packed_type(a1 / -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / b).str(), packed_type(-a1 / b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / d).str(), packed_type(a1 / d1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % b).str(), packed_type(a1 % b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % -b).str(), packed_type(a1 % -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % b).str(), packed_type(-a1 % b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % d).str(), packed_type(a1 % d1).str()); + // bitwise ops: + BOOST_CHECK_EQUAL(mpz_int(a|b).str(), packed_type(a1 | b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a|b).str(), packed_type(-a1 | b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a|-b).str(), packed_type(a1 | -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a|-b).str(), packed_type(-a1 | -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a&b).str(), packed_type(a1 & b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a&b).str(), packed_type(-a1 & b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a&-b).str(), packed_type(a1 & -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a&-b).str(), packed_type(-a1 & -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a^b).str(), packed_type(a1 ^ b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a^b).str(), packed_type(-a1 ^ b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a^-b).str(), packed_type(a1 ^ -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a^-b).str(), packed_type(-a1 ^ -b1).str()); + // Now check operations involving integers: + BOOST_CHECK_EQUAL(mpz_int(a + si).str(), packed_type(a1 + si).str()); + BOOST_CHECK_EQUAL(mpz_int(a + -si).str(), packed_type(a1 + -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a + si).str(), packed_type(-a1 + si).str()); + BOOST_CHECK_EQUAL(mpz_int(si + a).str(), packed_type(si + a1).str()); + BOOST_CHECK_EQUAL(mpz_int(a - si).str(), packed_type(a1 - si).str()); + BOOST_CHECK_EQUAL(mpz_int(a - -si).str(), packed_type(a1 - -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a - si).str(), packed_type(-a1 - si).str()); + BOOST_CHECK_EQUAL(mpz_int(si - a).str(), packed_type(si - a1).str()); + BOOST_CHECK_EQUAL(mpz_int(b * si).str(), packed_type(b1 * si).str()); + BOOST_CHECK_EQUAL(mpz_int(b * -si).str(), packed_type(b1 * -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-b * si).str(), packed_type(-b1 * si).str()); + BOOST_CHECK_EQUAL(mpz_int(si * b).str(), packed_type(si * b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / si).str(), packed_type(a1 / si).str()); + BOOST_CHECK_EQUAL(mpz_int(a / -si).str(), packed_type(a1 / -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / si).str(), packed_type(-a1 / si).str()); + BOOST_CHECK_EQUAL(mpz_int(a % si).str(), packed_type(a1 % si).str()); + BOOST_CHECK_EQUAL(mpz_int(a % -si).str(), packed_type(a1 % -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % si).str(), packed_type(-a1 % si).str()); + BOOST_CHECK_EQUAL(mpz_int(a|si).str(), packed_type(a1 | si).str()); + BOOST_CHECK_EQUAL(mpz_int(a&si).str(), packed_type(a1 & si).str()); + BOOST_CHECK_EQUAL(mpz_int(a^si).str(), packed_type(a1 ^ si).str()); + BOOST_CHECK_EQUAL(mpz_int(si|a).str(), packed_type(si|a1).str()); + BOOST_CHECK_EQUAL(mpz_int(si&a).str(), packed_type(si&a1).str()); + BOOST_CHECK_EQUAL(mpz_int(si^a).str(), packed_type(si^a1).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(a, b)).str(), packed_type(gcd(a1, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, d)).str(), packed_type(lcm(c1, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, b)).str(), packed_type(gcd(-a1, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, d)).str(), packed_type(lcm(-c1, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, -b)).str(), packed_type(gcd(-a1, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, -d)).str(), packed_type(lcm(-c1, -d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(a, -b)).str(), packed_type(gcd(a1, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, -d)).str(), packed_type(lcm(c1, -d1)).str()); + if(last_error_count != boost::detail::test_errors()) + { + last_error_count = boost::detail::test_errors(); + std::cout << std::hex << std::showbase; + + std::cout << "a = " << a << std::endl; + std::cout << "a1 = " << a1 << std::endl; + std::cout << "b = " << b << std::endl; + std::cout << "b1 = " << b1 << std::endl; + std::cout << "c = " << c << std::endl; + std::cout << "c1 = " << c1 << std::endl; + std::cout << "d = " << d << std::endl; + std::cout << "d1 = " << d1 << std::endl; + std::cout << "a + b = " << a+b << std::endl; + std::cout << "a1 + b1 = " << a1+b1 << std::endl; + std::cout << std::dec; + std::cout << "a - b = " << a-b << std::endl; + std::cout << "a1 - b1 = " << a1-b1 << std::endl; + std::cout << "-a + b = " << mpz_int(-a)+b << std::endl; + std::cout << "-a1 + b1 = " << packed_type(-a1)+b1 << std::endl; + std::cout << "-a - b = " << mpz_int(-a)-b << std::endl; + std::cout << "-a1 - b1 = " << packed_type(-a1)-b1 << std::endl; + std::cout << "c*d = " << c*d << std::endl; + std::cout << "c1*d1 = " << c1*d1 << std::endl; + std::cout << "b*c = " << b*c << std::endl; + std::cout << "b1*c1 = " << b1*c1 << std::endl; + std::cout << "a/b = " << a/b << std::endl; + std::cout << "a1/b1 = " << a1/b1 << std::endl; + std::cout << "a/d = " << a/d << std::endl; + std::cout << "a1/d1 = " << a1/d1 << std::endl; + std::cout << "a%b = " << a%b << std::endl; + std::cout << "a1%b1 = " << a1%b1 << std::endl; + std::cout << "a%d = " << a%d << std::endl; + std::cout << "a1%d1 = " << a1%d1 << std::endl; + } + } + return boost::report_errors(); +} + + + diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index 6cc53374..ddec4db1 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -9,7 +9,9 @@ #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && !defined(TEST_TOMMATH) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \ + !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && \ + !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) && !defined(TEST_FIXED_INT) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND @@ -19,6 +21,8 @@ # define TEST_CPP_DEC_FLOAT # define TEST_MPQ # define TEST_TOMMATH +# define TEST_FIXED_INT +# define TEST_CPP_INT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -44,6 +48,12 @@ #ifdef TEST_TOMMATH #include #endif +#ifdef TEST_FIXED_INT +#include +#endif +#ifdef TEST_CPP_INT +#include +#endif #define PRINT(x)\ std::cout << BOOST_STRINGIZE(x) << " = " << std::numeric_limits::x << std::endl; @@ -206,6 +216,15 @@ int main() #endif #ifdef TEST_TOMMATH test(); +#endif +#ifdef TEST_FIXED_INT + test(); + test(); + test(); + test(); +#endif +#ifdef TEST_CPP_INT + test(); #endif return boost::report_errors(); } From f2cb591accfdfa4c196cda8f9f085562ab2bbf8c Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 29 Feb 2012 18:26:34 +0000 Subject: [PATCH 118/256] Fix a few GCC C++0x warnings and errors [SVN r77143] --- .../concepts/mp_number_architypes.hpp | 18 +++++++++--------- include/boost/multiprecision/cpp_int.hpp | 6 +++--- include/boost/multiprecision/fixed_int.hpp | 4 ++-- include/boost/multiprecision/mpfr.hpp | 18 +++++++++--------- 4 files changed, 23 insertions(+), 23 deletions(-) diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index bfa941be..61de59c7 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -198,15 +198,15 @@ class numeric_limits typedef std::numeric_limits base_type; typedef boost::multiprecision::concepts::mp_number_float_architype number_type; public: - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; } - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } + static number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } + static number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } + static number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } + static number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); } + static number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; } + static number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); } + static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); } + static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); } + static number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } }; } diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 6ffe9f8a..e68c7a93 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -130,7 +130,7 @@ public: } } - cpp_int_backend() : m_limbs(1), m_internal(true), m_sign(false) + cpp_int_backend() : m_limbs(1), m_sign(false), m_internal(true) { *limbs() = 0; } @@ -149,7 +149,7 @@ public: } else { - data.ld = o.data.ld; + m_data.ld = o.m_data.ld; o.m_limbs = 0; o.m_internal = true; } @@ -1703,7 +1703,7 @@ inline typename enable_if, void>::type convert_to(R* result, cons { *result += static_cast(backend.limbs()[i]) << shift; shift += cpp_int_backend::limb_bits; - if(shift > std::numeric_limits::digits) + if(shift > static_cast(std::numeric_limits::digits)) break; } if(backend.sign()) diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index 5ea5be09..051fab4f 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -24,7 +24,7 @@ typedef boost::int64_t signed_double_limb_type; static const limb_type max_block_10 = 1000000000; static const limb_type digits_per_block_10 = 9; -inline limb_type block_multiplier(int count) +inline limb_type block_multiplier(unsigned count) { static const limb_type values[digits_per_block_10] = { 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 }; @@ -941,7 +941,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1] % y; return; } - else if(r_order == static_cast(fixed_int::limb_count) - 2) + else if(r_order == static_cast(fixed_int::limb_count) - 2) { double_limb_type a; a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1]; diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index aed383e2..fc7e7f05 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -1156,9 +1156,9 @@ class numeric_limits > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type (min)() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type (max)() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type lowest() BOOST_MP_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR int digits = 0; BOOST_STATIC_CONSTEXPR int digits10 = 0; BOOST_STATIC_CONSTEXPR int max_digits10 = 0; @@ -1166,8 +1166,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 0; - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type round_error() BOOST_MP_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -1177,10 +1177,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type infinity() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; From d45e66bc36c6c29e1298ce1c051a886dfd444b68 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 2 Mar 2012 18:41:33 +0000 Subject: [PATCH 119/256] Improve subtract performance. [SVN r77156] --- include/boost/multiprecision/cpp_int.hpp | 10 ++++------ 1 file changed, 4 insertions(+), 6 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index e68c7a93..ef485f4f 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -760,22 +760,20 @@ inline void subtract_unsigned(cpp_int_backend& result, } unsigned i = 0; - BOOST_STATIC_CONSTANT(double_limb_type, borrow_value = static_cast(cpp_int_backend::max_limb_value) + 1); // First where a and b overlap: while(i < m) { - borrow += pb[i]; - borrow = (borrow_value + static_cast(pa[i])) - borrow; + borrow = static_cast(pa[i]) - static_cast(pb[i]) - borrow; pr[i] = static_cast(borrow); - borrow = borrow & borrow_value ? 0 : 1; + borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; ++i; } // Now where only a has digits, only as long as we've borrowed: while(borrow && (i < x)) { - borrow = (borrow_value + static_cast(pa[i])) - borrow; + borrow = static_cast(pa[i]) - borrow; pr[i] = static_cast(borrow); - borrow = borrow & borrow_value ? 0 : 1; + borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; ++i; } // Any remaining digits are the same as those in pa: From 8f0e6e12b2c373df487cef6d4cba54e1d5d389e6 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 3 Mar 2012 15:25:35 +0000 Subject: [PATCH 120/256] Fix range error [SVN r77175] --- include/boost/multiprecision/cpp_int.hpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index ef485f4f..2b55369b 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1507,7 +1507,7 @@ void bitwise_op(cpp_int_backend& result, const cpp_int // // Strip leading zeros: // - while(result.limbs()[result.size()-1] == 0) + while((result.size() > 1) && (result.limbs()[result.size()-1] == 0)) result.resize(result.size()-1); } From 6e494e59fdbe9acded02f61588a919f5d193aa3b Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 3 Mar 2012 18:39:37 +0000 Subject: [PATCH 121/256] Begin refactoring cpp_int code. [SVN r77180] --- include/boost/multiprecision/cpp_int.hpp | 33 +------------- .../multiprecision/detail/cpp_int_core.hpp | 44 +++++++++++++++++++ include/boost/multiprecision/fixed_int.hpp | 16 +------ 3 files changed, 46 insertions(+), 47 deletions(-) create mode 100644 include/boost/multiprecision/detail/cpp_int_core.hpp diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 2b55369b..63c47bc9 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -13,43 +13,12 @@ #include #include #include -#include +#include #include namespace boost{ namespace multiprecision{ - /* -typedef boost::uint32_t limb_type; -typedef boost::int32_t signed_limb_type; -typedef boost::uint64_t double_limb_type; -typedef boost::int64_t signed_double_limb_type; -static const limb_type max_block_10 = 1000000000; -static const limb_type digits_per_block_10 = 9; - -inline limb_type block_multiplier(int count) -{ - static const limb_type values[digits_per_block_10] - = { 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 }; - BOOST_ASSERT(count < digits_per_block_10); - return values[count]; -} -*/ -template -inline void minmax(const T& a, const T& b, T& aa, T& bb) -{ - if(a < b) - { - aa = a; - bb = b; - } - else - { - aa = b; - bb = a; - } -} - template > struct cpp_int_backend : private Allocator::template rebind::other { diff --git a/include/boost/multiprecision/detail/cpp_int_core.hpp b/include/boost/multiprecision/detail/cpp_int_core.hpp new file mode 100644 index 00000000..338eab26 --- /dev/null +++ b/include/boost/multiprecision/detail/cpp_int_core.hpp @@ -0,0 +1,44 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_CPP_INT_CORE_HPP +#define BOOST_MP_CPP_INT_CORE_HPP + +namespace boost{ namespace multiprecision{ + +typedef boost::uint32_t limb_type; +typedef boost::int32_t signed_limb_type; +typedef boost::uint64_t double_limb_type; +typedef boost::int64_t signed_double_limb_type; +static const limb_type max_block_10 = 1000000000; +static const limb_type digits_per_block_10 = 9; + +inline limb_type block_multiplier(unsigned count) +{ + static const limb_type values[digits_per_block_10] + = { 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 }; + BOOST_ASSERT(count < digits_per_block_10); + return values[count]; +} + +template +inline void minmax(const T& a, const T& b, T& aa, T& bb) +{ + if(a < b) + { + aa = a; + bb = b; + } + else + { + aa = b; + bb = a; + } +} + +}} + +#endif // BOOST_MP_CPP_INT_CORE_HPP + diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index 051fab4f..d183b6dd 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -10,6 +10,7 @@ #include #include #include +#include #include #include #include @@ -17,21 +18,6 @@ namespace boost{ namespace multiprecision{ -typedef boost::uint32_t limb_type; -typedef boost::int32_t signed_limb_type; -typedef boost::uint64_t double_limb_type; -typedef boost::int64_t signed_double_limb_type; -static const limb_type max_block_10 = 1000000000; -static const limb_type digits_per_block_10 = 9; - -inline limb_type block_multiplier(unsigned count) -{ - static const limb_type values[digits_per_block_10] - = { 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 }; - BOOST_ASSERT(count < digits_per_block_10); - return values[count]; -} - template struct fixed_int { From 5500ad3ea86cd187fc5f743066bfbaab6f75f112 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 8 Mar 2012 10:34:37 +0000 Subject: [PATCH 122/256] Add support for fixed precision and unsigned cpp_int's. [SVN r77260] --- include/boost/multiprecision/cpp_int.hpp | 1074 +++++++++++++++------- test/test_arithmetic.cpp | 2 + test/test_cpp_int.cpp | 144 +-- test/test_numeric_limits.cpp | 13 +- 4 files changed, 846 insertions(+), 387 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 63c47bc9..9efa5147 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -19,8 +19,11 @@ namespace boost{ namespace multiprecision{ -template > -struct cpp_int_backend : private Allocator::template rebind::other +template > +struct cpp_int_backend; + +template > +struct cpp_int_base : private Allocator::template rebind::other { typedef typename Allocator::template rebind::other allocator_type; typedef typename allocator_type::pointer limb_pointer; @@ -34,17 +37,18 @@ private: }; public: - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list float_types; - BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT); BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u)); BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << (limb_bits - 1)); - BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = InternalLimbs ? InternalLimbs : sizeof(limb_data) / sizeof(limb_type)); + BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = + MinBits + ? MinBits / limb_bits + (MinBits % limb_bits ? 1 : 0) + : sizeof(limb_data) / sizeof(limb_type)); + BOOST_STATIC_CONSTANT(bool, variable = true); + + BOOST_STATIC_ASSERT_MESSAGE(Signed, "There is curently no support for unsigned arbitrary precision integers."); private: - union data_type { limb_data ld; @@ -56,7 +60,6 @@ private: bool m_sign, m_internal; public: - // // Helper functions for getting at our internal data, and manipulating storage: // @@ -98,19 +101,24 @@ public: m_limbs = new_size; } } + void normalize() + { + limb_pointer p = limbs(); + while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; + } - cpp_int_backend() : m_limbs(1), m_sign(false), m_internal(true) + cpp_int_base() : m_limbs(1), m_sign(false), m_internal(true) { *limbs() = 0; } - cpp_int_backend(const cpp_int_backend& o) : m_limbs(0), m_internal(true) + cpp_int_base(const cpp_int_base& o) : m_limbs(0), m_internal(true) { resize(o.size()); std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); m_sign = o.m_sign; } #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_backend(cpp_int_backend&& o) : m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) + cpp_int_base(cpp_int_base&& o) : m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) { if(m_internal) { @@ -124,12 +132,12 @@ public: } } #endif - ~cpp_int_backend() + ~cpp_int_base() { if(!m_internal) allocator().deallocate(limbs(), capacity()); } - cpp_int_backend& operator = (const cpp_int_backend& o) + void assign(const cpp_int_base& o) { if(this != &o) { @@ -138,20 +146,242 @@ public: std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); m_sign = o.m_sign; } + } + void negate() + { + m_sign = !m_sign; + // Check for zero value: + if(m_sign && (m_limbs == 1)) + { + if(limbs()[0] == 0) + m_sign = false; + } + } + bool isneg()const + { + return m_sign; + } + void do_swap(cpp_int_base& o) + { + std::swap(m_data, o.m_data); + std::swap(m_sign, o.m_sign); + std::swap(m_internal, o.m_internal); + std::swap(m_limbs, o.m_limbs); + } +}; + +template +struct cpp_int_base +{ + typedef limb_type* limb_pointer; + typedef const limb_type* const_limb_pointer; + +public: + BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT); + BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u)); + BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << (limb_bits - 1)); + BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = MinBits / limb_bits + (MinBits % limb_bits ? 1 : 0)); + BOOST_STATIC_CONSTANT(bool, variable = false); + BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs"); + +private: + limb_type m_data[internal_limb_count]; + boost::uint16_t m_limbs; + bool m_sign; + +public: + // + // Helper functions for getting at our internal data, and manipulating storage: + // + unsigned size()const { return m_limbs; } + limb_pointer limbs() { return m_data; } + const_limb_pointer limbs()const { return m_data; } + bool sign()const { return m_sign; } + void sign(bool b) + { + m_sign = b; + // Check for zero value: + if(m_sign && (m_limbs == 1)) + { + if(limbs()[0] == 0) + m_sign = false; + } + } + void resize(unsigned new_size) + { + m_limbs = (std::min)(new_size, internal_limb_count); + } + void normalize() + { + limb_pointer p = limbs(); + while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; + } + + cpp_int_base() : m_limbs(1), m_sign(false) + { + *limbs() = 0; + } + cpp_int_base(const cpp_int_base& o) : m_limbs(0) + { + resize(o.size()); + std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + m_sign = o.m_sign; + } +#ifndef BOOST_NO_RVALUE_REFERENCES + cpp_int_base(cpp_int_base&& o) : m_limbs(o.m_limbs), m_sign(o.m_sign) + { + std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + } +#endif + ~cpp_int_base() {} + void assign(const cpp_int_base& o) + { + if(this != &o) + { + resize(o.size()); + std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + m_sign = o.m_sign; + } + } + void negate() + { + m_sign = !m_sign; + // Check for zero value: + if(m_sign && (m_limbs == 1)) + { + if(limbs()[0] == 0) + m_sign = false; + } + } + bool isneg()const + { + return m_sign; + } + void do_swap(cpp_int_base& o) + { + for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i) + std::swap(m_data[i], o.m_data[i]); + std::swap(m_sign, o.m_sign); + std::swap(m_limbs, o.m_limbs); + } +}; + +template +struct cpp_int_base +{ + typedef limb_type* limb_pointer; + typedef const limb_type* const_limb_pointer; + +public: + BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT); + BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u)); + BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << (limb_bits - 1)); + BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = MinBits / limb_bits + (MinBits % limb_bits ? 1 : 0)); + BOOST_STATIC_CONSTANT(bool, variable = false); + BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs"); + +private: + limb_type m_data[internal_limb_count]; + limb_type m_limbs; + +public: + // + // Helper functions for getting at our internal data, and manipulating storage: + // + unsigned size()const { return m_limbs; } + limb_pointer limbs() { return m_data; } + const_limb_pointer limbs()const { return m_data; } + bool sign()const { return false; } + void sign(bool b) { if(b) negate(); } + void resize(unsigned new_size) + { + m_limbs = (std::min)(new_size, internal_limb_count); + } + void normalize() + { + limb_pointer p = limbs(); + while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; + } + + cpp_int_base() : m_limbs(1) + { + *limbs() = 0; + } + cpp_int_base(const cpp_int_base& o) : m_limbs(0) + { + resize(o.size()); + std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + } +#ifndef BOOST_NO_RVALUE_REFERENCES + cpp_int_base(cpp_int_base&& o) : m_limbs(o.m_limbs) + { + std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + } +#endif + ~cpp_int_base() {} + void assign(const cpp_int_base& o) + { + if(this != &o) + { + resize(o.size()); + std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + } + } + void negate() + { + // Not so much a negate as a complement - this gets called when subtraction + // would result in a "negative" number: + unsigned i; + for(i = m_limbs; i < internal_limb_count; ++i) + m_data[i] = 0; + m_limbs = internal_limb_count; + for(i = 0; i < internal_limb_count; ++i) + m_data[i] = ~m_data[i]; + normalize(); + increment(static_cast& >(*this)); + } + bool isneg()const + { + return false; + } + void do_swap(cpp_int_base& o) + { + for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i) + std::swap(m_data[i], o.m_data[i]); + std::swap(m_limbs, o.m_limbs); + } +}; + +template +struct cpp_int_backend : public cpp_int_base +{ +public: + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list float_types; + + cpp_int_backend(){} + cpp_int_backend(const cpp_int_backend& o) : cpp_int_base(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + cpp_int_backend(cpp_int_backend&& o) : cpp_int_base(o) {} +#endif + cpp_int_backend& operator = (const cpp_int_backend& o) + { + this->assign(o); return *this; } cpp_int_backend& operator = (limb_type i) { - m_limbs = 1; - *limbs() = i; - m_sign = false; + this->resize(1); + *this->limbs() = i; + this->sign(false); return *this; } cpp_int_backend& operator = (signed_limb_type i) { - m_limbs = 1; - *limbs() = static_cast(std::abs(i)); - m_sign = i < 0; + this->resize(1); + *this->limbs() = static_cast(std::abs(i)); + this->sign(i < 0); return *this; } cpp_int_backend& operator = (double_limb_type i) @@ -161,25 +391,27 @@ public: limb_pointer p = limbs(); *p = static_cast(i); p[1] = static_cast(i >> limb_bits); - m_limbs = p[1] ? 2 : 1; - m_sign = false; + this->resize(p[1] ? 2 : 1); + this->sign(false); return *this; } cpp_int_backend& operator = (signed_double_limb_type i) { BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type)); BOOST_STATIC_ASSERT(internal_limb_count >= 2); + bool s = false; if(i < 0) { - m_sign = true; + s = true; i = -i; } else - m_sign = false; - limb_pointer p = limbs(); + this->sign(false); + limb_pointer p = this->limbs(); *p = static_cast(i); p[1] = static_cast(i >> limb_bits); - m_limbs = p[1] ? 2 : 1; + resize(p[1] ? 2 : 1); + this->sign(s); return *this; } @@ -329,10 +561,7 @@ public: } void swap(cpp_int_backend& o) { - std::swap(m_data, o.m_data); - std::swap(m_sign, o.m_sign); - std::swap(m_internal, o.m_internal); - std::swap(m_limbs, o.m_limbs); + this->do_swap(o); } std::string str(std::streamsize digits, std::ios_base::fmtflags f)const { @@ -347,6 +576,8 @@ public: if(base == 8 || base == 16) { + if(this->sign()) + BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported.")); limb_type shift = base == 8 ? 3 : 4; limb_type mask = static_cast((1u << shift) - 1); cpp_int_backend t(*this); @@ -428,41 +659,27 @@ public: } return result; } - void negate() - { - m_sign = !m_sign; - // Check for zero value: - if(m_sign && (m_limbs == 1)) - { - if(limbs()[0] == 0) - m_sign = false; - } - } - bool isneg()const - { - return m_sign; - } int compare(const cpp_int_backend& o)const { - if(m_sign != o.m_sign) - return m_sign ? -1 : 1; + if(sign() != o.sign()) + return sign() ? -1 : 1; int result = 0; // Only do the compare if the same sign: result = compare_unsigned(o); - if(m_sign) + if(sign()) result = -result; return result; } int compare_unsigned(const cpp_int_backend& o)const { - if(m_limbs != o.m_limbs) + if(size() != o.size()) { - return m_limbs > o.m_limbs ? 1 : -1; + return size() > o.size() ? 1 : -1; } const_limb_pointer pa = limbs(); const_limb_pointer pb = o.limbs(); - for(int i = m_limbs - 1; i >= 0; --i) + for(int i = size() - 1; i >= 0; --i) { if(pa[i] != pb[i]) return pa[i] > pb[i] ? 1 : -1; @@ -479,23 +696,23 @@ public: } }; -template -const unsigned cpp_int_backend::limb_bits; -template -const limb_type cpp_int_backend::max_limb_value; -template -const limb_type cpp_int_backend::sign_bit_mask; -template -const unsigned cpp_int_backend::internal_limb_count; +template +const unsigned cpp_int_backend::limb_bits; +template +const limb_type cpp_int_backend::max_limb_value; +template +const limb_type cpp_int_backend::sign_bit_mask; +template +const unsigned cpp_int_backend::internal_limb_count; -template -inline void add(cpp_int_backend& result, const cpp_int_backend& o) +template +inline void add(cpp_int_backend& result, const cpp_int_backend& o) { add(result, result, o); } -template -inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { using std::swap; @@ -511,10 +728,10 @@ inline void add_unsigned(cpp_int_backend& result, cons return; } result.resize(x); - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); - typename cpp_int_backend::const_limb_pointer pb = b.limbs(); - typename cpp_int_backend::limb_pointer pr = result.limbs(); - typename cpp_int_backend::limb_pointer pr_end = pr + m; + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr_end = pr + m; if(a.size() < b.size()) swap(pa, pb); @@ -524,7 +741,7 @@ inline void add_unsigned(cpp_int_backend& result, cons { carry += static_cast(*pa) + static_cast(*pb); *pr = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; ++pr, ++pa, ++pb; } pr_end += x - m; @@ -539,19 +756,21 @@ inline void add_unsigned(cpp_int_backend& result, cons } carry += static_cast(*pa); *pr = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; ++pr, ++pa; } if(carry) { result.resize(x + 1); // We overflowed, need to add one more limb: - result.limbs()[x] = static_cast(carry); + if(cpp_int_backend::variable || (result.size() > x)) + result.limbs()[x] = static_cast(carry); } + result.normalize(); result.sign(a.sign()); } -template -inline void add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +inline void add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { if(a.sign() != b.sign()) { @@ -561,22 +780,31 @@ inline void add(cpp_int_backend& result, const cpp_int add_unsigned(result, a, b); } -template -inline void add_unsigned(cpp_int_backend& result, const limb_type& o) +template +inline void add_unsigned(cpp_int_backend& result, const limb_type& o) { // Addition using modular arithmatic. // Nothing fancy, just let uintmax_t take the strain: double_limb_type carry = o; - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); for(unsigned i = 0; carry && (i < result.size()); ++i) { carry += static_cast(pr[i]); pr[i] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } + if(carry) + { + unsigned x = result.size(); + result.resize(x + 1); + // We overflowed, need to add one more limb: + if(cpp_int_backend::variable || (result.size() > x)) + result.limbs()[x] = static_cast(carry); + } + result.normalize(); } -template -inline void add(cpp_int_backend& result, const limb_type& o) +template +inline void add(cpp_int_backend& result, const limb_type& o) { if(result.sign()) { @@ -585,8 +813,8 @@ inline void add(cpp_int_backend& result, const limb_ty else add_unsigned(result, o); } -template -inline void add(cpp_int_backend& result, const signed_limb_type& o) +template +inline void add(cpp_int_backend& result, const signed_limb_type& o) { if(o < 0) subtract(result, static_cast(-o)); @@ -594,13 +822,13 @@ inline void add(cpp_int_backend& result, const signed_ add(result, static_cast(o)); } -template -inline void subtract_unsigned(cpp_int_backend& result, const limb_type& o) +template +inline void subtract_unsigned(cpp_int_backend& result, const limb_type& o) { // Subtract one limb. // Nothing fancy, just let uintmax_t take the strain: - BOOST_STATIC_CONSTANT(double_limb_type, borrow = static_cast(cpp_int_backend::max_limb_value) + 1); - typename cpp_int_backend::limb_pointer p = result.limbs(); + BOOST_STATIC_CONSTANT(double_limb_type, borrow = static_cast(cpp_int_backend::max_limb_value) + 1); + typename cpp_int_backend::limb_pointer p = result.limbs(); if(*p > o) { *p -= o; @@ -616,24 +844,23 @@ inline void subtract_unsigned(cpp_int_backend& result, ++p; while(!*p) { - *p = cpp_int_backend::max_limb_value; + *p = cpp_int_backend::max_limb_value; ++p; } --*p; - if(!result.limbs()[result.size() - 1]) - result.resize(result.size() - 1); + result.normalize(); } } -template -inline void subtract(cpp_int_backend& result, const limb_type& o) +template +inline void subtract(cpp_int_backend& result, const limb_type& o) { if(result.sign()) add_unsigned(result, o); else subtract_unsigned(result, o); } -template -inline void subtract(cpp_int_backend& result, const signed_limb_type& o) +template +inline void subtract(cpp_int_backend& result, const signed_limb_type& o) { if(o) { @@ -643,35 +870,35 @@ inline void subtract(cpp_int_backend& result, const si subtract(result, static_cast(o)); } } -template -inline void increment(cpp_int_backend& result) +template +inline void increment(cpp_int_backend& result) { static const limb_type one = 1; - if(!result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) + if(!result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) ++result.limbs()[0]; else if(result.sign() && result.limbs()[0]) --result.limbs()[0]; else add(result, one); } -template -inline void decrement(cpp_int_backend& result) +template +inline void decrement(cpp_int_backend& result) { static const limb_type one = 1; if(!result.sign() && result.limbs()[0]) --result.limbs()[0]; - else if(result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) + else if(result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) ++result.limbs()[0]; else subtract(result, one); } -template -inline void subtract(cpp_int_backend& result, const cpp_int_backend& o) +template +inline void subtract(cpp_int_backend& result, const cpp_int_backend& o) { subtract(result, result, o); } -template -inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { using std::swap; @@ -695,26 +922,11 @@ inline void subtract_unsigned(cpp_int_backend& result, result = al - bl; result.sign(s); return; - }/* - else if(m == 1) - { - if(b.size() == 1) - { - result = a; - subtract_unsigned(result, *b.limbs()); - } - else - { - result = b; - subtract_unsigned(result, *a.limbs()); - result.negate(); - } - return; - }*/ + } result.resize(x); - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); - typename cpp_int_backend::const_limb_pointer pb = b.limbs(); - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); bool swapped = false; int c = a.compare_unsigned(b); if(c < 0) @@ -734,7 +946,7 @@ inline void subtract_unsigned(cpp_int_backend& result, { borrow = static_cast(pa[i]) - static_cast(pb[i]) - borrow; pr[i] = static_cast(borrow); - borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; + borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; ++i; } // Now where only a has digits, only as long as we've borrowed: @@ -742,7 +954,7 @@ inline void subtract_unsigned(cpp_int_backend& result, { borrow = static_cast(pa[i]) - borrow; pr[i] = static_cast(borrow); - borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; + borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; ++i; } // Any remaining digits are the same as those in pa: @@ -753,18 +965,13 @@ inline void subtract_unsigned(cpp_int_backend& result, // // We may have lost digits, if so update limb usage count: // - i = result.size() - 1; - while(!pr[i] && i) - { - --i; - } - result.resize(i + 1); + result.normalize(); result.sign(a.sign()); if(swapped) result.negate(); } -template -inline void subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +inline void subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { if(a.sign() != b.sign()) { @@ -773,8 +980,8 @@ inline void subtract(cpp_int_backend& result, const cp } subtract_unsigned(result, a, b); } -template -inline void multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +inline void multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { // Very simple long multiplication, only usable for small numbers of limb_type's // but that's the typical use case for this type anyway: @@ -783,8 +990,8 @@ inline void multiply(cpp_int_backend& result, const cp // unsigned as = a.size(); unsigned bs = b.size(); - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); - typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); if(as == 1) { bool s = b.sign() != a.sign(); @@ -813,55 +1020,50 @@ inline void multiply(cpp_int_backend& result, const cp if(&result == &a) { - cpp_int_backend t(a); + cpp_int_backend t(a); multiply(result, t, b); return; } if(&result == &b) { - cpp_int_backend t(b); + cpp_int_backend t(b); multiply(result, a, t); return; } result.resize(as + bs); - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); double_limb_type carry = 0; std::memset(pr, 0, (as + bs) * sizeof(limb_type)); + unsigned inner_limit = result.size() - as; for(unsigned i = 0; i < as; ++i) { - for(unsigned j = 0; j < bs; ++j) + for(unsigned j = 0; j < inner_limit; ++j) { + BOOST_ASSERT(i+j < result.size()); carry += static_cast(pa[i]) * static_cast(pb[j]); carry += pr[i + j]; pr[i + j] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } - pr[i + bs] = static_cast(carry); + if(cpp_int_backend::variable || (i + bs < result.size())) + pr[i + bs] = static_cast(carry); carry = 0; } - // - // We may not have filled all the digits, if so update limb usage count: - // - unsigned i = result.size() - 1; - while(!pr[i] && i) - { - --i; - } - result.resize(i + 1); + result.normalize(); // // Set the sign of the result: // result.sign(a.sign() != b.sign()); } -template -inline void multiply(cpp_int_backend& result, const cpp_int_backend& a) +template +inline void multiply(cpp_int_backend& result, const cpp_int_backend& a) { multiply(result, result, a); } -template -inline void multiply(cpp_int_backend& result, cpp_int_backend& a, const limb_type& val) +template +inline void multiply(cpp_int_backend& result, cpp_int_backend& a, const limb_type& val) { if(!val) { @@ -869,29 +1071,33 @@ inline void multiply(cpp_int_backend& result, cpp_int_ return; } double_limb_type carry = 0; - typename cpp_int_backend::limb_pointer p = result.limbs(); - typename cpp_int_backend::limb_pointer pe = result.limbs() + result.size(); - typename cpp_int_backend::limb_pointer pa = a.limbs(); + typename cpp_int_backend::limb_pointer p = result.limbs(); + typename cpp_int_backend::limb_pointer pe = result.limbs() + result.size(); + typename cpp_int_backend::limb_pointer pa = a.limbs(); while(p != pe) { carry += static_cast(*pa * static_cast(val)); *p = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; ++p, ++pa; } if(carry) { - result.resize(result.size() + 1); - result.limbs()[result.size() - 1] = static_cast(carry); + unsigned i = result.size(); + result.resize(i + 1); + if(cpp_int_backend::variable || (result.size() > i)) + result.limbs()[i] = static_cast(carry); } + if(!cpp_int_backend::variable) + result.normalize(); } -template -inline void multiply(cpp_int_backend& result, const limb_type& val) +template +inline void multiply(cpp_int_backend& result, const limb_type& val) { multiply(result, result, val); } -template -inline void multiply(cpp_int_backend& result, cpp_int_backend& a, const signed_limb_type& val) +template +inline void multiply(cpp_int_backend& result, cpp_int_backend& a, const signed_limb_type& val) { if(val > 0) multiply(result, a, static_cast(val)); @@ -901,23 +1107,23 @@ inline void multiply(cpp_int_backend& result, cpp_int_ result.negate(); } } -template -inline void multiply(cpp_int_backend& result, const signed_limb_type& val) +template +inline void multiply(cpp_int_backend& result, const signed_limb_type& val) { multiply(result, result, val); } -template -void divide_unsigned_helper(cpp_int_backend& result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) +template +void divide_unsigned_helper(cpp_int_backend& result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) { if((&result == &x) || (&r == &x)) { - cpp_int_backend t(x); + cpp_int_backend t(x); divide_unsigned_helper(result, t, y, r); return; } if((&result == &y) || (&r == &y)) { - cpp_int_backend t(y); + cpp_int_backend t(y); divide_unsigned_helper(result, x, t, r); return; } @@ -945,7 +1151,7 @@ void divide_unsigned_helper(cpp_int_backend& result, c if(&result == &r) { - cpp_int_backend rem; + cpp_int_backend rem; divide_unsigned_helper(result, x, y, rem); r = rem; return; @@ -967,8 +1173,8 @@ void divide_unsigned_helper(cpp_int_backend& result, c return; } - typename cpp_int_backend::const_limb_pointer px = x.limbs(); - typename cpp_int_backend::const_limb_pointer py = y.limbs(); + typename cpp_int_backend::const_limb_pointer px = x.limbs(); + typename cpp_int_backend::const_limb_pointer py = y.limbs(); limb_type r_order = x.size() - 1; if((r_order == 0) && (*px == 0)) @@ -995,7 +1201,7 @@ void divide_unsigned_helper(cpp_int_backend& result, c } } - cpp_int_backend t; + cpp_int_backend t; bool r_neg = false; // @@ -1010,9 +1216,9 @@ void divide_unsigned_helper(cpp_int_backend& result, c else if(r_order == 1) { double_limb_type a, b; - a = (static_cast(px[1]) << cpp_int_backend::limb_bits) | px[0]; + a = (static_cast(px[1]) << cpp_int_backend::limb_bits) | px[0]; b = y_order > 1 ? - (static_cast(py[1]) << cpp_int_backend::limb_bits) | py[0] + (static_cast(py[1]) << cpp_int_backend::limb_bits) | py[0] : py[0]; result = a / b; r = a % b; @@ -1022,8 +1228,8 @@ void divide_unsigned_helper(cpp_int_backend& result, c // prepare result: // result.resize(1 + r_order - y_order); - typename cpp_int_backend::const_limb_pointer prem = r.limbs(); - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::const_limb_pointer prem = r.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); for(unsigned i = 1; i < 1 + r_order - y_order; ++i) pr[i] = 0; bool first_pass = true; @@ -1041,10 +1247,10 @@ void divide_unsigned_helper(cpp_int_backend& result, c if((prem[r_order] <= py[y_order]) && (r_order > 0)) { double_limb_type a, b, v; - a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; + a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; b = py[y_order]; v = a / b; - if(v > cpp_int_backend::max_limb_value) + if(v > cpp_int_backend::max_limb_value) guess = 1; else { @@ -1059,8 +1265,8 @@ void divide_unsigned_helper(cpp_int_backend& result, c else { double_limb_type a, b, v; - a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; - b = (y_order > 0) ? (static_cast(py[y_order]) << cpp_int_backend::limb_bits) | py[y_order - 1] : (static_cast(py[y_order]) << cpp_int_backend::limb_bits); + a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; + b = (y_order > 0) ? (static_cast(py[y_order]) << cpp_int_backend::limb_bits) | py[y_order - 1] : (static_cast(py[y_order]) << cpp_int_backend::limb_bits); v = a / b; guess = static_cast(v); } @@ -1082,7 +1288,7 @@ void divide_unsigned_helper(cpp_int_backend& result, c subtract(result, t); } } - else if(cpp_int_backend::max_limb_value - pr[shift] > guess) + else if(cpp_int_backend::max_limb_value - pr[shift] > guess) pr[shift] += guess; else { @@ -1098,14 +1304,14 @@ void divide_unsigned_helper(cpp_int_backend& result, c // double_limb_type carry = 0; t.resize(y.size() + shift + 1); - typename cpp_int_backend::limb_pointer pt = t.limbs(); + typename cpp_int_backend::limb_pointer pt = t.limbs(); for(unsigned i = 0; i < shift; ++i) pt[i] = 0; for(unsigned i = 0; i < y.size(); ++i) { carry += static_cast(py[i]) * static_cast(guess); pt[i + shift] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } if(carry) { @@ -1156,19 +1362,19 @@ void divide_unsigned_helper(cpp_int_backend& result, c BOOST_ASSERT(r.compare_unsigned(y) < 0); // remainder must be less than the divisor or our code has failed } -template -void divide_unsigned_helper(cpp_int_backend& result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) +template +void divide_unsigned_helper(cpp_int_backend& result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) { if((&result == &x) || (&r == &x)) { - cpp_int_backend t(x); + cpp_int_backend t(x); divide_unsigned_helper(result, t, y, r); return; } if(&result == &r) { - cpp_int_backend rem; + cpp_int_backend rem; divide_unsigned_helper(result, x, y, rem); r = rem; return; @@ -1192,7 +1398,7 @@ void divide_unsigned_helper(cpp_int_backend& result, c // r = x; r.sign(false); - typename cpp_int_backend::limb_pointer pr = r.limbs(); + typename cpp_int_backend::limb_pointer pr = r.limbs(); if((r_order == 0) && (*pr == 0)) { @@ -1223,7 +1429,7 @@ void divide_unsigned_helper(cpp_int_backend& result, c else if(r_order == 1) { double_limb_type a; - a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[0]; + a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[0]; result = a / y; result.sign(x.sign()); r = a % y; @@ -1232,7 +1438,7 @@ void divide_unsigned_helper(cpp_int_backend& result, c } result.resize(r_order + 1); - typename cpp_int_backend::limb_pointer pres = result.limbs(); + typename cpp_int_backend::limb_pointer pres = result.limbs(); pres[r_order] = 0; // just in case we don't set the most significant limb below. do @@ -1243,7 +1449,7 @@ void divide_unsigned_helper(cpp_int_backend& result, c if((pr[r_order] < y) && r_order) { double_limb_type a, b; - a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[r_order - 1]; + a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[r_order - 1]; b = a % y; r.resize(r.size() - 1); --r_order; @@ -1269,90 +1475,90 @@ void divide_unsigned_helper(cpp_int_backend& result, c BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed } -template -inline void divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +inline void divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(result, a, b, r); result.sign(a.sign() != b.sign()); } -template -inline void divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) +template +inline void divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(result, a, b, r); } -template -inline void divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) +template +inline void divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(result, a, std::abs(b), r); if(b < 0) result.negate(); } -template -inline void divide(cpp_int_backend& result, const cpp_int_backend& b) +template +inline void divide(cpp_int_backend& result, const cpp_int_backend& b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); divide(result, a, b); } -template -inline void divide(cpp_int_backend& result, limb_type b) +template +inline void divide(cpp_int_backend& result, limb_type b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); divide(result, a, b); } -template -inline void divide(cpp_int_backend& result, signed_limb_type b) +template +inline void divide(cpp_int_backend& result, signed_limb_type b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); divide(result, a, b); } -template -inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(r, a, b, result); result.sign(a.sign()); } -template -inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) +template +inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(r, a, b, result); } -template -inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) +template +inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(r, a, static_cast(std::abs(b)), result); } -template -inline void modulus(cpp_int_backend& result, const cpp_int_backend& b) +template +inline void modulus(cpp_int_backend& result, const cpp_int_backend& b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); modulus(result, a, b); } -template -inline void modulus(cpp_int_backend& result, limb_type b) +template +inline void modulus(cpp_int_backend& result, limb_type b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); modulus(result, a, b); } -template -inline void modulus(cpp_int_backend& result, signed_limb_type b) +template +inline void modulus(cpp_int_backend& result, signed_limb_type b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); modulus(result, a, b); } -template -void bitwise_op(cpp_int_backend& result, const cpp_int_backend& o, Op op) +template +void bitwise_op(cpp_int_backend& result, const cpp_int_backend& o, Op op) { // // There are 4 cases: @@ -1371,8 +1577,8 @@ void bitwise_op(cpp_int_backend& result, const cpp_int unsigned m, x; minmax(rs, os, m, x); result.resize(x); - typename cpp_int_backend::limb_pointer pr = result.limbs(); - typename cpp_int_backend::const_limb_pointer po = o.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::const_limb_pointer po = o.limbs(); for(unsigned i = rs; i < x; ++i) pr[i] = 0; @@ -1395,13 +1601,13 @@ void bitwise_op(cpp_int_backend& result, const cpp_int { carry += static_cast(~po[i]); pr[i] = op(pr[i], static_cast(carry)); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } for(unsigned i = os; i < x; ++i) { carry += static_cast(~limb_type(0)); pr[i] = op(pr[i], static_cast(carry)); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } // Set the overflow into the "extra" limb: carry += static_cast(~limb_type(0)); @@ -1418,13 +1624,13 @@ void bitwise_op(cpp_int_backend& result, const cpp_int { carry += static_cast(~pr[i]); pr[i] = op(static_cast(carry), po[i]); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } for(unsigned i = os; i < x; ++i) { carry += static_cast(~pr[i]); pr[i] = op(static_cast(carry), limb_type(0)); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } // Set the overflow into the "extra" limb: carry += static_cast(~limb_type(0)); @@ -1440,16 +1646,16 @@ void bitwise_op(cpp_int_backend& result, const cpp_int r_carry += static_cast(~pr[i]); o_carry += static_cast(~po[i]); pr[i] = op(static_cast(r_carry), static_cast(o_carry)); - r_carry >>= cpp_int_backend::limb_bits; - o_carry >>= cpp_int_backend::limb_bits; + r_carry >>= cpp_int_backend::limb_bits; + o_carry >>= cpp_int_backend::limb_bits; } for(unsigned i = os; i < x; ++i) { r_carry += static_cast(~pr[i]); o_carry += static_cast(~limb_type(0)); pr[i] = op(static_cast(r_carry), static_cast(o_carry)); - r_carry >>= cpp_int_backend::limb_bits; - o_carry >>= cpp_int_backend::limb_bits; + r_carry >>= cpp_int_backend::limb_bits; + o_carry >>= cpp_int_backend::limb_bits; } // Set the overflow into the "extra" limb: r_carry += static_cast(~limb_type(0)); @@ -1468,106 +1674,179 @@ void bitwise_op(cpp_int_backend& result, const cpp_int { carry += static_cast(~pr[i]); pr[i] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } } else result.sign(false); - // - // Strip leading zeros: - // - while((result.size() > 1) && (result.limbs()[result.size()-1] == 0)) - result.resize(result.size()-1); + + result.normalize(); } struct bit_and{ limb_type operator()(limb_type a, limb_type b)const{ return a & b; } }; struct bit_or{ limb_type operator()(limb_type a, limb_type b)const{ return a | b; } }; struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const{ return a ^ b; } }; -template -inline void bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) +template +inline void bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) { bitwise_op(result, o, bit_and()); } #if 0 -template -inline void bitwise_and(cpp_int_backend& result, limb_type o) +template +inline void bitwise_and(cpp_int_backend& result, limb_type o) { - result.data()[cpp_int_backend::limb_count - 1] &= o; - for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) + result.data()[cpp_int_backend::limb_count - 1] &= o; + for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) result.data()[i] = 0; } -template -inline void bitwise_and(cpp_int_backend& result, signed_limb_type o) +template +inline void bitwise_and(cpp_int_backend& result, signed_limb_type o) { - result.data()[cpp_int_backend::limb_count - 1] &= o; - limb_type mask = o < 0 ? cpp_int_backend::max_limb_value : 0; - for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) + result.data()[cpp_int_backend::limb_count - 1] &= o; + limb_type mask = o < 0 ? cpp_int_backend::max_limb_value : 0; + for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) result.data()[i] &= mask; } -template -inline void bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) +template +inline void bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) { - for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count; ++i) + for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count; ++i) result.data()[i] |= o.data()[i]; } -template -inline void bitwise_or(cpp_int_backend& result, limb_type o) +template +inline void bitwise_or(cpp_int_backend& result, limb_type o) { - result.data()[cpp_int_backend::limb_count - 1] |= o; + result.data()[cpp_int_backend::limb_count - 1] |= o; } #endif -template -inline void bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) +template +inline void bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) { bitwise_op(result, o, bit_or()); } -template -inline void bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) +template +inline void bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) { bitwise_op(result, o, bit_xor()); } #if 0 -template -inline void bitwise_xor(cpp_int_backend& result, limb_type o) +template +inline void bitwise_xor(cpp_int_backend& result, limb_type o) { - result.data()[cpp_int_backend::limb_count - 1] ^= o; + result.data()[cpp_int_backend::limb_count - 1] ^= o; } -template -inline void bitwise_xor(cpp_int_backend& result, signed_limb_type o) +template +inline void bitwise_xor(cpp_int_backend& result, signed_limb_type o) { - result.data()[cpp_int_backend::limb_count - 1] ^= o; - limb_type mask = o < 0 ? cpp_int_backend::max_limb_value : 0; - for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) + result.data()[cpp_int_backend::limb_count - 1] ^= o; + limb_type mask = o < 0 ? cpp_int_backend::max_limb_value : 0; + for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) result.data()[i] ^= mask; } #endif -template -inline void complement(cpp_int_backend& result, const cpp_int_backend& o) +template +inline void complement(cpp_int_backend& result, const cpp_int_backend& o) { // Increment and negate: result = o; increment(result); result.negate(); } -template -inline void left_shift(cpp_int_backend& result, double_limb_type s) +template +inline void left_shift(cpp_int_backend& result, double_limb_type s) { if(!s) return; - limb_type offset = static_cast(s / cpp_int_backend::limb_bits); - limb_type shift = static_cast(s % cpp_int_backend::limb_bits); + limb_type offset = static_cast(s / cpp_int_backend::limb_bits); + limb_type shift = static_cast(s % cpp_int_backend::limb_bits); + + if(offset > cpp_int_backend::internal_limb_count) + { + result = static_cast(0); + return; + } unsigned ors = result.size(); if((ors == 1) && (!*result.limbs())) return; // shifting zero yields zero. unsigned rs = ors; - if(shift && (result.limbs()[rs - 1] >> (cpp_int_backend::limb_bits - shift))) + if(shift && (result.limbs()[rs - 1] >> (cpp_int_backend::limb_bits - shift))) ++rs; // Most significant limb will overflow when shifted rs += offset; result.resize(rs); - typename cpp_int_backend::limb_pointer pr = result.limbs(); + bool truncated = result.size() != rs; + if(truncated) + rs = result.size(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + + unsigned i = 0; + if(shift) + { + // This code only works when shift is non-zero, otherwise we invoke undefined behaviour! + i = 0; + if(!truncated) + { + if(rs > ors) + { + pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift); + --rs; + } + else + { + pr[rs - 1 - i] = pr[ors - 1 - i] << shift; + if(ors > 1) + pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); + ++i; + } + } + for(; ors > 1 + i; ++i) + { + pr[rs - 1 - i] = pr[ors - 1 - i] << shift; + pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); + } + if(ors >= 1 + i) + { + pr[rs - 1 - i] = pr[ors - 1 - i] << shift; + ++i; + } + for(; i < rs; ++i) + pr[rs - 1 - i] = 0; + } + else + { + for(; i < ors; ++i) + pr[rs - 1 - i] = pr[ors - 1 - i]; + for(; i < rs; ++i) + pr[rs - 1 - i] = 0; + } + // + // We may have shifted off the end and have leading zeros: + // + if(truncated) + { + result.normalize(); + } +} +template +inline void left_shift(cpp_int_backend& result, double_limb_type s) +{ + if(!s) + return; + + limb_type offset = static_cast(s / cpp_int_backend::limb_bits); + limb_type shift = static_cast(s % cpp_int_backend::limb_bits); + + unsigned ors = result.size(); + if((ors == 1) && (!*result.limbs())) + return; // shifting zero yields zero. + unsigned rs = ors; + if(shift && (result.limbs()[rs - 1] >> (cpp_int_backend::limb_bits - shift))) + ++rs; // Most significant limb will overflow when shifted + rs += offset; + result.resize(rs); + typename cpp_int_backend::limb_pointer pr = result.limbs(); unsigned i = 0; if(shift) @@ -1576,20 +1855,20 @@ inline void left_shift(cpp_int_backend& result, double i = 0; if(rs > ors) { - pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift); + pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift); --rs; } else { pr[rs - 1 - i] = pr[ors - 1 - i] << shift; if(ors > 1) - pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); + pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); ++i; } for(; ors > 1 + i; ++i) { pr[rs - 1 - i] = pr[ors - 1 - i] << shift; - pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); + pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); } if(ors >= 1 + i) { @@ -1607,14 +1886,14 @@ inline void left_shift(cpp_int_backend& result, double pr[rs - 1 - i] = 0; } } -template -inline void right_shift(cpp_int_backend& result, double_limb_type s) +template +inline void right_shift(cpp_int_backend& result, double_limb_type s) { if(!s) return; - limb_type offset = static_cast(s / cpp_int_backend::limb_bits); - limb_type shift = static_cast(s % cpp_int_backend::limb_bits); + limb_type offset = static_cast(s / cpp_int_backend::limb_bits); + limb_type shift = static_cast(s % cpp_int_backend::limb_bits); unsigned ors = result.size(); unsigned rs = ors; if(offset >= rs) @@ -1623,7 +1902,7 @@ inline void right_shift(cpp_int_backend& result, doubl return; } rs -= offset; - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); if((pr[ors - 1] >> shift) == 0) --rs; if(rs == 0) @@ -1638,7 +1917,7 @@ inline void right_shift(cpp_int_backend& result, doubl for(; i + offset + 1 < ors; ++i) { pr[i] = pr[i + offset] >> shift; - pr[i] |= pr[i + offset + 1] << (cpp_int_backend::limb_bits - shift); + pr[i] |= pr[i + offset + 1] << (cpp_int_backend::limb_bits - shift); } pr[i] = pr[i + offset] >> shift; } @@ -1661,15 +1940,15 @@ inline Integer negate_integer(Integer i, const mpl::false_&) return ~--i; } -template -inline typename enable_if, void>::type convert_to(R* result, const cpp_int_backend& backend) +template +inline typename enable_if, void>::type convert_to(R* result, const cpp_int_backend& backend) { *result = static_cast(backend.limbs()[0]); - unsigned shift = cpp_int_backend::limb_bits; + unsigned shift = cpp_int_backend::limb_bits; for(unsigned i = 1; i < backend.size(); ++i) { *result += static_cast(backend.limbs()[i]) << shift; - shift += cpp_int_backend::limb_bits; + shift += cpp_int_backend::limb_bits; if(shift > static_cast(std::numeric_limits::digits)) break; } @@ -1679,28 +1958,28 @@ inline typename enable_if, void>::type convert_to(R* result, cons } } -template -inline typename enable_if, void>::type convert_to(R* result, const cpp_int_backend& backend) +template +inline typename enable_if, void>::type convert_to(R* result, const cpp_int_backend& backend) { - typename cpp_int_backend::const_limb_pointer p = backend.limbs(); - unsigned shift = cpp_int_backend::limb_bits; + typename cpp_int_backend::const_limb_pointer p = backend.limbs(); + unsigned shift = cpp_int_backend::limb_bits; *result = static_cast(*p); for(unsigned i = 1; i < backend.size(); ++i) { *result += static_cast(std::ldexp(static_cast(p[i]), shift)); - shift += cpp_int_backend::limb_bits; + shift += cpp_int_backend::limb_bits; } if(backend.sign()) *result = -*result; } -template -inline bool is_zero(const cpp_int_backend& val) +template +inline bool is_zero(const cpp_int_backend& val) { return (val.size() == 1) && (val.limbs()[0] == 0); } -template -inline int get_sign(const cpp_int_backend& val) +template +inline int get_sign(const cpp_int_backend& val) { return is_zero(val) ? 0 : val.sign() ? -1 : 1; } @@ -1709,8 +1988,8 @@ namespace detail{ // // Get the location of the least-significant-bit: // -template -inline unsigned get_lsb(const cpp_int_backend& a) +template +inline unsigned get_lsb(const cpp_int_backend& a) { BOOST_ASSERT(get_sign(a) != 0); @@ -1731,17 +2010,17 @@ inline unsigned get_lsb(const cpp_int_backend& a) ++result; } - return result + index * cpp_int_backend::limb_bits; + return result + index * cpp_int_backend::limb_bits; } } -template -inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { int shift; - cpp_int_backend u(a), v(b); + cpp_int_backend u(a), v(b); int s = get_sign(u); @@ -1796,10 +2075,10 @@ inline void eval_gcd(cpp_int_backend& result, const cp left_shift(result, shift); } -template -inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { - cpp_int_backend t; + cpp_int_backend t; eval_gcd(t, a, b); if(is_zero(t)) @@ -1815,8 +2094,8 @@ inline void eval_lcm(cpp_int_backend& result, const cp result.negate(); } -template -struct number_category > : public mpl::int_{}; +template +struct number_category > : public mpl::int_{}; typedef mp_number > cpp_int; typedef rational_adapter > cpp_rational_backend; @@ -1827,10 +2106,10 @@ typedef mp_number cpp_rational; namespace std{ -template -class numeric_limits > > +template +class numeric_limits > > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; @@ -1877,6 +2156,165 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; +template +class numeric_limits > > +{ + typedef boost::multiprecision::mp_number > number_type; + + struct inititializer + { + inititializer() + { + (std::numeric_limits::max)(); + (std::numeric_limits::min)(); + } + void do_nothing()const{} + }; + + static const inititializer init; + +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + // + // Largest and smallest numbers are bounded only by available memory, set + // to zero: + // + static number_type (min)() BOOST_MP_NOEXCEPT + { + return -(max)(); + } + static number_type (max)() BOOST_MP_NOEXCEPT + { + typedef typename number_type::backend_type backend_type; + init.do_nothing(); + static bool init = false; + static number_type val; + if(!init) + { + boost::multiprecision::limb_type l = ~static_cast(0); + unsigned c = MinBits / backend_type::limb_bits + (MinBits % backend_type::limb_bits ? 1 : 0); + for(unsigned i = 0; i < c; ++i) + { + val <<= backend_type::limb_bits; + val |= l; + } + init = true; + } + return val; + } + static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + BOOST_STATIC_CONSTEXPR int digits = MinBits; + BOOST_STATIC_CONSTEXPR int digits10 = static_cast(MinBits * 301L / 1000L); + BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = true; + BOOST_STATIC_CONSTEXPR bool is_exact = true; + BOOST_STATIC_CONSTEXPR int radix = 2; + static number_type epsilon() BOOST_MP_NOEXCEPT { return 0; } + static number_type round_error() BOOST_MP_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + static number_type infinity() BOOST_MP_NOEXCEPT { return 0; } + static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return 0; } + static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return 0; } + static number_type denorm_min() BOOST_MP_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = true; + BOOST_STATIC_CONSTEXPR bool is_modulo = true; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + +template +const typename numeric_limits > >::inititializer numeric_limits > >::init; + +template +class numeric_limits > > +{ + typedef boost::multiprecision::mp_number > number_type; + + struct inititializer + { + inititializer() + { + (std::numeric_limits::max)(); + } + void do_nothing()const{} + }; + + static const inititializer init; + +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + // + // Largest and smallest numbers are bounded only by available memory, set + // to zero: + // + static number_type (min)() BOOST_MP_NOEXCEPT + { + return number_type(0); + } + static number_type (max)() BOOST_MP_NOEXCEPT + { + typedef typename number_type::backend_type backend_type; + init.do_nothing(); + static bool init = false; + static number_type val(0); + if(!init) + { + boost::multiprecision::limb_type l = ~static_cast(0); + unsigned c = MinBits / backend_type::limb_bits + (MinBits % backend_type::limb_bits ? 1 : 0); + for(unsigned i = 0; i < c; ++i) + { + val <<= backend_type::limb_bits; + val |= l; + } + init = true; + } + return val; + } + static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + BOOST_STATIC_CONSTEXPR int digits = MinBits; + BOOST_STATIC_CONSTEXPR int digits10 = static_cast(MinBits * 301L / 1000L); + BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; + BOOST_STATIC_CONSTEXPR bool is_signed = false; + BOOST_STATIC_CONSTEXPR bool is_integer = true; + BOOST_STATIC_CONSTEXPR bool is_exact = true; + BOOST_STATIC_CONSTEXPR int radix = 2; + static number_type epsilon() BOOST_MP_NOEXCEPT { return 0; } + static number_type round_error() BOOST_MP_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR int min_exponent = 0; + BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; + BOOST_STATIC_CONSTEXPR int max_exponent = 0; + BOOST_STATIC_CONSTEXPR int max_exponent10 = 0; + BOOST_STATIC_CONSTEXPR bool has_infinity = false; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + static number_type infinity() BOOST_MP_NOEXCEPT { return 0; } + static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return 0; } + static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return 0; } + static number_type denorm_min() BOOST_MP_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = true; + BOOST_STATIC_CONSTEXPR bool is_modulo = true; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; +}; + +template +const typename numeric_limits > >::inititializer numeric_limits > >::init; + } #endif diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index eb2a7de0..5d5d47ea 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -1047,6 +1047,8 @@ int main() #endif #ifdef TEST_CPP_INT test(); + test > >(); + test > >(); #endif #ifdef TEST_CPP_INT_BR test(); diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp index ee6bcde2..ee83b641 100644 --- a/test/test_cpp_int.cpp +++ b/test/test_cpp_int.cpp @@ -51,10 +51,11 @@ T generate_random(unsigned bits_wanted) return val; } -int main() +template +void test() { using namespace boost::multiprecision; - typedef cpp_int packed_type; + typedef Number test_type; unsigned last_error_count = 0; for(int i = 0; i < 1000; ++i) { @@ -65,77 +66,77 @@ int main() int si = d.convert_to(); - packed_type a1 = a.str(); - packed_type b1 = b.str(); - packed_type c1 = c.str(); - packed_type d1 = d.str(); + test_type a1 = a.str(); + test_type b1 = b.str(); + test_type c1 = c.str(); + test_type d1 = d.str(); BOOST_CHECK_EQUAL(a.str(), a1.str()); BOOST_CHECK_EQUAL(b.str(), b1.str()); BOOST_CHECK_EQUAL(c.str(), c1.str()); BOOST_CHECK_EQUAL(d.str(), d1.str()); - BOOST_CHECK_EQUAL(mpz_int(a+b).str(), packed_type(a1 + b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a-b).str(), packed_type(a1 - b1).str()); - BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)+b).str(), packed_type(packed_type(-a1) + b1).str()); - BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)-b).str(), packed_type(packed_type(-a1) - b1).str()); - BOOST_CHECK_EQUAL(mpz_int(c * d).str(), packed_type(c1 * d1).str()); - BOOST_CHECK_EQUAL(mpz_int(c * -d).str(), packed_type(c1 * -d1).str()); - BOOST_CHECK_EQUAL(mpz_int(-c * d).str(), packed_type(-c1 * d1).str()); - BOOST_CHECK_EQUAL(mpz_int(b * c).str(), packed_type(b1 * c1).str()); - BOOST_CHECK_EQUAL(mpz_int(a / b).str(), packed_type(a1 / b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a / -b).str(), packed_type(a1 / -b1).str()); - BOOST_CHECK_EQUAL(mpz_int(-a / b).str(), packed_type(-a1 / b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a / d).str(), packed_type(a1 / d1).str()); - BOOST_CHECK_EQUAL(mpz_int(a % b).str(), packed_type(a1 % b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a % -b).str(), packed_type(a1 % -b1).str()); - BOOST_CHECK_EQUAL(mpz_int(-a % b).str(), packed_type(-a1 % b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a % d).str(), packed_type(a1 % d1).str()); + BOOST_CHECK_EQUAL(mpz_int(a+b).str(), test_type(a1 + b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a-b).str(), test_type(a1 - b1).str()); + BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)+b).str(), test_type(test_type(-a1) + b1).str()); + BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)-b).str(), test_type(test_type(-a1) - b1).str()); + BOOST_CHECK_EQUAL(mpz_int(c * d).str(), test_type(c1 * d1).str()); + BOOST_CHECK_EQUAL(mpz_int(c * -d).str(), test_type(c1 * -d1).str()); + BOOST_CHECK_EQUAL(mpz_int(-c * d).str(), test_type(-c1 * d1).str()); + BOOST_CHECK_EQUAL(mpz_int(b * c).str(), test_type(b1 * c1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / b).str(), test_type(a1 / b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / -b).str(), test_type(a1 / -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / b).str(), test_type(-a1 / b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / d).str(), test_type(a1 / d1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % b).str(), test_type(a1 % b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % -b).str(), test_type(a1 % -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % b).str(), test_type(-a1 % b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % d).str(), test_type(a1 % d1).str()); // bitwise ops: - BOOST_CHECK_EQUAL(mpz_int(a|b).str(), packed_type(a1 | b1).str()); - BOOST_CHECK_EQUAL(mpz_int(-a|b).str(), packed_type(-a1 | b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a|-b).str(), packed_type(a1 | -b1).str()); - BOOST_CHECK_EQUAL(mpz_int(-a|-b).str(), packed_type(-a1 | -b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a&b).str(), packed_type(a1 & b1).str()); - BOOST_CHECK_EQUAL(mpz_int(-a&b).str(), packed_type(-a1 & b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a&-b).str(), packed_type(a1 & -b1).str()); - BOOST_CHECK_EQUAL(mpz_int(-a&-b).str(), packed_type(-a1 & -b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a^b).str(), packed_type(a1 ^ b1).str()); - BOOST_CHECK_EQUAL(mpz_int(-a^b).str(), packed_type(-a1 ^ b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a^-b).str(), packed_type(a1 ^ -b1).str()); - BOOST_CHECK_EQUAL(mpz_int(-a^-b).str(), packed_type(-a1 ^ -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a|b).str(), test_type(a1 | b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a|b).str(), test_type(-a1 | b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a|-b).str(), test_type(a1 | -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a|-b).str(), test_type(-a1 | -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a&b).str(), test_type(a1 & b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a&b).str(), test_type(-a1 & b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a&-b).str(), test_type(a1 & -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a&-b).str(), test_type(-a1 & -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a^b).str(), test_type(a1 ^ b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a^b).str(), test_type(-a1 ^ b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a^-b).str(), test_type(a1 ^ -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a^-b).str(), test_type(-a1 ^ -b1).str()); // Now check operations involving integers: - BOOST_CHECK_EQUAL(mpz_int(a + si).str(), packed_type(a1 + si).str()); - BOOST_CHECK_EQUAL(mpz_int(a + -si).str(), packed_type(a1 + -si).str()); - BOOST_CHECK_EQUAL(mpz_int(-a + si).str(), packed_type(-a1 + si).str()); - BOOST_CHECK_EQUAL(mpz_int(si + a).str(), packed_type(si + a1).str()); - BOOST_CHECK_EQUAL(mpz_int(a - si).str(), packed_type(a1 - si).str()); - BOOST_CHECK_EQUAL(mpz_int(a - -si).str(), packed_type(a1 - -si).str()); - BOOST_CHECK_EQUAL(mpz_int(-a - si).str(), packed_type(-a1 - si).str()); - BOOST_CHECK_EQUAL(mpz_int(si - a).str(), packed_type(si - a1).str()); - BOOST_CHECK_EQUAL(mpz_int(b * si).str(), packed_type(b1 * si).str()); - BOOST_CHECK_EQUAL(mpz_int(b * -si).str(), packed_type(b1 * -si).str()); - BOOST_CHECK_EQUAL(mpz_int(-b * si).str(), packed_type(-b1 * si).str()); - BOOST_CHECK_EQUAL(mpz_int(si * b).str(), packed_type(si * b1).str()); - BOOST_CHECK_EQUAL(mpz_int(a / si).str(), packed_type(a1 / si).str()); - BOOST_CHECK_EQUAL(mpz_int(a / -si).str(), packed_type(a1 / -si).str()); - BOOST_CHECK_EQUAL(mpz_int(-a / si).str(), packed_type(-a1 / si).str()); - BOOST_CHECK_EQUAL(mpz_int(a % si).str(), packed_type(a1 % si).str()); - BOOST_CHECK_EQUAL(mpz_int(a % -si).str(), packed_type(a1 % -si).str()); - BOOST_CHECK_EQUAL(mpz_int(-a % si).str(), packed_type(-a1 % si).str()); - BOOST_CHECK_EQUAL(mpz_int(a|si).str(), packed_type(a1 | si).str()); - BOOST_CHECK_EQUAL(mpz_int(a&si).str(), packed_type(a1 & si).str()); - BOOST_CHECK_EQUAL(mpz_int(a^si).str(), packed_type(a1 ^ si).str()); - BOOST_CHECK_EQUAL(mpz_int(si|a).str(), packed_type(si|a1).str()); - BOOST_CHECK_EQUAL(mpz_int(si&a).str(), packed_type(si&a1).str()); - BOOST_CHECK_EQUAL(mpz_int(si^a).str(), packed_type(si^a1).str()); - BOOST_CHECK_EQUAL(mpz_int(gcd(a, b)).str(), packed_type(gcd(a1, b1)).str()); - BOOST_CHECK_EQUAL(mpz_int(lcm(c, d)).str(), packed_type(lcm(c1, d1)).str()); - BOOST_CHECK_EQUAL(mpz_int(gcd(-a, b)).str(), packed_type(gcd(-a1, b1)).str()); - BOOST_CHECK_EQUAL(mpz_int(lcm(-c, d)).str(), packed_type(lcm(-c1, d1)).str()); - BOOST_CHECK_EQUAL(mpz_int(gcd(-a, -b)).str(), packed_type(gcd(-a1, -b1)).str()); - BOOST_CHECK_EQUAL(mpz_int(lcm(-c, -d)).str(), packed_type(lcm(-c1, -d1)).str()); - BOOST_CHECK_EQUAL(mpz_int(gcd(a, -b)).str(), packed_type(gcd(a1, -b1)).str()); - BOOST_CHECK_EQUAL(mpz_int(lcm(c, -d)).str(), packed_type(lcm(c1, -d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(a + si).str(), test_type(a1 + si).str()); + BOOST_CHECK_EQUAL(mpz_int(a + -si).str(), test_type(a1 + -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a + si).str(), test_type(-a1 + si).str()); + BOOST_CHECK_EQUAL(mpz_int(si + a).str(), test_type(si + a1).str()); + BOOST_CHECK_EQUAL(mpz_int(a - si).str(), test_type(a1 - si).str()); + BOOST_CHECK_EQUAL(mpz_int(a - -si).str(), test_type(a1 - -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a - si).str(), test_type(-a1 - si).str()); + BOOST_CHECK_EQUAL(mpz_int(si - a).str(), test_type(si - a1).str()); + BOOST_CHECK_EQUAL(mpz_int(b * si).str(), test_type(b1 * si).str()); + BOOST_CHECK_EQUAL(mpz_int(b * -si).str(), test_type(b1 * -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-b * si).str(), test_type(-b1 * si).str()); + BOOST_CHECK_EQUAL(mpz_int(si * b).str(), test_type(si * b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / si).str(), test_type(a1 / si).str()); + BOOST_CHECK_EQUAL(mpz_int(a / -si).str(), test_type(a1 / -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / si).str(), test_type(-a1 / si).str()); + BOOST_CHECK_EQUAL(mpz_int(a % si).str(), test_type(a1 % si).str()); + BOOST_CHECK_EQUAL(mpz_int(a % -si).str(), test_type(a1 % -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % si).str(), test_type(-a1 % si).str()); + BOOST_CHECK_EQUAL(mpz_int(a|si).str(), test_type(a1 | si).str()); + BOOST_CHECK_EQUAL(mpz_int(a&si).str(), test_type(a1 & si).str()); + BOOST_CHECK_EQUAL(mpz_int(a^si).str(), test_type(a1 ^ si).str()); + BOOST_CHECK_EQUAL(mpz_int(si|a).str(), test_type(si|a1).str()); + BOOST_CHECK_EQUAL(mpz_int(si&a).str(), test_type(si&a1).str()); + BOOST_CHECK_EQUAL(mpz_int(si^a).str(), test_type(si^a1).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(a, b)).str(), test_type(gcd(a1, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, d)).str(), test_type(lcm(c1, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, b)).str(), test_type(gcd(-a1, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, d)).str(), test_type(lcm(-c1, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, -b)).str(), test_type(gcd(-a1, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, -d)).str(), test_type(lcm(-c1, -d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(a, -b)).str(), test_type(gcd(a1, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, -d)).str(), test_type(lcm(c1, -d1)).str()); if(last_error_count != boost::detail::test_errors()) { last_error_count = boost::detail::test_errors(); @@ -155,9 +156,9 @@ int main() std::cout << "a - b = " << a-b << std::endl; std::cout << "a1 - b1 = " << a1-b1 << std::endl; std::cout << "-a + b = " << mpz_int(-a)+b << std::endl; - std::cout << "-a1 + b1 = " << packed_type(-a1)+b1 << std::endl; + std::cout << "-a1 + b1 = " << test_type(-a1)+b1 << std::endl; std::cout << "-a - b = " << mpz_int(-a)-b << std::endl; - std::cout << "-a1 - b1 = " << packed_type(-a1)-b1 << std::endl; + std::cout << "-a1 - b1 = " << test_type(-a1)-b1 << std::endl; std::cout << "c*d = " << c*d << std::endl; std::cout << "c1*d1 = " << c1*d1 << std::endl; std::cout << "b*c = " << b*c << std::endl; @@ -172,6 +173,13 @@ int main() std::cout << "a1%d1 = " << a1%d1 << std::endl; } } +} + +int main() +{ + using namespace boost::multiprecision; + test(); + test > >(); return boost::report_errors(); } diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index ddec4db1..3d988fc1 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -134,8 +134,17 @@ void test() std::cout << "numeric_limits values for type " << typeid(Number).name() << std::endl; PRINT(is_specialized); - PRINT(min()); + if(std::numeric_limits::is_integer) + { + std::cout << std::hex << std::showbase; + } PRINT(max()); + if(std::numeric_limits::is_integer) + { + std::cout << std::dec; + } + PRINT(max()); + PRINT(min()); #ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST PRINT(lowest()); #endif @@ -225,6 +234,8 @@ int main() #endif #ifdef TEST_CPP_INT test(); + test > >(); + test > >(); #endif return boost::report_errors(); } From c82710fee6e49074bd4ca912e60ba21eaa6b9f37 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 8 Mar 2012 13:01:36 +0000 Subject: [PATCH 123/256] Fix gcc compiler errors. [SVN r77261] --- include/boost/multiprecision/cpp_int.hpp | 89 +++++++++++++++--------- 1 file changed, 57 insertions(+), 32 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 9efa5147..f46e574b 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -46,7 +46,7 @@ public: : sizeof(limb_data) / sizeof(limb_type)); BOOST_STATIC_CONSTANT(bool, variable = true); - BOOST_STATIC_ASSERT_MESSAGE(Signed, "There is curently no support for unsigned arbitrary precision integers."); + BOOST_STATIC_ASSERT_MSG(Signed, "There is curently no support for unsigned arbitrary precision integers."); private: union data_type @@ -352,18 +352,52 @@ public: } }; +template +const unsigned cpp_int_base::limb_bits; +template +const limb_type cpp_int_base::max_limb_value; +template +const limb_type cpp_int_base::sign_bit_mask; +template +const unsigned cpp_int_base::internal_limb_count; +template +const bool cpp_int_base::variable; + +template +const unsigned cpp_int_base::limb_bits; +template +const limb_type cpp_int_base::max_limb_value; +template +const limb_type cpp_int_base::sign_bit_mask; +template +const unsigned cpp_int_base::internal_limb_count; +template +const bool cpp_int_base::variable; + +template +const unsigned cpp_int_base::limb_bits; +template +const limb_type cpp_int_base::max_limb_value; +template +const limb_type cpp_int_base::sign_bit_mask; +template +const unsigned cpp_int_base::internal_limb_count; +template +const bool cpp_int_base::variable; + template struct cpp_int_backend : public cpp_int_base { + typedef cpp_int_base base_type; public: typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list float_types; cpp_int_backend(){} - cpp_int_backend(const cpp_int_backend& o) : cpp_int_base(o) {} + cpp_int_backend(const cpp_int_backend& o) : base_type(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_backend(cpp_int_backend&& o) : cpp_int_base(o) {} + cpp_int_backend(cpp_int_backend&& o) : base_type(o) {} #endif cpp_int_backend& operator = (const cpp_int_backend& o) { @@ -387,10 +421,10 @@ public: cpp_int_backend& operator = (double_limb_type i) { BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type)); - BOOST_STATIC_ASSERT(internal_limb_count >= 2); - limb_pointer p = limbs(); + BOOST_STATIC_ASSERT(base_type::internal_limb_count >= 2); + typename base_type::limb_pointer p = this->limbs(); *p = static_cast(i); - p[1] = static_cast(i >> limb_bits); + p[1] = static_cast(i >> base_type::limb_bits); this->resize(p[1] ? 2 : 1); this->sign(false); return *this; @@ -398,7 +432,7 @@ public: cpp_int_backend& operator = (signed_double_limb_type i) { BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type)); - BOOST_STATIC_ASSERT(internal_limb_count >= 2); + BOOST_STATIC_ASSERT(base_type::internal_limb_count >= 2); bool s = false; if(i < 0) { @@ -407,9 +441,9 @@ public: } else this->sign(false); - limb_pointer p = this->limbs(); + typename base_type::limb_pointer p = this->limbs(); *p = static_cast(i); - p[1] = static_cast(i >> limb_bits); + p[1] = static_cast(i >> base_type::limb_bits); resize(p[1] ? 2 : 1); this->sign(s); return *this; @@ -494,7 +528,7 @@ public: if(radix == 8 || radix == 16) { unsigned shift = radix == 8 ? 3 : 4; - unsigned block_count = limb_bits / shift; + unsigned block_count = base_type::limb_bits / shift; unsigned block_shift = shift * block_count; limb_type val, block; while(*s) @@ -509,7 +543,7 @@ public: else if(*s >= 'A' && *s <= 'F') val = 10 + *s - 'A'; else - val = max_limb_value; + val = base_type::max_limb_value; if(val > radix) { BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string.")); @@ -524,7 +558,7 @@ public: } } left_shift(*this, block_shift); - limbs()[0] |= block; + this->limbs()[0] |= block; } } else @@ -556,7 +590,7 @@ public: } } if(isneg) - negate(); + this->negate(); return *this; } void swap(cpp_int_backend& o) @@ -572,7 +606,7 @@ public: base = 16; std::string result; - unsigned Bits = size() * limb_bits; + unsigned Bits = this->size() * base_type::limb_bits; if(base == 8 || base == 16) { @@ -624,7 +658,7 @@ public: t.negate(); neg = true; } - if(size() == 1) + if(this->size() == 1) { result = boost::lexical_cast(t.limbs()[0]); } @@ -661,25 +695,25 @@ public: } int compare(const cpp_int_backend& o)const { - if(sign() != o.sign()) - return sign() ? -1 : 1; + if(this->sign() != o.sign()) + return this->sign() ? -1 : 1; int result = 0; // Only do the compare if the same sign: result = compare_unsigned(o); - if(sign()) + if(this->sign()) result = -result; return result; } int compare_unsigned(const cpp_int_backend& o)const { - if(size() != o.size()) + if(this->size() != o.size()) { - return size() > o.size() ? 1 : -1; + return this->size() > o.size() ? 1 : -1; } - const_limb_pointer pa = limbs(); - const_limb_pointer pb = o.limbs(); - for(int i = size() - 1; i >= 0; --i) + typename base_type::const_limb_pointer pa = this->limbs(); + typename base_type::const_limb_pointer pb = o.limbs(); + for(int i = this->size() - 1; i >= 0; --i) { if(pa[i] != pb[i]) return pa[i] > pb[i] ? 1 : -1; @@ -696,15 +730,6 @@ public: } }; -template -const unsigned cpp_int_backend::limb_bits; -template -const limb_type cpp_int_backend::max_limb_value; -template -const limb_type cpp_int_backend::sign_bit_mask; -template -const unsigned cpp_int_backend::internal_limb_count; - template inline void add(cpp_int_backend& result, const cpp_int_backend& o) From 78cfa00b07fb4bad113a85e8e1df620d0c6590b5 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 8 Mar 2012 13:17:13 +0000 Subject: [PATCH 124/256] Fix Clang failure. [SVN r77262] --- include/boost/multiprecision/cpp_int.hpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index f46e574b..20dab2ee 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -444,7 +444,7 @@ public: typename base_type::limb_pointer p = this->limbs(); *p = static_cast(i); p[1] = static_cast(i >> base_type::limb_bits); - resize(p[1] ? 2 : 1); + this->resize(p[1] ? 2 : 1); this->sign(s); return *this; } From b680077687ad6a13055e19e3610d0830362452de Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 8 Mar 2012 16:56:32 +0000 Subject: [PATCH 125/256] enable 128-bit arithmetic on x64 systems. [SVN r77265] --- include/boost/multiprecision/cpp_int.hpp | 6 +- .../multiprecision/detail/cpp_int_core.hpp | 21 + include/boost/multiprecision/fixed_int.hpp | 12 +- performance/performance_test-gcc-linux.log | 1045 ++++++++--------- performance/performance_test-intel-linux.log | 811 ++++++------- performance/performance_test.cpp | 5 + 6 files changed, 881 insertions(+), 1019 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 20dab2ee..6c0addf1 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -961,7 +961,7 @@ inline void subtract_unsigned(cpp_int_backend& resul } else if(c == 0) { - result = 0; + result = static_cast(0); return; } @@ -1092,7 +1092,7 @@ inline void multiply(cpp_int_backend& result, cpp_in { if(!val) { - result = 0; + result = static_cast(0); return; } double_limb_type carry = 0; @@ -2108,7 +2108,7 @@ inline void eval_lcm(cpp_int_backend& result, const if(is_zero(t)) { - result = 0; + result = static_cast(0); } else { diff --git a/include/boost/multiprecision/detail/cpp_int_core.hpp b/include/boost/multiprecision/detail/cpp_int_core.hpp index 338eab26..63d9efbf 100644 --- a/include/boost/multiprecision/detail/cpp_int_core.hpp +++ b/include/boost/multiprecision/detail/cpp_int_core.hpp @@ -8,6 +8,25 @@ namespace boost{ namespace multiprecision{ +#if defined(__GNUC__) && !defined(BOOST_INTEL) && defined(__x86_64__) + +typedef boost::uint64_t limb_type; +typedef boost::int64_t signed_limb_type; +typedef unsigned __int128 double_limb_type; +typedef __int128 signed_double_limb_type; +static const limb_type max_block_10 = 1000000000000000000uLL; +static const limb_type digits_per_block_10 = 18; + +inline limb_type block_multiplier(unsigned count) +{ + static const limb_type values[digits_per_block_10] + = { 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000 }; + BOOST_ASSERT(count < digits_per_block_10); + return values[count]; +} + +#else + typedef boost::uint32_t limb_type; typedef boost::int32_t signed_limb_type; typedef boost::uint64_t double_limb_type; @@ -23,6 +42,8 @@ inline limb_type block_multiplier(unsigned count) return values[count]; } +#endif + template inline void minmax(const T& a, const T& b, T& aa, T& bb) { diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index d183b6dd..1127079d 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -30,7 +30,7 @@ struct fixed_int BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u)); BOOST_STATIC_CONSTANT(limb_type, upper_limb_mask = (Bits % limb_bits ? (1 << (Bits % limb_bits)) - 1 : max_limb_value)); BOOST_STATIC_CONSTANT(limb_type, upper_limb_not_mask = ~upper_limb_mask); - BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << ((Bits % limb_bits ? Bits % limb_bits : limb_bits) - 1)); + BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = limb_type(1u) << ((Bits % limb_bits ? Bits % limb_bits : limb_bits) - 1)); typedef boost::array data_type; fixed_int(){} @@ -427,7 +427,7 @@ inline void subtract(fixed_int& result, const limb_type& o) carry >>= fixed_int::limb_bits; for(int i = static_cast(fixed_int::limb_count) - 2; (carry != 1) && (i >= 0); --i) { - carry += static_cast(result.data()[i]) + 0xFFFFFFFF; + carry += static_cast(result.data()[i]) + fixed_int::max_limb_value; result.data()[i] = static_cast(carry); carry >>= fixed_int::limb_bits; } @@ -748,7 +748,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1] % y.data()[fixed_int::limb_count - 1]; return; } - else if(r_order == static_cast(fixed_int::limb_count) - 2) + else if(r_order == static_cast(fixed_int::limb_count) - 2) { double_limb_type a, b; a = (static_cast(r.data()[r_order]) << fixed_int::limb_bits) | r.data()[r_order + 1]; @@ -1335,7 +1335,7 @@ template inline typename enable_if, void>::type convert_to(R* result, const fixed_int& backend, const mpl::false_&) { unsigned shift = (fixed_int::limb_count - 1) * fixed_int::limb_bits; - *result = 0; + *result = static_cast(0); for(unsigned i = 0; i < fixed_int::limb_count; ++i) { *result += static_cast(backend.data()[i]) << shift; @@ -1362,7 +1362,7 @@ inline typename enable_if, void>::type convert_to(R* result return; } unsigned shift = (fixed_int::limb_count - 1) * fixed_int::limb_bits; - *result = 0; + *result = static_cast(0); for(unsigned i = 0; i < fixed_int::limb_count; ++i) { *result += static_cast(std::ldexp(static_cast(backend.data()[i]), shift)); @@ -1490,7 +1490,7 @@ inline void eval_lcm(fixed_int& result, const fixed_int(0); } else { diff --git a/performance/performance_test-gcc-linux.log b/performance/performance_test-gcc-linux.log index 8ef6ee7b..4fc1d067 100644 --- a/performance/performance_test-gcc-linux.log +++ b/performance/performance_test-gcc-linux.log @@ -1,621 +1,542 @@ -gmp_float 50 + 0.0172634 -gmp_float 50 - 0.0190593 -gmp_float 50 * 0.0496313 -gmp_float 50 / 0.270376 -gmp_float 50 str 0.00338283 -gmp_float 50 +(int)0.0107627 -gmp_float 50 -(int)0.0189185 -gmp_float 50 *(int)0.0161546 -gmp_float 50 /(int)0.0751156 -gmp_float 100 + 0.0189236 -gmp_float 100 - 0.0210418 -gmp_float 100 * 0.0892922 -gmp_float 100 / 0.376385 -gmp_float 100 str 0.00695061 -gmp_float 100 +(int)0.0120513 -gmp_float 100 -(int)0.0198354 -gmp_float 100 *(int)0.0195997 -gmp_float 100 /(int)0.0947924 -gmp_float 500 + 0.0301919 -gmp_float 500 - 0.0323239 -gmp_float 500 * 0.870235 -gmp_float 500 / 1.42311 -gmp_float 500 str 0.0313911 -gmp_float 500 +(int)0.0179283 -gmp_float 500 -(int)0.0258331 -gmp_float 500 *(int)0.0407228 -gmp_float 500 /(int)0.231398 -gmp_int 64 + 0.0169318 -gmp_int 64 - 0.0173731 -gmp_int 64 * 0.0113175 -gmp_int 64 / 0.169581 -gmp_int 64 str 0.000400819 -gmp_int 64 +(int)0.00684333 -gmp_int 64 -(int)0.00707918 -gmp_int 64 *(int)0.00855311 -gmp_int 64 /(int)0.0451154 -gmp_int 64 % 0.157075 -gmp_int 64 | 0.00932794 -gmp_int 64 & 0.00932918 -gmp_int 64 ^ 0.00974691 -gmp_int 64 << 0.00891992 -gmp_int 64 >> 0.00890735 -gmp_int 64 %(int)0.0278521 -gmp_int 64 |(int)0.0381401 -gmp_int 64 &(int)0.039882 -gmp_int 64 ^(int)0.0387007 -gmp_int 128 + 0.0187076 -gmp_int 128 - 0.0183551 -gmp_int 128 * 0.0156906 -gmp_int 128 / 0.191252 -gmp_int 128 str 0.000364851 -gmp_int 128 +(int)0.0102801 -gmp_int 128 -(int)0.00860256 -gmp_int 128 *(int)0.0114853 -gmp_int 128 /(int)0.0523559 -gmp_int 128 % 0.15528 -gmp_int 128 | 0.0103394 -gmp_int 128 & 0.0110643 -gmp_int 128 ^ 0.0109019 -gmp_int 128 << 0.00971087 -gmp_int 128 >> 0.00747274 -gmp_int 128 %(int)0.0344314 -gmp_int 128 |(int)0.0397332 -gmp_int 128 &(int)0.0413597 -gmp_int 128 ^(int)0.0404831 -gmp_int 256 + 0.022606 -gmp_int 256 - 0.0247961 -gmp_int 256 * 0.0417861 -gmp_int 256 / 0.234977 -gmp_int 256 str 0.00059847 -gmp_int 256 +(int)0.0109994 -gmp_int 256 -(int)0.0115691 -gmp_int 256 *(int)0.0135361 -gmp_int 256 /(int)0.0654383 -gmp_int 256 % 0.186922 -gmp_int 256 | 0.0128787 -gmp_int 256 & 0.0126536 -gmp_int 256 ^ 0.0133999 -gmp_int 256 << 0.01177 -gmp_int 256 >> 0.00803845 -gmp_int 256 %(int)0.0470174 -gmp_int 256 |(int)0.0405797 -gmp_int 256 &(int)0.0422895 -gmp_int 256 ^(int)0.0411956 -gmp_int 512 + 0.0277407 -gmp_int 512 - 0.0314653 -gmp_int 512 * 0.09803 -gmp_int 512 / 0.267598 -gmp_int 512 str 0.00121866 -gmp_int 512 +(int)0.0135739 -gmp_int 512 -(int)0.0143368 -gmp_int 512 *(int)0.0181278 -gmp_int 512 /(int)0.0892225 -gmp_int 512 % 0.217246 -gmp_int 512 | 0.0173872 -gmp_int 512 & 0.016516 -gmp_int 512 ^ 0.0185213 -gmp_int 512 << 0.0143127 -gmp_int 512 >> 0.00949988 -gmp_int 512 %(int)0.0599828 -gmp_int 512 |(int)0.0437876 -gmp_int 512 &(int)0.0454139 -gmp_int 512 ^(int)0.0443687 -gmp_int 1024 + 0.0398652 -gmp_int 1024 - 0.0416822 -gmp_int 1024 * 0.316471 -gmp_int 1024 / 0.352869 -gmp_int 1024 str 0.00278974 -gmp_int 1024 +(int)0.0188639 -gmp_int 1024 -(int)0.0194421 -gmp_int 1024 *(int)0.0265822 -gmp_int 1024 /(int)0.140502 -gmp_int 1024 % 0.281408 -gmp_int 1024 | 0.0243975 -gmp_int 1024 & 0.0233641 -gmp_int 1024 ^ 0.0248742 -gmp_int 1024 << 0.0205595 -gmp_int 1024 >> 0.012374 -gmp_int 1024 %(int)0.075892 -gmp_int 1024 |(int)0.0475998 -gmp_int 1024 &(int)0.0492285 -gmp_int 1024 ^(int)0.0488719 -mpq_rational 64 + 0.248703 -mpq_rational 64 - 0.248085 -mpq_rational 64 * 0.415269 -mpq_rational 64 / 1.34308 -mpq_rational 64 str 0.000573396 -mpq_rational 64 +(int)0.287841 -mpq_rational 64 -(int)0.28346 -mpq_rational 64 *(int)0.310676 -mpq_rational 64 /(int)0.311221 -mpq_rational 128 + 0.525318 -mpq_rational 128 - 0.53016 -mpq_rational 128 * 0.933404 -mpq_rational 128 / 2.63133 -mpq_rational 128 str 0.000723346 -mpq_rational 128 +(int)0.144307 -mpq_rational 128 -(int)0.14385 -mpq_rational 128 *(int)0.172035 -mpq_rational 128 /(int)0.175494 -mpq_rational 256 + 2.26207 -mpq_rational 256 - 2.26907 -mpq_rational 256 * 4.28222 -mpq_rational 256 / 8.12755 -mpq_rational 256 str 0.00120085 -mpq_rational 256 +(int)0.162372 -mpq_rational 256 -(int)0.160533 -mpq_rational 256 *(int)0.192923 -mpq_rational 256 /(int)0.197356 -mpq_rational 512 + 5.07193 -mpq_rational 512 - 5.07942 -mpq_rational 512 * 9.65569 -mpq_rational 512 / 16.8657 -mpq_rational 512 str 0.00233842 -mpq_rational 512 +(int)0.197738 -mpq_rational 512 -(int)0.198744 -mpq_rational 512 *(int)0.240048 -mpq_rational 512 /(int)0.250338 -mpq_rational 1024 + 11.2925 -mpq_rational 1024 - 11.3536 -mpq_rational 1024 * 21.0382 -mpq_rational 1024 / 35.6477 -mpq_rational 1024 str 0.00549707 -mpq_rational 1024 +(int)0.269222 -mpq_rational 1024 -(int)0.267056 -mpq_rational 1024 *(int)0.324096 -mpq_rational 1024 /(int)0.338966 -tommath_int 64 + 0.0159939 -tommath_int 64 - 0.0250036 -tommath_int 64 * 0.0363444 -tommath_int 64 / 0.977073 -tommath_int 64 str 0.00445496 -tommath_int 64 +(int)0.164295 -tommath_int 64 -(int)0.162629 -tommath_int 64 *(int)0.179095 -tommath_int 64 /(int)0.842398 -tommath_int 64 % 0.977861 -tommath_int 64 | 0.0691489 -tommath_int 64 & 0.073788 -tommath_int 64 ^ 0.0709205 -tommath_int 64 << 0.0193922 -tommath_int 64 >> 0.124706 -tommath_int 64 %(int)0.727338 -tommath_int 64 |(int)0.239311 -tommath_int 64 &(int)0.217949 -tommath_int 64 ^(int)0.239579 -tommath_int 128 + 0.0164327 -tommath_int 128 - 0.0232398 -tommath_int 128 * 0.0548361 -tommath_int 128 / 1.08958 -tommath_int 128 str 0.00876306 -tommath_int 128 +(int)0.165193 -tommath_int 128 -(int)0.165879 -tommath_int 128 *(int)0.183198 -tommath_int 128 /(int)0.912304 -tommath_int 128 % 1.08174 -tommath_int 128 | 0.0704018 -tommath_int 128 & 0.0720242 -tommath_int 128 ^ 0.0707622 -tommath_int 128 << 0.0307909 -tommath_int 128 >> 0.135357 -tommath_int 128 %(int)0.838173 -tommath_int 128 |(int)0.239724 -tommath_int 128 &(int)0.216927 -tommath_int 128 ^(int)0.241914 -tommath_int 256 + 0.0186154 -tommath_int 256 - 0.0251722 -tommath_int 256 * 0.0904396 -tommath_int 256 / 1.35539 -tommath_int 256 str 0.0211627 -tommath_int 256 +(int)0.171325 -tommath_int 256 -(int)0.171589 -tommath_int 256 *(int)0.195625 -tommath_int 256 /(int)1.16415 -tommath_int 256 % 1.30947 -tommath_int 256 | 0.0732898 -tommath_int 256 & 0.0736961 -tommath_int 256 ^ 0.0734515 -tommath_int 256 << 0.038933 -tommath_int 256 >> 0.138079 -tommath_int 256 %(int)1.18164 -tommath_int 256 |(int)0.243102 -tommath_int 256 &(int)0.223836 -tommath_int 256 ^(int)0.245577 -tommath_int 512 + 0.0235136 -tommath_int 512 - 0.0288817 -tommath_int 512 * 0.192319 -tommath_int 512 / 1.91905 -tommath_int 512 str 0.0619139 -tommath_int 512 +(int)0.168344 -tommath_int 512 -(int)0.165763 -tommath_int 512 *(int)0.213072 -tommath_int 512 /(int)1.6709 -tommath_int 512 % 1.91623 -tommath_int 512 | 0.0782698 -tommath_int 512 & 0.0785497 -tommath_int 512 ^ 0.0787174 -tommath_int 512 << 0.0445723 -tommath_int 512 >> 0.148176 -tommath_int 512 %(int)1.724 -tommath_int 512 |(int)0.247972 -tommath_int 512 &(int)0.227986 -tommath_int 512 ^(int)0.245992 -tommath_int 1024 + 0.0353819 -tommath_int 1024 - 0.0411398 -tommath_int 1024 * 0.548938 -tommath_int 1024 / 3.19059 -tommath_int 1024 str 0.186976 -tommath_int 1024 +(int)0.179688 -tommath_int 1024 -(int)0.177946 -tommath_int 1024 *(int)0.257986 -tommath_int 1024 /(int)2.90617 -tommath_int 1024 % 3.17595 -tommath_int 1024 | 0.0928142 -tommath_int 1024 & 0.0989265 -tommath_int 1024 ^ 0.096274 -tommath_int 1024 << 0.0663455 -tommath_int 1024 >> 0.164607 -tommath_int 1024 %(int)2.83798 -tommath_int 1024 |(int)0.256182 -tommath_int 1024 &(int)0.241025 -tommath_int 1024 ^(int)0.258545 -fixed_int 64 + 0.00139124 -fixed_int 64 - 0.00164434 -fixed_int 64 * 0.00699488 -fixed_int 64 / 0.0516797 -fixed_int 64 str 0.000232222 -fixed_int 64 +(int)0.002316 -fixed_int 64 -(int)0.00191233 -fixed_int 64 *(int)0.00233361 -fixed_int 64 /(int)0.0232935 -fixed_int 64 % 0.0534904 -fixed_int 64 | 0.00176279 -fixed_int 64 & 0.00177991 -fixed_int 64 ^ 0.00173416 -fixed_int 64 << 0.000672222 -fixed_int 64 >> 0.000779919 -fixed_int 64 %(int)0.022105 -fixed_int 64 |(int)0.00108065 -fixed_int 64 &(int)0.00120958 -fixed_int 64 ^(int)0.00107863 -fixed_int 128 + 0.00260327 -fixed_int 128 - 0.00292914 -fixed_int 128 * 0.017405 -fixed_int 128 / 0.10547 -fixed_int 128 str 0.000458298 -fixed_int 128 +(int)0.00202532 -fixed_int 128 -(int)0.00163065 -fixed_int 128 *(int)0.0029341 -fixed_int 128 /(int)0.086585 -fixed_int 128 % 0.104705 -fixed_int 128 | 0.00262583 -fixed_int 128 & 0.00263365 -fixed_int 128 ^ 0.00261842 -fixed_int 128 << 0.00180218 -fixed_int 128 >> 0.00195989 -fixed_int 128 %(int)0.076707 -fixed_int 128 |(int)0.00127991 -fixed_int 128 &(int)0.00221857 -fixed_int 128 ^(int)0.00129423 -fixed_int 256 + 0.00544189 -fixed_int 256 - 0.00594733 -fixed_int 256 * 0.0716955 -fixed_int 256 / 0.18658 -fixed_int 256 str 0.0011329 -fixed_int 256 +(int)0.00239115 -fixed_int 256 -(int)0.00196589 -fixed_int 256 *(int)0.00536465 -fixed_int 256 /(int)0.177415 -fixed_int 256 % 0.18577 -fixed_int 256 | 0.00654441 -fixed_int 256 & 0.00658456 -fixed_int 256 ^ 0.00653302 -fixed_int 256 << 0.00366541 -fixed_int 256 >> 0.00345938 -fixed_int 256 %(int)0.146564 -fixed_int 256 |(int)0.00179758 -fixed_int 256 &(int)0.00406972 -fixed_int 256 ^(int)0.00174107 -fixed_int 512 + 0.0119663 -fixed_int 512 - 0.0122849 -fixed_int 512 * 0.250144 -fixed_int 512 / 0.362685 -fixed_int 512 str 0.00353655 -fixed_int 512 +(int)0.00525298 -fixed_int 512 -(int)0.0054428 -fixed_int 512 *(int)0.0104665 -fixed_int 512 /(int)0.35372 -fixed_int 512 % 0.364137 -fixed_int 512 | 0.0133848 -fixed_int 512 & 0.0134244 -fixed_int 512 ^ 0.0133775 -fixed_int 512 << 0.0111573 -fixed_int 512 >> 0.0104619 -fixed_int 512 %(int)0.293131 -fixed_int 512 |(int)0.00511566 -fixed_int 512 &(int)0.00944583 -fixed_int 512 ^(int)0.00520143 -fixed_int 1024 + 0.0265669 -fixed_int 1024 - 0.0305353 -fixed_int 1024 * 0.792037 -fixed_int 1024 / 0.758868 -fixed_int 1024 str 0.0137457 -fixed_int 1024 +(int)0.0101279 -fixed_int 1024 -(int)0.00950205 -fixed_int 1024 *(int)0.026544 -fixed_int 1024 /(int)0.709808 -fixed_int 1024 % 0.760095 -fixed_int 1024 | 0.0258782 -fixed_int 1024 & 0.0244113 -fixed_int 1024 ^ 0.0258119 -fixed_int 1024 << 0.0193046 -fixed_int 1024 >> 0.0195598 -fixed_int 1024 %(int)0.591454 -fixed_int 1024 |(int)0.010103 -fixed_int 1024 &(int)0.0249342 -fixed_int 1024 ^(int)0.0100668 -cpp_float 50 + 0.0135692 -cpp_float 50 - 0.014813 -cpp_float 50 * 0.121949 -cpp_float 50 / 1.86438 -cpp_float 50 str 0.00921786 -cpp_float 50 +(int)0.0231423 -cpp_float 50 -(int)0.0245803 -cpp_float 50 *(int)0.036823 -cpp_float 50 /(int)0.200073 -cpp_float 100 + 0.0194008 -cpp_float 100 - 0.0179391 -cpp_float 100 * 0.237444 -cpp_float 100 / 3.67594 -cpp_float 100 str 0.0156382 -cpp_float 100 +(int)0.032027 -cpp_float 100 -(int)0.0355546 -cpp_float 100 *(int)0.0596723 -cpp_float 100 /(int)0.341129 -cpp_float 500 + 0.0431376 -cpp_float 500 - 0.0441081 -cpp_float 500 * 2.11624 -cpp_float 500 / 25.3672 -cpp_float 500 str 0.0619948 -cpp_float 500 +(int)0.0717688 -cpp_float 500 -(int)0.0737847 -cpp_float 500 *(int)0.240091 -cpp_float 500 /(int)1.39098 -mpfr_float 50 + 0.018534 -mpfr_float 50 - 0.0219753 -mpfr_float 50 * 0.0573856 -mpfr_float 50 / 0.318134 -mpfr_float 50 str 0.00683453 -mpfr_float 50 +(int)0.0267235 -mpfr_float 50 -(int)0.0449984 -mpfr_float 50 *(int)0.0345749 -mpfr_float 50 /(int)0.0856313 -mpfr_float 100 + 0.0203895 -mpfr_float 100 - 0.023673 -mpfr_float 100 * 0.0922367 -mpfr_float 100 / 0.455272 -mpfr_float 100 str 0.00688747 -mpfr_float 100 +(int)0.0280739 -mpfr_float 100 -(int)0.048047 -mpfr_float 100 *(int)0.039831 -mpfr_float 100 /(int)0.107712 -mpfr_float 500 + 0.032386 -mpfr_float 500 - 0.0362805 -mpfr_float 500 * 0.853213 -mpfr_float 500 / 2.82089 -mpfr_float 500 str 0.0336548 -mpfr_float 500 +(int)0.0383341 -mpfr_float 500 -(int)0.0587852 -mpfr_float 500 *(int)0.0845355 -mpfr_float 500 /(int)0.252175 -[section:float_performance Float Type Perfomance] -[table Operator * -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.45709 (0.121949s)][2.65918 (0.237444s)][2.48032 (2.11624s)]] -[[gmp_float][[*1] (0.0496313s)][[*1] (0.0892922s)][1.01995 (0.870235s)]] -[[mpfr_float][1.15624 (0.0573856s)][1.03298 (0.0922367s)][[*1] (0.853213s)]] -] -[table Operator *(int) -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.27942 (0.036823s)][3.04455 (0.0596723s)][5.89573 (0.240091s)]] -[[gmp_float][[*1] (0.0161546s)][[*1] (0.0195997s)][[*1] (0.0407228s)]] -[[mpfr_float][2.14025 (0.0345749s)][2.03222 (0.039831s)][2.07588 (0.0845355s)]] -] -[table Operator + -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][[*1] (0.0135692s)][1.02522 (0.0194008s)][1.42878 (0.0431376s)]] -[[gmp_float][1.27225 (0.0172634s)][[*1] (0.0189236s)][[*1] (0.0301919s)]] -[[mpfr_float][1.36589 (0.018534s)][1.07746 (0.0203895s)][1.07267 (0.032386s)]] -] -[table Operator +(int) -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.15023 (0.0231423s)][2.65755 (0.032027s)][4.0031 (0.0717688s)]] -[[gmp_float][[*1] (0.0107627s)][[*1] (0.0120513s)][[*1] (0.0179283s)]] -[[mpfr_float][2.48298 (0.0267235s)][2.32953 (0.0280739s)][2.13819 (0.0383341s)]] -] -[table Operator - -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][[*1] (0.014813s)][[*1] (0.0179391s)][1.36457 (0.0441081s)]] -[[gmp_float][1.28666 (0.0190593s)][1.17296 (0.0210418s)][[*1] (0.0323239s)]] -[[mpfr_float][1.48351 (0.0219753s)][1.31963 (0.023673s)][1.12241 (0.0362805s)]] -] -[table Operator -(int) -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][1.29928 (0.0245803s)][1.79248 (0.0355546s)][2.85621 (0.0737847s)]] -[[gmp_float][[*1] (0.0189185s)][[*1] (0.0198354s)][[*1] (0.0258331s)]] -[[mpfr_float][2.37854 (0.0449984s)][2.42229 (0.048047s)][2.27558 (0.0587852s)]] -] -[table Operator / -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][6.89549 (1.86438s)][9.76642 (3.67594s)][17.8252 (25.3672s)]] -[[gmp_float][[*1] (0.270376s)][[*1] (0.376385s)][[*1] (1.42311s)]] -[[mpfr_float][1.17664 (0.318134s)][1.20959 (0.455272s)][1.9822 (2.82089s)]] -] -[table Operator /(int) -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.66353 (0.200073s)][3.59869 (0.341129s)][6.01121 (1.39098s)]] -[[gmp_float][[*1] (0.0751156s)][[*1] (0.0947924s)][[*1] (0.231398s)]] -[[mpfr_float][1.13999 (0.0856313s)][1.1363 (0.107712s)][1.08979 (0.252175s)]] -] -[table Operator str -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.72489 (0.00921786s)][2.27053 (0.0156382s)][1.97491 (0.0619948s)]] -[[gmp_float][[*1] (0.00338283s)][1.00917 (0.00695061s)][[*1] (0.0313911s)]] -[[mpfr_float][2.02036 (0.00683453s)][[*1] (0.00688747s)][1.07211 (0.0336548s)]] -] -[endsect] +gmp_int 64 + 0.0168195 +gmp_int 64 - 0.0186168 +gmp_int 64 * 0.0114224 +gmp_int 64 / 0.168483 +gmp_int 64 str 0.000337753 +gmp_int 64 +(int)0.00683062 +gmp_int 64 -(int)0.00706193 +gmp_int 64 *(int)0.00869587 +gmp_int 64 /(int)0.0453323 +gmp_int 64 % 0.157804 +gmp_int 64 | 0.00932423 +gmp_int 64 & 0.00944499 +gmp_int 64 ^ 0.00996572 +gmp_int 64 << 0.00922261 +gmp_int 64 >> 0.00918099 +gmp_int 64 %(int)0.0281261 +gmp_int 64 |(int)0.0397808 +gmp_int 64 &(int)0.0415959 +gmp_int 64 ^(int)0.0404741 +gmp_int 64 gcd 0.176988 +gmp_int 128 + 0.0179677 +gmp_int 128 - 0.0189371 +gmp_int 128 * 0.0161959 +gmp_int 128 / 0.190813 +gmp_int 128 str 0.000372045 +gmp_int 128 +(int)0.00848258 +gmp_int 128 -(int)0.00875216 +gmp_int 128 *(int)0.0113487 +gmp_int 128 /(int)0.0525228 +gmp_int 128 % 0.15826 +gmp_int 128 | 0.0106091 +gmp_int 128 & 0.0112477 +gmp_int 128 ^ 0.0113254 +gmp_int 128 << 0.0100071 +gmp_int 128 >> 0.00769246 +gmp_int 128 %(int)0.0347099 +gmp_int 128 |(int)0.0407317 +gmp_int 128 &(int)0.0426387 +gmp_int 128 ^(int)0.041833 +gmp_int 128 gcd 0.432692 +gmp_int 256 + 0.0228276 +gmp_int 256 - 0.0253604 +gmp_int 256 * 0.0424289 +gmp_int 256 / 0.232371 +gmp_int 256 str 0.000590578 +gmp_int 256 +(int)0.0111117 +gmp_int 256 -(int)0.0119104 +gmp_int 256 *(int)0.0138547 +gmp_int 256 /(int)0.0658471 +gmp_int 256 % 0.189604 +gmp_int 256 | 0.0128476 +gmp_int 256 & 0.0148126 +gmp_int 256 ^ 0.0134169 +gmp_int 256 << 0.0117499 +gmp_int 256 >> 0.00808343 +gmp_int 256 %(int)0.0471351 +gmp_int 256 |(int)0.0423473 +gmp_int 256 &(int)0.0436809 +gmp_int 256 ^(int)0.0426564 +gmp_int 256 gcd 2.06786 +gmp_int 512 + 0.0274004 +gmp_int 512 - 0.0318076 +gmp_int 512 * 0.097384 +gmp_int 512 / 0.272392 +gmp_int 512 str 0.0012598 +gmp_int 512 +(int)0.0142198 +gmp_int 512 -(int)0.0148327 +gmp_int 512 *(int)0.0179982 +gmp_int 512 /(int)0.0906272 +gmp_int 512 % 0.22163 +gmp_int 512 | 0.0211022 +gmp_int 512 & 0.0165864 +gmp_int 512 ^ 0.0218245 +gmp_int 512 << 0.0145569 +gmp_int 512 >> 0.00978776 +gmp_int 512 %(int)0.0601084 +gmp_int 512 |(int)0.0460084 +gmp_int 512 &(int)0.0466719 +gmp_int 512 ^(int)0.045828 +gmp_int 512 gcd 4.69155 +gmp_int 1024 + 0.038508 +gmp_int 1024 - 0.0417826 +gmp_int 1024 * 0.315222 +gmp_int 1024 / 0.352494 +gmp_int 1024 str 0.00274057 +gmp_int 1024 +(int)0.0187457 +gmp_int 1024 -(int)0.0194778 +gmp_int 1024 *(int)0.0259764 +gmp_int 1024 /(int)0.140287 +gmp_int 1024 % 0.284404 +gmp_int 1024 | 0.0242278 +gmp_int 1024 & 0.0235658 +gmp_int 1024 ^ 0.0249122 +gmp_int 1024 << 0.0202809 +gmp_int 1024 >> 0.0127441 +gmp_int 1024 %(int)0.0758432 +gmp_int 1024 |(int)0.0495155 +gmp_int 1024 &(int)0.0503542 +gmp_int 1024 ^(int)0.0510615 +gmp_int 1024 gcd 10.1136 +cpp_int 64 + 0.0157994 +cpp_int 64 - 0.0256769 +cpp_int 64 * 0.0226198 +cpp_int 64 / 0.102281 +cpp_int 64 str 0.000380146 +cpp_int 64 +(int)0.0103873 +cpp_int 64 -(int)0.00898962 +cpp_int 64 *(int)0.0159193 +cpp_int 64 /(int)0.0522854 +cpp_int 64 % 0.0999552 +cpp_int 64 | 0.0203489 +cpp_int 64 & 0.0202989 +cpp_int 64 ^ 0.020334 +cpp_int 64 << 0.0166545 +cpp_int 64 >> 0.0143805 +cpp_int 64 %(int)0.0389361 +cpp_int 64 |(int)0.0198498 +cpp_int 64 &(int)0.024074 +cpp_int 64 ^(int)0.0198061 +cpp_int 64 gcd 1.72384 +cpp_int 128 + 0.0182643 +cpp_int 128 - 0.0271678 +cpp_int 128 * 0.0408988 +cpp_int 128 / 0.172852 +cpp_int 128 str 0.000693873 +cpp_int 128 +(int)0.0116175 +cpp_int 128 -(int)0.0104572 +cpp_int 128 *(int)0.0187569 +cpp_int 128 /(int)0.108782 +cpp_int 128 % 0.179562 +cpp_int 128 | 0.0245406 +cpp_int 128 & 0.0245186 +cpp_int 128 ^ 0.0247923 +cpp_int 128 << 0.0196597 +cpp_int 128 >> 0.0157968 +cpp_int 128 %(int)0.0940069 +cpp_int 128 |(int)0.0210111 +cpp_int 128 &(int)0.0322746 +cpp_int 128 ^(int)0.0210955 +cpp_int 128 gcd 3.97787 +cpp_int 256 + 0.0236538 +cpp_int 256 - 0.0339319 +cpp_int 256 * 0.107568 +cpp_int 256 / 0.376559 +cpp_int 256 str 0.00192567 +cpp_int 256 +(int)0.0156148 +cpp_int 256 -(int)0.0125633 +cpp_int 256 *(int)0.0227126 +cpp_int 256 /(int)0.240023 +cpp_int 256 % 0.324919 +cpp_int 256 | 0.0273651 +cpp_int 256 & 0.0268812 +cpp_int 256 ^ 0.027153 +cpp_int 256 << 0.0240014 +cpp_int 256 >> 0.0178114 +cpp_int 256 %(int)0.196223 +cpp_int 256 |(int)0.0238206 +cpp_int 256 &(int)0.0518555 +cpp_int 256 ^(int)0.0237059 +cpp_int 256 gcd 9.44724 +cpp_int 512 + 0.0286286 +cpp_int 512 - 0.0473463 +cpp_int 512 * 0.36983 +cpp_int 512 / 0.53608 +cpp_int 512 str 0.00489147 +cpp_int 512 +(int)0.0165983 +cpp_int 512 -(int)0.0157028 +cpp_int 512 *(int)0.0327202 +cpp_int 512 /(int)0.39506 +cpp_int 512 % 0.484383 +cpp_int 512 | 0.0336779 +cpp_int 512 & 0.0332565 +cpp_int 512 ^ 0.033731 +cpp_int 512 << 0.032593 +cpp_int 512 >> 0.0249415 +cpp_int 512 %(int)0.347801 +cpp_int 512 |(int)0.0270701 +cpp_int 512 &(int)0.0847243 +cpp_int 512 ^(int)0.0270095 +cpp_int 512 gcd 22.6824 +cpp_int 1024 + 0.041093 +cpp_int 1024 - 0.065839 +cpp_int 1024 * 1.36107 +cpp_int 1024 / 0.91127 +cpp_int 1024 str 0.0150341 +cpp_int 1024 +(int)0.0212673 +cpp_int 1024 -(int)0.0207903 +cpp_int 1024 *(int)0.0482894 +cpp_int 1024 /(int)0.711756 +cpp_int 1024 % 0.853306 +cpp_int 1024 | 0.0459271 +cpp_int 1024 & 0.0455113 +cpp_int 1024 ^ 0.0457905 +cpp_int 1024 << 0.053456 +cpp_int 1024 >> 0.0339107 +cpp_int 1024 %(int)0.653379 +cpp_int 1024 |(int)0.0323199 +cpp_int 1024 &(int)0.152555 +cpp_int 1024 ^(int)0.032137 +cpp_int 1024 gcd 59.7424 +tommath_int 64 + 0.0166687 +tommath_int 64 - 0.0270094 +tommath_int 64 * 0.0386521 +tommath_int 64 / 0.98286 +tommath_int 64 str 0.00413258 +tommath_int 64 +(int)0.174336 +tommath_int 64 -(int)0.174454 +tommath_int 64 *(int)0.191871 +tommath_int 64 /(int)0.886522 +tommath_int 64 % 0.980074 +tommath_int 64 | 0.0716826 +tommath_int 64 & 0.0777977 +tommath_int 64 ^ 0.0730863 +tommath_int 64 << 0.0200111 +tommath_int 64 >> 0.124855 +tommath_int 64 %(int)0.734449 +tommath_int 64 |(int)0.254639 +tommath_int 64 &(int)0.226047 +tommath_int 64 ^(int)0.252631 +tommath_int 64 gcd 3.80432 +tommath_int 128 + 0.0169388 +tommath_int 128 - 0.0247515 +tommath_int 128 * 0.0588799 +tommath_int 128 / 1.11408 +tommath_int 128 str 0.00853237 +tommath_int 128 +(int)0.17465 +tommath_int 128 -(int)0.169003 +tommath_int 128 *(int)0.193938 +tommath_int 128 /(int)0.901904 +tommath_int 128 % 1.09735 +tommath_int 128 | 0.0714914 +tommath_int 128 & 0.0734869 +tommath_int 128 ^ 0.0724281 +tommath_int 128 << 0.0315817 +tommath_int 128 >> 0.137548 +tommath_int 128 %(int)0.835579 +tommath_int 128 |(int)0.25282 +tommath_int 128 &(int)0.22947 +tommath_int 128 ^(int)0.253212 +tommath_int 128 gcd 7.29351 +tommath_int 256 + 0.0191982 +tommath_int 256 - 0.0260308 +tommath_int 256 * 0.0850765 +tommath_int 256 / 1.3375 +tommath_int 256 str 0.0217479 +tommath_int 256 +(int)0.173229 +tommath_int 256 -(int)0.17296 +tommath_int 256 *(int)0.201834 +tommath_int 256 /(int)1.153 +tommath_int 256 % 1.34044 +tommath_int 256 | 0.074755 +tommath_int 256 & 0.0755475 +tommath_int 256 ^ 0.0805466 +tommath_int 256 << 0.0382785 +tommath_int 256 >> 0.141309 +tommath_int 256 %(int)1.19796 +tommath_int 256 |(int)0.255801 +tommath_int 256 &(int)0.233997 +tommath_int 256 ^(int)0.25474 +tommath_int 256 gcd 15.3331 +tommath_int 512 + 0.0240257 +tommath_int 512 - 0.0303227 +tommath_int 512 * 0.195612 +tommath_int 512 / 1.96548 +tommath_int 512 str 0.0563537 +tommath_int 512 +(int)0.174848 +tommath_int 512 -(int)0.176184 +tommath_int 512 *(int)0.223672 +tommath_int 512 /(int)1.68054 +tommath_int 512 % 1.95689 +tommath_int 512 | 0.0801272 +tommath_int 512 & 0.0806169 +tommath_int 512 ^ 0.080112 +tommath_int 512 << 0.0451545 +tommath_int 512 >> 0.151606 +tommath_int 512 %(int)1.74812 +tommath_int 512 |(int)0.260477 +tommath_int 512 &(int)0.237892 +tommath_int 512 ^(int)0.259232 +tommath_int 512 gcd 31.9471 +tommath_int 1024 + 0.035905 +tommath_int 1024 - 0.0429664 +tommath_int 1024 * 0.564578 +tommath_int 1024 / 3.17298 +tommath_int 1024 str 0.187413 +tommath_int 1024 +(int)0.190852 +tommath_int 1024 -(int)0.189438 +tommath_int 1024 *(int)0.271175 +tommath_int 1024 /(int)2.92342 +tommath_int 1024 % 3.20126 +tommath_int 1024 | 0.0939085 +tommath_int 1024 & 0.10264 +tommath_int 1024 ^ 0.0957583 +tommath_int 1024 << 0.0670281 +tommath_int 1024 >> 0.166781 +tommath_int 1024 %(int)2.88178 +tommath_int 1024 |(int)0.267844 +tommath_int 1024 &(int)0.252612 +tommath_int 1024 ^(int)0.270201 +tommath_int 1024 gcd 68.3106 +fixed_int 64 + 0.00139312 +fixed_int 64 - 0.00162339 +fixed_int 64 * 0.00699782 +fixed_int 64 / 0.0526074 +fixed_int 64 str 0.000220769 +fixed_int 64 +(int)0.00224121 +fixed_int 64 -(int)0.00194005 +fixed_int 64 *(int)0.0023299 +fixed_int 64 /(int)0.0222776 +fixed_int 64 % 0.0533221 +fixed_int 64 | 0.00173919 +fixed_int 64 & 0.00172375 +fixed_int 64 ^ 0.00173786 +fixed_int 64 << 0.000542177 +fixed_int 64 >> 0.000774259 +fixed_int 64 %(int)0.0213357 +fixed_int 64 |(int)0.00111648 +fixed_int 64 &(int)0.00122907 +fixed_int 64 ^(int)0.00107255 +fixed_int 64 gcd 0.694716 +fixed_int 128 + 0.00257987 +fixed_int 128 - 0.00292488 +fixed_int 128 * 0.0224222 +fixed_int 128 / 0.104045 +fixed_int 128 str 0.000463955 +fixed_int 128 +(int)0.00201262 +fixed_int 128 -(int)0.00162514 +fixed_int 128 *(int)0.0029339 +fixed_int 128 /(int)0.0854855 +fixed_int 128 % 0.104704 +fixed_int 128 | 0.00262052 +fixed_int 128 & 0.00263811 +fixed_int 128 ^ 0.00262317 +fixed_int 128 << 0.00169023 +fixed_int 128 >> 0.00194871 +fixed_int 128 %(int)0.0765247 +fixed_int 128 |(int)0.0012695 +fixed_int 128 &(int)0.00213023 +fixed_int 128 ^(int)0.00126692 +fixed_int 128 gcd 1.94748 +fixed_int 256 + 0.00534754 +fixed_int 256 - 0.0057397 +fixed_int 256 * 0.0746728 +fixed_int 256 / 0.188237 +fixed_int 256 str 0.00110489 +fixed_int 256 +(int)0.00239737 +fixed_int 256 -(int)0.00190618 +fixed_int 256 *(int)0.00532854 +fixed_int 256 /(int)0.176302 +fixed_int 256 % 0.185671 +fixed_int 256 | 0.00635312 +fixed_int 256 & 0.00641492 +fixed_int 256 ^ 0.00637518 +fixed_int 256 << 0.00364634 +fixed_int 256 >> 0.00339513 +fixed_int 256 %(int)0.148628 +fixed_int 256 |(int)0.00172278 +fixed_int 256 &(int)0.00394582 +fixed_int 256 ^(int)0.0017306 +fixed_int 256 gcd 5.69938 +fixed_int 512 + 0.0104641 +fixed_int 512 - 0.0108643 +fixed_int 512 * 0.244289 +fixed_int 512 / 0.361312 +fixed_int 512 str 0.00355548 +fixed_int 512 +(int)0.00521225 +fixed_int 512 -(int)0.00508137 +fixed_int 512 *(int)0.0104497 +fixed_int 512 /(int)0.347573 +fixed_int 512 % 0.359133 +fixed_int 512 | 0.0127562 +fixed_int 512 & 0.0127079 +fixed_int 512 ^ 0.0128838 +fixed_int 512 << 0.00909235 +fixed_int 512 >> 0.0100095 +fixed_int 512 %(int)0.294967 +fixed_int 512 |(int)0.00510309 +fixed_int 512 &(int)0.0108019 +fixed_int 512 ^(int)0.00519878 +fixed_int 512 gcd 18.0766 +fixed_int 1024 + 0.0269036 +fixed_int 1024 - 0.0307375 +fixed_int 1024 * 0.794034 +fixed_int 1024 / 0.761903 +fixed_int 1024 str 0.0139069 +fixed_int 1024 +(int)0.0107717 +fixed_int 1024 -(int)0.0107214 +fixed_int 1024 *(int)0.0264201 +fixed_int 1024 /(int)0.710635 +fixed_int 1024 % 0.762693 +fixed_int 1024 | 0.0266044 +fixed_int 1024 & 0.0265946 +fixed_int 1024 ^ 0.0266218 +fixed_int 1024 << 0.0208209 +fixed_int 1024 >> 0.0199434 +fixed_int 1024 %(int)0.591732 +fixed_int 1024 |(int)0.0107572 +fixed_int 1024 &(int)0.0279165 +fixed_int 1024 ^(int)0.0107153 +fixed_int 1024 gcd 72.0083 [section:integer_performance Integer Type Perfomance] [table Operator % [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0534904s)][[*1] (0.104705s)][[*1] (0.18577s)][1.67615 (0.364137s)][2.70105 (0.760095s)]] -[[gmp_int][2.93651 (0.157075s)][1.48303 (0.15528s)][1.0062 (0.186922s)][[*1] (0.217246s)][[*1] (0.281408s)]] -[[tommath_int][18.2811 (0.977861s)][10.3314 (1.08174s)][7.04886 (1.30947s)][8.82054 (1.91623s)][11.2859 (3.17595s)]] +[[cpp_int][1.87455 (0.0999552s)][1.71496 (0.179562s)][1.74997 (0.324919s)][2.18555 (0.484383s)][3.00033 (0.853306s)]] +[[fixed_int][[*1] (0.0533221s)][[*1] (0.104704s)][[*1] (0.185671s)][1.62042 (0.359133s)][2.68172 (0.762693s)]] +[[gmp_int][2.95944 (0.157804s)][1.51151 (0.15826s)][1.02118 (0.189604s)][[*1] (0.22163s)][[*1] (0.284404s)]] +[[tommath_int][18.3802 (0.980074s)][10.4805 (1.09735s)][7.21942 (1.34044s)][8.82954 (1.95689s)][11.256 (3.20126s)]] ] [table Operator %(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.022105s)][2.22782 (0.076707s)][3.11723 (0.146564s)][4.88691 (0.293131s)][7.79337 (0.591454s)]] -[[gmp_int][1.25999 (0.0278521s)][[*1] (0.0344314s)][[*1] (0.0470174s)][[*1] (0.0599828s)][[*1] (0.075892s)]] -[[tommath_int][32.9037 (0.727338s)][24.3433 (0.838173s)][25.1319 (1.18164s)][28.7415 (1.724s)][37.3949 (2.83798s)]] +[[cpp_int][1.82492 (0.0389361s)][2.70836 (0.0940069s)][4.16298 (0.196223s)][5.78623 (0.347801s)][8.61488 (0.653379s)]] +[[fixed_int][[*1] (0.0213357s)][2.2047 (0.0765247s)][3.15324 (0.148628s)][4.90725 (0.294967s)][7.80205 (0.591732s)]] +[[gmp_int][1.31826 (0.0281261s)][[*1] (0.0347099s)][[*1] (0.0471351s)][[*1] (0.0601084s)][[*1] (0.0758432s)]] +[[tommath_int][34.4234 (0.734449s)][24.0732 (0.835579s)][25.4154 (1.19796s)][29.0828 (1.74812s)][37.9966 (2.88178s)]] ] [table Operator & [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00177991s)][[*1] (0.00263365s)][[*1] (0.00658456s)][[*1] (0.0134244s)][1.04482 (0.0244113s)]] -[[gmp_int][5.24139 (0.00932918s)][4.20114 (0.0110643s)][1.9217 (0.0126536s)][1.2303 (0.016516s)][[*1] (0.0233641s)]] -[[tommath_int][41.4562 (0.073788s)][27.3477 (0.0720242s)][11.1923 (0.0736961s)][5.85126 (0.0785497s)][4.23413 (0.0989265s)]] +[[cpp_int][11.776 (0.0202989s)][9.29397 (0.0245186s)][4.19042 (0.0268812s)][2.61699 (0.0332565s)][1.93124 (0.0455113s)]] +[[fixed_int][[*1] (0.00172375s)][[*1] (0.00263811s)][[*1] (0.00641492s)][[*1] (0.0127079s)][1.12853 (0.0265946s)]] +[[gmp_int][5.47931 (0.00944499s)][4.26352 (0.0112477s)][2.30908 (0.0148126s)][1.3052 (0.0165864s)][[*1] (0.0235658s)]] +[[tommath_int][45.1327 (0.0777977s)][27.8558 (0.0734869s)][11.7768 (0.0755475s)][6.34384 (0.0806169s)][4.35544 (0.10264s)]] ] [table Operator &(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00120958s)][[*1] (0.00221857s)][[*1] (0.00406972s)][[*1] (0.00944583s)][[*1] (0.0249342s)]] -[[gmp_int][32.9717 (0.039882s)][18.6425 (0.0413597s)][10.3913 (0.0422895s)][4.80782 (0.0454139s)][1.97433 (0.0492285s)]] -[[tommath_int][180.185 (0.217949s)][97.7774 (0.216927s)][55.0003 (0.223836s)][24.1362 (0.227986s)][9.6664 (0.241025s)]] +[[cpp_int][19.5872 (0.024074s)][15.1507 (0.0322746s)][13.1419 (0.0518555s)][7.84344 (0.0847243s)][5.46467 (0.152555s)]] +[[fixed_int][[*1] (0.00122907s)][[*1] (0.00213023s)][[*1] (0.00394582s)][[*1] (0.0108019s)][[*1] (0.0279165s)]] +[[gmp_int][33.8435 (0.0415959s)][20.016 (0.0426387s)][11.0702 (0.0436809s)][4.3207 (0.0466719s)][1.80374 (0.0503542s)]] +[[tommath_int][183.918 (0.226047s)][107.721 (0.22947s)][59.3026 (0.233997s)][22.0231 (0.237892s)][9.04882 (0.252612s)]] ] [table Operator * [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00699488s)][1.10926 (0.017405s)][1.71577 (0.0716955s)][2.55171 (0.250144s)][2.50272 (0.792037s)]] -[[gmp_int][1.61797 (0.0113175s)][[*1] (0.0156906s)][[*1] (0.0417861s)][[*1] (0.09803s)][[*1] (0.316471s)]] -[[tommath_int][5.19586 (0.0363444s)][3.49483 (0.0548361s)][2.16435 (0.0904396s)][1.96183 (0.192319s)][1.73456 (0.548938s)]] +[[cpp_int][3.2324 (0.0226198s)][2.52526 (0.0408988s)][2.53525 (0.107568s)][3.79765 (0.36983s)][4.31781 (1.36107s)]] +[[fixed_int][[*1] (0.00699782s)][1.38444 (0.0224222s)][1.75995 (0.0746728s)][2.50851 (0.244289s)][2.51897 (0.794034s)]] +[[gmp_int][1.63228 (0.0114224s)][[*1] (0.0161959s)][[*1] (0.0424289s)][[*1] (0.097384s)][[*1] (0.315222s)]] +[[tommath_int][5.52344 (0.0386521s)][3.63548 (0.0588799s)][2.00515 (0.0850765s)][2.00866 (0.195612s)][1.79105 (0.564578s)]] ] [table Operator *(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00233361s)][[*1] (0.0029341s)][[*1] (0.00536465s)][[*1] (0.0104665s)][[*1] (0.026544s)]] -[[gmp_int][3.66519 (0.00855311s)][3.9144 (0.0114853s)][2.52321 (0.0135361s)][1.73199 (0.0181278s)][1.00144 (0.0265822s)]] -[[tommath_int][76.7461 (0.179095s)][62.4375 (0.183198s)][36.4656 (0.195625s)][20.3576 (0.213072s)][9.71918 (0.257986s)]] +[[cpp_int][6.83259 (0.0159193s)][6.39316 (0.0187569s)][4.26244 (0.0227126s)][3.13123 (0.0327202s)][1.85897 (0.0482894s)]] +[[fixed_int][[*1] (0.0023299s)][[*1] (0.0029339s)][[*1] (0.00532854s)][[*1] (0.0104497s)][1.01708 (0.0264201s)]] +[[gmp_int][3.73229 (0.00869587s)][3.86814 (0.0113487s)][2.60009 (0.0138547s)][1.72238 (0.0179982s)][[*1] (0.0259764s)]] +[[tommath_int][82.3516 (0.191871s)][66.1027 (0.193938s)][37.8779 (0.201834s)][21.4047 (0.223672s)][10.4393 (0.271175s)]] ] [table Operator + [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00139124s)][[*1] (0.00260327s)][[*1] (0.00544189s)][[*1] (0.0119663s)][[*1] (0.0265669s)]] -[[gmp_int][12.1703 (0.0169318s)][7.18621 (0.0187076s)][4.15407 (0.022606s)][2.31823 (0.0277407s)][1.50056 (0.0398652s)]] -[[tommath_int][11.4962 (0.0159939s)][6.31236 (0.0164327s)][3.42075 (0.0186154s)][1.96498 (0.0235136s)][1.33181 (0.0353819s)]] +[[cpp_int][11.341 (0.0157994s)][7.07953 (0.0182643s)][4.42331 (0.0236538s)][2.73588 (0.0286286s)][1.52741 (0.041093s)]] +[[fixed_int][[*1] (0.00139312s)][[*1] (0.00257987s)][[*1] (0.00534754s)][[*1] (0.0104641s)][[*1] (0.0269036s)]] +[[gmp_int][12.0732 (0.0168195s)][6.96456 (0.0179677s)][4.26881 (0.0228276s)][2.61851 (0.0274004s)][1.43133 (0.038508s)]] +[[tommath_int][11.965 (0.0166687s)][6.56577 (0.0169388s)][3.5901 (0.0191982s)][2.29601 (0.0240257s)][1.33458 (0.035905s)]] ] [table Operator +(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.002316s)][[*1] (0.00202532s)][[*1] (0.00239115s)][[*1] (0.00525298s)][[*1] (0.0101279s)]] -[[gmp_int][2.9548 (0.00684333s)][5.07577 (0.0102801s)][4.60003 (0.0109994s)][2.58403 (0.0135739s)][1.86257 (0.0188639s)]] -[[tommath_int][70.9391 (0.164295s)][81.5638 (0.165193s)][71.6493 (0.171325s)][32.0474 (0.168344s)][17.7419 (0.179688s)]] +[[cpp_int][4.63468 (0.0103873s)][5.77235 (0.0116175s)][6.51328 (0.0156148s)][3.18449 (0.0165983s)][1.97437 (0.0212673s)]] +[[fixed_int][[*1] (0.00224121s)][[*1] (0.00201262s)][[*1] (0.00239737s)][[*1] (0.00521225s)][[*1] (0.0107717s)]] +[[gmp_int][3.04774 (0.00683062s)][4.2147 (0.00848258s)][4.63494 (0.0111117s)][2.72815 (0.0142198s)][1.74027 (0.0187457s)]] +[[tommath_int][77.7866 (0.174336s)][86.7776 (0.17465s)][72.258 (0.173229s)][33.5455 (0.174848s)][17.718 (0.190852s)]] ] [table Operator - [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00164434s)][[*1] (0.00292914s)][[*1] (0.00594733s)][[*1] (0.0122849s)][[*1] (0.0305353s)]] -[[gmp_int][10.5654 (0.0173731s)][6.26638 (0.0183551s)][4.16928 (0.0247961s)][2.56129 (0.0314653s)][1.36505 (0.0416822s)]] -[[tommath_int][15.2058 (0.0250036s)][7.934 (0.0232398s)][4.23252 (0.0251722s)][2.35098 (0.0288817s)][1.34729 (0.0411398s)]] +[[cpp_int][15.8168 (0.0256769s)][9.28853 (0.0271678s)][5.91179 (0.0339319s)][4.35797 (0.0473463s)][2.14198 (0.065839s)]] +[[fixed_int][[*1] (0.00162339s)][[*1] (0.00292488s)][[*1] (0.0057397s)][[*1] (0.0108643s)][[*1] (0.0307375s)]] +[[gmp_int][11.4678 (0.0186168s)][6.47449 (0.0189371s)][4.41843 (0.0253604s)][2.92772 (0.0318076s)][1.35934 (0.0417826s)]] +[[tommath_int][16.6376 (0.0270094s)][8.46239 (0.0247515s)][4.53521 (0.0260308s)][2.79104 (0.0303227s)][1.39785 (0.0429664s)]] ] [table Operator -(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00191233s)][[*1] (0.00163065s)][[*1] (0.00196589s)][[*1] (0.0054428s)][[*1] (0.00950205s)]] -[[gmp_int][3.70187 (0.00707918s)][5.27553 (0.00860256s)][5.88489 (0.0115691s)][2.63409 (0.0143368s)][2.04609 (0.0194421s)]] -[[tommath_int][85.0424 (0.162629s)][101.726 (0.165879s)][87.2831 (0.171589s)][30.4554 (0.165763s)][18.7271 (0.177946s)]] +[[cpp_int][4.63371 (0.00898962s)][6.43466 (0.0104572s)][6.59084 (0.0125633s)][3.09026 (0.0157028s)][1.93914 (0.0207903s)]] +[[fixed_int][[*1] (0.00194005s)][[*1] (0.00162514s)][[*1] (0.00190618s)][[*1] (0.00508137s)][[*1] (0.0107214s)]] +[[gmp_int][3.64008 (0.00706193s)][5.38549 (0.00875216s)][6.2483 (0.0119104s)][2.91903 (0.0148327s)][1.81672 (0.0194778s)]] +[[tommath_int][89.9224 (0.174454s)][103.993 (0.169003s)][90.7363 (0.17296s)][34.6724 (0.176184s)][17.6692 (0.189438s)]] ] [table Operator / [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0516797s)][[*1] (0.10547s)][[*1] (0.18658s)][1.35534 (0.362685s)][2.15056 (0.758868s)]] -[[gmp_int][3.28139 (0.169581s)][1.81332 (0.191252s)][1.25939 (0.234977s)][[*1] (0.267598s)][[*1] (0.352869s)]] -[[tommath_int][18.9063 (0.977073s)][10.3307 (1.08958s)][7.26443 (1.35539s)][7.17138 (1.91905s)][9.04185 (3.19059s)]] +[[cpp_int][1.94422 (0.102281s)][1.66132 (0.172852s)][2.00045 (0.376559s)][1.96804 (0.53608s)][2.58521 (0.91127s)]] +[[fixed_int][[*1] (0.0526074s)][[*1] (0.104045s)][[*1] (0.188237s)][1.32644 (0.361312s)][2.16146 (0.761903s)]] +[[gmp_int][3.20265 (0.168483s)][1.83394 (0.190813s)][1.23446 (0.232371s)][[*1] (0.272392s)][[*1] (0.352494s)]] +[[tommath_int][18.6829 (0.98286s)][10.7076 (1.11408s)][7.10542 (1.3375s)][7.21562 (1.96548s)][9.00151 (3.17298s)]] ] [table Operator /(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0232935s)][1.65378 (0.086585s)][2.71117 (0.177415s)][3.96447 (0.35372s)][5.05194 (0.709808s)]] -[[gmp_int][1.93682 (0.0451154s)][[*1] (0.0523559s)][[*1] (0.0654383s)][[*1] (0.0892225s)][[*1] (0.140502s)]] -[[tommath_int][36.1645 (0.842398s)][17.4251 (0.912304s)][17.7901 (1.16415s)][18.7273 (1.6709s)][20.6842 (2.90617s)]] +[[cpp_int][2.34699 (0.0522854s)][2.07114 (0.108782s)][3.64515 (0.240023s)][4.35917 (0.39506s)][5.07357 (0.711756s)]] +[[fixed_int][[*1] (0.0222776s)][1.62759 (0.0854855s)][2.67744 (0.176302s)][3.83519 (0.347573s)][5.06558 (0.710635s)]] +[[gmp_int][2.03488 (0.0453323s)][[*1] (0.0525228s)][[*1] (0.0658471s)][[*1] (0.0906272s)][[*1] (0.140287s)]] +[[tommath_int][39.7943 (0.886522s)][17.1717 (0.901904s)][17.5103 (1.153s)][18.5434 (1.68054s)][20.8389 (2.92342s)]] ] [table Operator << [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.000672222s)][[*1] (0.00180218s)][[*1] (0.00366541s)][[*1] (0.0111573s)][[*1] (0.0193046s)]] -[[gmp_int][13.2693 (0.00891992s)][5.38839 (0.00971087s)][3.2111 (0.01177s)][1.28281 (0.0143127s)][1.06501 (0.0205595s)]] -[[tommath_int][28.8479 (0.0193922s)][17.0853 (0.0307909s)][10.6217 (0.038933s)][3.99491 (0.0445723s)][3.43678 (0.0663455s)]] +[[cpp_int][30.7178 (0.0166545s)][11.6314 (0.0196597s)][6.58232 (0.0240014s)][3.58466 (0.032593s)][2.63577 (0.053456s)]] +[[fixed_int][[*1] (0.000542177s)][[*1] (0.00169023s)][[*1] (0.00364634s)][[*1] (0.00909235s)][1.02663 (0.0208209s)]] +[[gmp_int][17.0103 (0.00922261s)][5.92058 (0.0100071s)][3.22238 (0.0117499s)][1.601 (0.0145569s)][[*1] (0.0202809s)]] +[[tommath_int][36.9087 (0.0200111s)][18.6848 (0.0315817s)][10.4978 (0.0382785s)][4.9662 (0.0451545s)][3.30498 (0.0670281s)]] ] [table Operator >> [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.000779919s)][[*1] (0.00195989s)][[*1] (0.00345938s)][1.10127 (0.0104619s)][1.58072 (0.0195598s)]] -[[gmp_int][11.4209 (0.00890735s)][3.81284 (0.00747274s)][2.32367 (0.00803845s)][[*1] (0.00949988s)][[*1] (0.012374s)]] -[[tommath_int][159.896 (0.124706s)][69.0639 (0.135357s)][39.9143 (0.138079s)][15.5977 (0.148176s)][13.3026 (0.164607s)]] +[[cpp_int][18.5732 (0.0143805s)][8.1063 (0.0157968s)][5.24617 (0.0178114s)][2.54823 (0.0249415s)][2.66089 (0.0339107s)]] +[[fixed_int][[*1] (0.000774259s)][[*1] (0.00194871s)][[*1] (0.00339513s)][1.02266 (0.0100095s)][1.56491 (0.0199434s)]] +[[gmp_int][11.8578 (0.00918099s)][3.94746 (0.00769246s)][2.38089 (0.00808343s)][[*1] (0.00978776s)][[*1] (0.0127441s)]] +[[tommath_int][161.257 (0.124855s)][70.5839 (0.137548s)][41.6211 (0.141309s)][15.4893 (0.151606s)][13.0869 (0.166781s)]] ] [table Operator ^ [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00173416s)][[*1] (0.00261842s)][[*1] (0.00653302s)][[*1] (0.0133775s)][1.0377 (0.0258119s)]] -[[gmp_int][5.62054 (0.00974691s)][4.16356 (0.0109019s)][2.0511 (0.0133999s)][1.38452 (0.0185213s)][[*1] (0.0248742s)]] -[[tommath_int][40.8962 (0.0709205s)][27.0248 (0.0707622s)][11.2431 (0.0734515s)][5.88433 (0.0787174s)][3.87044 (0.096274s)]] +[[cpp_int][11.7006 (0.020334s)][9.45127 (0.0247923s)][4.25917 (0.027153s)][2.6181 (0.033731s)][1.83807 (0.0457905s)]] +[[fixed_int][[*1] (0.00173786s)][[*1] (0.00262317s)][[*1] (0.00637518s)][[*1] (0.0128838s)][1.06862 (0.0266218s)]] +[[gmp_int][5.73448 (0.00996572s)][4.31745 (0.0113254s)][2.10455 (0.0134169s)][1.69395 (0.0218245s)][[*1] (0.0249122s)]] +[[tommath_int][42.0554 (0.0730863s)][27.6109 (0.0724281s)][12.6344 (0.0805466s)][6.21806 (0.080112s)][3.84383 (0.0957583s)]] ] [table Operator ^(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00107863s)][[*1] (0.00129423s)][[*1] (0.00174107s)][[*1] (0.00520143s)][[*1] (0.0100668s)]] -[[gmp_int][35.8795 (0.0387007s)][31.2797 (0.0404831s)][23.661 (0.0411956s)][8.5301 (0.0443687s)][4.85477 (0.0488719s)]] -[[tommath_int][222.114 (0.239579s)][186.918 (0.241914s)][141.049 (0.245577s)][47.2931 (0.245992s)][25.683 (0.258545s)]] +[[cpp_int][18.4664 (0.0198061s)][16.651 (0.0210955s)][13.6981 (0.0237059s)][5.19536 (0.0270095s)][2.99916 (0.032137s)]] +[[fixed_int][[*1] (0.00107255s)][[*1] (0.00126692s)][[*1] (0.0017306s)][[*1] (0.00519878s)][[*1] (0.0107153s)]] +[[gmp_int][37.7363 (0.0404741s)][33.0195 (0.041833s)][24.6483 (0.0426564s)][8.81514 (0.045828s)][4.76527 (0.0510615s)]] +[[tommath_int][235.542 (0.252631s)][199.864 (0.253212s)][147.197 (0.25474s)][49.864 (0.259232s)][25.2164 (0.270201s)]] +] +[table Operator gcd +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][9.7399 (1.72384s)][9.19332 (3.97787s)][4.5686 (9.44724s)][4.83474 (22.6824s)][5.90712 (59.7424s)]] +[[fixed_int][3.92522 (0.694716s)][4.50085 (1.94748s)][2.75617 (5.69938s)][3.85301 (18.0766s)][7.11994 (72.0083s)]] +[[gmp_int][[*1] (0.176988s)][[*1] (0.432692s)][[*1] (2.06786s)][[*1] (4.69155s)][[*1] (10.1136s)]] +[[tommath_int][21.4948 (3.80432s)][16.8561 (7.29351s)][7.41497 (15.3331s)][6.8095 (31.9471s)][6.75432 (68.3106s)]] ] [table Operator str [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.000232222s)][1.25612 (0.000458298s)][1.89299 (0.0011329s)][2.90199 (0.00353655s)][4.92723 (0.0137457s)]] -[[gmp_int][1.72602 (0.000400819s)][[*1] (0.000364851s)][[*1] (0.00059847s)][[*1] (0.00121866s)][[*1] (0.00278974s)]] -[[tommath_int][19.1841 (0.00445496s)][24.0182 (0.00876306s)][35.3614 (0.0211627s)][50.8048 (0.0619139s)][67.0227 (0.186976s)]] +[[cpp_int][1.72192 (0.000380146s)][1.86502 (0.000693873s)][3.26065 (0.00192567s)][3.88275 (0.00489147s)][5.48576 (0.0150341s)]] +[[fixed_int][[*1] (0.000220769s)][1.24704 (0.000463955s)][1.87086 (0.00110489s)][2.82227 (0.00355548s)][5.07444 (0.0139069s)]] +[[gmp_int][1.52989 (0.000337753s)][[*1] (0.000372045s)][[*1] (0.000590578s)][[*1] (0.0012598s)][[*1] (0.00274057s)]] +[[tommath_int][18.719 (0.00413258s)][22.9337 (0.00853237s)][36.8247 (0.0217479s)][44.7324 (0.0563537s)][68.3845 (0.187413s)]] ] [table Operator | [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00176279s)][[*1] (0.00262583s)][[*1] (0.00654441s)][[*1] (0.0133848s)][1.06069 (0.0258782s)]] -[[gmp_int][5.29157 (0.00932794s)][3.93757 (0.0103394s)][1.96789 (0.0128787s)][1.29902 (0.0173872s)][[*1] (0.0243975s)]] -[[tommath_int][39.2269 (0.0691489s)][26.8113 (0.0704018s)][11.1988 (0.0732898s)][5.84766 (0.0782698s)][3.80426 (0.0928142s)]] +[[cpp_int][11.7002 (0.0203489s)][9.3648 (0.0245406s)][4.30735 (0.0273651s)][2.64011 (0.0336779s)][1.89563 (0.0459271s)]] +[[fixed_int][[*1] (0.00173919s)][[*1] (0.00262052s)][[*1] (0.00635312s)][[*1] (0.0127562s)][1.0981 (0.0266044s)]] +[[gmp_int][5.36125 (0.00932423s)][4.04848 (0.0106091s)][2.02225 (0.0128476s)][1.65427 (0.0211022s)][[*1] (0.0242278s)]] +[[tommath_int][41.2161 (0.0716826s)][27.2814 (0.0714914s)][11.7667 (0.074755s)][6.28141 (0.0801272s)][3.87606 (0.0939085s)]] ] [table Operator |(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00108065s)][[*1] (0.00127991s)][[*1] (0.00179758s)][[*1] (0.00511566s)][[*1] (0.010103s)]] -[[gmp_int][35.2935 (0.0381401s)][31.0437 (0.0397332s)][22.5747 (0.0405797s)][8.55952 (0.0437876s)][4.71147 (0.0475998s)]] -[[tommath_int][221.45 (0.239311s)][187.298 (0.239724s)][135.239 (0.243102s)][48.473 (0.247972s)][25.3571 (0.256182s)]] -] -[endsect] -[section:rational_performance Rational Type Perfomance] -[table Operator * -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.415269s)][[*1] (0.933404s)][[*1] (4.28222s)][[*1] (9.65569s)][[*1] (21.0382s)]] -] -[table Operator *(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.310676s)][[*1] (0.172035s)][[*1] (0.192923s)][[*1] (0.240048s)][[*1] (0.324096s)]] -] -[table Operator + -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.248703s)][[*1] (0.525318s)][[*1] (2.26207s)][[*1] (5.07193s)][[*1] (11.2925s)]] -] -[table Operator +(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.287841s)][[*1] (0.144307s)][[*1] (0.162372s)][[*1] (0.197738s)][[*1] (0.269222s)]] -] -[table Operator - -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.248085s)][[*1] (0.53016s)][[*1] (2.26907s)][[*1] (5.07942s)][[*1] (11.3536s)]] -] -[table Operator -(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.28346s)][[*1] (0.14385s)][[*1] (0.160533s)][[*1] (0.198744s)][[*1] (0.267056s)]] -] -[table Operator / -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (1.34308s)][[*1] (2.63133s)][[*1] (8.12755s)][[*1] (16.8657s)][[*1] (35.6477s)]] -] -[table Operator /(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.311221s)][[*1] (0.175494s)][[*1] (0.197356s)][[*1] (0.250338s)][[*1] (0.338966s)]] -] -[table Operator str -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.000573396s)][[*1] (0.000723346s)][[*1] (0.00120085s)][[*1] (0.00233842s)][[*1] (0.00549707s)]] +[[cpp_int][17.7789 (0.0198498s)][16.5506 (0.0210111s)][13.8268 (0.0238206s)][5.30465 (0.0270701s)][3.00448 (0.0323199s)]] +[[fixed_int][[*1] (0.00111648s)][[*1] (0.0012695s)][[*1] (0.00172278s)][[*1] (0.00510309s)][[*1] (0.0107572s)]] +[[gmp_int][35.6305 (0.0397808s)][32.0847 (0.0407317s)][24.5808 (0.0423473s)][9.0158 (0.0460084s)][4.603 (0.0495155s)]] +[[tommath_int][228.073 (0.254639s)][199.149 (0.25282s)][148.482 (0.255801s)][51.0429 (0.260477s)][24.899 (0.267844s)]] ] [endsect] diff --git a/performance/performance_test-intel-linux.log b/performance/performance_test-intel-linux.log index cacc4056..e721729e 100644 --- a/performance/performance_test-intel-linux.log +++ b/performance/performance_test-intel-linux.log @@ -1,507 +1,422 @@ -gmp_float 50 + 0.0180644 -gmp_float 50 - 0.0194673 -gmp_float 50 * 0.0505578 -gmp_float 50 / 0.278179 -gmp_float 50 str 0.00357972 -gmp_float 50 +(int)0.0115205 -gmp_float 50 -(int)0.0197263 -gmp_float 50 *(int)0.0165976 -gmp_float 50 /(int)0.0758893 -gmp_float 100 + 0.019475 -gmp_float 100 - 0.0218422 -gmp_float 100 * 0.090686 -gmp_float 100 / 0.378055 -gmp_float 100 str 0.00557522 -gmp_float 100 +(int)0.0127856 -gmp_float 100 -(int)0.0205184 -gmp_float 100 *(int)0.0200577 -gmp_float 100 /(int)0.0948556 -gmp_float 500 + 0.0317241 -gmp_float 500 - 0.0335304 -gmp_float 500 * 0.947017 -gmp_float 500 / 1.5881 -gmp_float 500 str 0.0313793 -gmp_float 500 +(int)0.0187639 -gmp_float 500 -(int)0.0265882 -gmp_float 500 *(int)0.0415067 -gmp_float 500 /(int)0.232493 -gmp_int 64 + 0.0167521 -gmp_int 64 - 0.0188881 -gmp_int 64 * 0.011645 -gmp_int 64 / 0.1697 -gmp_int 64 str 0.000336635 -gmp_int 64 +(int)0.00723269 -gmp_int 64 -(int)0.00741945 -gmp_int 64 *(int)0.0120496 -gmp_int 64 /(int)0.0501068 -gmp_int 64 % 0.16582 -gmp_int 64 | 0.0115873 -gmp_int 64 & 0.0125951 -gmp_int 64 ^ 0.0129732 -gmp_int 64 << 0.00969083 -gmp_int 64 >> 0.0130601 -gmp_int 64 %(int)0.034786 -gmp_int 64 |(int)0.0424747 -gmp_int 64 &(int)0.0441868 -gmp_int 64 ^(int)0.0442481 -gmp_int 128 + 0.0192114 -gmp_int 128 - 0.0219479 -gmp_int 128 * 0.0182506 -gmp_int 128 / 0.196561 -gmp_int 128 str 0.00232097 -gmp_int 128 +(int)0.00871277 -gmp_int 128 -(int)0.0130434 -gmp_int 128 *(int)0.0127078 -gmp_int 128 /(int)0.0568248 -gmp_int 128 % 0.164977 -gmp_int 128 | 0.0134681 -gmp_int 128 & 0.01436 -gmp_int 128 ^ 0.0140653 -gmp_int 128 << 0.0131179 -gmp_int 128 >> 0.0107065 -gmp_int 128 %(int)0.0405959 -gmp_int 128 |(int)0.0440289 -gmp_int 128 &(int)0.0453998 -gmp_int 128 ^(int)0.0468496 -gmp_int 256 + 0.0230482 -gmp_int 256 - 0.0289896 -gmp_int 256 * 0.0476911 -gmp_int 256 / 0.240552 -gmp_int 256 str 0.000971703 -gmp_int 256 +(int)0.0145101 -gmp_int 256 -(int)0.0148337 -gmp_int 256 *(int)0.0170638 -gmp_int 256 /(int)0.0686065 -gmp_int 256 % 0.197103 -gmp_int 256 | 0.0159192 -gmp_int 256 & 0.015575 -gmp_int 256 ^ 0.0166751 -gmp_int 256 << 0.0148945 -gmp_int 256 >> 0.0111136 -gmp_int 256 %(int)0.0516333 -gmp_int 256 |(int)0.0474723 -gmp_int 256 &(int)0.0466442 -gmp_int 256 ^(int)0.0465869 -gmp_int 512 + 0.028268 -gmp_int 512 - 0.0352221 -gmp_int 512 * 0.103105 -gmp_int 512 / 0.281226 -gmp_int 512 str 0.00167382 -gmp_int 512 +(int)0.0170154 -gmp_int 512 -(int)0.0179625 -gmp_int 512 *(int)0.021358 -gmp_int 512 /(int)0.0950571 -gmp_int 512 % 0.230214 -gmp_int 512 | 0.0208511 -gmp_int 512 & 0.019777 -gmp_int 512 ^ 0.025011 -gmp_int 512 << 0.0182795 -gmp_int 512 >> 0.0121814 -gmp_int 512 %(int)0.0651899 -gmp_int 512 |(int)0.0493584 -gmp_int 512 &(int)0.0498514 -gmp_int 512 ^(int)0.049668 -gmp_int 1024 + 0.0408966 -gmp_int 1024 - 0.0463151 -gmp_int 1024 * 0.326898 -gmp_int 1024 / 0.36922 -gmp_int 1024 str 0.00297363 -gmp_int 1024 +(int)0.0197647 -gmp_int 1024 -(int)0.0199956 -gmp_int 1024 *(int)0.0300116 -gmp_int 1024 /(int)0.144581 -gmp_int 1024 % 0.302132 -gmp_int 1024 | 0.0284821 -gmp_int 1024 & 0.0266602 -gmp_int 1024 ^ 0.0299441 -gmp_int 1024 << 0.0247868 -gmp_int 1024 >> 0.0162548 -gmp_int 1024 %(int)0.0799406 -gmp_int 1024 |(int)0.0525727 -gmp_int 1024 &(int)0.0539474 -gmp_int 1024 ^(int)0.0539722 -mpq_rational 64 + 0.254473 -mpq_rational 64 - 0.260331 -mpq_rational 64 * 0.426868 -mpq_rational 64 / 1.50105 -mpq_rational 64 str 0.000927423 -mpq_rational 64 +(int)0.309729 -mpq_rational 64 -(int)0.306598 -mpq_rational 64 *(int)0.344178 -mpq_rational 64 /(int)0.32842 -mpq_rational 128 + 0.542374 -mpq_rational 128 - 0.545764 -mpq_rational 128 * 0.968054 -mpq_rational 128 / 2.78757 -mpq_rational 128 str 0.00111655 -mpq_rational 128 +(int)0.154116 -mpq_rational 128 -(int)0.151187 -mpq_rational 128 *(int)0.179899 -mpq_rational 128 /(int)0.184167 -mpq_rational 256 + 2.34795 -mpq_rational 256 - 2.3565 -mpq_rational 256 * 4.39195 -mpq_rational 256 / 8.9203 -mpq_rational 256 str 0.00175742 -mpq_rational 256 +(int)0.177483 -mpq_rational 256 -(int)0.16783 -mpq_rational 256 *(int)0.200539 -mpq_rational 256 /(int)0.206129 -mpq_rational 512 + 5.10523 -mpq_rational 512 - 5.08802 -mpq_rational 512 * 9.6344 -mpq_rational 512 / 16.8502 -mpq_rational 512 str 0.00246714 -mpq_rational 512 +(int)0.212807 -mpq_rational 512 -(int)0.212048 -mpq_rational 512 *(int)0.254142 -mpq_rational 512 /(int)0.262442 -mpq_rational 1024 + 11.2331 -mpq_rational 1024 - 11.2446 -mpq_rational 1024 * 20.9879 -mpq_rational 1024 / 35.6472 -mpq_rational 1024 str 0.00550783 -mpq_rational 1024 +(int)0.27756 -mpq_rational 1024 -(int)0.271845 -mpq_rational 1024 *(int)0.328602 -mpq_rational 1024 /(int)0.350883 -fixed_int 64 + 0.00207163 -fixed_int 64 - 0.00216403 -fixed_int 64 * 0.00392745 -fixed_int 64 / 0.0556903 -fixed_int 64 str 0.000302762 -fixed_int 64 +(int)0.00358307 -fixed_int 64 -(int)0.00354668 -fixed_int 64 *(int)0.00294381 -fixed_int 64 /(int)0.0169012 -fixed_int 64 % 0.054413 -fixed_int 64 | 0.00257616 -fixed_int 64 & 0.00259593 -fixed_int 64 ^ 0.00256688 -fixed_int 64 << 0.00115455 -fixed_int 64 >> 0.00147407 -fixed_int 64 %(int)0.0243407 -fixed_int 64 |(int)0.00208078 -fixed_int 64 &(int)0.00209559 -fixed_int 64 ^(int)0.00202777 -fixed_int 128 + 0.00326026 -fixed_int 128 - 0.00372498 -fixed_int 128 * 0.0104772 -fixed_int 128 / 0.105756 -fixed_int 128 str 0.000500691 -fixed_int 128 +(int)0.00359962 -fixed_int 128 -(int)0.00360689 -fixed_int 128 *(int)0.00422148 -fixed_int 128 /(int)0.0634475 -fixed_int 128 % 0.106105 -fixed_int 128 | 0.00363433 -fixed_int 128 & 0.00361924 -fixed_int 128 ^ 0.00361813 -fixed_int 128 << 0.00632357 -fixed_int 128 >> 0.00238745 -fixed_int 128 %(int)0.0811764 -fixed_int 128 |(int)0.00190869 -fixed_int 128 &(int)0.00245967 -fixed_int 128 ^(int)0.00237775 -fixed_int 256 + 0.00834722 -fixed_int 256 - 0.00653903 -fixed_int 256 * 0.0324122 -fixed_int 256 / 0.198305 -fixed_int 256 str 0.00111683 -fixed_int 256 +(int)0.00405163 -fixed_int 256 -(int)0.00385712 -fixed_int 256 *(int)0.00849409 -fixed_int 256 /(int)0.127666 -fixed_int 256 % 0.19685 -fixed_int 256 | 0.0108232 -fixed_int 256 & 0.0108415 -fixed_int 256 ^ 0.0108455 -fixed_int 256 << 0.00826823 -fixed_int 256 >> 0.00854822 -fixed_int 256 %(int)0.15306 -fixed_int 256 |(int)0.00275195 -fixed_int 256 &(int)0.00419648 -fixed_int 256 ^(int)0.0027653 -fixed_int 512 + 0.0128543 -fixed_int 512 - 0.0120433 -fixed_int 512 * 0.201059 -fixed_int 512 / 0.385977 -fixed_int 512 str 0.00286314 -fixed_int 512 +(int)0.00694047 -fixed_int 512 -(int)0.00681002 -fixed_int 512 *(int)0.015882 -fixed_int 512 /(int)0.244657 -fixed_int 512 % 0.385184 -fixed_int 512 | 0.0131341 -fixed_int 512 & 0.013122 -fixed_int 512 ^ 0.013116 -fixed_int 512 << 0.0150546 -fixed_int 512 >> 0.0134889 -fixed_int 512 %(int)0.303051 -fixed_int 512 |(int)0.00618124 -fixed_int 512 &(int)0.00836021 -fixed_int 512 ^(int)0.00608555 -fixed_int 1024 + 0.0330379 -fixed_int 1024 - 0.0311489 -fixed_int 1024 * 0.701951 -fixed_int 1024 / 0.708393 -fixed_int 1024 str 0.00872206 -fixed_int 1024 +(int)0.0116939 -fixed_int 1024 -(int)0.0116182 -fixed_int 1024 *(int)0.0346698 -fixed_int 1024 /(int)0.692818 -fixed_int 1024 % 0.711308 -fixed_int 1024 | 0.0176472 -fixed_int 1024 & 0.0176585 -fixed_int 1024 ^ 0.0177043 -fixed_int 1024 << 0.0242721 -fixed_int 1024 >> 0.0248274 -fixed_int 1024 %(int)0.584615 -fixed_int 1024 |(int)0.0107899 -fixed_int 1024 &(int)0.0166854 -fixed_int 1024 ^(int)0.0108555 -cpp_float 50 + 0.0142302 -cpp_float 50 - 0.0153931 -cpp_float 50 * 0.137722 -cpp_float 50 / 2.0214 -cpp_float 50 str 0.00924301 -cpp_float 50 +(int)0.0240351 -cpp_float 50 -(int)0.0252498 -cpp_float 50 *(int)0.0387713 -cpp_float 50 /(int)0.199003 -cpp_float 100 + 0.0178132 -cpp_float 100 - 0.0189367 -cpp_float 100 * 0.293407 -cpp_float 100 / 4.24891 -cpp_float 100 str 0.0160219 -cpp_float 100 +(int)0.0334828 -cpp_float 100 -(int)0.0326407 -cpp_float 100 *(int)0.063236 -cpp_float 100 /(int)0.341837 -cpp_float 500 + 0.044608 -cpp_float 500 - 0.0457737 -cpp_float 500 * 2.88591 -cpp_float 500 / 31.8072 -cpp_float 500 str 0.0639606 -cpp_float 500 +(int)0.0947227 -cpp_float 500 -(int)0.0966926 -cpp_float 500 *(int)0.224258 -cpp_float 500 /(int)1.39765 -mpfr_float 50 + 0.0194724 -mpfr_float 50 - 0.0228715 -mpfr_float 50 * 0.0587051 -mpfr_float 50 / 0.319258 -mpfr_float 50 str 0.00735177 -mpfr_float 50 +(int)0.0285879 -mpfr_float 50 -(int)0.0468028 -mpfr_float 50 *(int)0.03626 -mpfr_float 50 /(int)0.0889091 -mpfr_float 100 + 0.0211419 -mpfr_float 100 - 0.0251794 -mpfr_float 100 * 0.0946069 -mpfr_float 100 / 0.464237 -mpfr_float 100 str 0.00743083 -mpfr_float 100 +(int)0.0302544 -mpfr_float 100 -(int)0.0478439 -mpfr_float 100 *(int)0.0407275 -mpfr_float 100 /(int)0.109517 -mpfr_float 500 + 0.0338 -mpfr_float 500 - 0.037242 -mpfr_float 500 * 0.852196 -mpfr_float 500 / 2.80673 -mpfr_float 500 str 0.0339866 -mpfr_float 500 +(int)0.0427411 -mpfr_float 500 -(int)0.060913 -mpfr_float 500 *(int)0.0814603 -mpfr_float 500 /(int)0.254409 -[section:float_performance Float Type Perfomance] -[table Operator * -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.72405 (0.137722s)][3.23542 (0.293407s)][3.38644 (2.88591s)]] -[[gmp_float][[*1] (0.0505578s)][[*1] (0.090686s)][1.11127 (0.947017s)]] -[[mpfr_float][1.16115 (0.0587051s)][1.04324 (0.0946069s)][[*1] (0.852196s)]] -] -[table Operator *(int) -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.33595 (0.0387713s)][3.1527 (0.063236s)][5.40294 (0.224258s)]] -[[gmp_float][[*1] (0.0165976s)][[*1] (0.0200577s)][[*1] (0.0415067s)]] -[[mpfr_float][2.18465 (0.03626s)][2.03052 (0.0407275s)][1.96258 (0.0814603s)]] -] -[table Operator + -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][[*1] (0.0142302s)][[*1] (0.0178132s)][1.40612 (0.044608s)]] -[[gmp_float][1.26944 (0.0180644s)][1.09329 (0.019475s)][[*1] (0.0317241s)]] -[[mpfr_float][1.36838 (0.0194724s)][1.18686 (0.0211419s)][1.06543 (0.0338s)]] -] -[table Operator +(int) -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.08629 (0.0240351s)][2.61878 (0.0334828s)][5.04813 (0.0947227s)]] -[[gmp_float][[*1] (0.0115205s)][[*1] (0.0127856s)][[*1] (0.0187639s)]] -[[mpfr_float][2.48148 (0.0285879s)][2.36628 (0.0302544s)][2.27784 (0.0427411s)]] -] -[table Operator - -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][[*1] (0.0153931s)][[*1] (0.0189367s)][1.36514 (0.0457737s)]] -[[gmp_float][1.26468 (0.0194673s)][1.15343 (0.0218422s)][[*1] (0.0335304s)]] -[[mpfr_float][1.48583 (0.0228715s)][1.32966 (0.0251794s)][1.11069 (0.037242s)]] -] -[table Operator -(int) -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][1.28001 (0.0252498s)][1.5908 (0.0326407s)][3.63667 (0.0966926s)]] -[[gmp_float][[*1] (0.0197263s)][[*1] (0.0205184s)][[*1] (0.0265882s)]] -[[mpfr_float][2.37262 (0.0468028s)][2.33176 (0.0478439s)][2.29098 (0.060913s)]] -] -[table Operator / -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][7.26654 (2.0214s)][11.2389 (4.24891s)][20.0284 (31.8072s)]] -[[gmp_float][[*1] (0.278179s)][[*1] (0.378055s)][[*1] (1.5881s)]] -[[mpfr_float][1.14767 (0.319258s)][1.22796 (0.464237s)][1.76735 (2.80673s)]] -] -[table Operator /(int) -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.62228 (0.199003s)][3.60376 (0.341837s)][6.01157 (1.39765s)]] -[[gmp_float][[*1] (0.0758893s)][[*1] (0.0948556s)][[*1] (0.232493s)]] -[[mpfr_float][1.17156 (0.0889091s)][1.15457 (0.109517s)][1.09427 (0.254409s)]] -] -[table Operator str -[[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.58205 (0.00924301s)][2.87378 (0.0160219s)][2.03831 (0.0639606s)]] -[[gmp_float][[*1] (0.00357972s)][[*1] (0.00557522s)][[*1] (0.0313793s)]] -[[mpfr_float][2.05373 (0.00735177s)][1.33283 (0.00743083s)][1.08309 (0.0339866s)]] -] -[endsect] +gmp_int 64 + 0.016582 +gmp_int 64 - 0.0174517 +gmp_int 64 * 0.0112253 +gmp_int 64 / 0.170951 +gmp_int 64 str 0.000343689 +gmp_int 64 +(int)0.00688382 +gmp_int 64 -(int)0.00734613 +gmp_int 64 *(int)0.00881438 +gmp_int 64 /(int)0.0465651 +gmp_int 64 % 0.164576 +gmp_int 64 | 0.0101555 +gmp_int 64 & 0.00955666 +gmp_int 64 ^ 0.00987346 +gmp_int 64 << 0.0106043 +gmp_int 64 >> 0.0093887 +gmp_int 64 %(int)0.0297463 +gmp_int 64 |(int)0.0403338 +gmp_int 64 &(int)0.0417288 +gmp_int 64 ^(int)0.0405779 +gmp_int 64 gcd 0.173816 +gmp_int 128 + 0.0183088 +gmp_int 128 - 0.0189266 +gmp_int 128 * 0.0161084 +gmp_int 128 / 0.191775 +gmp_int 128 str 0.000374699 +gmp_int 128 +(int)0.00866339 +gmp_int 128 -(int)0.0089443 +gmp_int 128 *(int)0.0114143 +gmp_int 128 /(int)0.0534638 +gmp_int 128 % 0.161212 +gmp_int 128 | 0.0107201 +gmp_int 128 & 0.0113559 +gmp_int 128 ^ 0.0112116 +gmp_int 128 << 0.0103295 +gmp_int 128 >> 0.00813413 +gmp_int 128 %(int)0.03692 +gmp_int 128 |(int)0.0412168 +gmp_int 128 &(int)0.0428359 +gmp_int 128 ^(int)0.0418522 +gmp_int 128 gcd 0.43131 +gmp_int 256 + 0.0224834 +gmp_int 256 - 0.025062 +gmp_int 256 * 0.0417471 +gmp_int 256 / 0.233656 +gmp_int 256 str 0.00059903 +gmp_int 256 +(int)0.0112071 +gmp_int 256 -(int)0.0116302 +gmp_int 256 *(int)0.0137181 +gmp_int 256 /(int)0.0667669 +gmp_int 256 % 0.191884 +gmp_int 256 | 0.0129489 +gmp_int 256 & 0.012778 +gmp_int 256 ^ 0.0134548 +gmp_int 256 << 0.0121471 +gmp_int 256 >> 0.00832878 +gmp_int 256 %(int)0.0474363 +gmp_int 256 |(int)0.0425591 +gmp_int 256 &(int)0.0436742 +gmp_int 256 ^(int)0.0425636 +gmp_int 256 gcd 2.06855 +gmp_int 512 + 0.0277439 +gmp_int 512 - 0.0318874 +gmp_int 512 * 0.0991032 +gmp_int 512 / 0.274993 +gmp_int 512 str 0.00129458 +gmp_int 512 +(int)0.014283 +gmp_int 512 -(int)0.0149874 +gmp_int 512 *(int)0.0180512 +gmp_int 512 /(int)0.0906691 +gmp_int 512 % 0.222477 +gmp_int 512 | 0.0217103 +gmp_int 512 & 0.0165285 +gmp_int 512 ^ 0.0208848 +gmp_int 512 << 0.014839 +gmp_int 512 >> 0.00988994 +gmp_int 512 %(int)0.0605682 +gmp_int 512 |(int)0.0462909 +gmp_int 512 &(int)0.046599 +gmp_int 512 ^(int)0.0456608 +gmp_int 512 gcd 4.68499 +gmp_int 1024 + 0.0397479 +gmp_int 1024 - 0.042232 +gmp_int 1024 * 0.31703 +gmp_int 1024 / 0.345984 +gmp_int 1024 str 0.00271592 +gmp_int 1024 +(int)0.0189969 +gmp_int 1024 -(int)0.0195046 +gmp_int 1024 *(int)0.0260306 +gmp_int 1024 /(int)0.140151 +gmp_int 1024 % 0.286399 +gmp_int 1024 | 0.0261953 +gmp_int 1024 & 0.023083 +gmp_int 1024 ^ 0.0248084 +gmp_int 1024 << 0.0202635 +gmp_int 1024 >> 0.0127909 +gmp_int 1024 %(int)0.0761102 +gmp_int 1024 |(int)0.049175 +gmp_int 1024 &(int)0.0499195 +gmp_int 1024 ^(int)0.0487102 +gmp_int 1024 gcd 10.1127 +cpp_int 64 + 0.0152915 +cpp_int 64 - 0.0191821 +cpp_int 64 * 0.0326218 +cpp_int 64 / 0.0951094 +cpp_int 64 str 0.000428547 +cpp_int 64 +(int)0.0132027 +cpp_int 64 -(int)0.0126144 +cpp_int 64 *(int)0.0151037 +cpp_int 64 /(int)0.0491116 +cpp_int 64 % 0.0951581 +cpp_int 64 | 0.0199629 +cpp_int 64 & 0.0196969 +cpp_int 64 ^ 0.0208608 +cpp_int 64 << 0.0179372 +cpp_int 64 >> 0.0146206 +cpp_int 64 %(int)0.0229261 +cpp_int 64 |(int)0.0185797 +cpp_int 64 &(int)0.0225055 +cpp_int 64 ^(int)0.0191337 +cpp_int 64 gcd 1.50205 +cpp_int 128 + 0.0170788 +cpp_int 128 - 0.0228373 +cpp_int 128 * 0.0375831 +cpp_int 128 / 0.163958 +cpp_int 128 str 0.000744647 +cpp_int 128 +(int)0.0144833 +cpp_int 128 -(int)0.013922 +cpp_int 128 *(int)0.0176402 +cpp_int 128 /(int)0.0972057 +cpp_int 128 % 0.169015 +cpp_int 128 | 0.0229631 +cpp_int 128 & 0.023126 +cpp_int 128 ^ 0.0229278 +cpp_int 128 << 0.0215749 +cpp_int 128 >> 0.0149198 +cpp_int 128 %(int)0.0476063 +cpp_int 128 |(int)0.0194697 +cpp_int 128 &(int)0.0270183 +cpp_int 128 ^(int)0.0194481 +cpp_int 128 gcd 3.36986 +cpp_int 256 + 0.0231877 +cpp_int 256 - 0.0293424 +cpp_int 256 * 0.113247 +cpp_int 256 / 0.336287 +cpp_int 256 str 0.00190436 +cpp_int 256 +(int)0.0161733 +cpp_int 256 -(int)0.0173225 +cpp_int 256 *(int)0.0199426 +cpp_int 256 /(int)0.229286 +cpp_int 256 % 0.306542 +cpp_int 256 | 0.0257191 +cpp_int 256 & 0.0254172 +cpp_int 256 ^ 0.0259082 +cpp_int 256 << 0.0253994 +cpp_int 256 >> 0.0172635 +cpp_int 256 %(int)0.116093 +cpp_int 256 |(int)0.0233559 +cpp_int 256 &(int)0.0367792 +cpp_int 256 ^(int)0.0232914 +cpp_int 256 gcd 7.88882 +cpp_int 512 + 0.0291058 +cpp_int 512 - 0.0380025 +cpp_int 512 * 0.337161 +cpp_int 512 / 0.487075 +cpp_int 512 str 0.00494162 +cpp_int 512 +(int)0.0201989 +cpp_int 512 -(int)0.0200688 +cpp_int 512 *(int)0.0311497 +cpp_int 512 /(int)0.375279 +cpp_int 512 % 0.459737 +cpp_int 512 | 0.0297101 +cpp_int 512 & 0.0297235 +cpp_int 512 ^ 0.0296913 +cpp_int 512 << 0.0328422 +cpp_int 512 >> 0.0234706 +cpp_int 512 %(int)0.194709 +cpp_int 512 |(int)0.0258992 +cpp_int 512 &(int)0.0529542 +cpp_int 512 ^(int)0.0258749 +cpp_int 512 gcd 19.7141 +cpp_int 1024 + 0.0410101 +cpp_int 1024 - 0.0576733 +cpp_int 1024 * 1.19319 +cpp_int 1024 / 0.850798 +cpp_int 1024 str 0.0149378 +cpp_int 1024 +(int)0.0222435 +cpp_int 1024 -(int)0.0219408 +cpp_int 1024 *(int)0.0435058 +cpp_int 1024 /(int)0.6795 +cpp_int 1024 % 0.800961 +cpp_int 1024 | 0.0369613 +cpp_int 1024 & 0.0368423 +cpp_int 1024 ^ 0.0371252 +cpp_int 1024 << 0.0474759 +cpp_int 1024 >> 0.0297527 +cpp_int 1024 %(int)0.360619 +cpp_int 1024 |(int)0.0326194 +cpp_int 1024 &(int)0.0801744 +cpp_int 1024 ^(int)0.0319848 +cpp_int 1024 gcd 53.3224 +fixed_int 64 + 0.00207275 +fixed_int 64 - 0.00214524 +fixed_int 64 * 0.00391097 +fixed_int 64 / 0.0608466 +fixed_int 64 str 0.000292286 +fixed_int 64 +(int)0.00357336 +fixed_int 64 -(int)0.00352796 +fixed_int 64 *(int)0.00292725 +fixed_int 64 /(int)0.0243018 +fixed_int 64 % 0.0603067 +fixed_int 64 | 0.00258063 +fixed_int 64 & 0.00257379 +fixed_int 64 ^ 0.00258525 +fixed_int 64 << 0.00134947 +fixed_int 64 >> 0.00560378 +fixed_int 64 %(int)0.0241499 +fixed_int 64 |(int)0.00201939 +fixed_int 64 &(int)0.00206716 +fixed_int 64 ^(int)0.00201848 +fixed_int 64 gcd 0.82127 +fixed_int 128 + 0.00325349 +fixed_int 128 - 0.00366953 +fixed_int 128 * 0.010445 +fixed_int 128 / 0.113697 +fixed_int 128 str 0.000564877 +fixed_int 128 +(int)0.00377625 +fixed_int 128 -(int)0.00360179 +fixed_int 128 *(int)0.00418426 +fixed_int 128 /(int)0.091141 +fixed_int 128 % 0.113804 +fixed_int 128 | 0.00360961 +fixed_int 128 & 0.00359913 +fixed_int 128 ^ 0.00361317 +fixed_int 128 << 0.0065905 +fixed_int 128 >> 0.00654308 +fixed_int 128 %(int)0.0809135 +fixed_int 128 |(int)0.00237125 +fixed_int 128 &(int)0.00231056 +fixed_int 128 ^(int)0.00190464 +fixed_int 128 gcd 2.05126 +fixed_int 256 + 0.00785776 +fixed_int 256 - 0.00635884 +fixed_int 256 * 0.0323875 +fixed_int 256 / 0.203194 +fixed_int 256 str 0.0013816 +fixed_int 256 +(int)0.00413397 +fixed_int 256 -(int)0.00379699 +fixed_int 256 *(int)0.00852456 +fixed_int 256 /(int)0.183053 +fixed_int 256 % 0.200368 +fixed_int 256 | 0.0105747 +fixed_int 256 & 0.0105856 +fixed_int 256 ^ 0.0105755 +fixed_int 256 << 0.00874545 +fixed_int 256 >> 0.00906624 +fixed_int 256 %(int)0.152826 +fixed_int 256 |(int)0.00261619 +fixed_int 256 &(int)0.00424202 +fixed_int 256 ^(int)0.00263274 +fixed_int 256 gcd 5.42715 +fixed_int 512 + 0.0131311 +fixed_int 512 - 0.0122513 +fixed_int 512 * 0.205979 +fixed_int 512 / 0.383601 +fixed_int 512 str 0.0043558 +fixed_int 512 +(int)0.00639746 +fixed_int 512 -(int)0.00641876 +fixed_int 512 *(int)0.0152369 +fixed_int 512 /(int)0.363289 +fixed_int 512 % 0.38201 +fixed_int 512 | 0.0131075 +fixed_int 512 & 0.0131292 +fixed_int 512 ^ 0.01314 +fixed_int 512 << 0.0130248 +fixed_int 512 >> 0.0131451 +fixed_int 512 %(int)0.304714 +fixed_int 512 |(int)0.00574368 +fixed_int 512 &(int)0.00810836 +fixed_int 512 ^(int)0.00576694 +fixed_int 512 gcd 16.6269 +fixed_int 1024 + 0.0322386 +fixed_int 1024 - 0.0312142 +fixed_int 1024 * 0.716002 +fixed_int 1024 / 0.728338 +fixed_int 1024 str 0.0135445 +fixed_int 1024 +(int)0.011986 +fixed_int 1024 -(int)0.0119838 +fixed_int 1024 *(int)0.0349878 +fixed_int 1024 /(int)0.708856 +fixed_int 1024 % 0.723622 +fixed_int 1024 | 0.0181468 +fixed_int 1024 & 0.0182648 +fixed_int 1024 ^ 0.018185 +fixed_int 1024 << 0.0252997 +fixed_int 1024 >> 0.0257832 +fixed_int 1024 %(int)0.597535 +fixed_int 1024 |(int)0.0116417 +fixed_int 1024 &(int)0.0172111 +fixed_int 1024 ^(int)0.011526 +fixed_int 1024 gcd 70.6396 [section:integer_performance Integer Type Perfomance] [table Operator % [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.054413s)][[*1] (0.106105s)][[*1] (0.19685s)][1.67316 (0.385184s)][2.3543 (0.711308s)]] -[[gmp_int][3.04743 (0.16582s)][1.55485 (0.164977s)][1.00128 (0.197103s)][[*1] (0.230214s)][[*1] (0.302132s)]] +[[cpp_int][1.5779 (0.0951581s)][1.48514 (0.169015s)][1.59753 (0.306542s)][2.06645 (0.459737s)][2.79666 (0.800961s)]] +[[fixed_int][[*1] (0.0603067s)][[*1] (0.113804s)][1.04421 (0.200368s)][1.71708 (0.38201s)][2.52662 (0.723622s)]] +[[gmp_int][2.72898 (0.164576s)][1.41658 (0.161212s)][[*1] (0.191884s)][[*1] (0.222477s)][[*1] (0.286399s)]] ] [table Operator %(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0243407s)][1.99962 (0.0811764s)][2.96437 (0.15306s)][4.64875 (0.303051s)][7.31311 (0.584615s)]] -[[gmp_int][1.42913 (0.034786s)][[*1] (0.0405959s)][[*1] (0.0516333s)][[*1] (0.0651899s)][[*1] (0.0799406s)]] +[[cpp_int][[*1] (0.0229261s)][1.28944 (0.0476063s)][2.44735 (0.116093s)][3.21471 (0.194709s)][4.73812 (0.360619s)]] +[[fixed_int][1.05338 (0.0241499s)][2.19159 (0.0809135s)][3.22171 (0.152826s)][5.03092 (0.304714s)][7.85093 (0.597535s)]] +[[gmp_int][1.29749 (0.0297463s)][[*1] (0.03692s)][[*1] (0.0474363s)][[*1] (0.0605682s)][[*1] (0.0761102s)]] ] [table Operator & [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00259593s)][[*1] (0.00361924s)][[*1] (0.0108415s)][[*1] (0.013122s)][[*1] (0.0176585s)]] -[[gmp_int][4.85187 (0.0125951s)][3.96768 (0.01436s)][1.43661 (0.015575s)][1.50716 (0.019777s)][1.50977 (0.0266602s)]] +[[cpp_int][7.65289 (0.0196969s)][6.42545 (0.023126s)][2.4011 (0.0254172s)][2.26393 (0.0297235s)][2.01712 (0.0368423s)]] +[[fixed_int][[*1] (0.00257379s)][[*1] (0.00359913s)][[*1] (0.0105856s)][[*1] (0.0131292s)][[*1] (0.0182648s)]] +[[gmp_int][3.71307 (0.00955666s)][3.15518 (0.0113559s)][1.2071 (0.012778s)][1.25891 (0.0165285s)][1.2638 (0.023083s)]] ] [table Operator &(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00209559s)][[*1] (0.00245967s)][[*1] (0.00419648s)][[*1] (0.00836021s)][[*1] (0.0166854s)]] -[[gmp_int][21.0856 (0.0441868s)][18.4577 (0.0453998s)][11.1151 (0.0466442s)][5.96293 (0.0498514s)][3.23322 (0.0539474s)]] +[[cpp_int][10.8871 (0.0225055s)][11.6934 (0.0270183s)][8.67021 (0.0367792s)][6.53082 (0.0529542s)][4.65829 (0.0801744s)]] +[[fixed_int][[*1] (0.00206716s)][[*1] (0.00231056s)][[*1] (0.00424202s)][[*1] (0.00810836s)][[*1] (0.0172111s)]] +[[gmp_int][20.1865 (0.0417288s)][18.5392 (0.0428359s)][10.2956 (0.0436742s)][5.74703 (0.046599s)][2.90042 (0.0499195s)]] ] [table Operator * [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00392745s)][[*1] (0.0104772s)][[*1] (0.0324122s)][1.95004 (0.201059s)][2.14731 (0.701951s)]] -[[gmp_int][2.96502 (0.011645s)][1.74194 (0.0182506s)][1.4714 (0.0476911s)][[*1] (0.103105s)][[*1] (0.326898s)]] +[[cpp_int][8.34111 (0.0326218s)][3.59818 (0.0375831s)][3.49662 (0.113247s)][3.40211 (0.337161s)][3.76364 (1.19319s)]] +[[fixed_int][[*1] (0.00391097s)][[*1] (0.010445s)][[*1] (0.0323875s)][2.07843 (0.205979s)][2.25847 (0.716002s)]] +[[gmp_int][2.87022 (0.0112253s)][1.54221 (0.0161084s)][1.28899 (0.0417471s)][[*1] (0.0991032s)][[*1] (0.31703s)]] ] [table Operator *(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00294381s)][[*1] (0.00422148s)][[*1] (0.00849409s)][[*1] (0.015882s)][1.15522 (0.0346698s)]] -[[gmp_int][4.09319 (0.0120496s)][3.01026 (0.0127078s)][2.0089 (0.0170638s)][1.34479 (0.021358s)][[*1] (0.0300116s)]] +[[cpp_int][5.15967 (0.0151037s)][4.21584 (0.0176402s)][2.33943 (0.0199426s)][2.04436 (0.0311497s)][1.67133 (0.0435058s)]] +[[fixed_int][[*1] (0.00292725s)][[*1] (0.00418426s)][[*1] (0.00852456s)][[*1] (0.0152369s)][1.3441 (0.0349878s)]] +[[gmp_int][3.01114 (0.00881438s)][2.72791 (0.0114143s)][1.60924 (0.0137181s)][1.1847 (0.0180512s)][[*1] (0.0260306s)]] ] [table Operator + [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00207163s)][[*1] (0.00326026s)][[*1] (0.00834722s)][[*1] (0.0128543s)][[*1] (0.0330379s)]] -[[gmp_int][8.08642 (0.0167521s)][5.89259 (0.0192114s)][2.76118 (0.0230482s)][2.19911 (0.028268s)][1.23787 (0.0408966s)]] +[[cpp_int][7.37741 (0.0152915s)][5.2494 (0.0170788s)][2.95092 (0.0231877s)][2.21655 (0.0291058s)][1.27208 (0.0410101s)]] +[[fixed_int][[*1] (0.00207275s)][[*1] (0.00325349s)][[*1] (0.00785776s)][[*1] (0.0131311s)][[*1] (0.0322386s)]] +[[gmp_int][7.99998 (0.016582s)][5.62745 (0.0183088s)][2.86129 (0.0224834s)][2.11283 (0.0277439s)][1.23293 (0.0397479s)]] ] [table Operator +(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00358307s)][[*1] (0.00359962s)][[*1] (0.00405163s)][[*1] (0.00694047s)][[*1] (0.0116939s)]] -[[gmp_int][2.01857 (0.00723269s)][2.42047 (0.00871277s)][3.5813 (0.0145101s)][2.45162 (0.0170154s)][1.69017 (0.0197647s)]] +[[cpp_int][3.69474 (0.0132027s)][3.83536 (0.0144833s)][3.91229 (0.0161733s)][3.15733 (0.0201989s)][1.85579 (0.0222435s)]] +[[fixed_int][[*1] (0.00357336s)][[*1] (0.00377625s)][[*1] (0.00413397s)][[*1] (0.00639746s)][[*1] (0.011986s)]] +[[gmp_int][1.92643 (0.00688382s)][2.29418 (0.00866339s)][2.71097 (0.0112071s)][2.23261 (0.014283s)][1.58492 (0.0189969s)]] ] [table Operator - [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00216403s)][[*1] (0.00372498s)][[*1] (0.00653903s)][[*1] (0.0120433s)][[*1] (0.0311489s)]] -[[gmp_int][8.72818 (0.0188881s)][5.89208 (0.0219479s)][4.43331 (0.0289896s)][2.92463 (0.0352221s)][1.48689 (0.0463151s)]] +[[cpp_int][8.94166 (0.0191821s)][6.22351 (0.0228373s)][4.61443 (0.0293424s)][3.10192 (0.0380025s)][1.84766 (0.0576733s)]] +[[fixed_int][[*1] (0.00214524s)][[*1] (0.00366953s)][[*1] (0.00635884s)][[*1] (0.0122513s)][[*1] (0.0312142s)]] +[[gmp_int][8.13505 (0.0174517s)][5.15777 (0.0189266s)][3.94128 (0.025062s)][2.60278 (0.0318874s)][1.35297 (0.042232s)]] ] [table Operator -(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00354668s)][[*1] (0.00360689s)][[*1] (0.00385712s)][[*1] (0.00681002s)][[*1] (0.0116182s)]] -[[gmp_int][2.09194 (0.00741945s)][3.61625 (0.0130434s)][3.8458 (0.0148337s)][2.63767 (0.0179625s)][1.72107 (0.0199956s)]] +[[cpp_int][3.57555 (0.0126144s)][3.86529 (0.013922s)][4.56215 (0.0173225s)][3.12658 (0.0200688s)][1.83087 (0.0219408s)]] +[[fixed_int][[*1] (0.00352796s)][[*1] (0.00360179s)][[*1] (0.00379699s)][[*1] (0.00641876s)][[*1] (0.0119838s)]] +[[gmp_int][2.08226 (0.00734613s)][2.4833 (0.0089443s)][3.063 (0.0116302s)][2.33493 (0.0149874s)][1.62759 (0.0195046s)]] ] [table Operator / [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0556903s)][[*1] (0.105756s)][[*1] (0.198305s)][1.37248 (0.385977s)][1.91862 (0.708393s)]] -[[gmp_int][3.04721 (0.1697s)][1.85862 (0.196561s)][1.21304 (0.240552s)][[*1] (0.281226s)][[*1] (0.36922s)]] +[[cpp_int][1.5631 (0.0951094s)][1.44205 (0.163958s)][1.655 (0.336287s)][1.77123 (0.487075s)][2.45907 (0.850798s)]] +[[fixed_int][[*1] (0.0608466s)][[*1] (0.113697s)][[*1] (0.203194s)][1.39495 (0.383601s)][2.10512 (0.728338s)]] +[[gmp_int][2.80954 (0.170951s)][1.68671 (0.191775s)][1.14992 (0.233656s)][[*1] (0.274993s)][[*1] (0.345984s)]] ] [table Operator /(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0169012s)][1.11654 (0.0634475s)][1.86084 (0.127666s)][2.57379 (0.244657s)][4.79191 (0.692818s)]] -[[gmp_int][2.96468 (0.0501068s)][[*1] (0.0568248s)][[*1] (0.0686065s)][[*1] (0.0950571s)][[*1] (0.144581s)]] +[[cpp_int][2.0209 (0.0491116s)][1.81816 (0.0972057s)][3.43412 (0.229286s)][4.13899 (0.375279s)][4.84836 (0.6795s)]] +[[fixed_int][[*1] (0.0243018s)][1.70472 (0.091141s)][2.74167 (0.183053s)][4.00675 (0.363289s)][5.05782 (0.708856s)]] +[[gmp_int][1.91611 (0.0465651s)][[*1] (0.0534638s)][[*1] (0.0667669s)][[*1] (0.0906691s)][[*1] (0.140151s)]] ] [table Operator << [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00115455s)][[*1] (0.00632357s)][[*1] (0.00826823s)][[*1] (0.0150546s)][[*1] (0.0242721s)]] -[[gmp_int][8.39362 (0.00969083s)][2.07445 (0.0131179s)][1.80141 (0.0148945s)][1.21421 (0.0182795s)][1.02121 (0.0247868s)]] +[[cpp_int][13.292 (0.0179372s)][3.27363 (0.0215749s)][2.9043 (0.0253994s)][2.52151 (0.0328422s)][2.34293 (0.0474759s)]] +[[fixed_int][[*1] (0.00134947s)][[*1] (0.0065905s)][[*1] (0.00874545s)][[*1] (0.0130248s)][1.24854 (0.0252997s)]] +[[gmp_int][7.85814 (0.0106043s)][1.56732 (0.0103295s)][1.38897 (0.0121471s)][1.13928 (0.014839s)][[*1] (0.0202635s)]] ] [table Operator >> [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00147407s)][[*1] (0.00238745s)][[*1] (0.00854822s)][1.10734 (0.0134889s)][1.52739 (0.0248274s)]] -[[gmp_int][8.85991 (0.0130601s)][4.4845 (0.0107065s)][1.30011 (0.0111136s)][[*1] (0.0121814s)][[*1] (0.0162548s)]] +[[cpp_int][2.60907 (0.0146206s)][2.28025 (0.0149198s)][2.07275 (0.0172635s)][2.37318 (0.0234706s)][2.32609 (0.0297527s)]] +[[fixed_int][[*1] (0.00560378s)][[*1] (0.00654308s)][1.08854 (0.00906624s)][1.32914 (0.0131451s)][2.01575 (0.0257832s)]] +[[gmp_int][1.67542 (0.0093887s)][1.24317 (0.00813413s)][[*1] (0.00832878s)][[*1] (0.00988994s)][[*1] (0.0127909s)]] ] [table Operator ^ [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00256688s)][[*1] (0.00361813s)][[*1] (0.0108455s)][[*1] (0.013116s)][[*1] (0.0177043s)]] -[[gmp_int][5.05409 (0.0129732s)][3.88746 (0.0140653s)][1.53751 (0.0166751s)][1.90691 (0.025011s)][1.69135 (0.0299441s)]] +[[cpp_int][8.06918 (0.0208608s)][6.34562 (0.0229278s)][2.44983 (0.0259082s)][2.25961 (0.0296913s)][2.04153 (0.0371252s)]] +[[fixed_int][[*1] (0.00258525s)][[*1] (0.00361317s)][[*1] (0.0105755s)][[*1] (0.01314s)][[*1] (0.018185s)]] +[[gmp_int][3.81916 (0.00987346s)][3.10299 (0.0112116s)][1.27226 (0.0134548s)][1.5894 (0.0208848s)][1.36422 (0.0248084s)]] ] [table Operator ^(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00202777s)][[*1] (0.00237775s)][[*1] (0.0027653s)][[*1] (0.00608555s)][[*1] (0.0108555s)]] -[[gmp_int][21.821 (0.0442481s)][19.7034 (0.0468496s)][16.847 (0.0465869s)][8.16164 (0.049668s)][4.97188 (0.0539722s)]] +[[cpp_int][9.47925 (0.0191337s)][10.2109 (0.0194481s)][8.84686 (0.0232914s)][4.48677 (0.0258749s)][2.775 (0.0319848s)]] +[[fixed_int][[*1] (0.00201848s)][[*1] (0.00190464s)][[*1] (0.00263274s)][[*1] (0.00576694s)][[*1] (0.011526s)]] +[[gmp_int][20.1032 (0.0405779s)][21.9738 (0.0418522s)][16.1671 (0.0425636s)][7.91768 (0.0456608s)][4.2261 (0.0487102s)]] +] +[table Operator gcd +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][8.64165 (1.50205s)][7.81307 (3.36986s)][3.81369 (7.88882s)][4.20792 (19.7141s)][5.27284 (53.3224s)]] +[[fixed_int][4.72495 (0.82127s)][4.75589 (2.05126s)][2.62364 (5.42715s)][3.54898 (16.6269s)][6.98527 (70.6396s)]] +[[gmp_int][[*1] (0.173816s)][[*1] (0.43131s)][[*1] (2.06855s)][[*1] (4.68499s)][[*1] (10.1127s)]] ] [table Operator str [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.000302762s)][[*1] (0.000500691s)][1.14936 (0.00111683s)][1.71055 (0.00286314s)][2.93313 (0.00872206s)]] -[[gmp_int][1.11188 (0.000336635s)][4.63553 (0.00232097s)][[*1] (0.000971703s)][[*1] (0.00167382s)][[*1] (0.00297363s)]] +[[cpp_int][1.46619 (0.000428547s)][1.98732 (0.000744647s)][3.17907 (0.00190436s)][3.81717 (0.00494162s)][5.50009 (0.0149378s)]] +[[fixed_int][[*1] (0.000292286s)][1.50755 (0.000564877s)][2.30639 (0.0013816s)][3.36465 (0.0043558s)][4.98706 (0.0135445s)]] +[[gmp_int][1.17587 (0.000343689s)][[*1] (0.000374699s)][[*1] (0.00059903s)][[*1] (0.00129458s)][[*1] (0.00271592s)]] ] [table Operator | [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00257616s)][[*1] (0.00363433s)][[*1] (0.0108232s)][[*1] (0.0131341s)][[*1] (0.0176472s)]] -[[gmp_int][4.49789 (0.0115873s)][3.7058 (0.0134681s)][1.47085 (0.0159192s)][1.58756 (0.0208511s)][1.61398 (0.0284821s)]] +[[cpp_int][7.73565 (0.0199629s)][6.36166 (0.0229631s)][2.43214 (0.0257191s)][2.26665 (0.0297101s)][2.0368 (0.0369613s)]] +[[fixed_int][[*1] (0.00258063s)][[*1] (0.00360961s)][[*1] (0.0105747s)][[*1] (0.0131075s)][[*1] (0.0181468s)]] +[[gmp_int][3.9353 (0.0101555s)][2.96987 (0.0107201s)][1.22452 (0.0129489s)][1.65632 (0.0217103s)][1.44352 (0.0261953s)]] ] [table Operator |(int) [[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00208078s)][[*1] (0.00190869s)][[*1] (0.00275195s)][[*1] (0.00618124s)][[*1] (0.0107899s)]] -[[gmp_int][20.4129 (0.0424747s)][23.0676 (0.0440289s)][17.2504 (0.0474723s)][7.98521 (0.0493584s)][4.87243 (0.0525727s)]] -] -[endsect] -[section:rational_performance Rational Type Perfomance] -[table Operator * -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.426868s)][[*1] (0.968054s)][[*1] (4.39195s)][[*1] (9.6344s)][[*1] (20.9879s)]] -] -[table Operator *(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.344178s)][[*1] (0.179899s)][[*1] (0.200539s)][[*1] (0.254142s)][[*1] (0.328602s)]] -] -[table Operator + -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.254473s)][[*1] (0.542374s)][[*1] (2.34795s)][[*1] (5.10523s)][[*1] (11.2331s)]] -] -[table Operator +(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.309729s)][[*1] (0.154116s)][[*1] (0.177483s)][[*1] (0.212807s)][[*1] (0.27756s)]] -] -[table Operator - -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.260331s)][[*1] (0.545764s)][[*1] (2.3565s)][[*1] (5.08802s)][[*1] (11.2446s)]] -] -[table Operator -(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.306598s)][[*1] (0.151187s)][[*1] (0.16783s)][[*1] (0.212048s)][[*1] (0.271845s)]] -] -[table Operator / -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (1.50105s)][[*1] (2.78757s)][[*1] (8.9203s)][[*1] (16.8502s)][[*1] (35.6472s)]] -] -[table Operator /(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.32842s)][[*1] (0.184167s)][[*1] (0.206129s)][[*1] (0.262442s)][[*1] (0.350883s)]] -] -[table Operator str -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.000927423s)][[*1] (0.00111655s)][[*1] (0.00175742s)][[*1] (0.00246714s)][[*1] (0.00550783s)]] +[[cpp_int][9.20066 (0.0185797s)][8.21071 (0.0194697s)][8.92746 (0.0233559s)][4.50916 (0.0258992s)][2.80194 (0.0326194s)]] +[[fixed_int][[*1] (0.00201939s)][[*1] (0.00237125s)][[*1] (0.00261619s)][[*1] (0.00574368s)][[*1] (0.0116417s)]] +[[gmp_int][19.9733 (0.0403338s)][17.3819 (0.0412168s)][16.2676 (0.0425591s)][8.05945 (0.0462909s)][4.22404 (0.049175s)]] ] [endsect] diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index 72ef2938..dbf6b539 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -587,6 +587,11 @@ int main() test("cpp_int", 256); test("cpp_int", 512); test("cpp_int", 1024); + + test > >("cpp_int(fixed)", 128); + test > >("cpp_int(fixed)", 256); + test > >("cpp_int(fixed)", 512); + test > >("cpp_int(fixed)", 1024); #endif #ifdef TEST_MPQ test("mpq_rational", 64); From 2178bef843a0b12e6247339181b0828f4ab58911 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 8 Mar 2012 17:54:28 +0000 Subject: [PATCH 126/256] Fix some bugs in division and addition code [SVN r77266] --- include/boost/multiprecision/cpp_int.hpp | 4 +- performance/performance_test-gcc-linux.log | 665 ++++----------------- performance/performance_test.cpp | 3 +- 3 files changed, 127 insertions(+), 545 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 6c0addf1..548c0e33 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1060,7 +1060,7 @@ inline void multiply(cpp_int_backend& result, const typename cpp_int_backend::limb_pointer pr = result.limbs(); double_limb_type carry = 0; - std::memset(pr, 0, (as + bs) * sizeof(limb_type)); + std::memset(pr, 0, result.size() * sizeof(limb_type)); unsigned inner_limit = result.size() - as; for(unsigned i = 0; i < as; ++i) { @@ -1242,7 +1242,7 @@ void divide_unsigned_helper(cpp_int_backend& result, { double_limb_type a, b; a = (static_cast(px[1]) << cpp_int_backend::limb_bits) | px[0]; - b = y_order > 1 ? + b = y_order ? (static_cast(py[1]) << cpp_int_backend::limb_bits) | py[0] : py[0]; result = a / b; diff --git a/performance/performance_test-gcc-linux.log b/performance/performance_test-gcc-linux.log index 4fc1d067..6df495e4 100644 --- a/performance/performance_test-gcc-linux.log +++ b/performance/performance_test-gcc-linux.log @@ -1,542 +1,123 @@ -gmp_int 64 + 0.0168195 -gmp_int 64 - 0.0186168 -gmp_int 64 * 0.0114224 -gmp_int 64 / 0.168483 -gmp_int 64 str 0.000337753 -gmp_int 64 +(int)0.00683062 -gmp_int 64 -(int)0.00706193 -gmp_int 64 *(int)0.00869587 -gmp_int 64 /(int)0.0453323 -gmp_int 64 % 0.157804 -gmp_int 64 | 0.00932423 -gmp_int 64 & 0.00944499 -gmp_int 64 ^ 0.00996572 -gmp_int 64 << 0.00922261 -gmp_int 64 >> 0.00918099 -gmp_int 64 %(int)0.0281261 -gmp_int 64 |(int)0.0397808 -gmp_int 64 &(int)0.0415959 -gmp_int 64 ^(int)0.0404741 -gmp_int 64 gcd 0.176988 -gmp_int 128 + 0.0179677 -gmp_int 128 - 0.0189371 -gmp_int 128 * 0.0161959 -gmp_int 128 / 0.190813 -gmp_int 128 str 0.000372045 -gmp_int 128 +(int)0.00848258 -gmp_int 128 -(int)0.00875216 -gmp_int 128 *(int)0.0113487 -gmp_int 128 /(int)0.0525228 -gmp_int 128 % 0.15826 -gmp_int 128 | 0.0106091 -gmp_int 128 & 0.0112477 -gmp_int 128 ^ 0.0113254 -gmp_int 128 << 0.0100071 -gmp_int 128 >> 0.00769246 -gmp_int 128 %(int)0.0347099 -gmp_int 128 |(int)0.0407317 -gmp_int 128 &(int)0.0426387 -gmp_int 128 ^(int)0.041833 -gmp_int 128 gcd 0.432692 -gmp_int 256 + 0.0228276 -gmp_int 256 - 0.0253604 -gmp_int 256 * 0.0424289 -gmp_int 256 / 0.232371 -gmp_int 256 str 0.000590578 -gmp_int 256 +(int)0.0111117 -gmp_int 256 -(int)0.0119104 -gmp_int 256 *(int)0.0138547 -gmp_int 256 /(int)0.0658471 -gmp_int 256 % 0.189604 -gmp_int 256 | 0.0128476 -gmp_int 256 & 0.0148126 -gmp_int 256 ^ 0.0134169 -gmp_int 256 << 0.0117499 -gmp_int 256 >> 0.00808343 -gmp_int 256 %(int)0.0471351 -gmp_int 256 |(int)0.0423473 -gmp_int 256 &(int)0.0436809 -gmp_int 256 ^(int)0.0426564 -gmp_int 256 gcd 2.06786 -gmp_int 512 + 0.0274004 -gmp_int 512 - 0.0318076 -gmp_int 512 * 0.097384 -gmp_int 512 / 0.272392 -gmp_int 512 str 0.0012598 -gmp_int 512 +(int)0.0142198 -gmp_int 512 -(int)0.0148327 -gmp_int 512 *(int)0.0179982 -gmp_int 512 /(int)0.0906272 -gmp_int 512 % 0.22163 -gmp_int 512 | 0.0211022 -gmp_int 512 & 0.0165864 -gmp_int 512 ^ 0.0218245 -gmp_int 512 << 0.0145569 -gmp_int 512 >> 0.00978776 -gmp_int 512 %(int)0.0601084 -gmp_int 512 |(int)0.0460084 -gmp_int 512 &(int)0.0466719 -gmp_int 512 ^(int)0.045828 -gmp_int 512 gcd 4.69155 -gmp_int 1024 + 0.038508 -gmp_int 1024 - 0.0417826 -gmp_int 1024 * 0.315222 -gmp_int 1024 / 0.352494 -gmp_int 1024 str 0.00274057 -gmp_int 1024 +(int)0.0187457 -gmp_int 1024 -(int)0.0194778 -gmp_int 1024 *(int)0.0259764 -gmp_int 1024 /(int)0.140287 -gmp_int 1024 % 0.284404 -gmp_int 1024 | 0.0242278 -gmp_int 1024 & 0.0235658 -gmp_int 1024 ^ 0.0249122 -gmp_int 1024 << 0.0202809 -gmp_int 1024 >> 0.0127441 -gmp_int 1024 %(int)0.0758432 -gmp_int 1024 |(int)0.0495155 -gmp_int 1024 &(int)0.0503542 -gmp_int 1024 ^(int)0.0510615 -gmp_int 1024 gcd 10.1136 -cpp_int 64 + 0.0157994 -cpp_int 64 - 0.0256769 -cpp_int 64 * 0.0226198 -cpp_int 64 / 0.102281 -cpp_int 64 str 0.000380146 -cpp_int 64 +(int)0.0103873 -cpp_int 64 -(int)0.00898962 -cpp_int 64 *(int)0.0159193 -cpp_int 64 /(int)0.0522854 -cpp_int 64 % 0.0999552 -cpp_int 64 | 0.0203489 -cpp_int 64 & 0.0202989 -cpp_int 64 ^ 0.020334 -cpp_int 64 << 0.0166545 -cpp_int 64 >> 0.0143805 -cpp_int 64 %(int)0.0389361 -cpp_int 64 |(int)0.0198498 -cpp_int 64 &(int)0.024074 -cpp_int 64 ^(int)0.0198061 -cpp_int 64 gcd 1.72384 -cpp_int 128 + 0.0182643 -cpp_int 128 - 0.0271678 -cpp_int 128 * 0.0408988 -cpp_int 128 / 0.172852 -cpp_int 128 str 0.000693873 -cpp_int 128 +(int)0.0116175 -cpp_int 128 -(int)0.0104572 -cpp_int 128 *(int)0.0187569 -cpp_int 128 /(int)0.108782 -cpp_int 128 % 0.179562 -cpp_int 128 | 0.0245406 -cpp_int 128 & 0.0245186 -cpp_int 128 ^ 0.0247923 -cpp_int 128 << 0.0196597 -cpp_int 128 >> 0.0157968 -cpp_int 128 %(int)0.0940069 -cpp_int 128 |(int)0.0210111 -cpp_int 128 &(int)0.0322746 -cpp_int 128 ^(int)0.0210955 -cpp_int 128 gcd 3.97787 -cpp_int 256 + 0.0236538 -cpp_int 256 - 0.0339319 -cpp_int 256 * 0.107568 -cpp_int 256 / 0.376559 -cpp_int 256 str 0.00192567 -cpp_int 256 +(int)0.0156148 -cpp_int 256 -(int)0.0125633 -cpp_int 256 *(int)0.0227126 -cpp_int 256 /(int)0.240023 -cpp_int 256 % 0.324919 -cpp_int 256 | 0.0273651 -cpp_int 256 & 0.0268812 -cpp_int 256 ^ 0.027153 -cpp_int 256 << 0.0240014 -cpp_int 256 >> 0.0178114 -cpp_int 256 %(int)0.196223 -cpp_int 256 |(int)0.0238206 -cpp_int 256 &(int)0.0518555 -cpp_int 256 ^(int)0.0237059 -cpp_int 256 gcd 9.44724 -cpp_int 512 + 0.0286286 -cpp_int 512 - 0.0473463 -cpp_int 512 * 0.36983 -cpp_int 512 / 0.53608 -cpp_int 512 str 0.00489147 -cpp_int 512 +(int)0.0165983 -cpp_int 512 -(int)0.0157028 -cpp_int 512 *(int)0.0327202 -cpp_int 512 /(int)0.39506 -cpp_int 512 % 0.484383 -cpp_int 512 | 0.0336779 -cpp_int 512 & 0.0332565 -cpp_int 512 ^ 0.033731 -cpp_int 512 << 0.032593 -cpp_int 512 >> 0.0249415 -cpp_int 512 %(int)0.347801 -cpp_int 512 |(int)0.0270701 -cpp_int 512 &(int)0.0847243 -cpp_int 512 ^(int)0.0270095 -cpp_int 512 gcd 22.6824 -cpp_int 1024 + 0.041093 -cpp_int 1024 - 0.065839 -cpp_int 1024 * 1.36107 -cpp_int 1024 / 0.91127 -cpp_int 1024 str 0.0150341 -cpp_int 1024 +(int)0.0212673 -cpp_int 1024 -(int)0.0207903 -cpp_int 1024 *(int)0.0482894 -cpp_int 1024 /(int)0.711756 -cpp_int 1024 % 0.853306 -cpp_int 1024 | 0.0459271 -cpp_int 1024 & 0.0455113 -cpp_int 1024 ^ 0.0457905 -cpp_int 1024 << 0.053456 -cpp_int 1024 >> 0.0339107 -cpp_int 1024 %(int)0.653379 -cpp_int 1024 |(int)0.0323199 -cpp_int 1024 &(int)0.152555 -cpp_int 1024 ^(int)0.032137 -cpp_int 1024 gcd 59.7424 -tommath_int 64 + 0.0166687 -tommath_int 64 - 0.0270094 -tommath_int 64 * 0.0386521 -tommath_int 64 / 0.98286 -tommath_int 64 str 0.00413258 -tommath_int 64 +(int)0.174336 -tommath_int 64 -(int)0.174454 -tommath_int 64 *(int)0.191871 -tommath_int 64 /(int)0.886522 -tommath_int 64 % 0.980074 -tommath_int 64 | 0.0716826 -tommath_int 64 & 0.0777977 -tommath_int 64 ^ 0.0730863 -tommath_int 64 << 0.0200111 -tommath_int 64 >> 0.124855 -tommath_int 64 %(int)0.734449 -tommath_int 64 |(int)0.254639 -tommath_int 64 &(int)0.226047 -tommath_int 64 ^(int)0.252631 -tommath_int 64 gcd 3.80432 -tommath_int 128 + 0.0169388 -tommath_int 128 - 0.0247515 -tommath_int 128 * 0.0588799 -tommath_int 128 / 1.11408 -tommath_int 128 str 0.00853237 -tommath_int 128 +(int)0.17465 -tommath_int 128 -(int)0.169003 -tommath_int 128 *(int)0.193938 -tommath_int 128 /(int)0.901904 -tommath_int 128 % 1.09735 -tommath_int 128 | 0.0714914 -tommath_int 128 & 0.0734869 -tommath_int 128 ^ 0.0724281 -tommath_int 128 << 0.0315817 -tommath_int 128 >> 0.137548 -tommath_int 128 %(int)0.835579 -tommath_int 128 |(int)0.25282 -tommath_int 128 &(int)0.22947 -tommath_int 128 ^(int)0.253212 -tommath_int 128 gcd 7.29351 -tommath_int 256 + 0.0191982 -tommath_int 256 - 0.0260308 -tommath_int 256 * 0.0850765 -tommath_int 256 / 1.3375 -tommath_int 256 str 0.0217479 -tommath_int 256 +(int)0.173229 -tommath_int 256 -(int)0.17296 -tommath_int 256 *(int)0.201834 -tommath_int 256 /(int)1.153 -tommath_int 256 % 1.34044 -tommath_int 256 | 0.074755 -tommath_int 256 & 0.0755475 -tommath_int 256 ^ 0.0805466 -tommath_int 256 << 0.0382785 -tommath_int 256 >> 0.141309 -tommath_int 256 %(int)1.19796 -tommath_int 256 |(int)0.255801 -tommath_int 256 &(int)0.233997 -tommath_int 256 ^(int)0.25474 -tommath_int 256 gcd 15.3331 -tommath_int 512 + 0.0240257 -tommath_int 512 - 0.0303227 -tommath_int 512 * 0.195612 -tommath_int 512 / 1.96548 -tommath_int 512 str 0.0563537 -tommath_int 512 +(int)0.174848 -tommath_int 512 -(int)0.176184 -tommath_int 512 *(int)0.223672 -tommath_int 512 /(int)1.68054 -tommath_int 512 % 1.95689 -tommath_int 512 | 0.0801272 -tommath_int 512 & 0.0806169 -tommath_int 512 ^ 0.080112 -tommath_int 512 << 0.0451545 -tommath_int 512 >> 0.151606 -tommath_int 512 %(int)1.74812 -tommath_int 512 |(int)0.260477 -tommath_int 512 &(int)0.237892 -tommath_int 512 ^(int)0.259232 -tommath_int 512 gcd 31.9471 -tommath_int 1024 + 0.035905 -tommath_int 1024 - 0.0429664 -tommath_int 1024 * 0.564578 -tommath_int 1024 / 3.17298 -tommath_int 1024 str 0.187413 -tommath_int 1024 +(int)0.190852 -tommath_int 1024 -(int)0.189438 -tommath_int 1024 *(int)0.271175 -tommath_int 1024 /(int)2.92342 -tommath_int 1024 % 3.20126 -tommath_int 1024 | 0.0939085 -tommath_int 1024 & 0.10264 -tommath_int 1024 ^ 0.0957583 -tommath_int 1024 << 0.0670281 -tommath_int 1024 >> 0.166781 -tommath_int 1024 %(int)2.88178 -tommath_int 1024 |(int)0.267844 -tommath_int 1024 &(int)0.252612 -tommath_int 1024 ^(int)0.270201 -tommath_int 1024 gcd 68.3106 -fixed_int 64 + 0.00139312 -fixed_int 64 - 0.00162339 -fixed_int 64 * 0.00699782 -fixed_int 64 / 0.0526074 -fixed_int 64 str 0.000220769 -fixed_int 64 +(int)0.00224121 -fixed_int 64 -(int)0.00194005 -fixed_int 64 *(int)0.0023299 -fixed_int 64 /(int)0.0222776 -fixed_int 64 % 0.0533221 -fixed_int 64 | 0.00173919 -fixed_int 64 & 0.00172375 -fixed_int 64 ^ 0.00173786 -fixed_int 64 << 0.000542177 -fixed_int 64 >> 0.000774259 -fixed_int 64 %(int)0.0213357 -fixed_int 64 |(int)0.00111648 -fixed_int 64 &(int)0.00122907 -fixed_int 64 ^(int)0.00107255 -fixed_int 64 gcd 0.694716 -fixed_int 128 + 0.00257987 -fixed_int 128 - 0.00292488 -fixed_int 128 * 0.0224222 -fixed_int 128 / 0.104045 -fixed_int 128 str 0.000463955 -fixed_int 128 +(int)0.00201262 -fixed_int 128 -(int)0.00162514 -fixed_int 128 *(int)0.0029339 -fixed_int 128 /(int)0.0854855 -fixed_int 128 % 0.104704 -fixed_int 128 | 0.00262052 -fixed_int 128 & 0.00263811 -fixed_int 128 ^ 0.00262317 -fixed_int 128 << 0.00169023 -fixed_int 128 >> 0.00194871 -fixed_int 128 %(int)0.0765247 -fixed_int 128 |(int)0.0012695 -fixed_int 128 &(int)0.00213023 -fixed_int 128 ^(int)0.00126692 -fixed_int 128 gcd 1.94748 -fixed_int 256 + 0.00534754 -fixed_int 256 - 0.0057397 -fixed_int 256 * 0.0746728 -fixed_int 256 / 0.188237 -fixed_int 256 str 0.00110489 -fixed_int 256 +(int)0.00239737 -fixed_int 256 -(int)0.00190618 -fixed_int 256 *(int)0.00532854 -fixed_int 256 /(int)0.176302 -fixed_int 256 % 0.185671 -fixed_int 256 | 0.00635312 -fixed_int 256 & 0.00641492 -fixed_int 256 ^ 0.00637518 -fixed_int 256 << 0.00364634 -fixed_int 256 >> 0.00339513 -fixed_int 256 %(int)0.148628 -fixed_int 256 |(int)0.00172278 -fixed_int 256 &(int)0.00394582 -fixed_int 256 ^(int)0.0017306 -fixed_int 256 gcd 5.69938 -fixed_int 512 + 0.0104641 -fixed_int 512 - 0.0108643 -fixed_int 512 * 0.244289 -fixed_int 512 / 0.361312 -fixed_int 512 str 0.00355548 -fixed_int 512 +(int)0.00521225 -fixed_int 512 -(int)0.00508137 -fixed_int 512 *(int)0.0104497 -fixed_int 512 /(int)0.347573 -fixed_int 512 % 0.359133 -fixed_int 512 | 0.0127562 -fixed_int 512 & 0.0127079 -fixed_int 512 ^ 0.0128838 -fixed_int 512 << 0.00909235 -fixed_int 512 >> 0.0100095 -fixed_int 512 %(int)0.294967 -fixed_int 512 |(int)0.00510309 -fixed_int 512 &(int)0.0108019 -fixed_int 512 ^(int)0.00519878 -fixed_int 512 gcd 18.0766 -fixed_int 1024 + 0.0269036 -fixed_int 1024 - 0.0307375 -fixed_int 1024 * 0.794034 -fixed_int 1024 / 0.761903 -fixed_int 1024 str 0.0139069 -fixed_int 1024 +(int)0.0107717 -fixed_int 1024 -(int)0.0107214 -fixed_int 1024 *(int)0.0264201 -fixed_int 1024 /(int)0.710635 -fixed_int 1024 % 0.762693 -fixed_int 1024 | 0.0266044 -fixed_int 1024 & 0.0265946 -fixed_int 1024 ^ 0.0266218 -fixed_int 1024 << 0.0208209 -fixed_int 1024 >> 0.0199434 -fixed_int 1024 %(int)0.591732 -fixed_int 1024 |(int)0.0107572 -fixed_int 1024 &(int)0.0279165 -fixed_int 1024 ^(int)0.0107153 -fixed_int 1024 gcd 72.0083 -[section:integer_performance Integer Type Perfomance] -[table Operator % -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][1.87455 (0.0999552s)][1.71496 (0.179562s)][1.74997 (0.324919s)][2.18555 (0.484383s)][3.00033 (0.853306s)]] -[[fixed_int][[*1] (0.0533221s)][[*1] (0.104704s)][[*1] (0.185671s)][1.62042 (0.359133s)][2.68172 (0.762693s)]] -[[gmp_int][2.95944 (0.157804s)][1.51151 (0.15826s)][1.02118 (0.189604s)][[*1] (0.22163s)][[*1] (0.284404s)]] -[[tommath_int][18.3802 (0.980074s)][10.4805 (1.09735s)][7.21942 (1.34044s)][8.82954 (1.95689s)][11.256 (3.20126s)]] -] -[table Operator %(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][1.82492 (0.0389361s)][2.70836 (0.0940069s)][4.16298 (0.196223s)][5.78623 (0.347801s)][8.61488 (0.653379s)]] -[[fixed_int][[*1] (0.0213357s)][2.2047 (0.0765247s)][3.15324 (0.148628s)][4.90725 (0.294967s)][7.80205 (0.591732s)]] -[[gmp_int][1.31826 (0.0281261s)][[*1] (0.0347099s)][[*1] (0.0471351s)][[*1] (0.0601084s)][[*1] (0.0758432s)]] -[[tommath_int][34.4234 (0.734449s)][24.0732 (0.835579s)][25.4154 (1.19796s)][29.0828 (1.74812s)][37.9966 (2.88178s)]] -] -[table Operator & -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][11.776 (0.0202989s)][9.29397 (0.0245186s)][4.19042 (0.0268812s)][2.61699 (0.0332565s)][1.93124 (0.0455113s)]] -[[fixed_int][[*1] (0.00172375s)][[*1] (0.00263811s)][[*1] (0.00641492s)][[*1] (0.0127079s)][1.12853 (0.0265946s)]] -[[gmp_int][5.47931 (0.00944499s)][4.26352 (0.0112477s)][2.30908 (0.0148126s)][1.3052 (0.0165864s)][[*1] (0.0235658s)]] -[[tommath_int][45.1327 (0.0777977s)][27.8558 (0.0734869s)][11.7768 (0.0755475s)][6.34384 (0.0806169s)][4.35544 (0.10264s)]] -] -[table Operator &(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][19.5872 (0.024074s)][15.1507 (0.0322746s)][13.1419 (0.0518555s)][7.84344 (0.0847243s)][5.46467 (0.152555s)]] -[[fixed_int][[*1] (0.00122907s)][[*1] (0.00213023s)][[*1] (0.00394582s)][[*1] (0.0108019s)][[*1] (0.0279165s)]] -[[gmp_int][33.8435 (0.0415959s)][20.016 (0.0426387s)][11.0702 (0.0436809s)][4.3207 (0.0466719s)][1.80374 (0.0503542s)]] -[[tommath_int][183.918 (0.226047s)][107.721 (0.22947s)][59.3026 (0.233997s)][22.0231 (0.237892s)][9.04882 (0.252612s)]] -] -[table Operator * -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][3.2324 (0.0226198s)][2.52526 (0.0408988s)][2.53525 (0.107568s)][3.79765 (0.36983s)][4.31781 (1.36107s)]] -[[fixed_int][[*1] (0.00699782s)][1.38444 (0.0224222s)][1.75995 (0.0746728s)][2.50851 (0.244289s)][2.51897 (0.794034s)]] -[[gmp_int][1.63228 (0.0114224s)][[*1] (0.0161959s)][[*1] (0.0424289s)][[*1] (0.097384s)][[*1] (0.315222s)]] -[[tommath_int][5.52344 (0.0386521s)][3.63548 (0.0588799s)][2.00515 (0.0850765s)][2.00866 (0.195612s)][1.79105 (0.564578s)]] -] -[table Operator *(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][6.83259 (0.0159193s)][6.39316 (0.0187569s)][4.26244 (0.0227126s)][3.13123 (0.0327202s)][1.85897 (0.0482894s)]] -[[fixed_int][[*1] (0.0023299s)][[*1] (0.0029339s)][[*1] (0.00532854s)][[*1] (0.0104497s)][1.01708 (0.0264201s)]] -[[gmp_int][3.73229 (0.00869587s)][3.86814 (0.0113487s)][2.60009 (0.0138547s)][1.72238 (0.0179982s)][[*1] (0.0259764s)]] -[[tommath_int][82.3516 (0.191871s)][66.1027 (0.193938s)][37.8779 (0.201834s)][21.4047 (0.223672s)][10.4393 (0.271175s)]] -] -[table Operator + -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][11.341 (0.0157994s)][7.07953 (0.0182643s)][4.42331 (0.0236538s)][2.73588 (0.0286286s)][1.52741 (0.041093s)]] -[[fixed_int][[*1] (0.00139312s)][[*1] (0.00257987s)][[*1] (0.00534754s)][[*1] (0.0104641s)][[*1] (0.0269036s)]] -[[gmp_int][12.0732 (0.0168195s)][6.96456 (0.0179677s)][4.26881 (0.0228276s)][2.61851 (0.0274004s)][1.43133 (0.038508s)]] -[[tommath_int][11.965 (0.0166687s)][6.56577 (0.0169388s)][3.5901 (0.0191982s)][2.29601 (0.0240257s)][1.33458 (0.035905s)]] -] -[table Operator +(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][4.63468 (0.0103873s)][5.77235 (0.0116175s)][6.51328 (0.0156148s)][3.18449 (0.0165983s)][1.97437 (0.0212673s)]] -[[fixed_int][[*1] (0.00224121s)][[*1] (0.00201262s)][[*1] (0.00239737s)][[*1] (0.00521225s)][[*1] (0.0107717s)]] -[[gmp_int][3.04774 (0.00683062s)][4.2147 (0.00848258s)][4.63494 (0.0111117s)][2.72815 (0.0142198s)][1.74027 (0.0187457s)]] -[[tommath_int][77.7866 (0.174336s)][86.7776 (0.17465s)][72.258 (0.173229s)][33.5455 (0.174848s)][17.718 (0.190852s)]] -] -[table Operator - -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][15.8168 (0.0256769s)][9.28853 (0.0271678s)][5.91179 (0.0339319s)][4.35797 (0.0473463s)][2.14198 (0.065839s)]] -[[fixed_int][[*1] (0.00162339s)][[*1] (0.00292488s)][[*1] (0.0057397s)][[*1] (0.0108643s)][[*1] (0.0307375s)]] -[[gmp_int][11.4678 (0.0186168s)][6.47449 (0.0189371s)][4.41843 (0.0253604s)][2.92772 (0.0318076s)][1.35934 (0.0417826s)]] -[[tommath_int][16.6376 (0.0270094s)][8.46239 (0.0247515s)][4.53521 (0.0260308s)][2.79104 (0.0303227s)][1.39785 (0.0429664s)]] -] -[table Operator -(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][4.63371 (0.00898962s)][6.43466 (0.0104572s)][6.59084 (0.0125633s)][3.09026 (0.0157028s)][1.93914 (0.0207903s)]] -[[fixed_int][[*1] (0.00194005s)][[*1] (0.00162514s)][[*1] (0.00190618s)][[*1] (0.00508137s)][[*1] (0.0107214s)]] -[[gmp_int][3.64008 (0.00706193s)][5.38549 (0.00875216s)][6.2483 (0.0119104s)][2.91903 (0.0148327s)][1.81672 (0.0194778s)]] -[[tommath_int][89.9224 (0.174454s)][103.993 (0.169003s)][90.7363 (0.17296s)][34.6724 (0.176184s)][17.6692 (0.189438s)]] -] -[table Operator / -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][1.94422 (0.102281s)][1.66132 (0.172852s)][2.00045 (0.376559s)][1.96804 (0.53608s)][2.58521 (0.91127s)]] -[[fixed_int][[*1] (0.0526074s)][[*1] (0.104045s)][[*1] (0.188237s)][1.32644 (0.361312s)][2.16146 (0.761903s)]] -[[gmp_int][3.20265 (0.168483s)][1.83394 (0.190813s)][1.23446 (0.232371s)][[*1] (0.272392s)][[*1] (0.352494s)]] -[[tommath_int][18.6829 (0.98286s)][10.7076 (1.11408s)][7.10542 (1.3375s)][7.21562 (1.96548s)][9.00151 (3.17298s)]] -] -[table Operator /(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][2.34699 (0.0522854s)][2.07114 (0.108782s)][3.64515 (0.240023s)][4.35917 (0.39506s)][5.07357 (0.711756s)]] -[[fixed_int][[*1] (0.0222776s)][1.62759 (0.0854855s)][2.67744 (0.176302s)][3.83519 (0.347573s)][5.06558 (0.710635s)]] -[[gmp_int][2.03488 (0.0453323s)][[*1] (0.0525228s)][[*1] (0.0658471s)][[*1] (0.0906272s)][[*1] (0.140287s)]] -[[tommath_int][39.7943 (0.886522s)][17.1717 (0.901904s)][17.5103 (1.153s)][18.5434 (1.68054s)][20.8389 (2.92342s)]] -] -[table Operator << -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][30.7178 (0.0166545s)][11.6314 (0.0196597s)][6.58232 (0.0240014s)][3.58466 (0.032593s)][2.63577 (0.053456s)]] -[[fixed_int][[*1] (0.000542177s)][[*1] (0.00169023s)][[*1] (0.00364634s)][[*1] (0.00909235s)][1.02663 (0.0208209s)]] -[[gmp_int][17.0103 (0.00922261s)][5.92058 (0.0100071s)][3.22238 (0.0117499s)][1.601 (0.0145569s)][[*1] (0.0202809s)]] -[[tommath_int][36.9087 (0.0200111s)][18.6848 (0.0315817s)][10.4978 (0.0382785s)][4.9662 (0.0451545s)][3.30498 (0.0670281s)]] -] -[table Operator >> -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][18.5732 (0.0143805s)][8.1063 (0.0157968s)][5.24617 (0.0178114s)][2.54823 (0.0249415s)][2.66089 (0.0339107s)]] -[[fixed_int][[*1] (0.000774259s)][[*1] (0.00194871s)][[*1] (0.00339513s)][1.02266 (0.0100095s)][1.56491 (0.0199434s)]] -[[gmp_int][11.8578 (0.00918099s)][3.94746 (0.00769246s)][2.38089 (0.00808343s)][[*1] (0.00978776s)][[*1] (0.0127441s)]] -[[tommath_int][161.257 (0.124855s)][70.5839 (0.137548s)][41.6211 (0.141309s)][15.4893 (0.151606s)][13.0869 (0.166781s)]] -] -[table Operator ^ -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][11.7006 (0.020334s)][9.45127 (0.0247923s)][4.25917 (0.027153s)][2.6181 (0.033731s)][1.83807 (0.0457905s)]] -[[fixed_int][[*1] (0.00173786s)][[*1] (0.00262317s)][[*1] (0.00637518s)][[*1] (0.0128838s)][1.06862 (0.0266218s)]] -[[gmp_int][5.73448 (0.00996572s)][4.31745 (0.0113254s)][2.10455 (0.0134169s)][1.69395 (0.0218245s)][[*1] (0.0249122s)]] -[[tommath_int][42.0554 (0.0730863s)][27.6109 (0.0724281s)][12.6344 (0.0805466s)][6.21806 (0.080112s)][3.84383 (0.0957583s)]] -] -[table Operator ^(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][18.4664 (0.0198061s)][16.651 (0.0210955s)][13.6981 (0.0237059s)][5.19536 (0.0270095s)][2.99916 (0.032137s)]] -[[fixed_int][[*1] (0.00107255s)][[*1] (0.00126692s)][[*1] (0.0017306s)][[*1] (0.00519878s)][[*1] (0.0107153s)]] -[[gmp_int][37.7363 (0.0404741s)][33.0195 (0.041833s)][24.6483 (0.0426564s)][8.81514 (0.045828s)][4.76527 (0.0510615s)]] -[[tommath_int][235.542 (0.252631s)][199.864 (0.253212s)][147.197 (0.25474s)][49.864 (0.259232s)][25.2164 (0.270201s)]] -] -[table Operator gcd -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][9.7399 (1.72384s)][9.19332 (3.97787s)][4.5686 (9.44724s)][4.83474 (22.6824s)][5.90712 (59.7424s)]] -[[fixed_int][3.92522 (0.694716s)][4.50085 (1.94748s)][2.75617 (5.69938s)][3.85301 (18.0766s)][7.11994 (72.0083s)]] -[[gmp_int][[*1] (0.176988s)][[*1] (0.432692s)][[*1] (2.06786s)][[*1] (4.69155s)][[*1] (10.1136s)]] -[[tommath_int][21.4948 (3.80432s)][16.8561 (7.29351s)][7.41497 (15.3331s)][6.8095 (31.9471s)][6.75432 (68.3106s)]] -] -[table Operator str -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][1.72192 (0.000380146s)][1.86502 (0.000693873s)][3.26065 (0.00192567s)][3.88275 (0.00489147s)][5.48576 (0.0150341s)]] -[[fixed_int][[*1] (0.000220769s)][1.24704 (0.000463955s)][1.87086 (0.00110489s)][2.82227 (0.00355548s)][5.07444 (0.0139069s)]] -[[gmp_int][1.52989 (0.000337753s)][[*1] (0.000372045s)][[*1] (0.000590578s)][[*1] (0.0012598s)][[*1] (0.00274057s)]] -[[tommath_int][18.719 (0.00413258s)][22.9337 (0.00853237s)][36.8247 (0.0217479s)][44.7324 (0.0563537s)][68.3845 (0.187413s)]] -] -[table Operator | -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][11.7002 (0.0203489s)][9.3648 (0.0245406s)][4.30735 (0.0273651s)][2.64011 (0.0336779s)][1.89563 (0.0459271s)]] -[[fixed_int][[*1] (0.00173919s)][[*1] (0.00262052s)][[*1] (0.00635312s)][[*1] (0.0127562s)][1.0981 (0.0266044s)]] -[[gmp_int][5.36125 (0.00932423s)][4.04848 (0.0106091s)][2.02225 (0.0128476s)][1.65427 (0.0211022s)][[*1] (0.0242278s)]] -[[tommath_int][41.2161 (0.0716826s)][27.2814 (0.0714914s)][11.7667 (0.074755s)][6.28141 (0.0801272s)][3.87606 (0.0939085s)]] -] -[table Operator |(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[cpp_int][17.7789 (0.0198498s)][16.5506 (0.0210111s)][13.8268 (0.0238206s)][5.30465 (0.0270701s)][3.00448 (0.0323199s)]] -[[fixed_int][[*1] (0.00111648s)][[*1] (0.0012695s)][[*1] (0.00172278s)][[*1] (0.00510309s)][[*1] (0.0107572s)]] -[[gmp_int][35.6305 (0.0397808s)][32.0847 (0.0407317s)][24.5808 (0.0423473s)][9.0158 (0.0460084s)][4.603 (0.0495155s)]] -[[tommath_int][228.073 (0.254639s)][199.149 (0.25282s)][148.482 (0.255801s)][51.0429 (0.260477s)][24.899 (0.267844s)]] -] -[endsect] +gmp_int 64 + 0.0168163 +gmp_int 64 - 0.0186614 +gmp_int 64 * 0.0117134 +gmp_int 64 / 0.169732 +gmp_int 64 str 0.000328882 +gmp_int 64 +(int)0.00662982 +gmp_int 64 -(int)0.00709197 +gmp_int 64 *(int)0.0088044 +gmp_int 64 /(int)0.0460225 +gmp_int 64 % 0.158198 +gmp_int 64 | 0.00933212 +gmp_int 64 & 0.00941153 +gmp_int 64 ^ 0.0100066 +gmp_int 64 << 0.00917854 +gmp_int 64 >> 0.00925083 +gmp_int 64 %(int)0.0280589 +gmp_int 64 |(int)0.0400043 +gmp_int 64 &(int)0.0417312 +gmp_int 64 ^(int)0.040751 +gmp_int 64 gcd 0.176467 +gmp_int 128 + 0.0178204 +gmp_int 128 - 0.0189183 +gmp_int 128 * 0.0162167 +gmp_int 128 / 0.188989 +gmp_int 128 str 0.00036981 +gmp_int 128 +(int)0.00848453 +gmp_int 128 -(int)0.00871131 +gmp_int 128 *(int)0.0113603 +gmp_int 128 /(int)0.0532432 +gmp_int 128 % 0.156838 +gmp_int 128 | 0.0106143 +gmp_int 128 & 0.0112662 +gmp_int 128 ^ 0.0113 +gmp_int 128 << 0.0100873 +gmp_int 128 >> 0.0078452 +gmp_int 128 %(int)0.0347183 +gmp_int 128 |(int)0.0411793 +gmp_int 128 &(int)0.0429282 +gmp_int 128 ^(int)0.0423867 +gmp_int 128 gcd 0.433341 +gmp_int 256 + 0.0227099 +gmp_int 256 - 0.0253696 +gmp_int 256 * 0.0419669 +gmp_int 256 / 0.231062 +gmp_int 256 str 0.00059791 +gmp_int 256 +(int)0.011126 +gmp_int 256 -(int)0.0118753 +gmp_int 256 *(int)0.0134931 +gmp_int 256 /(int)0.0656163 +gmp_int 256 % 0.188537 +gmp_int 256 | 0.0128192 +gmp_int 256 & 0.0127349 +gmp_int 256 ^ 0.0133922 +gmp_int 256 << 0.0118988 +gmp_int 256 >> 0.00811877 +gmp_int 256 %(int)0.0471091 +gmp_int 256 |(int)0.042799 +gmp_int 256 &(int)0.0458343 +gmp_int 256 ^(int)0.043002 +gmp_int 256 gcd 2.06647 +gmp_int 512 + 0.0273102 +gmp_int 512 - 0.0317526 +gmp_int 512 * 0.0977565 +gmp_int 512 / 0.271981 +gmp_int 512 str 0.0012591 +gmp_int 512 +(int)0.0141478 +gmp_int 512 -(int)0.0148129 +gmp_int 512 *(int)0.0180329 +gmp_int 512 /(int)0.0904515 +gmp_int 512 % 0.22083 +gmp_int 512 | 0.020649 +gmp_int 512 & 0.0165353 +gmp_int 512 ^ 0.0222088 +gmp_int 512 << 0.0146297 +gmp_int 512 >> 0.0098618 +gmp_int 512 %(int)0.0601431 +gmp_int 512 |(int)0.0461385 +gmp_int 512 &(int)0.0469244 +gmp_int 512 ^(int)0.0460041 +gmp_int 512 gcd 4.68119 +gmp_int 1024 + 0.0392733 +gmp_int 1024 - 0.0423657 +gmp_int 1024 * 0.314956 +gmp_int 1024 / 0.351788 +gmp_int 1024 str 0.00268616 +gmp_int 1024 +(int)0.0187891 +gmp_int 1024 -(int)0.0194118 +gmp_int 1024 *(int)0.0259443 +gmp_int 1024 /(int)0.140347 +gmp_int 1024 % 0.283657 +gmp_int 1024 | 0.0242247 +gmp_int 1024 & 0.023592 +gmp_int 1024 ^ 0.0249 +gmp_int 1024 << 0.0204313 +gmp_int 1024 >> 0.0128395 +gmp_int 1024 %(int)0.0758694 +gmp_int 1024 |(int)0.0495895 +gmp_int 1024 &(int)0.0506897 +gmp_int 1024 ^(int)0.049433 +gmp_int 1024 gcd 10.1293 +cpp_int(fixed) 128 + 0.0181676 +cpp_int(fixed) 128 - 0.0184343 +cpp_int(fixed) 128 * 0.014376 +cpp_int(fixed) 128 / 0.202558 +cpp_int(fixed) 128 str 0.000652736 +cpp_int(fixed) 128 +(int)0.00948536 +cpp_int(fixed) 128 -(int)0.00886251 +cpp_int(fixed) 128 *(int)0.0173963 +cpp_int(fixed) 128 /(int)0.106251 +cpp_int(fixed) 128 % 0.20362 +cpp_int(fixed) 128 | 0.0137212 +cpp_int(fixed) 128 & 0.0144157 +cpp_int(fixed) 128 ^ 0.0137219 +cpp_int(fixed) 128 << 0.0125872 +cpp_int(fixed) 128 >> 0.00905059 +cpp_int(fixed) 128 %(int)0.109447 +cpp_int(fixed) 128 |(int)0.014533 +cpp_int(fixed) 128 &(int)0.0162133 +cpp_int(fixed) 128 ^(int)0.0131589 +cpp_int(fixed) 128 gcd 2.86508 +cpp_int(fixed) 256 + 0.0216349 +cpp_int(fixed) 256 - 0.0208758 +cpp_int(fixed) 256 * 0.0210219 diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index dbf6b539..c615e19f 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -582,12 +582,13 @@ int main() test("gmp_int", 1024); #endif #ifdef TEST_CPP_INT +/* test("cpp_int", 64); test("cpp_int", 128); test("cpp_int", 256); test("cpp_int", 512); test("cpp_int", 1024); - +*/ test > >("cpp_int(fixed)", 128); test > >("cpp_int(fixed)", 256); test > >("cpp_int(fixed)", 512); From 5cf1ff427a7008a76f0791bff73c33c61d349827 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 8 Mar 2012 17:55:54 +0000 Subject: [PATCH 127/256] Ooops committed too much in last commit, revert. [SVN r77267] --- performance/performance_test.cpp | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index c615e19f..dbf6b539 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -582,13 +582,12 @@ int main() test("gmp_int", 1024); #endif #ifdef TEST_CPP_INT -/* test("cpp_int", 64); test("cpp_int", 128); test("cpp_int", 256); test("cpp_int", 512); test("cpp_int", 1024); -*/ + test > >("cpp_int(fixed)", 128); test > >("cpp_int(fixed)", 256); test > >("cpp_int(fixed)", 512); From b42208c5df62c39354a8f78552a36ccd3be335f9 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 11 Mar 2012 16:43:31 +0000 Subject: [PATCH 128/256] Fix several division algorithm bugs. Add cpp_rational to performance tests. Add modular arithmetic test to test cases. [SVN r77303] --- include/boost/multiprecision/cpp_int.hpp | 39 ++++++++++++++++-------- performance/performance_test.cpp | 15 ++++----- test/test_cpp_int.cpp | 18 +++++++++++ 3 files changed, 52 insertions(+), 20 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 548c0e33..a6f38a98 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1061,9 +1061,9 @@ inline void multiply(cpp_int_backend& result, const double_limb_type carry = 0; std::memset(pr, 0, result.size() * sizeof(limb_type)); - unsigned inner_limit = result.size() - as; for(unsigned i = 0; i < as; ++i) { + unsigned inner_limit = (std::min)(result.size() - i, b.size()); for(unsigned j = 0; j < inner_limit; ++j) { BOOST_ASSERT(i+j < result.size()); @@ -1261,10 +1261,6 @@ void divide_unsigned_helper(cpp_int_backend& result, do { - // - // Update r_order, this can't run past the end as r must be non-zero at this point: - // - r_order = r.size() - 1; // // Calculate our best guess for how many times y divides into r: // @@ -1329,6 +1325,7 @@ void divide_unsigned_helper(cpp_int_backend& result, // double_limb_type carry = 0; t.resize(y.size() + shift + 1); + bool truncated_t = !cpp_int_backend::variable && (t.size() != y.size() + shift + 1); typename cpp_int_backend::limb_pointer pt = t.limbs(); for(unsigned i = 0; i < shift; ++i) pt[i] = 0; @@ -1338,11 +1335,11 @@ void divide_unsigned_helper(cpp_int_backend& result, pt[i + shift] = static_cast(carry); carry >>= cpp_int_backend::limb_bits; } - if(carry) + if(carry && !truncated_t) { pt[t.size() - 1] = static_cast(carry); } - else + else if(!truncated_t) { t.resize(t.size() - 1); } @@ -1365,15 +1362,21 @@ void divide_unsigned_helper(cpp_int_backend& result, while(pr[result.size() - 1] == 0) result.resize(result.size() - 1); } + // + // Update r_order: + // + r_order = r.size() - 1; + if(r_order < y_order) + break; } - // Termination condition is really just a check that r > y, but with two common - // short-circuit cases handled first: - while((r_order > y_order) || (prem[r_order] > py[y_order]) || (r.compare_unsigned(y) > 0)); + // Termination condition is really just a check that r > y, but with a common + // short-circuit case handled first: + while((r_order > y_order) || (r.compare_unsigned(y) >= 0)); // // We now just have to normalise the result: // - if(r_neg) + if(r_neg && get_sign(r)) { // We have one too many in the result: decrement(result); @@ -1480,19 +1483,29 @@ void divide_unsigned_helper(cpp_int_backend& result, --r_order; pr[r_order] = static_cast(b); pres[r_order] = static_cast(a / y); + if(r_order && pr[r_order] == 0) + { + --r_order; // No remainder, division was exact. + r.resize(r.size() - 1); + } } else { pres[r_order] = pr[r_order] / y; pr[r_order] %= y; + if(r_order && pr[r_order] == 0) + { + --r_order; // No remainder, division was exact. + r.resize(r.size() - 1); + } } } // Termination condition is really just a check that r > y, but with two common // short-circuit cases handled first: while(r_order || (pr[r_order] > y)); - if(pres[result.size() - 1] == 0) - result.resize(result.size() - 1); + result.normalize(); + r.normalize(); result.sign(x.sign()); r.sign(x.sign()); diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index dbf6b539..7a541b02 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -12,7 +12,7 @@ #if !defined(TEST_MPF) && !defined(TEST_MPZ) && \ !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPQ) \ && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\ - && !defined(TEST_FIXED_INT) && !defined(TEST_CPP_INT) + && !defined(TEST_FIXED_INT) && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_RATIONAL) # define TEST_MPF # define TEST_MPZ # define TEST_MPQ @@ -22,6 +22,7 @@ # define TEST_TOMMATH # define TEST_FIXED_INT # define TEST_CPP_INT +# define TEST_CPP_INT_RATIONAL #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -575,14 +576,12 @@ int main() test("gmp_float", 500); #endif #ifdef TEST_MPZ - test("gmp_int", 64); test("gmp_int", 128); test("gmp_int", 256); test("gmp_int", 512); test("gmp_int", 1024); #endif #ifdef TEST_CPP_INT - test("cpp_int", 64); test("cpp_int", 128); test("cpp_int", 256); test("cpp_int", 512); @@ -593,15 +592,19 @@ int main() test > >("cpp_int(fixed)", 512); test > >("cpp_int(fixed)", 1024); #endif +#ifdef TEST_CPP_INT_RATIONAL + test("cpp_rational", 128); + test("cpp_rational", 256); + test("cpp_rational", 512); + test("cpp_rational", 1024); +#endif #ifdef TEST_MPQ - test("mpq_rational", 64); test("mpq_rational", 128); test("mpq_rational", 256); test("mpq_rational", 512); test("mpq_rational", 1024); #endif #ifdef TEST_TOMMATH - test("tommath_int", 64); test("tommath_int", 128); test("tommath_int", 256); test("tommath_int", 512); @@ -610,7 +613,6 @@ int main() // // These are actually too slow to test!!! // - test("mp_rational", 64); test("mp_rational", 128); test("mp_rational", 256); test("mp_rational", 512); @@ -618,7 +620,6 @@ int main() */ #endif #ifdef TEST_FIXED_INT - test > >("fixed_int", 64); test("fixed_int", 128); test("fixed_int", 256); test("fixed_int", 512); diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp index ee83b641..6cc69def 100644 --- a/test/test_cpp_int.cpp +++ b/test/test_cpp_int.cpp @@ -137,6 +137,24 @@ void test() BOOST_CHECK_EQUAL(mpz_int(lcm(-c, -d)).str(), test_type(lcm(-c1, -d1)).str()); BOOST_CHECK_EQUAL(mpz_int(gcd(a, -b)).str(), test_type(gcd(a1, -b1)).str()); BOOST_CHECK_EQUAL(mpz_int(lcm(c, -d)).str(), test_type(lcm(c1, -d1)).str()); + + if(std::numeric_limits::is_modulo) + { + static mpz_int m = mpz_int(1) << std::numeric_limits::digits; + mpz_int t(a); + test_type t1(a1); + for(unsigned i = 0; i < 10; ++i) + { + t *= a; + t %= m; + t += a; + t %= m; + t1 *= a1; + t1 += a1; + } + BOOST_CHECK_EQUAL(t.str(), t1.str()); + } + if(last_error_count != boost::detail::test_errors()) { last_error_count = boost::detail::test_errors(); From 5caa15f798456c1c8260c8f66cb2f2fcd536423f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 12 Mar 2012 09:18:44 +0000 Subject: [PATCH 129/256] Reorganisation: rename methods "eval_foo" rather than "foo" to avoid conflict with classes of the same name (GCC bug). Move backends into sub-namespaces to avoid namespace pollution. [SVN r77312] --- doc/multiprecision.qbk | 108 ++++---- .../multiprecision/arithmetic_backend.hpp | 13 +- .../concepts/mp_number_architypes.hpp | 14 +- .../boost/multiprecision/cpp_dec_float.hpp | 39 +-- include/boost/multiprecision/cpp_int.hpp | 230 ++++++++--------- .../multiprecision/detail/default_ops.hpp | 170 ++++++------- .../detail/functions/constants.hpp | 46 ++-- .../multiprecision/detail/functions/pow.hpp | 160 ++++++------ .../multiprecision/detail/functions/trig.hpp | 224 ++++++++--------- include/boost/multiprecision/fixed_int.hpp | 214 ++++++++-------- include/boost/multiprecision/gmp.hpp | 235 ++++++++--------- include/boost/multiprecision/mp_number.hpp | 238 +++++++++--------- include/boost/multiprecision/mpfr.hpp | 92 +++---- .../boost/multiprecision/rational_adapter.hpp | 23 +- include/boost/multiprecision/tommath.hpp | 75 +++--- test/test_arithmetic.cpp | 1 + 16 files changed, 958 insertions(+), 924 deletions(-) diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 3c18dd73..677a5336 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -621,13 +621,13 @@ So for example, given an integer backend type `MyIntegerBackend`, the use would // swap: void swap(mp_number& other); // Sign: - bool is_zero()const; + bool eval_is_zero()const; int sign()const; // string conversion: std::string str()const; // Generic conversion mechanism template - T convert_to()const; + T eval_convert_to()const; // precision control: static unsigned default_precision(); static void default_precision(unsigned digits10); @@ -801,7 +801,7 @@ This operator also enables the use of `mp_number` with any of the following oper Swaps `*this` with `other`. - bool is_zero()const; + bool eval_is_zero()const; Returns `true` is `*this` is zero, otherwise `false`. @@ -816,7 +816,7 @@ Returns the number formatted as a string, with at least /precision/ digits, and if /scientific/ is true. template - T convert_to()const; + T eval_convert_to()const; Provides a generic conversion mechanism to convert `*this` to type `T`. Type `T` may be any arithmetic type. Optionally other types may also be supported by specific `Backend` types. @@ -1043,18 +1043,18 @@ of type B2. [[`cb.compare(a)`][`int`][Compares `cb` and `a`, returns a value less than zero if `cb < a`, a value greater than zero if `cb > a` and zero if `cb == a`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`add(b, cb)`][`void`][Adds `cb` to `b`.]] -[[`subtract(b, cb)`][`void`][Subtracts `cb` from `b`.]] -[[`multiply(b, cb)`][`void`][Multiplies `b` by `cb`.]] -[[`divide(b, cb)`][`void`][Divides `b` by `cb`.]] -[[`modulus(b, cb)`][`void`][Computes `b %= cb`, only required when `B` is an integer type.]] -[[`bitwise_and(b, cb)`][`void`][Computes `b &= cb`, only required when `B` is an integer type.]] -[[`bitwise_or(b, cb)`][`void`][Computes `b |= cb`, only required when `B` is an integer type.]] -[[`bitwise_xor(b, cb)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type.]] -[[`complement(b, cb)`][`void`][Computes the ones-complement of `cb` and stores the result in `b`, only required when `B` is an integer type.]] -[[`left_shift(b, ui)`][`void`][Computes `b <<= ui`, only required when `B` is an integer type.]] -[[`right_shift(b, ui)`][`void`][Computes `b >>= ui`, only required when `B` is an integer type.]] -[[`convert_to(pa, cb)`][`void`][Converts `cb` to the type of `*pa` and store the result in `*pa`. Type `B` shall support +[[`eval_add(b, cb)`][`void`][Adds `cb` to `b`.]] +[[`eval_subtract(b, cb)`][`void`][Subtracts `cb` from `b`.]] +[[`eval_multiply(b, cb)`][`void`][Multiplies `b` by `cb`.]] +[[`eval_divide(b, cb)`][`void`][Divides `b` by `cb`.]] +[[`eval_modulus(b, cb)`][`void`][Computes `b %= cb`, only required when `B` is an integer type.]] +[[`eval_bitwise_and(b, cb)`][`void`][Computes `b &= cb`, only required when `B` is an integer type.]] +[[`eval_bitwise_or(b, cb)`][`void`][Computes `b |= cb`, only required when `B` is an integer type.]] +[[`eval_bitwise_xor(b, cb)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type.]] +[[`eval_complement(b, cb)`][`void`][Computes the ones-complement of `cb` and stores the result in `b`, only required when `B` is an integer type.]] +[[`eval_left_shift(b, ui)`][`void`][Computes `b <<= ui`, only required when `B` is an integer type.]] +[[`eval_right_shift(b, ui)`][`void`][Computes `b >>= ui`, only required when `B` is an integer type.]] +[[`eval_convert_to(pa, cb)`][`void`][Converts `cb` to the type of `*pa` and store the result in `*pa`. Type `B` shall support conversion to at least types `std::intmax_t`, `std::uintmax_t` and `long long`. Conversion to other arithmetic types can then be synthesised using other operations. Conversions to other types are entirely optional.]] @@ -1075,68 +1075,68 @@ of type B2. Only applies to rational and complex number types.]] [[`assign_components(b, b2, b2)`][`void`][Assigns to `b` the two components in the following arguments. Only applies to rational and complex number types.]] -[[`add(b, a)`][`void`][Adds `a` to `b`. The type of `a` shall be listed in one of the type lists +[[`eval_add(b, a)`][`void`][Adds `a` to `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`subtract(b, a)`][`void`][Subtracts `a` from `b`. The type of `a` shall be listed in one of the type lists +[[`eval_subtract(b, a)`][`void`][Subtracts `a` from `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`multiply(b, a)`][`void`][Multiplies `b` by `a`. The type of `a` shall be listed in one of the type lists +[[`eval_multiply(b, a)`][`void`][Multiplies `b` by `a`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`divide(b, a)`][`void`][Divides `b` by `a`. The type of `a` shall be listed in one of the type lists +[[`eval_divide(b, a)`][`void`][Divides `b` by `a`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`modulus(b, a)`][`void`][Computes `b %= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_modulus(b, a)`][`void`][Computes `b %= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`bitwise_and(b, a)`][`void`][Computes `b &= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_bitwise_and(b, a)`][`void`][Computes `b &= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`bitwise_or(b, a)`][`void`][Computes `b |= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_bitwise_or(b, a)`][`void`][Computes `b |= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`bitwise_xor(b, a)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_bitwise_xor(b, a)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`add(b, cb, cb2)`][`void`][Add `cb` to `cb2` and stores the result in `b`.]] -[[`subtract(b, cb, cb2)`][`void`][Subtracts `cb2` from `cb` and stores the result in `b`.]] -[[`multiply(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and stores the result in `b`.]] -[[`divide(b, cb, cb2)`][`void`][Divides `cb` by `cb2` and stores the result in `b`.]] -[[`add(b, cb, a)`][`void`][Add `cb` to `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists +[[`eval_add(b, cb, cb2)`][`void`][Add `cb` to `cb2` and stores the result in `b`.]] +[[`eval_subtract(b, cb, cb2)`][`void`][Subtracts `cb2` from `cb` and stores the result in `b`.]] +[[`eval_multiply(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and stores the result in `b`.]] +[[`eval_divide(b, cb, cb2)`][`void`][Divides `cb` by `cb2` and stores the result in `b`.]] +[[`eval_add(b, cb, a)`][`void`][Add `cb` to `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`subtract(b, cb, a)`][`void`][Subtracts `a` from `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists +[[`eval_subtract(b, cb, a)`][`void`][Subtracts `a` from `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`multiply(b, cb, a)`][`void`][Multiplies `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists +[[`eval_multiply(b, cb, a)`][`void`][Multiplies `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`divide(b, cb, a)`][`void`][Divides `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists +[[`eval_divide(b, cb, a)`][`void`][Divides `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`modulus(b, cb, cb2)`][`void`][Computes `cb % cb2` and stores the result in `b`, only required when `B` is an integer type.]] -[[`bitwise_and(b, cb, cb2)`][`void`][Computes `cb & cb2` and stores the result in `b`, only required when `B` is an integer type.]] -[[`bitwise_or(b, cb, cb2)`][`void`][Computes `cb | cb2` and stores the result in `b`, only required when `B` is an integer type.]] -[[`bitwise_xor(b, cb, cb2)`][`void`][Computes `cb ^ cb2` and stores the result in `b`, only required when `B` is an integer type.]] -[[`add(b, a, cb)`][`void`][Add `a` to `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists +[[`eval_modulus(b, cb, cb2)`][`void`][Computes `cb % cb2` and stores the result in `b`, only required when `B` is an integer type.]] +[[`eval_bitwise_and(b, cb, cb2)`][`void`][Computes `cb & cb2` and stores the result in `b`, only required when `B` is an integer type.]] +[[`eval_bitwise_or(b, cb, cb2)`][`void`][Computes `cb | cb2` and stores the result in `b`, only required when `B` is an integer type.]] +[[`eval_bitwise_xor(b, cb, cb2)`][`void`][Computes `cb ^ cb2` and stores the result in `b`, only required when `B` is an integer type.]] +[[`eval_add(b, a, cb)`][`void`][Add `a` to `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`subtract(b, a, cb)`][`void`][Subtracts `cb` from `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists +[[`eval_subtract(b, a, cb)`][`void`][Subtracts `cb` from `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`multiply(b, a, cb)`][`void`][Multiplies `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists +[[`eval_multiply(b, a, cb)`][`void`][Multiplies `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`divide(b, a, cb)`][`void`][Divides `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists +[[`eval_divide(b, a, cb)`][`void`][Divides `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`modulus(b, cb, a)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_modulus(b, cb, a)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`bitwise_and(b, cb, a)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_bitwise_and(b, cb, a)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`bitwise_or(b, cb, a)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_bitwise_or(b, cb, a)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`bitwise_xor(b, cb, a)`][`void`][Computes `cb ^ a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_bitwise_xor(b, cb, a)`][`void`][Computes `cb ^ a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`modulus(b, a, cb)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_modulus(b, a, cb)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`bitwise_and(b, a, cb)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_bitwise_and(b, a, cb)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`bitwise_or(b, a, cb)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_bitwise_or(b, a, cb)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`bitwise_xor(b, a, cb)`][`void`][Computes `a ^ cb` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists +[[`eval_bitwise_xor(b, a, cb)`][`void`][Computes `a ^ cb` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`left_shift(b, cb, ui)`][`void`][Computes `cb << ui` and stores the result in `b`, only required when `B` is an integer type.]] -[[`right_shift(b, cb, ui)`][`void`][Computes `cb >> ui` and stores the result in `b`, only required when `B` is an integer type.]] -[[`increment(b)`][void][Increments the value of `b` by one.]] -[[`decrement(b)`][void][Decrements the value of `b` by one.]] -[[`is_zero(cb)`][`bool`][Returns `true` if `cb` is zero, otherwise `false`]] -[[`get_sign(cb)`][`int`][Returns a value < zero if `cb` is negative, a value > zero if `cb` is positive, and zero if `cb` is zero.]] +[[`eval_left_shift(b, cb, ui)`][`void`][Computes `cb << ui` and stores the result in `b`, only required when `B` is an integer type.]] +[[`eval_right_shift(b, cb, ui)`][`void`][Computes `cb >> ui` and stores the result in `b`, only required when `B` is an integer type.]] +[[`eval_increment(b)`][void][Increments the value of `b` by one.]] +[[`eval_decrement(b)`][void][Decrements the value of `b` by one.]] +[[`eval_is_zero(cb)`][`bool`][Returns `true` if `cb` is zero, otherwise `false`]] +[[`eval_get_sign(cb)`][`int`][Returns a value < zero if `cb` is negative, a value > zero if `cb` is positive, and zero if `cb` is zero.]] [[`eval_abs(b, cb)`][`void`][Set `b` to the absolute value of `cb`.]] [[`eval_fabs(b, cb)`][`void`][Set `b` to the absolute value of `cb`.]] [[`eval_fpclassify(cb)`][`int`][Returns one of the same values returned by `std::fpclassify`. Only required when `B` is an floating-point type.]] diff --git a/include/boost/multiprecision/arithmetic_backend.hpp b/include/boost/multiprecision/arithmetic_backend.hpp index 8225bd0e..5d9111b2 100644 --- a/include/boost/multiprecision/arithmetic_backend.hpp +++ b/include/boost/multiprecision/arithmetic_backend.hpp @@ -15,6 +15,7 @@ namespace boost{ namespace multiprecision{ +namespace backends{ template struct arithmetic_backend @@ -97,26 +98,30 @@ private: }; template -inline void add(arithmetic_backend& result, const arithmetic_backend& o) +inline void eval_add(arithmetic_backend& result, const arithmetic_backend& o) { result.data() += o.data(); } template -inline void subtract(arithmetic_backend& result, const arithmetic_backend& o) +inline void eval_subtract(arithmetic_backend& result, const arithmetic_backend& o) { result.data() -= o.data(); } template -inline void multiply(arithmetic_backend& result, const arithmetic_backend& o) +inline void eval_multiply(arithmetic_backend& result, const arithmetic_backend& o) { result.data() *= o.data(); } template -inline void divide(arithmetic_backend& result, const arithmetic_backend& o) +inline void eval_divide(arithmetic_backend& result, const arithmetic_backend& o) { result.data() /= o.data(); } +} // namespace backends + +using boost::multiprecision::backends::arithmetic_backend; + }} // namespaces diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index 61de59c7..72e97842 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -122,36 +122,36 @@ struct mp_number_backend_float_architype long double m_value; }; -inline void add(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) +inline void eval_add(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) { std::cout << "Addition (" << result.m_value << " += " << o.m_value << ")" << std::endl; result.m_value += o.m_value; } -inline void subtract(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) +inline void eval_subtract(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) { std::cout << "Subtraction (" << result.m_value << " -= " << o.m_value << ")" << std::endl; result.m_value -= o.m_value; } -inline void multiply(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) +inline void eval_multiply(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) { std::cout << "Multiplication (" << result.m_value << " *= " << o.m_value << ")" << std::endl; result.m_value *= o.m_value; } -inline void divide(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) +inline void eval_divide(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o) { std::cout << "Division (" << result.m_value << " /= " << o.m_value << ")" << std::endl; result.m_value /= o.m_value; } -inline void convert_to(unsigned long long* result, const mp_number_backend_float_architype& val) +inline void eval_convert_to(unsigned long long* result, const mp_number_backend_float_architype& val) { *result = static_cast(val.m_value); } -inline void convert_to(long long* result, const mp_number_backend_float_architype& val) +inline void eval_convert_to(long long* result, const mp_number_backend_float_architype& val) { *result = static_cast(val.m_value); } -inline void convert_to(long double* result, mp_number_backend_float_architype& val) +inline void eval_convert_to(long double* result, mp_number_backend_float_architype& val) { *result = val.m_value; } diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index dfe947ae..a77dcc3b 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -24,6 +24,7 @@ namespace boost{ namespace multiprecision{ +namespace backends{ template class cpp_dec_float @@ -2535,49 +2536,49 @@ cpp_dec_float cpp_dec_float::pow2(const long long p) template -inline void add(cpp_dec_float& result, const cpp_dec_float& o) +inline void eval_add(cpp_dec_float& result, const cpp_dec_float& o) { result += o; } template -inline void subtract(cpp_dec_float& result, const cpp_dec_float& o) +inline void eval_subtract(cpp_dec_float& result, const cpp_dec_float& o) { result -= o; } template -inline void multiply(cpp_dec_float& result, const cpp_dec_float& o) +inline void eval_multiply(cpp_dec_float& result, const cpp_dec_float& o) { result *= o; } template -inline void divide(cpp_dec_float& result, const cpp_dec_float& o) +inline void eval_divide(cpp_dec_float& result, const cpp_dec_float& o) { result /= o; } template -inline void add(cpp_dec_float& result, const unsigned long long& o) +inline void eval_add(cpp_dec_float& result, const unsigned long long& o) { result.add_unsigned_long_long(o); } template -inline void subtract(cpp_dec_float& result, const unsigned long long& o) +inline void eval_subtract(cpp_dec_float& result, const unsigned long long& o) { result.sub_unsigned_long_long(o); } template -inline void multiply(cpp_dec_float& result, const unsigned long long& o) +inline void eval_multiply(cpp_dec_float& result, const unsigned long long& o) { result.mul_unsigned_long_long(o); } template -inline void divide(cpp_dec_float& result, const unsigned long long& o) +inline void eval_divide(cpp_dec_float& result, const unsigned long long& o) { result.div_unsigned_long_long(o); } template -inline void add(cpp_dec_float& result, long long o) +inline void eval_add(cpp_dec_float& result, long long o) { if(o < 0) result.sub_unsigned_long_long(-o); @@ -2585,7 +2586,7 @@ inline void add(cpp_dec_float& result, long long o) result.add_unsigned_long_long(o); } template -inline void subtract(cpp_dec_float& result, long long o) +inline void eval_subtract(cpp_dec_float& result, long long o) { if(o < 0) result.add_unsigned_long_long(-o); @@ -2593,7 +2594,7 @@ inline void subtract(cpp_dec_float& result, long long o) result.sub_unsigned_long_long(o); } template -inline void multiply(cpp_dec_float& result, long long o) +inline void eval_multiply(cpp_dec_float& result, long long o) { if(o < 0) { @@ -2604,7 +2605,7 @@ inline void multiply(cpp_dec_float& result, long long o) result.mul_unsigned_long_long(o); } template -inline void divide(cpp_dec_float& result, long long o) +inline void eval_divide(cpp_dec_float& result, long long o) { if(o < 0) { @@ -2616,17 +2617,17 @@ inline void divide(cpp_dec_float& result, long long o) } template -inline void convert_to(unsigned long long* result, const cpp_dec_float& val) +inline void eval_convert_to(unsigned long long* result, const cpp_dec_float& val) { *result = val.extract_unsigned_long_long(); } template -inline void convert_to(long long* result, const cpp_dec_float& val) +inline void eval_convert_to(long long* result, const cpp_dec_float& val) { *result = val.extract_signed_long_long(); } template -inline void convert_to(long double* result, cpp_dec_float& val) +inline void eval_convert_to(long double* result, cpp_dec_float& val) { *result = val.extract_long_double(); } @@ -2799,16 +2800,20 @@ inline void eval_frexp(cpp_dec_float& result, const cpp_dec_float -inline bool is_zero(const cpp_dec_float& val) +inline bool eval_is_zero(const cpp_dec_float& val) { return val.iszero(); } template -inline int get_sign(const cpp_dec_float& val) +inline int eval_get_sign(const cpp_dec_float& val) { return val.iszero() ? 0 : val.isneg() ? -1 : 1; } +} // namespace backends + +using boost::multiprecision::backends::cpp_dec_float; + typedef mp_number > cpp_dec_float_50; typedef mp_number > cpp_dec_float_100; diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index a6f38a98..65f5eb3b 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -18,6 +18,7 @@ namespace boost{ namespace multiprecision{ +namespace backends{ template > struct cpp_int_backend; @@ -338,7 +339,7 @@ public: for(i = 0; i < internal_limb_count; ++i) m_data[i] = ~m_data[i]; normalize(); - increment(static_cast& >(*this)); + eval_increment(static_cast& >(*this)); } bool isneg()const { @@ -451,8 +452,8 @@ public: cpp_int_backend& operator = (long double a) { - using default_ops::add; - using default_ops::subtract; + using default_ops::eval_add; + using default_ops::eval_subtract; using std::frexp; using std::ldexp; using std::floor; @@ -482,23 +483,23 @@ public: f = ldexp(f, shift); term = floor(f); e -= shift; - left_shift(*this, shift); + eval_left_shift(*this, shift); if(term > 0) - add(*this, static_cast(term)); + eval_add(*this, static_cast(term)); else - subtract(*this, static_cast(-term)); + eval_subtract(*this, static_cast(-term)); f -= term; } if(e > 0) - left_shift(*this, e); + eval_left_shift(*this, e); else if(e < 0) - right_shift(*this, -e); + eval_right_shift(*this, -e); return *this; } cpp_int_backend& operator = (const char* s) { - using default_ops::multiply; - using default_ops::add; + using default_ops::eval_multiply; + using default_ops::eval_add; std::size_t n = s ? std::strlen(s) : 0; *this = static_cast(0u); unsigned radix = 10; @@ -557,7 +558,7 @@ public: break; } } - left_shift(*this, block_shift); + eval_left_shift(*this, block_shift); this->limbs()[0] |= block; } } @@ -584,8 +585,8 @@ public: break; } } - multiply(*this, block_mult); - add(*this, block); + eval_multiply(*this, block_mult); + eval_add(*this, block); } } } @@ -623,7 +624,7 @@ public: if(c > '9') c += 'A' - '9' - 1; result[pos--] = c; - right_shift(t, shift); + eval_right_shift(t, shift); } if(Bits % shift) { @@ -666,7 +667,7 @@ public: { cpp_int_backend block10; block10 = max_block_10; - while(get_sign(t) != 0) + while(eval_get_sign(t) != 0) { cpp_int_backend t2; divide_unsigned_helper(t2, t, block10, r); @@ -732,9 +733,9 @@ public: template -inline void add(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) { - add(result, result, o); + eval_add(result, result, o); } template inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) @@ -795,7 +796,7 @@ inline void add_unsigned(cpp_int_backend& result, co result.sign(a.sign()); } template -inline void add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { if(a.sign() != b.sign()) { @@ -829,7 +830,7 @@ inline void add_unsigned(cpp_int_backend& result, co result.normalize(); } template -inline void add(cpp_int_backend& result, const limb_type& o) +inline void eval_add(cpp_int_backend& result, const limb_type& o) { if(result.sign()) { @@ -839,12 +840,12 @@ inline void add(cpp_int_backend& result, const limb_ add_unsigned(result, o); } template -inline void add(cpp_int_backend& result, const signed_limb_type& o) +inline void eval_add(cpp_int_backend& result, const signed_limb_type& o) { if(o < 0) - subtract(result, static_cast(-o)); + eval_subtract(result, static_cast(-o)); else if(o > 0) - add(result, static_cast(o)); + eval_add(result, static_cast(o)); } template @@ -877,7 +878,7 @@ inline void subtract_unsigned(cpp_int_backend& resul } } template -inline void subtract(cpp_int_backend& result, const limb_type& o) +inline void eval_subtract(cpp_int_backend& result, const limb_type& o) { if(result.sign()) add_unsigned(result, o); @@ -885,18 +886,18 @@ inline void subtract(cpp_int_backend& result, const subtract_unsigned(result, o); } template -inline void subtract(cpp_int_backend& result, const signed_limb_type& o) +inline void eval_subtract(cpp_int_backend& result, const signed_limb_type& o) { if(o) { if(o < 0) - add(result, static_cast(-o)); + eval_add(result, static_cast(-o)); else - subtract(result, static_cast(o)); + eval_subtract(result, static_cast(o)); } } template -inline void increment(cpp_int_backend& result) +inline void eval_increment(cpp_int_backend& result) { static const limb_type one = 1; if(!result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) @@ -904,10 +905,10 @@ inline void increment(cpp_int_backend& result) else if(result.sign() && result.limbs()[0]) --result.limbs()[0]; else - add(result, one); + eval_add(result, one); } template -inline void decrement(cpp_int_backend& result) +inline void eval_decrement(cpp_int_backend& result) { static const limb_type one = 1; if(!result.sign() && result.limbs()[0]) @@ -915,12 +916,12 @@ inline void decrement(cpp_int_backend& result) else if(result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) ++result.limbs()[0]; else - subtract(result, one); + eval_subtract(result, one); } template -inline void subtract(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) { - subtract(result, result, o); + eval_subtract(result, result, o); } template inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) @@ -996,7 +997,7 @@ inline void subtract_unsigned(cpp_int_backend& resul result.negate(); } template -inline void subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { if(a.sign() != b.sign()) { @@ -1006,7 +1007,7 @@ inline void subtract(cpp_int_backend& result, const subtract_unsigned(result, a, b); } template -inline void multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { // Very simple long multiplication, only usable for small numbers of limb_type's // but that's the typical use case for this type anyway: @@ -1028,7 +1029,7 @@ inline void multiply(cpp_int_backend& result, const { limb_type l = *pa; result = b; - multiply(result, l); + eval_multiply(result, l); } result.sign(s); return; @@ -1038,7 +1039,7 @@ inline void multiply(cpp_int_backend& result, const limb_type l = *pb; bool s = b.sign() != a.sign(); result = a; - multiply(result, l); + eval_multiply(result, l); result.sign(s); return; } @@ -1046,13 +1047,13 @@ inline void multiply(cpp_int_backend& result, const if(&result == &a) { cpp_int_backend t(a); - multiply(result, t, b); + eval_multiply(result, t, b); return; } if(&result == &b) { cpp_int_backend t(b); - multiply(result, a, t); + eval_multiply(result, a, t); return; } @@ -1063,7 +1064,7 @@ inline void multiply(cpp_int_backend& result, const std::memset(pr, 0, result.size() * sizeof(limb_type)); for(unsigned i = 0; i < as; ++i) { - unsigned inner_limit = (std::min)(result.size() - i, b.size()); + unsigned inner_limit = cpp_int_backend::variable ? bs : (std::min)(result.size() - i, bs); for(unsigned j = 0; j < inner_limit; ++j) { BOOST_ASSERT(i+j < result.size()); @@ -1083,12 +1084,12 @@ inline void multiply(cpp_int_backend& result, const result.sign(a.sign() != b.sign()); } template -inline void multiply(cpp_int_backend& result, const cpp_int_backend& a) +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a) { - multiply(result, result, a); + eval_multiply(result, result, a); } template -inline void multiply(cpp_int_backend& result, cpp_int_backend& a, const limb_type& val) +inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const limb_type& val) { if(!val) { @@ -1117,25 +1118,25 @@ inline void multiply(cpp_int_backend& result, cpp_in result.normalize(); } template -inline void multiply(cpp_int_backend& result, const limb_type& val) +inline void eval_multiply(cpp_int_backend& result, const limb_type& val) { - multiply(result, result, val); + eval_multiply(result, result, val); } template -inline void multiply(cpp_int_backend& result, cpp_int_backend& a, const signed_limb_type& val) +inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const signed_limb_type& val) { if(val > 0) - multiply(result, a, static_cast(val)); + eval_multiply(result, a, static_cast(val)); else { - multiply(result, a, static_cast(-val)); + eval_multiply(result, a, static_cast(-val)); result.negate(); } } template -inline void multiply(cpp_int_backend& result, const signed_limb_type& val) +inline void eval_multiply(cpp_int_backend& result, const signed_limb_type& val) { - multiply(result, result, val); + eval_multiply(result, result, val); } template void divide_unsigned_helper(cpp_int_backend& result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) @@ -1172,7 +1173,7 @@ void divide_unsigned_helper(cpp_int_backend& result, */ - using default_ops::subtract; + using default_ops::eval_subtract; if(&result == &r) { @@ -1306,7 +1307,7 @@ void divide_unsigned_helper(cpp_int_backend& result, t.limbs()[shift] = guess; for(unsigned i = 0; i < shift; ++i) t.limbs()[i] = 0; - subtract(result, t); + eval_subtract(result, t); } } else if(cpp_int_backend::max_limb_value - pr[shift] > guess) @@ -1317,7 +1318,7 @@ void divide_unsigned_helper(cpp_int_backend& result, t.limbs()[shift] = guess; for(unsigned i = 0; i < shift; ++i) t.limbs()[i] = 0; - add(result, t); + eval_add(result, t); } // // Calculate guess * y, we use a fused mutiply-shift O(N) for this @@ -1346,7 +1347,7 @@ void divide_unsigned_helper(cpp_int_backend& result, // // Update r: // - subtract(r, t); + eval_subtract(r, t); if(r.isneg()) { r.negate(); @@ -1376,15 +1377,15 @@ void divide_unsigned_helper(cpp_int_backend& result, // // We now just have to normalise the result: // - if(r_neg && get_sign(r)) + if(r_neg && eval_get_sign(r)) { // We have one too many in the result: - decrement(result); + eval_decrement(result); r.negate(); if(y.sign()) - subtract(r, y); + eval_subtract(r, y); else - add(r, y); + eval_add(r, y); } BOOST_ASSERT(r.compare_unsigned(y) < 0); // remainder must be less than the divisor or our code has failed @@ -1410,7 +1411,7 @@ void divide_unsigned_helper(cpp_int_backend& result, // As above, but simplified for integer divisor: - using default_ops::subtract; + using default_ops::eval_subtract; if(y == 0) { @@ -1514,20 +1515,20 @@ void divide_unsigned_helper(cpp_int_backend& result, } template -inline void divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { cpp_int_backend r; divide_unsigned_helper(result, a, b, r); result.sign(a.sign() != b.sign()); } template -inline void divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) { cpp_int_backend r; divide_unsigned_helper(result, a, b, r); } template -inline void divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) { cpp_int_backend r; divide_unsigned_helper(result, a, std::abs(b), r); @@ -1535,65 +1536,65 @@ inline void divide(cpp_int_backend& result, const cp result.negate(); } template -inline void divide(cpp_int_backend& result, const cpp_int_backend& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& b) { // There is no in place divide: cpp_int_backend a(result); - divide(result, a, b); + eval_divide(result, a, b); } template -inline void divide(cpp_int_backend& result, limb_type b) +inline void eval_divide(cpp_int_backend& result, limb_type b) { // There is no in place divide: cpp_int_backend a(result); - divide(result, a, b); + eval_divide(result, a, b); } template -inline void divide(cpp_int_backend& result, signed_limb_type b) +inline void eval_divide(cpp_int_backend& result, signed_limb_type b) { // There is no in place divide: cpp_int_backend a(result); - divide(result, a, b); + eval_divide(result, a, b); } template -inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { cpp_int_backend r; divide_unsigned_helper(r, a, b, result); result.sign(a.sign()); } template -inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) { cpp_int_backend r; divide_unsigned_helper(r, a, b, result); } template -inline void modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) { cpp_int_backend r; divide_unsigned_helper(r, a, static_cast(std::abs(b)), result); } template -inline void modulus(cpp_int_backend& result, const cpp_int_backend& b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) { // There is no in place divide: cpp_int_backend a(result); - modulus(result, a, b); + eval_modulus(result, a, b); } template -inline void modulus(cpp_int_backend& result, limb_type b) +inline void eval_modulus(cpp_int_backend& result, limb_type b) { // There is no in place divide: cpp_int_backend a(result); - modulus(result, a, b); + eval_modulus(result, a, b); } template -inline void modulus(cpp_int_backend& result, signed_limb_type b) +inline void eval_modulus(cpp_int_backend& result, signed_limb_type b) { // There is no in place divide: cpp_int_backend a(result); - modulus(result, a, b); + eval_modulus(result, a, b); } template void bitwise_op(cpp_int_backend& result, const cpp_int_backend& o, Op op) @@ -1726,20 +1727,20 @@ struct bit_or{ limb_type operator()(limb_type a, limb_type b)const{ return a | b struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const{ return a ^ b; } }; template -inline void bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) { bitwise_op(result, o, bit_and()); } #if 0 template -inline void bitwise_and(cpp_int_backend& result, limb_type o) +inline void eval_bitwise_and(cpp_int_backend& result, limb_type o) { result.data()[cpp_int_backend::limb_count - 1] &= o; for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) result.data()[i] = 0; } template -inline void bitwise_and(cpp_int_backend& result, signed_limb_type o) +inline void eval_bitwise_and(cpp_int_backend& result, signed_limb_type o) { result.data()[cpp_int_backend::limb_count - 1] &= o; limb_type mask = o < 0 ? cpp_int_backend::max_limb_value : 0; @@ -1747,35 +1748,35 @@ inline void bitwise_and(cpp_int_backend& result, sig result.data()[i] &= mask; } template -inline void bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) { for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count; ++i) result.data()[i] |= o.data()[i]; } template -inline void bitwise_or(cpp_int_backend& result, limb_type o) +inline void eval_bitwise_or(cpp_int_backend& result, limb_type o) { result.data()[cpp_int_backend::limb_count - 1] |= o; } #endif template -inline void bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) { bitwise_op(result, o, bit_or()); } template -inline void bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) { bitwise_op(result, o, bit_xor()); } #if 0 template -inline void bitwise_xor(cpp_int_backend& result, limb_type o) +inline void eval_bitwise_xor(cpp_int_backend& result, limb_type o) { result.data()[cpp_int_backend::limb_count - 1] ^= o; } template -inline void bitwise_xor(cpp_int_backend& result, signed_limb_type o) +inline void eval_bitwise_xor(cpp_int_backend& result, signed_limb_type o) { result.data()[cpp_int_backend::limb_count - 1] ^= o; limb_type mask = o < 0 ? cpp_int_backend::max_limb_value : 0; @@ -1784,15 +1785,15 @@ inline void bitwise_xor(cpp_int_backend& result, sig } #endif template -inline void complement(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) { // Increment and negate: result = o; - increment(result); + eval_increment(result); result.negate(); } template -inline void left_shift(cpp_int_backend& result, double_limb_type s) +inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) { if(!s) return; @@ -1868,7 +1869,7 @@ inline void left_shift(cpp_int_backend& result, double_li } } template -inline void left_shift(cpp_int_backend& result, double_limb_type s) +inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) { if(!s) return; @@ -1925,7 +1926,7 @@ inline void left_shift(cpp_int_backend& result, doub } } template -inline void right_shift(cpp_int_backend& result, double_limb_type s) +inline void eval_right_shift(cpp_int_backend& result, double_limb_type s) { if(!s) return; @@ -1979,7 +1980,7 @@ inline Integer negate_integer(Integer i, const mpl::false_&) } template -inline typename enable_if, void>::type convert_to(R* result, const cpp_int_backend& backend) +inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) { *result = static_cast(backend.limbs()[0]); unsigned shift = cpp_int_backend::limb_bits; @@ -1997,7 +1998,7 @@ inline typename enable_if, void>::type convert_to(R* result, cons } template -inline typename enable_if, void>::type convert_to(R* result, const cpp_int_backend& backend) +inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) { typename cpp_int_backend::const_limb_pointer p = backend.limbs(); unsigned shift = cpp_int_backend::limb_bits; @@ -2012,24 +2013,23 @@ inline typename enable_if, void>::type convert_to(R* result } template -inline bool is_zero(const cpp_int_backend& val) +inline bool eval_is_zero(const cpp_int_backend& val) { return (val.size() == 1) && (val.limbs()[0] == 0); } template -inline int get_sign(const cpp_int_backend& val) +inline int eval_get_sign(const cpp_int_backend& val) { - return is_zero(val) ? 0 : val.sign() ? -1 : 1; + return eval_is_zero(val) ? 0 : val.sign() ? -1 : 1; } -namespace detail{ // // Get the location of the least-significant-bit: // template inline unsigned get_lsb(const cpp_int_backend& a) { - BOOST_ASSERT(get_sign(a) != 0); + BOOST_ASSERT(eval_get_sign(a) != 0); unsigned result = 0; // @@ -2051,8 +2051,6 @@ inline unsigned get_lsb(const cpp_int_backend& a) return result + index * cpp_int_backend::limb_bits; } -} - template inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { @@ -2060,7 +2058,7 @@ inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend u(a), v(b); - int s = get_sign(u); + int s = eval_get_sign(u); /* GCD(0,x) := x */ if(s < 0) @@ -2072,7 +2070,7 @@ inline void eval_gcd(cpp_int_backend& result, const result = v; return; } - s = get_sign(v); + s = eval_get_sign(v); if(s < 0) { v.negate(); @@ -2086,11 +2084,11 @@ inline void eval_gcd(cpp_int_backend& result, const /* Let shift := lg K, where K is the greatest power of 2 dividing both u and v. */ - unsigned us = detail::get_lsb(u); - unsigned vs = detail::get_lsb(v); + unsigned us = get_lsb(u); + unsigned vs = get_lsb(v); shift = (std::min)(us, vs); - right_shift(u, us); - right_shift(v, vs); + eval_right_shift(u, us); + eval_right_shift(v, vs); do { @@ -2098,19 +2096,19 @@ inline void eval_gcd(cpp_int_backend& result, const Let u = min(u, v), v = diff(u, v)/2. */ if(u.compare(v) > 0) u.swap(v); - subtract(v, u); + eval_subtract(v, u); // Termination condition tries not to do a full compare if possible: - if(!v.limbs()[0] && is_zero(v)) + if(!v.limbs()[0] && eval_is_zero(v)) break; - vs = detail::get_lsb(v); - right_shift(v, vs); + vs = get_lsb(v); + eval_right_shift(v, vs); BOOST_ASSERT((v.limbs()[0] & 1)); BOOST_ASSERT((u.limbs()[0] & 1)); } while(true); result = u; - left_shift(result, shift); + eval_left_shift(result, shift); } template @@ -2119,19 +2117,23 @@ inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend t; eval_gcd(t, a, b); - if(is_zero(t)) + if(eval_is_zero(t)) { result = static_cast(0); } else { - divide(result, a, t); - multiply(result, b); + eval_divide(result, a, t); + eval_multiply(result, b); } - if(get_sign(result) < 0) + if(eval_get_sign(result) < 0) result.negate(); } +} // namespace backends; + +using boost::multiprecision::backends::cpp_int_backend; + template struct number_category > : public mpl::int_{}; diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 4f098147..6a7dfc67 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -32,76 +32,76 @@ namespace boost{ namespace multiprecision{ namespace default_ops{ // template inline typename enable_if, is_convertible, is_same > >::type - add(T& result, V const& v) + eval_add(T& result, V const& v) { T t; t = v; - add(result, t); + eval_add(result, t); } template inline typename enable_if, is_convertible, is_same > >::type - subtract(T& result, V const& v) + eval_subtract(T& result, V const& v) { T t; t = v; - subtract(result, t); + eval_subtract(result, t); } template inline typename enable_if, is_convertible, is_same > >::type - multiply(T& result, V const& v) + eval_multiply(T& result, V const& v) { T t; t = v; - multiply(result, t); + eval_multiply(result, t); } template inline typename enable_if, is_convertible, is_same > >::type - divide(T& result, V const& v) + eval_divide(T& result, V const& v) { T t; t = v; - divide(result, t); + eval_divide(result, t); } template inline typename enable_if, is_convertible, is_same > >::type - modulus(T& result, V const& v) + eval_modulus(T& result, V const& v) { T t; t = v; - modulus(result, t); + eval_modulus(result, t); } template inline typename enable_if, is_convertible, is_same > >::type - bitwise_and(T& result, V const& v) + eval_bitwise_and(T& result, V const& v) { T t; t = v; - bitwise_and(result, t); + eval_bitwise_and(result, t); } template inline typename enable_if, is_convertible, is_same > >::type - bitwise_or(T& result, V const& v) + eval_bitwise_or(T& result, V const& v) { T t; t = v; - bitwise_or(result, t); + eval_bitwise_or(result, t); } template inline typename enable_if, is_convertible, is_same > >::type - bitwise_xor(T& result, V const& v) + eval_bitwise_xor(T& result, V const& v) { T t; t = v; - bitwise_xor(result, t); + eval_bitwise_xor(result, t); } template inline typename enable_if, is_convertible, is_same > >::type - complement(T& result, V const& v) + eval_complement(T& result, V const& v) { T t; t = v; - complement(result, t); + eval_complement(result, t); } template @@ -115,196 +115,196 @@ inline bool is_same_object(const T& u, const U&v) // Default versions of 3-arg arithmetic functions, these just forward to the 2 arg versions: // template -inline void add(T& t, const U& u, const V& v) +inline void eval_add(T& t, const U& u, const V& v) { if(is_same_object(t, v)) { - add(t, u); + eval_add(t, u); } else if(is_same_object(t, u)) { - add(t, v); + eval_add(t, v); } else { t = u; - add(t, v); + eval_add(t, v); } } template -inline typename disable_if >::type add(T& t, const U& a, const T& b) +inline typename disable_if >::type eval_add(T& t, const U& a, const T& b) { - return add(t, b, a); + return eval_add(t, b, a); } template -inline void subtract(T& t, const U& u, const V& v) +inline void eval_subtract(T& t, const U& u, const V& v) { if(is_same_object(t, u)) - subtract(t, v); + eval_subtract(t, v); else if(is_same_object(t, v)) { - subtract(t, u); + eval_subtract(t, u); t.negate(); } else { t = u; - subtract(t, v); + eval_subtract(t, v); } } template -inline typename disable_if >::type subtract(T& t, const U& a, const T& b) +inline typename disable_if >::type eval_subtract(T& t, const U& a, const T& b) { - subtract(t, b, a); + eval_subtract(t, b, a); t.negate(); } template -inline void multiply(T& t, const U& u, const V& v) +inline void eval_multiply(T& t, const U& u, const V& v) { if(is_same_object(t, u)) - multiply(t, v); + eval_multiply(t, v); else if(is_same_object(t, v)) - multiply(t, u); + eval_multiply(t, u); else { t = u; - multiply(t, v); + eval_multiply(t, v); } } template -inline typename disable_if >::type multiply(T& t, const U& a, const T& b) +inline typename disable_if >::type eval_multiply(T& t, const U& a, const T& b) { - multiply(t, b, a); + eval_multiply(t, b, a); } template -inline void divide(T& t, const U& u, const V& v) +inline void eval_divide(T& t, const U& u, const V& v) { if(is_same_object(t, u)) - divide(t, v); + eval_divide(t, v); else if(is_same_object(t, v)) { T temp = t; - divide(temp, u, v); + eval_divide(temp, u, v); temp.swap(t); } else { t = u; - divide(t, v); + eval_divide(t, v); } } template -inline void modulus(T& t, const U& u, const V& v) +inline void eval_modulus(T& t, const U& u, const V& v) { if(is_same_object(t, u)) - modulus(t, v); + eval_modulus(t, v); else if(is_same_object(t, v)) { T temp; - modulus(temp, u, v); + eval_modulus(temp, u, v); temp.swap(t); } else { t = u; - modulus(t, v); + eval_modulus(t, v); } } template -inline void bitwise_and(T& t, const U& u, const V& v) +inline void eval_bitwise_and(T& t, const U& u, const V& v) { if(is_same_object(t, u)) - bitwise_and(t, v); + eval_bitwise_and(t, v); else if(is_same_object(t, v)) - bitwise_and(t, u); + eval_bitwise_and(t, u); else { t = u; - bitwise_and(t, v); + eval_bitwise_and(t, v); } } template -inline typename disable_if >::type bitwise_and(T& t, const U& a, const T& b) +inline typename disable_if >::type eval_bitwise_and(T& t, const U& a, const T& b) { - bitwise_and(t, b, a); + eval_bitwise_and(t, b, a); } template -inline void bitwise_or(T& t, const U& u, const V& v) +inline void eval_bitwise_or(T& t, const U& u, const V& v) { if(is_same_object(t, u)) - bitwise_or(t, v); + eval_bitwise_or(t, v); else if(is_same_object(t, v)) - bitwise_or(t, u); + eval_bitwise_or(t, u); else { t = u; - bitwise_or(t, v); + eval_bitwise_or(t, v); } } template -inline typename disable_if >::type bitwise_or(T& t, const U& a, const T& b) +inline typename disable_if >::type eval_bitwise_or(T& t, const U& a, const T& b) { - bitwise_or(t, b, a); + eval_bitwise_or(t, b, a); } template -inline void bitwise_xor(T& t, const U& u, const V& v) +inline void eval_bitwise_xor(T& t, const U& u, const V& v) { if(is_same_object(t, u)) - bitwise_xor(t, v); + eval_bitwise_xor(t, v); else if(is_same_object(t, v)) - bitwise_xor(t, u); + eval_bitwise_xor(t, u); else { t = u; - bitwise_xor(t, v); + eval_bitwise_xor(t, v); } } template -inline typename disable_if >::type bitwise_xor(T& t, const U& a, const T& b) +inline typename disable_if >::type eval_bitwise_xor(T& t, const U& a, const T& b) { - bitwise_xor(t, b, a); + eval_bitwise_xor(t, b, a); } template -inline void increment(T& val) +inline void eval_increment(T& val) { typedef typename mpl::front::type ui_type; - add(val, static_cast(1u)); + eval_add(val, static_cast(1u)); } template -inline void decrement(T& val) +inline void eval_decrement(T& val) { typedef typename mpl::front::type ui_type; - subtract(val, static_cast(1u)); + eval_subtract(val, static_cast(1u)); } template -inline void left_shift(T& result, const T& arg, const V val) +inline void eval_left_shift(T& result, const T& arg, const V val) { result = arg; - left_shift(result, val); + eval_left_shift(result, val); } template -inline void right_shift(T& result, const T& arg, const V val) +inline void eval_right_shift(T& result, const T& arg, const V val) { result = arg; - right_shift(result, val); + eval_right_shift(result, val); } template -inline bool is_zero(const T& val) +inline bool eval_is_zero(const T& val) { typedef typename mpl::front::type ui_type; return val.compare(static_cast(0)) == 0; } template -inline int get_sign(const T& val) +inline int eval_get_sign(const T& val) { typedef typename mpl::front::type ui_type; return val.compare(static_cast(0)); @@ -316,7 +316,7 @@ inline void assign_components_imp(T& result, const V& v1, const V& v2, const mpl result = v1; T t; t = v2; - divide(result, t); + eval_divide(result, t); } template @@ -367,11 +367,11 @@ struct calculate_next_larger_type }; template -inline void convert_to(R* result, const B& backend) +inline void eval_convert_to(R* result, const B& backend) { typedef typename calculate_next_larger_type::type next_type; next_type n; - convert_to(&n, backend); + eval_convert_to(&n, backend); if(std::numeric_limits::is_specialized && (n > (std::numeric_limits::max)())) { *result = (std::numeric_limits::max)(); @@ -381,7 +381,7 @@ inline void convert_to(R* result, const B& backend) } template -inline void convert_to(terminal* result, const B& backend) +inline void eval_convert_to(terminal* result, const B& backend) { // // We ran out of types to try for the convertion, try @@ -417,7 +417,7 @@ template inline int eval_fpclassify(const Backend& arg) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_floating_point, "The fpclassify function is only valid for floating point types."); - return is_zero(arg) ? FP_ZERO : FP_NORMAL; + return eval_is_zero(arg) ? FP_ZERO : FP_NORMAL; } template @@ -432,13 +432,13 @@ inline void eval_fmod(T& result, const T& a, const T& b) return; } T n; - divide(result, a, b); - if(get_sign(a) < 0) + eval_divide(result, a, b); + if(eval_get_sign(a) < 0) eval_ceil(n, result); else eval_floor(n, result); - multiply(n, b); - subtract(result, a, n); + eval_multiply(n, b); + eval_subtract(result, a, n); } template inline void eval_trunc(T& result, const T& a) @@ -450,7 +450,7 @@ inline void eval_trunc(T& result, const T& a) result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number(a), 0, boost::math::policies::policy<>()).backend(); return; } - if(get_sign(a) < 0) + if(eval_get_sign(a) < 0) eval_ceil(result, a); else eval_floor(result, a); @@ -467,14 +467,14 @@ inline void eval_round(T& result, const T& a) result = boost::math::policies::raise_rounding_error("boost::multiprecision::round<%1%>(%1%)", 0, mp_number(a), 0, boost::math::policies::policy<>()).backend(); return; } - if(get_sign(a) < 0) + if(eval_get_sign(a) < 0) { - subtract(result, a, fp_type(0.5f)); + eval_subtract(result, a, fp_type(0.5f)); eval_ceil(result, result); } else { - add(result, a, fp_type(0.5f)); + eval_add(result, a, fp_type(0.5f)); eval_floor(result, result); } } diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp index dab1e2c3..677ed49d 100644 --- a/include/boost/multiprecision/detail/functions/constants.hpp +++ b/include/boost/multiprecision/detail/functions/constants.hpp @@ -28,21 +28,21 @@ void calc_log2(T& num, unsigned digits) for(ui_type n = 6; n < limit; ++n) { temp = static_cast(2); - multiply(temp, ui_type(2 * n)); - multiply(temp, ui_type(2 * n + 1)); - multiply(num, temp); - multiply(denom, temp); + eval_multiply(temp, ui_type(2 * n)); + eval_multiply(temp, ui_type(2 * n + 1)); + eval_multiply(num, temp); + eval_multiply(denom, temp); sign = -sign; - multiply(next_term, n); - multiply(temp, next_term, next_term); - multiply(temp, sign); - add(num, temp); + eval_multiply(next_term, n); + eval_multiply(temp, next_term, next_term); + eval_multiply(temp, sign); + eval_add(num, temp); } - multiply(denom, ui_type(4)); - multiply(num, ui_type(3)); + eval_multiply(denom, ui_type(4)); + eval_multiply(num, ui_type(3)); INSTRUMENT_BACKEND(denom); INSTRUMENT_BACKEND(num); - divide(num, denom); + eval_divide(num, denom); INSTRUMENT_BACKEND(num); } @@ -60,12 +60,12 @@ void calc_e(T& result, unsigned digits) denom = ui_type(1); ui_type i = 2; do{ - multiply(denom, i); - multiply(result, i); - add(result, ui_type(1)); + eval_multiply(denom, i); + eval_multiply(result, i); + eval_add(result, ui_type(1)); ++i; }while(denom.compare(lim) <= 0); - divide(result, denom); + eval_divide(result, denom); } template @@ -91,16 +91,16 @@ void calc_pi(T& result, unsigned digits) do { - add(result, A, B); + eval_add(result, A, B); eval_ldexp(result, result, -2); eval_sqrt(b, B); - add(a, b); + eval_add(a, b); eval_ldexp(a, a, -1); - multiply(A, a, a); - subtract(B, A, result); + eval_multiply(A, a, a); + eval_subtract(B, A, result); eval_ldexp(B, B, 1); - subtract(result, A, B); - bool neg = get_sign(result) < 0; + eval_subtract(result, A, B); + bool neg = eval_get_sign(result) < 0; if(neg) result.negate(); if(result.compare(lim) <= 0) @@ -108,13 +108,13 @@ void calc_pi(T& result, unsigned digits) if(neg) result.negate(); eval_ldexp(result, result, k - 1); - subtract(D, result); + eval_subtract(D, result); ++k; eval_ldexp(lim, lim, 1); } while(true); - divide(result, B, D); + eval_divide(result, B, D); } template diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 23ee1895..f9f2e37b 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -35,7 +35,7 @@ inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) temp = static_cast(1); T denom; pow_imp(denom, t, -p, mpl::true_()); - divide(result, temp, denom); + eval_divide(result, temp, denom); return; } @@ -48,15 +48,15 @@ inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) result = t; break; case 2: - multiply(result, t, t); + eval_multiply(result, t, t); break; case 3: - multiply(result, t, t); - multiply(result, t); + eval_multiply(result, t, t); + eval_multiply(result, t); break; case 4: - multiply(result, t, t); - multiply(result, result); + eval_multiply(result, t, t); + eval_multiply(result, result); break; default: { @@ -65,7 +65,7 @@ inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) for(n = static_cast(1); n <= static_cast(p / static_cast(2)); n *= static_cast(2)) { - multiply(result, result); + eval_multiply(result, result); } const U p_minus_n = static_cast(p - n); @@ -75,7 +75,7 @@ inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) { T temp; pow_imp(temp, t, p_minus_n, mpl::true_()); - multiply(result, temp); + eval_multiply(result, temp); } } } @@ -106,11 +106,11 @@ void hyp0F0(T& H0F0, const T& x) T x_pow_n_div_n_fact(x); - add(H0F0, x_pow_n_div_n_fact, ui_type(1)); + eval_add(H0F0, x_pow_n_div_n_fact, ui_type(1)); T lim; eval_ldexp(lim, H0F0, 1 - tol); - if(get_sign(lim) < 0) + if(eval_get_sign(lim) < 0) lim.negate(); ui_type n; @@ -118,10 +118,10 @@ void hyp0F0(T& H0F0, const T& x) // Series expansion of hyperg_0f0(; ; x). for(n = 2; n < 300; ++n) { - multiply(x_pow_n_div_n_fact, x); - divide(x_pow_n_div_n_fact, n); - add(H0F0, x_pow_n_div_n_fact); - bool neg = get_sign(x_pow_n_div_n_fact) < 0; + eval_multiply(x_pow_n_div_n_fact, x); + eval_divide(x_pow_n_div_n_fact, n); + eval_add(H0F0, x_pow_n_div_n_fact); + bool neg = eval_get_sign(x_pow_n_div_n_fact) < 0; if(neg) x_pow_n_div_n_fact.negate(); if(lim.compare(x_pow_n_div_n_fact) > 0) @@ -154,11 +154,11 @@ void hyp1F0(T& H1F0, const T& a, const T& x) T pochham_a (a); T ap (a); - multiply(H1F0, pochham_a, x_pow_n_div_n_fact); - add(H1F0, si_type(1)); + eval_multiply(H1F0, pochham_a, x_pow_n_div_n_fact); + eval_add(H1F0, si_type(1)); T lim; eval_ldexp(lim, H1F0, 1 - boost::multiprecision::detail::digits2 >::value); - if(get_sign(lim) < 0) + if(eval_get_sign(lim) < 0) lim.negate(); si_type n; @@ -167,13 +167,13 @@ void hyp1F0(T& H1F0, const T& a, const T& x) // Series expansion of hyperg_1f0(a; ; x). for(n = 2; n < boost::multiprecision::detail::digits2 >::value + 10; n++) { - multiply(x_pow_n_div_n_fact, x); - divide(x_pow_n_div_n_fact, n); - increment(ap); - multiply(pochham_a, ap); - multiply(term, pochham_a, x_pow_n_div_n_fact); - add(H1F0, term); - if(get_sign(term) < 0) + eval_multiply(x_pow_n_div_n_fact, x); + eval_divide(x_pow_n_div_n_fact, n); + eval_increment(ap); + eval_multiply(pochham_a, ap); + eval_multiply(term, pochham_a, x_pow_n_div_n_fact); + eval_add(H1F0, term); + if(eval_get_sign(term) < 0) term.negate(); if(lim.compare(term) >= 0) break; @@ -201,7 +201,7 @@ void eval_exp(T& result, const T& x) // Handle special arguments. int type = eval_fpclassify(x); - bool isneg = get_sign(x) < 0; + bool isneg = eval_get_sign(x) < 0; if(type == FP_NAN) { result = std::numeric_limits >::quiet_NaN().backend(); @@ -250,21 +250,21 @@ void eval_exp(T& result, const T& x) exp_series = xx; result = si_type(1); if(isneg) - subtract(result, exp_series); + eval_subtract(result, exp_series); else - add(result, exp_series); - multiply(exp_series, xx); - divide(exp_series, ui_type(k)); - add(result, exp_series); + eval_add(result, exp_series); + eval_multiply(exp_series, xx); + eval_divide(exp_series, ui_type(k)); + eval_add(result, exp_series); while(exp_series.compare(lim) > 0) { ++k; - multiply(exp_series, xx); - divide(exp_series, ui_type(k)); + eval_multiply(exp_series, xx); + eval_divide(exp_series, ui_type(k)); if(isneg && (k&1)) - subtract(result, exp_series); + eval_subtract(result, exp_series); else - add(result, exp_series); + eval_add(result, exp_series); } return; } @@ -272,7 +272,7 @@ void eval_exp(T& result, const T& x) // Check for pure-integer arguments which can be either signed or unsigned. long long ll; eval_trunc(exp_series, x); - convert_to(&ll, exp_series); + eval_convert_to(&ll, exp_series); if(x.compare(ll) == 0) { detail::pow_imp(result, get_constant_e(), ll, mpl::true_()); @@ -293,23 +293,23 @@ void eval_exp(T& result, const T& x) if(b_scale) { - divide(result, xx, get_constant_ln2()); + eval_divide(result, xx, get_constant_ln2()); exp_type n; - convert_to(&n, result); + eval_convert_to(&n, result); // The scaling is 2^11 = 2048. static const si_type p2 = static_cast(si_type(1) << 11); - multiply(exp_series, get_constant_ln2(), static_cast(n)); - subtract(exp_series, xx); - divide(exp_series, p2); + eval_multiply(exp_series, get_constant_ln2(), static_cast(n)); + eval_subtract(exp_series, xx); + eval_divide(exp_series, p2); exp_series.negate(); hyp0F0(result, exp_series); detail::pow_imp(exp_series, result, p2, mpl::true_()); result = ui_type(1); eval_ldexp(result, result, n); - multiply(exp_series, result); + eval_multiply(exp_series, result); } else { @@ -317,7 +317,7 @@ void eval_exp(T& result, const T& x) } if(isneg) - divide(result, ui_type(1), exp_series); + eval_divide(result, ui_type(1), exp_series); else result = exp_series; } @@ -358,9 +358,9 @@ void eval_log(T& result, const T& arg) --e; } - multiply(result, get_constant_ln2(), canonical_exp_type(e)); + eval_multiply(result, get_constant_ln2(), canonical_exp_type(e)); INSTRUMENT_BACKEND(result); - subtract(t, ui_type(1)); /* -0.3 <= t <= 0.3 */ + eval_subtract(t, ui_type(1)); /* -0.3 <= t <= 0.3 */ if(!alternate) t.negate(); /* 0 <= t <= 0.33333 */ T pow = t; @@ -368,12 +368,12 @@ void eval_log(T& result, const T& arg) T t2; if(alternate) - add(result, t); + eval_add(result, t); else - subtract(result, t); + eval_subtract(result, t); - multiply(lim, result, std::numeric_limits >::epsilon().backend()); - if(get_sign(lim) < 0) + eval_multiply(lim, result, std::numeric_limits >::epsilon().backend()); + if(eval_get_sign(lim) < 0) lim.negate(); INSTRUMENT_BACKEND(lim); @@ -381,13 +381,13 @@ void eval_log(T& result, const T& arg) do { ++k; - multiply(pow, t); - divide(t2, pow, k); + eval_multiply(pow, t); + eval_divide(t2, pow, k); INSTRUMENT_BACKEND(t2); if(alternate && ((k & 1) != 0)) - add(result, t2); + eval_add(result, t2); else - subtract(result, t2); + eval_subtract(result, t2); INSTRUMENT_BACKEND(result); }while(lim.compare(t2) < 0); } @@ -415,7 +415,7 @@ void eval_log10(T& result, const T& arg) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_floating_point, "The fabs function is only valid for floating point types."); eval_log(result, arg); - divide(result, get_constant_log10()); + eval_divide(result, get_constant_log10()); } template @@ -457,35 +457,35 @@ inline void eval_pow(T& result, const T& x, const T& a) default: ; } - if(get_sign(a) == 0) + if(eval_get_sign(a) == 0) { result = si_type(1); return; } long long an; - convert_to(&an, a); + eval_convert_to(&an, a); const bool bo_a_isint = a.compare(an) == 0; - if((get_sign(x) < 0) && !bo_a_isint) + if((eval_get_sign(x) < 0) && !bo_a_isint) { result = std::numeric_limits >::quiet_NaN().backend(); } T t; T da(a); - subtract(da, an); + eval_subtract(da, an); if(a.compare(si_type(-1)) < 0) { t = a; t.negate(); eval_pow(da, x, t); - divide(result, si_type(1), da); + eval_divide(result, si_type(1), da); return; } - subtract(da, a, an); + eval_subtract(da, a, an); if(bo_a_isint) { @@ -493,13 +493,13 @@ inline void eval_pow(T& result, const T& x, const T& a) return; } - if((get_sign(x) > 0) && (x.compare(fp_type(0.5)) >= 0) && (x.compare(fp_type(0.9)) < 0)) + if((eval_get_sign(x) > 0) && (x.compare(fp_type(0.5)) >= 0) && (x.compare(fp_type(0.9)) < 0)) { if(a.compare(fp_type(1e-5f)) <= 0) { // Series expansion for small a. eval_log(t, x); - multiply(t, a); + eval_multiply(t, a); hyp0F0(result, t); return; } @@ -511,17 +511,17 @@ inline void eval_pow(T& result, const T& x, const T& a) { da.negate(); t = si_type(1); - subtract(t, x); + eval_subtract(t, x); hyp1F0(result, da, t); detail::pow_imp(t, x, an, mpl::true_()); - multiply(result, t); + eval_multiply(result, t); } else { da = a; da.negate(); t = si_type(1); - subtract(t, x); + eval_subtract(t, x); hyp1F0(result, da, t); } } @@ -533,15 +533,15 @@ inline void eval_pow(T& result, const T& x, const T& a) if(an) { eval_log(t, x); - multiply(t, da); + eval_multiply(t, da); eval_exp(result, t); detail::pow_imp(t, x, an, mpl::true_()); - multiply(result, t); + eval_multiply(result, t); } else { eval_log(t, x); - multiply(t, a); + eval_multiply(t, a); eval_exp(result, t); } } @@ -553,12 +553,12 @@ namespace detail{ void small_sinh_series(T x, T& result) { typedef typename boost::multiprecision::detail::canonical::type ui_type; - bool neg = get_sign(x) < 0; + bool neg = eval_get_sign(x) < 0; if(neg) x.negate(); T p(x); T mult(x); - multiply(mult, x); + eval_multiply(mult, x); result = x; ui_type k = 1; @@ -567,10 +567,10 @@ namespace detail{ do { - multiply(p, mult); - divide(p, ++k); - divide(p, ++k); - add(result, p); + eval_multiply(p, mult); + eval_divide(p, ++k); + eval_divide(p, ++k); + eval_add(result, p); }while(p.compare(lim) >= 0); if(neg) result.negate(); @@ -605,12 +605,12 @@ namespace detail{ T e_px, e_mx; - bool small_sinh = get_sign(x) < 0 ? e_px.compare(fp_type(-0.5)) > 0 : e_px.compare(fp_type(0.5)) < 0; + bool small_sinh = eval_get_sign(x) < 0 ? e_px.compare(fp_type(-0.5)) > 0 : e_px.compare(fp_type(0.5)) < 0; if(p_cosh || !small_sinh) { eval_exp(e_px, x); - divide(e_mx, ui_type(1), e_px); + eval_divide(e_mx, ui_type(1), e_px); if(p_sinh) { @@ -620,14 +620,14 @@ namespace detail{ } else { - subtract(*p_sinh, e_px, e_mx); - divide(*p_sinh, ui_type(2)); + eval_subtract(*p_sinh, e_px, e_mx); + eval_divide(*p_sinh, ui_type(2)); } } if(p_cosh) { - add(*p_cosh, e_px, e_mx); - divide(*p_cosh, ui_type(2)); + eval_add(*p_cosh, e_px, e_mx); + eval_divide(*p_cosh, ui_type(2)); } } else @@ -658,6 +658,6 @@ inline void eval_tanh(T& result, const T& x) BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_floating_point, "The tanh function is only valid for floating point types."); T c; detail::sinhcosh(x, &result, &c); - divide(result, c); + eval_divide(result, c); } diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index 58c24cd4..dbe134fd 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -29,31 +29,31 @@ void hyp0F1(T& result, const T& b, const T& x) T pochham_b (b); T bp (b); - divide(result, x_pow_n_div_n_fact, pochham_b); - add(result, ui_type(1)); + eval_divide(result, x_pow_n_div_n_fact, pochham_b); + eval_add(result, ui_type(1)); si_type n; T tol; tol = ui_type(1); eval_ldexp(tol, tol, 1 - boost::multiprecision::detail::digits2 >::value); - multiply(tol, result); - if(get_sign(tol) < 0) + eval_multiply(tol, result); + if(eval_get_sign(tol) < 0) tol.negate(); T term; // Series expansion of hyperg_0f1(; b; x). for(n = 2; n < 300; ++n) { - multiply(x_pow_n_div_n_fact, x); - divide(x_pow_n_div_n_fact, n); - increment(bp); - multiply(pochham_b, bp); + eval_multiply(x_pow_n_div_n_fact, x); + eval_divide(x_pow_n_div_n_fact, n); + eval_increment(bp); + eval_multiply(pochham_b, bp); - divide(term, x_pow_n_div_n_fact, pochham_b); - add(result, term); + eval_divide(term, x_pow_n_div_n_fact, pochham_b); + eval_add(result, term); - bool neg_term = get_sign(term) < 0; + bool neg_term = eval_get_sign(term) < 0; if(neg_term) term.negate(); if(term.compare(tol) <= 0) @@ -103,7 +103,7 @@ void eval_sin(T& result, const T& x) // The argument xx will be reduced to 0 <= xx <= pi/2. bool b_negate_sin = false; - if(get_sign(x) < 0) + if(eval_get_sign(x) < 0) { xx.negate(); b_negate_sin = !b_negate_sin; @@ -113,13 +113,13 @@ void eval_sin(T& result, const T& x) // Remove even multiples of pi. if(xx.compare(get_constant_pi()) > 0) { - divide(n_pi, xx, get_constant_pi()); + eval_divide(n_pi, xx, get_constant_pi()); eval_trunc(n_pi, n_pi); t = ui_type(2); eval_fmod(t, n_pi, t); - const bool b_n_pi_is_even = get_sign(t) == 0; - multiply(n_pi, get_constant_pi()); - subtract(xx, n_pi); + const bool b_n_pi_is_even = eval_get_sign(t) == 0; + eval_multiply(n_pi, get_constant_pi()); + eval_subtract(xx, n_pi); BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific)); BOOST_MATH_INSTRUMENT_CODE(n_pi.str(0, std::ios_base::scientific)); @@ -135,13 +135,13 @@ void eval_sin(T& result, const T& x) eval_ldexp(t, get_constant_pi(), -1); if(xx.compare(t) > 0) { - subtract(xx, get_constant_pi(), xx); + eval_subtract(xx, get_constant_pi(), xx); BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific)); } - subtract(t, xx); - const bool b_zero = get_sign(xx) == 0; - const bool b_pi_half = get_sign(t) == 0; + eval_subtract(t, xx); + const bool b_zero = eval_get_sign(xx) == 0; + const bool b_pi_half = eval_get_sign(t) == 0; // Check if the reduced argument is very close to 0 or pi/2. const bool b_near_zero = xx.compare(fp_type(1e-1)) < 0; @@ -157,18 +157,18 @@ void eval_sin(T& result, const T& x) } else if(b_near_zero) { - multiply(t, xx, xx); - divide(t, si_type(-4)); + eval_multiply(t, xx, xx); + eval_divide(t, si_type(-4)); T t2; t2 = fp_type(1.5); hyp0F1(result, t2, t); BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific)); - multiply(result, xx); + eval_multiply(result, xx); } else if(b_near_pi_half) { - multiply(t, t); - divide(t, si_type(-4)); + eval_multiply(t, t); + eval_divide(t, si_type(-4)); T t2; t2 = fp_type(0.5); hyp0F1(result, t2, t); @@ -184,26 +184,26 @@ void eval_sin(T& result, const T& x) static const si_type n_scale = 9; static const si_type n_three_pow_scale = static_cast(19683L); - divide(xx, n_three_pow_scale); + eval_divide(xx, n_three_pow_scale); // Now with small arguments, we are ready for a series expansion. - multiply(t, xx, xx); - divide(t, si_type(-4)); + eval_multiply(t, xx, xx); + eval_divide(t, si_type(-4)); T t2; t2 = fp_type(1.5); hyp0F1(result, t2, t); BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific)); - multiply(result, xx); + eval_multiply(result, xx); // Convert back using multiple angle identity. for(boost::int32_t k = static_cast(0); k < n_scale; k++) { // Rescale the cosine value using the multiple angle identity. - multiply(t2, result, ui_type(3)); - multiply(t, result, result); - multiply(t, result); - multiply(t, ui_type(4)); - subtract(result, t2, t); + eval_multiply(t2, result, ui_type(3)); + eval_multiply(t, result, result); + eval_multiply(t, result); + eval_multiply(t, ui_type(4)); + eval_subtract(result, t2, t); } } @@ -249,7 +249,7 @@ void eval_cos(T& result, const T& x) // The argument xx will be reduced to 0 <= xx <= pi/2. bool b_negate_cos = false; - if(get_sign(x) < 0) + if(eval_get_sign(x) < 0) { xx.negate(); } @@ -258,18 +258,18 @@ void eval_cos(T& result, const T& x) // Remove even multiples of pi. if(xx.compare(get_constant_pi()) > 0) { - divide(t, xx, get_constant_pi()); + eval_divide(t, xx, get_constant_pi()); eval_trunc(n_pi, t); BOOST_MATH_INSTRUMENT_CODE(n_pi.str(0, std::ios_base::scientific)); - multiply(t, n_pi, get_constant_pi()); + eval_multiply(t, n_pi, get_constant_pi()); BOOST_MATH_INSTRUMENT_CODE(t.str(0, std::ios_base::scientific)); - subtract(xx, t); + eval_subtract(xx, t); BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific)); // Adjust signs if the multiple of pi is not even. t = ui_type(2); eval_fmod(t, n_pi, t); - const bool b_n_pi_is_even = get_sign(t) == 0; + const bool b_n_pi_is_even = eval_get_sign(t) == 0; if(!b_n_pi_is_even) { @@ -282,17 +282,17 @@ void eval_cos(T& result, const T& x) int com = xx.compare(t); if(com > 0) { - subtract(xx, get_constant_pi(), xx); + eval_subtract(xx, get_constant_pi(), xx); b_negate_cos = !b_negate_cos; BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific)); } - const bool b_zero = get_sign(xx) == 0; + const bool b_zero = eval_get_sign(xx) == 0; const bool b_pi_half = com == 0; // Check if the reduced argument is very close to 0 or pi/2. const bool b_near_zero = xx.compare(fp_type(1e-4)) < 0; - subtract(t, xx); + eval_subtract(t, xx); const bool b_near_pi_half = t.compare(fp_type(1e-4)) < 0; if(b_zero) @@ -305,8 +305,8 @@ void eval_cos(T& result, const T& x) } else if(b_near_zero) { - multiply(t, xx, xx); - divide(t, si_type(-4)); + eval_multiply(t, xx, xx); + eval_divide(t, si_type(-4)); n_pi = fp_type(0.5f); hyp0F1(result, n_pi, t); BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific)); @@ -314,11 +314,11 @@ void eval_cos(T& result, const T& x) else if(b_near_pi_half) { T t2(t); - multiply(t, t); - divide(t, si_type(-4)); + eval_multiply(t, t); + eval_divide(t, si_type(-4)); n_pi = fp_type(1.5f); hyp0F1(result, n_pi, t); - multiply(result, t2); + eval_multiply(result, t2); BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific)); } else @@ -330,10 +330,10 @@ void eval_cos(T& result, const T& x) static const ui_type n_scale = 9; static const ui_type n_three_pow_scale = 19683; - divide(xx, n_three_pow_scale); + eval_divide(xx, n_three_pow_scale); - multiply(t, xx, xx); - divide(t, si_type(-4)); + eval_multiply(t, xx, xx); + eval_divide(t, si_type(-4)); n_pi = fp_type(0.5f); // Now with small arguments, we are ready for a series expansion. @@ -343,11 +343,11 @@ void eval_cos(T& result, const T& x) // Convert back using multiple angle identity. for(ui_type k = 0; k < n_scale; k++) { - multiply(t, result, result); - multiply(t, result); - multiply(t, ui_type(4)); - multiply(result, si_type(-3)); - add(result, t); + eval_multiply(t, result, result); + eval_multiply(t, result); + eval_multiply(t, ui_type(4)); + eval_multiply(result, si_type(-3)); + eval_add(result, t); } } if(b_negate_cos) @@ -361,7 +361,7 @@ void eval_tan(T& result, const T& x) T t; eval_sin(result, x); eval_cos(t, x); - divide(result, t); + eval_divide(result, t); } template @@ -385,15 +385,15 @@ void hyp2F1(T& result, const T& a, const T& b, const T& c, const T& x) T bp (b); T cp (c); - multiply(result, pochham_a, pochham_b); - divide(result, pochham_c); - multiply(result, x_pow_n_div_n_fact); - add(result, ui_type(1)); + eval_multiply(result, pochham_a, pochham_b); + eval_divide(result, pochham_c); + eval_multiply(result, x_pow_n_div_n_fact); + eval_add(result, ui_type(1)); T lim; eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value); - if(get_sign(lim) < 0) + if(eval_get_sign(lim) < 0) lim.negate(); ui_type n; @@ -402,22 +402,22 @@ void hyp2F1(T& result, const T& a, const T& b, const T& c, const T& x) // Series expansion of hyperg_2f1(a, b; c; x). for(n = 2; n < 300; ++n) { - multiply(x_pow_n_div_n_fact, x); - divide(x_pow_n_div_n_fact, n); + eval_multiply(x_pow_n_div_n_fact, x); + eval_divide(x_pow_n_div_n_fact, n); - increment(ap); - multiply(pochham_a, ap); - increment(bp); - multiply(pochham_b, bp); - increment(cp); - multiply(pochham_c, cp); + eval_increment(ap); + eval_multiply(pochham_a, ap); + eval_increment(bp); + eval_multiply(pochham_b, bp); + eval_increment(cp); + eval_multiply(pochham_c, cp); - multiply(term, pochham_a, pochham_b); - divide(term, pochham_c); - multiply(term, x_pow_n_div_n_fact); - add(result, term); + eval_multiply(term, pochham_a, pochham_b); + eval_divide(term, pochham_c); + eval_multiply(term, x_pow_n_div_n_fact); + eval_add(result, term); - if(get_sign(term) < 0) + if(eval_get_sign(term) < 0) term.negate(); if(lim.compare(term) >= 0) break; @@ -455,7 +455,7 @@ void eval_asin(T& result, const T& x) default: ; } - const bool b_neg = get_sign(x) < 0; + const bool b_neg = eval_get_sign(x) < 0; T xx(x); if(b_neg) @@ -479,29 +479,29 @@ void eval_asin(T& result, const T& x) if(xx.compare(fp_type(1e-4)) < 0) { // http://functions.wolfram.com/ElementaryFunctions/ArcSin/26/01/01/ - multiply(xx, xx); + eval_multiply(xx, xx); T t1, t2; t1 = fp_type(0.5f); t2 = fp_type(1.5f); hyp2F1(result, t1, t1, t2, xx); - multiply(result, x); + eval_multiply(result, x); return; } else if(xx.compare(fp_type(1 - 1e-4f)) > 0) { T dx1; T t1, t2; - subtract(dx1, ui_type(1), xx); + eval_subtract(dx1, ui_type(1), xx); t1 = fp_type(0.5f); t2 = fp_type(1.5f); eval_ldexp(dx1, dx1, -1); hyp2F1(result, t1, t1, t2, dx1); eval_ldexp(dx1, dx1, 2); eval_sqrt(t1, dx1); - multiply(result, t1); + eval_multiply(result, t1); eval_ldexp(t1, get_constant_pi(), -1); result.negate(); - add(result, t1); + eval_add(result, t1); if(b_neg) result.negate(); return; @@ -509,7 +509,7 @@ void eval_asin(T& result, const T& x) // Get initial estimate using standard math function asin. double dd; - convert_to(&dd, xx); + eval_convert_to(&dd, xx); result = fp_type(std::asin(dd)); @@ -519,15 +519,15 @@ void eval_asin(T& result, const T& x) T s, c; eval_sin(s, result); eval_cos(c, result); - subtract(s, xx); - divide(s, c); - subtract(result, s); + eval_subtract(s, xx); + eval_divide(s, c); + eval_subtract(result, s); T lim; eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value); - if(get_sign(s) < 0) + if(eval_get_sign(s) < 0) s.negate(); - if(get_sign(lim) < 0) + if(eval_get_sign(lim) < 0) lim.negate(); if(lim.compare(s) >= 0) break; @@ -564,7 +564,7 @@ inline void eval_acos(T& result, const T& x) } else if(c == 0) { - if(get_sign(x) < 0) + if(eval_get_sign(x) < 0) result = get_constant_pi(); else result = ui_type(0); @@ -574,7 +574,7 @@ inline void eval_acos(T& result, const T& x) eval_asin(result, x); T t; eval_ldexp(t, get_constant_pi(), -1); - subtract(result, t); + eval_subtract(result, t); result.negate(); } @@ -597,7 +597,7 @@ void eval_atan(T& result, const T& x) result = ui_type(0); return; case FP_INFINITE: - if(get_sign(x) < 0) + if(eval_get_sign(x) < 0) { eval_ldexp(result, get_constant_pi(), -1); result.negate(); @@ -608,7 +608,7 @@ void eval_atan(T& result, const T& x) default: ; } - const bool b_neg = get_sign(x) < 0; + const bool b_neg = eval_get_sign(x) < 0; T xx(x); if(b_neg) @@ -620,10 +620,10 @@ void eval_atan(T& result, const T& x) t1 = ui_type(1); t2 = fp_type(0.5f); t3 = fp_type(1.5f); - multiply(xx, xx); + eval_multiply(xx, xx); xx.negate(); hyp2F1(result, t1, t2, t3, xx); - multiply(result, x); + eval_multiply(result, x); return; } @@ -633,14 +633,14 @@ void eval_atan(T& result, const T& x) t1 = fp_type(0.5f); t2 = ui_type(1u); t3 = fp_type(1.5f); - multiply(xx, xx); - divide(xx, si_type(-1), xx); + eval_multiply(xx, xx); + eval_divide(xx, si_type(-1), xx); hyp2F1(result, t1, t2, t3, xx); - divide(result, x); + eval_divide(result, x); if(!b_neg) result.negate(); eval_ldexp(t1, get_constant_pi(), -1); - add(result, t1); + eval_add(result, t1); if(b_neg) result.negate(); return; @@ -649,7 +649,7 @@ void eval_atan(T& result, const T& x) // Get initial estimate using standard math function atan. fp_type d; - convert_to(&d, xx); + eval_convert_to(&d, xx); result = fp_type(std::atan(d)); // Newton-Raphson iteration @@ -660,10 +660,10 @@ void eval_atan(T& result, const T& x) { eval_sin(s, result); eval_cos(c, result); - multiply(t, xx, c); - subtract(t, s); - multiply(s, t, c); - add(result, s); + eval_multiply(t, xx, c); + eval_subtract(t, s); + eval_multiply(s, t, c); + eval_add(result, s); } if(b_neg) result.negate(); @@ -699,7 +699,7 @@ void eval_atan2(T& result, const T& y, const T& x) return; case FP_ZERO: { - int c = get_sign(x); + int c = eval_get_sign(x); if(c < 0) result = get_constant_pi(); else if(c >= 0) @@ -715,7 +715,7 @@ void eval_atan2(T& result, const T& y, const T& x) else { eval_ldexp(result, get_constant_pi(), -1); - if(get_sign(y) < 0) + if(eval_get_sign(y) < 0) result.negate(); } return; @@ -730,30 +730,30 @@ void eval_atan2(T& result, const T& y, const T& x) case FP_ZERO: { eval_ldexp(result, get_constant_pi(), -1); - if(get_sign(y) < 0) + if(eval_get_sign(y) < 0) result.negate(); return; } case FP_INFINITE: - if(get_sign(x) > 0) + if(eval_get_sign(x) > 0) result = ui_type(0); else result = get_constant_pi(); - if(get_sign(y) < 0) + if(eval_get_sign(y) < 0) result.negate(); return; } T xx; - divide(xx, y, x); - if(get_sign(xx) < 0) + eval_divide(xx, y, x); + if(eval_get_sign(xx) < 0) xx.negate(); eval_atan(result, xx); // Determine quadrant (sign) based on signs of x, y - const bool y_neg = get_sign(y) < 0; - const bool x_neg = get_sign(x) < 0; + const bool y_neg = eval_get_sign(y) < 0; + const bool x_neg = eval_get_sign(x) < 0; if(y_neg != x_neg) result.negate(); @@ -761,9 +761,9 @@ void eval_atan2(T& result, const T& y, const T& x) if(x_neg) { if(y_neg) - subtract(result, get_constant_pi()); + eval_subtract(result, get_constant_pi()); else - add(result, get_constant_pi()); + eval_add(result, get_constant_pi()); } } diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index 1127079d..85a6d339 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -127,17 +127,17 @@ struct fixed_int f = ldexp(f, shift); term = floor(f); e -= shift; - left_shift(*this, shift); + eval_left_shift(*this, shift); if(term > 0) - add(*this, static_cast(term)); + eval_add(*this, static_cast(term)); else - subtract(*this, static_cast(-term)); + eval_subtract(*this, static_cast(-term)); f -= term; } if(e > 0) - left_shift(*this, e); + eval_left_shift(*this, e); else if(e < 0) - right_shift(*this, -e); + eval_right_shift(*this, -e); data()[0] &= fixed_int::upper_limb_mask; return *this; } @@ -202,7 +202,7 @@ struct fixed_int break; } } - left_shift(*this, block_shift); + eval_left_shift(*this, block_shift); m_value[limb_count - 1] |= block; } } @@ -229,8 +229,8 @@ struct fixed_int break; } } - multiply(*this, block_mult); - add(*this, block); + eval_multiply(*this, block_mult); + eval_add(*this, block); } } } @@ -265,7 +265,7 @@ struct fixed_int if(c > '9') c += 'A' - '9' - 1; result[pos--] = c; - right_shift(t, shift); + eval_right_shift(t, shift); } if(Bits % shift) { @@ -306,7 +306,7 @@ struct fixed_int } else { - while(get_sign(t) != 0) + while(eval_get_sign(t) != 0) { fixed_int t2; divide_unsigned_helper(t2, t, max_block_10, r); @@ -376,12 +376,12 @@ private: }; template -inline void add(fixed_int& result, const fixed_int& o) +inline void eval_add(fixed_int& result, const fixed_int& o) { - add(result, result, o); + eval_add(result, result, o); } template -inline void add(fixed_int& result, const fixed_int& a, const fixed_int& b) +inline void eval_add(fixed_int& result, const fixed_int& a, const fixed_int& b) { // Addition using modular arithmatic. // Nothing fancy, just let uintmax_t take the strain: @@ -395,7 +395,7 @@ inline void add(fixed_int& result, const fixed_int& result.data()[0] &= fixed_int::upper_limb_mask; } template -inline void add(fixed_int& result, const limb_type& o) +inline void eval_add(fixed_int& result, const limb_type& o) { // Addition using modular arithmatic. // Nothing fancy, just let uintmax_t take the strain: @@ -409,15 +409,15 @@ inline void add(fixed_int& result, const limb_type& o) result.data()[0] &= fixed_int::upper_limb_mask; } template -inline void add(fixed_int& result, const signed_limb_type& o) +inline void eval_add(fixed_int& result, const signed_limb_type& o) { if(o < 0) - subtract(result, static_cast(-o)); + eval_subtract(result, static_cast(-o)); else if(o > 0) - add(result, static_cast(o)); + eval_add(result, static_cast(o)); } template -inline void subtract(fixed_int& result, const limb_type& o) +inline void eval_subtract(fixed_int& result, const limb_type& o) { // Subtract using modular arithmatic. // This is the same code as for addition, with the twist that we negate o "on the fly": @@ -434,41 +434,41 @@ inline void subtract(fixed_int& result, const limb_type& o) result.data()[0] &= fixed_int::upper_limb_mask; } template -inline void subtract(fixed_int& result, const signed_limb_type& o) +inline void eval_subtract(fixed_int& result, const signed_limb_type& o) { if(o) { if(o < 0) - add(result, static_cast(-o)); + eval_add(result, static_cast(-o)); else - subtract(result, static_cast(o)); + eval_subtract(result, static_cast(o)); } } template -inline void increment(fixed_int& result) +inline void eval_increment(fixed_int& result) { static const limb_type one = 1; if(result.data().elems[fixed_int::limb_count - 1] < fixed_int::max_limb_value) ++result.data().elems[fixed_int::limb_count - 1]; else - add(result, one); + eval_add(result, one); } template -inline void decrement(fixed_int& result) +inline void eval_decrement(fixed_int& result) { static const limb_type one = 1; if(result.data().elems[fixed_int::limb_count - 1]) --result.data().elems[fixed_int::limb_count - 1]; else - subtract(result, one); + eval_subtract(result, one); } template -inline void subtract(fixed_int& result, const fixed_int& o) +inline void eval_subtract(fixed_int& result, const fixed_int& o) { - subtract(result, result, o); + eval_subtract(result, result, o); } template -inline void subtract(fixed_int& result, const fixed_int& a, const fixed_int& b) +inline void eval_subtract(fixed_int& result, const fixed_int& a, const fixed_int& b) { // Subtract using modular arithmatic. // This is the same code as for addition, with the twist that we negate b "on the fly": @@ -482,20 +482,20 @@ inline void subtract(fixed_int& result, const fixed_int::upper_limb_mask; } template -inline void multiply(fixed_int& result, const fixed_int& a, const fixed_int& b) +inline void eval_multiply(fixed_int& result, const fixed_int& a, const fixed_int& b) { // Very simple long multiplication, only usable for small numbers of limb_type's // but that's the typical use case for this type anyway: if(&result == &a) { fixed_int t(a); - multiply(result, t, b); + eval_multiply(result, t, b); return; } if(&result == &b) { fixed_int t(b); - multiply(result, a, t); + eval_multiply(result, a, t); return; } double_limb_type carry = 0; @@ -515,14 +515,14 @@ inline void multiply(fixed_int& result, const fixed_int::upper_limb_mask; } template -inline void multiply(fixed_int& result, const fixed_int& a) +inline void eval_multiply(fixed_int& result, const fixed_int& a) { // There is no in-place multiply: fixed_int b(result); - multiply(result, b, a); + eval_multiply(result, b, a); } template -inline void multiply(fixed_int& result, const limb_type& a) +inline void eval_multiply(fixed_int& result, const limb_type& a) { double_limb_type carry = 0; for(int i = fixed_int::limb_count - 1; i >= 0; --i) @@ -534,13 +534,13 @@ inline void multiply(fixed_int& result, const limb_type& a) result.data()[0] &= fixed_int::upper_limb_mask; } template -inline void multiply(fixed_int& result, const signed_limb_type& a) +inline void eval_multiply(fixed_int& result, const signed_limb_type& a) { if(a > 0) - multiply(result, static_cast(a)); + eval_multiply(result, static_cast(a)); else { - multiply(result, static_cast(-a)); + eval_multiply(result, static_cast(-a)); result.negate(); } } @@ -580,17 +580,17 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int& result, const fixed_int(1u); - subtract(r, y); + eval_subtract(r, y); return; } @@ -626,18 +626,18 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1 - n / fixed_int::limb_bits; limb_type mask = static_cast(1u) << n % fixed_int::limb_bits; fixed_int t(y); - left_shift(t, n); + eval_left_shift(t, n); while(mask_index < fixed_int::limb_count) { int comp = r.compare(t); if(comp >= 0) { result.data()[mask_index] |= mask; - subtract(r, t); + eval_subtract(r, t); if(comp == 0) break; // no remainder left - we have an exact result! } - right_shift(t, 1u); + eval_right_shift(t, 1u); if(0 == (mask >>= 1)) { ++mask_index; @@ -682,7 +682,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int& result, const fixed_int::limb_count - 1 - shift] = guess; - subtract(result, t); + eval_subtract(result, t); } } else if(fixed_int::max_limb_value - result.data()[fixed_int::limb_count - 1 - shift] > guess) @@ -821,7 +821,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::limb_count - 1 - shift] = guess; - add(result, t); + eval_add(result, t); } // // Calculate guess * y, we use a fused mutiply-shift O(N) for this @@ -840,7 +840,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int::sign_bit_mask) { r.negate(); @@ -857,9 +857,9 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int& result, const fixed_int& result, const fixed_int -inline void divide(fixed_int& result, const fixed_int& a, const fixed_int& b) +inline void eval_divide(fixed_int& result, const fixed_int& a, const fixed_int& b) { fixed_int r; if(Signed && (a.data()[0] & fixed_int::sign_bit_mask)) @@ -1003,7 +1003,7 @@ inline void divide(fixed_int& result, const fixed_int -inline void divide(fixed_int& result, const fixed_int& a, limb_type& b) +inline void eval_divide(fixed_int& result, const fixed_int& a, limb_type& b) { fixed_int r; if(Signed && (a.data()[0] & fixed_int::sign_bit_mask)) @@ -1019,7 +1019,7 @@ inline void divide(fixed_int& result, const fixed_int -inline void divide(fixed_int& result, const fixed_int& a, signed_limb_type& b) +inline void eval_divide(fixed_int& result, const fixed_int& a, signed_limb_type& b) { fixed_int r; if(Signed && (a.data()[0] & fixed_int::sign_bit_mask)) @@ -1049,28 +1049,28 @@ inline void divide(fixed_int& result, const fixed_int -inline void divide(fixed_int& result, const fixed_int& b) +inline void eval_divide(fixed_int& result, const fixed_int& b) { // There is no in place divide: fixed_int a(result); - divide(result, a, b); + eval_divide(result, a, b); } template -inline void divide(fixed_int& result, limb_type b) +inline void eval_divide(fixed_int& result, limb_type b) { // There is no in place divide: fixed_int a(result); - divide(result, a, b); + eval_divide(result, a, b); } template -inline void divide(fixed_int& result, signed_limb_type b) +inline void eval_divide(fixed_int& result, signed_limb_type b) { // There is no in place divide: fixed_int a(result); - divide(result, a, b); + eval_divide(result, a, b); } template -inline void modulus(fixed_int& result, const fixed_int& a, const fixed_int& b) +inline void eval_modulus(fixed_int& result, const fixed_int& a, const fixed_int& b) { fixed_int r; if(Signed && (a.data()[0] & fixed_int::sign_bit_mask)) @@ -1103,7 +1103,7 @@ inline void modulus(fixed_int& result, const fixed_int -inline void modulus(fixed_int& result, const fixed_int& a, limb_type b) +inline void eval_modulus(fixed_int& result, const fixed_int& a, limb_type b) { fixed_int r; if(Signed && (a.data()[0] & fixed_int::sign_bit_mask)) @@ -1119,7 +1119,7 @@ inline void modulus(fixed_int& result, const fixed_int -inline void modulus(fixed_int& result, const fixed_int& a, signed_limb_type b) +inline void eval_modulus(fixed_int& result, const fixed_int& a, signed_limb_type b) { fixed_int r; if(Signed && (a.data()[0] & fixed_int::sign_bit_mask)) @@ -1149,42 +1149,42 @@ inline void modulus(fixed_int& result, const fixed_int -inline void modulus(fixed_int& result, const fixed_int& b) +inline void eval_modulus(fixed_int& result, const fixed_int& b) { // There is no in place divide: fixed_int a(result); - modulus(result, a, b); + eval_modulus(result, a, b); } template -inline void modulus(fixed_int& result, limb_type b) +inline void eval_modulus(fixed_int& result, limb_type b) { // There is no in place divide: fixed_int a(result); - modulus(result, a, b); + eval_modulus(result, a, b); } template -inline void modulus(fixed_int& result, signed_limb_type b) +inline void eval_modulus(fixed_int& result, signed_limb_type b) { // There is no in place divide: fixed_int a(result); - modulus(result, a, b); + eval_modulus(result, a, b); } template -inline void bitwise_and(fixed_int& result, const fixed_int& o) +inline void eval_bitwise_and(fixed_int& result, const fixed_int& o) { for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i) result.data()[i] &= o.data()[i]; } template -inline void bitwise_and(fixed_int& result, limb_type o) +inline void eval_bitwise_and(fixed_int& result, limb_type o) { result.data()[fixed_int::limb_count - 1] &= o; for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count - 1; ++i) result.data()[i] = 0; } template -inline void bitwise_and(fixed_int& result, signed_limb_type o) +inline void eval_bitwise_and(fixed_int& result, signed_limb_type o) { result.data()[fixed_int::limb_count - 1] &= o; limb_type mask = o < 0 ? fixed_int::max_limb_value : 0; @@ -1192,18 +1192,18 @@ inline void bitwise_and(fixed_int& result, signed_limb_type o) result.data()[i] &= mask; } template -inline void bitwise_or(fixed_int& result, const fixed_int& o) +inline void eval_bitwise_or(fixed_int& result, const fixed_int& o) { for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i) result.data()[i] |= o.data()[i]; } template -inline void bitwise_or(fixed_int& result, limb_type o) +inline void eval_bitwise_or(fixed_int& result, limb_type o) { result.data()[fixed_int::limb_count - 1] |= o; } template -inline void bitwise_or(fixed_int& result, signed_limb_type o) +inline void eval_bitwise_or(fixed_int& result, signed_limb_type o) { result.data()[fixed_int::limb_count - 1] |= o; limb_type mask = o < 0 ? fixed_int::max_limb_value : 0; @@ -1211,19 +1211,19 @@ inline void bitwise_or(fixed_int& result, signed_limb_type o) result.data()[i] |= mask; } template -inline void bitwise_xor(fixed_int& result, const fixed_int& o) +inline void eval_bitwise_xor(fixed_int& result, const fixed_int& o) { for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i) result.data()[i] ^= o.data()[i]; result.data()[0] &= fixed_int::upper_limb_mask; } template -inline void bitwise_xor(fixed_int& result, limb_type o) +inline void eval_bitwise_xor(fixed_int& result, limb_type o) { result.data()[fixed_int::limb_count - 1] ^= o; } template -inline void bitwise_xor(fixed_int& result, signed_limb_type o) +inline void eval_bitwise_xor(fixed_int& result, signed_limb_type o) { result.data()[fixed_int::limb_count - 1] ^= o; limb_type mask = o < 0 ? fixed_int::max_limb_value : 0; @@ -1231,14 +1231,14 @@ inline void bitwise_xor(fixed_int& result, signed_limb_type o) result.data()[i] ^= mask; } template -inline void complement(fixed_int& result, const fixed_int& o) +inline void eval_complement(fixed_int& result, const fixed_int& o) { for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i) result.data()[i] = ~o.data()[i]; result.data()[0] &= fixed_int::upper_limb_mask; } template -inline void left_shift(fixed_int& result, double_limb_type s) +inline void eval_left_shift(fixed_int& result, double_limb_type s) { if(!s) return; @@ -1273,7 +1273,7 @@ inline void left_shift(fixed_int& result, double_limb_type s) result.data()[0] &= fixed_int::upper_limb_mask; } template -inline void right_shift(fixed_int& result, double_limb_type s) +inline void eval_right_shift(fixed_int& result, double_limb_type s) { if(!s) return; @@ -1317,22 +1317,22 @@ inline void right_shift(fixed_int& result, double_limb_type s) } template -inline typename enable_if, void>::type convert_to(R* result, const fixed_int& backend, const mpl::true_&) +inline typename enable_if, void>::type eval_convert_to(R* result, const fixed_int& backend, const mpl::true_&) { if(backend.data()[0] & fixed_int::sign_bit_mask) { fixed_int t(backend); t.negate(); - convert_to(result, t, mpl::false_()); + eval_convert_to(result, t, mpl::false_()); *result = -*result; return; } else - convert_to(result, backend, mpl::false_()); + eval_convert_to(result, backend, mpl::false_()); } template -inline typename enable_if, void>::type convert_to(R* result, const fixed_int& backend, const mpl::false_&) +inline typename enable_if, void>::type eval_convert_to(R* result, const fixed_int& backend, const mpl::false_&) { unsigned shift = (fixed_int::limb_count - 1) * fixed_int::limb_bits; *result = static_cast(0); @@ -1344,20 +1344,20 @@ inline typename enable_if, void>::type convert_to(R* result, cons } template -inline typename enable_if, void>::type convert_to(R* result, const fixed_int& backend) +inline typename enable_if, void>::type eval_convert_to(R* result, const fixed_int& backend) { typedef mpl::bool_::is_signed> tag_type; - convert_to(result, backend, tag_type()); + eval_convert_to(result, backend, tag_type()); } template -inline typename enable_if, void>::type convert_to(R* result, const fixed_int& backend) +inline typename enable_if, void>::type eval_convert_to(R* result, const fixed_int& backend) { if(Signed && (backend.data()[0] & fixed_int::sign_bit_mask)) { fixed_int t(backend); t.negate(); - convert_to(result, t); + eval_convert_to(result, t); *result = -*result; return; } @@ -1371,7 +1371,7 @@ inline typename enable_if, void>::type convert_to(R* result } template -inline bool is_zero(const fixed_int& val) +inline bool eval_is_zero(const fixed_int& val) { for(typename fixed_int::data_type::size_type i = 0; i < fixed_int::limb_count; ++i) { @@ -1381,14 +1381,14 @@ inline bool is_zero(const fixed_int& val) return true; } template -inline int get_sign(const fixed_int& val) +inline int eval_get_sign(const fixed_int& val) { - return is_zero(val) ? 0 : 1; + return eval_is_zero(val) ? 0 : 1; } template -inline int get_sign(const fixed_int& val) +inline int eval_get_sign(const fixed_int& val) { - return is_zero(val) ? 0 : val.data()[0] & fixed_int::sign_bit_mask ? -1 : 1; + return eval_is_zero(val) ? 0 : val.data()[0] & fixed_int::sign_bit_mask ? -1 : 1; } namespace detail{ @@ -1398,7 +1398,7 @@ namespace detail{ template inline unsigned get_lsb(const fixed_int& a) { - BOOST_ASSERT(get_sign(a) != 0); + BOOST_ASSERT(eval_get_sign(a) != 0); unsigned result = 0; // @@ -1429,7 +1429,7 @@ inline void eval_gcd(fixed_int& result, const fixed_int u(a), v(b); - int s = get_sign(u); + int s = eval_get_sign(u); /* GCD(0,x) := x */ if(s < 0) @@ -1441,7 +1441,7 @@ inline void eval_gcd(fixed_int& result, const fixed_int& result, const fixed_int& result, const fixed_int 0) u.swap(v); - subtract(v, u); + eval_subtract(v, u); // Termination condition tries not to do a full compare if possible: - if(!v.data()[fixed_int::limb_count - 1] && is_zero(v)) + if(!v.data()[fixed_int::limb_count - 1] && eval_is_zero(v)) break; vs = detail::get_lsb(v); - right_shift(v, vs); + eval_right_shift(v, vs); BOOST_ASSERT((v.data()[fixed_int::limb_count - 1] & 1)); BOOST_ASSERT((u.data()[fixed_int::limb_count - 1] & 1)); } while(true); result = u; - left_shift(result, shift); + eval_left_shift(result, shift); } template @@ -1488,16 +1488,16 @@ inline void eval_lcm(fixed_int& result, const fixed_int t; eval_gcd(t, a, b); - if(is_zero(t)) + if(eval_is_zero(t)) { result = static_cast(0); } else { - divide(result, a, t); - multiply(result, b); + eval_divide(result, a, t); + eval_multiply(result, b); } - if(get_sign(result) < 0) + if(eval_get_sign(result) < 0) result.negate(); } diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 648d60c5..f2104de9 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -16,7 +16,9 @@ #include #include -namespace boost{ namespace multiprecision{ +namespace boost{ +namespace multiprecision{ +namespace backends{ template struct gmp_float; @@ -473,47 +475,47 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> }; template -inline void add(gmp_float& result, const gmp_float& o) +inline void eval_add(gmp_float& result, const gmp_float& o) { mpf_add(result.data(), result.data(), o.data()); } template -inline void subtract(gmp_float& result, const gmp_float& o) +inline void eval_subtract(gmp_float& result, const gmp_float& o) { mpf_sub(result.data(), result.data(), o.data()); } template -inline void multiply(gmp_float& result, const gmp_float& o) +inline void eval_multiply(gmp_float& result, const gmp_float& o) { mpf_mul(result.data(), result.data(), o.data()); } template -inline void divide(gmp_float& result, const gmp_float& o) +inline void eval_divide(gmp_float& result, const gmp_float& o) { mpf_div(result.data(), result.data(), o.data()); } template -inline void add(gmp_float& result, unsigned long i) +inline void eval_add(gmp_float& result, unsigned long i) { mpf_add_ui(result.data(), result.data(), i); } template -inline void subtract(gmp_float& result, unsigned long i) +inline void eval_subtract(gmp_float& result, unsigned long i) { mpf_sub_ui(result.data(), result.data(), i); } template -inline void multiply(gmp_float& result, unsigned long i) +inline void eval_multiply(gmp_float& result, unsigned long i) { mpf_mul_ui(result.data(), result.data(), i); } template -inline void divide(gmp_float& result, unsigned long i) +inline void eval_divide(gmp_float& result, unsigned long i) { mpf_div_ui(result.data(), result.data(), i); } template -inline void add(gmp_float& result, long i) +inline void eval_add(gmp_float& result, long i) { if(i > 0) mpf_add_ui(result.data(), result.data(), i); @@ -521,7 +523,7 @@ inline void add(gmp_float& result, long i) mpf_sub_ui(result.data(), result.data(), std::abs(i)); } template -inline void subtract(gmp_float& result, long i) +inline void eval_subtract(gmp_float& result, long i) { if(i > 0) mpf_sub_ui(result.data(), result.data(), i); @@ -529,14 +531,14 @@ inline void subtract(gmp_float& result, long i) mpf_add_ui(result.data(), result.data(), std::abs(i)); } template -inline void multiply(gmp_float& result, long i) +inline void eval_multiply(gmp_float& result, long i) { mpf_mul_ui(result.data(), result.data(), std::abs(i)); if(i < 0) mpf_neg(result.data(), result.data()); } template -inline void divide(gmp_float& result, long i) +inline void eval_divide(gmp_float& result, long i) { mpf_div_ui(result.data(), result.data(), std::abs(i)); if(i < 0) @@ -546,17 +548,17 @@ inline void divide(gmp_float& result, long i) // Specialised 3 arg versions of the basic operators: // template -inline void add(gmp_float& a, const gmp_float& x, const gmp_float& y) +inline void eval_add(gmp_float& a, const gmp_float& x, const gmp_float& y) { mpf_add(a.data(), x.data(), y.data()); } template -inline void add(gmp_float& a, const gmp_float& x, unsigned long y) +inline void eval_add(gmp_float& a, const gmp_float& x, unsigned long y) { mpf_add_ui(a.data(), x.data(), y); } template -inline void add(gmp_float& a, const gmp_float& x, long y) +inline void eval_add(gmp_float& a, const gmp_float& x, long y) { if(y < 0) mpf_sub_ui(a.data(), x.data(), -y); @@ -564,12 +566,12 @@ inline void add(gmp_float& a, const gmp_float& x, long y) mpf_add_ui(a.data(), x.data(), y); } template -inline void add(gmp_float& a, unsigned long x, const gmp_float& y) +inline void eval_add(gmp_float& a, unsigned long x, const gmp_float& y) { mpf_add_ui(a.data(), y.data(), x); } template -inline void add(gmp_float& a, long x, const gmp_float& y) +inline void eval_add(gmp_float& a, long x, const gmp_float& y) { if(x < 0) { @@ -580,17 +582,17 @@ inline void add(gmp_float& a, long x, const gmp_float& y) mpf_add_ui(a.data(), y.data(), x); } template -inline void subtract(gmp_float& a, const gmp_float& x, const gmp_float& y) +inline void eval_subtract(gmp_float& a, const gmp_float& x, const gmp_float& y) { mpf_sub(a.data(), x.data(), y.data()); } template -inline void subtract(gmp_float& a, const gmp_float& x, unsigned long y) +inline void eval_subtract(gmp_float& a, const gmp_float& x, unsigned long y) { mpf_sub_ui(a.data(), x.data(), y); } template -inline void subtract(gmp_float& a, const gmp_float& x, long y) +inline void eval_subtract(gmp_float& a, const gmp_float& x, long y) { if(y < 0) mpf_add_ui(a.data(), x.data(), -y); @@ -598,12 +600,12 @@ inline void subtract(gmp_float& a, const gmp_float& x, long mpf_sub_ui(a.data(), x.data(), y); } template -inline void subtract(gmp_float& a, unsigned long x, const gmp_float& y) +inline void eval_subtract(gmp_float& a, unsigned long x, const gmp_float& y) { mpf_ui_sub(a.data(), x, y.data()); } template -inline void subtract(gmp_float& a, long x, const gmp_float& y) +inline void eval_subtract(gmp_float& a, long x, const gmp_float& y) { if(x < 0) { @@ -615,17 +617,17 @@ inline void subtract(gmp_float& a, long x, const gmp_float& } template -inline void multiply(gmp_float& a, const gmp_float& x, const gmp_float& y) +inline void eval_multiply(gmp_float& a, const gmp_float& x, const gmp_float& y) { mpf_mul(a.data(), x.data(), y.data()); } template -inline void multiply(gmp_float& a, const gmp_float& x, unsigned long y) +inline void eval_multiply(gmp_float& a, const gmp_float& x, unsigned long y) { mpf_mul_ui(a.data(), x.data(), y); } template -inline void multiply(gmp_float& a, const gmp_float& x, long y) +inline void eval_multiply(gmp_float& a, const gmp_float& x, long y) { if(y < 0) { @@ -636,12 +638,12 @@ inline void multiply(gmp_float& a, const gmp_float& x, long mpf_mul_ui(a.data(), x.data(), y); } template -inline void multiply(gmp_float& a, unsigned long x, const gmp_float& y) +inline void eval_multiply(gmp_float& a, unsigned long x, const gmp_float& y) { mpf_mul_ui(a.data(), y.data(), x); } template -inline void multiply(gmp_float& a, long x, const gmp_float& y) +inline void eval_multiply(gmp_float& a, long x, const gmp_float& y) { if(x < 0) { @@ -653,17 +655,17 @@ inline void multiply(gmp_float& a, long x, const gmp_float& } template -inline void divide(gmp_float& a, const gmp_float& x, const gmp_float& y) +inline void eval_divide(gmp_float& a, const gmp_float& x, const gmp_float& y) { mpf_div(a.data(), x.data(), y.data()); } template -inline void divide(gmp_float& a, const gmp_float& x, unsigned long y) +inline void eval_divide(gmp_float& a, const gmp_float& x, unsigned long y) { mpf_div_ui(a.data(), x.data(), y); } template -inline void divide(gmp_float& a, const gmp_float& x, long y) +inline void eval_divide(gmp_float& a, const gmp_float& x, long y) { if(y < 0) { @@ -674,12 +676,12 @@ inline void divide(gmp_float& a, const gmp_float& x, long y) mpf_div_ui(a.data(), x.data(), y); } template -inline void divide(gmp_float& a, unsigned long x, const gmp_float& y) +inline void eval_divide(gmp_float& a, unsigned long x, const gmp_float& y) { mpf_ui_div(a.data(), x, y.data()); } template -inline void divide(gmp_float& a, long x, const gmp_float& y) +inline void eval_divide(gmp_float& a, long x, const gmp_float& y) { if(x < 0) { @@ -691,18 +693,18 @@ inline void divide(gmp_float& a, long x, const gmp_float& y) } template -inline bool is_zero(const gmp_float& val) +inline bool eval_is_zero(const gmp_float& val) { return mpf_sgn(val.data()) == 0; } template -inline int get_sign(const gmp_float& val) +inline int eval_get_sign(const gmp_float& val) { return mpf_sgn(val.data()); } template -inline void convert_to(unsigned long* result, const gmp_float& val) +inline void eval_convert_to(unsigned long* result, const gmp_float& val) { if(0 == mpf_fits_ulong_p(val.data())) *result = (std::numeric_limits::max)(); @@ -710,7 +712,7 @@ inline void convert_to(unsigned long* result, const gmp_float& val) *result = mpf_get_ui(val.data()); } template -inline void convert_to(long* result, const gmp_float& val) +inline void eval_convert_to(long* result, const gmp_float& val) { if(0 == mpf_fits_slong_p(val.data())) { @@ -721,16 +723,16 @@ inline void convert_to(long* result, const gmp_float& val) *result = mpf_get_si(val.data()); } template -inline void convert_to(double* result, const gmp_float& val) +inline void eval_convert_to(double* result, const gmp_float& val) { *result = mpf_get_d(val.data()); } #ifdef BOOST_HAS_LONG_LONG template -inline void convert_to(long long* result, const gmp_float& val) +inline void eval_convert_to(long long* result, const gmp_float& val) { gmp_float t(val); - if(get_sign(t) < 0) + if(eval_get_sign(t) < 0) t.negate(); long digits = std::numeric_limits::digits - std::numeric_limits::digits; @@ -740,7 +742,7 @@ inline void convert_to(long long* result, const gmp_float& val) if(!mpf_fits_slong_p(t.data())) { - if(get_sign(val) < 0) + if(eval_get_sign(val) < 0) *result = (std::numeric_limits::min)(); else *result = (std::numeric_limits::max)(); @@ -758,11 +760,11 @@ inline void convert_to(long long* result, const gmp_float& val) l >>= -digits; *result |= l; } - if(get_sign(val) < 0) + if(eval_get_sign(val) < 0) *result = -*result; } template -inline void convert_to(unsigned long long* result, const gmp_float& val) +inline void eval_convert_to(unsigned long long* result, const gmp_float& val) { gmp_float t(val); @@ -1094,23 +1096,23 @@ protected: mpz_t m_data; }; -inline void add(gmp_int& t, const gmp_int& o) +inline void eval_add(gmp_int& t, const gmp_int& o) { mpz_add(t.data(), t.data(), o.data()); } -inline void subtract(gmp_int& t, const gmp_int& o) +inline void eval_subtract(gmp_int& t, const gmp_int& o) { mpz_sub(t.data(), t.data(), o.data()); } -inline void multiply(gmp_int& t, const gmp_int& o) +inline void eval_multiply(gmp_int& t, const gmp_int& o) { mpz_mul(t.data(), t.data(), o.data()); } -inline void divide(gmp_int& t, const gmp_int& o) +inline void eval_divide(gmp_int& t, const gmp_int& o) { mpz_div(t.data(), t.data(), o.data()); } -inline void modulus(gmp_int& t, const gmp_int& o) +inline void eval_modulus(gmp_int& t, const gmp_int& o) { bool neg = mpz_sgn(t.data()) < 0; bool neg2 = mpz_sgn(o.data()) < 0; @@ -1124,19 +1126,19 @@ inline void modulus(gmp_int& t, const gmp_int& o) t.negate(); } } -inline void add(gmp_int& t, unsigned long i) +inline void eval_add(gmp_int& t, unsigned long i) { mpz_add_ui(t.data(), t.data(), i); } -inline void subtract(gmp_int& t, unsigned long i) +inline void eval_subtract(gmp_int& t, unsigned long i) { mpz_sub_ui(t.data(), t.data(), i); } -inline void multiply(gmp_int& t, unsigned long i) +inline void eval_multiply(gmp_int& t, unsigned long i) { mpz_mul_ui(t.data(), t.data(), i); } -inline void modulus(gmp_int& t, unsigned long i) +inline void eval_modulus(gmp_int& t, unsigned long i) { bool neg = mpz_sgn(t.data()) < 0; mpz_mod_ui(t.data(), t.data(), i); @@ -1147,31 +1149,31 @@ inline void modulus(gmp_int& t, unsigned long i) t.negate(); } } -inline void divide(gmp_int& t, unsigned long i) +inline void eval_divide(gmp_int& t, unsigned long i) { mpz_div_ui(t.data(), t.data(), i); } -inline void add(gmp_int& t, long i) +inline void eval_add(gmp_int& t, long i) { if(i > 0) mpz_add_ui(t.data(), t.data(), i); else mpz_sub_ui(t.data(), t.data(), -i); } -inline void subtract(gmp_int& t, long i) +inline void eval_subtract(gmp_int& t, long i) { if(i > 0) mpz_sub_ui(t.data(), t.data(), i); else mpz_add_ui(t.data(), t.data(), -i); } -inline void multiply(gmp_int& t, long i) +inline void eval_multiply(gmp_int& t, long i) { mpz_mul_ui(t.data(), t.data(), std::abs(i)); if(i < 0) mpz_neg(t.data(), t.data()); } -inline void modulus(gmp_int& t, long i) +inline void eval_modulus(gmp_int& t, long i) { bool neg = mpz_sgn(t.data()) < 0; bool neg2 = i < 0; @@ -1190,65 +1192,65 @@ inline void modulus(gmp_int& t, long i) } } } -inline void divide(gmp_int& t, long i) +inline void eval_divide(gmp_int& t, long i) { mpz_div_ui(t.data(), t.data(), std::abs(i)); if(i < 0) mpz_neg(t.data(), t.data()); } template -inline void left_shift(gmp_int& t, UI i) +inline void eval_left_shift(gmp_int& t, UI i) { mpz_mul_2exp(t.data(), t.data(), static_cast(i)); } template -inline void right_shift(gmp_int& t, UI i) +inline void eval_right_shift(gmp_int& t, UI i) { mpz_fdiv_q_2exp(t.data(), t.data(), static_cast(i)); } template -inline void left_shift(gmp_int& t, const gmp_int& v, UI i) +inline void eval_left_shift(gmp_int& t, const gmp_int& v, UI i) { mpz_mul_2exp(t.data(), v.data(), static_cast(i)); } template -inline void right_shift(gmp_int& t, const gmp_int& v, UI i) +inline void eval_right_shift(gmp_int& t, const gmp_int& v, UI i) { mpz_fdiv_q_2exp(t.data(), v.data(), static_cast(i)); } -inline void bitwise_and(gmp_int& result, const gmp_int& v) +inline void eval_bitwise_and(gmp_int& result, const gmp_int& v) { mpz_and(result.data(), result.data(), v.data()); } -inline void bitwise_or(gmp_int& result, const gmp_int& v) +inline void eval_bitwise_or(gmp_int& result, const gmp_int& v) { mpz_ior(result.data(), result.data(), v.data()); } -inline void bitwise_xor(gmp_int& result, const gmp_int& v) +inline void eval_bitwise_xor(gmp_int& result, const gmp_int& v) { mpz_xor(result.data(), result.data(), v.data()); } -inline void add(gmp_int& t, const gmp_int& p, const gmp_int& o) +inline void eval_add(gmp_int& t, const gmp_int& p, const gmp_int& o) { mpz_add(t.data(), p.data(), o.data()); } -inline void subtract(gmp_int& t, const gmp_int& p, const gmp_int& o) +inline void eval_subtract(gmp_int& t, const gmp_int& p, const gmp_int& o) { mpz_sub(t.data(), p.data(), o.data()); } -inline void multiply(gmp_int& t, const gmp_int& p, const gmp_int& o) +inline void eval_multiply(gmp_int& t, const gmp_int& p, const gmp_int& o) { mpz_mul(t.data(), p.data(), o.data()); } -inline void divide(gmp_int& t, const gmp_int& p, const gmp_int& o) +inline void eval_divide(gmp_int& t, const gmp_int& p, const gmp_int& o) { mpz_div(t.data(), p.data(), o.data()); } -inline void modulus(gmp_int& t, const gmp_int& p, const gmp_int& o) +inline void eval_modulus(gmp_int& t, const gmp_int& p, const gmp_int& o) { bool neg = mpz_sgn(p.data()) < 0; bool neg2 = mpz_sgn(o.data()) < 0; @@ -1262,19 +1264,19 @@ inline void modulus(gmp_int& t, const gmp_int& p, const gmp_int& o) t.negate(); } } -inline void add(gmp_int& t, const gmp_int& p, unsigned long i) +inline void eval_add(gmp_int& t, const gmp_int& p, unsigned long i) { mpz_add_ui(t.data(), p.data(), i); } -inline void subtract(gmp_int& t, const gmp_int& p, unsigned long i) +inline void eval_subtract(gmp_int& t, const gmp_int& p, unsigned long i) { mpz_sub_ui(t.data(), p.data(), i); } -inline void multiply(gmp_int& t, const gmp_int& p, unsigned long i) +inline void eval_multiply(gmp_int& t, const gmp_int& p, unsigned long i) { mpz_mul_ui(t.data(), p.data(), i); } -inline void modulus(gmp_int& t, const gmp_int& p, unsigned long i) +inline void eval_modulus(gmp_int& t, const gmp_int& p, unsigned long i) { bool neg = mpz_sgn(p.data()) < 0; mpz_mod_ui(t.data(), p.data(), i); @@ -1285,31 +1287,31 @@ inline void modulus(gmp_int& t, const gmp_int& p, unsigned long i) t.negate(); } } -inline void divide(gmp_int& t, const gmp_int& p, unsigned long i) +inline void eval_divide(gmp_int& t, const gmp_int& p, unsigned long i) { mpz_div_ui(t.data(), p.data(), i); } -inline void add(gmp_int& t, const gmp_int& p, long i) +inline void eval_add(gmp_int& t, const gmp_int& p, long i) { if(i > 0) mpz_add_ui(t.data(), p.data(), i); else mpz_sub_ui(t.data(), p.data(), -i); } -inline void subtract(gmp_int& t, const gmp_int& p, long i) +inline void eval_subtract(gmp_int& t, const gmp_int& p, long i) { if(i > 0) mpz_sub_ui(t.data(), p.data(), i); else mpz_add_ui(t.data(), p.data(), -i); } -inline void multiply(gmp_int& t, const gmp_int& p, long i) +inline void eval_multiply(gmp_int& t, const gmp_int& p, long i) { mpz_mul_ui(t.data(), p.data(), std::abs(i)); if(i < 0) mpz_neg(t.data(), t.data()); } -inline void modulus(gmp_int& t, const gmp_int& p, long i) +inline void eval_modulus(gmp_int& t, const gmp_int& p, long i) { bool neg = mpz_sgn(p.data()) < 0; bool neg2 = i < 0; @@ -1328,42 +1330,42 @@ inline void modulus(gmp_int& t, const gmp_int& p, long i) } } } -inline void divide(gmp_int& t, const gmp_int& p, long i) +inline void eval_divide(gmp_int& t, const gmp_int& p, long i) { mpz_div_ui(t.data(), p.data(), std::abs(i)); if(i < 0) mpz_neg(t.data(), t.data()); } -inline void bitwise_and(gmp_int& result, const gmp_int& u, const gmp_int& v) +inline void eval_bitwise_and(gmp_int& result, const gmp_int& u, const gmp_int& v) { mpz_and(result.data(), u.data(), v.data()); } -inline void bitwise_or(gmp_int& result, const gmp_int& u, const gmp_int& v) +inline void eval_bitwise_or(gmp_int& result, const gmp_int& u, const gmp_int& v) { mpz_ior(result.data(), u.data(), v.data()); } -inline void bitwise_xor(gmp_int& result, const gmp_int& u, const gmp_int& v) +inline void eval_bitwise_xor(gmp_int& result, const gmp_int& u, const gmp_int& v) { mpz_xor(result.data(), u.data(), v.data()); } -inline void complement(gmp_int& result, const gmp_int& u) +inline void eval_complement(gmp_int& result, const gmp_int& u) { mpz_com(result.data(), u.data()); } -inline bool is_zero(const gmp_int& val) +inline bool eval_is_zero(const gmp_int& val) { return mpz_sgn(val.data()) == 0; } -inline int get_sign(const gmp_int& val) +inline int eval_get_sign(const gmp_int& val) { return mpz_sgn(val.data()); } -inline void convert_to(unsigned long* result, const gmp_int& val) +inline void eval_convert_to(unsigned long* result, const gmp_int& val) { if(0 == mpz_fits_ulong_p(val.data())) { @@ -1372,7 +1374,7 @@ inline void convert_to(unsigned long* result, const gmp_int& val) else *result = mpz_get_ui(val.data()); } -inline void convert_to(long* result, const gmp_int& val) +inline void eval_convert_to(long* result, const gmp_int& val) { if(0 == mpz_fits_slong_p(val.data())) { @@ -1382,7 +1384,7 @@ inline void convert_to(long* result, const gmp_int& val) else *result = mpz_get_si(val.data()); } -inline void convert_to(double* result, const gmp_int& val) +inline void eval_convert_to(double* result, const gmp_int& val) { *result = mpz_get_d(val.data()); } @@ -1418,7 +1420,7 @@ inline void eval_lcm(gmp_int& result, const gmp_int& a, const long b) } struct gmp_rational; -void add(gmp_rational& t, const gmp_rational& o); +void eval_add(gmp_rational& t, const gmp_rational& o); struct gmp_rational { @@ -1503,8 +1505,8 @@ struct gmp_rational using std::frexp; using std::ldexp; using std::floor; - using default_ops::add; - using default_ops::subtract; + using default_ops::eval_add; + using default_ops::eval_subtract; if (a == 0) { mpq_set_si(m_data, 0, 1); @@ -1537,7 +1539,7 @@ struct gmp_rational e -= shift; mpq_mul_2exp(m_data, m_data, shift); t = static_cast(term); - add(*this, t); + eval_add(*this, t); f -= term; } if(e > 0) @@ -1628,69 +1630,63 @@ inline mp_number denominator(const mp_number& val) return result; } -template <> -struct component_type > -{ - typedef mp_number type; -}; - -inline void add(gmp_rational& t, const gmp_rational& o) +inline void eval_add(gmp_rational& t, const gmp_rational& o) { mpq_add(t.data(), t.data(), o.data()); } -inline void subtract(gmp_rational& t, const gmp_rational& o) +inline void eval_subtract(gmp_rational& t, const gmp_rational& o) { mpq_sub(t.data(), t.data(), o.data()); } -inline void multiply(gmp_rational& t, const gmp_rational& o) +inline void eval_multiply(gmp_rational& t, const gmp_rational& o) { mpq_mul(t.data(), t.data(), o.data()); } -inline void divide(gmp_rational& t, const gmp_rational& o) +inline void eval_divide(gmp_rational& t, const gmp_rational& o) { mpq_div(t.data(), t.data(), o.data()); } -inline void add(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +inline void eval_add(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) { mpq_add(t.data(), p.data(), o.data()); } -inline void subtract(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +inline void eval_subtract(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) { mpq_sub(t.data(), p.data(), o.data()); } -inline void multiply(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +inline void eval_multiply(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) { mpq_mul(t.data(), p.data(), o.data()); } -inline void divide(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) +inline void eval_divide(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) { mpq_div(t.data(), p.data(), o.data()); } -inline bool is_zero(const gmp_rational& val) +inline bool eval_is_zero(const gmp_rational& val) { return mpq_sgn(val.data()) == 0; } -inline int get_sign(const gmp_rational& val) +inline int eval_get_sign(const gmp_rational& val) { return mpq_sgn(val.data()); } -inline void convert_to(double* result, const gmp_rational& val) +inline void eval_convert_to(double* result, const gmp_rational& val) { *result = mpq_get_d(val.data()); } -inline void convert_to(long* result, const gmp_rational& val) +inline void eval_convert_to(long* result, const gmp_rational& val) { double r; - convert_to(&r, val); + eval_convert_to(&r, val); *result = static_cast(r); } -inline void convert_to(unsigned long* result, const gmp_rational& val) +inline void eval_convert_to(unsigned long* result, const gmp_rational& val) { double r; - convert_to(&r, val); + eval_convert_to(&r, val); *result = static_cast(r); } @@ -1788,6 +1784,17 @@ inline gmp_int& gmp_int::operator=(const gmp_rational& o) return *this; } +} //namespace backends + +using boost::multiprecision::backends::gmp_int; +using boost::multiprecision::backends::gmp_rational; +using boost::multiprecision::backends::gmp_float; + +template <> +struct component_type > +{ + typedef mp_number type; +}; template<> struct number_category : public mpl::int_{}; diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index bb48f629..22e18403 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -150,8 +150,8 @@ public: typename enable_if, mp_number& >::type operator+=(const V& v) { - using default_ops::add; - add(m_backend, canonical_value(v)); + using default_ops::eval_add; + eval_add(m_backend, canonical_value(v)); return *this; } @@ -181,8 +181,8 @@ public: typename enable_if, mp_number& >::type operator-=(const V& v) { - using default_ops::subtract; - subtract(m_backend, canonical_value(v)); + using default_ops::eval_subtract; + eval_subtract(m_backend, canonical_value(v)); return *this; } @@ -214,8 +214,8 @@ public: typename enable_if, mp_number& >::type operator*=(const V& v) { - using default_ops::multiply; - multiply(m_backend, canonical_value(v)); + using default_ops::eval_multiply; + eval_multiply(m_backend, canonical_value(v)); return *this; } @@ -246,8 +246,8 @@ public: operator%=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using default_ops::modulus; - modulus(m_backend, canonical_value(v)); + using default_ops::eval_modulus; + eval_modulus(m_backend, canonical_value(v)); return *this; } @@ -261,31 +261,31 @@ public: // mp_number& operator++() { - using default_ops::increment; - increment(m_backend); + using default_ops::eval_increment; + eval_increment(m_backend); return *this; } mp_number& operator--() { - using default_ops::decrement; - decrement(m_backend); + using default_ops::eval_decrement; + eval_decrement(m_backend); return *this; } mp_number operator++(int) { - using default_ops::increment; + using default_ops::eval_increment; self_type temp(*this); - increment(m_backend); + eval_increment(m_backend); return temp; } mp_number operator--(int) { - using default_ops::decrement; + using default_ops::eval_decrement; self_type temp(*this); - decrement(m_backend); + eval_decrement(m_backend); return temp; } @@ -294,7 +294,7 @@ public: { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left-shift operation is only valid for integer types"); check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); - left_shift(m_backend, canonical_value(val)); + eval_left_shift(m_backend, canonical_value(val)); return *this; } @@ -303,7 +303,7 @@ public: { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right-shift operation is only valid for integer types"); check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); - right_shift(m_backend, canonical_value(val)); + eval_right_shift(m_backend, canonical_value(val)); return *this; } @@ -333,8 +333,8 @@ public: typename enable_if, mp_number& >::type operator/=(const V& v) { - using default_ops::divide; - divide(m_backend, canonical_value(v)); + using default_ops::eval_divide; + eval_divide(m_backend, canonical_value(v)); return *this; } @@ -368,8 +368,8 @@ public: operator&=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); - using default_ops::bitwise_and; - bitwise_and(m_backend, canonical_value(v)); + using default_ops::eval_bitwise_and; + eval_bitwise_and(m_backend, canonical_value(v)); return *this; } @@ -403,8 +403,8 @@ public: operator|=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); - using default_ops::bitwise_or; - bitwise_or(m_backend, canonical_value(v)); + using default_ops::eval_bitwise_or; + eval_bitwise_or(m_backend, canonical_value(v)); return *this; } @@ -436,8 +436,8 @@ public: operator^=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); - using default_ops::bitwise_xor; - bitwise_xor(m_backend, canonical_value(v)); + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(m_backend, canonical_value(v)); return *this; } // @@ -462,13 +462,13 @@ public: // bool is_zero()const { - using default_ops::is_zero; - return is_zero(m_backend); + using default_ops::eval_is_zero; + return eval_is_zero(m_backend); } int sign()const { - using default_ops::get_sign; - return get_sign(m_backend); + using default_ops::eval_get_sign; + return eval_get_sign(m_backend); } // // String conversion functions: @@ -480,9 +480,9 @@ public: template T convert_to()const { - using default_ops::convert_to; + using default_ops::eval_convert_to; T result; - convert_to(&result, m_backend); + eval_convert_to(&result, m_backend); return result; } // @@ -514,9 +514,9 @@ public: template typename enable_if, int>::type compare(const V& o)const { - using default_ops::get_sign; + using default_ops::eval_get_sign; if(o == 0) - return get_sign(m_backend); + return eval_get_sign(m_backend); return m_backend.compare(canonical_value(o)); } Backend& backend() @@ -554,36 +554,36 @@ private: template void do_assign(const Exp& e, const detail::add_immediates&) { - using default_ops::add; - add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + using default_ops::eval_add; + eval_add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } /* template void do_assign(const Exp& e, const detail::add_and_negate_immediates&) { - using default_ops::add; - add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + using default_ops::eval_add; + eval_add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); m_backend.negate(); } */ template void do_assign(const Exp& e, const detail::subtract_immediates&) { - using default_ops::subtract; - subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + using default_ops::eval_subtract; + eval_subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template void do_assign(const Exp& e, const detail::multiply_immediates&) { - using default_ops::multiply; - multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + using default_ops::eval_multiply; + eval_multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template void do_assign(const Exp& e, const detail::divide_immediates&) { - using default_ops::divide; - divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + using default_ops::eval_divide; + eval_divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template @@ -768,8 +768,8 @@ private: void do_assign(const Exp& e, const detail::modulus_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using default_ops::modulus; - modulus(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + using default_ops::eval_modulus; + eval_modulus(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template @@ -813,8 +813,8 @@ private: void do_assign(const Exp& e, const detail::bitwise_and_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - using default_ops::bitwise_and; - bitwise_and(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + using default_ops::eval_bitwise_and; + eval_bitwise_and(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template @@ -858,8 +858,8 @@ private: void do_assign(const Exp& e, const detail::bitwise_or_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - using default_ops::bitwise_or; - bitwise_or(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + using default_ops::eval_bitwise_or; + eval_bitwise_or(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template @@ -903,8 +903,8 @@ private: void do_assign(const Exp& e, const detail::bitwise_xor_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "Bitwise operations are only valid for integer types"); - using default_ops::bitwise_xor; - bitwise_xor(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template void do_assign(const Exp& e, const detail::terminal&) @@ -952,51 +952,51 @@ private: void do_assign(const Exp& e, const detail::bitwise_complement&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ~ operation is only valid for integer types"); - using default_ops::complement; + using default_ops::eval_complement; self_type temp(e.left()); - complement(m_backend, temp.backend()); + eval_complement(m_backend, temp.backend()); } template void do_assign(const Exp& e, const detail::complement_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ~ operation is only valid for integer types"); - using default_ops::complement; - complement(m_backend, canonical_value(e.left().value())); + using default_ops::eval_complement; + eval_complement(m_backend, canonical_value(e.left().value())); } template void do_assign_right_shift(const Exp& e, const Val& val, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right shift operation is only valid for integer types"); - using default_ops::right_shift; - right_shift(m_backend, canonical_value(e.value()), val); + using default_ops::eval_right_shift; + eval_right_shift(m_backend, canonical_value(e.value()), val); } template void do_assign_left_shift(const Exp& e, const Val& val, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left shift operation is only valid for integer types"); - using default_ops::left_shift; - left_shift(m_backend, canonical_value(e.value()), val); + using default_ops::eval_left_shift; + eval_left_shift(m_backend, canonical_value(e.value()), val); } template void do_assign_right_shift(const Exp& e, const Val& val, const Tag&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right shift operation is only valid for integer types"); - using default_ops::right_shift; + using default_ops::eval_right_shift; self_type temp(e); - right_shift(m_backend, temp.backend(), val); + eval_right_shift(m_backend, temp.backend(), val); } template void do_assign_left_shift(const Exp& e, const Val& val, const Tag&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left shift operation is only valid for integer types"); - using default_ops::left_shift; + using default_ops::eval_left_shift; self_type temp(e); - left_shift(m_backend, temp.backend(), val); + eval_left_shift(m_backend, temp.backend(), val); } template @@ -1059,8 +1059,8 @@ private: template void do_add(const Exp& e, const detail::terminal&) { - using default_ops::add; - add(m_backend, canonical_value(e.value())); + using default_ops::eval_add; + eval_add(m_backend, canonical_value(e.value())); } template @@ -1098,23 +1098,23 @@ private: template void do_add(const Exp& e, const detail::add_immediates&) { - using default_ops::add; - add(m_backend, canonical_value(e.left().value())); - add(m_backend, canonical_value(e.right().value())); + using default_ops::eval_add; + eval_add(m_backend, canonical_value(e.left().value())); + eval_add(m_backend, canonical_value(e.right().value())); } template void do_add(const Exp& e, const detail::subtract_immediates&) { - using default_ops::add; - using default_ops::subtract; - add(m_backend, canonical_value(e.left().value())); - subtract(m_backend, canonical_value(e.right().value())); + using default_ops::eval_add; + using default_ops::eval_subtract; + eval_add(m_backend, canonical_value(e.left().value())); + eval_subtract(m_backend, canonical_value(e.right().value())); } template void do_subtract(const Exp& e, const detail::terminal&) { - using default_ops::subtract; - subtract(m_backend, canonical_value(e.value())); + using default_ops::eval_subtract; + eval_subtract(m_backend, canonical_value(e.value())); } template @@ -1144,17 +1144,17 @@ private: template void do_subtract(const Exp& e, const detail::add_immediates&) { - using default_ops::subtract; - subtract(m_backend, canonical_value(e.left().value())); - subtract(m_backend, canonical_value(e.right().value())); + using default_ops::eval_subtract; + eval_subtract(m_backend, canonical_value(e.left().value())); + eval_subtract(m_backend, canonical_value(e.right().value())); } template void do_subtract(const Exp& e, const detail::subtract_immediates&) { - using default_ops::add; - using default_ops::subtract; - subtract(m_backend, canonical_value(e.left().value())); - add(m_backend, canonical_value(e.right().value())); + using default_ops::eval_add; + using default_ops::eval_subtract; + eval_subtract(m_backend, canonical_value(e.left().value())); + eval_add(m_backend, canonical_value(e.right().value())); } template void do_subtract(const Exp& e, const unknown&) @@ -1166,8 +1166,8 @@ private: template void do_multiplies(const Exp& e, const detail::terminal&) { - using default_ops::multiply; - multiply(m_backend, canonical_value(e.value())); + using default_ops::eval_multiply; + eval_multiply(m_backend, canonical_value(e.value())); } template @@ -1199,31 +1199,31 @@ private: template void do_multiplies(const Exp& e, const detail::multiply_immediates&) { - using default_ops::multiply; - multiply(m_backend, canonical_value(e.left().value())); - multiply(m_backend, canonical_value(e.right().value())); + using default_ops::eval_multiply; + eval_multiply(m_backend, canonical_value(e.left().value())); + eval_multiply(m_backend, canonical_value(e.right().value())); } template void do_multiplies(const Exp& e, const detail::divide_immediates&) { - using default_ops::multiply; - using default_ops::divide; - multiply(m_backend, canonical_value(e.left().value())); - divide(m_backend, canonical_value(e.right().value())); + using default_ops::eval_multiply; + using default_ops::eval_divide; + eval_multiply(m_backend, canonical_value(e.left().value())); + eval_divide(m_backend, canonical_value(e.right().value())); } template void do_multiplies(const Exp& e, const unknown&) { - using default_ops::multiply; + using default_ops::eval_multiply; self_type temp(e); - multiply(m_backend, temp.m_backend); + eval_multiply(m_backend, temp.m_backend); } template void do_divide(const Exp& e, const detail::terminal&) { - using default_ops::divide; - divide(m_backend, canonical_value(e.value())); + using default_ops::eval_divide; + eval_divide(m_backend, canonical_value(e.value())); } template @@ -1255,50 +1255,50 @@ private: template void do_divides(const Exp& e, const detail::multiply_immediates&) { - using default_ops::divide; - divide(m_backend, canonical_value(e.left().value())); - divide(m_backend, canonical_value(e.right().value())); + using default_ops::eval_divide; + eval_divide(m_backend, canonical_value(e.left().value())); + eval_divide(m_backend, canonical_value(e.right().value())); } template void do_divides(const Exp& e, const detail::divide_immediates&) { - using default_ops::multiply; - using default_ops::divide; - divide(m_backend, canonical_value(e.left().value())); + using default_ops::eval_multiply; + using default_ops::eval_divide; + eval_divide(m_backend, canonical_value(e.left().value())); mutiply(m_backend, canonical_value(e.right().value())); } template void do_divide(const Exp& e, const unknown&) { - using default_ops::multiply; + using default_ops::eval_multiply; self_type temp(e); - divide(m_backend, temp.m_backend); + eval_divide(m_backend, temp.m_backend); } template void do_modulus(const Exp& e, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using default_ops::modulus; - modulus(m_backend, canonical_value(e.value())); + using default_ops::eval_modulus; + eval_modulus(m_backend, canonical_value(e.value())); } template void do_modulus(const Exp& e, const Unknown&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - using default_ops::modulus; + using default_ops::eval_modulus; self_type temp(e); - modulus(m_backend, canonical_value(temp)); + eval_modulus(m_backend, canonical_value(temp)); } template void do_bitwise_and(const Exp& e, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); - using default_ops::bitwise_and; - bitwise_and(m_backend, canonical_value(e.value())); + using default_ops::eval_bitwise_and; + eval_bitwise_and(m_backend, canonical_value(e.value())); } template void do_bitwise_and(const Exp& e, const detail::bitwise_and&) @@ -1313,17 +1313,17 @@ private: void do_bitwise_and(const Exp& e, const unknown&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); - using default_ops::bitwise_and; + using default_ops::eval_bitwise_and; self_type temp(e); - bitwise_and(m_backend, temp.m_backend); + eval_bitwise_and(m_backend, temp.m_backend); } template void do_bitwise_or(const Exp& e, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); - using default_ops::bitwise_or; - bitwise_or(m_backend, canonical_value(e.value())); + using default_ops::eval_bitwise_or; + eval_bitwise_or(m_backend, canonical_value(e.value())); } template void do_bitwise_or(const Exp& e, const detail::bitwise_or&) @@ -1338,17 +1338,17 @@ private: void do_bitwise_or(const Exp& e, const unknown&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); - using default_ops::bitwise_or; + using default_ops::eval_bitwise_or; self_type temp(e); - bitwise_or(m_backend, temp.m_backend); + eval_bitwise_or(m_backend, temp.m_backend); } template void do_bitwise_xor(const Exp& e, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); - using default_ops::bitwise_xor; - bitwise_xor(m_backend, canonical_value(e.value())); + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(m_backend, canonical_value(e.value())); } template void do_bitwise_xor(const Exp& e, const detail::bitwise_xor&) @@ -1363,9 +1363,9 @@ private: void do_bitwise_xor(const Exp& e, const unknown&) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); - using default_ops::bitwise_xor; + using default_ops::eval_bitwise_xor; self_type temp(e); - bitwise_xor(m_backend, temp.m_backend); + eval_bitwise_xor(m_backend, temp.m_backend); } // Tests if the expression contains a reference to *this: diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index fc7e7f05..9f5e3ce1 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -16,7 +16,9 @@ #include #include -namespace boost{ namespace multiprecision{ +namespace boost{ +namespace multiprecision{ +namespace backends{ template struct mpfr_float_backend; @@ -560,47 +562,47 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> }; template -inline void add(mpfr_float_backend& result, const mpfr_float_backend& o) +inline void eval_add(mpfr_float_backend& result, const mpfr_float_backend& o) { mpfr_add(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void subtract(mpfr_float_backend& result, const mpfr_float_backend& o) +inline void eval_subtract(mpfr_float_backend& result, const mpfr_float_backend& o) { mpfr_sub(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void multiply(mpfr_float_backend& result, const mpfr_float_backend& o) +inline void eval_multiply(mpfr_float_backend& result, const mpfr_float_backend& o) { mpfr_mul(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void divide(mpfr_float_backend& result, const mpfr_float_backend& o) +inline void eval_divide(mpfr_float_backend& result, const mpfr_float_backend& o) { mpfr_div(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void add(mpfr_float_backend& result, unsigned long i) +inline void eval_add(mpfr_float_backend& result, unsigned long i) { mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void subtract(mpfr_float_backend& result, unsigned long i) +inline void eval_subtract(mpfr_float_backend& result, unsigned long i) { mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void multiply(mpfr_float_backend& result, unsigned long i) +inline void eval_multiply(mpfr_float_backend& result, unsigned long i) { mpfr_mul_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void divide(mpfr_float_backend& result, unsigned long i) +inline void eval_divide(mpfr_float_backend& result, unsigned long i) { mpfr_div_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void add(mpfr_float_backend& result, long i) +inline void eval_add(mpfr_float_backend& result, long i) { if(i > 0) mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); @@ -608,7 +610,7 @@ inline void add(mpfr_float_backend& result, long i) mpfr_sub_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); } template -inline void subtract(mpfr_float_backend& result, long i) +inline void eval_subtract(mpfr_float_backend& result, long i) { if(i > 0) mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); @@ -616,14 +618,14 @@ inline void subtract(mpfr_float_backend& result, long i) mpfr_add_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); } template -inline void multiply(mpfr_float_backend& result, long i) +inline void eval_multiply(mpfr_float_backend& result, long i) { mpfr_mul_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); if(i < 0) mpfr_neg(result.data(), result.data(), GMP_RNDN); } template -inline void divide(mpfr_float_backend& result, long i) +inline void eval_divide(mpfr_float_backend& result, long i) { mpfr_div_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); if(i < 0) @@ -633,17 +635,17 @@ inline void divide(mpfr_float_backend& result, long i) // Specialised 3 arg versions of the basic operators: // template -inline void add(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) { mpfr_add(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void add(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) { mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void add(mpfr_float_backend& a, const mpfr_float_backend& x, long y) +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, long y) { if(y < 0) mpfr_sub_ui(a.data(), x.data(), -y, GMP_RNDN); @@ -651,12 +653,12 @@ inline void add(mpfr_float_backend& a, const mpfr_float_backend -inline void add(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) +inline void eval_add(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) { mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } template -inline void add(mpfr_float_backend& a, long x, const mpfr_float_backend& y) +inline void eval_add(mpfr_float_backend& a, long x, const mpfr_float_backend& y) { if(x < 0) { @@ -667,17 +669,17 @@ inline void add(mpfr_float_backend& a, long x, const mpfr_float_backen mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } template -inline void subtract(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) { mpfr_sub(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void subtract(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) { mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void subtract(mpfr_float_backend& a, const mpfr_float_backend& x, long y) +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, long y) { if(y < 0) mpfr_add_ui(a.data(), x.data(), -y, GMP_RNDN); @@ -685,12 +687,12 @@ inline void subtract(mpfr_float_backend& a, const mpfr_float_backend -inline void subtract(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) +inline void eval_subtract(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) { mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); } template -inline void subtract(mpfr_float_backend& a, long x, const mpfr_float_backend& y) +inline void eval_subtract(mpfr_float_backend& a, long x, const mpfr_float_backend& y) { if(x < 0) { @@ -702,17 +704,17 @@ inline void subtract(mpfr_float_backend& a, long x, const mpfr_float_b } template -inline void multiply(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) { mpfr_mul(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void multiply(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) { mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void multiply(mpfr_float_backend& a, const mpfr_float_backend& x, long y) +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, long y) { if(y < 0) { @@ -723,12 +725,12 @@ inline void multiply(mpfr_float_backend& a, const mpfr_float_backend -inline void multiply(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) +inline void eval_multiply(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) { mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); } template -inline void multiply(mpfr_float_backend& a, long x, const mpfr_float_backend& y) +inline void eval_multiply(mpfr_float_backend& a, long x, const mpfr_float_backend& y) { if(x < 0) { @@ -740,17 +742,17 @@ inline void multiply(mpfr_float_backend& a, long x, const mpfr_float_b } template -inline void divide(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) +inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) { mpfr_div(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void divide(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) +inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) { mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void divide(mpfr_float_backend& a, const mpfr_float_backend& x, long y) +inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, long y) { if(y < 0) { @@ -761,12 +763,12 @@ inline void divide(mpfr_float_backend& a, const mpfr_float_backend -inline void divide(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) +inline void eval_divide(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) { mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); } template -inline void divide(mpfr_float_backend& a, long x, const mpfr_float_backend& y) +inline void eval_divide(mpfr_float_backend& a, long x, const mpfr_float_backend& y) { if(x < 0) { @@ -778,45 +780,45 @@ inline void divide(mpfr_float_backend& a, long x, const mpfr_float_bac } template -inline bool is_zero(const mpfr_float_backend& val) +inline bool eval_is_zero(const mpfr_float_backend& val) { return 0 != mpfr_zero_p(val.data()); } template -inline int get_sign(const mpfr_float_backend& val) +inline int eval_get_sign(const mpfr_float_backend& val) { return mpfr_sgn(val.data()); } template -inline void convert_to(unsigned long* result, const mpfr_float_backend& val) +inline void eval_convert_to(unsigned long* result, const mpfr_float_backend& val) { *result = mpfr_get_ui(val.data(), GMP_RNDN); } template -inline void convert_to(long* result, const mpfr_float_backend& val) +inline void eval_convert_to(long* result, const mpfr_float_backend& val) { *result = mpfr_get_si(val.data(), GMP_RNDN); } #ifdef _MPFR_H_HAVE_INTMAX_T template -inline void convert_to(unsigned long long* result, const mpfr_float_backend& val) +inline void eval_convert_to(unsigned long long* result, const mpfr_float_backend& val) { *result = mpfr_get_uj(val.data(), GMP_RNDN); } template -inline void convert_to(long long* result, const mpfr_float_backend& val) +inline void eval_convert_to(long long* result, const mpfr_float_backend& val) { *result = mpfr_get_sj(val.data(), GMP_RNDN); } #endif template -inline void convert_to(double* result, const mpfr_float_backend& val) +inline void eval_convert_to(double* result, const mpfr_float_backend& val) { *result = mpfr_get_d(val.data(), GMP_RNDN); } template -inline void convert_to(long double* result, const mpfr_float_backend& val) +inline void eval_convert_to(long double* result, const mpfr_float_backend& val) { *result = mpfr_get_ld(val.data(), GMP_RNDN); } @@ -988,13 +990,17 @@ inline void eval_tanh(mpfr_float_backend& result, const mpfr_float_bac mpfr_tanh(result.data(), arg.data(), GMP_RNDN); } +} // namespace backends + +using boost::multiprecision::backends::mpfr_float_backend; + typedef mp_number > mpfr_float_50; typedef mp_number > mpfr_float_100; typedef mp_number > mpfr_float_500; typedef mp_number > mpfr_float_1000; typedef mp_number > mpfr_float; -} // namespace boost +} // namespace multiprecision namespace math{ @@ -1003,7 +1009,7 @@ namespace tools{ template <> inline int digits() { - return boost::multiprecision::detail::get_default_precision(); + return boost::multiprecision::backends::detail::get_default_precision(); } } diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index cc0e786b..2436147f 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -16,6 +16,7 @@ namespace boost{ namespace multiprecision{ +namespace backends{ template struct rational_adapter @@ -123,42 +124,42 @@ private: }; template -inline void add(rational_adapter& result, const rational_adapter& o) +inline void eval_add(rational_adapter& result, const rational_adapter& o) { result.data() += o.data(); } template -inline void subtract(rational_adapter& result, const rational_adapter& o) +inline void eval_subtract(rational_adapter& result, const rational_adapter& o) { result.data() -= o.data(); } template -inline void multiply(rational_adapter& result, const rational_adapter& o) +inline void eval_multiply(rational_adapter& result, const rational_adapter& o) { result.data() *= o.data(); } template -inline void divide(rational_adapter& result, const rational_adapter& o) +inline void eval_divide(rational_adapter& result, const rational_adapter& o) { result.data() /= o.data(); } template -inline void convert_to(R* result, const rational_adapter& backend) +inline void eval_convert_to(R* result, const rational_adapter& backend) { *result = backend.data().numerator().template convert_to(); *result /= backend.data().denominator().template convert_to(); } template -inline bool is_zero(const rational_adapter& val) +inline bool eval_is_zero(const rational_adapter& val) { - return is_zero(val.data().numerator().backend()); + return eval_is_zero(val.data().numerator().backend()); } template -inline int get_sign(const rational_adapter& val) +inline int eval_get_sign(const rational_adapter& val) { - return get_sign(val.data().numerator().backend()); + return eval_get_sign(val.data().numerator().backend()); } template @@ -181,6 +182,10 @@ inline void assign_components(rational_adapter& result, const V& v1, template struct number_category > : public mpl::int_{}; +} // namespace backends + +using boost::multiprecision::backends::rational_adapter; + template struct component_type > { diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 683d5e5b..a30a3868 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -17,7 +17,7 @@ #include #include -namespace boost{ namespace multiprecision{ +namespace boost{ namespace multiprecision{ namespace backends{ namespace detail{ @@ -241,31 +241,31 @@ protected: if(SIGN(&x.data()))\ BOOST_THROW_EXCEPTION(std::runtime_error("Bitwise operations on libtommath negative valued integers are disabled as they produce unpredictable results")) -int get_sign(const tommath_int& val); +int eval_get_sign(const tommath_int& val); -inline void add(tommath_int& t, const tommath_int& o) +inline void eval_add(tommath_int& t, const tommath_int& o) { detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); } -inline void subtract(tommath_int& t, const tommath_int& o) +inline void eval_subtract(tommath_int& t, const tommath_int& o) { detail::check_tommath_result(mp_sub(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); } -inline void multiply(tommath_int& t, const tommath_int& o) +inline void eval_multiply(tommath_int& t, const tommath_int& o) { detail::check_tommath_result(mp_mul(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); } -inline void divide(tommath_int& t, const tommath_int& o) +inline void eval_divide(tommath_int& t, const tommath_int& o) { tommath_int temp; detail::check_tommath_result(mp_div(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data(), &temp.data())); } -inline void modulus(tommath_int& t, const tommath_int& o) +inline void eval_modulus(tommath_int& t, const tommath_int& o) { - bool neg = get_sign(t) < 0; - bool neg2 = get_sign(o) < 0; + bool neg = eval_get_sign(t) < 0; + bool neg2 = eval_get_sign(o) < 0; detail::check_tommath_result(mp_mod(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); - if((neg != neg2) && (get_sign(t) != 0)) + if((neg != neg2) && (eval_get_sign(t) != 0)) { t.negate(); detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); @@ -277,72 +277,72 @@ inline void modulus(tommath_int& t, const tommath_int& o) } } template -inline void left_shift(tommath_int& t, UI i) +inline void eval_left_shift(tommath_int& t, UI i) { detail::check_tommath_result(mp_mul_2d(&t.data(), static_cast(i), &t.data())); } template -inline void right_shift(tommath_int& t, UI i) +inline void eval_right_shift(tommath_int& t, UI i) { tommath_int d; detail::check_tommath_result(mp_div_2d(&t.data(), static_cast(i), &t.data(), &d.data())); } template -inline void left_shift(tommath_int& t, const tommath_int& v, UI i) +inline void eval_left_shift(tommath_int& t, const tommath_int& v, UI i) { detail::check_tommath_result(mp_mul_2d(const_cast< ::mp_int*>(&v.data()), static_cast(i), &t.data())); } template -inline void right_shift(tommath_int& t, const tommath_int& v, UI i) +inline void eval_right_shift(tommath_int& t, const tommath_int& v, UI i) { tommath_int d; detail::check_tommath_result(mp_div_2d(const_cast< ::mp_int*>(&v.data()), static_cast(i), &t.data(), &d.data())); } -inline void bitwise_and(tommath_int& result, const tommath_int& v) +inline void eval_bitwise_and(tommath_int& result, const tommath_int& v) { BOOST_MP_TOMMATH_BIT_OP_CHECK(result); BOOST_MP_TOMMATH_BIT_OP_CHECK(v); detail::check_tommath_result(mp_and(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data())); } -inline void bitwise_or(tommath_int& result, const tommath_int& v) +inline void eval_bitwise_or(tommath_int& result, const tommath_int& v) { BOOST_MP_TOMMATH_BIT_OP_CHECK(result); BOOST_MP_TOMMATH_BIT_OP_CHECK(v); detail::check_tommath_result(mp_or(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data())); } -inline void bitwise_xor(tommath_int& result, const tommath_int& v) +inline void eval_bitwise_xor(tommath_int& result, const tommath_int& v) { BOOST_MP_TOMMATH_BIT_OP_CHECK(result); BOOST_MP_TOMMATH_BIT_OP_CHECK(v); detail::check_tommath_result(mp_xor(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data())); } -inline void add(tommath_int& t, const tommath_int& p, const tommath_int& o) +inline void eval_add(tommath_int& t, const tommath_int& p, const tommath_int& o) { detail::check_tommath_result(mp_add(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data())); } -inline void subtract(tommath_int& t, const tommath_int& p, const tommath_int& o) +inline void eval_subtract(tommath_int& t, const tommath_int& p, const tommath_int& o) { detail::check_tommath_result(mp_sub(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data())); } -inline void multiply(tommath_int& t, const tommath_int& p, const tommath_int& o) +inline void eval_multiply(tommath_int& t, const tommath_int& p, const tommath_int& o) { detail::check_tommath_result(mp_mul(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data())); } -inline void divide(tommath_int& t, const tommath_int& p, const tommath_int& o) +inline void eval_divide(tommath_int& t, const tommath_int& p, const tommath_int& o) { tommath_int d; detail::check_tommath_result(mp_div(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data(), &d.data())); } -inline void modulus(tommath_int& t, const tommath_int& p, const tommath_int& o) +inline void eval_modulus(tommath_int& t, const tommath_int& p, const tommath_int& o) { - bool neg = get_sign(p) < 0; - bool neg2 = get_sign(o) < 0; + bool neg = eval_get_sign(p) < 0; + bool neg2 = eval_get_sign(o) < 0; detail::check_tommath_result(mp_mod(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data())); - if((neg != neg2) && (get_sign(t) != 0)) + if((neg != neg2) && (eval_get_sign(t) != 0)) { t.negate(); detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); @@ -354,28 +354,28 @@ inline void modulus(tommath_int& t, const tommath_int& p, const tommath_int& o) } } -inline void bitwise_and(tommath_int& result, const tommath_int& u, const tommath_int& v) +inline void eval_bitwise_and(tommath_int& result, const tommath_int& u, const tommath_int& v) { BOOST_MP_TOMMATH_BIT_OP_CHECK(u); BOOST_MP_TOMMATH_BIT_OP_CHECK(v); detail::check_tommath_result(mp_and(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data())); } -inline void bitwise_or(tommath_int& result, const tommath_int& u, const tommath_int& v) +inline void eval_bitwise_or(tommath_int& result, const tommath_int& u, const tommath_int& v) { BOOST_MP_TOMMATH_BIT_OP_CHECK(u); BOOST_MP_TOMMATH_BIT_OP_CHECK(v); detail::check_tommath_result(mp_or(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data())); } -inline void bitwise_xor(tommath_int& result, const tommath_int& u, const tommath_int& v) +inline void eval_bitwise_xor(tommath_int& result, const tommath_int& u, const tommath_int& v) { BOOST_MP_TOMMATH_BIT_OP_CHECK(u); BOOST_MP_TOMMATH_BIT_OP_CHECK(v); detail::check_tommath_result(mp_xor(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data())); } /* -inline void complement(tommath_int& result, const tommath_int& u) +inline void eval_complement(tommath_int& result, const tommath_int& u) { // // Although this code works, it doesn't really do what the user might expect.... @@ -400,32 +400,32 @@ inline void complement(tommath_int& result, const tommath_int& u) // Create a mask providing the extra bits we need and add to result: tommath_int mask; mask = static_cast((1u << padding) - 1); - left_shift(mask, shift); + eval_left_shift(mask, shift); add(result, mask); } */ -inline bool is_zero(const tommath_int& val) +inline bool eval_is_zero(const tommath_int& val) { return mp_iszero(&val.data()); } -inline int get_sign(const tommath_int& val) +inline int eval_get_sign(const tommath_int& val) { return mp_iszero(&val.data()) ? 0 : SIGN(&val.data()) ? -1 : 1; } template -inline void convert_to(A* result, const tommath_int& val) +inline void eval_convert_to(A* result, const tommath_int& val) { *result = boost::lexical_cast(val.str(0, std::ios_base::fmtflags(0))); } -inline void convert_to(char* result, const tommath_int& val) +inline void eval_convert_to(char* result, const tommath_int& val) { *result = static_cast(boost::lexical_cast(val.str(0, std::ios_base::fmtflags(0)))); } -inline void convert_to(unsigned char* result, const tommath_int& val) +inline void eval_convert_to(unsigned char* result, const tommath_int& val) { *result = static_cast(boost::lexical_cast(val.str(0, std::ios_base::fmtflags(0)))); } -inline void convert_to(signed char* result, const tommath_int& val) +inline void eval_convert_to(signed char* result, const tommath_int& val) { *result = static_cast(boost::lexical_cast(val.str(0, std::ios_base::fmtflags(0)))); } @@ -442,6 +442,9 @@ inline void eval_lcm(tommath_int& result, const tommath_int& a, const tommath_in detail::check_tommath_result(mp_lcm(const_cast< ::mp_int*>(&a.data()), const_cast< ::mp_int*>(&b.data()), const_cast< ::mp_int*>(&result.data()))); } +} // namespace backends + +using boost::multiprecision::backends::tommath_int; template<> struct number_category : public mpl::int_{}; diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 5d5d47ea..b7e53e1d 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -1049,6 +1049,7 @@ int main() test(); test > >(); test > >(); + test(); #endif #ifdef TEST_CPP_INT_BR test(); From 7bed8d02f9170590d2e903cd011d7e8268f0eedd Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 13 Mar 2012 18:30:18 +0000 Subject: [PATCH 130/256] Add support for disabling expression templates via a second template parameter to mp_number. Begin to update docs to reflect new cpp_int code. [SVN r77323] --- doc/multiprecision.qbk | 193 ++++++-- .../multiprecision/arithmetic_backend.hpp | 6 +- .../concepts/mp_number_architypes.hpp | 6 +- .../boost/multiprecision/cpp_dec_float.hpp | 26 +- include/boost/multiprecision/cpp_int.hpp | 26 +- .../multiprecision/detail/big_lanczos.hpp | 6 +- .../multiprecision/detail/default_ops.hpp | 201 +++++--- .../multiprecision/detail/mp_number_base.hpp | 468 +++++++++--------- include/boost/multiprecision/fixed_int.hpp | 12 +- include/boost/multiprecision/gmp.hpp | 28 +- include/boost/multiprecision/mp_number.hpp | 128 ++--- include/boost/multiprecision/mpfr.hpp | 21 +- .../boost/multiprecision/rational_adapter.hpp | 6 +- include/boost/multiprecision/tommath.hpp | 6 +- test/Jamfile.v2 | 49 +- test/mp_number_concept_check.cpp | 8 +- test/test_arithmetic.cpp | 2 + test/test_int_io.cpp | 11 +- 18 files changed, 677 insertions(+), 526 deletions(-) diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 677a5336..d7c313d7 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -60,6 +60,17 @@ so instead we compose our own: my_float a, b, c; // These variables have 300 decimal digits precision +We can repeat the above example, but with the expression templates disabled (for faster compile times, but slower runtimes) +by passing a second template argument to `mp_number`: + + #include // Defines the Backend type that wraps MPFR + + namespace mp = boost::multiprecision; // Reduce the typing a bit later... + + typedef mp::mp_number, false> my_float; + + my_float a, b, c; // These variables have 300 decimal digits precision + [h4 Expression Templates] Class `mp_number` is expression-template-enabled: that means that rather than having a multiplication @@ -176,6 +187,9 @@ magic by converting out-of-place operators to in-place ones, we necessarily take transformation is more efficient than creating the extra temporary variable, just not by as much as one would hope. +Finally, note that `mp_number` takes a second template argument, which, when set to `false` disables all +the expression template machinary. The result is much faster to compile, but slower at runtime. + We'll conclude this section by providing some more performance comparisons between these three libraries, again, all are using [mpfr] to carry out the underlying arithmetic, and all are operating at the same precision (50 decimal digits): @@ -209,7 +223,8 @@ The following backends provide integer arithmetic: [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] [[`gmp_int`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient backend.][Dependency on GNU licenced [gmp] library.]] [[`mp_int`][boost/multiprecision/tommath.hpp][2][libtommath][Public domain backend with no licence restrictions.][Slower than [gmp].]] -[[`fixed_int`][boost/multiprecision/fixed_int.hpp][2][None][Boost licenced fixed precision modular arithmetic integer.][Slower than [gmp].]] +[[`cpp_int`][boost/multiprecision/cpp_int.hpp][2][None] + [Very versatile, Boost licenced, all C++ integer type which support both arbitrary precision and fixed precision integer types.][Slower than [gmp].]] ] [h4 gmp_int] @@ -277,46 +292,76 @@ as a result performing formatted output on this type when the argument is negati [tommath_eg] -[h4 fixed_int] +[h4 cpp_int] namespace boost{ namespace multiprecision{ - template - class fixed_int; + typedef unspecified-type limb_type; - typedef mp_number > mp_uint128_t; - typedef mp_number > mp_uint256_t; - typedef mp_number > mp_uint512_t; + template > + class cpp_int_backend; - typedef mp_number > mp_int128_t; - typedef mp_number > mp_int256_t; - typedef mp_number > mp_int512_t; + typedef mp_number > cpp_int; // arbitrary precision integer + typedef rational_adapter > cpp_rational_backend; + typedef mp_number cpp_rational; // arbitrary precision rational number + + // Fixed precision unsigned types: + typedef mp_number > mp_uint128_t; + typedef mp_number > mp_uint256_t; + typedef mp_number > mp_uint512_t; + + // Fixed precision signed types: + typedef mp_number > mp_int128_t; + typedef mp_number > mp_int256_t; + typedef mp_number > mp_int512_t; }} // namespaces -The `fixed_int` backend is used via one of the typedefs `boost::multiprecision::mp_uint128_t`, `boost::multiprecision::mp_uint256_t`, +The `cpp_int_backend` type is used via one of the typedefs `boost::multiprecision::cpp_int`, +`boost::multiprecision::mp_uint128_t`, `boost::multiprecision::mp_uint256_t`, `boost::multiprecision::mp_uint512_t`, `boost::multiprecision::mp_int128_t`, `boost::multiprecision::mp_int256_t` -or `boost::multiprecision::mp_int512_t`. It provides both signed and unsigned integer types with a fixed precision -and modular arithmetic with a 2's complement representation for negative values. In other words it's designed to work just -like a typical built in integer type, but with larger precision. +or `boost::multiprecision::mp_int512_t`. + +This backend is the "Swiss Army Knife" of integer types as it can represent both fixed and arbitrary precision +integer types, and both signed and unsigned types. There are three template arguments: + +[variablelist +[[MinBits][Determines the number of Bits to store directly within the object before resorting to dynamic memory + allocation. When zero, this field is determined automatically based on how many bits can be stored + in union with the dynamic storage header: setting a larger value may improve performance as larger integer + values will be stored internally before memory allocation is required. + When the Allocator parameter is type `void`, then this field + determines the total number of bits in the resulting fixed precision type.]] +[[Signed][Determines whether the resulting type is signed or not. Note that for arbitrary precision types + (where the Allocator parameter is non-void), then this parameter must be `true`. For fixed precision + types then this type may be either `true` (type is signed), or `false` (type is unsigned).]] +[[Allocator][The allocator to use for dymamic memory allocation, or type `void` if this is to be a fixed precision type.]] +] Things you should know when using this type: -* Default constructed `fixed_int`'s have indeterminate value - just like normal built in integers. +* Default constructed `cpp_int_backend`'s have the value zero. * Division by zero results in a `std::runtime_error` being thrown. * Construction from a string that contains invalid non-numeric characters results in a `std::runtime_error` being thrown. -* Since the precision of `fixed_int` is necessarily limited, care should be taken to avoid numeric overflow when using this type +* Since the precision of `cpp_int_backend` is necessarily limited when the allocator parameter is void, +care should be taken to avoid numeric overflow when using this type unless you actually want modulo-arithmetic behavior. +* The type uses a sign-magnitude representation internally, so type `mp_int128_t` has 128-bits of precision plus an extra sign bit. +In this respect the behaviour of these types differs from built-in 2's complement types. In might be tempting to use a +127-bit type instead, and indeed this does work, but behaviour is still slightly different from a 2's complement built-in type +as the min and max values are identical (apart from the sign), where as they differ by one for a true 2's complement type. +That said it should be noted that there's no requirement for built-in types to be 2's complement either - it's simply that this +is the most common format by far. [h5 Example:] -[fixed_int_eg] +[cpp_int_eg] [endsect] -[section:reals Real Numbers] +[section:reals Floating Point Numbers] -The following backends provide real number arithmetic: +The following backends provide floating point arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] @@ -471,7 +516,8 @@ The following backends provide rational number arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] [[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient backend.][Dependency on GNU licenced [gmp] library.]] -[[`tommath_rational`][boost/multiprecision/tommath.hpp][2][libtommath][All C/C++ implementation that's Boost Software Licence compatible.][Slower than [gmp].]] +[[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licenced implementation.][[Slower than [gmp].]] +[[`tommath_rational`][boost/multiprecision/tommath.hpp][2][libtommath][All C/C++ implementation that's Boost Software Licence compatible.] [[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any inetger backend type to be used as a rational type.][Requires an underlying integer backend type.]] [[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `mp_number` integer type.][The expression templates used by `mp_number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]] ] @@ -516,6 +562,38 @@ Things you should know when using this type: [mpq_eg] +[h4 cpp_rational] + + namespace boost{ namespace multiprecision{ + + typedef rational_adapter > cpp_rational_backend; + + typedef mp_number cpp_rational; + + }} // namespaces + +The `cpp_rational_backend` type is used via the typedef `boost::multiprecision::cpp_rational`. It provides +a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. + +As well as the usual conversions from arithmetic and string types, instances of `cpp_rational` are copy constructible +and assignable from type `cpp_int`. + +There are also non-member functions: + + cpp_int numerator(const cpp_rational&); + cpp_int denominator(const cpp_rational&); + +which return the numerator and denominator of the number. + +Things you should know when using this type: + +* Default constructed `cpp_rational`'s have the value zero. +* Division by zero results in a `std::rumtime_error` being thrown. + +[h5 Example:] + +[cpp_rational_eg] + [h4 tommath_rational] namespace boost{ namespace multiprecision{ @@ -592,7 +670,7 @@ So for example, given an integer backend type `MyIntegerBackend`, the use would namespace boost{ namespace multiprecision{ - template + template class mp_number { mp_number(); @@ -621,13 +699,13 @@ So for example, given an integer backend type `MyIntegerBackend`, the use would // swap: void swap(mp_number& other); // Sign: - bool eval_is_zero()const; + bool is_zero()const; int sign()const; // string conversion: std::string str()const; // Generic conversion mechanism template - T eval_convert_to()const; + T convert_to()const; // precision control: static unsigned default_precision(); static void default_precision(unsigned digits10); @@ -663,15 +741,15 @@ So for example, given an integer backend type `MyIntegerBackend`, the use would bool operator>=(const ``['see-below]``&, const ``['see-below]``&); // Swap: - template - void swap(mp_number& a, mp_number& b); + template + void swap(mp_number& a, mp_number& b); // iostream support: - template - std::ostream& operator << (std::ostream& os, const mp_number& r); + template + std::ostream& operator << (std::ostream& os, const mp_number& r); std::ostream& operator << (std::ostream& os, const ``['unmentionable-expression-template-type]``& r); - template - std::istream& operator >> (std::istream& is, mp_number& r); + template + std::istream& operator >> (std::istream& is, mp_number& r); // Non-member function standard library support: ``['unmentionable-expression-template-type]`` abs (const ``['mp_number-or-expression-template-type]``&); @@ -732,8 +810,8 @@ So for example, given an integer backend type `MyIntegerBackend`, the use would // numeric_limits support: namespace std{ - template - struct numeric_limits > + template + struct numeric_limits > { /* Usual members here */ }; @@ -742,6 +820,16 @@ So for example, given an integer backend type `MyIntegerBackend`, the use would [h4 Description] + template + class mp_number; + +Class `mp_number` has two template arguments: + +[variablelist +[[Backend][The actual arithmetic backend that does all the work.]] +[[ExpressionTemplates][A boolean value: when true, then expression templates are enabled, otherwise they are disabled.]] +] + mp_number(); mp_number(see-below); mp_number& operator=(see-below); @@ -781,7 +869,7 @@ These operators all take their usual arithmetic meanings. The arguments to these operators is either: -* Another `mp_number`. +* Another `mp_number`. * A builtin arithmetic type. * An expression template derived from `mp_number`. @@ -801,7 +889,7 @@ This operator also enables the use of `mp_number` with any of the following oper Swaps `*this` with `other`. - bool eval_is_zero()const; + bool is_zero()const; Returns `true` is `*this` is zero, otherwise `false`. @@ -816,7 +904,7 @@ Returns the number formatted as a string, with at least /precision/ digits, and if /scientific/ is true. template - T eval_convert_to()const; + T convert_to()const; Provides a generic conversion mechanism to convert `*this` to type `T`. Type `T` may be any arithmetic type. Optionally other types may also be supported by specific `Backend` types. @@ -830,7 +918,7 @@ Optionally other types may also be supported by specific `Backend` types. These functions are only available if the Backend template parameter supports runtime changes to precision. They get and set the default precision and the precision of `*this` respectively. - int compare(const mp_number& o)const; + int compare(const mp_number& o)const; template typename enable_if, int>::type compare(const V& other)const; @@ -876,28 +964,30 @@ The arguments to these functions must contain at least one of the following: In addition, one of the two arguments may be a builtin arithmetic type. -With the exception of the comparison operators (which always evaluate their arguments and return a `bool` result), -these operators return an "unmentionable" expression template type which defers evaluation of the operator -until the result is actually required. +The return type of these operators is either: + +* An ['unmentionable-type] expression template type when `ExpressionTemplates` is `true`. +* Type `mp_number` when `ExpressionTemplates` is `false`. +* Type `bool` if the operator is a comparison operator. Finally note that the second argument to the left and right shift operations must be a builtin integer type, and that the argument must be positive (negative arguments result in a `std::runtime_error` being thrown). [h4 swap] - template - void swap(mp_number& a, mp_number& b); + template + void swap(mp_number& a, mp_number& b); Swaps `a` and `b`. [h4 Iostream Support] - template - std::ostream& operator << (std::ostream& os, const mp_number& r); - template + template + std::ostream& operator << (std::ostream& os, const mp_number& r); + template std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r); - template - inline std::istream& operator >> (std::istream& is, mp_number& r) + template + inline std::istream& operator >> (std::istream& is, mp_number& r) These operators provided formatted input-output operations on `mp_number` types, and expression templates derived from them. @@ -939,7 +1029,8 @@ this library support all of the iostream formatting flags, field width and preci ``['unmentionable-expression-template-type]`` atan2 (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); These functions all behave exactly as their standard library counterparts do: their argument is either an instance of `mp_number` or -an expression template derived from it; their return value is always an expression template. +an expression template derived from it; If the argument is of type `mp_number,Backend, false>` then that is also the return type, +otherwise the return type is an expression template. These functions are normally implemented by the Backend type. However, default versions are provided for Backend types that don't have native support for these functions. Please note however, that this default support requires the precision of the type @@ -990,8 +1081,8 @@ specialized or overloaded to ensure interoperability. namespace std{ - template - struct numeric_limits > + template + struct numeric_limits > { /* Usual members here */ }; @@ -1159,6 +1250,10 @@ of type B2. [[`eval_atan2(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::atan` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] ] +[note +The non-member functions are all named with an "eval_" prefix to avoid conflicts with template classes of the same name - +in point of fact this naming convension shouldn't be necessary, but rather works around some compiler bugs.] + [endsect] [endsect] @@ -1417,4 +1512,4 @@ More a list of what ['could] be done, rather than what ['should] be done (which [endsect] -[endsect] \ No newline at end of file +[endsect] diff --git a/include/boost/multiprecision/arithmetic_backend.hpp b/include/boost/multiprecision/arithmetic_backend.hpp index 5d9111b2..af26b1ca 100644 --- a/include/boost/multiprecision/arithmetic_backend.hpp +++ b/include/boost/multiprecision/arithmetic_backend.hpp @@ -127,11 +127,11 @@ using boost::multiprecision::backends::arithmetic_backend; namespace std{ -template -class numeric_limits > > : public std::numeric_limits +template +class numeric_limits, ExpressionTemplates > > : public std::numeric_limits { typedef std::numeric_limits base_type; - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index 72e97842..ea29ecde 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -192,11 +192,11 @@ typedef boost::multiprecision::mp_number mp_n namespace std{ -template <> -class numeric_limits : public std::numeric_limits +template +class numeric_limits > : public std::numeric_limits { typedef std::numeric_limits base_type; - typedef boost::multiprecision::concepts::mp_number_float_architype number_type; + typedef boost::multiprecision::mp_number number_type; public: static number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } static number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index a77dcc3b..da5dfe56 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -2822,8 +2822,8 @@ typedef mp_number > cpp_dec_float_100; namespace std { - template - class numeric_limits > > + template + class numeric_limits, ExpressionTemplates> > { public: static const bool is_specialized = true; @@ -2850,15 +2850,15 @@ namespace std static const bool traps = false; static const bool tinyness_before = false; - static const boost::multiprecision::mp_number > (min) (void) { return (boost::multiprecision::cpp_dec_float::min)(); } - static const boost::multiprecision::mp_number > (max) (void) { return (boost::multiprecision::cpp_dec_float::max)(); } - static const boost::multiprecision::mp_number > lowest (void) { return boost::multiprecision::cpp_dec_float::zero(); } - static const boost::multiprecision::mp_number > epsilon (void) { return boost::multiprecision::cpp_dec_float::eps(); } - static const boost::multiprecision::mp_number > round_error (void) { return 0.5L; } - static const boost::multiprecision::mp_number > infinity (void) { return boost::multiprecision::cpp_dec_float::inf(); } - static const boost::multiprecision::mp_number > quiet_NaN (void) { return boost::multiprecision::cpp_dec_float::nan(); } - static const boost::multiprecision::mp_number > signaling_NaN(void) { return boost::multiprecision::cpp_dec_float::zero(); } - static const boost::multiprecision::mp_number > denorm_min (void) { return boost::multiprecision::cpp_dec_float::zero(); } + static const boost::multiprecision::mp_number, ExpressionTemplates> (min) (void) { return (boost::multiprecision::cpp_dec_float::min)(); } + static const boost::multiprecision::mp_number, ExpressionTemplates> (max) (void) { return (boost::multiprecision::cpp_dec_float::max)(); } + static const boost::multiprecision::mp_number, ExpressionTemplates> lowest (void) { return boost::multiprecision::cpp_dec_float::zero(); } + static const boost::multiprecision::mp_number, ExpressionTemplates> epsilon (void) { return boost::multiprecision::cpp_dec_float::eps(); } + static const boost::multiprecision::mp_number, ExpressionTemplates> round_error (void) { return 0.5L; } + static const boost::multiprecision::mp_number, ExpressionTemplates> infinity (void) { return boost::multiprecision::cpp_dec_float::inf(); } + static const boost::multiprecision::mp_number, ExpressionTemplates> quiet_NaN (void) { return boost::multiprecision::cpp_dec_float::nan(); } + static const boost::multiprecision::mp_number, ExpressionTemplates> signaling_NaN(void) { return boost::multiprecision::cpp_dec_float::zero(); } + static const boost::multiprecision::mp_number, ExpressionTemplates> denorm_min (void) { return boost::multiprecision::cpp_dec_float::zero(); } }; } @@ -2866,8 +2866,8 @@ namespace boost{ namespace math{ namespace policies{ -template -struct precision< boost::multiprecision::mp_number >, Policy> +template +struct precision< boost::multiprecision::mp_number, ExpressionTemplates>, Policy> { typedef typename Policy::precision_type precision_type; typedef digits2<((Digits10 + 1) * 1000L) / 301L> digits_2; diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 65f5eb3b..b087fe5f 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -2146,10 +2146,10 @@ typedef mp_number cpp_rational; namespace std{ -template -class numeric_limits > > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; @@ -2196,10 +2196,10 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template -class numeric_limits > > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; struct inititializer { @@ -2273,13 +2273,13 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template -const typename numeric_limits > >::inititializer numeric_limits > >::init; +template +const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; -template -class numeric_limits > > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; struct inititializer { @@ -2352,8 +2352,8 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template -const typename numeric_limits > >::inititializer numeric_limits > >::init; +template +const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; } diff --git a/include/boost/multiprecision/detail/big_lanczos.hpp b/include/boost/multiprecision/detail/big_lanczos.hpp index a3dd8cb2..998d5dca 100644 --- a/include/boost/multiprecision/detail/big_lanczos.hpp +++ b/include/boost/multiprecision/detail/big_lanczos.hpp @@ -16,10 +16,10 @@ namespace lanczos{ template struct lanczos; -template -struct lanczos, Policy> +template +struct lanczos, Policy> { - typedef typename boost::math::policies::precision, Policy>::type precision_type; + typedef typename boost::math::policies::precision, Policy>::type precision_type; typedef typename mpl::if_c< precision_type::value <= 73, lanczos13UDT, diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 6a7dfc67..6fcf64f7 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -531,16 +531,13 @@ typename enable_if_c::type eval_frexp(); } -template -class mp_number; - } // namespace multiprecision namespace math{ // // Default versions of floating point classification routines: // -template -inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) +template +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { using multiprecision::default_ops::eval_fpclassify; return eval_fpclassify(arg.backend()); @@ -551,8 +548,8 @@ inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::det typedef typename multiprecision::detail::mp_exp::result_type value_type; return fpclassify(value_type(arg)); } -template -inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) +template +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { int v = fpclassify(arg); return (v != FP_INFINITE) && (v != FP_NAN); @@ -563,8 +560,8 @@ inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::deta typedef typename multiprecision::detail::mp_exp::result_type value_type; return isfinite(value_type(arg)); } -template -inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) +template +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { return fpclassify(arg) == FP_NAN; } @@ -574,8 +571,8 @@ inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail: typedef typename multiprecision::detail::mp_exp::result_type value_type; return isnan(value_type(arg)); } -template -inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) +template +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { return fpclassify(arg) == FP_INFINITE; } @@ -585,8 +582,8 @@ inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail: typedef typename multiprecision::detail::mp_exp::result_type value_type; return isinf(value_type(arg)); } -template -inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) +template +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) { return fpclassify(arg) == FP_NORMAL; } @@ -607,11 +604,11 @@ inline typename detail::mp_exp::result_type trunc(const detail: return trunc(number_type(v), pol); } -template -inline mp_number trunc(const mp_number& v, const Policy& pol) +template +inline mp_number trunc(const mp_number& v, const Policy& pol) { using default_ops::eval_trunc; - mp_number result; + mp_number result; eval_trunc(result.backend(), v.backend()); return result; } @@ -630,16 +627,16 @@ inline int itrunc(const detail::mp_exp& v) { return itrunc(v, boost::math::policies::policy<>()); } -template -inline int itrunc(const mp_number& v, const Policy& pol) +template +inline int itrunc(const mp_number& v, const Policy& pol) { - mp_number r = trunc(v, pol); + mp_number r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } -template -inline int itrunc(const mp_number& v) +template +inline int itrunc(const mp_number& v) { return itrunc(v, boost::math::policies::policy<>()); } @@ -657,16 +654,16 @@ inline long ltrunc(const detail::mp_exp& v) { return ltrunc(v, boost::math::policies::policy<>()); } -template -inline long ltrunc(const mp_number& v, const Policy& pol) +template +inline long ltrunc(const mp_number& v, const Policy& pol) { - mp_number r = trunc(v, pol); + mp_number r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } -template -inline long ltrunc(const mp_number& v) +template +inline long ltrunc(const mp_number& v) { return ltrunc(v, boost::math::policies::policy<>()); } @@ -685,16 +682,16 @@ inline long long lltrunc(const detail::mp_exp& v) { return lltrunc(v, boost::math::policies::policy<>()); } -template -inline long long lltrunc(const mp_number& v, const Policy& pol) +template +inline long long lltrunc(const mp_number& v, const Policy& pol) { - mp_number r = trunc(v, pol); + mp_number r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } -template -inline long long lltrunc(const mp_number& v) +template +inline long long lltrunc(const mp_number& v) { return lltrunc(v, boost::math::policies::policy<>()); } @@ -705,11 +702,11 @@ inline typename detail::mp_exp::result_type round(const detail: typedef typename detail::mp_exp::result_type number_type; return round(static_cast(v), pol); } -template -inline mp_number round(const mp_number& v, const Policy& pol) +template +inline mp_number round(const mp_number& v, const Policy& pol) { using default_ops::eval_round; - mp_number result; + mp_number result; eval_round(result.backend(), v.backend()); return result; } @@ -728,16 +725,16 @@ inline int iround(const detail::mp_exp& v) { return iround(v, boost::math::policies::policy<>()); } -template -inline int iround(const mp_number& v, const Policy& pol) +template +inline int iround(const mp_number& v, const Policy& pol) { - mp_number r = round(v, pol); + mp_number r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } -template -inline int iround(const mp_number& v) +template +inline int iround(const mp_number& v) { return iround(v, boost::math::policies::policy<>()); } @@ -755,16 +752,16 @@ inline long lround(const detail::mp_exp& v) { return lround(v, boost::math::policies::policy<>()); } -template -inline long lround(const mp_number& v, const Policy& pol) +template +inline long lround(const mp_number& v, const Policy& pol) { - mp_number r = round(v, pol); + mp_number r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } -template -inline long lround(const mp_number& v) +template +inline long lround(const mp_number& v) { return lround(v, boost::math::policies::policy<>()); } @@ -783,16 +780,16 @@ inline long long llround(const detail::mp_exp& v) { return llround(v, boost::math::policies::policy<>()); } -template -inline long long llround(const mp_number& v, const Policy& pol) +template +inline long long llround(const mp_number& v, const Policy& pol) { - mp_number r = round(v, pol); + mp_number r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } -template -inline long long llround(const mp_number& v) +template +inline long long llround(const mp_number& v) { return llround(v, boost::math::policies::policy<>()); } @@ -813,7 +810,7 @@ struct BOOST_JOIN(func, _funct)\ }\ \ template \ -detail::mp_exp<\ +inline detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) >::type> \ , detail::mp_exp \ @@ -830,7 +827,7 @@ func(const detail::mp_exp& arg)\ );\ }\ template \ -detail::mp_exp<\ +inline detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , mp_number \ @@ -845,6 +842,15 @@ func(const mp_number& arg)\ detail::BOOST_JOIN(func, _funct)() \ , arg \ );\ +}\ +template \ +inline mp_number \ +func(const mp_number& arg)\ +{\ + mp_number result;\ + using default_ops::BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result.backend(), arg.backend());\ + return result;\ } #define BINARY_OP_FUNCTOR(func)\ @@ -873,7 +879,7 @@ struct BOOST_JOIN(func, _funct)\ \ }\ template \ -detail::mp_exp<\ +inline detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , mp_number \ @@ -893,7 +899,7 @@ func(const mp_number& arg, const mp_number& a)\ );\ }\ template \ -detail::mp_exp<\ +inline detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , mp_number \ @@ -913,7 +919,7 @@ func(const mp_number& arg, const detail::mp_exp& a)\ );\ }\ template \ -detail::mp_exp<\ +inline detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , detail::mp_exp \ @@ -933,7 +939,7 @@ func(const detail::mp_exp& arg, const mp_number& a)\ );\ }\ template \ -detail::mp_exp<\ +inline detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) >::type> \ , detail::mp_exp \ @@ -953,7 +959,7 @@ func(const detail::mp_exp& arg, const detail::mp_exp \ -typename enable_if<\ +inline typename enable_if<\ is_arithmetic,\ detail::mp_exp<\ detail::function\ @@ -976,7 +982,7 @@ func(const mp_number& arg, const Arithmetic& a)\ );\ }\ template \ -typename enable_if<\ +inline typename enable_if<\ is_arithmetic,\ detail::mp_exp<\ detail::function\ @@ -999,13 +1005,13 @@ func(const detail::mp_exp& arg, const Arithmetic& a)\ );\ }\ template \ -typename enable_if<\ +inline typename enable_if<\ is_arithmetic,\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , Arithmetic \ - , mp_number\ + , mp_number \ > \ >::type \ func(const Arithmetic& arg, const mp_number& a)\ @@ -1014,7 +1020,7 @@ func(const Arithmetic& arg, const mp_number& a)\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , Arithmetic \ - , mp_number\ + , mp_number \ >(\ detail::BOOST_JOIN(func, _funct)() \ , arg,\ @@ -1022,13 +1028,13 @@ func(const Arithmetic& arg, const mp_number& a)\ );\ }\ template \ -typename enable_if<\ +inline typename enable_if<\ is_arithmetic,\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) >::type> \ , Arithmetic \ - , detail::mp_exp\ + , detail::mp_exp \ > \ >::type \ func(const Arithmetic& arg, const detail::mp_exp& a)\ @@ -1037,13 +1043,48 @@ func(const Arithmetic& arg, const detail::mp_exp& a)\ detail::function\ , detail::BOOST_JOIN(func, _funct) >::type> \ , Arithmetic \ - , detail::mp_exp\ + , detail::mp_exp \ >(\ detail::BOOST_JOIN(func, _funct) >::type>() \ , arg,\ a\ );\ }\ +template \ +inline mp_number \ +func(const mp_number& arg, const mp_number& a)\ +{\ + mp_number result;\ + using default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), a.backend());\ + return result;\ +}\ +template \ +inline typename enable_if<\ + is_arithmetic,\ + mp_number \ +>::type \ +func(const mp_number& arg, const Arithmetic& a)\ +{\ + typedef typename detail::canonical::type canonical_type;\ + mp_number result;\ + using default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), static_cast(a));\ + return result;\ +}\ +template \ +inline typename enable_if<\ + is_arithmetic,\ + mp_number \ +>::type \ +func(const Arithmetic& a, const mp_number& arg)\ +{\ + typedef typename detail::canonical::type canonical_type;\ + mp_number result;\ + using default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result.backend(), static_cast(a), arg.backend());\ + return result;\ +}\ #define HETERO_BINARY_OP_FUNCTOR(func, Arg2)\ @@ -1061,7 +1102,7 @@ struct BOOST_JOIN(func, _funct)\ }\ \ template \ -detail::mp_exp<\ +inline detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) >::type> \ , detail::mp_exp \ @@ -1080,7 +1121,7 @@ func(const detail::mp_exp& arg, Arg2 const& a)\ );\ }\ template \ -detail::mp_exp<\ +inline detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , mp_number \ @@ -1099,6 +1140,15 @@ func(const mp_number& arg, Arg2 const& a)\ a\ );\ }\ +template \ +inline mp_number \ +func(const mp_number& arg, Arg2 const& a)\ +{\ + mp_number result;\ + using default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), a);\ + return result;\ +}\ UNARY_OP_FUNCTOR(abs) UNARY_OP_FUNCTOR(fabs) @@ -1146,26 +1196,26 @@ namespace detail{ template T sinc_pi_imp(T); template T sinhc_pi_imp(T); } -template -inline multiprecision::mp_number sinc_pi(const multiprecision::mp_number& x) +template +inline multiprecision::mp_number sinc_pi(const multiprecision::mp_number& x) { return detail::sinc_pi_imp(x); } -template -inline multiprecision::mp_number sinc_pi(const multiprecision::mp_number& x, const Policy&) +template +inline multiprecision::mp_number sinc_pi(const multiprecision::mp_number& x, const Policy&) { return detail::sinc_pi_imp(x); } -template -inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x) +template +inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x) { return detail::sinhc_pi_imp(x); } -template -inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x, const Policy&) +template +inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x, const Policy&) { return boost::math::sinhc_pi(x); } @@ -1173,5 +1223,10 @@ inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_numb } // namespace math } // namespace boost +// +// This has to come last of all: +// +#include + #endif diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 870adace..ba349fe4 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -19,7 +19,7 @@ namespace boost{ namespace multiprecision{ -template +template class mp_number; namespace detail{ @@ -138,8 +138,8 @@ struct function{}; template struct backend_type; -template -struct backend_type > +template +struct backend_type > { typedef T type; }; @@ -153,8 +153,8 @@ struct backend_type > template struct is_mp_number : public mpl::false_{}; -template -struct is_mp_number > : public mpl::true_{}; +template +struct is_mp_number > : public mpl::true_{}; template struct is_mp_number_exp : public mpl::false_{}; template @@ -163,22 +163,22 @@ struct is_mp_number_exp struct combine_expression; -template -struct combine_expression, T2> +template +struct combine_expression, T2> { - typedef mp_number type; + typedef mp_number type; }; -template -struct combine_expression > +template +struct combine_expression > { - typedef mp_number type; + typedef mp_number type; }; -template -struct combine_expression, mp_number > +template +struct combine_expression, mp_number > { - typedef mp_number type; + typedef mp_number type; }; template @@ -500,50 +500,50 @@ void format_float_string(S& str, boost::intmax_t my_exp, boost::intmax_t digits, // // Unary operators first: // -template -inline const mp_number& operator + (const mp_number& v) { return v; } +template +inline const mp_number& operator + (const mp_number& v) { return v; } template inline const detail::mp_exp& operator + (const detail::mp_exp& v) { return v; } template -inline detail::mp_exp > operator - (const mp_number& v) { return detail::mp_exp >(v); } +inline detail::mp_exp > operator - (const mp_number& v) { return detail::mp_exp >(v); } template inline detail::mp_exp > operator - (const detail::mp_exp& v) { return detail::mp_exp >(v); } template -inline detail::mp_exp > operator ~ (const mp_number& v) { return detail::mp_exp >(v); } +inline detail::mp_exp > operator ~ (const mp_number& v) { return detail::mp_exp >(v); } template inline detail::mp_exp > operator ~ (const detail::mp_exp& v) { return detail::mp_exp >(v); } // // Then addition: // template -inline detail::mp_exp, mp_number > - operator + (const mp_number& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator + (const mp_number& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template -inline typename enable_if, detail::mp_exp, V > >::type - operator + (const mp_number& a, const V& b) +inline typename enable_if, detail::mp_exp, V > >::type + operator + (const mp_number& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } template -inline typename enable_if, detail::mp_exp > >::type - operator + (const V& a, const mp_number& b) +inline typename enable_if, detail::mp_exp > >::type + operator + (const V& a, const mp_number& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } template -inline detail::mp_exp, detail::mp_exp > - operator + (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, detail::mp_exp > + operator + (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } template -inline detail::mp_exp, mp_number > - operator + (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator + (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template inline detail::mp_exp, detail::mp_exp > @@ -567,73 +567,73 @@ inline typename enable_if, detail::mp_exp -inline detail::mp_exp, typename detail::mp_exp::left_type > - operator + (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, typename detail::mp_exp::left_type > + operator + (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); + return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); } template -inline detail::mp_exp, typename detail::mp_exp::left_type > - operator + (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, typename detail::mp_exp::left_type > + operator + (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref()); + return detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref()); } template -inline detail::mp_exp, mp_number > - operator + (const mp_number& a, const detail::mp_exp >& b) +inline detail::mp_exp, mp_number > + operator + (const mp_number& a, const detail::mp_exp >& b) { - return detail::mp_exp, mp_number >(a, b.left_ref()); + return detail::mp_exp, mp_number >(a, b.left_ref()); } template -inline detail::mp_exp, mp_number > - operator + (const detail::mp_exp >& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator + (const detail::mp_exp >& a, const mp_number& b) { - return detail::mp_exp, mp_number >(b, a.left_ref()); + return detail::mp_exp, mp_number >(b, a.left_ref()); } template -inline typename enable_if, detail::mp_exp > >::type - operator + (const detail::mp_exp >& a, const V& b) +inline typename enable_if, detail::mp_exp > >::type + operator + (const detail::mp_exp >& a, const V& b) { - return detail::mp_exp >(b, a.left_ref()); + return detail::mp_exp >(b, a.left_ref()); } template -inline typename enable_if, detail::mp_exp > >::type - operator + (const V& a, const detail::mp_exp >& b) +inline typename enable_if, detail::mp_exp > >::type + operator + (const V& a, const detail::mp_exp >& b) { - return detail::mp_exp, mp_number >(a, b.left_ref()); + return detail::mp_exp, mp_number >(a, b.left_ref()); } // // Subtraction: // template -inline detail::mp_exp, mp_number > - operator - (const mp_number& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator - (const mp_number& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template -inline typename enable_if, detail::mp_exp, V > >::type - operator - (const mp_number& a, const V& b) +inline typename enable_if, detail::mp_exp, V > >::type + operator - (const mp_number& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } template -inline typename enable_if, detail::mp_exp > >::type - operator - (const V& a, const mp_number& b) +inline typename enable_if, detail::mp_exp > >::type + operator - (const V& a, const mp_number& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } template -inline detail::mp_exp, detail::mp_exp > - operator - (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, detail::mp_exp > + operator - (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } template -inline detail::mp_exp, mp_number > - operator - (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator - (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template inline detail::mp_exp, detail::mp_exp > @@ -657,75 +657,75 @@ inline typename enable_if, detail::mp_exp -inline detail::mp_exp, typename detail::mp_exp::left_type > - operator - (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, typename detail::mp_exp::left_type > + operator - (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); + return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); } template -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator - (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator - (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); } template -inline detail::mp_exp, mp_number > - operator - (const mp_number& a, const detail::mp_exp >& b) +inline detail::mp_exp, mp_number > + operator - (const mp_number& a, const detail::mp_exp >& b) { - return detail::mp_exp, mp_number >(a, b.left_ref()); + return detail::mp_exp, mp_number >(a, b.left_ref()); } template -inline detail::mp_exp, mp_number > > - operator - (const detail::mp_exp >& a, const mp_number& b) +inline detail::mp_exp, mp_number > > + operator - (const detail::mp_exp >& a, const mp_number& b) { - return detail::mp_exp, mp_number > >( - detail::mp_exp, mp_number >(b, a.left_ref())); + return detail::mp_exp, mp_number > >( + detail::mp_exp, mp_number >(b, a.left_ref())); } template -inline typename enable_if, detail::mp_exp, V > > >::type - operator - (const detail::mp_exp >& a, const V& b) +inline typename enable_if, detail::mp_exp, V > > >::type + operator - (const detail::mp_exp >& a, const V& b) { - return detail::mp_exp, V > >(detail::mp_exp, V >(a.left_ref(), b)); + return detail::mp_exp, V > >(detail::mp_exp, V >(a.left_ref(), b)); } template -inline typename enable_if, detail::mp_exp > >::type - operator - (const V& a, const detail::mp_exp >& b) +inline typename enable_if, detail::mp_exp > >::type + operator - (const V& a, const detail::mp_exp >& b) { - return detail::mp_exp >(a, b.left_ref()); + return detail::mp_exp >(a, b.left_ref()); } // // Multiplication: // template -inline detail::mp_exp, mp_number > - operator * (const mp_number& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator * (const mp_number& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template -inline typename enable_if, detail::mp_exp, V > >::type - operator * (const mp_number& a, const V& b) +inline typename enable_if, detail::mp_exp, V > >::type + operator * (const mp_number& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } template -inline typename enable_if, detail::mp_exp > >::type - operator * (const V& a, const mp_number& b) +inline typename enable_if, detail::mp_exp > >::type + operator * (const V& a, const mp_number& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } template -inline detail::mp_exp, detail::mp_exp > - operator * (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, detail::mp_exp > + operator * (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } template -inline detail::mp_exp, mp_number > - operator * (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator * (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template inline detail::mp_exp, detail::mp_exp > @@ -749,79 +749,79 @@ inline typename enable_if, detail::mp_exp -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator * (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator * (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type > (a, b.left_ref())); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type > (a, b.left_ref())); } template -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator * (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator * (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); } template -inline detail::mp_exp, mp_number > > - operator * (const mp_number& a, const detail::mp_exp >& b) +inline detail::mp_exp, mp_number > > + operator * (const mp_number& a, const detail::mp_exp >& b) { - return detail::mp_exp, mp_number > >( - detail::mp_exp, mp_number >(a, b.left_ref())); + return detail::mp_exp, mp_number > >( + detail::mp_exp, mp_number >(a, b.left_ref())); } template -inline detail::mp_exp, mp_number > > - operator * (const detail::mp_exp >& a, const mp_number& b) +inline detail::mp_exp, mp_number > > + operator * (const detail::mp_exp >& a, const mp_number& b) { - return detail::mp_exp, mp_number > >( - detail::mp_exp, mp_number >(b, a.left_ref())); + return detail::mp_exp, mp_number > >( + detail::mp_exp, mp_number >(b, a.left_ref())); } template -inline typename enable_if, detail::mp_exp, V > > >::type - operator * (const detail::mp_exp >& a, const V& b) +inline typename enable_if, detail::mp_exp, V > > >::type + operator * (const detail::mp_exp >& a, const V& b) { - return detail::mp_exp, V > > ( - detail::mp_exp, V >(a.left_ref(), b)); + return detail::mp_exp, V > > ( + detail::mp_exp, V >(a.left_ref(), b)); } template -inline typename enable_if, detail::mp_exp, V > > >::type - operator * (const V& a, const detail::mp_exp >& b) +inline typename enable_if, detail::mp_exp, V > > >::type + operator * (const V& a, const detail::mp_exp >& b) { - return detail::mp_exp, V > >( - detail::mp_exp, V >(b.left_ref(), a)); + return detail::mp_exp, V > >( + detail::mp_exp, V >(b.left_ref(), a)); } // // Division: // template -inline detail::mp_exp, mp_number > - operator / (const mp_number& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator / (const mp_number& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template -inline typename enable_if, detail::mp_exp, V > >::type - operator / (const mp_number& a, const V& b) +inline typename enable_if, detail::mp_exp, V > >::type + operator / (const mp_number& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } template -inline typename enable_if, detail::mp_exp > >::type - operator / (const V& a, const mp_number& b) +inline typename enable_if, detail::mp_exp > >::type + operator / (const V& a, const mp_number& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } template -inline detail::mp_exp, detail::mp_exp > - operator / (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, detail::mp_exp > + operator / (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } template -inline detail::mp_exp, mp_number > - operator / (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator / (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template inline detail::mp_exp, detail::mp_exp > @@ -845,79 +845,79 @@ inline typename enable_if, detail::mp_exp -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator / (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator / (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref())); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref())); } template -inline detail::mp_exp::left_type, mp_number > > - operator / (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp::left_type, mp_number > > + operator / (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp::left_type, mp_number > >( - detail::mp_exp::left_type, mp_number >(a.left_ref(), b)); + return detail::mp_exp::left_type, mp_number > >( + detail::mp_exp::left_type, mp_number >(a.left_ref(), b)); } template -inline detail::mp_exp, mp_number > > - operator / (const mp_number& a, const detail::mp_exp >& b) +inline detail::mp_exp, mp_number > > + operator / (const mp_number& a, const detail::mp_exp >& b) { - return detail::mp_exp, mp_number > >( - detail::mp_exp, mp_number >(a, b.left_ref())); + return detail::mp_exp, mp_number > >( + detail::mp_exp, mp_number >(a, b.left_ref())); } template -inline detail::mp_exp, mp_number > > - operator / (const detail::mp_exp >& a, const mp_number& b) +inline detail::mp_exp, mp_number > > + operator / (const detail::mp_exp >& a, const mp_number& b) { - return detail::mp_exp, mp_number > >( - detail::mp_exp, mp_number >(a.left_ref(), b)); + return detail::mp_exp, mp_number > >( + detail::mp_exp, mp_number >(a.left_ref(), b)); } template -inline typename enable_if, detail::mp_exp, V > > >::type - operator / (const detail::mp_exp >& a, const V& b) +inline typename enable_if, detail::mp_exp, V > > >::type + operator / (const detail::mp_exp >& a, const V& b) { - return detail::mp_exp, V > >( - detail::mp_exp, V>(a.left_ref(), b)); + return detail::mp_exp, V > >( + detail::mp_exp, V>(a.left_ref(), b)); } template -inline typename enable_if, detail::mp_exp > > >::type - operator / (const V& a, const detail::mp_exp >& b) +inline typename enable_if, detail::mp_exp > > >::type + operator / (const V& a, const detail::mp_exp >& b) { - return detail::mp_exp > >( - detail::mp_exp >(a, b.left_ref())); + return detail::mp_exp > >( + detail::mp_exp >(a, b.left_ref())); } // // Modulus: // template -inline detail::mp_exp, mp_number > - operator % (const mp_number& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator % (const mp_number& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template -inline typename enable_if, detail::mp_exp, V > >::type - operator % (const mp_number& a, const V& b) +inline typename enable_if, detail::mp_exp, V > >::type + operator % (const mp_number& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } template -inline typename enable_if, detail::mp_exp > >::type - operator % (const V& a, const mp_number& b) +inline typename enable_if, detail::mp_exp > >::type + operator % (const V& a, const mp_number& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } template -inline detail::mp_exp, detail::mp_exp > - operator % (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, detail::mp_exp > + operator % (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } template -inline detail::mp_exp, mp_number > - operator % (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator % (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template inline detail::mp_exp, detail::mp_exp > @@ -941,10 +941,10 @@ inline typename enable_if, detail::mp_exp -inline typename enable_if, detail::mp_exp, I > >::type - operator << (const mp_number& a, const I& b) +inline typename enable_if, detail::mp_exp, I > >::type + operator << (const mp_number& a, const I& b) { - return detail::mp_exp, I>(a, b); + return detail::mp_exp, I>(a, b); } template inline typename enable_if, detail::mp_exp, I> >::type @@ -956,10 +956,10 @@ inline typename enable_if, detail::mp_exp -inline typename enable_if, detail::mp_exp, I > >::type - operator >> (const mp_number& a, const I& b) +inline typename enable_if, detail::mp_exp, I > >::type + operator >> (const mp_number& a, const I& b) { - return detail::mp_exp, I>(a, b); + return detail::mp_exp, I>(a, b); } template inline typename enable_if, detail::mp_exp, I> >::type @@ -971,34 +971,34 @@ inline typename enable_if, detail::mp_exp -inline detail::mp_exp, mp_number > - operator & (const mp_number& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator & (const mp_number& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template -inline typename enable_if, detail::mp_exp, V > >::type - operator & (const mp_number& a, const V& b) +inline typename enable_if, detail::mp_exp, V > >::type + operator & (const mp_number& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } template -inline typename enable_if, detail::mp_exp > >::type - operator & (const V& a, const mp_number& b) +inline typename enable_if, detail::mp_exp > >::type + operator & (const V& a, const mp_number& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } template -inline detail::mp_exp, detail::mp_exp > - operator & (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, detail::mp_exp > + operator & (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } template -inline detail::mp_exp, mp_number > - operator & (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator & (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template inline detail::mp_exp, detail::mp_exp > @@ -1022,34 +1022,34 @@ inline typename enable_if, detail::mp_exp -inline detail::mp_exp, mp_number > - operator| (const mp_number& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator| (const mp_number& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template -inline typename enable_if, detail::mp_exp, V > >::type - operator| (const mp_number& a, const V& b) +inline typename enable_if, detail::mp_exp, V > >::type + operator| (const mp_number& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } template -inline typename enable_if, detail::mp_exp > >::type - operator| (const V& a, const mp_number& b) +inline typename enable_if, detail::mp_exp > >::type + operator| (const V& a, const mp_number& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } template -inline detail::mp_exp, detail::mp_exp > - operator| (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, detail::mp_exp > + operator| (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } template -inline detail::mp_exp, mp_number > - operator| (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator| (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template inline detail::mp_exp, detail::mp_exp > @@ -1073,34 +1073,34 @@ inline typename enable_if, detail::mp_exp -inline detail::mp_exp, mp_number > - operator^ (const mp_number& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator^ (const mp_number& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template -inline typename enable_if, detail::mp_exp, V > >::type - operator^ (const mp_number& a, const V& b) +inline typename enable_if, detail::mp_exp, V > >::type + operator^ (const mp_number& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } template -inline typename enable_if, detail::mp_exp > >::type - operator^ (const V& a, const mp_number& b) +inline typename enable_if, detail::mp_exp > >::type + operator^ (const V& a, const mp_number& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } template -inline detail::mp_exp, detail::mp_exp > - operator^ (const mp_number& a, const detail::mp_exp& b) +inline detail::mp_exp, detail::mp_exp > + operator^ (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } template -inline detail::mp_exp, mp_number > - operator^ (const detail::mp_exp& a, const mp_number& b) +inline detail::mp_exp, mp_number > + operator^ (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } template inline detail::mp_exp, detail::mp_exp > @@ -1134,15 +1134,15 @@ enum number_category_type template struct number_category : public mpl::int_ {}; -template -struct number_category > : public number_category{}; +template +struct number_category > : public number_category{}; template struct number_category > : public number_category::result_type>{}; template struct component_type; -template -struct component_type > : public component_type{}; +template +struct component_type > : public component_type{}; template struct component_type > : public component_type::result_type>{}; diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/fixed_int.hpp index 85a6d339..ff59dbef 100644 --- a/include/boost/multiprecision/fixed_int.hpp +++ b/include/boost/multiprecision/fixed_int.hpp @@ -1517,10 +1517,10 @@ typedef mp_number > mp_int512_t; namespace std{ -template -class numeric_limits > > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; struct initializer { @@ -1591,9 +1591,9 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template -typename numeric_limits > >::initializer const - numeric_limits > >::init; +template +typename numeric_limits, ExpressionTemplates> >::initializer const + numeric_limits, ExpressionTemplates> >::init; } #endif diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index f2104de9..47eb5f1b 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1816,10 +1816,10 @@ namespace std{ // // numeric_limits [partial] specializations for the types declared in this header: // -template -class numeric_limits > > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; // @@ -1924,13 +1924,13 @@ private: static const data_initializer initializer; }; -template -const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; +template +const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; -template<> -class numeric_limits > > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; static number_type (min)() BOOST_MP_NOEXCEPT { return number_type(); } @@ -1966,10 +1966,10 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template<> -class numeric_limits +template +class numeric_limits > { - typedef boost::multiprecision::mpz_int number_type; + typedef boost::multiprecision::mp_number number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; // @@ -2015,10 +2015,10 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template<> -class numeric_limits +template +class numeric_limits > { - typedef boost::multiprecision::mpq_rational number_type; + typedef boost::multiprecision::mp_number number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; // diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 22e18403..2c139de8 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -23,10 +23,10 @@ namespace boost{ namespace multiprecision{ -template +template class mp_number { - typedef mp_number self_type; + typedef mp_number self_type; public: typedef Backend backend_type; mp_number(){} @@ -49,8 +49,11 @@ public: m_backend = canonical_value(v); } */ - template - mp_number(const mp_number& val, typename enable_if >::type* dummy1 = 0) + template + mp_number(const mp_number& val) : m_backend(val.m_backend) {} + + template + mp_number(const mp_number& val, typename enable_if >::type* dummy1 = 0) { m_backend = val.backend(); } @@ -60,8 +63,8 @@ public: using default_ops::assign_components; assign_components(m_backend, canonical_value(v1), canonical_value(v2)); } - template - mp_number(const mp_number& v1, const mp_number& v2, typename enable_if >::type* dummy1 = 0) + template + mp_number(const mp_number& v1, const mp_number& v2, typename enable_if >::type* dummy1 = 0) { using default_ops::assign_components; assign_components(m_backend, v1.backend(), v2.backend()); @@ -85,7 +88,7 @@ public: } template - typename enable_if, is_same, is_convertible >, mp_number& >::type + typename enable_if, is_same, is_convertible >, mp_number& >::type operator=(const V& v) { m_backend = canonical_value(v); @@ -93,15 +96,22 @@ public: } template - typename enable_if, mpl::not_, is_same, is_convertible > > >, mp_number& >::type + typename enable_if, mpl::not_, is_same, is_convertible > > >, mp_number& >::type operator=(const V& v) { m_backend = v; return *this; } + template + mp_number& operator=(const mp_number& v) + { + m_backend = v.backend(); + return *this; + } + template - typename enable_if, mp_number& >::type + typename enable_if, mp_number& >::type operator=(const mp_number& v) { m_backend = v.backend(); @@ -147,7 +157,7 @@ public: } template - typename enable_if, mp_number& >::type + typename enable_if, mp_number& >::type operator+=(const V& v) { using default_ops::eval_add; @@ -178,7 +188,7 @@ public: } template - typename enable_if, mp_number& >::type + typename enable_if, mp_number& >::type operator-=(const V& v) { using default_ops::eval_subtract; @@ -211,7 +221,7 @@ public: } template - typename enable_if, mp_number& >::type + typename enable_if, mp_number& >::type operator*=(const V& v) { using default_ops::eval_multiply; @@ -242,7 +252,7 @@ public: return *this; } template - typename enable_if, mp_number& >::type + typename enable_if, mp_number& >::type operator%=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); @@ -330,7 +340,7 @@ public: } template - typename enable_if, mp_number& >::type + typename enable_if, mp_number& >::type operator/=(const V& v) { using default_ops::eval_divide; @@ -364,7 +374,7 @@ public: } template - typename enable_if, mp_number& >::type + typename enable_if, mp_number& >::type operator&=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); @@ -399,7 +409,7 @@ public: } template - typename enable_if, mp_number& >::type + typename enable_if, mp_number& >::type operator|=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); @@ -432,7 +442,7 @@ public: } template - typename enable_if, mp_number& >::type + typename enable_if, mp_number& >::type operator^=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); @@ -507,7 +517,7 @@ public: // // Comparison: // - int compare(const mp_number& o)const + int compare(const mp_number& o)const { return m_backend.compare(o.m_backend); } @@ -1377,7 +1387,7 @@ private: template bool contains_self(const Exp& e, mpl::int_<0> const&)const { - return is_floatly_self(e.value()); + return is_realy_self(e.value()); } template bool contains_self(const Exp& e, mpl::int_<1> const&)const @@ -1413,7 +1423,7 @@ private: template bool is_self(const Exp& e, mpl::int_<0> const&)const { - return is_floatly_self(e.value()); + return is_realy_self(e.value()); } template bool is_self(const Exp& e, mpl::int_ const&)const @@ -1422,8 +1432,8 @@ private: } template - bool is_floatly_self(const Val&)const { return false; } - bool is_floatly_self(const self_type& v)const { return &v == this; } + bool is_realy_self(const Val&)const { return false; } + bool is_realy_self(const self_type& v)const { return &v == this; } static const Backend& canonical_value(const self_type& v){ return v.m_backend; } template @@ -1439,32 +1449,32 @@ private: namespace detail { -template -inline int mp_number_compare(const mp_number& a, const mp_number& b) +template +inline int mp_number_compare(const mp_number& a, const mp_number& b) { return a.compare(b); } -template -inline int mp_number_compare(const mp_number& a, const mp_exp& b) +template +inline int mp_number_compare(const mp_number& a, const mp_exp& b) { - return a.compare(mp_number(b)); + return a.compare(mp_number(b)); } -template -inline int mp_number_compare(const mp_exp& a, const mp_number& b) +template +inline int mp_number_compare(const mp_exp& a, const mp_number& b) { - return -b.compare(mp_number(a)); + return -b.compare(mp_number(a)); } -template -inline int mp_number_compare(const mp_number& a, const Val b) +template +inline int mp_number_compare(const mp_number& a, const Val b) { return a.compare(b); } -template -inline int mp_number_compare(const Val a, const mp_number& b) +template +inline int mp_number_compare(const Val a, const mp_number& b) { return -b.compare(a); } @@ -1569,8 +1579,8 @@ inline typename boost::enable_if, bool>: return 0 < detail::mp_number_compare(a, b); } -template -inline std::ostream& operator << (std::ostream& os, const mp_number& r) +template +inline std::ostream& operator << (std::ostream& os, const mp_number& r) { std::streamsize d = os.precision(); std::string s = r.str(d, os.flags()); @@ -1598,8 +1608,8 @@ inline std::ostream& operator << (std::ostream& os, const mp_exp -inline std::istream& operator >> (std::istream& is, mp_number& r) +template +inline std::istream& operator >> (std::istream& is, mp_number& r) { std::string s; is >> s; @@ -1607,8 +1617,8 @@ inline std::istream& operator >> (std::istream& is, mp_number& r) return is; } -template -inline void swap(mp_number& a, mp_number& b) +template +inline void swap(mp_number& a, mp_number& b) { a.swap(b); } @@ -1618,11 +1628,11 @@ inline void swap(mp_number& a, mp_number& b) template class rational; -template -inline std::istream& operator >> (std::istream& is, rational >& r) +template +inline std::istream& operator >> (std::istream& is, rational >& r) { std::string s1; - multiprecision::mp_number v1, v2; + multiprecision::mp_number v1, v2; char c; bool have_hex = false; @@ -1653,38 +1663,38 @@ inline std::istream& operator >> (std::istream& is, rational -typename enable_if, bool>::type operator == (const rational >& a, const Arithmetic& b) +template +typename enable_if, bool>::type operator == (const rational >& a, const Arithmetic& b) { - return a == multiprecision::mp_number(b); + return a == multiprecision::mp_number(b); } -template -typename enable_if, bool>::type operator == (const Arithmetic& b, const rational >& a) +template +typename enable_if, bool>::type operator == (const Arithmetic& b, const rational >& a) { - return a == multiprecision::mp_number(b); + return a == multiprecision::mp_number(b); } -template -typename enable_if, bool>::type operator != (const rational >& a, const Arithmetic& b) +template +typename enable_if, bool>::type operator != (const rational >& a, const Arithmetic& b) { - return a != multiprecision::mp_number(b); + return a != multiprecision::mp_number(b); } -template -typename enable_if, bool>::type operator != (const Arithmetic& b, const rational >& a) +template +typename enable_if, bool>::type operator != (const Arithmetic& b, const rational >& a) { - return a != multiprecision::mp_number(b); + return a != multiprecision::mp_number(b); } -template -inline multiprecision::mp_number numerator(const rational >& a) +template +inline multiprecision::mp_number numerator(const rational >& a) { return a.numerator(); } -template -inline multiprecision::mp_number denominator(const rational >& a) +template +inline multiprecision::mp_number denominator(const rational >& a) { return a.denominator(); } diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 9f5e3ce1..cdb38d26 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -1011,6 +1011,11 @@ inline int digits() { return boost::multiprecision::backends::detail::get_default_precision(); } +template <> +inline int digits, false> >() +{ + return boost::multiprecision::backends::detail::get_default_precision(); +} } @@ -1021,10 +1026,10 @@ namespace std{ // // numeric_limits [partial] specializations for the types declared in this header: // -template -class numeric_limits > > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT @@ -1153,13 +1158,13 @@ private: static const data_initializer initializer; }; -template -const typename numeric_limits > >::data_initializer numeric_limits > >::initializer; +template +const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; -template<> -class numeric_limits > > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number > number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; static number_type (min)() BOOST_MP_NOEXCEPT { return number_type(0); } diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index 2436147f..c01af0fd 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -179,11 +179,11 @@ inline void assign_components(rational_adapter& result, const V& v1, result.data().assign(v1, v2); } -template -struct number_category > : public mpl::int_{}; - } // namespace backends +template +struct number_category > : public mpl::int_{}; + using boost::multiprecision::backends::rational_adapter; template diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index a30a3868..50bc1785 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -457,10 +457,10 @@ typedef mp_number mp_rational; namespace std{ -template<> -class numeric_limits +template +class numeric_limits > { - typedef boost::multiprecision::mp_int number_type; + typedef boost::multiprecision::mp_number number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; // diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 47dc5082..31d1bf74 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -128,26 +128,12 @@ run test_arithmetic.cpp $(TOMMATH) [ check-target-builds ../config//has_tommath : : no ] : test_arithmetic_tommath_br ; -run test_arithmetic.cpp - : # command line - : # input files - : # requirements - TEST_FIXED_INT1 - : test_arithmetic_fixed_int1 ; - -run test_arithmetic.cpp - : # command line - : # input files - : # requirements - TEST_FIXED_INT2 - : test_arithmetic_fixed_int2 ; - run test_arithmetic.cpp : # command line : # input files : # requirements TEST_CPP_INT - : test_arithmetic_fixed_cpp_int ; + : test_arithmetic_cpp_int ; run test_arithmetic.cpp : # command line @@ -233,13 +219,6 @@ run test_numeric_limits.cpp TEST_CPP_INT : test_numeric_limits_cpp_int ; -run test_numeric_limits.cpp - : # command line - : # input files - : # requirements - TEST_FIXED_INT - : test_numeric_limits_fixed_int ; - run test_exp.cpp gmp : # command line : # input files @@ -612,23 +591,8 @@ run test_int_io.cpp : # command line : # input files : # requirements - TEST_FIXED_INT1 - : test_int_io_fixed_int1 ; - -run test_int_io.cpp - : # command line - : # input files - : # requirements - TEST_FIXED_INT2 - : test_int_io_fixed_int2 ; - -run test_fixed_int.cpp gmp - : # command line - : # input files - : # requirements - [ check-target-builds ../config//has_gmp : : no ] - release # otherwise runtime is too slow!! - ; + TEST_CPP_INT + : test_int_io_cpp_int ; run test_cpp_int.cpp gmp : # command line @@ -772,6 +736,13 @@ if ! $(disable-concepts) TEST_CPP_DEC_FLOAT : mp_number_concept_check_cpp_dec_float ; + run mp_number_concept_check.cpp + : # command line + : # input files + : # requirements + TEST_CPP_DEC_FLOAT_NO_ET + : mp_number_concept_check_cpp_dec_float_no_et ; + run mp_number_concept_check.cpp : # command line : # input files diff --git a/test/mp_number_concept_check.cpp b/test/mp_number_concept_check.cpp index 15d56a27..07c6861a 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -22,7 +22,7 @@ #if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ - && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) # define TEST_MPF_50 # define TEST_BACKEND # define TEST_MPZ @@ -32,6 +32,7 @@ # define TEST_MPFR_17 # define TEST_MPFR_30 # define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -48,7 +49,7 @@ #ifdef TEST_BACKEND #include #endif -#ifdef TEST_CPP_DEC_FLOAT +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) #include #endif #if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) @@ -84,6 +85,9 @@ void foo() #ifdef TEST_CPP_DEC_FLOAT instantiate(boost::multiprecision::cpp_dec_float_50()); #endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + instantiate(boost::multiprecision::mp_number, false>()); +#endif } int main() diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index b7e53e1d..ea66d0cf 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -1012,6 +1012,7 @@ int main() #endif #ifdef TEST_CPP_DEC_FLOAT test(); + test, false> >(); #endif #ifdef TEST_MPFR test(); @@ -1050,6 +1051,7 @@ int main() test > >(); test > >(); test(); + test, false> >(); #endif #ifdef TEST_CPP_INT_BR test(); diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp index 1078ac8e..704ec26c 100644 --- a/test/test_int_io.cpp +++ b/test/test_int_io.cpp @@ -9,11 +9,12 @@ # define _SCL_SECURE_NO_WARNINGS #endif -#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) && !defined(TEST_FIXED_INT1) && !defined(TEST_FIXED_INT2) +#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) && !defined(TEST_FIXED_INT1) && !defined(TEST_FIXED_INT2) && !defined(TEST_CPP_INT) # define TEST_TOMMATH # define TEST_MPZ # define TEST_FIXED_INT1 # define TEST_FIXED_INT2 +# define TEST_CPP_INT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -33,6 +34,9 @@ #if defined(TEST_FIXED_INT1) || defined(TEST_FIXED_INT2) #include #endif +#ifdef TEST_CPP_INT +#include +#endif #include #include @@ -136,6 +140,11 @@ int main() test_round_trip(); test_round_trip > >(); test_round_trip > >(); +#endif +#ifdef TEST_CPP_INT + test_round_trip > >(); + test_round_trip > >(); + test_round_trip > >(); #endif return boost::report_errors(); } From e1b23af8f5b903a5925aea8d1ed36dccc2892de1 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 13 Mar 2012 18:40:52 +0000 Subject: [PATCH 131/256] Add files missing from last commit, and add new examples to tests. [SVN r77324] --- doc/multiprecision.qbk | 2 +- example/cpp_int_snips.cpp | 64 ++++ example/fixed_int_snips.cpp | 34 -- .../boost/multiprecision/detail/no_et_ops.hpp | 303 ++++++++++++++++++ test/Jamfile.v2 | 1 + 5 files changed, 369 insertions(+), 35 deletions(-) create mode 100644 example/cpp_int_snips.cpp delete mode 100644 example/fixed_int_snips.cpp create mode 100644 include/boost/multiprecision/detail/no_et_ops.hpp diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index d7c313d7..52f85764 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -22,7 +22,7 @@ [import ../example/mpfr_snips.cpp] [import ../example/cpp_dec_float_snips.cpp] [import ../example/tommath_snips.cpp] -[import ../example/fixed_int_snips.cpp] +[import ../example/cpp_int_snips.cpp] [template mpfr[] [@http://www.mpfr.org MPFR]] [template gmp[] [@http://gmplib.org GMP]] diff --git a/example/cpp_int_snips.cpp b/example/cpp_int_snips.cpp new file mode 100644 index 00000000..eb2827c7 --- /dev/null +++ b/example/cpp_int_snips.cpp @@ -0,0 +1,64 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include + +void t1() +{ + //[cpp_int_eg + //=#include + + using namespace boost::multiprecision; + + mp_int128_t v = 1; + + // Do some fixed precision arithmetic: + for(unsigned i = 1; i <= 20; ++i) + v *= i; + + std::cout << v << std::endl; // prints 20! + + // Try again at arbitrary precision: + cpp_int u = 1; + for(unsigned i = 1; i <= 100; ++i) + u *= i; + + std::cout << u << std::endl; // prints 100! + + //] +} + +void t3() +{ + //[cpp_rat_eg + //=#include + + using namespace boost::multiprecision; + + cpp_rational v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + v /= 10; + + std::cout << v << std::endl; // prints 1000! / 10 + std::cout << numerator(v) << std::endl; + std::cout << denominator(v) << std::endl; + + cpp_rational w(2, 3); // component wise constructor + std::cout << w << std::endl; // prints 2/3 + //] +} + + +int main() +{ + t1(); + t3(); + return 0; +} + diff --git a/example/fixed_int_snips.cpp b/example/fixed_int_snips.cpp deleted file mode 100644 index e076b60f..00000000 --- a/example/fixed_int_snips.cpp +++ /dev/null @@ -1,34 +0,0 @@ -/////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ - -#include -#include - -void t1() -{ - //[fixed_int_eg - //=#include - - using namespace boost::multiprecision; - - mp_int128_t v = 1; - - // Do some arithmetic: - for(unsigned i = 1; i <= 20; ++i) - v *= i; - - std::cout << v << std::endl; // prints 20! - v = -v; - std::cout << std::hex << v << std::endl; // prints 2's complement representation - - //] -} - -int main() -{ - t1(); - return 0; -} - diff --git a/include/boost/multiprecision/detail/no_et_ops.hpp b/include/boost/multiprecision/detail/no_et_ops.hpp new file mode 100644 index 00000000..3710c644 --- /dev/null +++ b/include/boost/multiprecision/detail/no_et_ops.hpp @@ -0,0 +1,303 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MP_NO_ET_OPS_HPP +#define BOOST_MP_NO_ET_OPS_HPP + +namespace boost{ +namespace multiprecision{ + +// +// Operators for non-expression template enabled mp_number. +// NOTE: this is not a complete header - really just a suffix to default_ops.hpp. +// NOTE: these operators have to be defined after the methods in default_ops.hpp. +// +template +inline mp_number operator - (const mp_number& v) +{ + mp_number result(v); + result.backend().negate(); + return result; +} +template +inline mp_number operator ~ (const mp_number& v) +{ + mp_number result; + eval_complement(result.backend(), v.backend()); + return result; +} +// +// Addition: +// +template +inline mp_number operator + (const mp_number& a, const mp_number& b) +{ + mp_number result; + using default_ops::eval_add; + eval_add(result.backend(), a.backend(), b.backend()); + return result; +} +template +inline typename enable_if, mp_number >::type + operator + (const mp_number& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_add; + eval_add(result.backend(), a.backend(), static_cast(b)); + return result; +} +template +inline typename enable_if, mp_number >::type + operator + (const V& a, const mp_number& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_add; + eval_add(result.backend(), b.backend(), static_cast(a)); + return result; +} +// +// Subtraction: +// +template +inline mp_number operator - (const mp_number& a, const mp_number& b) +{ + mp_number result; + using default_ops::eval_subtract; + eval_subtract(result.backend(), a.backend(), b.backend()); + return result; +} +template +inline typename enable_if, mp_number >::type + operator - (const mp_number& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_subtract; + eval_subtract(result.backend(), a.backend(), static_cast(b)); + return result; +} +template +inline typename enable_if, mp_number >::type + operator - (const V& a, const mp_number& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_subtract; + eval_subtract(result.backend(), static_cast(a), b.backend()); + return result; +} +// +// Multiply: +// +template +inline mp_number operator * (const mp_number& a, const mp_number& b) +{ + mp_number result; + using default_ops::eval_multiply; + eval_multiply(result.backend(), a.backend(), b.backend()); + return result; +} +template +inline typename enable_if, mp_number >::type + operator * (const mp_number& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_multiply; + eval_multiply(result.backend(), a.backend(), static_cast(b)); + return result; +} +template +inline typename enable_if, mp_number >::type + operator * (const V& a, const mp_number& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_multiply; + eval_multiply(result.backend(), b.backend(), static_cast(a)); + return result; +} +// +// divide: +// +template +inline mp_number operator / (const mp_number& a, const mp_number& b) +{ + mp_number result; + using default_ops::eval_divide; + eval_divide(result.backend(), a.backend(), b.backend()); + return result; +} +template +inline typename enable_if, mp_number >::type + operator / (const mp_number& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_divide; + eval_divide(result.backend(), a.backend(), static_cast(b)); + return result; +} +template +inline typename enable_if, mp_number >::type + operator / (const V& a, const mp_number& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_divide; + eval_divide(result.backend(), static_cast(a), b.backend()); + return result; +} +// +// modulus: +// +template +inline mp_number operator % (const mp_number& a, const mp_number& b) +{ + mp_number result; + using default_ops::eval_modulus; + eval_modulus(result.backend(), a.backend(), b.backend()); + return result; +} +template +inline typename enable_if, mp_number >::type + operator % (const mp_number& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_modulus; + eval_modulus(result.backend(), a.backend(), static_cast(b)); + return result; +} +template +inline typename enable_if, mp_number >::type + operator % (const V& a, const mp_number& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_modulus; + eval_modulus(result.backend(), static_cast(a), b.backend()); + return result; +} +// +// Bitwise or: +// +template +inline mp_number operator | (const mp_number& a, const mp_number& b) +{ + mp_number result; + using default_ops::eval_bitwise_or; + eval_bitwise_or(result.backend(), a.backend(), b.backend()); + return result; +} +template +inline typename enable_if, mp_number >::type + operator | (const mp_number& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_bitwise_or; + eval_bitwise_or(result.backend(), a.backend(), static_cast(b)); + return result; +} +template +inline typename enable_if, mp_number >::type + operator | (const V& a, const mp_number& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_bitwise_or; + eval_bitwise_or(result.backend(), b.backend(), static_cast(a)); + return result; +} +// +// Bitwise xor: +// +template +inline mp_number operator ^ (const mp_number& a, const mp_number& b) +{ + mp_number result; + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(result.backend(), a.backend(), b.backend()); + return result; +} +template +inline typename enable_if, mp_number >::type + operator ^ (const mp_number& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(result.backend(), a.backend(), static_cast(b)); + return result; +} +template +inline typename enable_if, mp_number >::type + operator ^ (const V& a, const mp_number& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(result.backend(), b.backend(), static_cast(a)); + return result; +} +// +// Bitwise and: +// +template +inline mp_number operator & (const mp_number& a, const mp_number& b) +{ + mp_number result; + using default_ops::eval_bitwise_and; + eval_bitwise_and(result.backend(), a.backend(), b.backend()); + return result; +} +template +inline typename enable_if, mp_number >::type + operator & (const mp_number& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_bitwise_and; + eval_bitwise_and(result.backend(), a.backend(), static_cast(b)); + return result; +} +template +inline typename enable_if, mp_number >::type + operator & (const V& a, const mp_number& b) +{ + typedef typename detail::canonical::type canonical_type; + mp_number result; + using default_ops::eval_bitwise_and; + eval_bitwise_and(result.backend(), b.backend(), static_cast(a)); + return result; +} +// +// shifts: +// +template +inline typename enable_if, mp_number >::type + operator << (const mp_number& a, const I& b) +{ + mp_number result(a); + using default_ops::eval_left_shift; + eval_left_shift(result.backend(), b); + return result; +} +template +inline typename enable_if, mp_number >::type + operator >> (const mp_number& a, const I& b) +{ + mp_number result(a); + using default_ops::eval_right_shift; + eval_right_shift(result.backend(), b); + return result; +} + +}} // namespaces + +#endif // BOOST_MP_NO_ET_OPS_HPP diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 31d1bf74..511e14fb 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -631,6 +631,7 @@ run ../example/mpfr_snips.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] ; run ../example/cpp_dec_float_snips.cpp ; +run ../example/cpp_int_snips.cpp ; run ../example/tommath_snips.cpp $(TOMMATH) : # command line From d82fa61c8131166436783f6694868ee337b047ea Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 14 Mar 2012 18:23:44 +0000 Subject: [PATCH 132/256] Mostly remove references to fixed_int. Update docs. [SVN r77335] --- doc/html/boost_multiprecision/intro.html | 19 +++ .../boost_multiprecision/ref/backendconc.html | 145 ++++++++---------- .../boost_multiprecision/ref/mp_number.html | 90 +++++++---- doc/html/boost_multiprecision/tut.html | 2 +- doc/html/boost_multiprecision/tut/ints.html | 122 +++++++++++---- .../boost_multiprecision/tut/rational.html | 122 ++++++++++++++- doc/html/boost_multiprecision/tut/reals.html | 6 +- doc/html/index.html | 4 +- doc/multiprecision.qbk | 24 +-- example/cpp_int_snips.cpp | 2 +- include/boost/multiprecision/cpp_int.hpp | 11 ++ performance/Jamfile.v2 | 2 +- performance/performance_test.cpp | 12 +- test/test_arithmetic.cpp | 27 +--- test/test_int_io.cpp | 21 +-- test/test_numeric_limits.cpp | 16 +- 16 files changed, 392 insertions(+), 233 deletions(-) diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index 59d5fc82..25367098 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -55,6 +55,19 @@ typedef mp::mp_number<mp::mpfr_float_backend<300> > my_float; +my_float a, b, c; // These variables have 300 decimal digits precision + +

    + We can repeat the above example, but with the expression templates disabled + (for faster compile times, but slower runtimes) by passing a second template + argument to mp_number: +

    +
    #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
+
+namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
+
+typedef mp::mp_number<mp::mpfr_float_backend<300>, false>  my_float;
+
 my_float a, b, c; // These variables have 300 decimal digits precision
    @@ -303,6 +316,12 @@ as one would hope.
    +

    + Finally, note that mp_number + takes a second template argument, which, when set to false + disables all the expression template machinary. The result is much faster to + compile, but slower at runtime. +

    We'll conclude this section by providing some more performance comparisons between these three libraries, again, all are using MPFR diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index 95fe4403..d9633266 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -330,7 +330,7 @@

    - add(b, + eval_add(b, cb)

    @@ -348,7 +348,7 @@

    - subtract(b, + eval_subtract(b, cb)

    @@ -367,7 +367,7 @@

    - multiply(b, + eval_multiply(b, cb)

    @@ -386,7 +386,7 @@

    - divide(b, + eval_divide(b, cb)

    @@ -404,7 +404,7 @@

    - modulus(b, + eval_modulus(b, cb)

    @@ -425,8 +425,7 @@

    - bitwise_and(b, - cb) + eval_bitwise_and(b, cb)

    @@ -446,8 +445,7 @@

    - bitwise_or(b, - cb) + eval_bitwise_or(b, cb)

    @@ -467,8 +465,7 @@

    - bitwise_xor(b, - cb) + eval_bitwise_xor(b, cb)

    @@ -488,8 +485,7 @@

    - complement(b, - cb) + eval_complement(b, cb)

    @@ -509,8 +505,7 @@

    - left_shift(b, - ui) + eval_left_shift(b, ui)

    @@ -530,8 +525,7 @@

    - right_shift(b, - ui) + eval_right_shift(b, ui)

    @@ -551,8 +545,7 @@

    - convert_to(pa, - cb) + eval_convert_to(pa, cb)

    @@ -807,7 +800,7 @@

    - add(b, + eval_add(b, a)

    @@ -827,7 +820,7 @@

    - subtract(b, + eval_subtract(b, a)

    @@ -849,7 +842,7 @@

    - multiply(b, + eval_multiply(b, a)

    @@ -871,7 +864,7 @@

    - divide(b, + eval_divide(b, a)

    @@ -891,7 +884,7 @@

    - modulus(b, + eval_modulus(b, a)

    @@ -914,8 +907,7 @@

    - bitwise_and(b, - a) + eval_bitwise_and(b, a)

    @@ -937,8 +929,7 @@

    - bitwise_or(b, - a) + eval_bitwise_or(b, a)

    @@ -960,8 +951,7 @@

    - bitwise_xor(b, - a) + eval_bitwise_xor(b, a)

    @@ -983,7 +973,7 @@

    - add(b, + eval_add(b, cb, cb2)

    @@ -1003,7 +993,7 @@

    - subtract(b, + eval_subtract(b, cb, cb2)

    @@ -1024,7 +1014,7 @@

    - multiply(b, + eval_multiply(b, cb, cb2)

    @@ -1045,7 +1035,7 @@

    - divide(b, + eval_divide(b, cb, cb2)

    @@ -1066,7 +1056,7 @@

    - add(b, + eval_add(b, cb, a)

    @@ -1087,7 +1077,7 @@

    - subtract(b, + eval_subtract(b, cb, a)

    @@ -1111,7 +1101,7 @@

    - multiply(b, + eval_multiply(b, cb, a)

    @@ -1135,7 +1125,7 @@

    - divide(b, + eval_divide(b, cb, a)

    @@ -1159,7 +1149,7 @@

    - modulus(b, + eval_modulus(b, cb, cb2)

    @@ -1182,9 +1172,7 @@

    - bitwise_and(b, - cb, - cb2) + eval_bitwise_and(b, cb, cb2)

    @@ -1205,9 +1193,7 @@

    - bitwise_or(b, - cb, - cb2) + eval_bitwise_or(b, cb, cb2)

    @@ -1228,9 +1214,7 @@

    - bitwise_xor(b, - cb, - cb2) + eval_bitwise_xor(b, cb, cb2)

    @@ -1251,7 +1235,7 @@

    - add(b, + eval_add(b, a, cb)

    @@ -1274,7 +1258,7 @@

    - subtract(b, + eval_subtract(b, a, cb)

    @@ -1298,7 +1282,7 @@

    - multiply(b, + eval_multiply(b, a, cb)

    @@ -1322,7 +1306,7 @@

    - divide(b, + eval_divide(b, a, cb)

    @@ -1345,7 +1329,7 @@

    - modulus(b, + eval_modulus(b, cb, a)

    @@ -1370,9 +1354,7 @@

    - bitwise_and(b, - cb, - a) + eval_bitwise_and(b, cb, a)

    @@ -1395,9 +1377,7 @@

    - bitwise_or(b, - cb, - a) + eval_bitwise_or(b, cb, a)

    @@ -1420,9 +1400,7 @@

    - bitwise_xor(b, - cb, - a) + eval_bitwise_xor(b, cb, a)

    @@ -1445,7 +1423,7 @@

    - modulus(b, + eval_modulus(b, a, cb)

    @@ -1470,9 +1448,7 @@

    - bitwise_and(b, - a, - cb) + eval_bitwise_and(b, a, cb)

    @@ -1495,9 +1471,7 @@

    - bitwise_or(b, - a, - cb) + eval_bitwise_or(b, a, cb)

    @@ -1520,9 +1494,7 @@

    - bitwise_xor(b, - a, - cb) + eval_bitwise_xor(b, a, cb)

    @@ -1545,9 +1517,7 @@

    - left_shift(b, - cb, - ui) + eval_left_shift(b, cb, ui)

    @@ -1568,9 +1538,7 @@

    - right_shift(b, - cb, - ui) + eval_right_shift(b, cb, ui)

    @@ -1591,7 +1559,7 @@

    - increment(b) + eval_increment(b)

    @@ -1609,7 +1577,7 @@

    - decrement(b) + eval_decrement(b)

    @@ -1627,7 +1595,7 @@

    - is_zero(cb) + eval_is_zero(cb)

    @@ -1644,7 +1612,7 @@

    - get_sign(cb) + eval_get_sign(cb)

    @@ -2102,7 +2070,18 @@
    -
    +
    + + + + + +
    [Note]Note

    + The non-member functions are all named with an "eval_" prefix + to avoid conflicts with template classes of the same name - in point of + fact this naming convension shouldn't be necessary, but rather works around + some compiler bugs. +

    diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html index f039c147..a68c1649 100644 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -23,7 +23,7 @@ 
    namespace boost{ namespace multiprecision{
 
-template <class Backend>
+template <class Backend, bool ExpressionTemplates = true>
 class mp_number
 {
    mp_number();
@@ -94,15 +94,15 @@
 bool operator>=(const see-below&, const see-below&);
 
 // Swap:
-template <class Backend>
-void swap(mp_number<Backend>& a, mp_number<Backend>& b);
+template <class Backend, bool ExpressionTemplates>
+void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
 
 // iostream support:
-template <class Backend>
-std::ostream& operator << (std::ostream& os, const mp_number<Backend>& r);
+template <class Backend, bool ExpressionTemplates>
+std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
 std::ostream& operator << (std::ostream& os, const unmentionable-expression-template-type& r);
-template <class Backend>
-std::istream& operator >> (std::istream& is, mp_number<Backend>& r);
+template <class Backend, bool ExpressionTemplates>
+std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r);
 
 // Non-member function standard library support:
 unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
@@ -163,8 +163,8 @@
 // numeric_limits support:
 namespace std{
 
-template <class Backend>
-struct numeric_limits<boost::multiprecision<Backend> >
+template <class Backend, bool ExpressionTemplates>
+struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
 {
    /* Usual members here */
 };
@@ -175,6 +175,27 @@
 
         Description
       
+
    template <class Backend, bool ExpressionTemplates = true>
+class mp_number;
+
    
+
    
+        Class mp_number has two template
+        arguments:
+      
    
+
    
+
    
+
    
+
    Backend
    
+
    
+              The actual arithmetic backend that does all the work.
+            
    
+
    ExpressionTemplates
    
+
    
+              A boolean value: when true, then expression templates are enabled,
+              otherwise they are disabled.
+            
    
+
    
+
    
 
    mp_number();
 mp_number(see-below);
 mp_number& operator=(see-below);
@@ -235,7 +256,8 @@
       
    
 
      
 
    • 
-            Another mp_number<Backend>.
+            Another mp_number<Backend,
+            ExpressionTemplates>.
           
      • 
 
    • 
             A builtin arithmetic type.
@@ -309,7 +331,7 @@
         the precision of *this
         respectively.
       
      
-
      int compare(const mp_number<Backend>& o)const;
+
      int compare(const mp_number<Backend, ExpressionTemplates>& o)const;
 template <class V>
 typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
 
      
@@ -377,12 +399,25 @@
         In addition, one of the two arguments may be a builtin arithmetic type.
       
      
 
      
-        With the exception of the comparison operators (which always evaluate their
-        arguments and return a bool
-        result), these operators return an "unmentionable" expression template
-        type which defers evaluation of the operator until the result is actually
-        required.
+        The return type of these operators is either:
       
      
+
        
+
      • 
+            An unmentionable-type expression template type when
+            ExpressionTemplates is
+            true.
+          
        • 
+
      • 
+            Type mp_number<Backend,
+            false>
+            when ExpressionTemplates
+            is false.
+          
        • 
+
      • 
+            Type bool if the operator
+            is a comparison operator.
+          
        • 
+
      
 
      
         Finally note that the second argument to the left and right shift operations
         must be a builtin integer type, and that the argument must be positive (negative
@@ -393,8 +428,8 @@
 
         swap
       
-
      template <class Backend>
-void swap(mp_number<Backend>& a, mp_number<Backend>& b);
+
      template <class Backend, ExpressionTemplates>
+void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
 
      
 
      
         Swaps a and b.
@@ -404,12 +439,12 @@
         Iostream
         Support
       
-
      template <class Backend>
-std::ostream& operator << (std::ostream& os, const mp_number<Backend>& r);
-template <class Backend>
+
      template <class Backend, bool ExpressionTemplates>
+std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
+template <class Unspecified...>
 std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r);
-template <class Backend>
-inline std::istream& operator >> (std::istream& is, mp_number<Backend>& r)
+template <class Backend, bool ExpressionTemplates>
+inline std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r)
 
      
 
      
         These operators provided formatted input-output operations on mp_number types, and expression templates
@@ -460,8 +495,9 @@
 
      
         These functions all behave exactly as their standard library counterparts
         do: their argument is either an instance of mp_number
-        or an expression template derived from it; their return value is always an
-        expression template.
+        or an expression template derived from it; If the argument is of type mp_number<Backend, false>
+        then that is also the return type, otherwise the return type is an expression
+        template.
       
      
 
      
         These functions are normally implemented by the Backend type. However, default
@@ -541,8 +577,8 @@
       
 
      namespace std{
 
-template <class Backend>
-struct numeric_limits<boost::multiprecision<Backend> >
+template <class Backend, ExpressionTemplates>
+struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
 {
    /* Usual members here */
 };
diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html
index 896c5a8d..cb05f329 100644
--- a/doc/html/boost_multiprecision/tut.html
+++ b/doc/html/boost_multiprecision/tut.html
@@ -19,7 +19,7 @@
 
    
 
    
 
    Integer Types
    
-
    Real Numbers
    
+
    Floating Point Numbers
    
 
    Rational Number Types
    
 
    
 
    
diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html
index c59d3f9a..e0b55bd3 100644
--- a/doc/html/boost_multiprecision/tut/ints.html
+++ b/doc/html/boost_multiprecision/tut/ints.html
@@ -7,7 +7,7 @@
 
 
 
-
+
 
 
 
    
@@ -130,12 +130,12 @@
    + + + + + + + +

    - fixed_int + cpp_int

    - boost/multiprecision/fixed_int.hpp + boost/multiprecision/cpp_int.hpp

    		@@ -150,7 +150,8 @@

    - Boost licenced fixed precision modular arithmetic integer. + Very versatile, Boost licenced, all C++ integer type which support + both arbitrary precision and fixed precision integer types.

    		@@ -336,47 +337,83 @@ { std::cout << e.what() << std::endl; } -

    - fixed_int + cpp_int 
    namespace boost{ namespace multiprecision{
 
-template <unsigned Digits, bool Signed>
-class fixed_int;
+typedef unspecified-type limb_type;
 
-typedef mp_number<fixed_int<128, false> > mp_uint128_t;
-typedef mp_number<fixed_int<256, false> > mp_uint256_t;
-typedef mp_number<fixed_int<512, false> > mp_uint512_t;
+template <unsigned MinDigits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
+class cpp_int_backend;
 
-typedef mp_number<fixed_int<128, true> > mp_int128_t;
-typedef mp_number<fixed_int<256, true> > mp_int256_t;
-typedef mp_number<fixed_int<512, true> > mp_int512_t;
+typedef mp_number<cpp_int_backend<> >           cpp_int;    // arbitrary precision integer
+typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
+typedef mp_number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
+
+// Fixed precision unsigned types:
+typedef mp_number<cpp_int_backend<128, false, void> >   mp_uint128_t;
+typedef mp_number<cpp_int_backend<256, false, void> >   mp_uint256_t;
+typedef mp_number<cpp_int_backend<512, false, void> >   mp_uint512_t;
+
+// Fixed precision signed types:
+typedef mp_number<cpp_int_backend<128, true, void> >    mp_int128_t;
+typedef mp_number<cpp_int_backend<256, true, void> >    mp_int256_t;
+typedef mp_number<cpp_int_backend<512, true, void> >    mp_int512_t;
 
 }} // namespaces

    - The fixed_int backend is - used via one of the typedefs boost::multiprecision::mp_uint128_t, - boost::multiprecision::mp_uint256_t, boost::multiprecision::mp_uint512_t, - boost::multiprecision::mp_int128_t, boost::multiprecision::mp_int256_t - or boost::multiprecision::mp_int512_t. It provides both signed and - unsigned integer types with a fixed precision and modular arithmetic with - a 2's complement representation for negative values. In other words it's - designed to work just like a typical built in integer type, but with larger - precision. + The cpp_int_backend type + is used via one of the typedefs boost::multiprecision::cpp_int, + boost::multiprecision::mp_uint128_t, boost::multiprecision::mp_uint256_t, + boost::multiprecision::mp_uint512_t, boost::multiprecision::mp_int128_t, + boost::multiprecision::mp_int256_t or boost::multiprecision::mp_int512_t.

    +

    + This backend is the "Swiss Army Knife" of integer types as it can + represent both fixed and arbitrary precision integer types, and both signed + and unsigned types. There are three template arguments: +

    +
    +

    +
    +
    MinBits
    +

    + Determines the number of Bits to store directly within the object before + resorting to dynamic memory allocation. When zero, this field is determined + automatically based on how many bits can be stored in union with the + dynamic storage header: setting a larger value may improve performance + as larger integer values will be stored internally before memory allocation + is required. When the Allocator parameter is type void, + then this field determines the total number of bits in the resulting + fixed precision type. +

    +
    Signed
    +

    + Determines whether the resulting type is signed or not. Note that for + arbitrary precision types (where the Allocator parameter is non-void), + then this parameter must be true. + For fixed precision types then this type may be either true (type is signed), or false (type is unsigned). +

    +
    Allocator
    +

    + The allocator to use for dymamic memory allocation, or type void if this is to be a fixed precision + type. +

    +
    +

    Things you should know when using this type:

    • - Default constructed fixed_int's - have indeterminate value - just like normal built in integers. + Default constructed cpp_int_backend's + have the value zero.
    • Division by zero results in a std::runtime_error @@ -387,9 +424,26 @@ results in a std::runtime_error being thrown.
    • - Since the precision of fixed_int - is necessarily limited, care should be taken to avoid numeric overflow - when using this type unless you actually want modulo-arithmetic behavior. + Since the precision of cpp_int_backend + is necessarily limited when the allocator parameter is void, care should + be taken to avoid numeric overflow when using this type unless you actually + want modulo-arithmetic behavior. +
      • +
    • + The type uses a sign-magnitude representation internally, so type mp_int128_t has 128-bits of precision + plus an extra sign bit. In this respect the behaviour of these types + differs from built-in 2's complement types. In might be tempting to use + a 127-bit type instead, and indeed this does work, but behaviour is still + slightly different from a 2's complement built-in type as the min and + max values are identical (apart from the sign), where as they differ + by one for a true 2's complement type. That said it should be noted that + there's no requirement for built-in types to be 2's complement either + - it's simply that this is the most common format by far. +
      • +
    • + Attempting to print negative values as either an Octal or Hexadecimal + string results in a std::runtime_error + being thrown, this is a direct consequence of the sign-magnitude representation.
    @@ -398,20 +452,24 @@

    -
    #include <boost/multiprecision/fixed_int.hpp>
+
    #include <boost/multiprecision/cpp_int.hpp>
 
 using namespace boost::multiprecision;
 
 mp_int128_t v = 1;
 
-// Do some arithmetic:
+// Do some fixed precision arithmetic:
 for(unsigned i = 1; i <= 20; ++i)
    v *= i;
 
 std::cout << v << std::endl; // prints 20!
-v = -v;
-std::cout << std::hex << v << std::endl; // prints 2's complement representation
 
+// Try again at arbitrary precision:
+cpp_int u = 1;
+for(unsigned i = 1; i <= 100; ++i)
+   u *= i;
+
+std::cout << u << std::endl; // prints 100!
 
    
 
    
       
    
diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html
index 13d4cbb0..505e9393 100644
--- a/doc/html/boost_multiprecision/tut/rational.html
+++ b/doc/html/boost_multiprecision/tut/rational.html
@@ -6,7 +6,7 @@
 
 
 
-
+
 
 
 
@@ -96,6 +96,38 @@
    +

    + cpp_rational +

    +     		+

    + boost/multiprecision/cpp_int.hpp +

    +     		+

    + 2 +

    +     		+

    + None +

    +     		+

    + An all C++ Boost-licenced implementation. +

    +     		+

    + Slower than GMP. +

    +

    tommath_rational @@ -229,6 +261,10 @@ mp_number<gmp_int>. +

    + There is also a two-argument constructor that accepts a numerator and denominator + (both of type mp_number<gmp_int>). +

    There are also non-member functions:

    @@ -298,6 +334,81 @@

    + cpp_rational +
    +
    namespace boost{ namespace multiprecision{
+
+typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
+
+typedef mp_number<cpp_rational_backend>         cpp_rational;
+
+}} // namespaces
+
    +

    + The cpp_rational_backend + type is used via the typedef boost::multiprecision::cpp_rational. + It provides a rational number type that is a drop-in replacement for the + native C++ number types, but with unlimited precision. +

    +

    + As well as the usual conversions from arithmetic and string types, instances + of cpp_rational are copy + constructible and assignable from type cpp_int. +

    +

    + There is also a two argument constructor that accepts a numerator and denominator: + both of type cpp_int. +

    +

    + There are also non-member functions: +

    +
    cpp_int numerator(const cpp_rational&);
+cpp_int denominator(const cpp_rational&);
+
    +

    + which return the numerator and denominator of the number. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed cpp_rational's + have the value zero. +
      • +
    • + Division by zero results in a std::rumtime_error + being thrown. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+
+using namespace boost::multiprecision;
+
+cpp_rational v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+v /= 10;
+
+std::cout << v << std::endl; // prints 1000! / 10
+std::cout << numerator(v) << std::endl;
+std::cout << denominator(v) << std::endl;
+
+cpp_rational w(2, 3);  // component wise constructor
+std::cout << w << std::endl; // prints 2/3
+
    +

    +

    +
    + tommath_rational 
    namespace boost{ namespace multiprecision{
@@ -351,8 +462,8 @@
           
 
 
    
-
-        Example:
+
+        Example:
       
    
 
    
 
    
@@ -373,12 +484,11 @@
 
 mp_rational w(2, 3); // Component wise constructor
 std::cout << w << std::endl; // prints 2/3
-

    - + Use With Boost.Rational
    @@ -391,7 +501,7 @@ expression templates in mp_number.

    - + rational_adapter 
    namespace boost{ namespace multiprecision{
diff --git a/doc/html/boost_multiprecision/tut/reals.html b/doc/html/boost_multiprecision/tut/reals.html
index fee37a92..fe118cb9 100644
--- a/doc/html/boost_multiprecision/tut/reals.html
+++ b/doc/html/boost_multiprecision/tut/reals.html
@@ -1,7 +1,7 @@
 
 
 
-Real Numbers
+Floating Point Numbers
 
 
 
@@ -15,10 +15,10 @@
 
 
    
 
    
 
    
-        The following backends provide real number arithmetic:
+        The following backends provide floating point arithmetic:
       
    
 
    diff --git a/doc/html/index.html b/doc/html/index.html
index 19da3604..1d74c1b0 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -31,7 +31,7 @@
 
    Tutorial
    
 
    Integer Types
    
-
    Real Numbers
    
+
    Floating Point Numbers
    
 
    Rational Number Types
    
 
    Reference
    
@@ -56,7 +56,7 @@
 
    
 

 
 
 
 
    
-
+
    Last revised: February 15, 2012 at 18:08:37 GMT
    Last revised: March 13, 2012 at 19:12:03 GMT
    		
 
    		
 
    
 
    
diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk
index 52f85764..7b7ee9ff 100644
--- a/doc/multiprecision.qbk
+++ b/doc/multiprecision.qbk
@@ -306,14 +306,14 @@ as a result performing formatted output on this type when the argument is negati
    typedef mp_number         cpp_rational; // arbitrary precision rational number
 
    // Fixed precision unsigned types:
-   typedef mp_number >   mp_uint128_t;
-   typedef mp_number > mp_uint256_t;
-   typedef mp_number > mp_uint512_t;
+   typedef mp_number >   mp_uint128_t;
+   typedef mp_number >   mp_uint256_t;
+   typedef mp_number >   mp_uint512_t;
 
    // Fixed precision signed types:
-   typedef mp_number >  mp_int128_t;
-   typedef mp_number >  mp_int256_t;
-   typedef mp_number >  mp_int512_t;
+   typedef mp_number >    mp_int128_t;
+   typedef mp_number >    mp_int256_t;
+   typedef mp_number >    mp_int512_t;
 
    }} // namespaces
 
@@ -352,6 +352,8 @@ In this respect the behaviour of these types differs from built-in 2's complemen
 as the min and max values are identical (apart from the sign), where as they differ by one for a true 2's complement type.
 That said it should be noted that there's no requirement for built-in types to be 2's complement either - it's simply that this
 is the most common format by far.
+* Attempting to print negative values as either an Octal or Hexadecimal string results in a `std::runtime_error` being thrown,
+this is a direct consequence of the sign-magnitude representation.
 
 [h5 Example:]
 
@@ -516,8 +518,8 @@ The following backends provide rational number arithmetic:
 [table
 [[Backend Type][Header][Radix][Dependencies][Pros][Cons]]
 [[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient backend.][Dependency on GNU licenced [gmp] library.]]
-[[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licenced implementation.][[Slower than [gmp].]]
-[[`tommath_rational`][boost/multiprecision/tommath.hpp][2][libtommath][All C/C++ implementation that's Boost Software Licence compatible.]
+[[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licenced implementation.][Slower than [gmp].]]
+[[`tommath_rational`][boost/multiprecision/tommath.hpp][2][libtommath][All C/C++ implementation that's Boost Software Licence compatible.][Slower than [gmp].]]
 [[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any inetger backend type to be used as a rational type.][Requires an underlying integer backend type.]]
 [[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `mp_number` integer type.][The expression templates used by `mp_number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]]
 ]
@@ -541,6 +543,8 @@ and assignable from:
 * The [gmp] native types: `mpz_t`, `mpq_t`.
 * `mp_number`.
 
+There is also a two-argument constructor that accepts a numerator and denominator (both of type `mp_number`).
+
 There are also non-member functions:
 
    mpz_int numerator(const mpq_rational&);
@@ -578,6 +582,8 @@ a rational number type that is a drop-in replacement for the native C++ number t
 As well as the usual conversions from arithmetic and string types, instances of `cpp_rational` are copy constructible
 and assignable from type `cpp_int`.
 
+There is also a two argument constructor that accepts a numerator and denominator: both of type `cpp_int`.
+
 There are also non-member functions:
 
    cpp_int numerator(const cpp_rational&);
@@ -1029,7 +1035,7 @@ this library support all of the iostream formatting flags, field width and preci
    ``['unmentionable-expression-template-type]``    atan2 (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&);
 
 These functions all behave exactly as their standard library counterparts do: their argument is either an instance of `mp_number` or
-an expression template derived from it; If the argument is of type `mp_number,Backend, false>` then that is also the return type,
+an expression template derived from it; If the argument is of type `mp_number` then that is also the return type,
 otherwise the return type is an expression template.
 
 These functions are normally implemented by the Backend type.  However, default versions are provided for Backend types that
diff --git a/example/cpp_int_snips.cpp b/example/cpp_int_snips.cpp
index eb2827c7..942f27d6 100644
--- a/example/cpp_int_snips.cpp
+++ b/example/cpp_int_snips.cpp
@@ -33,7 +33,7 @@ void t1()
 
 void t3()
 {
-   //[cpp_rat_eg
+   //[cpp_rational_eg
    //=#include 
 
    using namespace boost::multiprecision;
diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp
index b087fe5f..60d9cc50 100644
--- a/include/boost/multiprecision/cpp_int.hpp
+++ b/include/boost/multiprecision/cpp_int.hpp
@@ -2141,6 +2141,17 @@ typedef mp_number >          cpp_int;
 typedef rational_adapter >   cpp_rational_backend;
 typedef mp_number        cpp_rational;
 
+// Fixed precision unsigned types:
+typedef mp_number >   mp_uint128_t;
+typedef mp_number >   mp_uint256_t;
+typedef mp_number >   mp_uint512_t;
+
+// Fixed precision signed types:
+typedef mp_number >    mp_int128_t;
+typedef mp_number >    mp_int256_t;
+typedef mp_number >    mp_int512_t;
+
+
 }} // namespaces
 
 
diff --git a/performance/Jamfile.v2 b/performance/Jamfile.v2
index 37c1017c..54fd7e52 100644
--- a/performance/Jamfile.v2
+++ b/performance/Jamfile.v2
@@ -50,7 +50,7 @@ exe performance_test : performance_test.cpp /boost/system//boost_system
           [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr : ]
           [ check-target-builds ../config//has_tommath : TEST_TOMMATH $(TOMMATH) : ]
           TEST_CPP_DEC_FLOAT
-          TEST_FIXED_INT
+          TEST_CPP_INT
           ;
 
 exe sf_performance : sf_performance.cpp /boost/system//boost_system
diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp
index 7a541b02..6fc2d9cf 100644
--- a/performance/performance_test.cpp
+++ b/performance/performance_test.cpp
@@ -12,7 +12,7 @@
 #if !defined(TEST_MPF) && !defined(TEST_MPZ) && \
    !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPQ) \
    && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\
-   && !defined(TEST_FIXED_INT) && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_RATIONAL)
+   && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_RATIONAL)
 #  define TEST_MPF
 #  define TEST_MPZ
 #  define TEST_MPQ
@@ -20,7 +20,6 @@
 #  define TEST_CPP_DEC_FLOAT
 #  define TEST_MPQ
 #  define TEST_TOMMATH
-#  define TEST_FIXED_INT
 #  define TEST_CPP_INT
 #  define TEST_CPP_INT_RATIONAL
 
@@ -47,9 +46,6 @@
 #include 
 #include 
 #endif
-#if defined(TEST_FIXED_INT)
-#include 
-#endif
 #if defined(TEST_CPP_INT)
 #include 
 #endif
@@ -619,12 +615,6 @@ int main()
    test("mp_rational", 1024);
    */
 #endif
-#ifdef TEST_FIXED_INT
-   test("fixed_int", 128);
-   test("fixed_int", 256);
-   test("fixed_int", 512);
-   test > >("fixed_int", 1024);
-#endif
 #ifdef TEST_CPP_DEC_FLOAT
    test("cpp_dec_float", 50);
    test("cpp_dec_float", 100);
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index ea66d0cf..e22c8a1c 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -18,7 +18,7 @@
 #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \
    !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) \
    && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\
-   && !defined(TEST_FIXED_INT1) && !defined(TEST_FIXED_INT2) && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_BR)
+   && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_BR)
 #  define TEST_MPF_50
 #  define TEST_MPF
 #  define TEST_BACKEND
@@ -28,8 +28,6 @@
 #  define TEST_CPP_DEC_FLOAT
 #  define TEST_MPQ
 #  define TEST_TOMMATH
-#  define TEST_FIXED_INT1
-#  define TEST_FIXED_INT2
 #  define TEST_CPP_INT
 #  define TEST_CPP_INT_BR
 
@@ -59,9 +57,6 @@
 #include 
 #include 
 #endif
-#if defined(TEST_FIXED_INT1) || defined(TEST_FIXED_INT2)
-#include 
-#endif
 #if defined(TEST_CPP_INT) || defined(TEST_CPP_INT_BR)
 #include 
 #endif
@@ -1030,26 +1025,10 @@ int main()
 #ifdef TEST_MPZ_BOOST_RATIONAL
    test >();
 #endif
-#ifdef TEST_FIXED_INT1
-   test > >();
-   test();
-   test();
-   test > >();
-#endif
-#ifdef TEST_FIXED_INT2
-   //
-   // Can't test 64-bit signed ints - they don't have enough bits
-   // to interoperate with uint64_t without loss:
-   //
-   //test();
-   test();
-   test();
-   test > >();
-#endif
 #ifdef TEST_CPP_INT
    test();
-   test > >();
-   test > >();
+   test();
+   test();
    test();
    test, false> >();
 #endif
diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp
index 704ec26c..9fac176d 100644
--- a/test/test_int_io.cpp
+++ b/test/test_int_io.cpp
@@ -9,11 +9,9 @@
 #  define _SCL_SECURE_NO_WARNINGS
 #endif
 
-#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) && !defined(TEST_FIXED_INT1) && !defined(TEST_FIXED_INT2) && !defined(TEST_CPP_INT)
+#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT)
 #  define TEST_TOMMATH
 #  define TEST_MPZ
-#  define TEST_FIXED_INT1
-#  define TEST_FIXED_INT2
 #  define TEST_CPP_INT
 
 #ifdef _MSC_VER
@@ -31,9 +29,6 @@
 #if defined(TEST_TOMMATH)
 #include 
 #endif
-#if defined(TEST_FIXED_INT1) || defined(TEST_FIXED_INT2)
-#include 
-#endif
 #ifdef TEST_CPP_INT
 #include 
 #endif
@@ -127,20 +122,6 @@ int main()
 #ifdef TEST_TOMMATH
    test_round_trip();
 #endif
-#ifdef TEST_FIXED_INT1
-   test_round_trip > >();
-   test_round_trip();
-   test_round_trip();
-   test_round_trip > >();
-   test_round_trip > >();
-#endif
-#ifdef TEST_FIXED_INT2
-   test_round_trip > >();
-   test_round_trip();
-   test_round_trip();
-   test_round_trip > >();
-   test_round_trip > >();
-#endif
 #ifdef TEST_CPP_INT
    test_round_trip > >();
    test_round_trip > >();
diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp
index 3d988fc1..bb2d64c6 100644
--- a/test/test_numeric_limits.cpp
+++ b/test/test_numeric_limits.cpp
@@ -11,7 +11,7 @@
 
 #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \
    !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && \
-   !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) && !defined(TEST_FIXED_INT)
+   !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT)
 #  define TEST_MPF_50
 #  define TEST_MPF
 #  define TEST_BACKEND
@@ -21,7 +21,6 @@
 #  define TEST_CPP_DEC_FLOAT
 #  define TEST_MPQ
 #  define TEST_TOMMATH
-#  define TEST_FIXED_INT
 #  define TEST_CPP_INT
 
 #ifdef _MSC_VER
@@ -48,9 +47,6 @@
 #ifdef TEST_TOMMATH
 #include 
 #endif
-#ifdef TEST_FIXED_INT
-#include 
-#endif
 #ifdef TEST_CPP_INT
 #include 
 #endif
@@ -226,16 +222,10 @@ int main()
 #ifdef TEST_TOMMATH
    test();
 #endif
-#ifdef TEST_FIXED_INT
-   test();
-   test();
-   test();
-   test();
-#endif
 #ifdef TEST_CPP_INT
    test();
-   test > >();
-   test > >();
+   test();
+   test();
 #endif
    return boost::report_errors();
 }

From fe94baae5077a8b30b696571258ef47ebbef1c68 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 15 Mar 2012 10:47:48 +0000
Subject: [PATCH 133/256] Allow construction/assignment from expression
 templates that yield a different type to *this.

[SVN r77340]
---
 include/boost/multiprecision/mp_number.hpp | 21 +++++++++++++++++++--
 1 file changed, 19 insertions(+), 2 deletions(-)

diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp
index 2c139de8..33c3c9ba 100644
--- a/include/boost/multiprecision/mp_number.hpp
+++ b/include/boost/multiprecision/mp_number.hpp
@@ -77,7 +77,8 @@ public:
    template 
    mp_number& operator=(const detail::mp_exp& e)
    {
-      do_assign(e, tag());
+      typedef typename is_same::result_type>::type tag_type;
+      do_assign(e, tag_type());
       return *this;
    }
 
@@ -121,7 +122,7 @@ public:
    template 
    mp_number(const detail::mp_exp& e)
    {
-      do_assign(e, tag());
+      *this = e;
    }
 
 #ifndef BOOST_NO_RVALUE_REFERENCES
@@ -538,6 +539,22 @@ public:
       return m_backend;
    }
 private:
+   template 
+   void do_assign(const detail::mp_exp& e, const mpl::true_&)
+   {
+      do_assign(e, tag());
+   }
+   template 
+   void do_assign(const detail::mp_exp& e, const mpl::false_&)
+   {
+      // The result of the expression isn't the same type as this -
+      // create a temporary result and assign it to *this:
+      typedef typename detail::mp_exp::result_type temp_type;
+      temp_type t(e);
+      *this = t;
+   }
+
+
    template 
    void check_shift_range(V val, const mpl::true_&, const mpl::true_&)
    {

From 0f6a527ceee411617ac98ad6b8cce6cbb9941ad5 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 15 Mar 2012 18:41:00 +0000
Subject: [PATCH 134/256] Add random number support.

[SVN r77344]
---
 doc/html/boost_multiprecision/ref.html        |   6 +-
 doc/html/boost_multiprecision/tut.html        |   1 +
 .../boost_multiprecision/tut/rational.html    |   6 +-
 doc/html/index.html                           |   3 +-
 doc/multiprecision.qbk                        |  32 +
 example/random_snips.cpp                      | 118 +++
 include/boost/multiprecision/random.hpp       | 559 ++++++++++++
 performance/performance_test-gcc-linux.log    | 841 +++++++++++++++---
 8 files changed, 1436 insertions(+), 130 deletions(-)
 create mode 100644 example/random_snips.cpp
 create mode 100644 include/boost/multiprecision/random.hpp

diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html
index d909f999..d975490b 100644
--- a/doc/html/boost_multiprecision/ref.html
+++ b/doc/html/boost_multiprecision/ref.html
@@ -6,12 +6,12 @@
 
 
 
-
+
 
 
 
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -32,7 +32,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html index cb05f329..0ac5b703 100644 --- a/doc/html/boost_multiprecision/tut.html +++ b/doc/html/boost_multiprecision/tut.html @@ -21,6 +21,7 @@
    Integer Types
    Floating Point Numbers
    Rational Number Types
    +
    Generating Random Numbers

    In order to use this library you need to make two choices: what kind of number diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 505e9393..3c2cefcf 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -7,11 +7,11 @@ - +

    -PrevUpHomeNext +PrevUpHomeNext

    @@ -539,7 +539,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/index.html b/doc/html/index.html index 1d74c1b0..5d80f737 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -33,6 +33,7 @@
    Integer Types
    Floating Point Numbers
    Rational Number Types
    +
    Generating Random Numbers
    Reference
    @@ -56,7 +57,7 @@

    - +

    Last revised: March 13, 2012 at 19:12:03 GMT

    Last revised: March 15, 2012 at 18:34:52 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 7b7ee9ff..fe1cd9d4 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -23,6 +23,7 @@ [import ../example/cpp_dec_float_snips.cpp] [import ../example/tommath_snips.cpp] [import ../example/cpp_int_snips.cpp] +[import ../example/random_snips.cpp] [template mpfr[] [@http://www.mpfr.org MPFR]] [template gmp[] [@http://gmplib.org GMP]] @@ -664,6 +665,37 @@ So for example, given an integer backend type `MyIntegerBackend`, the use would assert(i == 2); +[endsect] + +[section:random Generating Random Numbers] + +Random numbers are generated in conjunction with Boost.Random. However, since Boost.Random is unaware +of arbitrary precision numbers, it's necessary to include the header: + + #include + +In order to act as a bridge between the two libraries. + +Integers with /N/ random bits are generated using `independent_bits_engine`: + +[random_eg1] + +Alternatively we can generate integers in a given range using `uniform_int_distribution`, this will +invoke the underlying engine multiple times to build up the required number of bits in the result: + +[random_eg2] + +Floating point values in \[0,1) are generated using `uniform_01`, the trick here is to ensure +that the underlying generator produces as many random bits as there are digits in the floating +point type. As above `independent_bits_engine` can be used for this purpose, note that we also have to +convert decimal digits (in the floating point type) to bits (in the random number generator): + +[random_eg3] + +Finally, we can modify the above example to produce numbers distributed according to some distribution: + +[random_eg4] + [endsect] [endsect] diff --git a/example/random_snips.cpp b/example/random_snips.cpp new file mode 100644 index 00000000..8880f06e --- /dev/null +++ b/example/random_snips.cpp @@ -0,0 +1,118 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include +#include +#include + +void t1() +{ + //[random_eg1 + //=#include + //=#include + + using namespace boost::multiprecision; + using namespace boost::random; + + // + // Declare our random number generator type, the underlying generator + // is the Mersenne twister mt19937 engine, and 256 bits are generated: + // + typedef independent_bits_engine generator_type; + generator_type gen; + // + // Generate some values: + // + std::cout << std::hex << std::showbase; + for(unsigned i = 0; i < 10; ++i) + std::cout << gen() << std::endl; + //] +} + +void t2() +{ + //[random_eg2 + //=#include + //=#include + + using namespace boost::multiprecision; + using namespace boost::random; + + // + // Generate integers in a given range using uniform_int, + // the underlying generator is invoked multiple times + // to generate enough bits: + // + mt19937 mt; + uniform_int_distribution ui(0, mpz_int(1) << 256); + // + // Generate the numbers: + // + std::cout << std::hex << std::showbase; + for(unsigned i = 0; i < 10; ++i) + std::cout << ui(mt) << std::endl; + + //] +} + +void t3() +{ + //[random_eg3 + //=#include + //=#include + + using namespace boost::multiprecision; + using namespace boost::random; + // + // We need an underlying generator with at least as many bits as the + // floating point type to generate numbers in [0, 1) with all the bits + // in the floating point type randomly filled: + // + uniform_01 uf; + independent_bits_engine gen; + // + // Generate the values: + // + std::cout << std::setprecision(50); + for(unsigned i = 0; i < 20; ++i) + std::cout << uf(gen) << std::endl; + //] +} + +void t4() +{ + //[random_eg4 + //=#include + //=#include + + using namespace boost::multiprecision; + using namespace boost::random; + // + // We can repeat the above example, with other distributions: + // + uniform_real_distribution ur(-20, 20); + gamma_distribution gd(20); + independent_bits_engine gen; + // + // Generate some values: + // + std::cout << std::setprecision(50); + for(unsigned i = 0; i < 20; ++i) + std::cout << ur(gen) << std::endl; + for(unsigned i = 0; i < 20; ++i) + std::cout << gd(gen) << std::endl; + //] +} + +int main() +{ + t1(); + t2(); + t3(); + t4(); + return 0; +} + diff --git a/include/boost/multiprecision/random.hpp b/include/boost/multiprecision/random.hpp new file mode 100644 index 00000000..096ab8f1 --- /dev/null +++ b/include/boost/multiprecision/random.hpp @@ -0,0 +1,559 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_RANDOM_HPP +#define BOOST_MP_RANDOM_HPP + +#include +#include +#include + +namespace boost{ +namespace random{ +namespace detail{ + +template +struct subtract, true> +{ + typedef boost::multiprecision::mp_number result_type; + result_type operator()(result_type const& x, result_type const& y) { return x - y; } +}; + +} + +template +class independent_bits_engine > +{ +public: + typedef Engine base_type; + typedef boost::multiprecision::mp_number result_type; + + static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () + { return 0; } + // This is the only function we modify compared to the primary template: + static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () + { return (result_type(1) << w) - 1; } + + independent_bits_engine() { } + + BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(independent_bits_engine, + result_type, seed_arg) + { + _base.seed(seed_arg); + } + + BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(independent_bits_engine, + SeedSeq, seq) + { _base.seed(seq); } + + independent_bits_engine(const base_type& base_arg) : _base(base_arg) {} + + template + independent_bits_engine(It& first, It last) : _base(first, last) { } + + void seed() { _base.seed(); } + + BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(independent_bits_engine, + result_type, seed_arg) + { _base.seed(seed_arg); } + + BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(independent_bits_engine, + SeedSeq, seq) + { _base.seed(seq); } + + template void seed(It& first, It last) + { _base.seed(first, last); } + + result_type operator()() + { + // While it may seem wasteful to recalculate this + // every time, both msvc and gcc can propagate + // constants, resolving this at compile time. + base_unsigned range = + detail::subtract()((_base.max)(), (_base.min)()); + std::size_t m = + (range == (std::numeric_limits::max)()) ? + std::numeric_limits::digits : + detail::integer_log2(range + 1); + std::size_t n = (w + m - 1) / m; + std::size_t w0, n0; + base_unsigned y0, y1; + base_unsigned y0_mask, y1_mask; + calc_params(n, range, w0, n0, y0, y1, y0_mask, y1_mask); + if(base_unsigned(range - y0 + 1) > y0 / n) { + // increment n and try again. + ++n; + calc_params(n, range, w0, n0, y0, y1, y0_mask, y1_mask); + } + + BOOST_ASSERT(n0*w0 + (n - n0)*(w0 + 1) == w); + + result_type S = 0; + for(std::size_t k = 0; k < n0; ++k) { + base_unsigned u; + do { + u = detail::subtract()(_base(), (_base.min)()); + } while(u > base_unsigned(y0 - 1)); + S = (S << w0) + (u & y0_mask); + } + for(std::size_t k = 0; k < (n - n0); ++k) { + base_unsigned u; + do { + u = detail::subtract()(_base(), (_base.min)()); + } while(u > base_unsigned(y1 - 1)); + S = (S << (w0 + 1)) + (u & y1_mask); + } + return S; + } + + /** Fills a range with random values */ + template + void generate(Iter first, Iter last) + { detail::generate_from_int(*this, first, last); } + + /** Advances the state of the generator by @c z. */ + void discard(boost::uintmax_t z) + { + for(boost::uintmax_t i = 0; i < z; ++i) { + (*this)(); + } + } + + const base_type& base() const { return _base; } + + /** + * Writes the textual representation if the generator to a @c std::ostream. + * The textual representation of the engine is the textual representation + * of the base engine. + */ + BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, independent_bits_engine, r) + { + os << r._base; + return os; + } + + /** + * Reads the state of an @c independent_bits_engine from a + * @c std::istream. + */ + BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, independent_bits_engine, r) + { + is >> r._base; + return is; + } + + /** + * Returns: true iff the two @c independent_bits_engines will + * produce the same sequence of values. + */ + BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(independent_bits_engine, x, y) + { return x._base == y._base; } + /** + * Returns: true iff the two @c independent_bits_engines will + * produce different sequences of values. + */ + BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(independent_bits_engine) + +private: + + /// \cond show_private + typedef typename base_type::result_type base_result; + typedef typename make_unsigned::type base_unsigned; + + void calc_params( + std::size_t n, base_unsigned range, + std::size_t& w0, std::size_t& n0, + base_unsigned& y0, base_unsigned& y1, + base_unsigned& y0_mask, base_unsigned& y1_mask) + { + BOOST_ASSERT(w >= n); + w0 = w/n; + n0 = n - w % n; + y0_mask = (base_unsigned(2) << (w0 - 1)) - 1; + y1_mask = (y0_mask << 1) | 1; + y0 = (range + 1) & ~y0_mask; + y1 = (range + 1) & ~y1_mask; + BOOST_ASSERT(y0 != 0 || base_unsigned(range + 1) == 0); + } + /// \endcond + + Engine _base; +}; + +template +class uniform_smallint > +{ +public: + typedef boost::multiprecision::mp_number input_type; + typedef boost::multiprecision::mp_number result_type; + + class param_type + { + public: + + typedef uniform_smallint distribution_type; + + /** constructs the parameters of a @c uniform_smallint distribution. */ + param_type(result_type const& min_arg = 0, result_type const& max_arg = 9) + : _min(min_arg), _max(max_arg) + { + BOOST_ASSERT(_min <= _max); + } + + /** Returns the minimum value. */ + result_type a() const { return _min; } + /** Returns the maximum value. */ + result_type b() const { return _max; } + + + /** Writes the parameters to a @c std::ostream. */ + BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm) + { + os << parm._min << " " << parm._max; + return os; + } + + /** Reads the parameters from a @c std::istream. */ + BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm) + { + is >> parm._min >> std::ws >> parm._max; + return is; + } + + /** Returns true if the two sets of parameters are equal. */ + BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs) + { return lhs._min == rhs._min && lhs._max == rhs._max; } + + /** Returns true if the two sets of parameters are different. */ + BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type) + + private: + result_type _min; + result_type _max; + }; + + /** + * Constructs a @c uniform_smallint. @c min and @c max are the + * lower and upper bounds of the output range, respectively. + */ + explicit uniform_smallint(result_type const& min_arg = 0, result_type const& max_arg = 9) + : _min(min_arg), _max(max_arg) {} + + /** + * Constructs a @c uniform_smallint from its parameters. + */ + explicit uniform_smallint(const param_type& parm) + : _min(parm.a()), _max(parm.b()) {} + + /** Returns the minimum value of the distribution. */ + result_type a() const { return _min; } + /** Returns the maximum value of the distribution. */ + result_type b() const { return _max; } + /** Returns the minimum value of the distribution. */ + result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _min; } + /** Returns the maximum value of the distribution. */ + result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _max; } + + /** Returns the parameters of the distribution. */ + param_type param() const { return param_type(_min, _max); } + /** Sets the parameters of the distribution. */ + void param(const param_type& parm) + { + _min = parm.a(); + _max = parm.b(); + } + + /** + * Effects: Subsequent uses of the distribution do not depend + * on values produced by any engine prior to invoking reset. + */ + void reset() { } + + /** Returns a value uniformly distributed in the range [min(), max()]. */ + template + result_type operator()(Engine& eng) const + { + typedef typename Engine::result_type base_result; + return generate(eng, boost::is_integral()); + } + + /** Returns a value uniformly distributed in the range [param.a(), param.b()]. */ + template + result_type operator()(Engine& eng, const param_type& parm) const + { return uniform_smallint(parm)(eng); } + + /** Writes the distribution to a @c std::ostream. */ + BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, uniform_smallint, ud) + { + os << ud._min << " " << ud._max; + return os; + } + + /** Reads the distribution from a @c std::istream. */ + BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, uniform_smallint, ud) + { + is >> ud._min >> std::ws >> ud._max; + return is; + } + + /** + * Returns true if the two distributions will produce identical + * sequences of values given equal generators. + */ + BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(uniform_smallint, lhs, rhs) + { return lhs._min == rhs._min && lhs._max == rhs._max; } + + /** + * Returns true if the two distributions may produce different + * sequences of values given equal generators. + */ + BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(uniform_smallint) + +private: + + // \cond show_private + template + result_type generate(Engine& eng, boost::mpl::true_) const + { + // equivalent to (eng() - eng.min()) % (_max - _min + 1) + _min, + // but guarantees no overflow. + typedef typename Engine::result_type base_result; + typedef typename boost::make_unsigned::type base_unsigned; + typedef result_type range_type; + range_type range = random::detail::subtract()(_max, _min); + base_unsigned base_range = + random::detail::subtract()((eng.max)(), (eng.min)()); + base_unsigned val = + random::detail::subtract()(eng(), (eng.min)()); + if(range >= base_range) { + return boost::random::detail::add()( + static_cast(val), _min); + } else { + base_unsigned modulus = static_cast(range) + 1; + return boost::random::detail::add()( + static_cast(val % modulus), _min); + } + } + + template + result_type generate(Engine& eng, boost::mpl::false_) const + { + typedef typename Engine::result_type base_result; + typedef result_type range_type; + range_type range = random::detail::subtract()(_max, _min); + base_result val = boost::uniform_01()(eng); + // what is the worst that can possibly happen here? + // base_result may not be able to represent all the values in [0, range] + // exactly. If this happens, it will cause round off error and we + // won't be able to produce all the values in the range. We don't + // care about this because the user has already told us not to by + // using uniform_smallint. However, we do need to be careful + // to clamp the result, or floating point rounding can produce + // an out of range result. + range_type offset = static_cast(val * (range + 1)); + if(offset > range) return _max; + return boost::random::detail::add()(offset , _min); + } + // \endcond + + result_type _min; + result_type _max; +}; + + +namespace detail{ + +template +struct select_uniform_01 > +{ + template + struct apply + { + typedef new_uniform_01 > type; + }; +}; + +template +boost::multiprecision::mp_number + generate_uniform_int( + Engine& eng, const boost::multiprecision::mp_number& min_value, const boost::multiprecision::mp_number& max_value, + boost::mpl::true_ /** is_integral */) +{ + typedef boost::multiprecision::mp_number result_type; + // Since we're using big-numbers, use the result type for all internal calculations: + typedef result_type range_type; + typedef result_type base_result; + typedef result_type base_unsigned; + const range_type range = random::detail::subtract()(max_value, min_value); + const base_result bmin = (eng.min)(); + const base_unsigned brange = + random::detail::subtract()((eng.max)(), (eng.min)()); + + if(range == 0) { + return min_value; + } else if(brange == range) { + // this will probably never happen in real life + // basically nothing to do; just take care we don't overflow / underflow + base_unsigned v = random::detail::subtract()(eng(), bmin); + return random::detail::add()(v, min_value); + } else if(brange < range) { + // use rejection method to handle things like 0..3 --> 0..4 + for(;;) { + // concatenate several invocations of the base RNG + // take extra care to avoid overflows + + // limit == floor((range+1)/(brange+1)) + // Therefore limit*(brange+1) <= range+1 + range_type limit; + if(std::numeric_limits::is_bounded && (range == (std::numeric_limits::max)())) { + limit = range/(range_type(brange)+1); + if(range % (range_type(brange)+1) == range_type(brange)) + ++limit; + } else { + limit = (range+1)/(range_type(brange)+1); + } + + // We consider "result" as expressed to base (brange+1): + // For every power of (brange+1), we determine a random factor + range_type result = range_type(0); + range_type mult = range_type(1); + + // loop invariants: + // result < mult + // mult <= range + while(mult <= limit) { + // Postcondition: result <= range, thus no overflow + // + // limit*(brange+1)<=range+1 def. of limit (1) + // eng()-bmin<=brange eng() post. (2) + // and mult<=limit. loop condition (3) + // Therefore mult*(eng()-bmin+1)<=range+1 by (1),(2),(3) (4) + // Therefore mult*(eng()-bmin)+mult<=range+1 rearranging (4) (5) + // result(random::detail::subtract()(eng(), bmin) * mult); + + // equivalent to (mult * (brange+1)) == range+1, but avoids overflow. + if(mult * range_type(brange) == range - mult + 1) { + // The destination range is an integer power of + // the generator's range. + return(result); + } + + // Postcondition: mult <= range + // + // limit*(brange+1)<=range+1 def. of limit (1) + // mult<=limit loop condition (2) + // Therefore mult*(brange+1)<=range+1 by (1), (2) (3) + // mult*(brange+1)!=range+1 preceding if (4) + // Therefore mult*(brange+1) limit loop condition (1) + // Suppose range/mult >= brange+1 Assumption (2) + // range >= mult*(brange+1) by (2) (3) + // range+1 > mult*(brange+1) by (3) (4) + // range+1 > (limit+1)*(brange+1) by (1), (4) (5) + // (range+1)/(brange+1) > limit+1 by (5) (6) + // limit < floor((range+1)/(brange+1)) by (6) (7) + // limit==floor((range+1)/(brange+1)) def. of limit (8) + // not (2) reductio (9) + // + // loop postcondition: (range/mult)*mult+(mult-1) >= range + // + // (range/mult)*mult + range%mult == range identity (1) + // range%mult < mult def. of % (2) + // (range/mult)*mult+mult > range by (1), (2) (3) + // (range/mult)*mult+(mult-1) >= range by (3) (4) + // + // Note that the maximum value of result at this point is (mult-1), + // so after this final step, we generate numbers that can be + // at least as large as range. We have to really careful to avoid + // overflow in this final addition and in the rejection. Anything + // that overflows is larger than range and can thus be rejected. + + // range/mult < brange+1 -> no endless loop + range_type result_increment = + generate_uniform_int( + eng, + static_cast(0), + static_cast(range/mult), + boost::mpl::true_()); + if(std::numeric_limits::is_bounded && ((std::numeric_limits::max)() / mult < result_increment)) { + // The multiplcation would overflow. Reject immediately. + continue; + } + result_increment *= mult; + // unsigned integers are guaranteed to wrap on overflow. + result += result_increment; + if(result < result_increment) { + // The addition overflowed. Reject. + continue; + } + if(result > range) { + // Too big. Reject. + continue; + } + return random::detail::add()(result, min_value); + } + } else { // brange > range + range_type bucket_size; + // it's safe to add 1 to range, as long as we cast it first, + // because we know that it is less than brange. However, + // we do need to be careful not to cause overflow by adding 1 + // to brange. + if(std::numeric_limits::is_bounded && (brange == (std::numeric_limits::max)())) { + bucket_size = brange / (range+1); + if(brange % (range+1) == range) { + ++bucket_size; + } + } else { + bucket_size = (brange+1) / (range+1); + } + for(;;) { + range_type result = + random::detail::subtract()(eng(), bmin); + result /= bucket_size; + // result and range are non-negative, and result is possibly larger + // than range, so the cast is safe + if(result <= range) + return result + min_value; + } + } +} + +template +inline boost::multiprecision::mp_number + generate_uniform_int(Engine& eng, const boost::multiprecision::mp_number& min_value, const boost::multiprecision::mp_number& max_value) +{ + typedef typename Engine::result_type base_result; + typedef typename mpl::or_, mpl::bool_::value == boost::multiprecision::number_kind_integer> >::type tag_type; + return generate_uniform_int(eng, min_value, max_value, + tag_type()); +} + +} // detail + + +}} // namespaces + +#endif diff --git a/performance/performance_test-gcc-linux.log b/performance/performance_test-gcc-linux.log index 6df495e4..83b15004 100644 --- a/performance/performance_test-gcc-linux.log +++ b/performance/performance_test-gcc-linux.log @@ -1,123 +1,718 @@ -gmp_int 64 + 0.0168163 -gmp_int 64 - 0.0186614 -gmp_int 64 * 0.0117134 -gmp_int 64 / 0.169732 -gmp_int 64 str 0.000328882 -gmp_int 64 +(int)0.00662982 -gmp_int 64 -(int)0.00709197 -gmp_int 64 *(int)0.0088044 -gmp_int 64 /(int)0.0460225 -gmp_int 64 % 0.158198 -gmp_int 64 | 0.00933212 -gmp_int 64 & 0.00941153 -gmp_int 64 ^ 0.0100066 -gmp_int 64 << 0.00917854 -gmp_int 64 >> 0.00925083 -gmp_int 64 %(int)0.0280589 -gmp_int 64 |(int)0.0400043 -gmp_int 64 &(int)0.0417312 -gmp_int 64 ^(int)0.040751 -gmp_int 64 gcd 0.176467 -gmp_int 128 + 0.0178204 -gmp_int 128 - 0.0189183 -gmp_int 128 * 0.0162167 -gmp_int 128 / 0.188989 -gmp_int 128 str 0.00036981 -gmp_int 128 +(int)0.00848453 -gmp_int 128 -(int)0.00871131 -gmp_int 128 *(int)0.0113603 -gmp_int 128 /(int)0.0532432 -gmp_int 128 % 0.156838 -gmp_int 128 | 0.0106143 -gmp_int 128 & 0.0112662 -gmp_int 128 ^ 0.0113 -gmp_int 128 << 0.0100873 -gmp_int 128 >> 0.0078452 -gmp_int 128 %(int)0.0347183 -gmp_int 128 |(int)0.0411793 -gmp_int 128 &(int)0.0429282 -gmp_int 128 ^(int)0.0423867 -gmp_int 128 gcd 0.433341 -gmp_int 256 + 0.0227099 -gmp_int 256 - 0.0253696 -gmp_int 256 * 0.0419669 -gmp_int 256 / 0.231062 -gmp_int 256 str 0.00059791 -gmp_int 256 +(int)0.011126 -gmp_int 256 -(int)0.0118753 -gmp_int 256 *(int)0.0134931 -gmp_int 256 /(int)0.0656163 -gmp_int 256 % 0.188537 -gmp_int 256 | 0.0128192 -gmp_int 256 & 0.0127349 -gmp_int 256 ^ 0.0133922 -gmp_int 256 << 0.0118988 -gmp_int 256 >> 0.00811877 -gmp_int 256 %(int)0.0471091 -gmp_int 256 |(int)0.042799 -gmp_int 256 &(int)0.0458343 -gmp_int 256 ^(int)0.043002 -gmp_int 256 gcd 2.06647 -gmp_int 512 + 0.0273102 -gmp_int 512 - 0.0317526 -gmp_int 512 * 0.0977565 -gmp_int 512 / 0.271981 -gmp_int 512 str 0.0012591 -gmp_int 512 +(int)0.0141478 -gmp_int 512 -(int)0.0148129 -gmp_int 512 *(int)0.0180329 -gmp_int 512 /(int)0.0904515 -gmp_int 512 % 0.22083 -gmp_int 512 | 0.020649 -gmp_int 512 & 0.0165353 -gmp_int 512 ^ 0.0222088 -gmp_int 512 << 0.0146297 -gmp_int 512 >> 0.0098618 -gmp_int 512 %(int)0.0601431 -gmp_int 512 |(int)0.0461385 -gmp_int 512 &(int)0.0469244 -gmp_int 512 ^(int)0.0460041 -gmp_int 512 gcd 4.68119 -gmp_int 1024 + 0.0392733 -gmp_int 1024 - 0.0423657 -gmp_int 1024 * 0.314956 -gmp_int 1024 / 0.351788 -gmp_int 1024 str 0.00268616 -gmp_int 1024 +(int)0.0187891 -gmp_int 1024 -(int)0.0194118 -gmp_int 1024 *(int)0.0259443 -gmp_int 1024 /(int)0.140347 -gmp_int 1024 % 0.283657 -gmp_int 1024 | 0.0242247 -gmp_int 1024 & 0.023592 -gmp_int 1024 ^ 0.0249 -gmp_int 1024 << 0.0204313 -gmp_int 1024 >> 0.0128395 -gmp_int 1024 %(int)0.0758694 -gmp_int 1024 |(int)0.0495895 -gmp_int 1024 &(int)0.0506897 -gmp_int 1024 ^(int)0.049433 -gmp_int 1024 gcd 10.1293 -cpp_int(fixed) 128 + 0.0181676 -cpp_int(fixed) 128 - 0.0184343 -cpp_int(fixed) 128 * 0.014376 -cpp_int(fixed) 128 / 0.202558 -cpp_int(fixed) 128 str 0.000652736 -cpp_int(fixed) 128 +(int)0.00948536 -cpp_int(fixed) 128 -(int)0.00886251 -cpp_int(fixed) 128 *(int)0.0173963 -cpp_int(fixed) 128 /(int)0.106251 -cpp_int(fixed) 128 % 0.20362 -cpp_int(fixed) 128 | 0.0137212 -cpp_int(fixed) 128 & 0.0144157 -cpp_int(fixed) 128 ^ 0.0137219 -cpp_int(fixed) 128 << 0.0125872 -cpp_int(fixed) 128 >> 0.00905059 -cpp_int(fixed) 128 %(int)0.109447 -cpp_int(fixed) 128 |(int)0.014533 -cpp_int(fixed) 128 &(int)0.0162133 -cpp_int(fixed) 128 ^(int)0.0131589 -cpp_int(fixed) 128 gcd 2.86508 -cpp_int(fixed) 256 + 0.0216349 -cpp_int(fixed) 256 - 0.0208758 -cpp_int(fixed) 256 * 0.0210219 +gmp_float 50 + 0.0180885 +gmp_float 50 - 0.0227712 +gmp_float 50 * 0.0567584 +gmp_float 50 / 0.289062 +gmp_float 50 str 0.00354863 +gmp_float 50 +(int)0.0129337 +gmp_float 50 -(int)0.0256267 +gmp_float 50 *(int)0.0197258 +gmp_float 50 /(int)0.087785 +gmp_float 100 + 0.0196977 +gmp_float 100 - 0.024745 +gmp_float 100 * 0.0972 +gmp_float 100 / 0.393792 +gmp_float 100 str 0.00528245 +gmp_float 100 +(int)0.0154802 +gmp_float 100 -(int)0.0242376 +gmp_float 100 *(int)0.0251239 +gmp_float 100 /(int)0.100588 +gmp_float 500 + 0.034133 +gmp_float 500 - 0.0411447 +gmp_float 500 * 0.938779 +gmp_float 500 / 1.5973 +gmp_float 500 str 0.0406575 +gmp_float 500 +(int)0.0220839 +gmp_float 500 -(int)0.0310849 +gmp_float 500 *(int)0.046899 +gmp_float 500 /(int)0.240511 +gmp_int 128 + 0.0236625 +gmp_int 128 - 0.0255431 +gmp_int 128 * 0.0164612 +gmp_int 128 / 0.20205 +gmp_int 128 str 0.000397397 +gmp_int 128 +(int)0.00907029 +gmp_int 128 -(int)0.0120936 +gmp_int 128 *(int)0.0139764 +gmp_int 128 /(int)0.061181 +gmp_int 128 % 0.167724 +gmp_int 128 | 0.0126627 +gmp_int 128 & 0.0129377 +gmp_int 128 ^ 0.0136018 +gmp_int 128 << 0.0109566 +gmp_int 128 >> 0.0107283 +gmp_int 128 %(int)0.0408971 +gmp_int 128 |(int)0.0463637 +gmp_int 128 &(int)0.0502028 +gmp_int 128 ^(int)0.047593 +gmp_int 128 gcd 0.452707 +gmp_int 256 + 0.0257277 +gmp_int 256 - 0.0314085 +gmp_int 256 * 0.0495293 +gmp_int 256 / 0.242695 +gmp_int 256 str 0.000617745 +gmp_int 256 +(int)0.0129046 +gmp_int 256 -(int)0.0163165 +gmp_int 256 *(int)0.0153128 +gmp_int 256 /(int)0.0730963 +gmp_int 256 % 0.203102 +gmp_int 256 | 0.0149383 +gmp_int 256 & 0.0170717 +gmp_int 256 ^ 0.0160796 +gmp_int 256 << 0.0146023 +gmp_int 256 >> 0.010293 +gmp_int 256 %(int)0.0525884 +gmp_int 256 |(int)0.0501017 +gmp_int 256 &(int)0.0508389 +gmp_int 256 ^(int)0.0498771 +gmp_int 256 gcd 2.17179 +gmp_int 512 + 0.0283556 +gmp_int 512 - 0.0398509 +gmp_int 512 * 0.104633 +gmp_int 512 / 0.294206 +gmp_int 512 str 0.00125749 +gmp_int 512 +(int)0.0156938 +gmp_int 512 -(int)0.0204795 +gmp_int 512 *(int)0.0190714 +gmp_int 512 /(int)0.09638 +gmp_int 512 % 0.23687 +gmp_int 512 | 0.0244134 +gmp_int 512 & 0.0209509 +gmp_int 512 ^ 0.0266707 +gmp_int 512 << 0.0178981 +gmp_int 512 >> 0.0122496 +gmp_int 512 %(int)0.0655264 +gmp_int 512 |(int)0.0536497 +gmp_int 512 &(int)0.0532932 +gmp_int 512 ^(int)0.0540655 +gmp_int 512 gcd 4.86569 +gmp_int 1024 + 0.0417292 +gmp_int 1024 - 0.0504965 +gmp_int 1024 * 0.330741 +gmp_int 1024 / 0.376529 +gmp_int 1024 str 0.00295526 +gmp_int 1024 +(int)0.0258726 +gmp_int 1024 -(int)0.0235972 +gmp_int 1024 *(int)0.0326542 +gmp_int 1024 /(int)0.148103 +gmp_int 1024 % 0.301177 +gmp_int 1024 | 0.0262977 +gmp_int 1024 & 0.0235786 +gmp_int 1024 ^ 0.0254182 +gmp_int 1024 << 0.0206225 +gmp_int 1024 >> 0.012848 +gmp_int 1024 %(int)0.0765616 +gmp_int 1024 |(int)0.0495613 +gmp_int 1024 &(int)0.0512979 +gmp_int 1024 ^(int)0.0491785 +gmp_int 1024 gcd 10.2899 +cpp_int 128 + 0.0226262 +cpp_int 128 - 0.0256171 +cpp_int 128 * 0.0363846 +cpp_int 128 / 0.227187 +cpp_int 128 str 0.000703371 +cpp_int 128 +(int)0.0156956 +cpp_int 128 -(int)0.0122229 +cpp_int 128 *(int)0.0257193 +cpp_int 128 /(int)0.129609 +cpp_int 128 % 0.226534 +cpp_int 128 | 0.0242976 +cpp_int 128 & 0.0244482 +cpp_int 128 ^ 0.0243197 +cpp_int 128 << 0.0182175 +cpp_int 128 >> 0.0215535 +cpp_int 128 %(int)0.181554 +cpp_int 128 |(int)0.0454215 +cpp_int 128 &(int)0.0426893 +cpp_int 128 ^(int)0.0404509 +cpp_int 128 gcd 4.16823 +cpp_int 256 + 0.0275581 +cpp_int 256 - 0.0305114 +cpp_int 256 * 0.100083 +cpp_int 256 / 0.467116 +cpp_int 256 str 0.00181769 +cpp_int 256 +(int)0.017033 +cpp_int 256 -(int)0.0143035 +cpp_int 256 *(int)0.0294836 +cpp_int 256 /(int)0.303922 +cpp_int 256 % 0.435207 +cpp_int 256 | 0.0281237 +cpp_int 256 & 0.028049 +cpp_int 256 ^ 0.0280192 +cpp_int 256 << 0.0210768 +cpp_int 256 >> 0.0175781 +cpp_int 256 %(int)0.279274 +cpp_int 256 |(int)0.0323883 +cpp_int 256 &(int)0.0338674 +cpp_int 256 ^(int)0.0299941 +cpp_int 256 gcd 8.51244 +cpp_int 512 + 0.033691 +cpp_int 512 - 0.0422701 +cpp_int 512 * 0.343683 +cpp_int 512 / 0.755608 +cpp_int 512 str 0.00434022 +cpp_int 512 +(int)0.0196755 +cpp_int 512 -(int)0.0171212 +cpp_int 512 *(int)0.039305 +cpp_int 512 /(int)0.535727 +cpp_int 512 % 0.719958 +cpp_int 512 | 0.0339623 +cpp_int 512 & 0.0342017 +cpp_int 512 ^ 0.033929 +cpp_int 512 << 0.0269161 +cpp_int 512 >> 0.0216914 +cpp_int 512 %(int)0.53345 +cpp_int 512 |(int)0.0324562 +cpp_int 512 &(int)0.0424884 +cpp_int 512 ^(int)0.0323887 +cpp_int 512 gcd 19.489 +cpp_int 1024 + 0.0456764 +cpp_int 1024 - 0.0574919 +cpp_int 1024 * 1.28548 +cpp_int 1024 / 1.30086 +cpp_int 1024 str 0.0122363 +cpp_int 1024 +(int)0.0241476 +cpp_int 1024 -(int)0.0212992 +cpp_int 1024 *(int)0.0540818 +cpp_int 1024 /(int)1.00179 +cpp_int 1024 % 1.27181 +cpp_int 1024 | 0.0457886 +cpp_int 1024 & 0.0456006 +cpp_int 1024 ^ 0.0456494 +cpp_int 1024 << 0.0394128 +cpp_int 1024 >> 0.0294462 +cpp_int 1024 %(int)0.962651 +cpp_int 1024 |(int)0.0372077 +cpp_int 1024 &(int)0.0577198 +cpp_int 1024 ^(int)0.0372218 +cpp_int 1024 gcd 47.7651 +cpp_int(fixed) 128 + 0.0183948 +cpp_int(fixed) 128 - 0.0182905 +cpp_int(fixed) 128 * 0.0201727 +cpp_int(fixed) 128 / 0.206852 +cpp_int(fixed) 128 str 0.000630107 +cpp_int(fixed) 128 +(int)0.00967714 +cpp_int(fixed) 128 -(int)0.00810627 +cpp_int(fixed) 128 *(int)0.0183201 +cpp_int(fixed) 128 /(int)0.111309 +cpp_int(fixed) 128 % 0.204164 +cpp_int(fixed) 128 | 0.0136789 +cpp_int(fixed) 128 & 0.0143848 +cpp_int(fixed) 128 ^ 0.0137773 +cpp_int(fixed) 128 << 0.0131154 +cpp_int(fixed) 128 >> 0.00912176 +cpp_int(fixed) 128 %(int)0.115583 +cpp_int(fixed) 128 |(int)0.0164462 +cpp_int(fixed) 128 &(int)0.0169816 +cpp_int(fixed) 128 ^(int)0.014607 +cpp_int(fixed) 128 gcd 2.87326 +cpp_int(fixed) 256 + 0.0217614 +cpp_int(fixed) 256 - 0.0208437 +cpp_int(fixed) 256 * 0.0385279 +cpp_int(fixed) 256 / 0.321272 +cpp_int(fixed) 256 str 0.00149991 +cpp_int(fixed) 256 +(int)0.0102395 +cpp_int(fixed) 256 -(int)0.00923316 +cpp_int(fixed) 256 *(int)0.021549 +cpp_int(fixed) 256 /(int)0.219146 +cpp_int(fixed) 256 % 0.321039 +cpp_int(fixed) 256 | 0.0154596 +cpp_int(fixed) 256 & 0.0156443 +cpp_int(fixed) 256 ^ 0.015493 +cpp_int(fixed) 256 << 0.0169546 +cpp_int(fixed) 256 >> 0.0114138 +cpp_int(fixed) 256 %(int)0.238857 +cpp_int(fixed) 256 |(int)0.015725 +cpp_int(fixed) 256 &(int)0.021641 +cpp_int(fixed) 256 ^(int)0.0163443 +cpp_int(fixed) 256 gcd 6.68597 +cpp_int(fixed) 512 + 0.0284799 +cpp_int(fixed) 512 - 0.028304 +cpp_int(fixed) 512 * 0.119904 +cpp_int(fixed) 512 / 0.616699 +cpp_int(fixed) 512 str 0.00415653 +cpp_int(fixed) 512 +(int)0.0122821 +cpp_int(fixed) 512 -(int)0.0110103 +cpp_int(fixed) 512 *(int)0.0283635 +cpp_int(fixed) 512 /(int)0.451373 +cpp_int(fixed) 512 % 0.620217 +cpp_int(fixed) 512 | 0.0189862 +cpp_int(fixed) 512 & 0.0192657 +cpp_int(fixed) 512 ^ 0.018973 +cpp_int(fixed) 512 << 0.0188263 +cpp_int(fixed) 512 >> 0.0152103 +cpp_int(fixed) 512 %(int)0.491398 +cpp_int(fixed) 512 |(int)0.0182191 +cpp_int(fixed) 512 &(int)0.0277722 +cpp_int(fixed) 512 ^(int)0.0182565 +cpp_int(fixed) 512 gcd 16.1788 +cpp_int(fixed) 1024 + 0.0396571 +cpp_int(fixed) 1024 - 0.0413187 +cpp_int(fixed) 1024 * 0.371065 +cpp_int(fixed) 1024 / 1.09072 +cpp_int(fixed) 1024 str 0.011546 +cpp_int(fixed) 1024 +(int)0.0254102 +cpp_int(fixed) 1024 -(int)0.020939 +cpp_int(fixed) 1024 *(int)0.0494233 +cpp_int(fixed) 1024 /(int)0.870306 +cpp_int(fixed) 1024 % 1.09888 +cpp_int(fixed) 1024 | 0.0393824 +cpp_int(fixed) 1024 & 0.0397966 +cpp_int(fixed) 1024 ^ 0.0394082 +cpp_int(fixed) 1024 << 0.0392477 +cpp_int(fixed) 1024 >> 0.0214742 +cpp_int(fixed) 1024 %(int)0.941513 +cpp_int(fixed) 1024 |(int)0.0304613 +cpp_int(fixed) 1024 &(int)0.0497983 +cpp_int(fixed) 1024 ^(int)0.0333848 +cpp_int(fixed) 1024 gcd 41.9178 +cpp_rational 128 + 8.33358 +cpp_rational 128 - 8.3543 +cpp_rational 128 * 15.3196 +cpp_rational 128 / 31.794 +cpp_rational 128 str 0.00980984 +cpp_rational 128 +(int)1.14042 +cpp_rational 128 -(int)1.13947 +cpp_rational 128 *(int)1.3425 +cpp_rational 128 /(int)1.35276 +cpp_rational 256 + 24.5753 +cpp_rational 256 - 24.3831 +cpp_rational 256 * 45.9283 +cpp_rational 256 / 80.7871 +cpp_rational 256 str 0.0288878 +cpp_rational 256 +(int)1.54697 +cpp_rational 256 -(int)1.55711 +cpp_rational 256 *(int)2.05921 +cpp_rational 256 /(int)2.12933 +cpp_rational 512 + 58.1983 +cpp_rational 512 - 58.3044 +cpp_rational 512 * 111.528 +cpp_rational 512 / 184.73 +cpp_rational 512 str 0.067039 +cpp_rational 512 +(int)1.83113 +cpp_rational 512 -(int)1.82889 +cpp_rational 512 *(int)2.75206 +cpp_rational 512 /(int)2.75885 +cpp_rational 1024 + 139.884 +cpp_rational 1024 - 139.665 +cpp_rational 1024 * 270.253 +cpp_rational 1024 / 436.471 +cpp_rational 1024 str 0.165057 +cpp_rational 1024 +(int)2.65768 +cpp_rational 1024 -(int)2.68279 +cpp_rational 1024 *(int)4.26866 +cpp_rational 1024 /(int)4.27228 +mpq_rational 128 + 0.518878 +mpq_rational 128 - 0.520249 +mpq_rational 128 * 0.940549 +mpq_rational 128 / 2.63335 +mpq_rational 128 str 0.000732008 +mpq_rational 128 +(int)0.145745 +mpq_rational 128 -(int)0.142505 +mpq_rational 128 *(int)0.173305 +mpq_rational 128 /(int)0.178914 +mpq_rational 256 + 2.2747 +mpq_rational 256 - 2.27886 +mpq_rational 256 * 4.27402 +mpq_rational 256 / 8.07149 +mpq_rational 256 str 0.00123256 +mpq_rational 256 +(int)0.164417 +mpq_rational 256 -(int)0.161741 +mpq_rational 256 *(int)0.193095 +mpq_rational 256 /(int)0.202255 +mpq_rational 512 + 5.09463 +mpq_rational 512 - 5.09757 +mpq_rational 512 * 9.6481 +mpq_rational 512 / 16.9064 +mpq_rational 512 str 0.00244388 +mpq_rational 512 +(int)0.202901 +mpq_rational 512 -(int)0.200644 +mpq_rational 512 *(int)0.248942 +mpq_rational 512 /(int)0.251928 +mpq_rational 1024 + 11.2492 +mpq_rational 1024 - 11.2528 +mpq_rational 1024 * 21.0227 +mpq_rational 1024 / 35.7647 +mpq_rational 1024 str 0.00559869 +mpq_rational 1024 +(int)0.287349 +mpq_rational 1024 -(int)0.28136 +mpq_rational 1024 *(int)0.337805 +mpq_rational 1024 /(int)0.351164 +tommath_int 128 + 0.0169999 +tommath_int 128 - 0.025088 +tommath_int 128 * 0.0608098 +tommath_int 128 / 1.14807 +tommath_int 128 str 0.00864677 +tommath_int 128 +(int)0.170239 +tommath_int 128 -(int)0.169805 +tommath_int 128 *(int)0.18998 +tommath_int 128 /(int)0.936106 +tommath_int 128 % 1.10993 +tommath_int 128 | 0.0742258 +tommath_int 128 & 0.0747022 +tommath_int 128 ^ 0.0734074 +tommath_int 128 << 0.0316344 +tommath_int 128 >> 0.139155 +tommath_int 128 %(int)0.871093 +tommath_int 128 |(int)0.249135 +tommath_int 128 &(int)0.224394 +tommath_int 128 ^(int)0.248407 +tommath_int 128 gcd 7.6073 +tommath_int 256 + 0.0191462 +tommath_int 256 - 0.0267191 +tommath_int 256 * 0.0843842 +tommath_int 256 / 1.34052 +tommath_int 256 str 0.0212684 +tommath_int 256 +(int)0.173633 +tommath_int 256 -(int)0.173084 +tommath_int 256 *(int)0.20074 +tommath_int 256 /(int)1.17192 +tommath_int 256 % 1.33781 +tommath_int 256 | 0.0740269 +tommath_int 256 & 0.0747001 +tommath_int 256 ^ 0.0741847 +tommath_int 256 << 0.0379471 +tommath_int 256 >> 0.14164 +tommath_int 256 %(int)1.52193 +tommath_int 256 |(int)0.251418 +tommath_int 256 &(int)0.230435 +tommath_int 256 ^(int)0.249516 +tommath_int 256 gcd 15.8851 +tommath_int 512 + 0.0241933 +tommath_int 512 - 0.032154 +tommath_int 512 * 0.195855 +tommath_int 512 / 2.061 +tommath_int 512 str 0.0827649 +tommath_int 512 +(int)0.25223 +tommath_int 512 -(int)0.25482 +tommath_int 512 *(int)0.305608 +tommath_int 512 /(int)1.76155 +tommath_int 512 % 1.97453 +tommath_int 512 | 0.0795209 +tommath_int 512 & 0.0815029 +tommath_int 512 ^ 0.0793004 +tommath_int 512 << 0.0449753 +tommath_int 512 >> 0.149597 +tommath_int 512 %(int)1.74258 +tommath_int 512 |(int)0.253519 +tommath_int 512 &(int)0.235246 +tommath_int 512 ^(int)0.261762 +tommath_int 512 gcd 33.8904 +tommath_int 1024 + 0.0356467 +tommath_int 1024 - 0.0426379 +tommath_int 1024 * 0.563154 +tommath_int 1024 / 3.3106 +tommath_int 1024 str 0.200351 +tommath_int 1024 +(int)0.183982 +tommath_int 1024 -(int)0.182348 +tommath_int 1024 *(int)0.265242 +tommath_int 1024 /(int)2.99248 +tommath_int 1024 % 3.36442 +tommath_int 1024 | 0.0935681 +tommath_int 1024 & 0.0990244 +tommath_int 1024 ^ 0.0948247 +tommath_int 1024 << 0.0671463 +tommath_int 1024 >> 0.167341 +tommath_int 1024 %(int)2.8911 +tommath_int 1024 |(int)0.26358 +tommath_int 1024 &(int)0.244976 +tommath_int 1024 ^(int)0.261357 +tommath_int 1024 gcd 67.1657 +cpp_dec_float 50 + 0.0139248 +cpp_dec_float 50 - 0.0142418 +cpp_dec_float 50 * 0.118247 +cpp_dec_float 50 / 1.82747 +cpp_dec_float 50 str 0.00932849 +cpp_dec_float 50 +(int)0.0253923 +cpp_dec_float 50 -(int)0.0248418 +cpp_dec_float 50 *(int)0.0371704 +cpp_dec_float 50 /(int)0.199883 +cpp_dec_float 100 + 0.0171021 +cpp_dec_float 100 - 0.0176287 +cpp_dec_float 100 * 0.237033 +cpp_dec_float 100 / 3.63766 +cpp_dec_float 100 str 0.0201057 +cpp_dec_float 100 +(int)0.0330663 +cpp_dec_float 100 -(int)0.0332922 +cpp_dec_float 100 *(int)0.0606472 +cpp_dec_float 100 /(int)0.343778 +cpp_dec_float 500 + 0.043194 +cpp_dec_float 500 - 0.0443422 +cpp_dec_float 500 * 2.12299 +cpp_dec_float 500 / 25.7245 +cpp_dec_float 500 str 0.0655127 +cpp_dec_float 500 +(int)0.0706977 +cpp_dec_float 500 -(int)0.0727089 +cpp_dec_float 500 *(int)0.239796 +cpp_dec_float 500 /(int)1.39609 +mpfr_float 50 + 0.019179 +mpfr_float 50 - 0.0225632 +mpfr_float 50 * 0.0588765 +mpfr_float 50 / 0.317276 +mpfr_float 50 str 0.00725414 +mpfr_float 50 +(int)0.0286079 +mpfr_float 50 -(int)0.0465151 +mpfr_float 50 *(int)0.0362579 +mpfr_float 50 /(int)0.0888645 +mpfr_float 100 + 0.0210236 +mpfr_float 100 - 0.0250703 +mpfr_float 100 * 0.0946262 +mpfr_float 100 / 0.456375 +mpfr_float 100 str 0.00900848 +mpfr_float 100 +(int)0.0320443 +mpfr_float 100 -(int)0.0487733 +mpfr_float 100 *(int)0.0437034 +mpfr_float 100 /(int)0.154203 +mpfr_float 500 + 0.033691 +mpfr_float 500 - 0.0371954 +mpfr_float 500 * 0.851721 +mpfr_float 500 / 2.7946 +mpfr_float 500 str 0.0342011 +mpfr_float 500 +(int)0.0414774 +mpfr_float 500 -(int)0.0616173 +mpfr_float 500 *(int)0.0826485 +mpfr_float 500 /(int)0.254227 +[section:float_performance Float Type Perfomance] +[table Operator * +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.08334 (0.118247s)][2.50494 (0.237033s)][2.49259 (2.12299s)]] +[[gmp_float][[*1] (0.0567584s)][1.0272 (0.0972s)][1.10221 (0.938779s)]] +[[mpfr_float][1.03732 (0.0588765s)][[*1] (0.0946262s)][[*1] (0.851721s)]] +] +[table Operator *(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][1.88436 (0.0371704s)][2.41392 (0.0606472s)][5.11303 (0.239796s)]] +[[gmp_float][[*1] (0.0197258s)][[*1] (0.0251239s)][[*1] (0.046899s)]] +[[mpfr_float][1.8381 (0.0362579s)][1.73951 (0.0437034s)][1.76227 (0.0826485s)]] +] +[table Operator + +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0139248s)][[*1] (0.0171021s)][1.28206 (0.043194s)]] +[[gmp_float][1.29901 (0.0180885s)][1.15177 (0.0196977s)][1.01312 (0.034133s)]] +[[mpfr_float][1.37732 (0.019179s)][1.2293 (0.0210236s)][[*1] (0.033691s)]] +] +[table Operator +(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][1.96327 (0.0253923s)][2.13604 (0.0330663s)][3.20133 (0.0706977s)]] +[[gmp_float][[*1] (0.0129337s)][[*1] (0.0154802s)][[*1] (0.0220839s)]] +[[mpfr_float][2.21189 (0.0286079s)][2.07002 (0.0320443s)][1.87818 (0.0414774s)]] +] +[table Operator - +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0142418s)][[*1] (0.0176287s)][1.19214 (0.0443422s)]] +[[gmp_float][1.5989 (0.0227712s)][1.40368 (0.024745s)][1.10618 (0.0411447s)]] +[[mpfr_float][1.5843 (0.0225632s)][1.42213 (0.0250703s)][[*1] (0.0371954s)]] +] +[table Operator -(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0248418s)][1.37357 (0.0332922s)][2.33904 (0.0727089s)]] +[[gmp_float][1.03159 (0.0256267s)][[*1] (0.0242376s)][[*1] (0.0310849s)]] +[[mpfr_float][1.87245 (0.0465151s)][2.0123 (0.0487733s)][1.98223 (0.0616173s)]] +] +[table Operator / +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][6.32206 (1.82747s)][9.23752 (3.63766s)][16.1049 (25.7245s)]] +[[gmp_float][[*1] (0.289062s)][[*1] (0.393792s)][[*1] (1.5973s)]] +[[mpfr_float][1.09761 (0.317276s)][1.15892 (0.456375s)][1.74957 (2.7946s)]] +] +[table Operator /(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.27696 (0.199883s)][3.41769 (0.343778s)][5.8047 (1.39609s)]] +[[gmp_float][[*1] (0.087785s)][[*1] (0.100588s)][[*1] (0.240511s)]] +[[mpfr_float][1.0123 (0.0888645s)][1.53302 (0.154203s)][1.05703 (0.254227s)]] +] +[table Operator str +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.62876 (0.00932849s)][3.80613 (0.0201057s)][1.91552 (0.0655127s)]] +[[gmp_float][[*1] (0.00354863s)][[*1] (0.00528245s)][1.18878 (0.0406575s)]] +[[mpfr_float][2.04421 (0.00725414s)][1.70536 (0.00900848s)][[*1] (0.0342011s)]] +] +[endsect] +[section:integer_performance Integer Type Perfomance] +[table Operator % +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.35064 (0.226534s)][2.1428 (0.435207s)][3.03946 (0.719958s)][4.22281 (1.27181s)]] +[[cpp_int(fixed)][1.21726 (0.204164s)][1.58068 (0.321039s)][2.61838 (0.620217s)][3.6486 (1.09888s)]] +[[gmp_int][[*1] (0.167724s)][[*1] (0.203102s)][[*1] (0.23687s)][[*1] (0.301177s)]] +[[tommath_int][6.61759 (1.10993s)][6.58689 (1.33781s)][8.33593 (1.97453s)][11.1709 (3.36442s)]] +] +[table Operator %(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][4.43928 (0.181554s)][5.31056 (0.279274s)][8.141 (0.53345s)][12.5735 (0.962651s)]] +[[cpp_int(fixed)][2.82619 (0.115583s)][4.54202 (0.238857s)][7.49924 (0.491398s)][12.2974 (0.941513s)]] +[[gmp_int][[*1] (0.0408971s)][[*1] (0.0525884s)][[*1] (0.0655264s)][[*1] (0.0765616s)]] +[[tommath_int][21.2996 (0.871093s)][28.9405 (1.52193s)][26.5936 (1.74258s)][37.7618 (2.8911s)]] +] +[table Operator & +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.88968 (0.0244482s)][1.79292 (0.028049s)][1.77526 (0.0342017s)][1.93398 (0.0456006s)]] +[[cpp_int(fixed)][1.11185 (0.0143848s)][[*1] (0.0156443s)][[*1] (0.0192657s)][1.68783 (0.0397966s)]] +[[gmp_int][[*1] (0.0129377s)][1.09124 (0.0170717s)][1.08747 (0.0209509s)][[*1] (0.0235786s)]] +[[tommath_int][5.77397 (0.0747022s)][4.7749 (0.0747001s)][4.23046 (0.0815029s)][4.19976 (0.0990244s)]] +] +[table Operator &(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.51385 (0.0426893s)][1.56497 (0.0338674s)][1.52989 (0.0424884s)][1.15907 (0.0577198s)]] +[[cpp_int(fixed)][[*1] (0.0169816s)][[*1] (0.021641s)][[*1] (0.0277722s)][[*1] (0.0497983s)]] +[[gmp_int][2.9563 (0.0502028s)][2.3492 (0.0508389s)][1.91894 (0.0532932s)][1.03011 (0.0512979s)]] +[[tommath_int][13.2139 (0.224394s)][10.6481 (0.230435s)][8.47057 (0.235246s)][4.91936 (0.244976s)]] +] +[table Operator * +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.21032 (0.0363846s)][2.59769 (0.100083s)][3.28466 (0.343683s)][3.88666 (1.28548s)]] +[[cpp_int(fixed)][1.22547 (0.0201727s)][[*1] (0.0385279s)][1.14595 (0.119904s)][1.12192 (0.371065s)]] +[[gmp_int][[*1] (0.0164612s)][1.28554 (0.0495293s)][[*1] (0.104633s)][[*1] (0.330741s)]] +[[tommath_int][3.69412 (0.0608098s)][2.19021 (0.0843842s)][1.87184 (0.195855s)][1.70271 (0.563154s)]] +] +[table Operator *(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.8402 (0.0257193s)][1.92542 (0.0294836s)][2.06094 (0.039305s)][1.6562 (0.0540818s)]] +[[cpp_int(fixed)][1.3108 (0.0183201s)][1.40725 (0.021549s)][1.48723 (0.0283635s)][1.51354 (0.0494233s)]] +[[gmp_int][[*1] (0.0139764s)][[*1] (0.0153128s)][[*1] (0.0190714s)][[*1] (0.0326542s)]] +[[tommath_int][13.593 (0.18998s)][13.1093 (0.20074s)][16.0244 (0.305608s)][8.12274 (0.265242s)]] +] +[table Operator + +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.33096 (0.0226262s)][1.43935 (0.0275581s)][1.39258 (0.033691s)][1.28136 (0.0456764s)]] +[[cpp_int(fixed)][1.08205 (0.0183948s)][1.13659 (0.0217614s)][1.17718 (0.0284799s)][1.1125 (0.0396571s)]] +[[gmp_int][1.39192 (0.0236625s)][1.34375 (0.0257277s)][1.17204 (0.0283556s)][1.17063 (0.0417292s)]] +[[tommath_int][[*1] (0.0169999s)][[*1] (0.0191462s)][[*1] (0.0241933s)][[*1] (0.0356467s)]] +] +[table Operator +(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.73044 (0.0156956s)][1.66346 (0.017033s)][1.60196 (0.0196755s)][[*1] (0.0241476s)]] +[[cpp_int(fixed)][1.06691 (0.00967714s)][[*1] (0.0102395s)][[*1] (0.0122821s)][1.05229 (0.0254102s)]] +[[gmp_int][[*1] (0.00907029s)][1.26028 (0.0129046s)][1.27777 (0.0156938s)][1.07144 (0.0258726s)]] +[[tommath_int][18.7688 (0.170239s)][16.9572 (0.173633s)][20.5363 (0.25223s)][7.61905 (0.183982s)]] +] +[table Operator - +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.40057 (0.0256171s)][1.46382 (0.0305114s)][1.49343 (0.0422701s)][1.39142 (0.0574919s)]] +[[cpp_int(fixed)][[*1] (0.0182905s)][[*1] (0.0208437s)][[*1] (0.028304s)][[*1] (0.0413187s)]] +[[gmp_int][1.39653 (0.0255431s)][1.50686 (0.0314085s)][1.40796 (0.0398509s)][1.22212 (0.0504965s)]] +[[tommath_int][1.37164 (0.025088s)][1.28188 (0.0267191s)][1.13602 (0.032154s)][1.03193 (0.0426379s)]] +] +[table Operator -(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.50784 (0.0122229s)][1.54914 (0.0143035s)][1.55501 (0.0171212s)][1.0172 (0.0212992s)]] +[[cpp_int(fixed)][[*1] (0.00810627s)][[*1] (0.00923316s)][[*1] (0.0110103s)][[*1] (0.020939s)]] +[[gmp_int][1.49189 (0.0120936s)][1.76716 (0.0163165s)][1.86002 (0.0204795s)][1.12695 (0.0235972s)]] +[[tommath_int][20.9474 (0.169805s)][18.7459 (0.173084s)][23.1437 (0.25482s)][8.70855 (0.182348s)]] +] +[table Operator / +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.12441 (0.227187s)][1.92471 (0.467116s)][2.5683 (0.755608s)][3.45487 (1.30086s)]] +[[cpp_int(fixed)][1.02377 (0.206852s)][1.32377 (0.321272s)][2.09615 (0.616699s)][2.89679 (1.09072s)]] +[[gmp_int][[*1] (0.20205s)][[*1] (0.242695s)][[*1] (0.294206s)][[*1] (0.376529s)]] +[[tommath_int][5.68214 (1.14807s)][5.52349 (1.34052s)][7.00529 (2.061s)][8.79242 (3.3106s)]] +] +[table Operator /(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.11845 (0.129609s)][4.15783 (0.303922s)][5.55849 (0.535727s)][6.76415 (1.00179s)]] +[[cpp_int(fixed)][1.81934 (0.111309s)][2.99804 (0.219146s)][4.68327 (0.451373s)][5.87635 (0.870306s)]] +[[gmp_int][[*1] (0.061181s)][[*1] (0.0730963s)][[*1] (0.09638s)][[*1] (0.148103s)]] +[[tommath_int][15.3006 (0.936106s)][16.0325 (1.17192s)][18.2771 (1.76155s)][20.2054 (2.99248s)]] +] +[table Operator << +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.66271 (0.0182175s)][1.44338 (0.0210768s)][1.50386 (0.0269161s)][1.91115 (0.0394128s)]] +[[cpp_int(fixed)][1.19703 (0.0131154s)][1.16109 (0.0169546s)][1.05186 (0.0188263s)][1.90315 (0.0392477s)]] +[[gmp_int][[*1] (0.0109566s)][[*1] (0.0146023s)][[*1] (0.0178981s)][[*1] (0.0206225s)]] +[[tommath_int][2.88726 (0.0316344s)][2.5987 (0.0379471s)][2.51285 (0.0449753s)][3.25597 (0.0671463s)]] +] +[table Operator >> +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.36287 (0.0215535s)][1.70778 (0.0175781s)][1.77078 (0.0216914s)][2.29189 (0.0294462s)]] +[[cpp_int(fixed)][[*1] (0.00912176s)][1.10889 (0.0114138s)][1.2417 (0.0152103s)][1.6714 (0.0214742s)]] +[[gmp_int][1.17612 (0.0107283s)][[*1] (0.010293s)][[*1] (0.0122496s)][[*1] (0.012848s)]] +[[tommath_int][15.2553 (0.139155s)][13.7608 (0.14164s)][12.2124 (0.149597s)][13.0247 (0.167341s)]] +] +[table Operator ^ +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.78798 (0.0243197s)][1.8085 (0.0280192s)][1.78828 (0.033929s)][1.79594 (0.0456494s)]] +[[cpp_int(fixed)][1.0129 (0.0137773s)][[*1] (0.015493s)][[*1] (0.018973s)][1.5504 (0.0394082s)]] +[[gmp_int][[*1] (0.0136018s)][1.03786 (0.0160796s)][1.40572 (0.0266707s)][[*1] (0.0254182s)]] +[[tommath_int][5.39689 (0.0734074s)][4.78827 (0.0741847s)][4.17964 (0.0793004s)][3.73059 (0.0948247s)]] +] +[table Operator ^(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.76928 (0.0404509s)][1.83515 (0.0299941s)][1.77409 (0.0323887s)][1.11493 (0.0372218s)]] +[[cpp_int(fixed)][[*1] (0.014607s)][[*1] (0.0163443s)][[*1] (0.0182565s)][[*1] (0.0333848s)]] +[[gmp_int][3.25823 (0.047593s)][3.05166 (0.0498771s)][2.96144 (0.0540655s)][1.47308 (0.0491785s)]] +[[tommath_int][17.006 (0.248407s)][15.2663 (0.249516s)][14.338 (0.261762s)][7.82864 (0.261357s)]] +] +[table Operator gcd +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][9.20736 (4.16823s)][3.91955 (8.51244s)][4.00539 (19.489s)][4.64192 (47.7651s)]] +[[cpp_int(fixed)][6.34685 (2.87326s)][3.07855 (6.68597s)][3.32507 (16.1788s)][4.07366 (41.9178s)]] +[[gmp_int][[*1] (0.452707s)][[*1] (2.17179s)][[*1] (4.86569s)][[*1] (10.2899s)]] +[[tommath_int][16.804 (7.6073s)][7.31428 (15.8851s)][6.96518 (33.8904s)][6.52732 (67.1657s)]] +] +[table Operator str +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.76995 (0.000703371s)][2.94246 (0.00181769s)][3.45149 (0.00434022s)][4.14052 (0.0122363s)]] +[[cpp_int(fixed)][1.58559 (0.000630107s)][2.42804 (0.00149991s)][3.30542 (0.00415653s)][3.90693 (0.011546s)]] +[[gmp_int][[*1] (0.000397397s)][[*1] (0.000617745s)][[*1] (0.00125749s)][[*1] (0.00295526s)]] +[[tommath_int][21.7585 (0.00864677s)][34.4291 (0.0212684s)][65.8175 (0.0827649s)][67.7946 (0.200351s)]] +] +[table Operator | +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.91883 (0.0242976s)][1.88265 (0.0281237s)][1.78879 (0.0339623s)][1.74117 (0.0457886s)]] +[[cpp_int(fixed)][1.08025 (0.0136789s)][1.03489 (0.0154596s)][[*1] (0.0189862s)][1.49756 (0.0393824s)]] +[[gmp_int][[*1] (0.0126627s)][[*1] (0.0149383s)][1.28585 (0.0244134s)][[*1] (0.0262977s)]] +[[tommath_int][5.86177 (0.0742258s)][4.9555 (0.0740269s)][4.18835 (0.0795209s)][3.55804 (0.0935681s)]] +] +[table Operator |(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.76183 (0.0454215s)][2.05967 (0.0323883s)][1.78143 (0.0324562s)][1.22147 (0.0372077s)]] +[[cpp_int(fixed)][[*1] (0.0164462s)][[*1] (0.015725s)][[*1] (0.0182191s)][[*1] (0.0304613s)]] +[[gmp_int][2.81912 (0.0463637s)][3.18611 (0.0501017s)][2.94469 (0.0536497s)][1.62702 (0.0495613s)]] +[[tommath_int][15.1485 (0.249135s)][15.9884 (0.251418s)][13.915 (0.253519s)][8.65293 (0.26358s)]] +] +[endsect] +[section:rational_performance Rational Type Perfomance] +[table Operator * +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][16.2879 (15.3196s)][10.7459 (45.9283s)][11.5596 (111.528s)][12.8553 (270.253s)]] +[[mpq_rational][[*1] (0.940549s)][[*1] (4.27402s)][[*1] (9.6481s)][[*1] (21.0227s)]] +] +[table Operator *(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][7.7465 (1.3425s)][10.6643 (2.05921s)][11.055 (2.75206s)][12.6365 (4.26866s)]] +[[mpq_rational][[*1] (0.173305s)][[*1] (0.193095s)][[*1] (0.248942s)][[*1] (0.337805s)]] +] +[table Operator + +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][16.0608 (8.33358s)][10.8037 (24.5753s)][11.4235 (58.1983s)][12.435 (139.884s)]] +[[mpq_rational][[*1] (0.518878s)][[*1] (2.2747s)][[*1] (5.09463s)][[*1] (11.2492s)]] +] +[table Operator +(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][7.82472 (1.14042s)][9.40883 (1.54697s)][9.02478 (1.83113s)][9.24894 (2.65768s)]] +[[mpq_rational][[*1] (0.145745s)][[*1] (0.164417s)][[*1] (0.202901s)][[*1] (0.287349s)]] +] +[table Operator - +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][16.0583 (8.3543s)][10.6997 (24.3831s)][11.4377 (58.3044s)][12.4116 (139.665s)]] +[[mpq_rational][[*1] (0.520249s)][[*1] (2.27886s)][[*1] (5.09757s)][[*1] (11.2528s)]] +] +[table Operator -(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][7.99602 (1.13947s)][9.62717 (1.55711s)][9.1151 (1.82889s)][9.53508 (2.68279s)]] +[[mpq_rational][[*1] (0.142505s)][[*1] (0.161741s)][[*1] (0.200644s)][[*1] (0.28136s)]] +] +[table Operator / +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][12.0736 (31.794s)][10.0089 (80.7871s)][10.9267 (184.73s)][12.204 (436.471s)]] +[[mpq_rational][[*1] (2.63335s)][[*1] (8.07149s)][[*1] (16.9064s)][[*1] (35.7647s)]] +] +[table Operator /(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][7.56092 (1.35276s)][10.5279 (2.12933s)][10.9509 (2.75885s)][12.166 (4.27228s)]] +[[mpq_rational][[*1] (0.178914s)][[*1] (0.202255s)][[*1] (0.251928s)][[*1] (0.351164s)]] +] +[table Operator str +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][13.4013 (0.00980984s)][23.4372 (0.0288878s)][27.4314 (0.067039s)][29.4814 (0.165057s)]] +[[mpq_rational][[*1] (0.000732008s)][[*1] (0.00123256s)][[*1] (0.00244388s)][[*1] (0.00559869s)]] +] +[endsect] From 45a08da90e7d1e6d58e17e587773fe599da10ac8 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 17 Mar 2012 09:18:20 +0000 Subject: [PATCH 135/256] Add simple version of the Miller Rabin test [SVN r77353] --- doc/html/boost_multiprecision/ref.html | 6 +- doc/html/boost_multiprecision/tut.html | 1 + doc/html/index.html | 3 +- doc/multiprecision.qbk | 28 +++++ example/safe_prime.cpp | 45 ++++++++ include/boost/multiprecision/miller_rabin.hpp | 106 ++++++++++++++++++ include/boost/multiprecision/random.hpp | 2 + test/Jamfile.v2 | 8 ++ test/test_miller_rabin.cpp | 47 ++++++++ 9 files changed, 242 insertions(+), 4 deletions(-) create mode 100644 example/safe_prime.cpp create mode 100644 include/boost/multiprecision/miller_rabin.hpp create mode 100644 test/test_miller_rabin.cpp diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html index d975490b..a31f61bb 100644 --- a/doc/html/boost_multiprecision/ref.html +++ b/doc/html/boost_multiprecision/ref.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -32,7 +32,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html index 0ac5b703..4d71a28e 100644 --- a/doc/html/boost_multiprecision/tut.html +++ b/doc/html/boost_multiprecision/tut.html @@ -22,6 +22,7 @@
    Floating Point Numbers
    Rational Number Types
    Generating Random Numbers
    +
    Primality Testing

    In order to use this library you need to make two choices: what kind of number diff --git a/doc/html/index.html b/doc/html/index.html index 5d80f737..abfa54c5 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -34,6 +34,7 @@

    Floating Point Numbers
    Rational Number Types
    Generating Random Numbers
    +
    Primality Testing
    Reference
    @@ -57,7 +58,7 @@
    - +

    Last revised: March 15, 2012 at 18:34:52 GMT

    Last revised: March 17, 2012 at 09:04:10 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index fe1cd9d4..9f174569 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -24,6 +24,7 @@ [import ../example/tommath_snips.cpp] [import ../example/cpp_int_snips.cpp] [import ../example/random_snips.cpp] +[import ../example/safe_prime.cpp] [template mpfr[] [@http://www.mpfr.org MPFR]] [template gmp[] [@http://gmplib.org GMP]] @@ -698,6 +699,33 @@ Finally, we can modify the above example to produce numbers distributed accordin [endsect] +[section:primetest Primality Testing] + +The library implements a fairly basic (meaning unoptimized, and possibly slow) Miller-Rabin test for primality: + + #include + + template + bool miller_rabin_test(const mp_number& n, unsigned trials, Engine& gen); + + template + bool miller_rabin_test(const mp_number& n, unsigned trials); + +These functions perform a Miller-Rabin test for primality, if the result is `false` then /n/ is definitely composite, +while if the result is `true` then /n/ is prime with probability 0.25^trials. The algorithm used is straight out of +Knuth Vol 2, which recomends 25 trials for a pretty strong likelyhood that /n/ is prime. + +The third optional argument is for a Uniform Random Number Generator from Boost.Random. When not provided the `mt19937` +generator is used. Note that when producing random primes then you should probably use a different random number generator +to produce possible primes, than used internally for testing whether the value is prime. It also helps of course to seed the +generators with some source of randomness. + +The following example searches for a prime `p` for which `(p-1)/2` is also probably prime: + +[safe_prime] + +[endsect] + [endsect] [section:ref Reference] diff --git a/example/safe_prime.cpp b/example/safe_prime.cpp new file mode 100644 index 00000000..12684659 --- /dev/null +++ b/example/safe_prime.cpp @@ -0,0 +1,45 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +//[safe_prime + +#include +#include +#include +#include + +int main() +{ + using namespace boost::random; + using namespace boost::multiprecision; + + typedef mpz_int int_type; + mt11213b base_gen(clock()); + independent_bits_engine gen(base_gen); + // + // We must use a different generator for the tests and number generation, otherwise + // we get false positives. + // + mt19937 gen2(clock()); + + for(unsigned i = 0; i < 100000; ++i) + { + int_type n = gen(); + if(miller_rabin_test(n, 25, gen2)) + { + // Value n is probably prime, see if (n-1)/2 is also prime: + std::cout << "We have a probable prime with value: " << std::hex << std::showbase << n << std::endl; + if(miller_rabin_test((n-1)/2, 25, gen2)) + { + std::cout << "We have a safe prime with value: " << std::hex << std::showbase << n << std::endl; + return 0; + } + } + } + std::cout << "Ooops, no safe primes were found" << std::endl; + return 1; +} + +//] diff --git a/include/boost/multiprecision/miller_rabin.hpp b/include/boost/multiprecision/miller_rabin.hpp new file mode 100644 index 00000000..f95713db --- /dev/null +++ b/include/boost/multiprecision/miller_rabin.hpp @@ -0,0 +1,106 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_MR_HPP +#define BOOST_MP_MR_HPP + +#include + +namespace boost{ +namespace multiprecision{ +// +// Calculate (a^b)%c: +// +template +void expmod(const mp_number& a, mp_number b, const mp_number& c, mp_number& result) +{ + typedef mp_number number_type; + number_type x(1), y(a); + while(b > 0) + { + if(b & 1) + { + x = (x * y) % c; + } + y = (y * y) % c; + b /= 2; + } + result = x % c; +} + +template +bool miller_rabin_test(const mp_number& n, unsigned trials, Engine& gen) +{ + typedef mp_number number_type; + + static const unsigned small_factors[] = { + 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u, 29u, 31u, 37u, 41u, 43u, 47u, 53u }; + + if(n < 2) + return false; + if((n & 1) == 0) + return false; + // + // Sanity check for small factors: + // + + number_type q = (n - 1) >> 1; + unsigned k = 1; + while((q & 1) == 0) + { + q >>= 1; + ++k; + } + // Declare our random number generator: + boost::random::uniform_int_distribution dist(0, n); + number_type nm1 = n - 1; + // + // Execute the trials: + // + for(unsigned i = 0; i < trials; ++i) + { + number_type x = dist(gen); + number_type y; + expmod(x, q, n, y); + unsigned j = 0; + while(true) + { + if((y == nm1) || ((y == 1) && (j == 0))) + break; + if(y == 1) + return false; // test failed + if(++j == k) + return false; // failed + y = (y * y) % n; + } + } + return true; // Yeheh! probably prime. +} + +template +bool miller_rabin_test(const mp_number& x, unsigned trials) +{ + static mt19937 gen; + return miller_rabin_test(x, trials, gen); +} + +template +bool miller_rabin_test(const detail::mp_exp & n, unsigned trials, Engine& gen) +{ + typedef typename detail::mp_exp::result_type number_type; + return miller_rabin_test(number_type(n), trials, gen); +} + +template +bool miller_rabin_test(const detail::mp_exp & n, unsigned trials) +{ + typedef typename detail::mp_exp::result_type number_type; + return miller_rabin_test(number_type(n), trials); +} + +}} // namespaces + +#endif + diff --git a/include/boost/multiprecision/random.hpp b/include/boost/multiprecision/random.hpp index 096ab8f1..4d82fedb 100644 --- a/include/boost/multiprecision/random.hpp +++ b/include/boost/multiprecision/random.hpp @@ -1,4 +1,6 @@ /////////////////////////////////////////////////////////////// +// Copyright Jens Maurer 2006-1011 +// Copyright Steven Watanabe 2011 // Copyright 2012 John Maddock. Distributed under the Boost // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 511e14fb..eeed5577 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -602,6 +602,14 @@ run test_cpp_int.cpp gmp release # otherwise runtime is too slow!! ; +run test_miller_rabin.cpp gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : no ] + release # otherwise runtime is too slow!! + ; + run test_rational_io.cpp $(TOMMATH) : # command line : # input files diff --git a/test/test_miller_rabin.cpp b/test/test_miller_rabin.cpp new file mode 100644 index 00000000..084d1ffb --- /dev/null +++ b/test/test_miller_rabin.cpp @@ -0,0 +1,47 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include +#include +#include +#include "test.hpp" + +int main() +{ + // + // Very simple test program to verify that the GMP's Miller-Rabin + // implementation and this one agree on whether some random numbers + // are prime or not. Of course these are probabilistic tests so there's + // no reason why they should actually agree - except the probability of + // disagreement for 25 trials is almost infinitely small. + // + using namespace boost::random; + using namespace boost::multiprecision; + independent_bits_engine gen; + // + // We must use a different generator for the tests and number generation, otherwise + // we get false positives. Further we use the same random number engine for the + // Miller Rabin test as GMP uses internally: + // + mt19937 gen2; + + for(unsigned i = 0; i < 10000; ++i) + { + mpz_int n = gen(); + bool is_prime_boost = miller_rabin_test(n, 25, gen2); + bool is_gmp_prime = mpz_probab_prime_p(n.backend().data(), 25); + if(is_prime_boost && is_gmp_prime) + { + std::cout << "We have a prime: " << std::hex << std::showbase << n << std::endl; + } + if(is_prime_boost != is_gmp_prime) + std::cout << std::hex << std::showbase << "n = " << n << std::endl; + BOOST_CHECK_EQUAL(is_prime_boost, is_gmp_prime); + } + return 0; +} + + From 6deafa525bafcfee27611a53eec9b1e809087bef Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 17 Mar 2012 13:23:32 +0000 Subject: [PATCH 136/256] Fix bug in cpp_int shown up by random number generations and change example to use it. [SVN r77359] --- doc/html/index.html | 2 +- example/safe_prime.cpp | 4 ++-- include/boost/multiprecision/cpp_int.hpp | 6 ++++-- 3 files changed, 7 insertions(+), 5 deletions(-) diff --git a/doc/html/index.html b/doc/html/index.html index abfa54c5..bc91e441 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -58,7 +58,7 @@
    - +

    Last revised: March 17, 2012 at 09:04:10 GMT

    Last revised: March 17, 2012 at 13:19:03 GMT
    diff --git a/example/safe_prime.cpp b/example/safe_prime.cpp index 12684659..71adf4f3 100644 --- a/example/safe_prime.cpp +++ b/example/safe_prime.cpp @@ -5,7 +5,7 @@ //[safe_prime -#include +#include #include #include #include @@ -15,7 +15,7 @@ int main() using namespace boost::random; using namespace boost::multiprecision; - typedef mpz_int int_type; + typedef cpp_int int_type; mt11213b base_gen(clock()); independent_bits_engine gen(base_gen); // diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 60d9cc50..667bd3d8 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -745,7 +745,9 @@ inline void add_unsigned(cpp_int_backend& result, co // Nothing fancy, just let uintmax_t take the strain: double_limb_type carry = 0; unsigned m, x; - minmax(a.size(), b.size(), m, x); + unsigned as = a.size(); + unsigned bs = b.size(); + minmax(as, bs, m, x); if(x == 1) { bool s = a.sign(); @@ -759,7 +761,7 @@ inline void add_unsigned(cpp_int_backend& result, co typename cpp_int_backend::limb_pointer pr = result.limbs(); typename cpp_int_backend::limb_pointer pr_end = pr + m; - if(a.size() < b.size()) + if(as < bs) swap(pa, pb); // First where a and b overlap: From 2349943cdb2487a547ba5c508016f40280beda92 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 17 Mar 2012 19:43:26 +0000 Subject: [PATCH 137/256] Fix some GMP int errors, and simplify modulus code. Fix some cpp_int errors. Improve cpp_int tests. [SVN r77362] --- include/boost/multiprecision/cpp_int.hpp | 2 +- include/boost/multiprecision/gmp.hpp | 88 +++------------------- test/test_cpp_int.cpp | 94 +++++++++++++++++++++++- 3 files changed, 105 insertions(+), 79 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 667bd3d8..b022d658 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1104,7 +1104,7 @@ inline void eval_multiply(cpp_int_backend& result, c typename cpp_int_backend::limb_pointer pa = a.limbs(); while(p != pe) { - carry += static_cast(*pa * static_cast(val)); + carry += static_cast(*pa) * static_cast(val); *p = static_cast(carry); carry >>= cpp_int_backend::limb_bits; ++p, ++pa; diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 47eb5f1b..f59b198f 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1110,21 +1110,11 @@ inline void eval_multiply(gmp_int& t, const gmp_int& o) } inline void eval_divide(gmp_int& t, const gmp_int& o) { - mpz_div(t.data(), t.data(), o.data()); + mpz_tdiv_q(t.data(), t.data(), o.data()); } inline void eval_modulus(gmp_int& t, const gmp_int& o) { - bool neg = mpz_sgn(t.data()) < 0; - bool neg2 = mpz_sgn(o.data()) < 0; - mpz_mod(t.data(), t.data(), o.data()); - if(neg && mpz_sgn(t.data()) != 0) - { - if(!neg2) - t.negate(); - mpz_add(t.data(), t.data(), o.data()); - if(!neg2) - t.negate(); - } + mpz_tdiv_r(t.data(), t.data(), o.data()); } inline void eval_add(gmp_int& t, unsigned long i) { @@ -1140,18 +1130,11 @@ inline void eval_multiply(gmp_int& t, unsigned long i) } inline void eval_modulus(gmp_int& t, unsigned long i) { - bool neg = mpz_sgn(t.data()) < 0; - mpz_mod_ui(t.data(), t.data(), i); - if(neg && mpz_sgn(t.data()) != 0) - { - t.negate(); - mpz_add_ui(t.data(), t.data(), i); - t.negate(); - } + mpz_tdiv_r_ui(t.data(), t.data(), i); } inline void eval_divide(gmp_int& t, unsigned long i) { - mpz_div_ui(t.data(), t.data(), i); + mpz_tdiv_q_ui(t.data(), t.data(), i); } inline void eval_add(gmp_int& t, long i) { @@ -1175,26 +1158,11 @@ inline void eval_multiply(gmp_int& t, long i) } inline void eval_modulus(gmp_int& t, long i) { - bool neg = mpz_sgn(t.data()) < 0; - bool neg2 = i < 0; - mpz_mod_ui(t.data(), t.data(), std::abs(i)); - if(neg && mpz_sgn(t.data()) != 0) - { - if(!neg2) - { - t.negate(); - mpz_add_ui(t.data(), t.data(), std::abs(i)); - t.negate(); - } - else - { - mpz_sub_ui(t.data(), t.data(), std::abs(i)); - } - } + mpz_tdiv_r_ui(t.data(), t.data(), std::abs(i)); } inline void eval_divide(gmp_int& t, long i) { - mpz_div_ui(t.data(), t.data(), std::abs(i)); + mpz_tdiv_q_ui(t.data(), t.data(), std::abs(i)); if(i < 0) mpz_neg(t.data(), t.data()); } @@ -1248,21 +1216,11 @@ inline void eval_multiply(gmp_int& t, const gmp_int& p, const gmp_int& o) } inline void eval_divide(gmp_int& t, const gmp_int& p, const gmp_int& o) { - mpz_div(t.data(), p.data(), o.data()); + mpz_tdiv_q(t.data(), p.data(), o.data()); } inline void eval_modulus(gmp_int& t, const gmp_int& p, const gmp_int& o) { - bool neg = mpz_sgn(p.data()) < 0; - bool neg2 = mpz_sgn(o.data()) < 0; - mpz_mod(t.data(), p.data(), o.data()); - if(neg && mpz_sgn(t.data()) != 0) - { - if(!neg2) - t.negate(); - mpz_add(t.data(), t.data(), o.data()); - if(!neg2) - t.negate(); - } + mpz_tdiv_r(t.data(), p.data(), o.data()); } inline void eval_add(gmp_int& t, const gmp_int& p, unsigned long i) { @@ -1278,18 +1236,11 @@ inline void eval_multiply(gmp_int& t, const gmp_int& p, unsigned long i) } inline void eval_modulus(gmp_int& t, const gmp_int& p, unsigned long i) { - bool neg = mpz_sgn(p.data()) < 0; - mpz_mod_ui(t.data(), p.data(), i); - if(neg && mpz_sgn(t.data()) != 0) - { - t.negate(); - mpz_add_ui(t.data(), t.data(), i); - t.negate(); - } + mpz_tdiv_r_ui(t.data(), p.data(), i); } inline void eval_divide(gmp_int& t, const gmp_int& p, unsigned long i) { - mpz_div_ui(t.data(), p.data(), i); + mpz_tdiv_q_ui(t.data(), p.data(), i); } inline void eval_add(gmp_int& t, const gmp_int& p, long i) { @@ -1313,26 +1264,11 @@ inline void eval_multiply(gmp_int& t, const gmp_int& p, long i) } inline void eval_modulus(gmp_int& t, const gmp_int& p, long i) { - bool neg = mpz_sgn(p.data()) < 0; - bool neg2 = i < 0; - mpz_mod_ui(t.data(), p.data(), std::abs(i)); - if(neg && mpz_sgn(t.data()) != 0) - { - if(!neg2) - { - t.negate(); - mpz_add_ui(t.data(), t.data(), std::abs(i)); - t.negate(); - } - else - { - mpz_sub_ui(t.data(), t.data(), std::abs(i)); - } - } + mpz_tdiv_r_ui(t.data(), p.data(), std::abs(i)); } inline void eval_divide(gmp_int& t, const gmp_int& p, long i) { - mpz_div_ui(t.data(), p.data(), std::abs(i)); + mpz_tdiv_q_ui(t.data(), p.data(), std::abs(i)); if(i < 0) mpz_neg(t.data(), t.data()); } diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp index 6cc69def..f806f125 100644 --- a/test/test_cpp_int.cpp +++ b/test/test_cpp_int.cpp @@ -65,6 +65,7 @@ void test() mpz_int d = generate_random(32); int si = d.convert_to(); + unsigned ui = si; test_type a1 = a.str(); test_type b1 = b.str(); @@ -76,56 +77,104 @@ void test() BOOST_CHECK_EQUAL(c.str(), c1.str()); BOOST_CHECK_EQUAL(d.str(), d1.str()); BOOST_CHECK_EQUAL(mpz_int(a+b).str(), test_type(a1 + b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)+=b).str(), (test_type(a1) += b1).str()); + BOOST_CHECK_EQUAL((mpz_int(b)+=a).str(), (test_type(b1) += a1).str()); BOOST_CHECK_EQUAL(mpz_int(a-b).str(), test_type(a1 - b1).str()); BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)+b).str(), test_type(test_type(-a1) + b1).str()); BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)-b).str(), test_type(test_type(-a1) - b1).str()); BOOST_CHECK_EQUAL(mpz_int(c * d).str(), test_type(c1 * d1).str()); + BOOST_CHECK_EQUAL((mpz_int(c)*=d).str(), (test_type(c1) *= d1).str()); + BOOST_CHECK_EQUAL((mpz_int(d)*=c).str(), (test_type(d1) *= c1).str()); BOOST_CHECK_EQUAL(mpz_int(c * -d).str(), test_type(c1 * -d1).str()); BOOST_CHECK_EQUAL(mpz_int(-c * d).str(), test_type(-c1 * d1).str()); + BOOST_CHECK_EQUAL((mpz_int(c)*=-d).str(), (test_type(c1) *= -d1).str()); + BOOST_CHECK_EQUAL((mpz_int(-d)*=c).str(), (test_type(-d1) *= c1).str()); BOOST_CHECK_EQUAL(mpz_int(b * c).str(), test_type(b1 * c1).str()); BOOST_CHECK_EQUAL(mpz_int(a / b).str(), test_type(a1 / b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)/=b).str(), (test_type(a1) /= b1).str()); BOOST_CHECK_EQUAL(mpz_int(a / -b).str(), test_type(a1 / -b1).str()); BOOST_CHECK_EQUAL(mpz_int(-a / b).str(), test_type(-a1 / b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)/=-b).str(), (test_type(a1) /= -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)/=b).str(), (test_type(-a1) /= b1).str()); BOOST_CHECK_EQUAL(mpz_int(a / d).str(), test_type(a1 / d1).str()); BOOST_CHECK_EQUAL(mpz_int(a % b).str(), test_type(a1 % b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=b).str(), (test_type(a1) %= b1).str()); BOOST_CHECK_EQUAL(mpz_int(a % -b).str(), test_type(a1 % -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=-b).str(), (test_type(a1) %= -b1).str()); BOOST_CHECK_EQUAL(mpz_int(-a % b).str(), test_type(-a1 % b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)%=b).str(), (test_type(-a1) %= b1).str()); BOOST_CHECK_EQUAL(mpz_int(a % d).str(), test_type(a1 % d1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=d).str(), (test_type(a1) %= d1).str()); // bitwise ops: BOOST_CHECK_EQUAL(mpz_int(a|b).str(), test_type(a1 | b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)|=b).str(), (test_type(a1) |= b1).str()); BOOST_CHECK_EQUAL(mpz_int(-a|b).str(), test_type(-a1 | b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)|=b).str(), (test_type(-a1) |= b1).str()); BOOST_CHECK_EQUAL(mpz_int(a|-b).str(), test_type(a1 | -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)|=-b).str(), (test_type(a1) |= -b1).str()); BOOST_CHECK_EQUAL(mpz_int(-a|-b).str(), test_type(-a1 | -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)|=-b).str(), (test_type(-a1) |= -b1).str()); BOOST_CHECK_EQUAL(mpz_int(a&b).str(), test_type(a1 & b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)&=b).str(), (test_type(a1) &= b1).str()); BOOST_CHECK_EQUAL(mpz_int(-a&b).str(), test_type(-a1 & b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)&=b).str(), (test_type(-a1) &= b1).str()); BOOST_CHECK_EQUAL(mpz_int(a&-b).str(), test_type(a1 & -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)&=-b).str(), (test_type(a1) &= -b1).str()); BOOST_CHECK_EQUAL(mpz_int(-a&-b).str(), test_type(-a1 & -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)&=-b).str(), (test_type(-a1) &= -b1).str()); BOOST_CHECK_EQUAL(mpz_int(a^b).str(), test_type(a1 ^ b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)^=b).str(), (test_type(a1) ^= b1).str()); BOOST_CHECK_EQUAL(mpz_int(-a^b).str(), test_type(-a1 ^ b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)^=b).str(), (test_type(-a1) ^= b1).str()); BOOST_CHECK_EQUAL(mpz_int(a^-b).str(), test_type(a1 ^ -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)^=-b).str(), (test_type(a1) ^= -b1).str()); BOOST_CHECK_EQUAL(mpz_int(-a^-b).str(), test_type(-a1 ^ -b1).str()); - // Now check operations involving integers: + BOOST_CHECK_EQUAL((mpz_int(-a)^=-b).str(), (test_type(-a1) ^= -b1).str()); + // Now check operations involving signed integers: BOOST_CHECK_EQUAL(mpz_int(a + si).str(), test_type(a1 + si).str()); BOOST_CHECK_EQUAL(mpz_int(a + -si).str(), test_type(a1 + -si).str()); BOOST_CHECK_EQUAL(mpz_int(-a + si).str(), test_type(-a1 + si).str()); BOOST_CHECK_EQUAL(mpz_int(si + a).str(), test_type(si + a1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)+=si).str(), (test_type(a1) += si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)+=-si).str(), (test_type(a1) += -si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)+=si).str(), (test_type(-a1) += si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)+=-si).str(), (test_type(-a1) += -si).str()); BOOST_CHECK_EQUAL(mpz_int(a - si).str(), test_type(a1 - si).str()); BOOST_CHECK_EQUAL(mpz_int(a - -si).str(), test_type(a1 - -si).str()); BOOST_CHECK_EQUAL(mpz_int(-a - si).str(), test_type(-a1 - si).str()); BOOST_CHECK_EQUAL(mpz_int(si - a).str(), test_type(si - a1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)-=si).str(), (test_type(a1) -= si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)-=-si).str(), (test_type(a1) -= -si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)-=si).str(), (test_type(-a1) -= si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)-=-si).str(), (test_type(-a1) -= -si).str()); BOOST_CHECK_EQUAL(mpz_int(b * si).str(), test_type(b1 * si).str()); BOOST_CHECK_EQUAL(mpz_int(b * -si).str(), test_type(b1 * -si).str()); BOOST_CHECK_EQUAL(mpz_int(-b * si).str(), test_type(-b1 * si).str()); BOOST_CHECK_EQUAL(mpz_int(si * b).str(), test_type(si * b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)*=si).str(), (test_type(a1) *= si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)*=-si).str(), (test_type(a1) *= -si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)*=si).str(), (test_type(-a1) *= si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)*=-si).str(), (test_type(-a1) *= -si).str()); BOOST_CHECK_EQUAL(mpz_int(a / si).str(), test_type(a1 / si).str()); BOOST_CHECK_EQUAL(mpz_int(a / -si).str(), test_type(a1 / -si).str()); BOOST_CHECK_EQUAL(mpz_int(-a / si).str(), test_type(-a1 / si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)/=si).str(), (test_type(a1) /= si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)/=-si).str(), (test_type(a1) /= -si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)/=si).str(), (test_type(-a1) /= si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)/=-si).str(), (test_type(-a1) /= -si).str()); BOOST_CHECK_EQUAL(mpz_int(a % si).str(), test_type(a1 % si).str()); BOOST_CHECK_EQUAL(mpz_int(a % -si).str(), test_type(a1 % -si).str()); BOOST_CHECK_EQUAL(mpz_int(-a % si).str(), test_type(-a1 % si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=si).str(), (test_type(a1) %= si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=-si).str(), (test_type(a1) %= -si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)%=si).str(), (test_type(-a1) %= si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)%=-si).str(), (test_type(-a1) %= -si).str()); BOOST_CHECK_EQUAL(mpz_int(a|si).str(), test_type(a1 | si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)|=si).str(), (test_type(a1) |= si).str()); BOOST_CHECK_EQUAL(mpz_int(a&si).str(), test_type(a1 & si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)&=si).str(), (test_type(a1) &= si).str()); BOOST_CHECK_EQUAL(mpz_int(a^si).str(), test_type(a1 ^ si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)^=si).str(), (test_type(a1) ^= si).str()); BOOST_CHECK_EQUAL(mpz_int(si|a).str(), test_type(si|a1).str()); BOOST_CHECK_EQUAL(mpz_int(si&a).str(), test_type(si&a1).str()); BOOST_CHECK_EQUAL(mpz_int(si^a).str(), test_type(si^a1).str()); @@ -137,6 +186,47 @@ void test() BOOST_CHECK_EQUAL(mpz_int(lcm(-c, -d)).str(), test_type(lcm(-c1, -d1)).str()); BOOST_CHECK_EQUAL(mpz_int(gcd(a, -b)).str(), test_type(gcd(a1, -b1)).str()); BOOST_CHECK_EQUAL(mpz_int(lcm(c, -d)).str(), test_type(lcm(c1, -d1)).str()); + // Now check operations involving unsigned integers: + BOOST_CHECK_EQUAL(mpz_int(a + ui).str(), test_type(a1 + ui).str()); + BOOST_CHECK_EQUAL(mpz_int(-a + ui).str(), test_type(-a1 + ui).str()); + BOOST_CHECK_EQUAL(mpz_int(ui + a).str(), test_type(ui + a1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)+=ui).str(), (test_type(a1) += ui).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)+=ui).str(), (test_type(-a1) += ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a - ui).str(), test_type(a1 - ui).str()); + BOOST_CHECK_EQUAL(mpz_int(-a - ui).str(), test_type(-a1 - ui).str()); + BOOST_CHECK_EQUAL(mpz_int(ui - a).str(), test_type(ui - a1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)-=ui).str(), (test_type(a1) -= ui).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)-=ui).str(), (test_type(-a1) -= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(b * ui).str(), test_type(b1 * ui).str()); + BOOST_CHECK_EQUAL(mpz_int(-b * ui).str(), test_type(-b1 * ui).str()); + BOOST_CHECK_EQUAL(mpz_int(ui * b).str(), test_type(ui * b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)*=ui).str(), (test_type(a1) *= ui).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)*=ui).str(), (test_type(-a1) *= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a / ui).str(), test_type(a1 / ui).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / ui).str(), test_type(-a1 / ui).str()); + BOOST_CHECK_EQUAL((mpz_int(a)/=ui).str(), (test_type(a1) /= ui).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)/=ui).str(), (test_type(-a1) /= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a % ui).str(), test_type(a1 % ui).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % ui).str(), test_type(-a1 % ui).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=ui).str(), (test_type(a1) %= ui).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)%=ui).str(), (test_type(-a1) %= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a|ui).str(), test_type(a1 | ui).str()); + BOOST_CHECK_EQUAL((mpz_int(a)|=ui).str(), (test_type(a1) |= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a&ui).str(), test_type(a1 & ui).str()); + BOOST_CHECK_EQUAL((mpz_int(a)&=ui).str(), (test_type(a1) &= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a^ui).str(), test_type(a1 ^ ui).str()); + BOOST_CHECK_EQUAL((mpz_int(a)^=ui).str(), (test_type(a1) ^= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(ui|a).str(), test_type(ui|a1).str()); + BOOST_CHECK_EQUAL(mpz_int(ui&a).str(), test_type(ui&a1).str()); + BOOST_CHECK_EQUAL(mpz_int(ui^a).str(), test_type(ui^a1).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(a, b)).str(), test_type(gcd(a1, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, d)).str(), test_type(lcm(c1, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, b)).str(), test_type(gcd(-a1, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, d)).str(), test_type(lcm(-c1, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, -b)).str(), test_type(gcd(-a1, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, -d)).str(), test_type(lcm(-c1, -d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(a, -b)).str(), test_type(gcd(a1, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, -d)).str(), test_type(lcm(c1, -d1)).str()); if(std::numeric_limits::is_modulo) { @@ -197,7 +287,7 @@ int main() { using namespace boost::multiprecision; test(); - test > >(); + test > >(); return boost::report_errors(); } From 24cff33935d13b3ad9d362c083376f162c24a79c Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 21 Mar 2012 09:19:57 +0000 Subject: [PATCH 138/256] Update Miller Rabin test to use small prime filtering. Add some new integer type operations. Update performance tests to match. [SVN r77451] --- doc/html/boost_multiprecision/map.html | 6 +- doc/html/boost_multiprecision/perf.html | 9 +- .../perf/float_performance.html | 6 +- .../perf/int_real_world.html | 217 +++ .../perf/integer_performance.html | 1648 ++++++++++------- .../perf/rational_performance.html | 905 +++++++++ .../boost_multiprecision/perf/realworld.html | 11 +- doc/html/boost_multiprecision/tut/ints.html | 15 +- .../boost_multiprecision/tut/primetest.html | 107 ++ doc/html/boost_multiprecision/tut/random.html | 157 ++ .../boost_multiprecision/tut/rational.html | 7 +- doc/html/index.html | 9 +- doc/multiprecision.qbk | 296 ++- include/boost/multiprecision/cpp_int.hpp | 176 +- include/boost/multiprecision/gmp.hpp | 27 + include/boost/multiprecision/integer_ops.hpp | 62 + include/boost/multiprecision/miller_rabin.hpp | 79 +- include/boost/multiprecision/tommath.hpp | 29 + performance/miller_rabin_performance.cpp | 164 ++ performance/performance_test-msvc-10.log | 1161 ++++++------ test/test_arithmetic.cpp | 19 + test/test_cpp_int.cpp | 17 +- 22 files changed, 3727 insertions(+), 1400 deletions(-) create mode 100644 doc/html/boost_multiprecision/perf/int_real_world.html create mode 100644 doc/html/boost_multiprecision/perf/rational_performance.html create mode 100644 doc/html/boost_multiprecision/tut/primetest.html create mode 100644 doc/html/boost_multiprecision/tut/random.html create mode 100644 include/boost/multiprecision/integer_ops.hpp create mode 100644 performance/miller_rabin_performance.cpp diff --git a/doc/html/boost_multiprecision/map.html b/doc/html/boost_multiprecision/map.html index 891900e9..4f482f06 100644 --- a/doc/html/boost_multiprecision/map.html +++ b/doc/html/boost_multiprecision/map.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -32,7 +32,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/perf.html b/doc/html/boost_multiprecision/perf.html index e62c527a..d36eb092 100644 --- a/doc/html/boost_multiprecision/perf.html +++ b/doc/html/boost_multiprecision/perf.html @@ -7,7 +7,7 @@ - +
    @@ -18,11 +18,16 @@ Performance Comparison

    -
    Real World Tests
    +
    Floating Point Real + World Tests
    +
    Integer Real + World Tests
    Float Algorithm Perfomance
    Integer Algorithm Perfomance
    +
    Rational + Type Perfomance
    diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html index 2b46f507..61490d94 100644 --- a/doc/html/boost_multiprecision/perf/float_performance.html +++ b/doc/html/boost_multiprecision/perf/float_performance.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -955,7 +955,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html new file mode 100644 index 00000000..5705e869 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/int_real_world.html @@ -0,0 +1,217 @@ + + + +Integer Real World Tests + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + These tests + measure the time taken to generate 1000 128-bit random numbers and test for + primality using the Miller Rabin test. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and libtommath-0.42.0. + The tests were run on 32-bit Windows Vista machine. +

    +
    ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Integer Type +

    +     		+

    + Relative (and Absolute) Times +

    +
    +

    + cpp_int +

    +     		+

    + 1.45089(0.481248s) +

    +
    +

    + cpp_int (no Expression templates) +

    +     		+

    + 1.61489(0.535646s) +

    +
    +

    + cpp_int (64-bit cache) +

    +     		+

    + 1.39273(0.461956s) +

    +
    +

    + cpp_int (256-bit cache) +

    +     		+

    + 1.37743(0.456884s) +

    +
    +

    + cpp_int (512-bit cache) +

    +     		+

    + 1.0919(0.362175s) +

    +
    +

    + cpp_int (1024-bit cache) +

    +     		+

    + 1.10864(0.367726s) +

    +
    +

    + mp_int +

    +     		+

    + 3.92956(1.3034s) +

    +
    +

    + mp_int (no Expression templates) +

    +     		+

    + 4.02496(1.33505s) +

    +
    +

    + mp_int1024_t +

    +     		+

    + 1.01094(0.335322s) +

    +
    +

    + mp_int1024_t (no Expression templates) +

    +     		+

    + 1(0.331692s) +

    +
    +

    + mpz_int +

    +     		+

    + 1.08472(0.359793s) +

    +
    +

    + mpz_int (no Expression templates) +

    +     		+

    + 1.20865(0.400901s) +

    +
    +

    + It's interesting to note that expression templates have little effect here + - perhaps because the actual expressions involved are relatively trivial + in this case - so the time taken for multiplication and division tends to + dominate. Also note how increasing the internal cache size used by cpp_int is quite effective in this case + in cutting out memory allocations altogether - cutting about a third off + the total runtime. +

    +
    + + + +
    Copyright © 2011 John Maddock

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html index 4cca438f..b5cc5574 100644 --- a/doc/html/boost_multiprecision/perf/integer_performance.html +++ b/doc/html/boost_multiprecision/perf/integer_performance.html @@ -7,11 +7,11 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -33,9 +33,8 @@ The tests were run on 32-bit Windows Vista machine.

    - Note that Linux x64 tests showed significantly worse performance for fixed_int division than on Win32 (or possibly - GMP behaves much better in that case). - Otherwise the results are much the same. + Linux x86_64 results are broadly similar, except that libtommath performs + much better there.

    Table 1.17. Operator +

    @@ -46,7 +45,6 @@ - @@ -54,11 +52,6 @@ Backend

    - -

    - 64 Bits -

    -

    128 Bits @@ -84,32 +77,54 @@

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    - 1 (0.0163669s) + 1.25708 (0.0524047s)

    - 1 (0.0326567s) + 1.31488 (0.08777s) +

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    + 1 (0.0321268s) +

    + + +

    + 1.16171 (0.0484289s) +

    + + +

    + 1.24017 (0.0827832s)

    @@ -121,27 +136,22 @@

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    - 2.65628 (0.0434751s) + 1.19676 (0.0498904s)

    - 1.54295 (0.0503875s) -

    - - -

    - 1.16477 (0.0702458s) + 1 (0.0667514s)

    @@ -153,27 +163,22 @@

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    - 1.30199 (0.0425188s) -

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    - 1.18909 (0.0717123s) + 1.06344 (0.0709863s)

    @@ -189,7 +194,6 @@ - @@ -197,11 +201,6 @@ Backend

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    -

    128 Bits @@ -227,32 +226,54 @@

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    - 1 (0.0119345s) + 1.12424 (0.0317931s) +

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    + + +

    + 1 (0.0197719s) +

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    + 1 (0.0282796s)

    @@ -264,27 +285,22 @@

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    - - -

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    @@ -296,27 +312,22 @@

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    @@ -439,27 +461,22 @@

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    - 1.39777 (0.0488346s) -

    - - -

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    @@ -475,7 +492,6 @@ - @@ -483,11 +499,6 @@ Backend

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    -

    128 Bits @@ -513,32 +524,54 @@

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    - 1 (0.0103282s) + 1.29599 (0.0235066s)

    - 1 (0.0119127s) + 1.21534 (0.0266136s) +

    + + + + +

    + cpp_int(fixed)

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    + + +

    + 1 (0.0152482s) +

    + + +

    + 1 (0.018138s) +

    + + +

    + 1 (0.021898s)

    @@ -550,27 +583,22 @@

    - 12.093 (0.0303454s) + 2.7938 (0.0289568s)

    - 8.50898 (0.0304669s) + 2.55493 (0.038958s)

    - 3.9284 (0.0405733s) + 3.12248 (0.0566356s)

    - 5.03037 (0.0599252s) -

    - - -

    - 5.96617 (0.105058s) + 4.48855 (0.0982904s)

    @@ -582,27 +610,22 @@

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    - 21.3372 (0.220375s) + 13.4093 (0.243217s)

    - 23.526 (0.280258s) -

    - - -

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    -

    128 Bits @@ -656,32 +673,54 @@

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    - 1 (0.120353s) + 1.4363 (0.656569s)

    - 1 (0.439147s) + 1.63701 (2.47859s) +

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    + cpp_int(fixed)

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    + + +

    + 1.16604 (0.147138s) +

    + + +

    + 1 (0.457124s) +

    + + +

    + 1 (1.5141s)

    @@ -693,27 +732,22 @@

    - 2.50746 (0.0560369s) + 1.19574 (0.0674975s)

    - 1.76676 (0.0663044s) + 1 (0.126186s)

    - 1.06052 (0.127636s) + 1.16627 (0.53313s)

    - 1.22558 (0.53821s) -

    - - -

    - 1.03538 (1.52168s) + 1.02906 (1.5581s)

    @@ -725,27 +759,22 @@

    - 3.00028 (0.0670506s) + 1.97229 (0.111333s)

    - 2.97696 (0.111722s) + 2.67087 (0.337027s)

    - 2.86257 (0.34452s) + 2.13031 (0.973817s)

    - 2.26661 (0.995374s) -

    - - -

    - 2.12926 (3.12935s) + 2.05869 (3.11706s)

    @@ -761,7 +790,6 @@ - @@ -769,11 +797,6 @@ Backend

    - -

    - 64 Bits -

    -

    128 Bits @@ -799,32 +822,54 @@

    - fixed_int + cpp_int

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    - 1 (0.0135739s) + 1.57086 (0.0407838s)

    - 1 (0.0192615s) + 1.60154 (0.0542267s)

    - 1 (0.0328339s) + 1.67808 (0.0804984s) +

    + + + + +

    + cpp_int(fixed)

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    + + +

    + 1.58263 (0.0410894s) +

    + + +

    + 1.61543 (0.054697s) +

    + + +

    + 1.66841 (0.0800346s)

    @@ -836,27 +881,22 @@

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    - 1.32814 (0.025582s) + 1 (0.033859s)

    - 1.01453 (0.033311s) -

    - - -

    - 1 (0.048001s) + 1 (0.0479706s)

    @@ -868,27 +908,22 @@

    - 53.8709 (0.239357s) + 12.4278 (0.279882s)

    - 18.3773 (0.249452s) + 11.9045 (0.309074s)

    - 14.2088 (0.273682s) + 10.5973 (0.358813s)

    - 14.0907 (0.462652s) -

    - - -

    - 9.10761 (0.437175s) + 9.47384 (0.454466s)

    @@ -904,7 +939,6 @@ - @@ -912,11 +946,6 @@ Backend

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    - 64 Bits -

    -

    128 Bits @@ -942,32 +971,54 @@

    - fixed_int + cpp_int

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    - 1 (0.573815s) + 1.39251 (1.33801s) +

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    + + +

    + 1 (0.320389s) +

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    @@ -979,27 +1030,22 @@

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    - 2.93514 (0.908404s) + 1.96635 (1.04635s)

    - 1.80497 (1.03572s) -

    - - -

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    @@ -1011,27 +1057,22 @@

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    - 12.3939 (2.13582s) + 9.35941 (2.99865s)

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    - 8.74047 (5.01541s) -

    - - -

    - 10.8288 (11.517s) + 11.8316 (11.3684s)

    @@ -1047,7 +1088,6 @@ - @@ -1055,11 +1095,6 @@ Backend

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    - 64 Bits -

    -

    128 Bits @@ -1085,32 +1120,54 @@

    - fixed_int + cpp_int

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    - 2.18324 (0.229148s) + 3.55054 (0.634559s)

    - 2.36331 (0.442167s) + 2.97898 (1.03205s) +

    + + + + +

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    + + +

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    + 2.56716 (0.458808s) +

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    @@ -1154,27 +1206,22 @@

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    -

    128 Bits @@ -1371,32 +1418,54 @@

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    @@ -1440,27 +1504,22 @@

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    - - -

    - 25.0046 (8.682s) + 24.0694 (8.50676s)

    @@ -1468,150 +1527,7 @@


    -

    Table 1.27. Operator str

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 64 Bits -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - fixed_int -

    -     		-

    - 1 (0.000465841s) -

    -     		-

    - 1 (0.00102073s) -

    -     		-

    - 1 (0.00207212s) -

    -     		-

    - 1.02618 (0.0062017s) -

    -     		-

    - 1.32649 (0.0190043s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.83823 (0.00132216s) -

    -     		-

    - 2.17537 (0.00222046s) -

    -     		-

    - 1.46978 (0.00304557s) -

    -     		-

    - 1 (0.00604351s) -

    -     		-

    - 1 (0.0143268s) -

    -
    -

    - tommath_int -

    -     		-

    - 15.76 (0.00734164s) -

    -     		-

    - 15.9879 (0.0163193s) -

    -     		-

    - 21.7337 (0.0450349s) -

    -     		-

    - 19.7183 (0.119168s) -

    -     		-

    - 26.3445 (0.377431s) -

    -
    -
    -
    -

    Table 1.28. Operator <<

    +

    Table 1.27. Operator <<

    @@ -1619,7 +1535,6 @@ - - + + + + + + @@ -1694,27 +1626,22 @@ - @@ -1726,27 +1653,22 @@ - @@ -1754,7 +1676,7 @@
    @@ -1627,11 +1542,6 @@ Backend

    		-

    - 64 Bits -

    -

    128 Bits @@ -1657,32 +1567,54 @@

    - fixed_int + cpp_int

    - 1 (0.0119095s) + 1.20362 (0.0224696s)

    - 1 (0.0131746s) + 1.08555 (0.0294403s)

    - 1 (0.0213483s) + 1 (0.0360516s)

    - 1 (0.0247552s) + 1.07177 (0.0523935s) +

    +
    +

    + cpp_int(fixed)

    - 1 (0.0339579s) + 1 (0.0186683s) +

    +     		+

    + 1 (0.0271201s) +

    +     		+

    + 1.02126 (0.036818s) +

    +     		+

    + 1 (0.0488848s)

    - 1.9355 (0.0230509s) + 1.36706 (0.0255207s)

    - 1.94257 (0.0255925s) + 1.12042 (0.0303858s)

    - 1.49684 (0.031955s) + 1.24359 (0.0448335s)

    - 1.79202 (0.0443618s) -

    -     		-

    - 2.0846 (0.0707887s) + 1.40143 (0.0685085s)

    - 2.64273 (0.0314737s) + 2.09357 (0.0390833s)

    - 2.95612 (0.0389456s) + 2.4569 (0.0666312s)

    - 3.05842 (0.065292s) + 2.63592 (0.0950291s)

    - 3.79496 (0.0939451s) -

    -     		-

    - 4.82142 (0.163725s) + 3.43638 (0.167987s)


    -

    Table 1.29. Operator >>

    +

    Table 1.28. Operator >>

    @@ -1762,7 +1684,6 @@ - - + + + + + + @@ -1837,27 +1775,22 @@ - @@ -1869,27 +1802,22 @@ - @@ -1897,7 +1825,7 @@
    @@ -1770,11 +1691,6 @@ Backend

    		-

    - 64 Bits -

    -

    128 Bits @@ -1800,32 +1716,54 @@

    - fixed_int + cpp_int

    - 1 (0.006361s) + 1.33649 (0.0210319s)

    - 1 (0.00880189s) + 1.12919 (0.0266135s)

    - 1 (0.0180295s) + 1.10413 (0.0307184s)

    - 1 (0.0220786s) + 1.09267 (0.0399373s) +

    +
    +

    + cpp_int(fixed)

    - 1 (0.0325312s) + 1 (0.0157367s) +

    +     		+

    + 1 (0.0235686s) +

    +     		+

    + 1 (0.0278214s) +

    +     		+

    + 1.05198 (0.0384501s)

    - 4.26889 (0.0271544s) + 1.72135 (0.0270884s)

    - 3.14669 (0.0276968s) + 1.2078 (0.0284661s)

    - 1.74396 (0.0314426s) + 1.16066 (0.0322912s)

    - 1.45928 (0.0322188s) -

    -     		-

    - 1.24596 (0.0405327s) + 1 (0.0365503s)

    - 39.4379 (0.250865s) + 15.4381 (0.242945s)

    - 28.6225 (0.251932s) + 11.8797 (0.279987s)

    - 16.4543 (0.296661s) + 10.9043 (0.303374s)

    - 14.2167 (0.313884s) -

    -     		-

    - 15.5842 (0.506974s) + 14.0762 (0.514491s)


    -

    Table 1.30. Operator &

    +

    Table 1.29. Operator &

    @@ -1905,7 +1833,6 @@ - - + + + + + + @@ -1980,27 +1924,22 @@ - @@ -2012,27 +1951,22 @@ - @@ -2040,7 +1974,7 @@
    @@ -1913,11 +1840,6 @@ Backend

    		-

    - 64 Bits -

    -

    128 Bits @@ -1943,32 +1865,54 @@

    - fixed_int + cpp_int

    - 1 (0.00298048s) + 1.65829 (0.0314059s)

    - 1 (0.00546222s) + 1.42198 (0.0390384s)

    - 1 (0.0127546s) + 1.48578 (0.0498903s)

    - 1 (0.01985s) + 1.51243 (0.0770342s) +

    +
    +

    + cpp_int(fixed)

    - 1 (0.0349286s) + 1 (0.0189387s) +

    +     		+

    + 1 (0.0274536s) +

    +     		+

    + 1 (0.0335786s) +

    +     		+

    + 1 (0.0509341s)

    - 16.0105 (0.0477189s) + 2.80248 (0.0530755s)

    - 9.67027 (0.0528211s) + 2.39752 (0.0658206s)

    - 5.12678 (0.0653902s) + 2.66009 (0.089322s)

    - 4.62316 (0.0917698s) -

    -     		-

    - 4.00837 (0.140007s) + 2.73942 (0.13953s)

    - 43.6665 (0.130147s) + 6.95432 (0.131706s)

    - 23.8003 (0.130002s) + 5.4059 (0.148412s)

    - 11.4242 (0.145711s) + 4.56887 (0.153417s)

    - 7.83416 (0.155508s) -

    -     		-

    - 9.50103 (0.331858s) + 6.5696 (0.334616s)


    -

    Table 1.31. Operator &(int)

    +

    Table 1.30. Operator &(int)

    @@ -2048,7 +1982,6 @@ - - + + + + + + @@ -2123,27 +2073,22 @@ - @@ -2155,27 +2100,22 @@ - @@ -2183,7 +2123,7 @@
    @@ -2056,11 +1989,6 @@ Backend

    		-

    - 64 Bits -

    -

    128 Bits @@ -2086,32 +2014,54 @@

    - fixed_int + cpp_int

    - 1 (0.00222291s) + 1.63285 (0.0472296s)

    - 1 (0.0035522s) + 1.43344 (0.0588492s)

    - 1 (0.0110247s) + 1.33141 (0.0724386s)

    - 1 (0.0154281s) + 1.21353 (0.104144s) +

    +
    +

    + cpp_int(fixed)

    - 1 (0.0275044s) + 1 (0.0289247s) +

    +     		+

    + 1 (0.0410546s) +

    +     		+

    + 1 (0.0544075s) +

    +     		+

    + 1 (0.0858187s)

    - 70.8538 (0.157502s) + 5.24478 (0.151704s)

    - 42.1478 (0.149717s) + 3.81907 (0.15679s)

    - 13.9023 (0.153268s) + 2.77979 (0.151242s)

    - 10.3271 (0.159328s) -

    -     		-

    - 6.0529 (0.166481s) + 1.84209 (0.158086s)

    - 154.134 (0.342626s) + 11.7257 (0.339163s)

    - 93.2035 (0.331077s) + 8.6379 (0.354625s)

    - 31.9151 (0.351853s) + 6.90411 (0.375636s)

    - 23.6515 (0.364899s) -

    -     		-

    - 22.0042 (0.605213s) + 7.63253 (0.655013s)


    -

    Table 1.32. Operator ^

    +

    Table 1.31. Operator ^

    @@ -2191,7 +2131,6 @@ - - + + + + + + @@ -2266,27 +2222,22 @@ - @@ -2298,27 +2249,22 @@ - @@ -2326,7 +2272,7 @@
    @@ -2199,11 +2138,6 @@ Backend

    		-

    - 64 Bits -

    -

    128 Bits @@ -2229,32 +2163,54 @@

    - fixed_int + cpp_int

    - 1 (0.00307714s) + 1.39325 (0.0297525s)

    - 1 (0.00538197s) + 1.28821 (0.0385005s)

    - 1 (0.0127717s) + 1.18843 (0.0492426s)

    - 1 (0.0198304s) + 1.07724 (0.0758668s) +

    +
    +

    + cpp_int(fixed)

    - 1 (0.0345822s) + 1 (0.0213547s) +

    +     		+

    + 1 (0.0298868s) +

    +     		+

    + 1 (0.041435s) +

    +     		+

    + 1 (0.070427s)

    - 13.9543 (0.0429392s) + 2.28582 (0.048813s)

    - 9.92785 (0.0534314s) + 2.03478 (0.0608129s)

    - 4.80398 (0.0613552s) + 2.05655 (0.0852131s)

    - 4.35864 (0.0864335s) -

    -     		-

    - 3.887 (0.134421s) + 1.92381 (0.135488s)

    - 41.5958 (0.127996s) + 6.17078 (0.131775s)

    - 24.2396 (0.130457s) + 4.8567 (0.145151s)

    - 11.3666 (0.145171s) + 3.64659 (0.151097s)

    - 8.01016 (0.158845s) -

    -     		-

    - 9.84853 (0.340584s) + 4.78192 (0.336776s)


    -

    Table 1.33. Operator ^(int)

    +

    Table 1.32. Operator ^(int)

    @@ -2334,7 +2280,6 @@ - - + + + + + + @@ -2409,27 +2371,22 @@ - @@ -2441,27 +2398,22 @@ - @@ -2469,7 +2421,7 @@
    @@ -2342,11 +2287,6 @@ Backend

    		-

    - 64 Bits -

    -

    128 Bits @@ -2372,32 +2312,54 @@

    - fixed_int + cpp_int

    - 1 (0.00236664s) + 1.89396 (0.0383127s)

    - 1 (0.0035339s) + 1.64269 (0.043417s)

    - 1 (0.0100442s) + 1.5386 (0.0477162s)

    - 1 (0.0155814s) + 1.32247 (0.0568053s) +

    +
    +

    + cpp_int(fixed)

    - 1 (0.0293253s) + 1 (0.0202288s) +

    +     		+

    + 1 (0.0264305s) +

    +     		+

    + 1 (0.0310128s) +

    +     		+

    + 1 (0.0429539s)

    - 61.4272 (0.145376s) + 7.01953 (0.141997s)

    - 41.6319 (0.147123s) + 5.47513 (0.14471s)

    - 14.9744 (0.150405s) + 4.6627 (0.144603s)

    - 9.64857 (0.150338s) -

    -     		-

    - 5.46649 (0.160306s) + 3.59601 (0.154463s)

    - 145.509 (0.344367s) + 16.2706 (0.329134s)

    - 93.9055 (0.331853s) + 12.9494 (0.342258s)

    - 35.0456 (0.352003s) + 11.3305 (0.35139s)

    - 22.7371 (0.354275s) -

    -     		-

    - 19.1373 (0.561207s) + 14.1712 (0.608709s)


    -

    Table 1.34. Operator |

    +

    Table 1.33. Operator |

    @@ -2477,7 +2429,6 @@ - - + + + + + + @@ -2552,27 +2520,22 @@ - @@ -2584,27 +2547,22 @@ - @@ -2612,7 +2570,7 @@
    @@ -2485,11 +2436,6 @@ Backend

    		-

    - 64 Bits -

    -

    128 Bits @@ -2515,32 +2461,54 @@

    - fixed_int + cpp_int

    - 1 (0.00295261s) + 1.34742 (0.0296944s)

    - 1 (0.00560832s) + 1.25923 (0.0384846s)

    - 1 (0.0127056s) + 1.20517 (0.0493908s)

    - 1 (0.0200759s) + 1.10536 (0.0761343s) +

    +
    +

    + cpp_int(fixed)

    - 1 (0.034651s) + 1 (0.0220379s) +

    +     		+

    + 1 (0.030562s) +

    +     		+

    + 1 (0.0409823s) +

    +     		+

    + 1 (0.0688775s)

    - 14.1091 (0.0416586s) + 2.14429 (0.0472558s)

    - 8.52475 (0.0478096s) + 1.95901 (0.0598712s)

    - 4.74593 (0.0602998s) + 2.07584 (0.0850728s)

    - 4.19694 (0.0842575s) -

    -     		-

    - 3.85525 (0.133588s) + 1.94265 (0.133805s)

    - 44.8889 (0.132539s) + 5.98286 (0.13185s)

    - 25.2503 (0.141612s) + 4.65705 (0.142329s)

    - 11.0488 (0.140382s) + 3.85812 (0.158115s)

    - 7.39273 (0.148416s) -

    -     		-

    - 9.75809 (0.338127s) + 4.81524 (0.331662s)


    -

    Table 1.35. Operator |(int)

    +

    Table 1.34. Operator |(int)

    @@ -2620,7 +2578,6 @@ - - + + + + + + @@ -2695,27 +2669,22 @@ - @@ -2727,27 +2696,320 @@ + + +
    @@ -2628,11 +2585,6 @@ Backend

    		-

    - 64 Bits -

    -

    128 Bits @@ -2658,32 +2610,54 @@

    - fixed_int + cpp_int

    - 1 (0.00244005s) + 1.40808 (0.0389721s)

    - 1 (0.0040142s) + 1.65035 (0.0437872s)

    - 1 (0.00983777s) + 1.51667 (0.0466144s)

    - 1 (0.0155223s) + 1.37806 (0.0582842s) +

    +
    +

    + cpp_int(fixed)

    - 1 (0.0293444s) + 1 (0.0276775s) +

    +     		+

    + 1 (0.026532s) +

    +     		+

    + 1 (0.0307348s) +

    +     		+

    + 1 (0.0422945s)

    - 64.6148 (0.157663s) + 5.31451 (0.147092s)

    - 34.5827 (0.138822s) + 5.37333 (0.142565s)

    - 14.2764 (0.140448s) + 4.86508 (0.149527s)

    - 10.3248 (0.160264s) -

    -     		-

    - 5.33565 (0.156572s) + 3.74364 (0.158335s)

    - 137.825 (0.3363s) + 11.9312 (0.330226s)

    - 81.1074 (0.325581s) + 12.943 (0.343403s)

    - 34.8737 (0.343079s) + 11.4457 (0.35178s)

    - 22.3727 (0.347276s) + 14.4462 (0.610997s) +

    +
    +
    +
    +

    Table 1.35. Operator gcd

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int

    - 18.912 (0.554963s) + 1.82514 (4.45586s) +

    +     		+

    + 1.75955 (10.1748s) +

    +     		+

    + 1.87025 (25.23s) +

    +     		+

    + 2.11453 (68.8556s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1.57965 (3.85654s) +

    +     		+

    + 1.67404 (9.68027s) +

    +     		+

    + 1.8405 (24.8287s) +

    +     		+

    + 2.27588 (74.1096s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (2.44138s) +

    +     		+

    + 1 (5.78259s) +

    +     		+

    + 1 (13.4902s) +

    +     		+

    + 1 (32.5631s) +

    +
    +

    + tommath_int +

    +     		+

    + 5.01357 (12.24s) +

    +     		+

    + 4.38161 (25.337s) +

    +     		+

    + 4.08681 (55.1319s) +

    +     		+

    + 4.01045 (130.593s) +

    +
    +
    +
    +

    Table 1.36. Operator str

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + @@ -2766,7 +3028,7 @@
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.46421 (0.00195137s) +

    +     		+

    + 1.21669 (0.00319216s) +

    +     		+

    + 1.25041 (0.00765237s) +

    +     		+

    + 1.53339 (0.0218096s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.00133271s) +

    +     		+

    + 1 (0.00262366s) +

    +     		+

    + 1.0109 (0.00618661s) +

    +     		+

    + 1.24429 (0.0176978s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.7777 (0.00236916s) +

    +     		+

    + 1.27408 (0.00334274s) +

    +     		+

    + 1 (0.00611991s) +

    +     		+

    + 1 (0.0142232s) +

    +
    +

    + tommath_int +

    +     		+

    + 11.9797 (0.0159654s) +

    +     		+

    + 18.3349 (0.0481046s) +

    +     		+

    + 18.3681 (0.112411s) +

    +     		+

    + 25.0355 (0.356085s)

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/perf/rational_performance.html b/doc/html/boost_multiprecision/perf/rational_performance.html new file mode 100644 index 00000000..fd98e028 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/rational_performance.html @@ -0,0 +1,905 @@ + + + +Rational Type Perfomance + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticsm, and real-world + peformance may vary widely depending upon the specifics of the program. In + each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. + The tests were run on 32-bit Windows Vista machine. +

    +
    +

    Table 1.37. Operator +

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.91758 (18.1263s) +

    +     		+

    + 6.60754 (44.1182s) +

    +     		+

    + 6.65334 (103.169s) +

    +     		+

    + 6.44717 (244.055s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (3.06312s) +

    +     		+

    + 1 (6.67695s) +

    +     		+

    + 1 (15.5064s) +

    +     		+

    + 1 (37.8546s) +

    +
    +
    +
    +

    Table 1.38. Operator +(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 3.98512 (2.67249s) +

    +     		+

    + 4.24335 (3.04309s) +

    +     		+

    + 4.65009 (3.83046s) +

    +     		+

    + 5.45832 (5.08346s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (0.670618s) +

    +     		+

    + 1 (0.717144s) +

    +     		+

    + 1 (0.823739s) +

    +     		+

    + 1 (0.931322s) +

    +
    +
    +
    +

    Table 1.39. Operator -

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.91504 (18.2374s) +

    +     		+

    + 6.55676 (43.8659s) +

    +     		+

    + 6.66239 (103.481s) +

    +     		+

    + 6.47224 (244.887s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (3.08322s) +

    +     		+

    + 1 (6.69018s) +

    +     		+

    + 1 (15.5321s) +

    +     		+

    + 1 (37.8365s) +

    +
    +
    +
    +

    Table 1.40. Operator -(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 3.96173 (2.66785s) +

    +     		+

    + 4.36532 (3.09023s) +

    +     		+

    + 4.59363 (3.74494s) +

    +     		+

    + 5.43075 (5.09156s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (0.673405s) +

    +     		+

    + 1 (0.707904s) +

    +     		+

    + 1 (0.815246s) +

    +     		+

    + 1 (0.937541s) +

    +
    +
    +
    +

    Table 1.41. Operator *

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.59286 (32.3559s) +

    +     		+

    + 6.54125 (82.4247s) +

    +     		+

    + 6.8815 (197.198s) +

    +     		+

    + 6.84066 (473.057s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (5.78521s) +

    +     		+

    + 1 (12.6008s) +

    +     		+

    + 1 (28.6562s) +

    +     		+

    + 1 (69.1537s) +

    +
    +
    +
    +

    Table 1.42. Operator *(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 2.70193 (3.1466s) +

    +     		+

    + 3.10134 (3.79056s) +

    +     		+

    + 3.659 (4.93935s) +

    +     		+

    + 4.61372 (6.89845s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (1.16457s) +

    +     		+

    + 1 (1.22223s) +

    +     		+

    + 1 (1.34992s) +

    +     		+

    + 1 (1.4952s) +

    +
    +
    +
    +

    Table 1.43. Operator /

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 4.36846 (63.9498s) +

    +     		+

    + 5.52565 (145.045s) +

    +     		+

    + 6.18331 (328.069s) +

    +     		+

    + 6.49822 (784.806s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (14.639s) +

    +     		+

    + 1 (26.2494s) +

    +     		+

    + 1 (53.0571s) +

    +     		+

    + 1 (120.772s) +

    +
    +
    +
    +

    Table 1.44. Operator /(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 2.26643 (3.13785s) +

    +     		+

    + 2.57125 (3.76931s) +

    +     		+

    + 3.20872 (5.06758s) +

    +     		+

    + 4.02177 (7.17803s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (1.38449s) +

    +     		+

    + 1 (1.46594s) +

    +     		+

    + 1 (1.57931s) +

    +     		+

    + 1 (1.78479s) +

    +
    +
    +
    +

    Table 1.45. Operator str

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.40493 (0.0199393s) +

    +     		+

    + 8.55089 (0.0511907s) +

    +     		+

    + 9.91026 (0.118839s) +

    +     		+

    + 9.93546 (0.285367s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (0.00368909s) +

    +     		+

    + 1 (0.00598659s) +

    +     		+

    + 1 (0.0119915s) +

    +     		+

    + 1 (0.028722s) +

    +
    +
    +
    +
    + + + +
    Copyright © 2011 John Maddock

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html index 8c880e2e..68464c8d 100644 --- a/doc/html/boost_multiprecision/perf/realworld.html +++ b/doc/html/boost_multiprecision/perf/realworld.html @@ -1,21 +1,22 @@ -Real World Tests +Floating Point Real World Tests - +
    -PrevUpHomeNext +PrevUpHomeNext

    These tests test the total time taken to execute all of Boost.Math's test @@ -271,7 +272,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html index e0b55bd3..2cc70776 100644 --- a/doc/html/boost_multiprecision/tut/ints.html +++ b/doc/html/boost_multiprecision/tut/ints.html @@ -113,7 +113,7 @@

    - libtommath + libtommath

    @@ -271,16 +271,17 @@

    The tommath_int backend is used via the typedef boost::multiprecision::mp_int. - It acts as a thin wrapper around the libtommath mp_int - to provide an integer type that is a drop-in replacement for the native C++ - integer types, but with unlimited precision. + It acts as a thin wrapper around the libtommath + mp_int to provide an integer + type that is a drop-in replacement for the native C++ integer types, but + with unlimited precision.

    Things you should know when using this type:

    • - Default constructed objects have the value zero (this is libtommath's + Default constructed objects have the value zero (this is libtommath's default behavior).
    • @@ -300,7 +301,7 @@ will be thrown.
    • - Division by zero will result in a hardware signal being raised by libtommath. + Division by zero will result in a hardware signal being raised by libtommath.
    @@ -359,11 +360,13 @@ typedef mp_number<cpp_int_backend<128, false, void> > mp_uint128_t; typedef mp_number<cpp_int_backend<256, false, void> > mp_uint256_t; typedef mp_number<cpp_int_backend<512, false, void> > mp_uint512_t; +typedef mp_number<cpp_int_backend<1024, false, void> > mp_uint1024_t; // Fixed precision signed types: typedef mp_number<cpp_int_backend<128, true, void> > mp_int128_t; typedef mp_number<cpp_int_backend<256, true, void> > mp_int256_t; typedef mp_number<cpp_int_backend<512, true, void> > mp_int512_t; +typedef mp_number<cpp_int_backend<1024, true, void> > mp_int1024_t; }} // namespaces diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html new file mode 100644 index 00000000..32a761ea --- /dev/null +++ b/doc/html/boost_multiprecision/tut/primetest.html @@ -0,0 +1,107 @@ + + + +Primality Testing + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + The library implements a fairly basic (meaning unoptimized, and possibly + slow) Miller-Rabin test for primality: +

    +
    #include <boost/multiprecision/miller_rabin.hpp>
+
+template <class Backend, bool ExpressionTemplates, class Engine>
+bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials, Engine& gen);
+
+template <class Backend, bool ExpressionTemplates, class Engine>
+bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials);
+
    +

    + These functions perform a Miller-Rabin test for primality, if the result + is false then n + is definitely composite, while if the result is true + then n is prime with probability 0.25^trials. The algorithm + used is straight out of Knuth Vol 2, which recomends 25 trials for a pretty + strong likelyhood that n is prime. +

    +

    + The third optional argument is for a Uniform Random Number Generator from + Boost.Random. When not provided the mt19937 + generator is used. Note that when producing random primes then you should + probably use a different random number generator to produce possible primes, + than used internally for testing whether the value is prime. It also helps + of course to seed the generators with some source of randomness. +

    +

    + The following example searches for a prime p + for which (p-1)/2 is also probably prime: +

    +

    +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+#include <boost/multiprecision/miller_rabin.hpp>
+#include <iostream>
+#include <iomanip>
+
+int main()
+{
+   using namespace boost::random;
+   using namespace boost::multiprecision;
+
+   typedef cpp_int int_type;
+   mt11213b base_gen(clock());
+   independent_bits_engine<mt11213b, 256, int_type> gen(base_gen);
+   //
+   // We must use a different generator for the tests and number generation, otherwise
+   // we get false positives.
+   //
+   mt19937 gen2(clock());
+
+   for(unsigned i = 0; i < 100000; ++i)
+   {
+      int_type n = gen();
+      if(miller_rabin_test(n, 25, gen2))
+      {
+         // Value n is probably prime, see if (n-1)/2 is also prime:
+         std::cout << "We have a probable prime with value: " << std::hex << std::showbase << n << std::endl;
+         if(miller_rabin_test((n-1)/2, 25, gen2))
+         {
+            std::cout << "We have a safe prime with value: " << std::hex << std::showbase << n << std::endl;
+            return 0;
+         }
+      }
+   }
+   std::cout << "Ooops, no safe primes were found" << std::endl;
+   return 1;
+}
+
    +

    +

    +
    + + + +
    Copyright © 2011 John Maddock

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/random.html b/doc/html/boost_multiprecision/tut/random.html new file mode 100644 index 00000000..5c383672 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/random.html @@ -0,0 +1,157 @@ + + + +Generating Random Numbers + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Random numbers are generated in conjunction with Boost.Random. However, since + Boost.Random is unaware of arbitrary precision numbers, it's necessary to + include the header: +

    +
    #include <boost/multiprecision/random.hpp>
+
    +

    + In order to act as a bridge between the two libraries. +

    +

    + Integers with N random bits are generated using independent_bits_engine: +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+
+//
+// Declare our random number generator type, the underlying generator
+// is the Mersenne twister mt19937 engine, and 256 bits are generated:
+//
+typedef independent_bits_engine<mt19937, 256, mpz_int> generator_type;
+generator_type gen;
+//
+// Generate some values:
+//
+std::cout << std::hex << std::showbase;
+for(unsigned i = 0; i < 10; ++i)
+   std::cout << gen() << std::endl;
+
    +

    +

    +

    + Alternatively we can generate integers in a given range using uniform_int_distribution, this will invoke + the underlying engine multiple times to build up the required number of bits + in the result: +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+
+//
+// Generate integers in a given range using uniform_int,
+// the underlying generator is invoked multiple times
+// to generate enough bits:
+//
+mt19937 mt;
+uniform_int_distribution<mpz_int> ui(0, mpz_int(1) << 256);
+//
+// Generate the numbers:
+//
+std::cout << std::hex << std::showbase;
+for(unsigned i = 0; i < 10; ++i)
+   std::cout << ui(mt) << std::endl;
+
    +

    +

    +

    + Floating point values in [0,1) are generated using uniform_01, + the trick here is to ensure that the underlying generator produces as many + random bits as there are digits in the floating point type. As above independent_bits_engine can be used for + this purpose, note that we also have to convert decimal digits (in the floating + point type) to bits (in the random number generator): +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+//
+// We need an underlying generator with at least as many bits as the
+// floating point type to generate numbers in [0, 1) with all the bits
+// in the floating point type randomly filled:
+//
+uniform_01<mpf_float_50> uf;
+independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen;
+//
+// Generate the values:
+//
+std::cout << std::setprecision(50);
+for(unsigned i = 0; i < 20; ++i)
+   std::cout << uf(gen) << std::endl;
+
    +

    +

    +

    + Finally, we can modify the above example to produce numbers distributed according + to some distribution: +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+//
+// We can repeat the above example, with other distributions:
+//
+uniform_real_distribution<mpf_float_50> ur(-20, 20);
+gamma_distribution<mpf_float_50> gd(20);
+independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen;
+//
+// Generate some values:
+//
+std::cout << std::setprecision(50);
+for(unsigned i = 0; i < 20; ++i)
+   std::cout << ur(gen) << std::endl;
+for(unsigned i = 0; i < 20; ++i)
+   std::cout << gd(gen) << std::endl;
+
    +

    +

    +
    + + + +
    Copyright © 2011 John Maddock

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 3c2cefcf..b3cba087 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -145,7 +145,7 @@

    - libtommath + libtommath

    @@ -452,8 +452,9 @@ information).
  • - No changes are made to libtommath's global state, so this type can safely - coexist with other libtommath code. + No changes are made to libtommath's + global state, so this type can safely coexist with other libtommath + code.
  • Performance of this type has been found to be pretty poor - this need diff --git a/doc/html/index.html b/doc/html/index.html index bc91e441..cf7ed306 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -43,11 +43,16 @@
    Performance Comparison
    -
    Real World Tests
    +
    Floating Point Real + World Tests
    +
    Integer Real + World Tests
    Float Algorithm Perfomance
    Integer Algorithm Perfomance
    +
    Rational + Type Perfomance
    Roadmap
    @@ -58,7 +63,7 @@
    • - +

    Last revised: March 17, 2012 at 13:19:03 GMT

    Last revised: March 20, 2012 at 19:02:47 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 9f174569..5d9597ae 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -32,6 +32,8 @@ [template mpfr_class[] [@http://math.berkeley.edu/~wilken/code/gmpfrxx/ mpfr_class]] [template mpreal[] [@http://www.holoborodko.com/pavel/mpfr/ mpreal]] [template mpir[] [@http://mpir.org/ MPIR]] +[template tommath[] [@http://libtom.org/?page=features&newsitems=5&whatfile=ltm libtommath]] + [section:intro Introduction] @@ -224,7 +226,7 @@ The following backends provide integer arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] [[`gmp_int`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient backend.][Dependency on GNU licenced [gmp] library.]] -[[`mp_int`][boost/multiprecision/tommath.hpp][2][libtommath][Public domain backend with no licence restrictions.][Slower than [gmp].]] +[[`mp_int`][boost/multiprecision/tommath.hpp][2][[tommath]][Public domain backend with no licence restrictions.][Slower than [gmp].]] [[`cpp_int`][boost/multiprecision/cpp_int.hpp][2][None] [Very versatile, Boost licenced, all C++ integer type which support both arbitrary precision and fixed precision integer types.][Slower than [gmp].]] ] @@ -275,12 +277,12 @@ is recomended on Win32. }} // namespaces -The `tommath_int` backend is used via the typedef `boost::multiprecision::mp_int`. It acts as a thin wrapper around the libtommath `mp_int` +The `tommath_int` backend is used via the typedef `boost::multiprecision::mp_int`. It acts as a thin wrapper around the [tommath] `mp_int` to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. Things you should know when using this type: -* Default constructed objects have the value zero (this is libtommath's default behavior). +* Default constructed objects have the value zero (this is [tommath]'s default behavior). * Although `mp_int` is mostly a drop in replacement for the builtin integer types, it should be noted that it is a rather strange beast as it's a signed type that is not a 2's complement type. As a result the bitwise operations `| & ^` will throw a `std::runtime_error` exception if either of the arguments is negative. Similarly the complement @@ -288,7 +290,7 @@ operator`~` is deliberately not implemented for this type. * Formatted IO for this type does not support octal or hexadecimal notation for negative values, as a result performing formatted output on this type when the argument is negative and either of the flags `std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. -* Division by zero will result in a hardware signal being raised by libtommath. +* Division by zero will result in a hardware signal being raised by [tommath]. [h5 Example:] @@ -311,11 +313,13 @@ as a result performing formatted output on this type when the argument is negati typedef mp_number > mp_uint128_t; typedef mp_number > mp_uint256_t; typedef mp_number > mp_uint512_t; + typedef mp_number > mp_uint1024_t; // Fixed precision signed types: typedef mp_number > mp_int128_t; typedef mp_number > mp_int256_t; typedef mp_number > mp_int512_t; + typedef mp_number > mp_int1024_t; }} // namespaces @@ -521,7 +525,7 @@ The following backends provide rational number arithmetic: [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] [[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient backend.][Dependency on GNU licenced [gmp] library.]] [[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licenced implementation.][Slower than [gmp].]] -[[`tommath_rational`][boost/multiprecision/tommath.hpp][2][libtommath][All C/C++ implementation that's Boost Software Licence compatible.][Slower than [gmp].]] +[[`tommath_rational`][boost/multiprecision/tommath.hpp][2][[tommath]][All C/C++ implementation that's Boost Software Licence compatible.][Slower than [gmp].]] [[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any inetger backend type to be used as a rational type.][Requires an underlying integer backend type.]] [[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `mp_number` integer type.][The expression templates used by `mp_number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]] ] @@ -629,7 +633,7 @@ Things you should know when using this type: * Default constructed `mp_rational`'s have the value zero (this the inherited Boost.Rational behavior). * Division by zero results in a `boost::bad_rational` exception being thrown (see the rational number library's docs for more information). -* No changes are made to libtommath's global state, so this type can safely coexist with other libtommath code. +* No changes are made to [tommath]'s global state, so this type can safely coexist with other [tommath] code. * Performance of this type has been found to be pretty poor - this need further investigation - but it appears that Boost.Rational needs some improvement in this area. @@ -1326,7 +1330,7 @@ in point of fact this naming convension shouldn't be necessary, but rather works [section:perf Performance Comparison] -[section:realworld Real World Tests] +[section:realworld Floating Point Real World Tests] These tests test the total time taken to execute all of Boost.Math's test cases for these functions. In each case the best performing library gets a relative score of 1, with the total execution time @@ -1358,6 +1362,38 @@ Windows Vista machine. [endsect] +[section:int_real_world Integer Real World Tests] + +These [@../../performance/miller_rabin_performance.cpp tests] measure the time taken to generate 1000 128-bit +random numbers and test for primality using the Miller Rabin test. + +Test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and [tommath]-0.42.0. The tests were run on 32-bit +Windows Vista machine. + +[table +[[Integer Type][Relative (and Absolute) Times]] +[[cpp_int][1.45089(0.481248s)]] +[[cpp_int (no Expression templates)][1.61489(0.535646s)]] +[[cpp_int (64-bit cache)][1.39273(0.461956s)]] +[[cpp_int (256-bit cache)][1.37743(0.456884s)]] +[[cpp_int (512-bit cache)][1.0919(0.362175s)]] +[[cpp_int (1024-bit cache)][1.10864(0.367726s)]] +[[mp_int][3.92956(1.3034s)]] +[[mp_int (no Expression templates)][4.02496(1.33505s)]] +[[mp_int1024_t][1.01094(0.335322s)]] +[[mp_int1024_t (no Expression templates)][1(0.331692s)]] +[[mpz_int][1.08472(0.359793s)]] +[[mpz_int (no Expression templates)][1.20865(0.400901s)]] +] + +It's interesting to note that expression templates have little effect here - perhaps because the actual expressions involved +are relatively trivial in this case - so the time taken for multiplication and division tends to dominate. Also note +how increasing the internal cache size used by `cpp_int` is quite effective in this case in cutting out memory allocations +altogether - cutting about a third off the total runtime. + +[endsect] + [section:float_performance Float Algorithm Perfomance] Note that these tests are carefully designed to test performance of the underlying algorithms @@ -1441,123 +1477,207 @@ Test code was compiled with Microsoft Visual Studio 2010 with all optimisations turned on (/Ox), and used MPIR-2.3.0 and [mpfr]-3.0.0. The tests were run on 32-bit Windows Vista machine. -Note that Linux x64 tests showed significantly worse performance for `fixed_int` division -than on Win32 (or possibly [gmp] behaves much better in that case). Otherwise the results -are much the same. +Linux x86_64 results are broadly similar, except that libtommath performs much better there. [table Operator + -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0031291s)][[*1] (0.00703043s)][[*1] (0.0163669s)][[*1] (0.0326567s)][[*1] (0.0603087s)]] -[[gmp_int][12.4866 (0.0390717s)][6.01034 (0.0422553s)][2.65628 (0.0434751s)][1.54295 (0.0503875s)][1.16477 (0.0702458s)]] -[[tommath_int][6.03111 (0.018872s)][3.08173 (0.0216659s)][1.84243 (0.0301548s)][1.30199 (0.0425188s)][1.18909 (0.0717123s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.24574 (0.0270133s)][1.09665 (0.0352319s)][1.25708 (0.0524047s)][1.31488 (0.08777s)]] +[[cpp_int(fixed)][1.05787 (0.0229394s)][[*1] (0.0321268s)][1.16171 (0.0484289s)][1.24017 (0.0827832s)]] +[[gmp_int][2.08016 (0.0451073s)][1.33792 (0.042983s)][1.19676 (0.0498904s)][[*1] (0.0667514s)]] +[[tommath_int][[*1] (0.0216845s)][1.07779 (0.0346258s)][[*1] (0.0416877s)][1.06344 (0.0709863s)]] ] [table Operator +(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00335294s)][[*1] (0.00376116s)][[*1] (0.00985174s)][[*1] (0.0119345s)][[*1] (0.0170918s)]] -[[gmp_int][9.47407 (0.031766s)][8.44794 (0.0317741s)][4.23857 (0.0417573s)][5.40856 (0.0645488s)][6.31314 (0.107903s)]] -[[tommath_int][67.0025 (0.224655s)][60.4203 (0.22725s)][25.1834 (0.2481s)][23.2996 (0.27807s)][17.1743 (0.293538s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.46244 (0.0202077s)][1.20665 (0.0238576s)][1.17647 (0.0258293s)][1.12424 (0.0317931s)]] +[[cpp_int(fixed)][[*1] (0.0138178s)][[*1] (0.0197719s)][[*1] (0.0219548s)][[*1] (0.0282796s)]] +[[gmp_int][2.15321 (0.0297527s)][2.09834 (0.041488s)][2.89935 (0.0636546s)][3.70262 (0.104709s)]] +[[tommath_int][17.1419 (0.236864s)][12.9762 (0.256563s)][12.3275 (0.270648s)][10.7373 (0.303648s)]] ] [table Operator - -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00339191s)][[*1] (0.0073172s)][[*1] (0.0166428s)][[*1] (0.0349375s)][[*1] (0.0600083s)]] -[[gmp_int][12.5182 (0.0424608s)][5.57936 (0.0408253s)][2.78496 (0.0463496s)][1.48373 (0.051838s)][1.29928 (0.0779673s)]] -[[tommath_int][7.00782 (0.0237699s)][3.69919 (0.0270677s)][2.29645 (0.0382195s)][1.39777 (0.0488346s)][1.28243 (0.0769566s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.15385 (0.029665s)][1.08217 (0.0369886s)][1.05882 (0.051534s)][1.12132 (0.0822725s)]] +[[cpp_int(fixed)][[*1] (0.0257095s)][[*1] (0.0341801s)][[*1] (0.0486711s)][1.08659 (0.0797242s)]] +[[gmp_int][1.56685 (0.040283s)][1.32917 (0.0454312s)][1.06917 (0.0520378s)][[*1] (0.0733708s)]] +[[tommath_int][1.059 (0.0272264s)][1.16974 (0.0399818s)][1.01303 (0.0493054s)][1.03375 (0.0758472s)]] ] [table Operator -(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00250933s)][[*1] (0.00358055s)][[*1] (0.0103282s)][[*1] (0.0119127s)][[*1] (0.0176089s)]] -[[gmp_int][12.093 (0.0303454s)][8.50898 (0.0304669s)][3.9284 (0.0405733s)][5.03037 (0.0599252s)][5.96617 (0.105058s)]] -[[tommath_int][80.8477 (0.202873s)][57.8371 (0.207089s)][21.3372 (0.220375s)][23.526 (0.280258s)][14.793 (0.260488s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.51665 (0.0157196s)][1.31513 (0.0200533s)][1.29599 (0.0235066s)][1.21534 (0.0266136s)]] +[[cpp_int(fixed)][[*1] (0.0103647s)][[*1] (0.0152482s)][[*1] (0.018138s)][[*1] (0.021898s)]] +[[gmp_int][2.7938 (0.0289568s)][2.55493 (0.038958s)][3.12248 (0.0566356s)][4.48855 (0.0982904s)]] +[[tommath_int][20.8695 (0.216305s)][15.0705 (0.229797s)][13.4093 (0.243217s)][12.2599 (0.268468s)]] ] [table Operator * -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0223481s)][[*1] (0.0375288s)][[*1] (0.120353s)][[*1] (0.439147s)][[*1] (1.46969s)]] -[[gmp_int][2.50746 (0.0560369s)][1.76676 (0.0663044s)][1.06052 (0.127636s)][1.22558 (0.53821s)][1.03538 (1.52168s)]] -[[tommath_int][3.00028 (0.0670506s)][2.97696 (0.111722s)][2.86257 (0.34452s)][2.26661 (0.995374s)][2.12926 (3.12935s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.29504 (0.0731032s)][1.55431 (0.196132s)][1.4363 (0.656569s)][1.63701 (2.47859s)]] +[[cpp_int(fixed)][[*1] (0.0564485s)][1.16604 (0.147138s)][[*1] (0.457124s)][[*1] (1.5141s)]] +[[gmp_int][1.19574 (0.0674975s)][[*1] (0.126186s)][1.16627 (0.53313s)][1.02906 (1.5581s)]] +[[tommath_int][1.97229 (0.111333s)][2.67087 (0.337027s)][2.13031 (0.973817s)][2.05869 (3.11706s)]] ] [table Operator *(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00444316s)][[*1] (0.0135739s)][[*1] (0.0192615s)][[*1] (0.0328339s)][1.18198 (0.0567364s)]] -[[gmp_int][4.57776 (0.0203397s)][1.79901 (0.0244196s)][1.32814 (0.025582s)][1.01453 (0.033311s)][[*1] (0.048001s)]] -[[tommath_int][53.8709 (0.239357s)][18.3773 (0.249452s)][14.2088 (0.273682s)][14.0907 (0.462652s)][9.10761 (0.437175s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.34609 (0.030315s)][1.57086 (0.0407838s)][1.60154 (0.0542267s)][1.67808 (0.0804984s)]] +[[cpp_int(fixed)][1.29783 (0.0292279s)][1.58263 (0.0410894s)][1.61543 (0.054697s)][1.66841 (0.0800346s)]] +[[gmp_int][[*1] (0.0225207s)][[*1] (0.0259628s)][[*1] (0.033859s)][[*1] (0.0479706s)]] +[[tommath_int][12.4278 (0.279882s)][11.9045 (0.309074s)][10.5973 (0.358813s)][9.47384 (0.454466s)]] ] [table Operator / -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0991632s)][[*1] (0.172328s)][[*1] (0.309492s)][[*1] (0.573815s)][[*1] (1.06356s)]] -[[gmp_int][7.81859 (0.775316s)][5.11069 (0.880715s)][2.93514 (0.908404s)][1.80497 (1.03572s)][1.21878 (1.29625s)]] -[[tommath_int][18.0766 (1.79253s)][12.3939 (2.13582s)][9.80438 (3.03438s)][8.74047 (5.01541s)][10.8288 (11.517s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.86387 (0.593314s)][2.18375 (0.69965s)][1.72571 (0.918294s)][1.39251 (1.33801s)]] +[[cpp_int(fixed)][[*1] (0.207172s)][[*1] (0.320389s)][[*1] (0.532127s)][[*1] (0.960856s)]] +[[gmp_int][3.89115 (0.806137s)][2.87573 (0.921352s)][1.96635 (1.04635s)][1.29618 (1.24544s)]] +[[tommath_int][11.9483 (2.47535s)][9.35941 (2.99865s)][8.79014 (4.67747s)][11.8316 (11.3684s)]] ] [table Operator /(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][1.04098 (0.0443082s)][1.61317 (0.110308s)][2.18324 (0.229148s)][2.36331 (0.442167s)][2.45159 (0.866172s)]] -[[gmp_int][[*1] (0.042564s)][[*1] (0.06838s)][[*1] (0.104957s)][[*1] (0.187096s)][[*1] (0.35331s)]] -[[tommath_int][32.4072 (1.37938s)][23.7471 (1.62383s)][22.1907 (2.32908s)][19.9054 (3.72421s)][24.2219 (8.55783s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][5.77003 (0.313196s)][4.38067 (0.431864s)][3.55054 (0.634559s)][2.97898 (1.03205s)]] +[[cpp_int(fixed)][2.48952 (0.135131s)][2.59188 (0.255519s)][2.56716 (0.458808s)][2.52368 (0.874313s)]] +[[gmp_int][[*1] (0.0542797s)][[*1] (0.0985842s)][[*1] (0.178722s)][[*1] (0.346443s)]] +[[tommath_int][31.6477 (1.71783s)][22.8727 (2.25489s)][19.9248 (3.56101s)][24.3266 (8.42779s)]] ] [table Operator % -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0946529s)][[*1] (0.170561s)][[*1] (0.328458s)][[*1] (0.575884s)][[*1] (1.05006s)]] -[[gmp_int][7.77525 (0.73595s)][4.39387 (0.749422s)][2.35075 (0.772122s)][1.51922 (0.874894s)][1.02263 (1.07382s)]] -[[tommath_int][27.1503 (2.56986s)][12.8743 (2.19585s)][9.43965 (3.10053s)][8.24936 (4.75068s)][10.9719 (11.5211s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.9813 (0.357541s)][1.55667 (0.460146s)][1.35341 (0.681144s)][1.19906 (1.10138s)]] +[[cpp_int(fixed)][[*1] (0.180457s)][[*1] (0.295597s)][[*1] (0.503278s)][[*1] (0.918538s)]] +[[gmp_int][3.50213 (0.631985s)][2.33312 (0.689662s)][1.57264 (0.791475s)][1.07795 (0.99014s)]] +[[tommath_int][12.2393 (2.20868s)][10.1123 (2.98915s)][9.46676 (4.76442s)][12.1795 (11.1873s)]] ] [table Operator %(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][1.25034 (0.0425984s)][1.91617 (0.106226s)][2.02166 (0.195577s)][2.14437 (0.387067s)][2.23514 (0.776075s)]] -[[gmp_int][[*1] (0.0340695s)][[*1] (0.0554367s)][[*1] (0.0967406s)][[*1] (0.180504s)][[*1] (0.347216s)]] -[[tommath_int][42.8781 (1.46083s)][29.879 (1.65639s)][23.4323 (2.26685s)][19.932 (3.5978s)][25.0046 (8.682s)]] -] -[table Operator str -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.000465841s)][[*1] (0.00102073s)][[*1] (0.00207212s)][1.02618 (0.0062017s)][1.32649 (0.0190043s)]] -[[gmp_int][2.83823 (0.00132216s)][2.17537 (0.00222046s)][1.46978 (0.00304557s)][[*1] (0.00604351s)][[*1] (0.0143268s)]] -[[tommath_int][15.76 (0.00734164s)][15.9879 (0.0163193s)][21.7337 (0.0450349s)][19.7183 (0.119168s)][26.3445 (0.377431s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.88485 (0.105552s)][2.00194 (0.203711s)][2.08202 (0.380096s)][2.12794 (0.752068s)]] +[[cpp_int(fixed)][1.7474 (0.0978544s)][1.88457 (0.191768s)][2.0306 (0.37071s)][2.0851 (0.736929s)]] +[[gmp_int][[*1] (0.0560001s)][[*1] (0.101757s)][[*1] (0.182561s)][[*1] (0.353426s)]] +[[tommath_int][30.4466 (1.70501s)][22.2997 (2.26915s)][19.6199 (3.58184s)][24.0694 (8.50676s)]] ] [table Operator << -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0119095s)][[*1] (0.0131746s)][[*1] (0.0213483s)][[*1] (0.0247552s)][[*1] (0.0339579s)]] -[[gmp_int][1.9355 (0.0230509s)][1.94257 (0.0255925s)][1.49684 (0.031955s)][1.79202 (0.0443618s)][2.0846 (0.0707887s)]] -[[tommath_int][2.64273 (0.0314737s)][2.95612 (0.0389456s)][3.05842 (0.065292s)][3.79496 (0.0939451s)][4.82142 (0.163725s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.20362 (0.0224696s)][1.08555 (0.0294403s)][[*1] (0.0360516s)][1.07177 (0.0523935s)]] +[[cpp_int(fixed)][[*1] (0.0186683s)][[*1] (0.0271201s)][1.02126 (0.036818s)][[*1] (0.0488848s)]] +[[gmp_int][1.36706 (0.0255207s)][1.12042 (0.0303858s)][1.24359 (0.0448335s)][1.40143 (0.0685085s)]] +[[tommath_int][2.09357 (0.0390833s)][2.4569 (0.0666312s)][2.63592 (0.0950291s)][3.43638 (0.167987s)]] ] [table Operator >> -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.006361s)][[*1] (0.00880189s)][[*1] (0.0180295s)][[*1] (0.0220786s)][[*1] (0.0325312s)]] -[[gmp_int][4.26889 (0.0271544s)][3.14669 (0.0276968s)][1.74396 (0.0314426s)][1.45928 (0.0322188s)][1.24596 (0.0405327s)]] -[[tommath_int][39.4379 (0.250865s)][28.6225 (0.251932s)][16.4543 (0.296661s)][14.2167 (0.313884s)][15.5842 (0.506974s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.33649 (0.0210319s)][1.12919 (0.0266135s)][1.10413 (0.0307184s)][1.09267 (0.0399373s)]] +[[cpp_int(fixed)][[*1] (0.0157367s)][[*1] (0.0235686s)][[*1] (0.0278214s)][1.05198 (0.0384501s)]] +[[gmp_int][1.72135 (0.0270884s)][1.2078 (0.0284661s)][1.16066 (0.0322912s)][[*1] (0.0365503s)]] +[[tommath_int][15.4381 (0.242945s)][11.8797 (0.279987s)][10.9043 (0.303374s)][14.0762 (0.514491s)]] ] [table Operator & -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00298048s)][[*1] (0.00546222s)][[*1] (0.0127546s)][[*1] (0.01985s)][[*1] (0.0349286s)]] -[[gmp_int][16.0105 (0.0477189s)][9.67027 (0.0528211s)][5.12678 (0.0653902s)][4.62316 (0.0917698s)][4.00837 (0.140007s)]] -[[tommath_int][43.6665 (0.130147s)][23.8003 (0.130002s)][11.4242 (0.145711s)][7.83416 (0.155508s)][9.50103 (0.331858s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.65829 (0.0314059s)][1.42198 (0.0390384s)][1.48578 (0.0498903s)][1.51243 (0.0770342s)]] +[[cpp_int(fixed)][[*1] (0.0189387s)][[*1] (0.0274536s)][[*1] (0.0335786s)][[*1] (0.0509341s)]] +[[gmp_int][2.80248 (0.0530755s)][2.39752 (0.0658206s)][2.66009 (0.089322s)][2.73942 (0.13953s)]] +[[tommath_int][6.95432 (0.131706s)][5.4059 (0.148412s)][4.56887 (0.153417s)][6.5696 (0.334616s)]] ] [table Operator &(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00222291s)][[*1] (0.0035522s)][[*1] (0.0110247s)][[*1] (0.0154281s)][[*1] (0.0275044s)]] -[[gmp_int][70.8538 (0.157502s)][42.1478 (0.149717s)][13.9023 (0.153268s)][10.3271 (0.159328s)][6.0529 (0.166481s)]] -[[tommath_int][154.134 (0.342626s)][93.2035 (0.331077s)][31.9151 (0.351853s)][23.6515 (0.364899s)][22.0042 (0.605213s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.63285 (0.0472296s)][1.43344 (0.0588492s)][1.33141 (0.0724386s)][1.21353 (0.104144s)]] +[[cpp_int(fixed)][[*1] (0.0289247s)][[*1] (0.0410546s)][[*1] (0.0544075s)][[*1] (0.0858187s)]] +[[gmp_int][5.24478 (0.151704s)][3.81907 (0.15679s)][2.77979 (0.151242s)][1.84209 (0.158086s)]] +[[tommath_int][11.7257 (0.339163s)][8.6379 (0.354625s)][6.90411 (0.375636s)][7.63253 (0.655013s)]] ] [table Operator ^ -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00307714s)][[*1] (0.00538197s)][[*1] (0.0127717s)][[*1] (0.0198304s)][[*1] (0.0345822s)]] -[[gmp_int][13.9543 (0.0429392s)][9.92785 (0.0534314s)][4.80398 (0.0613552s)][4.35864 (0.0864335s)][3.887 (0.134421s)]] -[[tommath_int][41.5958 (0.127996s)][24.2396 (0.130457s)][11.3666 (0.145171s)][8.01016 (0.158845s)][9.84853 (0.340584s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.39325 (0.0297525s)][1.28821 (0.0385005s)][1.18843 (0.0492426s)][1.07724 (0.0758668s)]] +[[cpp_int(fixed)][[*1] (0.0213547s)][[*1] (0.0298868s)][[*1] (0.041435s)][[*1] (0.070427s)]] +[[gmp_int][2.28582 (0.048813s)][2.03478 (0.0608129s)][2.05655 (0.0852131s)][1.92381 (0.135488s)]] +[[tommath_int][6.17078 (0.131775s)][4.8567 (0.145151s)][3.64659 (0.151097s)][4.78192 (0.336776s)]] ] [table Operator ^(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00236664s)][[*1] (0.0035339s)][[*1] (0.0100442s)][[*1] (0.0155814s)][[*1] (0.0293253s)]] -[[gmp_int][61.4272 (0.145376s)][41.6319 (0.147123s)][14.9744 (0.150405s)][9.64857 (0.150338s)][5.46649 (0.160306s)]] -[[tommath_int][145.509 (0.344367s)][93.9055 (0.331853s)][35.0456 (0.352003s)][22.7371 (0.354275s)][19.1373 (0.561207s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.89396 (0.0383127s)][1.64269 (0.043417s)][1.5386 (0.0477162s)][1.32247 (0.0568053s)]] +[[cpp_int(fixed)][[*1] (0.0202288s)][[*1] (0.0264305s)][[*1] (0.0310128s)][[*1] (0.0429539s)]] +[[gmp_int][7.01953 (0.141997s)][5.47513 (0.14471s)][4.6627 (0.144603s)][3.59601 (0.154463s)]] +[[tommath_int][16.2706 (0.329134s)][12.9494 (0.342258s)][11.3305 (0.35139s)][14.1712 (0.608709s)]] ] [table Operator | -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00295261s)][[*1] (0.00560832s)][[*1] (0.0127056s)][[*1] (0.0200759s)][[*1] (0.034651s)]] -[[gmp_int][14.1091 (0.0416586s)][8.52475 (0.0478096s)][4.74593 (0.0602998s)][4.19694 (0.0842575s)][3.85525 (0.133588s)]] -[[tommath_int][44.8889 (0.132539s)][25.2503 (0.141612s)][11.0488 (0.140382s)][7.39273 (0.148416s)][9.75809 (0.338127s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.34742 (0.0296944s)][1.25923 (0.0384846s)][1.20517 (0.0493908s)][1.10536 (0.0761343s)]] +[[cpp_int(fixed)][[*1] (0.0220379s)][[*1] (0.030562s)][[*1] (0.0409823s)][[*1] (0.0688775s)]] +[[gmp_int][2.14429 (0.0472558s)][1.95901 (0.0598712s)][2.07584 (0.0850728s)][1.94265 (0.133805s)]] +[[tommath_int][5.98286 (0.13185s)][4.65705 (0.142329s)][3.85812 (0.158115s)][4.81524 (0.331662s)]] ] [table Operator |(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00244005s)][[*1] (0.0040142s)][[*1] (0.00983777s)][[*1] (0.0155223s)][[*1] (0.0293444s)]] -[[gmp_int][64.6148 (0.157663s)][34.5827 (0.138822s)][14.2764 (0.140448s)][10.3248 (0.160264s)][5.33565 (0.156572s)]] -[[tommath_int][137.825 (0.3363s)][81.1074 (0.325581s)][34.8737 (0.343079s)][22.3727 (0.347276s)][18.912 (0.554963s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.40808 (0.0389721s)][1.65035 (0.0437872s)][1.51667 (0.0466144s)][1.37806 (0.0582842s)]] +[[cpp_int(fixed)][[*1] (0.0276775s)][[*1] (0.026532s)][[*1] (0.0307348s)][[*1] (0.0422945s)]] +[[gmp_int][5.31451 (0.147092s)][5.37333 (0.142565s)][4.86508 (0.149527s)][3.74364 (0.158335s)]] +[[tommath_int][11.9312 (0.330226s)][12.943 (0.343403s)][11.4457 (0.35178s)][14.4462 (0.610997s)]] +] +[table Operator gcd +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.82514 (4.45586s)][1.75955 (10.1748s)][1.87025 (25.23s)][2.11453 (68.8556s)]] +[[cpp_int(fixed)][1.57965 (3.85654s)][1.67404 (9.68027s)][1.8405 (24.8287s)][2.27588 (74.1096s)]] +[[gmp_int][[*1] (2.44138s)][[*1] (5.78259s)][[*1] (13.4902s)][[*1] (32.5631s)]] +[[tommath_int][5.01357 (12.24s)][4.38161 (25.337s)][4.08681 (55.1319s)][4.01045 (130.593s)]] +] +[table Operator str +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.46421 (0.00195137s)][1.21669 (0.00319216s)][1.25041 (0.00765237s)][1.53339 (0.0218096s)]] +[[cpp_int(fixed)][[*1] (0.00133271s)][[*1] (0.00262366s)][1.0109 (0.00618661s)][1.24429 (0.0176978s)]] +[[gmp_int][1.7777 (0.00236916s)][1.27408 (0.00334274s)][[*1] (0.00611991s)][[*1] (0.0142232s)]] +[[tommath_int][11.9797 (0.0159654s)][18.3349 (0.0481046s)][18.3681 (0.112411s)][25.0355 (0.356085s)]] +] +[endsect] + +[section:rational_performance Rational Type Perfomance] + +Note that these tests are carefully designed to test performance of the underlying algorithms +and not memory allocation or variable copying. As usual, performance results should be taken +with a healthy dose of scepticsm, and real-world peformance may vary widely depending upon the +specifics of the program. In each table relative times are given first, with the best performer +given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 +operations. + +Test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and [mpfr]-3.0.0. The tests were run on 32-bit +Windows Vista machine. + +[table Operator + +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.91758 (18.1263s)][6.60754 (44.1182s)][6.65334 (103.169s)][6.44717 (244.055s)]] +[[mpq_rational][[*1] (3.06312s)][[*1] (6.67695s)][[*1] (15.5064s)][[*1] (37.8546s)]] +] +[table Operator +(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][3.98512 (2.67249s)][4.24335 (3.04309s)][4.65009 (3.83046s)][5.45832 (5.08346s)]] +[[mpq_rational][[*1] (0.670618s)][[*1] (0.717144s)][[*1] (0.823739s)][[*1] (0.931322s)]] +] +[table Operator - +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.91504 (18.2374s)][6.55676 (43.8659s)][6.66239 (103.481s)][6.47224 (244.887s)]] +[[mpq_rational][[*1] (3.08322s)][[*1] (6.69018s)][[*1] (15.5321s)][[*1] (37.8365s)]] +] +[table Operator -(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][3.96173 (2.66785s)][4.36532 (3.09023s)][4.59363 (3.74494s)][5.43075 (5.09156s)]] +[[mpq_rational][[*1] (0.673405s)][[*1] (0.707904s)][[*1] (0.815246s)][[*1] (0.937541s)]] +] +[table Operator * +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.59286 (32.3559s)][6.54125 (82.4247s)][6.8815 (197.198s)][6.84066 (473.057s)]] +[[mpq_rational][[*1] (5.78521s)][[*1] (12.6008s)][[*1] (28.6562s)][[*1] (69.1537s)]] +] +[table Operator *(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][2.70193 (3.1466s)][3.10134 (3.79056s)][3.659 (4.93935s)][4.61372 (6.89845s)]] +[[mpq_rational][[*1] (1.16457s)][[*1] (1.22223s)][[*1] (1.34992s)][[*1] (1.4952s)]] +] +[table Operator / +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][4.36846 (63.9498s)][5.52565 (145.045s)][6.18331 (328.069s)][6.49822 (784.806s)]] +[[mpq_rational][[*1] (14.639s)][[*1] (26.2494s)][[*1] (53.0571s)][[*1] (120.772s)]] +] +[table Operator /(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][2.26643 (3.13785s)][2.57125 (3.76931s)][3.20872 (5.06758s)][4.02177 (7.17803s)]] +[[mpq_rational][[*1] (1.38449s)][[*1] (1.46594s)][[*1] (1.57931s)][[*1] (1.78479s)]] +] +[table Operator str +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.40493 (0.0199393s)][8.55089 (0.0511907s)][9.91026 (0.118839s)][9.93546 (0.285367s)]] +[[mpq_rational][[*1] (0.00368909s)][[*1] (0.00598659s)][[*1] (0.0119915s)][[*1] (0.028722s)]] ] [endsect] diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index b022d658..43ddbe28 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -10,6 +10,7 @@ #include #include #include +#include #include #include #include @@ -670,7 +671,7 @@ public: while(eval_get_sign(t) != 0) { cpp_int_backend t2; - divide_unsigned_helper(t2, t, block10, r); + divide_unsigned_helper(&t2, t, block10, r); t = t2; limb_type v = r.limbs()[0]; for(unsigned i = 0; i < digits_per_block_10; ++i) @@ -1141,15 +1142,15 @@ inline void eval_multiply(cpp_int_backend& result, c eval_multiply(result, result, val); } template -void divide_unsigned_helper(cpp_int_backend& result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) +void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) { - if((&result == &x) || (&r == &x)) + if((result == &x) || (&r == &x)) { cpp_int_backend t(x); divide_unsigned_helper(result, t, y, r); return; } - if((&result == &y) || (&r == &y)) + if((result == &y) || (&r == &y)) { cpp_int_backend t(y); divide_unsigned_helper(result, x, t, r); @@ -1177,7 +1178,7 @@ void divide_unsigned_helper(cpp_int_backend& result, using default_ops::eval_subtract; - if(&result == &r) + if(result == &r) { cpp_int_backend rem; divide_unsigned_helper(result, x, y, rem); @@ -1209,13 +1210,15 @@ void divide_unsigned_helper(cpp_int_backend& result, { // x is zero, so is the result: r = y; - result = x; + if(result) + *result = x; return; } r = x; r.sign(false); - result = static_cast(0u); + if(result) + *result = static_cast(0u); // // Check if the remainder is already less than the divisor, if so // we already have the result. Note we try and avoid a full compare @@ -1237,7 +1240,8 @@ void divide_unsigned_helper(cpp_int_backend& result, // if(r_order == 0) { - result = px[0] / py[0]; + if(result) + *result = px[0] / py[0]; r = px[0] % py[0]; return; } @@ -1248,18 +1252,24 @@ void divide_unsigned_helper(cpp_int_backend& result, b = y_order ? (static_cast(py[1]) << cpp_int_backend::limb_bits) | py[0] : py[0]; - result = a / b; + if(result) + *result = a / b; r = a % b; return; } // // prepare result: // - result.resize(1 + r_order - y_order); + if(result) + result->resize(1 + r_order - y_order); typename cpp_int_backend::const_limb_pointer prem = r.limbs(); - typename cpp_int_backend::limb_pointer pr = result.limbs(); - for(unsigned i = 1; i < 1 + r_order - y_order; ++i) - pr[i] = 0; + typename cpp_int_backend::limb_pointer pr; + if(result) + { + pr = result->limbs(); + for(unsigned i = 1; i < 1 + r_order - y_order; ++i) + pr[i] = 0; + } bool first_pass = true; do @@ -1299,29 +1309,32 @@ void divide_unsigned_helper(cpp_int_backend& result, // Update result: // limb_type shift = r_order - y_order; - if(r_neg) + if(result) { - if(pr[shift] > guess) - pr[shift] -= guess; + if(r_neg) + { + if(pr[shift] > guess) + pr[shift] -= guess; + else + { + t.resize(shift + 1); + t.limbs()[shift] = guess; + for(unsigned i = 0; i < shift; ++i) + t.limbs()[i] = 0; + eval_subtract(*result, t); + } + } + else if(cpp_int_backend::max_limb_value - pr[shift] > guess) + pr[shift] += guess; else { t.resize(shift + 1); t.limbs()[shift] = guess; for(unsigned i = 0; i < shift; ++i) t.limbs()[i] = 0; - eval_subtract(result, t); + eval_add(*result, t); } } - else if(cpp_int_backend::max_limb_value - pr[shift] > guess) - pr[shift] += guess; - else - { - t.resize(shift + 1); - t.limbs()[shift] = guess; - for(unsigned i = 0; i < shift; ++i) - t.limbs()[i] = 0; - eval_add(result, t); - } // // Calculate guess * y, we use a fused mutiply-shift O(N) for this // rather than a full O(N^2) multiply: @@ -1359,11 +1372,11 @@ void divide_unsigned_helper(cpp_int_backend& result, // First time through we need to strip any leading zero, otherwise // the termination condition goes belly-up: // - if(first_pass) + if(result && first_pass) { first_pass = false; - while(pr[result.size() - 1] == 0) - result.resize(result.size() - 1); + while(pr[result->size() - 1] == 0) + result->resize(result->size() - 1); } // // Update r_order: @@ -1382,7 +1395,8 @@ void divide_unsigned_helper(cpp_int_backend& result, if(r_neg && eval_get_sign(r)) { // We have one too many in the result: - eval_decrement(result); + if(result) + eval_decrement(*result); r.negate(); if(y.sign()) eval_subtract(r, y); @@ -1394,16 +1408,16 @@ void divide_unsigned_helper(cpp_int_backend& result, } template -void divide_unsigned_helper(cpp_int_backend& result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) +void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) { - if((&result == &x) || (&r == &x)) + if((result == &x) || (&r == &x)) { cpp_int_backend t(x); divide_unsigned_helper(result, t, y, r); return; } - if(&result == &r) + if(result == &r) { cpp_int_backend rem; divide_unsigned_helper(result, x, y, rem); @@ -1442,7 +1456,8 @@ void divide_unsigned_helper(cpp_int_backend& result, // if((r_order == 0) && (*pr < y)) { - result = static_cast(0u); + if(result) + *result = static_cast(0u); return; } @@ -1451,8 +1466,11 @@ void divide_unsigned_helper(cpp_int_backend& result, // if(r_order == 0) { - result = *pr / y; - result.sign(x.sign()); + if(result) + { + *result = *pr / y; + result->sign(x.sign()); + } r.sign(x.sign()); *pr %= y; return; @@ -1461,16 +1479,23 @@ void divide_unsigned_helper(cpp_int_backend& result, { double_limb_type a; a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[0]; - result = a / y; - result.sign(x.sign()); + if(result) + { + *result = a / y; + result->sign(x.sign()); + } r = a % y; r.sign(x.sign()); return; } - result.resize(r_order + 1); - typename cpp_int_backend::limb_pointer pres = result.limbs(); - pres[r_order] = 0; // just in case we don't set the most significant limb below. + typename cpp_int_backend::limb_pointer pres; + if(result) + { + result->resize(r_order + 1); + pres = result->limbs(); + pres[r_order] = 0; // just in case we don't set the most significant limb below. + } do { @@ -1485,7 +1510,8 @@ void divide_unsigned_helper(cpp_int_backend& result, r.resize(r.size() - 1); --r_order; pr[r_order] = static_cast(b); - pres[r_order] = static_cast(a / y); + if(result) + pres[r_order] = static_cast(a / y); if(r_order && pr[r_order] == 0) { --r_order; // No remainder, division was exact. @@ -1494,7 +1520,8 @@ void divide_unsigned_helper(cpp_int_backend& result, } else { - pres[r_order] = pr[r_order] / y; + if(result) + pres[r_order] = pr[r_order] / y; pr[r_order] %= y; if(r_order && pr[r_order] == 0) { @@ -1507,10 +1534,12 @@ void divide_unsigned_helper(cpp_int_backend& result, // short-circuit cases handled first: while(r_order || (pr[r_order] > y)); - result.normalize(); + if(result) + { + result->normalize(); + result->sign(x.sign()); + } r.normalize(); - - result.sign(x.sign()); r.sign(x.sign()); BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed @@ -1520,20 +1549,20 @@ template inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { cpp_int_backend r; - divide_unsigned_helper(result, a, b, r); + divide_unsigned_helper(&result, a, b, r); result.sign(a.sign() != b.sign()); } template inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) { cpp_int_backend r; - divide_unsigned_helper(result, a, b, r); + divide_unsigned_helper(&result, a, b, r); } template inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) { cpp_int_backend r; - divide_unsigned_helper(result, a, std::abs(b), r); + divide_unsigned_helper(&result, a, std::abs(b), r); if(b < 0) result.negate(); } @@ -1561,21 +1590,18 @@ inline void eval_divide(cpp_int_backend& result, sig template inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { - cpp_int_backend r; - divide_unsigned_helper(r, a, b, result); + divide_unsigned_helper(static_cast* >(0), a, b, result); result.sign(a.sign()); } template inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) { - cpp_int_backend r; - divide_unsigned_helper(r, a, b, result); + divide_unsigned_helper(static_cast* >(0), a, b, result); } template inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) { - cpp_int_backend r; - divide_unsigned_helper(r, a, static_cast(std::abs(b)), result); + divide_unsigned_helper(static_cast* >(0), a, static_cast(std::abs(b)), result); } template inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) @@ -2024,6 +2050,12 @@ inline int eval_get_sign(const cpp_int_backend& val) { return eval_is_zero(val) ? 0 : val.sign() ? -1 : 1; } +template +inline void eval_abs(cpp_int_backend& result, const cpp_int_backend& val) +{ + result = val; + result.sign(false); +} // // Get the location of the least-significant-bit: @@ -2132,6 +2164,36 @@ inline void eval_lcm(cpp_int_backend& result, const result.negate(); } +template +inline void eval_qr(const cpp_int_backend& x, const cpp_int_backend& y, + cpp_int_backend& q, cpp_int_backend& r) +{ + divide_unsigned_helper(&q, x, y, r); + q.sign(x.sign() != y.sign()); + r.sign(x.sign()); +} + +template +inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) +{ + if((sizeof(Integer) <= sizeof(limb_type)) || (val <= (std::numeric_limits::max)())) + { + cpp_int_backend d; + divide_unsigned_helper(static_cast*>(0), x, val, d); + return d.limbs()[0]; + } + else + { + return default_ops::eval_integer_modulus(x, val); + } +} +template +inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) +{ + typedef typename make_unsigned::type unsigned_type; + return eval_integer_modulus(x, static_cast(std::abs(val))); +} + } // namespace backends; using boost::multiprecision::backends::cpp_int_backend; @@ -2147,11 +2209,13 @@ typedef mp_number cpp_rational; typedef mp_number > mp_uint128_t; typedef mp_number > mp_uint256_t; typedef mp_number > mp_uint512_t; +typedef mp_number > mp_uint1024_t; // Fixed precision signed types: typedef mp_number > mp_int128_t; typedef mp_number > mp_int256_t; typedef mp_number > mp_int512_t; +typedef mp_number > mp_int1024_t; }} // namespaces diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index f59b198f..2b7dc8cf 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -7,6 +7,7 @@ #define BOOST_MATH_ER_GMP_BACKEND_HPP #include +#include #include #include #include @@ -1355,6 +1356,32 @@ inline void eval_lcm(gmp_int& result, const gmp_int& a, const long b) mpz_lcm_ui(result.data(), a.data(), std::abs(b)); } +inline void eval_qr(const gmp_int& x, const gmp_int& y, + gmp_int& q, gmp_int& r) +{ + mpz_tdiv_qr(q.data(), r.data(), x.data(), y.data()); +} + +template +inline typename enable_if, Integer>::type eval_integer_modulus(const gmp_int& x, Integer val) +{ + if((sizeof(Integer) <= sizeof(long)) || (val <= (std::numeric_limits::max)())) + { + gmp_int r; + return mpz_tdiv_r_ui(r.data(), x.data(), val); + } + else + { + return default_ops::eval_integer_modulus(x, val); + } +} +template +inline typename enable_if, Integer>::type eval_integer_modulus(const gmp_int& x, Integer val) +{ + typedef typename make_unsigned::type unsigned_type; + return eval_integer_modulus(x, static_cast(std::abs(val))); +} + struct gmp_rational; void eval_add(gmp_rational& t, const gmp_rational& o); diff --git a/include/boost/multiprecision/integer_ops.hpp b/include/boost/multiprecision/integer_ops.hpp new file mode 100644 index 00000000..7bd1e6c8 --- /dev/null +++ b/include/boost/multiprecision/integer_ops.hpp @@ -0,0 +1,62 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_INT_FUNC_HPP +#define BOOST_MP_INT_FUNC_HPP + +#include + +namespace boost{ namespace multiprecision{ + +namespace default_ops +{ + +template +inline void eval_qr(const Backend& x, const Backend& y, Backend& q, Backend& r) +{ + eval_divide(q, x, y); + eval_modulus(r, x, y); +} + +template +inline typename enable_if, Integer>::type maybe_abs(Integer i) { return std::abs(i); } +template +inline typename enable_if, Integer>::type maybe_abs(Integer i) { return i; } + +template +inline Integer eval_integer_modulus(const Backend& x, Integer val) +{ + using default_ops::eval_modulus; + using default_ops::eval_convert_to; + typedef typename boost::multiprecision::detail::canonical::type int_type; + Backend t; + eval_modulus(t, x, static_cast(val)); + Integer result; + eval_convert_to(&result, t); + return maybe_abs(result); +} + +} + +template +inline void divide_qr(const mp_number& x, const mp_number& y, + mp_number& q, mp_number& r) +{ + using default_ops::eval_qr; + eval_qr(x.backend(), y.backend(), q.backend(), r.backend()); +} + +template +inline typename enable_if, Integer>::type integer_modulus(const mp_number& x, Integer val) +{ + using default_ops::eval_integer_modulus; + return eval_integer_modulus(x.backend(), val); +} + +}} //namespaces + +#endif + + diff --git a/include/boost/multiprecision/miller_rabin.hpp b/include/boost/multiprecision/miller_rabin.hpp index f95713db..506e9022 100644 --- a/include/boost/multiprecision/miller_rabin.hpp +++ b/include/boost/multiprecision/miller_rabin.hpp @@ -30,21 +30,88 @@ void expmod(const mp_number& a, mp_number +bool check_small_factors(const mp_number& n) +{ + static const boost::uint32_t small_factors1[] = { + 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u }; + static const boost::uint32_t pp1 = 223092870u; + + boost::uint32_t m1 = integer_modulus(n, pp1); + + for(unsigned i = 0; i < sizeof(small_factors1) / sizeof(small_factors1[0]); ++i) + { + BOOST_ASSERT(pp1 % small_factors1[i] == 0); + if(m1 % small_factors1[i] == 0) + return false; + } + + static const boost::uint32_t small_factors2[] = { + 29u, 31u, 37u, 41u, 43u, 47u }; + static const boost::uint32_t pp2 = 2756205443u; + + m1 = integer_modulus(n, pp2); + + for(unsigned i = 0; i < sizeof(small_factors2) / sizeof(small_factors2[0]); ++i) + { + BOOST_ASSERT(pp2 % small_factors2[i] == 0); + if(m1 % small_factors2[i] == 0) + return false; + } + + static const boost::uint32_t small_factors3[] = { + 53u, 59u, 61u, 67u, 71u }; + static const boost::uint32_t pp3 = 907383479u; + + m1 = integer_modulus(n, pp3); + + for(unsigned i = 0; i < sizeof(small_factors3) / sizeof(small_factors3[0]); ++i) + { + BOOST_ASSERT(pp3 % small_factors3[i] == 0); + if(m1 % small_factors3[i] == 0) + return false; + } + + static const boost::uint32_t small_factors4[] = { + 73u, 79u, 83u, 89u, 97u }; + static const boost::uint32_t pp4 = 4132280413u; + + m1 = integer_modulus(n, pp4); + + for(unsigned i = 0; i < sizeof(small_factors4) / sizeof(small_factors4[0]); ++i) + { + BOOST_ASSERT(pp4 % small_factors4[i] == 0); + if(m1 % small_factors4[i] == 0) + return false; + } + + static const boost::uint32_t small_factors5[] = { + 101u, 103u, 107u, 109u }; + static const boost::uint32_t pp5 = 121330189u; + + m1 = integer_modulus(n, pp5); + + for(unsigned i = 0; i < sizeof(small_factors5) / sizeof(small_factors5[0]); ++i) + { + BOOST_ASSERT(pp5 % small_factors5[i] == 0); + if(m1 % small_factors5[i] == 0) + return false; + } + return true; +} + template bool miller_rabin_test(const mp_number& n, unsigned trials, Engine& gen) { typedef mp_number number_type; - static const unsigned small_factors[] = { - 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u, 29u, 31u, 37u, 41u, 43u, 47u, 53u }; - if(n < 2) return false; if((n & 1) == 0) return false; - // - // Sanity check for small factors: - // + + if(!check_small_factors(n)) + return false; number_type q = (n - 1) >> 1; unsigned k = 1; diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 50bc1785..5a948940 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -8,6 +8,7 @@ #include #include +#include #include #include #include @@ -442,6 +443,34 @@ inline void eval_lcm(tommath_int& result, const tommath_int& a, const tommath_in detail::check_tommath_result(mp_lcm(const_cast< ::mp_int*>(&a.data()), const_cast< ::mp_int*>(&b.data()), const_cast< ::mp_int*>(&result.data()))); } +inline void eval_qr(const tommath_int& x, const tommath_int& y, + tommath_int& q, tommath_int& r) +{ + detail::check_tommath_result(mp_div(const_cast< ::mp_int*>(&x.data()), const_cast< ::mp_int*>(&y.data()), &q.data(), &r.data())); +} + +template +inline typename enable_if, Integer>::type eval_integer_modulus(const tommath_int& x, Integer val) +{ + static const mp_digit m = (static_cast(1) << DIGIT_BIT) - 1; + if(val <= m) + { + mp_digit d; + detail::check_tommath_result(mp_mod_d(const_cast< ::mp_int*>(&x.data()), static_cast(val), &d)); + return d; + } + else + { + return default_ops::eval_integer_modulus(x, val); + } +} +template +inline typename enable_if, Integer>::type eval_integer_modulus(const tommath_int& x, Integer val) +{ + typedef typename make_unsigned::type unsigned_type; + return eval_integer_modulus(x, static_cast(std::abs(val))); +} + } // namespace backends using boost::multiprecision::backends::tommath_int; diff --git a/performance/miller_rabin_performance.cpp b/performance/miller_rabin_performance.cpp new file mode 100644 index 00000000..1fbed9b7 --- /dev/null +++ b/performance/miller_rabin_performance.cpp @@ -0,0 +1,164 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#define BOOST_CHRONO_HEADER_ONLY + +#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) +# define TEST_MPZ +# define TEST_TOMMATH +# define TEST_CPP_INT +#endif + +#ifdef TEST_MPZ +#include +#endif +#ifdef TEST_TOMMATH +#include +#endif +#ifdef TEST_CPP_INT +#include +#endif +#include +#include +#include + +template +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + +unsigned allocation_count = 0; + +void *(*alloc_func_ptr) (size_t); +void *(*realloc_func_ptr) (void *, size_t, size_t); +void (*free_func_ptr) (void *, size_t); + +void *alloc_func(size_t n) +{ + ++allocation_count; + return (*alloc_func_ptr)(n); +} + +void free_func(void * p, size_t n) +{ + (*free_func_ptr)(p, n); +} + +void * realloc_func(void * p, size_t old, size_t n) +{ + ++allocation_count; + return (*realloc_func_ptr)(p, old, n); +} + +boost::chrono::duration test_miller_rabin_gmp() +{ + using namespace boost::random; + using namespace boost::multiprecision; + + stopwatch c; + + independent_bits_engine gen; + + for(unsigned i = 0; i < 1000; ++i) + { + mpz_int n = gen(); + mpz_probab_prime_p(n.backend().data(), 25); + } + return c.elapsed(); +} + +std::map results; +double min_time = (std::numeric_limits::max)(); + +template +boost::chrono::duration test_miller_rabin(const char* name) +{ + using namespace boost::random; + + stopwatch c; + + independent_bits_engine gen; + // + // We must use a different generator for the tests and number generation, otherwise + // we get false positives. + // + mt19937 gen2; + + for(unsigned i = 0; i < 1000; ++i) + { + IntType n = gen(); + miller_rabin_test(n, 25, gen2); + } + boost::chrono::duration t = c.elapsed(); + double d = t.count(); + if(d < min_time) + min_time = d; + results[name] = d; + std::cout << "Time for " << std::setw(30) << std::left << name << " = " << d << std::endl; + return t; +} + +void generate_quickbook() +{ + std::cout << "[table\n"; + + std::map::const_iterator i(results.begin()), j(results.end()); + + while(i != j) + { + double rel = i->second / min_time; + std::cout << "[[" << i->first << "][" << rel << "(" << i->second << "s)]]\n"; + ++i; + } + + std::cout << "]\n"; +} + +int main() +{ + using namespace boost::multiprecision; +#ifdef TEST_CPP_INT + test_miller_rabin, false> >("cpp_int (no Expression templates)"); + test_miller_rabin("cpp_int"); + test_miller_rabin, false> >("cpp_int (64-bit cache)"); + test_miller_rabin, false> >("cpp_int (256-bit cache)"); + test_miller_rabin, false> >("cpp_int (512-bit cache)"); + test_miller_rabin, false> >("cpp_int (1024-bit cache)"); + test_miller_rabin, false> >("mp_int1024_t (no Expression templates)"); + test_miller_rabin("mp_int1024_t"); +#endif +#ifdef TEST_MPZ + test_miller_rabin >("mpz_int (no Expression templates)"); + test_miller_rabin("mpz_int"); + std::cout << "Time for mpz_int (native Miller Rabin Test) = " << test_miller_rabin_gmp() << std::endl; +#endif +#ifdef TEST_TOMMATH + test_miller_rabin >("mp_int (no Expression templates)"); + test_miller_rabin("mp_int"); +#endif + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + mp_set_memory_functions(&alloc_func, &realloc_func, &free_func); + + generate_quickbook(); + + return 0; +} + diff --git a/performance/performance_test-msvc-10.log b/performance/performance_test-msvc-10.log index 86435ab4..a7a8386a 100644 --- a/performance/performance_test-msvc-10.log +++ b/performance/performance_test-msvc-10.log @@ -1,621 +1,718 @@ -gmp_float 50 + 0.108402 -gmp_float 50 - 0.124108 -gmp_float 50 * 0.268372 -gmp_float 50 / 1.23366 -gmp_float 50 str 0.0129107 -gmp_float 50 +(int)0.0336201 -gmp_float 50 -(int)0.133911 -gmp_float 50 *(int)0.0412457 -gmp_float 50 /(int)0.174836 -gmp_float 100 + 0.113853 -gmp_float 100 - 0.117253 -gmp_float 100 * 0.395718 -gmp_float 100 / 1.62424 -gmp_float 100 str 0.0203967 -gmp_float 100 +(int)0.0353951 -gmp_float 100 -(int)0.131355 -gmp_float 100 *(int)0.0433772 -gmp_float 100 /(int)0.22889 -gmp_float 500 + 0.15342 -gmp_float 500 - 0.165713 -gmp_float 500 * 3.28705 -gmp_float 500 / 7.9874 -gmp_float 500 str 0.138075 -gmp_float 500 +(int)0.0630232 -gmp_float 500 -(int)0.186319 -gmp_float 500 *(int)0.0821206 -gmp_float 500 /(int)0.694411 -gmp_int 64 + 0.0390717 -gmp_int 64 - 0.0424608 -gmp_int 64 * 0.0560369 -gmp_int 64 / 0.775316 -gmp_int 64 str 0.00132216 -gmp_int 64 +(int)0.031766 -gmp_int 64 -(int)0.0303454 -gmp_int 64 *(int)0.0203397 -gmp_int 64 /(int)0.042564 -gmp_int 64 % 0.73595 -gmp_int 64 | 0.0416586 -gmp_int 64 & 0.0477189 -gmp_int 64 ^ 0.0429392 -gmp_int 64 << 0.0230509 -gmp_int 64 >> 0.0271544 -gmp_int 64 %(int)0.0340695 -gmp_int 64 |(int)0.157663 -gmp_int 64 &(int)0.157502 -gmp_int 64 ^(int)0.145376 -gmp_int 128 + 0.0422553 -gmp_int 128 - 0.0408253 -gmp_int 128 * 0.0663044 -gmp_int 128 / 0.880715 -gmp_int 128 str 0.00222046 -gmp_int 128 +(int)0.0317741 -gmp_int 128 -(int)0.0304669 -gmp_int 128 *(int)0.0244196 -gmp_int 128 /(int)0.06838 -gmp_int 128 % 0.749422 -gmp_int 128 | 0.0478096 -gmp_int 128 & 0.0528211 -gmp_int 128 ^ 0.0534314 -gmp_int 128 << 0.0255925 -gmp_int 128 >> 0.0276968 -gmp_int 128 %(int)0.0554367 -gmp_int 128 |(int)0.138822 -gmp_int 128 &(int)0.149717 -gmp_int 128 ^(int)0.147123 -gmp_int 256 + 0.0434751 -gmp_int 256 - 0.0463496 -gmp_int 256 * 0.127636 -gmp_int 256 / 0.908404 -gmp_int 256 str 0.00304557 -gmp_int 256 +(int)0.0417573 -gmp_int 256 -(int)0.0405733 -gmp_int 256 *(int)0.025582 -gmp_int 256 /(int)0.104957 -gmp_int 256 % 0.772122 -gmp_int 256 | 0.0602998 -gmp_int 256 & 0.0653902 -gmp_int 256 ^ 0.0613552 -gmp_int 256 << 0.031955 -gmp_int 256 >> 0.0314426 -gmp_int 256 %(int)0.0967406 -gmp_int 256 |(int)0.140448 -gmp_int 256 &(int)0.153268 -gmp_int 256 ^(int)0.150405 -gmp_int 512 + 0.0503875 -gmp_int 512 - 0.051838 -gmp_int 512 * 0.53821 -gmp_int 512 / 1.03572 -gmp_int 512 str 0.00604351 -gmp_int 512 +(int)0.0645488 -gmp_int 512 -(int)0.0599252 -gmp_int 512 *(int)0.033311 -gmp_int 512 /(int)0.187096 -gmp_int 512 % 0.874894 -gmp_int 512 | 0.0842575 -gmp_int 512 & 0.0917698 -gmp_int 512 ^ 0.0864335 -gmp_int 512 << 0.0443618 -gmp_int 512 >> 0.0322188 -gmp_int 512 %(int)0.180504 -gmp_int 512 |(int)0.160264 -gmp_int 512 &(int)0.159328 -gmp_int 512 ^(int)0.150338 -gmp_int 1024 + 0.0702458 -gmp_int 1024 - 0.0779673 -gmp_int 1024 * 1.52168 -gmp_int 1024 / 1.29625 -gmp_int 1024 str 0.0143268 -gmp_int 1024 +(int)0.107903 -gmp_int 1024 -(int)0.105058 -gmp_int 1024 *(int)0.048001 -gmp_int 1024 /(int)0.35331 -gmp_int 1024 % 1.07382 -gmp_int 1024 | 0.133588 -gmp_int 1024 & 0.140007 -gmp_int 1024 ^ 0.134421 -gmp_int 1024 << 0.0707887 -gmp_int 1024 >> 0.0405327 -gmp_int 1024 %(int)0.347216 -gmp_int 1024 |(int)0.156572 -gmp_int 1024 &(int)0.166481 -gmp_int 1024 ^(int)0.160306 -mpq_rational 64 + 1.47032 -mpq_rational 64 - 1.48169 -mpq_rational 64 * 2.67402 -mpq_rational 64 / 9.26405 -mpq_rational 64 str 0.00265159 -mpq_rational 64 +(int)0.639153 -mpq_rational 64 -(int)0.650283 -mpq_rational 64 *(int)1.15673 -mpq_rational 64 /(int)1.40596 -mpq_rational 128 + 3.1599 -mpq_rational 128 - 3.17694 -mpq_rational 128 * 5.89806 -mpq_rational 128 / 14.7461 -mpq_rational 128 str 0.00363964 -mpq_rational 128 +(int)0.683218 -mpq_rational 128 -(int)0.669498 -mpq_rational 128 *(int)1.20559 -mpq_rational 128 /(int)1.42215 -mpq_rational 256 + 6.74926 -mpq_rational 256 - 6.75317 -mpq_rational 256 * 12.7524 -mpq_rational 256 / 26.4939 -mpq_rational 256 str 0.00677698 -mpq_rational 256 +(int)0.725686 -mpq_rational 256 -(int)0.707811 -mpq_rational 256 *(int)1.25776 -mpq_rational 256 /(int)1.50342 -mpq_rational 512 + 16.7334 -mpq_rational 512 - 15.9167 -mpq_rational 512 * 29.4044 -mpq_rational 512 / 54.0641 -mpq_rational 512 str 0.0117945 -mpq_rational 512 +(int)0.895283 -mpq_rational 512 -(int)0.83232 -mpq_rational 512 *(int)1.41413 -mpq_rational 512 /(int)1.62326 -mpq_rational 1024 + 38.5739 -mpq_rational 1024 - 39.0541 -mpq_rational 1024 * 70.1615 -mpq_rational 1024 / 126.261 -mpq_rational 1024 str 0.0283447 -mpq_rational 1024 +(int)0.931053 -mpq_rational 1024 -(int)1.06134 -mpq_rational 1024 *(int)1.59151 -mpq_rational 1024 /(int)1.7796 -tommath_int 64 + 0.018872 -tommath_int 64 - 0.0237699 -tommath_int 64 * 0.0670506 -tommath_int 64 / 1.79253 -tommath_int 64 str 0.00734164 -tommath_int 64 +(int)0.224655 -tommath_int 64 -(int)0.202873 -tommath_int 64 *(int)0.239357 -tommath_int 64 /(int)1.37938 -tommath_int 64 % 2.56986 -tommath_int 64 | 0.132539 -tommath_int 64 & 0.130147 -tommath_int 64 ^ 0.127996 -tommath_int 64 << 0.0314737 -tommath_int 64 >> 0.250865 -tommath_int 64 %(int)1.46083 -tommath_int 64 |(int)0.3363 -tommath_int 64 &(int)0.342626 -tommath_int 64 ^(int)0.344367 -tommath_int 128 + 0.0216659 -tommath_int 128 - 0.0270677 -tommath_int 128 * 0.111722 -tommath_int 128 / 2.13582 -tommath_int 128 str 0.0163193 -tommath_int 128 +(int)0.22725 -tommath_int 128 -(int)0.207089 -tommath_int 128 *(int)0.249452 -tommath_int 128 /(int)1.62383 -tommath_int 128 % 2.19585 -tommath_int 128 | 0.141612 -tommath_int 128 & 0.130002 -tommath_int 128 ^ 0.130457 -tommath_int 128 << 0.0389456 -tommath_int 128 >> 0.251932 -tommath_int 128 %(int)1.65639 -tommath_int 128 |(int)0.325581 -tommath_int 128 &(int)0.331077 -tommath_int 128 ^(int)0.331853 -tommath_int 256 + 0.0301548 -tommath_int 256 - 0.0382195 -tommath_int 256 * 0.34452 -tommath_int 256 / 3.03438 -tommath_int 256 str 0.0450349 -tommath_int 256 +(int)0.2481 -tommath_int 256 -(int)0.220375 -tommath_int 256 *(int)0.273682 -tommath_int 256 /(int)2.32908 -tommath_int 256 % 3.10053 -tommath_int 256 | 0.140382 -tommath_int 256 & 0.145711 -tommath_int 256 ^ 0.145171 -tommath_int 256 << 0.065292 -tommath_int 256 >> 0.296661 -tommath_int 256 %(int)2.26685 -tommath_int 256 |(int)0.343079 -tommath_int 256 &(int)0.351853 -tommath_int 256 ^(int)0.352003 -tommath_int 512 + 0.0425188 -tommath_int 512 - 0.0488346 -tommath_int 512 * 0.995374 -tommath_int 512 / 5.01541 -tommath_int 512 str 0.119168 -tommath_int 512 +(int)0.27807 -tommath_int 512 -(int)0.280258 -tommath_int 512 *(int)0.462652 -tommath_int 512 /(int)3.72421 -tommath_int 512 % 4.75068 -tommath_int 512 | 0.148416 -tommath_int 512 & 0.155508 -tommath_int 512 ^ 0.158845 -tommath_int 512 << 0.0939451 -tommath_int 512 >> 0.313884 -tommath_int 512 %(int)3.5978 -tommath_int 512 |(int)0.347276 -tommath_int 512 &(int)0.364899 -tommath_int 512 ^(int)0.354275 -tommath_int 1024 + 0.0717123 -tommath_int 1024 - 0.0769566 -tommath_int 1024 * 3.12935 -tommath_int 1024 / 11.517 -tommath_int 1024 str 0.377431 -tommath_int 1024 +(int)0.293538 -tommath_int 1024 -(int)0.260488 -tommath_int 1024 *(int)0.437175 -tommath_int 1024 /(int)8.55783 -tommath_int 1024 % 11.5211 -tommath_int 1024 | 0.338127 -tommath_int 1024 & 0.331858 -tommath_int 1024 ^ 0.340584 -tommath_int 1024 << 0.163725 -tommath_int 1024 >> 0.506974 -tommath_int 1024 %(int)8.682 -tommath_int 1024 |(int)0.554963 -tommath_int 1024 &(int)0.605213 -tommath_int 1024 ^(int)0.561207 -fixed_int 64 + 0.0031291 -fixed_int 64 - 0.00339191 -fixed_int 64 * 0.0223481 -fixed_int 64 / 0.0991632 -fixed_int 64 str 0.000465841 -fixed_int 64 +(int)0.00335294 -fixed_int 64 -(int)0.00250933 -fixed_int 64 *(int)0.00444316 -fixed_int 64 /(int)0.0443082 -fixed_int 64 % 0.0946529 -fixed_int 64 | 0.00295261 -fixed_int 64 & 0.00298048 -fixed_int 64 ^ 0.00307714 -fixed_int 64 << 0.0119095 -fixed_int 64 >> 0.006361 -fixed_int 64 %(int)0.0425984 -fixed_int 64 |(int)0.00244005 -fixed_int 64 &(int)0.00222291 -fixed_int 64 ^(int)0.00236664 -fixed_int 128 + 0.00703043 -fixed_int 128 - 0.0073172 -fixed_int 128 * 0.0375288 -fixed_int 128 / 0.172328 -fixed_int 128 str 0.00102073 -fixed_int 128 +(int)0.00376116 -fixed_int 128 -(int)0.00358055 -fixed_int 128 *(int)0.0135739 -fixed_int 128 /(int)0.110308 -fixed_int 128 % 0.170561 -fixed_int 128 | 0.00560832 -fixed_int 128 & 0.00546222 -fixed_int 128 ^ 0.00538197 -fixed_int 128 << 0.0131746 -fixed_int 128 >> 0.00880189 -fixed_int 128 %(int)0.106226 -fixed_int 128 |(int)0.0040142 -fixed_int 128 &(int)0.0035522 -fixed_int 128 ^(int)0.0035339 -fixed_int 256 + 0.0163669 -fixed_int 256 - 0.0166428 -fixed_int 256 * 0.120353 -fixed_int 256 / 0.309492 -fixed_int 256 str 0.00207212 -fixed_int 256 +(int)0.00985174 -fixed_int 256 -(int)0.0103282 -fixed_int 256 *(int)0.0192615 -fixed_int 256 /(int)0.229148 -fixed_int 256 % 0.328458 -fixed_int 256 | 0.0127056 -fixed_int 256 & 0.0127546 -fixed_int 256 ^ 0.0127717 -fixed_int 256 << 0.0213483 -fixed_int 256 >> 0.0180295 -fixed_int 256 %(int)0.195577 -fixed_int 256 |(int)0.00983777 -fixed_int 256 &(int)0.0110247 -fixed_int 256 ^(int)0.0100442 -fixed_int 512 + 0.0326567 -fixed_int 512 - 0.0349375 -fixed_int 512 * 0.439147 -fixed_int 512 / 0.573815 -fixed_int 512 str 0.0062017 -fixed_int 512 +(int)0.0119345 -fixed_int 512 -(int)0.0119127 -fixed_int 512 *(int)0.0328339 -fixed_int 512 /(int)0.442167 -fixed_int 512 % 0.575884 -fixed_int 512 | 0.0200759 -fixed_int 512 & 0.01985 -fixed_int 512 ^ 0.0198304 -fixed_int 512 << 0.0247552 -fixed_int 512 >> 0.0220786 -fixed_int 512 %(int)0.387067 -fixed_int 512 |(int)0.0155223 -fixed_int 512 &(int)0.0154281 -fixed_int 512 ^(int)0.0155814 -fixed_int 1024 + 0.0603087 -fixed_int 1024 - 0.0600083 -fixed_int 1024 * 1.46969 -fixed_int 1024 / 1.06356 -fixed_int 1024 str 0.0190043 -fixed_int 1024 +(int)0.0170918 -fixed_int 1024 -(int)0.0176089 -fixed_int 1024 *(int)0.0567364 -fixed_int 1024 /(int)0.866172 -fixed_int 1024 % 1.05006 -fixed_int 1024 | 0.034651 -fixed_int 1024 & 0.0349286 -fixed_int 1024 ^ 0.0345822 -fixed_int 1024 << 0.0339579 -fixed_int 1024 >> 0.0325312 -fixed_int 1024 %(int)0.776075 -fixed_int 1024 |(int)0.0293444 -fixed_int 1024 &(int)0.0275044 -fixed_int 1024 ^(int)0.0293253 -cpp_float 50 + 0.02382 -cpp_float 50 - 0.0265783 -cpp_float 50 * 0.287898 -cpp_float 50 / 4.00108 -cpp_float 50 str 0.0188303 -cpp_float 50 +(int)0.0527023 -cpp_float 50 -(int)0.0577674 -cpp_float 50 *(int)0.11959 -cpp_float 50 /(int)0.253675 -cpp_float 100 + 0.0294619 -cpp_float 100 - 0.031465 -cpp_float 100 * 0.584569 -cpp_float 100 / 8.12985 -cpp_float 100 str 0.03172 -cpp_float 100 +(int)0.0618102 -cpp_float 100 -(int)0.0633795 -cpp_float 100 *(int)0.197945 -cpp_float 100 /(int)0.419569 -cpp_float 500 + 0.058466 -cpp_float 500 - 0.0619405 -cpp_float 500 * 5.09969 -cpp_float 500 / 54.2796 -cpp_float 500 str 0.131962 -cpp_float 500 +(int)0.105927 -cpp_float 500 -(int)0.11146 -cpp_float 500 *(int)0.742044 -cpp_float 500 /(int)1.64187 -mpfr_float 50 + 0.060035 -mpfr_float 50 - 0.0741774 -mpfr_float 50 * 0.341642 -mpfr_float 50 / 1.63486 -mpfr_float 50 str 0.0282764 -mpfr_float 50 +(int)0.105861 -mpfr_float 50 -(int)0.141577 -mpfr_float 50 *(int)0.152407 -mpfr_float 50 /(int)0.204088 -mpfr_float 100 + 0.0643242 -mpfr_float 100 - 0.0782083 -mpfr_float 100 * 0.465557 -mpfr_float 100 / 2.25716 -mpfr_float 100 str 0.0376683 -mpfr_float 100 +(int)0.111671 -mpfr_float 100 -(int)0.145249 -mpfr_float 100 *(int)0.161353 -mpfr_float 100 /(int)0.259127 -mpfr_float 500 + 0.0805287 -mpfr_float 500 - 0.0934957 -mpfr_float 500 * 3.7482 -mpfr_float 500 / 13.7713 -mpfr_float 500 str 0.158743 -mpfr_float 500 +(int)0.121528 -mpfr_float 500 -(int)0.155487 -mpfr_float 500 *(int)0.271785 -mpfr_float 500 /(int)0.708513 +gmp_float 50 + 0.111016 +gmp_float 50 - 0.119562 +gmp_float 50 * 0.266947 +gmp_float 50 / 1.23608 +gmp_float 50 str 0.0299824 +gmp_float 50 +(int)0.0320709 +gmp_float 50 -(int)0.130453 +gmp_float 50 *(int)0.0391224 +gmp_float 50 /(int)0.178268 +gmp_float 100 + 0.108884 +gmp_float 100 - 0.118595 +gmp_float 100 * 0.401792 +gmp_float 100 / 1.60879 +gmp_float 100 str 0.0207461 +gmp_float 100 +(int)0.0346436 +gmp_float 100 -(int)0.131897 +gmp_float 100 *(int)0.0435089 +gmp_float 100 /(int)0.23715 +gmp_float 500 + 0.143065 +gmp_float 500 - 0.151427 +gmp_float 500 * 3.22591 +gmp_float 500 / 8.09281 +gmp_float 500 str 0.136249 +gmp_float 500 +(int)0.0567182 +gmp_float 500 -(int)0.164247 +gmp_float 500 *(int)0.0824826 +gmp_float 500 /(int)0.693418 +gmp_int 128 + 0.0416325 +gmp_int 128 - 0.0409536 +gmp_int 128 * 0.0673622 +gmp_int 128 / 0.8304 +gmp_int 128 str 0.00202218 +gmp_int 128 +(int)0.0297328 +gmp_int 128 -(int)0.0296573 +gmp_int 128 *(int)0.0225369 +gmp_int 128 /(int)0.0545672 +gmp_int 128 % 0.626244 +gmp_int 128 | 0.0491246 +gmp_int 128 & 0.0530007 +gmp_int 128 ^ 0.0485553 +gmp_int 128 << 0.0260055 +gmp_int 128 >> 0.0275053 +gmp_int 128 %(int)0.0553103 +gmp_int 128 |(int)0.14092 +gmp_int 128 &(int)0.146717 +gmp_int 128 ^(int)0.141446 +gmp_int 128 gcd 2.4583 +gmp_int 256 + 0.0437202 +gmp_int 256 - 0.0449331 +gmp_int 256 * 0.128456 +gmp_int 256 / 0.91168 +gmp_int 256 str 0.00293026 +gmp_int 256 +(int)0.0421762 +gmp_int 256 -(int)0.0392365 +gmp_int 256 *(int)0.0260961 +gmp_int 256 /(int)0.101468 +gmp_int 256 % 0.686075 +gmp_int 256 | 0.0605797 +gmp_int 256 & 0.0657431 +gmp_int 256 ^ 0.0628266 +gmp_int 256 << 0.0309127 +gmp_int 256 >> 0.028966 +gmp_int 256 %(int)0.0997194 +gmp_int 256 |(int)0.141959 +gmp_int 256 &(int)0.148873 +gmp_int 256 ^(int)0.145267 +gmp_int 256 gcd 5.7433 +gmp_int 512 + 0.0502054 +gmp_int 512 - 0.053661 +gmp_int 512 * 0.517967 +gmp_int 512 / 1.04166 +gmp_int 512 str 0.00589914 +gmp_int 512 +(int)0.0648096 +gmp_int 512 -(int)0.0579614 +gmp_int 512 *(int)0.0336047 +gmp_int 512 /(int)0.18882 +gmp_int 512 % 0.792461 +gmp_int 512 | 0.0862186 +gmp_int 512 & 0.0910233 +gmp_int 512 ^ 0.086449 +gmp_int 512 << 0.0480825 +gmp_int 512 >> 0.0323891 +gmp_int 512 %(int)0.183615 +gmp_int 512 |(int)0.150229 +gmp_int 512 &(int)0.154253 +gmp_int 512 ^(int)0.156314 +gmp_int 512 gcd 13.5018 +gmp_int 1024 + 0.065979 +gmp_int 1024 - 0.0703067 +gmp_int 1024 * 1.51138 +gmp_int 1024 / 1.26397 +gmp_int 1024 str 0.0145211 +gmp_int 1024 +(int)0.105223 +gmp_int 1024 -(int)0.0997431 +gmp_int 1024 *(int)0.0487139 +gmp_int 1024 /(int)0.374919 +gmp_int 1024 % 1.02412 +gmp_int 1024 | 0.134887 +gmp_int 1024 & 0.148173 +gmp_int 1024 ^ 0.136369 +gmp_int 1024 << 0.0702549 +gmp_int 1024 >> 0.037103 +gmp_int 1024 %(int)0.351263 +gmp_int 1024 |(int)0.155137 +gmp_int 1024 &(int)0.163801 +gmp_int 1024 ^(int)0.15826 +gmp_int 1024 gcd 32.5205 +cpp_int 128 + 0.0271391 +cpp_int 128 - 0.0302204 +cpp_int 128 * 0.0764199 +cpp_int 128 / 0.601063 +cpp_int 128 str 0.00186546 +cpp_int 128 +(int)0.0203604 +cpp_int 128 -(int)0.0155424 +cpp_int 128 *(int)0.0306376 +cpp_int 128 /(int)0.318461 +cpp_int 128 % 0.488484 +cpp_int 128 | 0.0295702 +cpp_int 128 & 0.0299046 +cpp_int 128 ^ 0.0300509 +cpp_int 128 << 0.0220286 +cpp_int 128 >> 0.0208765 +cpp_int 128 %(int)0.197942 +cpp_int 128 |(int)0.0385046 +cpp_int 128 &(int)0.0463351 +cpp_int 128 ^(int)0.0381023 +cpp_int 128 gcd 4.48165 +cpp_int 256 + 0.0354288 +cpp_int 256 - 0.03826 +cpp_int 256 * 0.193581 +cpp_int 256 / 0.694115 +cpp_int 256 str 0.00327905 +cpp_int 256 +(int)0.0238597 +cpp_int 256 -(int)0.0199724 +cpp_int 256 *(int)0.040404 +cpp_int 256 /(int)0.433035 +cpp_int 256 % 0.597931 +cpp_int 256 | 0.0378751 +cpp_int 256 & 0.0389208 +cpp_int 256 ^ 0.0381634 +cpp_int 256 << 0.0294239 +cpp_int 256 >> 0.0265325 +cpp_int 256 %(int)0.298382 +cpp_int 256 |(int)0.0425891 +cpp_int 256 &(int)0.0550224 +cpp_int 256 ^(int)0.0432356 +cpp_int 256 gcd 10.1686 +cpp_int 512 + 0.0536949 +cpp_int 512 - 0.0529947 +cpp_int 512 * 0.656832 +cpp_int 512 / 0.915068 +cpp_int 512 str 0.0076685 +cpp_int 512 +(int)0.0262742 +cpp_int 512 -(int)0.0223562 +cpp_int 512 *(int)0.0537717 +cpp_int 512 /(int)0.641615 +cpp_int 512 % 0.807811 +cpp_int 512 | 0.0523944 +cpp_int 512 & 0.04981 +cpp_int 512 ^ 0.0494246 +cpp_int 512 << 0.0365532 +cpp_int 512 >> 0.0304931 +cpp_int 512 %(int)0.478772 +cpp_int 512 |(int)0.0479629 +cpp_int 512 &(int)0.0697964 +cpp_int 512 ^(int)0.0466764 +cpp_int 512 gcd 25.1877 +cpp_int 1024 + 0.0884854 +cpp_int 1024 - 0.0822931 +cpp_int 1024 * 2.47851 +cpp_int 1024 / 1.36697 +cpp_int 1024 str 0.0217405 +cpp_int 1024 +(int)0.0296193 +cpp_int 1024 -(int)0.0246399 +cpp_int 1024 *(int)0.0790137 +cpp_int 1024 /(int)1.05122 +cpp_int 1024 % 1.24204 +cpp_int 1024 | 0.0751774 +cpp_int 1024 & 0.0745785 +cpp_int 1024 ^ 0.075182 +cpp_int 1024 << 0.0522035 +cpp_int 1024 >> 0.0383751 +cpp_int 1024 %(int)0.85137 +cpp_int 1024 |(int)0.0549147 +cpp_int 1024 &(int)0.101779 +cpp_int 1024 ^(int)0.0550852 +cpp_int 1024 gcd 69.0626 +cpp_int(fixed) 128 + 0.023195 +cpp_int(fixed) 128 - 0.0255758 +cpp_int(fixed) 128 * 0.0560495 +cpp_int(fixed) 128 / 0.20335 +cpp_int(fixed) 128 str 0.00107409 +cpp_int(fixed) 128 +(int)0.013729 +cpp_int(fixed) 128 -(int)0.0103816 +cpp_int(fixed) 128 *(int)0.0290285 +cpp_int(fixed) 128 /(int)0.134603 +cpp_int(fixed) 128 % 0.193104 +cpp_int(fixed) 128 | 0.0211746 +cpp_int(fixed) 128 & 0.0234269 +cpp_int(fixed) 128 ^ 0.0214753 +cpp_int(fixed) 128 << 0.0189966 +cpp_int(fixed) 128 >> 0.0164431 +cpp_int(fixed) 128 %(int)0.111723 +cpp_int(fixed) 128 |(int)0.020319 +cpp_int(fixed) 128 &(int)0.0281931 +cpp_int(fixed) 128 ^(int)0.0205145 +cpp_int(fixed) 128 gcd 3.69729 +cpp_int(fixed) 256 + 0.0316591 +cpp_int(fixed) 256 - 0.0387139 +cpp_int(fixed) 256 * 0.162173 +cpp_int(fixed) 256 / 0.313292 +cpp_int(fixed) 256 str 0.00227396 +cpp_int(fixed) 256 +(int)0.0195617 +cpp_int(fixed) 256 -(int)0.0153586 +cpp_int(fixed) 256 *(int)0.0403434 +cpp_int(fixed) 256 /(int)0.256092 +cpp_int(fixed) 256 % 0.314303 +cpp_int(fixed) 256 | 0.0329594 +cpp_int(fixed) 256 & 0.026925 +cpp_int(fixed) 256 ^ 0.0297291 +cpp_int(fixed) 256 << 0.0262879 +cpp_int(fixed) 256 >> 0.0222577 +cpp_int(fixed) 256 %(int)0.207915 +cpp_int(fixed) 256 |(int)0.0258999 +cpp_int(fixed) 256 &(int)0.0409067 +cpp_int(fixed) 256 ^(int)0.0260211 +cpp_int(fixed) 256 gcd 9.22552 +cpp_int(fixed) 512 + 0.0515755 +cpp_int(fixed) 512 - 0.0475007 +cpp_int(fixed) 512 * 0.462871 +cpp_int(fixed) 512 / 0.52874 +cpp_int(fixed) 512 str 0.00597122 +cpp_int(fixed) 512 +(int)0.0212179 +cpp_int(fixed) 512 -(int)0.0179683 +cpp_int(fixed) 512 *(int)0.0542558 +cpp_int(fixed) 512 /(int)0.459431 +cpp_int(fixed) 512 % 0.512737 +cpp_int(fixed) 512 | 0.0398115 +cpp_int(fixed) 512 & 0.032775 +cpp_int(fixed) 512 ^ 0.0394438 +cpp_int(fixed) 512 << 0.0317039 +cpp_int(fixed) 512 >> 0.0275545 +cpp_int(fixed) 512 %(int)0.38701 +cpp_int(fixed) 512 |(int)0.0306217 +cpp_int(fixed) 512 &(int)0.0539505 +cpp_int(fixed) 512 ^(int)0.0308272 +cpp_int(fixed) 512 gcd 24.8643 +cpp_int(fixed) 1024 + 0.0833072 +cpp_int(fixed) 1024 - 0.0864345 +cpp_int(fixed) 1024 * 1.61211 +cpp_int(fixed) 1024 / 0.965347 +cpp_int(fixed) 1024 str 0.0174989 +cpp_int(fixed) 1024 +(int)0.0286337 +cpp_int(fixed) 1024 -(int)0.0219173 +cpp_int(fixed) 1024 *(int)0.0826023 +cpp_int(fixed) 1024 /(int)0.855435 +cpp_int(fixed) 1024 % 0.944678 +cpp_int(fixed) 1024 | 0.071698 +cpp_int(fixed) 1024 & 0.0503183 +cpp_int(fixed) 1024 ^ 0.0721252 +cpp_int(fixed) 1024 << 0.0488381 +cpp_int(fixed) 1024 >> 0.0382038 +cpp_int(fixed) 1024 %(int)0.760262 +cpp_int(fixed) 1024 |(int)0.0426336 +cpp_int(fixed) 1024 &(int)0.0863606 +cpp_int(fixed) 1024 ^(int)0.0429944 +cpp_int(fixed) 1024 gcd 73.4335 +cpp_rational 128 + 18.1263 +cpp_rational 128 - 18.2374 +cpp_rational 128 * 32.3559 +cpp_rational 128 / 63.9498 +cpp_rational 128 str 0.0199393 +cpp_rational 128 +(int)2.67249 +cpp_rational 128 -(int)2.66785 +cpp_rational 128 *(int)3.1466 +cpp_rational 128 /(int)3.13785 +cpp_rational 256 + 44.1182 +cpp_rational 256 - 43.8659 +cpp_rational 256 * 82.4247 +cpp_rational 256 / 145.045 +cpp_rational 256 str 0.0511907 +cpp_rational 256 +(int)3.04309 +cpp_rational 256 -(int)3.09023 +cpp_rational 256 *(int)3.79056 +cpp_rational 256 /(int)3.76931 +cpp_rational 512 + 103.169 +cpp_rational 512 - 103.481 +cpp_rational 512 * 197.198 +cpp_rational 512 / 328.069 +cpp_rational 512 str 0.118839 +cpp_rational 512 +(int)3.83046 +cpp_rational 512 -(int)3.74494 +cpp_rational 512 *(int)4.93935 +cpp_rational 512 /(int)5.06758 +cpp_rational 1024 + 244.055 +cpp_rational 1024 - 244.887 +cpp_rational 1024 * 473.057 +cpp_rational 1024 / 784.806 +cpp_rational 1024 str 0.285367 +cpp_rational 1024 +(int)5.08346 +cpp_rational 1024 -(int)5.09156 +cpp_rational 1024 *(int)6.89845 +cpp_rational 1024 /(int)7.17803 +mpq_rational 128 + 3.06312 +mpq_rational 128 - 3.08322 +mpq_rational 128 * 5.78521 +mpq_rational 128 / 14.639 +mpq_rational 128 str 0.00368909 +mpq_rational 128 +(int)0.670618 +mpq_rational 128 -(int)0.673405 +mpq_rational 128 *(int)1.16457 +mpq_rational 128 /(int)1.38449 +mpq_rational 256 + 6.67695 +mpq_rational 256 - 6.69018 +mpq_rational 256 * 12.6008 +mpq_rational 256 / 26.2494 +mpq_rational 256 str 0.00598659 +mpq_rational 256 +(int)0.717144 +mpq_rational 256 -(int)0.707904 +mpq_rational 256 *(int)1.22223 +mpq_rational 256 /(int)1.46594 +mpq_rational 512 + 15.5064 +mpq_rational 512 - 15.5321 +mpq_rational 512 * 28.6562 +mpq_rational 512 / 53.0571 +mpq_rational 512 str 0.0119915 +mpq_rational 512 +(int)0.823739 +mpq_rational 512 -(int)0.815246 +mpq_rational 512 *(int)1.34992 +mpq_rational 512 /(int)1.57931 +mpq_rational 1024 + 37.8546 +mpq_rational 1024 - 37.8365 +mpq_rational 1024 * 69.1537 +mpq_rational 1024 / 120.772 +mpq_rational 1024 str 0.028722 +mpq_rational 1024 +(int)0.931322 +mpq_rational 1024 -(int)0.937541 +mpq_rational 1024 *(int)1.4952 +mpq_rational 1024 /(int)1.78479 +tommath_int 128 + 0.0217192 +tommath_int 128 - 0.0291902 +tommath_int 128 * 0.111627 +tommath_int 128 / 2.08463 +tommath_int 128 str 0.0168021 +tommath_int 128 +(int)0.257132 +tommath_int 128 -(int)0.203455 +tommath_int 128 *(int)0.238829 +tommath_int 128 /(int)1.59094 +tommath_int 128 % 2.85844 +tommath_int 128 | 0.129637 +tommath_int 128 & 0.131309 +tommath_int 128 ^ 0.130689 +tommath_int 128 << 0.0401547 +tommath_int 128 >> 0.23176 +tommath_int 128 %(int)1.79288 +tommath_int 128 |(int)0.335087 +tommath_int 128 &(int)0.340397 +tommath_int 128 ^(int)0.336121 +tommath_int 128 gcd 12.105 +tommath_int 256 + 0.0314797 +tommath_int 256 - 0.0397314 +tommath_int 256 * 0.339525 +tommath_int 256 / 2.90357 +tommath_int 256 str 0.0507118 +tommath_int 256 +(int)0.27657 +tommath_int 256 -(int)0.218347 +tommath_int 256 *(int)0.272846 +tommath_int 256 /(int)2.23033 +tommath_int 256 % 3.05431 +tommath_int 256 | 0.14062 +tommath_int 256 & 0.149703 +tommath_int 256 ^ 0.143938 +tommath_int 256 << 0.0663968 +tommath_int 256 >> 0.261181 +tommath_int 256 %(int)2.19631 +tommath_int 256 |(int)0.344931 +tommath_int 256 &(int)0.354773 +tommath_int 256 ^(int)0.337315 +tommath_int 256 gcd 25.2396 +tommath_int 512 + 0.0423742 +tommath_int 512 - 0.0520296 +tommath_int 512 * 0.974058 +tommath_int 512 / 4.55815 +tommath_int 512 str 0.123612 +tommath_int 512 +(int)0.293832 +tommath_int 512 -(int)0.23252 +tommath_int 512 *(int)0.325472 +tommath_int 512 /(int)3.45058 +tommath_int 512 % 4.64676 +tommath_int 512 | 0.149674 +tommath_int 512 & 0.15487 +tommath_int 512 ^ 0.150772 +tommath_int 512 << 0.0938596 +tommath_int 512 >> 0.289806 +tommath_int 512 %(int)3.43906 +tommath_int 512 |(int)0.350645 +tommath_int 512 &(int)0.364622 +tommath_int 512 ^(int)0.347472 +tommath_int 512 gcd 54.7712 +tommath_int 1024 + 0.0724498 +tommath_int 1024 - 0.0774105 +tommath_int 1024 * 3.11813 +tommath_int 1024 / 11.2594 +tommath_int 1024 str 0.380528 +tommath_int 1024 +(int)0.329666 +tommath_int 1024 -(int)0.261392 +tommath_int 1024 *(int)0.41516 +tommath_int 1024 /(int)8.38249 +tommath_int 1024 % 11.2704 +tommath_int 1024 | 0.414581 +tommath_int 1024 & 0.417234 +tommath_int 1024 ^ 0.419285 +tommath_int 1024 << 0.161738 +tommath_int 1024 >> 0.495316 +tommath_int 1024 %(int)8.45761 +tommath_int 1024 |(int)0.587063 +tommath_int 1024 &(int)0.613817 +tommath_int 1024 ^(int)0.587566 +tommath_int 1024 gcd 128.781 +cpp_dec_float 50 + 0.0238412 +cpp_dec_float 50 - 0.026085 +cpp_dec_float 50 * 0.292488 +cpp_dec_float 50 / 3.99158 +cpp_dec_float 50 str 0.0185371 +cpp_dec_float 50 +(int)0.0522868 +cpp_dec_float 50 -(int)0.0588879 +cpp_dec_float 50 *(int)0.118517 +cpp_dec_float 50 /(int)0.246362 +cpp_dec_float 100 + 0.0293132 +cpp_dec_float 100 - 0.0304546 +cpp_dec_float 100 * 0.583535 +cpp_dec_float 100 / 8.1132 +cpp_dec_float 100 str 0.0318154 +cpp_dec_float 100 +(int)0.0626744 +cpp_dec_float 100 -(int)0.0638241 +cpp_dec_float 100 *(int)0.191461 +cpp_dec_float 100 /(int)0.412828 +cpp_dec_float 500 + 0.0605518 +cpp_dec_float 500 - 0.0625459 +cpp_dec_float 500 * 5.08004 +cpp_dec_float 500 / 53.775 +cpp_dec_float 500 str 0.131303 +cpp_dec_float 500 +(int)0.105128 +cpp_dec_float 500 -(int)0.113107 +cpp_dec_float 500 *(int)0.736865 +cpp_dec_float 500 /(int)1.62534 +mpfr_float 50 + 0.0604351 +mpfr_float 50 - 0.073623 +mpfr_float 50 * 0.332216 +mpfr_float 50 / 1.65596 +mpfr_float 50 str 0.0292843 +mpfr_float 50 +(int)0.107103 +mpfr_float 50 -(int)0.141072 +mpfr_float 50 *(int)0.151189 +mpfr_float 50 /(int)0.202945 +mpfr_float 100 + 0.0651951 +mpfr_float 100 - 0.078328 +mpfr_float 100 * 0.462025 +mpfr_float 100 / 2.28108 +mpfr_float 100 str 0.0379418 +mpfr_float 100 +(int)0.112256 +mpfr_float 100 -(int)0.146486 +mpfr_float 100 *(int)0.160234 +mpfr_float 100 /(int)0.256434 +mpfr_float 500 + 0.0777324 +mpfr_float 500 - 0.089375 +mpfr_float 500 * 3.71393 +mpfr_float 500 / 13.6039 +mpfr_float 500 str 0.156426 +mpfr_float 500 +(int)0.123967 +mpfr_float 500 -(int)0.158239 +mpfr_float 500 *(int)0.265474 +mpfr_float 500 /(int)0.709137 [section:float_performance Float Type Perfomance] [table Operator * [[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][1.07276 (0.287898s)][1.47724 (0.584569s)][1.55145 (5.09969s)]] -[[gmp_float][[*1] (0.268372s)][[*1] (0.395718s)][[*1] (3.28705s)]] -[[mpfr_float][1.27302 (0.341642s)][1.17649 (0.465557s)][1.14029 (3.7482s)]] +[[cpp_dec_float][1.09568 (0.292488s)][1.45233 (0.583535s)][1.57476 (5.08004s)]] +[[gmp_float][[*1] (0.266947s)][[*1] (0.401792s)][[*1] (3.22591s)]] +[[mpfr_float][1.2445 (0.332216s)][1.14991 (0.462025s)][1.15128 (3.71393s)]] ] [table Operator *(int) [[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][2.89945 (0.11959s)][4.56335 (0.197945s)][9.03602 (0.742044s)]] -[[gmp_float][[*1] (0.0412457s)][[*1] (0.0433772s)][[*1] (0.0821206s)]] -[[mpfr_float][3.6951 (0.152407s)][3.71977 (0.161353s)][3.30958 (0.271785s)]] +[[cpp_dec_float][3.02939 (0.118517s)][4.40051 (0.191461s)][8.93358 (0.736865s)]] +[[gmp_float][[*1] (0.0391224s)][[*1] (0.0435089s)][[*1] (0.0824826s)]] +[[mpfr_float][3.8645 (0.151189s)][3.6828 (0.160234s)][3.21855 (0.265474s)]] ] [table Operator + [[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][[*1] (0.02382s)][[*1] (0.0294619s)][[*1] (0.058466s)]] -[[gmp_float][4.55086 (0.108402s)][3.86443 (0.113853s)][2.6241 (0.15342s)]] -[[mpfr_float][2.52036 (0.060035s)][2.1833 (0.0643242s)][1.37736 (0.0805287s)]] +[[cpp_dec_float][[*1] (0.0238412s)][[*1] (0.0293132s)][[*1] (0.0605518s)]] +[[gmp_float][4.65648 (0.111016s)][3.71451 (0.108884s)][2.36269 (0.143065s)]] +[[mpfr_float][2.5349 (0.0604351s)][2.22408 (0.0651951s)][1.28374 (0.0777324s)]] ] [table Operator +(int) [[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][1.56759 (0.0527023s)][1.74629 (0.0618102s)][1.68077 (0.105927s)]] -[[gmp_float][[*1] (0.0336201s)][[*1] (0.0353951s)][[*1] (0.0630232s)]] -[[mpfr_float][3.14875 (0.105861s)][3.15499 (0.111671s)][1.92831 (0.121528s)]] +[[cpp_dec_float][1.63035 (0.0522868s)][1.80912 (0.0626744s)][1.85351 (0.105128s)]] +[[gmp_float][[*1] (0.0320709s)][[*1] (0.0346436s)][[*1] (0.0567182s)]] +[[mpfr_float][3.33957 (0.107103s)][3.24031 (0.112256s)][2.18567 (0.123967s)]] ] [table Operator - [[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][[*1] (0.0265783s)][[*1] (0.031465s)][[*1] (0.0619405s)]] -[[gmp_float][4.66954 (0.124108s)][3.72645 (0.117253s)][2.67536 (0.165713s)]] -[[mpfr_float][2.7909 (0.0741774s)][2.48557 (0.0782083s)][1.50944 (0.0934957s)]] +[[cpp_dec_float][[*1] (0.026085s)][[*1] (0.0304546s)][[*1] (0.0625459s)]] +[[gmp_float][4.58354 (0.119562s)][3.89415 (0.118595s)][2.42105 (0.151427s)]] +[[mpfr_float][2.82243 (0.073623s)][2.57196 (0.078328s)][1.42895 (0.089375s)]] ] [table Operator -(int) [[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][[*1] (0.0577674s)][[*1] (0.0633795s)][[*1] (0.11146s)]] -[[gmp_float][2.31811 (0.133911s)][2.07251 (0.131355s)][1.67161 (0.186319s)]] -[[mpfr_float][2.45081 (0.141577s)][2.29174 (0.145249s)][1.395 (0.155487s)]] +[[cpp_dec_float][[*1] (0.0588879s)][[*1] (0.0638241s)][[*1] (0.113107s)]] +[[gmp_float][2.21528 (0.130453s)][2.06656 (0.131897s)][1.45214 (0.164247s)]] +[[mpfr_float][2.3956 (0.141072s)][2.29515 (0.146486s)][1.39903 (0.158239s)]] ] [table Operator / [[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][3.24327 (4.00108s)][5.00532 (8.12985s)][6.79566 (54.2796s)]] -[[gmp_float][[*1] (1.23366s)][[*1] (1.62424s)][[*1] (7.9874s)]] -[[mpfr_float][1.32521 (1.63486s)][1.38967 (2.25716s)][1.72413 (13.7713s)]] +[[cpp_dec_float][3.22921 (3.99158s)][5.04305 (8.1132s)][6.64479 (53.775s)]] +[[gmp_float][[*1] (1.23608s)][[*1] (1.60879s)][[*1] (8.09281s)]] +[[mpfr_float][1.33968 (1.65596s)][1.41789 (2.28108s)][1.68098 (13.6039s)]] ] [table Operator /(int) [[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][1.45093 (0.253675s)][1.83306 (0.419569s)][2.3644 (1.64187s)]] -[[gmp_float][[*1] (0.174836s)][[*1] (0.22889s)][[*1] (0.694411s)]] -[[mpfr_float][1.16731 (0.204088s)][1.13211 (0.259127s)][1.02031 (0.708513s)]] +[[cpp_dec_float][1.38197 (0.246362s)][1.74079 (0.412828s)][2.34395 (1.62534s)]] +[[gmp_float][[*1] (0.178268s)][[*1] (0.23715s)][[*1] (0.693418s)]] +[[mpfr_float][1.13843 (0.202945s)][1.08131 (0.256434s)][1.02267 (0.709137s)]] ] [table Operator str [[Backend][50 Bits][100 Bits][500 Bits]] -[[cpp_float][1.4585 (0.0188303s)][1.55515 (0.03172s)][[*1] (0.131962s)]] -[[gmp_float][[*1] (0.0129107s)][[*1] (0.0203967s)][1.04632 (0.138075s)]] -[[mpfr_float][2.19015 (0.0282764s)][1.84679 (0.0376683s)][1.20295 (0.158743s)]] +[[cpp_dec_float][[*1] (0.0185371s)][1.53356 (0.0318154s)][[*1] (0.131303s)]] +[[gmp_float][1.61743 (0.0299824s)][[*1] (0.0207461s)][1.03767 (0.136249s)]] +[[mpfr_float][1.57977 (0.0292843s)][1.82886 (0.0379418s)][1.19134 (0.156426s)]] ] [endsect] [section:integer_performance Integer Type Perfomance] [table Operator % -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0946529s)][[*1] (0.170561s)][[*1] (0.328458s)][[*1] (0.575884s)][[*1] (1.05006s)]] -[[gmp_int][7.77525 (0.73595s)][4.39387 (0.749422s)][2.35075 (0.772122s)][1.51922 (0.874894s)][1.02263 (1.07382s)]] -[[tommath_int][27.1503 (2.56986s)][12.8743 (2.19585s)][9.43965 (3.10053s)][8.24936 (4.75068s)][10.9719 (11.5211s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.52964 (0.488484s)][1.9024 (0.597931s)][1.57549 (0.807811s)][1.31477 (1.24204s)]] +[[cpp_int(fixed)][[*1] (0.193104s)][[*1] (0.314303s)][[*1] (0.512737s)][[*1] (0.944678s)]] +[[gmp_int][3.24303 (0.626244s)][2.18285 (0.686075s)][1.54555 (0.792461s)][1.0841 (1.02412s)]] +[[tommath_int][14.8026 (2.85844s)][9.7177 (3.05431s)][9.06266 (4.64676s)][11.9304 (11.2704s)]] ] [table Operator %(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][1.25034 (0.0425984s)][1.91617 (0.106226s)][2.02166 (0.195577s)][2.14437 (0.387067s)][2.23514 (0.776075s)]] -[[gmp_int][[*1] (0.0340695s)][[*1] (0.0554367s)][[*1] (0.0967406s)][[*1] (0.180504s)][[*1] (0.347216s)]] -[[tommath_int][42.8781 (1.46083s)][29.879 (1.65639s)][23.4323 (2.26685s)][19.932 (3.5978s)][25.0046 (8.682s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][3.57875 (0.197942s)][2.99222 (0.298382s)][2.60748 (0.478772s)][2.42374 (0.85137s)]] +[[cpp_int(fixed)][2.01994 (0.111723s)][2.085 (0.207915s)][2.10772 (0.38701s)][2.16437 (0.760262s)]] +[[gmp_int][[*1] (0.0553103s)][[*1] (0.0997194s)][[*1] (0.183615s)][[*1] (0.351263s)]] +[[tommath_int][32.4149 (1.79288s)][22.0249 (2.19631s)][18.7297 (3.43906s)][24.0777 (8.45761s)]] ] [table Operator & -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00298048s)][[*1] (0.00546222s)][[*1] (0.0127546s)][[*1] (0.01985s)][[*1] (0.0349286s)]] -[[gmp_int][16.0105 (0.0477189s)][9.67027 (0.0528211s)][5.12678 (0.0653902s)][4.62316 (0.0917698s)][4.00837 (0.140007s)]] -[[tommath_int][43.6665 (0.130147s)][23.8003 (0.130002s)][11.4242 (0.145711s)][7.83416 (0.155508s)][9.50103 (0.331858s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.27651 (0.0299046s)][1.44553 (0.0389208s)][1.51976 (0.04981s)][1.48214 (0.0745785s)]] +[[cpp_int(fixed)][[*1] (0.0234269s)][[*1] (0.026925s)][[*1] (0.032775s)][[*1] (0.0503183s)]] +[[gmp_int][2.26238 (0.0530007s)][2.44171 (0.0657431s)][2.77722 (0.0910233s)][2.94472 (0.148173s)]] +[[tommath_int][5.60505 (0.131309s)][5.56001 (0.149703s)][4.72526 (0.15487s)][8.2919 (0.417234s)]] ] [table Operator &(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00222291s)][[*1] (0.0035522s)][[*1] (0.0110247s)][[*1] (0.0154281s)][[*1] (0.0275044s)]] -[[gmp_int][70.8538 (0.157502s)][42.1478 (0.149717s)][13.9023 (0.153268s)][10.3271 (0.159328s)][6.0529 (0.166481s)]] -[[tommath_int][154.134 (0.342626s)][93.2035 (0.331077s)][31.9151 (0.351853s)][23.6515 (0.364899s)][22.0042 (0.605213s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.64349 (0.0463351s)][1.34507 (0.0550224s)][1.29371 (0.0697964s)][1.17854 (0.101779s)]] +[[cpp_int(fixed)][[*1] (0.0281931s)][[*1] (0.0409067s)][[*1] (0.0539505s)][[*1] (0.0863606s)]] +[[gmp_int][5.204 (0.146717s)][3.63933 (0.148873s)][2.85915 (0.154253s)][1.8967 (0.163801s)]] +[[tommath_int][12.0738 (0.340397s)][8.67273 (0.354773s)][6.75845 (0.364622s)][7.1076 (0.613817s)]] ] [table Operator * -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0223481s)][[*1] (0.0375288s)][[*1] (0.120353s)][[*1] (0.439147s)][[*1] (1.46969s)]] -[[gmp_int][2.50746 (0.0560369s)][1.76676 (0.0663044s)][1.06052 (0.127636s)][1.22558 (0.53821s)][1.03538 (1.52168s)]] -[[tommath_int][3.00028 (0.0670506s)][2.97696 (0.111722s)][2.86257 (0.34452s)][2.26661 (0.995374s)][2.12926 (3.12935s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.36344 (0.0764199s)][1.50698 (0.193581s)][1.41904 (0.656832s)][1.6399 (2.47851s)]] +[[cpp_int(fixed)][[*1] (0.0560495s)][1.26247 (0.162173s)][[*1] (0.462871s)][1.06665 (1.61211s)]] +[[gmp_int][1.20183 (0.0673622s)][[*1] (0.128456s)][1.11903 (0.517967s)][[*1] (1.51138s)]] +[[tommath_int][1.99157 (0.111627s)][2.64312 (0.339525s)][2.10438 (0.974058s)][2.0631 (3.11813s)]] ] [table Operator *(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00444316s)][[*1] (0.0135739s)][[*1] (0.0192615s)][[*1] (0.0328339s)][1.18198 (0.0567364s)]] -[[gmp_int][4.57776 (0.0203397s)][1.79901 (0.0244196s)][1.32814 (0.025582s)][1.01453 (0.033311s)][[*1] (0.048001s)]] -[[tommath_int][53.8709 (0.239357s)][18.3773 (0.249452s)][14.2088 (0.273682s)][14.0907 (0.462652s)][9.10761 (0.437175s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.35944 (0.0306376s)][1.54828 (0.040404s)][1.60013 (0.0537717s)][1.62199 (0.0790137s)]] +[[cpp_int(fixed)][1.28804 (0.0290285s)][1.54595 (0.0403434s)][1.61453 (0.0542558s)][1.69566 (0.0826023s)]] +[[gmp_int][[*1] (0.0225369s)][[*1] (0.0260961s)][[*1] (0.0336047s)][[*1] (0.0487139s)]] +[[tommath_int][10.5972 (0.238829s)][10.4554 (0.272846s)][9.6853 (0.325472s)][8.5224 (0.41516s)]] ] [table Operator + -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0031291s)][[*1] (0.00703043s)][[*1] (0.0163669s)][[*1] (0.0326567s)][[*1] (0.0603087s)]] -[[gmp_int][12.4866 (0.0390717s)][6.01034 (0.0422553s)][2.65628 (0.0434751s)][1.54295 (0.0503875s)][1.16477 (0.0702458s)]] -[[tommath_int][6.03111 (0.018872s)][3.08173 (0.0216659s)][1.84243 (0.0301548s)][1.30199 (0.0425188s)][1.18909 (0.0717123s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.24954 (0.0271391s)][1.12545 (0.0354288s)][1.26716 (0.0536949s)][1.34112 (0.0884854s)]] +[[cpp_int(fixed)][1.06795 (0.023195s)][1.0057 (0.0316591s)][1.21714 (0.0515755s)][1.26263 (0.0833072s)]] +[[gmp_int][1.91685 (0.0416325s)][1.38884 (0.0437202s)][1.18481 (0.0502054s)][[*1] (0.065979s)]] +[[tommath_int][[*1] (0.0217192s)][[*1] (0.0314797s)][[*1] (0.0423742s)][1.09807 (0.0724498s)]] ] [table Operator +(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00335294s)][[*1] (0.00376116s)][[*1] (0.00985174s)][[*1] (0.0119345s)][[*1] (0.0170918s)]] -[[gmp_int][9.47407 (0.031766s)][8.44794 (0.0317741s)][4.23857 (0.0417573s)][5.40856 (0.0645488s)][6.31314 (0.107903s)]] -[[tommath_int][67.0025 (0.224655s)][60.4203 (0.22725s)][25.1834 (0.2481s)][23.2996 (0.27807s)][17.1743 (0.293538s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.48302 (0.0203604s)][1.21971 (0.0238597s)][1.2383 (0.0262742s)][1.03442 (0.0296193s)]] +[[cpp_int(fixed)][[*1] (0.013729s)][[*1] (0.0195617s)][[*1] (0.0212179s)][[*1] (0.0286337s)]] +[[gmp_int][2.16569 (0.0297328s)][2.15606 (0.0421762s)][3.05447 (0.0648096s)][3.67481 (0.105223s)]] +[[tommath_int][18.7291 (0.257132s)][14.1384 (0.27657s)][13.8483 (0.293832s)][11.5132 (0.329666s)]] ] [table Operator - -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00339191s)][[*1] (0.0073172s)][[*1] (0.0166428s)][[*1] (0.0349375s)][[*1] (0.0600083s)]] -[[gmp_int][12.5182 (0.0424608s)][5.57936 (0.0408253s)][2.78496 (0.0463496s)][1.48373 (0.051838s)][1.29928 (0.0779673s)]] -[[tommath_int][7.00782 (0.0237699s)][3.69919 (0.0270677s)][2.29645 (0.0382195s)][1.39777 (0.0488346s)][1.28243 (0.0769566s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.1816 (0.0302204s)][[*1] (0.03826s)][1.11566 (0.0529947s)][1.17049 (0.0822931s)]] +[[cpp_int(fixed)][[*1] (0.0255758s)][1.01186 (0.0387139s)][[*1] (0.0475007s)][1.22939 (0.0864345s)]] +[[gmp_int][1.60126 (0.0409536s)][1.17441 (0.0449331s)][1.12969 (0.053661s)][[*1] (0.0703067s)]] +[[tommath_int][1.14132 (0.0291902s)][1.03846 (0.0397314s)][1.09534 (0.0520296s)][1.10104 (0.0774105s)]] ] [table Operator -(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00250933s)][[*1] (0.00358055s)][[*1] (0.0103282s)][[*1] (0.0119127s)][[*1] (0.0176089s)]] -[[gmp_int][12.093 (0.0303454s)][8.50898 (0.0304669s)][3.9284 (0.0405733s)][5.03037 (0.0599252s)][5.96617 (0.105058s)]] -[[tommath_int][80.8477 (0.202873s)][57.8371 (0.207089s)][21.3372 (0.220375s)][23.526 (0.280258s)][14.793 (0.260488s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.49712 (0.0155424s)][1.3004 (0.0199724s)][1.2442 (0.0223562s)][1.12422 (0.0246399s)]] +[[cpp_int(fixed)][[*1] (0.0103816s)][[*1] (0.0153586s)][[*1] (0.0179683s)][[*1] (0.0219173s)]] +[[gmp_int][2.85673 (0.0296573s)][2.55469 (0.0392365s)][3.22576 (0.0579614s)][4.55088 (0.0997431s)]] +[[tommath_int][19.5977 (0.203455s)][14.2166 (0.218347s)][12.9406 (0.23252s)][11.9263 (0.261392s)]] ] [table Operator / -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0991632s)][[*1] (0.172328s)][[*1] (0.309492s)][[*1] (0.573815s)][[*1] (1.06356s)]] -[[gmp_int][7.81859 (0.775316s)][5.11069 (0.880715s)][2.93514 (0.908404s)][1.80497 (1.03572s)][1.21878 (1.29625s)]] -[[tommath_int][18.0766 (1.79253s)][12.3939 (2.13582s)][9.80438 (3.03438s)][8.74047 (5.01541s)][10.8288 (11.517s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.9558 (0.601063s)][2.21555 (0.694115s)][1.73066 (0.915068s)][1.41604 (1.36697s)]] +[[cpp_int(fixed)][[*1] (0.20335s)][[*1] (0.313292s)][[*1] (0.52874s)][[*1] (0.965347s)]] +[[gmp_int][4.08359 (0.8304s)][2.91 (0.91168s)][1.97009 (1.04166s)][1.30934 (1.26397s)]] +[[tommath_int][10.2514 (2.08463s)][9.26794 (2.90357s)][8.62079 (4.55815s)][11.6636 (11.2594s)]] ] [table Operator /(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][1.04098 (0.0443082s)][1.61317 (0.110308s)][2.18324 (0.229148s)][2.36331 (0.442167s)][2.45159 (0.866172s)]] -[[gmp_int][[*1] (0.042564s)][[*1] (0.06838s)][[*1] (0.104957s)][[*1] (0.187096s)][[*1] (0.35331s)]] -[[tommath_int][32.4072 (1.37938s)][23.7471 (1.62383s)][22.1907 (2.32908s)][19.9054 (3.72421s)][24.2219 (8.55783s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][5.83613 (0.318461s)][4.26769 (0.433035s)][3.39803 (0.641615s)][2.80387 (1.05122s)]] +[[cpp_int(fixed)][2.46673 (0.134603s)][2.52386 (0.256092s)][2.43318 (0.459431s)][2.28165 (0.855435s)]] +[[gmp_int][[*1] (0.0545672s)][[*1] (0.101468s)][[*1] (0.18882s)][[*1] (0.374919s)]] +[[tommath_int][29.1556 (1.59094s)][21.9806 (2.23033s)][18.2745 (3.45058s)][22.3582 (8.38249s)]] ] [table Operator << -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.0119095s)][[*1] (0.0131746s)][[*1] (0.0213483s)][[*1] (0.0247552s)][[*1] (0.0339579s)]] -[[gmp_int][1.9355 (0.0230509s)][1.94257 (0.0255925s)][1.49684 (0.031955s)][1.79202 (0.0443618s)][2.0846 (0.0707887s)]] -[[tommath_int][2.64273 (0.0314737s)][2.95612 (0.0389456s)][3.05842 (0.065292s)][3.79496 (0.0939451s)][4.82142 (0.163725s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.1596 (0.0220286s)][1.11929 (0.0294239s)][1.15296 (0.0365532s)][1.06891 (0.0522035s)]] +[[cpp_int(fixed)][[*1] (0.0189966s)][[*1] (0.0262879s)][[*1] (0.0317039s)][[*1] (0.0488381s)]] +[[gmp_int][1.36896 (0.0260055s)][1.17593 (0.0309127s)][1.51661 (0.0480825s)][1.43853 (0.0702549s)]] +[[tommath_int][2.11378 (0.0401547s)][2.52576 (0.0663968s)][2.96051 (0.0938596s)][3.31171 (0.161738s)]] ] [table Operator >> -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.006361s)][[*1] (0.00880189s)][[*1] (0.0180295s)][[*1] (0.0220786s)][[*1] (0.0325312s)]] -[[gmp_int][4.26889 (0.0271544s)][3.14669 (0.0276968s)][1.74396 (0.0314426s)][1.45928 (0.0322188s)][1.24596 (0.0405327s)]] -[[tommath_int][39.4379 (0.250865s)][28.6225 (0.251932s)][16.4543 (0.296661s)][14.2167 (0.313884s)][15.5842 (0.506974s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.26962 (0.0208765s)][1.19206 (0.0265325s)][1.10665 (0.0304931s)][1.03429 (0.0383751s)]] +[[cpp_int(fixed)][[*1] (0.0164431s)][[*1] (0.0222577s)][[*1] (0.0275545s)][1.02967 (0.0382038s)]] +[[gmp_int][1.67276 (0.0275053s)][1.30139 (0.028966s)][1.17546 (0.0323891s)][[*1] (0.037103s)]] +[[tommath_int][14.0947 (0.23176s)][11.7344 (0.261181s)][10.5175 (0.289806s)][13.3498 (0.495316s)]] ] [table Operator ^ -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00307714s)][[*1] (0.00538197s)][[*1] (0.0127717s)][[*1] (0.0198304s)][[*1] (0.0345822s)]] -[[gmp_int][13.9543 (0.0429392s)][9.92785 (0.0534314s)][4.80398 (0.0613552s)][4.35864 (0.0864335s)][3.887 (0.134421s)]] -[[tommath_int][41.5958 (0.127996s)][24.2396 (0.130457s)][11.3666 (0.145171s)][8.01016 (0.158845s)][9.84853 (0.340584s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.39932 (0.0300509s)][1.28371 (0.0381634s)][1.25304 (0.0494246s)][1.04238 (0.075182s)]] +[[cpp_int(fixed)][[*1] (0.0214753s)][[*1] (0.0297291s)][[*1] (0.0394438s)][[*1] (0.0721252s)]] +[[gmp_int][2.26098 (0.0485553s)][2.11331 (0.0628266s)][2.1917 (0.086449s)][1.89072 (0.136369s)]] +[[tommath_int][6.08557 (0.130689s)][4.84167 (0.143938s)][3.82246 (0.150772s)][5.8133 (0.419285s)]] ] [table Operator ^(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00236664s)][[*1] (0.0035339s)][[*1] (0.0100442s)][[*1] (0.0155814s)][[*1] (0.0293253s)]] -[[gmp_int][61.4272 (0.145376s)][41.6319 (0.147123s)][14.9744 (0.150405s)][9.64857 (0.150338s)][5.46649 (0.160306s)]] -[[tommath_int][145.509 (0.344367s)][93.9055 (0.331853s)][35.0456 (0.352003s)][22.7371 (0.354275s)][19.1373 (0.561207s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.85734 (0.0381023s)][1.66156 (0.0432356s)][1.51413 (0.0466764s)][1.28122 (0.0550852s)]] +[[cpp_int(fixed)][[*1] (0.0205145s)][[*1] (0.0260211s)][[*1] (0.0308272s)][[*1] (0.0429944s)]] +[[gmp_int][6.89492 (0.141446s)][5.58265 (0.145267s)][5.07065 (0.156314s)][3.68095 (0.15826s)]] +[[tommath_int][16.3846 (0.336121s)][12.9631 (0.337315s)][11.2716 (0.347472s)][13.6661 (0.587566s)]] +] +[table Operator gcd +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.82307 (4.48165s)][1.77052 (10.1686s)][1.8655 (25.1877s)][2.12367 (69.0626s)]] +[[cpp_int(fixed)][1.504 (3.69729s)][1.60631 (9.22552s)][1.84155 (24.8643s)][2.25807 (73.4335s)]] +[[gmp_int][[*1] (2.4583s)][[*1] (5.7433s)][[*1] (13.5018s)][[*1] (32.5205s)]] +[[tommath_int][4.92412 (12.105s)][4.39462 (25.2396s)][4.05657 (54.7712s)][3.96001 (128.781s)]] ] [table Operator str -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.000465841s)][[*1] (0.00102073s)][[*1] (0.00207212s)][1.02618 (0.0062017s)][1.32649 (0.0190043s)]] -[[gmp_int][2.83823 (0.00132216s)][2.17537 (0.00222046s)][1.46978 (0.00304557s)][[*1] (0.00604351s)][[*1] (0.0143268s)]] -[[tommath_int][15.76 (0.00734164s)][15.9879 (0.0163193s)][21.7337 (0.0450349s)][19.7183 (0.119168s)][26.3445 (0.377431s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.73678 (0.00186546s)][1.442 (0.00327905s)][1.29994 (0.0076685s)][1.49716 (0.0217405s)]] +[[cpp_int(fixed)][[*1] (0.00107409s)][[*1] (0.00227396s)][1.01222 (0.00597122s)][1.20506 (0.0174989s)]] +[[gmp_int][1.8827 (0.00202218s)][1.28861 (0.00293026s)][[*1] (0.00589914s)][[*1] (0.0145211s)]] +[[tommath_int][15.6431 (0.0168021s)][22.3011 (0.0507118s)][20.9541 (0.123612s)][26.2052 (0.380528s)]] ] [table Operator | -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00295261s)][[*1] (0.00560832s)][[*1] (0.0127056s)][[*1] (0.0200759s)][[*1] (0.034651s)]] -[[gmp_int][14.1091 (0.0416586s)][8.52475 (0.0478096s)][4.74593 (0.0602998s)][4.19694 (0.0842575s)][3.85525 (0.133588s)]] -[[tommath_int][44.8889 (0.132539s)][25.2503 (0.141612s)][11.0488 (0.140382s)][7.39273 (0.148416s)][9.75809 (0.338127s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.39649 (0.0295702s)][1.14915 (0.0378751s)][1.31606 (0.0523944s)][1.04853 (0.0751774s)]] +[[cpp_int(fixed)][[*1] (0.0211746s)][[*1] (0.0329594s)][[*1] (0.0398115s)][[*1] (0.071698s)]] +[[gmp_int][2.31998 (0.0491246s)][1.83801 (0.0605797s)][2.16567 (0.0862186s)][1.88132 (0.134887s)]] +[[tommath_int][6.12227 (0.129637s)][4.26647 (0.14062s)][3.75956 (0.149674s)][5.78233 (0.414581s)]] ] [table Operator |(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[fixed_int][[*1] (0.00244005s)][[*1] (0.0040142s)][[*1] (0.00983777s)][[*1] (0.0155223s)][[*1] (0.0293444s)]] -[[gmp_int][64.6148 (0.157663s)][34.5827 (0.138822s)][14.2764 (0.140448s)][10.3248 (0.160264s)][5.33565 (0.156572s)]] -[[tommath_int][137.825 (0.3363s)][81.1074 (0.325581s)][34.8737 (0.343079s)][22.3727 (0.347276s)][18.912 (0.554963s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.89501 (0.0385046s)][1.64437 (0.0425891s)][1.56631 (0.0479629s)][1.28806 (0.0549147s)]] +[[cpp_int(fixed)][[*1] (0.020319s)][[*1] (0.0258999s)][[*1] (0.0306217s)][[*1] (0.0426336s)]] +[[gmp_int][6.93537 (0.14092s)][5.48104 (0.141959s)][4.90595 (0.150229s)][3.63885 (0.155137s)]] +[[tommath_int][16.4913 (0.335087s)][13.3178 (0.344931s)][11.4509 (0.350645s)][13.7699 (0.587063s)]] ] [endsect] [section:rational_performance Rational Type Perfomance] [table Operator * -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (2.67402s)][[*1] (5.89806s)][[*1] (12.7524s)][[*1] (29.4044s)][[*1] (70.1615s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.59286 (32.3559s)][6.54125 (82.4247s)][6.8815 (197.198s)][6.84066 (473.057s)]] +[[mpq_rational][[*1] (5.78521s)][[*1] (12.6008s)][[*1] (28.6562s)][[*1] (69.1537s)]] ] [table Operator *(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (1.15673s)][[*1] (1.20559s)][[*1] (1.25776s)][[*1] (1.41413s)][[*1] (1.59151s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][2.70193 (3.1466s)][3.10134 (3.79056s)][3.659 (4.93935s)][4.61372 (6.89845s)]] +[[mpq_rational][[*1] (1.16457s)][[*1] (1.22223s)][[*1] (1.34992s)][[*1] (1.4952s)]] ] [table Operator + -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (1.47032s)][[*1] (3.1599s)][[*1] (6.74926s)][[*1] (16.7334s)][[*1] (38.5739s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.91758 (18.1263s)][6.60754 (44.1182s)][6.65334 (103.169s)][6.44717 (244.055s)]] +[[mpq_rational][[*1] (3.06312s)][[*1] (6.67695s)][[*1] (15.5064s)][[*1] (37.8546s)]] ] [table Operator +(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.639153s)][[*1] (0.683218s)][[*1] (0.725686s)][[*1] (0.895283s)][[*1] (0.931053s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][3.98512 (2.67249s)][4.24335 (3.04309s)][4.65009 (3.83046s)][5.45832 (5.08346s)]] +[[mpq_rational][[*1] (0.670618s)][[*1] (0.717144s)][[*1] (0.823739s)][[*1] (0.931322s)]] ] [table Operator - -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (1.48169s)][[*1] (3.17694s)][[*1] (6.75317s)][[*1] (15.9167s)][[*1] (39.0541s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.91504 (18.2374s)][6.55676 (43.8659s)][6.66239 (103.481s)][6.47224 (244.887s)]] +[[mpq_rational][[*1] (3.08322s)][[*1] (6.69018s)][[*1] (15.5321s)][[*1] (37.8365s)]] ] [table Operator -(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.650283s)][[*1] (0.669498s)][[*1] (0.707811s)][[*1] (0.83232s)][[*1] (1.06134s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][3.96173 (2.66785s)][4.36532 (3.09023s)][4.59363 (3.74494s)][5.43075 (5.09156s)]] +[[mpq_rational][[*1] (0.673405s)][[*1] (0.707904s)][[*1] (0.815246s)][[*1] (0.937541s)]] ] [table Operator / -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (9.26405s)][[*1] (14.7461s)][[*1] (26.4939s)][[*1] (54.0641s)][[*1] (126.261s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][4.36846 (63.9498s)][5.52565 (145.045s)][6.18331 (328.069s)][6.49822 (784.806s)]] +[[mpq_rational][[*1] (14.639s)][[*1] (26.2494s)][[*1] (53.0571s)][[*1] (120.772s)]] ] [table Operator /(int) -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (1.40596s)][[*1] (1.42215s)][[*1] (1.50342s)][[*1] (1.62326s)][[*1] (1.7796s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][2.26643 (3.13785s)][2.57125 (3.76931s)][3.20872 (5.06758s)][4.02177 (7.17803s)]] +[[mpq_rational][[*1] (1.38449s)][[*1] (1.46594s)][[*1] (1.57931s)][[*1] (1.78479s)]] ] [table Operator str -[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] -[[mpq_rational][[*1] (0.00265159s)][[*1] (0.00363964s)][[*1] (0.00677698s)][[*1] (0.0117945s)][[*1] (0.0283447s)]] +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.40493 (0.0199393s)][8.55089 (0.0511907s)][9.91026 (0.118839s)][9.93546 (0.285367s)]] +[[mpq_rational][[*1] (0.00368909s)][[*1] (0.00598659s)][[*1] (0.0119915s)][[*1] (0.028722s)]] ] [endsect] diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index e22c8a1c..237760dd 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -358,6 +358,11 @@ void test_integer_ops(const boost::mpl::int_::is_signed) { a = -20; @@ -376,6 +381,20 @@ void test_integer_ops(const boost::mpl::int_ #include #include +#include #include "test.hpp" template @@ -57,7 +58,9 @@ void test() using namespace boost::multiprecision; typedef Number test_type; unsigned last_error_count = 0; - for(int i = 0; i < 1000; ++i) + boost::timer tim; + + for(int i = 0; i < 10000; ++i) { mpz_int a = generate_random(1000); mpz_int b = generate_random(512); @@ -280,6 +283,18 @@ void test() std::cout << "a%d = " << a%d << std::endl; std::cout << "a1%d1 = " << a1%d1 << std::endl; } + + // + // Check to see if test is taking too long. + // Tests run on the compiler farm time out after 300 seconds, + // so don't get too close to that: + // + if(tim.elapsed() > 100) + { + std::cout << "Timeout reached, aborting tests now....\n"; + break; + } + } } From 8433c691750535dc9505b7ce0a5e3e0e7e08889a Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 22 Mar 2012 10:29:30 +0000 Subject: [PATCH 139/256] Disable expression templates for fixed precision types. Restrict integer functions to integer types. Improve Miller Rabin performance by filtering out small primes etc. Improve Miller Rabin tests. Change mp_int to tom_int to avoid conflict with global ::mp_Int type. [SVN r77471] --- .../perf/int_real_world.html | 132 +---- .../boost_multiprecision/ref/mp_number.html | 48 +- doc/html/boost_multiprecision/tut/ints.html | 453 +++++++++--------- .../boost_multiprecision/tut/rational.html | 18 +- doc/html/index.html | 2 +- doc/multiprecision.qbk | 226 +++++---- example/tommath_snips.cpp | 6 +- include/boost/multiprecision/cpp_int.hpp | 16 +- include/boost/multiprecision/integer_ops.hpp | 38 +- include/boost/multiprecision/miller_rabin.hpp | 77 ++- include/boost/multiprecision/tommath.hpp | 10 +- performance/miller_rabin_performance.cpp | 4 +- performance/performance_test.cpp | 16 +- test/test_arithmetic.cpp | 17 +- test/test_int_io.cpp | 2 +- test/test_miller_rabin.cpp | 12 + test/test_numeric_limits.cpp | 2 +- test/test_rational_io.cpp | 4 +- 18 files changed, 579 insertions(+), 504 deletions(-) diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html index 5705e869..6033685c 100644 --- a/doc/html/boost_multiprecision/perf/int_real_world.html +++ b/doc/html/boost_multiprecision/perf/int_real_world.html @@ -47,126 +47,6 @@ - -

    - cpp_int -

    - - -

    - 1.45089(0.481248s) -

    - - - - -

    - cpp_int (no Expression templates) -

    - - -

    - 1.61489(0.535646s) -

    - - - - -

    - cpp_int (64-bit cache) -

    - - -

    - 1.39273(0.461956s) -

    - - - - -

    - cpp_int (256-bit cache) -

    - - -

    - 1.37743(0.456884s) -

    - - - - -

    - cpp_int (512-bit cache) -

    - - -

    - 1.0919(0.362175s) -

    - - - - -

    - cpp_int (1024-bit cache) -

    - - -

    - 1.10864(0.367726s) -

    - - - - -

    - mp_int -

    - - -

    - 3.92956(1.3034s) -

    - - - - -

    - mp_int (no Expression templates) -

    - - -

    - 4.02496(1.33505s) -

    - - - - -

    - mp_int1024_t -

    - - -

    - 1.01094(0.335322s) -

    - - - - -

    - mp_int1024_t (no Expression templates) -

    - - -

    - 1(0.331692s) -

    - - -

    mpz_int @@ -174,7 +54,7 @@

    - 1.08472(0.359793s) + 1.08279(0.370326s)

    @@ -186,12 +66,20 @@

    - 1.20865(0.400901s) + 1.1702(0.400222s)

    +

    + [[cpp_int][1.3612(0.465547s)]] [[cpp_int (no Expression templates)][1.33286(0.455854s)]] + [[cpp_int (64-bit cache)][1.33134(0.455333s)]] [[cpp_int (256-bit cache)][1.29367(0.442451s)]] + [[cpp_int (512-bit cache)][1.08821(0.37218s)]] [[cpp_int (1024-bit cache)][1.07902(0.369037s)]] + [[mp_int1024_t][1.02616(0.35096s)]] [[mp_int1024_t (no Expression templates)][1(0.342011s)]] + [[tom_int][3.74233(1.27992s)]] [[tom_int (no Expression templates)][3.97646(1.35999s)]] + ] +

    It's interesting to note that expression templates have little effect here - perhaps because the actual expressions involved are relatively trivial diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html index a68c1649..e1a98ef1 100644 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -143,6 +143,16 @@ template <class T> struct number_category; +// Integer specific functions: +template <class Backend, bool ExpressionTemplates> +bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y, + mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r); +template <class Integer> +Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val); +template <class Engine> +bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen); +bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials); + // Rational number support: typename component_type<mp_number-or-expression-template-type>::type numerator (const mp_number-or-expression-template-type&); typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&); @@ -537,6 +547,40 @@

    + Integer functions +
    +
    template <class Backend, bool ExpressionTemplates>
+bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
+               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
+
    +

    + Divides x by y and returns both the quotient and remainder. After the call + q = + x / y and r + = x % y. +

    +
    template <class Integer>
+Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
+
    +

    + Returns the absolute value of x + % val. +

    +
    template <class Engine>
+bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
+bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
+
    +

    + Tests to see if the number n is probably prime - the + test excludes the vast majority of composite numbers by excluding small prime + factors and performing a single Fermat test. Then performs trials + Miller-Rabin tests. Returns false + if n is definitely composite, or true + if n is probably prime with the probability of it being + composite less than 0.25^trials. +

    +
    + Rational Number Functions
    @@ -548,7 +592,7 @@ respectively.

    - + Boost.Math Interoperability Support
    @@ -571,7 +615,7 @@ to ensure interoperability.

    - + std::numeric_limits support
    diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html index 2cc70776..3c0e3371 100644 --- a/doc/html/boost_multiprecision/tut/ints.html +++ b/doc/html/boost_multiprecision/tut/ints.html @@ -63,6 +63,40 @@ + +

    + cpp_int +

    + + +

    + boost/multiprecision/cpp_int.hpp +

    + + +

    + 2 +

    + + +

    + None +

    + + +

    + Very versatile, Boost licenced, all C++ integer type which support + both arbitrary precision and fixed precision integer types. +

    + + +

    + Slower than GMP, though + typically not as slow as libtommath +

    + + +

    gmp_int @@ -98,7 +132,7 @@

    - mp_int + tom_int

    @@ -127,222 +161,10 @@

    - - -

    - cpp_int -

    - - -

    - boost/multiprecision/cpp_int.hpp -

    - - -

    - 2 -

    - - -

    - None -

    - - -

    - Very versatile, Boost licenced, all C++ integer type which support - both arbitrary precision and fixed precision integer types. -

    - - -

    - Slower than GMP. -

    - -
    - gmp_int -
    -
    namespace boost{ namespace multiprecision{
-
-class gmp_int;
-
-typedef mp_number<gmp_int >         mpz_int;
-
-}} // namespaces
-
    -

    - The gmp_int backend is used - via the typedef boost::multiprecision::mpz_int. It acts as a thin wrapper around - the GMP mpz_t - to provide an integer type that is a drop-in replacement for the native C++ - integer types, but with unlimited precision. -

    -

    - As well as the usual conversions from arithmetic and string types, type - mpz_int is copy constructible - and assignable from: -

    -
      -
    • - The GMP native types: mpf_t, mpz_t, - mpq_t. -
      • -
    • - Instances of mp_number<T> that are wrappers around those types: - mp_number<gmp_float<N> >, mp_number<gmp_rational>. -
      • -
    -

    - It's also possible to access the underlying mpz_t - via the data() - member function of gmp_int. -

    -

    - Things you should know when using this type: -

    -
      -
    • - No changes are made to the GMP library's global settings - so you can - safely mix this type with existing code that uses GMP. -
      • -
    • - Default constructed gmp_int's - have the value zero (this is GMP's default behavior). -
      • -
    • - Formatted IO for this type does not support octal or hexadecimal notation - for negative values, as a result performing formatted output on this - type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex - are set, will result in a std::runtime_error - will be thrown. -
      • -
    • - Division by zero is handled by the GMP - library - it will trigger a division by zero signal. -
      • -
    • - Although this type is a wrapper around GMP - it will work equally well with MPIR. - Indeed use of MPIR is recomended - on Win32. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-
-using namespace boost::multiprecision;
-
-mpz_int v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-
-std::cout << v << std::endl; // prints 1000!
-
-// Access the underlying representation:
-mpz_t z;
-mpz_init(z);
-mpz_set(z, v.backend().data());
-
    -

    -

    -
    - - mp_int -
    -
    namespace boost{ namespace multiprecision{
-
-class tommath_int;
-
-typedef mp_number<tommath_int >         mp_int;
-
-}} // namespaces
-
    -

    - The tommath_int backend is - used via the typedef boost::multiprecision::mp_int. - It acts as a thin wrapper around the libtommath - mp_int to provide an integer - type that is a drop-in replacement for the native C++ integer types, but - with unlimited precision. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed objects have the value zero (this is libtommath's - default behavior). -
      • -
    • - Although mp_int is mostly - a drop in replacement for the builtin integer types, it should be noted - that it is a rather strange beast as it's a signed type that is not a - 2's complement type. As a result the bitwise operations | & ^ will throw a std::runtime_error - exception if either of the arguments is negative. Similarly the complement - operator~ is deliberately - not implemented for this type. -
      • -
    • - Formatted IO for this type does not support octal or hexadecimal notation - for negative values, as a result performing formatted output on this - type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex - are set, will result in a std::runtime_error - will be thrown. -
      • -
    • - Division by zero will result in a hardware signal being raised by libtommath. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/tommath.hpp>
-
-boost::multiprecision::mp_int v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-
-std::cout << v << std::endl; // prints 1000!
-std::cout << std::hex << v << std::endl; // prints 1000! in hex format
-
-try{
-   std::cout << std::hex << -v << std::endl; // Ooops! can't print a negative value in hex format!
-}
-catch(const std::runtime_error& e)
-{
-   std::cout << e.what() << std::endl;
-}
-
-try{
-   // v is not a 2's complement type, bitwise operations are only supported
-   // on positive values:
-   v = -v & 2;
-}
-catch(const std::runtime_error& e)
-{
-   std::cout << e.what() << std::endl;
-}
-
    -

    -

    -
    - cpp_int 
    namespace boost{ namespace multiprecision{
@@ -357,16 +179,16 @@
 typedef mp_number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
 
 // Fixed precision unsigned types:
-typedef mp_number<cpp_int_backend<128, false, void> >   mp_uint128_t;
-typedef mp_number<cpp_int_backend<256, false, void> >   mp_uint256_t;
-typedef mp_number<cpp_int_backend<512, false, void> >   mp_uint512_t;
-typedef mp_number<cpp_int_backend<1024, false, void> >  mp_uint1024_t;
+typedef mp_number<cpp_int_backend<128, false, void>, false>   mp_uint128_t;
+typedef mp_number<cpp_int_backend<256, false, void>, false>   mp_uint256_t;
+typedef mp_number<cpp_int_backend<512, false, void>, false>   mp_uint512_t;
+typedef mp_number<cpp_int_backend<1024, false, void>, false>  mp_uint1024_t;
 
 // Fixed precision signed types:
-typedef mp_number<cpp_int_backend<128, true, void> >    mp_int128_t;
-typedef mp_number<cpp_int_backend<256, true, void> >    mp_int256_t;
-typedef mp_number<cpp_int_backend<512, true, void> >    mp_int512_t;
-typedef mp_number<cpp_int_backend<1024, true, void> >   mp_int1024_t;
+typedef mp_number<cpp_int_backend<128, true, void>, false>    mp_int128_t;
+typedef mp_number<cpp_int_backend<256, true, void>, false>    mp_int256_t;
+typedef mp_number<cpp_int_backend<512, true, void>, false>    mp_int512_t;
+typedef mp_number<cpp_int_backend<1024, true, void>, false>   mp_int1024_t;
 
 }} // namespaces
    @@ -448,10 +270,16 @@ string results in a std::runtime_error being thrown, this is a direct consequence of the sign-magnitude representation. +
  • + The fixed precision types mp_[u]intXXX_t + have expression template support turned off - it seems to make little + difference to the performance of these types either way - so we may as + well have the faster compile times by turning the feature off. +
    • - - Example: + + Example:

    @@ -474,6 +302,185 @@ std::cout << u << std::endl; // prints 100! +

    +

    +
    + + gmp_int +
    +
    namespace boost{ namespace multiprecision{
+
+class gmp_int;
+
+typedef mp_number<gmp_int >         mpz_int;
+
+}} // namespaces
+
    +

    + The gmp_int backend is used + via the typedef boost::multiprecision::mpz_int. It acts as a thin wrapper around + the GMP mpz_t + to provide an integer type that is a drop-in replacement for the native C++ + integer types, but with unlimited precision. +

    +

    + As well as the usual conversions from arithmetic and string types, type + mpz_int is copy constructible + and assignable from: +

    +
      +
    • + The GMP native types: mpf_t, mpz_t, + mpq_t. +
      • +
    • + Instances of mp_number<T> that are wrappers around those types: + mp_number<gmp_float<N> >, mp_number<gmp_rational>. +
      • +
    +

    + It's also possible to access the underlying mpz_t + via the data() + member function of gmp_int. +

    +

    + Things you should know when using this type: +

    +
      +
    • + No changes are made to the GMP library's global settings - so you can + safely mix this type with existing code that uses GMP. +
      • +
    • + Default constructed gmp_int's + have the value zero (this is GMP's default behavior). +
      • +
    • + Formatted IO for this type does not support octal or hexadecimal notation + for negative values, as a result performing formatted output on this + type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex + are set, will result in a std::runtime_error + will be thrown. +
      • +
    • + Division by zero is handled by the GMP + library - it will trigger a division by zero signal. +
      • +
    • + Although this type is a wrapper around GMP + it will work equally well with MPIR. + Indeed use of MPIR is recomended + on Win32. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+
+using namespace boost::multiprecision;
+
+mpz_int v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 1000!
+
+// Access the underlying representation:
+mpz_t z;
+mpz_init(z);
+mpz_set(z, v.backend().data());
+
    +

    +

    +
    + + tom_int +
    +
    namespace boost{ namespace multiprecision{
+
+class tommath_int;
+
+typedef mp_number<tommath_int >         tom_int;
+
+}} // namespaces
+
    +

    + The tommath_int backend is + used via the typedef boost::multiprecision::tom_int. + It acts as a thin wrapper around the libtommath + tom_int to provide an integer + type that is a drop-in replacement for the native C++ integer types, but + with unlimited precision. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed objects have the value zero (this is libtommath's + default behavior). +
      • +
    • + Although tom_int is mostly + a drop in replacement for the builtin integer types, it should be noted + that it is a rather strange beast as it's a signed type that is not a + 2's complement type. As a result the bitwise operations | & ^ will throw a std::runtime_error + exception if either of the arguments is negative. Similarly the complement + operator~ is deliberately + not implemented for this type. +
      • +
    • + Formatted IO for this type does not support octal or hexadecimal notation + for negative values, as a result performing formatted output on this + type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex + are set, will result in a std::runtime_error + will be thrown. +
      • +
    • + Division by zero will result in a hardware signal being raised by libtommath. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/tommath.hpp>
+
+boost::multiprecision::tom_int v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 1000!
+std::cout << std::hex << v << std::endl; // prints 1000! in hex format
+
+try{
+   std::cout << std::hex << -v << std::endl; // Ooops! can't print a negative value in hex format!
+}
+catch(const std::runtime_error& e)
+{
+   std::cout << e.what() << std::endl;
+}
+
+try{
+   // v is not a 2's complement type, bitwise operations are only supported
+   // on positive values:
+   v = -v & 2;
+}
+catch(const std::runtime_error& e)
+{
+   std::cout << e.what() << std::endl;
+}
+

    diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index b3cba087..2584d7db 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -414,26 +414,26 @@ 
    namespace boost{ namespace multiprecision{
 
 typedef rational_adpater<tommath_int>        tommath_rational;
-typedef mp_number<tommath_rational >         mp_rational;
+typedef mp_number<tommath_rational >         tom_rational;
 
 }} // namespaces

    The tommath_rational backend - is used via the typedef boost::multiprecision::mp_rational. - It acts as a thin wrapper around boost::rational<mp_int> to provide a rational number type that + is used via the typedef boost::multiprecision::tom_rational. + It acts as a thin wrapper around boost::rational<tom_int> to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision.

    - The advantage of using this type rather than boost::rational<mp_int> directly, is that it is expression-template + The advantage of using this type rather than boost::rational<tom_int> directly, is that it is expression-template enabled, greatly reducing the number of temporaries created in complex expressions.

    There are also non-member functions:

    -
    mp_int numerator(const mp_rational&);
-mp_int denominator(const mp_rational&);
+
    tom_int numerator(const tom_rational&);
+tom_int denominator(const tom_rational&);
 
    
 
    
         which return the numerator and denominator of the number.
@@ -443,7 +443,7 @@
       
    
 
      
 
    • 
-            Default constructed mp_rational's
+            Default constructed tom_rational's
             have the value zero (this the inherited Boost.Rational behavior).
           
      • 
 
    • 
@@ -472,7 +472,7 @@
 
 using namespace boost::multiprecision;
 
-mp_rational v = 1;
+tom_rational v = 1;
 
 // Do some arithmetic:
 for(unsigned i = 1; i <= 1000; ++i)
@@ -483,7 +483,7 @@
 std::cout << numerator(v) << std::endl;
 std::cout << denominator(v) << std::endl;
 
-mp_rational w(2, 3); // Component wise constructor
+tom_rational w(2, 3); // Component wise constructor
 std::cout << w << std::endl; // prints 2/3

    diff --git a/doc/html/index.html b/doc/html/index.html index cf7ed306..a81e493e 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -63,7 +63,7 @@

    - +

    Last revised: March 20, 2012 at 19:02:47 GMT

    Last revised: March 22, 2012 at 08:59:33 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 5d9597ae..c790c76e 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -225,77 +225,12 @@ The following backends provide integer arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] -[[`gmp_int`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient backend.][Dependency on GNU licenced [gmp] library.]] -[[`mp_int`][boost/multiprecision/tommath.hpp][2][[tommath]][Public domain backend with no licence restrictions.][Slower than [gmp].]] [[`cpp_int`][boost/multiprecision/cpp_int.hpp][2][None] - [Very versatile, Boost licenced, all C++ integer type which support both arbitrary precision and fixed precision integer types.][Slower than [gmp].]] + [Very versatile, Boost licenced, all C++ integer type which support both arbitrary precision and fixed precision integer types.][Slower than [gmp], though typically not as slow as [tommath]]] +[[`gmp_int`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient backend.][Dependency on GNU licenced [gmp] library.]] +[[`tom_int`][boost/multiprecision/tommath.hpp][2][[tommath]][Public domain backend with no licence restrictions.][Slower than [gmp].]] ] -[h4 gmp_int] - - namespace boost{ namespace multiprecision{ - - class gmp_int; - - typedef mp_number mpz_int; - - }} // namespaces - -The `gmp_int` backend is used via the typedef `boost::multiprecision::mpz_int`. It acts as a thin wrapper around the [gmp] `mpz_t` -to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. - -As well as the usual conversions from arithmetic and string types, type `mpz_int` is copy constructible and assignable from: - -* The [gmp] native types: `mpf_t`, `mpz_t`, `mpq_t`. -* Instances of `mp_number` that are wrappers around those types: `mp_number >`, `mp_number`. - -It's also possible to access the underlying `mpz_t` via the `data()` member function of `gmp_int`. - -Things you should know when using this type: - -* No changes are made to the GMP library's global settings - so you can safely mix this type with -existing code that uses [gmp]. -* Default constructed `gmp_int`'s have the value zero (this is GMP's default behavior). -* Formatted IO for this type does not support octal or hexadecimal notation for negative values, -as a result performing formatted output on this type when the argument is negative and either of the flags -`std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. -* Division by zero is handled by the [gmp] library - it will trigger a division by zero signal. -* Although this type is a wrapper around [gmp] it will work equally well with [mpir]. Indeed use of [mpir] -is recomended on Win32. - -[h5 Example:] - -[mpz_eg] - -[h4 mp_int] - - namespace boost{ namespace multiprecision{ - - class tommath_int; - - typedef mp_number mp_int; - - }} // namespaces - -The `tommath_int` backend is used via the typedef `boost::multiprecision::mp_int`. It acts as a thin wrapper around the [tommath] `mp_int` -to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. - -Things you should know when using this type: - -* Default constructed objects have the value zero (this is [tommath]'s default behavior). -* Although `mp_int` is mostly a drop in replacement for the builtin integer types, it should be noted that it is a -rather strange beast as it's a signed type that is not a 2's complement type. As a result the bitwise operations -`| & ^` will throw a `std::runtime_error` exception if either of the arguments is negative. Similarly the complement -operator`~` is deliberately not implemented for this type. -* Formatted IO for this type does not support octal or hexadecimal notation for negative values, -as a result performing formatted output on this type when the argument is negative and either of the flags -`std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. -* Division by zero will result in a hardware signal being raised by [tommath]. - -[h5 Example:] - -[tommath_eg] - [h4 cpp_int] namespace boost{ namespace multiprecision{ @@ -310,16 +245,16 @@ as a result performing formatted output on this type when the argument is negati typedef mp_number cpp_rational; // arbitrary precision rational number // Fixed precision unsigned types: - typedef mp_number > mp_uint128_t; - typedef mp_number > mp_uint256_t; - typedef mp_number > mp_uint512_t; - typedef mp_number > mp_uint1024_t; + typedef mp_number, false> mp_uint128_t; + typedef mp_number, false> mp_uint256_t; + typedef mp_number, false> mp_uint512_t; + typedef mp_number, false> mp_uint1024_t; // Fixed precision signed types: - typedef mp_number > mp_int128_t; - typedef mp_number > mp_int256_t; - typedef mp_number > mp_int512_t; - typedef mp_number > mp_int1024_t; + typedef mp_number, false> mp_int128_t; + typedef mp_number, false> mp_int256_t; + typedef mp_number, false> mp_int512_t; + typedef mp_number, false> mp_int1024_t; }} // namespaces @@ -360,11 +295,79 @@ That said it should be noted that there's no requirement for built-in types to b is the most common format by far. * Attempting to print negative values as either an Octal or Hexadecimal string results in a `std::runtime_error` being thrown, this is a direct consequence of the sign-magnitude representation. +* The fixed precision types `mp_[u]intXXX_t` have expression template support turned off - it seems to make little +difference to the performance of these types either way - so we may as well have the faster compile times by turning +the feature off. [h5 Example:] [cpp_int_eg] +[h4 gmp_int] + + namespace boost{ namespace multiprecision{ + + class gmp_int; + + typedef mp_number mpz_int; + + }} // namespaces + +The `gmp_int` backend is used via the typedef `boost::multiprecision::mpz_int`. It acts as a thin wrapper around the [gmp] `mpz_t` +to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. + +As well as the usual conversions from arithmetic and string types, type `mpz_int` is copy constructible and assignable from: + +* The [gmp] native types: `mpf_t`, `mpz_t`, `mpq_t`. +* Instances of `mp_number` that are wrappers around those types: `mp_number >`, `mp_number`. + +It's also possible to access the underlying `mpz_t` via the `data()` member function of `gmp_int`. + +Things you should know when using this type: + +* No changes are made to the GMP library's global settings - so you can safely mix this type with +existing code that uses [gmp]. +* Default constructed `gmp_int`'s have the value zero (this is GMP's default behavior). +* Formatted IO for this type does not support octal or hexadecimal notation for negative values, +as a result performing formatted output on this type when the argument is negative and either of the flags +`std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. +* Division by zero is handled by the [gmp] library - it will trigger a division by zero signal. +* Although this type is a wrapper around [gmp] it will work equally well with [mpir]. Indeed use of [mpir] +is recomended on Win32. + +[h5 Example:] + +[mpz_eg] + +[h4 tom_int] + + namespace boost{ namespace multiprecision{ + + class tommath_int; + + typedef mp_number tom_int; + + }} // namespaces + +The `tommath_int` backend is used via the typedef `boost::multiprecision::tom_int`. It acts as a thin wrapper around the [tommath] `tom_int` +to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. + +Things you should know when using this type: + +* Default constructed objects have the value zero (this is [tommath]'s default behavior). +* Although `tom_int` is mostly a drop in replacement for the builtin integer types, it should be noted that it is a +rather strange beast as it's a signed type that is not a 2's complement type. As a result the bitwise operations +`| & ^` will throw a `std::runtime_error` exception if either of the arguments is negative. Similarly the complement +operator`~` is deliberately not implemented for this type. +* Formatted IO for this type does not support octal or hexadecimal notation for negative values, +as a result performing formatted output on this type when the argument is negative and either of the flags +`std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. +* Division by zero will result in a hardware signal being raised by [tommath]. + +[h5 Example:] + +[tommath_eg] + [endsect] [section:reals Floating Point Numbers] @@ -611,27 +614,27 @@ Things you should know when using this type: namespace boost{ namespace multiprecision{ typedef rational_adpater tommath_rational; - typedef mp_number mp_rational; + typedef mp_number tom_rational; }} // namespaces -The `tommath_rational` backend is used via the typedef `boost::multiprecision::mp_rational`. It acts as a thin wrapper around -`boost::rational` +The `tommath_rational` backend is used via the typedef `boost::multiprecision::tom_rational`. It acts as a thin wrapper around +`boost::rational` to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. -The advantage of using this type rather than `boost::rational` directly, is that it is expression-template enabled, +The advantage of using this type rather than `boost::rational` directly, is that it is expression-template enabled, greatly reducing the number of temporaries created in complex expressions. There are also non-member functions: - mp_int numerator(const mp_rational&); - mp_int denominator(const mp_rational&); + tom_int numerator(const tom_rational&); + tom_int denominator(const tom_rational&); which return the numerator and denominator of the number. Things you should know when using this type: -* Default constructed `mp_rational`'s have the value zero (this the inherited Boost.Rational behavior). +* Default constructed `tom_rational`'s have the value zero (this the inherited Boost.Rational behavior). * Division by zero results in a `boost::bad_rational` exception being thrown (see the rational number library's docs for more information). * No changes are made to [tommath]'s global state, so this type can safely coexist with other [tommath] code. * Performance of this type has been found to be pretty poor - this need further investigation - but it appears that Boost.Rational @@ -860,6 +863,16 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba template struct number_category; + // Integer specific functions: + template + bool divide_qr(const ``['mp_number-or-expression-template-type]``& x, const ``['mp_number-or-expression-template-type]``& y, + mp_number& q, mp_number& r); + template + Integer integer_modulus(const ``['mp_number-or-expression-template-type]``& x, Integer val); + template + bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials, Engine& gen); + bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials); + // Rational number support: typename component_type<``['mp_number-or-expression-template-type]``>::type numerator (const ``['mp_number-or-expression-template-type]``&); typename component_type<``['mp_number-or-expression-template-type]``>::type denominator(const ``['mp_number-or-expression-template-type]``&); @@ -1123,6 +1136,29 @@ If this is a type with mutiple components (for example rational or complex types A traits class that inherits from `mpl::int_` where `N` is one of the enumerated values `number_kind_integer`, `number_kind_floating_point`, `number_kind_rational` or `number_kind_fixed_point`. + +[h4 Integer functions] + + template + bool divide_qr(const ``['mp_number-or-expression-template-type]``& x, const ``['mp_number-or-expression-template-type]``& y, + mp_number& q, mp_number& r); + +Divides x by y and returns both the quotient and remainder. After the call `q = x / y` and `r = x % y`. + + template + Integer integer_modulus(const ``['mp_number-or-expression-template-type]``& x, Integer val); + +Returns the absolute value of `x % val`. + + template + bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials, Engine& gen); + bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials); + +Tests to see if the number /n/ is probably prime - the test excludes the vast majority of composite numbers +by excluding small prime factors and performing a single Fermat test. Then performs /trials/ Miller-Rabin +tests. Returns `false` if /n/ is definitely composite, or `true` if /n/ is probably prime with the +probability of it being composite less than 0.25^trials. + [h4 Rational Number Functions] typename component_type<``['mp_number-or-expression-template-type]``>::type numerator (const ``['mp_number-or-expression-template-type]``&); @@ -1373,18 +1409,18 @@ Windows Vista machine. [table [[Integer Type][Relative (and Absolute) Times]] -[[cpp_int][1.45089(0.481248s)]] -[[cpp_int (no Expression templates)][1.61489(0.535646s)]] -[[cpp_int (64-bit cache)][1.39273(0.461956s)]] -[[cpp_int (256-bit cache)][1.37743(0.456884s)]] -[[cpp_int (512-bit cache)][1.0919(0.362175s)]] -[[cpp_int (1024-bit cache)][1.10864(0.367726s)]] -[[mp_int][3.92956(1.3034s)]] -[[mp_int (no Expression templates)][4.02496(1.33505s)]] -[[mp_int1024_t][1.01094(0.335322s)]] -[[mp_int1024_t (no Expression templates)][1(0.331692s)]] -[[mpz_int][1.08472(0.359793s)]] -[[mpz_int (no Expression templates)][1.20865(0.400901s)]] +[[mpz_int][1.08279(0.370326s)]] +[[mpz_int (no Expression templates)][1.1702(0.400222s)]]] +[[cpp_int][1.3612(0.465547s)]] +[[cpp_int (no Expression templates)][1.33286(0.455854s)]] +[[cpp_int (64-bit cache)][1.33134(0.455333s)]] +[[cpp_int (256-bit cache)][1.29367(0.442451s)]] +[[cpp_int (512-bit cache)][1.08821(0.37218s)]] +[[cpp_int (1024-bit cache)][1.07902(0.369037s)]] +[[mp_int1024_t][1.02616(0.35096s)]] +[[mp_int1024_t (no Expression templates)][1(0.342011s)]] +[[tom_int][3.74233(1.27992s)]] +[[tom_int (no Expression templates)][3.97646(1.35999s)]] ] It's interesting to note that expression templates have little effect here - perhaps because the actual expressions involved diff --git a/example/tommath_snips.cpp b/example/tommath_snips.cpp index 92fbaeed..6c0f73d2 100644 --- a/example/tommath_snips.cpp +++ b/example/tommath_snips.cpp @@ -11,7 +11,7 @@ void t1() //[tommath_eg //=#include - boost::multiprecision::mp_int v = 1; + boost::multiprecision::tom_int v = 1; // Do some arithmetic: for(unsigned i = 1; i <= 1000; ++i) @@ -48,7 +48,7 @@ void t3() using namespace boost::multiprecision; - mp_rational v = 1; + tom_rational v = 1; // Do some arithmetic: for(unsigned i = 1; i <= 1000; ++i) @@ -59,7 +59,7 @@ void t3() std::cout << numerator(v) << std::endl; std::cout << denominator(v) << std::endl; - mp_rational w(2, 3); // Component wise constructor + tom_rational w(2, 3); // Component wise constructor std::cout << w << std::endl; // prints 2/3 //] diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 43ddbe28..65923f7a 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -2206,16 +2206,16 @@ typedef rational_adapter > cpp_rational_backend; typedef mp_number cpp_rational; // Fixed precision unsigned types: -typedef mp_number > mp_uint128_t; -typedef mp_number > mp_uint256_t; -typedef mp_number > mp_uint512_t; -typedef mp_number > mp_uint1024_t; +typedef mp_number, false> mp_uint128_t; +typedef mp_number, false> mp_uint256_t; +typedef mp_number, false> mp_uint512_t; +typedef mp_number, false> mp_uint1024_t; // Fixed precision signed types: -typedef mp_number > mp_int128_t; -typedef mp_number > mp_int256_t; -typedef mp_number > mp_int512_t; -typedef mp_number > mp_int1024_t; +typedef mp_number, false> mp_int128_t; +typedef mp_number, false> mp_int256_t; +typedef mp_number, false> mp_int512_t; +typedef mp_number, false> mp_int1024_t; }} // namespaces diff --git a/include/boost/multiprecision/integer_ops.hpp b/include/boost/multiprecision/integer_ops.hpp index 7bd1e6c8..a98524b4 100644 --- a/include/boost/multiprecision/integer_ops.hpp +++ b/include/boost/multiprecision/integer_ops.hpp @@ -41,20 +41,54 @@ inline Integer eval_integer_modulus(const Backend& x, Integer val) } template -inline void divide_qr(const mp_number& x, const mp_number& y, +inline typename enable_if_c::value == number_kind_integer>::type + divide_qr(const mp_number& x, const mp_number& y, mp_number& q, mp_number& r) { using default_ops::eval_qr; eval_qr(x.backend(), y.backend(), q.backend(), r.backend()); } +template +inline typename enable_if_c::value == number_kind_integer>::type + divide_qr(const mp_number& x, const multiprecision::detail::mp_exp& y, + mp_number& q, mp_number& r) +{ + divide_qr(x, mp_number(y), q, r); +} + +template +inline typename enable_if_c::value == number_kind_integer>::type + divide_qr(const multiprecision::detail::mp_exp& x, const mp_number& y, + mp_number& q, mp_number& r) +{ + divide_qr(mp_number(x), y, q, r); +} + +template +inline typename enable_if_c::value == number_kind_integer>::type + divide_qr(const multiprecision::detail::mp_exp& x, const multiprecision::detail::mp_exp& y, + mp_number& q, mp_number& r) +{ + divide_qr(mp_number(x), mp_number(y), q, r); +} + template -inline typename enable_if, Integer>::type integer_modulus(const mp_number& x, Integer val) +inline typename enable_if, mpl::bool_::value == number_kind_integer> >, Integer>::type + integer_modulus(const mp_number& x, Integer val) { using default_ops::eval_integer_modulus; return eval_integer_modulus(x.backend(), val); } +template +inline typename enable_if, mpl::bool_::result_type>::value == number_kind_integer> >, Integer>::type + integer_modulus(const multiprecision::detail::mp_exp& x, Integer val) +{ + typedef typename multiprecision::detail::mp_exp::result_type result_type; + return integer_modulus(result_type(x), val); +} + }} //namespaces #endif diff --git a/include/boost/multiprecision/miller_rabin.hpp b/include/boost/multiprecision/miller_rabin.hpp index 506e9022..d804df38 100644 --- a/include/boost/multiprecision/miller_rabin.hpp +++ b/include/boost/multiprecision/miller_rabin.hpp @@ -85,35 +85,81 @@ bool check_small_factors(const mp_number& n) return false; } - static const boost::uint32_t small_factors5[] = { - 101u, 103u, 107u, 109u }; - static const boost::uint32_t pp5 = 121330189u; + static const boost::uint32_t small_factors5[6][4] = { + { 101u, 103u, 107u, 109u }, + { 113u, 127u, 131u, 137u }, + { 139u, 149u, 151u, 157u }, + { 163u, 167u, 173u, 179u }, + { 181u, 191u, 193u, 197u }, + { 199u, 211u, 223u, 227u } + }; + static const boost::uint32_t pp5[6] = + { + 121330189u, + 113u * 127u * 131u * 137u, + 139u * 149u * 151u * 157u, + 163u * 167u * 173u * 179u, + 181u * 191u * 193u * 197u, + 199u * 211u * 223u * 227u + }; - m1 = integer_modulus(n, pp5); - - for(unsigned i = 0; i < sizeof(small_factors5) / sizeof(small_factors5[0]); ++i) + for(unsigned k = 0; k < sizeof(pp5) / sizeof(*pp5); ++k) { - BOOST_ASSERT(pp5 % small_factors5[i] == 0); - if(m1 % small_factors5[i] == 0) - return false; + m1 = integer_modulus(n, pp5[k]); + + for(unsigned i = 0; i < 4; ++i) + { + BOOST_ASSERT(pp5[k] % small_factors5[k][i] == 0); + if(m1 % small_factors5[k][i] == 0) + return false; + } } return true; } +inline bool is_small_prime(unsigned n) +{ + static const unsigned char p[] = + { + 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u, 29u, 31u, + 37u, 41u, 43u, 47u, 53u, 59u, 61u, 67u, 71u, 73u, + 79u, 83u, 89u, 97u, 101u, 103u, 107u, 109u, 113u, + 127u, 131u, 137u, 139u, 149u, 151u, 157u, 163u, + 167u, 173u, 179u, 181u, 191u, 193u, 197u, 199u, + 211u, 223u, 227u + }; + for(unsigned i = 0; i < sizeof(p) / sizeof(*p); ++i) + { + if(n == p[i]) + return true; + } + return false; +} + template -bool miller_rabin_test(const mp_number& n, unsigned trials, Engine& gen) +typename enable_if_c::value == number_kind_integer, bool>::type + miller_rabin_test(const mp_number& n, unsigned trials, Engine& gen) { typedef mp_number number_type; - if(n < 2) - return false; + if(n <= 227) + return is_small_prime(n.template convert_to()); if((n & 1) == 0) return false; if(!check_small_factors(n)) return false; - number_type q = (n - 1) >> 1; + number_type nm1 = n - 1; + // + // Begin with a single Fermat test - it excludes a lot of candidates: + // + number_type q(228), x, y; // We know n is greater than this, as we've excluded small factors + expmod(q, nm1, n, x); + if(x != 1u) + return false; + + q = (n - 1) >> 1; unsigned k = 1; while((q & 1) == 0) { @@ -122,14 +168,13 @@ bool miller_rabin_test(const mp_number& n, unsigne } // Declare our random number generator: boost::random::uniform_int_distribution dist(0, n); - number_type nm1 = n - 1; // // Execute the trials: // for(unsigned i = 0; i < trials; ++i) { - number_type x = dist(gen); - number_type y; + x = dist(gen); + y; expmod(x, q, n, y); unsigned j = 0; while(true) diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 5a948940..f40043b3 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -228,14 +228,14 @@ struct tommath_int d = v; return t.compare(d); } - mp_int& data() { return m_data; } - const mp_int& data()const { return m_data; } + ::mp_int& data() { return m_data; } + const ::mp_int& data()const { return m_data; } void swap(tommath_int& o) { mp_exch(&m_data, &o.data()); } protected: - mp_int m_data; + ::mp_int m_data; }; #define BOOST_MP_TOMMATH_BIT_OP_CHECK(x)\ @@ -478,9 +478,9 @@ using boost::multiprecision::backends::tommath_int; template<> struct number_category : public mpl::int_{}; -typedef mp_number mp_int; +typedef mp_number tom_int; typedef rational_adapter tommath_rational; -typedef mp_number mp_rational; +typedef mp_number tom_rational; }} // namespaces diff --git a/performance/miller_rabin_performance.cpp b/performance/miller_rabin_performance.cpp index 1fbed9b7..e0c32dc3 100644 --- a/performance/miller_rabin_performance.cpp +++ b/performance/miller_rabin_performance.cpp @@ -151,8 +151,8 @@ int main() std::cout << "Time for mpz_int (native Miller Rabin Test) = " << test_miller_rabin_gmp() << std::endl; #endif #ifdef TEST_TOMMATH - test_miller_rabin >("mp_int (no Expression templates)"); - test_miller_rabin("mp_int"); + test_miller_rabin >("tom_int (no Expression templates)"); + test_miller_rabin("tom_int"); #endif mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); mp_set_memory_functions(&alloc_func, &realloc_func, &free_func); diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index 6fc2d9cf..da143eb9 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -601,18 +601,18 @@ int main() test("mpq_rational", 1024); #endif #ifdef TEST_TOMMATH - test("tommath_int", 128); - test("tommath_int", 256); - test("tommath_int", 512); - test("tommath_int", 1024); + test("tommath_int", 128); + test("tommath_int", 256); + test("tommath_int", 512); + test("tommath_int", 1024); /* // // These are actually too slow to test!!! // - test("mp_rational", 128); - test("mp_rational", 256); - test("mp_rational", 512); - test("mp_rational", 1024); + test("tom_rational", 128); + test("tom_rational", 256); + test("tom_rational", 512); + test("tom_rational", 1024); */ #endif #ifdef TEST_CPP_DEC_FLOAT diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 237760dd..62103ada 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -69,7 +69,7 @@ namespace boost{ namespace multiprecision{ #ifdef TEST_TOMMATH_BOOST_RATIONAL template<> -struct number_category > : public mpl::int_ {}; +struct number_category > : public mpl::int_ {}; #endif #ifdef TEST_MPZ_BOOST_RATIONAL template<> @@ -117,7 +117,7 @@ struct is_twos_complement_integer : public boost::mpl::true_ {}; #ifdef TEST_TOMMATH template <> -struct is_twos_complement_integer : public boost::mpl::false_ {}; +struct is_twos_complement_integer : public boost::mpl::false_ {}; #endif template @@ -362,6 +362,15 @@ void test_integer_ops(const boost::mpl::int_::is_signed) { @@ -1035,11 +1044,11 @@ int main() test(); #endif #ifdef TEST_TOMMATH - test(); + test(); test > >(); #endif #ifdef TEST_TOMMATH_BOOST_RATIONAL - test >(); + test >(); #endif #ifdef TEST_MPZ_BOOST_RATIONAL test >(); diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp index 9fac176d..87c79ec7 100644 --- a/test/test_int_io.cpp +++ b/test/test_int_io.cpp @@ -120,7 +120,7 @@ int main() test_round_trip(); #endif #ifdef TEST_TOMMATH - test_round_trip(); + test_round_trip(); #endif #ifdef TEST_CPP_INT test_round_trip > >(); diff --git a/test/test_miller_rabin.cpp b/test/test_miller_rabin.cpp index 084d1ffb..d8f9f9a2 100644 --- a/test/test_miller_rabin.cpp +++ b/test/test_miller_rabin.cpp @@ -5,6 +5,7 @@ #include #include +#include #include #include #include "test.hpp" @@ -20,6 +21,7 @@ int main() // using namespace boost::random; using namespace boost::multiprecision; + independent_bits_engine gen; // // We must use a different generator for the tests and number generation, otherwise @@ -28,6 +30,16 @@ int main() // mt19937 gen2; + // + // Begin by testing the primes in our table as all these should return true: + // + for(unsigned i = 1; i < boost::math::max_prime; ++i) + { + BOOST_TEST(miller_rabin_test(mpz_int(boost::math::prime(i)), 25, gen)); + } + // + // Now test some random values and compare GMP's native routine with ours. + // for(unsigned i = 0; i < 10000; ++i) { mpz_int n = gen(); diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index bb2d64c6..73c1fe7f 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -220,7 +220,7 @@ int main() test(); #endif #ifdef TEST_TOMMATH - test(); + test(); #endif #ifdef TEST_CPP_INT test(); diff --git a/test/test_rational_io.cpp b/test/test_rational_io.cpp index 05c037c7..4d629fb7 100644 --- a/test/test_rational_io.cpp +++ b/test/test_rational_io.cpp @@ -130,8 +130,8 @@ int main() test_round_trip > >(); #endif #ifdef TEST_TOMMATH - test_round_trip >(); - test_round_trip(); + test_round_trip >(); + test_round_trip(); #endif return boost::report_errors(); } From 6ead74422337cb69c98b915a3f02bfb6688fd4dc Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 22 Mar 2012 11:54:15 +0000 Subject: [PATCH 140/256] Fix fixed precision ints to work with non obvious bit counts. [SVN r77473] --- include/boost/multiprecision/cpp_int.hpp | 5 +++++ test/test_arithmetic.cpp | 1 + test/test_numeric_limits.cpp | 21 ++++++++++++++++++--- 3 files changed, 24 insertions(+), 3 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 65923f7a..77fca771 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -184,6 +184,7 @@ public: BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << (limb_bits - 1)); BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = MinBits / limb_bits + (MinBits % limb_bits ? 1 : 0)); BOOST_STATIC_CONSTANT(bool, variable = false); + BOOST_STATIC_CONSTANT(limb_type, upper_limb_mask = MinBits % limb_bits ? (limb_type(1) << (MinBits % limb_bits)) -1 : (~limb_type(0))); BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs"); private: @@ -216,7 +217,9 @@ public: void normalize() { limb_pointer p = limbs(); + p[internal_limb_count-1] &= upper_limb_mask; while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; + if((m_limbs == 1) && (!*p)) m_sign = false; // zero is always unsigned } cpp_int_base() : m_limbs(1), m_sign(false) @@ -280,6 +283,7 @@ public: BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << (limb_bits - 1)); BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = MinBits / limb_bits + (MinBits % limb_bits ? 1 : 0)); BOOST_STATIC_CONSTANT(bool, variable = false); + BOOST_STATIC_CONSTANT(limb_type, upper_limb_mask = MinBits % limb_bits ? (limb_type(1) << (MinBits % limb_bits)) -1 : (~limb_type(0))); BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs"); private: @@ -302,6 +306,7 @@ public: void normalize() { limb_pointer p = limbs(); + p[internal_limb_count-1] &= upper_limb_mask; while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; } diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 62103ada..eeb43056 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -1059,6 +1059,7 @@ int main() test(); test(); test, false> >(); + test > >(); #endif #ifdef TEST_CPP_INT_BR test(); diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index 73c1fe7f..da557a47 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -55,7 +55,7 @@ std::cout << BOOST_STRINGIZE(x) << " = " << std::numeric_limits::x << std::endl; template -void test_fp(const boost::mpl::int_&) +void test_specific(const boost::mpl::int_&) { Number minv, maxv; minv = (std::numeric_limits::min)(); @@ -116,8 +116,21 @@ void test_fp(const boost::mpl::int_ +void test_specific(const boost::mpl::int_&) +{ + if(std::numeric_limits::is_modulo) + { + if(!std::numeric_limits::is_signed) + { + BOOST_TEST(1 + (std::numeric_limits::max)() == 0); + BOOST_TEST(--Number(0) == (std::numeric_limits::max)()); + } + } +} + template -void test_fp(const T&) +void test_specific(const T&) { } @@ -181,7 +194,7 @@ void test() boost::mpl::int_<500> // not a number type >::type fp_test_type; - test_fp(fp_test_type()); + test_specific(fp_test_type()); } @@ -226,6 +239,8 @@ int main() test(); test(); test(); + test > >(); + test > >(); #endif return boost::report_errors(); } From f657a2fd592111a971acf0a2b08c70b1ad55b306 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 22 Mar 2012 13:27:12 +0000 Subject: [PATCH 141/256] Remove dead statement [SVN r77475] --- include/boost/multiprecision/miller_rabin.hpp | 1 - 1 file changed, 1 deletion(-) diff --git a/include/boost/multiprecision/miller_rabin.hpp b/include/boost/multiprecision/miller_rabin.hpp index d804df38..1e6bbe98 100644 --- a/include/boost/multiprecision/miller_rabin.hpp +++ b/include/boost/multiprecision/miller_rabin.hpp @@ -174,7 +174,6 @@ typename enable_if_c::value == number_kind_integer, boo for(unsigned i = 0; i < trials; ++i) { x = dist(gen); - y; expmod(x, q, n, y); unsigned j = 0; while(true) From 366ec67ddc8775eb611bd3fdb3f460521bacd613 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 22 Mar 2012 17:32:43 +0000 Subject: [PATCH 142/256] Fix GCC Random number and Miller Rabin build errors. [SVN r77478] --- include/boost/multiprecision/random.hpp | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/include/boost/multiprecision/random.hpp b/include/boost/multiprecision/random.hpp index 4d82fedb..a76372a5 100644 --- a/include/boost/multiprecision/random.hpp +++ b/include/boost/multiprecision/random.hpp @@ -9,6 +9,20 @@ #define BOOST_MP_RANDOM_HPP #include + +namespace boost{ namespace random{ namespace detail{ +// +// This is a horrible hack: this declaration has to appear before the definition of +// uniform_int_distribution, otherwise it won't be used... +// Need to find a better solution, like make Boost.Random safe to use with +// UDT's and depricate/remove this header altogether. +// +template +boost::multiprecision::mp_number + generate_uniform_int(Engine& eng, const boost::multiprecision::mp_number& min_value, const boost::multiprecision::mp_number& max_value); + +}}} + #include #include From 4c6065717b9f4d3b9318322d4540a1edad2763c2 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 27 Mar 2012 11:45:01 +0000 Subject: [PATCH 143/256] Add a few more integer specific bit-fiddling functions. Fix some bugs in cpp_int left shift code. Document some missing backend API's, and update docs. [SVN r77583] --- doc/html/boost_multiprecision/intro.html | 2 +- doc/html/boost_multiprecision/map.html | 2 +- doc/html/boost_multiprecision/map/hist.html | 2 +- doc/html/boost_multiprecision/map/todo.html | 14 +- doc/html/boost_multiprecision/perf.html | 2 +- .../perf/float_performance.html | 2 +- .../perf/int_real_world.html | 2 +- .../perf/integer_performance.html | 2 +- .../perf/rational_performance.html | 2 +- .../boost_multiprecision/perf/realworld.html | 2 +- doc/html/boost_multiprecision/ref.html | 2 +- .../boost_multiprecision/ref/backendconc.html | 126 ++++++++++++++++-- .../boost_multiprecision/ref/mp_number.html | 44 +++++- doc/html/boost_multiprecision/tut.html | 2 +- doc/html/boost_multiprecision/tut/ints.html | 2 +- .../boost_multiprecision/tut/primetest.html | 2 +- doc/html/boost_multiprecision/tut/random.html | 2 +- .../boost_multiprecision/tut/rational.html | 2 +- doc/html/boost_multiprecision/tut/reals.html | 2 +- doc/html/index.html | 9 +- doc/multiprecision.qbk | 54 +++++++- include/boost/multiprecision/cpp_int.hpp | 74 +++++++++- .../multiprecision/detail/default_ops.hpp | 65 +++++++++ include/boost/multiprecision/gmp.hpp | 25 ++++ include/boost/multiprecision/integer_ops.hpp | 63 +++++++++ include/boost/multiprecision/tommath.hpp | 5 + test/test_arithmetic.cpp | 14 ++ test/test_cpp_int.cpp | 9 ++ 28 files changed, 494 insertions(+), 40 deletions(-) diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index 25367098..9c1f2b6f 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -492,7 +492,7 @@ -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/map.html b/doc/html/boost_multiprecision/map.html index 4f482f06..d2f2120d 100644 --- a/doc/html/boost_multiprecision/map.html +++ b/doc/html/boost_multiprecision/map.html @@ -24,7 +24,7 @@
    -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html index 8c480119..28b46cd6 100644 --- a/doc/html/boost_multiprecision/map/hist.html +++ b/doc/html/boost_multiprecision/map/hist.html @@ -18,7 +18,7 @@
    -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index 3f92de36..838ead9b 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -27,11 +27,23 @@
  • Add an adapter backend for complex number types.
    • +
  • + Add a backend for MPFR interval arithmetic. +
    • +
  • + Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. +
    • +
  • + Add assembly level routines to cpp_int_backend. +
    • +
  • + Add an all C++ binary floating point type. +
    • -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/perf.html b/doc/html/boost_multiprecision/perf.html index d36eb092..7460f077 100644 --- a/doc/html/boost_multiprecision/perf.html +++ b/doc/html/boost_multiprecision/perf.html @@ -32,7 +32,7 @@
    -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html index 61490d94..ce1d7eec 100644 --- a/doc/html/boost_multiprecision/perf/float_performance.html +++ b/doc/html/boost_multiprecision/perf/float_performance.html @@ -947,7 +947,7 @@
    - + + + + + + + + - - - - - - - -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html index 6033685c..5d6c79ff 100644 --- a/doc/html/boost_multiprecision/perf/int_real_world.html +++ b/doc/html/boost_multiprecision/perf/int_real_world.html @@ -91,7 +91,7 @@
    -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html index b5cc5574..23fdd44c 100644 --- a/doc/html/boost_multiprecision/perf/integer_performance.html +++ b/doc/html/boost_multiprecision/perf/integer_performance.html @@ -3020,7 +3020,7 @@
    -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/perf/rational_performance.html b/doc/html/boost_multiprecision/perf/rational_performance.html index fd98e028..eab8d539 100644 --- a/doc/html/boost_multiprecision/perf/rational_performance.html +++ b/doc/html/boost_multiprecision/perf/rational_performance.html @@ -891,7 +891,7 @@
    -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html index 68464c8d..9137d2d1 100644 --- a/doc/html/boost_multiprecision/perf/realworld.html +++ b/doc/html/boost_multiprecision/perf/realworld.html @@ -264,7 +264,7 @@
    -+ + + + + + + + + + + + + + + + + + + + + + + + + + + @@ -809,7 +1098,13 @@ + @@ -828,7 +1123,13 @@

    Assigns to b the two components in the following arguments. Only applies to rational - and complex number types. + and complex number types. When not provided, arithmetic operations + are used to synthesise the result from the two values. +

    + + @@ -847,9 +1148,324 @@

    Assigns to b the two components in the following arguments. Only applies to rational - and complex number types. + and complex number types. When not provided, arithmetic operations + are used to synthesise the result from the two values.

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - @@ -1040,70 +1509,14 @@ - - - - - - - - - - - - - - @@ -1124,165 +1537,13 @@

    Add cb to a and stores the result in b. The type of a shall be listed in one of the type lists B::signed_types, B::unsigned_types - or B::float_types. -

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - @@ -1305,7 +1566,99 @@ b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_add(b, cb, a). +

    + + + + + + + + + + + + + + + + + + + + @@ -1329,7 +1682,99 @@ result in b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_subtract(b, cb, a); b.negate();. +

    + + + + + + + + + + + + + + + + + + + + @@ -1353,7 +1798,104 @@ result in b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_multiply(b, cb, a). +

    + + + + + + + + + + + + + + + + + + + + @@ -1376,7 +1918,137 @@ b. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_divide(b, B(a), cb). +

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + @@ -1401,76 +2073,13 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    - - - - - - - - - - - - - - - @@ -1495,7 +2104,97 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_modulus(b, B(a), cb). +

    + + + + + + + + + + + + + + + + + + + + @@ -1518,7 +2217,97 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_bitwise_and(b, cb, a). +

    + + + + + + + + + + + + + + + + + + + + @@ -1541,7 +2330,97 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_bitwise_or(b, cb, a). +

    + + + + + + + + + + + + + + + + + + + + @@ -1564,7 +2443,13 @@ when B is an integer type. The type of a shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_bitwise_xor(b, cb, a). +

    + + @@ -1585,7 +2470,13 @@ ui and stores the result in b, only required when B is an integer - type. + type. When not provided, does the equivalent of b + = cb; eval_left_shift(b, a);. +

    + + @@ -1606,517 +2497,13 @@ ui and stores the result in b, only required when B is an integer - type. + type. When not provided, does the equivalent of b + = cb; eval_right_shift(b, a);.

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - @@ -2141,7 +2528,13 @@ cb2 and b2 to the result of cb % cb2. Only required when B is an integer - type. + type. The default version of this function is synthesised from + other operations above. +

    + + @@ -2161,7 +2554,13 @@ Returns the result of cb % ui. Only required when B - is an integer type. + is an integer type. The default version of this function is synthesised + from other operations above. +

    + + @@ -2180,7 +2579,13 @@

    Returns the index of the least significant bit that is set. Only required when B - is an integer type. + is an integer type. The default version of this function is synthesised + from other operations above. +

    + + @@ -2201,7 +2606,13 @@ Returns true if cb has bit ui set. Only required when B - is an integer type. + is an integer type. The default version of this function is synthesised + from other operations above. +

    + + @@ -2222,7 +2633,13 @@ Sets the bit at index ui in b. Only required when B is an integer - type. + type. The default version of this function is synthesised from + other operations above. +

    + + @@ -2242,7 +2659,13 @@ Unsets the bit at index ui in b. Only required when B is an integer - type. + type. The default version of this function is synthesised from + other operations above. +

    + + @@ -2263,7 +2686,13 @@ Flips the bit at index ui in b. Only required when B is an integer - type. + type. The default version of this function is synthesised from + other operations above. +

    + + @@ -2286,7 +2715,13 @@ common divisor of cb and cb2. Only required when B is an integer - type. + type. The default version of this function is synthesised from + other operations above. +

    + + @@ -2309,7 +2744,836 @@ common multiple of cb and cb2. Only required when B is an integer - type. + type. The default version of this function is synthesised from + other operations above. +

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + @@ -2317,8 +3581,8 @@
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html index a31f61bb..12b46354 100644 --- a/doc/html/boost_multiprecision/ref.html +++ b/doc/html/boost_multiprecision/ref.html @@ -24,7 +24,7 @@
    - + + + + + + + + + + + + + + +
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index d9633266..c5507f4e 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -26,13 +26,16 @@

    In the following tables, type B is the Backend template arument to mp_number, - b is a variable of B, cb and cb2 - are constant variables of type B, a - is a variable of Arithmetic type, s - is a variable of type const char*, ui is a variable of type unsigned, bb - is a variable of type bool, - pa is a variable of type - pointer-to-arithmetic-type, exp + b and b2 + are a variables of type B, cb + and cb2 are constant variables + of type B, a is a variable + of Arithmetic type, s is + a variable of type const char*, ui + is a variable of type unsigned, + bb is a variable of type + bool, pa + is a variable of type pointer-to-arithmetic-type, exp is a variable of type B::exp_type, pexp is a variable of type B::exp_type*, B2 is another type that meets these requirements, b2 is a variable of type @@ -2067,6 +2070,113 @@

    +

    + eval_qr(cb, + cb2, + b, + b2) +

    +     		+

    + void +

    +     		+

    + Sets b to the result + of cb / + cb2 and b2 to the result of cb % + cb2. Only required when + B is an integer + type. +

    +
    +

    + eval_integer_modulus(cb, ui) +

    +     		+

    + unsigned +

    +     		+

    + Returns the result of cb + % ui. + Only required when B + is an integer type. +

    +
    +

    + eval_lsb(cb) +

    +     		+

    + unsigned +

    +     		+

    + Returns the index of the least significant bit that is set. + Only required + when B is an + integer type.]] [[eval_bit_test(cb, + ui)][bool][Returns + true if + cb has bit ui set. Only + required when + B is an + integer type.]] [[eval_bit_set(b, + ui)][void][Sets + the bit + at index + ui in b. Only + required when + B is an + integer type.]] [[eval_bit_unset(b, + ui)][void][Unsets + the bit + at index + ui in b. Only + required when + B is an + integer type.]] [[eval_bit_flip(b, + ui)][void][Flips + the bit + at index + ui in b. Only + required when + B is an + integer type.]] [[eval_gcd(b, + cb, cb2)][void][Sets + b to the + greatest common + divisor of + cb and cb2. Only + required when + B is an + integer type.]] [[eval_lcm(b, + cb, cb2)][void][Sets + b to the + least common + multiple of + cb and cb2. Only + required when + B` is an integer type. +

    +
    @@ -2085,7 +2195,7 @@ -+ + @@ -92,6 +106,11 @@ shall terminate in the type that is std::intmax_t.

    + + + + @@ -161,6 +196,11 @@ Default constructor.

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html index e1a98ef1..2a8ca1b3 100644 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -149,6 +149,15 @@ mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r); template <class Integer> Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val); +unsigned lsb(const mp_number-or-expression-template-type& x); +template <class Backend, class ExpressionTemplates> +bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index); +template <class Backend, class ExpressionTemplates> +mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index); +template <class Backend, class ExpressionTemplates> +mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index); +template <class Backend, class ExpressionTemplates> +mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index); template <class Engine> bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen); bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials); @@ -566,6 +575,39 @@ Returns the absolute value of x % val.

    +
    unsigned lsb(const mp_number-or-expression-template-type& x);
+
    +

    + Returns the index of the least significant bit that is set to 1. +

    +
    template <class Backend, class ExpressionTemplates>
+bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Returns true if the bit at + index in val is set. +

    +
    template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Sets the bit at index in val, and + returns val. +

    +
    template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Unsets the bit at index in val, + and returns val. +

    +
    template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Flips the bit at index in val, + and returns val. + 

    template <class Engine>
 bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
 bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
@@ -639,7 +681,7 @@
    - @@ -166,7 +166,7 @@ diff --git a/doc/html/boost_multiprecision/ref/mpf_ref.html b/doc/html/boost_multiprecision/ref/mpf_ref.html index 1eb8aad6..02f8e03b 100644 --- a/doc/html/boost_multiprecision/ref/mpf_ref.html +++ b/doc/html/boost_multiprecision/ref/mpf_ref.html @@ -22,11 +22,11 @@ template<unsignedDigits10>classgmp_float; -typedefmp_number<gmp_float<50>>mpf_float_50; -typedefmp_number<gmp_float<100>>mpf_float_100; -typedefmp_number<gmp_float<500>>mpf_float_500; -typedefmp_number<gmp_float<1000>>mpf_float_1000; -typedefmp_number<gmp_float<0>>mpf_float; +typedefnumber<gmp_float<50>>mpf_float_50; +typedefnumber<gmp_float<100>>mpf_float_100; +typedefnumber<gmp_float<500>>mpf_float_500; +typedefnumber<gmp_float<1000>>mpf_float_1000; +typedefnumber<gmp_float<0>>mpf_float;}}// namespaces @@ -40,7 +40,7 @@ The class takes a single template parameter - Digits10 - which is the number of decimal digits precision the type should support. When this parameter is zero, then the precision can be set at runtime via - mp_number::default_precision and mp_number::precision. + number::default_precision and number::precision. Note that this type does not in any way change the GMP library's global state (for example it does not change the default precision of the mpf_t data type), therefore you can safely mix this type with existing code that uses GMP, diff --git a/doc/html/boost_multiprecision/ref/mpfr_ref.html b/doc/html/boost_multiprecision/ref/mpfr_ref.html index a60f9563..a5e0ba30 100644 --- a/doc/html/boost_multiprecision/ref/mpfr_ref.html +++ b/doc/html/boost_multiprecision/ref/mpfr_ref.html @@ -22,11 +22,11 @@ template<unsignedDigits10>classmpfr_float_backend; -typedefmp_number<mpfr_float_backend<50>>mpfr_float_50; -typedefmp_number<mpfr_float_backend<100>>mpfr_float_100; -typedefmp_number<mpfr_float_backend<500>>mpfr_float_500; -typedefmp_number<mpfr_float_backend<1000>>mpfr_float_1000; -typedefmp_number<mpfr_float_backend<0>>mpfr_float; +typedefnumber<mpfr_float_backend<50>>mpfr_float_50; +typedefnumber<mpfr_float_backend<100>>mpfr_float_100; +typedefnumber<mpfr_float_backend<500>>mpfr_float_500; +typedefnumber<mpfr_float_backend<1000>>mpfr_float_1000; +typedefnumber<mpfr_float_backend<0>>mpfr_float;}}// namespaces @@ -40,7 +40,7 @@ The class takes a single template parameter - Digits10 - which is the number of decimal digits precision the type should support. When this parameter is zero, then the precision can be set at runtime via - mp_number::default_precision and mp_number::precision. + number::default_precision and number::precision. Note that this type does not in any way change the GMP or MPFR library's global state (for example it does not change the default precision of the mpfr_t data type), therefore you can safely mix this type with existing code diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/number.html similarity index 67% rename from doc/html/boost_multiprecision/ref/mp_number.html rename to doc/html/boost_multiprecision/ref/number.html index 5f2605b4..bf6d8b24 100644 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ b/doc/html/boost_multiprecision/ref/number.html @@ -1,7 +1,7 @@ -mp_number +number @@ -13,44 +13,44 @@
    PrevUpHomeNext
    -
    +
    - - Synopsis + + Synopsis 
    namespace boost{ namespace multiprecision{
 
 template <class Backend, bool ExpressionTemplates = true>
-class mp_number
+class number
 {
-   mp_number();
-   mp_number(see-below);
-   mp_number& operator=(see-below);
+   number();
+   number(see-below);
+   number& operator=(see-below);
 
    // Member operators
-   mp_number& operator+=(const see-below&);
-   mp_number& operator-=(const see-below&);
-   mp_number& operator*=(const see-below&);
-   mp_number& operator/=(const see-below&);
-   mp_number& operator++();
-   mp_number& operator--();
-   mp_number  operator++(int);
-   mp_number  operator--(int);
+   number& operator+=(const see-below&);
+   number& operator-=(const see-below&);
+   number& operator*=(const see-below&);
+   number& operator/=(const see-below&);
+   number& operator++();
+   number& operator--();
+   number  operator++(int);
+   number  operator--(int);
 
-   mp_number& operator%=(const see-below&);
-   mp_number& operator&=(const see-below&);
-   mp_number& operator|=(const see-below&);
-   mp_number& operator^=(const see-below&);
-   mp_number& operator<<=(const integer-type&);
-   mp_number& operator>>=(const integer-type&);
+   number& operator%=(const see-below&);
+   number& operator&=(const see-below&);
+   number& operator|=(const see-below&);
+   number& operator^=(const see-below&);
+   number& operator<<=(const integer-type&);
+   number& operator>>=(const integer-type&);
 
    // Use in Boolean context:
    operator convertible-to-bool-type()const;
    // swap:
-   void swap(mp_number& other);
+   void swap(number& other);
    // Sign:
    bool is_zero()const;
    int sign()const;
@@ -59,13 +59,15 @@
    // Generic conversion mechanism
    template <class T>
    T convert_to()const;
+   template <class T>
+   explicit operator T ()const;
    // precision control:
    static unsigned default_precision();
    static void default_precision(unsigned digits10);
    unsigned precision()const;
    void precision(unsigned digits10);
    // Comparison:
-   int compare(const mp_number<Backend>& o)const;
+   int compare(const number<Backend>& o)const;
    template <class V>
    typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
    // Access to the underlying implementation:
@@ -97,47 +99,47 @@
 
 // Swap:
 template <class Backend, bool ExpressionTemplates>
-void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
+void swap(number<Backend, ExpressionTemplates>& a, number<Backend, ExpressionTemplates>& b);
 
 // iostream support:
 template <class Backend, bool ExpressionTemplates>
-std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
+std::ostream& operator << (std::ostream& os, const number<Backend, ExpressionTemplates>& r);
 std::ostream& operator << (std::ostream& os, const unmentionable-expression-template-type& r);
 template <class Backend, bool ExpressionTemplates>
-std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r);
+std::istream& operator >> (std::istream& is, number<Backend, ExpressionTemplates>& r);
 
 // Non-member function standard library support:
-unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    abs    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    fabs   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    sqrt   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    floor  (const number-or-expression-template-type&);
+unmentionable-expression-template-type    ceil   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    trunc  (const number-or-expression-template-type&);
+unmentionable-expression-template-type    itrunc (const number-or-expression-template-type&);
+unmentionable-expression-template-type    ltrunc (const number-or-expression-template-type&);
+unmentionable-expression-template-type    lltrunc(const number-or-expression-template-type&);
+unmentionable-expression-template-type    round  (const number-or-expression-template-type&);
+unmentionable-expression-template-type    iround (const number-or-expression-template-type&);
+unmentionable-expression-template-type    lround (const number-or-expression-template-type&);
+unmentionable-expression-template-type    llround(const number-or-expression-template-type&);
+unmentionable-expression-template-type    exp    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    log    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    log10    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    cos    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    sin    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    tan    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    acos   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    asin   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    atan   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    cosh   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    sinh   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    tanh   (const number-or-expression-template-type&);
 
-unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
-unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
-unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ldexp (const number-or-expression-template-type&, int);
+unmentionable-expression-template-type    frexp (const number-or-expression-template-type&, int*);
+unmentionable-expression-template-type    pow   (const number-or-expression-template-type&, const number-or-expression-template-type&);
+unmentionable-expression-template-type    fmod  (const number-or-expression-template-type&, const number-or-expression-template-type&);
+unmentionable-expression-template-type    atan2 (const number-or-expression-template-type&, const number-or-expression-template-type&);
 
 // Traits support:
 template <class T>
@@ -146,40 +148,40 @@
 struct number_category;
 
 // Integer specific functions:
-unmentionable-expression-template-type    pow(const mp_number-or-expression-template-type&, unsigned);
-unmentionable-expression-template-type    powm(const mp_number-or-expression-template-type& b, const mp_number-or-expression-template-type& p, const mp_number-or-expression-template-type& m);
+unmentionable-expression-template-type    pow(const number-or-expression-template-type&, unsigned);
+unmentionable-expression-template-type    powm(const number-or-expression-template-type& b, const number-or-expression-template-type& p, const number-or-expression-template-type& m);
 template <class Backend, bool ExpressionTemplates>
-void divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
-               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
+void divide_qr(const number-or-expression-template-type& x, const number-or-expression-template-type& y,
+               number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r);
 template <class Integer>
-Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
-unsigned lsb(const mp_number-or-expression-template-type& x);
+Integer integer_modulus(const number-or-expression-template-type& x, Integer val);
+unsigned lsb(const number-or-expression-template-type& x);
 template <class Backend, class ExpressionTemplates>
-bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+bool bit_test(const number<Backend, ExpressionTemplates>& val, unsigned index);
 template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+number<Backend, ExpressionTemplates>& bit_set(number<Backend, ExpressionTemplates>& val, unsigned index);
 template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+number<Backend, ExpressionTemplates>& bit_unset(number<Backend, ExpressionTemplates>& val, unsigned index);
 template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+number<Backend, ExpressionTemplates>& bit_flip(number<Backend, ExpressionTemplates>& val, unsigned index);
 template <class Engine>
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
+bool miller_rabin_test(const number-or-expression-template-type& n, unsigned trials, Engine& gen);
+bool miller_rabin_test(const number-or-expression-template-type& n, unsigned trials);
 
 // Rational number support:
-typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
-typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
+typename component_type<number-or-expression-template-type>::type numerator  (const number-or-expression-template-type&);
+typename component_type<number-or-expression-template-type>::type denominator(const number-or-expression-template-type&);
 
 }} // namespaces
 
 namespace boost{ namespace math{
 
 // Boost.Math interoperability functions:
-int                                              fpclassify     (const mp_number-or-expression-template-type&, int);
-bool                                             isfinite       (const mp_number-or-expression-template-type&, int);
-bool                                             isnan          (const mp_number-or-expression-template-type&, int);
-bool                                             isinf          (const mp_number-or-expression-template-type&, int);
-bool                                             isnormal       (const mp_number-or-expression-template-type&, int);
+int                                              fpclassify     (const number-or-expression-template-type&, int);
+bool                                             isfinite       (const number-or-expression-template-type&, int);
+bool                                             isnan          (const number-or-expression-template-type&, int);
+bool                                             isinf          (const number-or-expression-template-type&, int);
+bool                                             isnormal       (const number-or-expression-template-type&, int);
 
 }} // namespaces
 
@@ -195,14 +197,14 @@
 }
    - - Description + + Description 
    template <class Backend, bool ExpressionTemplates = true>
-class mp_number;
+class number;

    - Class mp_number has two template + Class number has two template arguments:

    @@ -219,13 +221,13 @@

    -
    mp_number();
-mp_number(see-below);
-mp_number& operator=(see-below);
+
    number();
+number(see-below);
+number& operator=(see-below);
 
    
 
    
-        Type mp_number is default
-        constructible, and both copy constructible and assignable from:
+        Type number is default constructible,
+        and both copy constructible and assignable from:
       
    
 
      
 
    • 
@@ -245,7 +247,7 @@
             Any type that the Backend is constructible or assignable from.
           
      • 
 
    • 
-            An rvalue reference to another mp_number.
+            An rvalue reference to another number.
             Move-semantics are used for construction if the backend also supports
             rvalue reference construction. In the case of assignment, move semantics
             are always supported when the argument is an rvalue reference irrespective
@@ -256,27 +258,27 @@
         In addition, if the type has multiple components (for example rational or
         complex number types), then there is a two argument constructor:
       
      
-
      mp_number(arg1, arg2);
+
      number(arg1, arg2);
 
      
 
      
         Where the two args must either be arithmetic types, or types that are convertible
         to the two components of this.
       
      
-
      mp_number& operator+=(const see-below&);
-mp_number& operator-=(const see-below&);
-mp_number& operator*=(const see-below&);
-mp_number& operator/=(const see-below&);
-mp_number& operator++();
-mp_number& operator--();
-mp_number  operator++(int);
-mp_number  operator--(int);
+
      number& operator+=(const see-below&);
+number& operator-=(const see-below&);
+number& operator*=(const see-below&);
+number& operator/=(const see-below&);
+number& operator++();
+number& operator--();
+number  operator++(int);
+number  operator--(int);
 // Integer only operations:
-mp_number& operator%=(const see-below&);
-mp_number& operator&=(const see-below&);
-mp_number& operator|=(const see-below&);
-mp_number& operator^=(const see-below&);
-mp_number& operator<<=(const integer-type&);
-mp_number& operator>>=(const integer-type&);
+number& operator%=(const see-below&);
+number& operator&=(const see-below&);
+number& operator|=(const see-below&);
+number& operator^=(const see-below&);
+number& operator<<=(const integer-type&);
+number& operator>>=(const integer-type&);
 
      
 
      
         These operators all take their usual arithmetic meanings.
@@ -286,14 +288,14 @@
       
      
 
        
 
      • 
-            Another mp_number<Backend,
+            Another number<Backend,
             ExpressionTemplates>.
           
        • 
 
      • 
             A builtin arithmetic type.
           
        • 
 
      • 
-            An expression template derived from mp_number<Backend>.
+            An expression template derived from number<Backend>.
           
        • 
 
      
 
      
@@ -303,24 +305,24 @@
       
      
 
      
         Note that all the types involved in the expression must evaluate to the same
-        type - which is to say we cannot mix an mp_number<B1> with an mp_number<B2> where B1 and B2 are different types.
+        type - which is to say we cannot mix a number<B1> with a number<B2> where B1 and B2 are different types.
       
      
 
      operator convertible-to-bool-type()const;
 
      
 
      
         Returns an unmentionable-type that is usable in Boolean
-        contexts (this allows mp_number
+        contexts (this allows number
         to be used in any Boolean context - if statements, conditional statements,
-        or as an argument to a logical operator - without type mp_number
+        or as an argument to a logical operator - without type number
         being convertible to type bool.
       
      
 
      
-        This operator also enables the use of mp_number
+        This operator also enables the use of number
         with any of the following operators: !,
         ||, &&
         and ?:.
       
      
-
      void swap(mp_number& other);
+
      void swap(number& other);
 
      
 
      
         Swaps *this
@@ -348,6 +350,9 @@
       
      
 
      template <class T>
 T convert_to()const;
+
+template <class T>
+explicit operator T ()const;
 
      
 
      
         Provides a generic conversion mechanism to convert *this to type T.
@@ -365,7 +370,7 @@
         the precision of *this
         respectively.
       
      
-
      int compare(const mp_number<Backend, ExpressionTemplates>& o)const;
+
      int compare(const number<Backend, ExpressionTemplates>& o)const;
 template <class V>
 typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
 
      
@@ -391,8 +396,8 @@
         Returns the underlying back-end instance used by *this.
       
      
 
      
-
-        Non-member
+
+        Non-member
         operators
       
      
 
      // Non member operators:
@@ -425,10 +430,10 @@
       
      
 
        
 
      • 
-            An mp_number.
+            A number.
           
        • 
 
      • 
-            An expression template type derived from mp_number.
+            An expression template type derived from number.
           
        • 
 
      
 
      
@@ -444,7 +449,7 @@
             true.
           
      • 
 
    • 
-            Type mp_number<Backend,
+            Type number<Backend,
             false>
             when ExpressionTemplates
             is false.
@@ -456,7 +461,7 @@
 
    
 
    
         Note that all the types involved in the expression must evaluate to the same
-        type - which is to say we cannot mix an mp_number<B1> with an mp_number<B2> where B1 and B2 are different types.
+        type - which is to say we cannot mix a number<B1> with a number<B2> where B1 and B2 are different types.
       
    
 
    
         Finally note that the second argument to the left and right shift operations
@@ -465,29 +470,29 @@
         being thrown).
       
    
 
    
-
-        swap
+
+        swap
       
    
 
    template <class Backend, ExpressionTemplates>
-void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
+void swap(number<Backend, ExpressionTemplates>& a, number<Backend, ExpressionTemplates>& b);
 
    
 
    
         Swaps a and b.
       
    
 
    
-
-        Iostream
+
+        Iostream
         Support
       
    
 
    template <class Backend, bool ExpressionTemplates>
-std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
+std::ostream& operator << (std::ostream& os, const number<Backend, ExpressionTemplates>& r);
 template <class Unspecified...>
 std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r);
 template <class Backend, bool ExpressionTemplates>
-inline std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r)
+inline std::istream& operator >> (std::istream& is, number<Backend, ExpressionTemplates>& r)
 
    
 
    
-        These operators provided formatted input-output operations on mp_number types, and expression templates
+        These operators provided formatted input-output operations on number types, and expression templates
         derived from them.
       
    
 
    
@@ -496,46 +501,46 @@
         flags, field width and precision settings.
       
    
 
    
-
-        Non-member
+
+        Non-member
         standard library function support
       
    
-
    unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
+
    unmentionable-expression-template-type    abs    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    fabs   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    sqrt   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    floor  (const number-or-expression-template-type&);
+unmentionable-expression-template-type    ceil   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    trunc  (const number-or-expression-template-type&);
+unmentionable-expression-template-type    itrunc (const number-or-expression-template-type&);
+unmentionable-expression-template-type    ltrunc (const number-or-expression-template-type&);
+unmentionable-expression-template-type    lltrunc(const number-or-expression-template-type&);
+unmentionable-expression-template-type    round  (const number-or-expression-template-type&);
+unmentionable-expression-template-type    iround (const number-or-expression-template-type&);
+unmentionable-expression-template-type    lround (const number-or-expression-template-type&);
+unmentionable-expression-template-type    llround(const number-or-expression-template-type&);
+unmentionable-expression-template-type    exp    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    log    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    log10    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    cos    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    sin    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    tan    (const number-or-expression-template-type&);
+unmentionable-expression-template-type    acos   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    asin   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    atan   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    cosh   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    sinh   (const number-or-expression-template-type&);
+unmentionable-expression-template-type    tanh   (const number-or-expression-template-type&);
 
-unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
-unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
-unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ldexp (const number-or-expression-template-type&, int);
+unmentionable-expression-template-type    frexp (const number-or-expression-template-type&, int*);
+unmentionable-expression-template-type    pow   (const number-or-expression-template-type&, const number-or-expression-template-type&);
+unmentionable-expression-template-type    fmod  (const number-or-expression-template-type&, const number-or-expression-template-type&);
+unmentionable-expression-template-type    atan2 (const number-or-expression-template-type&, const number-or-expression-template-type&);
 
    
 
    
         These functions all behave exactly as their standard library counterparts
-        do: their argument is either an instance of mp_number
-        or an expression template derived from it; If the argument is of type mp_number<Backend, false>
+        do: their argument is either an instance of number
+        or an expression template derived from it; If the argument is of type number<Backend, false>
         then that is also the return type, otherwise the return type is an expression
         template.
       
    
@@ -555,9 +560,9 @@
         types).
       
    
 
    
-
-        Traits
-        Class Support
+
+        Traits Class
+        Support
       
    
 
    template <class T>
 struct component_type;
@@ -579,10 +584,11 @@
         number_kind_fixed_point.
       
    
 
    
-
-        Integer functions
+
+        Integer
+        functions
       
    
-
    unmentionable-expression-template-type    pow(const mp_number-or-expression-template-type& b, unsigned p);
+
    unmentionable-expression-template-type    pow(const number-or-expression-template-type& b, unsigned p);
 
    
 
    
         Returns bp as an expression template. Note that this
@@ -590,14 +596,14 @@
         as to take "effectively forever" to compute, or else simply run
         the host machine out of memory.
       
    
-
    unmentionable-expression-template-type    powm(const mp_number-or-expression-template-type& b, const mp_number-or-expression-template-type& p, const mp_number-or-expression-template-type& m);
+
    unmentionable-expression-template-type    powm(const number-or-expression-template-type& b, const number-or-expression-template-type& p, const number-or-expression-template-type& m);
 
    
 
    
         Returns bp mod m as an expression template.
       
    
 
    template <class Backend, bool ExpressionTemplates>
-bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
-               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
+bool divide_qr(const number-or-expression-template-type& x, const number-or-expression-template-type& y,
+               number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r);
 
    
 
    
         Divides x by y and returns both the quotient and remainder. After the call
@@ -606,48 +612,48 @@
         = x % y.
       
    
 
    template <class Integer>
-Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
+Integer integer_modulus(const number-or-expression-template-type& x, Integer val);
 
    
 
    
         Returns the absolute value of x
         % val.
       
    
-
    unsigned lsb(const mp_number-or-expression-template-type& x);
+
    unsigned lsb(const number-or-expression-template-type& x);
 
    
 
    
         Returns the index of the least significant bit that is set to 1.
       
    
 
    template <class Backend, class ExpressionTemplates>
-bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+bool bit_test(const number<Backend, ExpressionTemplates>& val, unsigned index);
 
    
 
    
         Returns true if the bit at
         index in val is set.
       
    
 
    template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+number<Backend, ExpressionTemplates>& bit_set(number<Backend, ExpressionTemplates>& val, unsigned index);
 
    
 
    
         Sets the bit at index in val, and
         returns val.
       
    
 
    template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+number<Backend, ExpressionTemplates>& bit_unset(number<Backend, ExpressionTemplates>& val, unsigned index);
 
    
 
    
         Unsets the bit at index in val,
         and returns val.
       
    
 
    template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+number<Backend, ExpressionTemplates>& bit_flip(number<Backend, ExpressionTemplates>& val, unsigned index);
 
    
 
    
         Flips the bit at index in val,
         and returns val.
       
    
 
    template <class Engine>
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
+bool miller_rabin_test(const number-or-expression-template-type& n, unsigned trials, Engine& gen);
+bool miller_rabin_test(const number-or-expression-template-type& n, unsigned trials);
 
    
 
    
         Tests to see if the number n is probably prime - the
@@ -659,29 +665,29 @@
         composite less than 0.25^trials.
       
    
 
    
-
-        Rational
+
+        Rational
         Number Functions
       
    
-
    typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
-typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
+
    typename component_type<number-or-expression-template-type>::type numerator  (const number-or-expression-template-type&);
+typename component_type<number-or-expression-template-type>::type denominator(const number-or-expression-template-type&);
 
    
 
    
         These functions return the numerator and denominator of a rational number
         respectively.
       
    
 
    
-
-        Boost.Math
+
+        Boost.Math
         Interoperability Support
       
    
 
    namespace boost{ namespace math{
 
-int  fpclassify     (const mp_number-or-expression-template-type&, int);
-bool isfinite       (const mp_number-or-expression-template-type&, int);
-bool isnan          (const mp_number-or-expression-template-type&, int);
-bool isinf          (const mp_number-or-expression-template-type&, int);
-bool isnormal       (const mp_number-or-expression-template-type&, int);
+int  fpclassify     (const number-or-expression-template-type&, int);
+bool isfinite       (const number-or-expression-template-type&, int);
+bool isnan          (const number-or-expression-template-type&, int);
+bool isinf          (const number-or-expression-template-type&, int);
+bool isnormal       (const number-or-expression-template-type&, int);
 
 }} // namespaces
 
    
@@ -694,8 +700,8 @@
         to ensure interoperability.
       
    
 
    
-
-        std::numeric_limits
+
+        std::numeric_limits
         support
       
    
 
    namespace std{
@@ -710,7 +716,7 @@
 
    
 
    
         Class template std::numeric_limits is specialized for all instantiations
-        of mp_number whose precision
+        of number whose precision
         is known at compile time, plus those types whose precision is unlimited (though
         it is much less useful in those cases). It is not specialized for types whose
         precision can vary at compile time (such as mpf_float).
diff --git a/doc/html/boost_multiprecision/ref/tom_int_ref.html b/doc/html/boost_multiprecision/ref/tom_int_ref.html
index c95e2112..5d7cf7bd 100644
--- a/doc/html/boost_multiprecision/ref/tom_int_ref.html
+++ b/doc/html/boost_multiprecision/ref/tom_int_ref.html
@@ -21,7 +21,7 @@
 
 class tommath_int;
 
-typedef mp_number<tommath_int >         tom_int;
+typedef number<tommath_int >         tom_int;
 
 }} // namespaces
 
    
diff --git a/doc/html/boost_multiprecision/tut/conversions.html b/doc/html/boost_multiprecision/tut/conversions.html
index 81632bc8..c288abe4 100644
--- a/doc/html/boost_multiprecision/tut/conversions.html
+++ b/doc/html/boost_multiprecision/tut/conversions.html
@@ -19,7 +19,7 @@
       Interconverting Between Number Types

    - All of the number types that are based on mp_number + All of the number types that are based on number have certain conversion rules in common. In particular:

    • @@ -29,6 +29,27 @@ 
      cpp_dec_float_50 df(0.5); // OK construction from double
 cpp_int          i(450);  // OK constructs from signed int
      +
      • + A number can be converted + to any built in type, via the convert_to + member function: +
      +
      mpz_int z(2);
+int i = z.template convert_to<int>(); // sets i to 2
+
      +

      + Additional conversions may be supported by particular backends. +

      +
      • + A number can be converted + to any built in type, via an explicit conversion operator: this functionality + is only available on compilers supporting C++11's explicit conversion + syntax. +
      +
      mpz_int z(2);
+int i = z;  // Error, implicit conversion not allowed.
+int j = static_cast<int>(z);  // OK explicit conversion.
+
      • Any number type can be constructed (or assigned) from a const char* or a std::string:
      @@ -93,17 +114,6 @@ More information on what additional types a backend supports conversions from are given in the tutorial for each backend.

      -
      • - An mp_number can be converted - to any built in type, via the convert_to - member function: -
      -
      mpz_int z(2);
-int i = z.template convert_to<int>(); // sets i to 2
-
      -

      - Additional conversions may be supported by particular backends. -

    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html index 4d71a28e..94671163 100644 --- a/doc/html/boost_multiprecision/tut.html +++ b/doc/html/boost_multiprecision/tut.html @@ -31,7 +31,7 @@
    - diff --git a/doc/html/index.html b/doc/html/index.html index 4e0ab81c..55b45c32 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -118,7 +118,7 @@
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html index 3c0e3371..a1a715d4 100644 --- a/doc/html/boost_multiprecision/tut/ints.html +++ b/doc/html/boost_multiprecision/tut/ints.html @@ -486,7 +486,7 @@
    -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html index 32a761ea..336c4d1f 100644 --- a/doc/html/boost_multiprecision/tut/primetest.html +++ b/doc/html/boost_multiprecision/tut/primetest.html @@ -93,7 +93,7 @@
    -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/random.html b/doc/html/boost_multiprecision/tut/random.html index 5c383672..6739f77a 100644 --- a/doc/html/boost_multiprecision/tut/random.html +++ b/doc/html/boost_multiprecision/tut/random.html @@ -143,7 +143,7 @@
    -
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 2584d7db..5b386e55 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -532,7 +532,7 @@
    - @@ -758,7 +758,7 @@ @@ -2128,52 +2128,138 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html index 2a8ca1b3..f3c1ecf5 100644 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -206,7 +206,7 @@
    Backend

    - The actual arithmetic backend that does all the work. + The actual arithmetic back-end that does all the work.

    ExpressionTemplates

    @@ -373,7 +373,7 @@ const Backend& backend()const;

    - Returns the underlying backend instance used by *this. + Returns the underlying back-end instance used by *this.

    @@ -470,8 +470,8 @@ derived from them.

    - It's down to the backend type to actually implement string conversion. However, - the backends provided with this library support all of the iostream formatting + It's down to the back-end type to actually implement string conversion. However, + the back-ends provided with this library support all of the iostream formatting flags, field width and precision settings.

    diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html index 94671163..ea39c242 100644 --- a/doc/html/boost_multiprecision/tut.html +++ b/doc/html/boost_multiprecision/tut.html @@ -26,7 +26,7 @@

    In order to use this library you need to make two choices: what kind of number - do I want, and which backend do I want to perform the actual arithmetic? + do I want, and which back-end do I want to perform the actual arithmetic?

    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/reals.html b/doc/html/boost_multiprecision/tut/reals.html index fe118cb9..58c5cf14 100644 --- a/doc/html/boost_multiprecision/tut/reals.html +++ b/doc/html/boost_multiprecision/tut/reals.html @@ -491,7 +491,7 @@
    - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    Copyright © 2011 John Maddock

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/index.html b/doc/html/index.html index a81e493e..77a81cd9 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -14,9 +14,12 @@

    Chapter 1. Boost.Multiprecision

    -various authors +John Maddock

    -

    Copyright © 2011 John Maddock

    +

    +Christopher Kormanyos +

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying @@ -63,7 +66,7 @@

    - +

    Last revised: March 22, 2012 at 08:59:33 GMT

    Last revised: March 26, 2012 at 17:54:45 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index c790c76e..97db0938 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -7,14 +7,14 @@ [library Boost.Multiprecision [quickbook 1.5] - [copyright 2011 John Maddock] + [copyright 2002-2012 John Maddock and Christopher Kormanyos] [purpose Multiprecision Number library] [license Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at [@http://www.boost.org/LICENSE_1_0.txt]) ] - [authors [authors, various]] + [authors [Maddock, John], [Kormanyos, Christopher]] [/last-revision $Date: 2011-07-08 18:51:46 +0100 (Fri, 08 Jul 2011) $] ] @@ -869,6 +869,15 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba mp_number& q, mp_number& r); template Integer integer_modulus(const ``['mp_number-or-expression-template-type]``& x, Integer val); + unsigned lsb(const ``['mp_number-or-expression-template-type]``& x); + template + bool bit_test(const mp_number& val, unsigned index); + template + mp_number& bit_set(mp_number& val, unsigned index); + template + mp_number& bit_unset(mp_number& val, unsigned index); + template + mp_number& bit_flip(mp_number& val, unsigned index); template bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials, Engine& gen); bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials); @@ -1150,6 +1159,30 @@ Divides x by y and returns both the quotient and remainder. After the call `q = Returns the absolute value of `x % val`. + unsigned lsb(const ``['mp_number-or-expression-template-type]``& x); + +Returns the index of the least significant bit that is set to 1. + + template + bool bit_test(const mp_number& val, unsigned index); + +Returns `true` if the bit at /index/ in /val/ is set. + + template + mp_number& bit_set(mp_number& val, unsigned index); + +Sets the bit at /index/ in /val/, and returns /val/. + + template + mp_number& bit_unset(mp_number& val, unsigned index); + +Unsets the bit at /index/ in /val/, and returns /val/. + + template + mp_number& bit_flip(mp_number& val, unsigned index); + +Flips the bit at /index/ in /val/, and returns /val/. + template bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials, Engine& gen); bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials); @@ -1209,8 +1242,8 @@ The requirements on the `Backend` template argument to `mp_number` are split up compulsory requirements, and optional requirements that are either to improve performance or provide optional features. -In the following tables, type B is the `Backend` template arument to `mp_number`, `b` is -a variable of B, `cb` and `cb2` are constant variables of type B, `a` is a variable of Arithmetic type, +In the following tables, type B is the `Backend` template arument to `mp_number`, `b` and `b2` are +a variables of type B, `cb` and `cb2` are constant variables of type B, `a` is a variable of Arithmetic type, `s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`, `pa` is a variable of type pointer-to-arithmetic-type, `exp` is a variable of type `B::exp_type`, `pexp` is a variable of type `B::exp_type*`, B2 is another type that meets these requirements, b2 is a variable @@ -1354,6 +1387,15 @@ of type B2. [[`eval_fmod(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::fmod` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] [[`eval_pow(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::pow` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] [[`eval_atan2(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::atan` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_qr(cb, cb2, b, b2)`][`void`][Sets `b` to the result of `cb / cb2` and `b2` to the result of `cb % cb2`. Only required when `B` is an integer type.]] +[[`eval_integer_modulus(cb, ui)`][`unsigned`][Returns the result of `cb % ui`. Only required when `B` is an integer type.]] +[[`eval_lsb(cb)`][`unsigned`][Returns the index of the least significant bit that is set.` Only required when `B` is an integer type.]] +[[`eval_bit_test(cb, ui)`][`bool`][Returns true if `cb` has bit `ui` set. Only required when `B` is an integer type.]] +[[`eval_bit_set(b, ui)`][`void`][Sets the bit at index `ui` in `b`. Only required when `B` is an integer type.]] +[[`eval_bit_unset(b, ui)`][`void`][Unsets the bit at index `ui` in `b`. Only required when `B` is an integer type.]] +[[`eval_bit_flip(b, ui)`][`void`][Flips the bit at index `ui` in `b`. Only required when `B` is an integer type.]] +[[`eval_gcd(b, cb, cb2)`][`void`][Sets `b` to the greatest common divisor of `cb` and `cb2`. Only required when `B` is an integer type.]] +[[`eval_lcm(b, cb, cb2)`][`void`][Sets `b` to the least common multiple of `cb` and `cb2`. Only required when `B` is an integer type.]] ] [note @@ -1731,6 +1773,10 @@ More a list of what ['could] be done, rather than what ['should] be done (which * Add backend support for libdecNumber. * Add an adapter backend for complex number types. +* Add a backend for MPFR interval arithmetic. +* Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. +* Add assembly level routines to cpp_int_backend. +* Add an all C++ binary floating point type. [endsect] diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 77fca771..1681a445 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1844,7 +1844,7 @@ inline void eval_left_shift(cpp_int_backend& result, doub if((ors == 1) && (!*result.limbs())) return; // shifting zero yields zero. unsigned rs = ors; - if(shift && (result.limbs()[rs - 1] >> (cpp_int_backend::limb_bits - shift))) + if(shift && (result.limbs()[ors - 1] >> (cpp_int_backend::limb_bits - shift))) ++rs; // Most significant limb will overflow when shifted rs += offset; result.resize(rs); @@ -1860,7 +1860,7 @@ inline void eval_left_shift(cpp_int_backend& result, doub i = 0; if(!truncated) { - if(rs > ors) + if(rs > ors + offset) { pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift); --rs; @@ -1925,7 +1925,7 @@ inline void eval_left_shift(cpp_int_backend& result, { // This code only works when shift is non-zero, otherwise we invoke undefined behaviour! i = 0; - if(rs > ors) + if(rs > ors + offset) { pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift); --rs; @@ -2066,7 +2066,7 @@ inline void eval_abs(cpp_int_backend& result, const // Get the location of the least-significant-bit: // template -inline unsigned get_lsb(const cpp_int_backend& a) +inline unsigned eval_lsb(const cpp_int_backend& a) { BOOST_ASSERT(eval_get_sign(a) != 0); @@ -2123,8 +2123,8 @@ inline void eval_gcd(cpp_int_backend& result, const /* Let shift := lg K, where K is the greatest power of 2 dividing both u and v. */ - unsigned us = get_lsb(u); - unsigned vs = get_lsb(v); + unsigned us = eval_lsb(u); + unsigned vs = eval_lsb(v); shift = (std::min)(us, vs); eval_right_shift(u, us); eval_right_shift(v, vs); @@ -2139,7 +2139,7 @@ inline void eval_gcd(cpp_int_backend& result, const // Termination condition tries not to do a full compare if possible: if(!v.limbs()[0] && eval_is_zero(v)) break; - vs = get_lsb(v); + vs = eval_lsb(v); eval_right_shift(v, vs); BOOST_ASSERT((v.limbs()[0] & 1)); BOOST_ASSERT((u.limbs()[0] & 1)); @@ -2150,6 +2150,66 @@ inline void eval_gcd(cpp_int_backend& result, const eval_left_shift(result, shift); } +template +inline bool eval_bit_test(const cpp_int_backend& val, unsigned index) +{ + unsigned offset = index / cpp_int_backend::limb_bits; + unsigned shift = index % cpp_int_backend::limb_bits; + limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u); + if(offset >= val.size()) + return false; + return val.limbs()[offset] & mask ? true : false; +} + +template +inline void eval_bit_set(cpp_int_backend& val, unsigned index) +{ + unsigned offset = index / cpp_int_backend::limb_bits; + unsigned shift = index % cpp_int_backend::limb_bits; + limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u); + if(offset >= val.size()) + { + unsigned os = val.size(); + val.resize(offset + 1); + if(offset >= val.size()) + return; // fixed precision overflow + for(unsigned i = os; i <= offset; ++i) + val.limbs()[i] = 0; + } + val.limbs()[offset] |= mask; +} + +template +inline void eval_bit_unset(cpp_int_backend& val, unsigned index) +{ + unsigned offset = index / cpp_int_backend::limb_bits; + unsigned shift = index % cpp_int_backend::limb_bits; + limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u); + if(offset >= val.size()) + return; + val.limbs()[offset] &= ~mask; + val.normalize(); +} + +template +inline void eval_bit_flip(cpp_int_backend& val, unsigned index) +{ + unsigned offset = index / cpp_int_backend::limb_bits; + unsigned shift = index % cpp_int_backend::limb_bits; + limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u); + if(offset >= val.size()) + { + unsigned os = val.size(); + val.resize(offset + 1); + if(offset >= val.size()) + return; // fixed precision overflow + for(unsigned i = os; i <= offset; ++i) + val.limbs()[i] = 0; + } + val.limbs()[offset] ^= mask; + val.normalize(); +} + template inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 6fcf64f7..9bd53ba7 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -506,6 +506,71 @@ inline typename enable_if >::type eval_lcm(T& result, co eval_lcm(result, b, a); } +template +inline unsigned eval_lsb(const T& val) +{ + typedef typename boost::multiprecision::detail::canonical::type ui_type; + unsigned result = 0; + T mask, t; + mask = ui_type(1); + do + { + eval_bitwise_and(t, mask, val); + ++result; + eval_left_shift(mask, 1); + } + while(eval_is_zero(t)); + + return --result; +} + +template +inline bool eval_bit_test(const T& val, unsigned index) +{ + typedef typename boost::multiprecision::detail::canonical::type ui_type; + unsigned result = 0; + T mask, t; + mask = ui_type(1); + eval_left_shift(mask, index); + eval_bitwise_and(t, mask, val); + return !eval_is_zero(t); +} + +template +inline void eval_bit_set(T& val, unsigned index) +{ + typedef typename boost::multiprecision::detail::canonical::type ui_type; + unsigned result = 0; + T mask; + mask = ui_type(1); + eval_left_shift(mask, index); + eval_bitwise_or(val, mask); +} + +template +inline void eval_bit_flip(T& val, unsigned index) +{ + typedef typename boost::multiprecision::detail::canonical::type ui_type; + unsigned result = 0; + T mask; + mask = ui_type(1); + eval_left_shift(mask, index); + eval_bitwise_xor(val, mask); +} + +template +inline void eval_bit_unset(T& val, unsigned index) +{ + typedef typename boost::multiprecision::detail::canonical::type ui_type; + unsigned result = 0; + T mask, t; + mask = ui_type(1); + eval_left_shift(mask, index); + eval_bitwise_and(t, mask, val); + if(!eval_is_zero(t)) + eval_bitwise_xor(val, mask); +} + // // These have to implemented by the backend, declared here so that our macro generated code compiles OK. // diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 2b7dc8cf..314fc4cd 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1356,6 +1356,31 @@ inline void eval_lcm(gmp_int& result, const gmp_int& a, const long b) mpz_lcm_ui(result.data(), a.data(), std::abs(b)); } +inline unsigned eval_lsb(const gmp_int& val) +{ + return mpz_scan1(val.data(), 0); +} + +inline bool eval_bit_test(const gmp_int& val, unsigned index) +{ + return mpz_tstbit(val.data(), index) ? true : false; +} + +inline void eval_bit_set(gmp_int& val, unsigned index) +{ + mpz_setbit(val.data(), index); +} + +inline void eval_bit_unset(gmp_int& val, unsigned index) +{ + mpz_clrbit(val.data(), index); +} + +inline void eval_bit_flip(gmp_int& val, unsigned index) +{ + mpz_combit(val.data(), index); +} + inline void eval_qr(const gmp_int& x, const gmp_int& y, gmp_int& q, gmp_int& r) { diff --git a/include/boost/multiprecision/integer_ops.hpp b/include/boost/multiprecision/integer_ops.hpp index a98524b4..6a83b2a6 100644 --- a/include/boost/multiprecision/integer_ops.hpp +++ b/include/boost/multiprecision/integer_ops.hpp @@ -89,6 +89,69 @@ inline typename enable_if, mpl::bool_ +inline typename enable_if_c::value == number_kind_integer, unsigned>::type + lsb(const mp_number& x) +{ + using default_ops::eval_lsb; + return eval_lsb(x.backend()); +} + +template +inline typename enable_if_c::result_type>::value == number_kind_integer, unsigned>::type + lsb(const multiprecision::detail::mp_exp& x) +{ + typedef typename multiprecision::detail::mp_exp::result_type number_type; + number_type n(x); + using default_ops::eval_lsb; + return eval_lsb(n.backend()); +} + +template +inline typename enable_if_c::value == number_kind_integer, bool>::type + bit_test(const mp_number& x, unsigned index) +{ + using default_ops::eval_bit_test; + return eval_bit_test(x.backend(), index); +} + +template +inline typename enable_if_c::result_type>::value == number_kind_integer, bool>::type + bit_test(const multiprecision::detail::mp_exp& x, unsigned index) +{ + typedef typename multiprecision::detail::mp_exp::result_type number_type; + number_type n(x); + using default_ops::eval_bit_test; + return eval_bit_test(n.backend(), index); +} + +template +inline typename enable_if_c::value == number_kind_integer, mp_number&>::type + bit_set(mp_number& x, unsigned index) +{ + using default_ops::eval_bit_set; + eval_bit_set(x.backend(), index); + return x; +} + +template +inline typename enable_if_c::value == number_kind_integer, mp_number&>::type + bit_unset(mp_number& x, unsigned index) +{ + using default_ops::eval_bit_unset; + eval_bit_unset(x.backend(), index); + return x; +} + +template +inline typename enable_if_c::value == number_kind_integer, mp_number&>::type + bit_flip(mp_number& x, unsigned index) +{ + using default_ops::eval_bit_flip; + eval_bit_flip(x.backend(), index); + return x; +} + }} //namespaces #endif diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index f40043b3..a6c9256b 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -449,6 +449,11 @@ inline void eval_qr(const tommath_int& x, const tommath_int& y, detail::check_tommath_result(mp_div(const_cast< ::mp_int*>(&x.data()), const_cast< ::mp_int*>(&y.data()), &q.data(), &r.data())); } +inline unsigned eval_lsb(const tommath_int& val) +{ + return mp_cnt_lsb(const_cast<::mp_int*>(&val.data())); +} + template inline typename enable_if, Integer>::type eval_integer_modulus(const tommath_int& x, Integer val) { diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index eeb43056..4b3da0a8 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -405,6 +405,20 @@ void test_integer_ops(const boost::mpl::int_::is_specialized && (!std::numeric_limits::is_bounded || (i * 17 < std::numeric_limits::digits))) + { + BOOST_TEST(lsb(Real(1) << (i * 17)) == i * 17); + BOOST_TEST(bit_test(Real(1) << (i * 17), i * 17)); + BOOST_TEST(!bit_test(Real(1) << (i * 17), i * 17 + 1)); + BOOST_TEST(!bit_test(Real(1) << (i * 17), i * 17 - 1)); + BOOST_TEST(bit_test(bit_set(Real(0), i * 17), i * 17)); + BOOST_TEST(bit_flip(Real(0), i*17) == Real(1) << i * 17); + BOOST_TEST(bit_flip(Real(Real(1) << i * 17), i * 17) == 0); + BOOST_TEST(bit_unset(Real(Real(1) << i * 17), i * 17) == 0); + } + } } template diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp index 33a0c276..fb836463 100644 --- a/test/test_cpp_int.cpp +++ b/test/test_cpp_int.cpp @@ -133,6 +133,15 @@ void test() BOOST_CHECK_EQUAL((mpz_int(a)^=-b).str(), (test_type(a1) ^= -b1).str()); BOOST_CHECK_EQUAL(mpz_int(-a^-b).str(), test_type(-a1 ^ -b1).str()); BOOST_CHECK_EQUAL((mpz_int(-a)^=-b).str(), (test_type(-a1) ^= -b1).str()); + // Shift ops: + for(unsigned i = 0; i < 128; ++i) + { + if(!std::numeric_limits::is_bounded) + { + BOOST_CHECK_EQUAL(mpz_int(a << i).str(), test_type(a1 << i).str()); + } + BOOST_CHECK_EQUAL(mpz_int(a >> i).str(), test_type(a1 >> i).str()); + } // Now check operations involving signed integers: BOOST_CHECK_EQUAL(mpz_int(a + si).str(), test_type(a1 + si).str()); BOOST_CHECK_EQUAL(mpz_int(a + -si).str(), test_type(a1 + -si).str()); From bb6393d69e2ecb31b129dd1b82e17930dd687d41 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 28 Mar 2012 17:26:20 +0000 Subject: [PATCH 144/256] Fix typos / issue spotted by Paul Bristow. [SVN r77605] --- doc/html/boost_multiprecision/intro.html | 27 ++- doc/html/boost_multiprecision/map/todo.html | 6 +- .../perf/float_performance.html | 2 +- .../perf/int_real_world.html | 128 +++++++++++- .../perf/integer_performance.html | 2 +- .../perf/rational_performance.html | 2 +- .../boost_multiprecision/perf/realworld.html | 2 +- .../boost_multiprecision/ref/backendconc.html | 182 +++++++++++++----- .../boost_multiprecision/ref/mp_number.html | 8 +- doc/html/boost_multiprecision/tut.html | 2 +- doc/html/boost_multiprecision/tut/ints.html | 22 +-- .../boost_multiprecision/tut/primetest.html | 13 +- .../boost_multiprecision/tut/rational.html | 26 +-- doc/html/boost_multiprecision/tut/reals.html | 21 +- doc/html/index.html | 2 +- doc/multiprecision.qbk | 124 ++++++------ 16 files changed, 398 insertions(+), 171 deletions(-) diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index 9c1f2b6f..134f9fea 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -17,21 +17,36 @@
    +

    + The Multiprecision Library provides User-defined integer, + rational and floating-point C++ types which try to emulate as closely as practicable + the C++ built-in types, but provide for more range and precision. Depending + upon the number type, precision may be arbitrarily large (limited only by available + memory), fixed at compile time values, for example 50 decimal digits, or a + variable controlled at run-time by member functions. The types are expression-template-enabled + for better performance than naive user-defined types. +

    The Multiprecision library comes in two distinct parts:

    • - An expression-template-enabled front end mp_number + An expression-template-enabled front-end mp_number that handles all the operator overloading, expression evaluation optimization, and code reduction.
    • - A selection of backends that implement the actual arithmetic operations, - and need conform only to the reduced interface requirements of the front - end. + A selection of back-ends that implement the actual arithmetic operations, + and need conform only to the reduced interface requirements of the front-end.
    +

    + Separation of front-end and back-end allows use of highly refined, but restricted + license libraries where possible, but provides Boost license alternatives for + users who must have a portable unconstrained license. Which is to say some + back-ends rely on 3rd party libraries, but a header-only Boost license version + is always available (if somewhat slower). +

    The library is often used via one of the predefined typedefs: for example if you wanted an arbitrary precision integer type using GMP @@ -44,7 +59,7 @@

    Alternatively, you can compose your own multiprecision type, by combining mp_number with one of the predefined - backend types. For example, suppose you wanted a 300 decimal digit floating-point + back-end types. For example, suppose you wanted a 300 decimal digit floating-point type based on the MPFR library. In this case, there's no predefined typedef with that level of precision, so instead we compose our own: @@ -161,7 +176,7 @@ tend to be slower to compile than their simpler cousins, they're also harder to debug (should you actually want to step through our code!), and rely on compiler optimizations being turned on to give really good performance. Also, - since the return type from expressions involving mp_number's + since the return type from expressions involving mp_numbers is an "unmentionable implementation detail", you have to be careful to cast the result of an expression to the actual number type when passing an expression to a template function. For example, given: diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index 838ead9b..e849897d 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -22,13 +22,13 @@

    • - Add backend support for libdecNumber. + Add back-end support for libdecNumber.
    • - Add an adapter backend for complex number types. + Add an adapter back-end for complex number types.
    • - Add a backend for MPFR interval arithmetic. + Add a back-end for MPFR interval arithmetic.
    • Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html index ce1d7eec..90f06dcc 100644 --- a/doc/html/boost_multiprecision/perf/float_performance.html +++ b/doc/html/boost_multiprecision/perf/float_performance.html @@ -21,7 +21,7 @@

      Note that these tests are carefully designed to test performance of the underlying algorithms and not memory allocation or variable copying. As usual, performance - results should be taken with a healthy dose of scepticsm, and real-world + results should be taken with a healthy dose of scepticism, and real-world peformance may vary widely depending upon the specifics of the program. In each table relative times are given first, with the best performer given a score of 1. Total actual times are given in brackets, measured in seconds diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html index 5d6c79ff..89278b58 100644 --- a/doc/html/boost_multiprecision/perf/int_real_world.html +++ b/doc/html/boost_multiprecision/perf/int_real_world.html @@ -70,16 +70,128 @@

    +

    + cpp_int +

    +     		+

    + 1.3612(0.465547s) +

    +
    +

    + cpp_int (no Expression templates) +

    +     		+

    + 1.33286(0.455854s) +

    +
    +

    + cpp_int (64-bit cache) +

    +     		+

    + 1.33134(0.455333s) +

    +
    +

    + cpp_int (256-bit cache) +

    +     		+

    + 1.29367(0.442451s) +

    +
    +

    + cpp_int (512-bit cache) +

    +     		+

    + 1.08821(0.37218s) +

    +
    +

    + cpp_int (1024-bit cache) +

    +     		+

    + 1.07902(0.369037s) +

    +
    +

    + mp_int1024_t +

    +     		+

    + 1.02616(0.35096s) +

    +
    +

    + mp_int1024_t (no Expression templates) +

    +     		+

    + 1(0.342011s) +

    +
    +

    + tom_int +

    +     		+

    + 3.74233(1.27992s) +

    +
    +

    + tom_int (no Expression templates) +

    +     		+

    + 3.97646(1.35999s) +

    +
    -

    - [[cpp_int][1.3612(0.465547s)]] [[cpp_int (no Expression templates)][1.33286(0.455854s)]] - [[cpp_int (64-bit cache)][1.33134(0.455333s)]] [[cpp_int (256-bit cache)][1.29367(0.442451s)]] - [[cpp_int (512-bit cache)][1.08821(0.37218s)]] [[cpp_int (1024-bit cache)][1.07902(0.369037s)]] - [[mp_int1024_t][1.02616(0.35096s)]] [[mp_int1024_t (no Expression templates)][1(0.342011s)]] - [[tom_int][3.74233(1.27992s)]] [[tom_int (no Expression templates)][3.97646(1.35999s)]] - ] -

    It's interesting to note that expression templates have little effect here - perhaps because the actual expressions involved are relatively trivial diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html index 23fdd44c..6ad820a4 100644 --- a/doc/html/boost_multiprecision/perf/integer_performance.html +++ b/doc/html/boost_multiprecision/perf/integer_performance.html @@ -21,7 +21,7 @@

    Note that these tests are carefully designed to test performance of the underlying algorithms and not memory allocation or variable copying. As usual, performance - results should be taken with a healthy dose of scepticsm, and real-world + results should be taken with a healthy dose of scepticism, and real-world peformance may vary widely depending upon the specifics of the program. In each table relative times are given first, with the best performer given a score of 1. Total actual times are given in brackets, measured in seconds diff --git a/doc/html/boost_multiprecision/perf/rational_performance.html b/doc/html/boost_multiprecision/perf/rational_performance.html index eab8d539..6754381e 100644 --- a/doc/html/boost_multiprecision/perf/rational_performance.html +++ b/doc/html/boost_multiprecision/perf/rational_performance.html @@ -21,7 +21,7 @@

    Note that these tests are carefully designed to test performance of the underlying algorithms and not memory allocation or variable copying. As usual, performance - results should be taken with a healthy dose of scepticsm, and real-world + results should be taken with a healthy dose of scepticism, and real-world peformance may vary widely depending upon the specifics of the program. In each table relative times are given first, with the best performer given a score of 1. Total actual times are given in brackets, measured in seconds diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html index 9137d2d1..4dd0d5ef 100644 --- a/doc/html/boost_multiprecision/perf/realworld.html +++ b/doc/html/boost_multiprecision/perf/realworld.html @@ -23,7 +23,7 @@ cases for these functions. In each case the best performing library gets a relative score of 1, with the total execution time given in brackets. The first three libraries listed are the various floating point types provided - by this library, while for comparison, two popular C++ frontends to MPFR ( mpfr_class + by this library, while for comparison, two popular C++ front-ends to MPFR ( mpfr_class and mpreal) are also shown.

    diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index c5507f4e..e56abc3b 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -740,7 +740,7 @@

    - Copy constructor from a different backend type. + Copy constructor from a different back-end type.

    - Assignment operator from a different backend type. + Assignment operator from a different back-end type.

    - Returns the index of the least significant bit that is set. - Only required - when B is an - integer type.]] [[eval_bit_test(cb, - ui)][bool][Returns - true if - cb has bit ui set. Only - required when - B is an - integer type.]] [[eval_bit_set(b, - ui)][void][Sets - the bit - at index - ui in b. Only - required when - B is an - integer type.]] [[eval_bit_unset(b, - ui)][void][Unsets - the bit - at index - ui in b. Only - required when - B is an - integer type.]] [[eval_bit_flip(b, - ui)][void][Flips - the bit - at index - ui in b. Only - required when - B is an - integer type.]] [[eval_gcd(b, - cb, cb2)][void][Sets - b to the - greatest common - divisor of - cb and cb2. Only - required when - B is an - integer type.]] [[eval_lcm(b, - cb, cb2)][void][Sets - b to the - least common - multiple of - cb and cb2. Only - required when - B` is an integer type. + Returns the index of the least significant bit that is set. Only + required when B + is an integer type. +

    +
    +

    + eval_bit_test(cb, + ui) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb + has bit ui set. + Only required when B + is an integer type. +

    +
    +

    + eval_bit_set(b, + ui) +

    +     		+

    + void +

    +     		+

    + Sets the bit at index ui + in b. Only required + when B is an integer + type. +

    +
    +

    + eval_bit_unset(b, ui) +

    +     		+

    + void +

    +     		+

    + Unsets the bit at index ui + in b. Only required + when B is an integer + type. +

    +
    +

    + eval_bit_flip(b, + ui) +

    +     		+

    + void +

    +     		+

    + Flips the bit at index ui + in b. Only required + when B is an integer + type. +

    +
    +

    + eval_gcd(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Sets b to the greatest + common divisor of cb + and cb2. Only required + when B is an integer + type. +

    +
    +

    + eval_lcm(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Sets b to the least + common multiple of cb + and cb2. Only required + when B is an integer + type.

    diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html index a1a715d4..591ab4be 100644 --- a/doc/html/boost_multiprecision/tut/ints.html +++ b/doc/html/boost_multiprecision/tut/ints.html @@ -18,7 +18,7 @@ Integer Types

    - The following backends provide integer arithmetic: + The following back-ends provide integer arithmetic:

    @@ -119,7 +119,7 @@

    - Very fast and efficient backend. + Very fast and efficient back-end.

    		@@ -152,7 +152,7 @@

    - Public domain backend with no licence restrictions. + Public domain back-end with no licence restrictions.

    		@@ -200,9 +200,9 @@ boost::multiprecision::mp_int256_t or boost::multiprecision::mp_int512_t.

    - This backend is the "Swiss Army Knife" of integer types as it can - represent both fixed and arbitrary precision integer types, and both signed - and unsigned types. There are three template arguments: + This back-end is the "Swiss Army Knife" of integer types as it + can represent both fixed and arbitrary precision integer types, and both + signed and unsigned types. There are three template arguments:

    @@ -237,7 +237,7 @@

    • - Default constructed cpp_int_backend's + Default constructed cpp_int_backends have the value zero.
    • @@ -317,7 +317,7 @@ }} // namespaces

      - The gmp_int backend is used + The gmp_int back-end is used via the typedef boost::multiprecision::mpz_int. It acts as a thin wrapper around the GMP mpz_t to provide an integer type that is a drop-in replacement for the native C++ @@ -352,7 +352,7 @@ safely mix this type with existing code that uses GMP.

    • - Default constructed gmp_int's + Default constructed gmp_ints have the value zero (this is GMP's default behavior).
    • @@ -411,8 +411,8 @@ }} // namespaces

      - The tommath_int backend is - used via the typedef boost::multiprecision::tom_int. + The tommath_int back-end + is used via the typedef boost::multiprecision::tom_int. It acts as a thin wrapper around the libtommath tom_int to provide an integer type that is a drop-in replacement for the native C++ integer types, but diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html index 336c4d1f..f1dac222 100644 --- a/doc/html/boost_multiprecision/tut/primetest.html +++ b/doc/html/boost_multiprecision/tut/primetest.html @@ -33,17 +33,18 @@ These functions perform a Miller-Rabin test for primality, if the result is false then n is definitely composite, while if the result is true - then n is prime with probability 0.25^trials. The algorithm - used is straight out of Knuth Vol 2, which recomends 25 trials for a pretty - strong likelyhood that n is prime. + then n is prime with probability 0.25^trials. + The algorithm used is straight out of Knuth Vol 2, which recomends 25 trials + for a pretty strong likelyhood that n is prime.

      The third optional argument is for a Uniform Random Number Generator from Boost.Random. When not provided the mt19937 generator is used. Note that when producing random primes then you should - probably use a different random number generator to produce possible primes, - than used internally for testing whether the value is prime. It also helps - of course to seed the generators with some source of randomness. + probably use a different random number generator to produce candidate prime + numbers for testing, than is used internally by miller_rabin_test + for determining whether the value is prime. It also helps of course to seed + the generators with some source of randomness.

      The following example searches for a prime p diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 5b386e55..65eca5a3 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -18,7 +18,7 @@ Rational Number Types

    - The following backends provide rational number arithmetic: + The following back-ends provide rational number arithmetic:

    @@ -85,7 +85,7 @@ @@ -241,7 +241,7 @@ }}// namespaces

    - The gmp_rational backend + The gmp_rational back-end is used via the typedef boost::multiprecision::mpq_rational. It acts as a thin wrapper around the GMP mpq_t to provide a rational @@ -284,7 +284,7 @@

    • - Default constructed mpq_rational's + Default constructed mpq_rationals have the value zero (this is the GMP default behavior).
      • @@ -373,7 +373,7 @@

      • - Default constructed cpp_rational's + Default constructed cpp_rationals have the value zero.
      • @@ -419,7 +419,7 @@ }} // namespaces

        - The tommath_rational backend + The tommath_rational back-end is used via the typedef boost::multiprecision::tom_rational. It acts as a thin wrapper around boost::rational<tom_int> to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited @@ -443,7 +443,7 @@

        • - Default constructed tom_rational's + Default constructed tom_rationals have the value zero (this the inherited Boost.Rational behavior).
        • @@ -494,7 +494,7 @@ Boost.Rational

          - All of the inetger types in this library can be used as template arguments + All of the integer types in this library can be used as template arguments to boost::rational<IntType>.

          @@ -514,11 +514,11 @@

          The class template rational_adapter - is a backend for mp_number - which converts any existing integer backend into a rational-number backend. + is a back-end for mp_number + which converts any existing integer back-end into a rational-number back-end.

          - So for example, given an integer backend type MyIntegerBackend, + So for example, given an integer back-end type MyIntegerBackend, the use would be something like: 

          typedef mp_number<MyIntegerBackend>                    MyInt;
diff --git a/doc/html/boost_multiprecision/tut/reals.html b/doc/html/boost_multiprecision/tut/reals.html
index 58c5cf14..23ea5d72 100644
--- a/doc/html/boost_multiprecision/tut/reals.html
+++ b/doc/html/boost_multiprecision/tut/reals.html
@@ -18,7 +18,7 @@
 Floating Point Numbers

    - The following backends provide floating point arithmetic: + The following back-ends provide floating point arithmetic:

    - Very fast and efficient backend. + Very fast and efficient back-end.

    		@@ -182,13 +182,13 @@

    - All C++ adapter that allows any inetger backend type to be used + All C++ adapter that allows any inetger back-end type to be used as a rational type.

    - Requires an underlying integer backend type. + Requires an underlying integer back-end type.

    @@ -85,7 +85,7 @@ @@ -182,7 +182,7 @@ }}// namespaces

    - The gmp_float backend is + The gmp_float back-end is used in conjunction with mp_number : it acts as a thin wrapper around the GMP mpf_t to provide an real-number @@ -196,7 +196,7 @@ to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision respectively. The typedef mpf_float provides a variable precision type whose - precision can be controlled via the mp_number's + precision can be controlled via the mp_numbers member functions.

    - Very fast and efficient backend. + Very fast and efficient back-end.

    		@@ -118,7 +118,7 @@

    - Very fast and efficient backend, with its own standard library + Very fast and efficient back-end, with its own standard library implementation.

    @@ -236,7 +236,7 @@

    • - Default constructed gmp_float's + Default constructed gmp_floats have the value zero (this is the GMP library's default behavior).
      • @@ -327,7 +327,7 @@ to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision respectively. The typedef mpfr_float provides a variable precision type whose - precision can be controlled via the mp_number's + precision can be controlled via the mp_numbers member functions.

    @@ -431,7 +431,7 @@ }}// namespaces

    - The cpp_dec_float backend + The cpp_dec_float back-end is used in conjunction with mp_number: It acts as an entirely C++ (header only and dependency free) real-number type that is a drop-in replacement for the native C++ floating-point types, @@ -440,7 +440,8 @@

    Type cpp_dec_float can be used at fixed precision by specifying a non-zero Digits10 - template parameter. The typedefs cpp_dec_float_50 and cpp_dec_float_100 provide + template parameter. The typedefs cpp_dec_float_50 + and cpp_dec_float_100 provide arithmetic types at 50 and 100 decimal digits precision respectively.

    @@ -452,7 +453,7 @@

    • - Default constructed cpp_dec_float's + Default constructed cpp_dec_floats have a value of zero.
    • diff --git a/doc/html/index.html b/doc/html/index.html index 77a81cd9..9b369d6c 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -66,7 +66,7 @@
    - +

    Last revised: March 26, 2012 at 17:54:45 GMT

    Last revised: March 28, 2012 at 17:05:42 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 97db0938..8cc647ac 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -37,12 +37,24 @@ [section:intro Introduction] +The Multiprecision Library provides ['User-defined] integer, rational and floating-point C++ types which +try to emulate as closely as practicable the C++ built-in types, but provide for more range and +precision. Depending upon the number type, precision may be arbitrarily large (limited only by available memory), +fixed at compile time values, for example 50 decimal +digits, or a variable controlled at run-time by member functions. The types are +expression-template-enabled for better performance than naive user-defined types. + The Multiprecision library comes in two distinct parts: -* An expression-template-enabled front end `mp_number` +* An expression-template-enabled front-end `mp_number` that handles all the operator overloading, expression evaluation optimization, and code reduction. -* A selection of backends that implement the actual arithmetic operations, and need conform only to the -reduced interface requirements of the front end. +* A selection of back-ends that implement the actual arithmetic operations, and need conform only to the +reduced interface requirements of the front-end. + +Separation of front-end and back-end allows use of highly refined, but restricted license libraries +where possible, but provides Boost license alternatives for users who must have a portable +unconstrained license. Which is to say some back-ends rely on 3rd party libraries, but a header-only Boost license version is always +available (if somewhat slower). The library is often used via one of the predefined typedefs: for example if you wanted an arbitrary precision integer type using [gmp] as the underlying implementation then you could use: @@ -52,7 +64,7 @@ integer type using [gmp] as the underlying implementation then you could use: boost::multiprecision::mpz_int myint; // Arbitrary precision integer type. Alternatively, you can compose your own multiprecision type, by combining `mp_number` with one of the -predefined backend types. For example, suppose you wanted a 300 decimal digit floating-point type +predefined back-end types. For example, suppose you wanted a 300 decimal digit floating-point type based on the [mpfr] library. In this case, there's no predefined typedef with that level of precision, so instead we compose our own: @@ -135,7 +147,7 @@ Given the comments above, you might be forgiven for thinking that expression-tem sadly though, all tricks like this have their downsides. For one thing, expression template libraries like this one, tend to be slower to compile than their simpler cousins, they're also harder to debug (should you actually want to step through our code!), and rely on compiler optimizations being turned -on to give really good performance. Also, since the return type from expressions involving `mp_number`'s +on to give really good performance. Also, since the return type from expressions involving `mp_number`s is an "unmentionable implementation detail", you have to be careful to cast the result of an expression to the actual number type when passing an expression to a template function. For example, given: @@ -217,18 +229,18 @@ again, all are using [mpfr] to carry out the underlying arithmetic, and all are [section:tut Tutorial] In order to use this library you need to make two choices: what kind of number do I want, and -which backend do I want to perform the actual arithmetic? +which back-end do I want to perform the actual arithmetic? [section:ints Integer Types] -The following backends provide integer arithmetic: +The following back-ends provide integer arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] [[`cpp_int`][boost/multiprecision/cpp_int.hpp][2][None] [Very versatile, Boost licenced, all C++ integer type which support both arbitrary precision and fixed precision integer types.][Slower than [gmp], though typically not as slow as [tommath]]] -[[`gmp_int`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient backend.][Dependency on GNU licenced [gmp] library.]] -[[`tom_int`][boost/multiprecision/tommath.hpp][2][[tommath]][Public domain backend with no licence restrictions.][Slower than [gmp].]] +[[`gmp_int`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licenced [gmp] library.]] +[[`tom_int`][boost/multiprecision/tommath.hpp][2][[tommath]][Public domain back-end with no licence restrictions.][Slower than [gmp].]] ] [h4 cpp_int] @@ -263,7 +275,7 @@ The `cpp_int_backend` type is used via one of the typedefs `boost::multiprecisio `boost::multiprecision::mp_uint512_t`, `boost::multiprecision::mp_int128_t`, `boost::multiprecision::mp_int256_t` or `boost::multiprecision::mp_int512_t`. -This backend is the "Swiss Army Knife" of integer types as it can represent both fixed and arbitrary precision +This back-end is the "Swiss Army Knife" of integer types as it can represent both fixed and arbitrary precision integer types, and both signed and unsigned types. There are three template arguments: [variablelist @@ -281,7 +293,7 @@ integer types, and both signed and unsigned types. There are three template arg Things you should know when using this type: -* Default constructed `cpp_int_backend`'s have the value zero. +* Default constructed `cpp_int_backend`s have the value zero. * Division by zero results in a `std::runtime_error` being thrown. * Construction from a string that contains invalid non-numeric characters results in a `std::runtime_error` being thrown. * Since the precision of `cpp_int_backend` is necessarily limited when the allocator parameter is void, @@ -313,7 +325,7 @@ the feature off. }} // namespaces -The `gmp_int` backend is used via the typedef `boost::multiprecision::mpz_int`. It acts as a thin wrapper around the [gmp] `mpz_t` +The `gmp_int` back-end is used via the typedef `boost::multiprecision::mpz_int`. It acts as a thin wrapper around the [gmp] `mpz_t` to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. As well as the usual conversions from arithmetic and string types, type `mpz_int` is copy constructible and assignable from: @@ -327,7 +339,7 @@ Things you should know when using this type: * No changes are made to the GMP library's global settings - so you can safely mix this type with existing code that uses [gmp]. -* Default constructed `gmp_int`'s have the value zero (this is GMP's default behavior). +* Default constructed `gmp_int`s have the value zero (this is GMP's default behavior). * Formatted IO for this type does not support octal or hexadecimal notation for negative values, as a result performing formatted output on this type when the argument is negative and either of the flags `std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. @@ -349,7 +361,7 @@ is recomended on Win32. }} // namespaces -The `tommath_int` backend is used via the typedef `boost::multiprecision::tom_int`. It acts as a thin wrapper around the [tommath] `tom_int` +The `tommath_int` back-end is used via the typedef `boost::multiprecision::tom_int`. It acts as a thin wrapper around the [tommath] `tom_int` to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. Things you should know when using this type: @@ -372,12 +384,12 @@ as a result performing formatted output on this type when the argument is negati [section:reals Floating Point Numbers] -The following backends provide floating point arithmetic: +The following back-ends provide floating point arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] -[[`mpf_float`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient backend.][Dependency on GNU licenced [gmp] library.]] -[[`mpfr_float`][boost/multiprecision/mpfr.hpp][2][[gmp] and [mpfr]][Very fast and efficient backend, with its own standard library implementation.][Dependency on GNU licenced [gmp] and [mpfr] libraries.]] +[[`mpf_float`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licenced [gmp] library.]] +[[`mpfr_float`][boost/multiprecision/mpfr.hpp][2][[gmp] and [mpfr]][Very fast and efficient back-end, with its own standard library implementation.][Dependency on GNU licenced [gmp] and [mpfr] libraries.]] [[`cpp_dec_float`][boost/multiprecision/cpp_dec_float.hpp][10][None][Header only, all C++ implementation. Boost licence.][Approximately 2x slower than the [mpfr] or [gmp] libraries.]] ] @@ -396,7 +408,7 @@ The following backends provide floating point arithmetic: }} // namespaces -The `gmp_float` backend is used in conjunction with `mp_number` : it acts as a thin wrapper around the [gmp] `mpf_t` +The `gmp_float` back-end is used in conjunction with `mp_number` : it acts as a thin wrapper around the [gmp] `mpf_t` to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. @@ -404,7 +416,7 @@ Type `gmp_float` can be used at fixed precision by specifying a non-zero `Digits at variable precision by setting the template argument to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision respectively. The typedef mpf_float provides a variable precision type whose precision can be controlled via the -`mp_number`'s member functions. +`mp_number`s member functions. [note This type only provides standard library and `numeric_limits` support when the precision is fixed at compile time.] @@ -418,7 +430,7 @@ It's also possible to access the underlying `mpf_t` via the `data()` member func Things you should know when using this type: -* Default constructed `gmp_float`'s have the value zero (this is the [gmp] library's default behavior). +* Default constructed `gmp_float`s have the value zero (this is the [gmp] library's default behavior). * No changes are made to the [gmp] library's global settings, so this type can be safely mixed with existing [gmp] code. * It is not possible to round-trip objects of this type to and from a string and get back @@ -458,7 +470,7 @@ Type `mpfr_float_backend` can be used at fixed precision by specifying a non-zer at variable precision by setting the template argument to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision respectively. The typedef mpfr_float provides a variable precision type whose precision can be controlled via the -`mp_number`'s member functions. +`mp_number`s member functions. [note This type only provides `numeric_limits` support when the precision is fixed at compile time.] @@ -495,19 +507,19 @@ Things you should know when using this type: }} // namespaces -The `cpp_dec_float` backend is used in conjunction with `mp_number`: It acts as an entirely C++ (header only and dependency free) +The `cpp_dec_float` back-end is used in conjunction with `mp_number`: It acts as an entirely C++ (header only and dependency free) real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. Type `cpp_dec_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter. -The typedefs cpp_dec_float_50 and cpp_dec_float_100 provide arithmetic types at 50 and 100 decimal digits precision +The typedefs `cpp_dec_float_50` and `cpp_dec_float_100` provide arithmetic types at 50 and 100 decimal digits precision respectively. There is full standard library and `numeric_limits` support available for this type. Things you should know when using this type: -* Default constructed `cpp_dec_float`'s have a value of zero. +* Default constructed `cpp_dec_float`s have a value of zero. * The radix of this type is 10. As a result it can behave subtly differently from base-2 types. * It is not possible to round-trip this type to and from a string and get back to exactly the same value (this is a result of the type having some hidden internal guard digits). @@ -522,14 +534,14 @@ Normally these should not be visible to the user. [section:rational Rational Number Types] -The following backends provide rational number arithmetic: +The following back-ends provide rational number arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] -[[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient backend.][Dependency on GNU licenced [gmp] library.]] +[[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licenced [gmp] library.]] [[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licenced implementation.][Slower than [gmp].]] [[`tommath_rational`][boost/multiprecision/tommath.hpp][2][[tommath]][All C/C++ implementation that's Boost Software Licence compatible.][Slower than [gmp].]] -[[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any inetger backend type to be used as a rational type.][Requires an underlying integer backend type.]] +[[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any inetger back-end type to be used as a rational type.][Requires an underlying integer back-end type.]] [[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `mp_number` integer type.][The expression templates used by `mp_number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]] ] @@ -543,7 +555,7 @@ The following backends provide rational number arithmetic: }} // namespaces -The `gmp_rational` backend is used via the typedef `boost::multiprecision::mpq_rational`. It acts as a thin wrapper around the [gmp] `mpq_t` +The `gmp_rational` back-end is used via the typedef `boost::multiprecision::mpq_rational`. It acts as a thin wrapper around the [gmp] `mpq_t` to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. As well as the usual conversions from arithmetic and string types, instances of `mp_number` are copy constructible @@ -565,7 +577,7 @@ It's also possible to access the underlying `mpq_t` via the `data()` member func Things you should know when using this type: -* Default constructed `mpq_rational`'s have the value zero (this is the [gmp] default behavior). +* Default constructed `mpq_rational`s have the value zero (this is the [gmp] default behavior). * Division by zero results in a hardware exception inside the [gmp] library. * No changes are made to the [gmp] library's global settings, so this type can coexist with existing [gmp] code. @@ -602,7 +614,7 @@ which return the numerator and denominator of the number. Things you should know when using this type: -* Default constructed `cpp_rational`'s have the value zero. +* Default constructed `cpp_rational`s have the value zero. * Division by zero results in a `std::rumtime_error` being thrown. [h5 Example:] @@ -618,7 +630,7 @@ Things you should know when using this type: }} // namespaces -The `tommath_rational` backend is used via the typedef `boost::multiprecision::tom_rational`. It acts as a thin wrapper around +The `tommath_rational` back-end is used via the typedef `boost::multiprecision::tom_rational`. It acts as a thin wrapper around `boost::rational` to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. @@ -634,7 +646,7 @@ which return the numerator and denominator of the number. Things you should know when using this type: -* Default constructed `tom_rational`'s have the value zero (this the inherited Boost.Rational behavior). +* Default constructed `tom_rational`s have the value zero (this the inherited Boost.Rational behavior). * Division by zero results in a `boost::bad_rational` exception being thrown (see the rational number library's docs for more information). * No changes are made to [tommath]'s global state, so this type can safely coexist with other [tommath] code. * Performance of this type has been found to be pretty poor - this need further investigation - but it appears that Boost.Rational @@ -646,7 +658,7 @@ needs some improvement in this area. [h4 Use With Boost.Rational] -All of the inetger types in this library can be used as template arguments to `boost::rational`. +All of the integer types in this library can be used as template arguments to `boost::rational`. Note that using the library in this way largely negates the effect of the expression templates in `mp_number`. @@ -659,10 +671,10 @@ Note that using the library in this way largely negates the effect of the expres }} -The class template `rational_adapter` is a backend for `mp_number` which converts any existing integer backend -into a rational-number backend. +The class template `rational_adapter` is a back-end for `mp_number` which converts any existing integer back-end +into a rational-number back-end. -So for example, given an integer backend type `MyIntegerBackend`, the use would be something like: +So for example, given an integer back-end type `MyIntegerBackend`, the use would be something like: typedef mp_number MyInt; typedef mp_number > MyRational; @@ -719,13 +731,13 @@ The library implements a fairly basic (meaning unoptimized, and possibly slow) M bool miller_rabin_test(const mp_number& n, unsigned trials); These functions perform a Miller-Rabin test for primality, if the result is `false` then /n/ is definitely composite, -while if the result is `true` then /n/ is prime with probability 0.25^trials. The algorithm used is straight out of +while if the result is `true` then /n/ is prime with probability ['0.25^trials]. The algorithm used is straight out of Knuth Vol 2, which recomends 25 trials for a pretty strong likelyhood that /n/ is prime. The third optional argument is for a Uniform Random Number Generator from Boost.Random. When not provided the `mt19937` generator is used. Note that when producing random primes then you should probably use a different random number generator -to produce possible primes, than used internally for testing whether the value is prime. It also helps of course to seed the -generators with some source of randomness. +to produce candidate prime numbers for testing, than is used internally by `miller_rabin_test` for determining +whether the value is prime. It also helps of course to seed the generators with some source of randomness. The following example searches for a prime `p` for which `(p-1)/2` is also probably prime: @@ -918,7 +930,7 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba Class `mp_number` has two template arguments: [variablelist -[[Backend][The actual arithmetic backend that does all the work.]] +[[Backend][The actual arithmetic back-end that does all the work.]] [[ExpressionTemplates][A boolean value: when true, then expression templates are enabled, otherwise they are disabled.]] ] @@ -1023,7 +1035,7 @@ Returns: Backend& backend(); const Backend& backend()const; -Returns the underlying backend instance used by `*this`. +Returns the underlying back-end instance used by `*this`. [h4 Non-member operators] @@ -1083,7 +1095,7 @@ Swaps `a` and `b`. These operators provided formatted input-output operations on `mp_number` types, and expression templates derived from them. -It's down to the backend type to actually implement string conversion. However, the backends provided with +It's down to the back-end type to actually implement string conversion. However, the back-ends provided with this library support all of the iostream formatting flags, field width and precision settings. [h4 Non-member standard library function support] @@ -1299,8 +1311,8 @@ of type B2. [table Optional Requirements on the Backend Type [[Expression][Returns][Comments]] -[[`B(b2)`][`B`][Copy constructor from a different backend type.]] -[[`b = b2`][`b&`][Assignment operator from a different backend type.]] +[[`B(b2)`][`B`][Copy constructor from a different back-end type.]] +[[`b = b2`][`b&`][Assignment operator from a different back-end type.]] [[`assign_components(b, a, a)`][`void`][Assigns to `b` the two components in the following arguments. Only applies to rational and complex number types.]] [[`assign_components(b, b2, b2)`][`void`][Assigns to `b` the two components in the following arguments. @@ -1389,13 +1401,13 @@ of type B2. [[`eval_atan2(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::atan` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] [[`eval_qr(cb, cb2, b, b2)`][`void`][Sets `b` to the result of `cb / cb2` and `b2` to the result of `cb % cb2`. Only required when `B` is an integer type.]] [[`eval_integer_modulus(cb, ui)`][`unsigned`][Returns the result of `cb % ui`. Only required when `B` is an integer type.]] -[[`eval_lsb(cb)`][`unsigned`][Returns the index of the least significant bit that is set.` Only required when `B` is an integer type.]] -[[`eval_bit_test(cb, ui)`][`bool`][Returns true if `cb` has bit `ui` set. Only required when `B` is an integer type.]] +[[`eval_lsb(cb)`][`unsigned`][Returns the index of the least significant bit that is set. Only required when `B` is an integer type.]] +[[`eval_bit_test(cb, ui)`][`bool`][Returns true if `cb` has bit `ui` set. Only required when `B` is an integer type.]] [[`eval_bit_set(b, ui)`][`void`][Sets the bit at index `ui` in `b`. Only required when `B` is an integer type.]] [[`eval_bit_unset(b, ui)`][`void`][Unsets the bit at index `ui` in `b`. Only required when `B` is an integer type.]] [[`eval_bit_flip(b, ui)`][`void`][Flips the bit at index `ui` in `b`. Only required when `B` is an integer type.]] -[[`eval_gcd(b, cb, cb2)`][`void`][Sets `b` to the greatest common divisor of `cb` and `cb2`. Only required when `B` is an integer type.]] -[[`eval_lcm(b, cb, cb2)`][`void`][Sets `b` to the least common multiple of `cb` and `cb2`. Only required when `B` is an integer type.]] +[[`eval_gcd(b, cb, cb2)`][`void`][Sets `b` to the greatest common divisor of `cb` and `cb2`. Only required when `B` is an integer type.]] +[[`eval_lcm(b, cb, cb2)`][`void`][Sets `b` to the least common multiple of `cb` and `cb2`. Only required when `B` is an integer type.]] ] [note @@ -1413,7 +1425,7 @@ in point of fact this naming convension shouldn't be necessary, but rather works These tests test the total time taken to execute all of Boost.Math's test cases for these functions. In each case the best performing library gets a relative score of 1, with the total execution time given in brackets. The first three libraries listed are the various floating point types provided -by this library, while for comparison, two popular C++ frontends to [mpfr] ([mpfr_class] and [mpreal]) +by this library, while for comparison, two popular C++ front-ends to [mpfr] ([mpfr_class] and [mpreal]) are also shown. Test code was compiled with Microsoft Visual Studio 2010 with all optimisations @@ -1452,7 +1464,7 @@ Windows Vista machine. [table [[Integer Type][Relative (and Absolute) Times]] [[mpz_int][1.08279(0.370326s)]] -[[mpz_int (no Expression templates)][1.1702(0.400222s)]]] +[[mpz_int (no Expression templates)][1.1702(0.400222s)]] [[cpp_int][1.3612(0.465547s)]] [[cpp_int (no Expression templates)][1.33286(0.455854s)]] [[cpp_int (64-bit cache)][1.33134(0.455333s)]] @@ -1476,7 +1488,7 @@ altogether - cutting about a third off the total runtime. Note that these tests are carefully designed to test performance of the underlying algorithms and not memory allocation or variable copying. As usual, performance results should be taken -with a healthy dose of scepticsm, and real-world peformance may vary widely depending upon the +with a healthy dose of scepticism, and real-world peformance may vary widely depending upon the specifics of the program. In each table relative times are given first, with the best performer given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 operations. @@ -1546,7 +1558,7 @@ Windows Vista machine. Note that these tests are carefully designed to test performance of the underlying algorithms and not memory allocation or variable copying. As usual, performance results should be taken -with a healthy dose of scepticsm, and real-world peformance may vary widely depending upon the +with a healthy dose of scepticism, and real-world peformance may vary widely depending upon the specifics of the program. In each table relative times are given first, with the best performer given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 operations. @@ -1703,7 +1715,7 @@ Linux x86_64 results are broadly similar, except that libtommath performs much b Note that these tests are carefully designed to test performance of the underlying algorithms and not memory allocation or variable copying. As usual, performance results should be taken -with a healthy dose of scepticsm, and real-world peformance may vary widely depending upon the +with a healthy dose of scepticism, and real-world peformance may vary widely depending upon the specifics of the program. In each table relative times are given first, with the best performer given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 operations. @@ -1771,9 +1783,9 @@ Windows Vista machine. More a list of what ['could] be done, rather than what ['should] be done (which may be a much smaller list!). -* Add backend support for libdecNumber. -* Add an adapter backend for complex number types. -* Add a backend for MPFR interval arithmetic. +* Add back-end support for libdecNumber. +* Add an adapter back-end for complex number types. +* Add a back-end for MPFR interval arithmetic. * Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. * Add assembly level routines to cpp_int_backend. * Add an all C++ binary floating point type. From 1cfbf792a38f08f9c21a7b00b63498e1046ef7e4 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 28 Mar 2012 17:35:38 +0000 Subject: [PATCH 145/256] Fix comment. [SVN r77606] --- example/cpp_int_snips.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/example/cpp_int_snips.cpp b/example/cpp_int_snips.cpp index 942f27d6..191fcecb 100644 --- a/example/cpp_int_snips.cpp +++ b/example/cpp_int_snips.cpp @@ -21,7 +21,7 @@ void t1() std::cout << v << std::endl; // prints 20! - // Try again at arbitrary precision: + // Repeat at arbitrary precision: cpp_int u = 1; for(unsigned i = 1; i <= 100; ++i) u *= i; From e47eee1e5e2d324fe972d8865759a772ed09c89b Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 28 Mar 2012 17:47:41 +0000 Subject: [PATCH 146/256] Update floating point examples to show Boost.Math usage. [SVN r77607] --- doc/html/boost_multiprecision/tut/ints.html | 2 +- doc/html/boost_multiprecision/tut/reals.html | 15 +++++++++++++++ doc/html/index.html | 2 +- example/cpp_dec_float_snips.cpp | 6 ++++++ example/gmp_snips.cpp | 6 ++++++ example/mpfr_snips.cpp | 6 ++++++ 6 files changed, 35 insertions(+), 2 deletions(-) diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html index 591ab4be..8f4c69d7 100644 --- a/doc/html/boost_multiprecision/tut/ints.html +++ b/doc/html/boost_multiprecision/tut/ints.html @@ -295,7 +295,7 @@ std::cout << v << std::endl; // prints 20! -// Try again at arbitrary precision: +// Repeat at arbitrary precision: cpp_int u = 1; for(unsigned i = 1; i <= 100; ++i) u *= i; diff --git a/doc/html/boost_multiprecision/tut/reals.html b/doc/html/boost_multiprecision/tut/reals.html index 23ea5d72..02d1064f 100644 --- a/doc/html/boost_multiprecision/tut/reals.html +++ b/doc/html/boost_multiprecision/tut/reals.html @@ -286,7 +286,12 @@ // Operations at fixed precision and full standard library support: mpf_float_100 b = 2; std::cout << std::numeric_limits<mpf_float_100>::digits << std::endl; +// We can use any C++ std lib function: std::cout << log(b) << std::endl; // print log(2) +// We can also use any function from Boost.Math: +std::cout << boost::math::tgamma(b) << std::endl; +// These even work when the argument is an expression template: +std::cout << boost::math::tgamma(b * b) << std::endl; // Access the underlying representation: mpf_t f; @@ -407,7 +412,12 @@ // Operations at fixed precision and full numeric_limits support: mpfr_float_100 b = 2; std::cout << std::numeric_limits<mpfr_float_100>::digits << std::endl; +// We can use any C++ std lib function: std::cout << log(b) << std::endl; // print log(2) +// We can also use any function from Boost.Math: +std::cout << boost::math::tgamma(b) << std::endl; +// These even work when the argument is an expression template: +std::cout << boost::math::tgamma(b * b) << std::endl; // Access the underlying data: mpfr_t r; @@ -485,7 +495,12 @@ // Operations at fixed precision and full numeric_limits support: cpp_dec_float_100 b = 2; std::cout << std::numeric_limits<cpp_dec_float_100>::digits << std::endl; +// We can use any C++ std lib function: std::cout << log(b) << std::endl; // print log(2) +// We can also use any function from Boost.Math: +std::cout << boost::math::tgamma(b) << std::endl; +// These even work when the argument is an expression template: +std::cout << boost::math::tgamma(b * b) << std::endl;

    diff --git a/doc/html/index.html b/doc/html/index.html index 9b369d6c..75c23b24 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -66,7 +66,7 @@
    - +

    Last revised: March 28, 2012 at 17:05:42 GMT

    Last revised: March 28, 2012 at 17:43:15 GMT
    diff --git a/example/cpp_dec_float_snips.cpp b/example/cpp_dec_float_snips.cpp index 7794c5fe..7f1ec443 100644 --- a/example/cpp_dec_float_snips.cpp +++ b/example/cpp_dec_float_snips.cpp @@ -4,6 +4,7 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ #include +#include #include void t1() @@ -16,7 +17,12 @@ void t1() // Operations at fixed precision and full numeric_limits support: cpp_dec_float_100 b = 2; std::cout << std::numeric_limits::digits << std::endl; + // We can use any C++ std lib function: std::cout << log(b) << std::endl; // print log(2) + // We can also use any function from Boost.Math: + std::cout << boost::math::tgamma(b) << std::endl; + // These even work when the argument is an expression template: + std::cout << boost::math::tgamma(b * b) << std::endl; //] } diff --git a/example/gmp_snips.cpp b/example/gmp_snips.cpp index 511a2894..4ea36103 100644 --- a/example/gmp_snips.cpp +++ b/example/gmp_snips.cpp @@ -4,6 +4,7 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ #include +#include #include void t1() @@ -44,7 +45,12 @@ void t2() // Operations at fixed precision and full standard library support: mpf_float_100 b = 2; std::cout << std::numeric_limits::digits << std::endl; + // We can use any C++ std lib function: std::cout << log(b) << std::endl; // print log(2) + // We can also use any function from Boost.Math: + std::cout << boost::math::tgamma(b) << std::endl; + // These even work when the argument is an expression template: + std::cout << boost::math::tgamma(b * b) << std::endl; // Access the underlying representation: mpf_t f; diff --git a/example/mpfr_snips.cpp b/example/mpfr_snips.cpp index 3eaf6f31..dfecf5e9 100644 --- a/example/mpfr_snips.cpp +++ b/example/mpfr_snips.cpp @@ -4,6 +4,7 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ #include +#include #include void t1() @@ -22,7 +23,12 @@ void t1() // Operations at fixed precision and full numeric_limits support: mpfr_float_100 b = 2; std::cout << std::numeric_limits::digits << std::endl; + // We can use any C++ std lib function: std::cout << log(b) << std::endl; // print log(2) + // We can also use any function from Boost.Math: + std::cout << boost::math::tgamma(b) << std::endl; + // These even work when the argument is an expression template: + std::cout << boost::math::tgamma(b * b) << std::endl; // Access the underlying data: mpfr_t r; From ada7aced0ad4962a99d932cb439a2cf9cccf5aa5 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 28 Mar 2012 17:53:35 +0000 Subject: [PATCH 147/256] Add links to arbitary precision definition. [SVN r77608] --- doc/html/boost_multiprecision/intro.html | 3 ++- doc/html/boost_multiprecision/tut/ints.html | 11 +++++++---- doc/html/boost_multiprecision/tut/random.html | 4 ++-- doc/html/index.html | 2 +- doc/multiprecision.qbk | 12 +++++++----- 5 files changed, 19 insertions(+), 13 deletions(-) diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index 134f9fea..5e4dfde1 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -49,7 +49,8 @@

    The library is often used via one of the predefined typedefs: for example if - you wanted an arbitrary precision integer type using GMP + you wanted an arbitrary + precision integer type using GMP as the underlying implementation then you could use: 

    #include <boost/multiprecision/gmp.hpp>  // Defines the wrappers around the GMP library's types
diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html
index 8f4c69d7..41862d34 100644
--- a/doc/html/boost_multiprecision/tut/ints.html
+++ b/doc/html/boost_multiprecision/tut/ints.html
@@ -86,7 +86,8 @@

    Very versatile, Boost licenced, all C++ integer type which support - both arbitrary precision and fixed precision integer types. + both arbitrary + precision and fixed precision integer types.

    		@@ -201,8 +202,9 @@

    This back-end is the "Swiss Army Knife" of integer types as it - can represent both fixed and arbitrary precision integer types, and both - signed and unsigned types. There are three template arguments: + can represent both fixed and arbitrary + precision integer types, and both signed and unsigned types. There + are three template arguments:

    @@ -221,7 +223,8 @@
    Signed

    Determines whether the resulting type is signed or not. Note that for - arbitrary precision types (where the Allocator parameter is non-void), + arbitrary + precision types (where the Allocator parameter is non-void), then this parameter must be true. For fixed precision types then this type may be either true (type is signed), or false (type is unsigned).

    diff --git a/doc/html/boost_multiprecision/tut/random.html b/doc/html/boost_multiprecision/tut/random.html index 6739f77a..5b7928ff 100644 --- a/doc/html/boost_multiprecision/tut/random.html +++ b/doc/html/boost_multiprecision/tut/random.html @@ -19,8 +19,8 @@

    Random numbers are generated in conjunction with Boost.Random. However, since - Boost.Random is unaware of arbitrary precision numbers, it's necessary to - include the header: + Boost.Random is unaware of arbitrary + precision numbers, it's necessary to include the header: 

    #include <boost/multiprecision/random.hpp>
    diff --git a/doc/html/index.html b/doc/html/index.html index 75c23b24..d6b3fc03 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -66,7 +66,7 @@ - +

    Last revised: March 28, 2012 at 17:43:15 GMT

    Last revised: March 28, 2012 at 17:52:12 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 8cc647ac..c31531b3 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -56,7 +56,7 @@ where possible, but provides Boost license alternatives for users who must have unconstrained license. Which is to say some back-ends rely on 3rd party libraries, but a header-only Boost license version is always available (if somewhat slower). -The library is often used via one of the predefined typedefs: for example if you wanted an arbitrary precision +The library is often used via one of the predefined typedefs: for example if you wanted an [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] integer type using [gmp] as the underlying implementation then you could use: #include // Defines the wrappers around the GMP library's types @@ -238,7 +238,7 @@ The following back-ends provide integer arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] [[`cpp_int`][boost/multiprecision/cpp_int.hpp][2][None] - [Very versatile, Boost licenced, all C++ integer type which support both arbitrary precision and fixed precision integer types.][Slower than [gmp], though typically not as slow as [tommath]]] + [Very versatile, Boost licenced, all C++ integer type which support both [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] and fixed precision integer types.][Slower than [gmp], though typically not as slow as [tommath]]] [[`gmp_int`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licenced [gmp] library.]] [[`tom_int`][boost/multiprecision/tommath.hpp][2][[tommath]][Public domain back-end with no licence restrictions.][Slower than [gmp].]] ] @@ -275,7 +275,8 @@ The `cpp_int_backend` type is used via one of the typedefs `boost::multiprecisio `boost::multiprecision::mp_uint512_t`, `boost::multiprecision::mp_int128_t`, `boost::multiprecision::mp_int256_t` or `boost::multiprecision::mp_int512_t`. -This back-end is the "Swiss Army Knife" of integer types as it can represent both fixed and arbitrary precision +This back-end is the "Swiss Army Knife" of integer types as it can represent both fixed and +[@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] integer types, and both signed and unsigned types. There are three template arguments: [variablelist @@ -285,7 +286,8 @@ integer types, and both signed and unsigned types. There are three template arg values will be stored internally before memory allocation is required. When the Allocator parameter is type `void`, then this field determines the total number of bits in the resulting fixed precision type.]] -[[Signed][Determines whether the resulting type is signed or not. Note that for arbitrary precision types +[[Signed][Determines whether the resulting type is signed or not. Note that for +[@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] types (where the Allocator parameter is non-void), then this parameter must be `true`. For fixed precision types then this type may be either `true` (type is signed), or `false` (type is unsigned).]] [[Allocator][The allocator to use for dymamic memory allocation, or type `void` if this is to be a fixed precision type.]] @@ -690,7 +692,7 @@ So for example, given an integer back-end type `MyIntegerBackend`, the use would [section:random Generating Random Numbers] Random numbers are generated in conjunction with Boost.Random. However, since Boost.Random is unaware -of arbitrary precision numbers, it's necessary to include the header: +of [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] numbers, it's necessary to include the header: #include From ead32b95631e93d70b792bc6a6f60f6d0015d778 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 29 Mar 2012 09:12:08 +0000 Subject: [PATCH 148/256] Squash some MSVC level 4 compiler warnings. [SVN r77623] --- include/boost/multiprecision/cpp_int.hpp | 23 ++++++++++++++----- .../multiprecision/detail/default_ops.hpp | 14 +++++++---- .../multiprecision/detail/mp_number_base.hpp | 4 ++++ include/boost/multiprecision/gmp.hpp | 12 +++++++++- include/boost/multiprecision/mp_number.hpp | 20 ++++++++++++---- test/test_arithmetic.cpp | 17 ++++++++++---- 6 files changed, 69 insertions(+), 21 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 1681a445..c1024a75 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -21,6 +21,12 @@ namespace boost{ namespace multiprecision{ namespace backends{ +#ifdef BOOST_MSVC +// warning C4127: conditional expression is constant +#pragma warning(push) +#pragma warning(disable:4127) +#endif + template > struct cpp_int_backend; @@ -212,7 +218,7 @@ public: } void resize(unsigned new_size) { - m_limbs = (std::min)(new_size, internal_limb_count); + m_limbs = static_cast((std::min)(new_size, internal_limb_count)); } void normalize() { @@ -604,7 +610,7 @@ public: { this->do_swap(o); } - std::string str(std::streamsize digits, std::ios_base::fmtflags f)const + std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const { int base = 10; if((f & std::ios_base::oct) == std::ios_base::oct) @@ -626,7 +632,7 @@ public: int pos = result.size() - 1; for(unsigned i = 0; i < Bits / shift; ++i) { - char c = '0' + (t.limbs()[0] & mask); + char c = '0' + static_cast(t.limbs()[0] & mask); if(c > '9') c += 'A' - '9' - 1; result[pos--] = c; @@ -635,7 +641,7 @@ public: if(Bits % shift) { mask = static_cast((1u << (Bits % shift)) - 1); - char c = '0' + (t.limbs()[0] & mask); + char c = '0' + static_cast(t.limbs()[0] & mask); if(c > '9') c += 'A' - '9'; result[pos] = c; @@ -1268,7 +1274,8 @@ void divide_unsigned_helper(cpp_int_backend* result, if(result) result->resize(1 + r_order - y_order); typename cpp_int_backend::const_limb_pointer prem = r.limbs(); - typename cpp_int_backend::limb_pointer pr; + // This is initialised just to keep the compiler from emitting useless warnings later on: + typename cpp_int_backend::limb_pointer pr = typename cpp_int_backend::limb_pointer(); if(result) { pr = result->limbs(); @@ -1494,7 +1501,8 @@ void divide_unsigned_helper(cpp_int_backend* result, return; } - typename cpp_int_backend::limb_pointer pres; + // This is initialised just to keep the compiler from emitting useless warnings later on: + typename cpp_int_backend::limb_pointer pres = typename cpp_int_backend::limb_pointer(); if(result) { result->resize(r_order + 1); @@ -2282,6 +2290,9 @@ typedef mp_number, false> mp_int256_t; typedef mp_number, false> mp_int512_t; typedef mp_number, false> mp_int1024_t; +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif }} // namespaces diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 9bd53ba7..f85e8194 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -26,6 +26,11 @@ namespace boost{ namespace multiprecision{ namespace default_ops{ +#ifdef BOOST_MSVC +// warning C4127: conditional expression is constant +#pragma warning(push) +#pragma warning(disable:4127) +#endif // // Default versions of mixed arithmetic, these just construct a temporary // from the arithmetic value and then do the arithmetic on that: @@ -108,7 +113,7 @@ template inline bool is_same_object(const T& u, const T&v) { return &u == &v; } template -inline bool is_same_object(const T& u, const U&v) +inline bool is_same_object(const T&, const U&) { return false; } // @@ -528,7 +533,6 @@ template inline bool eval_bit_test(const T& val, unsigned index) { typedef typename boost::multiprecision::detail::canonical::type ui_type; - unsigned result = 0; T mask, t; mask = ui_type(1); eval_left_shift(mask, index); @@ -540,7 +544,6 @@ template inline void eval_bit_set(T& val, unsigned index) { typedef typename boost::multiprecision::detail::canonical::type ui_type; - unsigned result = 0; T mask; mask = ui_type(1); eval_left_shift(mask, index); @@ -551,7 +554,6 @@ template inline void eval_bit_flip(T& val, unsigned index) { typedef typename boost::multiprecision::detail::canonical::type ui_type; - unsigned result = 0; T mask; mask = ui_type(1); eval_left_shift(mask, index); @@ -562,7 +564,6 @@ template inline void eval_bit_unset(T& val, unsigned index) { typedef typename boost::multiprecision::detail::canonical::type ui_type; - unsigned result = 0; T mask, t; mask = ui_type(1); eval_left_shift(mask, index); @@ -1285,6 +1286,9 @@ inline multiprecision::mp_number sinhc_pi(const mu return boost::math::sinhc_pi(x); } +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif } // namespace math } // namespace boost diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index ba349fe4..317462dd 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -249,6 +249,7 @@ struct mp_exp private: typename mp_exp_storage::type arg; + mp_exp& operator=(const mp_exp&); }; template @@ -271,6 +272,7 @@ struct mp_exp private: typename mp_exp_storage::type arg; + mp_exp& operator=(const mp_exp&); }; template @@ -303,6 +305,7 @@ struct mp_exp private: typename mp_exp_storage::type arg1; typename mp_exp_storage::type arg2; + mp_exp& operator=(const mp_exp&); }; template @@ -344,6 +347,7 @@ private: typename mp_exp_storage::type arg1; typename mp_exp_storage::type arg2; typename mp_exp_storage::type arg3; + mp_exp& operator=(const mp_exp&); }; template diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 314fc4cd..a4014cdd 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -21,6 +21,12 @@ namespace boost{ namespace multiprecision{ namespace backends{ +#ifdef BOOST_MSVC +// warning C4127: conditional expression is constant +#pragma warning(push) +#pragma warning(disable:4127) +#endif + template struct gmp_float; @@ -1560,7 +1566,7 @@ struct gmp_rational { mpq_swap(m_data, o.m_data); } - std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const + std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags /*f*/)const { // TODO make a better job of this including handling of f!! void *(*alloc_func_ptr) (size_t); @@ -2053,6 +2059,10 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + } // namespace std #endif diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 33c3c9ba..98df86ec 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -23,6 +23,12 @@ namespace boost{ namespace multiprecision{ +#ifdef BOOST_MSVC +// warning C4127: conditional expression is constant +#pragma warning(push) +#pragma warning(disable:4127) +#endif + template class mp_number { @@ -32,7 +38,7 @@ public: mp_number(){} mp_number(const mp_number& e) : m_backend(e.m_backend){} template - mp_number(V v, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) + mp_number(V v, typename enable_if, is_same, is_convertible > >::type* = 0) { m_backend = canonical_value(v); } @@ -71,7 +77,7 @@ public: } template - mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* dummy1 = 0) + mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) : m_backend(v){} template @@ -576,7 +582,7 @@ private: BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); } template - void check_shift_range(V val, const mpl::false_&, const mpl::false_&){} + void check_shift_range(V, const mpl::false_&, const mpl::false_&){} template void do_assign(const Exp& e, const detail::add_immediates&) @@ -1443,7 +1449,7 @@ private: return is_realy_self(e.value()); } template - bool is_self(const Exp& e, mpl::int_ const&)const + bool is_self(const Exp&, mpl::int_ const&)const { return false; } @@ -1454,7 +1460,7 @@ private: static const Backend& canonical_value(const self_type& v){ return v.m_backend; } template - static typename detail::canonical::type canonical_value(const V& v){ return v; } + static typename detail::canonical::type canonical_value(const V& v){ return static_cast::type>(v); } static typename detail::canonical::type canonical_value(const std::string& v){ return v.c_str(); } static const Backend& function_arg_value(const self_type& v) { return v.backend(); } @@ -1716,6 +1722,10 @@ inline multiprecision::mp_number denominator(const ratio return a.denominator(); } +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + } // namespaces #endif diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 4b3da0a8..ca7a39c1 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -80,6 +80,11 @@ struct number_category > : public mpl::int_ Date: Thu, 29 Mar 2012 12:15:05 +0000 Subject: [PATCH 149/256] Add licence and copyright. [SVN r77624] --- test/test.hpp | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/test/test.hpp b/test/test.hpp index b4d21e1c..2214491f 100644 --- a/test/test.hpp +++ b/test/test.hpp @@ -1,3 +1,8 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// #ifndef BOOST_MULTIPRECISION_TEST_HPP #define BOOST_MULTIPRECISION_TEST_HPP From 0cc1c727d831d717a6b92993c9625ce2042db72f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 29 Mar 2012 12:28:16 +0000 Subject: [PATCH 150/256] Squash some more MSVC level 4 warnings. [SVN r77625] --- include/boost/multiprecision/detail/default_ops.hpp | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index f85e8194..ee90315a 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -671,7 +671,7 @@ inline typename detail::mp_exp::result_type trunc(const detail: } template -inline mp_number trunc(const mp_number& v, const Policy& pol) +inline mp_number trunc(const mp_number& v, const Policy&) { using default_ops::eval_trunc; mp_number result; @@ -769,7 +769,7 @@ inline typename detail::mp_exp::result_type round(const detail: return round(static_cast(v), pol); } template -inline mp_number round(const mp_number& v, const Policy& pol) +inline mp_number round(const mp_number& v, const Policy&) { using default_ops::eval_round; mp_number result; From 43975488162e679e870e30e66f6224b7d6b8dec1 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 29 Mar 2012 12:28:31 +0000 Subject: [PATCH 151/256] Extend examples using Paul Bristow's comments. [SVN r77626] --- example/cpp_dec_float_snips.cpp | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/example/cpp_dec_float_snips.cpp b/example/cpp_dec_float_snips.cpp index 7f1ec443..012ad0ec 100644 --- a/example/cpp_dec_float_snips.cpp +++ b/example/cpp_dec_float_snips.cpp @@ -17,12 +17,18 @@ void t1() // Operations at fixed precision and full numeric_limits support: cpp_dec_float_100 b = 2; std::cout << std::numeric_limits::digits << std::endl; - // We can use any C++ std lib function: - std::cout << log(b) << std::endl; // print log(2) + // Note that digits10 is the same as digits, since we're base 10! : + std::cout << std::numeric_limits::digits10 << std::endl; + // We can use any C++ std lib function, lets print all the digits as well: + std::cout << std::setprecision(std::numeric_limits::max_digits10) + << log(b) << std::endl; // print log(2) // We can also use any function from Boost.Math: std::cout << boost::math::tgamma(b) << std::endl; // These even work when the argument is an expression template: std::cout << boost::math::tgamma(b * b) << std::endl; + // And since we have an extended exponent range we can generate some really large + // numbers here (4.0238726007709377354370243e+2564): + std::cout << boost::math::tgamma(cpp_dec_float_100(1000)) << std::endl; //] } From 3913771ea0984d7bbd43d00a27afb520ad615743 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 29 Mar 2012 18:00:06 +0000 Subject: [PATCH 152/256] Change cpp_dec_float string conversion to generate a better error message when conversion fails. Add generic inter-conversions and tests for them. Fix bug in cpp_int convert_to. [SVN r77630] --- .../boost/multiprecision/cpp_dec_float.hpp | 14 +- include/boost/multiprecision/cpp_int.hpp | 4 +- .../detail/generic_interconvert.hpp | 221 ++++++++++++++++++ include/boost/multiprecision/mp_number.hpp | 21 +- test/Jamfile.v2 | 11 + test/test_generic_conv.cpp | 148 ++++++++++++ 6 files changed, 414 insertions(+), 5 deletions(-) create mode 100644 include/boost/multiprecision/detail/generic_interconvert.hpp create mode 100644 test/test_generic_conv.cpp diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index da5dfe56..91a82f24 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -1804,6 +1804,8 @@ std::string cpp_dec_float::str(boost::intmax_t number_of_digits, std:: template bool cpp_dec_float::rd_string(const char* const s) { + try{ + std::string str(s); // Get a possible exponent and remove it. @@ -1849,7 +1851,7 @@ bool cpp_dec_float::rd_string(const char* const s) *this = this->inf(); return true; } - if((str.size() >= 3) && ((str.substr(0, 3) == "nan") || (str.substr(0, 3) == "NAN"))) + if((str.size() >= 3) && ((str.substr(0, 3) == "nan") || (str.substr(0, 3) == "NAN") || (str.substr(0, 3) == "NaN"))) { *this = this->nan(); return true; @@ -2056,6 +2058,16 @@ bool cpp_dec_float::rd_string(const char* const s) } } + } + catch(const bad_lexical_cast&) + { + // Rethrow with better error message: + std::string msg = "Unable to parse the string \""; + msg += s; + msg += "\" as a floating point value."; + throw std::runtime_error(msg); + } + return true; } diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index c1024a75..a72008c4 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -2025,12 +2025,10 @@ inline typename enable_if, void>::type eval_convert_to(R* result, { *result = static_cast(backend.limbs()[0]); unsigned shift = cpp_int_backend::limb_bits; - for(unsigned i = 1; i < backend.size(); ++i) + for(unsigned i = 1; (i < backend.size()) && (shift < static_cast(std::numeric_limits::digits)); ++i) { *result += static_cast(backend.limbs()[i]) << shift; shift += cpp_int_backend::limb_bits; - if(shift > static_cast(std::numeric_limits::digits)) - break; } if(backend.sign()) { diff --git a/include/boost/multiprecision/detail/generic_interconvert.hpp b/include/boost/multiprecision/detail/generic_interconvert.hpp new file mode 100644 index 00000000..4356e522 --- /dev/null +++ b/include/boost/multiprecision/detail/generic_interconvert.hpp @@ -0,0 +1,221 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MP_GENERIC_INTERCONVERT_HPP +#define BOOST_MP_GENERIC_INTERCONVERT_HPP + +#include + +namespace boost{ namespace multiprecision{ namespace detail{ + +template +void generic_interconvert(To& to, const From& from, const mpl::int_& /*to_type*/, const mpl::int_& /*from_type*/) +{ + using default_ops::eval_get_sign; + using default_ops::eval_bitwise_and; + using default_ops::eval_convert_to; + using default_ops::eval_right_shift; + using default_ops::eval_ldexp; + using default_ops::eval_add; + // smallest unsigned type handled natively by "From" is likely to be it's limb_type: + typedef typename canonical::type limb_type; + // get the corresponding type that we can assign to "To": + typedef typename canonical::type to_type; + From t(from); + bool is_neg = eval_get_sign(t) < 0; + if(is_neg) + t.negate(); + // Pick off the first limb: + limb_type limb; + limb_type mask = ~static_cast(0); + From fl; + eval_bitwise_and(fl, t, mask); + eval_convert_to(&limb, fl); + to = static_cast(limb); + eval_right_shift(t, std::numeric_limits::digits); + // + // Then keep picking off more limbs until "t" is zero: + // + To l; + unsigned shift = std::numeric_limits::digits; + while(!eval_is_zero(t)) + { + eval_bitwise_and(fl, t, mask); + eval_convert_to(&limb, fl); + l = static_cast(limb); + eval_right_shift(t, std::numeric_limits::digits); + eval_ldexp(l, l, shift); + eval_add(to, l); + shift += std::numeric_limits::digits; + } + // + // Finish off by setting the sign: + // + if(is_neg) + to.negate(); +} + +template +void generic_interconvert(To& to, const From& from, const mpl::int_& /*to_type*/, const mpl::int_& /*from_type*/) +{ + using default_ops::eval_get_sign; + using default_ops::eval_bitwise_and; + using default_ops::eval_convert_to; + using default_ops::eval_right_shift; + using default_ops::eval_left_shift; + using default_ops::eval_bitwise_or; + // smallest unsigned type handled natively by "From" is likely to be it's limb_type: + typedef typename canonical::type limb_type; + // get the corresponding type that we can assign to "To": + typedef typename canonical::type to_type; + From t(from); + bool is_neg = eval_get_sign(t) < 0; + if(is_neg) + t.negate(); + // Pick off the first limb: + limb_type limb; + limb_type mask = ~static_cast(0); + From fl; + eval_bitwise_and(fl, t, mask); + eval_convert_to(&limb, fl); + to = static_cast(limb); + eval_right_shift(t, std::numeric_limits::digits); + // + // Then keep picking off more limbs until "t" is zero: + // + To l; + unsigned shift = std::numeric_limits::digits; + while(!eval_is_zero(t)) + { + eval_bitwise_and(fl, t, mask); + eval_convert_to(&limb, fl); + l = static_cast(limb); + eval_right_shift(t, std::numeric_limits::digits); + eval_left_shift(l, shift); + eval_bitwise_or(to, l); + shift += std::numeric_limits::digits; + } + // + // Finish off by setting the sign: + // + if(is_neg) + to.negate(); +} + +template +void generic_interconvert(To& to, const From& from, const mpl::int_& /*to_type*/, const mpl::int_& /*from_type*/) +{ + // + // The code here only works when the radix of "From" is 2, we could try shifting by other + // radixes but it would complicate things.... use a string convertion when the radix is other + // than 2: + // + if(std::numeric_limits >::radix != 2) + { + to = from.str(0, std::ios_base::fmtflags()).c_str(); + return; + } + + + typedef typename canonical::type ui_type; + + using default_ops::eval_fpclassify; + using default_ops::eval_add; + using default_ops::eval_subtract; + using default_ops::eval_convert_to; + + // + // First classify the input, then handle the special cases: + // + int c = eval_fpclassify(from); + + if(c == FP_ZERO) + { + to = ui_type(0); + return; + } + else if(c == FP_NAN) + { + to = "nan"; + return; + } + else if(c == FP_INFINITE) + { + to = "inf"; + if(eval_get_sign(from) < 0) + to.negate(); + return; + } + + typename From::exponent_type e; + From f, term; + to = ui_type(0); + + eval_frexp(f, from, &e); + + static const int shift = std::numeric_limits::digits - 1; + + while(!eval_is_zero(f)) + { + // extract int sized bits from f: + eval_ldexp(f, f, shift); + eval_floor(term, f); + e -= shift; + eval_ldexp(to, to, shift); + long long ll; + eval_convert_to(&ll, term); + eval_add(to, ll); + eval_subtract(f, term); + } + typedef typename To::exponent_type to_exponent; + if((e > (std::numeric_limits::max)()) || (e < (std::numeric_limits::min)())) + { + to = "inf"; + if(eval_get_sign(from) < 0) + to.negate(); + return; + } + eval_ldexp(to, to, static_cast(e)); +} + +template +void generic_interconvert(To& to, const From& from, const mpl::int_& /*to_type*/, const mpl::int_& /*from_type*/) +{ + typedef typename component_type >::type from_component_type; + typedef typename component_type >::type to_component_type; + + mp_number t(from); + to_component_type n(numerator(t)), d(denominator(t)); + using default_ops::assign_components; + assign_components(to, n.backend(), d.backend()); +} + +template +void generic_interconvert(To& to, const From& from, const mpl::int_& /*to_type*/, const mpl::int_& /*from_type*/) +{ + typedef typename component_type >::type to_component_type; + + mp_number t(from); + to_component_type n(t), d(1); + using default_ops::assign_components; + assign_components(to, n.backend(), d.backend()); +} + +template +void generic_interconvert(To& to, const From& from, const mpl::int_& /*to_type*/, const mpl::int_& /*from_type*/) +{ + typedef typename component_type >::type from_component_type; + using default_ops::eval_divide; + + mp_number t(from); + from_component_type n(numerator(t)), d(denominator(t)); + mp_number fn(n), fd(d); + eval_divide(to, fn.backend(), fd.backend()); +} + +}}} // namespaces + +#endif // BOOST_MP_GENERIC_INTERCONVERT_HPP + diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 98df86ec..41f9106c 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -19,7 +19,7 @@ #include #include #include -#include +#include namespace boost{ namespace multiprecision{ @@ -63,6 +63,14 @@ public: { m_backend = val.backend(); } + template + mp_number(const mp_number& val, typename disable_if >::type* dummy1 = 0) + { + // + // Attempt a generic interconvertion: + // + detail::generic_interconvert(backend(), val.backend(), number_category(), number_category()); + } template mp_number(V v1, V v2, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) { @@ -125,6 +133,17 @@ public: return *this; } + template + typename disable_if, mp_number& >::type + operator=(const mp_number& v) + { + // + // Attempt a generic interconvertion: + // + detail::generic_interconvert(backend(), v.backend(), number_category(), number_category()); + return *this; + } + template mp_number(const detail::mp_exp& e) { diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index eeed5577..1e3087ee 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -626,6 +626,17 @@ run test_rational_io.cpp gmp [ check-target-builds ../config//has_gmp : : no ] : test_rational_io_mpz ; +run test_generic_conv.cpp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : TEST_GMP gmp : ] + [ check-target-builds ../config//has_tommath : TEST_TOMMATH $(TOMMATH) : ] + [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr : ] + release + ; + + run ../example/gmp_snips.cpp gmp : # command line : # input files diff --git a/test/test_generic_conv.cpp b/test/test_generic_conv.cpp new file mode 100644 index 00000000..df033f83 --- /dev/null +++ b/test/test_generic_conv.cpp @@ -0,0 +1,148 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include +#include +#include "test.hpp" + +#include +#include +#include + +#ifdef TEST_GMP +#include +#endif +#ifdef TEST_TOMMATH +#include +#endif +#ifdef TEST_MPFR +#include +#endif + +int main() +{ + using namespace boost::multiprecision; + using namespace boost::random; + + independent_bits_engine gen; + + for(unsigned i = 0; i < 100; ++i) + { + cpp_int c = gen(); + // + // Integer to integer conversions first: + // +#ifdef TEST_GMP + mpz_int z(c); + cpp_int t(z); + BOOST_CHECK_EQUAL(t, c); + z = -c; + t = -z; + BOOST_CHECK_EQUAL(t, c); +#endif +#ifdef TEST_TOMMATH + tom_int tom(c); + cpp_int t2(tom); + BOOST_CHECK_EQUAL(t2, c); + tom = -c; + t2 = -tom; + BOOST_CHECK_EQUAL(t2, c); +#endif + // + // Now integer to float: + // + typedef mp_number > dec_float_500; + dec_float_500 df(c); + dec_float_500 df2(c.str()); + BOOST_CHECK_EQUAL(df, df2); + df = -c; + df2 = -df2; + BOOST_CHECK_EQUAL(df, df2); +#ifdef TEST_GMP + typedef mp_number > mpf_type; + mpf_type mpf(c); + mpf_type mpf2(c.str()); + BOOST_CHECK_EQUAL(mpf, mpf2); + mpf = -c; + mpf2 = -mpf2; + BOOST_CHECK_EQUAL(mpf, mpf2); +#endif +#ifdef TEST_MPFR + typedef mp_number > mpfr_type; + mpfr_type mpfr(c); + mpfr_type mpfr2(c.str()); + BOOST_CHECK_EQUAL(mpfr, mpfr2); + mpfr = -c; + mpfr2 = -mpfr2; + BOOST_CHECK_EQUAL(mpfr, mpfr2); +#endif + // + // Now float to float: + // + df = c; + df /= dec_float_500(gen()); + dec_float_500 tol("1e-500"); +#ifdef TEST_GMP + mpf = df; + mpf2 = df.str(); + BOOST_CHECK_EQUAL(mpf, mpf2); + df = mpf; + df2 = mpf.str(); + BOOST_CHECK(fabs((df - df2) / df) < tol); +#endif +#ifdef TEST_MPFR + mpfr = df; + mpfr2 = df.str(); + BOOST_CHECK_EQUAL(mpfr, mpfr2); + df = mpfr; + df2 = mpfr.str(); + BOOST_CHECK(fabs((df - df2) / df) < tol); +#endif + // + // Rational to rational conversions: + // + cpp_rational cppr(c, gen()); +#ifdef TEST_GMP + mpq_rational mpq(cppr); + cpp_rational cppr2(mpq); + BOOST_CHECK_EQUAL(cppr, cppr2); +#endif +#ifdef TEST_TOMMATH + tom_rational tr(cppr); + cpp_rational cppr3(tr); + BOOST_CHECK_EQUAL(cppr, cppr3); +#endif + // + // Integer to rational conversions: + // +#ifdef TEST_GMP + mpq = c; + mpq_rational mpq2 = c.str(); + BOOST_CHECK_EQUAL(mpq, mpq2); +#endif +#ifdef TEST_TOMMATH + tr = c; + tom_rational tr2 = c.str(); + BOOST_CHECK_EQUAL(tr, tr2); +#endif + // + // Rational to float: + // + df = cppr; + df2 = numerator(cppr); + df2 /= dec_float_500(denominator(cppr)); + BOOST_CHECK(fabs(df - df2) / df2 < tol); + } + + return boost::report_errors(); +} + + + From 0e71a0c55e877e9eca523642feb86877fc4cc45d Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 30 Mar 2012 18:33:27 +0000 Subject: [PATCH 153/256] Documentation update, temporarily remove the HTML docs. [SVN r77651] --- doc/Jamfile.v2 | 10 + doc/html/boost_multiprecision/intro.html | 522 --- doc/html/boost_multiprecision/map.html | 38 - doc/html/boost_multiprecision/map/hist.html | 32 - doc/html/boost_multiprecision/map/todo.html | 57 - doc/html/boost_multiprecision/perf.html | 46 - .../perf/float_performance.html | 961 ------ .../perf/int_real_world.html | 217 -- .../perf/integer_performance.html | 3034 ----------------- .../perf/rational_performance.html | 905 ----- .../boost_multiprecision/perf/realworld.html | 278 -- doc/html/boost_multiprecision/ref.html | 38 - .../boost_multiprecision/ref/backendconc.html | 2295 ------------- .../boost_multiprecision/ref/mp_number.html | 695 ---- doc/html/boost_multiprecision/tut.html | 45 - doc/html/boost_multiprecision/tut/ints.html | 503 --- .../boost_multiprecision/tut/primetest.html | 108 - doc/html/boost_multiprecision/tut/random.html | 157 - .../boost_multiprecision/tut/rational.html | 546 --- doc/html/boost_multiprecision/tut/reals.html | 521 --- doc/html/index.html | 75 - doc/index.idx | 11 + doc/multiprecision.qbk | 360 +- 23 files changed, 353 insertions(+), 11101 deletions(-) delete mode 100644 doc/html/boost_multiprecision/intro.html delete mode 100644 doc/html/boost_multiprecision/map.html delete mode 100644 doc/html/boost_multiprecision/map/hist.html delete mode 100644 doc/html/boost_multiprecision/map/todo.html delete mode 100644 doc/html/boost_multiprecision/perf.html delete mode 100644 doc/html/boost_multiprecision/perf/float_performance.html delete mode 100644 doc/html/boost_multiprecision/perf/int_real_world.html delete mode 100644 doc/html/boost_multiprecision/perf/integer_performance.html delete mode 100644 doc/html/boost_multiprecision/perf/rational_performance.html delete mode 100644 doc/html/boost_multiprecision/perf/realworld.html delete mode 100644 doc/html/boost_multiprecision/ref.html delete mode 100644 doc/html/boost_multiprecision/ref/backendconc.html delete mode 100644 doc/html/boost_multiprecision/ref/mp_number.html delete mode 100644 doc/html/boost_multiprecision/tut.html delete mode 100644 doc/html/boost_multiprecision/tut/ints.html delete mode 100644 doc/html/boost_multiprecision/tut/primetest.html delete mode 100644 doc/html/boost_multiprecision/tut/random.html delete mode 100644 doc/html/boost_multiprecision/tut/rational.html delete mode 100644 doc/html/boost_multiprecision/tut/reals.html delete mode 100644 doc/html/index.html create mode 100644 doc/index.idx diff --git a/doc/Jamfile.v2 b/doc/Jamfile.v2 index 7cae9abc..c8568858 100644 --- a/doc/Jamfile.v2 +++ b/doc/Jamfile.v2 @@ -4,8 +4,10 @@ # file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) using quickbook ; +using auto-index ; path-constant images_location : html ; +path-constant here : . ; xml big_number : multiprecision.qbk ; boostbook standalone @@ -62,6 +64,14 @@ boostbook standalone pdf:img.src.path=$(images_location)/ pdf:draft.mode="no" pdf:boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/sf_and_dist/html + # Index generation: + on + $(here)/index.idx + $(here)/../../.. + on + html:on + enable_index + pdf:index.on.type=1 ; install pdf-install : standalone : . PDF ; diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html deleted file mode 100644 index 5e4dfde1..00000000 --- a/doc/html/boost_multiprecision/intro.html +++ /dev/null @@ -1,522 +0,0 @@ - - - -Introduction - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - The Multiprecision Library provides User-defined integer, - rational and floating-point C++ types which try to emulate as closely as practicable - the C++ built-in types, but provide for more range and precision. Depending - upon the number type, precision may be arbitrarily large (limited only by available - memory), fixed at compile time values, for example 50 decimal digits, or a - variable controlled at run-time by member functions. The types are expression-template-enabled - for better performance than naive user-defined types. -

    -

    - The Multiprecision library comes in two distinct parts: -

    -
      -
    • - An expression-template-enabled front-end mp_number - that handles all the operator overloading, expression evaluation optimization, - and code reduction. -
      • -
    • - A selection of back-ends that implement the actual arithmetic operations, - and need conform only to the reduced interface requirements of the front-end. -
      • -
    -

    - Separation of front-end and back-end allows use of highly refined, but restricted - license libraries where possible, but provides Boost license alternatives for - users who must have a portable unconstrained license. Which is to say some - back-ends rely on 3rd party libraries, but a header-only Boost license version - is always available (if somewhat slower). -

    -

    - The library is often used via one of the predefined typedefs: for example if - you wanted an arbitrary - precision integer type using GMP - as the underlying implementation then you could use: -

    -
    #include <boost/multiprecision/gmp.hpp>  // Defines the wrappers around the GMP library's types
-
-boost::multiprecision::mpz_int myint;    // Arbitrary precision integer type.
-
    -

    - Alternatively, you can compose your own multiprecision type, by combining - mp_number with one of the predefined - back-end types. For example, suppose you wanted a 300 decimal digit floating-point - type based on the MPFR library. In - this case, there's no predefined typedef with that level of precision, so instead - we compose our own: -

    -
    #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
-
-namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
-
-typedef mp::mp_number<mp::mpfr_float_backend<300> >  my_float;
-
-my_float a, b, c; // These variables have 300 decimal digits precision
-
    -

    - We can repeat the above example, but with the expression templates disabled - (for faster compile times, but slower runtimes) by passing a second template - argument to mp_number: -

    -
    #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
-
-namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
-
-typedef mp::mp_number<mp::mpfr_float_backend<300>, false>  my_float;
-
-my_float a, b, c; // These variables have 300 decimal digits precision
-
    -
    - - Expression - Templates -
    -

    - Class mp_number is expression-template-enabled: - that means that rather than having a multiplication operator that looks like - this: -

    -
    template <class Backend>
-mp_number<Backend> operator * (const mp_number<Backend>& a, const mp_number<Backend>& b)
-{
-   mp_number<Backend> result(a);
-   result *= b;
-   return result;
-}
-
    -

    - Instead the operator looks more like this: -

    -
    template <class Backend>
-unmentionable-type operator * (const mp_number<Backend>& a, const mp_number<Backend>& b);
-
    -

    - Where the "unmentionable" return type is an implementation detail - that, rather than containing the result of the multiplication, contains instructions - on how to compute the result. In effect it's just a pair of references to the - arguments of the function, plus some compile-time information that stores what - the operation is. -

    -

    - The great advantage of this method is the elimination of temporaries: - for example the "naive" implementation of operator* above, requires one temporary for computing - the result, and at least another one to return it. It's true that sometimes - this overhead can be reduced by using move-semantics, but it can't be eliminated - completely. For example, lets suppose we're evaluating a polynomial via Horners - method, something like this: -

    -
    T a[7] = { /* some values */ };
-//....
-y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0];
-
    -

    - If type T is an mp_number, then this expression is evaluated - without creating a single temporary value. In contrast, - if we were using the C++ wrapper that ships with GMP - - mpfr_class - - then this expression would result in no less than 11 temporaries (this is - true even though mpfr_class - does use expression templates to reduce the number of temporaries somewhat). - Had we used an even simpler wrapper around GMP - or MPFR like mpclass - things would have been even worse and no less that 24 temporaries are created - for this simple expression (note - we actually measure the number of memory - allocations performed rather than the number of temporaries directly). -

    -

    - This library also extends expression template support to standard library functions - like abs or sin - with mp_number arguments. This - means that an expression such as: -

    -
    y = abs(x);
-
    -

    - can be evaluated without a single temporary being calculated. Even expressions - like: -

    -
    y = sin(x);
-
    -

    - get this treatment, so that variable 'y' is used as "working storage" - within the implementation of sin, - thus reducing the number of temporaries used by one. Of course, should you - write: -

    -
    x = sin(x);
-
    -

    - Then we clearly can't use x - as working storage during the calculation, so then a temporary variable is - created in this case. -

    -

    - Given the comments above, you might be forgiven for thinking that expression-templates - are some kind of universal-panacea: sadly though, all tricks like this have - their downsides. For one thing, expression template libraries like this one, - tend to be slower to compile than their simpler cousins, they're also harder - to debug (should you actually want to step through our code!), and rely on - compiler optimizations being turned on to give really good performance. Also, - since the return type from expressions involving mp_numbers - is an "unmentionable implementation detail", you have to be careful - to cast the result of an expression to the actual number type when passing - an expression to a template function. For example, given: -

    -
    template <class T>
-void my_proc(const T&);
-
    -

    - Then calling: -

    -
    my_proc(a+b);
-
    -

    - Will very likely result in obscure error messages inside the body of my_proc - since we've passed it an expression - template type, and not a number type. Instead we probably need: -

    -
    my_proc(my_mp_number_type(a+b));
-
    -

    - Having said that, these situations don't occur that often - or indeed not at - all for non-template functions. In addition, all the functions in the Boost.Math - library will automatically convert expression-template arguments to the underlying - number type without you having to do anything, so: -

    -
    mpfr_float_100 a(20), delta(0.125);
-boost::math::gamma_p(a, a + delta);
-
    -

    - Will work just fine, with the a + delta expression - template argument getting converted to an mpfr_float_100 - internally by the Boost.Math library. -

    -

    - One other potential pitfall that's only possible in C++11: you should never - store an expression template using: -

    -
    auto my_expression = a + b - c;
-
    -

    - unless you're absolutely sure that the lifetimes of a, - b and c - will outlive that of my_expression. -

    -

    - And finally... the performance improvements from an expression template library - like this are often not as dramatic as the reduction in number of temporaries - would suggest. For example if we compare this library with mpfr_class - and mpreal, with - all three using the underlying MPFR - library at 50 decimal digits precision then we see the following typical results - for polynomial execution: -

    -
    -

    Table 1.1. Evaluation of Order 6 Polynomial.

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Library -

    -     		-

    - Relative Time -

    -     		-

    - Relative number of memory allocations -

    -
    -

    - mp_number -

    -     		-

    - 1.0 (0.00793s) -

    -     		-

    - 1.0 (2996 total) -

    -
    -

    - mpfr_class -

    -     		-

    - 1.2 (0.00931s) -

    -     		-

    - 4.3 (12976 total) -

    -
    -

    - mpreal -

    -     		-

    - 1.9 (0.0148s) -

    -     		-

    - 9.3 (27947 total) -

    -
    -
    -

    - As you can see, the execution time increases a lot more slowly than the number - of memory allocations. There are a number of reasons for this: -

    -
      -
    • - The cost of extended-precision multiplication and division is so great, - that the times taken for these tend to swamp everything else. -
      • -
    • - The cost of an in-place multiplication (using operator*=) tends to be more than an out-of-place - operator* - (typically operator *= - has to create a temporary workspace to carry out the multiplication, where - as operator* - can use the target variable as workspace). Since the expression templates - carry out their magic by converting out-of-place operators to in-place - ones, we necessarily take this hit. Even so the transformation is more - efficient than creating the extra temporary variable, just not by as much - as one would hope. -
      • -
    -

    - Finally, note that mp_number - takes a second template argument, which, when set to false - disables all the expression template machinary. The result is much faster to - compile, but slower at runtime. -

    -

    - We'll conclude this section by providing some more performance comparisons - between these three libraries, again, all are using MPFR - to carry out the underlying arithmetic, and all are operating at the same precision - (50 decimal digits): -

    -
    -

    Table 1.2. Evaluation of Boost.Math's Bessel function test data

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Library -

    -     		-

    - Relative Time -

    -     		-

    - Relative Number of Memory Allocations -

    -
    -

    - mp_number -

    -     		-

    - 1.0 (6.21s) -

    -     		-

    - 1.0 (2685469) -

    -
    -

    - mpfr_class -

    -     		-

    - 1.04 (6.45s) -

    -     		-

    - 1.47 (3946007) -

    -
    -

    - mpreal -

    -     		-

    - 1.53 (9.52s) -

    -     		-

    - 4.92 (13222940) -

    -
    -
    -
    -

    Table 1.3. Evaluation of Boost.Math's Non-Central T distribution test data

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Library -

    -     		-

    - Relative Time -

    -     		-

    - Relative Number of Memory Allocations -

    -
    -

    - mp_number -

    -     		-

    - 1.0 (269s) -

    -     		-

    - 1.0 (139082551) -

    -
    -

    - mpfr_class -

    -     		-

    - 1.04 (278s) -

    -     		-

    - 1.81 (252400791) -

    -
    -

    - mpreal -

    -     		-

    - 1.49 (401s) -

    -     		-

    - 3.22 (447009280) -

    -
    -
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/map.html b/doc/html/boost_multiprecision/map.html deleted file mode 100644 index d2f2120d..00000000 --- a/doc/html/boost_multiprecision/map.html +++ /dev/null @@ -1,38 +0,0 @@ - - - -Roadmap - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    -
    History
    -
    TODO
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html deleted file mode 100644 index 28b46cd6..00000000 --- a/doc/html/boost_multiprecision/map/hist.html +++ /dev/null @@ -1,32 +0,0 @@ - - - -History - - - - - - - - -
    -PrevUpHomeNext -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
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    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html deleted file mode 100644 index e849897d..00000000 --- a/doc/html/boost_multiprecision/map/todo.html +++ /dev/null @@ -1,57 +0,0 @@ - - - -TODO - - - - - - - -
    -PrevUpHome -
    -
    -

    -TODO -

    -

    - More a list of what could be done, rather than what - should be done (which may be a much smaller list!). -

    -
      -
    • - Add back-end support for libdecNumber. -
      • -
    • - Add an adapter back-end for complex number types. -
      • -
    • - Add a back-end for MPFR interval arithmetic. -
      • -
    • - Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. -
      • -
    • - Add assembly level routines to cpp_int_backend. -
      • -
    • - Add an all C++ binary floating point type. -
      • -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
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    -
    -PrevUpHome -
    - - diff --git a/doc/html/boost_multiprecision/perf.html b/doc/html/boost_multiprecision/perf.html deleted file mode 100644 index 7460f077..00000000 --- a/doc/html/boost_multiprecision/perf.html +++ /dev/null @@ -1,46 +0,0 @@ - - - -Performance Comparison - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    -
    Floating Point Real - World Tests
    -
    Integer Real - World Tests
    -
    Float Algorithm - Perfomance
    -
    Integer - Algorithm Perfomance
    -
    Rational - Type Perfomance
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
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    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html deleted file mode 100644 index 90f06dcc..00000000 --- a/doc/html/boost_multiprecision/perf/float_performance.html +++ /dev/null @@ -1,961 +0,0 @@ - - - -Float Algorithm Perfomance - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - Note that these tests are carefully designed to test performance of the underlying - algorithms and not memory allocation or variable copying. As usual, performance - results should be taken with a healthy dose of scepticism, and real-world - peformance may vary widely depending upon the specifics of the program. In - each table relative times are given first, with the best performer given - a score of 1. Total actual times are given in brackets, measured in seconds - for 500000 operations. -

    -

    - Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. - The tests were run on 32-bit Windows Vista machine. -

    -
    -

    Table 1.8. Operator +

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1 (0.02382s) -

    -     		-

    - 1 (0.0294619s) -

    -     		-

    - 1 (0.058466s) -

    -
    -

    - gmp_float -

    -     		-

    - 4.55086 (0.108402s) -

    -     		-

    - 3.86443 (0.113853s) -

    -     		-

    - 2.6241 (0.15342s) -

    -
    -

    - mpfr_float -

    -     		-

    - 2.52036 (0.060035s) -

    -     		-

    - 2.1833 (0.0643242s) -

    -     		-

    - 1.37736 (0.0805287s) -

    -
    -
    -
    -

    Table 1.9. Operator +(int)

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1.56759 (0.0527023s) -

    -     		-

    - 1.74629 (0.0618102s) -

    -     		-

    - 1.68077 (0.105927s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (0.0336201s) -

    -     		-

    - 1 (0.0353951s) -

    -     		-

    - 1 (0.0630232s) -

    -
    -

    - mpfr_float -

    -     		-

    - 3.14875 (0.105861s) -

    -     		-

    - 3.15499 (0.111671s) -

    -     		-

    - 1.92831 (0.121528s) -

    -
    -
    -
    -

    Table 1.10. Operator -

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1 (0.0265783s) -

    -     		-

    - 1 (0.031465s) -

    -     		-

    - 1 (0.0619405s) -

    -
    -

    - gmp_float -

    -     		-

    - 4.66954 (0.124108s) -

    -     		-

    - 3.72645 (0.117253s) -

    -     		-

    - 2.67536 (0.165713s) -

    -
    -

    - mpfr_float -

    -     		-

    - 2.7909 (0.0741774s) -

    -     		-

    - 2.48557 (0.0782083s) -

    -     		-

    - 1.50944 (0.0934957s) -

    -
    -
    -
    -

    Table 1.11. Operator -(int)

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1 (0.0577674s) -

    -     		-

    - 1 (0.0633795s) -

    -     		-

    - 1 (0.11146s) -

    -
    -

    - gmp_float -

    -     		-

    - 2.31811 (0.133911s) -

    -     		-

    - 2.07251 (0.131355s) -

    -     		-

    - 1.67161 (0.186319s) -

    -
    -

    - mpfr_float -

    -     		-

    - 2.45081 (0.141577s) -

    -     		-

    - 2.29174 (0.145249s) -

    -     		-

    - 1.395 (0.155487s) -

    -
    -
    -
    -

    Table 1.12. Operator *

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1.07276 (0.287898s) -

    -     		-

    - 1.47724 (0.584569s) -

    -     		-

    - 1.55145 (5.09969s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (0.268372s) -

    -     		-

    - 1 (0.395718s) -

    -     		-

    - 1 (3.28705s) -

    -
    -

    - mpfr_float -

    -     		-

    - 1.27302 (0.341642s) -

    -     		-

    - 1.17649 (0.465557s) -

    -     		-

    - 1.14029 (3.7482s) -

    -
    -
    -
    -

    Table 1.13. Operator *(int)

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 2.89945 (0.11959s) -

    -     		-

    - 4.56335 (0.197945s) -

    -     		-

    - 9.03602 (0.742044s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (0.0412457s) -

    -     		-

    - 1 (0.0433772s) -

    -     		-

    - 1 (0.0821206s) -

    -
    -

    - mpfr_float -

    -     		-

    - 3.6951 (0.152407s) -

    -     		-

    - 3.71977 (0.161353s) -

    -     		-

    - 3.30958 (0.271785s) -

    -
    -
    -
    -

    Table 1.14. Operator /

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 3.24327 (4.00108s) -

    -     		-

    - 5.00532 (8.12985s) -

    -     		-

    - 6.79566 (54.2796s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (1.23366s) -

    -     		-

    - 1 (1.62424s) -

    -     		-

    - 1 (7.9874s) -

    -
    -

    - mpfr_float -

    -     		-

    - 1.32521 (1.63486s) -

    -     		-

    - 1.38967 (2.25716s) -

    -     		-

    - 1.72413 (13.7713s) -

    -
    -
    -
    -

    Table 1.15. Operator /(int)

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1.45093 (0.253675s) -

    -     		-

    - 1.83306 (0.419569s) -

    -     		-

    - 2.3644 (1.64187s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (0.174836s) -

    -     		-

    - 1 (0.22889s) -

    -     		-

    - 1 (0.694411s) -

    -
    -

    - mpfr_float -

    -     		-

    - 1.16731 (0.204088s) -

    -     		-

    - 1.13211 (0.259127s) -

    -     		-

    - 1.02031 (0.708513s) -

    -
    -
    -
    -

    Table 1.16. Operator str

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1.4585 (0.0188303s) -

    -     		-

    - 1.55515 (0.03172s) -

    -     		-

    - 1 (0.131962s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (0.0129107s) -

    -     		-

    - 1 (0.0203967s) -

    -     		-

    - 1.04632 (0.138075s) -

    -
    -

    - mpfr_float -

    -     		-

    - 2.19015 (0.0282764s) -

    -     		-

    - 1.84679 (0.0376683s) -

    -     		-

    - 1.20295 (0.158743s) -

    -
    -
    -

    - ] -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html deleted file mode 100644 index 89278b58..00000000 --- a/doc/html/boost_multiprecision/perf/int_real_world.html +++ /dev/null @@ -1,217 +0,0 @@ - - - -Integer Real World Tests - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - These tests - measure the time taken to generate 1000 128-bit random numbers and test for - primality using the Miller Rabin test. -

    -

    - Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and libtommath-0.42.0. - The tests were run on 32-bit Windows Vista machine. -

    -
    ---- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Integer Type -

    -     		-

    - Relative (and Absolute) Times -

    -
    -

    - mpz_int -

    -     		-

    - 1.08279(0.370326s) -

    -
    -

    - mpz_int (no Expression templates) -

    -     		-

    - 1.1702(0.400222s) -

    -
    -

    - cpp_int -

    -     		-

    - 1.3612(0.465547s) -

    -
    -

    - cpp_int (no Expression templates) -

    -     		-

    - 1.33286(0.455854s) -

    -
    -

    - cpp_int (64-bit cache) -

    -     		-

    - 1.33134(0.455333s) -

    -
    -

    - cpp_int (256-bit cache) -

    -     		-

    - 1.29367(0.442451s) -

    -
    -

    - cpp_int (512-bit cache) -

    -     		-

    - 1.08821(0.37218s) -

    -
    -

    - cpp_int (1024-bit cache) -

    -     		-

    - 1.07902(0.369037s) -

    -
    -

    - mp_int1024_t -

    -     		-

    - 1.02616(0.35096s) -

    -
    -

    - mp_int1024_t (no Expression templates) -

    -     		-

    - 1(0.342011s) -

    -
    -

    - tom_int -

    -     		-

    - 3.74233(1.27992s) -

    -
    -

    - tom_int (no Expression templates) -

    -     		-

    - 3.97646(1.35999s) -

    -
    -

    - It's interesting to note that expression templates have little effect here - - perhaps because the actual expressions involved are relatively trivial - in this case - so the time taken for multiplication and division tends to - dominate. Also note how increasing the internal cache size used by cpp_int is quite effective in this case - in cutting out memory allocations altogether - cutting about a third off - the total runtime. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html deleted file mode 100644 index 6ad820a4..00000000 --- a/doc/html/boost_multiprecision/perf/integer_performance.html +++ /dev/null @@ -1,3034 +0,0 @@ - - - -Integer Algorithm Perfomance - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - Note that these tests are carefully designed to test performance of the underlying - algorithms and not memory allocation or variable copying. As usual, performance - results should be taken with a healthy dose of scepticism, and real-world - peformance may vary widely depending upon the specifics of the program. In - each table relative times are given first, with the best performer given - a score of 1. Total actual times are given in brackets, measured in seconds - for 500000 operations. -

    -

    - Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. - The tests were run on 32-bit Windows Vista machine. -

    -

    - Linux x86_64 results are broadly similar, except that libtommath performs - much better there. -

    -
    -

    Table 1.17. Operator +

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.24574 (0.0270133s) -

    -     		-

    - 1.09665 (0.0352319s) -

    -     		-

    - 1.25708 (0.0524047s) -

    -     		-

    - 1.31488 (0.08777s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1.05787 (0.0229394s) -

    -     		-

    - 1 (0.0321268s) -

    -     		-

    - 1.16171 (0.0484289s) -

    -     		-

    - 1.24017 (0.0827832s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.08016 (0.0451073s) -

    -     		-

    - 1.33792 (0.042983s) -

    -     		-

    - 1.19676 (0.0498904s) -

    -     		-

    - 1 (0.0667514s) -

    -
    -

    - tommath_int -

    -     		-

    - 1 (0.0216845s) -

    -     		-

    - 1.07779 (0.0346258s) -

    -     		-

    - 1 (0.0416877s) -

    -     		-

    - 1.06344 (0.0709863s) -

    -
    -
    -
    -

    Table 1.18. Operator +(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.46244 (0.0202077s) -

    -     		-

    - 1.20665 (0.0238576s) -

    -     		-

    - 1.17647 (0.0258293s) -

    -     		-

    - 1.12424 (0.0317931s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0138178s) -

    -     		-

    - 1 (0.0197719s) -

    -     		-

    - 1 (0.0219548s) -

    -     		-

    - 1 (0.0282796s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.15321 (0.0297527s) -

    -     		-

    - 2.09834 (0.041488s) -

    -     		-

    - 2.89935 (0.0636546s) -

    -     		-

    - 3.70262 (0.104709s) -

    -
    -

    - tommath_int -

    -     		-

    - 17.1419 (0.236864s) -

    -     		-

    - 12.9762 (0.256563s) -

    -     		-

    - 12.3275 (0.270648s) -

    -     		-

    - 10.7373 (0.303648s) -

    -
    -
    -
    -

    Table 1.19. Operator -

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.15385 (0.029665s) -

    -     		-

    - 1.08217 (0.0369886s) -

    -     		-

    - 1.05882 (0.051534s) -

    -     		-

    - 1.12132 (0.0822725s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0257095s) -

    -     		-

    - 1 (0.0341801s) -

    -     		-

    - 1 (0.0486711s) -

    -     		-

    - 1.08659 (0.0797242s) -

    -
    -

    - gmp_int -

    -     		-

    - 1.56685 (0.040283s) -

    -     		-

    - 1.32917 (0.0454312s) -

    -     		-

    - 1.06917 (0.0520378s) -

    -     		-

    - 1 (0.0733708s) -

    -
    -

    - tommath_int -

    -     		-

    - 1.059 (0.0272264s) -

    -     		-

    - 1.16974 (0.0399818s) -

    -     		-

    - 1.01303 (0.0493054s) -

    -     		-

    - 1.03375 (0.0758472s) -

    -
    -
    -
    -

    Table 1.20. Operator -(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.51665 (0.0157196s) -

    -     		-

    - 1.31513 (0.0200533s) -

    -     		-

    - 1.29599 (0.0235066s) -

    -     		-

    - 1.21534 (0.0266136s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0103647s) -

    -     		-

    - 1 (0.0152482s) -

    -     		-

    - 1 (0.018138s) -

    -     		-

    - 1 (0.021898s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.7938 (0.0289568s) -

    -     		-

    - 2.55493 (0.038958s) -

    -     		-

    - 3.12248 (0.0566356s) -

    -     		-

    - 4.48855 (0.0982904s) -

    -
    -

    - tommath_int -

    -     		-

    - 20.8695 (0.216305s) -

    -     		-

    - 15.0705 (0.229797s) -

    -     		-

    - 13.4093 (0.243217s) -

    -     		-

    - 12.2599 (0.268468s) -

    -
    -
    -
    -

    Table 1.21. Operator *

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.29504 (0.0731032s) -

    -     		-

    - 1.55431 (0.196132s) -

    -     		-

    - 1.4363 (0.656569s) -

    -     		-

    - 1.63701 (2.47859s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0564485s) -

    -     		-

    - 1.16604 (0.147138s) -

    -     		-

    - 1 (0.457124s) -

    -     		-

    - 1 (1.5141s) -

    -
    -

    - gmp_int -

    -     		-

    - 1.19574 (0.0674975s) -

    -     		-

    - 1 (0.126186s) -

    -     		-

    - 1.16627 (0.53313s) -

    -     		-

    - 1.02906 (1.5581s) -

    -
    -

    - tommath_int -

    -     		-

    - 1.97229 (0.111333s) -

    -     		-

    - 2.67087 (0.337027s) -

    -     		-

    - 2.13031 (0.973817s) -

    -     		-

    - 2.05869 (3.11706s) -

    -
    -
    -
    -

    Table 1.22. Operator *(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.34609 (0.030315s) -

    -     		-

    - 1.57086 (0.0407838s) -

    -     		-

    - 1.60154 (0.0542267s) -

    -     		-

    - 1.67808 (0.0804984s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1.29783 (0.0292279s) -

    -     		-

    - 1.58263 (0.0410894s) -

    -     		-

    - 1.61543 (0.054697s) -

    -     		-

    - 1.66841 (0.0800346s) -

    -
    -

    - gmp_int -

    -     		-

    - 1 (0.0225207s) -

    -     		-

    - 1 (0.0259628s) -

    -     		-

    - 1 (0.033859s) -

    -     		-

    - 1 (0.0479706s) -

    -
    -

    - tommath_int -

    -     		-

    - 12.4278 (0.279882s) -

    -     		-

    - 11.9045 (0.309074s) -

    -     		-

    - 10.5973 (0.358813s) -

    -     		-

    - 9.47384 (0.454466s) -

    -
    -
    -
    -

    Table 1.23. Operator /

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 2.86387 (0.593314s) -

    -     		-

    - 2.18375 (0.69965s) -

    -     		-

    - 1.72571 (0.918294s) -

    -     		-

    - 1.39251 (1.33801s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.207172s) -

    -     		-

    - 1 (0.320389s) -

    -     		-

    - 1 (0.532127s) -

    -     		-

    - 1 (0.960856s) -

    -
    -

    - gmp_int -

    -     		-

    - 3.89115 (0.806137s) -

    -     		-

    - 2.87573 (0.921352s) -

    -     		-

    - 1.96635 (1.04635s) -

    -     		-

    - 1.29618 (1.24544s) -

    -
    -

    - tommath_int -

    -     		-

    - 11.9483 (2.47535s) -

    -     		-

    - 9.35941 (2.99865s) -

    -     		-

    - 8.79014 (4.67747s) -

    -     		-

    - 11.8316 (11.3684s) -

    -
    -
    -
    -

    Table 1.24. Operator /(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 5.77003 (0.313196s) -

    -     		-

    - 4.38067 (0.431864s) -

    -     		-

    - 3.55054 (0.634559s) -

    -     		-

    - 2.97898 (1.03205s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 2.48952 (0.135131s) -

    -     		-

    - 2.59188 (0.255519s) -

    -     		-

    - 2.56716 (0.458808s) -

    -     		-

    - 2.52368 (0.874313s) -

    -
    -

    - gmp_int -

    -     		-

    - 1 (0.0542797s) -

    -     		-

    - 1 (0.0985842s) -

    -     		-

    - 1 (0.178722s) -

    -     		-

    - 1 (0.346443s) -

    -
    -

    - tommath_int -

    -     		-

    - 31.6477 (1.71783s) -

    -     		-

    - 22.8727 (2.25489s) -

    -     		-

    - 19.9248 (3.56101s) -

    -     		-

    - 24.3266 (8.42779s) -

    -
    -
    -
    -

    Table 1.25. Operator %

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.9813 (0.357541s) -

    -     		-

    - 1.55667 (0.460146s) -

    -     		-

    - 1.35341 (0.681144s) -

    -     		-

    - 1.19906 (1.10138s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.180457s) -

    -     		-

    - 1 (0.295597s) -

    -     		-

    - 1 (0.503278s) -

    -     		-

    - 1 (0.918538s) -

    -
    -

    - gmp_int -

    -     		-

    - 3.50213 (0.631985s) -

    -     		-

    - 2.33312 (0.689662s) -

    -     		-

    - 1.57264 (0.791475s) -

    -     		-

    - 1.07795 (0.99014s) -

    -
    -

    - tommath_int -

    -     		-

    - 12.2393 (2.20868s) -

    -     		-

    - 10.1123 (2.98915s) -

    -     		-

    - 9.46676 (4.76442s) -

    -     		-

    - 12.1795 (11.1873s) -

    -
    -
    -
    -

    Table 1.26. Operator %(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.88485 (0.105552s) -

    -     		-

    - 2.00194 (0.203711s) -

    -     		-

    - 2.08202 (0.380096s) -

    -     		-

    - 2.12794 (0.752068s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1.7474 (0.0978544s) -

    -     		-

    - 1.88457 (0.191768s) -

    -     		-

    - 2.0306 (0.37071s) -

    -     		-

    - 2.0851 (0.736929s) -

    -
    -

    - gmp_int -

    -     		-

    - 1 (0.0560001s) -

    -     		-

    - 1 (0.101757s) -

    -     		-

    - 1 (0.182561s) -

    -     		-

    - 1 (0.353426s) -

    -
    -

    - tommath_int -

    -     		-

    - 30.4466 (1.70501s) -

    -     		-

    - 22.2997 (2.26915s) -

    -     		-

    - 19.6199 (3.58184s) -

    -     		-

    - 24.0694 (8.50676s) -

    -
    -
    -
    -

    Table 1.27. Operator <<

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.20362 (0.0224696s) -

    -     		-

    - 1.08555 (0.0294403s) -

    -     		-

    - 1 (0.0360516s) -

    -     		-

    - 1.07177 (0.0523935s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0186683s) -

    -     		-

    - 1 (0.0271201s) -

    -     		-

    - 1.02126 (0.036818s) -

    -     		-

    - 1 (0.0488848s) -

    -
    -

    - gmp_int -

    -     		-

    - 1.36706 (0.0255207s) -

    -     		-

    - 1.12042 (0.0303858s) -

    -     		-

    - 1.24359 (0.0448335s) -

    -     		-

    - 1.40143 (0.0685085s) -

    -
    -

    - tommath_int -

    -     		-

    - 2.09357 (0.0390833s) -

    -     		-

    - 2.4569 (0.0666312s) -

    -     		-

    - 2.63592 (0.0950291s) -

    -     		-

    - 3.43638 (0.167987s) -

    -
    -
    -
    -

    Table 1.28. Operator >>

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.33649 (0.0210319s) -

    -     		-

    - 1.12919 (0.0266135s) -

    -     		-

    - 1.10413 (0.0307184s) -

    -     		-

    - 1.09267 (0.0399373s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0157367s) -

    -     		-

    - 1 (0.0235686s) -

    -     		-

    - 1 (0.0278214s) -

    -     		-

    - 1.05198 (0.0384501s) -

    -
    -

    - gmp_int -

    -     		-

    - 1.72135 (0.0270884s) -

    -     		-

    - 1.2078 (0.0284661s) -

    -     		-

    - 1.16066 (0.0322912s) -

    -     		-

    - 1 (0.0365503s) -

    -
    -

    - tommath_int -

    -     		-

    - 15.4381 (0.242945s) -

    -     		-

    - 11.8797 (0.279987s) -

    -     		-

    - 10.9043 (0.303374s) -

    -     		-

    - 14.0762 (0.514491s) -

    -
    -
    -
    -

    Table 1.29. Operator &

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.65829 (0.0314059s) -

    -     		-

    - 1.42198 (0.0390384s) -

    -     		-

    - 1.48578 (0.0498903s) -

    -     		-

    - 1.51243 (0.0770342s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0189387s) -

    -     		-

    - 1 (0.0274536s) -

    -     		-

    - 1 (0.0335786s) -

    -     		-

    - 1 (0.0509341s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.80248 (0.0530755s) -

    -     		-

    - 2.39752 (0.0658206s) -

    -     		-

    - 2.66009 (0.089322s) -

    -     		-

    - 2.73942 (0.13953s) -

    -
    -

    - tommath_int -

    -     		-

    - 6.95432 (0.131706s) -

    -     		-

    - 5.4059 (0.148412s) -

    -     		-

    - 4.56887 (0.153417s) -

    -     		-

    - 6.5696 (0.334616s) -

    -
    -
    -
    -

    Table 1.30. Operator &(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.63285 (0.0472296s) -

    -     		-

    - 1.43344 (0.0588492s) -

    -     		-

    - 1.33141 (0.0724386s) -

    -     		-

    - 1.21353 (0.104144s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0289247s) -

    -     		-

    - 1 (0.0410546s) -

    -     		-

    - 1 (0.0544075s) -

    -     		-

    - 1 (0.0858187s) -

    -
    -

    - gmp_int -

    -     		-

    - 5.24478 (0.151704s) -

    -     		-

    - 3.81907 (0.15679s) -

    -     		-

    - 2.77979 (0.151242s) -

    -     		-

    - 1.84209 (0.158086s) -

    -
    -

    - tommath_int -

    -     		-

    - 11.7257 (0.339163s) -

    -     		-

    - 8.6379 (0.354625s) -

    -     		-

    - 6.90411 (0.375636s) -

    -     		-

    - 7.63253 (0.655013s) -

    -
    -
    -
    -

    Table 1.31. Operator ^

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.39325 (0.0297525s) -

    -     		-

    - 1.28821 (0.0385005s) -

    -     		-

    - 1.18843 (0.0492426s) -

    -     		-

    - 1.07724 (0.0758668s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0213547s) -

    -     		-

    - 1 (0.0298868s) -

    -     		-

    - 1 (0.041435s) -

    -     		-

    - 1 (0.070427s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.28582 (0.048813s) -

    -     		-

    - 2.03478 (0.0608129s) -

    -     		-

    - 2.05655 (0.0852131s) -

    -     		-

    - 1.92381 (0.135488s) -

    -
    -

    - tommath_int -

    -     		-

    - 6.17078 (0.131775s) -

    -     		-

    - 4.8567 (0.145151s) -

    -     		-

    - 3.64659 (0.151097s) -

    -     		-

    - 4.78192 (0.336776s) -

    -
    -
    -
    -

    Table 1.32. Operator ^(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.89396 (0.0383127s) -

    -     		-

    - 1.64269 (0.043417s) -

    -     		-

    - 1.5386 (0.0477162s) -

    -     		-

    - 1.32247 (0.0568053s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0202288s) -

    -     		-

    - 1 (0.0264305s) -

    -     		-

    - 1 (0.0310128s) -

    -     		-

    - 1 (0.0429539s) -

    -
    -

    - gmp_int -

    -     		-

    - 7.01953 (0.141997s) -

    -     		-

    - 5.47513 (0.14471s) -

    -     		-

    - 4.6627 (0.144603s) -

    -     		-

    - 3.59601 (0.154463s) -

    -
    -

    - tommath_int -

    -     		-

    - 16.2706 (0.329134s) -

    -     		-

    - 12.9494 (0.342258s) -

    -     		-

    - 11.3305 (0.35139s) -

    -     		-

    - 14.1712 (0.608709s) -

    -
    -
    -
    -

    Table 1.33. Operator |

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.34742 (0.0296944s) -

    -     		-

    - 1.25923 (0.0384846s) -

    -     		-

    - 1.20517 (0.0493908s) -

    -     		-

    - 1.10536 (0.0761343s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0220379s) -

    -     		-

    - 1 (0.030562s) -

    -     		-

    - 1 (0.0409823s) -

    -     		-

    - 1 (0.0688775s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.14429 (0.0472558s) -

    -     		-

    - 1.95901 (0.0598712s) -

    -     		-

    - 2.07584 (0.0850728s) -

    -     		-

    - 1.94265 (0.133805s) -

    -
    -

    - tommath_int -

    -     		-

    - 5.98286 (0.13185s) -

    -     		-

    - 4.65705 (0.142329s) -

    -     		-

    - 3.85812 (0.158115s) -

    -     		-

    - 4.81524 (0.331662s) -

    -
    -
    -
    -

    Table 1.34. Operator |(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.40808 (0.0389721s) -

    -     		-

    - 1.65035 (0.0437872s) -

    -     		-

    - 1.51667 (0.0466144s) -

    -     		-

    - 1.37806 (0.0582842s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0276775s) -

    -     		-

    - 1 (0.026532s) -

    -     		-

    - 1 (0.0307348s) -

    -     		-

    - 1 (0.0422945s) -

    -
    -

    - gmp_int -

    -     		-

    - 5.31451 (0.147092s) -

    -     		-

    - 5.37333 (0.142565s) -

    -     		-

    - 4.86508 (0.149527s) -

    -     		-

    - 3.74364 (0.158335s) -

    -
    -

    - tommath_int -

    -     		-

    - 11.9312 (0.330226s) -

    -     		-

    - 12.943 (0.343403s) -

    -     		-

    - 11.4457 (0.35178s) -

    -     		-

    - 14.4462 (0.610997s) -

    -
    -
    -
    -

    Table 1.35. Operator gcd

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.82514 (4.45586s) -

    -     		-

    - 1.75955 (10.1748s) -

    -     		-

    - 1.87025 (25.23s) -

    -     		-

    - 2.11453 (68.8556s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1.57965 (3.85654s) -

    -     		-

    - 1.67404 (9.68027s) -

    -     		-

    - 1.8405 (24.8287s) -

    -     		-

    - 2.27588 (74.1096s) -

    -
    -

    - gmp_int -

    -     		-

    - 1 (2.44138s) -

    -     		-

    - 1 (5.78259s) -

    -     		-

    - 1 (13.4902s) -

    -     		-

    - 1 (32.5631s) -

    -
    -

    - tommath_int -

    -     		-

    - 5.01357 (12.24s) -

    -     		-

    - 4.38161 (25.337s) -

    -     		-

    - 4.08681 (55.1319s) -

    -     		-

    - 4.01045 (130.593s) -

    -
    -
    -
    -

    Table 1.36. Operator str

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.46421 (0.00195137s) -

    -     		-

    - 1.21669 (0.00319216s) -

    -     		-

    - 1.25041 (0.00765237s) -

    -     		-

    - 1.53339 (0.0218096s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.00133271s) -

    -     		-

    - 1 (0.00262366s) -

    -     		-

    - 1.0109 (0.00618661s) -

    -     		-

    - 1.24429 (0.0176978s) -

    -
    -

    - gmp_int -

    -     		-

    - 1.7777 (0.00236916s) -

    -     		-

    - 1.27408 (0.00334274s) -

    -     		-

    - 1 (0.00611991s) -

    -     		-

    - 1 (0.0142232s) -

    -
    -

    - tommath_int -

    -     		-

    - 11.9797 (0.0159654s) -

    -     		-

    - 18.3349 (0.0481046s) -

    -     		-

    - 18.3681 (0.112411s) -

    -     		-

    - 25.0355 (0.356085s) -

    -
    -
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/perf/rational_performance.html b/doc/html/boost_multiprecision/perf/rational_performance.html deleted file mode 100644 index 6754381e..00000000 --- a/doc/html/boost_multiprecision/perf/rational_performance.html +++ /dev/null @@ -1,905 +0,0 @@ - - - -Rational Type Perfomance - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - Note that these tests are carefully designed to test performance of the underlying - algorithms and not memory allocation or variable copying. As usual, performance - results should be taken with a healthy dose of scepticism, and real-world - peformance may vary widely depending upon the specifics of the program. In - each table relative times are given first, with the best performer given - a score of 1. Total actual times are given in brackets, measured in seconds - for 500000 operations. -

    -

    - Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. - The tests were run on 32-bit Windows Vista machine. -

    -
    -

    Table 1.37. Operator +

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 5.91758 (18.1263s) -

    -     		-

    - 6.60754 (44.1182s) -

    -     		-

    - 6.65334 (103.169s) -

    -     		-

    - 6.44717 (244.055s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (3.06312s) -

    -     		-

    - 1 (6.67695s) -

    -     		-

    - 1 (15.5064s) -

    -     		-

    - 1 (37.8546s) -

    -
    -
    -
    -

    Table 1.38. Operator +(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 3.98512 (2.67249s) -

    -     		-

    - 4.24335 (3.04309s) -

    -     		-

    - 4.65009 (3.83046s) -

    -     		-

    - 5.45832 (5.08346s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (0.670618s) -

    -     		-

    - 1 (0.717144s) -

    -     		-

    - 1 (0.823739s) -

    -     		-

    - 1 (0.931322s) -

    -
    -
    -
    -

    Table 1.39. Operator -

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 5.91504 (18.2374s) -

    -     		-

    - 6.55676 (43.8659s) -

    -     		-

    - 6.66239 (103.481s) -

    -     		-

    - 6.47224 (244.887s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (3.08322s) -

    -     		-

    - 1 (6.69018s) -

    -     		-

    - 1 (15.5321s) -

    -     		-

    - 1 (37.8365s) -

    -
    -
    -
    -

    Table 1.40. Operator -(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 3.96173 (2.66785s) -

    -     		-

    - 4.36532 (3.09023s) -

    -     		-

    - 4.59363 (3.74494s) -

    -     		-

    - 5.43075 (5.09156s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (0.673405s) -

    -     		-

    - 1 (0.707904s) -

    -     		-

    - 1 (0.815246s) -

    -     		-

    - 1 (0.937541s) -

    -
    -
    -
    -

    Table 1.41. Operator *

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 5.59286 (32.3559s) -

    -     		-

    - 6.54125 (82.4247s) -

    -     		-

    - 6.8815 (197.198s) -

    -     		-

    - 6.84066 (473.057s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (5.78521s) -

    -     		-

    - 1 (12.6008s) -

    -     		-

    - 1 (28.6562s) -

    -     		-

    - 1 (69.1537s) -

    -
    -
    -
    -

    Table 1.42. Operator *(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 2.70193 (3.1466s) -

    -     		-

    - 3.10134 (3.79056s) -

    -     		-

    - 3.659 (4.93935s) -

    -     		-

    - 4.61372 (6.89845s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (1.16457s) -

    -     		-

    - 1 (1.22223s) -

    -     		-

    - 1 (1.34992s) -

    -     		-

    - 1 (1.4952s) -

    -
    -
    -
    -

    Table 1.43. Operator /

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 4.36846 (63.9498s) -

    -     		-

    - 5.52565 (145.045s) -

    -     		-

    - 6.18331 (328.069s) -

    -     		-

    - 6.49822 (784.806s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (14.639s) -

    -     		-

    - 1 (26.2494s) -

    -     		-

    - 1 (53.0571s) -

    -     		-

    - 1 (120.772s) -

    -
    -
    -
    -

    Table 1.44. Operator /(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 2.26643 (3.13785s) -

    -     		-

    - 2.57125 (3.76931s) -

    -     		-

    - 3.20872 (5.06758s) -

    -     		-

    - 4.02177 (7.17803s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (1.38449s) -

    -     		-

    - 1 (1.46594s) -

    -     		-

    - 1 (1.57931s) -

    -     		-

    - 1 (1.78479s) -

    -
    -
    -
    -

    Table 1.45. Operator str

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 5.40493 (0.0199393s) -

    -     		-

    - 8.55089 (0.0511907s) -

    -     		-

    - 9.91026 (0.118839s) -

    -     		-

    - 9.93546 (0.285367s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (0.00368909s) -

    -     		-

    - 1 (0.00598659s) -

    -     		-

    - 1 (0.0119915s) -

    -     		-

    - 1 (0.028722s) -

    -
    -
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html deleted file mode 100644 index 4dd0d5ef..00000000 --- a/doc/html/boost_multiprecision/perf/realworld.html +++ /dev/null @@ -1,278 +0,0 @@ - - - -Floating Point Real World Tests - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - These tests test the total time taken to execute all of Boost.Math's test - cases for these functions. In each case the best performing library gets - a relative score of 1, with the total execution time given in brackets. The - first three libraries listed are the various floating point types provided - by this library, while for comparison, two popular C++ front-ends to MPFR ( mpfr_class - and mpreal) are - also shown. -

    -

    - Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. - The tests were run on 32-bit Windows Vista machine. -

    -
    -

    Table 1.6. Bessel Function Performance

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Library -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -
    -

    - mpfr_float -

    -     		-

    - 1.0 (6.472s) -

    -     		-

    - 1.193 (10.154s) -

    -
    -

    - mpf_float -

    -     		-

    - 1.801 (11.662s) -

    -     		-

    - 1.0(8.511s) -

    -
    -

    - cpp_dec_float -

    -     		-

    - 3.13 (20.285s) -

    -     		-

    - 2.46 (21.019s) -

    -
    -

    - mpfr_class -

    -     		-

    - 1.001 (6.480s) -

    -     		-

    - 1.15(9.805s) -

    -
    -

    - mpreal -

    -     		-

    - 1.542 (9.981s) -

    -     		-

    - 1.61 (13.702s) -

    -
    -
    -
    -

    Table 1.7. Non-Central T Distribution Performance

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Library -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -
    -

    - mpfr_float -

    -     		-

    - 1.308 (258.09s) -

    -     		-

    - 1.30 (516.74s) -

    -
    -

    - mpf_float -

    -     		-

    - 1.0 (197.30s) -

    -     		-

    - 1.0(397.30s) -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1.695 (334.50s) -

    -     		-

    - 2.68 (1064.53s) -

    -
    -

    - mpfr_class -

    -     		-

    - 1.35 (266.39s) -

    -     		-

    - 1.323 (525.74s) -

    -
    -

    - mpreal -

    -     		-

    - 1.75 (346.64s) -

    -     		-

    - 1.635 (649.94s) -

    -
    -
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html deleted file mode 100644 index 12b46354..00000000 --- a/doc/html/boost_multiprecision/ref.html +++ /dev/null @@ -1,38 +0,0 @@ - - - -Reference - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    -
    mp_number
    -
    Backend Requirements
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html deleted file mode 100644 index e56abc3b..00000000 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ /dev/null @@ -1,2295 +0,0 @@ - - - -Backend Requirements - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - The requirements on the Backend - template argument to mp_number - are split up into compulsory requirements, and optional requirements that - are either to improve performance or provide optional features. -

    -

    - In the following tables, type B is the Backend - template arument to mp_number, - b and b2 - are a variables of type B, cb - and cb2 are constant variables - of type B, a is a variable - of Arithmetic type, s is - a variable of type const char*, ui - is a variable of type unsigned, - bb is a variable of type - bool, pa - is a variable of type pointer-to-arithmetic-type, exp - is a variable of type B::exp_type, pexp - is a variable of type B::exp_type*, - B2 is another type that meets these requirements, b2 is a variable of type - B2. -

    -
    -

    Table 1.4. Compulsory Requirements on the Backend type.

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Expression -

    -     		-

    - Return Type -

    -     		-

    - Comments -

    -
    -

    - B::signed_types -

    -     		-

    - mpl::list<type-list> -

    -     		-

    - A list of signed integral types that can be assigned to type B. - The types shall be listed in order of size, smallest first, and - shall terminate in the type that is std::intmax_t. -

    -
    -

    - B::unsigned_types -

    -     		-

    - mpl::list<type-list> -

    -     		-

    - A list of unsigned integral types that can be assigned to type - B. The types shall be listed in order of size, smallest first, - and shall terminate in the type that is std::uintmax_t. -

    -
    -

    - B::float_types -

    -     		-

    - mpl::list<type-list> -

    -     		-

    - A list of floating-point types that can be assigned to type B.The - types shall be listed in order of size, smallest first, and shall - terminate in type long double. -

    -
    -

    - B::exponent_type -

    -     		-

    - A signed integral type. -

    -     		-

    - The type of the exponent of type B. -

    -
    -

    - B() -

    -     		- -

    - Default constructor. -

    -
    -

    - B(cb) -

    -     		- -

    - Copy Constructor. -

    -
    -

    - b = - b -

    -     		-

    - B& -

    -     		-

    - Assignment operator. -

    -
    -

    - b = - a -

    -     		-

    - B& -

    -     		-

    - Assignment from an Arithmetic type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - b = - s -

    -     		-

    - B& -

    -     		-

    - Assignment from a string. -

    -
    -

    - b.swap(b) -

    -     		-

    - void -

    -     		-

    - Swaps the contents of its arguments. -

    -
    -

    - cb.str(ui, - bb) -

    -     		-

    - std::string -

    -     		-

    - Returns the string representation of b - with ui digits - and in scientific format if bb - is true. If ui is zero, then returns as many - digits as are required to reconstruct the original value. -

    -
    -

    - b.negate() -

    -     		-

    - void -

    -     		-

    - Negates b. -

    -
    -

    - cb.compare(cb2) -

    -     		-

    - int -

    -     		-

    - Compares cb and - cb2, returns a - value less than zero if cb - < cb2, - a value greater than zero if cb - > cb2 - and zero if cb == cb2. -

    -
    -

    - cb.compare(a) -

    -     		-

    - int -

    -     		-

    - Compares cb and - a, returns a value - less than zero if cb - < a, - a value greater than zero if cb - > a - and zero if cb == a. - The type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_add(b, - cb) -

    -     		-

    - void -

    -     		-

    - Adds cb to b. -

    -
    -

    - eval_subtract(b, - cb) -

    -     		-

    - void -

    -     		-

    - Subtracts cb from - b. -

    -
    -

    - eval_multiply(b, - cb) -

    -     		-

    - void -

    -     		-

    - Multiplies b by - cb. -

    -
    -

    - eval_divide(b, - cb) -

    -     		-

    - void -

    -     		-

    - Divides b by cb. -

    -
    -

    - eval_modulus(b, - cb) -

    -     		-

    - void -

    -     		-

    - Computes b %= - cb, only required when - B is an integer - type. -

    -
    -

    - eval_bitwise_and(b, cb) -

    -     		-

    - void -

    -     		-

    - Computes b &= - cb, only required when - B is an integer - type. -

    -
    -

    - eval_bitwise_or(b, cb) -

    -     		-

    - void -

    -     		-

    - Computes b |= - cb, only required when - B is an integer - type. -

    -
    -

    - eval_bitwise_xor(b, cb) -

    -     		-

    - void -

    -     		-

    - Computes b ^= - cb, only required when - B is an integer - type. -

    -
    -

    - eval_complement(b, cb) -

    -     		-

    - void -

    -     		-

    - Computes the ones-complement of cb - and stores the result in b, - only required when B - is an integer type. -

    -
    -

    - eval_left_shift(b, ui) -

    -     		-

    - void -

    -     		-

    - Computes b <<= - ui, only required when - B is an integer - type. -

    -
    -

    - eval_right_shift(b, ui) -

    -     		-

    - void -

    -     		-

    - Computes b >>= - ui, only required when - B is an integer - type. -

    -
    -

    - eval_convert_to(pa, cb) -

    -     		-

    - void -

    -     		-

    - Converts cb to - the type of *pa - and store the result in *pa. Type B - shall support conversion to at least types std::intmax_t, - std::uintmax_t and long - long. Conversion to other - arithmetic types can then be synthesised using other operations. - Conversions to other types are entirely optional. -

    -
    -

    - eval_frexp(b, - cb, - pexp) -

    -     		-

    - void -

    -     		-

    - Stores values in b - and *pexp - such that the value of cb - is b * 2*pexp, only required when B - is a floating-point type. -

    -
    -

    - eval_ldexp(b, - cb, - exp) -

    -     		-

    - void -

    -     		-

    - Stores a value in b - that is cb * 2exp, only required when B - is a floating-point type. -

    -
    -

    - eval_floor(b, - cb) -

    -     		-

    - void -

    -     		-

    - Stores the floor of cb - in b, only required - when B is a floating-point - type. -

    -
    -

    - eval_ceil(b, - cb) -

    -     		-

    - void -

    -     		-

    - Stores the ceiling of cb - in b, only required - when B is a floating-point - type. -

    -
    -

    - eval_sqrt(b, - cb) -

    -     		-

    - void -

    -     		-

    - Stores the square root of cb - in b, only required - when B is a floating-point - type. -

    -
    -

    - boost::multiprecision::number_category<B>::type -

    -     		-

    - mpl::int_<N> -

    -     		-

    - N is one of the - values number_kind_integer, - number_kind_floating_point, - number_kind_rational - or number_kind_fixed_point. - Defaults to number_kind_floating_point. -

    -
    -
    -
    -

    Table 1.5. Optional Requirements on the Backend Type

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Expression -

    -     		-

    - Returns -

    -     		-

    - Comments -

    -
    -

    - B(b2) -

    -     		-

    - B -

    -     		-

    - Copy constructor from a different back-end type. -

    -
    -

    - b = - b2 -

    -     		-

    - b& -

    -     		-

    - Assignment operator from a different back-end type. -

    -
    -

    - assign_components(b, a, a) -

    -     		-

    - void -

    -     		-

    - Assigns to b the - two components in the following arguments. Only applies to rational - and complex number types. -

    -
    -

    - assign_components(b, b2, b2) -

    -     		-

    - void -

    -     		-

    - Assigns to b the - two components in the following arguments. Only applies to rational - and complex number types. -

    -
    -

    - eval_add(b, - a) -

    -     		-

    - void -

    -     		-

    - Adds a to b. The type of a shall be listed in one of the - type lists B::signed_types, B::unsigned_types - or B::float_types. -

    -
    -

    - eval_subtract(b, - a) -

    -     		-

    - void -

    -     		-

    - Subtracts a from - b. The type of - a shall be listed - in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_multiply(b, - a) -

    -     		-

    - void -

    -     		-

    - Multiplies b by - a. The type of - a shall be listed - in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_divide(b, - a) -

    -     		-

    - void -

    -     		-

    - Divides b by a. The type of a shall be listed in one of the - type lists B::signed_types, B::unsigned_types - or B::float_types. -

    -
    -

    - eval_modulus(b, - a) -

    -     		-

    - void -

    -     		-

    - Computes b %= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_and(b, a) -

    -     		-

    - void -

    -     		-

    - Computes b &= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_or(b, a) -

    -     		-

    - void -

    -     		-

    - Computes b |= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_xor(b, a) -

    -     		-

    - void -

    -     		-

    - Computes b ^= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_add(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Add cb to cb2 and stores the result in - b. -

    -
    -

    - eval_subtract(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Subtracts cb2 from - cb and stores the - result in b. -

    -
    -

    - eval_multiply(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Multiplies cb by - cb2 and stores - the result in b. -

    -
    -

    - eval_divide(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Divides cb by - cb2 and stores - the result in b. -

    -
    -

    - eval_add(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Add cb to a and stores the result in b. The type of a shall be listed in one of the - type lists B::signed_types, B::unsigned_types - or B::float_types. -

    -
    -

    - eval_subtract(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Subtracts a from - cb and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_multiply(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Multiplies cb by - a and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_divide(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Divides cb by - a and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_modulus(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb % - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_bitwise_and(b, cb, cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb & - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_bitwise_or(b, cb, cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb | - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_bitwise_xor(b, cb, cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb ^ - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_add(b, - a, - cb) -

    -     		-

    - void -

    -     		-

    - Add a to cb and stores the result in - b. The type of - a shall be listed - in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_subtract(b, - a, - cb) -

    -     		-

    - void -

    -     		-

    - Subtracts cb from - a and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_multiply(b, - a, - cb) -

    -     		-

    - void -

    -     		-

    - Multiplies a by - cb and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_divide(b, - a, - cb) -

    -     		-

    - void -

    -     		-

    - Divides a by cb and stores the result in - b. The type of - a shall be listed - in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_modulus(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Computes cb % - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_and(b, cb, a) -

    -     		-

    - void -

    -     		-

    - Computes cb & - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_or(b, cb, a) -

    -     		-

    - void -

    -     		-

    - Computes cb | - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_xor(b, cb, a) -

    -     		-

    - void -

    -     		-

    - Computes cb ^ - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_modulus(b, - a, - cb) -

    -     		-

    - void -

    -     		-

    - Computes cb % - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_and(b, a, cb) -

    -     		-

    - void -

    -     		-

    - Computes cb & - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_or(b, a, cb) -

    -     		-

    - void -

    -     		-

    - Computes cb | - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_xor(b, a, cb) -

    -     		-

    - void -

    -     		-

    - Computes a ^ - cb and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_left_shift(b, cb, ui) -

    -     		-

    - void -

    -     		-

    - Computes cb << - ui and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_right_shift(b, cb, ui) -

    -     		-

    - void -

    -     		-

    - Computes cb >> - ui and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_increment(b) -

    -     		-

    - void -

    -     		-

    - Increments the value of b - by one. -

    -
    -

    - eval_decrement(b) -

    -     		-

    - void -

    -     		-

    - Decrements the value of b - by one. -

    -
    -

    - eval_is_zero(cb) -

    -     		-

    - bool -

    -     		-

    - Returns true if cb is zero, otherwise false -

    -
    -

    - eval_get_sign(cb) -

    -     		-

    - int -

    -     		-

    - Returns a value < zero if cb - is negative, a value > zero if cb - is positive, and zero if cb - is zero. -

    -
    -

    - eval_abs(b, - cb) -

    -     		-

    - void -

    -     		-

    - Set b to the absolute - value of cb. -

    -
    -

    - eval_fabs(b, - cb) -

    -     		-

    - void -

    -     		-

    - Set b to the absolute - value of cb. -

    -
    -

    - eval_fpclassify(cb) -

    -     		-

    - int -

    -     		-

    - Returns one of the same values returned by std::fpclassify. - Only required when B - is an floating-point type. -

    -
    -

    - eval_trunc(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::trunc - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_round(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::round - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_exp(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::exp - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_log(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::log - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_log10(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::log10 - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_sin(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::sin - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_cos(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::cos - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_tan(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::exp - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_asin(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::asin - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_acos(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::acos - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_atan(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::atan - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_sinh(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::sinh - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_cosh(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::cosh - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_tanh(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::tanh - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_fmod(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::fmod - on arguments cb - and cb2, and store - the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_pow(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::pow - on arguments cb - and cb2, and store - the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_atan2(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::atan - on arguments cb - and cb2, and store - the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_qr(cb, - cb2, - b, - b2) -

    -     		-

    - void -

    -     		-

    - Sets b to the result - of cb / - cb2 and b2 to the result of cb % - cb2. Only required when - B is an integer - type. -

    -
    -

    - eval_integer_modulus(cb, ui) -

    -     		-

    - unsigned -

    -     		-

    - Returns the result of cb - % ui. - Only required when B - is an integer type. -

    -
    -

    - eval_lsb(cb) -

    -     		-

    - unsigned -

    -     		-

    - Returns the index of the least significant bit that is set. Only - required when B - is an integer type. -

    -
    -

    - eval_bit_test(cb, - ui) -

    -     		-

    - bool -

    -     		-

    - Returns true if cb - has bit ui set. - Only required when B - is an integer type. -

    -
    -

    - eval_bit_set(b, - ui) -

    -     		-

    - void -

    -     		-

    - Sets the bit at index ui - in b. Only required - when B is an integer - type. -

    -
    -

    - eval_bit_unset(b, ui) -

    -     		-

    - void -

    -     		-

    - Unsets the bit at index ui - in b. Only required - when B is an integer - type. -

    -
    -

    - eval_bit_flip(b, - ui) -

    -     		-

    - void -

    -     		-

    - Flips the bit at index ui - in b. Only required - when B is an integer - type. -

    -
    -

    - eval_gcd(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Sets b to the greatest - common divisor of cb - and cb2. Only required - when B is an integer - type. -

    -
    -

    - eval_lcm(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Sets b to the least - common multiple of cb - and cb2. Only required - when B is an integer - type. -

    -
    -
    -
    - - - - - -
    [Note]Note

    - The non-member functions are all named with an "eval_" prefix - to avoid conflicts with template classes of the same name - in point of - fact this naming convension shouldn't be necessary, but rather works around - some compiler bugs. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html deleted file mode 100644 index f3c1ecf5..00000000 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ /dev/null @@ -1,695 +0,0 @@ - - - -mp_number - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    - - Synopsis -
    -
    namespace boost{ namespace multiprecision{
-
-template <class Backend, bool ExpressionTemplates = true>
-class mp_number
-{
-   mp_number();
-   mp_number(see-below);
-   mp_number& operator=(see-below);
-
-   // Member operators
-   mp_number& operator+=(const see-below&);
-   mp_number& operator-=(const see-below&);
-   mp_number& operator*=(const see-below&);
-   mp_number& operator/=(const see-below&);
-   mp_number& operator++();
-   mp_number& operator--();
-   mp_number  operator++(int);
-   mp_number  operator--(int);
-
-   mp_number& operator%=(const see-below&);
-   mp_number& operator&=(const see-below&);
-   mp_number& operator|=(const see-below&);
-   mp_number& operator^=(const see-below&);
-   mp_number& operator<<=(const integer-type&);
-   mp_number& operator>>=(const integer-type&);
-
-   // Use in Boolean context:
-   operator convertible-to-bool-type()const;
-   // swap:
-   void swap(mp_number& other);
-   // Sign:
-   bool is_zero()const;
-   int sign()const;
-   // string conversion:
-   std::string str()const;
-   // Generic conversion mechanism
-   template <class T>
-   T convert_to()const;
-   // precision control:
-   static unsigned default_precision();
-   static void default_precision(unsigned digits10);
-   unsigned precision()const;
-   void precision(unsigned digits10);
-   // Comparison:
-   int compare(const mp_number<Backend>& o)const;
-   template <class V>
-   typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
-   // Access to the underlying implementation:
-   Backend& backend();
-   const Backend& backend()const;
-};
-
-// Non member operators:
-unmentionable-expression-template-type operator+(const see-below&, const see-below&);
-unmentionable-expression-template-type operator-(const see-below&, const see-below&);
-unmentionable-expression-template-type operator*(const see-below&, const see-below&);
-unmentionable-expression-template-type operator/(const see-below&, const see-below&);
-// Integer only operations:
-unmentionable-expression-template-type operator%(const see-below&, const see-below&);
-unmentionable-expression-template-type operator&(const see-below&, const see-below&);
-unmentionable-expression-template-type operator|(const see-below&, const see-below&);
-unmentionable-expression-template-type operator^(const see-below&, const see-below&);
-unmentionable-expression-template-type operator<<(const see-below&, const integer-type&);
-unmentionable-expression-template-type operator>>(const see-below&, const integer-type&);
-// Comparison operators:
-bool operator==(const see-below&, const see-below&);
-bool operator!=(const see-below&, const see-below&);
-bool operator< (const see-below&, const see-below&);
-bool operator> (const see-below&, const see-below&);
-bool operator<=(const see-below&, const see-below&);
-bool operator>=(const see-below&, const see-below&);
-
-// Swap:
-template <class Backend, bool ExpressionTemplates>
-void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
-
-// iostream support:
-template <class Backend, bool ExpressionTemplates>
-std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
-std::ostream& operator << (std::ostream& os, const unmentionable-expression-template-type& r);
-template <class Backend, bool ExpressionTemplates>
-std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r);
-
-// Non-member function standard library support:
-unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
-
-unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
-unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
-unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-
-// Traits support:
-template <class T>
-struct component_type;
-template <class T>
-struct number_category;
-
-// Integer specific functions:
-template <class Backend, bool ExpressionTemplates>
-bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
-               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
-template <class Integer>
-Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
-unsigned lsb(const mp_number-or-expression-template-type& x);
-template <class Backend, class ExpressionTemplates>
-bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-template <class Engine>
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
-
-// Rational number support:
-typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
-typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
-
-}} // namespaces
-
-namespace boost{ namespace math{
-
-// Boost.Math interoperability functions:
-int                                              fpclassify     (const mp_number-or-expression-template-type&, int);
-bool                                             isfinite       (const mp_number-or-expression-template-type&, int);
-bool                                             isnan          (const mp_number-or-expression-template-type&, int);
-bool                                             isinf          (const mp_number-or-expression-template-type&, int);
-bool                                             isnormal       (const mp_number-or-expression-template-type&, int);
-
-}} // namespaces
-
-// numeric_limits support:
-namespace std{
-
-template <class Backend, bool ExpressionTemplates>
-struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
-{
-   /* Usual members here */
-};
-
-}
-
    -
    - - Description -
    -
    template <class Backend, bool ExpressionTemplates = true>
-class mp_number;
-
    -

    - Class mp_number has two template - arguments: -

    -
    -

    -
    -
    Backend
    -

    - The actual arithmetic back-end that does all the work. -

    -
    ExpressionTemplates
    -

    - A boolean value: when true, then expression templates are enabled, - otherwise they are disabled. -

    -
    -
    -
    mp_number();
-mp_number(see-below);
-mp_number& operator=(see-below);
-
    -

    - Type mp_number is default - constructible, and both copy constructible and assignable from: -

    -
      -
    • - Itself. -
      • -
    • - An expression template which is the result of one of the arithmetic operators. -
      • -
    • - Any builtin arithmetic type. -
      • -
    • - A std::string or any type which is convertible - to const char*. -
      • -
    • - Any type that the Backend is constructible or assignable from. -
      • -
    -

    - In addition, if the type has multiple components (for example rational or - complex number types), then there is a two argument constructor: -

    -
    mp_number(arg1, arg2);
-
    -

    - Where the two args must either be arithmetic types, or types that are convertible - to the two components of this. -

    -
    mp_number& operator+=(const see-below&);
-mp_number& operator-=(const see-below&);
-mp_number& operator*=(const see-below&);
-mp_number& operator/=(const see-below&);
-mp_number& operator++();
-mp_number& operator--();
-mp_number  operator++(int);
-mp_number  operator--(int);
-// Integer only operations:
-mp_number& operator%=(const see-below&);
-mp_number& operator&=(const see-below&);
-mp_number& operator|=(const see-below&);
-mp_number& operator^=(const see-below&);
-mp_number& operator<<=(const integer-type&);
-mp_number& operator>>=(const integer-type&);
-
    -

    - These operators all take their usual arithmetic meanings. -

    -

    - The arguments to these operators is either: -

    -
      -
    • - Another mp_number<Backend, - ExpressionTemplates>. -
      • -
    • - A builtin arithmetic type. -
      • -
    • - An expression template derived from mp_number<Backend>. -
      • -
    -

    - For the left and right shift operations, the argument must be a builtin integer - type with a positive value (negative values result in a std::runtime_error - being thrown). -

    -
    operator convertible-to-bool-type()const;
-
    -

    - Returns an unmentionable-type that is usable in Boolean - contexts (this allows mp_number - to be used in any Boolean context - if statements, conditional statements, - or as an argument to a logical operator - without type mp_number - being convertible to type bool. -

    -

    - This operator also enables the use of mp_number - with any of the following operators: !, - ||, && - and ?:. -

    -
    void swap(mp_number& other);
-
    -

    - Swaps *this - with other. -

    -
    bool is_zero()const;
-
    -

    - Returns true is *this is zero, - otherwise false. -

    -
    int sign()const;
-
    -

    - Returns a value less than zero if *this is negative, a value greater than zero - if *this - is positive, and zero if *this - is zero. -

    -
    std::string str(unsigned precision, bool scientific = true)const;
-
    -

    - Returns the number formatted as a string, with at least precision - digits, and in scientific format if scientific is true. -

    -
    template <class T>
-T convert_to()const;
-
    -

    - Provides a generic conversion mechanism to convert *this to type T. - Type T may be any arithmetic - type. Optionally other types may also be supported by specific Backend types. -

    -
    static unsigned default_precision();
-static void default_precision(unsigned digits10);
-unsigned precision()const;
-void precision(unsigned digits10);
-
    -

    - These functions are only available if the Backend template parameter supports - runtime changes to precision. They get and set the default precision and - the precision of *this - respectively. -

    -
    int compare(const mp_number<Backend, ExpressionTemplates>& o)const;
-template <class V>
-typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
-
    -

    - Returns: -

    -
      -
    • - A value less that 0 for *this < other -
      • -
    • - A value greater that 0 for *this > other -
      • -
    • - Zero for *this - == other -
      • -
    -
    Backend& backend();
-const Backend& backend()const;
-
    -

    - Returns the underlying back-end instance used by *this. -

    -
    - - Non-member - operators -
    -
    // Non member operators:
-unmentionable-expression-template-type operator+(const see-below&, const see-below&);
-unmentionable-expression-template-type operator-(const see-below&, const see-below&);
-unmentionable-expression-template-type operator*(const see-below&, const see-below&);
-unmentionable-expression-template-type operator/(const see-below&, const see-below&);
-// Integer only operations:
-unmentionable-expression-template-type operator%(const see-below&, const see-below&);
-unmentionable-expression-template-type operator&(const see-below&, const see-below&);
-unmentionable-expression-template-type operator|(const see-below&, const see-below&);
-unmentionable-expression-template-type operator^(const see-below&, const see-below&);
-unmentionable-expression-template-type operator<<(const see-below&, const integer-type&);
-unmentionable-expression-template-type operator>>(const see-below&, const integer-type&);
-// Comparison operators:
-bool operator==(const see-below&, const see-below&);
-bool operator!=(const see-below&, const see-below&);
-bool operator< (const see-below&, const see-below&);
-bool operator> (const see-below&, const see-below&);
-bool operator<=(const see-below&, const see-below&);
-bool operator>=(const see-below&, const see-below&);
-
    -

    - These operators all take their usual arithmetic meanings. -

    -

    - The arguments to these functions must contain at least one of the following: -

    -
      -
    • - An mp_number. -
      • -
    • - An expression template type derived from mp_number. -
      • -
    -

    - In addition, one of the two arguments may be a builtin arithmetic type. -

    -

    - The return type of these operators is either: -

    -
      -
    • - An unmentionable-type expression template type when - ExpressionTemplates is - true. -
      • -
    • - Type mp_number<Backend, - false> - when ExpressionTemplates - is false. -
      • -
    • - Type bool if the operator - is a comparison operator. -
      • -
    -

    - Finally note that the second argument to the left and right shift operations - must be a builtin integer type, and that the argument must be positive (negative - arguments result in a std::runtime_error - being thrown). -

    -
    - - swap -
    -
    template <class Backend, ExpressionTemplates>
-void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
-
    -

    - Swaps a and b. -

    -
    - - Iostream - Support -
    -
    template <class Backend, bool ExpressionTemplates>
-std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
-template <class Unspecified...>
-std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r);
-template <class Backend, bool ExpressionTemplates>
-inline std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r)
-
    -

    - These operators provided formatted input-output operations on mp_number types, and expression templates - derived from them. -

    -

    - It's down to the back-end type to actually implement string conversion. However, - the back-ends provided with this library support all of the iostream formatting - flags, field width and precision settings. -

    -
    - - Non-member - standard library function support -
    -
    unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
-
-unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
-unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
-unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-
    -

    - These functions all behave exactly as their standard library counterparts - do: their argument is either an instance of mp_number - or an expression template derived from it; If the argument is of type mp_number<Backend, false> - then that is also the return type, otherwise the return type is an expression - template. -

    -

    - These functions are normally implemented by the Backend type. However, default - versions are provided for Backend types that don't have native support for - these functions. Please note however, that this default support requires - the precision of the type to be a compile time constant - this means for - example that the GMP MPF Backend will - not work with these functions when that type is used at variable precision. -

    -

    - Also note that with the exception of abs - that these functions can only be used with floating-point Backend types. -

    -
    - - Traits - Class Support -
    -
    template <class T>
-struct component_type;
-
    -

    - If this is a type with mutiple components (for example rational or complex - types), then this trait has a single member type - that is the type of those components. -

    -
    template <class T>
-struct number_category;
-
    -

    - A traits class that inherits from mpl::int_<N> - where N is one of the enumerated - values number_kind_integer, - number_kind_floating_point, - number_kind_rational or - number_kind_fixed_point. -

    -
    - - Integer functions -
    -
    template <class Backend, bool ExpressionTemplates>
-bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
-               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
-
    -

    - Divides x by y and returns both the quotient and remainder. After the call - q = - x / y and r - = x % y. -

    -
    template <class Integer>
-Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
-
    -

    - Returns the absolute value of x - % val. -

    -
    unsigned lsb(const mp_number-or-expression-template-type& x);
-
    -

    - Returns the index of the least significant bit that is set to 1. -

    -
    template <class Backend, class ExpressionTemplates>
-bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-
    -

    - Returns true if the bit at - index in val is set. -

    -
    template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-
    -

    - Sets the bit at index in val, and - returns val. -

    -
    template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-
    -

    - Unsets the bit at index in val, - and returns val. -

    -
    template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-
    -

    - Flips the bit at index in val, - and returns val. -

    -
    template <class Engine>
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
-
    -

    - Tests to see if the number n is probably prime - the - test excludes the vast majority of composite numbers by excluding small prime - factors and performing a single Fermat test. Then performs trials - Miller-Rabin tests. Returns false - if n is definitely composite, or true - if n is probably prime with the probability of it being - composite less than 0.25^trials. -

    -
    - - Rational - Number Functions -
    -
    typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
-typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
-
    -

    - These functions return the numerator and denominator of a rational number - respectively. -

    -
    - - Boost.Math - Interoperability Support -
    -
    namespace boost{ namespace math{
-
-int  fpclassify     (const mp_number-or-expression-template-type&, int);
-bool isfinite       (const mp_number-or-expression-template-type&, int);
-bool isnan          (const mp_number-or-expression-template-type&, int);
-bool isinf          (const mp_number-or-expression-template-type&, int);
-bool isnormal       (const mp_number-or-expression-template-type&, int);
-
-}} // namespaces
-
    -

    - These floating-point classification functions behave exactly as their Boost.Math - equivalents. -

    -

    - Other Boost.Math functions and templates may also be specialized or overloaded - to ensure interoperability. -

    -
    - - std::numeric_limits - support -
    -
    namespace std{
-
-template <class Backend, ExpressionTemplates>
-struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
-{
-   /* Usual members here */
-};
-
-}
-
    -

    - Class template std::numeric_limits is specialized for all instantiations - of mp_number whose precision - is known at compile time, plus those types whose precision is unlimited (though - it is much less useful in those cases). It is not specialized for types whose - precision can vary at compile time (such as mpf_float). -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html deleted file mode 100644 index ea39c242..00000000 --- a/doc/html/boost_multiprecision/tut.html +++ /dev/null @@ -1,45 +0,0 @@ - - - -Tutorial - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    -
    Integer Types
    -
    Floating Point Numbers
    -
    Rational Number Types
    -
    Generating Random Numbers
    -
    Primality Testing
    -
    -

    - In order to use this library you need to make two choices: what kind of number - do I want, and which back-end do I want to perform the actual arithmetic? -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html deleted file mode 100644 index 41862d34..00000000 --- a/doc/html/boost_multiprecision/tut/ints.html +++ /dev/null @@ -1,503 +0,0 @@ - - - -Integer Types - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - The following back-ends provide integer arithmetic: -

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend Type -

    -     		-

    - Header -

    -     		-

    - Radix -

    -     		-

    - Dependencies -

    -     		-

    - Pros -

    -     		-

    - Cons -

    -
    -

    - cpp_int -

    -     		-

    - boost/multiprecision/cpp_int.hpp -

    -     		-

    - 2 -

    -     		-

    - None -

    -     		-

    - Very versatile, Boost licenced, all C++ integer type which support - both arbitrary - precision and fixed precision integer types. -

    -     		-

    - Slower than GMP, though - typically not as slow as libtommath -

    -
    -

    - gmp_int -

    -     		-

    - boost/multiprecision/gmp.hpp -

    -     		-

    - 2 -

    -     		-

    - GMP -

    -     		-

    - Very fast and efficient back-end. -

    -     		-

    - Dependency on GNU licenced GMP - library. -

    -
    -

    - tom_int -

    -     		-

    - boost/multiprecision/tommath.hpp -

    -     		-

    - 2 -

    -     		-

    - libtommath -

    -     		-

    - Public domain back-end with no licence restrictions. -

    -     		-

    - Slower than GMP. -

    -
    -
    - - cpp_int -
    -
    namespace boost{ namespace multiprecision{
-
-typedef unspecified-type limb_type;
-
-template <unsigned MinDigits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
-class cpp_int_backend;
-
-typedef mp_number<cpp_int_backend<> >           cpp_int;    // arbitrary precision integer
-typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
-typedef mp_number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
-
-// Fixed precision unsigned types:
-typedef mp_number<cpp_int_backend<128, false, void>, false>   mp_uint128_t;
-typedef mp_number<cpp_int_backend<256, false, void>, false>   mp_uint256_t;
-typedef mp_number<cpp_int_backend<512, false, void>, false>   mp_uint512_t;
-typedef mp_number<cpp_int_backend<1024, false, void>, false>  mp_uint1024_t;
-
-// Fixed precision signed types:
-typedef mp_number<cpp_int_backend<128, true, void>, false>    mp_int128_t;
-typedef mp_number<cpp_int_backend<256, true, void>, false>    mp_int256_t;
-typedef mp_number<cpp_int_backend<512, true, void>, false>    mp_int512_t;
-typedef mp_number<cpp_int_backend<1024, true, void>, false>   mp_int1024_t;
-
-}} // namespaces
-
    -

    - The cpp_int_backend type - is used via one of the typedefs boost::multiprecision::cpp_int, - boost::multiprecision::mp_uint128_t, boost::multiprecision::mp_uint256_t, - boost::multiprecision::mp_uint512_t, boost::multiprecision::mp_int128_t, - boost::multiprecision::mp_int256_t or boost::multiprecision::mp_int512_t. -

    -

    - This back-end is the "Swiss Army Knife" of integer types as it - can represent both fixed and arbitrary - precision integer types, and both signed and unsigned types. There - are three template arguments: -

    -
    -

    -
    -
    MinBits
    -

    - Determines the number of Bits to store directly within the object before - resorting to dynamic memory allocation. When zero, this field is determined - automatically based on how many bits can be stored in union with the - dynamic storage header: setting a larger value may improve performance - as larger integer values will be stored internally before memory allocation - is required. When the Allocator parameter is type void, - then this field determines the total number of bits in the resulting - fixed precision type. -

    -
    Signed
    -

    - Determines whether the resulting type is signed or not. Note that for - arbitrary - precision types (where the Allocator parameter is non-void), - then this parameter must be true. - For fixed precision types then this type may be either true (type is signed), or false (type is unsigned). -

    -
    Allocator
    -

    - The allocator to use for dymamic memory allocation, or type void if this is to be a fixed precision - type. -

    -
    -
    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed cpp_int_backends - have the value zero. -
      • -
    • - Division by zero results in a std::runtime_error - being thrown. -
      • -
    • - Construction from a string that contains invalid non-numeric characters - results in a std::runtime_error being thrown. -
      • -
    • - Since the precision of cpp_int_backend - is necessarily limited when the allocator parameter is void, care should - be taken to avoid numeric overflow when using this type unless you actually - want modulo-arithmetic behavior. -
      • -
    • - The type uses a sign-magnitude representation internally, so type mp_int128_t has 128-bits of precision - plus an extra sign bit. In this respect the behaviour of these types - differs from built-in 2's complement types. In might be tempting to use - a 127-bit type instead, and indeed this does work, but behaviour is still - slightly different from a 2's complement built-in type as the min and - max values are identical (apart from the sign), where as they differ - by one for a true 2's complement type. That said it should be noted that - there's no requirement for built-in types to be 2's complement either - - it's simply that this is the most common format by far. -
      • -
    • - Attempting to print negative values as either an Octal or Hexadecimal - string results in a std::runtime_error - being thrown, this is a direct consequence of the sign-magnitude representation. -
      • -
    • - The fixed precision types mp_[u]intXXX_t - have expression template support turned off - it seems to make little - difference to the performance of these types either way - so we may as - well have the faster compile times by turning the feature off. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/cpp_int.hpp>
-
-using namespace boost::multiprecision;
-
-mp_int128_t v = 1;
-
-// Do some fixed precision arithmetic:
-for(unsigned i = 1; i <= 20; ++i)
-   v *= i;
-
-std::cout << v << std::endl; // prints 20!
-
-// Repeat at arbitrary precision:
-cpp_int u = 1;
-for(unsigned i = 1; i <= 100; ++i)
-   u *= i;
-
-std::cout << u << std::endl; // prints 100!
-
    -

    -

    -
    - - gmp_int -
    -
    namespace boost{ namespace multiprecision{
-
-class gmp_int;
-
-typedef mp_number<gmp_int >         mpz_int;
-
-}} // namespaces
-
    -

    - The gmp_int back-end is used - via the typedef boost::multiprecision::mpz_int. It acts as a thin wrapper around - the GMP mpz_t - to provide an integer type that is a drop-in replacement for the native C++ - integer types, but with unlimited precision. -

    -

    - As well as the usual conversions from arithmetic and string types, type - mpz_int is copy constructible - and assignable from: -

    -
      -
    • - The GMP native types: mpf_t, mpz_t, - mpq_t. -
      • -
    • - Instances of mp_number<T> that are wrappers around those types: - mp_number<gmp_float<N> >, mp_number<gmp_rational>. -
      • -
    -

    - It's also possible to access the underlying mpz_t - via the data() - member function of gmp_int. -

    -

    - Things you should know when using this type: -

    -
      -
    • - No changes are made to the GMP library's global settings - so you can - safely mix this type with existing code that uses GMP. -
      • -
    • - Default constructed gmp_ints - have the value zero (this is GMP's default behavior). -
      • -
    • - Formatted IO for this type does not support octal or hexadecimal notation - for negative values, as a result performing formatted output on this - type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex - are set, will result in a std::runtime_error - will be thrown. -
      • -
    • - Division by zero is handled by the GMP - library - it will trigger a division by zero signal. -
      • -
    • - Although this type is a wrapper around GMP - it will work equally well with MPIR. - Indeed use of MPIR is recomended - on Win32. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-
-using namespace boost::multiprecision;
-
-mpz_int v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-
-std::cout << v << std::endl; // prints 1000!
-
-// Access the underlying representation:
-mpz_t z;
-mpz_init(z);
-mpz_set(z, v.backend().data());
-
    -

    -

    -
    - - tom_int -
    -
    namespace boost{ namespace multiprecision{
-
-class tommath_int;
-
-typedef mp_number<tommath_int >         tom_int;
-
-}} // namespaces
-
    -

    - The tommath_int back-end - is used via the typedef boost::multiprecision::tom_int. - It acts as a thin wrapper around the libtommath - tom_int to provide an integer - type that is a drop-in replacement for the native C++ integer types, but - with unlimited precision. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed objects have the value zero (this is libtommath's - default behavior). -
      • -
    • - Although tom_int is mostly - a drop in replacement for the builtin integer types, it should be noted - that it is a rather strange beast as it's a signed type that is not a - 2's complement type. As a result the bitwise operations | & ^ will throw a std::runtime_error - exception if either of the arguments is negative. Similarly the complement - operator~ is deliberately - not implemented for this type. -
      • -
    • - Formatted IO for this type does not support octal or hexadecimal notation - for negative values, as a result performing formatted output on this - type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex - are set, will result in a std::runtime_error - will be thrown. -
      • -
    • - Division by zero will result in a hardware signal being raised by libtommath. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/tommath.hpp>
-
-boost::multiprecision::tom_int v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-
-std::cout << v << std::endl; // prints 1000!
-std::cout << std::hex << v << std::endl; // prints 1000! in hex format
-
-try{
-   std::cout << std::hex << -v << std::endl; // Ooops! can't print a negative value in hex format!
-}
-catch(const std::runtime_error& e)
-{
-   std::cout << e.what() << std::endl;
-}
-
-try{
-   // v is not a 2's complement type, bitwise operations are only supported
-   // on positive values:
-   v = -v & 2;
-}
-catch(const std::runtime_error& e)
-{
-   std::cout << e.what() << std::endl;
-}
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html deleted file mode 100644 index f1dac222..00000000 --- a/doc/html/boost_multiprecision/tut/primetest.html +++ /dev/null @@ -1,108 +0,0 @@ - - - -Primality Testing - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - The library implements a fairly basic (meaning unoptimized, and possibly - slow) Miller-Rabin test for primality: -

    -
    #include <boost/multiprecision/miller_rabin.hpp>
-
-template <class Backend, bool ExpressionTemplates, class Engine>
-bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials, Engine& gen);
-
-template <class Backend, bool ExpressionTemplates, class Engine>
-bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials);
-
    -

    - These functions perform a Miller-Rabin test for primality, if the result - is false then n - is definitely composite, while if the result is true - then n is prime with probability 0.25^trials. - The algorithm used is straight out of Knuth Vol 2, which recomends 25 trials - for a pretty strong likelyhood that n is prime. -

    -

    - The third optional argument is for a Uniform Random Number Generator from - Boost.Random. When not provided the mt19937 - generator is used. Note that when producing random primes then you should - probably use a different random number generator to produce candidate prime - numbers for testing, than is used internally by miller_rabin_test - for determining whether the value is prime. It also helps of course to seed - the generators with some source of randomness. -

    -

    - The following example searches for a prime p - for which (p-1)/2 is also probably prime: -

    -

    -

    -
    #include <boost/multiprecision/cpp_int.hpp>
-#include <boost/multiprecision/miller_rabin.hpp>
-#include <iostream>
-#include <iomanip>
-
-int main()
-{
-   using namespace boost::random;
-   using namespace boost::multiprecision;
-
-   typedef cpp_int int_type;
-   mt11213b base_gen(clock());
-   independent_bits_engine<mt11213b, 256, int_type> gen(base_gen);
-   //
-   // We must use a different generator for the tests and number generation, otherwise
-   // we get false positives.
-   //
-   mt19937 gen2(clock());
-
-   for(unsigned i = 0; i < 100000; ++i)
-   {
-      int_type n = gen();
-      if(miller_rabin_test(n, 25, gen2))
-      {
-         // Value n is probably prime, see if (n-1)/2 is also prime:
-         std::cout << "We have a probable prime with value: " << std::hex << std::showbase << n << std::endl;
-         if(miller_rabin_test((n-1)/2, 25, gen2))
-         {
-            std::cout << "We have a safe prime with value: " << std::hex << std::showbase << n << std::endl;
-            return 0;
-         }
-      }
-   }
-   std::cout << "Ooops, no safe primes were found" << std::endl;
-   return 1;
-}
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/random.html b/doc/html/boost_multiprecision/tut/random.html deleted file mode 100644 index 5b7928ff..00000000 --- a/doc/html/boost_multiprecision/tut/random.html +++ /dev/null @@ -1,157 +0,0 @@ - - - -Generating Random Numbers - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - Random numbers are generated in conjunction with Boost.Random. However, since - Boost.Random is unaware of arbitrary - precision numbers, it's necessary to include the header: -

    -
    #include <boost/multiprecision/random.hpp>
-
    -

    - In order to act as a bridge between the two libraries. -

    -

    - Integers with N random bits are generated using independent_bits_engine: -

    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-#include <boost/multiprecision/random.hpp>
-
-using namespace boost::multiprecision;
-using namespace boost::random;
-
-//
-// Declare our random number generator type, the underlying generator
-// is the Mersenne twister mt19937 engine, and 256 bits are generated:
-//
-typedef independent_bits_engine<mt19937, 256, mpz_int> generator_type;
-generator_type gen;
-//
-// Generate some values:
-//
-std::cout << std::hex << std::showbase;
-for(unsigned i = 0; i < 10; ++i)
-   std::cout << gen() << std::endl;
-
    -

    -

    -

    - Alternatively we can generate integers in a given range using uniform_int_distribution, this will invoke - the underlying engine multiple times to build up the required number of bits - in the result: -

    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-#include <boost/multiprecision/random.hpp>
-
-using namespace boost::multiprecision;
-using namespace boost::random;
-
-//
-// Generate integers in a given range using uniform_int,
-// the underlying generator is invoked multiple times
-// to generate enough bits:
-//
-mt19937 mt;
-uniform_int_distribution<mpz_int> ui(0, mpz_int(1) << 256);
-//
-// Generate the numbers:
-//
-std::cout << std::hex << std::showbase;
-for(unsigned i = 0; i < 10; ++i)
-   std::cout << ui(mt) << std::endl;
-
    -

    -

    -

    - Floating point values in [0,1) are generated using uniform_01, - the trick here is to ensure that the underlying generator produces as many - random bits as there are digits in the floating point type. As above independent_bits_engine can be used for - this purpose, note that we also have to convert decimal digits (in the floating - point type) to bits (in the random number generator): -

    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-#include <boost/multiprecision/random.hpp>
-
-using namespace boost::multiprecision;
-using namespace boost::random;
-//
-// We need an underlying generator with at least as many bits as the
-// floating point type to generate numbers in [0, 1) with all the bits
-// in the floating point type randomly filled:
-//
-uniform_01<mpf_float_50> uf;
-independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen;
-//
-// Generate the values:
-//
-std::cout << std::setprecision(50);
-for(unsigned i = 0; i < 20; ++i)
-   std::cout << uf(gen) << std::endl;
-
    -

    -

    -

    - Finally, we can modify the above example to produce numbers distributed according - to some distribution: -

    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-#include <boost/multiprecision/random.hpp>
-
-using namespace boost::multiprecision;
-using namespace boost::random;
-//
-// We can repeat the above example, with other distributions:
-//
-uniform_real_distribution<mpf_float_50> ur(-20, 20);
-gamma_distribution<mpf_float_50> gd(20);
-independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen;
-//
-// Generate some values:
-//
-std::cout << std::setprecision(50);
-for(unsigned i = 0; i < 20; ++i)
-   std::cout << ur(gen) << std::endl;
-for(unsigned i = 0; i < 20; ++i)
-   std::cout << gd(gen) << std::endl;
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html deleted file mode 100644 index 65eca5a3..00000000 --- a/doc/html/boost_multiprecision/tut/rational.html +++ /dev/null @@ -1,546 +0,0 @@ - - - -Rational Number Types - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - The following back-ends provide rational number arithmetic: -

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend Type -

    -     		-

    - Header -

    -     		-

    - Radix -

    -     		-

    - Dependencies -

    -     		-

    - Pros -

    -     		-

    - Cons -

    -
    -

    - gmp_rational -

    -     		-

    - boost/multiprecision/gmp.hpp -

    -     		-

    - 2 -

    -     		-

    - GMP -

    -     		-

    - Very fast and efficient back-end. -

    -     		-

    - Dependency on GNU licenced GMP - library. -

    -
    -

    - cpp_rational -

    -     		-

    - boost/multiprecision/cpp_int.hpp -

    -     		-

    - 2 -

    -     		-

    - None -

    -     		-

    - An all C++ Boost-licenced implementation. -

    -     		-

    - Slower than GMP. -

    -
    -

    - tommath_rational -

    -     		-

    - boost/multiprecision/tommath.hpp -

    -     		-

    - 2 -

    -     		-

    - libtommath -

    -     		-

    - All C/C++ implementation that's Boost Software Licence compatible. -

    -     		-

    - Slower than GMP. -

    -
    -

    - rational_adapter -

    -     		-

    - boost/multiprecision/rational_adapter.hpp -

    -     		-

    - N/A -

    -     		-

    - none -

    -     		-

    - All C++ adapter that allows any inetger back-end type to be used - as a rational type. -

    -     		-

    - Requires an underlying integer back-end type. -

    -
    -

    - boost::rational -

    -     		-

    - boost/rational.hpp -

    -     		-

    - N/A -

    -     		-

    - None -

    -     		-

    - A C++ rational number type that can used with any mp_number integer type. -

    -     		-

    - The expression templates used by mp_number - end up being "hidden" inside boost::rational: - performance may well suffer as a result. -

    -
    -
    - - gmp_rational -
    -
    namespace boost{ namespace multiprecision{
-
-class gmp_rational;
-
-typedef mp_number<gmp_rational >         mpq_rational;
-
-}} // namespaces
-
    -

    - The gmp_rational back-end - is used via the typedef boost::multiprecision::mpq_rational. - It acts as a thin wrapper around the GMP - mpq_t to provide a rational - number type that is a drop-in replacement for the native C++ number types, - but with unlimited precision. -

    -

    - As well as the usual conversions from arithmetic and string types, instances - of mp_number<gmp_rational> - are copy constructible and assignable from: -

    -
      -
    • - The GMP native types: mpz_t, mpq_t. -
      • -
    • - mp_number<gmp_int>. -
      • -
    -

    - There is also a two-argument constructor that accepts a numerator and denominator - (both of type mp_number<gmp_int>). -

    -

    - There are also non-member functions: -

    -
    mpz_int numerator(const mpq_rational&);
-mpz_int denominator(const mpq_rational&);
-
    -

    - which return the numerator and denominator of the number. -

    -

    - It's also possible to access the underlying mpq_t - via the data() - member function of mpq_rational. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed mpq_rationals - have the value zero (this is the GMP - default behavior). -
      • -
    • - Division by zero results in a hardware exception inside the GMP - library. -
      • -
    • - No changes are made to the GMP - library's global settings, so this type can coexist with existing GMP code. -
      • -
    • - The code can equally be used with MPIR - as the underlying library - indeed that is the prefered option on Win32. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-
-using namespace boost::multiprecision;
-
-mpq_rational v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-v /= 10;
-
-std::cout << v << std::endl; // prints 1000! / 10
-std::cout << numerator(v) << std::endl;
-std::cout << denominator(v) << std::endl;
-
-mpq_rational w(2, 3);  // component wise constructor
-std::cout << w << std::endl; // prints 2/3
-
-// Access the underlying data:
-mpq_t q;
-mpq_init(q);
-mpq_set(q, v.backend().data());
-
    -

    -

    -
    - - cpp_rational -
    -
    namespace boost{ namespace multiprecision{
-
-typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
-
-typedef mp_number<cpp_rational_backend>         cpp_rational;
-
-}} // namespaces
-
    -

    - The cpp_rational_backend - type is used via the typedef boost::multiprecision::cpp_rational. - It provides a rational number type that is a drop-in replacement for the - native C++ number types, but with unlimited precision. -

    -

    - As well as the usual conversions from arithmetic and string types, instances - of cpp_rational are copy - constructible and assignable from type cpp_int. -

    -

    - There is also a two argument constructor that accepts a numerator and denominator: - both of type cpp_int. -

    -

    - There are also non-member functions: -

    -
    cpp_int numerator(const cpp_rational&);
-cpp_int denominator(const cpp_rational&);
-
    -

    - which return the numerator and denominator of the number. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed cpp_rationals - have the value zero. -
      • -
    • - Division by zero results in a std::rumtime_error - being thrown. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/cpp_int.hpp>
-
-using namespace boost::multiprecision;
-
-cpp_rational v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-v /= 10;
-
-std::cout << v << std::endl; // prints 1000! / 10
-std::cout << numerator(v) << std::endl;
-std::cout << denominator(v) << std::endl;
-
-cpp_rational w(2, 3);  // component wise constructor
-std::cout << w << std::endl; // prints 2/3
-
    -

    -

    -
    - - tommath_rational -
    -
    namespace boost{ namespace multiprecision{
-
-typedef rational_adpater<tommath_int>        tommath_rational;
-typedef mp_number<tommath_rational >         tom_rational;
-
-}} // namespaces
-
    -

    - The tommath_rational back-end - is used via the typedef boost::multiprecision::tom_rational. - It acts as a thin wrapper around boost::rational<tom_int> to provide a rational number type that - is a drop-in replacement for the native C++ number types, but with unlimited - precision. -

    -

    - The advantage of using this type rather than boost::rational<tom_int> directly, is that it is expression-template - enabled, greatly reducing the number of temporaries created in complex expressions. -

    -

    - There are also non-member functions: -

    -
    tom_int numerator(const tom_rational&);
-tom_int denominator(const tom_rational&);
-
    -

    - which return the numerator and denominator of the number. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed tom_rationals - have the value zero (this the inherited Boost.Rational behavior). -
      • -
    • - Division by zero results in a boost::bad_rational - exception being thrown (see the rational number library's docs for more - information). -
      • -
    • - No changes are made to libtommath's - global state, so this type can safely coexist with other libtommath - code. -
      • -
    • - Performance of this type has been found to be pretty poor - this need - further investigation - but it appears that Boost.Rational needs some - improvement in this area. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/tommath.hpp>
-
-using namespace boost::multiprecision;
-
-tom_rational v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-v /= 10;
-
-std::cout << v << std::endl; // prints 1000! / 10
-std::cout << numerator(v) << std::endl;
-std::cout << denominator(v) << std::endl;
-
-tom_rational w(2, 3); // Component wise constructor
-std::cout << w << std::endl; // prints 2/3
-
    -

    -

    -
    - - Use With - Boost.Rational -
    -

    - All of the integer types in this library can be used as template arguments - to boost::rational<IntType>. -

    -

    - Note that using the library in this way largely negates the effect of the - expression templates in mp_number. -

    -
    - - rational_adapter -
    -
    namespace boost{ namespace multiprecision{
-
-template <class IntBackend>
-class rational_adpater;
-
-}}
-
    -

    - The class template rational_adapter - is a back-end for mp_number - which converts any existing integer back-end into a rational-number back-end. -

    -

    - So for example, given an integer back-end type MyIntegerBackend, - the use would be something like: -

    -
    typedef mp_number<MyIntegerBackend>                    MyInt;
-typedef mp_number<rational_adapter<MyIntegerBackend> > MyRational;
-
-MyRational r = 2;
-r /= 3;
-MyInt i = numerator(r);
-assert(i == 2);
-
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/reals.html b/doc/html/boost_multiprecision/tut/reals.html deleted file mode 100644 index 02d1064f..00000000 --- a/doc/html/boost_multiprecision/tut/reals.html +++ /dev/null @@ -1,521 +0,0 @@ - - - -Floating Point Numbers - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - The following back-ends provide floating point arithmetic: -

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend Type -

    -     		-

    - Header -

    -     		-

    - Radix -

    -     		-

    - Dependencies -

    -     		-

    - Pros -

    -     		-

    - Cons -

    -
    -

    - mpf_float<N> -

    -     		-

    - boost/multiprecision/gmp.hpp -

    -     		-

    - 2 -

    -     		-

    - GMP -

    -     		-

    - Very fast and efficient back-end. -

    -     		-

    - Dependency on GNU licenced GMP - library. -

    -
    -

    - mpfr_float<N> -

    -     		-

    - boost/multiprecision/mpfr.hpp -

    -     		-

    - 2 -

    -     		-

    - GMP and MPFR -

    -     		-

    - Very fast and efficient back-end, with its own standard library - implementation. -

    -     		-

    - Dependency on GNU licenced GMP - and MPFR libraries. -

    -
    -

    - cpp_dec_float<N> -

    -     		-

    - boost/multiprecision/cpp_dec_float.hpp -

    -     		-

    - 10 -

    -     		-

    - None -

    -     		-

    - Header only, all C++ implementation. Boost licence. -

    -     		-

    - Approximately 2x slower than the MPFR - or GMP libraries. -

    -
    -
    - - gmp_float -
    -
    namespace boost{ namespace multiprecision{
-
-template <unsigned Digits10>
-class gmp_float;
-
-typedef mp_number<gmp_float<50> >    mpf_float_50;
-typedef mp_number<gmp_float<100> >   mpf_float_100;
-typedef mp_number<gmp_float<500> >   mpf_float_500;
-typedef mp_number<gmp_float<1000> >  mpf_float_1000;
-typedef mp_number<gmp_float<0> >     mpf_float;
-
-}} // namespaces
-
    -

    - The gmp_float back-end is - used in conjunction with mp_number - : it acts as a thin wrapper around the GMP - mpf_t to provide an real-number - type that is a drop-in replacement for the native C++ floating-point types, - but with much greater precision. -

    -

    - Type gmp_float can be used - at fixed precision by specifying a non-zero Digits10 - template parameter, or at variable precision by setting the template argument - to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 - provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision - respectively. The typedef mpf_float provides a variable precision type whose - precision can be controlled via the mp_numbers - member functions. -

    -
    - - - - - -
    [Note]Note

    - This type only provides standard library and numeric_limits - support when the precision is fixed at compile time. -

    -

    - As well as the usual conversions from arithmetic and string types, instances - of mp_number<mpf_float<N> > are copy constructible and assignable - from: -

    -
      -
    • - The GMP native types mpf_t, mpz_t, - mpq_t. -
      • -
    • - The mp_number wrappers - around those types: mp_number<mpf_float<M> >, - mp_number<gmp_int>, - mp_number<gmp_rational>. -
      • -
    -

    - It's also possible to access the underlying mpf_t - via the data() - member function of gmp_float. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed gmp_floats - have the value zero (this is the GMP - library's default behavior). -
      • -
    • - No changes are made to the GMP - library's global settings, so this type can be safely mixed with existing - GMP code. -
      • -
    • - It is not possible to round-trip objects of this type to and from a string - and get back exactly the same value. This appears to be a limitation - of GMP. -
      • -
    • - Since the underlying GMP types - have no notion of infinities or NaN's, care should be taken to avoid - numeric overflow or division by zero. That latter will trigger a hardware - exception, while generating excessively large exponents may result in - instability of the underlying GMP - library (in testing, converting a number with an excessively large or - small exponent to a string caused GMP - to segfault). -
      • -
    • - This type can equally be used with MPIR - as the underlying implementation - indeed that is the recommended option - on Win32. -
      • -
    -
    - - - GMP example: -
    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-
-using namespace boost::multiprecision;
-
-// Operations at variable precision and limited standard library support:
-mpf_float a = 2;
-mpf_float::default_precision(1000);
-std::cout << mpf_float::default_precision() << std::endl;
-std::cout << sqrt(a) << std::endl; // print root-2
-
-// Operations at fixed precision and full standard library support:
-mpf_float_100 b = 2;
-std::cout << std::numeric_limits<mpf_float_100>::digits << std::endl;
-// We can use any C++ std lib function:
-std::cout << log(b) << std::endl; // print log(2)
-// We can also use any function from Boost.Math:
-std::cout << boost::math::tgamma(b) << std::endl;
-// These even work when the argument is an expression template:
-std::cout << boost::math::tgamma(b * b) << std::endl;
-
-// Access the underlying representation:
-mpf_t f;
-mpf_init(f);
-mpf_set(f, a.backend().data());
-
    -

    -

    -
    - - mpfr_float -
    -
    namespace boost{ namespace multiprecision{
-
-template <unsigned Digits10>
-class mpfr_float_backend;
-
-typedef mp_number<mpfr_float_backend<50> >    mpfr_float_50;
-typedef mp_number<mpfr_float_backend<100> >   mpfr_float_100;
-typedef mp_number<mpfr_float_backend<500> >   mpfr_float_500;
-typedef mp_number<mpfr_float_backend<1000> >  mpfr_float_1000;
-typedef mp_number<mpfr_float_backend<0> >     mpfr_float;
-
-}} // namespaces
-
    -

    - The mpfr_float_backend type - is used in conjunction with mp_number: - It acts as a thin wrapper around the MPFR - mpfr_t to provide an real-number - type that is a drop-in replacement for the native C++ floating-point types, - but with much greater precision. -

    -

    - Type mpfr_float_backend can - be used at fixed precision by specifying a non-zero Digits10 - template parameter, or at variable precision by setting the template argument - to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 - provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision - respectively. The typedef mpfr_float provides a variable precision type whose - precision can be controlled via the mp_numbers - member functions. -

    -
    - - - - - -
    [Note]Note

    - This type only provides numeric_limits - support when the precision is fixed at compile time. -

    -

    - As well as the usual conversions from arithmetic and string types, instances - of mp_number<mpfr_float_backend<N> > are copy constructible and assignable - from: -

    -
      -
    • - The GMP native types mpf_t, mpz_t, - mpq_t. -
      • -
    • - The MPFR native type mpfr_t. -
      • -
    • - The mp_number wrappers - around those types: mp_number<mpfr_float_backend<M> >, - mp_number<mpf_float<M> >, mp_number<gmp_int>, mp_number<gmp_rational>. -
      • -
    -

    - It's also possible to access the underlying mpf_t - via the data() member function of gmp_float. -

    -

    - Things you should know when using this type: -

    -
      -
    • - A default constructed mpfr_float_backend - is set to a NaN (this is the default MPFR - behavior). -
      • -
    • - All operations use round to nearest. -
      • -
    • - No changes are made to GMP or - MPFR global settings, so this - type can coexist with existing MPFR - or GMP code. -
      • -
    • - The code can equally use MPIR in - place of GMP - indeed that is - the prefered option on Win32. -
      • -
    -
    - - - MPFR example: -
    -

    -

    -
    #include <boost/multiprecision/mpfr.hpp>
-
-using namespace boost::multiprecision;
-
-// Operations at variable precision and no numeric_limits support:
-mpfr_float a = 2;
-mpfr_float::default_precision(1000);
-std::cout << mpfr_float::default_precision() << std::endl;
-std::cout << sqrt(a) << std::endl; // print root-2
-
-// Operations at fixed precision and full numeric_limits support:
-mpfr_float_100 b = 2;
-std::cout << std::numeric_limits<mpfr_float_100>::digits << std::endl;
-// We can use any C++ std lib function:
-std::cout << log(b) << std::endl; // print log(2)
-// We can also use any function from Boost.Math:
-std::cout << boost::math::tgamma(b) << std::endl;
-// These even work when the argument is an expression template:
-std::cout << boost::math::tgamma(b * b) << std::endl;
-
-// Access the underlying data:
-mpfr_t r;
-mpfr_init(r);
-mpfr_set(r, b.backend().data(), GMP_RNDN);
-
    -

    -

    -
    - - cpp_dec_float -
    -
    namespace boost{ namespace multiprecision{
-
-template <unsigned Digits10>
-class cpp_dec_float;
-
-typedef mp_number<cpp_dec_float<50> > cpp_dec_float_50;
-typedef mp_number<cpp_dec_float<100> > cpp_dec_float_100;
-
-}} // namespaces
-
    -

    - The cpp_dec_float back-end - is used in conjunction with mp_number: - It acts as an entirely C++ (header only and dependency free) real-number - type that is a drop-in replacement for the native C++ floating-point types, - but with much greater precision. -

    -

    - Type cpp_dec_float can be - used at fixed precision by specifying a non-zero Digits10 - template parameter. The typedefs cpp_dec_float_50 - and cpp_dec_float_100 provide - arithmetic types at 50 and 100 decimal digits precision respectively. -

    -

    - There is full standard library and numeric_limits - support available for this type. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed cpp_dec_floats - have a value of zero. -
      • -
    • - The radix of this type is 10. As a result it can behave subtly differently - from base-2 types. -
      • -
    • - It is not possible to round-trip this type to and from a string and get - back to exactly the same value (this is a result of the type having some - hidden internal guard digits). -
      • -
    • - The type has a number of internal guard digits over and above those specified - in the template argument. Normally these should not be visible to the - user. -
      • -
    -
    - - cpp_dec_float - example: -
    -

    -

    -
    #include <boost/multiprecision/cpp_dec_float.hpp>
-
-using namespace boost::multiprecision;
-
-// Operations at fixed precision and full numeric_limits support:
-cpp_dec_float_100 b = 2;
-std::cout << std::numeric_limits<cpp_dec_float_100>::digits << std::endl;
-// We can use any C++ std lib function:
-std::cout << log(b) << std::endl; // print log(2)
-// We can also use any function from Boost.Math:
-std::cout << boost::math::tgamma(b) << std::endl;
-// These even work when the argument is an expression template:
-std::cout << boost::math::tgamma(b * b) << std::endl;
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/index.html b/doc/html/index.html deleted file mode 100644 index d6b3fc03..00000000 --- a/doc/html/index.html +++ /dev/null @@ -1,75 +0,0 @@ - - - -Chapter 1. Boost.Multiprecision - - - - - - -
    Next
    -
    -
    -

    -Chapter 1. Boost.Multiprecision

    -

    -John Maddock -

    -

    -Christopher Kormanyos -

    -

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    -
    -

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -

    Table of Contents

    -
    -
    Introduction
    -
    Tutorial
    -
    -
    Integer Types
    -
    Floating Point Numbers
    -
    Rational Number Types
    -
    Generating Random Numbers
    -
    Primality Testing
    -
    -
    Reference
    -
    -
    mp_number
    -
    Backend Requirements
    -
    -
    Performance Comparison
    -
    -
    Floating Point Real - World Tests
    -
    Integer Real - World Tests
    -
    Float Algorithm - Perfomance
    -
    Integer - Algorithm Perfomance
    -
    Rational - Type Perfomance
    -
    -
    Roadmap
    -
    -
    History
    -
    TODO
    -
    -
    -
    -
    - - - -

    Last revised: March 28, 2012 at 17:52:12 GMT

    -
    -
    Next
    - - diff --git a/doc/index.idx b/doc/index.idx new file mode 100644 index 00000000..fc9adc82 --- /dev/null +++ b/doc/index.idx @@ -0,0 +1,11 @@ + +!scan-path boost/multiprecision .*\.hpp true + + + + + + + + + diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index c31531b3..97cf9fad 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -204,7 +204,7 @@ transformation is more efficient than creating the extra temporary variable, jus one would hope. Finally, note that `mp_number` takes a second template argument, which, when set to `false` disables all -the expression template machinary. The result is much faster to compile, but slower at runtime. +the expression template machinery. The result is much faster to compile, but slower at runtime. We'll conclude this section by providing some more performance comparisons between these three libraries, again, all are using [mpfr] to carry out the underlying arithmetic, and all are operating at the same precision @@ -238,12 +238,14 @@ The following back-ends provide integer arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] [[`cpp_int`][boost/multiprecision/cpp_int.hpp][2][None] - [Very versatile, Boost licenced, all C++ integer type which support both [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] and fixed precision integer types.][Slower than [gmp], though typically not as slow as [tommath]]] -[[`gmp_int`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licenced [gmp] library.]] + [Very versatile, Boost licensed, all C++ integer type which support both [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] and fixed precision integer types.][Slower than [gmp], though typically not as slow as [tommath]]] +[[`gmp_int`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] [[`tom_int`][boost/multiprecision/tommath.hpp][2][[tommath]][Public domain back-end with no licence restrictions.][Slower than [gmp].]] ] -[h4 cpp_int] +[section:cpp_int cpp_int] + +`#include ` namespace boost{ namespace multiprecision{ @@ -290,7 +292,7 @@ integer types, and both signed and unsigned types. There are three template arg [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] types (where the Allocator parameter is non-void), then this parameter must be `true`. For fixed precision types then this type may be either `true` (type is signed), or `false` (type is unsigned).]] -[[Allocator][The allocator to use for dymamic memory allocation, or type `void` if this is to be a fixed precision type.]] +[[Allocator][The allocator to use for dynamic memory allocation, or type `void` if this is to be a fixed precision type.]] ] Things you should know when using this type: @@ -317,7 +319,11 @@ the feature off. [cpp_int_eg] -[h4 gmp_int] +[endsect] + +[section:gmp_int gmp_int] + +`#include ` namespace boost{ namespace multiprecision{ @@ -347,13 +353,17 @@ as a result performing formatted output on this type when the argument is negati `std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. * Division by zero is handled by the [gmp] library - it will trigger a division by zero signal. * Although this type is a wrapper around [gmp] it will work equally well with [mpir]. Indeed use of [mpir] -is recomended on Win32. +is recommended on Win32. [h5 Example:] [mpz_eg] -[h4 tom_int] +[endsect] + +[section:tom_int tom_int] + +`#include ` namespace boost{ namespace multiprecision{ @@ -384,18 +394,22 @@ as a result performing formatted output on this type when the argument is negati [endsect] -[section:reals Floating Point Numbers] +[endsect] + +[section:floats Floating Point Numbers] The following back-ends provide floating point arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] -[[`mpf_float`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licenced [gmp] library.]] -[[`mpfr_float`][boost/multiprecision/mpfr.hpp][2][[gmp] and [mpfr]][Very fast and efficient back-end, with its own standard library implementation.][Dependency on GNU licenced [gmp] and [mpfr] libraries.]] +[[`mpf_float`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] +[[`mpfr_float`][boost/multiprecision/mpfr.hpp][2][[gmp] and [mpfr]][Very fast and efficient back-end, with its own standard library implementation.][Dependency on GNU licensed [gmp] and [mpfr] libraries.]] [[`cpp_dec_float`][boost/multiprecision/cpp_dec_float.hpp][10][None][Header only, all C++ implementation. Boost licence.][Approximately 2x slower than the [mpfr] or [gmp] libraries.]] ] -[h4 gmp_float] +[section:gmp_float gmp_float] + +`#include ` namespace boost{ namespace multiprecision{ @@ -449,7 +463,11 @@ the recommended option on Win32. [mpf_eg] -[h4 mpfr_float] +[endsect] + +[section:mpfr_float mpfr_float] + +`#include ` namespace boost{ namespace multiprecision{ @@ -491,13 +509,17 @@ Things you should know when using this type: * All operations use round to nearest. * No changes are made to [gmp] or [mpfr] global settings, so this type can coexist with existing [mpfr] or [gmp] code. -* The code can equally use [mpir] in place of [gmp] - indeed that is the prefered option on Win32. +* The code can equally use [mpir] in place of [gmp] - indeed that is the preferred option on Win32. [h5 [mpfr] example:] [mpfr_eg] -[h4 cpp_dec_float] +[endsect] + +[section:cpp_dec_float cpp_dec_float] + +`#include ` namespace boost{ namespace multiprecision{ @@ -534,20 +556,24 @@ Normally these should not be visible to the user. [endsect] +[endsect] + [section:rational Rational Number Types] The following back-ends provide rational number arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] -[[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licenced [gmp] library.]] -[[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licenced implementation.][Slower than [gmp].]] +[[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] +[[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licensed implementation.][Slower than [gmp].]] [[`tommath_rational`][boost/multiprecision/tommath.hpp][2][[tommath]][All C/C++ implementation that's Boost Software Licence compatible.][Slower than [gmp].]] [[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any inetger back-end type to be used as a rational type.][Requires an underlying integer back-end type.]] [[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `mp_number` integer type.][The expression templates used by `mp_number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]] ] -[h4 gmp_rational] +[section:gmp_rational gmp_rational] + +`#include ` namespace boost{ namespace multiprecision{ @@ -583,13 +609,17 @@ Things you should know when using this type: * Division by zero results in a hardware exception inside the [gmp] library. * No changes are made to the [gmp] library's global settings, so this type can coexist with existing [gmp] code. -* The code can equally be used with [mpir] as the underlying library - indeed that is the prefered option on Win32. +* The code can equally be used with [mpir] as the underlying library - indeed that is the preferred option on Win32. [h5 Example:] [mpq_eg] -[h4 cpp_rational] +[endsect] + +[section:cpp_rational cpp_rational] + +`#include ` namespace boost{ namespace multiprecision{ @@ -623,7 +653,11 @@ Things you should know when using this type: [cpp_rational_eg] -[h4 tommath_rational] +[endsect] + +[section:tommath_rational tommath_rational] + +`#include ` namespace boost{ namespace multiprecision{ @@ -658,13 +692,17 @@ needs some improvement in this area. [mp_rat_eg] -[h4 Use With Boost.Rational] +[endsect] + +[section:br Use With Boost.Rational] All of the integer types in this library can be used as template arguments to `boost::rational`. Note that using the library in this way largely negates the effect of the expression templates in `mp_number`. -[h4 rational_adapter] +[endsect] + +[section:rational_adapter rational_adapter] namespace boost{ namespace multiprecision{ @@ -686,6 +724,72 @@ So for example, given an integer back-end type `MyIntegerBackend`, the use would MyInt i = numerator(r); assert(i == 2); +[endsect] + +[endsect] + +[section:conversions Constructing and Interconverting Between Number Types] + +All of the number types that are based on `mp_number` have certain conversion rules in common. +In particular: + +* Any number type can be constructed (or assigned) from any builtin arithmetic type: + + cpp_dec_float_50 df(0.5); // OK construction from double + cpp_int i(450); // OK constructs from signed int + +* Any number type can be constructed (or assigned) from a `const char*` or a `std::string`: + + // pi to 50 places from a string: + cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510"; + // Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly: + cpp_int i = "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000"; + // Invalid input always results in a std::runtime_error being thrown: + i = std::string("3.14"); + +* Any number type will interoperate with the builtin type in arithmetic expressions: + + // pi to 50 places from a string: + cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510"; + // Multiply by 2 - using an integer literal here is usually more efficient + // than constructing a temporary: + df *= 2; + + // There is a need to be careful with integer types though: + cpp_int i = 2; + // Ooops, this really just multiplies by 3: + i *= 3.14; + +* Any number type can be streamed to and from the C++ iostreams: + + + cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510"; + // Now print at full precision: + std::cout << std::setprecision(std::numeric_limits::max_digits10) + << df << std::endl + cpp_int i = 1; + i <<= 256; + // Now print in hex format with prefix: + std::cout << std::hex << std::showbase << i << std::endl; + +* Some intercomnversions between number types are completely generic, and are always available: + + cpp_int cppi(2); + // We can always convert between numbers of the same category - + // int to int, rational to rational, or float to float, so this is OK: + mpz_int z = cppi; + // We can always promote from int to rational, int to float, or rational to float: + cpp_rational cppr = cppi; // OK, int to rational + cpp_dec_float_50 df = cppi; // OK, int to float + df = cppr; // OK, rational to float + // However narrowing conversions always fail: + cppi = df; // Compiler error, conversion not allowed + +* Other interconversions may be allowed as special cases, whenever the backend allows it: + + mpf_t m; // Native GMP type. + mpf_init_set_ui(m, 0); // set to a value; + mpf_float i(m); // copies the value of the native type. [endsect] @@ -933,7 +1037,7 @@ Class `mp_number` has two template arguments: [variablelist [[Backend][The actual arithmetic back-end that does all the work.]] -[[ExpressionTemplates][A boolean value: when true, then expression templates are enabled, otherwise they are disabled.]] +[[ExpressionTemplates][A Boolean value: when true, then expression templates are enabled, otherwise they are disabled.]] ] mp_number(); @@ -1248,6 +1352,172 @@ whose precision can vary at compile time (such as `mpf_float`). [endsect] +[section:cpp_int_ref cpp_int] + + namespace boost{ namespace multiprecision{ + + template > + struct cpp_int_backend; + + typedef mp_number > cpp_int; // arbitrary precision integer + typedef rational_adapter > cpp_rational_backend; + typedef mp_number cpp_rational; // arbitrary precision rational number + + // Fixed precision unsigned types: + typedef mp_number, false> mp_uint128_t; + typedef mp_number, false> mp_uint256_t; + typedef mp_number, false> mp_uint512_t; + typedef mp_number, false> mp_uint1024_t; + + // Fixed precision signed types: + typedef mp_number, false> mp_int128_t; + typedef mp_number, false> mp_int256_t; + typedef mp_number, false> mp_int512_t; + typedef mp_number, false> mp_int1024_t; + + }} // namespaces + +Class template `cpp_int_backend` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The template arguments are: + +[variablelist +[[Argument][Meaning]] +[[MinBits] + [The number of Bits to reserve inside the class's internal cache. When constructing a value, + the object will use this internal cache if possible before resorting to dynamic memory allocation. + When this value is zero, then the size of the internal cache is `2*sizeof(void*)*CHAR_BIT`. + When the Allocator argument is `void`, then this parameter determines the precision of the type.]] +[[Signed][When `true` the type is signed, otherwise unsigned. Note that unsigned types are currently only + supported when the Allocator parameter is `void`.]] +[[Allocator][The allocator used for dynamic memory allocation. This parameter can be `void`, in which case + no dymanic memory will ever be allocated.]] +] + +More information on this type can be found in the [link boost_multiprecision.tut.ints.cpp_int tutorial]. + +[endsect] + +[section:gmp_int_ref gmp_int] + + namespace boost{ namespace multiprecision{ + + class gmp_int; + + typedef mp_number mpz_int; + + }} // namespaces + +Class template `gmp_int` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +More information on this type can be found in the [link boost_multiprecision.tut.ints.gmp_int tutorial]. + +[endsect] + +[section:tom_int_ref tom_int] + + namespace boost{ namespace multiprecision{ + + class tommath_int; + + typedef mp_number tom_int; + + }} // namespaces + +Class template `tommath_int` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +More information on this type can be found in the [link boost_multiprecision.tut.ints.tom_int tutorial]. + +[endsect] + +[section:mpf_ref gmp_float] + + namespace boost{ namespace multiprecision{ + + template + class gmp_float; + + typedef mp_number > mpf_float_50; + typedef mp_number > mpf_float_100; + typedef mp_number > mpf_float_500; + typedef mp_number > mpf_float_1000; + typedef mp_number > mpf_float; + + }} // namespaces + +Class template `gmp_float` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type +should support. When this parameter is zero, then the precision can be set at runtime via `mp_number::default_precision` +and `mp_number::precision`. Note that this type does not in any way change the GMP library's global state (for example +it does not change the default precision of the mpf_t data type), therefore you can safely mix this type with existing +code that uses GMP, and also mix `gmp_float`s of differing precision. + +More information on this type can be found in the [link boost_multiprecision.tut.floats.gmp_float tutorial]. + +[endsect] + +[section:mpfr_ref mpfr_float_backend] + + namespace boost{ namespace multiprecision{ + + template + class mpfr_float_backend; + + typedef mp_number > mpfr_float_50; + typedef mp_number > mpfr_float_100; + typedef mp_number > mpfr_float_500; + typedef mp_number > mpfr_float_1000; + typedef mp_number > mpfr_float; + + }} // namespaces + +Class template `mpfr_float_backend` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type +should support. When this parameter is zero, then the precision can be set at runtime via `mp_number::default_precision` +and `mp_number::precision`. Note that this type does not in any way change the GMP or MPFR library's global state (for example +it does not change the default precision of the mpfr_t data type), therefore you can safely mix this type with existing +code that uses GMP or MPFR, and also mix `mpfr_float_backend`s of differing precision. + +More information on this type can be found in the [link boost_multiprecision.tut.floats.mpfr_float tutorial]. + +[endsect] + +[section:cpp_dec_ref cpp_dec_float] + + namespace boost{ namespace multiprecision{ + + template + class cpp_dec_float; + + typedef mp_number > cpp_dec_float_50; + typedef mp_number > cpp_dec_float_100; + + }} // namespaces + +Class template `cpp_dec_float` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type +should support. Note that this type does not ever perform any dynamic memory allocation, as a result the `Digits10` +template argument should not be set too high or the classes size will grow unreasonably large. + +More information on this type can be found in the [link boost_multiprecision.tut.floats.cpp_dec_float tutorial]. + +[endsect] + [section:backendconc Backend Requirements] [template super[x]''''''[x]''''''] @@ -1414,7 +1684,7 @@ of type B2. [note The non-member functions are all named with an "eval_" prefix to avoid conflicts with template classes of the same name - -in point of fact this naming convension shouldn't be necessary, but rather works around some compiler bugs.] +in point of fact this naming convention shouldn't be necessary, but rather works around some compiler bugs.] [endsect] @@ -1490,7 +1760,7 @@ altogether - cutting about a third off the total runtime. Note that these tests are carefully designed to test performance of the underlying algorithms and not memory allocation or variable copying. As usual, performance results should be taken -with a healthy dose of scepticism, and real-world peformance may vary widely depending upon the +with a healthy dose of scepticism, and real-world performance may vary widely depending upon the specifics of the program. In each table relative times are given first, with the best performer given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 operations. @@ -1560,7 +1830,7 @@ Windows Vista machine. Note that these tests are carefully designed to test performance of the underlying algorithms and not memory allocation or variable copying. As usual, performance results should be taken -with a healthy dose of scepticism, and real-world peformance may vary widely depending upon the +with a healthy dose of scepticism, and real-world performance may vary widely depending upon the specifics of the program. In each table relative times are given first, with the best performer given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 operations. @@ -1717,7 +1987,7 @@ Linux x86_64 results are broadly similar, except that libtommath performs much b Note that these tests are carefully designed to test performance of the underlying algorithms and not memory allocation or variable copying. As usual, performance results should be taken -with a healthy dose of scepticism, and real-world peformance may vary widely depending upon the +with a healthy dose of scepticism, and real-world performance may vary widely depending upon the specifics of the program. In each table relative times are given first, with the best performer given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 operations. @@ -1779,6 +2049,16 @@ Windows Vista machine. [section:hist History] +*2011-2012, John Maddock adds an expression template enabled front end to Christopher's code, +and adds support for other backends. +* 2011, Christopher Kormanyos publishes the decimal floating point code under the Boost +Software Licence. The code is published as: [@http://doi.acm.org/10.1145/1916461.1916469 +"Algorithm 910: A Portable C++ Multiple-Precision +System for Special-Function Calculations"], in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, +2011. +* 2002-2011, Christopher Kormanyos develops the all C++ decimal arithmetic floating point +code. + [endsect] [section:todo TODO] @@ -1794,4 +2074,28 @@ More a list of what ['could] be done, rather than what ['should] be done (which [endsect] +[section:ack Acknowledgements] + +This library would not have happened without: + +* Christopher Kormanyos' C++ decimal number code. +* Paul Bristow for patiently testing, and commenting on the library. +* All the folks at GMP, MPFR and libtommath, for providing the "guts" that makes this library work. +* [@http://www-cs-faculty.stanford.edu/~uno/taocp.html "The Art Of Computer Programming"], +Donald E. Knuth, Volume 2: Seminumerical Algorithms, Third Edition +(Reading, Massachusetts: Addison-Wesley, 1997), xiv+762pp. ISBN 0-201-89684-2 + [endsect] + +[endsect] + +[section:indexes Indexes] + +[include ../../../../../trunk/tools/auto_index/include/auto_index_helpers.qbk] +[named_index function_name Function Index] +[named_index class_name Class Index] +[named_index typedef_name Typedef Index] +[index] + +[endsect] + From c984b2eaa7ddfdebf9ee6cd466dae9fcbca8b43c Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 30 Mar 2012 18:35:38 +0000 Subject: [PATCH 154/256] Add updated HTML docs. [SVN r77652] --- doc/html/boost_multiprecision/indexes.html | 40 + .../boost_multiprecision/indexes/s01.html | 237 ++ .../boost_multiprecision/indexes/s02.html | 46 + .../boost_multiprecision/indexes/s03.html | 189 + .../boost_multiprecision/indexes/s04.html | 519 +++ doc/html/boost_multiprecision/intro.html | 522 +++ doc/html/boost_multiprecision/map.html | 39 + doc/html/boost_multiprecision/map/ack.html | 55 + doc/html/boost_multiprecision/map/hist.html | 50 + doc/html/boost_multiprecision/map/todo.html | 58 + doc/html/boost_multiprecision/perf.html | 46 + .../perf/float_performance.html | 961 ++++++ .../perf/int_real_world.html | 217 ++ .../perf/integer_performance.html | 3034 +++++++++++++++++ .../perf/rational_performance.html | 905 +++++ .../boost_multiprecision/perf/realworld.html | 278 ++ doc/html/boost_multiprecision/ref.html | 44 + .../boost_multiprecision/ref/backendconc.html | 2295 +++++++++++++ .../boost_multiprecision/ref/cpp_dec_ref.html | 61 + 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    + The Multiprecision Library provides User-defined integer, + rational and floating-point C++ types which try to emulate as closely as practicable + the C++ built-in types, but provide for more range and precision. Depending + upon the number type, precision may be arbitrarily large (limited only by available + memory), fixed at compile time values, for example 50 decimal digits, or a + variable controlled at run-time by member functions. The types are expression-template-enabled + for better performance than naive user-defined types. +

    +

    + The Multiprecision library comes in two distinct parts: +

    +
      +
    • + An expression-template-enabled front-end mp_number + that handles all the operator overloading, expression evaluation optimization, + and code reduction. +
      • +
    • + A selection of back-ends that implement the actual arithmetic operations, + and need conform only to the reduced interface requirements of the front-end. +
      • +
    +

    + Separation of front-end and back-end allows use of highly refined, but restricted + license libraries where possible, but provides Boost license alternatives for + users who must have a portable unconstrained license. Which is to say some + back-ends rely on 3rd party libraries, but a header-only Boost license version + is always available (if somewhat slower). +

    +

    + The library is often used via one of the predefined typedefs: for example if + you wanted an arbitrary + precision integer type using GMP + as the underlying implementation then you could use: +

    +
    #include <boost/multiprecision/gmp.hpp>  // Defines the wrappers around the GMP library's types
+
+boost::multiprecision::mpz_int myint;    // Arbitrary precision integer type.
+
    +

    + Alternatively, you can compose your own multiprecision type, by combining + mp_number with one of the predefined + back-end types. For example, suppose you wanted a 300 decimal digit floating-point + type based on the MPFR library. In + this case, there's no predefined typedef with that level of precision, so instead + we compose our own: +

    +
    #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
+
+namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
+
+typedef mp::mp_number<mp::mpfr_float_backend<300> >  my_float;
+
+my_float a, b, c; // These variables have 300 decimal digits precision
+
    +

    + We can repeat the above example, but with the expression templates disabled + (for faster compile times, but slower runtimes) by passing a second template + argument to mp_number: +

    +
    #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
+
+namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
+
+typedef mp::mp_number<mp::mpfr_float_backend<300>, false>  my_float;
+
+my_float a, b, c; // These variables have 300 decimal digits precision
+
    +
    + + Expression + Templates +
    +

    + Class mp_number is expression-template-enabled: + that means that rather than having a multiplication operator that looks like + this: +

    +
    template <class Backend>
+mp_number<Backend> operator * (const mp_number<Backend>& a, const mp_number<Backend>& b)
+{
+   mp_number<Backend> result(a);
+   result *= b;
+   return result;
+}
+
    +

    + Instead the operator looks more like this: +

    +
    template <class Backend>
+unmentionable-type operator * (const mp_number<Backend>& a, const mp_number<Backend>& b);
+
    +

    + Where the "unmentionable" return type is an implementation detail + that, rather than containing the result of the multiplication, contains instructions + on how to compute the result. In effect it's just a pair of references to the + arguments of the function, plus some compile-time information that stores what + the operation is. +

    +

    + The great advantage of this method is the elimination of temporaries: + for example the "naive" implementation of operator* above, requires one temporary for computing + the result, and at least another one to return it. It's true that sometimes + this overhead can be reduced by using move-semantics, but it can't be eliminated + completely. For example, lets suppose we're evaluating a polynomial via Horners + method, something like this: +

    +
    T a[7] = { /* some values */ };
+//....
+y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0];
+
    +

    + If type T is an mp_number, then this expression is evaluated + without creating a single temporary value. In contrast, + if we were using the C++ wrapper that ships with GMP + - mpfr_class + - then this expression would result in no less than 11 temporaries (this is + true even though mpfr_class + does use expression templates to reduce the number of temporaries somewhat). + Had we used an even simpler wrapper around GMP + or MPFR like mpclass + things would have been even worse and no less that 24 temporaries are created + for this simple expression (note - we actually measure the number of memory + allocations performed rather than the number of temporaries directly). +

    +

    + This library also extends expression template support to standard library functions + like abs or sin + with mp_number arguments. This + means that an expression such as: +

    +
    y = abs(x);
+
    +

    + can be evaluated without a single temporary being calculated. Even expressions + like: +

    +
    y = sin(x);
+
    +

    + get this treatment, so that variable 'y' is used as "working storage" + within the implementation of sin, + thus reducing the number of temporaries used by one. Of course, should you + write: +

    +
    x = sin(x);
+
    +

    + Then we clearly can't use x + as working storage during the calculation, so then a temporary variable is + created in this case. +

    +

    + Given the comments above, you might be forgiven for thinking that expression-templates + are some kind of universal-panacea: sadly though, all tricks like this have + their downsides. For one thing, expression template libraries like this one, + tend to be slower to compile than their simpler cousins, they're also harder + to debug (should you actually want to step through our code!), and rely on + compiler optimizations being turned on to give really good performance. Also, + since the return type from expressions involving mp_numbers + is an "unmentionable implementation detail", you have to be careful + to cast the result of an expression to the actual number type when passing + an expression to a template function. For example, given: +

    +
    template <class T>
+void my_proc(const T&);
+
    +

    + Then calling: +

    +
    my_proc(a+b);
+
    +

    + Will very likely result in obscure error messages inside the body of my_proc - since we've passed it an expression + template type, and not a number type. Instead we probably need: +

    +
    my_proc(my_mp_number_type(a+b));
+
    +

    + Having said that, these situations don't occur that often - or indeed not at + all for non-template functions. In addition, all the functions in the Boost.Math + library will automatically convert expression-template arguments to the underlying + number type without you having to do anything, so: +

    +
    mpfr_float_100 a(20), delta(0.125);
+boost::math::gamma_p(a, a + delta);
+
    +

    + Will work just fine, with the a + delta expression + template argument getting converted to an mpfr_float_100 + internally by the Boost.Math library. +

    +

    + One other potential pitfall that's only possible in C++11: you should never + store an expression template using: +

    +
    auto my_expression = a + b - c;
+
    +

    + unless you're absolutely sure that the lifetimes of a, + b and c + will outlive that of my_expression. +

    +

    + And finally... the performance improvements from an expression template library + like this are often not as dramatic as the reduction in number of temporaries + would suggest. For example if we compare this library with mpfr_class + and mpreal, with + all three using the underlying MPFR + library at 50 decimal digits precision then we see the following typical results + for polynomial execution: +

    +
    +

    Table 1.1. Evaluation of Order 6 Polynomial.

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + Relative Time +

    +     		+

    + Relative number of memory allocations +

    +
    +

    + mp_number +

    +     		+

    + 1.0 (0.00793s) +

    +     		+

    + 1.0 (2996 total) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.2 (0.00931s) +

    +     		+

    + 4.3 (12976 total) +

    +
    +

    + mpreal +

    +     		+

    + 1.9 (0.0148s) +

    +     		+

    + 9.3 (27947 total) +

    +
    +
    +

    + As you can see, the execution time increases a lot more slowly than the number + of memory allocations. There are a number of reasons for this: +

    +
      +
    • + The cost of extended-precision multiplication and division is so great, + that the times taken for these tend to swamp everything else. +
      • +
    • + The cost of an in-place multiplication (using operator*=) tends to be more than an out-of-place + operator* + (typically operator *= + has to create a temporary workspace to carry out the multiplication, where + as operator* + can use the target variable as workspace). Since the expression templates + carry out their magic by converting out-of-place operators to in-place + ones, we necessarily take this hit. Even so the transformation is more + efficient than creating the extra temporary variable, just not by as much + as one would hope. +
      • +
    +

    + Finally, note that mp_number + takes a second template argument, which, when set to false + disables all the expression template machinery. The result is much faster to + compile, but slower at runtime. +

    +

    + We'll conclude this section by providing some more performance comparisons + between these three libraries, again, all are using MPFR + to carry out the underlying arithmetic, and all are operating at the same precision + (50 decimal digits): +

    +
    +

    Table 1.2. Evaluation of Boost.Math's Bessel function test data

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + Relative Time +

    +     		+

    + Relative Number of Memory Allocations +

    +
    +

    + mp_number +

    +     		+

    + 1.0 (6.21s) +

    +     		+

    + 1.0 (2685469) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.04 (6.45s) +

    +     		+

    + 1.47 (3946007) +

    +
    +

    + mpreal +

    +     		+

    + 1.53 (9.52s) +

    +     		+

    + 4.92 (13222940) +

    +
    +
    +
    +

    Table 1.3. Evaluation of Boost.Math's Non-Central T distribution test data

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + Relative Time +

    +     		+

    + Relative Number of Memory Allocations +

    +
    +

    + mp_number +

    +     		+

    + 1.0 (269s) +

    +     		+

    + 1.0 (139082551) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.04 (278s) +

    +     		+

    + 1.81 (252400791) +

    +
    +

    + mpreal +

    +     		+

    + 1.49 (401s) +

    +     		+

    + 3.22 (447009280) +

    +
    +
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

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    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

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    + This library would not have happened without: +

    +
      +
    • + Christopher Kormanyos' C++ decimal number code. +
      • +
    • + Paul Bristow for patiently testing, and commenting on the library. +
      • +
    • + All the folks at GMP, MPFR and libtommath, for providing the "guts" + that makes this library work. +
      • +
    • + "The + Art Of Computer Programming", Donald E. Knuth, Volume 2: + Seminumerical Algorithms, Third Edition (Reading, Massachusetts: Addison-Wesley, + 1997), xiv+762pp. ISBN 0-201-89684-2 +
      • +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html new file mode 100644 index 00000000..70462181 --- /dev/null +++ b/doc/html/boost_multiprecision/map/hist.html @@ -0,0 +1,50 @@ + + + +History + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
      +
    • + 2011-2012, John Maddock adds an expression template enabled front end + to Christopher's code, and adds support for other backends. +
      • +
    • + 2011, Christopher Kormanyos publishes the decimal floating point code + under the Boost Software Licence. The code is published as: "Algorithm + 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", + in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. +
      • +
    • + 2002-2011, Christopher Kormanyos develops the all C++ decimal arithmetic + floating point code. +
      • +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html new file mode 100644 index 00000000..1c188b18 --- /dev/null +++ b/doc/html/boost_multiprecision/map/todo.html @@ -0,0 +1,58 @@ + + + +TODO + + + + + + + + +
    +PrevUpHomeNext +
    +
    +

    +TODO +

    +

    + More a list of what could be done, rather than what + should be done (which may be a much smaller list!). +

    +
      +
    • + Add back-end support for libdecNumber. +
      • +
    • + Add an adapter back-end for complex number types. +
      • +
    • + Add a back-end for MPFR interval arithmetic. +
      • +
    • + Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. +
      • +
    • + Add assembly level routines to cpp_int_backend. +
      • +
    • + Add an all C++ binary floating point type. +
      • +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf.html b/doc/html/boost_multiprecision/perf.html new file mode 100644 index 00000000..7460f077 --- /dev/null +++ b/doc/html/boost_multiprecision/perf.html @@ -0,0 +1,46 @@ + + + +Performance Comparison + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    Floating Point Real + World Tests
    +
    Integer Real + World Tests
    +
    Float Algorithm + Perfomance
    +
    Integer + Algorithm Perfomance
    +
    Rational + Type Perfomance
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html new file mode 100644 index 00000000..9e9b8217 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/float_performance.html @@ -0,0 +1,961 @@ + + + +Float Algorithm Perfomance + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticism, and real-world + performance may vary widely depending upon the specifics of the program. + In each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. + The tests were run on 32-bit Windows Vista machine. +

    +
    +

    Table 1.8. Operator +

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1 (0.02382s) +

    +     		+

    + 1 (0.0294619s) +

    +     		+

    + 1 (0.058466s) +

    +
    +

    + gmp_float +

    +     		+

    + 4.55086 (0.108402s) +

    +     		+

    + 3.86443 (0.113853s) +

    +     		+

    + 2.6241 (0.15342s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.52036 (0.060035s) +

    +     		+

    + 2.1833 (0.0643242s) +

    +     		+

    + 1.37736 (0.0805287s) +

    +
    +
    +
    +

    Table 1.9. Operator +(int)

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1.56759 (0.0527023s) +

    +     		+

    + 1.74629 (0.0618102s) +

    +     		+

    + 1.68077 (0.105927s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.0336201s) +

    +     		+

    + 1 (0.0353951s) +

    +     		+

    + 1 (0.0630232s) +

    +
    +

    + mpfr_float +

    +     		+

    + 3.14875 (0.105861s) +

    +     		+

    + 3.15499 (0.111671s) +

    +     		+

    + 1.92831 (0.121528s) +

    +
    +
    +
    +

    Table 1.10. Operator -

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1 (0.0265783s) +

    +     		+

    + 1 (0.031465s) +

    +     		+

    + 1 (0.0619405s) +

    +
    +

    + gmp_float +

    +     		+

    + 4.66954 (0.124108s) +

    +     		+

    + 3.72645 (0.117253s) +

    +     		+

    + 2.67536 (0.165713s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.7909 (0.0741774s) +

    +     		+

    + 2.48557 (0.0782083s) +

    +     		+

    + 1.50944 (0.0934957s) +

    +
    +
    +
    +

    Table 1.11. Operator -(int)

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1 (0.0577674s) +

    +     		+

    + 1 (0.0633795s) +

    +     		+

    + 1 (0.11146s) +

    +
    +

    + gmp_float +

    +     		+

    + 2.31811 (0.133911s) +

    +     		+

    + 2.07251 (0.131355s) +

    +     		+

    + 1.67161 (0.186319s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.45081 (0.141577s) +

    +     		+

    + 2.29174 (0.145249s) +

    +     		+

    + 1.395 (0.155487s) +

    +
    +
    +
    +

    Table 1.12. Operator *

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1.07276 (0.287898s) +

    +     		+

    + 1.47724 (0.584569s) +

    +     		+

    + 1.55145 (5.09969s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.268372s) +

    +     		+

    + 1 (0.395718s) +

    +     		+

    + 1 (3.28705s) +

    +
    +

    + mpfr_float +

    +     		+

    + 1.27302 (0.341642s) +

    +     		+

    + 1.17649 (0.465557s) +

    +     		+

    + 1.14029 (3.7482s) +

    +
    +
    +
    +

    Table 1.13. Operator *(int)

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 2.89945 (0.11959s) +

    +     		+

    + 4.56335 (0.197945s) +

    +     		+

    + 9.03602 (0.742044s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.0412457s) +

    +     		+

    + 1 (0.0433772s) +

    +     		+

    + 1 (0.0821206s) +

    +
    +

    + mpfr_float +

    +     		+

    + 3.6951 (0.152407s) +

    +     		+

    + 3.71977 (0.161353s) +

    +     		+

    + 3.30958 (0.271785s) +

    +
    +
    +
    +

    Table 1.14. Operator /

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 3.24327 (4.00108s) +

    +     		+

    + 5.00532 (8.12985s) +

    +     		+

    + 6.79566 (54.2796s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (1.23366s) +

    +     		+

    + 1 (1.62424s) +

    +     		+

    + 1 (7.9874s) +

    +
    +

    + mpfr_float +

    +     		+

    + 1.32521 (1.63486s) +

    +     		+

    + 1.38967 (2.25716s) +

    +     		+

    + 1.72413 (13.7713s) +

    +
    +
    +
    +

    Table 1.15. Operator /(int)

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1.45093 (0.253675s) +

    +     		+

    + 1.83306 (0.419569s) +

    +     		+

    + 2.3644 (1.64187s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.174836s) +

    +     		+

    + 1 (0.22889s) +

    +     		+

    + 1 (0.694411s) +

    +
    +

    + mpfr_float +

    +     		+

    + 1.16731 (0.204088s) +

    +     		+

    + 1.13211 (0.259127s) +

    +     		+

    + 1.02031 (0.708513s) +

    +
    +
    +
    +

    Table 1.16. Operator str

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1.4585 (0.0188303s) +

    +     		+

    + 1.55515 (0.03172s) +

    +     		+

    + 1 (0.131962s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.0129107s) +

    +     		+

    + 1 (0.0203967s) +

    +     		+

    + 1.04632 (0.138075s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.19015 (0.0282764s) +

    +     		+

    + 1.84679 (0.0376683s) +

    +     		+

    + 1.20295 (0.158743s) +

    +
    +
    +

    + ] +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html new file mode 100644 index 00000000..89278b58 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/int_real_world.html @@ -0,0 +1,217 @@ + + + +Integer Real World Tests + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + These tests + measure the time taken to generate 1000 128-bit random numbers and test for + primality using the Miller Rabin test. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and libtommath-0.42.0. + The tests were run on 32-bit Windows Vista machine. +

    +
    ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Integer Type +

    +     		+

    + Relative (and Absolute) Times +

    +
    +

    + mpz_int +

    +     		+

    + 1.08279(0.370326s) +

    +
    +

    + mpz_int (no Expression templates) +

    +     		+

    + 1.1702(0.400222s) +

    +
    +

    + cpp_int +

    +     		+

    + 1.3612(0.465547s) +

    +
    +

    + cpp_int (no Expression templates) +

    +     		+

    + 1.33286(0.455854s) +

    +
    +

    + cpp_int (64-bit cache) +

    +     		+

    + 1.33134(0.455333s) +

    +
    +

    + cpp_int (256-bit cache) +

    +     		+

    + 1.29367(0.442451s) +

    +
    +

    + cpp_int (512-bit cache) +

    +     		+

    + 1.08821(0.37218s) +

    +
    +

    + cpp_int (1024-bit cache) +

    +     		+

    + 1.07902(0.369037s) +

    +
    +

    + mp_int1024_t +

    +     		+

    + 1.02616(0.35096s) +

    +
    +

    + mp_int1024_t (no Expression templates) +

    +     		+

    + 1(0.342011s) +

    +
    +

    + tom_int +

    +     		+

    + 3.74233(1.27992s) +

    +
    +

    + tom_int (no Expression templates) +

    +     		+

    + 3.97646(1.35999s) +

    +
    +

    + It's interesting to note that expression templates have little effect here + - perhaps because the actual expressions involved are relatively trivial + in this case - so the time taken for multiplication and division tends to + dominate. Also note how increasing the internal cache size used by cpp_int is quite effective in this case + in cutting out memory allocations altogether - cutting about a third off + the total runtime. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html new file mode 100644 index 00000000..b7bbe0e7 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/integer_performance.html @@ -0,0 +1,3034 @@ + + + +Integer Algorithm Perfomance + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticism, and real-world + performance may vary widely depending upon the specifics of the program. + In each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. + The tests were run on 32-bit Windows Vista machine. +

    +

    + Linux x86_64 results are broadly similar, except that libtommath performs + much better there. +

    +
    +

    Table 1.17. Operator +

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.24574 (0.0270133s) +

    +     		+

    + 1.09665 (0.0352319s) +

    +     		+

    + 1.25708 (0.0524047s) +

    +     		+

    + 1.31488 (0.08777s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1.05787 (0.0229394s) +

    +     		+

    + 1 (0.0321268s) +

    +     		+

    + 1.16171 (0.0484289s) +

    +     		+

    + 1.24017 (0.0827832s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.08016 (0.0451073s) +

    +     		+

    + 1.33792 (0.042983s) +

    +     		+

    + 1.19676 (0.0498904s) +

    +     		+

    + 1 (0.0667514s) +

    +
    +

    + tommath_int +

    +     		+

    + 1 (0.0216845s) +

    +     		+

    + 1.07779 (0.0346258s) +

    +     		+

    + 1 (0.0416877s) +

    +     		+

    + 1.06344 (0.0709863s) +

    +
    +
    +
    +

    Table 1.18. Operator +(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.46244 (0.0202077s) +

    +     		+

    + 1.20665 (0.0238576s) +

    +     		+

    + 1.17647 (0.0258293s) +

    +     		+

    + 1.12424 (0.0317931s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0138178s) +

    +     		+

    + 1 (0.0197719s) +

    +     		+

    + 1 (0.0219548s) +

    +     		+

    + 1 (0.0282796s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.15321 (0.0297527s) +

    +     		+

    + 2.09834 (0.041488s) +

    +     		+

    + 2.89935 (0.0636546s) +

    +     		+

    + 3.70262 (0.104709s) +

    +
    +

    + tommath_int +

    +     		+

    + 17.1419 (0.236864s) +

    +     		+

    + 12.9762 (0.256563s) +

    +     		+

    + 12.3275 (0.270648s) +

    +     		+

    + 10.7373 (0.303648s) +

    +
    +
    +
    +

    Table 1.19. Operator -

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.15385 (0.029665s) +

    +     		+

    + 1.08217 (0.0369886s) +

    +     		+

    + 1.05882 (0.051534s) +

    +     		+

    + 1.12132 (0.0822725s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0257095s) +

    +     		+

    + 1 (0.0341801s) +

    +     		+

    + 1 (0.0486711s) +

    +     		+

    + 1.08659 (0.0797242s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.56685 (0.040283s) +

    +     		+

    + 1.32917 (0.0454312s) +

    +     		+

    + 1.06917 (0.0520378s) +

    +     		+

    + 1 (0.0733708s) +

    +
    +

    + tommath_int +

    +     		+

    + 1.059 (0.0272264s) +

    +     		+

    + 1.16974 (0.0399818s) +

    +     		+

    + 1.01303 (0.0493054s) +

    +     		+

    + 1.03375 (0.0758472s) +

    +
    +
    +
    +

    Table 1.20. Operator -(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.51665 (0.0157196s) +

    +     		+

    + 1.31513 (0.0200533s) +

    +     		+

    + 1.29599 (0.0235066s) +

    +     		+

    + 1.21534 (0.0266136s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0103647s) +

    +     		+

    + 1 (0.0152482s) +

    +     		+

    + 1 (0.018138s) +

    +     		+

    + 1 (0.021898s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.7938 (0.0289568s) +

    +     		+

    + 2.55493 (0.038958s) +

    +     		+

    + 3.12248 (0.0566356s) +

    +     		+

    + 4.48855 (0.0982904s) +

    +
    +

    + tommath_int +

    +     		+

    + 20.8695 (0.216305s) +

    +     		+

    + 15.0705 (0.229797s) +

    +     		+

    + 13.4093 (0.243217s) +

    +     		+

    + 12.2599 (0.268468s) +

    +
    +
    +
    +

    Table 1.21. Operator *

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.29504 (0.0731032s) +

    +     		+

    + 1.55431 (0.196132s) +

    +     		+

    + 1.4363 (0.656569s) +

    +     		+

    + 1.63701 (2.47859s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0564485s) +

    +     		+

    + 1.16604 (0.147138s) +

    +     		+

    + 1 (0.457124s) +

    +     		+

    + 1 (1.5141s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.19574 (0.0674975s) +

    +     		+

    + 1 (0.126186s) +

    +     		+

    + 1.16627 (0.53313s) +

    +     		+

    + 1.02906 (1.5581s) +

    +
    +

    + tommath_int +

    +     		+

    + 1.97229 (0.111333s) +

    +     		+

    + 2.67087 (0.337027s) +

    +     		+

    + 2.13031 (0.973817s) +

    +     		+

    + 2.05869 (3.11706s) +

    +
    +
    +
    +

    Table 1.22. Operator *(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.34609 (0.030315s) +

    +     		+

    + 1.57086 (0.0407838s) +

    +     		+

    + 1.60154 (0.0542267s) +

    +     		+

    + 1.67808 (0.0804984s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1.29783 (0.0292279s) +

    +     		+

    + 1.58263 (0.0410894s) +

    +     		+

    + 1.61543 (0.054697s) +

    +     		+

    + 1.66841 (0.0800346s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (0.0225207s) +

    +     		+

    + 1 (0.0259628s) +

    +     		+

    + 1 (0.033859s) +

    +     		+

    + 1 (0.0479706s) +

    +
    +

    + tommath_int +

    +     		+

    + 12.4278 (0.279882s) +

    +     		+

    + 11.9045 (0.309074s) +

    +     		+

    + 10.5973 (0.358813s) +

    +     		+

    + 9.47384 (0.454466s) +

    +
    +
    +
    +

    Table 1.23. Operator /

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 2.86387 (0.593314s) +

    +     		+

    + 2.18375 (0.69965s) +

    +     		+

    + 1.72571 (0.918294s) +

    +     		+

    + 1.39251 (1.33801s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.207172s) +

    +     		+

    + 1 (0.320389s) +

    +     		+

    + 1 (0.532127s) +

    +     		+

    + 1 (0.960856s) +

    +
    +

    + gmp_int +

    +     		+

    + 3.89115 (0.806137s) +

    +     		+

    + 2.87573 (0.921352s) +

    +     		+

    + 1.96635 (1.04635s) +

    +     		+

    + 1.29618 (1.24544s) +

    +
    +

    + tommath_int +

    +     		+

    + 11.9483 (2.47535s) +

    +     		+

    + 9.35941 (2.99865s) +

    +     		+

    + 8.79014 (4.67747s) +

    +     		+

    + 11.8316 (11.3684s) +

    +
    +
    +
    +

    Table 1.24. Operator /(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 5.77003 (0.313196s) +

    +     		+

    + 4.38067 (0.431864s) +

    +     		+

    + 3.55054 (0.634559s) +

    +     		+

    + 2.97898 (1.03205s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 2.48952 (0.135131s) +

    +     		+

    + 2.59188 (0.255519s) +

    +     		+

    + 2.56716 (0.458808s) +

    +     		+

    + 2.52368 (0.874313s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (0.0542797s) +

    +     		+

    + 1 (0.0985842s) +

    +     		+

    + 1 (0.178722s) +

    +     		+

    + 1 (0.346443s) +

    +
    +

    + tommath_int +

    +     		+

    + 31.6477 (1.71783s) +

    +     		+

    + 22.8727 (2.25489s) +

    +     		+

    + 19.9248 (3.56101s) +

    +     		+

    + 24.3266 (8.42779s) +

    +
    +
    +
    +

    Table 1.25. Operator %

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.9813 (0.357541s) +

    +     		+

    + 1.55667 (0.460146s) +

    +     		+

    + 1.35341 (0.681144s) +

    +     		+

    + 1.19906 (1.10138s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.180457s) +

    +     		+

    + 1 (0.295597s) +

    +     		+

    + 1 (0.503278s) +

    +     		+

    + 1 (0.918538s) +

    +
    +

    + gmp_int +

    +     		+

    + 3.50213 (0.631985s) +

    +     		+

    + 2.33312 (0.689662s) +

    +     		+

    + 1.57264 (0.791475s) +

    +     		+

    + 1.07795 (0.99014s) +

    +
    +

    + tommath_int +

    +     		+

    + 12.2393 (2.20868s) +

    +     		+

    + 10.1123 (2.98915s) +

    +     		+

    + 9.46676 (4.76442s) +

    +     		+

    + 12.1795 (11.1873s) +

    +
    +
    +
    +

    Table 1.26. Operator %(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.88485 (0.105552s) +

    +     		+

    + 2.00194 (0.203711s) +

    +     		+

    + 2.08202 (0.380096s) +

    +     		+

    + 2.12794 (0.752068s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1.7474 (0.0978544s) +

    +     		+

    + 1.88457 (0.191768s) +

    +     		+

    + 2.0306 (0.37071s) +

    +     		+

    + 2.0851 (0.736929s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (0.0560001s) +

    +     		+

    + 1 (0.101757s) +

    +     		+

    + 1 (0.182561s) +

    +     		+

    + 1 (0.353426s) +

    +
    +

    + tommath_int +

    +     		+

    + 30.4466 (1.70501s) +

    +     		+

    + 22.2997 (2.26915s) +

    +     		+

    + 19.6199 (3.58184s) +

    +     		+

    + 24.0694 (8.50676s) +

    +
    +
    +
    +

    Table 1.27. Operator <<

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.20362 (0.0224696s) +

    +     		+

    + 1.08555 (0.0294403s) +

    +     		+

    + 1 (0.0360516s) +

    +     		+

    + 1.07177 (0.0523935s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0186683s) +

    +     		+

    + 1 (0.0271201s) +

    +     		+

    + 1.02126 (0.036818s) +

    +     		+

    + 1 (0.0488848s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.36706 (0.0255207s) +

    +     		+

    + 1.12042 (0.0303858s) +

    +     		+

    + 1.24359 (0.0448335s) +

    +     		+

    + 1.40143 (0.0685085s) +

    +
    +

    + tommath_int +

    +     		+

    + 2.09357 (0.0390833s) +

    +     		+

    + 2.4569 (0.0666312s) +

    +     		+

    + 2.63592 (0.0950291s) +

    +     		+

    + 3.43638 (0.167987s) +

    +
    +
    +
    +

    Table 1.28. Operator >>

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.33649 (0.0210319s) +

    +     		+

    + 1.12919 (0.0266135s) +

    +     		+

    + 1.10413 (0.0307184s) +

    +     		+

    + 1.09267 (0.0399373s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0157367s) +

    +     		+

    + 1 (0.0235686s) +

    +     		+

    + 1 (0.0278214s) +

    +     		+

    + 1.05198 (0.0384501s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.72135 (0.0270884s) +

    +     		+

    + 1.2078 (0.0284661s) +

    +     		+

    + 1.16066 (0.0322912s) +

    +     		+

    + 1 (0.0365503s) +

    +
    +

    + tommath_int +

    +     		+

    + 15.4381 (0.242945s) +

    +     		+

    + 11.8797 (0.279987s) +

    +     		+

    + 10.9043 (0.303374s) +

    +     		+

    + 14.0762 (0.514491s) +

    +
    +
    +
    +

    Table 1.29. Operator &

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.65829 (0.0314059s) +

    +     		+

    + 1.42198 (0.0390384s) +

    +     		+

    + 1.48578 (0.0498903s) +

    +     		+

    + 1.51243 (0.0770342s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0189387s) +

    +     		+

    + 1 (0.0274536s) +

    +     		+

    + 1 (0.0335786s) +

    +     		+

    + 1 (0.0509341s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.80248 (0.0530755s) +

    +     		+

    + 2.39752 (0.0658206s) +

    +     		+

    + 2.66009 (0.089322s) +

    +     		+

    + 2.73942 (0.13953s) +

    +
    +

    + tommath_int +

    +     		+

    + 6.95432 (0.131706s) +

    +     		+

    + 5.4059 (0.148412s) +

    +     		+

    + 4.56887 (0.153417s) +

    +     		+

    + 6.5696 (0.334616s) +

    +
    +
    +
    +

    Table 1.30. Operator &(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.63285 (0.0472296s) +

    +     		+

    + 1.43344 (0.0588492s) +

    +     		+

    + 1.33141 (0.0724386s) +

    +     		+

    + 1.21353 (0.104144s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0289247s) +

    +     		+

    + 1 (0.0410546s) +

    +     		+

    + 1 (0.0544075s) +

    +     		+

    + 1 (0.0858187s) +

    +
    +

    + gmp_int +

    +     		+

    + 5.24478 (0.151704s) +

    +     		+

    + 3.81907 (0.15679s) +

    +     		+

    + 2.77979 (0.151242s) +

    +     		+

    + 1.84209 (0.158086s) +

    +
    +

    + tommath_int +

    +     		+

    + 11.7257 (0.339163s) +

    +     		+

    + 8.6379 (0.354625s) +

    +     		+

    + 6.90411 (0.375636s) +

    +     		+

    + 7.63253 (0.655013s) +

    +
    +
    +
    +

    Table 1.31. Operator ^

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.39325 (0.0297525s) +

    +     		+

    + 1.28821 (0.0385005s) +

    +     		+

    + 1.18843 (0.0492426s) +

    +     		+

    + 1.07724 (0.0758668s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0213547s) +

    +     		+

    + 1 (0.0298868s) +

    +     		+

    + 1 (0.041435s) +

    +     		+

    + 1 (0.070427s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.28582 (0.048813s) +

    +     		+

    + 2.03478 (0.0608129s) +

    +     		+

    + 2.05655 (0.0852131s) +

    +     		+

    + 1.92381 (0.135488s) +

    +
    +

    + tommath_int +

    +     		+

    + 6.17078 (0.131775s) +

    +     		+

    + 4.8567 (0.145151s) +

    +     		+

    + 3.64659 (0.151097s) +

    +     		+

    + 4.78192 (0.336776s) +

    +
    +
    +
    +

    Table 1.32. Operator ^(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.89396 (0.0383127s) +

    +     		+

    + 1.64269 (0.043417s) +

    +     		+

    + 1.5386 (0.0477162s) +

    +     		+

    + 1.32247 (0.0568053s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0202288s) +

    +     		+

    + 1 (0.0264305s) +

    +     		+

    + 1 (0.0310128s) +

    +     		+

    + 1 (0.0429539s) +

    +
    +

    + gmp_int +

    +     		+

    + 7.01953 (0.141997s) +

    +     		+

    + 5.47513 (0.14471s) +

    +     		+

    + 4.6627 (0.144603s) +

    +     		+

    + 3.59601 (0.154463s) +

    +
    +

    + tommath_int +

    +     		+

    + 16.2706 (0.329134s) +

    +     		+

    + 12.9494 (0.342258s) +

    +     		+

    + 11.3305 (0.35139s) +

    +     		+

    + 14.1712 (0.608709s) +

    +
    +
    +
    +

    Table 1.33. Operator |

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.34742 (0.0296944s) +

    +     		+

    + 1.25923 (0.0384846s) +

    +     		+

    + 1.20517 (0.0493908s) +

    +     		+

    + 1.10536 (0.0761343s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0220379s) +

    +     		+

    + 1 (0.030562s) +

    +     		+

    + 1 (0.0409823s) +

    +     		+

    + 1 (0.0688775s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.14429 (0.0472558s) +

    +     		+

    + 1.95901 (0.0598712s) +

    +     		+

    + 2.07584 (0.0850728s) +

    +     		+

    + 1.94265 (0.133805s) +

    +
    +

    + tommath_int +

    +     		+

    + 5.98286 (0.13185s) +

    +     		+

    + 4.65705 (0.142329s) +

    +     		+

    + 3.85812 (0.158115s) +

    +     		+

    + 4.81524 (0.331662s) +

    +
    +
    +
    +

    Table 1.34. Operator |(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.40808 (0.0389721s) +

    +     		+

    + 1.65035 (0.0437872s) +

    +     		+

    + 1.51667 (0.0466144s) +

    +     		+

    + 1.37806 (0.0582842s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0276775s) +

    +     		+

    + 1 (0.026532s) +

    +     		+

    + 1 (0.0307348s) +

    +     		+

    + 1 (0.0422945s) +

    +
    +

    + gmp_int +

    +     		+

    + 5.31451 (0.147092s) +

    +     		+

    + 5.37333 (0.142565s) +

    +     		+

    + 4.86508 (0.149527s) +

    +     		+

    + 3.74364 (0.158335s) +

    +
    +

    + tommath_int +

    +     		+

    + 11.9312 (0.330226s) +

    +     		+

    + 12.943 (0.343403s) +

    +     		+

    + 11.4457 (0.35178s) +

    +     		+

    + 14.4462 (0.610997s) +

    +
    +
    +
    +

    Table 1.35. Operator gcd

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.82514 (4.45586s) +

    +     		+

    + 1.75955 (10.1748s) +

    +     		+

    + 1.87025 (25.23s) +

    +     		+

    + 2.11453 (68.8556s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1.57965 (3.85654s) +

    +     		+

    + 1.67404 (9.68027s) +

    +     		+

    + 1.8405 (24.8287s) +

    +     		+

    + 2.27588 (74.1096s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (2.44138s) +

    +     		+

    + 1 (5.78259s) +

    +     		+

    + 1 (13.4902s) +

    +     		+

    + 1 (32.5631s) +

    +
    +

    + tommath_int +

    +     		+

    + 5.01357 (12.24s) +

    +     		+

    + 4.38161 (25.337s) +

    +     		+

    + 4.08681 (55.1319s) +

    +     		+

    + 4.01045 (130.593s) +

    +
    +
    +
    +

    Table 1.36. Operator str

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.46421 (0.00195137s) +

    +     		+

    + 1.21669 (0.00319216s) +

    +     		+

    + 1.25041 (0.00765237s) +

    +     		+

    + 1.53339 (0.0218096s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.00133271s) +

    +     		+

    + 1 (0.00262366s) +

    +     		+

    + 1.0109 (0.00618661s) +

    +     		+

    + 1.24429 (0.0176978s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.7777 (0.00236916s) +

    +     		+

    + 1.27408 (0.00334274s) +

    +     		+

    + 1 (0.00611991s) +

    +     		+

    + 1 (0.0142232s) +

    +
    +

    + tommath_int +

    +     		+

    + 11.9797 (0.0159654s) +

    +     		+

    + 18.3349 (0.0481046s) +

    +     		+

    + 18.3681 (0.112411s) +

    +     		+

    + 25.0355 (0.356085s) +

    +
    +
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/rational_performance.html b/doc/html/boost_multiprecision/perf/rational_performance.html new file mode 100644 index 00000000..6736d065 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/rational_performance.html @@ -0,0 +1,905 @@ + + + +Rational Type Perfomance + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticism, and real-world + performance may vary widely depending upon the specifics of the program. + In each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. + The tests were run on 32-bit Windows Vista machine. +

    +
    +

    Table 1.37. Operator +

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.91758 (18.1263s) +

    +     		+

    + 6.60754 (44.1182s) +

    +     		+

    + 6.65334 (103.169s) +

    +     		+

    + 6.44717 (244.055s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (3.06312s) +

    +     		+

    + 1 (6.67695s) +

    +     		+

    + 1 (15.5064s) +

    +     		+

    + 1 (37.8546s) +

    +
    +
    +
    +

    Table 1.38. Operator +(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 3.98512 (2.67249s) +

    +     		+

    + 4.24335 (3.04309s) +

    +     		+

    + 4.65009 (3.83046s) +

    +     		+

    + 5.45832 (5.08346s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (0.670618s) +

    +     		+

    + 1 (0.717144s) +

    +     		+

    + 1 (0.823739s) +

    +     		+

    + 1 (0.931322s) +

    +
    +
    +
    +

    Table 1.39. Operator -

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.91504 (18.2374s) +

    +     		+

    + 6.55676 (43.8659s) +

    +     		+

    + 6.66239 (103.481s) +

    +     		+

    + 6.47224 (244.887s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (3.08322s) +

    +     		+

    + 1 (6.69018s) +

    +     		+

    + 1 (15.5321s) +

    +     		+

    + 1 (37.8365s) +

    +
    +
    +
    +

    Table 1.40. Operator -(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 3.96173 (2.66785s) +

    +     		+

    + 4.36532 (3.09023s) +

    +     		+

    + 4.59363 (3.74494s) +

    +     		+

    + 5.43075 (5.09156s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (0.673405s) +

    +     		+

    + 1 (0.707904s) +

    +     		+

    + 1 (0.815246s) +

    +     		+

    + 1 (0.937541s) +

    +
    +
    +
    +

    Table 1.41. Operator *

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.59286 (32.3559s) +

    +     		+

    + 6.54125 (82.4247s) +

    +     		+

    + 6.8815 (197.198s) +

    +     		+

    + 6.84066 (473.057s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (5.78521s) +

    +     		+

    + 1 (12.6008s) +

    +     		+

    + 1 (28.6562s) +

    +     		+

    + 1 (69.1537s) +

    +
    +
    +
    +

    Table 1.42. Operator *(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 2.70193 (3.1466s) +

    +     		+

    + 3.10134 (3.79056s) +

    +     		+

    + 3.659 (4.93935s) +

    +     		+

    + 4.61372 (6.89845s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (1.16457s) +

    +     		+

    + 1 (1.22223s) +

    +     		+

    + 1 (1.34992s) +

    +     		+

    + 1 (1.4952s) +

    +
    +
    +
    +

    Table 1.43. Operator /

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 4.36846 (63.9498s) +

    +     		+

    + 5.52565 (145.045s) +

    +     		+

    + 6.18331 (328.069s) +

    +     		+

    + 6.49822 (784.806s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (14.639s) +

    +     		+

    + 1 (26.2494s) +

    +     		+

    + 1 (53.0571s) +

    +     		+

    + 1 (120.772s) +

    +
    +
    +
    +

    Table 1.44. Operator /(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 2.26643 (3.13785s) +

    +     		+

    + 2.57125 (3.76931s) +

    +     		+

    + 3.20872 (5.06758s) +

    +     		+

    + 4.02177 (7.17803s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (1.38449s) +

    +     		+

    + 1 (1.46594s) +

    +     		+

    + 1 (1.57931s) +

    +     		+

    + 1 (1.78479s) +

    +
    +
    +
    +

    Table 1.45. Operator str

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.40493 (0.0199393s) +

    +     		+

    + 8.55089 (0.0511907s) +

    +     		+

    + 9.91026 (0.118839s) +

    +     		+

    + 9.93546 (0.285367s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (0.00368909s) +

    +     		+

    + 1 (0.00598659s) +

    +     		+

    + 1 (0.0119915s) +

    +     		+

    + 1 (0.028722s) +

    +
    +
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html new file mode 100644 index 00000000..4dd0d5ef --- /dev/null +++ b/doc/html/boost_multiprecision/perf/realworld.html @@ -0,0 +1,278 @@ + + + +Floating Point Real World Tests + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + These tests test the total time taken to execute all of Boost.Math's test + cases for these functions. In each case the best performing library gets + a relative score of 1, with the total execution time given in brackets. The + first three libraries listed are the various floating point types provided + by this library, while for comparison, two popular C++ front-ends to MPFR ( mpfr_class + and mpreal) are + also shown. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. + The tests were run on 32-bit Windows Vista machine. +

    +
    +

    Table 1.6. Bessel Function Performance

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +
    +

    + mpfr_float +

    +     		+

    + 1.0 (6.472s) +

    +     		+

    + 1.193 (10.154s) +

    +
    +

    + mpf_float +

    +     		+

    + 1.801 (11.662s) +

    +     		+

    + 1.0(8.511s) +

    +
    +

    + cpp_dec_float +

    +     		+

    + 3.13 (20.285s) +

    +     		+

    + 2.46 (21.019s) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.001 (6.480s) +

    +     		+

    + 1.15(9.805s) +

    +
    +

    + mpreal +

    +     		+

    + 1.542 (9.981s) +

    +     		+

    + 1.61 (13.702s) +

    +
    +
    +
    +

    Table 1.7. Non-Central T Distribution Performance

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +
    +

    + mpfr_float +

    +     		+

    + 1.308 (258.09s) +

    +     		+

    + 1.30 (516.74s) +

    +
    +

    + mpf_float +

    +     		+

    + 1.0 (197.30s) +

    +     		+

    + 1.0(397.30s) +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1.695 (334.50s) +

    +     		+

    + 2.68 (1064.53s) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.35 (266.39s) +

    +     		+

    + 1.323 (525.74s) +

    +
    +

    + mpreal +

    +     		+

    + 1.75 (346.64s) +

    +     		+

    + 1.635 (649.94s) +

    +
    +
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html new file mode 100644 index 00000000..35ad59f4 --- /dev/null +++ b/doc/html/boost_multiprecision/ref.html @@ -0,0 +1,44 @@ + + + +Reference + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    mp_number
    +
    cpp_int
    +
    gmp_int
    +
    tom_int
    +
    gmp_float
    +
    mpfr_float_backend
    +
    cpp_dec_float
    +
    Backend Requirements
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html new file mode 100644 index 00000000..3bf6b60f --- /dev/null +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -0,0 +1,2295 @@ + + + +Backend Requirements + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + The requirements on the Backend + template argument to mp_number + are split up into compulsory requirements, and optional requirements that + are either to improve performance or provide optional features. +

    +

    + In the following tables, type B is the Backend + template arument to mp_number, + b and b2 + are a variables of type B, cb + and cb2 are constant variables + of type B, a is a variable + of Arithmetic type, s is + a variable of type const char*, ui + is a variable of type unsigned, + bb is a variable of type + bool, pa + is a variable of type pointer-to-arithmetic-type, exp + is a variable of type B::exp_type, pexp + is a variable of type B::exp_type*, + B2 is another type that meets these requirements, b2 is a variable of type + B2. +

    +
    +

    Table 1.4. Compulsory Requirements on the Backend type.

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Expression +

    +     		+

    + Return Type +

    +     		+

    + Comments +

    +
    +

    + B::signed_types +

    +     		+

    + mpl::list<type-list> +

    +     		+

    + A list of signed integral types that can be assigned to type B. + The types shall be listed in order of size, smallest first, and + shall terminate in the type that is std::intmax_t. +

    +
    +

    + B::unsigned_types +

    +     		+

    + mpl::list<type-list> +

    +     		+

    + A list of unsigned integral types that can be assigned to type + B. The types shall be listed in order of size, smallest first, + and shall terminate in the type that is std::uintmax_t. +

    +
    +

    + B::float_types +

    +     		+

    + mpl::list<type-list> +

    +     		+

    + A list of floating-point types that can be assigned to type B.The + types shall be listed in order of size, smallest first, and shall + terminate in type long double. +

    +
    +

    + B::exponent_type +

    +     		+

    + A signed integral type. +

    +     		+

    + The type of the exponent of type B. +

    +
    +

    + B() +

    +     		+ +

    + Default constructor. +

    +
    +

    + B(cb) +

    +     		+ +

    + Copy Constructor. +

    +
    +

    + b = + b +

    +     		+

    + B& +

    +     		+

    + Assignment operator. +

    +
    +

    + b = + a +

    +     		+

    + B& +

    +     		+

    + Assignment from an Arithmetic type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + b = + s +

    +     		+

    + B& +

    +     		+

    + Assignment from a string. +

    +
    +

    + b.swap(b) +

    +     		+

    + void +

    +     		+

    + Swaps the contents of its arguments. +

    +
    +

    + cb.str(ui, + bb) +

    +     		+

    + std::string +

    +     		+

    + Returns the string representation of b + with ui digits + and in scientific format if bb + is true. If ui is zero, then returns as many + digits as are required to reconstruct the original value. +

    +
    +

    + b.negate() +

    +     		+

    + void +

    +     		+

    + Negates b. +

    +
    +

    + cb.compare(cb2) +

    +     		+

    + int +

    +     		+

    + Compares cb and + cb2, returns a + value less than zero if cb + < cb2, + a value greater than zero if cb + > cb2 + and zero if cb == cb2. +

    +
    +

    + cb.compare(a) +

    +     		+

    + int +

    +     		+

    + Compares cb and + a, returns a value + less than zero if cb + < a, + a value greater than zero if cb + > a + and zero if cb == a. + The type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_add(b, + cb) +

    +     		+

    + void +

    +     		+

    + Adds cb to b. +

    +
    +

    + eval_subtract(b, + cb) +

    +     		+

    + void +

    +     		+

    + Subtracts cb from + b. +

    +
    +

    + eval_multiply(b, + cb) +

    +     		+

    + void +

    +     		+

    + Multiplies b by + cb. +

    +
    +

    + eval_divide(b, + cb) +

    +     		+

    + void +

    +     		+

    + Divides b by cb. +

    +
    +

    + eval_modulus(b, + cb) +

    +     		+

    + void +

    +     		+

    + Computes b %= + cb, only required when + B is an integer + type. +

    +
    +

    + eval_bitwise_and(b, cb) +

    +     		+

    + void +

    +     		+

    + Computes b &= + cb, only required when + B is an integer + type. +

    +
    +

    + eval_bitwise_or(b, cb) +

    +     		+

    + void +

    +     		+

    + Computes b |= + cb, only required when + B is an integer + type. +

    +
    +

    + eval_bitwise_xor(b, cb) +

    +     		+

    + void +

    +     		+

    + Computes b ^= + cb, only required when + B is an integer + type. +

    +
    +

    + eval_complement(b, cb) +

    +     		+

    + void +

    +     		+

    + Computes the ones-complement of cb + and stores the result in b, + only required when B + is an integer type. +

    +
    +

    + eval_left_shift(b, ui) +

    +     		+

    + void +

    +     		+

    + Computes b <<= + ui, only required when + B is an integer + type. +

    +
    +

    + eval_right_shift(b, ui) +

    +     		+

    + void +

    +     		+

    + Computes b >>= + ui, only required when + B is an integer + type. +

    +
    +

    + eval_convert_to(pa, cb) +

    +     		+

    + void +

    +     		+

    + Converts cb to + the type of *pa + and store the result in *pa. Type B + shall support conversion to at least types std::intmax_t, + std::uintmax_t and long + long. Conversion to other + arithmetic types can then be synthesised using other operations. + Conversions to other types are entirely optional. +

    +
    +

    + eval_frexp(b, + cb, + pexp) +

    +     		+

    + void +

    +     		+

    + Stores values in b + and *pexp + such that the value of cb + is b * 2*pexp, only required when B + is a floating-point type. +

    +
    +

    + eval_ldexp(b, + cb, + exp) +

    +     		+

    + void +

    +     		+

    + Stores a value in b + that is cb * 2exp, only required when B + is a floating-point type. +

    +
    +

    + eval_floor(b, + cb) +

    +     		+

    + void +

    +     		+

    + Stores the floor of cb + in b, only required + when B is a floating-point + type. +

    +
    +

    + eval_ceil(b, + cb) +

    +     		+

    + void +

    +     		+

    + Stores the ceiling of cb + in b, only required + when B is a floating-point + type. +

    +
    +

    + eval_sqrt(b, + cb) +

    +     		+

    + void +

    +     		+

    + Stores the square root of cb + in b, only required + when B is a floating-point + type. +

    +
    +

    + boost::multiprecision::number_category<B>::type +

    +     		+

    + mpl::int_<N> +

    +     		+

    + N is one of the + values number_kind_integer, + number_kind_floating_point, + number_kind_rational + or number_kind_fixed_point. + Defaults to number_kind_floating_point. +

    +
    +
    +
    +

    Table 1.5. Optional Requirements on the Backend Type

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Expression +

    +     		+

    + Returns +

    +     		+

    + Comments +

    +
    +

    + B(b2) +

    +     		+

    + B +

    +     		+

    + Copy constructor from a different back-end type. +

    +
    +

    + b = + b2 +

    +     		+

    + b& +

    +     		+

    + Assignment operator from a different back-end type. +

    +
    +

    + assign_components(b, a, a) +

    +     		+

    + void +

    +     		+

    + Assigns to b the + two components in the following arguments. Only applies to rational + and complex number types. +

    +
    +

    + assign_components(b, b2, b2) +

    +     		+

    + void +

    +     		+

    + Assigns to b the + two components in the following arguments. Only applies to rational + and complex number types. +

    +
    +

    + eval_add(b, + a) +

    +     		+

    + void +

    +     		+

    + Adds a to b. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. +

    +
    +

    + eval_subtract(b, + a) +

    +     		+

    + void +

    +     		+

    + Subtracts a from + b. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_multiply(b, + a) +

    +     		+

    + void +

    +     		+

    + Multiplies b by + a. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_divide(b, + a) +

    +     		+

    + void +

    +     		+

    + Divides b by a. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. +

    +
    +

    + eval_modulus(b, + a) +

    +     		+

    + void +

    +     		+

    + Computes b %= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_and(b, a) +

    +     		+

    + void +

    +     		+

    + Computes b &= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_or(b, a) +

    +     		+

    + void +

    +     		+

    + Computes b |= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_xor(b, a) +

    +     		+

    + void +

    +     		+

    + Computes b ^= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_add(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Add cb to cb2 and stores the result in + b. +

    +
    +

    + eval_subtract(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Subtracts cb2 from + cb and stores the + result in b. +

    +
    +

    + eval_multiply(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Multiplies cb by + cb2 and stores + the result in b. +

    +
    +

    + eval_divide(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Divides cb by + cb2 and stores + the result in b. +

    +
    +

    + eval_add(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Add cb to a and stores the result in b. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. +

    +
    +

    + eval_subtract(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Subtracts a from + cb and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_multiply(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Multiplies cb by + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_divide(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Divides cb by + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_modulus(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb % + cb2 and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_bitwise_and(b, cb, cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb & + cb2 and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_bitwise_or(b, cb, cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb | + cb2 and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_bitwise_xor(b, cb, cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb ^ + cb2 and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_add(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Add a to cb and stores the result in + b. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_subtract(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Subtracts cb from + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_multiply(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Multiplies a by + cb and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_divide(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Divides a by cb and stores the result in + b. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_modulus(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Computes cb % + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_and(b, cb, a) +

    +     		+

    + void +

    +     		+

    + Computes cb & + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_or(b, cb, a) +

    +     		+

    + void +

    +     		+

    + Computes cb | + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_xor(b, cb, a) +

    +     		+

    + void +

    +     		+

    + Computes cb ^ + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_modulus(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Computes cb % + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_and(b, a, cb) +

    +     		+

    + void +

    +     		+

    + Computes cb & + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_or(b, a, cb) +

    +     		+

    + void +

    +     		+

    + Computes cb | + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_xor(b, a, cb) +

    +     		+

    + void +

    +     		+

    + Computes a ^ + cb and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_left_shift(b, cb, ui) +

    +     		+

    + void +

    +     		+

    + Computes cb << + ui and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_right_shift(b, cb, ui) +

    +     		+

    + void +

    +     		+

    + Computes cb >> + ui and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_increment(b) +

    +     		+

    + void +

    +     		+

    + Increments the value of b + by one. +

    +
    +

    + eval_decrement(b) +

    +     		+

    + void +

    +     		+

    + Decrements the value of b + by one. +

    +
    +

    + eval_is_zero(cb) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb is zero, otherwise false +

    +
    +

    + eval_get_sign(cb) +

    +     		+

    + int +

    +     		+

    + Returns a value < zero if cb + is negative, a value > zero if cb + is positive, and zero if cb + is zero. +

    +
    +

    + eval_abs(b, + cb) +

    +     		+

    + void +

    +     		+

    + Set b to the absolute + value of cb. +

    +
    +

    + eval_fabs(b, + cb) +

    +     		+

    + void +

    +     		+

    + Set b to the absolute + value of cb. +

    +
    +

    + eval_fpclassify(cb) +

    +     		+

    + int +

    +     		+

    + Returns one of the same values returned by std::fpclassify. + Only required when B + is an floating-point type. +

    +
    +

    + eval_trunc(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::trunc + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_round(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::round + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_exp(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::exp + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_log(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::log + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_log10(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::log10 + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_sin(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::sin + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_cos(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::cos + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_tan(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::exp + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_asin(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::asin + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_acos(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::acos + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_atan(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::atan + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_sinh(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::sinh + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_cosh(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::cosh + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_tanh(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::tanh + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_fmod(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::fmod + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_pow(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::pow + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_atan2(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::atan + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_qr(cb, + cb2, + b, + b2) +

    +     		+

    + void +

    +     		+

    + Sets b to the result + of cb / + cb2 and b2 to the result of cb % + cb2. Only required when + B is an integer + type. +

    +
    +

    + eval_integer_modulus(cb, ui) +

    +     		+

    + unsigned +

    +     		+

    + Returns the result of cb + % ui. + Only required when B + is an integer type. +

    +
    +

    + eval_lsb(cb) +

    +     		+

    + unsigned +

    +     		+

    + Returns the index of the least significant bit that is set. Only + required when B + is an integer type. +

    +
    +

    + eval_bit_test(cb, + ui) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb + has bit ui set. + Only required when B + is an integer type. +

    +
    +

    + eval_bit_set(b, + ui) +

    +     		+

    + void +

    +     		+

    + Sets the bit at index ui + in b. Only required + when B is an integer + type. +

    +
    +

    + eval_bit_unset(b, ui) +

    +     		+

    + void +

    +     		+

    + Unsets the bit at index ui + in b. Only required + when B is an integer + type. +

    +
    +

    + eval_bit_flip(b, + ui) +

    +     		+

    + void +

    +     		+

    + Flips the bit at index ui + in b. Only required + when B is an integer + type. +

    +
    +

    + eval_gcd(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Sets b to the greatest + common divisor of cb + and cb2. Only required + when B is an integer + type. +

    +
    +

    + eval_lcm(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Sets b to the least + common multiple of cb + and cb2. Only required + when B is an integer + type. +

    +
    +
    +
    + + + + + +
    [Note]Note

    + The non-member functions are all named with an "eval_" prefix + to avoid conflicts with template classes of the same name - in point of + fact this naming convention shouldn't be necessary, but rather works around + some compiler bugs. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html new file mode 100644 index 00000000..9d34b1e6 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html @@ -0,0 +1,61 @@ + + + +cpp_dec_float + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class cpp_dec_float;
+
+typedef mp_number<cpp_dec_float<50> > cpp_dec_float_50;
+typedef mp_number<cpp_dec_float<100> > cpp_dec_float_100;
+
+}} // namespaces
+
    +

    + Class template cpp_dec_float + fulfills all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + The class takes a single template parameter - Digits10 + - which is the number of decimal digits precision the type should support. + Note that this type does not ever perform any dynamic memory allocation, + as a result the Digits10 + template argument should not be set too high or the classes size will grow + unreasonably large. +

    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html new file mode 100644 index 00000000..40530e86 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/cpp_int_ref.html @@ -0,0 +1,99 @@ + + + +cpp_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned MinBits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
+struct cpp_int_backend;
+
+typedef mp_number<cpp_int_backend<> >           cpp_int;    // arbitrary precision integer
+typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
+typedef mp_number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
+
+// Fixed precision unsigned types:
+typedef mp_number<cpp_int_backend<128, false, void>, false>   mp_uint128_t;
+typedef mp_number<cpp_int_backend<256, false, void>, false>   mp_uint256_t;
+typedef mp_number<cpp_int_backend<512, false, void>, false>   mp_uint512_t;
+typedef mp_number<cpp_int_backend<1024, false, void>, false>  mp_uint1024_t;
+
+// Fixed precision signed types:
+typedef mp_number<cpp_int_backend<128, true, void>, false>    mp_int128_t;
+typedef mp_number<cpp_int_backend<256, true, void>, false>    mp_int256_t;
+typedef mp_number<cpp_int_backend<512, true, void>, false>    mp_int512_t;
+typedef mp_number<cpp_int_backend<1024, true, void>, false>   mp_int1024_t;
+
+}} // namespaces
+
    +

    + Class template cpp_int_backend + fulfills all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + The template arguments are: +

    +
    +

    +
    +
    Argument
    +

    + Meaning +

    +
    MinBits
    +

    + The number of Bits to reserve inside the class's internal cache. When + constructing a value, the object will use this internal cache if possible + before resorting to dynamic memory allocation. When this value is zero, + then the size of the internal cache is 2*sizeof(void*)*CHAR_BIT. + When the Allocator argument is void, + then this parameter determines the precision of the type. +

    +
    Signed
    +

    + When true the type is + signed, otherwise unsigned. Note that unsigned types are currently + only supported when the Allocator parameter is void. +

    +
    Allocator
    +

    + The allocator used for dynamic memory allocation. This parameter can + be void, in which case + no dymanic memory will ever be allocated. +

    +
    +
    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/gmp_int_ref.html b/doc/html/boost_multiprecision/ref/gmp_int_ref.html new file mode 100644 index 00000000..71dfb0ae --- /dev/null +++ b/doc/html/boost_multiprecision/ref/gmp_int_ref.html @@ -0,0 +1,51 @@ + + + +gmp_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+class gmp_int;
+
+typedef mp_number<gmp_int >         mpz_int;
+
+}} // namespaces
+
    +

    + Class template gmp_int fulfills + all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html new file mode 100644 index 00000000..b883aa18 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -0,0 +1,695 @@ + + + +mp_number + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    + + Synopsis +
    +
    namespace boost{ namespace multiprecision{
+
+template <class Backend, bool ExpressionTemplates = true>
+class mp_number
+{
+   mp_number();
+   mp_number(see-below);
+   mp_number& operator=(see-below);
+
+   // Member operators
+   mp_number& operator+=(const see-below&);
+   mp_number& operator-=(const see-below&);
+   mp_number& operator*=(const see-below&);
+   mp_number& operator/=(const see-below&);
+   mp_number& operator++();
+   mp_number& operator--();
+   mp_number  operator++(int);
+   mp_number  operator--(int);
+
+   mp_number& operator%=(const see-below&);
+   mp_number& operator&=(const see-below&);
+   mp_number& operator|=(const see-below&);
+   mp_number& operator^=(const see-below&);
+   mp_number& operator<<=(const integer-type&);
+   mp_number& operator>>=(const integer-type&);
+
+   // Use in Boolean context:
+   operator convertible-to-bool-type()const;
+   // swap:
+   void swap(mp_number& other);
+   // Sign:
+   bool is_zero()const;
+   int sign()const;
+   // string conversion:
+   std::string str()const;
+   // Generic conversion mechanism
+   template <class T>
+   T convert_to()const;
+   // precision control:
+   static unsigned default_precision();
+   static void default_precision(unsigned digits10);
+   unsigned precision()const;
+   void precision(unsigned digits10);
+   // Comparison:
+   int compare(const mp_number<Backend>& o)const;
+   template <class V>
+   typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
+   // Access to the underlying implementation:
+   Backend& backend();
+   const Backend& backend()const;
+};
+
+// Non member operators:
+unmentionable-expression-template-type operator+(const see-below&, const see-below&);
+unmentionable-expression-template-type operator-(const see-below&, const see-below&);
+unmentionable-expression-template-type operator*(const see-below&, const see-below&);
+unmentionable-expression-template-type operator/(const see-below&, const see-below&);
+// Integer only operations:
+unmentionable-expression-template-type operator%(const see-below&, const see-below&);
+unmentionable-expression-template-type operator&(const see-below&, const see-below&);
+unmentionable-expression-template-type operator|(const see-below&, const see-below&);
+unmentionable-expression-template-type operator^(const see-below&, const see-below&);
+unmentionable-expression-template-type operator<<(const see-below&, const integer-type&);
+unmentionable-expression-template-type operator>>(const see-below&, const integer-type&);
+// Comparison operators:
+bool operator==(const see-below&, const see-below&);
+bool operator!=(const see-below&, const see-below&);
+bool operator< (const see-below&, const see-below&);
+bool operator> (const see-below&, const see-below&);
+bool operator<=(const see-below&, const see-below&);
+bool operator>=(const see-below&, const see-below&);
+
+// Swap:
+template <class Backend, bool ExpressionTemplates>
+void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
+
+// iostream support:
+template <class Backend, bool ExpressionTemplates>
+std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
+std::ostream& operator << (std::ostream& os, const unmentionable-expression-template-type& r);
+template <class Backend, bool ExpressionTemplates>
+std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r);
+
+// Non-member function standard library support:
+unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
+
+unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
+unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
+unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+
+// Traits support:
+template <class T>
+struct component_type;
+template <class T>
+struct number_category;
+
+// Integer specific functions:
+template <class Backend, bool ExpressionTemplates>
+bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
+               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
+template <class Integer>
+Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
+unsigned lsb(const mp_number-or-expression-template-type& x);
+template <class Backend, class ExpressionTemplates>
+bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+template <class Engine>
+bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
+bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
+
+// Rational number support:
+typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
+typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
+
+}} // namespaces
+
+namespace boost{ namespace math{
+
+// Boost.Math interoperability functions:
+int                                              fpclassify     (const mp_number-or-expression-template-type&, int);
+bool                                             isfinite       (const mp_number-or-expression-template-type&, int);
+bool                                             isnan          (const mp_number-or-expression-template-type&, int);
+bool                                             isinf          (const mp_number-or-expression-template-type&, int);
+bool                                             isnormal       (const mp_number-or-expression-template-type&, int);
+
+}} // namespaces
+
+// numeric_limits support:
+namespace std{
+
+template <class Backend, bool ExpressionTemplates>
+struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
+{
+   /* Usual members here */
+};
+
+}
+
    +
    + + Description +
    +
    template <class Backend, bool ExpressionTemplates = true>
+class mp_number;
+
    +

    + Class mp_number has two template + arguments: +

    +
    +

    +
    +
    Backend
    +

    + The actual arithmetic back-end that does all the work. +

    +
    ExpressionTemplates
    +

    + A Boolean value: when true, then expression templates are enabled, + otherwise they are disabled. +

    +
    +
    +
    mp_number();
+mp_number(see-below);
+mp_number& operator=(see-below);
+
    +

    + Type mp_number is default + constructible, and both copy constructible and assignable from: +

    +
      +
    • + Itself. +
      • +
    • + An expression template which is the result of one of the arithmetic operators. +
      • +
    • + Any builtin arithmetic type. +
      • +
    • + A std::string or any type which is convertible + to const char*. +
      • +
    • + Any type that the Backend is constructible or assignable from. +
      • +
    +

    + In addition, if the type has multiple components (for example rational or + complex number types), then there is a two argument constructor: +

    +
    mp_number(arg1, arg2);
+
    +

    + Where the two args must either be arithmetic types, or types that are convertible + to the two components of this. +

    +
    mp_number& operator+=(const see-below&);
+mp_number& operator-=(const see-below&);
+mp_number& operator*=(const see-below&);
+mp_number& operator/=(const see-below&);
+mp_number& operator++();
+mp_number& operator--();
+mp_number  operator++(int);
+mp_number  operator--(int);
+// Integer only operations:
+mp_number& operator%=(const see-below&);
+mp_number& operator&=(const see-below&);
+mp_number& operator|=(const see-below&);
+mp_number& operator^=(const see-below&);
+mp_number& operator<<=(const integer-type&);
+mp_number& operator>>=(const integer-type&);
+
    +

    + These operators all take their usual arithmetic meanings. +

    +

    + The arguments to these operators is either: +

    +
      +
    • + Another mp_number<Backend, + ExpressionTemplates>. +
      • +
    • + A builtin arithmetic type. +
      • +
    • + An expression template derived from mp_number<Backend>. +
      • +
    +

    + For the left and right shift operations, the argument must be a builtin integer + type with a positive value (negative values result in a std::runtime_error + being thrown). +

    +
    operator convertible-to-bool-type()const;
+
    +

    + Returns an unmentionable-type that is usable in Boolean + contexts (this allows mp_number + to be used in any Boolean context - if statements, conditional statements, + or as an argument to a logical operator - without type mp_number + being convertible to type bool. +

    +

    + This operator also enables the use of mp_number + with any of the following operators: !, + ||, && + and ?:. +

    +
    void swap(mp_number& other);
+
    +

    + Swaps *this + with other. +

    +
    bool is_zero()const;
+
    +

    + Returns true is *this is zero, + otherwise false. +

    +
    int sign()const;
+
    +

    + Returns a value less than zero if *this is negative, a value greater than zero + if *this + is positive, and zero if *this + is zero. +

    +
    std::string str(unsigned precision, bool scientific = true)const;
+
    +

    + Returns the number formatted as a string, with at least precision + digits, and in scientific format if scientific is true. +

    +
    template <class T>
+T convert_to()const;
+
    +

    + Provides a generic conversion mechanism to convert *this to type T. + Type T may be any arithmetic + type. Optionally other types may also be supported by specific Backend types. +

    +
    static unsigned default_precision();
+static void default_precision(unsigned digits10);
+unsigned precision()const;
+void precision(unsigned digits10);
+
    +

    + These functions are only available if the Backend template parameter supports + runtime changes to precision. They get and set the default precision and + the precision of *this + respectively. +

    +
    int compare(const mp_number<Backend, ExpressionTemplates>& o)const;
+template <class V>
+typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
+
    +

    + Returns: +

    +
      +
    • + A value less that 0 for *this < other +
      • +
    • + A value greater that 0 for *this > other +
      • +
    • + Zero for *this + == other +
      • +
    +
    Backend& backend();
+const Backend& backend()const;
+
    +

    + Returns the underlying back-end instance used by *this. +

    +
    + + Non-member + operators +
    +
    // Non member operators:
+unmentionable-expression-template-type operator+(const see-below&, const see-below&);
+unmentionable-expression-template-type operator-(const see-below&, const see-below&);
+unmentionable-expression-template-type operator*(const see-below&, const see-below&);
+unmentionable-expression-template-type operator/(const see-below&, const see-below&);
+// Integer only operations:
+unmentionable-expression-template-type operator%(const see-below&, const see-below&);
+unmentionable-expression-template-type operator&(const see-below&, const see-below&);
+unmentionable-expression-template-type operator|(const see-below&, const see-below&);
+unmentionable-expression-template-type operator^(const see-below&, const see-below&);
+unmentionable-expression-template-type operator<<(const see-below&, const integer-type&);
+unmentionable-expression-template-type operator>>(const see-below&, const integer-type&);
+// Comparison operators:
+bool operator==(const see-below&, const see-below&);
+bool operator!=(const see-below&, const see-below&);
+bool operator< (const see-below&, const see-below&);
+bool operator> (const see-below&, const see-below&);
+bool operator<=(const see-below&, const see-below&);
+bool operator>=(const see-below&, const see-below&);
+
    +

    + These operators all take their usual arithmetic meanings. +

    +

    + The arguments to these functions must contain at least one of the following: +

    +
      +
    • + An mp_number. +
      • +
    • + An expression template type derived from mp_number. +
      • +
    +

    + In addition, one of the two arguments may be a builtin arithmetic type. +

    +

    + The return type of these operators is either: +

    +
      +
    • + An unmentionable-type expression template type when + ExpressionTemplates is + true. +
      • +
    • + Type mp_number<Backend, + false> + when ExpressionTemplates + is false. +
      • +
    • + Type bool if the operator + is a comparison operator. +
      • +
    +

    + Finally note that the second argument to the left and right shift operations + must be a builtin integer type, and that the argument must be positive (negative + arguments result in a std::runtime_error + being thrown). +

    +
    + + swap +
    +
    template <class Backend, ExpressionTemplates>
+void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
+
    +

    + Swaps a and b. +

    +
    + + Iostream + Support +
    +
    template <class Backend, bool ExpressionTemplates>
+std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
+template <class Unspecified...>
+std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r);
+template <class Backend, bool ExpressionTemplates>
+inline std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r)
+
    +

    + These operators provided formatted input-output operations on mp_number types, and expression templates + derived from them. +

    +

    + It's down to the back-end type to actually implement string conversion. However, + the back-ends provided with this library support all of the iostream formatting + flags, field width and precision settings. +

    +
    + + Non-member + standard library function support +
    +
    unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
+
+unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
+unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
+unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+
    +

    + These functions all behave exactly as their standard library counterparts + do: their argument is either an instance of mp_number + or an expression template derived from it; If the argument is of type mp_number<Backend, false> + then that is also the return type, otherwise the return type is an expression + template. +

    +

    + These functions are normally implemented by the Backend type. However, default + versions are provided for Backend types that don't have native support for + these functions. Please note however, that this default support requires + the precision of the type to be a compile time constant - this means for + example that the GMP MPF Backend will + not work with these functions when that type is used at variable precision. +

    +

    + Also note that with the exception of abs + that these functions can only be used with floating-point Backend types. +

    +
    + + Traits + Class Support +
    +
    template <class T>
+struct component_type;
+
    +

    + If this is a type with mutiple components (for example rational or complex + types), then this trait has a single member type + that is the type of those components. +

    +
    template <class T>
+struct number_category;
+
    +

    + A traits class that inherits from mpl::int_<N> + where N is one of the enumerated + values number_kind_integer, + number_kind_floating_point, + number_kind_rational or + number_kind_fixed_point. +

    +
    + + Integer functions +
    +
    template <class Backend, bool ExpressionTemplates>
+bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
+               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
+
    +

    + Divides x by y and returns both the quotient and remainder. After the call + q = + x / y and r + = x % y. +

    +
    template <class Integer>
+Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
+
    +

    + Returns the absolute value of x + % val. +

    +
    unsigned lsb(const mp_number-or-expression-template-type& x);
+
    +

    + Returns the index of the least significant bit that is set to 1. +

    +
    template <class Backend, class ExpressionTemplates>
+bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Returns true if the bit at + index in val is set. +

    +
    template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Sets the bit at index in val, and + returns val. +

    +
    template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Unsets the bit at index in val, + and returns val. +

    +
    template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Flips the bit at index in val, + and returns val. +

    +
    template <class Engine>
+bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
+bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
+
    +

    + Tests to see if the number n is probably prime - the + test excludes the vast majority of composite numbers by excluding small prime + factors and performing a single Fermat test. Then performs trials + Miller-Rabin tests. Returns false + if n is definitely composite, or true + if n is probably prime with the probability of it being + composite less than 0.25^trials. +

    +
    + + Rational + Number Functions +
    +
    typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
+typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
+
    +

    + These functions return the numerator and denominator of a rational number + respectively. +

    +
    + + Boost.Math + Interoperability Support +
    +
    namespace boost{ namespace math{
+
+int  fpclassify     (const mp_number-or-expression-template-type&, int);
+bool isfinite       (const mp_number-or-expression-template-type&, int);
+bool isnan          (const mp_number-or-expression-template-type&, int);
+bool isinf          (const mp_number-or-expression-template-type&, int);
+bool isnormal       (const mp_number-or-expression-template-type&, int);
+
+}} // namespaces
+
    +

    + These floating-point classification functions behave exactly as their Boost.Math + equivalents. +

    +

    + Other Boost.Math functions and templates may also be specialized or overloaded + to ensure interoperability. +

    +
    + + std::numeric_limits + support +
    +
    namespace std{
+
+template <class Backend, ExpressionTemplates>
+struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
+{
+   /* Usual members here */
+};
+
+}
+
    +

    + Class template std::numeric_limits is specialized for all instantiations + of mp_number whose precision + is known at compile time, plus those types whose precision is unlimited (though + it is much less useful in those cases). It is not specialized for types whose + precision can vary at compile time (such as mpf_float). +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/mpf_ref.html b/doc/html/boost_multiprecision/ref/mpf_ref.html new file mode 100644 index 00000000..fd2d8f50 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/mpf_ref.html @@ -0,0 +1,67 @@ + + + +gmp_float + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class gmp_float;
+
+typedef mp_number<gmp_float<50> >    mpf_float_50;
+typedef mp_number<gmp_float<100> >   mpf_float_100;
+typedef mp_number<gmp_float<500> >   mpf_float_500;
+typedef mp_number<gmp_float<1000> >  mpf_float_1000;
+typedef mp_number<gmp_float<0> >     mpf_float;
+
+}} // namespaces
+
    +

    + Class template gmp_float + fulfills all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + The class takes a single template parameter - Digits10 + - which is the number of decimal digits precision the type should support. + When this parameter is zero, then the precision can be set at runtime via + mp_number::default_precision and mp_number::precision. + Note that this type does not in any way change the GMP library's global state + (for example it does not change the default precision of the mpf_t data type), + therefore you can safely mix this type with existing code that uses GMP, + and also mix gmp_floats of + differing precision. +

    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/mpfr_ref.html b/doc/html/boost_multiprecision/ref/mpfr_ref.html new file mode 100644 index 00000000..7588f301 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/mpfr_ref.html @@ -0,0 +1,67 @@ + + + +mpfr_float_backend + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class mpfr_float_backend;
+
+typedef mp_number<mpfr_float_backend<50> >    mpfr_float_50;
+typedef mp_number<mpfr_float_backend<100> >   mpfr_float_100;
+typedef mp_number<mpfr_float_backend<500> >   mpfr_float_500;
+typedef mp_number<mpfr_float_backend<1000> >  mpfr_float_1000;
+typedef mp_number<mpfr_float_backend<0> >     mpfr_float;
+
+}} // namespaces
+
    +

    + Class template mpfr_float_backend + fulfills all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + The class takes a single template parameter - Digits10 + - which is the number of decimal digits precision the type should support. + When this parameter is zero, then the precision can be set at runtime via + mp_number::default_precision and mp_number::precision. + Note that this type does not in any way change the GMP or MPFR library's + global state (for example it does not change the default precision of the + mpfr_t data type), therefore you can safely mix this type with existing code + that uses GMP or MPFR, and also mix mpfr_float_backends + of differing precision. +

    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/tom_int_ref.html b/doc/html/boost_multiprecision/ref/tom_int_ref.html new file mode 100644 index 00000000..95abdcbe --- /dev/null +++ b/doc/html/boost_multiprecision/ref/tom_int_ref.html @@ -0,0 +1,51 @@ + + + +tom_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+class tommath_int;
+
+typedef mp_number<tommath_int >         tom_int;
+
+}} // namespaces
+
    +

    + Class template tommath_int + fulfills all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html new file mode 100644 index 00000000..d42d37ac --- /dev/null +++ b/doc/html/boost_multiprecision/tut.html @@ -0,0 +1,64 @@ + + + +Tutorial + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    Integer Types
    +
    +
    cpp_int
    +
    gmp_int
    +
    tom_int
    +
    +
    Floating Point Numbers
    +
    +
    gmp_float
    +
    mpfr_float
    +
    cpp_dec_float
    +
    +
    Rational Number Types
    +
    +
    gmp_rational
    +
    cpp_rational
    +
    tommath_rational
    +
    Use With Boost.Rational
    +
    rational_adapter
    +
    +
    Constructing and + Interconverting Between Number Types
    +
    Generating Random Numbers
    +
    Primality Testing
    +
    +

    + In order to use this library you need to make two choices: what kind of number + do I want, and which back-end do I want to perform the actual arithmetic? +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/conversions.html b/doc/html/boost_multiprecision/tut/conversions.html new file mode 100644 index 00000000..b34da26c --- /dev/null +++ b/doc/html/boost_multiprecision/tut/conversions.html @@ -0,0 +1,106 @@ + + + +Constructing and Interconverting Between Number Types + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + All of the number types that are based on mp_number + have certain conversion rules in common. In particular: +

    +
    • + Any number type can be constructed (or assigned) from any builtin arithmetic + type: +
    +
    cpp_dec_float_50 df(0.5); // OK construction from double
+cpp_int          i(450);  // OK constructs from signed int
+
    +
    • + Any number type can be constructed (or assigned) from a const char* or a std::string: +
    +
    // pi to 50 places from a string:
+cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
+// Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly:
+cpp_int          i  = "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000";
+// Invalid input always results in a std::runtime_error being thrown:
+i = std::string("3.14");
+
    +
    • + Any number type will interoperate with the builtin type in arithmetic + expressions: +
    +
    // pi to 50 places from a string:
+cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
+// Multiply by 2 - using an integer literal here is usually more efficient
+// than constructing a temporary:
+df *= 2;
+
+// There is a need to be careful with integer types though:
+cpp_int i = 2;
+// Ooops, this really just multiplies by 3:
+i *= 3.14;
+
    +
    • + Any number type can be streamed to and from the C++ iostreams: +
    +
    cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
+// Now print at full precision:
+std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_50>::max_digits10)
+   << df << std::endl
+cpp_int i = 1;
+i <<= 256;
+// Now print in hex format with prefix:
+std::cout << std::hex << std::showbase << i << std::endl;
+
    +
    • + Some intercomnversions between number types are completely generic, and + are always available: +
    +
    cpp_int cppi(2);
+// We can always convert between numbers of the same category - 
+// int to int, rational to rational, or float to float, so this is OK:
+mpz_int z = cppi;
+// We can always promote from int to rational, int to float, or rational to float:
+cpp_rational     cppr = cppi;  // OK, int to rational
+cpp_dec_float_50 df =   cppi;  // OK, int to float
+df                  =   cppr;  // OK, rational to float
+// However narrowing conversions always fail:
+cppi                =   df;    // Compiler error, conversion not allowed
+
    +
    • + Other interconversions may be allowed as special cases, whenever the + backend allows it: +
    +
    mpf_t     m;           // Native GMP type.
+mpf_init_set_ui(m, 0); // set to a value;
+mpf_float i(m);        // copies the value of the native type.
+
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats.html b/doc/html/boost_multiprecision/tut/floats.html new file mode 100644 index 00000000..a3b605f0 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats.html @@ -0,0 +1,186 @@ + + + +Floating Point Numbers + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    gmp_float
    +
    mpfr_float
    +
    cpp_dec_float
    +
    +

    + The following back-ends provide floating point arithmetic: +

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend Type +

    +     		+

    + Header +

    +     		+

    + Radix +

    +     		+

    + Dependencies +

    +     		+

    + Pros +

    +     		+

    + Cons +

    +
    +

    + mpf_float<N> +

    +     		+

    + boost/multiprecision/gmp.hpp +

    +     		+

    + 2 +

    +     		+

    + GMP +

    +     		+

    + Very fast and efficient back-end. +

    +     		+

    + Dependency on GNU licensed GMP + library. +

    +
    +

    + mpfr_float<N> +

    +     		+

    + boost/multiprecision/mpfr.hpp +

    +     		+

    + 2 +

    +     		+

    + GMP and MPFR +

    +     		+

    + Very fast and efficient back-end, with its own standard library + implementation. +

    +     		+

    + Dependency on GNU licensed GMP + and MPFR libraries. +

    +
    +

    + cpp_dec_float<N> +

    +     		+

    + boost/multiprecision/cpp_dec_float.hpp +

    +     		+

    + 10 +

    +     		+

    + None +

    +     		+

    + Header only, all C++ implementation. Boost licence. +

    +     		+

    + Approximately 2x slower than the MPFR + or GMP libraries. +

    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html new file mode 100644 index 00000000..ca15017c --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html @@ -0,0 +1,117 @@ + + + +cpp_dec_float + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/cpp_dec_float.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class cpp_dec_float;
+
+typedef mp_number<cpp_dec_float<50> > cpp_dec_float_50;
+typedef mp_number<cpp_dec_float<100> > cpp_dec_float_100;
+
+}} // namespaces
+
    +

    + The cpp_dec_float back-end + is used in conjunction with mp_number: + It acts as an entirely C++ (header only and dependency free) real-number + type that is a drop-in replacement for the native C++ floating-point types, + but with much greater precision. +

    +

    + Type cpp_dec_float can + be used at fixed precision by specifying a non-zero Digits10 + template parameter. The typedefs cpp_dec_float_50 + and cpp_dec_float_100 provide + arithmetic types at 50 and 100 decimal digits precision respectively. +

    +

    + There is full standard library and numeric_limits + support available for this type. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed cpp_dec_floats + have a value of zero. +
      • +
    • + The radix of this type is 10. As a result it can behave subtly differently + from base-2 types. +
      • +
    • + It is not possible to round-trip this type to and from a string and + get back to exactly the same value (this is a result of the type having + some hidden internal guard digits). +
      • +
    • + The type has a number of internal guard digits over and above those + specified in the template argument. Normally these should not be visible + to the user. +
      • +
    +
    + + cpp_dec_float + example: +
    +

    +

    +
    #include <boost/multiprecision/cpp_dec_float.hpp>
+
+using namespace boost::multiprecision;
+
+// Operations at fixed precision and full numeric_limits support:
+cpp_dec_float_100 b = 2;
+std::cout << std::numeric_limits<cpp_dec_float_100>::digits << std::endl;
+// Note that digits10 is the same as digits, since we're base 10! :
+std::cout << std::numeric_limits<cpp_dec_float_100>::digits10 << std::endl;
+// We can use any C++ std lib function, lets print all the digits as well:
+std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_100>::max_digits10)
+   << log(b) << std::endl; // print log(2)
+// We can also use any function from Boost.Math:
+std::cout << boost::math::tgamma(b) << std::endl;
+// These even work when the argument is an expression template:
+std::cout << boost::math::tgamma(b * b) << std::endl;
+// And since we have an extended exponent range we can generate some really large 
+// numbers here (4.0238726007709377354370243e+2564):
+std::cout << boost::math::tgamma(cpp_dec_float_100(1000)) << std::endl;
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/gmp_float.html b/doc/html/boost_multiprecision/tut/floats/gmp_float.html new file mode 100644 index 00000000..3b104b2e --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/gmp_float.html @@ -0,0 +1,169 @@ + + + +gmp_float + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/gmp.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class gmp_float;
+
+typedef mp_number<gmp_float<50> >    mpf_float_50;
+typedef mp_number<gmp_float<100> >   mpf_float_100;
+typedef mp_number<gmp_float<500> >   mpf_float_500;
+typedef mp_number<gmp_float<1000> >  mpf_float_1000;
+typedef mp_number<gmp_float<0> >     mpf_float;
+
+}} // namespaces
+
    +

    + The gmp_float back-end + is used in conjunction with mp_number + : it acts as a thin wrapper around the GMP + mpf_t to provide an real-number + type that is a drop-in replacement for the native C++ floating-point types, + but with much greater precision. +

    +

    + Type gmp_float can be used + at fixed precision by specifying a non-zero Digits10 + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpf_float provides a variable precision type + whose precision can be controlled via the mp_numbers + member functions. +

    +
    + + + + + +
    [Note]Note

    + This type only provides standard library and numeric_limits + support when the precision is fixed at compile time. +

    +

    + As well as the usual conversions from arithmetic and string types, instances + of mp_number<mpf_float<N> > are copy constructible and assignable + from: +

    +
      +
    • + The GMP native types mpf_t, mpz_t, + mpq_t. +
      • +
    • + The mp_number wrappers + around those types: mp_number<mpf_float<M> >, + mp_number<gmp_int>, + mp_number<gmp_rational>. +
      • +
    +

    + It's also possible to access the underlying mpf_t + via the data() + member function of gmp_float. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed gmp_floats + have the value zero (this is the GMP + library's default behavior). +
      • +
    • + No changes are made to the GMP + library's global settings, so this type can be safely mixed with existing + GMP code. +
      • +
    • + It is not possible to round-trip objects of this type to and from a + string and get back exactly the same value. This appears to be a limitation + of GMP. +
      • +
    • + Since the underlying GMP types + have no notion of infinities or NaN's, care should be taken to avoid + numeric overflow or division by zero. That latter will trigger a hardware + exception, while generating excessively large exponents may result + in instability of the underlying GMP + library (in testing, converting a number with an excessively large + or small exponent to a string caused GMP + to segfault). +
      • +
    • + This type can equally be used with MPIR + as the underlying implementation - indeed that is the recommended option + on Win32. +
      • +
    +
    + + + GMP example: +
    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+
+using namespace boost::multiprecision;
+
+// Operations at variable precision and limited standard library support:
+mpf_float a = 2;
+mpf_float::default_precision(1000);
+std::cout << mpf_float::default_precision() << std::endl;
+std::cout << sqrt(a) << std::endl; // print root-2
+
+// Operations at fixed precision and full standard library support:
+mpf_float_100 b = 2;
+std::cout << std::numeric_limits<mpf_float_100>::digits << std::endl;
+// We can use any C++ std lib function:
+std::cout << log(b) << std::endl; // print log(2)
+// We can also use any function from Boost.Math:
+std::cout << boost::math::tgamma(b) << std::endl;
+// These even work when the argument is an expression template:
+std::cout << boost::math::tgamma(b * b) << std::endl;
+
+// Access the underlying representation:
+mpf_t f;
+mpf_init(f);
+mpf_set(f, a.backend().data());
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html new file mode 100644 index 00000000..595e9d2c --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html @@ -0,0 +1,159 @@ + + + +mpfr_float + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/mpfr_float.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class mpfr_float_backend;
+
+typedef mp_number<mpfr_float_backend<50> >    mpfr_float_50;
+typedef mp_number<mpfr_float_backend<100> >   mpfr_float_100;
+typedef mp_number<mpfr_float_backend<500> >   mpfr_float_500;
+typedef mp_number<mpfr_float_backend<1000> >  mpfr_float_1000;
+typedef mp_number<mpfr_float_backend<0> >     mpfr_float;
+
+}} // namespaces
+
    +

    + The mpfr_float_backend + type is used in conjunction with mp_number: + It acts as a thin wrapper around the MPFR + mpfr_t to provide an real-number + type that is a drop-in replacement for the native C++ floating-point types, + but with much greater precision. +

    +

    + Type mpfr_float_backend + can be used at fixed precision by specifying a non-zero Digits10 + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpfr_float provides a variable precision type + whose precision can be controlled via the mp_numbers + member functions. +

    +
    + + + + + +
    [Note]Note

    + This type only provides numeric_limits + support when the precision is fixed at compile time. +

    +

    + As well as the usual conversions from arithmetic and string types, instances + of mp_number<mpfr_float_backend<N> > are copy constructible and assignable + from: +

    +
      +
    • + The GMP native types mpf_t, mpz_t, + mpq_t. +
      • +
    • + The MPFR native type mpfr_t. +
      • +
    • + The mp_number wrappers + around those types: mp_number<mpfr_float_backend<M> >, + mp_number<mpf_float<M> >, mp_number<gmp_int>, mp_number<gmp_rational>. +
      • +
    +

    + It's also possible to access the underlying mpf_t + via the data() member function of gmp_float. +

    +

    + Things you should know when using this type: +

    +
      +
    • + A default constructed mpfr_float_backend + is set to a NaN (this is the default MPFR + behavior). +
      • +
    • + All operations use round to nearest. +
      • +
    • + No changes are made to GMP or + MPFR global settings, so this + type can coexist with existing MPFR + or GMP code. +
      • +
    • + The code can equally use MPIR + in place of GMP - indeed that + is the preferred option on Win32. +
      • +
    +
    + + + MPFR example: +
    +

    +

    +
    #include <boost/multiprecision/mpfr.hpp>
+
+using namespace boost::multiprecision;
+
+// Operations at variable precision and no numeric_limits support:
+mpfr_float a = 2;
+mpfr_float::default_precision(1000);
+std::cout << mpfr_float::default_precision() << std::endl;
+std::cout << sqrt(a) << std::endl; // print root-2
+
+// Operations at fixed precision and full numeric_limits support:
+mpfr_float_100 b = 2;
+std::cout << std::numeric_limits<mpfr_float_100>::digits << std::endl;
+// We can use any C++ std lib function:
+std::cout << log(b) << std::endl; // print log(2)
+// We can also use any function from Boost.Math:
+std::cout << boost::math::tgamma(b) << std::endl;
+// These even work when the argument is an expression template:
+std::cout << boost::math::tgamma(b * b) << std::endl;
+
+// Access the underlying data:
+mpfr_t r;
+mpfr_init(r);
+mpfr_set(r, b.backend().data(), GMP_RNDN);
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html new file mode 100644 index 00000000..b5504ee0 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints.html @@ -0,0 +1,186 @@ + + + +Integer Types + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    cpp_int
    +
    gmp_int
    +
    tom_int
    +
    +

    + The following back-ends provide integer arithmetic: +

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend Type +

    +     		+

    + Header +

    +     		+

    + Radix +

    +     		+

    + Dependencies +

    +     		+

    + Pros +

    +     		+

    + Cons +

    +
    +

    + cpp_int +

    +     		+

    + boost/multiprecision/cpp_int.hpp +

    +     		+

    + 2 +

    +     		+

    + None +

    +     		+

    + Very versatile, Boost licensed, all C++ integer type which support + both arbitrary + precision and fixed precision integer types. +

    +     		+

    + Slower than GMP, though + typically not as slow as libtommath +

    +
    +

    + gmp_int +

    +     		+

    + boost/multiprecision/gmp.hpp +

    +     		+

    + 2 +

    +     		+

    + GMP +

    +     		+

    + Very fast and efficient back-end. +

    +     		+

    + Dependency on GNU licensed GMP + library. +

    +
    +

    + tom_int +

    +     		+

    + boost/multiprecision/tommath.hpp +

    +     		+

    + 2 +

    +     		+

    + libtommath +

    +     		+

    + Public domain back-end with no licence restrictions. +

    +     		+

    + Slower than GMP. +

    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html new file mode 100644 index 00000000..98340475 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints/cpp_int.html @@ -0,0 +1,179 @@ + + + +cpp_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/cpp_int.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+typedef unspecified-type limb_type;
+
+template <unsigned MinDigits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
+class cpp_int_backend;
+
+typedef mp_number<cpp_int_backend<> >           cpp_int;    // arbitrary precision integer
+typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
+typedef mp_number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
+
+// Fixed precision unsigned types:
+typedef mp_number<cpp_int_backend<128, false, void>, false>   mp_uint128_t;
+typedef mp_number<cpp_int_backend<256, false, void>, false>   mp_uint256_t;
+typedef mp_number<cpp_int_backend<512, false, void>, false>   mp_uint512_t;
+typedef mp_number<cpp_int_backend<1024, false, void>, false>  mp_uint1024_t;
+
+// Fixed precision signed types:
+typedef mp_number<cpp_int_backend<128, true, void>, false>    mp_int128_t;
+typedef mp_number<cpp_int_backend<256, true, void>, false>    mp_int256_t;
+typedef mp_number<cpp_int_backend<512, true, void>, false>    mp_int512_t;
+typedef mp_number<cpp_int_backend<1024, true, void>, false>   mp_int1024_t;
+
+}} // namespaces
+
    +

    + The cpp_int_backend type + is used via one of the typedefs boost::multiprecision::cpp_int, + boost::multiprecision::mp_uint128_t, boost::multiprecision::mp_uint256_t, + boost::multiprecision::mp_uint512_t, boost::multiprecision::mp_int128_t, + boost::multiprecision::mp_int256_t or boost::multiprecision::mp_int512_t. +

    +

    + This back-end is the "Swiss Army Knife" of integer types as it + can represent both fixed and arbitrary + precision integer types, and both signed and unsigned types. There + are three template arguments: +

    +
    +

    +
    +
    MinBits
    +

    + Determines the number of Bits to store directly within the object + before resorting to dynamic memory allocation. When zero, this field + is determined automatically based on how many bits can be stored + in union with the dynamic storage header: setting a larger value + may improve performance as larger integer values will be stored internally + before memory allocation is required. When the Allocator parameter + is type void, then this + field determines the total number of bits in the resulting fixed + precision type. +

    +
    Signed
    +

    + Determines whether the resulting type is signed or not. Note that + for arbitrary + precision types (where the Allocator parameter is non-void), + then this parameter must be true. + For fixed precision types then this type may be either true (type is signed), or false (type is unsigned). +

    +
    Allocator
    +

    + The allocator to use for dynamic memory allocation, or type void if this is to be a fixed precision + type. +

    +
    +
    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed cpp_int_backends + have the value zero. +
      • +
    • + Division by zero results in a std::runtime_error + being thrown. +
      • +
    • + Construction from a string that contains invalid non-numeric characters + results in a std::runtime_error being thrown. +
      • +
    • + Since the precision of cpp_int_backend + is necessarily limited when the allocator parameter is void, care should + be taken to avoid numeric overflow when using this type unless you + actually want modulo-arithmetic behavior. +
      • +
    • + The type uses a sign-magnitude representation internally, so type + mp_int128_t has 128-bits + of precision plus an extra sign bit. In this respect the behaviour + of these types differs from built-in 2's complement types. In might + be tempting to use a 127-bit type instead, and indeed this does work, + but behaviour is still slightly different from a 2's complement built-in + type as the min and max values are identical (apart from the sign), + where as they differ by one for a true 2's complement type. That said + it should be noted that there's no requirement for built-in types to + be 2's complement either - it's simply that this is the most common + format by far. +
      • +
    • + Attempting to print negative values as either an Octal or Hexadecimal + string results in a std::runtime_error + being thrown, this is a direct consequence of the sign-magnitude representation. +
      • +
    • + The fixed precision types mp_[u]intXXX_t + have expression template support turned off - it seems to make little + difference to the performance of these types either way - so we may + as well have the faster compile times by turning the feature off. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+
+using namespace boost::multiprecision;
+
+mp_int128_t v = 1;
+
+// Do some fixed precision arithmetic:
+for(unsigned i = 1; i <= 20; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 20!
+
+// Repeat at arbitrary precision:
+cpp_int u = 1;
+for(unsigned i = 1; i <= 100; ++i)
+   u *= i;
+
+std::cout << u << std::endl; // prints 100!
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints/gmp_int.html b/doc/html/boost_multiprecision/tut/ints/gmp_int.html new file mode 100644 index 00000000..1bf12605 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints/gmp_int.html @@ -0,0 +1,128 @@ + + + +gmp_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/gmp.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+class gmp_int;
+
+typedef mp_number<gmp_int >         mpz_int;
+
+}} // namespaces
+
    +

    + The gmp_int back-end is + used via the typedef boost::multiprecision::mpz_int. + It acts as a thin wrapper around the GMP + mpz_t to provide an integer + type that is a drop-in replacement for the native C++ integer types, but + with unlimited precision. +

    +

    + As well as the usual conversions from arithmetic and string types, type + mpz_int is copy constructible + and assignable from: +

    +
      +
    • + The GMP native types: mpf_t, mpz_t, + mpq_t. +
      • +
    • + Instances of mp_number<T> that are wrappers around those + types: mp_number<gmp_float<N> >, mp_number<gmp_rational>. +
      • +
    +

    + It's also possible to access the underlying mpz_t + via the data() + member function of gmp_int. +

    +

    + Things you should know when using this type: +

    +
      +
    • + No changes are made to the GMP library's global settings - so you can + safely mix this type with existing code that uses GMP. +
      • +
    • + Default constructed gmp_ints + have the value zero (this is GMP's default behavior). +
      • +
    • + Formatted IO for this type does not support octal or hexadecimal notation + for negative values, as a result performing formatted output on this + type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex + are set, will result in a std::runtime_error + will be thrown. +
      • +
    • + Division by zero is handled by the GMP + library - it will trigger a division by zero signal. +
      • +
    • + Although this type is a wrapper around GMP + it will work equally well with MPIR. + Indeed use of MPIR is recommended + on Win32. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+
+using namespace boost::multiprecision;
+
+mpz_int v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 1000!
+
+// Access the underlying representation:
+mpz_t z;
+mpz_init(z);
+mpz_set(z, v.backend().data());
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints/tom_int.html b/doc/html/boost_multiprecision/tut/ints/tom_int.html new file mode 100644 index 00000000..2ea5acf4 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints/tom_int.html @@ -0,0 +1,119 @@ + + + +tom_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/tommath.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+class tommath_int;
+
+typedef mp_number<tommath_int >         tom_int;
+
+}} // namespaces
+
    +

    + The tommath_int back-end + is used via the typedef boost::multiprecision::tom_int. + It acts as a thin wrapper around the libtommath + tom_int to provide an integer + type that is a drop-in replacement for the native C++ integer types, but + with unlimited precision. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed objects have the value zero (this is libtommath's + default behavior). +
      • +
    • + Although tom_int is + mostly a drop in replacement for the builtin integer types, it should + be noted that it is a rather strange beast as it's a signed type that + is not a 2's complement type. As a result the bitwise operations | & ^ will throw a std::runtime_error + exception if either of the arguments is negative. Similarly the complement + operator~ is deliberately + not implemented for this type. +
      • +
    • + Formatted IO for this type does not support octal or hexadecimal notation + for negative values, as a result performing formatted output on this + type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex + are set, will result in a std::runtime_error + will be thrown. +
      • +
    • + Division by zero will result in a hardware signal being raised by + libtommath. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/tommath.hpp>
+
+boost::multiprecision::tom_int v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 1000!
+std::cout << std::hex << v << std::endl; // prints 1000! in hex format
+
+try{
+   std::cout << std::hex << -v << std::endl; // Ooops! can't print a negative value in hex format!
+}
+catch(const std::runtime_error& e)
+{
+   std::cout << e.what() << std::endl;
+}
+
+try{
+   // v is not a 2's complement type, bitwise operations are only supported
+   // on positive values:
+   v = -v & 2;
+}
+catch(const std::runtime_error& e)
+{
+   std::cout << e.what() << std::endl;
+}
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html new file mode 100644 index 00000000..f1dac222 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/primetest.html @@ -0,0 +1,108 @@ + + + +Primality Testing + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + The library implements a fairly basic (meaning unoptimized, and possibly + slow) Miller-Rabin test for primality: +

    +
    #include <boost/multiprecision/miller_rabin.hpp>
+
+template <class Backend, bool ExpressionTemplates, class Engine>
+bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials, Engine& gen);
+
+template <class Backend, bool ExpressionTemplates, class Engine>
+bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials);
+
    +

    + These functions perform a Miller-Rabin test for primality, if the result + is false then n + is definitely composite, while if the result is true + then n is prime with probability 0.25^trials. + The algorithm used is straight out of Knuth Vol 2, which recomends 25 trials + for a pretty strong likelyhood that n is prime. +

    +

    + The third optional argument is for a Uniform Random Number Generator from + Boost.Random. When not provided the mt19937 + generator is used. Note that when producing random primes then you should + probably use a different random number generator to produce candidate prime + numbers for testing, than is used internally by miller_rabin_test + for determining whether the value is prime. It also helps of course to seed + the generators with some source of randomness. +

    +

    + The following example searches for a prime p + for which (p-1)/2 is also probably prime: +

    +

    +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+#include <boost/multiprecision/miller_rabin.hpp>
+#include <iostream>
+#include <iomanip>
+
+int main()
+{
+   using namespace boost::random;
+   using namespace boost::multiprecision;
+
+   typedef cpp_int int_type;
+   mt11213b base_gen(clock());
+   independent_bits_engine<mt11213b, 256, int_type> gen(base_gen);
+   //
+   // We must use a different generator for the tests and number generation, otherwise
+   // we get false positives.
+   //
+   mt19937 gen2(clock());
+
+   for(unsigned i = 0; i < 100000; ++i)
+   {
+      int_type n = gen();
+      if(miller_rabin_test(n, 25, gen2))
+      {
+         // Value n is probably prime, see if (n-1)/2 is also prime:
+         std::cout << "We have a probable prime with value: " << std::hex << std::showbase << n << std::endl;
+         if(miller_rabin_test((n-1)/2, 25, gen2))
+         {
+            std::cout << "We have a safe prime with value: " << std::hex << std::showbase << n << std::endl;
+            return 0;
+         }
+      }
+   }
+   std::cout << "Ooops, no safe primes were found" << std::endl;
+   return 1;
+}
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/random.html b/doc/html/boost_multiprecision/tut/random.html new file mode 100644 index 00000000..6f0d438b --- /dev/null +++ b/doc/html/boost_multiprecision/tut/random.html @@ -0,0 +1,157 @@ + + + +Generating Random Numbers + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Random numbers are generated in conjunction with Boost.Random. However, since + Boost.Random is unaware of arbitrary + precision numbers, it's necessary to include the header: +

    +
    #include <boost/multiprecision/random.hpp>
+
    +

    + In order to act as a bridge between the two libraries. +

    +

    + Integers with N random bits are generated using independent_bits_engine: +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+
+//
+// Declare our random number generator type, the underlying generator
+// is the Mersenne twister mt19937 engine, and 256 bits are generated:
+//
+typedef independent_bits_engine<mt19937, 256, mpz_int> generator_type;
+generator_type gen;
+//
+// Generate some values:
+//
+std::cout << std::hex << std::showbase;
+for(unsigned i = 0; i < 10; ++i)
+   std::cout << gen() << std::endl;
+
    +

    +

    +

    + Alternatively we can generate integers in a given range using uniform_int_distribution, this will invoke + the underlying engine multiple times to build up the required number of bits + in the result: +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+
+//
+// Generate integers in a given range using uniform_int,
+// the underlying generator is invoked multiple times
+// to generate enough bits:
+//
+mt19937 mt;
+uniform_int_distribution<mpz_int> ui(0, mpz_int(1) << 256);
+//
+// Generate the numbers:
+//
+std::cout << std::hex << std::showbase;
+for(unsigned i = 0; i < 10; ++i)
+   std::cout << ui(mt) << std::endl;
+
    +

    +

    +

    + Floating point values in [0,1) are generated using uniform_01, + the trick here is to ensure that the underlying generator produces as many + random bits as there are digits in the floating point type. As above independent_bits_engine can be used for + this purpose, note that we also have to convert decimal digits (in the floating + point type) to bits (in the random number generator): +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+//
+// We need an underlying generator with at least as many bits as the
+// floating point type to generate numbers in [0, 1) with all the bits
+// in the floating point type randomly filled:
+//
+uniform_01<mpf_float_50> uf;
+independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen;
+//
+// Generate the values:
+//
+std::cout << std::setprecision(50);
+for(unsigned i = 0; i < 20; ++i)
+   std::cout << uf(gen) << std::endl;
+
    +

    +

    +

    + Finally, we can modify the above example to produce numbers distributed according + to some distribution: +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+//
+// We can repeat the above example, with other distributions:
+//
+uniform_real_distribution<mpf_float_50> ur(-20, 20);
+gamma_distribution<mpf_float_50> gd(20);
+independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen;
+//
+// Generate some values:
+//
+std::cout << std::setprecision(50);
+for(unsigned i = 0; i < 20; ++i)
+   std::cout << ur(gen) << std::endl;
+for(unsigned i = 0; i < 20; ++i)
+   std::cout << gd(gen) << std::endl;
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html new file mode 100644 index 00000000..0336d8e2 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -0,0 +1,252 @@ + + + +Rational Number Types + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    gmp_rational
    +
    cpp_rational
    +
    tommath_rational
    +
    Use With Boost.Rational
    +
    rational_adapter
    +
    +

    + The following back-ends provide rational number arithmetic: +

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend Type +

    +     		+

    + Header +

    +     		+

    + Radix +

    +     		+

    + Dependencies +

    +     		+

    + Pros +

    +     		+

    + Cons +

    +
    +

    + gmp_rational +

    +     		+

    + boost/multiprecision/gmp.hpp +

    +     		+

    + 2 +

    +     		+

    + GMP +

    +     		+

    + Very fast and efficient back-end. +

    +     		+

    + Dependency on GNU licensed GMP + library. +

    +
    +

    + cpp_rational +

    +     		+

    + boost/multiprecision/cpp_int.hpp +

    +     		+

    + 2 +

    +     		+

    + None +

    +     		+

    + An all C++ Boost-licensed implementation. +

    +     		+

    + Slower than GMP. +

    +
    +

    + tommath_rational +

    +     		+

    + boost/multiprecision/tommath.hpp +

    +     		+

    + 2 +

    +     		+

    + libtommath +

    +     		+

    + All C/C++ implementation that's Boost Software Licence compatible. +

    +     		+

    + Slower than GMP. +

    +
    +

    + rational_adapter +

    +     		+

    + boost/multiprecision/rational_adapter.hpp +

    +     		+

    + N/A +

    +     		+

    + none +

    +     		+

    + All C++ adapter that allows any inetger back-end type to be used + as a rational type. +

    +     		+

    + Requires an underlying integer back-end type. +

    +
    +

    + boost::rational +

    +     		+

    + boost/rational.hpp +

    +     		+

    + N/A +

    +     		+

    + None +

    +     		+

    + A C++ rational number type that can used with any mp_number integer type. +

    +     		+

    + The expression templates used by mp_number + end up being "hidden" inside boost::rational: + performance may well suffer as a result. +

    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational/br.html b/doc/html/boost_multiprecision/tut/rational/br.html new file mode 100644 index 00000000..a3efdfa6 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational/br.html @@ -0,0 +1,42 @@ + + + +Use With Boost.Rational + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + All of the integer types in this library can be used as template arguments + to boost::rational<IntType>. +

    +

    + Note that using the library in this way largely negates the effect of the + expression templates in mp_number. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html new file mode 100644 index 00000000..ea6b42a8 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html @@ -0,0 +1,108 @@ + + + +cpp_rational + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/cpp_int.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
+
+typedef mp_number<cpp_rational_backend>         cpp_rational;
+
+}} // namespaces
+
    +

    + The cpp_rational_backend + type is used via the typedef boost::multiprecision::cpp_rational. + It provides a rational number type that is a drop-in replacement for the + native C++ number types, but with unlimited precision. +

    +

    + As well as the usual conversions from arithmetic and string types, instances + of cpp_rational are copy + constructible and assignable from type cpp_int. +

    +

    + There is also a two argument constructor that accepts a numerator and denominator: + both of type cpp_int. +

    +

    + There are also non-member functions: +

    +
    cpp_int numerator(const cpp_rational&);
+cpp_int denominator(const cpp_rational&);
+
    +

    + which return the numerator and denominator of the number. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed cpp_rationals + have the value zero. +
      • +
    • + Division by zero results in a std::rumtime_error + being thrown. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+
+using namespace boost::multiprecision;
+
+cpp_rational v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+v /= 10;
+
+std::cout << v << std::endl; // prints 1000! / 10
+std::cout << numerator(v) << std::endl;
+std::cout << denominator(v) << std::endl;
+
+cpp_rational w(2, 3);  // component wise constructor
+std::cout << w << std::endl; // prints 2/3
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html new file mode 100644 index 00000000..8f1f28fe --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html @@ -0,0 +1,138 @@ + + + +gmp_rational + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/gmp.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+class gmp_rational;
+
+typedef mp_number<gmp_rational >         mpq_rational;
+
+}} // namespaces
+
    +

    + The gmp_rational back-end + is used via the typedef boost::multiprecision::mpq_rational. + It acts as a thin wrapper around the GMP + mpq_t to provide a rational + number type that is a drop-in replacement for the native C++ number types, + but with unlimited precision. +

    +

    + As well as the usual conversions from arithmetic and string types, instances + of mp_number<gmp_rational> + are copy constructible and assignable from: +

    +
      +
    • + The GMP native types: mpz_t, mpq_t. +
      • +
    • + mp_number<gmp_int>. +
      • +
    +

    + There is also a two-argument constructor that accepts a numerator and denominator + (both of type mp_number<gmp_int>). +

    +

    + There are also non-member functions: +

    +
    mpz_int numerator(const mpq_rational&);
+mpz_int denominator(const mpq_rational&);
+
    +

    + which return the numerator and denominator of the number. +

    +

    + It's also possible to access the underlying mpq_t + via the data() + member function of mpq_rational. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed mpq_rationals + have the value zero (this is the GMP + default behavior). +
      • +
    • + Division by zero results in a hardware exception inside the GMP library. +
      • +
    • + No changes are made to the GMP + library's global settings, so this type can coexist with existing + GMP code. +
      • +
    • + The code can equally be used with MPIR + as the underlying library - indeed that is the preferred option on + Win32. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+
+using namespace boost::multiprecision;
+
+mpq_rational v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+v /= 10;
+
+std::cout << v << std::endl; // prints 1000! / 10
+std::cout << numerator(v) << std::endl;
+std::cout << denominator(v) << std::endl;
+
+mpq_rational w(2, 3);  // component wise constructor
+std::cout << w << std::endl; // prints 2/3
+
+// Access the underlying data:
+mpq_t q;
+mpq_init(q);
+mpq_set(q, v.backend().data());
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational/rational_adapter.html b/doc/html/boost_multiprecision/tut/rational/rational_adapter.html new file mode 100644 index 00000000..6b4853f1 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational/rational_adapter.html @@ -0,0 +1,58 @@ + + + +rational_adapter + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+template <class IntBackend>
+class rational_adpater;
+
+}}
+
    +

    + The class template rational_adapter + is a back-end for mp_number + which converts any existing integer back-end into a rational-number back-end. +

    +

    + So for example, given an integer back-end type MyIntegerBackend, + the use would be something like: +

    +
    typedef mp_number<MyIntegerBackend>                    MyInt;
+typedef mp_number<rational_adapter<MyIntegerBackend> > MyRational;
+
+MyRational r = 2;
+r /= 3;
+MyInt i = numerator(r);
+assert(i == 2);
+
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html new file mode 100644 index 00000000..25520372 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html @@ -0,0 +1,115 @@ + + + +tommath_rational + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/tommath.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+typedef rational_adpater<tommath_int>        tommath_rational;
+typedef mp_number<tommath_rational >         tom_rational;
+
+}} // namespaces
+
    +

    + The tommath_rational back-end + is used via the typedef boost::multiprecision::tom_rational. + It acts as a thin wrapper around boost::rational<tom_int> to provide a rational number type that + is a drop-in replacement for the native C++ number types, but with unlimited + precision. +

    +

    + The advantage of using this type rather than boost::rational<tom_int> directly, is that it is expression-template + enabled, greatly reducing the number of temporaries created in complex + expressions. +

    +

    + There are also non-member functions: +

    +
    tom_int numerator(const tom_rational&);
+tom_int denominator(const tom_rational&);
+
    +

    + which return the numerator and denominator of the number. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed tom_rationals + have the value zero (this the inherited Boost.Rational behavior). +
      • +
    • + Division by zero results in a boost::bad_rational + exception being thrown (see the rational number library's docs for + more information). +
      • +
    • + No changes are made to libtommath's + global state, so this type can safely coexist with other libtommath + code. +
      • +
    • + Performance of this type has been found to be pretty poor - this need + further investigation - but it appears that Boost.Rational needs some + improvement in this area. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/tommath.hpp>
+
+using namespace boost::multiprecision;
+
+tom_rational v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+v /= 10;
+
+std::cout << v << std::endl; // prints 1000! / 10
+std::cout << numerator(v) << std::endl;
+std::cout << denominator(v) << std::endl;
+
+tom_rational w(2, 3); // Component wise constructor
+std::cout << w << std::endl; // prints 2/3
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/index.html b/doc/html/index.html new file mode 100644 index 00000000..3f79382c --- /dev/null +++ b/doc/html/index.html @@ -0,0 +1,108 @@ + + + +Chapter 1. Boost.Multiprecision + + + + + + +
    Next
    +
    +
    +

    +Chapter 1. Boost.Multiprecision

    +

    +John Maddock +

    +

    +Christopher Kormanyos +

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +
    +

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +

    Table of Contents

    +
    +
    Introduction
    +
    Tutorial
    +
    +
    Integer Types
    +
    +
    cpp_int
    +
    gmp_int
    +
    tom_int
    +
    +
    Floating Point Numbers
    +
    +
    gmp_float
    +
    mpfr_float
    +
    cpp_dec_float
    +
    +
    Rational Number Types
    +
    +
    gmp_rational
    +
    cpp_rational
    +
    tommath_rational
    +
    Use With Boost.Rational
    +
    rational_adapter
    +
    +
    Constructing and + Interconverting Between Number Types
    +
    Generating Random Numbers
    +
    Primality Testing
    +
    +
    Reference
    +
    +
    mp_number
    +
    cpp_int
    +
    gmp_int
    +
    tom_int
    +
    gmp_float
    +
    mpfr_float_backend
    +
    cpp_dec_float
    +
    Backend Requirements
    +
    +
    Performance Comparison
    +
    +
    Floating Point Real + World Tests
    +
    Integer Real + World Tests
    +
    Float Algorithm + Perfomance
    +
    Integer + Algorithm Perfomance
    +
    Rational + Type Perfomance
    +
    +
    Roadmap
    +
    +
    History
    +
    TODO
    +
    Acknowledgements
    +
    +
    Indexes
    +
    +
    Function Index
    +
    Class Index
    +
    Typedef Index
    +
    Index
    +
    +
    +
    +
    + + + +

    Last revised: March 30, 2012 at 18:33:57 GMT

    +
    +
    Next
    + + From 3d3d58e04090445b90d5447765e207e0dd0737c6 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 3 Apr 2012 16:20:11 +0000 Subject: [PATCH 155/256] Tidy up code, and add multi-threaded test case. [SVN r77741] --- performance/sf_performance.cpp | 376 ++++++++++++--------------------- 1 file changed, 135 insertions(+), 241 deletions(-) diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index 195b991c..e2183f7f 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -3,15 +3,15 @@ // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ -#define BOOST_CHRONO_HEADER_ONLY #define BOOST_MATH_MAX_ROOT_ITERATION_POLICY 500 -#if !defined(TEST_MPFR) && !defined(TEST_MP_REAL) && !defined(TEST_MPF) +#if !defined(TEST_MPFR) && !defined(TEST_MPREAL) && !defined(TEST_MPF) && !defined(TEST_MPREAL) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_CLASS) # define TEST_MPFR # define TEST_MPF -# define TEST_MPF # define TEST_CPP_DEC_FLOAT # define TEST_MPFR_CLASS +# define TEST_MPREAL #endif #ifdef TEST_MPFR_CLASS @@ -20,7 +20,7 @@ #ifdef TEST_MPFR #include #endif -#ifdef TEST_MP_REAL +#ifdef TEST_MPREAL #include #endif #ifdef TEST_MPF @@ -35,6 +35,7 @@ #include #include #include +#include template Real test_bessel(); @@ -63,48 +64,54 @@ private: template Real test_bessel() { + try{ # define T double # define SC_(x) x # include "libs/math/test/bessel_i_int_data.ipp" # include "libs/math/test/bessel_i_data.ipp" - Real r; + Real r; - for(unsigned i = 0; i < bessel_i_int_data.size(); ++i) - { - r += boost::math::cyl_bessel_i(Real(bessel_i_int_data[i][0]), Real(bessel_i_int_data[i][1])); - } - for(unsigned i = 0; i < bessel_i_data.size(); ++i) - { - r += boost::math::cyl_bessel_i(Real(bessel_i_data[i][0]), Real(bessel_i_data[i][1])); - } + for(unsigned i = 0; i < bessel_i_int_data.size(); ++i) + { + r += boost::math::cyl_bessel_i(Real(bessel_i_int_data[i][0]), Real(bessel_i_int_data[i][1])); + } + for(unsigned i = 0; i < bessel_i_data.size(); ++i) + { + r += boost::math::cyl_bessel_i(Real(bessel_i_data[i][0]), Real(bessel_i_data[i][1])); + } #include "libs/math/test/bessel_j_int_data.ipp" - for(unsigned i = 0; i < bessel_j_int_data.size(); ++i) - { - r += boost::math::cyl_bessel_j(Real(bessel_j_int_data[i][0]), Real(bessel_j_int_data[i][1])); - } + for(unsigned i = 0; i < bessel_j_int_data.size(); ++i) + { + r += boost::math::cyl_bessel_j(Real(bessel_j_int_data[i][0]), Real(bessel_j_int_data[i][1])); + } #include "libs/math/test/bessel_j_data.ipp" - for(unsigned i = 0; i < bessel_j_data.size(); ++i) - { - r += boost::math::cyl_bessel_j(Real(bessel_j_data[i][0]), Real(bessel_j_data[i][1])); - } + for(unsigned i = 0; i < bessel_j_data.size(); ++i) + { + r += boost::math::cyl_bessel_j(Real(bessel_j_data[i][0]), Real(bessel_j_data[i][1])); + } #include "libs/math/test/bessel_j_large_data.ipp" - for(unsigned i = 0; i < bessel_j_large_data.size(); ++i) - { - r += boost::math::cyl_bessel_j(Real(bessel_j_large_data[i][0]), Real(bessel_j_large_data[i][1])); - } + for(unsigned i = 0; i < bessel_j_large_data.size(); ++i) + { + r += boost::math::cyl_bessel_j(Real(bessel_j_large_data[i][0]), Real(bessel_j_large_data[i][1])); + } #include "libs/math/test/sph_bessel_data.ipp" - for(unsigned i = 0; i < sph_bessel_data.size(); ++i) - { - r += boost::math::sph_bessel(static_cast(sph_bessel_data[i][0]), Real(sph_bessel_data[i][1])); + for(unsigned i = 0; i < sph_bessel_data.size(); ++i) + { + r += boost::math::sph_bessel(static_cast(sph_bessel_data[i][0]), Real(sph_bessel_data[i][1])); + } + + return r; } - - - return r; + catch(const std::exception& e) + { + std::cout << e.what() << std::endl; + } + return 0; } template @@ -161,54 +168,89 @@ void * realloc_func(void * p, size_t old, size_t n) return (*realloc_func_ptr)(p, old, n); } +template +void basic_allocation_test(const char* name, Real x) +{ + static const unsigned a[] = { 2, 3, 4, 5, 6, 7, 8 }; + allocation_count = 0; + Real result = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; + std::cout << "Allocation count for type " << name << " = " << allocation_count << std::endl; +} + +template +void poly_allocation_test(const char* name, Real x) +{ + static const unsigned a[] = { 2, 3, 4, 5, 6, 7, 8 }; + allocation_count = 0; + Real result = boost::math::tools::evaluate_polynomial(a, x); + std::cout << "Allocation count for type " << name << " = " << allocation_count << std::endl; +} + +template +void time_proc(const char* name, Real (*proc)(), unsigned threads = 1) +{ + try{ + static Real total = 0; + allocation_count = 0; + boost::chrono::duration time; + stopwatch c; + total += proc(); + time = c.elapsed(); + std::cout << "Time for " << name << " = " << time << std::endl; + std::cout << "Total allocations for " << name << " = " << allocation_count << std::endl; + + for(unsigned thread_count = 1; thread_count < threads; ++thread_count) + { + c.reset(); + boost::thread_group g; + for(unsigned i = 0; i <= thread_count; ++i) + g.create_thread(proc); + g.join_all(); + time = c.elapsed(); + std::cout << "Time for " << name << " (" << (thread_count + 1) << " threads) = " << time << std::endl; + std::cout << "Total allocations for " << name << " = " << allocation_count << std::endl; + } + } + catch(const std::exception& e) + { + std::cout << e.what() << std::endl; + } +} + int main() { + using namespace boost::multiprecision; +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) || defined(TEST_MPREAL) mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); mp_set_memory_functions(&alloc_func, &realloc_func, &free_func); +#endif - static const unsigned a[] = { - 2, 3, 4, 5, 6, 7, 8 }; + std::cout << "Allocation Counts for Horner Evaluation:\n"; #ifdef TEST_MPFR - boost::multiprecision::mpfr_float_50 result, x(2); - allocation_count = 0; - result = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; - std::cout << allocation_count << std::endl; + basic_allocation_test("mpfr_float_50", mpfr_float_50(2)); #endif #ifdef TEST_MPFR_CLASS - mpfr_class r, x2(2); - allocation_count = 0; - r = (((((a[6] * x2 + a[5]) * x2 + a[4]) * x2 + a[3]) * x2 + a[2]) * x2 + a[1]) * x2 + a[0]; - std::cout << allocation_count << std::endl; + basic_allocation_test("mpfr_class", mpfr_class(2)); #endif #ifdef TEST_MPREAL - mpfr::mpreal r2, x3(2); - allocation_count = 0; - r2 = (((((a[6] * x3 + a[5]) * x3 + a[4]) * x3 + a[3]) * x3 + a[2]) * x3 + a[1]) * x3 + a[0]; - std::cout << allocation_count << std::endl; + basic_allocation_test("mpfr::mpreal", mpfr::mpreal(2)); #endif - allocation_count = 0; + std::cout << "Allocation Counts for boost::math::tools::evaluate_polynomial:\n"; #ifdef TEST_MPFR - result = boost::math::tools::evaluate_polynomial(a, x); - std::cout << allocation_count << std::endl; - allocation_count = 0; + poly_allocation_test("mpfr_float_50", mpfr_float_50(2)); #endif #ifdef TEST_MPFR_CLASS - r = boost::math::tools::evaluate_polynomial(a, x2); - std::cout << allocation_count << std::endl; - allocation_count = 0; + poly_allocation_test("mpfr_class", mpfr_class(2)); #endif #ifdef TEST_MPREAL - r2 = boost::math::tools::evaluate_polynomial(a, x3); - std::cout << allocation_count << std::endl; + poly_allocation_test("mpfr::mpreal", mpfr::mpreal(2)); #endif - boost::chrono::duration time; - stopwatch c; // // 50 digits first: // - std::cout << "Testing Bessel Functions....." << std::endl; + std::cout << "Testing Bessel Functions at 50 digits....." << std::endl; #if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) mpfr_set_default_prec(50 * 1000L / 301L); #endif @@ -216,48 +258,25 @@ int main() mpfr::mpreal::set_default_prec(50 * 1000L / 301L); #endif #ifdef TEST_MPFR - c.reset(); - test_bessel(); - time = c.elapsed(); - std::cout << "Time for mpfr_float_50 = " << time << std::endl; - std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_float_50", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); #endif #ifdef TEST_MPF - c.reset(); - test_bessel(); - time = c.elapsed(); - std::cout << "Time for mpf_float_50 = " << time << std::endl; - std::cout << "Total allocations for mpf_float_50 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpf_float_50", test_bessel, 3); + time_proc("mpf_float_50 (no expression templates", test_bessel, false> >, 3); #endif #ifdef TEST_CPP_DEC_FLOAT - c.reset(); - test_bessel(); - time = c.elapsed(); - std::cout << "Time for cpp_dec_float_50 = " << time << std::endl; - std::cout << "Total allocations for cpp_dec_float_50 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("cpp_dec_float_50", test_bessel, 3); #endif #ifdef TEST_MPFR_CLASS - c.reset(); - test_bessel(); - time = c.elapsed(); - std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl; - std::cout << "Total allocations for mpfr_class (50 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_class", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); #endif #ifdef TEST_MP_REAL - c.reset(); - test_bessel(); - time = c.elapsed(); - std::cout << "Time for mpreal (50 digits) = " << time << std::endl; - std::cout << "Total allocations for mpreal (50 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr::mpreal", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); #endif // // Then 100 digits: // + std::cout << "Testing Bessel Functions at 100 digits....." << std::endl; #if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) mpfr_set_default_prec(100 * 1000L / 301L); #endif @@ -265,51 +284,25 @@ int main() mpfr::mpreal::set_default_prec(100 * 1000L / 301L); #endif #ifdef TEST_MPFR - c.reset(); - test_bessel(); - time = c.elapsed(); - std::cout << "Time for mpfr_float_100 = " << time << std::endl; - std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_float_100", test_bessel); #endif #ifdef TEST_MPF - c.reset(); - test_bessel(); - time = c.elapsed(); - std::cout << "Time for mpf_float_100 = " << time << std::endl; - std::cout << "Total allocations for mpf_float_100 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpf_float_100", test_bessel); #endif #ifdef TEST_CPP_DEC_FLOAT - c.reset(); - test_bessel(); - time = c.elapsed(); - std::cout << "Time for cpp_dec_float_100 = " << time << std::endl; - std::cout << "Total allocations for cpp_dec_float_100 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("cpp_dec_float_100", test_bessel); #endif #ifdef TEST_MPFR_CLASS - c.reset(); - test_bessel(); - time = c.elapsed(); - std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl; - std::cout << "Total allocations for mpfr_class (100 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_class", test_bessel); #endif #ifdef TEST_MPREAL - c.reset(); - test_bessel(); - time = c.elapsed(); - std::cout << "Time for mpreal (100 digits) = " << time << std::endl; - std::cout << "Total allocations for mpreal (100 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr::mpreal", test_bessel); #endif // // 50 digits first: // - c.reset(); - std::cout << "Testing Polynomial Evaluation....." << std::endl; + std::cout << "Testing Polynomial Evaluation at 50 digits....." << std::endl; #if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) mpfr_set_default_prec(50 * 1000L / 301L); #endif @@ -317,48 +310,24 @@ int main() mpfr::mpreal::set_default_prec(50 * 1000L / 301L); #endif #ifdef TEST_MPFR - c.reset(); - test_polynomial(); - time = c.elapsed(); - std::cout << "Time for mpfr_float_50 = " << time << std::endl; - std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_float_50", test_polynomial); #endif #ifdef TEST_MPF - c.reset(); - test_polynomial(); - time = c.elapsed(); - std::cout << "Time for mpf_float_50 = " << time << std::endl; - std::cout << "Total allocations for mpf_float_50 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpf_float_50", test_polynomial); #endif #ifdef TEST_CPP_DEC_FLOAT - c.reset(); - test_polynomial(); - time = c.elapsed(); - std::cout << "Time for cpp_dec_float_50 = " << time << std::endl; - std::cout << "Total allocations for cpp_dec_float_50 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("cpp_dec_float_50", test_polynomial); #endif #ifdef TEST_MPFR_CLASS - c.reset(); - test_polynomial(); - time = c.elapsed(); - std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl; - std::cout << "Total allocations for mpfr_class (50 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_class", test_polynomial); #endif #ifdef TEST_MPREAL - c.reset(); - test_polynomial(); - time = c.elapsed(); - std::cout << "Time for mpreal (50 digits) = " << time << std::endl; - std::cout << "Total allocations for mpreal (50 digits = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr::mpreal", test_polynomial); #endif // // Then 100 digits: // + std::cout << "Testing Polynomial Evaluation at 100 digits....." << std::endl; #ifdef TEST_MPFR_CLASS mpfr_set_default_prec(100 * 1000L / 301L); #endif @@ -366,50 +335,24 @@ int main() mpfr::mpreal::set_default_prec(100 * 1000L / 301L); #endif #ifdef TEST_MPFR - c.reset(); - test_polynomial(); - time = c.elapsed(); - std::cout << "Time for mpfr_float_100 = " << time << std::endl; - std::cout << "Total allocations for mpfr_float_100 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_float_100", test_polynomial); #endif #ifdef TEST_MPF - c.reset(); - test_polynomial(); - time = c.elapsed(); - std::cout << "Time for mpf_float_100 = " << time << std::endl; - std::cout << "Total allocations for mpf_float_100 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpf_float_100", test_polynomial); #endif #ifdef TEST_CPP_DEC_FLOAT - c.reset(); - test_polynomial(); - time = c.elapsed(); - std::cout << "Time for cpp_dec_float_100 = " << time << std::endl; - std::cout << "Total allocations for cpp_dec_float_100 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("cpp_dec_float_100", test_polynomial); #endif #ifdef TEST_MPFR_CLASS - c.reset(); - test_polynomial(); - time = c.elapsed(); - std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl; - std::cout << "Total allocations for mpfr_class (100 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_class", test_polynomial); #endif #ifdef TEST_MPREAL - c.reset(); - test_polynomial(); - time = c.elapsed(); - std::cout << "Time for mpreal (100 digits) = " << time << std::endl; - std::cout << "Total allocations for mpreal (100 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr::mpreal", test_polynomial); #endif // // 50 digits first: // - c.reset(); - std::cout << "Testing Non-Central T....." << std::endl; + std::cout << "Testing Non-Central T at 50 digits....." << std::endl; #ifdef TEST_MPFR_CLASS mpfr_set_default_prec(50 * 1000L / 301L); #endif @@ -417,48 +360,24 @@ int main() mpfr::mpreal::set_default_prec(50 * 1000L / 301L); #endif #ifdef TEST_MPFR - c.reset(); - test_nct(); - time = c.elapsed(); - std::cout << "Time for mpfr_float_50 = " << time << std::endl; - std::cout << "Total allocations for mpfr_float_50 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_float_50", test_nct); #endif #ifdef TEST_MPF - c.reset(); - test_nct(); - time = c.elapsed(); - std::cout << "Time for mpf_float_50 = " << time << std::endl; - std::cout << "Total allocations for mpf_float_50 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpf_float_50", test_nct); #endif #ifdef TEST_CPP_DEC_FLOAT - c.reset(); - test_nct(); - time = c.elapsed(); - std::cout << "Time for cpp_dec_float_50 = " << time << std::endl; - std::cout << "Total allocations for cpp_dec_float_50 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("cpp_dec_float_50", test_nct); #endif #ifdef TEST_MPFR_CLASS - c.reset(); - test_nct(); - time = c.elapsed(); - std::cout << "Time for mpfr_class (50 digits) = " << time << std::endl; - std::cout << "Total allocations for mpfr_class (50 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_class", test_nct); #endif #ifdef TEST_MP_REAL - c.reset(); - test_nct(); - time = c.elapsed(); - std::cout << "Time for mpreal (50 digits) = " << time << std::endl; - std::cout << "Total allocations for mpreal (50 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr::mpreal", test_nct); #endif // // Then 100 digits: // + std::cout << "Testing Non-Central T at 100 digits....." << std::endl; #ifdef TEST_MPFR_CLASS mpfr_set_default_prec(100 * 1000L / 301L); #endif @@ -466,44 +385,19 @@ int main() mpfr::mpreal::set_default_prec(100 * 1000L / 301L); #endif #ifdef TEST_MPFR - c.reset(); - test_nct(); - time = c.elapsed(); - std::cout << "Time for mpfr_float_100 = " << time << std::endl; - std::cout << "Total allocations for mpfr_float_100 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_float_100", test_nct); #endif #ifdef TEST_MPF - c.reset(); - test_nct(); - time = c.elapsed(); - std::cout << "Time for mpf_float_100 = " << time << std::endl; - std::cout << "Total allocations for mpf_float_100 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpf_float_100", test_nct); #endif #ifdef TEST_CPP_DEC_FLOAT - c.reset(); - test_nct(); - time = c.elapsed(); - std::cout << "Time for cpp_dec_float_100 = " << time << std::endl; - std::cout << "Total allocations for cpp_dec_float_100 = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("cpp_dec_float_100", test_nct); #endif #ifdef TEST_MPFR_CLASS - c.reset(); - test_nct(); - time = c.elapsed(); - std::cout << "Time for mpfr_class (100 digits) = " << time << std::endl; - std::cout << "Total allocations for mpfr_class (100 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr_class", test_nct); #endif #ifdef TEST_MPREAL - c.reset(); - test_nct(); - time = c.elapsed(); - std::cout << "Time for mpreal (100 digits) = " << time << std::endl; - std::cout << "Total allocations for mpreal (100 digits) = " << allocation_count << std::endl; - allocation_count = 0; + time_proc("mpfr::mpreal", test_nct); #endif } From 4a15673dd47a211fed9556733dabee4086c01390 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 3 Apr 2012 16:21:08 +0000 Subject: [PATCH 156/256] Update Jamfile to match new sf_performance.cpp code. [SVN r77742] --- performance/Jamfile.v2 | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/performance/Jamfile.v2 b/performance/Jamfile.v2 index 54fd7e52..be2cc779 100644 --- a/performance/Jamfile.v2 +++ b/performance/Jamfile.v2 @@ -53,7 +53,7 @@ exe performance_test : performance_test.cpp /boost/system//boost_system TEST_CPP_INT ; -exe sf_performance : sf_performance.cpp /boost/system//boost_system +exe sf_performance : sf_performance.cpp /boost/system//boost_system /boost/system//boost_chrono /boost/system//boost_thread : release [ check-target-builds ../config//has_gmp : TEST_MPF TEST_MPZ gmp : ] [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr : ] From 149af697bc4a091f575109c01abb2eaba96759f1 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 3 Apr 2012 16:22:27 +0000 Subject: [PATCH 157/256] Add log of comments. [SVN r77743] --- .../boost_multiprecision/indexes/s01.html | 4 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 4 +- doc/html/boost_multiprecision/map/todo.html | 43 +++++++++++++++++++ doc/html/index.html | 2 +- doc/multiprecision.qbk | 15 +++++++ 7 files changed, 67 insertions(+), 9 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 59767df1..985e46bb 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
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    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 3ac7ed2e..d7638e3e 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
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    diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index 1c188b18..315bd765 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -41,6 +41,49 @@ Add an all C++ binary floating point type.
    +
    + + Pre-Review + Comments +
    +
      +
    • + Make the exponent type for cpp_dec_float a templare parameter, maybe + include support for big-integer exponents. Open question - what should + be the default - int32_t or int64_t? +
      • +
    • + Document the size requirements of fixed precision ints. +
      • +
    • + Document std lib function accuracy. +
      • +
    • + Make fixed precision orthogonal to Allocator type in cpp_int. Possible + solution - add an additional MaxBits template argument that defaults + to 0 (meaning keep going till no more space/memory). +
      • +
    • + Add support for fused multiply add (and subtract). GMP mpz_t could use + this. +
      • +
    • + Be a bit clearer on the effects of sign-magnitude representation of cpp_int + - min == -max etc. +
      • +
    • + Document cpp_dec_float precision, rounding, and exponent size. +
      • +
    • + Can we be clearer in the docs that mixed arithmetic doesn't work? +
      • +
    • + Document round functions behaviour better (they behave as in C99). +
      • +
    • + Should there be a choice of rounding mode (probably MPFR specific)? +
      • +
    diff --git a/doc/html/index.html b/doc/html/index.html index 3f79382c..2609da49 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -99,7 +99,7 @@
    - +

    Last revised: March 30, 2012 at 18:33:57 GMT

    Last revised: April 03, 2012 at 15:58:48 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 97cf9fad..4b3e4dba 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -2072,6 +2072,21 @@ More a list of what ['could] be done, rather than what ['should] be done (which * Add assembly level routines to cpp_int_backend. * Add an all C++ binary floating point type. +[h4 Pre-Review Comments] + +* Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents. +Open question - what should be the default - int32_t or int64_t? +* Document the size requirements of fixed precision ints. +* Document std lib function accuracy. +* Make fixed precision orthogonal to Allocator type in cpp_int. Possible solution - add an additional MaxBits +template argument that defaults to 0 (meaning keep going till no more space/memory). +* Add support for fused multiply add (and subtract). GMP mpz_t could use this. +* Be a bit clearer on the effects of sign-magnitude representation of cpp_int - min == -max etc. +* Document cpp_dec_float precision, rounding, and exponent size. +* Can we be clearer in the docs that mixed arithmetic doesn't work? +* Document round functions behaviour better (they behave as in C99). +* Should there be a choice of rounding mode (probably MPFR specific)? + [endsect] [section:ack Acknowledgements] From 0488e551b995ff2625cfe5840d0b55accb1817a0 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 3 Apr 2012 18:20:35 +0000 Subject: [PATCH 158/256] Add extended floating point example. [SVN r77746] --- .../boost_multiprecision/indexes/s01.html | 8 +- .../boost_multiprecision/indexes/s02.html | 15 +- .../boost_multiprecision/indexes/s03.html | 16 +- .../boost_multiprecision/indexes/s04.html | 49 ++-- doc/html/boost_multiprecision/tut.html | 2 + doc/html/boost_multiprecision/tut/floats.html | 2 + .../tut/floats/cpp_dec_float.html | 6 +- .../boost_multiprecision/tut/floats/jel.html | 222 ++++++++++++++++++ .../boost_multiprecision/tut/rational.html | 6 +- doc/html/index.html | 4 +- doc/multiprecision.qbk | 8 + example/floating_point_examples.cpp | 194 +++++++++++++++ 12 files changed, 490 insertions(+), 42 deletions(-) create mode 100644 doc/html/boost_multiprecision/tut/floats/jel.html create mode 100644 example/floating_point_examples.cpp diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 985e46bb..5e18e6c7 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,10 +13,10 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    -

    A B C D E F I L M P R S T Z

    +Function Index
    +

    A B C D E F I L M P R S T Z

    A @@ -207,7 +207,7 @@
    -Z +Z

    • zero

      diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index 730aadba..9207a2a7 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,13 +13,13 @@
      PrevUpHomeNext
      -
      +

      -Class Index

      -

      M

      +Class Index
    +

    M T

    -M +M
    +
    +T +
    +
    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 9208e9f5..9aecc85a 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,13 +13,13 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    -

    C I L M T

    +Typedef Index
    +

    C I L M T

    -C +C
    • @@ -47,21 +47,21 @@
    -I +I
    -L +L
    -M +M
    • @@ -161,7 +161,7 @@
    -T +T

    • tommath_rational

      • diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index d7638e3e..a079ef1a 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,20 +12,20 @@
      PrevUpHome
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      -Index

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      A B C D E F G I L M O P R S T Z

      +Index
    +

    A B C D E F G I L M O P R S T W Z

    -A +A
    -B +B
    • @@ -50,7 +50,7 @@
    -C +C
    • @@ -106,7 +106,7 @@
    -D +D
    • @@ -128,21 +128,21 @@
    -E +E
    -F +F
    -G +G
    • @@ -175,7 +175,7 @@
    -I +I
    • @@ -223,7 +223,7 @@
    -L +L
    • @@ -252,7 +252,7 @@
    -M +M
    • @@ -410,14 +410,14 @@
    -O +O
    -P +P
    • @@ -437,14 +437,14 @@
    -R +R
    -S +S
    • @@ -461,7 +461,7 @@
    -T +T
    -Z +W +
    +
    • +

      Worked Example: defining a mathematical function.

      +
      +
    +
    +Z
    Rational Number Types
    diff --git a/doc/html/boost_multiprecision/tut/floats.html b/doc/html/boost_multiprecision/tut/floats.html index a3b605f0..f9b841f4 100644 --- a/doc/html/boost_multiprecision/tut/floats.html +++ b/doc/html/boost_multiprecision/tut/floats.html @@ -21,6 +21,8 @@
    gmp_float
    mpfr_float
    cpp_dec_float
    +
    Worked Example: + defining a mathematical function.

    The following back-ends provide floating point arithmetic: diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html index ca15017c..cc7b16ca 100644 --- a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html +++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html @@ -7,11 +7,11 @@ - +

    -PrevUpHomeNext +PrevUpHomeNext

    @@ -111,7 +111,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/floats/jel.html b/doc/html/boost_multiprecision/tut/floats/jel.html new file mode 100644 index 00000000..9a6a4ba8 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/jel.html @@ -0,0 +1,222 @@ + + + +Worked Example: defining a mathematical function. + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + In this example we'll show several implementations of the Jahnke + and Emden Lambda function, each implementation a little more sophisticated + than the last. +

    +

    + The Jahnke-Emden Lambda function is defined by the equation: +

    +

    + JahnkeEmden(v, z) = Gamma(v+1) * J[v](z) / (z / 2)^v +

    +

    + If we were to implement this at double precision using Boost.Math's facilities + for the Gamma and Bessel function calls it would look like this: +

    +

    +

    +
    double JEL1(double v, double z)
+{
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / std::pow(z / 2, v);
+}
+
    +

    +

    +

    + Calling this function as: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10);
+std::cout << JEL1(2.5, 0.5) << std::endl;
+
    +

    + Yields the output: +

    +
    9.822663964796047e-001
    +

    + Now lets implement the function again, but this time using the multiprecision + type cpp_dec_float_50 as + the argument type: +

    +

    +

    +
    boost::multiprecision::cpp_dec_float_50
+   JEL2(boost::multiprecision::cpp_dec_float_50 v, boost::multiprecision::cpp_dec_float_50 z)
+{
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / boost::multiprecision::pow(z / 2, v);
+}
+
    +

    +

    +

    + The implementation is almost the same as before, but with one key difference + - we can no longer call std::pow, + instead we must call the version inside the boost::multiprecision + namespace. In point of fact, we could have omitted the namespace prefix + on the call to pow since + the right overload would have been found via argument + dependent lookup in any case. +

    +

    + Note also that the first argument to pow + along with the argument to tgamma + in the above code are actually expression templates. The pow and tgamma + functions will handle these arguments just fine. +

    +

    + Here's an example of how the function may be called: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10);
+std::cout << JEL2(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl;
+
    +

    + Which outputs: +

    +
    9.82266396479604757017335009796882833995903762577173e-01
    +

    + Now that we've seen some non-template examples, lets repeat the code again, + but this time as a template that can be called either with a builtin type + (float, double + etc), or with a multiprecision type: +

    +

    +

    +
    template <class Float>
+Float JEL3(Float v, Float z)
+{
+   using std::pow;
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
+}
+
    +

    +

    +

    + Once again the code is almost the same as before, but the call to pow has changed yet again. We need the + call to resolve to either std::pow + (when the argument is a builtin type), or to boost::multiprecision::pow + (when the argument is a multiprecision type). We do that by making the + call unqualified so that versions of pow + defined in the same namespace as type Float + are found via argument dependent lookup, while the using + std::pow directive makes the standard library + versions visible for builtin floating point types. +

    +

    + Let's call the function with both double + and multiprecision arguments: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10);
+std::cout << JEL3(2.5, 0.5) << std::endl;
+std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10);
+std::cout << JEL3(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl;
+
    +

    + Which outputs: +

    +
    9.822663964796047e-001
+9.82266396479604757017335009796882833995903762577173e-01
+
    +

    + Unfortunately there is a problem with this version: if we were to call + it like this: +

    +
    boost::multiprecision::cpp_dec_float_50 v(2), z(0.5);
+JEL3(v + 0.5, z);
+
    +

    + Then we would get a long and inscrutable error message from the compiler: + the problem here is that the first argument to JEL3 + is not a number type, but an expression template. We could obviously add + a typecast to fix the issue: +

    +
    JEL(cpp_dec_float_50(v + 0.5), z);
+
    +

    + However, if we want the function JEL to be truely reusable, then a better + solution might be preferred. To achieve this we can borrow some code from + Boost.Math which calculates the return type of mixed-argument functions, + here's how the new code looks now: +

    +

    +

    +
    template <class Float1, class Float2>
+typename boost::math::tools::promote_args<Float1, Float2>::type
+   JEL4(Float1 v, Float2 z)
+{
+   using std::pow;
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
+}
+
    +

    +

    +

    + As you can see the two arguments to the function are now separate template + types, and the return type is computed using the promote_args + metafunction from Boost.Math. +

    +

    + Now we can call: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_100>::digits10);
+std::cout << JEL4(cpp_dec_float_100(2) + 0.5, cpp_dec_float_100(0.5)) << std::endl;
+
    +

    + And get 100 digits of output: +

    +
    9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01
    +

    + As a bonus, we can now call the function not just with expression templates, + but with other mixed types as well: for example float + and double or int and double, + and the correct return type will be computed in each case. +

    +

    + Note that while in this case we didn't have to change the body of the function, + in the general case any function like this which creates local variables + internally would have to use promote_args + to work out what type those variables should be, for example: +

    +
    template <class Float1, class Float2>
+typename boost::math::tools::promote_args<Float1, Float2>::type
+   JEL5(Float1 v, Float2 z)
+{
+   using std::pow;
+   typedef typename boost::math::tools::promote_args<Float1, Float2>::type variable_type;
+   variable_type t = pow(z / 2, v);
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / t;
+}
+
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 0336d8e2..318cba56 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -246,7 +246,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/index.html b/doc/html/index.html index 2609da49..013c47c5 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -44,6 +44,8 @@
    gmp_float
    mpfr_float
    cpp_dec_float
    +
    Worked Example: + defining a mathematical function.
    Rational Number Types
    @@ -99,7 +101,7 @@ - +

    Last revised: April 03, 2012 at 15:58:48 GMT

    Last revised: April 03, 2012 at 18:14:12 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 4b3e4dba..4d7e2a49 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -556,6 +556,14 @@ Normally these should not be visible to the user. [endsect] +[section:jel Worked Example: defining a mathematical function.] + +[import ../example/floating_point_examples.cpp] + +[JEL] + +[endsect] + [endsect] [section:rational Rational Number Types] diff --git a/example/floating_point_examples.cpp b/example/floating_point_examples.cpp new file mode 100644 index 00000000..9aa134e9 --- /dev/null +++ b/example/floating_point_examples.cpp @@ -0,0 +1,194 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include +#include +#include +#include + +//[JEL + +/*` +In this example we'll show several implementations of the +[@http://mathworld.wolfram.com/LambdaFunction.html Jahnke and Emden Lambda function], +each implementation a little more sophisticated than the last. + +The Jahnke-Emden Lambda function is defined by the equation: + +JahnkeEmden(v, z) = Gamma(v+1) * J[v](z) / (z / 2)^v + +If we were to implement this at double precision using Boost.Math's facilities for the Gamma and Bessel +function calls it would look like this: + +*/ + +double JEL1(double v, double z) +{ + return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / std::pow(z / 2, v); +} + +/*` +Calling this function as: + + std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); + std::cout << JEL1(2.5, 0.5) << std::endl; + +Yields the output: + +[pre 9.822663964796047e-001] + +Now lets implement the function again, but this time using the multiprecision type +`cpp_dec_float_50` as the argument type: + +*/ + +boost::multiprecision::cpp_dec_float_50 + JEL2(boost::multiprecision::cpp_dec_float_50 v, boost::multiprecision::cpp_dec_float_50 z) +{ + return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / boost::multiprecision::pow(z / 2, v); +} + +/*` +The implementation is almost the same as before, but with one key difference - we can no longer call +`std::pow`, instead we must call the version inside the `boost::multiprecision` namespace. In point of +fact, we could have omitted the namespace prefix on the call to `pow` since the right overload would +have been found via [@http://en.wikipedia.org/wiki/Argument-dependent_name_lookup +argument dependent lookup] in any case. + +Note also that the first argument to `pow` along with the argument to `tgamma` in the above code +are actually expression templates. The `pow` and `tgamma` functions will handle these arguments +just fine. + +Here's an example of how the function may be called: + + std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); + std::cout << JEL2(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl; + +Which outputs: + +[pre 9.82266396479604757017335009796882833995903762577173e-01] + +Now that we've seen some non-template examples, lets repeat the code again, but this time as a template +that can be called either with a builtin type (`float`, `double` etc), or with a multiprecision type: + +*/ + +template +Float JEL3(Float v, Float z) +{ + using std::pow; + return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v); +} + +/*` + +Once again the code is almost the same as before, but the call to `pow` has changed yet again. +We need the call to resolve to either `std::pow` (when the argument is a builtin type), or +to `boost::multiprecision::pow` (when the argument is a multiprecision type). We do that by +making the call unqualified so that versions of `pow` defined in the same namespace as type +`Float` are found via argument dependent lookup, while the `using std::pow` directive makes +the standard library versions visible for builtin floating point types. + +Let's call the function with both `double` and multiprecision arguments: + + std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); + std::cout << JEL3(2.5, 0.5) << std::endl; + std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); + std::cout << JEL3(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl; + +Which outputs: + +[pre +9.822663964796047e-001 +9.82266396479604757017335009796882833995903762577173e-01 +] + +Unfortunately there is a problem with this version: if we were to call it like this: + + boost::multiprecision::cpp_dec_float_50 v(2), z(0.5); + JEL3(v + 0.5, z); + +Then we would get a long and inscrutable error message from the compiler: the problem here is that the first +argument to `JEL3` is not a number type, but an expression template. We could obviously add a typecast to +fix the issue: + + JEL(cpp_dec_float_50(v + 0.5), z); + +However, if we want the function JEL to be truely reusable, then a better solution might be preferred. +To achieve this we can borrow some code from Boost.Math which calculates the return type of mixed-argument +functions, here's how the new code looks now: + +*/ + +template +typename boost::math::tools::promote_args::type + JEL4(Float1 v, Float2 z) +{ + using std::pow; + return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v); +} + +/*` + +As you can see the two arguments to the function are now separate template types, and +the return type is computed using the `promote_args` metafunction from Boost.Math. + +Now we can call: + + std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); + std::cout << JEL4(cpp_dec_float_100(2) + 0.5, cpp_dec_float_100(0.5)) << std::endl; + +And get 100 digits of output: + +[pre 9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01] + +As a bonus, we can now call the function not just with expression templates, but with other mixed types as well: +for example `float` and `double` or `int` and `double`, and the correct return type will be computed in each case. + +Note that while in this case we didn't have to change the body of the function, in the general case +any function like this which creates local variables internally would have to use `promote_args` +to work out what type those variables should be, for example: + + template + typename boost::math::tools::promote_args::type + JEL5(Float1 v, Float2 z) + { + using std::pow; + typedef typename boost::math::tools::promote_args::type variable_type; + variable_type t = pow(z / 2, v); + return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / t; + } + +*/ + +//] + +int main() +{ + using namespace boost::multiprecision; + std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); + std::cout << JEL1(2.5, 0.5) << std::endl; + std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); + std::cout << JEL2(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl; + std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); + std::cout << JEL3(2.5, 0.5) << std::endl; + std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); + std::cout << JEL3(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl; + std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); + std::cout << JEL4(cpp_dec_float_100(2) + 0.5, cpp_dec_float_100(0.5)) << std::endl; + return 0; +} + +/* + +Program output: + +9.822663964796047e-001 +9.82266396479604757017335009796882833995903762577173e-01 +9.822663964796047e-001 +9.82266396479604757017335009796882833995903762577173e-01 +9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01 +*/ \ No newline at end of file From 68a4a8743844348ce2a56aa85985a36e0355365e Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 4 Apr 2012 17:04:00 +0000 Subject: [PATCH 159/256] Add string versions of constants for faster (and more accurate) constant initialization. [SVN r77758] --- .../detail/functions/constants.hpp | 70 +++++++++++++++++++ test/Jamfile.v2 | 12 +++- 2 files changed, 80 insertions(+), 2 deletions(-) diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp index 677ed49d..40a13fa6 100644 --- a/include/boost/multiprecision/detail/functions/constants.hpp +++ b/include/boost/multiprecision/detail/functions/constants.hpp @@ -17,6 +17,29 @@ void calc_log2(T& num, unsigned digits) typedef typename mpl::deref::type ui_type; typedef typename mpl::front::type si_type; + // + // String value with 1100 digits: + // + static const char* string_val = "0." + "6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875" + "4200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335" + "0115364497955239120475172681574932065155524734139525882950453007095326366642654104239157814952043740" + "4303855008019441706416715186447128399681717845469570262716310645461502572074024816377733896385506952" + "6066834113727387372292895649354702576265209885969320196505855476470330679365443254763274495125040606" + "9438147104689946506220167720424524529612687946546193165174681392672504103802546259656869144192871608" + "2938031727143677826548775664850856740776484514644399404614226031930967354025744460703080960850474866" + "3852313818167675143866747664789088143714198549423151997354880375165861275352916610007105355824987941" + "4729509293113897155998205654392871700072180857610252368892132449713893203784393530887748259701715591" + "0708823683627589842589185353024363421436706118923678919237231467232172053401649256872747782344535347" + "6481149418642386776774406069562657379600867076257199184734022651462837904883062033061144630073719489"; + // + // Check if we can just construct from string: + // + if(digits * 1000L / 301 < 1100) + { + num = string_val; + return; + } num = static_cast(1180509120u); T denom, next_term, temp; denom = static_cast(1277337600u); @@ -51,6 +74,30 @@ void calc_e(T& result, unsigned digits) { typedef typename mpl::front::type ui_type; typedef typename mpl::front::type real_type; + // + // 1100 digits in string form: + // + const char* string_val = "2." + "7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274" + "2746639193200305992181741359662904357290033429526059563073813232862794349076323382988075319525101901" + "1573834187930702154089149934884167509244761460668082264800168477411853742345442437107539077744992069" + "5517027618386062613313845830007520449338265602976067371132007093287091274437470472306969772093101416" + "9283681902551510865746377211125238978442505695369677078544996996794686445490598793163688923009879312" + "7736178215424999229576351482208269895193668033182528869398496465105820939239829488793320362509443117" + "3012381970684161403970198376793206832823764648042953118023287825098194558153017567173613320698112509" + "9618188159304169035159888851934580727386673858942287922849989208680582574927961048419844436346324496" + "8487560233624827041978623209002160990235304369941849146314093431738143640546253152096183690888707016" + "7683964243781405927145635490613031072085103837505101157477041718986106873969655212671546889570350354" + "0212340784981933432106817012100562788023519303322474501585390473041995777709350366041699732972508869"; + // + // Check if we can just construct from string: + // + if(digits * 1000L / 301 < 1100) + { + result = string_val; + return; + } + T lim; lim = ui_type(1); eval_ldexp(lim, lim, digits); @@ -73,6 +120,29 @@ void calc_pi(T& result, unsigned digits) { typedef typename mpl::front::type ui_type; typedef typename mpl::front::type real_type; + // + // 1100 digits in string form: + // + const char* string_val = "3." + "1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679" + "8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196" + "4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273" + "7245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094" + "3305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912" + "9833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132" + "0005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235" + "4201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859" + "5024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303" + "5982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989" + "3809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913152"; + // + // Check if we can just construct from string: + // + if(digits * 1000L / 301 < 1100) + { + result = string_val; + return; + } T a; a = ui_type(1); diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 1e3087ee..7087da06 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -553,6 +553,7 @@ run test_float_io.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT + release # Otherwise runtime is slow : test_float_io_cpp_dec_float ; run test_float_io.cpp gmp @@ -560,6 +561,7 @@ run test_float_io.cpp gmp : # input files : # requirements TEST_MPF_50 + release # Otherwise runtime is slow [ check-target-builds ../config//has_gmp : : no ] : test_float_io_mpf ; @@ -568,6 +570,7 @@ run test_float_io.cpp mpfr gmp : # input files : # requirements TEST_MPFR_50 + release # Otherwise runtime is slow [ check-target-builds ../config//has_mpfr : : no ] : test_float_io_mpfr ; @@ -576,6 +579,7 @@ run test_int_io.cpp $(TOMMATH) : # input files : # requirements TEST_TOMMATH + release # Otherwise runtime is slow [ check-target-builds ../config//has_tommath : : no ] : test_int_io_tommath ; @@ -584,6 +588,7 @@ run test_int_io.cpp gmp : # input files : # requirements TEST_MPZ + release # Otherwise runtime is slow [ check-target-builds ../config//has_gmp : : no ] : test_int_io_mpz ; @@ -592,6 +597,7 @@ run test_int_io.cpp : # input files : # requirements TEST_CPP_INT + release # Otherwise runtime is slow : test_int_io_cpp_int ; run test_cpp_int.cpp gmp @@ -616,6 +622,7 @@ run test_rational_io.cpp $(TOMMATH) : # requirements TEST_TOMMATH [ check-target-builds ../config//has_tommath : : no ] + release # Otherwise runtime is slow : test_rational_io_tommath ; run test_rational_io.cpp gmp @@ -624,6 +631,7 @@ run test_rational_io.cpp gmp : # requirements TEST_MPQ [ check-target-builds ../config//has_gmp : : no ] + release # Otherwise runtime is slow : test_rational_io_mpz ; run test_generic_conv.cpp @@ -633,7 +641,7 @@ run test_generic_conv.cpp [ check-target-builds ../config//has_gmp : TEST_GMP gmp : ] [ check-target-builds ../config//has_tommath : TEST_TOMMATH $(TOMMATH) : ] [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr : ] - release + release # Otherwise runtime is slow ; @@ -657,7 +665,7 @@ run ../example/tommath_snips.cpp $(TOMMATH) : # input files : # requirements [ check-target-builds ../config//has_tommath : : no ] ; - +run ../example/floating_point_examples.cpp ; if $(enable-specfun) { From d98d1ccf7d3ecd546c08a84d3a9222ba95eda9b0 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 4 Apr 2012 17:10:39 +0000 Subject: [PATCH 160/256] Change max_digits10 to allow some headroom for subsequent calculations. [SVN r77759] --- include/boost/multiprecision/cpp_dec_float.hpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 91a82f24..5b08ee23 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -40,7 +40,7 @@ public: static const boost::int32_t cpp_dec_float_digits = Digits10; static const boost::int32_t cpp_dec_float_digits10_setting = Digits10; - static const boost::int32_t cpp_dec_float_digits10_limit = boost::integer_traits::const_max; + static const boost::int32_t cpp_dec_float_digits10_limit = boost::integer_traits::const_max - 100; static const boost::int32_t cpp_dec_float_digits10 = ((cpp_dec_float_digits10_setting < static_cast(30)) ? static_cast(30) : ((cpp_dec_float_digits10_setting > cpp_dec_float_digits10_limit) ? cpp_dec_float_digits10_limit : cpp_dec_float_digits10_setting)); static const boost::int32_t cpp_dec_float_digits10_extra = static_cast(((static_cast(cpp_dec_float_digits10) * 15LL) + 50LL) / 100LL); static const boost::int32_t cpp_dec_float_max_digits10 = static_cast(cpp_dec_float_digits10 + ((cpp_dec_float_digits10_extra < static_cast(5)) ? static_cast(5) : ((cpp_dec_float_digits10_extra > static_cast(30)) ? static_cast(30) : cpp_dec_float_digits10_extra))); From d873049821ea8ec31ae34a2bc64e38b4a98dfc6c Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 4 Apr 2012 17:14:00 +0000 Subject: [PATCH 161/256] Update notes on comments. [SVN r77760] --- doc/multiprecision.qbk | 1 + 1 file changed, 1 insertion(+) diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 4d7e2a49..5f0f244c 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -2094,6 +2094,7 @@ template argument that defaults to 0 (meaning keep going till no more space/memo * Can we be clearer in the docs that mixed arithmetic doesn't work? * Document round functions behaviour better (they behave as in C99). * Should there be a choice of rounding mode (probably MPFR specific)? +* Document limits on size of cpp_dec_float. [endsect] From 19113e841a5840cfccb7d090c786ea5487de4413 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 5 Apr 2012 07:54:09 +0000 Subject: [PATCH 162/256] Correct logic to detect when string representation has enough bits. [SVN r77774] --- include/boost/multiprecision/detail/functions/constants.hpp | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp index 40a13fa6..685b04e0 100644 --- a/include/boost/multiprecision/detail/functions/constants.hpp +++ b/include/boost/multiprecision/detail/functions/constants.hpp @@ -35,7 +35,7 @@ void calc_log2(T& num, unsigned digits) // // Check if we can just construct from string: // - if(digits * 1000L / 301 < 1100) + if(digits < 3640) { num = string_val; return; @@ -92,7 +92,7 @@ void calc_e(T& result, unsigned digits) // // Check if we can just construct from string: // - if(digits * 1000L / 301 < 1100) + if(digits < 3640) { result = string_val; return; @@ -138,7 +138,7 @@ void calc_pi(T& result, unsigned digits) // // Check if we can just construct from string: // - if(digits * 1000L / 301 < 1100) + if(digits < 3640) { result = string_val; return; From cd398028e8af2c53f283407bf5562bbe0889e849 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 5 Apr 2012 08:22:20 +0000 Subject: [PATCH 163/256] Add static assert to protect multiplication algorithm from excessive limb counts. [SVN r77775] --- include/boost/multiprecision/cpp_dec_float.hpp | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 5b08ee23..cce91bc3 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -2208,6 +2208,14 @@ void cpp_dec_float::from_unsigned_long_long(const unsigned long long u template void cpp_dec_float::mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p) { + // + // There is a limit on how many limbs this algorithm can handle without dropping digits + // due to overflow in the carry, it is: + // + // FLOOR( (2^64 - 1) / (10^8 * 10^8) ) == 1844 + // + BOOST_STATIC_ASSERT_MSG(mp_elem_number < 1800, "Too many limbs in the data type for the multiplication algorithm - unsupported precision in cpp_dec_float."); + boost::uint64_t carry = static_cast(0u); for(boost::int32_t j = static_cast(p - 1u); j >= static_cast(0); j--) From 426430a233922b452e92915e96dbc513d2ed7b62 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 5 Apr 2012 17:19:57 +0000 Subject: [PATCH 164/256] Fix MPFR error rates on Linux x86 64 [SVN r77782] --- test/math/test_bessel_j.cpp | 23 ++++++++++++++++++++++- test/math/test_bessel_y.cpp | 14 ++++++++++++++ test/math/test_beta.cpp | 11 +++++++++-- test/math/test_binomial_coeff.cpp | 2 +- test/math/test_digamma.cpp | 7 +++++++ test/math/test_ellint_1.cpp | 7 +++++++ test/math/test_ellint_2.cpp | 2 +- test/math/test_ellint_3.cpp | 7 +++++++ test/math/test_gamma.cpp | 2 +- test/math/test_ibeta.cpp | 7 +++++++ test/math/test_ibeta_inv_1.cpp | 7 +++++++ test/math/test_ibeta_inv_ab_4.cpp | 2 +- test/math/test_igamma_inv.cpp | 9 ++++++++- test/math/test_tgamma_ratio.cpp | 9 ++++++++- test/math/test_zeta.cpp | 2 +- 15 files changed, 101 insertions(+), 10 deletions(-) diff --git a/test/math/test_bessel_j.cpp b/test/math/test_bessel_j.cpp index c85bd12f..f5b70f1c 100644 --- a/test/math/test_bessel_j.cpp +++ b/test/math/test_bessel_j.cpp @@ -53,6 +53,13 @@ void expected_results() // various compilers and platforms. // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*J0.*Tricky.*", // test data group + ".*", 10000000000L, 5000000000L); // test function add_expected_result( ".*", // compiler ".*", // stdlib @@ -60,6 +67,13 @@ void expected_results() ".*", // test type(s) ".*J0.*Tricky.*", // test data group ".*", 400000000, 400000000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*J1.*Tricky.*", // test data group + ".*", 1000000000L, 500000000L); // test function add_expected_result( ".*", // compiler ".*", // stdlib @@ -74,13 +88,20 @@ void expected_results() ".*", // test type(s) ".*JN.*Integer.*", // test data group ".*", 40000, 10000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*(JN|j).*|.*Tricky.*", // test data group + ".*", 70000, 7000); // test function add_expected_result( ".*", // compiler ".*", // stdlib ".*", // platform ".*", // test type(s) ".*(JN|j).*|.*Tricky.*", // test data group - ".*", 4000, 700); // test function + ".*", 7000, 3000); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp index 2ec7595c..68a94851 100644 --- a/test/math/test_bessel_y.cpp +++ b/test/math/test_bessel_y.cpp @@ -52,6 +52,13 @@ void expected_results() // Define the max and mean errors expected for // various compilers and platforms. // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*(Y[nv]|y).*Random.*", // test data group + ".*", 200000, 10000); // test function add_expected_result( ".*", // compiler ".*", // stdlib @@ -73,6 +80,13 @@ void expected_results() ".*", // test type(s) ".*Y0.*", // test data group ".*", 800, 400); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*Yn.*", // test data group + ".*", 200000, 70000); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_beta.cpp b/test/math/test_beta.cpp index f2983d8e..73e33f04 100644 --- a/test/math/test_beta.cpp +++ b/test/math/test_beta.cpp @@ -66,6 +66,13 @@ void expected_results() ".*gmp.*", // test type(s) "Beta Function: Divergent.*", // test data group "boost::math::beta", 2200, 1000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + "Beta Function: Small.*", // test data group + "boost::math::beta", 200, 200); // test function add_expected_result( ".*", // compiler ".*", // stdlib @@ -79,14 +86,14 @@ void expected_results() ".*", // platform ".*", // test type(s) "Beta Function: Medium.*", // test data group - "boost::math::beta", 160, 35); // test function + "boost::math::beta", 260, 200); // test function add_expected_result( ".*", // compiler ".*", // stdlib ".*", // platform ".*", // test type(s) "Beta Function: Divergent.*", // test data group - "boost::math::beta", 30, 6); // test function + "boost::math::beta", 200, 200); // test function // // Finish off by printing out the compiler/stdlib/platform names, // we do this to make it easier to mark up expected error rates. diff --git a/test/math/test_binomial_coeff.cpp b/test/math/test_binomial_coeff.cpp index 3a31939a..291361e3 100644 --- a/test/math/test_binomial_coeff.cpp +++ b/test/math/test_binomial_coeff.cpp @@ -65,7 +65,7 @@ void expected_results() ".*", // platform ".*mpfr_float_backend<18>.*", // test type(s) ".*", // test data group - ".*", 500, 100); // test function + ".*", 500, 150); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_digamma.cpp b/test/math/test_digamma.cpp index 2f687c64..7767b46c 100644 --- a/test/math/test_digamma.cpp +++ b/test/math/test_digamma.cpp @@ -48,6 +48,13 @@ void expected_results() // Define the max and mean errors expected for // various compilers and platforms. // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*Negative.*", // test data group + ".*", 20000, 2000); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_ellint_1.cpp b/test/math/test_ellint_1.cpp index ebe1bb03..7ba717cf 100644 --- a/test/math/test_ellint_1.cpp +++ b/test/math/test_ellint_1.cpp @@ -48,6 +48,13 @@ void expected_results() // Define the max and mean errors expected for // various compilers and platforms. // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 1000, 200); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_ellint_2.cpp b/test/math/test_ellint_2.cpp index 2642dd03..534cbd84 100644 --- a/test/math/test_ellint_2.cpp +++ b/test/math/test_ellint_2.cpp @@ -54,7 +54,7 @@ void expected_results() ".*", // platform ".*", // test type(s) ".*", // test data group - ".*", 60, 30); // test function + ".*", 300, 200); // test function // // Finish off by printing out the compiler/stdlib/platform names, // we do this to make it easier to mark up expected error rates. diff --git a/test/math/test_ellint_3.cpp b/test/math/test_ellint_3.cpp index 03d9c363..95fe73e1 100644 --- a/test/math/test_ellint_3.cpp +++ b/test/math/test_ellint_3.cpp @@ -55,6 +55,13 @@ void expected_results() ".*gmp_float<18>.*", // test type(s) ".*", // test data group ".*", 3000, 500); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 10000, 3000); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_gamma.cpp b/test/math/test_gamma.cpp index 514a7f1f..42c2cb02 100644 --- a/test/math/test_gamma.cpp +++ b/test/math/test_gamma.cpp @@ -75,7 +75,7 @@ void expected_results() ".*", // platform ".*", // test type(s) "near.*", // test data group - "boost::math::tgamma", 80, 60); // test function + "boost::math::tgamma", 200, 100); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_ibeta.cpp b/test/math/test_ibeta.cpp index 78493503..167b8f31 100644 --- a/test/math/test_ibeta.cpp +++ b/test/math/test_ibeta.cpp @@ -58,6 +58,13 @@ void expected_results() ".*gmp_float<18>.*", // test type(s) "(?i).*small.*", // test data group ".*", 3000, 1000); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + "(?i).*small.*", // test data group + ".*", 400, 200); // test function add_expected_result( "[^|]*", // compiler "[^|]*", // stdlib diff --git a/test/math/test_ibeta_inv_1.cpp b/test/math/test_ibeta_inv_1.cpp index f4e87f83..fd2b3e5f 100644 --- a/test/math/test_ibeta_inv_1.cpp +++ b/test/math/test_ibeta_inv_1.cpp @@ -51,6 +51,13 @@ void expected_results() // Define the max and mean errors expected for // various compilers and platforms. // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 20000000, 2000000); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_ibeta_inv_ab_4.cpp b/test/math/test_ibeta_inv_ab_4.cpp index b4b41a02..eb91e02d 100644 --- a/test/math/test_ibeta_inv_ab_4.cpp +++ b/test/math/test_ibeta_inv_ab_4.cpp @@ -57,7 +57,7 @@ void expected_results() ".*", // platform ".*", // test type(s) ".*", // test data group - ".*", 1000, 100); // test function + ".*", 2000, 200); // test function // // Finish off by printing out the compiler/stdlib/platform names, // we do this to make it easier to mark up expected error rates. diff --git a/test/math/test_igamma_inv.cpp b/test/math/test_igamma_inv.cpp index 39d57132..010c3762 100644 --- a/test/math/test_igamma_inv.cpp +++ b/test/math/test_igamma_inv.cpp @@ -56,13 +56,20 @@ void expected_results() ".*gmp_float<18>.*", // test type(s) ".*small.*", // test data group ".*", 2000000000L, 300000000L); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*small.*", // test data group + ".*", 30000000L, 5000000L); // test function add_expected_result( ".*", // compiler ".*", // stdlib ".*", // platform ".*", // test type(s) ".*small.*", // test data group - ".*", 10000000L, 2000000L); // test function + ".*", 10000000L, 2500000L); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_tgamma_ratio.cpp b/test/math/test_tgamma_ratio.cpp index a37dd322..1084d843 100644 --- a/test/math/test_tgamma_ratio.cpp +++ b/test/math/test_tgamma_ratio.cpp @@ -55,13 +55,20 @@ void expected_results() ".*gmp_float<18>.*", // test type(s) ".*", // test data group ".*", 4000, 2000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 20000, 7000); // test function add_expected_result( ".*", // compiler ".*", // stdlib ".*", // platform ".*", // test type(s) ".*", // test data group - ".*", 1000, 200); // test function + ".*", 2000, 500); // test function // // Finish off by printing out the compiler/stdlib/platform names, // we do this to make it easier to mark up expected error rates. diff --git a/test/math/test_zeta.cpp b/test/math/test_zeta.cpp index fccc7e65..e9db0af5 100644 --- a/test/math/test_zeta.cpp +++ b/test/math/test_zeta.cpp @@ -54,7 +54,7 @@ void expected_results() ".*", // platform ".*", // test type(s) ".*Random values less than 1", // test data group - ".*", 5000, 2000); // test function + ".*", 6000, 3000); // test function add_expected_result( ".*", // compiler ".*", // stdlib From b424123c9d5344c67865f79e9f7dbc573bf88d5f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 5 Apr 2012 17:20:50 +0000 Subject: [PATCH 165/256] Fix GCC compile failure [SVN r77783] --- include/boost/multiprecision/tommath.hpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index a6c9256b..ece8e039 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -451,7 +451,7 @@ inline void eval_qr(const tommath_int& x, const tommath_int& y, inline unsigned eval_lsb(const tommath_int& val) { - return mp_cnt_lsb(const_cast<::mp_int*>(&val.data())); + return mp_cnt_lsb(const_cast< ::mp_int*>(&val.data())); } template From 43a86370a56bd49b858134a246988841b5e74083 Mon Sep 17 00:00:00 2001 From: Christopher Kormanyos Date: Fri, 6 Apr 2012 22:09:09 +0000 Subject: [PATCH 166/256] Added examples of generic numeric programming using built-in and MP types. [SVN r77794] --- .../generic_numerics/generic_numerics.pdf | Bin 0 -> 98380 bytes .../generic_area_of_a_circle.cpp | 45 ++++++++ .../generic_derivative.cpp | 79 +++++++++++++ .../generic_numerics_src/generic_integral.cpp | 104 ++++++++++++++++++ 4 files changed, 228 insertions(+) create mode 100644 example/generic_numerics_examples/generic_numerics/generic_numerics.pdf create mode 100644 example/generic_numerics_examples/generic_numerics_src/generic_area_of_a_circle.cpp create mode 100644 example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp create mode 100644 example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp diff --git a/example/generic_numerics_examples/generic_numerics/generic_numerics.pdf b/example/generic_numerics_examples/generic_numerics/generic_numerics.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cee1fb74db16f8a5ea552fb10c32a77af1425982 GIT binary patch literal 98380 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zqCDFlk?g&A0sZsEn16#JqbV*SsR2My)&3I}Vu!oDvJ(pNGRv<3{S4*rWP$Fy1MWa%?@Sir!!IoSdjdp!{v|W_zd^YwEh8$e#H~sI)*h^_ zv8uC`Jg=%H7EdsMqJV2Fd-52$FL$836Pft*D|>!M_qU^VYT*5E;Qmc7aCd9XKgu;Fo1^n-6{b#Vms`>wArj+OvZ3Pu>d3z@_1#7(ZzFb7?TT|gX*D+va z|Lx14dW`?#OX&VBTnT#vX9pZ~tnGpI9XP|tnHdvzaAL)Qpg+0I!;)7N3;8rKKSjk0(M>Gc~gV0pCBN@&1Gcg7IMha7Y-4^A||2 z9UH5YEzX1-0zyH^0Y%Thzkss@638DD(BC#F1_L;f_yxlMW8>!sJiglofe<%=T{a97 zg8`~yw+#?*1y-ItHaHxJ*=`#WL5$-b8$WU9-fcr6A^XRL@$Y*t3bk)s2m<~G8;qFA zyT*XPps>9*3=)X~_TydcFh~?;Z#xJI1$b_EI|vHFzZWwEfrReEjD#Zg+8}6t^u96B z=>79Rp^53f3m*i7!0hV}14jc3%kFk)3~j|~XsKFk;tbRQNB3b8LYFqr*uL!kDL zi^1%h8x(@vHwIuMo|<-Hh60Y>I}a!zRJ#`+6p94oTlc&dMy!xMHVlNg6YU-Y14HiZ z4~Bxn_Rbdul+fNW;Bd^o`T(?aQG3TlK>7EzL%@Kj@4q4(wnKMb+2KYkehz8u0J_VVH1b{z!@g~+FVz`LMNLdMxt`Hg_j*>z^ zAmZY1xC9C&iUHCRA|` + +using boost::math::constants::pi; + +template +inline T area_of_a_circle(T r) +{ + return pi() * (r * r); +} + +#include +#include +#include + +using boost::multiprecision::cpp_dec_float_50; + +int main(int, char**) +{ + const float r_f(float(123) / 100); + const float a_f = area_of_a_circle(r_f); + + const double r_d(double(123) / 100); + const double a_d = area_of_a_circle(r_d); + + const cpp_dec_float_50 r_mp(cpp_dec_float_50(123) / 100); + const cpp_dec_float_50 a_mp = area_of_a_circle(r_mp); + + // 4.75292 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_f + << std::endl; + + // 4.752915525616 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_d + << std::endl; + + // 4.7529155256159981904701331745635599135018975843146 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_mp + << std::endl; +} diff --git a/example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp b/example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp new file mode 100644 index 00000000..ccf0ad97 --- /dev/null +++ b/example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp @@ -0,0 +1,79 @@ +template +value_type derivative(const value_type x, + const value_type dx, + function_type func) +{ + // Compute d/dx[func(*first)] using a three-point + // central difference rule of O(dx^6). + + const value_type dx1 = dx; + const value_type dx2 = dx1 * 2; + const value_type dx3 = dx1 * 3; + + const value_type m1 = ( func(x + dx1) + - func(x - dx1)) / 2; + const value_type m2 = ( func(x + dx2) + - func(x - dx2)) / 4; + const value_type m3 = ( func(x + dx3) + - func(x - dx3)) / 6; + + const value_type fifteen_m1 = 15 * m1; + const value_type six_m2 = 6 * m2; + const value_type ten_dx1 = 10 * dx1; + + return ((fifteen_m1 - six_m2) + m3) / ten_dx1; +} + +#include +#include +#include +#include + +using boost::math::constants::pi; +using boost::multiprecision::cpp_dec_float_50; + +int main(int, char**) +{ + const float d_f = + derivative(float(pi() / 3), + 0.01F, + [](const float x) -> float + { + return ::sin(x); + }); + + const double d_d = + derivative(double(pi() / 3), + 0.001, + [](const double x) -> double + { + return ::sin(x); + }); + + const cpp_dec_float_50 d_mp = + derivative(cpp_dec_float_50(pi() / 3), + cpp_dec_float_50(1.0E-9), + [](const cpp_dec_float_50 x) -> cpp_dec_float_50 + { + return boost::multiprecision::sin(x); + }); + + // 0.500003 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_f + << std::endl; + + // 0.499999999999888 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_d + << std::endl; + + // 0.50000000000000000000000000000000000000000003925935 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_mp + << std::endl; +} diff --git a/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp b/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp new file mode 100644 index 00000000..6e7495b1 --- /dev/null +++ b/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp @@ -0,0 +1,104 @@ +template +inline value_type integral(const value_type a, + const value_type b, + const value_type tol, + function_type func) +{ + unsigned n = 1U; + + value_type h = (b - a); + value_type I = (func(a) + func(b)) * (h / 2); + + for(unsigned k = 0U; k < 8U; k++) + { + h /= 2; + + value_type sum(0); + for(unsigned j = 1U; j <= n; j++) + { + sum += func(a + (value_type((j * 2) - 1) * h)); + } + + const value_type I0 = I; + I = (I / 2) + (h * sum); + + const value_type ratio = I0 / I; + const value_type delta = ratio - 1; + const value_type delta_abs = ((delta < 0) ? -delta : delta); + + if((k > 1U) && (delta_abs < tol)) + { + break; + } + + n *= 2U; + } + + return I; +} + +#include +#include +#include +#include + +template +class cyl_bessel_j_integral_rep +{ +public: + cyl_bessel_j_integral_rep(const unsigned N, + const value_type& X) : n(N), x(X) { } + + value_type operator()(const value_type& t) const + { + // pi * Jn(x) = Int_0^pi [cos(x * sin(t) - n*t) dt] + return cos(x * sin(t) - (n * t)); + } + +private: + const unsigned n; + const value_type x; +}; + +using boost::math::constants::pi; +typedef boost::multiprecision::cpp_dec_float_50 mp_type; + +int main(int, char**) +{ + const float j2_f = + integral(0.0F, + pi(), + 0.01F, + cyl_bessel_j_integral_rep(2U, 1.23F)) / pi(); + + const double j2_d = + integral(0.0, + pi(), + 0.0001, + cyl_bessel_j_integral_rep(2U, 1.23)) / pi(); + + const mp_type j2_mp = + integral(mp_type(0), + pi(), + mp_type(1.0E-20), + cyl_bessel_j_integral_rep(2U, mp_type(123) / 100)) / pi(); + + // 0.166369 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_f + << std::endl; + + // 0.166369383786814 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_d + << std::endl; + + // 0.16636938378681407351267852431513159437103348245333 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_mp + << std::endl; +} From 2b1f19fa2bda6edd6d14a7e9c2c7b50969f73a1c Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 9 Apr 2012 16:58:30 +0000 Subject: [PATCH 167/256] Integrate Chris's FP examples into the docs. [SVN r77851] --- .../boost_multiprecision/indexes/s01.html | 8 +- .../boost_multiprecision/indexes/s02.html | 12 +- .../boost_multiprecision/indexes/s03.html | 16 +- .../boost_multiprecision/indexes/s04.html | 51 ++- doc/html/boost_multiprecision/map/todo.html | 3 + doc/html/boost_multiprecision/tut.html | 13 +- doc/html/boost_multiprecision/tut/floats.html | 13 +- .../tut/floats/cpp_dec_float.html | 6 +- .../tut/floats/fp_eg.html | 44 +++ .../tut/floats/fp_eg/GI.html | 161 ++++++++ .../tut/floats/fp_eg/aos.html | 118 ++++++ .../tut/floats/fp_eg/jel.html | 222 +++++++++++ .../tut/floats/fp_eg/nd.html | 202 ++++++++++ .../boost_multiprecision/tut/rational.html | 6 +- doc/html/index.html | 15 +- doc/html4_symbols.qbk | 215 ++++++++++ doc/multiprecision.qbk | 44 ++- example/floating_point_examples.cpp | 373 +++++++++++++++++- .../generic_numerics_src/generic_integral.cpp | 65 +-- 19 files changed, 1493 insertions(+), 94 deletions(-) create mode 100644 doc/html/boost_multiprecision/tut/floats/fp_eg.html create mode 100644 doc/html/boost_multiprecision/tut/floats/fp_eg/GI.html create mode 100644 doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html create mode 100644 doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html create mode 100644 doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html create mode 100644 doc/html4_symbols.qbk diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 5e18e6c7..a54c0f55 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,10 +13,10 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    -

    A B C D E F I L M P R S T Z

    +Function Index
    +

    A B C D E F I L M P R S T Z

    A @@ -207,7 +207,7 @@
    -Z +Z

    • zero

      diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index 9207a2a7..a25a7a5b 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,13 +13,13 @@
      PrevUpHomeNext
      -
      +

      -Class Index

      -

      M T

      +Class Index
    +

    M T

    -M +M

    • mp_number

      @@ -29,11 +29,11 @@
    -T +T
    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 9aecc85a..9806196f 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,13 +13,13 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    -

    C I L M T

    +Typedef Index
    +

    C I L M T

    -C +C
    • @@ -47,21 +47,21 @@
    -I +I
    -L +L
    -M +M
    • @@ -161,7 +161,7 @@
    -T +T

    • tommath_rational

      • diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index a079ef1a..f6c4c3ed 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,20 +12,20 @@
      PrevUpHome
      -
      +

      -Index

      -

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      +Index
    +

    A B C D E F G I L M O P R S T Z

    -A +A
    -B +B
    • @@ -50,7 +50,7 @@
    -C +C
    • @@ -106,7 +106,7 @@
    -D +D
    -E +E
    -F +F
    -G +G
    • @@ -175,7 +179,7 @@
    -I +I
    • @@ -223,7 +227,7 @@
    -L +L
    • @@ -252,7 +256,7 @@
    -M +M
    • @@ -410,14 +414,14 @@
    -O +O
    -P +P
    • @@ -437,14 +441,14 @@
    -R +R
    -S +S
    • @@ -461,7 +465,7 @@
    -T +T
    -W -
    -
    • -

      Worked Example: defining a mathematical function.

      -
      -
    -
    -Z +Z

    • zero

      diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index 315bd765..00d93f94 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -83,6 +83,9 @@
    • Should there be a choice of rounding mode (probably MPFR specific)?
      • +
    • + Document limits on size of cpp_dec_float. +
    diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html index 621eb176..38896477 100644 --- a/doc/html/boost_multiprecision/tut.html +++ b/doc/html/boost_multiprecision/tut.html @@ -29,8 +29,17 @@
    gmp_float
    mpfr_float
    cpp_dec_float
    -
    Worked Example: - defining a mathematical function.
    +
    Examples
    +
    +
    Area of + Circle
    +
    Defining + a Lambda Function.
    +
    Calculating + a Derivative
    +
    Calculating + an Integral
    +
    Rational Number Types
    diff --git a/doc/html/boost_multiprecision/tut/floats.html b/doc/html/boost_multiprecision/tut/floats.html index f9b841f4..e441517f 100644 --- a/doc/html/boost_multiprecision/tut/floats.html +++ b/doc/html/boost_multiprecision/tut/floats.html @@ -21,8 +21,17 @@
    gmp_float
    mpfr_float
    cpp_dec_float
    -
    Worked Example: - defining a mathematical function.
    +
    Examples
    +
    +
    Area of + Circle
    +
    Defining + a Lambda Function.
    +
    Calculating + a Derivative
    +
    Calculating + an Integral
    +

    The following back-ends provide floating point arithmetic: diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html index cc7b16ca..aea653f8 100644 --- a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html +++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html @@ -7,11 +7,11 @@ - +

    -PrevUpHomeNext +PrevUpHomeNext

    @@ -111,7 +111,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg.html new file mode 100644 index 00000000..c5e07650 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg.html @@ -0,0 +1,44 @@ + + + +Examples + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    Area of + Circle
    +
    Defining + a Lambda Function.
    +
    Calculating + a Derivative
    +
    Calculating + an Integral
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/GI.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/GI.html new file mode 100644 index 00000000..7b30997c --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/GI.html @@ -0,0 +1,161 @@ + + + +Calculating an Integral + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Similar to the generic derivative example, we can calculate integrals + in a similar manner: +

    +

    +

    +
    template<typename value_type, typename function_type>
+inline value_type integral(const value_type a,
+                           const value_type b,
+                           const value_type tol,
+                           function_type func)
+{
+   unsigned n = 1U;
+
+   value_type h = (b - a);
+   value_type I = (func(a) + func(b)) * (h / 2);
+
+   for(unsigned k = 0U; k < 8U; k++)
+   {
+      h /= 2;
+
+      value_type sum(0);
+      for(unsigned j = 1U; j <= n; j++)
+      {
+         sum += func(a + (value_type((j * 2) - 1) * h));
+      }
+
+      const value_type I0 = I;
+      I = (I / 2) + (h * sum);
+
+      const value_type ratio     = I0 / I;
+      const value_type delta     = ratio - 1;
+      const value_type delta_abs = ((delta < 0) ? -delta : delta);
+
+      if((k > 1U) && (delta_abs < tol))
+      {
+         break;
+      }
+
+      n *= 2U;
+   }
+
+   return I;
+}
+
    +

    +

    +

    + The following sample program shows how the function can be called, we + begin by defining a function object, which when integrated should yield + the Bessel J function: +

    +

    +

    +
    template<typename value_type>
+class cyl_bessel_j_integral_rep
+{
+public:
+   cyl_bessel_j_integral_rep(const unsigned N,
+      const value_type& X) : n(N), x(X) { }
+
+   value_type operator()(const value_type& t) const
+   {
+      // pi * Jn(x) = Int_0^pi [cos(x * sin(t) - n*t) dt]
+      return cos(x * sin(t) - (n * t));
+   }
+
+private:
+   const unsigned n;
+   const value_type x;
+};
+
    +

    +

    +

    +

    +
       /* The function can now be called as follows: */
+int main(int, char**)
+{
+   using boost::math::constants::pi;
+   typedef boost::multiprecision::cpp_dec_float_50 mp_type;
+
+   const float j2_f =
+      integral(0.0F,
+      pi<float>(),
+      0.01F,
+      cyl_bessel_j_integral_rep<float>(2U, 1.23F)) / pi<float>();
+
+   const double j2_d =
+      integral(0.0,
+      pi<double>(),
+      0.0001,
+      cyl_bessel_j_integral_rep<double>(2U, 1.23)) / pi<double>();
+
+   const mp_type j2_mp =
+      integral(mp_type(0),
+      pi<mp_type>(),
+      mp_type(1.0E-20),
+      cyl_bessel_j_integral_rep<mp_type>(2U, mp_type(123) / 100)) / pi<mp_type>();
+
+   // 0.166369
+   std::cout
+      << std::setprecision(std::numeric_limits<float>::digits10)
+      << j2_f
+      << std::endl;
+
+   // 0.166369383786814
+   std::cout
+      << std::setprecision(std::numeric_limits<double>::digits10)
+      << j2_d
+      << std::endl;
+
+   // 0.16636938378681407351267852431513159437103348245333
+   std::cout
+      << std::setprecision(std::numeric_limits<mp_type>::digits10)
+      << j2_mp
+      << std::endl;
+
+   //
+   // Print true value for comparison:
+   // 0.166369383786814073512678524315131594371033482453329
+   std::cout << boost::math::cyl_bessel_j(2, mp_type(123) / 100) << std::endl;
+}
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html new file mode 100644 index 00000000..46500c20 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html @@ -0,0 +1,118 @@ + + + +Area of Circle + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Generic numeric programming employs templates to use the same code for + different floating-point types and functions. Consider the area of a + circle a of radius r, given by +

    +

    + a = π * r2 +

    +

    + The area of a circle can be computed in generic programming using Boost.Math + for the constant π as shown below: +

    +

    +

    +
    #include <boost/math/constants/constants.hpp>
+
+template<typename T>
+inline T area_of_a_circle(T r)
+{
+   using boost::math::constants::pi;
+   return pi<T>() * r * r;
+}
+
    +

    +

    +

    + It is possible to use area_of_a_circle() with built-in floating-point types + as well as floating-point types from Boost.Multiprecision. In particular, + consider a system with 4-byte single-precision float, 8-byte double-precision + double and also the cpp_dec_float_50 + data type from Boost.Multiprecision with 50 decimal digits of precision. +

    +

    + We can compute and print the approximate area of a circle with radius + 123/100 for float, double and cpp_dec_float_50 + with the program below. +

    +

    +

    +
    #include <iostream>
+#include <iomanip>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+
+using boost::multiprecision::cpp_dec_float_50;
+
+int main(int, char**)
+{
+   const float r_f(float(123) / 100);
+   const float a_f = area_of_a_circle(r_f);
+
+   const double r_d(double(123) / 100);
+   const double a_d = area_of_a_circle(r_d);
+
+   const cpp_dec_float_50 r_mp(cpp_dec_float_50(123) / 100);
+   const cpp_dec_float_50 a_mp = area_of_a_circle(r_mp);
+
+   // 4.75292
+   std::cout
+      << std::setprecision(std::numeric_limits<float>::digits10)
+      << a_f
+      << std::endl;
+
+   // 4.752915525616
+   std::cout
+      << std::setprecision(std::numeric_limits<double>::digits10)
+      << a_d
+      << std::endl;
+
+   // 4.7529155256159981904701331745635599135018975843146
+   std::cout
+      << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10)
+      << a_mp
+      << std::endl;
+}
+
    +

    +

    +

    + In the next example we'll look at calling both standard library and Boost.Math + functions from within generic code. We'll also show how to cope with + template arguments which are expression-templates rather than number + types. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html new file mode 100644 index 00000000..981d684d --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html @@ -0,0 +1,222 @@ + + + +Defining a Lambda Function. + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + In this example we'll show several implementations of the Jahnke + and Emden Lambda function, each implementation a little more + sophisticated than the last. +

    +

    + The Jahnke-Emden Lambda function is defined by the equation: +

    +

    + JahnkeEmden(v, z) = Γ(v+1) * Jv(z) / (z / 2)v +

    +

    + If we were to implement this at double precision using Boost.Math's facilities + for the Gamma and Bessel function calls it would look like this: +

    +

    +

    +
    double JEL1(double v, double z)
+{
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / std::pow(z / 2, v);
+}
+
    +

    +

    +

    + Calling this function as: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10);
+std::cout << JEL1(2.5, 0.5) << std::endl;
+
    +

    + Yields the output: +

    +
    9.822663964796047e-001
    +

    + Now lets implement the function again, but this time using the multiprecision + type cpp_dec_float_50 + as the argument type: +

    +

    +

    +
    boost::multiprecision::cpp_dec_float_50
+   JEL2(boost::multiprecision::cpp_dec_float_50 v, boost::multiprecision::cpp_dec_float_50 z)
+{
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / boost::multiprecision::pow(z / 2, v);
+}
+
    +

    +

    +

    + The implementation is almost the same as before, but with one key difference + - we can no longer call std::pow, + instead we must call the version inside the boost::multiprecision + namespace. In point of fact, we could have omitted the namespace prefix + on the call to pow since + the right overload would have been found via argument + dependent lookup in any case. +

    +

    + Note also that the first argument to pow + along with the argument to tgamma + in the above code are actually expression templates. The pow and tgamma + functions will handle these arguments just fine. +

    +

    + Here's an example of how the function may be called: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10);
+std::cout << JEL2(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl;
+
    +

    + Which outputs: +

    +
    9.82266396479604757017335009796882833995903762577173e-01
    +

    + Now that we've seen some non-template examples, lets repeat the code + again, but this time as a template that can be called either with a builtin + type (float, double etc), or with a multiprecision + type: +

    +

    +

    +
    template <class Float>
+Float JEL3(Float v, Float z)
+{
+   using std::pow;
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
+}
+
    +

    +

    +

    + Once again the code is almost the same as before, but the call to pow has changed yet again. We need + the call to resolve to either std::pow + (when the argument is a builtin type), or to boost::multiprecision::pow + (when the argument is a multiprecision type). We do that by making the + call unqualified so that versions of pow + defined in the same namespace as type Float + are found via argument dependent lookup, while the using + std::pow directive makes the standard library + versions visible for builtin floating point types. +

    +

    + Let's call the function with both double + and multiprecision arguments: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10);
+std::cout << JEL3(2.5, 0.5) << std::endl;
+std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10);
+std::cout << JEL3(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl;
+
    +

    + Which outputs: +

    +
    9.822663964796047e-001
+9.82266396479604757017335009796882833995903762577173e-01
+
    +

    + Unfortunately there is a problem with this version: if we were to call + it like this: +

    +
    boost::multiprecision::cpp_dec_float_50 v(2), z(0.5);
+JEL3(v + 0.5, z);
+
    +

    + Then we would get a long and inscrutable error message from the compiler: + the problem here is that the first argument to JEL3 + is not a number type, but an expression template. We could obviously + add a typecast to fix the issue: +

    +
    JEL(cpp_dec_float_50(v + 0.5), z);
+
    +

    + However, if we want the function JEL to be truely reusable, then a better + solution might be preferred. To achieve this we can borrow some code + from Boost.Math which calculates the return type of mixed-argument functions, + here's how the new code looks now: +

    +

    +

    +
    template <class Float1, class Float2>
+typename boost::math::tools::promote_args<Float1, Float2>::type
+   JEL4(Float1 v, Float2 z)
+{
+   using std::pow;
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
+}
+
    +

    +

    +

    + As you can see the two arguments to the function are now separate template + types, and the return type is computed using the promote_args + metafunction from Boost.Math. +

    +

    + Now we can call: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_100>::digits10);
+std::cout << JEL4(cpp_dec_float_100(2) + 0.5, cpp_dec_float_100(0.5)) << std::endl;
+
    +

    + And get 100 digits of output: +

    +
    9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01
    +

    + As a bonus, we can now call the function not just with expression templates, + but with other mixed types as well: for example float + and double or int and double, + and the correct return type will be computed in each case. +

    +

    + Note that while in this case we didn't have to change the body of the + function, in the general case any function like this which creates local + variables internally would have to use promote_args + to work out what type those variables should be, for example: +

    +
    template <class Float1, class Float2>
+typename boost::math::tools::promote_args<Float1, Float2>::type
+   JEL5(Float1 v, Float2 z)
+{
+   using std::pow;
+   typedef typename boost::math::tools::promote_args<Float1, Float2>::type variable_type;
+   variable_type t = pow(z / 2, v);
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / t;
+}
+
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html new file mode 100644 index 00000000..460c86c4 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html @@ -0,0 +1,202 @@ + + + +Calculating a Derivative + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + In this example we'll add even more power to generic numeric programming + using not only different floating-point types but also function objects + as template parameters. Consider some well-known central difference rules + for numerically computing the first derivative of a function f′(x) + with x ∈ ℜ: +

    +

    + +

    +

    + Where the difference terms mn are given by: +

    +

    + +

    +

    + and dx is the step-size of the derivative. +

    +

    + The third formula in Equation 1 is a three-point central difference rule. + It calculates the first derivative of f′(x) to O(dx6), + where dx is the given step-size. For example, if + the step-size is 0.01 this derivative calculation has about 6 decimal + digits of precision - just about right for the 7 decimal digits of single-precision + float. Let's make a generic template subroutine using this three-point + central difference rule. In particular: +

    +

    +

    +
    template<typename value_type, typename function_type>
+   value_type derivative(const value_type x, const value_type dx, function_type func)
+{
+   // Compute d/dx[func(*first)] using a three-point
+   // central difference rule of O(dx^6).
+
+   const value_type dx1 = dx;
+   const value_type dx2 = dx1 * 2;
+   const value_type dx3 = dx1 * 3;
+
+   const value_type m1 = (func(x + dx1) - func(x - dx1)) / 2;
+   const value_type m2 = (func(x + dx2) - func(x - dx2)) / 4;
+   const value_type m3 = (func(x + dx3) - func(x - dx3)) / 6;
+
+   const value_type fifteen_m1 = 15 * m1;
+   const value_type six_m2     =  6 * m2;
+   const value_type ten_dx1    = 10 * dx1;
+
+   return ((fifteen_m1 - six_m2) + m3) / ten_dx1;
+}
+
    +

    +

    +

    + The derivative() + template function can be used to compute the first derivative of any + function to O(dx6). For example, consider the first + derivative of sin(x) evaluated at x = + π/3. In other words, +

    +

    + +

    +

    + The code below computes the derivative in Equation 3 for float, double + and boost's multiple-precision type cpp_dec_float_50. +

    +

    +

    +
    #include <iostream>
+#include <iomanip>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+#include <boost/math/constants/constants.hpp>
+
+
+int main(int, char**)
+{
+   using boost::math::constants::pi;
+   using boost::multiprecision::cpp_dec_float_50;
+   //
+   // We'll pass a function pointer for the function object passed to derivative,
+   // the typecast is needed to select the correct overload of std::sin:
+   //
+   const float d_f = derivative(
+      pi<float>() / 3,
+      0.01F,
+      static_cast<float(*)(float)>(std::sin)
+   );
+
+   const double d_d = derivative(
+      pi<double>() / 3,
+      0.001,
+      static_cast<double(*)(double)>(std::sin)
+      );
+   //
+   // In the cpp_dec_float_50 case, the sin function is multiply overloaded
+   // to handle expression templates etc.  As a result it's hard to take it's
+   // address without knowing about its implementation details.  We'll use a 
+   // C++11 lambda expression to capture the call.
+   // We also need a typecast on the first argument so we don't accidently pass
+   // an expression template to a template function:
+   //
+   const cpp_dec_float_50 d_mp = derivative(
+      cpp_dec_float_50(pi<cpp_dec_float_50>() / 3),
+      cpp_dec_float_50(1.0E-9),
+      [](const cpp_dec_float_50& x) -> cpp_dec_float_50
+      {
+         return sin(x);
+      }
+      );
+
+   // 5.000029e-001
+   std::cout
+      << std::setprecision(std::numeric_limits<float>::digits10)
+      << d_f
+      << std::endl;
+
+   // 4.999999999998876e-001
+   std::cout
+      << std::setprecision(std::numeric_limits<double>::digits10)
+      << d_d
+      << std::endl;
+
+   // 4.99999999999999999999999999999999999999999999999999e-01
+   std::cout
+      << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10)
+      << d_mp
+      << std::endl;
+}
+
    +

    +

    +

    + The expected value of the derivative is 0.5. This central difference + rule in this example is ill-conditioned, meaning it suffers from slight + loss of precision. With that in mind, the results agree with the expected + value of 0.5. +

    +

    + We can take this a step further and use our derivative function to compute + a partial derivative. For example if we take the incomplete gamma function + P(a, z), and take the derivative with respect to + z at (2,2) then we can calculate + the result as shown below, for good measure we'll compare with the "correct" + result obtained from a call to gamma_p_derivative, + the results agree to approximately 44 digits: +

    +

    +

    +
    cpp_dec_float_50 gd = derivative(
+   cpp_dec_float_50(2),
+   cpp_dec_float_50(1.0E-9),
+   [](const cpp_dec_float_50& x) ->cpp_dec_float_50
+   {
+      return boost::math::gamma_p(2, x);
+   }
+);
+// 2.70670566473225383787998989944968806815263091819151e-01
+std::cout
+   << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10)
+   << gd
+   << std::endl;
+// 2.70670566473225383787998989944968806815253190143120e-01
+std::cout << boost::math::gamma_p_derivative(cpp_dec_float_50(2), cpp_dec_float_50(2)) << std::endl;
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 318cba56..614d612e 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -246,7 +246,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/index.html b/doc/html/index.html index 013c47c5..4ed88ab7 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -44,8 +44,17 @@
    gmp_float
    mpfr_float
    cpp_dec_float
    -
    Worked Example: - defining a mathematical function.
    +
    Examples
    +
    +
    Area of + Circle
    +
    Defining + a Lambda Function.
    +
    Calculating + a Derivative
    +
    Calculating + an Integral
    +
    Rational Number Types
    @@ -101,7 +110,7 @@ - +

    Last revised: April 03, 2012 at 18:14:12 GMT

    Last revised: April 09, 2012 at 16:55:19 GMT
    diff --git a/doc/html4_symbols.qbk b/doc/html4_symbols.qbk new file mode 100644 index 00000000..55bf6588 --- /dev/null +++ b/doc/html4_symbols.qbk @@ -0,0 +1,215 @@ +[/ Symbols and Greek letters (about 120) from HTML4.] +[/ File HTML4_symbols.qbk] +[/ See http://www.htmlhelp.com/reference/html40/entities/symbols.html] +[/ See also http://en.wikipedia.org/wiki/List_of_XML_and_HTML_character_entity_references] +[/ http://www.alanwood.net/demos/ent4_frame.html] +[/ http://www.unicode.org/charts/PDF/U2200.pdf and others] +[/ All (except 2 angle brackets) show OK on Firefox 2.0] + +[/ See also Latin-1 aka Western (ISO-8859-1) in latin1_symbols.qbk] +[/ http://www.htmlhelp.com/reference/html40/entities/latin1.html] +[/Unicode Latin extended http://www.unicode.org/charts/U0080.pdf] + +[/ Also some miscellaneous math charaters added to this list - see the end.] +[/ For others see also math_symbols.qbk] + +[/ To use, enclose the template name in square brackets.] + +[template fnof[]'''ƒ'''] [/ ƒ Latin small f with hook = function = florin] +[/ Capital Greek start with capital letter, lower case all small.] +[template Alpha[]'''Α'''] [/ ? Greek capital letter alpha] +[template Beta[]'''Β'''] [/ ? Greek capital letter beta] +[template Gamma[]'''Γ'''] [/ G Greek capital letter gamma] +[template Delta[]'''Δ'''] [/ ? Greek capital letter delta] +[template Epsilon[]'''Ε'''] [/ ? Greek capital letter epsilon] +[template Zeta[]'''Ζ'''] [/ ? Greek capital letter zeta] +[template Eta[]'''Η'''] [/ ? Greek capital letter eta] +[template Theta[]'''Θ'''] [/ T Greek capital letter theta] +[template Iota[]'''Ι'''] [/ ? Greek capital letter iota] +[template Kappa[]'''Κ'''] [/ ? Greek capital letter kappa] +[template Lambda[]'''Λ'''] [/ ? Greek capital letter lambda] +[template Mu[]'''Μ'''] [/ ? Greek capital letter mu] +[template Nu[]'''Ν'''] [/ ? Greek capital letter nu] +[template Xi[]'''Ξ'''] [/ ? Greek capital letter xi] +[template Omicron[]'''Ο'''] [/ ? Greek capital letter omicron] +[template Pi[]'''Π'''] [/ ? Greek capital letter pi] +[template Rho[]'''Ρ'''] [/ ? Greek capital letter rho] +[template Sigma[]'''Σ'''] [/ S Greek capital letter sigma] +[template Tau[]'''Τ'''] [/ ? Greek capital letter tau] +[template Upsilon[]'''Υ'''] [/ ? Greek capital letter upsilon] +[template Phi[]'''Φ'''] [/ F Greek capital letter phi] +[template Chi[]'''Χ'''] [/ ? Greek capital letter chi] +[template Psi[]'''Ψ'''] [/ ? Greek capital letter psi] +[template Omega[]'''Ω'''] [/ O Greek capital letter omega] +[template alpha[]'''α'''] [/ a Greek small letter alpha] +[template beta[]'''β'''] [/ ß Greek small letter beta] +[template gamma[]'''γ'''] [/ ? Greek small letter gamma] +[template delta[]'''δ'''] [/ d Greek small letter delta] +[template epsilon[]'''ε'''] [/ e Greek small letter epsilon] +[template zeta[]'''ζ'''] [/ ? Greek small letter zeta] +[template eta[]'''η'''] [/ ? Greek small letter eta] +[template theta[]'''θ'''] [/ ? Greek small letter theta] +[template iota[]'''ι'''] [/ ? Greek small letter iota] +[template kappa[]'''κ'''] [/ ? Greek small letter kappa] +[template lambda[]'''λ'''] [/ ? Greek small letter lambda] +[template mu[]'''μ'''] [/ µ Greek small letter mu] +[template nu[]'''ν'''] [/ ? Greek small letter nu] +[template xi[]'''ξ'''] [/ ? Greek small letter xi] +[template omicron[]'''ο'''] [/ ? Greek small letter omicron] +[template pi[]'''π'''] [/ p Greek small letter pi] +[template rho[]'''ρ'''] [/ ? Greek small letter rho] +[template sigmaf[]'''ς'''] [/ ? Greek small letter final sigma] +[template sigma[]'''σ'''] [/ s Greek small letter sigma] +[template tau[]'''τ'''] [/ t Greek small letter tau] +[template upsilon[]'''υ'''] [/ ? Greek small letter upsilon] +[template phi[]'''φ'''] [/ f Greek small letter phi] +[template chi[]'''χ'''] [/ ? Greek small letter chi] +[template psi[]'''ψ'''] [/ ? Greek small letter psi] +[template omega[]'''ω'''] [/ ? Greek small letter omega] +[template thetasym[]'''ϑ'''] [/ ? Greek small letter theta symbol] +[template upsih[]'''ϒ'''] [/ ? Greek upsilon with hook symbol] +[template piv[]'''ϖ'''] [/ ? Greek pi symbol] + +[template bull[]'''•'''] [/ • bullet = black small circle] +[template hellip[]'''…'''] [/ … horizontal ellipsis = three dot leader] +[template prime[]'''′'''] [/ ' prime = minutes = feet] +[template Prime[]'''″'''] [/ ? double prime = seconds = inches] +[template oline[]'''‾'''] [/ ? overline = spacing overscore] +[template frasl[]'''⁄'''] [/ / fraction slash] +[template weierp[]'''℘'''] [/ P script capital P = power set = Weierstrass p] +[template image[]'''ℑ'''] [/ I blackletter capital I = imaginary part] +[template real[]'''ℜ'''] [/ R blackletter capital R = real part symbol] +[template trade[]'''™'''] [/ ™ trade mark sign] +[template alefsym[]'''ℵ'''] [/ ? alef symbol = first transfinite cardinal] +[template larr[]'''←'''] [/ ? leftwards arrow] +[template uarr[]'''↑'''] [/ ? upwards arrow] +[template rarr[]'''→'''] [/ ? rightwards arrow] +[template darr[]'''↓'''] [/ ? downwards arrow] +[template harr[]'''↔'''] [/ ? left right arrow] +[template crarr[]'''↵'''] [/ ? downwards arrow with corner leftwards = CR] +[template lArr[]'''⇐'''] [/ ? leftwards double arrow] +[template uArr[]'''⇑'''] [/ ? upwards double arrow] +[template rArr[]'''⇒'''] [/ ? rightwards double arrow] +[template dArr[]'''⇓'''] [/ ? downwards double arrow] +[template hArr[]'''⇔'''] [/ ? left right double arrow] +[template forall[]'''∀'''] [/ ? for all] +[template part[]'''∂'''] [/ ? partial differential] +[template exist[]'''∃'''] [/ ? there exists] +[template empty[]'''∅'''] [/ Ø empty set = null set = diameter] +[template nabla[]'''∇'''] [/ ? nabla = backward difference] +[template isin[]'''∈'''] [/ ? element of] +[template notin[]'''∉'''] [/ ? not an element of] +[template ni[]'''∋'''] [/ ? contains as member] +[template prod[]'''∏'''] [/ ? n-ary product = product sign] +[template sum[]'''∑'''] [/ ? n-ary sumation] +[template minus[]'''−'''] [/ - minus sign] +[template lowast[]'''∗'''] [/ * asterisk operator] +[template radic[]'''√'''] [/ v square root = radical sign] +[template prop[]'''∝'''] [/ ? proportional to] +[template infin[]'''∞'''] [/ 8 infinity] +[template ang[]'''∠'''] [/ ? angle] +[template and[]'''∧'''] [/ ? logical and = wedge] +[template or[]'''∨'''] [/ ? logical or = vee] +[template cap[]'''∩'''] [/ n intersection = cap] +[template cup[]'''∪'''] [/ ? union = cup] +[template int[]'''∫'''] [/ ? integral] +[template there4[]'''∴'''] [/ ? therefore] +[template sim[]'''∼'''] [/ ~ tilde operator = varies with = similar to] +[template cong[]'''≅'''] [/ ? approximately equal to] +[template asymp[]'''≈'''] [/ ˜ almost equal to = asymptotic to] +[template ne[]'''≠'''] [/ ? not equal to] +[template equiv[]'''≡'''] [/ = identical to] +[template le[]'''≤'''] [/ = less-than or equal to] +[template ge[]'''≥'''] [/ = greater-than or equal to] +[template subset[]'''⊂'''] [/ ? subset of] +[template superset[]'''⊃'''] [/ ? superset of] +[template nsubset[]'''⊄'''] [/ ? not a subset of] +[template sube[]'''⊆'''] [/ ? subset of or equal to] +[template supe[]'''⊇'''] [/ ? superset of or equal to] +[template oplus[]'''⊕'''] [/ ? circled plus = direct sum] +[template otimes[]'''⊗'''] [/ ? circled times = vector product] +[template perp[]'''⊥'''] [/ ? up tack = orthogonal to = perpendicular] +[template sdot[]'''⋅'''] [/ · dot operator] +[template lceil[]'''⌈'''] [/ ? left ceiling = APL upstile] +[template rceil[]'''⌉'''] [/ ? right ceiling] +[template lfloor[]'''⌊'''] [/ ? left floor = APL downstile] +[template rfloor[]'''⌋'''] [/ ? right floor] +[template lang[]'''〈'''] [/ < left-pointing angle bracket = bra (Firefox shows ?)] +[template rang[]'''〉'''] [/ > right-pointing angle bracket = ket (Firefox shows ?)] +[template loz[]'''◊'''] [/ ? lozenge] +[template spades[]'''♠'''] [/ ? black spade suit] +[template clubs[]'''♣'''] [/ ? black club suit = shamrock] +[template hearts[]'''♥'''] [/ ? black heart suit = valentine] +[template diams[]'''♦'''] [/ ? black diamond suit] +[template euro[]'''€'''] [/ ? Euro currency symbol] +[template lchev[]'''⟨'''] [/ ? left chevron] +[template rchev[]'''⟩'''] [/ right chevron] +[template rflat[]'''⟮'''] [/ right flat bracket Misc Math Symbol A] +[template lflat[]'''⟮'''] [/ left flat bracket] +[/ U2000.pdf punctuation] +[template endash[]'''–'''] [/ em width dash] +[template emdash[]'''—'''] [/ en width dash] +[template hbar[]'''―'''] [/ ? horizontal bar - introducing quoted text] +[template vert2bar[]'''‖'''] [/ ? double vertical bar] +[template line2[]'''‖'''] [/ ? double low line bar] +[template dagger[]'''†'''] [/ ? dagger] +[template dagger2[]'''‡'''] [/ ? double dagger] +[template dot[]'''․'''] [/ dot leader] +[template dot2[]'''‥'''] [/ ? dots leader] +[template ellipsis[]'''…'''] [/ horizontal ellipsis] + +[template dotover[]'''̇'''] [/ dot over symbol] +[template recur[]''' ̇'''] [/ math recurring symbol, eg after 0.333] +[/ Note use of a thin space before digit, so that dot isn't placed directly over the digit.] +[/ Use:1[recur]] + +[/ Other symbols, not in the HTML4 list:] +[template enquad[] ''' '''] [/ en quad space] +[template emquad[] ''' '''] [/ em quad space] +[template enspace[] ''' '''] [/ em half en space] +[template emspace[] ''' '''] [/ em space type size in points] +[template thickspace[] ''' '''] [/ 3 per em space] +[template midspace[] ''' '''] [/ 4 per em space] +[template sixemspace[] ''' '''] [/ 6 em space] +[template figspace[] ''' '''] [/ space = width fixed font digit] +[template punctspace[] ''' '''] [/ space = width punctuation] +[template thin[] ''' '''] [/ thin space ] +[template hair[] ''' '''] [/ hair space] +[template nbsp[] ''' '''] [/ non-breaking space] +[template space[] ''' '''] [/ plain non-breaking space] + +[template nospace[] '''​'''] [/ zero width space] +[template wordjoin[] '''⁠'''] [/ word joiner - no line break either side] +[template narrownbsp[] ''' '''] [/ narrow non-breaking space] +[template hyphen[] '''‐'''] [/ soft hyphen] +[template nbhyphen[] '''‑'''] [/ non-breaking hyphen] + +[template plusminus[]'''±'''] [/ ? plus or minus sign] +[template sqrt[]'''√'''] [/ ? square root sqrt symbol] +[/template pow2[]'''⁳'''] [/ 2073 is NOT superscript 2 character] +[template pow2[]'''²'''] [/ superscript 2 character] +[template pow3[]'''³'''] [/ superscript 3 character] +[template pown[]'''ⁿ'''] [/ superscript n character] +[template frac12[]'''½'''] [/ fraction half] +[template frac14[]'''¼'''] [/ fraction quarter] +[template frac34[]'''¾'''] [/ fraction three quarter] +[template sup1[]'''¹'''] [/ superscript one = superscript digit one ] +[template sup2[]'''²'''] [/ superscript two = superscript digit two = squared ] +[template cubed[]'''³'''] [/ superscript three = superscript digit three = cubed ] +[template macron[]'''¯'''] [/ macron = spacing macron = overline = APL overbar ] +[template deg[]'''°'''] [/ degree sign ] +[template plusmn[]'''±'''] [/ plus-minus sign = plus-or-minus sign ] +[template micro[]'''µ'''] [/ micro sign ] +[template cedil[]'''¸'''] [/ cedilla = spacing cedilla ] +[template ordm[]'''º'''] [/ masculine ordinal indicator ] +[template ordf[]'''ª'''] [/ feminine ordinal indicator ] +[template laquo[]'''«'''] [/ left-pointing double angle quotation mark = left pointing guillemet ] +[template raquo[]'''»'''] [/ right-pointing double angle quotation mark = right pointing guillemet ] + +[/ +Copyright 2007, 2010 Paul A. Bristow. +Distributed under the Boost Software License, Version 1.0. +(See accompanying file LICENSE_1_0.txt or copy at +http://www.boost.org/LICENSE_1_0.txt). +] + diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 5f0f244c..f1bf2c33 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -18,6 +18,7 @@ [/last-revision $Date: 2011-07-08 18:51:46 +0100 (Fri, 08 Jul 2011) $] ] +[include html4_symbols.qbk] [import ../example/gmp_snips.cpp] [import ../example/mpfr_snips.cpp] [import ../example/cpp_dec_float_snips.cpp] @@ -34,6 +35,18 @@ [template mpir[] [@http://mpir.org/ MPIR]] [template tommath[] [@http://libtom.org/?page=features&newsitems=5&whatfile=ltm libtommath]] +[template super[x]''''''[x]''''''] +[template sub[x]''''''[x]''''''] + +[template equation[name] ''' + + + + + + +'''] + [section:intro Introduction] @@ -556,14 +569,41 @@ Normally these should not be visible to the user. [endsect] -[section:jel Worked Example: defining a mathematical function.] +[section:fp_eg Examples] [import ../example/floating_point_examples.cpp] +[section:aos Area of Circle] + +[AOS1] +[AOS2] +[AOS3] + +[endsect] + +[section:jel Defining a Lambda Function.] + [JEL] [endsect] +[section:nd Calculating a Derivative] + +[ND1] +[ND2] +[ND3] + +[endsect] + +[section:GI Calculating an Integral] + +[GI1] +[GI2] + +[endsect] + +[endsect] + [endsect] [section:rational Rational Number Types] @@ -1528,8 +1568,6 @@ More information on this type can be found in the [link boost_multiprecision.tut [section:backendconc Backend Requirements] -[template super[x]''''''[x]''''''] - The requirements on the `Backend` template argument to `mp_number` are split up into compulsory requirements, and optional requirements that are either to improve performance or provide optional features. diff --git a/example/floating_point_examples.cpp b/example/floating_point_examples.cpp index 9aa134e9..81fccd70 100644 --- a/example/floating_point_examples.cpp +++ b/example/floating_point_examples.cpp @@ -9,6 +9,48 @@ #include #include +//[AOS1 + +/*`Generic numeric programming employs templates to use the same code for different +floating-point types and functions. Consider the area of a circle a of radius r, given by + +[:['a = [pi] * r[super 2]]] + +The area of a circle can be computed in generic programming using Boost.Math +for the constant [pi] as shown below: + +*/ + +//=#include + +template +inline T area_of_a_circle(T r) +{ + using boost::math::constants::pi; + return pi() * r * r; +} + +/*` +It is possible to use `area_of_a_circle()` with built-in floating-point types as +well as floating-point types from Boost.Multiprecision. In particular, consider a +system with 4-byte single-precision float, 8-byte double-precision double and also the +`cpp_dec_float_50` data type from Boost.Multiprecision with 50 decimal digits +of precision. + +We can compute and print the approximate area of a circle with radius 123/100 for +`float`, `double` and `cpp_dec_float_50` with the program below. + +*/ + +//] + +//[AOS3 + +/*`In the next example we'll look at calling both standard library and Boost.Math functions from within generic code. +We'll also show how to cope with template arguments which are expression-templates rather than number types.*/ + +//] + //[JEL /*` @@ -18,7 +60,7 @@ each implementation a little more sophisticated than the last. The Jahnke-Emden Lambda function is defined by the equation: -JahnkeEmden(v, z) = Gamma(v+1) * J[v](z) / (z / 2)^v +[:['JahnkeEmden(v, z) = [Gamma](v+1) * J[sub v](z) / (z / 2)[super v]]] If we were to implement this at double precision using Boost.Math's facilities for the Gamma and Bessel function calls it would look like this: @@ -164,6 +206,136 @@ to work out what type those variables should be, for example: */ +//] + +//[ND1 + +/*` +In this example we'll add even more power to generic numeric programming using not only different +floating-point types but also function objects as template parameters. Consider +some well-known central difference rules for numerically computing the first derivative +of a function ['f[prime](x)] with ['x [isin] [real]]: + +[equation floating_point_eg1] + +Where the difference terms ['m[sub n]] are given by: + +[equation floating_point_eg2] + +and ['dx] is the step-size of the derivative. + +The third formula in Equation 1 is a three-point central difference rule. It calculates +the first derivative of ['f[prime](x)] to ['O(dx[super 6])], where ['dx] is the given step-size. +For example, if +the step-size is 0.01 this derivative calculation has about 6 decimal digits of precision - +just about right for the 7 decimal digits of single-precision float. +Let's make a generic template subroutine using this three-point central difference +rule. In particular: +*/ + +template + value_type derivative(const value_type x, const value_type dx, function_type func) +{ + // Compute d/dx[func(*first)] using a three-point + // central difference rule of O(dx^6). + + const value_type dx1 = dx; + const value_type dx2 = dx1 * 2; + const value_type dx3 = dx1 * 3; + + const value_type m1 = (func(x + dx1) - func(x - dx1)) / 2; + const value_type m2 = (func(x + dx2) - func(x - dx2)) / 4; + const value_type m3 = (func(x + dx3) - func(x - dx3)) / 6; + + const value_type fifteen_m1 = 15 * m1; + const value_type six_m2 = 6 * m2; + const value_type ten_dx1 = 10 * dx1; + + return ((fifteen_m1 - six_m2) + m3) / ten_dx1; +} + +/*`The `derivative()` template function can be used to compute the first derivative +of any function to ['O(dx[super 6])]. For example, consider the first derivative of ['sin(x)] evaluated +at ['x = [pi]/3]. In other words, + +[equation floating_point_eg3] + +The code below computes the derivative in Equation 3 for float, double and boost's +multiple-precision type cpp_dec_float_50. +*/ + +//] + +//[GI1 + +/*` +Similar to the generic derivative example, we can calculate integrals in a similar manner: +*/ + +template +inline value_type integral(const value_type a, + const value_type b, + const value_type tol, + function_type func) +{ + unsigned n = 1U; + + value_type h = (b - a); + value_type I = (func(a) + func(b)) * (h / 2); + + for(unsigned k = 0U; k < 8U; k++) + { + h /= 2; + + value_type sum(0); + for(unsigned j = 1U; j <= n; j++) + { + sum += func(a + (value_type((j * 2) - 1) * h)); + } + + const value_type I0 = I; + I = (I / 2) + (h * sum); + + const value_type ratio = I0 / I; + const value_type delta = ratio - 1; + const value_type delta_abs = ((delta < 0) ? -delta : delta); + + if((k > 1U) && (delta_abs < tol)) + { + break; + } + + n *= 2U; + } + + return I; +} + +/*` +The following sample program shows how the function can be called, we begin +by defining a function object, which when integrated should yield the Bessel J +function: +*/ + +template +class cyl_bessel_j_integral_rep +{ +public: + cyl_bessel_j_integral_rep(const unsigned N, + const value_type& X) : n(N), x(X) { } + + value_type operator()(const value_type& t) const + { + // pi * Jn(x) = Int_0^pi [cos(x * sin(t) - n*t) dt] + return cos(x * sin(t) - (n * t)); + } + +private: + const unsigned n; + const value_type x; +}; + + //] int main() @@ -179,6 +351,197 @@ int main() std::cout << JEL3(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl; std::cout << std::scientific << std::setprecision(std::numeric_limits::digits10); std::cout << JEL4(cpp_dec_float_100(2) + 0.5, cpp_dec_float_100(0.5)) << std::endl; + + //[AOS2 + +/*=#include +#include +#include + +using boost::multiprecision::cpp_dec_float_50; + +int main(int, char**) +{*/ + const float r_f(float(123) / 100); + const float a_f = area_of_a_circle(r_f); + + const double r_d(double(123) / 100); + const double a_d = area_of_a_circle(r_d); + + const cpp_dec_float_50 r_mp(cpp_dec_float_50(123) / 100); + const cpp_dec_float_50 a_mp = area_of_a_circle(r_mp); + + // 4.75292 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_f + << std::endl; + + // 4.752915525616 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_d + << std::endl; + + // 4.7529155256159981904701331745635599135018975843146 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_mp + << std::endl; +/*=}*/ + + //] + + //[ND2 +/*= +#include +#include +#include +#include + + +int main(int, char**) +{*/ + using boost::math::constants::pi; + using boost::multiprecision::cpp_dec_float_50; + // + // We'll pass a function pointer for the function object passed to derivative, + // the typecast is needed to select the correct overload of std::sin: + // + const float d_f = derivative( + pi() / 3, + 0.01F, + static_cast(std::sin) + ); + + const double d_d = derivative( + pi() / 3, + 0.001, + static_cast(std::sin) + ); + // + // In the cpp_dec_float_50 case, the sin function is multiply overloaded + // to handle expression templates etc. As a result it's hard to take it's + // address without knowing about its implementation details. We'll use a + // C++11 lambda expression to capture the call. + // We also need a typecast on the first argument so we don't accidently pass + // an expression template to a template function: + // + const cpp_dec_float_50 d_mp = derivative( + cpp_dec_float_50(pi() / 3), + cpp_dec_float_50(1.0E-9), + [](const cpp_dec_float_50& x) -> cpp_dec_float_50 + { + return sin(x); + } + ); + + // 5.000029e-001 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_f + << std::endl; + + // 4.999999999998876e-001 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_d + << std::endl; + + // 4.99999999999999999999999999999999999999999999999999e-01 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_mp + << std::endl; +//=} + + /*` + The expected value of the derivative is 0.5. This central difference rule in this + example is ill-conditioned, meaning it suffers from slight loss of precision. With that + in mind, the results agree with the expected value of 0.5.*/ + + //] + + //[ND3 + + /*` + We can take this a step further and use our derivative function to compute + a partial derivative. For example if we take the incomplete gamma function + ['P(a, z)], and take the derivative with respect to /z/ at /(2,2)/ then we + can calculate the result as shown below, for good measure we'll compare with + the "correct" result obtained from a call to ['gamma_p_derivative], the results + agree to approximately 44 digits: + */ + + cpp_dec_float_50 gd = derivative( + cpp_dec_float_50(2), + cpp_dec_float_50(1.0E-9), + [](const cpp_dec_float_50& x) ->cpp_dec_float_50 + { + return boost::math::gamma_p(2, x); + } + ); + // 2.70670566473225383787998989944968806815263091819151e-01 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << gd + << std::endl; + // 2.70670566473225383787998989944968806815253190143120e-01 + std::cout << boost::math::gamma_p_derivative(cpp_dec_float_50(2), cpp_dec_float_50(2)) << std::endl; + //] + + //[GI2 + + /* The function can now be called as follows: */ +/*=int main(int, char**) +{*/ + using boost::math::constants::pi; + typedef boost::multiprecision::cpp_dec_float_50 mp_type; + + const float j2_f = + integral(0.0F, + pi(), + 0.01F, + cyl_bessel_j_integral_rep(2U, 1.23F)) / pi(); + + const double j2_d = + integral(0.0, + pi(), + 0.0001, + cyl_bessel_j_integral_rep(2U, 1.23)) / pi(); + + const mp_type j2_mp = + integral(mp_type(0), + pi(), + mp_type(1.0E-20), + cyl_bessel_j_integral_rep(2U, mp_type(123) / 100)) / pi(); + + // 0.166369 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_f + << std::endl; + + // 0.166369383786814 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_d + << std::endl; + + // 0.16636938378681407351267852431513159437103348245333 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_mp + << std::endl; + + // + // Print true value for comparison: + // 0.166369383786814073512678524315131594371033482453329 + std::cout << boost::math::cyl_bessel_j(2, mp_type(123) / 100) << std::endl; +//=} + + //] + return 0; } @@ -191,4 +554,12 @@ Program output: 9.822663964796047e-001 9.82266396479604757017335009796882833995903762577173e-01 9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01 +4.752916e+000 +4.752915525615998e+000 +4.75291552561599819047013317456355991350189758431460e+00 +5.000029e-001 +4.999999999998876e-001 +4.99999999999999999999999999999999999999999999999999e-01 +2.70670566473225383787998989944968806815263091819151e-01 +2.70670566473225383787998989944968806815253190143120e-01 */ \ No newline at end of file diff --git a/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp b/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp index 6e7495b1..787de062 100644 --- a/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp +++ b/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp @@ -61,44 +61,45 @@ private: const value_type x; }; -using boost::math::constants::pi; -typedef boost::multiprecision::cpp_dec_float_50 mp_type; int main(int, char**) { - const float j2_f = - integral(0.0F, - pi(), - 0.01F, - cyl_bessel_j_integral_rep(2U, 1.23F)) / pi(); + using boost::math::constants::pi; + typedef boost::multiprecision::cpp_dec_float_50 mp_type; - const double j2_d = - integral(0.0, - pi(), - 0.0001, - cyl_bessel_j_integral_rep(2U, 1.23)) / pi(); + const float j2_f = + integral(0.0F, + pi(), + 0.01F, + cyl_bessel_j_integral_rep(2U, 1.23F)) / pi(); - const mp_type j2_mp = - integral(mp_type(0), - pi(), - mp_type(1.0E-20), - cyl_bessel_j_integral_rep(2U, mp_type(123) / 100)) / pi(); + const double j2_d = + integral(0.0, + pi(), + 0.0001, + cyl_bessel_j_integral_rep(2U, 1.23)) / pi(); - // 0.166369 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << j2_f - << std::endl; + const mp_type j2_mp = + integral(mp_type(0), + pi(), + mp_type(1.0E-20), + cyl_bessel_j_integral_rep(2U, mp_type(123) / 100)) / pi(); - // 0.166369383786814 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << j2_d - << std::endl; + // 0.166369 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_f + << std::endl; - // 0.16636938378681407351267852431513159437103348245333 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << j2_mp - << std::endl; + // 0.166369383786814 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_d + << std::endl; + + // 0.16636938378681407351267852431513159437103348245333 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_mp + << std::endl; } From d4a2c46ac6feae8c001358508e936d59fdec3e4d Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 13 Apr 2012 15:38:28 +0000 Subject: [PATCH 168/256] Update examples, reorganise docs, temporarily remove HTML before rebuilding. Enhance test cases, including enabling loopback testing on cpp_dec_float io. 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00000000..27d1d5ef --- /dev/null +++ b/doc/generate.sh @@ -0,0 +1,33 @@ +# Copyright John Maddock 2008. +# Use, modification and distribution are subject to the +# Boost Software License, Version 1.0. (See accompanying file +# LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +# +# Generates SVG and PNG files from the MML masters. +# +# Paths to tools come first, change these to match your system: +# +math2svg='m:\download\open\SVGMath-0.3.1\math2svg.py' +python=/cygdrive/c/Python26/python.exe +inkscape=/cygdrive/c/progra~1/Inkscape/inkscape +# Image DPI: +dpi=120 + +for mmlfile in $*; do + svgfile=$(basename $mmlfile .mml).svg + pngfile=$(basename $svgfile .svg).png + tempfile=temp.mml + # strip html wrappers put in by MathCast: + cat $mmlfile | tr -d "\r\n" | sed -e 's/.*\(]*>.*<\/math>\).*/\1/' > $tempfile + + echo Generating $svgfile + $python $math2svg $tempfile > $svgfile + echo Generating $pngfile + $inkscape -d $dpi -e $(cygpath -a -w $pngfile) $(cygpath -a -w $svgfile) + rm $tempfile +done + + + + + diff --git a/doc/html/boost_multiprecision/indexes.html b/doc/html/boost_multiprecision/indexes.html deleted file mode 100644 index e3925a4f..00000000 --- a/doc/html/boost_multiprecision/indexes.html +++ /dev/null @@ -1,40 +0,0 @@ - - - -Indexes - - - - - - - - -
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    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

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    - The Multiprecision Library provides User-defined integer, - rational and floating-point C++ types which try to emulate as closely as practicable - the C++ built-in types, but provide for more range and precision. Depending - upon the number type, precision may be arbitrarily large (limited only by available - memory), fixed at compile time values, for example 50 decimal digits, or a - variable controlled at run-time by member functions. The types are expression-template-enabled - for better performance than naive user-defined types. -

    -

    - The Multiprecision library comes in two distinct parts: -

    -
      -
    • - An expression-template-enabled front-end mp_number - that handles all the operator overloading, expression evaluation optimization, - and code reduction. -
      • -
    • - A selection of back-ends that implement the actual arithmetic operations, - and need conform only to the reduced interface requirements of the front-end. -
      • -
    -

    - Separation of front-end and back-end allows use of highly refined, but restricted - license libraries where possible, but provides Boost license alternatives for - users who must have a portable unconstrained license. Which is to say some - back-ends rely on 3rd party libraries, but a header-only Boost license version - is always available (if somewhat slower). -

    -

    - The library is often used via one of the predefined typedefs: for example if - you wanted an arbitrary - precision integer type using GMP - as the underlying implementation then you could use: -

    -
    #include <boost/multiprecision/gmp.hpp>  // Defines the wrappers around the GMP library's types
-
-boost::multiprecision::mpz_int myint;    // Arbitrary precision integer type.
-
    -

    - Alternatively, you can compose your own multiprecision type, by combining - mp_number with one of the predefined - back-end types. For example, suppose you wanted a 300 decimal digit floating-point - type based on the MPFR library. In - this case, there's no predefined typedef with that level of precision, so instead - we compose our own: -

    -
    #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
-
-namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
-
-typedef mp::mp_number<mp::mpfr_float_backend<300> >  my_float;
-
-my_float a, b, c; // These variables have 300 decimal digits precision
-
    -

    - We can repeat the above example, but with the expression templates disabled - (for faster compile times, but slower runtimes) by passing a second template - argument to mp_number: -

    -
    #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
-
-namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
-
-typedef mp::mp_number<mp::mpfr_float_backend<300>, false>  my_float;
-
-my_float a, b, c; // These variables have 300 decimal digits precision
-
    -
    - - Expression - Templates -
    -

    - Class mp_number is expression-template-enabled: - that means that rather than having a multiplication operator that looks like - this: -

    -
    template <class Backend>
-mp_number<Backend> operator * (const mp_number<Backend>& a, const mp_number<Backend>& b)
-{
-   mp_number<Backend> result(a);
-   result *= b;
-   return result;
-}
-
    -

    - Instead the operator looks more like this: -

    -
    template <class Backend>
-unmentionable-type operator * (const mp_number<Backend>& a, const mp_number<Backend>& b);
-
    -

    - Where the "unmentionable" return type is an implementation detail - that, rather than containing the result of the multiplication, contains instructions - on how to compute the result. In effect it's just a pair of references to the - arguments of the function, plus some compile-time information that stores what - the operation is. -

    -

    - The great advantage of this method is the elimination of temporaries: - for example the "naive" implementation of operator* above, requires one temporary for computing - the result, and at least another one to return it. It's true that sometimes - this overhead can be reduced by using move-semantics, but it can't be eliminated - completely. For example, lets suppose we're evaluating a polynomial via Horners - method, something like this: -

    -
    T a[7] = { /* some values */ };
-//....
-y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0];
-
    -

    - If type T is an mp_number, then this expression is evaluated - without creating a single temporary value. In contrast, - if we were using the C++ wrapper that ships with GMP - - mpfr_class - - then this expression would result in no less than 11 temporaries (this is - true even though mpfr_class - does use expression templates to reduce the number of temporaries somewhat). - Had we used an even simpler wrapper around GMP - or MPFR like mpclass - things would have been even worse and no less that 24 temporaries are created - for this simple expression (note - we actually measure the number of memory - allocations performed rather than the number of temporaries directly). -

    -

    - This library also extends expression template support to standard library functions - like abs or sin - with mp_number arguments. This - means that an expression such as: -

    -
    y = abs(x);
-
    -

    - can be evaluated without a single temporary being calculated. Even expressions - like: -

    -
    y = sin(x);
-
    -

    - get this treatment, so that variable 'y' is used as "working storage" - within the implementation of sin, - thus reducing the number of temporaries used by one. Of course, should you - write: -

    -
    x = sin(x);
-
    -

    - Then we clearly can't use x - as working storage during the calculation, so then a temporary variable is - created in this case. -

    -

    - Given the comments above, you might be forgiven for thinking that expression-templates - are some kind of universal-panacea: sadly though, all tricks like this have - their downsides. For one thing, expression template libraries like this one, - tend to be slower to compile than their simpler cousins, they're also harder - to debug (should you actually want to step through our code!), and rely on - compiler optimizations being turned on to give really good performance. Also, - since the return type from expressions involving mp_numbers - is an "unmentionable implementation detail", you have to be careful - to cast the result of an expression to the actual number type when passing - an expression to a template function. For example, given: -

    -
    template <class T>
-void my_proc(const T&);
-
    -

    - Then calling: -

    -
    my_proc(a+b);
-
    -

    - Will very likely result in obscure error messages inside the body of my_proc - since we've passed it an expression - template type, and not a number type. Instead we probably need: -

    -
    my_proc(my_mp_number_type(a+b));
-
    -

    - Having said that, these situations don't occur that often - or indeed not at - all for non-template functions. In addition, all the functions in the Boost.Math - library will automatically convert expression-template arguments to the underlying - number type without you having to do anything, so: -

    -
    mpfr_float_100 a(20), delta(0.125);
-boost::math::gamma_p(a, a + delta);
-
    -

    - Will work just fine, with the a + delta expression - template argument getting converted to an mpfr_float_100 - internally by the Boost.Math library. -

    -

    - One other potential pitfall that's only possible in C++11: you should never - store an expression template using: -

    -
    auto my_expression = a + b - c;
-
    -

    - unless you're absolutely sure that the lifetimes of a, - b and c - will outlive that of my_expression. -

    -

    - And finally... the performance improvements from an expression template library - like this are often not as dramatic as the reduction in number of temporaries - would suggest. For example if we compare this library with mpfr_class - and mpreal, with - all three using the underlying MPFR - library at 50 decimal digits precision then we see the following typical results - for polynomial execution: -

    -
    -

    Table 1.1. Evaluation of Order 6 Polynomial.

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Library -

    -     		-

    - Relative Time -

    -     		-

    - Relative number of memory allocations -

    -
    -

    - mp_number -

    -     		-

    - 1.0 (0.00793s) -

    -     		-

    - 1.0 (2996 total) -

    -
    -

    - mpfr_class -

    -     		-

    - 1.2 (0.00931s) -

    -     		-

    - 4.3 (12976 total) -

    -
    -

    - mpreal -

    -     		-

    - 1.9 (0.0148s) -

    -     		-

    - 9.3 (27947 total) -

    -
    -
    -

    - As you can see, the execution time increases a lot more slowly than the number - of memory allocations. There are a number of reasons for this: -

    -
      -
    • - The cost of extended-precision multiplication and division is so great, - that the times taken for these tend to swamp everything else. -
      • -
    • - The cost of an in-place multiplication (using operator*=) tends to be more than an out-of-place - operator* - (typically operator *= - has to create a temporary workspace to carry out the multiplication, where - as operator* - can use the target variable as workspace). Since the expression templates - carry out their magic by converting out-of-place operators to in-place - ones, we necessarily take this hit. Even so the transformation is more - efficient than creating the extra temporary variable, just not by as much - as one would hope. -
      • -
    -

    - Finally, note that mp_number - takes a second template argument, which, when set to false - disables all the expression template machinery. The result is much faster to - compile, but slower at runtime. -

    -

    - We'll conclude this section by providing some more performance comparisons - between these three libraries, again, all are using MPFR - to carry out the underlying arithmetic, and all are operating at the same precision - (50 decimal digits): -

    -
    -

    Table 1.2. Evaluation of Boost.Math's Bessel function test data

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Library -

    -     		-

    - Relative Time -

    -     		-

    - Relative Number of Memory Allocations -

    -
    -

    - mp_number -

    -     		-

    - 1.0 (6.21s) -

    -     		-

    - 1.0 (2685469) -

    -
    -

    - mpfr_class -

    -     		-

    - 1.04 (6.45s) -

    -     		-

    - 1.47 (3946007) -

    -
    -

    - mpreal -

    -     		-

    - 1.53 (9.52s) -

    -     		-

    - 4.92 (13222940) -

    -
    -
    -
    -

    Table 1.3. Evaluation of Boost.Math's Non-Central T distribution test data

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Library -

    -     		-

    - Relative Time -

    -     		-

    - Relative Number of Memory Allocations -

    -
    -

    - mp_number -

    -     		-

    - 1.0 (269s) -

    -     		-

    - 1.0 (139082551) -

    -
    -

    - mpfr_class -

    -     		-

    - 1.04 (278s) -

    -     		-

    - 1.81 (252400791) -

    -
    -

    - mpreal -

    -     		-

    - 1.49 (401s) -

    -     		-

    - 3.22 (447009280) -

    -
    -
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
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    -PrevUpHomeNext -
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    -PrevUpHomeNext -
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    History
    -
    TODO
    -
    Acknowledgements
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

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    - - diff --git a/doc/html/boost_multiprecision/map/ack.html b/doc/html/boost_multiprecision/map/ack.html deleted file mode 100644 index 4de1bb82..00000000 --- a/doc/html/boost_multiprecision/map/ack.html +++ /dev/null @@ -1,55 +0,0 @@ - - - -Acknowledgements - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - This library would not have happened without: -

    -
      -
    • - Christopher Kormanyos' C++ decimal number code. -
      • -
    • - Paul Bristow for patiently testing, and commenting on the library. -
      • -
    • - All the folks at GMP, MPFR and libtommath, for providing the "guts" - that makes this library work. -
      • -
    • - "The - Art Of Computer Programming", Donald E. Knuth, Volume 2: - Seminumerical Algorithms, Third Edition (Reading, Massachusetts: Addison-Wesley, - 1997), xiv+762pp. ISBN 0-201-89684-2 -
      • -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
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    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html deleted file mode 100644 index 70462181..00000000 --- a/doc/html/boost_multiprecision/map/hist.html +++ /dev/null @@ -1,50 +0,0 @@ - - - -History - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
      -
    • - 2011-2012, John Maddock adds an expression template enabled front end - to Christopher's code, and adds support for other backends. -
      • -
    • - 2011, Christopher Kormanyos publishes the decimal floating point code - under the Boost Software Licence. The code is published as: "Algorithm - 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", - in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. -
      • -
    • - 2002-2011, Christopher Kormanyos develops the all C++ decimal arithmetic - floating point code. -
      • -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

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    -PrevUpHomeNext -
    -
    -

    -TODO -

    -

    - More a list of what could be done, rather than what - should be done (which may be a much smaller list!). -

    -
      -
    • - Add back-end support for libdecNumber. -
      • -
    • - Add an adapter back-end for complex number types. -
      • -
    • - Add a back-end for MPFR interval arithmetic. -
      • -
    • - Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. -
      • -
    • - Add assembly level routines to cpp_int_backend. -
      • -
    • - Add an all C++ binary floating point type. -
      • -
    -
    - - Pre-Review - Comments -
    -
      -
    • - Make the exponent type for cpp_dec_float a templare parameter, maybe - include support for big-integer exponents. Open question - what should - be the default - int32_t or int64_t? -
      • -
    • - Document the size requirements of fixed precision ints. -
      • -
    • - Document std lib function accuracy. -
      • -
    • - Make fixed precision orthogonal to Allocator type in cpp_int. Possible - solution - add an additional MaxBits template argument that defaults - to 0 (meaning keep going till no more space/memory). -
      • -
    • - Add support for fused multiply add (and subtract). GMP mpz_t could use - this. -
      • -
    • - Be a bit clearer on the effects of sign-magnitude representation of cpp_int - - min == -max etc. -
      • -
    • - Document cpp_dec_float precision, rounding, and exponent size. -
      • -
    • - Can we be clearer in the docs that mixed arithmetic doesn't work? -
      • -
    • - Document round functions behaviour better (they behave as in C99). -
      • -
    • - Should there be a choice of rounding mode (probably MPFR specific)? -
      • -
    • - Document limits on size of cpp_dec_float. -
      • -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

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    - - diff --git a/doc/html/boost_multiprecision/perf.html b/doc/html/boost_multiprecision/perf.html deleted file mode 100644 index 7460f077..00000000 --- a/doc/html/boost_multiprecision/perf.html +++ /dev/null @@ -1,46 +0,0 @@ - - - -Performance Comparison - - - - - - - - -
    -PrevUpHomeNext -
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    -
    -
    Floating Point Real - World Tests
    -
    Integer Real - World Tests
    -
    Float Algorithm - Perfomance
    -
    Integer - Algorithm Perfomance
    -
    Rational - Type Perfomance
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

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    -PrevUpHomeNext -
    -
    -
    -

    - Note that these tests are carefully designed to test performance of the underlying - algorithms and not memory allocation or variable copying. As usual, performance - results should be taken with a healthy dose of scepticism, and real-world - performance may vary widely depending upon the specifics of the program. - In each table relative times are given first, with the best performer given - a score of 1. Total actual times are given in brackets, measured in seconds - for 500000 operations. -

    -

    - Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. - The tests were run on 32-bit Windows Vista machine. -

    -
    -

    Table 1.8. Operator +

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1 (0.02382s) -

    -     		-

    - 1 (0.0294619s) -

    -     		-

    - 1 (0.058466s) -

    -
    -

    - gmp_float -

    -     		-

    - 4.55086 (0.108402s) -

    -     		-

    - 3.86443 (0.113853s) -

    -     		-

    - 2.6241 (0.15342s) -

    -
    -

    - mpfr_float -

    -     		-

    - 2.52036 (0.060035s) -

    -     		-

    - 2.1833 (0.0643242s) -

    -     		-

    - 1.37736 (0.0805287s) -

    -
    -
    -
    -

    Table 1.9. Operator +(int)

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1.56759 (0.0527023s) -

    -     		-

    - 1.74629 (0.0618102s) -

    -     		-

    - 1.68077 (0.105927s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (0.0336201s) -

    -     		-

    - 1 (0.0353951s) -

    -     		-

    - 1 (0.0630232s) -

    -
    -

    - mpfr_float -

    -     		-

    - 3.14875 (0.105861s) -

    -     		-

    - 3.15499 (0.111671s) -

    -     		-

    - 1.92831 (0.121528s) -

    -
    -
    -
    -

    Table 1.10. Operator -

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1 (0.0265783s) -

    -     		-

    - 1 (0.031465s) -

    -     		-

    - 1 (0.0619405s) -

    -
    -

    - gmp_float -

    -     		-

    - 4.66954 (0.124108s) -

    -     		-

    - 3.72645 (0.117253s) -

    -     		-

    - 2.67536 (0.165713s) -

    -
    -

    - mpfr_float -

    -     		-

    - 2.7909 (0.0741774s) -

    -     		-

    - 2.48557 (0.0782083s) -

    -     		-

    - 1.50944 (0.0934957s) -

    -
    -
    -
    -

    Table 1.11. Operator -(int)

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1 (0.0577674s) -

    -     		-

    - 1 (0.0633795s) -

    -     		-

    - 1 (0.11146s) -

    -
    -

    - gmp_float -

    -     		-

    - 2.31811 (0.133911s) -

    -     		-

    - 2.07251 (0.131355s) -

    -     		-

    - 1.67161 (0.186319s) -

    -
    -

    - mpfr_float -

    -     		-

    - 2.45081 (0.141577s) -

    -     		-

    - 2.29174 (0.145249s) -

    -     		-

    - 1.395 (0.155487s) -

    -
    -
    -
    -

    Table 1.12. Operator *

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1.07276 (0.287898s) -

    -     		-

    - 1.47724 (0.584569s) -

    -     		-

    - 1.55145 (5.09969s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (0.268372s) -

    -     		-

    - 1 (0.395718s) -

    -     		-

    - 1 (3.28705s) -

    -
    -

    - mpfr_float -

    -     		-

    - 1.27302 (0.341642s) -

    -     		-

    - 1.17649 (0.465557s) -

    -     		-

    - 1.14029 (3.7482s) -

    -
    -
    -
    -

    Table 1.13. Operator *(int)

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 2.89945 (0.11959s) -

    -     		-

    - 4.56335 (0.197945s) -

    -     		-

    - 9.03602 (0.742044s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (0.0412457s) -

    -     		-

    - 1 (0.0433772s) -

    -     		-

    - 1 (0.0821206s) -

    -
    -

    - mpfr_float -

    -     		-

    - 3.6951 (0.152407s) -

    -     		-

    - 3.71977 (0.161353s) -

    -     		-

    - 3.30958 (0.271785s) -

    -
    -
    -
    -

    Table 1.14. Operator /

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 3.24327 (4.00108s) -

    -     		-

    - 5.00532 (8.12985s) -

    -     		-

    - 6.79566 (54.2796s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (1.23366s) -

    -     		-

    - 1 (1.62424s) -

    -     		-

    - 1 (7.9874s) -

    -
    -

    - mpfr_float -

    -     		-

    - 1.32521 (1.63486s) -

    -     		-

    - 1.38967 (2.25716s) -

    -     		-

    - 1.72413 (13.7713s) -

    -
    -
    -
    -

    Table 1.15. Operator /(int)

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1.45093 (0.253675s) -

    -     		-

    - 1.83306 (0.419569s) -

    -     		-

    - 2.3644 (1.64187s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (0.174836s) -

    -     		-

    - 1 (0.22889s) -

    -     		-

    - 1 (0.694411s) -

    -
    -

    - mpfr_float -

    -     		-

    - 1.16731 (0.204088s) -

    -     		-

    - 1.13211 (0.259127s) -

    -     		-

    - 1.02031 (0.708513s) -

    -
    -
    -
    -

    Table 1.16. Operator str

    -
    ------ - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -     		-

    - 500 Decimal Digits -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1.4585 (0.0188303s) -

    -     		-

    - 1.55515 (0.03172s) -

    -     		-

    - 1 (0.131962s) -

    -
    -

    - gmp_float -

    -     		-

    - 1 (0.0129107s) -

    -     		-

    - 1 (0.0203967s) -

    -     		-

    - 1.04632 (0.138075s) -

    -
    -

    - mpfr_float -

    -     		-

    - 2.19015 (0.0282764s) -

    -     		-

    - 1.84679 (0.0376683s) -

    -     		-

    - 1.20295 (0.158743s) -

    -
    -
    -

    - ] -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html deleted file mode 100644 index 89278b58..00000000 --- a/doc/html/boost_multiprecision/perf/int_real_world.html +++ /dev/null @@ -1,217 +0,0 @@ - - - -Integer Real World Tests - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - These tests - measure the time taken to generate 1000 128-bit random numbers and test for - primality using the Miller Rabin test. -

    -

    - Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and libtommath-0.42.0. - The tests were run on 32-bit Windows Vista machine. -

    -
    ---- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Integer Type -

    -     		-

    - Relative (and Absolute) Times -

    -
    -

    - mpz_int -

    -     		-

    - 1.08279(0.370326s) -

    -
    -

    - mpz_int (no Expression templates) -

    -     		-

    - 1.1702(0.400222s) -

    -
    -

    - cpp_int -

    -     		-

    - 1.3612(0.465547s) -

    -
    -

    - cpp_int (no Expression templates) -

    -     		-

    - 1.33286(0.455854s) -

    -
    -

    - cpp_int (64-bit cache) -

    -     		-

    - 1.33134(0.455333s) -

    -
    -

    - cpp_int (256-bit cache) -

    -     		-

    - 1.29367(0.442451s) -

    -
    -

    - cpp_int (512-bit cache) -

    -     		-

    - 1.08821(0.37218s) -

    -
    -

    - cpp_int (1024-bit cache) -

    -     		-

    - 1.07902(0.369037s) -

    -
    -

    - mp_int1024_t -

    -     		-

    - 1.02616(0.35096s) -

    -
    -

    - mp_int1024_t (no Expression templates) -

    -     		-

    - 1(0.342011s) -

    -
    -

    - tom_int -

    -     		-

    - 3.74233(1.27992s) -

    -
    -

    - tom_int (no Expression templates) -

    -     		-

    - 3.97646(1.35999s) -

    -
    -

    - It's interesting to note that expression templates have little effect here - - perhaps because the actual expressions involved are relatively trivial - in this case - so the time taken for multiplication and division tends to - dominate. Also note how increasing the internal cache size used by cpp_int is quite effective in this case - in cutting out memory allocations altogether - cutting about a third off - the total runtime. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html deleted file mode 100644 index b7bbe0e7..00000000 --- a/doc/html/boost_multiprecision/perf/integer_performance.html +++ /dev/null @@ -1,3034 +0,0 @@ - - - -Integer Algorithm Perfomance - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - Note that these tests are carefully designed to test performance of the underlying - algorithms and not memory allocation or variable copying. As usual, performance - results should be taken with a healthy dose of scepticism, and real-world - performance may vary widely depending upon the specifics of the program. - In each table relative times are given first, with the best performer given - a score of 1. Total actual times are given in brackets, measured in seconds - for 500000 operations. -

    -

    - Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. - The tests were run on 32-bit Windows Vista machine. -

    -

    - Linux x86_64 results are broadly similar, except that libtommath performs - much better there. -

    -
    -

    Table 1.17. Operator +

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.24574 (0.0270133s) -

    -     		-

    - 1.09665 (0.0352319s) -

    -     		-

    - 1.25708 (0.0524047s) -

    -     		-

    - 1.31488 (0.08777s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1.05787 (0.0229394s) -

    -     		-

    - 1 (0.0321268s) -

    -     		-

    - 1.16171 (0.0484289s) -

    -     		-

    - 1.24017 (0.0827832s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.08016 (0.0451073s) -

    -     		-

    - 1.33792 (0.042983s) -

    -     		-

    - 1.19676 (0.0498904s) -

    -     		-

    - 1 (0.0667514s) -

    -
    -

    - tommath_int -

    -     		-

    - 1 (0.0216845s) -

    -     		-

    - 1.07779 (0.0346258s) -

    -     		-

    - 1 (0.0416877s) -

    -     		-

    - 1.06344 (0.0709863s) -

    -
    -
    -
    -

    Table 1.18. Operator +(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.46244 (0.0202077s) -

    -     		-

    - 1.20665 (0.0238576s) -

    -     		-

    - 1.17647 (0.0258293s) -

    -     		-

    - 1.12424 (0.0317931s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0138178s) -

    -     		-

    - 1 (0.0197719s) -

    -     		-

    - 1 (0.0219548s) -

    -     		-

    - 1 (0.0282796s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.15321 (0.0297527s) -

    -     		-

    - 2.09834 (0.041488s) -

    -     		-

    - 2.89935 (0.0636546s) -

    -     		-

    - 3.70262 (0.104709s) -

    -
    -

    - tommath_int -

    -     		-

    - 17.1419 (0.236864s) -

    -     		-

    - 12.9762 (0.256563s) -

    -     		-

    - 12.3275 (0.270648s) -

    -     		-

    - 10.7373 (0.303648s) -

    -
    -
    -
    -

    Table 1.19. Operator -

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.15385 (0.029665s) -

    -     		-

    - 1.08217 (0.0369886s) -

    -     		-

    - 1.05882 (0.051534s) -

    -     		-

    - 1.12132 (0.0822725s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0257095s) -

    -     		-

    - 1 (0.0341801s) -

    -     		-

    - 1 (0.0486711s) -

    -     		-

    - 1.08659 (0.0797242s) -

    -
    -

    - gmp_int -

    -     		-

    - 1.56685 (0.040283s) -

    -     		-

    - 1.32917 (0.0454312s) -

    -     		-

    - 1.06917 (0.0520378s) -

    -     		-

    - 1 (0.0733708s) -

    -
    -

    - tommath_int -

    -     		-

    - 1.059 (0.0272264s) -

    -     		-

    - 1.16974 (0.0399818s) -

    -     		-

    - 1.01303 (0.0493054s) -

    -     		-

    - 1.03375 (0.0758472s) -

    -
    -
    -
    -

    Table 1.20. Operator -(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.51665 (0.0157196s) -

    -     		-

    - 1.31513 (0.0200533s) -

    -     		-

    - 1.29599 (0.0235066s) -

    -     		-

    - 1.21534 (0.0266136s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0103647s) -

    -     		-

    - 1 (0.0152482s) -

    -     		-

    - 1 (0.018138s) -

    -     		-

    - 1 (0.021898s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.7938 (0.0289568s) -

    -     		-

    - 2.55493 (0.038958s) -

    -     		-

    - 3.12248 (0.0566356s) -

    -     		-

    - 4.48855 (0.0982904s) -

    -
    -

    - tommath_int -

    -     		-

    - 20.8695 (0.216305s) -

    -     		-

    - 15.0705 (0.229797s) -

    -     		-

    - 13.4093 (0.243217s) -

    -     		-

    - 12.2599 (0.268468s) -

    -
    -
    -
    -

    Table 1.21. Operator *

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.29504 (0.0731032s) -

    -     		-

    - 1.55431 (0.196132s) -

    -     		-

    - 1.4363 (0.656569s) -

    -     		-

    - 1.63701 (2.47859s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0564485s) -

    -     		-

    - 1.16604 (0.147138s) -

    -     		-

    - 1 (0.457124s) -

    -     		-

    - 1 (1.5141s) -

    -
    -

    - gmp_int -

    -     		-

    - 1.19574 (0.0674975s) -

    -     		-

    - 1 (0.126186s) -

    -     		-

    - 1.16627 (0.53313s) -

    -     		-

    - 1.02906 (1.5581s) -

    -
    -

    - tommath_int -

    -     		-

    - 1.97229 (0.111333s) -

    -     		-

    - 2.67087 (0.337027s) -

    -     		-

    - 2.13031 (0.973817s) -

    -     		-

    - 2.05869 (3.11706s) -

    -
    -
    -
    -

    Table 1.22. Operator *(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.34609 (0.030315s) -

    -     		-

    - 1.57086 (0.0407838s) -

    -     		-

    - 1.60154 (0.0542267s) -

    -     		-

    - 1.67808 (0.0804984s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1.29783 (0.0292279s) -

    -     		-

    - 1.58263 (0.0410894s) -

    -     		-

    - 1.61543 (0.054697s) -

    -     		-

    - 1.66841 (0.0800346s) -

    -
    -

    - gmp_int -

    -     		-

    - 1 (0.0225207s) -

    -     		-

    - 1 (0.0259628s) -

    -     		-

    - 1 (0.033859s) -

    -     		-

    - 1 (0.0479706s) -

    -
    -

    - tommath_int -

    -     		-

    - 12.4278 (0.279882s) -

    -     		-

    - 11.9045 (0.309074s) -

    -     		-

    - 10.5973 (0.358813s) -

    -     		-

    - 9.47384 (0.454466s) -

    -
    -
    -
    -

    Table 1.23. Operator /

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 2.86387 (0.593314s) -

    -     		-

    - 2.18375 (0.69965s) -

    -     		-

    - 1.72571 (0.918294s) -

    -     		-

    - 1.39251 (1.33801s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.207172s) -

    -     		-

    - 1 (0.320389s) -

    -     		-

    - 1 (0.532127s) -

    -     		-

    - 1 (0.960856s) -

    -
    -

    - gmp_int -

    -     		-

    - 3.89115 (0.806137s) -

    -     		-

    - 2.87573 (0.921352s) -

    -     		-

    - 1.96635 (1.04635s) -

    -     		-

    - 1.29618 (1.24544s) -

    -
    -

    - tommath_int -

    -     		-

    - 11.9483 (2.47535s) -

    -     		-

    - 9.35941 (2.99865s) -

    -     		-

    - 8.79014 (4.67747s) -

    -     		-

    - 11.8316 (11.3684s) -

    -
    -
    -
    -

    Table 1.24. Operator /(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 5.77003 (0.313196s) -

    -     		-

    - 4.38067 (0.431864s) -

    -     		-

    - 3.55054 (0.634559s) -

    -     		-

    - 2.97898 (1.03205s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 2.48952 (0.135131s) -

    -     		-

    - 2.59188 (0.255519s) -

    -     		-

    - 2.56716 (0.458808s) -

    -     		-

    - 2.52368 (0.874313s) -

    -
    -

    - gmp_int -

    -     		-

    - 1 (0.0542797s) -

    -     		-

    - 1 (0.0985842s) -

    -     		-

    - 1 (0.178722s) -

    -     		-

    - 1 (0.346443s) -

    -
    -

    - tommath_int -

    -     		-

    - 31.6477 (1.71783s) -

    -     		-

    - 22.8727 (2.25489s) -

    -     		-

    - 19.9248 (3.56101s) -

    -     		-

    - 24.3266 (8.42779s) -

    -
    -
    -
    -

    Table 1.25. Operator %

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.9813 (0.357541s) -

    -     		-

    - 1.55667 (0.460146s) -

    -     		-

    - 1.35341 (0.681144s) -

    -     		-

    - 1.19906 (1.10138s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.180457s) -

    -     		-

    - 1 (0.295597s) -

    -     		-

    - 1 (0.503278s) -

    -     		-

    - 1 (0.918538s) -

    -
    -

    - gmp_int -

    -     		-

    - 3.50213 (0.631985s) -

    -     		-

    - 2.33312 (0.689662s) -

    -     		-

    - 1.57264 (0.791475s) -

    -     		-

    - 1.07795 (0.99014s) -

    -
    -

    - tommath_int -

    -     		-

    - 12.2393 (2.20868s) -

    -     		-

    - 10.1123 (2.98915s) -

    -     		-

    - 9.46676 (4.76442s) -

    -     		-

    - 12.1795 (11.1873s) -

    -
    -
    -
    -

    Table 1.26. Operator %(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.88485 (0.105552s) -

    -     		-

    - 2.00194 (0.203711s) -

    -     		-

    - 2.08202 (0.380096s) -

    -     		-

    - 2.12794 (0.752068s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1.7474 (0.0978544s) -

    -     		-

    - 1.88457 (0.191768s) -

    -     		-

    - 2.0306 (0.37071s) -

    -     		-

    - 2.0851 (0.736929s) -

    -
    -

    - gmp_int -

    -     		-

    - 1 (0.0560001s) -

    -     		-

    - 1 (0.101757s) -

    -     		-

    - 1 (0.182561s) -

    -     		-

    - 1 (0.353426s) -

    -
    -

    - tommath_int -

    -     		-

    - 30.4466 (1.70501s) -

    -     		-

    - 22.2997 (2.26915s) -

    -     		-

    - 19.6199 (3.58184s) -

    -     		-

    - 24.0694 (8.50676s) -

    -
    -
    -
    -

    Table 1.27. Operator <<

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.20362 (0.0224696s) -

    -     		-

    - 1.08555 (0.0294403s) -

    -     		-

    - 1 (0.0360516s) -

    -     		-

    - 1.07177 (0.0523935s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0186683s) -

    -     		-

    - 1 (0.0271201s) -

    -     		-

    - 1.02126 (0.036818s) -

    -     		-

    - 1 (0.0488848s) -

    -
    -

    - gmp_int -

    -     		-

    - 1.36706 (0.0255207s) -

    -     		-

    - 1.12042 (0.0303858s) -

    -     		-

    - 1.24359 (0.0448335s) -

    -     		-

    - 1.40143 (0.0685085s) -

    -
    -

    - tommath_int -

    -     		-

    - 2.09357 (0.0390833s) -

    -     		-

    - 2.4569 (0.0666312s) -

    -     		-

    - 2.63592 (0.0950291s) -

    -     		-

    - 3.43638 (0.167987s) -

    -
    -
    -
    -

    Table 1.28. Operator >>

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.33649 (0.0210319s) -

    -     		-

    - 1.12919 (0.0266135s) -

    -     		-

    - 1.10413 (0.0307184s) -

    -     		-

    - 1.09267 (0.0399373s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0157367s) -

    -     		-

    - 1 (0.0235686s) -

    -     		-

    - 1 (0.0278214s) -

    -     		-

    - 1.05198 (0.0384501s) -

    -
    -

    - gmp_int -

    -     		-

    - 1.72135 (0.0270884s) -

    -     		-

    - 1.2078 (0.0284661s) -

    -     		-

    - 1.16066 (0.0322912s) -

    -     		-

    - 1 (0.0365503s) -

    -
    -

    - tommath_int -

    -     		-

    - 15.4381 (0.242945s) -

    -     		-

    - 11.8797 (0.279987s) -

    -     		-

    - 10.9043 (0.303374s) -

    -     		-

    - 14.0762 (0.514491s) -

    -
    -
    -
    -

    Table 1.29. Operator &

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.65829 (0.0314059s) -

    -     		-

    - 1.42198 (0.0390384s) -

    -     		-

    - 1.48578 (0.0498903s) -

    -     		-

    - 1.51243 (0.0770342s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0189387s) -

    -     		-

    - 1 (0.0274536s) -

    -     		-

    - 1 (0.0335786s) -

    -     		-

    - 1 (0.0509341s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.80248 (0.0530755s) -

    -     		-

    - 2.39752 (0.0658206s) -

    -     		-

    - 2.66009 (0.089322s) -

    -     		-

    - 2.73942 (0.13953s) -

    -
    -

    - tommath_int -

    -     		-

    - 6.95432 (0.131706s) -

    -     		-

    - 5.4059 (0.148412s) -

    -     		-

    - 4.56887 (0.153417s) -

    -     		-

    - 6.5696 (0.334616s) -

    -
    -
    -
    -

    Table 1.30. Operator &(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.63285 (0.0472296s) -

    -     		-

    - 1.43344 (0.0588492s) -

    -     		-

    - 1.33141 (0.0724386s) -

    -     		-

    - 1.21353 (0.104144s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0289247s) -

    -     		-

    - 1 (0.0410546s) -

    -     		-

    - 1 (0.0544075s) -

    -     		-

    - 1 (0.0858187s) -

    -
    -

    - gmp_int -

    -     		-

    - 5.24478 (0.151704s) -

    -     		-

    - 3.81907 (0.15679s) -

    -     		-

    - 2.77979 (0.151242s) -

    -     		-

    - 1.84209 (0.158086s) -

    -
    -

    - tommath_int -

    -     		-

    - 11.7257 (0.339163s) -

    -     		-

    - 8.6379 (0.354625s) -

    -     		-

    - 6.90411 (0.375636s) -

    -     		-

    - 7.63253 (0.655013s) -

    -
    -
    -
    -

    Table 1.31. Operator ^

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.39325 (0.0297525s) -

    -     		-

    - 1.28821 (0.0385005s) -

    -     		-

    - 1.18843 (0.0492426s) -

    -     		-

    - 1.07724 (0.0758668s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0213547s) -

    -     		-

    - 1 (0.0298868s) -

    -     		-

    - 1 (0.041435s) -

    -     		-

    - 1 (0.070427s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.28582 (0.048813s) -

    -     		-

    - 2.03478 (0.0608129s) -

    -     		-

    - 2.05655 (0.0852131s) -

    -     		-

    - 1.92381 (0.135488s) -

    -
    -

    - tommath_int -

    -     		-

    - 6.17078 (0.131775s) -

    -     		-

    - 4.8567 (0.145151s) -

    -     		-

    - 3.64659 (0.151097s) -

    -     		-

    - 4.78192 (0.336776s) -

    -
    -
    -
    -

    Table 1.32. Operator ^(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.89396 (0.0383127s) -

    -     		-

    - 1.64269 (0.043417s) -

    -     		-

    - 1.5386 (0.0477162s) -

    -     		-

    - 1.32247 (0.0568053s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0202288s) -

    -     		-

    - 1 (0.0264305s) -

    -     		-

    - 1 (0.0310128s) -

    -     		-

    - 1 (0.0429539s) -

    -
    -

    - gmp_int -

    -     		-

    - 7.01953 (0.141997s) -

    -     		-

    - 5.47513 (0.14471s) -

    -     		-

    - 4.6627 (0.144603s) -

    -     		-

    - 3.59601 (0.154463s) -

    -
    -

    - tommath_int -

    -     		-

    - 16.2706 (0.329134s) -

    -     		-

    - 12.9494 (0.342258s) -

    -     		-

    - 11.3305 (0.35139s) -

    -     		-

    - 14.1712 (0.608709s) -

    -
    -
    -
    -

    Table 1.33. Operator |

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.34742 (0.0296944s) -

    -     		-

    - 1.25923 (0.0384846s) -

    -     		-

    - 1.20517 (0.0493908s) -

    -     		-

    - 1.10536 (0.0761343s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0220379s) -

    -     		-

    - 1 (0.030562s) -

    -     		-

    - 1 (0.0409823s) -

    -     		-

    - 1 (0.0688775s) -

    -
    -

    - gmp_int -

    -     		-

    - 2.14429 (0.0472558s) -

    -     		-

    - 1.95901 (0.0598712s) -

    -     		-

    - 2.07584 (0.0850728s) -

    -     		-

    - 1.94265 (0.133805s) -

    -
    -

    - tommath_int -

    -     		-

    - 5.98286 (0.13185s) -

    -     		-

    - 4.65705 (0.142329s) -

    -     		-

    - 3.85812 (0.158115s) -

    -     		-

    - 4.81524 (0.331662s) -

    -
    -
    -
    -

    Table 1.34. Operator |(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.40808 (0.0389721s) -

    -     		-

    - 1.65035 (0.0437872s) -

    -     		-

    - 1.51667 (0.0466144s) -

    -     		-

    - 1.37806 (0.0582842s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.0276775s) -

    -     		-

    - 1 (0.026532s) -

    -     		-

    - 1 (0.0307348s) -

    -     		-

    - 1 (0.0422945s) -

    -
    -

    - gmp_int -

    -     		-

    - 5.31451 (0.147092s) -

    -     		-

    - 5.37333 (0.142565s) -

    -     		-

    - 4.86508 (0.149527s) -

    -     		-

    - 3.74364 (0.158335s) -

    -
    -

    - tommath_int -

    -     		-

    - 11.9312 (0.330226s) -

    -     		-

    - 12.943 (0.343403s) -

    -     		-

    - 11.4457 (0.35178s) -

    -     		-

    - 14.4462 (0.610997s) -

    -
    -
    -
    -

    Table 1.35. Operator gcd

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.82514 (4.45586s) -

    -     		-

    - 1.75955 (10.1748s) -

    -     		-

    - 1.87025 (25.23s) -

    -     		-

    - 2.11453 (68.8556s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1.57965 (3.85654s) -

    -     		-

    - 1.67404 (9.68027s) -

    -     		-

    - 1.8405 (24.8287s) -

    -     		-

    - 2.27588 (74.1096s) -

    -
    -

    - gmp_int -

    -     		-

    - 1 (2.44138s) -

    -     		-

    - 1 (5.78259s) -

    -     		-

    - 1 (13.4902s) -

    -     		-

    - 1 (32.5631s) -

    -
    -

    - tommath_int -

    -     		-

    - 5.01357 (12.24s) -

    -     		-

    - 4.38161 (25.337s) -

    -     		-

    - 4.08681 (55.1319s) -

    -     		-

    - 4.01045 (130.593s) -

    -
    -
    -
    -

    Table 1.36. Operator str

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_int -

    -     		-

    - 1.46421 (0.00195137s) -

    -     		-

    - 1.21669 (0.00319216s) -

    -     		-

    - 1.25041 (0.00765237s) -

    -     		-

    - 1.53339 (0.0218096s) -

    -
    -

    - cpp_int(fixed) -

    -     		-

    - 1 (0.00133271s) -

    -     		-

    - 1 (0.00262366s) -

    -     		-

    - 1.0109 (0.00618661s) -

    -     		-

    - 1.24429 (0.0176978s) -

    -
    -

    - gmp_int -

    -     		-

    - 1.7777 (0.00236916s) -

    -     		-

    - 1.27408 (0.00334274s) -

    -     		-

    - 1 (0.00611991s) -

    -     		-

    - 1 (0.0142232s) -

    -
    -

    - tommath_int -

    -     		-

    - 11.9797 (0.0159654s) -

    -     		-

    - 18.3349 (0.0481046s) -

    -     		-

    - 18.3681 (0.112411s) -

    -     		-

    - 25.0355 (0.356085s) -

    -
    -
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/perf/rational_performance.html b/doc/html/boost_multiprecision/perf/rational_performance.html deleted file mode 100644 index 6736d065..00000000 --- a/doc/html/boost_multiprecision/perf/rational_performance.html +++ /dev/null @@ -1,905 +0,0 @@ - - - -Rational Type Perfomance - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - Note that these tests are carefully designed to test performance of the underlying - algorithms and not memory allocation or variable copying. As usual, performance - results should be taken with a healthy dose of scepticism, and real-world - performance may vary widely depending upon the specifics of the program. - In each table relative times are given first, with the best performer given - a score of 1. Total actual times are given in brackets, measured in seconds - for 500000 operations. -

    -

    - Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. - The tests were run on 32-bit Windows Vista machine. -

    -
    -

    Table 1.37. Operator +

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 5.91758 (18.1263s) -

    -     		-

    - 6.60754 (44.1182s) -

    -     		-

    - 6.65334 (103.169s) -

    -     		-

    - 6.44717 (244.055s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (3.06312s) -

    -     		-

    - 1 (6.67695s) -

    -     		-

    - 1 (15.5064s) -

    -     		-

    - 1 (37.8546s) -

    -
    -
    -
    -

    Table 1.38. Operator +(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 3.98512 (2.67249s) -

    -     		-

    - 4.24335 (3.04309s) -

    -     		-

    - 4.65009 (3.83046s) -

    -     		-

    - 5.45832 (5.08346s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (0.670618s) -

    -     		-

    - 1 (0.717144s) -

    -     		-

    - 1 (0.823739s) -

    -     		-

    - 1 (0.931322s) -

    -
    -
    -
    -

    Table 1.39. Operator -

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 5.91504 (18.2374s) -

    -     		-

    - 6.55676 (43.8659s) -

    -     		-

    - 6.66239 (103.481s) -

    -     		-

    - 6.47224 (244.887s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (3.08322s) -

    -     		-

    - 1 (6.69018s) -

    -     		-

    - 1 (15.5321s) -

    -     		-

    - 1 (37.8365s) -

    -
    -
    -
    -

    Table 1.40. Operator -(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 3.96173 (2.66785s) -

    -     		-

    - 4.36532 (3.09023s) -

    -     		-

    - 4.59363 (3.74494s) -

    -     		-

    - 5.43075 (5.09156s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (0.673405s) -

    -     		-

    - 1 (0.707904s) -

    -     		-

    - 1 (0.815246s) -

    -     		-

    - 1 (0.937541s) -

    -
    -
    -
    -

    Table 1.41. Operator *

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 5.59286 (32.3559s) -

    -     		-

    - 6.54125 (82.4247s) -

    -     		-

    - 6.8815 (197.198s) -

    -     		-

    - 6.84066 (473.057s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (5.78521s) -

    -     		-

    - 1 (12.6008s) -

    -     		-

    - 1 (28.6562s) -

    -     		-

    - 1 (69.1537s) -

    -
    -
    -
    -

    Table 1.42. Operator *(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 2.70193 (3.1466s) -

    -     		-

    - 3.10134 (3.79056s) -

    -     		-

    - 3.659 (4.93935s) -

    -     		-

    - 4.61372 (6.89845s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (1.16457s) -

    -     		-

    - 1 (1.22223s) -

    -     		-

    - 1 (1.34992s) -

    -     		-

    - 1 (1.4952s) -

    -
    -
    -
    -

    Table 1.43. Operator /

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 4.36846 (63.9498s) -

    -     		-

    - 5.52565 (145.045s) -

    -     		-

    - 6.18331 (328.069s) -

    -     		-

    - 6.49822 (784.806s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (14.639s) -

    -     		-

    - 1 (26.2494s) -

    -     		-

    - 1 (53.0571s) -

    -     		-

    - 1 (120.772s) -

    -
    -
    -
    -

    Table 1.44. Operator /(int)

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 2.26643 (3.13785s) -

    -     		-

    - 2.57125 (3.76931s) -

    -     		-

    - 3.20872 (5.06758s) -

    -     		-

    - 4.02177 (7.17803s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (1.38449s) -

    -     		-

    - 1 (1.46594s) -

    -     		-

    - 1 (1.57931s) -

    -     		-

    - 1 (1.78479s) -

    -
    -
    -
    -

    Table 1.45. Operator str

    -
    ------- - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend -

    -     		-

    - 128 Bits -

    -     		-

    - 256 Bits -

    -     		-

    - 512 Bits -

    -     		-

    - 1024 Bits -

    -
    -

    - cpp_rational -

    -     		-

    - 5.40493 (0.0199393s) -

    -     		-

    - 8.55089 (0.0511907s) -

    -     		-

    - 9.91026 (0.118839s) -

    -     		-

    - 9.93546 (0.285367s) -

    -
    -

    - mpq_rational -

    -     		-

    - 1 (0.00368909s) -

    -     		-

    - 1 (0.00598659s) -

    -     		-

    - 1 (0.0119915s) -

    -     		-

    - 1 (0.028722s) -

    -
    -
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html deleted file mode 100644 index 4dd0d5ef..00000000 --- a/doc/html/boost_multiprecision/perf/realworld.html +++ /dev/null @@ -1,278 +0,0 @@ - - - -Floating Point Real World Tests - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - These tests test the total time taken to execute all of Boost.Math's test - cases for these functions. In each case the best performing library gets - a relative score of 1, with the total execution time given in brackets. The - first three libraries listed are the various floating point types provided - by this library, while for comparison, two popular C++ front-ends to MPFR ( mpfr_class - and mpreal) are - also shown. -

    -

    - Test code was compiled with Microsoft Visual Studio 2010 with all optimisations - turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. - The tests were run on 32-bit Windows Vista machine. -

    -
    -

    Table 1.6. Bessel Function Performance

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Library -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -
    -

    - mpfr_float -

    -     		-

    - 1.0 (6.472s) -

    -     		-

    - 1.193 (10.154s) -

    -
    -

    - mpf_float -

    -     		-

    - 1.801 (11.662s) -

    -     		-

    - 1.0(8.511s) -

    -
    -

    - cpp_dec_float -

    -     		-

    - 3.13 (20.285s) -

    -     		-

    - 2.46 (21.019s) -

    -
    -

    - mpfr_class -

    -     		-

    - 1.001 (6.480s) -

    -     		-

    - 1.15(9.805s) -

    -
    -

    - mpreal -

    -     		-

    - 1.542 (9.981s) -

    -     		-

    - 1.61 (13.702s) -

    -
    -
    -
    -

    Table 1.7. Non-Central T Distribution Performance

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Library -

    -     		-

    - 50 Decimal Digits -

    -     		-

    - 100 Decimal Digits -

    -
    -

    - mpfr_float -

    -     		-

    - 1.308 (258.09s) -

    -     		-

    - 1.30 (516.74s) -

    -
    -

    - mpf_float -

    -     		-

    - 1.0 (197.30s) -

    -     		-

    - 1.0(397.30s) -

    -
    -

    - cpp_dec_float -

    -     		-

    - 1.695 (334.50s) -

    -     		-

    - 2.68 (1064.53s) -

    -
    -

    - mpfr_class -

    -     		-

    - 1.35 (266.39s) -

    -     		-

    - 1.323 (525.74s) -

    -
    -

    - mpreal -

    -     		-

    - 1.75 (346.64s) -

    -     		-

    - 1.635 (649.94s) -

    -
    -
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html deleted file mode 100644 index 35ad59f4..00000000 --- a/doc/html/boost_multiprecision/ref.html +++ /dev/null @@ -1,44 +0,0 @@ - - - -Reference - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    -
    mp_number
    -
    cpp_int
    -
    gmp_int
    -
    tom_int
    -
    gmp_float
    -
    mpfr_float_backend
    -
    cpp_dec_float
    -
    Backend Requirements
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html deleted file mode 100644 index 3bf6b60f..00000000 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ /dev/null @@ -1,2295 +0,0 @@ - - - -Backend Requirements - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - The requirements on the Backend - template argument to mp_number - are split up into compulsory requirements, and optional requirements that - are either to improve performance or provide optional features. -

    -

    - In the following tables, type B is the Backend - template arument to mp_number, - b and b2 - are a variables of type B, cb - and cb2 are constant variables - of type B, a is a variable - of Arithmetic type, s is - a variable of type const char*, ui - is a variable of type unsigned, - bb is a variable of type - bool, pa - is a variable of type pointer-to-arithmetic-type, exp - is a variable of type B::exp_type, pexp - is a variable of type B::exp_type*, - B2 is another type that meets these requirements, b2 is a variable of type - B2. -

    -
    -

    Table 1.4. Compulsory Requirements on the Backend type.

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Expression -

    -     		-

    - Return Type -

    -     		-

    - Comments -

    -
    -

    - B::signed_types -

    -     		-

    - mpl::list<type-list> -

    -     		-

    - A list of signed integral types that can be assigned to type B. - The types shall be listed in order of size, smallest first, and - shall terminate in the type that is std::intmax_t. -

    -
    -

    - B::unsigned_types -

    -     		-

    - mpl::list<type-list> -

    -     		-

    - A list of unsigned integral types that can be assigned to type - B. The types shall be listed in order of size, smallest first, - and shall terminate in the type that is std::uintmax_t. -

    -
    -

    - B::float_types -

    -     		-

    - mpl::list<type-list> -

    -     		-

    - A list of floating-point types that can be assigned to type B.The - types shall be listed in order of size, smallest first, and shall - terminate in type long double. -

    -
    -

    - B::exponent_type -

    -     		-

    - A signed integral type. -

    -     		-

    - The type of the exponent of type B. -

    -
    -

    - B() -

    -     		- -

    - Default constructor. -

    -
    -

    - B(cb) -

    -     		- -

    - Copy Constructor. -

    -
    -

    - b = - b -

    -     		-

    - B& -

    -     		-

    - Assignment operator. -

    -
    -

    - b = - a -

    -     		-

    - B& -

    -     		-

    - Assignment from an Arithmetic type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - b = - s -

    -     		-

    - B& -

    -     		-

    - Assignment from a string. -

    -
    -

    - b.swap(b) -

    -     		-

    - void -

    -     		-

    - Swaps the contents of its arguments. -

    -
    -

    - cb.str(ui, - bb) -

    -     		-

    - std::string -

    -     		-

    - Returns the string representation of b - with ui digits - and in scientific format if bb - is true. If ui is zero, then returns as many - digits as are required to reconstruct the original value. -

    -
    -

    - b.negate() -

    -     		-

    - void -

    -     		-

    - Negates b. -

    -
    -

    - cb.compare(cb2) -

    -     		-

    - int -

    -     		-

    - Compares cb and - cb2, returns a - value less than zero if cb - < cb2, - a value greater than zero if cb - > cb2 - and zero if cb == cb2. -

    -
    -

    - cb.compare(a) -

    -     		-

    - int -

    -     		-

    - Compares cb and - a, returns a value - less than zero if cb - < a, - a value greater than zero if cb - > a - and zero if cb == a. - The type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_add(b, - cb) -

    -     		-

    - void -

    -     		-

    - Adds cb to b. -

    -
    -

    - eval_subtract(b, - cb) -

    -     		-

    - void -

    -     		-

    - Subtracts cb from - b. -

    -
    -

    - eval_multiply(b, - cb) -

    -     		-

    - void -

    -     		-

    - Multiplies b by - cb. -

    -
    -

    - eval_divide(b, - cb) -

    -     		-

    - void -

    -     		-

    - Divides b by cb. -

    -
    -

    - eval_modulus(b, - cb) -

    -     		-

    - void -

    -     		-

    - Computes b %= - cb, only required when - B is an integer - type. -

    -
    -

    - eval_bitwise_and(b, cb) -

    -     		-

    - void -

    -     		-

    - Computes b &= - cb, only required when - B is an integer - type. -

    -
    -

    - eval_bitwise_or(b, cb) -

    -     		-

    - void -

    -     		-

    - Computes b |= - cb, only required when - B is an integer - type. -

    -
    -

    - eval_bitwise_xor(b, cb) -

    -     		-

    - void -

    -     		-

    - Computes b ^= - cb, only required when - B is an integer - type. -

    -
    -

    - eval_complement(b, cb) -

    -     		-

    - void -

    -     		-

    - Computes the ones-complement of cb - and stores the result in b, - only required when B - is an integer type. -

    -
    -

    - eval_left_shift(b, ui) -

    -     		-

    - void -

    -     		-

    - Computes b <<= - ui, only required when - B is an integer - type. -

    -
    -

    - eval_right_shift(b, ui) -

    -     		-

    - void -

    -     		-

    - Computes b >>= - ui, only required when - B is an integer - type. -

    -
    -

    - eval_convert_to(pa, cb) -

    -     		-

    - void -

    -     		-

    - Converts cb to - the type of *pa - and store the result in *pa. Type B - shall support conversion to at least types std::intmax_t, - std::uintmax_t and long - long. Conversion to other - arithmetic types can then be synthesised using other operations. - Conversions to other types are entirely optional. -

    -
    -

    - eval_frexp(b, - cb, - pexp) -

    -     		-

    - void -

    -     		-

    - Stores values in b - and *pexp - such that the value of cb - is b * 2*pexp, only required when B - is a floating-point type. -

    -
    -

    - eval_ldexp(b, - cb, - exp) -

    -     		-

    - void -

    -     		-

    - Stores a value in b - that is cb * 2exp, only required when B - is a floating-point type. -

    -
    -

    - eval_floor(b, - cb) -

    -     		-

    - void -

    -     		-

    - Stores the floor of cb - in b, only required - when B is a floating-point - type. -

    -
    -

    - eval_ceil(b, - cb) -

    -     		-

    - void -

    -     		-

    - Stores the ceiling of cb - in b, only required - when B is a floating-point - type. -

    -
    -

    - eval_sqrt(b, - cb) -

    -     		-

    - void -

    -     		-

    - Stores the square root of cb - in b, only required - when B is a floating-point - type. -

    -
    -

    - boost::multiprecision::number_category<B>::type -

    -     		-

    - mpl::int_<N> -

    -     		-

    - N is one of the - values number_kind_integer, - number_kind_floating_point, - number_kind_rational - or number_kind_fixed_point. - Defaults to number_kind_floating_point. -

    -
    -
    -
    -

    Table 1.5. Optional Requirements on the Backend Type

    -
    ----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Expression -

    -     		-

    - Returns -

    -     		-

    - Comments -

    -
    -

    - B(b2) -

    -     		-

    - B -

    -     		-

    - Copy constructor from a different back-end type. -

    -
    -

    - b = - b2 -

    -     		-

    - b& -

    -     		-

    - Assignment operator from a different back-end type. -

    -
    -

    - assign_components(b, a, a) -

    -     		-

    - void -

    -     		-

    - Assigns to b the - two components in the following arguments. Only applies to rational - and complex number types. -

    -
    -

    - assign_components(b, b2, b2) -

    -     		-

    - void -

    -     		-

    - Assigns to b the - two components in the following arguments. Only applies to rational - and complex number types. -

    -
    -

    - eval_add(b, - a) -

    -     		-

    - void -

    -     		-

    - Adds a to b. The type of a shall be listed in one of the - type lists B::signed_types, B::unsigned_types - or B::float_types. -

    -
    -

    - eval_subtract(b, - a) -

    -     		-

    - void -

    -     		-

    - Subtracts a from - b. The type of - a shall be listed - in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_multiply(b, - a) -

    -     		-

    - void -

    -     		-

    - Multiplies b by - a. The type of - a shall be listed - in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_divide(b, - a) -

    -     		-

    - void -

    -     		-

    - Divides b by a. The type of a shall be listed in one of the - type lists B::signed_types, B::unsigned_types - or B::float_types. -

    -
    -

    - eval_modulus(b, - a) -

    -     		-

    - void -

    -     		-

    - Computes b %= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_and(b, a) -

    -     		-

    - void -

    -     		-

    - Computes b &= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_or(b, a) -

    -     		-

    - void -

    -     		-

    - Computes b |= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_xor(b, a) -

    -     		-

    - void -

    -     		-

    - Computes b ^= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_add(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Add cb to cb2 and stores the result in - b. -

    -
    -

    - eval_subtract(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Subtracts cb2 from - cb and stores the - result in b. -

    -
    -

    - eval_multiply(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Multiplies cb by - cb2 and stores - the result in b. -

    -
    -

    - eval_divide(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Divides cb by - cb2 and stores - the result in b. -

    -
    -

    - eval_add(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Add cb to a and stores the result in b. The type of a shall be listed in one of the - type lists B::signed_types, B::unsigned_types - or B::float_types. -

    -
    -

    - eval_subtract(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Subtracts a from - cb and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_multiply(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Multiplies cb by - a and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_divide(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Divides cb by - a and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_modulus(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb % - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_bitwise_and(b, cb, cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb & - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_bitwise_or(b, cb, cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb | - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_bitwise_xor(b, cb, cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb ^ - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_add(b, - a, - cb) -

    -     		-

    - void -

    -     		-

    - Add a to cb and stores the result in - b. The type of - a shall be listed - in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_subtract(b, - a, - cb) -

    -     		-

    - void -

    -     		-

    - Subtracts cb from - a and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_multiply(b, - a, - cb) -

    -     		-

    - void -

    -     		-

    - Multiplies a by - cb and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_divide(b, - a, - cb) -

    -     		-

    - void -

    -     		-

    - Divides a by cb and stores the result in - b. The type of - a shall be listed - in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_modulus(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Computes cb % - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_and(b, cb, a) -

    -     		-

    - void -

    -     		-

    - Computes cb & - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_or(b, cb, a) -

    -     		-

    - void -

    -     		-

    - Computes cb | - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_xor(b, cb, a) -

    -     		-

    - void -

    -     		-

    - Computes cb ^ - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_modulus(b, - a, - cb) -

    -     		-

    - void -

    -     		-

    - Computes cb % - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_and(b, a, cb) -

    -     		-

    - void -

    -     		-

    - Computes cb & - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_or(b, a, cb) -

    -     		-

    - void -

    -     		-

    - Computes cb | - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_xor(b, a, cb) -

    -     		-

    - void -

    -     		-

    - Computes a ^ - cb and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_left_shift(b, cb, ui) -

    -     		-

    - void -

    -     		-

    - Computes cb << - ui and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_right_shift(b, cb, ui) -

    -     		-

    - void -

    -     		-

    - Computes cb >> - ui and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_increment(b) -

    -     		-

    - void -

    -     		-

    - Increments the value of b - by one. -

    -
    -

    - eval_decrement(b) -

    -     		-

    - void -

    -     		-

    - Decrements the value of b - by one. -

    -
    -

    - eval_is_zero(cb) -

    -     		-

    - bool -

    -     		-

    - Returns true if cb is zero, otherwise false -

    -
    -

    - eval_get_sign(cb) -

    -     		-

    - int -

    -     		-

    - Returns a value < zero if cb - is negative, a value > zero if cb - is positive, and zero if cb - is zero. -

    -
    -

    - eval_abs(b, - cb) -

    -     		-

    - void -

    -     		-

    - Set b to the absolute - value of cb. -

    -
    -

    - eval_fabs(b, - cb) -

    -     		-

    - void -

    -     		-

    - Set b to the absolute - value of cb. -

    -
    -

    - eval_fpclassify(cb) -

    -     		-

    - int -

    -     		-

    - Returns one of the same values returned by std::fpclassify. - Only required when B - is an floating-point type. -

    -
    -

    - eval_trunc(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::trunc - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_round(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::round - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_exp(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::exp - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_log(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::log - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_log10(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::log10 - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_sin(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::sin - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_cos(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::cos - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_tan(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::exp - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_asin(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::asin - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_acos(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::acos - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_atan(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::atan - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_sinh(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::sinh - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_cosh(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::cosh - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_tanh(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::tanh - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_fmod(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::fmod - on arguments cb - and cb2, and store - the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_pow(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::pow - on arguments cb - and cb2, and store - the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_atan2(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::atan - on arguments cb - and cb2, and store - the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_qr(cb, - cb2, - b, - b2) -

    -     		-

    - void -

    -     		-

    - Sets b to the result - of cb / - cb2 and b2 to the result of cb % - cb2. Only required when - B is an integer - type. -

    -
    -

    - eval_integer_modulus(cb, ui) -

    -     		-

    - unsigned -

    -     		-

    - Returns the result of cb - % ui. - Only required when B - is an integer type. -

    -
    -

    - eval_lsb(cb) -

    -     		-

    - unsigned -

    -     		-

    - Returns the index of the least significant bit that is set. Only - required when B - is an integer type. -

    -
    -

    - eval_bit_test(cb, - ui) -

    -     		-

    - bool -

    -     		-

    - Returns true if cb - has bit ui set. - Only required when B - is an integer type. -

    -
    -

    - eval_bit_set(b, - ui) -

    -     		-

    - void -

    -     		-

    - Sets the bit at index ui - in b. Only required - when B is an integer - type. -

    -
    -

    - eval_bit_unset(b, ui) -

    -     		-

    - void -

    -     		-

    - Unsets the bit at index ui - in b. Only required - when B is an integer - type. -

    -
    -

    - eval_bit_flip(b, - ui) -

    -     		-

    - void -

    -     		-

    - Flips the bit at index ui - in b. Only required - when B is an integer - type. -

    -
    -

    - eval_gcd(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Sets b to the greatest - common divisor of cb - and cb2. Only required - when B is an integer - type. -

    -
    -

    - eval_lcm(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Sets b to the least - common multiple of cb - and cb2. Only required - when B is an integer - type. -

    -
    -
    -
    - - - - - -
    [Note]Note

    - The non-member functions are all named with an "eval_" prefix - to avoid conflicts with template classes of the same name - in point of - fact this naming convention shouldn't be necessary, but rather works around - some compiler bugs. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html deleted file mode 100644 index 9d34b1e6..00000000 --- a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html +++ /dev/null @@ -1,61 +0,0 @@ - - - -cpp_dec_float - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    namespace boost{ namespace multiprecision{
-
-template <unsigned Digits10>
-class cpp_dec_float;
-
-typedef mp_number<cpp_dec_float<50> > cpp_dec_float_50;
-typedef mp_number<cpp_dec_float<100> > cpp_dec_float_100;
-
-}} // namespaces
-
    -

    - Class template cpp_dec_float - fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: - these are considered implementation details that are subject to change. -

    -

    - The class takes a single template parameter - Digits10 - - which is the number of decimal digits precision the type should support. - Note that this type does not ever perform any dynamic memory allocation, - as a result the Digits10 - template argument should not be set too high or the classes size will grow - unreasonably large. -

    -

    - More information on this type can be found in the tutorial. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html deleted file mode 100644 index 40530e86..00000000 --- a/doc/html/boost_multiprecision/ref/cpp_int_ref.html +++ /dev/null @@ -1,99 +0,0 @@ - - - -cpp_int - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    namespace boost{ namespace multiprecision{
-
-template <unsigned MinBits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
-struct cpp_int_backend;
-
-typedef mp_number<cpp_int_backend<> >           cpp_int;    // arbitrary precision integer
-typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
-typedef mp_number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
-
-// Fixed precision unsigned types:
-typedef mp_number<cpp_int_backend<128, false, void>, false>   mp_uint128_t;
-typedef mp_number<cpp_int_backend<256, false, void>, false>   mp_uint256_t;
-typedef mp_number<cpp_int_backend<512, false, void>, false>   mp_uint512_t;
-typedef mp_number<cpp_int_backend<1024, false, void>, false>  mp_uint1024_t;
-
-// Fixed precision signed types:
-typedef mp_number<cpp_int_backend<128, true, void>, false>    mp_int128_t;
-typedef mp_number<cpp_int_backend<256, true, void>, false>    mp_int256_t;
-typedef mp_number<cpp_int_backend<512, true, void>, false>    mp_int512_t;
-typedef mp_number<cpp_int_backend<1024, true, void>, false>   mp_int1024_t;
-
-}} // namespaces
-
    -

    - Class template cpp_int_backend - fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: - these are considered implementation details that are subject to change. -

    -

    - The template arguments are: -

    -
    -

    -
    -
    Argument
    -

    - Meaning -

    -
    MinBits
    -

    - The number of Bits to reserve inside the class's internal cache. When - constructing a value, the object will use this internal cache if possible - before resorting to dynamic memory allocation. When this value is zero, - then the size of the internal cache is 2*sizeof(void*)*CHAR_BIT. - When the Allocator argument is void, - then this parameter determines the precision of the type. -

    -
    Signed
    -

    - When true the type is - signed, otherwise unsigned. Note that unsigned types are currently - only supported when the Allocator parameter is void. -

    -
    Allocator
    -

    - The allocator used for dynamic memory allocation. This parameter can - be void, in which case - no dymanic memory will ever be allocated. -

    -
    -
    -

    - More information on this type can be found in the tutorial. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref/gmp_int_ref.html b/doc/html/boost_multiprecision/ref/gmp_int_ref.html deleted file mode 100644 index 71dfb0ae..00000000 --- a/doc/html/boost_multiprecision/ref/gmp_int_ref.html +++ /dev/null @@ -1,51 +0,0 @@ - - - -gmp_int - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    namespace boost{ namespace multiprecision{
-
-class gmp_int;
-
-typedef mp_number<gmp_int >         mpz_int;
-
-}} // namespaces
-
    -

    - Class template gmp_int fulfills - all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: - these are considered implementation details that are subject to change. -

    -

    - More information on this type can be found in the tutorial. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html deleted file mode 100644 index b883aa18..00000000 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ /dev/null @@ -1,695 +0,0 @@ - - - -mp_number - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    - - Synopsis -
    -
    namespace boost{ namespace multiprecision{
-
-template <class Backend, bool ExpressionTemplates = true>
-class mp_number
-{
-   mp_number();
-   mp_number(see-below);
-   mp_number& operator=(see-below);
-
-   // Member operators
-   mp_number& operator+=(const see-below&);
-   mp_number& operator-=(const see-below&);
-   mp_number& operator*=(const see-below&);
-   mp_number& operator/=(const see-below&);
-   mp_number& operator++();
-   mp_number& operator--();
-   mp_number  operator++(int);
-   mp_number  operator--(int);
-
-   mp_number& operator%=(const see-below&);
-   mp_number& operator&=(const see-below&);
-   mp_number& operator|=(const see-below&);
-   mp_number& operator^=(const see-below&);
-   mp_number& operator<<=(const integer-type&);
-   mp_number& operator>>=(const integer-type&);
-
-   // Use in Boolean context:
-   operator convertible-to-bool-type()const;
-   // swap:
-   void swap(mp_number& other);
-   // Sign:
-   bool is_zero()const;
-   int sign()const;
-   // string conversion:
-   std::string str()const;
-   // Generic conversion mechanism
-   template <class T>
-   T convert_to()const;
-   // precision control:
-   static unsigned default_precision();
-   static void default_precision(unsigned digits10);
-   unsigned precision()const;
-   void precision(unsigned digits10);
-   // Comparison:
-   int compare(const mp_number<Backend>& o)const;
-   template <class V>
-   typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
-   // Access to the underlying implementation:
-   Backend& backend();
-   const Backend& backend()const;
-};
-
-// Non member operators:
-unmentionable-expression-template-type operator+(const see-below&, const see-below&);
-unmentionable-expression-template-type operator-(const see-below&, const see-below&);
-unmentionable-expression-template-type operator*(const see-below&, const see-below&);
-unmentionable-expression-template-type operator/(const see-below&, const see-below&);
-// Integer only operations:
-unmentionable-expression-template-type operator%(const see-below&, const see-below&);
-unmentionable-expression-template-type operator&(const see-below&, const see-below&);
-unmentionable-expression-template-type operator|(const see-below&, const see-below&);
-unmentionable-expression-template-type operator^(const see-below&, const see-below&);
-unmentionable-expression-template-type operator<<(const see-below&, const integer-type&);
-unmentionable-expression-template-type operator>>(const see-below&, const integer-type&);
-// Comparison operators:
-bool operator==(const see-below&, const see-below&);
-bool operator!=(const see-below&, const see-below&);
-bool operator< (const see-below&, const see-below&);
-bool operator> (const see-below&, const see-below&);
-bool operator<=(const see-below&, const see-below&);
-bool operator>=(const see-below&, const see-below&);
-
-// Swap:
-template <class Backend, bool ExpressionTemplates>
-void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
-
-// iostream support:
-template <class Backend, bool ExpressionTemplates>
-std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
-std::ostream& operator << (std::ostream& os, const unmentionable-expression-template-type& r);
-template <class Backend, bool ExpressionTemplates>
-std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r);
-
-// Non-member function standard library support:
-unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
-
-unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
-unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
-unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-
-// Traits support:
-template <class T>
-struct component_type;
-template <class T>
-struct number_category;
-
-// Integer specific functions:
-template <class Backend, bool ExpressionTemplates>
-bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
-               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
-template <class Integer>
-Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
-unsigned lsb(const mp_number-or-expression-template-type& x);
-template <class Backend, class ExpressionTemplates>
-bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-template <class Engine>
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
-
-// Rational number support:
-typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
-typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
-
-}} // namespaces
-
-namespace boost{ namespace math{
-
-// Boost.Math interoperability functions:
-int                                              fpclassify     (const mp_number-or-expression-template-type&, int);
-bool                                             isfinite       (const mp_number-or-expression-template-type&, int);
-bool                                             isnan          (const mp_number-or-expression-template-type&, int);
-bool                                             isinf          (const mp_number-or-expression-template-type&, int);
-bool                                             isnormal       (const mp_number-or-expression-template-type&, int);
-
-}} // namespaces
-
-// numeric_limits support:
-namespace std{
-
-template <class Backend, bool ExpressionTemplates>
-struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
-{
-   /* Usual members here */
-};
-
-}
-
    -
    - - Description -
    -
    template <class Backend, bool ExpressionTemplates = true>
-class mp_number;
-
    -

    - Class mp_number has two template - arguments: -

    -
    -

    -
    -
    Backend
    -

    - The actual arithmetic back-end that does all the work. -

    -
    ExpressionTemplates
    -

    - A Boolean value: when true, then expression templates are enabled, - otherwise they are disabled. -

    -
    -
    -
    mp_number();
-mp_number(see-below);
-mp_number& operator=(see-below);
-
    -

    - Type mp_number is default - constructible, and both copy constructible and assignable from: -

    -
      -
    • - Itself. -
      • -
    • - An expression template which is the result of one of the arithmetic operators. -
      • -
    • - Any builtin arithmetic type. -
      • -
    • - A std::string or any type which is convertible - to const char*. -
      • -
    • - Any type that the Backend is constructible or assignable from. -
      • -
    -

    - In addition, if the type has multiple components (for example rational or - complex number types), then there is a two argument constructor: -

    -
    mp_number(arg1, arg2);
-
    -

    - Where the two args must either be arithmetic types, or types that are convertible - to the two components of this. -

    -
    mp_number& operator+=(const see-below&);
-mp_number& operator-=(const see-below&);
-mp_number& operator*=(const see-below&);
-mp_number& operator/=(const see-below&);
-mp_number& operator++();
-mp_number& operator--();
-mp_number  operator++(int);
-mp_number  operator--(int);
-// Integer only operations:
-mp_number& operator%=(const see-below&);
-mp_number& operator&=(const see-below&);
-mp_number& operator|=(const see-below&);
-mp_number& operator^=(const see-below&);
-mp_number& operator<<=(const integer-type&);
-mp_number& operator>>=(const integer-type&);
-
    -

    - These operators all take their usual arithmetic meanings. -

    -

    - The arguments to these operators is either: -

    -
      -
    • - Another mp_number<Backend, - ExpressionTemplates>. -
      • -
    • - A builtin arithmetic type. -
      • -
    • - An expression template derived from mp_number<Backend>. -
      • -
    -

    - For the left and right shift operations, the argument must be a builtin integer - type with a positive value (negative values result in a std::runtime_error - being thrown). -

    -
    operator convertible-to-bool-type()const;
-
    -

    - Returns an unmentionable-type that is usable in Boolean - contexts (this allows mp_number - to be used in any Boolean context - if statements, conditional statements, - or as an argument to a logical operator - without type mp_number - being convertible to type bool. -

    -

    - This operator also enables the use of mp_number - with any of the following operators: !, - ||, && - and ?:. -

    -
    void swap(mp_number& other);
-
    -

    - Swaps *this - with other. -

    -
    bool is_zero()const;
-
    -

    - Returns true is *this is zero, - otherwise false. -

    -
    int sign()const;
-
    -

    - Returns a value less than zero if *this is negative, a value greater than zero - if *this - is positive, and zero if *this - is zero. -

    -
    std::string str(unsigned precision, bool scientific = true)const;
-
    -

    - Returns the number formatted as a string, with at least precision - digits, and in scientific format if scientific is true. -

    -
    template <class T>
-T convert_to()const;
-
    -

    - Provides a generic conversion mechanism to convert *this to type T. - Type T may be any arithmetic - type. Optionally other types may also be supported by specific Backend types. -

    -
    static unsigned default_precision();
-static void default_precision(unsigned digits10);
-unsigned precision()const;
-void precision(unsigned digits10);
-
    -

    - These functions are only available if the Backend template parameter supports - runtime changes to precision. They get and set the default precision and - the precision of *this - respectively. -

    -
    int compare(const mp_number<Backend, ExpressionTemplates>& o)const;
-template <class V>
-typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
-
    -

    - Returns: -

    -
      -
    • - A value less that 0 for *this < other -
      • -
    • - A value greater that 0 for *this > other -
      • -
    • - Zero for *this - == other -
      • -
    -
    Backend& backend();
-const Backend& backend()const;
-
    -

    - Returns the underlying back-end instance used by *this. -

    -
    - - Non-member - operators -
    -
    // Non member operators:
-unmentionable-expression-template-type operator+(const see-below&, const see-below&);
-unmentionable-expression-template-type operator-(const see-below&, const see-below&);
-unmentionable-expression-template-type operator*(const see-below&, const see-below&);
-unmentionable-expression-template-type operator/(const see-below&, const see-below&);
-// Integer only operations:
-unmentionable-expression-template-type operator%(const see-below&, const see-below&);
-unmentionable-expression-template-type operator&(const see-below&, const see-below&);
-unmentionable-expression-template-type operator|(const see-below&, const see-below&);
-unmentionable-expression-template-type operator^(const see-below&, const see-below&);
-unmentionable-expression-template-type operator<<(const see-below&, const integer-type&);
-unmentionable-expression-template-type operator>>(const see-below&, const integer-type&);
-// Comparison operators:
-bool operator==(const see-below&, const see-below&);
-bool operator!=(const see-below&, const see-below&);
-bool operator< (const see-below&, const see-below&);
-bool operator> (const see-below&, const see-below&);
-bool operator<=(const see-below&, const see-below&);
-bool operator>=(const see-below&, const see-below&);
-
    -

    - These operators all take their usual arithmetic meanings. -

    -

    - The arguments to these functions must contain at least one of the following: -

    -
      -
    • - An mp_number. -
      • -
    • - An expression template type derived from mp_number. -
      • -
    -

    - In addition, one of the two arguments may be a builtin arithmetic type. -

    -

    - The return type of these operators is either: -

    -
      -
    • - An unmentionable-type expression template type when - ExpressionTemplates is - true. -
      • -
    • - Type mp_number<Backend, - false> - when ExpressionTemplates - is false. -
      • -
    • - Type bool if the operator - is a comparison operator. -
      • -
    -

    - Finally note that the second argument to the left and right shift operations - must be a builtin integer type, and that the argument must be positive (negative - arguments result in a std::runtime_error - being thrown). -

    -
    - - swap -
    -
    template <class Backend, ExpressionTemplates>
-void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
-
    -

    - Swaps a and b. -

    -
    - - Iostream - Support -
    -
    template <class Backend, bool ExpressionTemplates>
-std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
-template <class Unspecified...>
-std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r);
-template <class Backend, bool ExpressionTemplates>
-inline std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r)
-
    -

    - These operators provided formatted input-output operations on mp_number types, and expression templates - derived from them. -

    -

    - It's down to the back-end type to actually implement string conversion. However, - the back-ends provided with this library support all of the iostream formatting - flags, field width and precision settings. -

    -
    - - Non-member - standard library function support -
    -
    unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
-
-unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
-unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
-unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
-
    -

    - These functions all behave exactly as their standard library counterparts - do: their argument is either an instance of mp_number - or an expression template derived from it; If the argument is of type mp_number<Backend, false> - then that is also the return type, otherwise the return type is an expression - template. -

    -

    - These functions are normally implemented by the Backend type. However, default - versions are provided for Backend types that don't have native support for - these functions. Please note however, that this default support requires - the precision of the type to be a compile time constant - this means for - example that the GMP MPF Backend will - not work with these functions when that type is used at variable precision. -

    -

    - Also note that with the exception of abs - that these functions can only be used with floating-point Backend types. -

    -
    - - Traits - Class Support -
    -
    template <class T>
-struct component_type;
-
    -

    - If this is a type with mutiple components (for example rational or complex - types), then this trait has a single member type - that is the type of those components. -

    -
    template <class T>
-struct number_category;
-
    -

    - A traits class that inherits from mpl::int_<N> - where N is one of the enumerated - values number_kind_integer, - number_kind_floating_point, - number_kind_rational or - number_kind_fixed_point. -

    -
    - - Integer functions -
    -
    template <class Backend, bool ExpressionTemplates>
-bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
-               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
-
    -

    - Divides x by y and returns both the quotient and remainder. After the call - q = - x / y and r - = x % y. -

    -
    template <class Integer>
-Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
-
    -

    - Returns the absolute value of x - % val. -

    -
    unsigned lsb(const mp_number-or-expression-template-type& x);
-
    -

    - Returns the index of the least significant bit that is set to 1. -

    -
    template <class Backend, class ExpressionTemplates>
-bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-
    -

    - Returns true if the bit at - index in val is set. -

    -
    template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-
    -

    - Sets the bit at index in val, and - returns val. -

    -
    template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-
    -

    - Unsets the bit at index in val, - and returns val. -

    -
    template <class Backend, class ExpressionTemplates>
-mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
-
    -

    - Flips the bit at index in val, - and returns val. -

    -
    template <class Engine>
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
-bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
-
    -

    - Tests to see if the number n is probably prime - the - test excludes the vast majority of composite numbers by excluding small prime - factors and performing a single Fermat test. Then performs trials - Miller-Rabin tests. Returns false - if n is definitely composite, or true - if n is probably prime with the probability of it being - composite less than 0.25^trials. -

    -
    - - Rational - Number Functions -
    -
    typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
-typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
-
    -

    - These functions return the numerator and denominator of a rational number - respectively. -

    -
    - - Boost.Math - Interoperability Support -
    -
    namespace boost{ namespace math{
-
-int  fpclassify     (const mp_number-or-expression-template-type&, int);
-bool isfinite       (const mp_number-or-expression-template-type&, int);
-bool isnan          (const mp_number-or-expression-template-type&, int);
-bool isinf          (const mp_number-or-expression-template-type&, int);
-bool isnormal       (const mp_number-or-expression-template-type&, int);
-
-}} // namespaces
-
    -

    - These floating-point classification functions behave exactly as their Boost.Math - equivalents. -

    -

    - Other Boost.Math functions and templates may also be specialized or overloaded - to ensure interoperability. -

    -
    - - std::numeric_limits - support -
    -
    namespace std{
-
-template <class Backend, ExpressionTemplates>
-struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
-{
-   /* Usual members here */
-};
-
-}
-
    -

    - Class template std::numeric_limits is specialized for all instantiations - of mp_number whose precision - is known at compile time, plus those types whose precision is unlimited (though - it is much less useful in those cases). It is not specialized for types whose - precision can vary at compile time (such as mpf_float). -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref/mpf_ref.html b/doc/html/boost_multiprecision/ref/mpf_ref.html deleted file mode 100644 index fd2d8f50..00000000 --- a/doc/html/boost_multiprecision/ref/mpf_ref.html +++ /dev/null @@ -1,67 +0,0 @@ - - - -gmp_float - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    namespace boost{ namespace multiprecision{
-
-template <unsigned Digits10>
-class gmp_float;
-
-typedef mp_number<gmp_float<50> >    mpf_float_50;
-typedef mp_number<gmp_float<100> >   mpf_float_100;
-typedef mp_number<gmp_float<500> >   mpf_float_500;
-typedef mp_number<gmp_float<1000> >  mpf_float_1000;
-typedef mp_number<gmp_float<0> >     mpf_float;
-
-}} // namespaces
-
    -

    - Class template gmp_float - fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: - these are considered implementation details that are subject to change. -

    -

    - The class takes a single template parameter - Digits10 - - which is the number of decimal digits precision the type should support. - When this parameter is zero, then the precision can be set at runtime via - mp_number::default_precision and mp_number::precision. - Note that this type does not in any way change the GMP library's global state - (for example it does not change the default precision of the mpf_t data type), - therefore you can safely mix this type with existing code that uses GMP, - and also mix gmp_floats of - differing precision. -

    -

    - More information on this type can be found in the tutorial. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref/mpfr_ref.html b/doc/html/boost_multiprecision/ref/mpfr_ref.html deleted file mode 100644 index 7588f301..00000000 --- a/doc/html/boost_multiprecision/ref/mpfr_ref.html +++ /dev/null @@ -1,67 +0,0 @@ - - - -mpfr_float_backend - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    namespace boost{ namespace multiprecision{
-
-template <unsigned Digits10>
-class mpfr_float_backend;
-
-typedef mp_number<mpfr_float_backend<50> >    mpfr_float_50;
-typedef mp_number<mpfr_float_backend<100> >   mpfr_float_100;
-typedef mp_number<mpfr_float_backend<500> >   mpfr_float_500;
-typedef mp_number<mpfr_float_backend<1000> >  mpfr_float_1000;
-typedef mp_number<mpfr_float_backend<0> >     mpfr_float;
-
-}} // namespaces
-
    -

    - Class template mpfr_float_backend - fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: - these are considered implementation details that are subject to change. -

    -

    - The class takes a single template parameter - Digits10 - - which is the number of decimal digits precision the type should support. - When this parameter is zero, then the precision can be set at runtime via - mp_number::default_precision and mp_number::precision. - Note that this type does not in any way change the GMP or MPFR library's - global state (for example it does not change the default precision of the - mpfr_t data type), therefore you can safely mix this type with existing code - that uses GMP or MPFR, and also mix mpfr_float_backends - of differing precision. -

    -

    - More information on this type can be found in the tutorial. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/ref/tom_int_ref.html b/doc/html/boost_multiprecision/ref/tom_int_ref.html deleted file mode 100644 index 95abdcbe..00000000 --- a/doc/html/boost_multiprecision/ref/tom_int_ref.html +++ /dev/null @@ -1,51 +0,0 @@ - - - -tom_int - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    namespace boost{ namespace multiprecision{
-
-class tommath_int;
-
-typedef mp_number<tommath_int >         tom_int;
-
-}} // namespaces
-
    -

    - Class template tommath_int - fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: - these are considered implementation details that are subject to change. -

    -

    - More information on this type can be found in the tutorial. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html deleted file mode 100644 index 38896477..00000000 --- a/doc/html/boost_multiprecision/tut.html +++ /dev/null @@ -1,75 +0,0 @@ - - - -Tutorial - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    -
    Integer Types
    -
    -
    cpp_int
    -
    gmp_int
    -
    tom_int
    -
    -
    Floating Point Numbers
    -
    -
    gmp_float
    -
    mpfr_float
    -
    cpp_dec_float
    -
    Examples
    -
    -
    Area of - Circle
    -
    Defining - a Lambda Function.
    -
    Calculating - a Derivative
    -
    Calculating - an Integral
    -
    -
    -
    Rational Number Types
    -
    -
    gmp_rational
    -
    cpp_rational
    -
    tommath_rational
    -
    Use With Boost.Rational
    -
    rational_adapter
    -
    -
    Constructing and - Interconverting Between Number Types
    -
    Generating Random Numbers
    -
    Primality Testing
    -
    -

    - In order to use this library you need to make two choices: what kind of number - do I want, and which back-end do I want to perform the actual arithmetic? -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/conversions.html b/doc/html/boost_multiprecision/tut/conversions.html deleted file mode 100644 index b34da26c..00000000 --- a/doc/html/boost_multiprecision/tut/conversions.html +++ /dev/null @@ -1,106 +0,0 @@ - - - -Constructing and Interconverting Between Number Types - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - All of the number types that are based on mp_number - have certain conversion rules in common. In particular: -

    -
    • - Any number type can be constructed (or assigned) from any builtin arithmetic - type: -
    -
    cpp_dec_float_50 df(0.5); // OK construction from double
-cpp_int          i(450);  // OK constructs from signed int
-
    -
    • - Any number type can be constructed (or assigned) from a const char* or a std::string: -
    -
    // pi to 50 places from a string:
-cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
-// Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly:
-cpp_int          i  = "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000";
-// Invalid input always results in a std::runtime_error being thrown:
-i = std::string("3.14");
-
    -
    • - Any number type will interoperate with the builtin type in arithmetic - expressions: -
    -
    // pi to 50 places from a string:
-cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
-// Multiply by 2 - using an integer literal here is usually more efficient
-// than constructing a temporary:
-df *= 2;
-
-// There is a need to be careful with integer types though:
-cpp_int i = 2;
-// Ooops, this really just multiplies by 3:
-i *= 3.14;
-
    -
    • - Any number type can be streamed to and from the C++ iostreams: -
    -
    cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
-// Now print at full precision:
-std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_50>::max_digits10)
-   << df << std::endl
-cpp_int i = 1;
-i <<= 256;
-// Now print in hex format with prefix:
-std::cout << std::hex << std::showbase << i << std::endl;
-
    -
    • - Some intercomnversions between number types are completely generic, and - are always available: -
    -
    cpp_int cppi(2);
-// We can always convert between numbers of the same category - 
-// int to int, rational to rational, or float to float, so this is OK:
-mpz_int z = cppi;
-// We can always promote from int to rational, int to float, or rational to float:
-cpp_rational     cppr = cppi;  // OK, int to rational
-cpp_dec_float_50 df =   cppi;  // OK, int to float
-df                  =   cppr;  // OK, rational to float
-// However narrowing conversions always fail:
-cppi                =   df;    // Compiler error, conversion not allowed
-
    -
    • - Other interconversions may be allowed as special cases, whenever the - backend allows it: -
    -
    mpf_t     m;           // Native GMP type.
-mpf_init_set_ui(m, 0); // set to a value;
-mpf_float i(m);        // copies the value of the native type.
-
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/floats.html b/doc/html/boost_multiprecision/tut/floats.html deleted file mode 100644 index e441517f..00000000 --- a/doc/html/boost_multiprecision/tut/floats.html +++ /dev/null @@ -1,197 +0,0 @@ - - - -Floating Point Numbers - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    -
    gmp_float
    -
    mpfr_float
    -
    cpp_dec_float
    -
    Examples
    -
    -
    Area of - Circle
    -
    Defining - a Lambda Function.
    -
    Calculating - a Derivative
    -
    Calculating - an Integral
    -
    -
    -

    - The following back-ends provide floating point arithmetic: -

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend Type -

    -     		-

    - Header -

    -     		-

    - Radix -

    -     		-

    - Dependencies -

    -     		-

    - Pros -

    -     		-

    - Cons -

    -
    -

    - mpf_float<N> -

    -     		-

    - boost/multiprecision/gmp.hpp -

    -     		-

    - 2 -

    -     		-

    - GMP -

    -     		-

    - Very fast and efficient back-end. -

    -     		-

    - Dependency on GNU licensed GMP - library. -

    -
    -

    - mpfr_float<N> -

    -     		-

    - boost/multiprecision/mpfr.hpp -

    -     		-

    - 2 -

    -     		-

    - GMP and MPFR -

    -     		-

    - Very fast and efficient back-end, with its own standard library - implementation. -

    -     		-

    - Dependency on GNU licensed GMP - and MPFR libraries. -

    -
    -

    - cpp_dec_float<N> -

    -     		-

    - boost/multiprecision/cpp_dec_float.hpp -

    -     		-

    - 10 -

    -     		-

    - None -

    -     		-

    - Header only, all C++ implementation. Boost licence. -

    -     		-

    - Approximately 2x slower than the MPFR - or GMP libraries. -

    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html deleted file mode 100644 index aea653f8..00000000 --- a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html +++ /dev/null @@ -1,117 +0,0 @@ - - - -cpp_dec_float - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - #include <boost/multiprecision/cpp_dec_float.hpp> -

    -
    namespace boost{ namespace multiprecision{
-
-template <unsigned Digits10>
-class cpp_dec_float;
-
-typedef mp_number<cpp_dec_float<50> > cpp_dec_float_50;
-typedef mp_number<cpp_dec_float<100> > cpp_dec_float_100;
-
-}} // namespaces
-
    -

    - The cpp_dec_float back-end - is used in conjunction with mp_number: - It acts as an entirely C++ (header only and dependency free) real-number - type that is a drop-in replacement for the native C++ floating-point types, - but with much greater precision. -

    -

    - Type cpp_dec_float can - be used at fixed precision by specifying a non-zero Digits10 - template parameter. The typedefs cpp_dec_float_50 - and cpp_dec_float_100 provide - arithmetic types at 50 and 100 decimal digits precision respectively. -

    -

    - There is full standard library and numeric_limits - support available for this type. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed cpp_dec_floats - have a value of zero. -
      • -
    • - The radix of this type is 10. As a result it can behave subtly differently - from base-2 types. -
      • -
    • - It is not possible to round-trip this type to and from a string and - get back to exactly the same value (this is a result of the type having - some hidden internal guard digits). -
      • -
    • - The type has a number of internal guard digits over and above those - specified in the template argument. Normally these should not be visible - to the user. -
      • -
    -
    - - cpp_dec_float - example: -
    -

    -

    -
    #include <boost/multiprecision/cpp_dec_float.hpp>
-
-using namespace boost::multiprecision;
-
-// Operations at fixed precision and full numeric_limits support:
-cpp_dec_float_100 b = 2;
-std::cout << std::numeric_limits<cpp_dec_float_100>::digits << std::endl;
-// Note that digits10 is the same as digits, since we're base 10! :
-std::cout << std::numeric_limits<cpp_dec_float_100>::digits10 << std::endl;
-// We can use any C++ std lib function, lets print all the digits as well:
-std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_100>::max_digits10)
-   << log(b) << std::endl; // print log(2)
-// We can also use any function from Boost.Math:
-std::cout << boost::math::tgamma(b) << std::endl;
-// These even work when the argument is an expression template:
-std::cout << boost::math::tgamma(b * b) << std::endl;
-// And since we have an extended exponent range we can generate some really large 
-// numbers here (4.0238726007709377354370243e+2564):
-std::cout << boost::math::tgamma(cpp_dec_float_100(1000)) << std::endl;
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg.html deleted file mode 100644 index c5e07650..00000000 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg.html +++ /dev/null @@ -1,44 +0,0 @@ - - - -Examples - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    -
    Area of - Circle
    -
    Defining - a Lambda Function.
    -
    Calculating - a Derivative
    -
    Calculating - an Integral
    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/GI.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/GI.html deleted file mode 100644 index 7b30997c..00000000 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/GI.html +++ /dev/null @@ -1,161 +0,0 @@ - - - -Calculating an Integral - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - Similar to the generic derivative example, we can calculate integrals - in a similar manner: -

    -

    -

    -
    template<typename value_type, typename function_type>
-inline value_type integral(const value_type a,
-                           const value_type b,
-                           const value_type tol,
-                           function_type func)
-{
-   unsigned n = 1U;
-
-   value_type h = (b - a);
-   value_type I = (func(a) + func(b)) * (h / 2);
-
-   for(unsigned k = 0U; k < 8U; k++)
-   {
-      h /= 2;
-
-      value_type sum(0);
-      for(unsigned j = 1U; j <= n; j++)
-      {
-         sum += func(a + (value_type((j * 2) - 1) * h));
-      }
-
-      const value_type I0 = I;
-      I = (I / 2) + (h * sum);
-
-      const value_type ratio     = I0 / I;
-      const value_type delta     = ratio - 1;
-      const value_type delta_abs = ((delta < 0) ? -delta : delta);
-
-      if((k > 1U) && (delta_abs < tol))
-      {
-         break;
-      }
-
-      n *= 2U;
-   }
-
-   return I;
-}
-
    -

    -

    -

    - The following sample program shows how the function can be called, we - begin by defining a function object, which when integrated should yield - the Bessel J function: -

    -

    -

    -
    template<typename value_type>
-class cyl_bessel_j_integral_rep
-{
-public:
-   cyl_bessel_j_integral_rep(const unsigned N,
-      const value_type& X) : n(N), x(X) { }
-
-   value_type operator()(const value_type& t) const
-   {
-      // pi * Jn(x) = Int_0^pi [cos(x * sin(t) - n*t) dt]
-      return cos(x * sin(t) - (n * t));
-   }
-
-private:
-   const unsigned n;
-   const value_type x;
-};
-
    -

    -

    -

    -

    -
       /* The function can now be called as follows: */
-int main(int, char**)
-{
-   using boost::math::constants::pi;
-   typedef boost::multiprecision::cpp_dec_float_50 mp_type;
-
-   const float j2_f =
-      integral(0.0F,
-      pi<float>(),
-      0.01F,
-      cyl_bessel_j_integral_rep<float>(2U, 1.23F)) / pi<float>();
-
-   const double j2_d =
-      integral(0.0,
-      pi<double>(),
-      0.0001,
-      cyl_bessel_j_integral_rep<double>(2U, 1.23)) / pi<double>();
-
-   const mp_type j2_mp =
-      integral(mp_type(0),
-      pi<mp_type>(),
-      mp_type(1.0E-20),
-      cyl_bessel_j_integral_rep<mp_type>(2U, mp_type(123) / 100)) / pi<mp_type>();
-
-   // 0.166369
-   std::cout
-      << std::setprecision(std::numeric_limits<float>::digits10)
-      << j2_f
-      << std::endl;
-
-   // 0.166369383786814
-   std::cout
-      << std::setprecision(std::numeric_limits<double>::digits10)
-      << j2_d
-      << std::endl;
-
-   // 0.16636938378681407351267852431513159437103348245333
-   std::cout
-      << std::setprecision(std::numeric_limits<mp_type>::digits10)
-      << j2_mp
-      << std::endl;
-
-   //
-   // Print true value for comparison:
-   // 0.166369383786814073512678524315131594371033482453329
-   std::cout << boost::math::cyl_bessel_j(2, mp_type(123) / 100) << std::endl;
-}
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html deleted file mode 100644 index 46500c20..00000000 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html +++ /dev/null @@ -1,118 +0,0 @@ - - - -Area of Circle - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - Generic numeric programming employs templates to use the same code for - different floating-point types and functions. Consider the area of a - circle a of radius r, given by -

    -

    - a = π * r2 -

    -

    - The area of a circle can be computed in generic programming using Boost.Math - for the constant π as shown below: -

    -

    -

    -
    #include <boost/math/constants/constants.hpp>
-
-template<typename T>
-inline T area_of_a_circle(T r)
-{
-   using boost::math::constants::pi;
-   return pi<T>() * r * r;
-}
-
    -

    -

    -

    - It is possible to use area_of_a_circle() with built-in floating-point types - as well as floating-point types from Boost.Multiprecision. In particular, - consider a system with 4-byte single-precision float, 8-byte double-precision - double and also the cpp_dec_float_50 - data type from Boost.Multiprecision with 50 decimal digits of precision. -

    -

    - We can compute and print the approximate area of a circle with radius - 123/100 for float, double and cpp_dec_float_50 - with the program below. -

    -

    -

    -
    #include <iostream>
-#include <iomanip>
-#include <boost/multiprecision/cpp_dec_float.hpp>
-
-using boost::multiprecision::cpp_dec_float_50;
-
-int main(int, char**)
-{
-   const float r_f(float(123) / 100);
-   const float a_f = area_of_a_circle(r_f);
-
-   const double r_d(double(123) / 100);
-   const double a_d = area_of_a_circle(r_d);
-
-   const cpp_dec_float_50 r_mp(cpp_dec_float_50(123) / 100);
-   const cpp_dec_float_50 a_mp = area_of_a_circle(r_mp);
-
-   // 4.75292
-   std::cout
-      << std::setprecision(std::numeric_limits<float>::digits10)
-      << a_f
-      << std::endl;
-
-   // 4.752915525616
-   std::cout
-      << std::setprecision(std::numeric_limits<double>::digits10)
-      << a_d
-      << std::endl;
-
-   // 4.7529155256159981904701331745635599135018975843146
-   std::cout
-      << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10)
-      << a_mp
-      << std::endl;
-}
-
    -

    -

    -

    - In the next example we'll look at calling both standard library and Boost.Math - functions from within generic code. We'll also show how to cope with - template arguments which are expression-templates rather than number - types. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html deleted file mode 100644 index 981d684d..00000000 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html +++ /dev/null @@ -1,222 +0,0 @@ - - - -Defining a Lambda Function. - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - In this example we'll show several implementations of the Jahnke - and Emden Lambda function, each implementation a little more - sophisticated than the last. -

    -

    - The Jahnke-Emden Lambda function is defined by the equation: -

    -

    - JahnkeEmden(v, z) = Γ(v+1) * Jv(z) / (z / 2)v -

    -

    - If we were to implement this at double precision using Boost.Math's facilities - for the Gamma and Bessel function calls it would look like this: -

    -

    -

    -
    double JEL1(double v, double z)
-{
-   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / std::pow(z / 2, v);
-}
-
    -

    -

    -

    - Calling this function as: -

    -
    std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10);
-std::cout << JEL1(2.5, 0.5) << std::endl;
-
    -

    - Yields the output: -

    -
    9.822663964796047e-001
    -

    - Now lets implement the function again, but this time using the multiprecision - type cpp_dec_float_50 - as the argument type: -

    -

    -

    -
    boost::multiprecision::cpp_dec_float_50
-   JEL2(boost::multiprecision::cpp_dec_float_50 v, boost::multiprecision::cpp_dec_float_50 z)
-{
-   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / boost::multiprecision::pow(z / 2, v);
-}
-
    -

    -

    -

    - The implementation is almost the same as before, but with one key difference - - we can no longer call std::pow, - instead we must call the version inside the boost::multiprecision - namespace. In point of fact, we could have omitted the namespace prefix - on the call to pow since - the right overload would have been found via argument - dependent lookup in any case. -

    -

    - Note also that the first argument to pow - along with the argument to tgamma - in the above code are actually expression templates. The pow and tgamma - functions will handle these arguments just fine. -

    -

    - Here's an example of how the function may be called: -

    -
    std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10);
-std::cout << JEL2(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl;
-
    -

    - Which outputs: -

    -
    9.82266396479604757017335009796882833995903762577173e-01
    -

    - Now that we've seen some non-template examples, lets repeat the code - again, but this time as a template that can be called either with a builtin - type (float, double etc), or with a multiprecision - type: -

    -

    -

    -
    template <class Float>
-Float JEL3(Float v, Float z)
-{
-   using std::pow;
-   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
-}
-
    -

    -

    -

    - Once again the code is almost the same as before, but the call to pow has changed yet again. We need - the call to resolve to either std::pow - (when the argument is a builtin type), or to boost::multiprecision::pow - (when the argument is a multiprecision type). We do that by making the - call unqualified so that versions of pow - defined in the same namespace as type Float - are found via argument dependent lookup, while the using - std::pow directive makes the standard library - versions visible for builtin floating point types. -

    -

    - Let's call the function with both double - and multiprecision arguments: -

    -
    std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10);
-std::cout << JEL3(2.5, 0.5) << std::endl;
-std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10);
-std::cout << JEL3(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl;
-
    -

    - Which outputs: -

    -
    9.822663964796047e-001
-9.82266396479604757017335009796882833995903762577173e-01
-
    -

    - Unfortunately there is a problem with this version: if we were to call - it like this: -

    -
    boost::multiprecision::cpp_dec_float_50 v(2), z(0.5);
-JEL3(v + 0.5, z);
-
    -

    - Then we would get a long and inscrutable error message from the compiler: - the problem here is that the first argument to JEL3 - is not a number type, but an expression template. We could obviously - add a typecast to fix the issue: -

    -
    JEL(cpp_dec_float_50(v + 0.5), z);
-
    -

    - However, if we want the function JEL to be truely reusable, then a better - solution might be preferred. To achieve this we can borrow some code - from Boost.Math which calculates the return type of mixed-argument functions, - here's how the new code looks now: -

    -

    -

    -
    template <class Float1, class Float2>
-typename boost::math::tools::promote_args<Float1, Float2>::type
-   JEL4(Float1 v, Float2 z)
-{
-   using std::pow;
-   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
-}
-
    -

    -

    -

    - As you can see the two arguments to the function are now separate template - types, and the return type is computed using the promote_args - metafunction from Boost.Math. -

    -

    - Now we can call: -

    -
    std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_100>::digits10);
-std::cout << JEL4(cpp_dec_float_100(2) + 0.5, cpp_dec_float_100(0.5)) << std::endl;
-
    -

    - And get 100 digits of output: -

    -
    9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01
    -

    - As a bonus, we can now call the function not just with expression templates, - but with other mixed types as well: for example float - and double or int and double, - and the correct return type will be computed in each case. -

    -

    - Note that while in this case we didn't have to change the body of the - function, in the general case any function like this which creates local - variables internally would have to use promote_args - to work out what type those variables should be, for example: -

    -
    template <class Float1, class Float2>
-typename boost::math::tools::promote_args<Float1, Float2>::type
-   JEL5(Float1 v, Float2 z)
-{
-   using std::pow;
-   typedef typename boost::math::tools::promote_args<Float1, Float2>::type variable_type;
-   variable_type t = pow(z / 2, v);
-   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / t;
-}
-
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html deleted file mode 100644 index 460c86c4..00000000 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html +++ /dev/null @@ -1,202 +0,0 @@ - - - -Calculating a Derivative - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - In this example we'll add even more power to generic numeric programming - using not only different floating-point types but also function objects - as template parameters. Consider some well-known central difference rules - for numerically computing the first derivative of a function f′(x) - with x ∈ ℜ: -

    -

    - -

    -

    - Where the difference terms mn are given by: -

    -

    - -

    -

    - and dx is the step-size of the derivative. -

    -

    - The third formula in Equation 1 is a three-point central difference rule. - It calculates the first derivative of f′(x) to O(dx6), - where dx is the given step-size. For example, if - the step-size is 0.01 this derivative calculation has about 6 decimal - digits of precision - just about right for the 7 decimal digits of single-precision - float. Let's make a generic template subroutine using this three-point - central difference rule. In particular: -

    -

    -

    -
    template<typename value_type, typename function_type>
-   value_type derivative(const value_type x, const value_type dx, function_type func)
-{
-   // Compute d/dx[func(*first)] using a three-point
-   // central difference rule of O(dx^6).
-
-   const value_type dx1 = dx;
-   const value_type dx2 = dx1 * 2;
-   const value_type dx3 = dx1 * 3;
-
-   const value_type m1 = (func(x + dx1) - func(x - dx1)) / 2;
-   const value_type m2 = (func(x + dx2) - func(x - dx2)) / 4;
-   const value_type m3 = (func(x + dx3) - func(x - dx3)) / 6;
-
-   const value_type fifteen_m1 = 15 * m1;
-   const value_type six_m2     =  6 * m2;
-   const value_type ten_dx1    = 10 * dx1;
-
-   return ((fifteen_m1 - six_m2) + m3) / ten_dx1;
-}
-
    -

    -

    -

    - The derivative() - template function can be used to compute the first derivative of any - function to O(dx6). For example, consider the first - derivative of sin(x) evaluated at x = - π/3. In other words, -

    -

    - -

    -

    - The code below computes the derivative in Equation 3 for float, double - and boost's multiple-precision type cpp_dec_float_50. -

    -

    -

    -
    #include <iostream>
-#include <iomanip>
-#include <boost/multiprecision/cpp_dec_float.hpp>
-#include <boost/math/constants/constants.hpp>
-
-
-int main(int, char**)
-{
-   using boost::math::constants::pi;
-   using boost::multiprecision::cpp_dec_float_50;
-   //
-   // We'll pass a function pointer for the function object passed to derivative,
-   // the typecast is needed to select the correct overload of std::sin:
-   //
-   const float d_f = derivative(
-      pi<float>() / 3,
-      0.01F,
-      static_cast<float(*)(float)>(std::sin)
-   );
-
-   const double d_d = derivative(
-      pi<double>() / 3,
-      0.001,
-      static_cast<double(*)(double)>(std::sin)
-      );
-   //
-   // In the cpp_dec_float_50 case, the sin function is multiply overloaded
-   // to handle expression templates etc.  As a result it's hard to take it's
-   // address without knowing about its implementation details.  We'll use a 
-   // C++11 lambda expression to capture the call.
-   // We also need a typecast on the first argument so we don't accidently pass
-   // an expression template to a template function:
-   //
-   const cpp_dec_float_50 d_mp = derivative(
-      cpp_dec_float_50(pi<cpp_dec_float_50>() / 3),
-      cpp_dec_float_50(1.0E-9),
-      [](const cpp_dec_float_50& x) -> cpp_dec_float_50
-      {
-         return sin(x);
-      }
-      );
-
-   // 5.000029e-001
-   std::cout
-      << std::setprecision(std::numeric_limits<float>::digits10)
-      << d_f
-      << std::endl;
-
-   // 4.999999999998876e-001
-   std::cout
-      << std::setprecision(std::numeric_limits<double>::digits10)
-      << d_d
-      << std::endl;
-
-   // 4.99999999999999999999999999999999999999999999999999e-01
-   std::cout
-      << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10)
-      << d_mp
-      << std::endl;
-}
-
    -

    -

    -

    - The expected value of the derivative is 0.5. This central difference - rule in this example is ill-conditioned, meaning it suffers from slight - loss of precision. With that in mind, the results agree with the expected - value of 0.5. -

    -

    - We can take this a step further and use our derivative function to compute - a partial derivative. For example if we take the incomplete gamma function - P(a, z), and take the derivative with respect to - z at (2,2) then we can calculate - the result as shown below, for good measure we'll compare with the "correct" - result obtained from a call to gamma_p_derivative, - the results agree to approximately 44 digits: -

    -

    -

    -
    cpp_dec_float_50 gd = derivative(
-   cpp_dec_float_50(2),
-   cpp_dec_float_50(1.0E-9),
-   [](const cpp_dec_float_50& x) ->cpp_dec_float_50
-   {
-      return boost::math::gamma_p(2, x);
-   }
-);
-// 2.70670566473225383787998989944968806815263091819151e-01
-std::cout
-   << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10)
-   << gd
-   << std::endl;
-// 2.70670566473225383787998989944968806815253190143120e-01
-std::cout << boost::math::gamma_p_derivative(cpp_dec_float_50(2), cpp_dec_float_50(2)) << std::endl;
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/floats/gmp_float.html b/doc/html/boost_multiprecision/tut/floats/gmp_float.html deleted file mode 100644 index 3b104b2e..00000000 --- a/doc/html/boost_multiprecision/tut/floats/gmp_float.html +++ /dev/null @@ -1,169 +0,0 @@ - - - -gmp_float - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - #include <boost/multiprecision/gmp.hpp> -

    -
    namespace boost{ namespace multiprecision{
-
-template <unsigned Digits10>
-class gmp_float;
-
-typedef mp_number<gmp_float<50> >    mpf_float_50;
-typedef mp_number<gmp_float<100> >   mpf_float_100;
-typedef mp_number<gmp_float<500> >   mpf_float_500;
-typedef mp_number<gmp_float<1000> >  mpf_float_1000;
-typedef mp_number<gmp_float<0> >     mpf_float;
-
-}} // namespaces
-
    -

    - The gmp_float back-end - is used in conjunction with mp_number - : it acts as a thin wrapper around the GMP - mpf_t to provide an real-number - type that is a drop-in replacement for the native C++ floating-point types, - but with much greater precision. -

    -

    - Type gmp_float can be used - at fixed precision by specifying a non-zero Digits10 - template parameter, or at variable precision by setting the template argument - to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 - provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision - respectively. The typedef mpf_float provides a variable precision type - whose precision can be controlled via the mp_numbers - member functions. -

    -
    - - - - - -
    [Note]Note

    - This type only provides standard library and numeric_limits - support when the precision is fixed at compile time. -

    -

    - As well as the usual conversions from arithmetic and string types, instances - of mp_number<mpf_float<N> > are copy constructible and assignable - from: -

    -
      -
    • - The GMP native types mpf_t, mpz_t, - mpq_t. -
      • -
    • - The mp_number wrappers - around those types: mp_number<mpf_float<M> >, - mp_number<gmp_int>, - mp_number<gmp_rational>. -
      • -
    -

    - It's also possible to access the underlying mpf_t - via the data() - member function of gmp_float. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed gmp_floats - have the value zero (this is the GMP - library's default behavior). -
      • -
    • - No changes are made to the GMP - library's global settings, so this type can be safely mixed with existing - GMP code. -
      • -
    • - It is not possible to round-trip objects of this type to and from a - string and get back exactly the same value. This appears to be a limitation - of GMP. -
      • -
    • - Since the underlying GMP types - have no notion of infinities or NaN's, care should be taken to avoid - numeric overflow or division by zero. That latter will trigger a hardware - exception, while generating excessively large exponents may result - in instability of the underlying GMP - library (in testing, converting a number with an excessively large - or small exponent to a string caused GMP - to segfault). -
      • -
    • - This type can equally be used with MPIR - as the underlying implementation - indeed that is the recommended option - on Win32. -
      • -
    -
    - - - GMP example: -
    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-
-using namespace boost::multiprecision;
-
-// Operations at variable precision and limited standard library support:
-mpf_float a = 2;
-mpf_float::default_precision(1000);
-std::cout << mpf_float::default_precision() << std::endl;
-std::cout << sqrt(a) << std::endl; // print root-2
-
-// Operations at fixed precision and full standard library support:
-mpf_float_100 b = 2;
-std::cout << std::numeric_limits<mpf_float_100>::digits << std::endl;
-// We can use any C++ std lib function:
-std::cout << log(b) << std::endl; // print log(2)
-// We can also use any function from Boost.Math:
-std::cout << boost::math::tgamma(b) << std::endl;
-// These even work when the argument is an expression template:
-std::cout << boost::math::tgamma(b * b) << std::endl;
-
-// Access the underlying representation:
-mpf_t f;
-mpf_init(f);
-mpf_set(f, a.backend().data());
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/floats/jel.html b/doc/html/boost_multiprecision/tut/floats/jel.html deleted file mode 100644 index 9a6a4ba8..00000000 --- a/doc/html/boost_multiprecision/tut/floats/jel.html +++ /dev/null @@ -1,222 +0,0 @@ - - - -Worked Example: defining a mathematical function. - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - In this example we'll show several implementations of the Jahnke - and Emden Lambda function, each implementation a little more sophisticated - than the last. -

    -

    - The Jahnke-Emden Lambda function is defined by the equation: -

    -

    - JahnkeEmden(v, z) = Gamma(v+1) * J[v](z) / (z / 2)^v -

    -

    - If we were to implement this at double precision using Boost.Math's facilities - for the Gamma and Bessel function calls it would look like this: -

    -

    -

    -
    double JEL1(double v, double z)
-{
-   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / std::pow(z / 2, v);
-}
-
    -

    -

    -

    - Calling this function as: -

    -
    std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10);
-std::cout << JEL1(2.5, 0.5) << std::endl;
-
    -

    - Yields the output: -

    -
    9.822663964796047e-001
    -

    - Now lets implement the function again, but this time using the multiprecision - type cpp_dec_float_50 as - the argument type: -

    -

    -

    -
    boost::multiprecision::cpp_dec_float_50
-   JEL2(boost::multiprecision::cpp_dec_float_50 v, boost::multiprecision::cpp_dec_float_50 z)
-{
-   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / boost::multiprecision::pow(z / 2, v);
-}
-
    -

    -

    -

    - The implementation is almost the same as before, but with one key difference - - we can no longer call std::pow, - instead we must call the version inside the boost::multiprecision - namespace. In point of fact, we could have omitted the namespace prefix - on the call to pow since - the right overload would have been found via argument - dependent lookup in any case. -

    -

    - Note also that the first argument to pow - along with the argument to tgamma - in the above code are actually expression templates. The pow and tgamma - functions will handle these arguments just fine. -

    -

    - Here's an example of how the function may be called: -

    -
    std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10);
-std::cout << JEL2(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl;
-
    -

    - Which outputs: -

    -
    9.82266396479604757017335009796882833995903762577173e-01
    -

    - Now that we've seen some non-template examples, lets repeat the code again, - but this time as a template that can be called either with a builtin type - (float, double - etc), or with a multiprecision type: -

    -

    -

    -
    template <class Float>
-Float JEL3(Float v, Float z)
-{
-   using std::pow;
-   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
-}
-
    -

    -

    -

    - Once again the code is almost the same as before, but the call to pow has changed yet again. We need the - call to resolve to either std::pow - (when the argument is a builtin type), or to boost::multiprecision::pow - (when the argument is a multiprecision type). We do that by making the - call unqualified so that versions of pow - defined in the same namespace as type Float - are found via argument dependent lookup, while the using - std::pow directive makes the standard library - versions visible for builtin floating point types. -

    -

    - Let's call the function with both double - and multiprecision arguments: -

    -
    std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10);
-std::cout << JEL3(2.5, 0.5) << std::endl;
-std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10);
-std::cout << JEL3(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl;
-
    -

    - Which outputs: -

    -
    9.822663964796047e-001
-9.82266396479604757017335009796882833995903762577173e-01
-
    -

    - Unfortunately there is a problem with this version: if we were to call - it like this: -

    -
    boost::multiprecision::cpp_dec_float_50 v(2), z(0.5);
-JEL3(v + 0.5, z);
-
    -

    - Then we would get a long and inscrutable error message from the compiler: - the problem here is that the first argument to JEL3 - is not a number type, but an expression template. We could obviously add - a typecast to fix the issue: -

    -
    JEL(cpp_dec_float_50(v + 0.5), z);
-
    -

    - However, if we want the function JEL to be truely reusable, then a better - solution might be preferred. To achieve this we can borrow some code from - Boost.Math which calculates the return type of mixed-argument functions, - here's how the new code looks now: -

    -

    -

    -
    template <class Float1, class Float2>
-typename boost::math::tools::promote_args<Float1, Float2>::type
-   JEL4(Float1 v, Float2 z)
-{
-   using std::pow;
-   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
-}
-
    -

    -

    -

    - As you can see the two arguments to the function are now separate template - types, and the return type is computed using the promote_args - metafunction from Boost.Math. -

    -

    - Now we can call: -

    -
    std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_100>::digits10);
-std::cout << JEL4(cpp_dec_float_100(2) + 0.5, cpp_dec_float_100(0.5)) << std::endl;
-
    -

    - And get 100 digits of output: -

    -
    9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01
    -

    - As a bonus, we can now call the function not just with expression templates, - but with other mixed types as well: for example float - and double or int and double, - and the correct return type will be computed in each case. -

    -

    - Note that while in this case we didn't have to change the body of the function, - in the general case any function like this which creates local variables - internally would have to use promote_args - to work out what type those variables should be, for example: -

    -
    template <class Float1, class Float2>
-typename boost::math::tools::promote_args<Float1, Float2>::type
-   JEL5(Float1 v, Float2 z)
-{
-   using std::pow;
-   typedef typename boost::math::tools::promote_args<Float1, Float2>::type variable_type;
-   variable_type t = pow(z / 2, v);
-   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / t;
-}
-
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html deleted file mode 100644 index 595e9d2c..00000000 --- a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html +++ /dev/null @@ -1,159 +0,0 @@ - - - -mpfr_float - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - #include <boost/multiprecision/mpfr_float.hpp> -

    -
    namespace boost{ namespace multiprecision{
-
-template <unsigned Digits10>
-class mpfr_float_backend;
-
-typedef mp_number<mpfr_float_backend<50> >    mpfr_float_50;
-typedef mp_number<mpfr_float_backend<100> >   mpfr_float_100;
-typedef mp_number<mpfr_float_backend<500> >   mpfr_float_500;
-typedef mp_number<mpfr_float_backend<1000> >  mpfr_float_1000;
-typedef mp_number<mpfr_float_backend<0> >     mpfr_float;
-
-}} // namespaces
-
    -

    - The mpfr_float_backend - type is used in conjunction with mp_number: - It acts as a thin wrapper around the MPFR - mpfr_t to provide an real-number - type that is a drop-in replacement for the native C++ floating-point types, - but with much greater precision. -

    -

    - Type mpfr_float_backend - can be used at fixed precision by specifying a non-zero Digits10 - template parameter, or at variable precision by setting the template argument - to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 - provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision - respectively. The typedef mpfr_float provides a variable precision type - whose precision can be controlled via the mp_numbers - member functions. -

    -
    - - - - - -
    [Note]Note

    - This type only provides numeric_limits - support when the precision is fixed at compile time. -

    -

    - As well as the usual conversions from arithmetic and string types, instances - of mp_number<mpfr_float_backend<N> > are copy constructible and assignable - from: -

    -
      -
    • - The GMP native types mpf_t, mpz_t, - mpq_t. -
      • -
    • - The MPFR native type mpfr_t. -
      • -
    • - The mp_number wrappers - around those types: mp_number<mpfr_float_backend<M> >, - mp_number<mpf_float<M> >, mp_number<gmp_int>, mp_number<gmp_rational>. -
      • -
    -

    - It's also possible to access the underlying mpf_t - via the data() member function of gmp_float. -

    -

    - Things you should know when using this type: -

    -
      -
    • - A default constructed mpfr_float_backend - is set to a NaN (this is the default MPFR - behavior). -
      • -
    • - All operations use round to nearest. -
      • -
    • - No changes are made to GMP or - MPFR global settings, so this - type can coexist with existing MPFR - or GMP code. -
      • -
    • - The code can equally use MPIR - in place of GMP - indeed that - is the preferred option on Win32. -
      • -
    -
    - - - MPFR example: -
    -

    -

    -
    #include <boost/multiprecision/mpfr.hpp>
-
-using namespace boost::multiprecision;
-
-// Operations at variable precision and no numeric_limits support:
-mpfr_float a = 2;
-mpfr_float::default_precision(1000);
-std::cout << mpfr_float::default_precision() << std::endl;
-std::cout << sqrt(a) << std::endl; // print root-2
-
-// Operations at fixed precision and full numeric_limits support:
-mpfr_float_100 b = 2;
-std::cout << std::numeric_limits<mpfr_float_100>::digits << std::endl;
-// We can use any C++ std lib function:
-std::cout << log(b) << std::endl; // print log(2)
-// We can also use any function from Boost.Math:
-std::cout << boost::math::tgamma(b) << std::endl;
-// These even work when the argument is an expression template:
-std::cout << boost::math::tgamma(b * b) << std::endl;
-
-// Access the underlying data:
-mpfr_t r;
-mpfr_init(r);
-mpfr_set(r, b.backend().data(), GMP_RNDN);
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html deleted file mode 100644 index b5504ee0..00000000 --- a/doc/html/boost_multiprecision/tut/ints.html +++ /dev/null @@ -1,186 +0,0 @@ - - - -Integer Types - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    -
    cpp_int
    -
    gmp_int
    -
    tom_int
    -
    -

    - The following back-ends provide integer arithmetic: -

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend Type -

    -     		-

    - Header -

    -     		-

    - Radix -

    -     		-

    - Dependencies -

    -     		-

    - Pros -

    -     		-

    - Cons -

    -
    -

    - cpp_int -

    -     		-

    - boost/multiprecision/cpp_int.hpp -

    -     		-

    - 2 -

    -     		-

    - None -

    -     		-

    - Very versatile, Boost licensed, all C++ integer type which support - both arbitrary - precision and fixed precision integer types. -

    -     		-

    - Slower than GMP, though - typically not as slow as libtommath -

    -
    -

    - gmp_int -

    -     		-

    - boost/multiprecision/gmp.hpp -

    -     		-

    - 2 -

    -     		-

    - GMP -

    -     		-

    - Very fast and efficient back-end. -

    -     		-

    - Dependency on GNU licensed GMP - library. -

    -
    -

    - tom_int -

    -     		-

    - boost/multiprecision/tommath.hpp -

    -     		-

    - 2 -

    -     		-

    - libtommath -

    -     		-

    - Public domain back-end with no licence restrictions. -

    -     		-

    - Slower than GMP. -

    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html deleted file mode 100644 index 98340475..00000000 --- a/doc/html/boost_multiprecision/tut/ints/cpp_int.html +++ /dev/null @@ -1,179 +0,0 @@ - - - -cpp_int - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - #include <boost/multiprecision/cpp_int.hpp> -

    -
    namespace boost{ namespace multiprecision{
-
-typedef unspecified-type limb_type;
-
-template <unsigned MinDigits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
-class cpp_int_backend;
-
-typedef mp_number<cpp_int_backend<> >           cpp_int;    // arbitrary precision integer
-typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
-typedef mp_number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
-
-// Fixed precision unsigned types:
-typedef mp_number<cpp_int_backend<128, false, void>, false>   mp_uint128_t;
-typedef mp_number<cpp_int_backend<256, false, void>, false>   mp_uint256_t;
-typedef mp_number<cpp_int_backend<512, false, void>, false>   mp_uint512_t;
-typedef mp_number<cpp_int_backend<1024, false, void>, false>  mp_uint1024_t;
-
-// Fixed precision signed types:
-typedef mp_number<cpp_int_backend<128, true, void>, false>    mp_int128_t;
-typedef mp_number<cpp_int_backend<256, true, void>, false>    mp_int256_t;
-typedef mp_number<cpp_int_backend<512, true, void>, false>    mp_int512_t;
-typedef mp_number<cpp_int_backend<1024, true, void>, false>   mp_int1024_t;
-
-}} // namespaces
-
    -

    - The cpp_int_backend type - is used via one of the typedefs boost::multiprecision::cpp_int, - boost::multiprecision::mp_uint128_t, boost::multiprecision::mp_uint256_t, - boost::multiprecision::mp_uint512_t, boost::multiprecision::mp_int128_t, - boost::multiprecision::mp_int256_t or boost::multiprecision::mp_int512_t. -

    -

    - This back-end is the "Swiss Army Knife" of integer types as it - can represent both fixed and arbitrary - precision integer types, and both signed and unsigned types. There - are three template arguments: -

    -
    -

    -
    -
    MinBits
    -

    - Determines the number of Bits to store directly within the object - before resorting to dynamic memory allocation. When zero, this field - is determined automatically based on how many bits can be stored - in union with the dynamic storage header: setting a larger value - may improve performance as larger integer values will be stored internally - before memory allocation is required. When the Allocator parameter - is type void, then this - field determines the total number of bits in the resulting fixed - precision type. -

    -
    Signed
    -

    - Determines whether the resulting type is signed or not. Note that - for arbitrary - precision types (where the Allocator parameter is non-void), - then this parameter must be true. - For fixed precision types then this type may be either true (type is signed), or false (type is unsigned). -

    -
    Allocator
    -

    - The allocator to use for dynamic memory allocation, or type void if this is to be a fixed precision - type. -

    -
    -
    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed cpp_int_backends - have the value zero. -
      • -
    • - Division by zero results in a std::runtime_error - being thrown. -
      • -
    • - Construction from a string that contains invalid non-numeric characters - results in a std::runtime_error being thrown. -
      • -
    • - Since the precision of cpp_int_backend - is necessarily limited when the allocator parameter is void, care should - be taken to avoid numeric overflow when using this type unless you - actually want modulo-arithmetic behavior. -
      • -
    • - The type uses a sign-magnitude representation internally, so type - mp_int128_t has 128-bits - of precision plus an extra sign bit. In this respect the behaviour - of these types differs from built-in 2's complement types. In might - be tempting to use a 127-bit type instead, and indeed this does work, - but behaviour is still slightly different from a 2's complement built-in - type as the min and max values are identical (apart from the sign), - where as they differ by one for a true 2's complement type. That said - it should be noted that there's no requirement for built-in types to - be 2's complement either - it's simply that this is the most common - format by far. -
      • -
    • - Attempting to print negative values as either an Octal or Hexadecimal - string results in a std::runtime_error - being thrown, this is a direct consequence of the sign-magnitude representation. -
      • -
    • - The fixed precision types mp_[u]intXXX_t - have expression template support turned off - it seems to make little - difference to the performance of these types either way - so we may - as well have the faster compile times by turning the feature off. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/cpp_int.hpp>
-
-using namespace boost::multiprecision;
-
-mp_int128_t v = 1;
-
-// Do some fixed precision arithmetic:
-for(unsigned i = 1; i <= 20; ++i)
-   v *= i;
-
-std::cout << v << std::endl; // prints 20!
-
-// Repeat at arbitrary precision:
-cpp_int u = 1;
-for(unsigned i = 1; i <= 100; ++i)
-   u *= i;
-
-std::cout << u << std::endl; // prints 100!
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/ints/gmp_int.html b/doc/html/boost_multiprecision/tut/ints/gmp_int.html deleted file mode 100644 index 1bf12605..00000000 --- a/doc/html/boost_multiprecision/tut/ints/gmp_int.html +++ /dev/null @@ -1,128 +0,0 @@ - - - -gmp_int - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - #include <boost/multiprecision/gmp.hpp> -

    -
    namespace boost{ namespace multiprecision{
-
-class gmp_int;
-
-typedef mp_number<gmp_int >         mpz_int;
-
-}} // namespaces
-
    -

    - The gmp_int back-end is - used via the typedef boost::multiprecision::mpz_int. - It acts as a thin wrapper around the GMP - mpz_t to provide an integer - type that is a drop-in replacement for the native C++ integer types, but - with unlimited precision. -

    -

    - As well as the usual conversions from arithmetic and string types, type - mpz_int is copy constructible - and assignable from: -

    -
      -
    • - The GMP native types: mpf_t, mpz_t, - mpq_t. -
      • -
    • - Instances of mp_number<T> that are wrappers around those - types: mp_number<gmp_float<N> >, mp_number<gmp_rational>. -
      • -
    -

    - It's also possible to access the underlying mpz_t - via the data() - member function of gmp_int. -

    -

    - Things you should know when using this type: -

    -
      -
    • - No changes are made to the GMP library's global settings - so you can - safely mix this type with existing code that uses GMP. -
      • -
    • - Default constructed gmp_ints - have the value zero (this is GMP's default behavior). -
      • -
    • - Formatted IO for this type does not support octal or hexadecimal notation - for negative values, as a result performing formatted output on this - type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex - are set, will result in a std::runtime_error - will be thrown. -
      • -
    • - Division by zero is handled by the GMP - library - it will trigger a division by zero signal. -
      • -
    • - Although this type is a wrapper around GMP - it will work equally well with MPIR. - Indeed use of MPIR is recommended - on Win32. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-
-using namespace boost::multiprecision;
-
-mpz_int v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-
-std::cout << v << std::endl; // prints 1000!
-
-// Access the underlying representation:
-mpz_t z;
-mpz_init(z);
-mpz_set(z, v.backend().data());
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/ints/tom_int.html b/doc/html/boost_multiprecision/tut/ints/tom_int.html deleted file mode 100644 index 2ea5acf4..00000000 --- a/doc/html/boost_multiprecision/tut/ints/tom_int.html +++ /dev/null @@ -1,119 +0,0 @@ - - - -tom_int - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - #include <boost/multiprecision/tommath.hpp> -

    -
    namespace boost{ namespace multiprecision{
-
-class tommath_int;
-
-typedef mp_number<tommath_int >         tom_int;
-
-}} // namespaces
-
    -

    - The tommath_int back-end - is used via the typedef boost::multiprecision::tom_int. - It acts as a thin wrapper around the libtommath - tom_int to provide an integer - type that is a drop-in replacement for the native C++ integer types, but - with unlimited precision. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed objects have the value zero (this is libtommath's - default behavior). -
      • -
    • - Although tom_int is - mostly a drop in replacement for the builtin integer types, it should - be noted that it is a rather strange beast as it's a signed type that - is not a 2's complement type. As a result the bitwise operations | & ^ will throw a std::runtime_error - exception if either of the arguments is negative. Similarly the complement - operator~ is deliberately - not implemented for this type. -
      • -
    • - Formatted IO for this type does not support octal or hexadecimal notation - for negative values, as a result performing formatted output on this - type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex - are set, will result in a std::runtime_error - will be thrown. -
      • -
    • - Division by zero will result in a hardware signal being raised by - libtommath. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/tommath.hpp>
-
-boost::multiprecision::tom_int v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-
-std::cout << v << std::endl; // prints 1000!
-std::cout << std::hex << v << std::endl; // prints 1000! in hex format
-
-try{
-   std::cout << std::hex << -v << std::endl; // Ooops! can't print a negative value in hex format!
-}
-catch(const std::runtime_error& e)
-{
-   std::cout << e.what() << std::endl;
-}
-
-try{
-   // v is not a 2's complement type, bitwise operations are only supported
-   // on positive values:
-   v = -v & 2;
-}
-catch(const std::runtime_error& e)
-{
-   std::cout << e.what() << std::endl;
-}
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html deleted file mode 100644 index f1dac222..00000000 --- a/doc/html/boost_multiprecision/tut/primetest.html +++ /dev/null @@ -1,108 +0,0 @@ - - - -Primality Testing - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - The library implements a fairly basic (meaning unoptimized, and possibly - slow) Miller-Rabin test for primality: -

    -
    #include <boost/multiprecision/miller_rabin.hpp>
-
-template <class Backend, bool ExpressionTemplates, class Engine>
-bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials, Engine& gen);
-
-template <class Backend, bool ExpressionTemplates, class Engine>
-bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials);
-
    -

    - These functions perform a Miller-Rabin test for primality, if the result - is false then n - is definitely composite, while if the result is true - then n is prime with probability 0.25^trials. - The algorithm used is straight out of Knuth Vol 2, which recomends 25 trials - for a pretty strong likelyhood that n is prime. -

    -

    - The third optional argument is for a Uniform Random Number Generator from - Boost.Random. When not provided the mt19937 - generator is used. Note that when producing random primes then you should - probably use a different random number generator to produce candidate prime - numbers for testing, than is used internally by miller_rabin_test - for determining whether the value is prime. It also helps of course to seed - the generators with some source of randomness. -

    -

    - The following example searches for a prime p - for which (p-1)/2 is also probably prime: -

    -

    -

    -
    #include <boost/multiprecision/cpp_int.hpp>
-#include <boost/multiprecision/miller_rabin.hpp>
-#include <iostream>
-#include <iomanip>
-
-int main()
-{
-   using namespace boost::random;
-   using namespace boost::multiprecision;
-
-   typedef cpp_int int_type;
-   mt11213b base_gen(clock());
-   independent_bits_engine<mt11213b, 256, int_type> gen(base_gen);
-   //
-   // We must use a different generator for the tests and number generation, otherwise
-   // we get false positives.
-   //
-   mt19937 gen2(clock());
-
-   for(unsigned i = 0; i < 100000; ++i)
-   {
-      int_type n = gen();
-      if(miller_rabin_test(n, 25, gen2))
-      {
-         // Value n is probably prime, see if (n-1)/2 is also prime:
-         std::cout << "We have a probable prime with value: " << std::hex << std::showbase << n << std::endl;
-         if(miller_rabin_test((n-1)/2, 25, gen2))
-         {
-            std::cout << "We have a safe prime with value: " << std::hex << std::showbase << n << std::endl;
-            return 0;
-         }
-      }
-   }
-   std::cout << "Ooops, no safe primes were found" << std::endl;
-   return 1;
-}
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/random.html b/doc/html/boost_multiprecision/tut/random.html deleted file mode 100644 index 6f0d438b..00000000 --- a/doc/html/boost_multiprecision/tut/random.html +++ /dev/null @@ -1,157 +0,0 @@ - - - -Generating Random Numbers - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - Random numbers are generated in conjunction with Boost.Random. However, since - Boost.Random is unaware of arbitrary - precision numbers, it's necessary to include the header: -

    -
    #include <boost/multiprecision/random.hpp>
-
    -

    - In order to act as a bridge between the two libraries. -

    -

    - Integers with N random bits are generated using independent_bits_engine: -

    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-#include <boost/multiprecision/random.hpp>
-
-using namespace boost::multiprecision;
-using namespace boost::random;
-
-//
-// Declare our random number generator type, the underlying generator
-// is the Mersenne twister mt19937 engine, and 256 bits are generated:
-//
-typedef independent_bits_engine<mt19937, 256, mpz_int> generator_type;
-generator_type gen;
-//
-// Generate some values:
-//
-std::cout << std::hex << std::showbase;
-for(unsigned i = 0; i < 10; ++i)
-   std::cout << gen() << std::endl;
-
    -

    -

    -

    - Alternatively we can generate integers in a given range using uniform_int_distribution, this will invoke - the underlying engine multiple times to build up the required number of bits - in the result: -

    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-#include <boost/multiprecision/random.hpp>
-
-using namespace boost::multiprecision;
-using namespace boost::random;
-
-//
-// Generate integers in a given range using uniform_int,
-// the underlying generator is invoked multiple times
-// to generate enough bits:
-//
-mt19937 mt;
-uniform_int_distribution<mpz_int> ui(0, mpz_int(1) << 256);
-//
-// Generate the numbers:
-//
-std::cout << std::hex << std::showbase;
-for(unsigned i = 0; i < 10; ++i)
-   std::cout << ui(mt) << std::endl;
-
    -

    -

    -

    - Floating point values in [0,1) are generated using uniform_01, - the trick here is to ensure that the underlying generator produces as many - random bits as there are digits in the floating point type. As above independent_bits_engine can be used for - this purpose, note that we also have to convert decimal digits (in the floating - point type) to bits (in the random number generator): -

    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-#include <boost/multiprecision/random.hpp>
-
-using namespace boost::multiprecision;
-using namespace boost::random;
-//
-// We need an underlying generator with at least as many bits as the
-// floating point type to generate numbers in [0, 1) with all the bits
-// in the floating point type randomly filled:
-//
-uniform_01<mpf_float_50> uf;
-independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen;
-//
-// Generate the values:
-//
-std::cout << std::setprecision(50);
-for(unsigned i = 0; i < 20; ++i)
-   std::cout << uf(gen) << std::endl;
-
    -

    -

    -

    - Finally, we can modify the above example to produce numbers distributed according - to some distribution: -

    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-#include <boost/multiprecision/random.hpp>
-
-using namespace boost::multiprecision;
-using namespace boost::random;
-//
-// We can repeat the above example, with other distributions:
-//
-uniform_real_distribution<mpf_float_50> ur(-20, 20);
-gamma_distribution<mpf_float_50> gd(20);
-independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen;
-//
-// Generate some values:
-//
-std::cout << std::setprecision(50);
-for(unsigned i = 0; i < 20; ++i)
-   std::cout << ur(gen) << std::endl;
-for(unsigned i = 0; i < 20; ++i)
-   std::cout << gd(gen) << std::endl;
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html deleted file mode 100644 index 614d612e..00000000 --- a/doc/html/boost_multiprecision/tut/rational.html +++ /dev/null @@ -1,252 +0,0 @@ - - - -Rational Number Types - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    -
    gmp_rational
    -
    cpp_rational
    -
    tommath_rational
    -
    Use With Boost.Rational
    -
    rational_adapter
    -
    -

    - The following back-ends provide rational number arithmetic: -

    -
    -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    -

    - Backend Type -

    -     		-

    - Header -

    -     		-

    - Radix -

    -     		-

    - Dependencies -

    -     		-

    - Pros -

    -     		-

    - Cons -

    -
    -

    - gmp_rational -

    -     		-

    - boost/multiprecision/gmp.hpp -

    -     		-

    - 2 -

    -     		-

    - GMP -

    -     		-

    - Very fast and efficient back-end. -

    -     		-

    - Dependency on GNU licensed GMP - library. -

    -
    -

    - cpp_rational -

    -     		-

    - boost/multiprecision/cpp_int.hpp -

    -     		-

    - 2 -

    -     		-

    - None -

    -     		-

    - An all C++ Boost-licensed implementation. -

    -     		-

    - Slower than GMP. -

    -
    -

    - tommath_rational -

    -     		-

    - boost/multiprecision/tommath.hpp -

    -     		-

    - 2 -

    -     		-

    - libtommath -

    -     		-

    - All C/C++ implementation that's Boost Software Licence compatible. -

    -     		-

    - Slower than GMP. -

    -
    -

    - rational_adapter -

    -     		-

    - boost/multiprecision/rational_adapter.hpp -

    -     		-

    - N/A -

    -     		-

    - none -

    -     		-

    - All C++ adapter that allows any inetger back-end type to be used - as a rational type. -

    -     		-

    - Requires an underlying integer back-end type. -

    -
    -

    - boost::rational -

    -     		-

    - boost/rational.hpp -

    -     		-

    - N/A -

    -     		-

    - None -

    -     		-

    - A C++ rational number type that can used with any mp_number integer type. -

    -     		-

    - The expression templates used by mp_number - end up being "hidden" inside boost::rational: - performance may well suffer as a result. -

    -
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/rational/br.html b/doc/html/boost_multiprecision/tut/rational/br.html deleted file mode 100644 index a3efdfa6..00000000 --- a/doc/html/boost_multiprecision/tut/rational/br.html +++ /dev/null @@ -1,42 +0,0 @@ - - - -Use With Boost.Rational - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - All of the integer types in this library can be used as template arguments - to boost::rational<IntType>. -

    -

    - Note that using the library in this way largely negates the effect of the - expression templates in mp_number. -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html deleted file mode 100644 index ea6b42a8..00000000 --- a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html +++ /dev/null @@ -1,108 +0,0 @@ - - - -cpp_rational - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - #include <boost/multiprecision/cpp_int.hpp> -

    -
    namespace boost{ namespace multiprecision{
-
-typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
-
-typedef mp_number<cpp_rational_backend>         cpp_rational;
-
-}} // namespaces
-
    -

    - The cpp_rational_backend - type is used via the typedef boost::multiprecision::cpp_rational. - It provides a rational number type that is a drop-in replacement for the - native C++ number types, but with unlimited precision. -

    -

    - As well as the usual conversions from arithmetic and string types, instances - of cpp_rational are copy - constructible and assignable from type cpp_int. -

    -

    - There is also a two argument constructor that accepts a numerator and denominator: - both of type cpp_int. -

    -

    - There are also non-member functions: -

    -
    cpp_int numerator(const cpp_rational&);
-cpp_int denominator(const cpp_rational&);
-
    -

    - which return the numerator and denominator of the number. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed cpp_rationals - have the value zero. -
      • -
    • - Division by zero results in a std::rumtime_error - being thrown. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/cpp_int.hpp>
-
-using namespace boost::multiprecision;
-
-cpp_rational v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-v /= 10;
-
-std::cout << v << std::endl; // prints 1000! / 10
-std::cout << numerator(v) << std::endl;
-std::cout << denominator(v) << std::endl;
-
-cpp_rational w(2, 3);  // component wise constructor
-std::cout << w << std::endl; // prints 2/3
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html deleted file mode 100644 index 8f1f28fe..00000000 --- a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html +++ /dev/null @@ -1,138 +0,0 @@ - - - -gmp_rational - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - #include <boost/multiprecision/gmp.hpp> -

    -
    namespace boost{ namespace multiprecision{
-
-class gmp_rational;
-
-typedef mp_number<gmp_rational >         mpq_rational;
-
-}} // namespaces
-
    -

    - The gmp_rational back-end - is used via the typedef boost::multiprecision::mpq_rational. - It acts as a thin wrapper around the GMP - mpq_t to provide a rational - number type that is a drop-in replacement for the native C++ number types, - but with unlimited precision. -

    -

    - As well as the usual conversions from arithmetic and string types, instances - of mp_number<gmp_rational> - are copy constructible and assignable from: -

    -
      -
    • - The GMP native types: mpz_t, mpq_t. -
      • -
    • - mp_number<gmp_int>. -
      • -
    -

    - There is also a two-argument constructor that accepts a numerator and denominator - (both of type mp_number<gmp_int>). -

    -

    - There are also non-member functions: -

    -
    mpz_int numerator(const mpq_rational&);
-mpz_int denominator(const mpq_rational&);
-
    -

    - which return the numerator and denominator of the number. -

    -

    - It's also possible to access the underlying mpq_t - via the data() - member function of mpq_rational. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed mpq_rationals - have the value zero (this is the GMP - default behavior). -
      • -
    • - Division by zero results in a hardware exception inside the GMP library. -
      • -
    • - No changes are made to the GMP - library's global settings, so this type can coexist with existing - GMP code. -
      • -
    • - The code can equally be used with MPIR - as the underlying library - indeed that is the preferred option on - Win32. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/gmp.hpp>
-
-using namespace boost::multiprecision;
-
-mpq_rational v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-v /= 10;
-
-std::cout << v << std::endl; // prints 1000! / 10
-std::cout << numerator(v) << std::endl;
-std::cout << denominator(v) << std::endl;
-
-mpq_rational w(2, 3);  // component wise constructor
-std::cout << w << std::endl; // prints 2/3
-
-// Access the underlying data:
-mpq_t q;
-mpq_init(q);
-mpq_set(q, v.backend().data());
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/rational/rational_adapter.html b/doc/html/boost_multiprecision/tut/rational/rational_adapter.html deleted file mode 100644 index 6b4853f1..00000000 --- a/doc/html/boost_multiprecision/tut/rational/rational_adapter.html +++ /dev/null @@ -1,58 +0,0 @@ - - - -rational_adapter - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -
    namespace boost{ namespace multiprecision{
-
-template <class IntBackend>
-class rational_adpater;
-
-}}
-
    -

    - The class template rational_adapter - is a back-end for mp_number - which converts any existing integer back-end into a rational-number back-end. -

    -

    - So for example, given an integer back-end type MyIntegerBackend, - the use would be something like: -

    -
    typedef mp_number<MyIntegerBackend>                    MyInt;
-typedef mp_number<rational_adapter<MyIntegerBackend> > MyRational;
-
-MyRational r = 2;
-r /= 3;
-MyInt i = numerator(r);
-assert(i == 2);
-
    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html deleted file mode 100644 index 25520372..00000000 --- a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html +++ /dev/null @@ -1,115 +0,0 @@ - - - -tommath_rational - - - - - - - - -
    -PrevUpHomeNext -
    -
    -
    -

    - #include <boost/multiprecision/tommath.hpp> -

    -
    namespace boost{ namespace multiprecision{
-
-typedef rational_adpater<tommath_int>        tommath_rational;
-typedef mp_number<tommath_rational >         tom_rational;
-
-}} // namespaces
-
    -

    - The tommath_rational back-end - is used via the typedef boost::multiprecision::tom_rational. - It acts as a thin wrapper around boost::rational<tom_int> to provide a rational number type that - is a drop-in replacement for the native C++ number types, but with unlimited - precision. -

    -

    - The advantage of using this type rather than boost::rational<tom_int> directly, is that it is expression-template - enabled, greatly reducing the number of temporaries created in complex - expressions. -

    -

    - There are also non-member functions: -

    -
    tom_int numerator(const tom_rational&);
-tom_int denominator(const tom_rational&);
-
    -

    - which return the numerator and denominator of the number. -

    -

    - Things you should know when using this type: -

    -
      -
    • - Default constructed tom_rationals - have the value zero (this the inherited Boost.Rational behavior). -
      • -
    • - Division by zero results in a boost::bad_rational - exception being thrown (see the rational number library's docs for - more information). -
      • -
    • - No changes are made to libtommath's - global state, so this type can safely coexist with other libtommath - code. -
      • -
    • - Performance of this type has been found to be pretty poor - this need - further investigation - but it appears that Boost.Rational needs some - improvement in this area. -
      • -
    -
    - - Example: -
    -

    -

    -
    #include <boost/multiprecision/tommath.hpp>
-
-using namespace boost::multiprecision;
-
-tom_rational v = 1;
-
-// Do some arithmetic:
-for(unsigned i = 1; i <= 1000; ++i)
-   v *= i;
-v /= 10;
-
-std::cout << v << std::endl; // prints 1000! / 10
-std::cout << numerator(v) << std::endl;
-std::cout << denominator(v) << std::endl;
-
-tom_rational w(2, 3); // Component wise constructor
-std::cout << w << std::endl; // prints 2/3
-
    -

    -

    -
    - - - -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -PrevUpHomeNext -
    - - diff --git a/doc/html/index.html b/doc/html/index.html deleted file mode 100644 index 4ed88ab7..00000000 --- a/doc/html/index.html +++ /dev/null @@ -1,119 +0,0 @@ - - - -Chapter 1. Boost.Multiprecision - - - - - - -
    Next
    -
    -
    -

    -Chapter 1. Boost.Multiprecision

    -

    -John Maddock -

    -

    -Christopher Kormanyos -

    -

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    -
    -

    - Distributed under the Boost Software License, Version 1.0. (See accompanying - file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -

    -
    -
    -
    -

    Table of Contents

    -
    -
    Introduction
    -
    Tutorial
    -
    -
    Integer Types
    -
    -
    cpp_int
    -
    gmp_int
    -
    tom_int
    -
    -
    Floating Point Numbers
    -
    -
    gmp_float
    -
    mpfr_float
    -
    cpp_dec_float
    -
    Examples
    -
    -
    Area of - Circle
    -
    Defining - a Lambda Function.
    -
    Calculating - a Derivative
    -
    Calculating - an Integral
    -
    -
    -
    Rational Number Types
    -
    -
    gmp_rational
    -
    cpp_rational
    -
    tommath_rational
    -
    Use With Boost.Rational
    -
    rational_adapter
    -
    -
    Constructing and - Interconverting Between Number Types
    -
    Generating Random Numbers
    -
    Primality Testing
    -
    -
    Reference
    -
    -
    mp_number
    -
    cpp_int
    -
    gmp_int
    -
    tom_int
    -
    gmp_float
    -
    mpfr_float_backend
    -
    cpp_dec_float
    -
    Backend Requirements
    -
    -
    Performance Comparison
    -
    -
    Floating Point Real - World Tests
    -
    Integer Real - World Tests
    -
    Float Algorithm - Perfomance
    -
    Integer - Algorithm Perfomance
    -
    Rational - Type Perfomance
    -
    -
    Roadmap
    -
    -
    History
    -
    TODO
    -
    Acknowledgements
    -
    -
    Indexes
    -
    -
    Function Index
    -
    Class Index
    -
    Typedef Index
    -
    Index
    -
    -
    -
    -
    - - - -

    Last revised: April 09, 2012 at 16:55:19 GMT

    -
    -
    Next
    - - diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index f1bf2c33..4804fd6d 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -407,6 +407,20 @@ as a result performing formatted output on this type when the argument is negati [endsect] +[section:egs Examples] + +[import ../example/integer_examples.cpp] + +[section:factorials Factorials] +[FAC1] +[endsect] + +[section:bitops Bit Operations] +[BITOPS] +[endsect] + +[endsect] + [endsect] [section:floats Floating Point Numbers] @@ -595,13 +609,19 @@ Normally these should not be visible to the user. [endsect] -[section:GI Calculating an Integral] +[section:gi Calculating an Integral] [GI1] [GI2] [endsect] +[section:poly_eg Polynomial Evaluation] + +[POLY] + +[endsect] + [endsect] [endsect] @@ -874,7 +894,7 @@ Finally, we can modify the above example to produce numbers distributed accordin [section:primetest Primality Testing] -The library implements a fairly basic (meaning unoptimized, and possibly slow) Miller-Rabin test for primality: +The library implements a Miller-Rabin test for primality: #include @@ -885,7 +905,9 @@ The library implements a fairly basic (meaning unoptimized, and possibly slow) M bool miller_rabin_test(const mp_number& n, unsigned trials); These functions perform a Miller-Rabin test for primality, if the result is `false` then /n/ is definitely composite, -while if the result is `true` then /n/ is prime with probability ['0.25^trials]. The algorithm used is straight out of +while if the result is `true` then /n/ is prime with probability ['0.25^trials]. The algorithm used performs some +trial divisions to exclude small prime factors, does one Fermat test to exclude many more composites, and then +uses the Miller-Rabin algorithm straight out of Knuth Vol 2, which recomends 25 trials for a pretty strong likelyhood that /n/ is prime. The third optional argument is for a Uniform Random Number Generator from Boost.Random. When not provided the `mt19937` diff --git a/example/floating_point_examples.cpp b/example/floating_point_examples.cpp index 81fccd70..701d4b0b 100644 --- a/example/floating_point_examples.cpp +++ b/example/floating_point_examples.cpp @@ -8,6 +8,7 @@ #include #include #include +#include //[AOS1 @@ -338,6 +339,120 @@ private: //] +//[POLY + +/*` +In this example we'll look at polynomial evaluation, this is not only an important +use case, but it's one that `mp_number` performs particularly well at because the +expression templates ['completely eliminate all temporaries] from a +[@http://en.wikipedia.org/wiki/Horner%27s_method Horner polynomial +evaluation scheme]. + +The following code evaluates `sin(x)` as a polynomial, accurate to at least 64 decimal places: + +*/ + +using boost::multiprecision::cpp_dec_float; +typedef boost::multiprecision::mp_number > mp_type; + +mp_type mysin(const mp_type& x) +{ + // Approximation of sin(x * pi/2) for -1 <= x <= 1, using an order 63 polynomial. + static const std::array coefs = + {{ + mp_type("+1.5707963267948966192313216916397514420985846996875529104874722961539082031431044993140174126711"), //"), + mp_type("-0.64596409750624625365575656389794573337969351178927307696134454382929989411386887578263960484"), // ^3 + mp_type("+0.07969262624616704512050554949047802252091164235106119545663865720995702920146198554317279"), // ^5 + mp_type("-0.0046817541353186881006854639339534378594950280185010575749538605102665157913157426229824"), // ^7 + mp_type("+0.00016044118478735982187266087016347332970280754062061156858775174056686380286868007443"), // ^9 + mp_type("-3.598843235212085340458540018208389404888495232432127661083907575106196374913134E-6"), // ^11 + mp_type("+5.692172921967926811775255303592184372902829756054598109818158853197797542565E-8"), // ^13 + mp_type("-6.688035109811467232478226335783138689956270985704278659373558497256423498E-10"), // ^15 + mp_type("+6.066935731106195667101445665327140070166203261129845646380005577490472E-12"), // ^17 + mp_type("-4.377065467313742277184271313776319094862897030084226361576452003432E-14"), // ^19 + mp_type("+2.571422892860473866153865950420487369167895373255729246889168337E-16"), // ^21 + mp_type("-1.253899540535457665340073300390626396596970180355253776711660E-18"), // ^23 + mp_type("+5.15645517658028233395375998562329055050964428219501277474E-21"), // ^25 + mp_type("-1.812399312848887477410034071087545686586497030654642705E-23"), // ^27 + mp_type("+5.50728578652238583570585513920522536675023562254864E-26"), // ^29 + mp_type("-1.461148710664467988723468673933026649943084902958E-28"), // ^31 + mp_type("+3.41405297003316172502972039913417222912445427E-31"), // ^33 + mp_type("-7.07885550810745570069916712806856538290251E-34"), // ^35 + mp_type("+1.31128947968267628970845439024155655665E-36"), // ^37 + mp_type("-2.18318293181145698535113946654065918E-39"), // ^39 + mp_type("+3.28462680978498856345937578502923E-42"), // ^41 + mp_type("-4.48753699028101089490067137298E-45"), // ^43 + mp_type("+5.59219884208696457859353716E-48"), // ^45 + mp_type("-6.38214503973500471720565E-51"), // ^47 + mp_type("+6.69528558381794452556E-54"), // ^49 + mp_type("-6.47841373182350206E-57"), // ^51 + mp_type("+5.800016389666445E-60"), // ^53 + mp_type("-4.818507347289E-63"), // ^55 + mp_type("+3.724683686E-66"), // ^57 + mp_type("-2.6856479E-69"), // ^59 + mp_type("+1.81046E-72"), // ^61 + mp_type("-1.133E-75"), // ^63 + }}; + + const mp_type v = x * 2 / boost::math::constants::pi(); + const mp_type x2 = (v * v); + // + // Polynomial evaluation follows, if mp_type allocates memory then + // just one such allocation occurs - to initialize the variable "sum" - + // and no temporaries are created at all. + // + const mp_type sum = ((((((((((((((((((((((((((((((( + coefs[31U] + * x2 + coefs[30U]) + * x2 + coefs[29U]) + * x2 + coefs[28U]) + * x2 + coefs[27U]) + * x2 + coefs[26U]) + * x2 + coefs[25U]) + * x2 + coefs[24U]) + * x2 + coefs[23U]) + * x2 + coefs[22U]) + * x2 + coefs[21U]) + * x2 + coefs[20U]) + * x2 + coefs[19U]) + * x2 + coefs[18U]) + * x2 + coefs[17U]) + * x2 + coefs[16U]) + * x2 + coefs[15U]) + * x2 + coefs[14U]) + * x2 + coefs[13U]) + * x2 + coefs[12U]) + * x2 + coefs[11U]) + * x2 + coefs[10U]) + * x2 + coefs[9U]) + * x2 + coefs[8U]) + * x2 + coefs[7U]) + * x2 + coefs[6U]) + * x2 + coefs[5U]) + * x2 + coefs[4U]) + * x2 + coefs[3U]) + * x2 + coefs[2U]) + * x2 + coefs[1U]) + * x2 + coefs[0U]) + * v; + + return sum; +} + +/*` +Calling the function like so: + + std::cout << std::setprecision(std::numeric_limits<::mp_type>::digits10) << std::scientific; + std::cout << mysin(mp_type(1)) << std::endl; + +Yields the expected output: + +[pre 7.0710678118654752440084436210484903928483593768847403658833986900e-01] + +*/ + +//] + + int main() { using namespace boost::multiprecision; @@ -542,6 +657,10 @@ int main(int, char**) //] + std::cout << std::setprecision(std::numeric_limits<::mp_type>::digits10) << std::scientific; + std::cout << mysin(boost::math::constants::pi<::mp_type>() / 4) << std::endl; + std::cout << boost::multiprecision::sin(boost::math::constants::pi<::mp_type>() / 4) << std::endl; + return 0; } @@ -562,4 +681,6 @@ Program output: 4.99999999999999999999999999999999999999999999999999e-01 2.70670566473225383787998989944968806815263091819151e-01 2.70670566473225383787998989944968806815253190143120e-01 +7.0710678118654752440084436210484903928483593768847403658833986900e-01 +7.0710678118654752440084436210484903928483593768847403658833986900e-01 */ \ No newline at end of file diff --git a/example/integer_examples.cpp b/example/integer_examples.cpp new file mode 100644 index 00000000..68cb0653 --- /dev/null +++ b/example/integer_examples.cpp @@ -0,0 +1,231 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include +#include +#include + +//[FAC1 + +/*` +In this simple example, we'll write a routine to print out all of the factorials +which will fit into a 128-bit integer. At the end of the routine we do some +fancy iostream formatting of the results: +*/ +/*= +#include +#include +#include +#include +*/ + +void print_factorials() +{ + using boost::multiprecision::cpp_int; + // + // Print all the factorials that will fit inside a 128-bit integer. + // + // Begin by building a big table of factorials, once we know just how + // large the largest is, we'll be able to "pretty format" the results. + // + // Calculate the largest number that will fit inside 128 bits, we could + // also have used numeric_limits::max() for this value: + cpp_int limit = (cpp_int(1) << 128) - 1; + // + // Our table of values: + std::vector results; + // + // Initial values: + unsigned i = 1; + cpp_int factorial = 1; + // + // Cycle through the factorials till we reach the limit: + while(factorial < limit) + { + results.push_back(factorial); + ++i; + factorial *= i; + } + // + // Lets see how many digits the largest factorial was: + unsigned digits = results.back().str().size(); + // + // Now print them out, using right justification, while we're at it + // we'll indicate the limit of each integer type, so begin by defining + // the limits for 16, 32, 64 etc bit integers: + cpp_int limits[] = { + (cpp_int(1) << 16) - 1, + (cpp_int(1) << 32) - 1, + (cpp_int(1) << 64) - 1, + (cpp_int(1) << 128) - 1, + }; + std::string bit_counts[] = { "16", "32", "64", "128" }; + unsigned current_limit = 0; + for(unsigned j = 0; j < results.size(); ++j) + { + if(limits[current_limit] < results[j]) + { + std::string message = "Limit of " + bit_counts[current_limit] + " bit integers"; + std::cout << std::setfill('.') << std::setw(digits+1) << std::right << message << std::setfill(' ') << std::endl; + ++current_limit; + } + std::cout << std::setw(digits + 1) << std::right << results[j] << std::endl; + } +} + +/*` +The output from this routine is: +[template nul[]] [# fix for quickbook bug] +[pre [nul] + 1 + 2 + 6 + 24 + 120 + 720 + 5040 + 40320 +................Limit of 16 bit integers + 362880 + 3628800 + 39916800 + 479001600 +................Limit of 32 bit integers + 6227020800 + 87178291200 + 1307674368000 + 20922789888000 + 355687428096000 + 6402373705728000 + 121645100408832000 + 2432902008176640000 +................Limit of 64 bit integers + 51090942171709440000 + 1124000727777607680000 + 25852016738884976640000 + 620448401733239439360000 + 15511210043330985984000000 + 403291461126605635584000000 + 10888869450418352160768000000 + 304888344611713860501504000000 + 8841761993739701954543616000000 + 265252859812191058636308480000000 + 8222838654177922817725562880000000 + 263130836933693530167218012160000000 + 8683317618811886495518194401280000000 + 295232799039604140847618609643520000000 +] +*/ + +//] + +//[BITOPS + +/*` +In this example we'll show how individual bits within an integer may be manipulated, +we'll start with an often needed calculation of ['2[super n] - 1], which we could obviously +implement like this: +*/ + +using boost::multiprecision::cpp_int; + +cpp_int b1(unsigned n) +{ + cpp_int r(1); + return (r << n) - 1; +} + +/*` +Calling: + + std::cout << std::hex << std::showbase << b1(200) << std::endl; + +Yields as expected: + +[pre 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF] + +However, we could equally just set the n'th bit in the result, like this: +*/ + +cpp_int b2(unsigned n) +{ + cpp_int r(0); + return --bit_set(r, n); +} + +/*` +Note how the `bit_set` function sets the specified bit in it's argument and then returns a reference to the result - +which we can then simply decrement. The result from a call to `b2` is the same as that to `b1`. + +We can equally test bits, so for example the n'th bit of the result returned from `b2` shouldn't be set +unless we increment it first: + + assert(!bit_test(b1(200), 200)); // OK + assert(bit_test(++b1(200), 200)); // OK + +And of course if we flip the n'th bit after increment, then we should get back to zero: + + assert(!bit_flip(++b1(200), 200)); // OK +*/ + +//] + +int main() +{ + print_factorials(); + + std::cout << std::hex << std::showbase << b1(200) << std::endl; + std::cout << std::hex << std::showbase << b2(200) << std::endl; + assert(!bit_test(b1(200), 200)); // OK + assert(bit_test(++b1(200), 200)); // OK + assert(!bit_flip(++b1(200), 200)); // OK + return 0; +} + +/* + +Program output: + + 1 + 2 + 6 + 24 + 120 + 720 + 5040 + 40320 +................Limit of 16 bit integers + 362880 + 3628800 + 39916800 + 479001600 +................Limit of 32 bit integers + 6227020800 + 87178291200 + 1307674368000 + 20922789888000 + 355687428096000 + 6402373705728000 + 121645100408832000 + 2432902008176640000 +................Limit of 64 bit integers + 51090942171709440000 + 1124000727777607680000 + 25852016738884976640000 + 620448401733239439360000 + 15511210043330985984000000 + 403291461126605635584000000 + 10888869450418352160768000000 + 304888344611713860501504000000 + 8841761993739701954543616000000 + 265252859812191058636308480000000 + 8222838654177922817725562880000000 + 263130836933693530167218012160000000 + 8683317618811886495518194401280000000 + 295232799039604140847618609643520000000 + 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF + 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF + */ \ No newline at end of file diff --git a/test/test_acos.cpp b/test/test_acos.cpp index de5957c1..a827fc48 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -102,6 +102,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index ca7a39c1..c230a9cd 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -447,7 +447,7 @@ void test_float_ops(const boost::mpl::int_(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_atan.cpp b/test/test_atan.cpp index ae0886d0..d1ee181c 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -244,6 +244,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_cos.cpp b/test/test_cos.cpp index 81138810..71c0c9b3 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -298,6 +298,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index ef6b372c..ad609a88 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -140,6 +140,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_exp.cpp b/test/test_exp.cpp index 34a19a35..7bd32666 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -180,6 +180,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp index caeb2c02..17bc33d5 100644 --- a/test/test_float_io.cpp +++ b/test/test_float_io.cpp @@ -191,6 +191,7 @@ void test() template T generate_random() { + typedef typename T::backend_type::exponent_type e_type; static boost::random::mt19937 gen; T val = gen(); T prev_val = -1; @@ -200,10 +201,9 @@ T generate_random() prev_val = val; val += gen(); } - int e; + e_type e; val = frexp(val, &e); - typedef typename T::backend_type::exponent_type e_type; static boost::random::uniform_int_distribution ui(0, std::numeric_limits::max_exponent - 10); return ldexp(val, ui(gen)); } @@ -260,11 +260,11 @@ int main() test(); test(); - /* + // cpp_dec_float has extra guard digits that messes this up: test_round_trip(); test_round_trip(); - */ + #endif #ifdef TEST_MPF_50 test(); diff --git a/test/test_log.cpp b/test/test_log.cpp index a8a743d3..fcd628f6 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -208,6 +208,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_pow.cpp b/test/test_pow.cpp index 3c909653..e98be847 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -583,6 +583,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_round.cpp b/test/test_round.cpp index 4efa024a..f6058668 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -389,6 +389,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif #ifdef TEST_BACKEND test >(); diff --git a/test/test_sin.cpp b/test/test_sin.cpp index 23470635..708fe5e8 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -291,6 +291,16 @@ int main() #endif #ifdef TEST_CPP_DEC_FLOAT test(); + test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index cfa84bdb..8ba7078b 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -216,6 +216,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp index ec801267..df50cf9f 100644 --- a/test/test_sqrt.cpp +++ b/test/test_sqrt.cpp @@ -186,6 +186,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index 71a05174..93052dd7 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -135,6 +135,15 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } From 5c9d22ae8e51cdc9fe5c76505c46f3c153c205e7 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 13 Apr 2012 15:40:50 +0000 Subject: [PATCH 169/256] Commit revised docs. 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    + The Multiprecision Library provides User-defined integer, + rational and floating-point C++ types which try to emulate as closely as practicable + the C++ built-in types, but provide for more range and precision. Depending + upon the number type, precision may be arbitrarily large (limited only by available + memory), fixed at compile time values, for example 50 decimal digits, or a + variable controlled at run-time by member functions. The types are expression-template-enabled + for better performance than naive user-defined types. +

    +

    + The Multiprecision library comes in two distinct parts: +

    +
      +
    • + An expression-template-enabled front-end mp_number + that handles all the operator overloading, expression evaluation optimization, + and code reduction. +
      • +
    • + A selection of back-ends that implement the actual arithmetic operations, + and need conform only to the reduced interface requirements of the front-end. +
      • +
    +

    + Separation of front-end and back-end allows use of highly refined, but restricted + license libraries where possible, but provides Boost license alternatives for + users who must have a portable unconstrained license. Which is to say some + back-ends rely on 3rd party libraries, but a header-only Boost license version + is always available (if somewhat slower). +

    +

    + The library is often used via one of the predefined typedefs: for example if + you wanted an arbitrary + precision integer type using GMP + as the underlying implementation then you could use: +

    +
    #include <boost/multiprecision/gmp.hpp>  // Defines the wrappers around the GMP library's types
+
+boost::multiprecision::mpz_int myint;    // Arbitrary precision integer type.
+
    +

    + Alternatively, you can compose your own multiprecision type, by combining + mp_number with one of the predefined + back-end types. For example, suppose you wanted a 300 decimal digit floating-point + type based on the MPFR library. In + this case, there's no predefined typedef with that level of precision, so instead + we compose our own: +

    +
    #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
+
+namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
+
+typedef mp::mp_number<mp::mpfr_float_backend<300> >  my_float;
+
+my_float a, b, c; // These variables have 300 decimal digits precision
+
    +

    + We can repeat the above example, but with the expression templates disabled + (for faster compile times, but slower runtimes) by passing a second template + argument to mp_number: +

    +
    #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
+
+namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
+
+typedef mp::mp_number<mp::mpfr_float_backend<300>, false>  my_float;
+
+my_float a, b, c; // These variables have 300 decimal digits precision
+
    +
    + + Expression + Templates +
    +

    + Class mp_number is expression-template-enabled: + that means that rather than having a multiplication operator that looks like + this: +

    +
    template <class Backend>
+mp_number<Backend> operator * (const mp_number<Backend>& a, const mp_number<Backend>& b)
+{
+   mp_number<Backend> result(a);
+   result *= b;
+   return result;
+}
+
    +

    + Instead the operator looks more like this: +

    +
    template <class Backend>
+unmentionable-type operator * (const mp_number<Backend>& a, const mp_number<Backend>& b);
+
    +

    + Where the "unmentionable" return type is an implementation detail + that, rather than containing the result of the multiplication, contains instructions + on how to compute the result. In effect it's just a pair of references to the + arguments of the function, plus some compile-time information that stores what + the operation is. +

    +

    + The great advantage of this method is the elimination of temporaries: + for example the "naive" implementation of operator* above, requires one temporary for computing + the result, and at least another one to return it. It's true that sometimes + this overhead can be reduced by using move-semantics, but it can't be eliminated + completely. For example, lets suppose we're evaluating a polynomial via Horners + method, something like this: +

    +
    T a[7] = { /* some values */ };
+//....
+y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0];
+
    +

    + If type T is an mp_number, then this expression is evaluated + without creating a single temporary value. In contrast, + if we were using the C++ wrapper that ships with GMP + - mpfr_class + - then this expression would result in no less than 11 temporaries (this is + true even though mpfr_class + does use expression templates to reduce the number of temporaries somewhat). + Had we used an even simpler wrapper around GMP + or MPFR like mpclass + things would have been even worse and no less that 24 temporaries are created + for this simple expression (note - we actually measure the number of memory + allocations performed rather than the number of temporaries directly). +

    +

    + This library also extends expression template support to standard library functions + like abs or sin + with mp_number arguments. This + means that an expression such as: +

    +
    y = abs(x);
+
    +

    + can be evaluated without a single temporary being calculated. Even expressions + like: +

    +
    y = sin(x);
+
    +

    + get this treatment, so that variable 'y' is used as "working storage" + within the implementation of sin, + thus reducing the number of temporaries used by one. Of course, should you + write: +

    +
    x = sin(x);
+
    +

    + Then we clearly can't use x + as working storage during the calculation, so then a temporary variable is + created in this case. +

    +

    + Given the comments above, you might be forgiven for thinking that expression-templates + are some kind of universal-panacea: sadly though, all tricks like this have + their downsides. For one thing, expression template libraries like this one, + tend to be slower to compile than their simpler cousins, they're also harder + to debug (should you actually want to step through our code!), and rely on + compiler optimizations being turned on to give really good performance. Also, + since the return type from expressions involving mp_numbers + is an "unmentionable implementation detail", you have to be careful + to cast the result of an expression to the actual number type when passing + an expression to a template function. For example, given: +

    +
    template <class T>
+void my_proc(const T&);
+
    +

    + Then calling: +

    +
    my_proc(a+b);
+
    +

    + Will very likely result in obscure error messages inside the body of my_proc - since we've passed it an expression + template type, and not a number type. Instead we probably need: +

    +
    my_proc(my_mp_number_type(a+b));
+
    +

    + Having said that, these situations don't occur that often - or indeed not at + all for non-template functions. In addition, all the functions in the Boost.Math + library will automatically convert expression-template arguments to the underlying + number type without you having to do anything, so: +

    +
    mpfr_float_100 a(20), delta(0.125);
+boost::math::gamma_p(a, a + delta);
+
    +

    + Will work just fine, with the a + delta expression + template argument getting converted to an mpfr_float_100 + internally by the Boost.Math library. +

    +

    + One other potential pitfall that's only possible in C++11: you should never + store an expression template using: +

    +
    auto my_expression = a + b - c;
+
    +

    + unless you're absolutely sure that the lifetimes of a, + b and c + will outlive that of my_expression. +

    +

    + And finally... the performance improvements from an expression template library + like this are often not as dramatic as the reduction in number of temporaries + would suggest. For example if we compare this library with mpfr_class + and mpreal, with + all three using the underlying MPFR + library at 50 decimal digits precision then we see the following typical results + for polynomial execution: +

    +
    +

    Table 1.1. Evaluation of Order 6 Polynomial.

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + Relative Time +

    +     		+

    + Relative number of memory allocations +

    +
    +

    + mp_number +

    +     		+

    + 1.0 (0.00793s) +

    +     		+

    + 1.0 (2996 total) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.2 (0.00931s) +

    +     		+

    + 4.3 (12976 total) +

    +
    +

    + mpreal +

    +     		+

    + 1.9 (0.0148s) +

    +     		+

    + 9.3 (27947 total) +

    +
    +
    +

    + As you can see, the execution time increases a lot more slowly than the number + of memory allocations. There are a number of reasons for this: +

    +
      +
    • + The cost of extended-precision multiplication and division is so great, + that the times taken for these tend to swamp everything else. +
      • +
    • + The cost of an in-place multiplication (using operator*=) tends to be more than an out-of-place + operator* + (typically operator *= + has to create a temporary workspace to carry out the multiplication, where + as operator* + can use the target variable as workspace). Since the expression templates + carry out their magic by converting out-of-place operators to in-place + ones, we necessarily take this hit. Even so the transformation is more + efficient than creating the extra temporary variable, just not by as much + as one would hope. +
      • +
    +

    + Finally, note that mp_number + takes a second template argument, which, when set to false + disables all the expression template machinery. The result is much faster to + compile, but slower at runtime. +

    +

    + We'll conclude this section by providing some more performance comparisons + between these three libraries, again, all are using MPFR + to carry out the underlying arithmetic, and all are operating at the same precision + (50 decimal digits): +

    +
    +

    Table 1.2. Evaluation of Boost.Math's Bessel function test data

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + Relative Time +

    +     		+

    + Relative Number of Memory Allocations +

    +
    +

    + mp_number +

    +     		+

    + 1.0 (6.21s) +

    +     		+

    + 1.0 (2685469) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.04 (6.45s) +

    +     		+

    + 1.47 (3946007) +

    +
    +

    + mpreal +

    +     		+

    + 1.53 (9.52s) +

    +     		+

    + 4.92 (13222940) +

    +
    +
    +
    +

    Table 1.3. Evaluation of Boost.Math's Non-Central T distribution test data

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + Relative Time +

    +     		+

    + Relative Number of Memory Allocations +

    +
    +

    + mp_number +

    +     		+

    + 1.0 (269s) +

    +     		+

    + 1.0 (139082551) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.04 (278s) +

    +     		+

    + 1.81 (252400791) +

    +
    +

    + mpreal +

    +     		+

    + 1.49 (401s) +

    +     		+

    + 3.22 (447009280) +

    +
    +
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

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    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

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    + This library would not have happened without: +

    +
      +
    • + Christopher Kormanyos' C++ decimal number code. +
      • +
    • + Paul Bristow for patiently testing, and commenting on the library. +
      • +
    • + All the folks at GMP, MPFR and libtommath, for providing the "guts" + that makes this library work. +
      • +
    • + "The + Art Of Computer Programming", Donald E. Knuth, Volume 2: + Seminumerical Algorithms, Third Edition (Reading, Massachusetts: Addison-Wesley, + 1997), xiv+762pp. ISBN 0-201-89684-2 +
      • +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

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      +
    • + 2011-2012, John Maddock adds an expression template enabled front end + to Christopher's code, and adds support for other backends. +
      • +
    • + 2011, Christopher Kormanyos publishes the decimal floating point code + under the Boost Software Licence. The code is published as: "Algorithm + 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", + in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. +
      • +
    • + 2002-2011, Christopher Kormanyos develops the all C++ decimal arithmetic + floating point code. +
      • +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html new file mode 100644 index 00000000..00d93f94 --- /dev/null +++ b/doc/html/boost_multiprecision/map/todo.html @@ -0,0 +1,104 @@ + + + +TODO + + + + + + + + +
    +PrevUpHomeNext +
    +
    +

    +TODO +

    +

    + More a list of what could be done, rather than what + should be done (which may be a much smaller list!). +

    +
      +
    • + Add back-end support for libdecNumber. +
      • +
    • + Add an adapter back-end for complex number types. +
      • +
    • + Add a back-end for MPFR interval arithmetic. +
      • +
    • + Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. +
      • +
    • + Add assembly level routines to cpp_int_backend. +
      • +
    • + Add an all C++ binary floating point type. +
      • +
    +
    + + Pre-Review + Comments +
    +
      +
    • + Make the exponent type for cpp_dec_float a templare parameter, maybe + include support for big-integer exponents. Open question - what should + be the default - int32_t or int64_t? +
      • +
    • + Document the size requirements of fixed precision ints. +
      • +
    • + Document std lib function accuracy. +
      • +
    • + Make fixed precision orthogonal to Allocator type in cpp_int. Possible + solution - add an additional MaxBits template argument that defaults + to 0 (meaning keep going till no more space/memory). +
      • +
    • + Add support for fused multiply add (and subtract). GMP mpz_t could use + this. +
      • +
    • + Be a bit clearer on the effects of sign-magnitude representation of cpp_int + - min == -max etc. +
      • +
    • + Document cpp_dec_float precision, rounding, and exponent size. +
      • +
    • + Can we be clearer in the docs that mixed arithmetic doesn't work? +
      • +
    • + Document round functions behaviour better (they behave as in C99). +
      • +
    • + Should there be a choice of rounding mode (probably MPFR specific)? +
      • +
    • + Document limits on size of cpp_dec_float. +
      • +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf.html b/doc/html/boost_multiprecision/perf.html new file mode 100644 index 00000000..7460f077 --- /dev/null +++ b/doc/html/boost_multiprecision/perf.html @@ -0,0 +1,46 @@ + + + +Performance Comparison + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    Floating Point Real + World Tests
    +
    Integer Real + World Tests
    +
    Float Algorithm + Perfomance
    +
    Integer + Algorithm Perfomance
    +
    Rational + Type Perfomance
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html new file mode 100644 index 00000000..9e9b8217 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/float_performance.html @@ -0,0 +1,961 @@ + + + +Float Algorithm Perfomance + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticism, and real-world + performance may vary widely depending upon the specifics of the program. + In each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. + The tests were run on 32-bit Windows Vista machine. +

    +
    +

    Table 1.8. Operator +

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1 (0.02382s) +

    +     		+

    + 1 (0.0294619s) +

    +     		+

    + 1 (0.058466s) +

    +
    +

    + gmp_float +

    +     		+

    + 4.55086 (0.108402s) +

    +     		+

    + 3.86443 (0.113853s) +

    +     		+

    + 2.6241 (0.15342s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.52036 (0.060035s) +

    +     		+

    + 2.1833 (0.0643242s) +

    +     		+

    + 1.37736 (0.0805287s) +

    +
    +
    +
    +

    Table 1.9. Operator +(int)

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1.56759 (0.0527023s) +

    +     		+

    + 1.74629 (0.0618102s) +

    +     		+

    + 1.68077 (0.105927s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.0336201s) +

    +     		+

    + 1 (0.0353951s) +

    +     		+

    + 1 (0.0630232s) +

    +
    +

    + mpfr_float +

    +     		+

    + 3.14875 (0.105861s) +

    +     		+

    + 3.15499 (0.111671s) +

    +     		+

    + 1.92831 (0.121528s) +

    +
    +
    +
    +

    Table 1.10. Operator -

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1 (0.0265783s) +

    +     		+

    + 1 (0.031465s) +

    +     		+

    + 1 (0.0619405s) +

    +
    +

    + gmp_float +

    +     		+

    + 4.66954 (0.124108s) +

    +     		+

    + 3.72645 (0.117253s) +

    +     		+

    + 2.67536 (0.165713s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.7909 (0.0741774s) +

    +     		+

    + 2.48557 (0.0782083s) +

    +     		+

    + 1.50944 (0.0934957s) +

    +
    +
    +
    +

    Table 1.11. Operator -(int)

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1 (0.0577674s) +

    +     		+

    + 1 (0.0633795s) +

    +     		+

    + 1 (0.11146s) +

    +
    +

    + gmp_float +

    +     		+

    + 2.31811 (0.133911s) +

    +     		+

    + 2.07251 (0.131355s) +

    +     		+

    + 1.67161 (0.186319s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.45081 (0.141577s) +

    +     		+

    + 2.29174 (0.145249s) +

    +     		+

    + 1.395 (0.155487s) +

    +
    +
    +
    +

    Table 1.12. Operator *

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1.07276 (0.287898s) +

    +     		+

    + 1.47724 (0.584569s) +

    +     		+

    + 1.55145 (5.09969s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.268372s) +

    +     		+

    + 1 (0.395718s) +

    +     		+

    + 1 (3.28705s) +

    +
    +

    + mpfr_float +

    +     		+

    + 1.27302 (0.341642s) +

    +     		+

    + 1.17649 (0.465557s) +

    +     		+

    + 1.14029 (3.7482s) +

    +
    +
    +
    +

    Table 1.13. Operator *(int)

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 2.89945 (0.11959s) +

    +     		+

    + 4.56335 (0.197945s) +

    +     		+

    + 9.03602 (0.742044s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.0412457s) +

    +     		+

    + 1 (0.0433772s) +

    +     		+

    + 1 (0.0821206s) +

    +
    +

    + mpfr_float +

    +     		+

    + 3.6951 (0.152407s) +

    +     		+

    + 3.71977 (0.161353s) +

    +     		+

    + 3.30958 (0.271785s) +

    +
    +
    +
    +

    Table 1.14. Operator /

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 3.24327 (4.00108s) +

    +     		+

    + 5.00532 (8.12985s) +

    +     		+

    + 6.79566 (54.2796s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (1.23366s) +

    +     		+

    + 1 (1.62424s) +

    +     		+

    + 1 (7.9874s) +

    +
    +

    + mpfr_float +

    +     		+

    + 1.32521 (1.63486s) +

    +     		+

    + 1.38967 (2.25716s) +

    +     		+

    + 1.72413 (13.7713s) +

    +
    +
    +
    +

    Table 1.15. Operator /(int)

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1.45093 (0.253675s) +

    +     		+

    + 1.83306 (0.419569s) +

    +     		+

    + 2.3644 (1.64187s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.174836s) +

    +     		+

    + 1 (0.22889s) +

    +     		+

    + 1 (0.694411s) +

    +
    +

    + mpfr_float +

    +     		+

    + 1.16731 (0.204088s) +

    +     		+

    + 1.13211 (0.259127s) +

    +     		+

    + 1.02031 (0.708513s) +

    +
    +
    +
    +

    Table 1.16. Operator str

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +     		+

    + 500 Decimal Digits +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1.4585 (0.0188303s) +

    +     		+

    + 1.55515 (0.03172s) +

    +     		+

    + 1 (0.131962s) +

    +
    +

    + gmp_float +

    +     		+

    + 1 (0.0129107s) +

    +     		+

    + 1 (0.0203967s) +

    +     		+

    + 1.04632 (0.138075s) +

    +
    +

    + mpfr_float +

    +     		+

    + 2.19015 (0.0282764s) +

    +     		+

    + 1.84679 (0.0376683s) +

    +     		+

    + 1.20295 (0.158743s) +

    +
    +
    +

    + ] +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html new file mode 100644 index 00000000..89278b58 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/int_real_world.html @@ -0,0 +1,217 @@ + + + +Integer Real World Tests + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + These tests + measure the time taken to generate 1000 128-bit random numbers and test for + primality using the Miller Rabin test. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and libtommath-0.42.0. + The tests were run on 32-bit Windows Vista machine. +

    +
    ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Integer Type +

    +     		+

    + Relative (and Absolute) Times +

    +
    +

    + mpz_int +

    +     		+

    + 1.08279(0.370326s) +

    +
    +

    + mpz_int (no Expression templates) +

    +     		+

    + 1.1702(0.400222s) +

    +
    +

    + cpp_int +

    +     		+

    + 1.3612(0.465547s) +

    +
    +

    + cpp_int (no Expression templates) +

    +     		+

    + 1.33286(0.455854s) +

    +
    +

    + cpp_int (64-bit cache) +

    +     		+

    + 1.33134(0.455333s) +

    +
    +

    + cpp_int (256-bit cache) +

    +     		+

    + 1.29367(0.442451s) +

    +
    +

    + cpp_int (512-bit cache) +

    +     		+

    + 1.08821(0.37218s) +

    +
    +

    + cpp_int (1024-bit cache) +

    +     		+

    + 1.07902(0.369037s) +

    +
    +

    + mp_int1024_t +

    +     		+

    + 1.02616(0.35096s) +

    +
    +

    + mp_int1024_t (no Expression templates) +

    +     		+

    + 1(0.342011s) +

    +
    +

    + tom_int +

    +     		+

    + 3.74233(1.27992s) +

    +
    +

    + tom_int (no Expression templates) +

    +     		+

    + 3.97646(1.35999s) +

    +
    +

    + It's interesting to note that expression templates have little effect here + - perhaps because the actual expressions involved are relatively trivial + in this case - so the time taken for multiplication and division tends to + dominate. Also note how increasing the internal cache size used by cpp_int is quite effective in this case + in cutting out memory allocations altogether - cutting about a third off + the total runtime. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html new file mode 100644 index 00000000..b7bbe0e7 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/integer_performance.html @@ -0,0 +1,3034 @@ + + + +Integer Algorithm Perfomance + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticism, and real-world + performance may vary widely depending upon the specifics of the program. + In each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. + The tests were run on 32-bit Windows Vista machine. +

    +

    + Linux x86_64 results are broadly similar, except that libtommath performs + much better there. +

    +
    +

    Table 1.17. Operator +

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.24574 (0.0270133s) +

    +     		+

    + 1.09665 (0.0352319s) +

    +     		+

    + 1.25708 (0.0524047s) +

    +     		+

    + 1.31488 (0.08777s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1.05787 (0.0229394s) +

    +     		+

    + 1 (0.0321268s) +

    +     		+

    + 1.16171 (0.0484289s) +

    +     		+

    + 1.24017 (0.0827832s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.08016 (0.0451073s) +

    +     		+

    + 1.33792 (0.042983s) +

    +     		+

    + 1.19676 (0.0498904s) +

    +     		+

    + 1 (0.0667514s) +

    +
    +

    + tommath_int +

    +     		+

    + 1 (0.0216845s) +

    +     		+

    + 1.07779 (0.0346258s) +

    +     		+

    + 1 (0.0416877s) +

    +     		+

    + 1.06344 (0.0709863s) +

    +
    +
    +
    +

    Table 1.18. Operator +(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.46244 (0.0202077s) +

    +     		+

    + 1.20665 (0.0238576s) +

    +     		+

    + 1.17647 (0.0258293s) +

    +     		+

    + 1.12424 (0.0317931s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0138178s) +

    +     		+

    + 1 (0.0197719s) +

    +     		+

    + 1 (0.0219548s) +

    +     		+

    + 1 (0.0282796s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.15321 (0.0297527s) +

    +     		+

    + 2.09834 (0.041488s) +

    +     		+

    + 2.89935 (0.0636546s) +

    +     		+

    + 3.70262 (0.104709s) +

    +
    +

    + tommath_int +

    +     		+

    + 17.1419 (0.236864s) +

    +     		+

    + 12.9762 (0.256563s) +

    +     		+

    + 12.3275 (0.270648s) +

    +     		+

    + 10.7373 (0.303648s) +

    +
    +
    +
    +

    Table 1.19. Operator -

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.15385 (0.029665s) +

    +     		+

    + 1.08217 (0.0369886s) +

    +     		+

    + 1.05882 (0.051534s) +

    +     		+

    + 1.12132 (0.0822725s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0257095s) +

    +     		+

    + 1 (0.0341801s) +

    +     		+

    + 1 (0.0486711s) +

    +     		+

    + 1.08659 (0.0797242s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.56685 (0.040283s) +

    +     		+

    + 1.32917 (0.0454312s) +

    +     		+

    + 1.06917 (0.0520378s) +

    +     		+

    + 1 (0.0733708s) +

    +
    +

    + tommath_int +

    +     		+

    + 1.059 (0.0272264s) +

    +     		+

    + 1.16974 (0.0399818s) +

    +     		+

    + 1.01303 (0.0493054s) +

    +     		+

    + 1.03375 (0.0758472s) +

    +
    +
    +
    +

    Table 1.20. Operator -(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.51665 (0.0157196s) +

    +     		+

    + 1.31513 (0.0200533s) +

    +     		+

    + 1.29599 (0.0235066s) +

    +     		+

    + 1.21534 (0.0266136s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0103647s) +

    +     		+

    + 1 (0.0152482s) +

    +     		+

    + 1 (0.018138s) +

    +     		+

    + 1 (0.021898s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.7938 (0.0289568s) +

    +     		+

    + 2.55493 (0.038958s) +

    +     		+

    + 3.12248 (0.0566356s) +

    +     		+

    + 4.48855 (0.0982904s) +

    +
    +

    + tommath_int +

    +     		+

    + 20.8695 (0.216305s) +

    +     		+

    + 15.0705 (0.229797s) +

    +     		+

    + 13.4093 (0.243217s) +

    +     		+

    + 12.2599 (0.268468s) +

    +
    +
    +
    +

    Table 1.21. Operator *

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.29504 (0.0731032s) +

    +     		+

    + 1.55431 (0.196132s) +

    +     		+

    + 1.4363 (0.656569s) +

    +     		+

    + 1.63701 (2.47859s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0564485s) +

    +     		+

    + 1.16604 (0.147138s) +

    +     		+

    + 1 (0.457124s) +

    +     		+

    + 1 (1.5141s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.19574 (0.0674975s) +

    +     		+

    + 1 (0.126186s) +

    +     		+

    + 1.16627 (0.53313s) +

    +     		+

    + 1.02906 (1.5581s) +

    +
    +

    + tommath_int +

    +     		+

    + 1.97229 (0.111333s) +

    +     		+

    + 2.67087 (0.337027s) +

    +     		+

    + 2.13031 (0.973817s) +

    +     		+

    + 2.05869 (3.11706s) +

    +
    +
    +
    +

    Table 1.22. Operator *(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.34609 (0.030315s) +

    +     		+

    + 1.57086 (0.0407838s) +

    +     		+

    + 1.60154 (0.0542267s) +

    +     		+

    + 1.67808 (0.0804984s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1.29783 (0.0292279s) +

    +     		+

    + 1.58263 (0.0410894s) +

    +     		+

    + 1.61543 (0.054697s) +

    +     		+

    + 1.66841 (0.0800346s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (0.0225207s) +

    +     		+

    + 1 (0.0259628s) +

    +     		+

    + 1 (0.033859s) +

    +     		+

    + 1 (0.0479706s) +

    +
    +

    + tommath_int +

    +     		+

    + 12.4278 (0.279882s) +

    +     		+

    + 11.9045 (0.309074s) +

    +     		+

    + 10.5973 (0.358813s) +

    +     		+

    + 9.47384 (0.454466s) +

    +
    +
    +
    +

    Table 1.23. Operator /

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 2.86387 (0.593314s) +

    +     		+

    + 2.18375 (0.69965s) +

    +     		+

    + 1.72571 (0.918294s) +

    +     		+

    + 1.39251 (1.33801s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.207172s) +

    +     		+

    + 1 (0.320389s) +

    +     		+

    + 1 (0.532127s) +

    +     		+

    + 1 (0.960856s) +

    +
    +

    + gmp_int +

    +     		+

    + 3.89115 (0.806137s) +

    +     		+

    + 2.87573 (0.921352s) +

    +     		+

    + 1.96635 (1.04635s) +

    +     		+

    + 1.29618 (1.24544s) +

    +
    +

    + tommath_int +

    +     		+

    + 11.9483 (2.47535s) +

    +     		+

    + 9.35941 (2.99865s) +

    +     		+

    + 8.79014 (4.67747s) +

    +     		+

    + 11.8316 (11.3684s) +

    +
    +
    +
    +

    Table 1.24. Operator /(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 5.77003 (0.313196s) +

    +     		+

    + 4.38067 (0.431864s) +

    +     		+

    + 3.55054 (0.634559s) +

    +     		+

    + 2.97898 (1.03205s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 2.48952 (0.135131s) +

    +     		+

    + 2.59188 (0.255519s) +

    +     		+

    + 2.56716 (0.458808s) +

    +     		+

    + 2.52368 (0.874313s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (0.0542797s) +

    +     		+

    + 1 (0.0985842s) +

    +     		+

    + 1 (0.178722s) +

    +     		+

    + 1 (0.346443s) +

    +
    +

    + tommath_int +

    +     		+

    + 31.6477 (1.71783s) +

    +     		+

    + 22.8727 (2.25489s) +

    +     		+

    + 19.9248 (3.56101s) +

    +     		+

    + 24.3266 (8.42779s) +

    +
    +
    +
    +

    Table 1.25. Operator %

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.9813 (0.357541s) +

    +     		+

    + 1.55667 (0.460146s) +

    +     		+

    + 1.35341 (0.681144s) +

    +     		+

    + 1.19906 (1.10138s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.180457s) +

    +     		+

    + 1 (0.295597s) +

    +     		+

    + 1 (0.503278s) +

    +     		+

    + 1 (0.918538s) +

    +
    +

    + gmp_int +

    +     		+

    + 3.50213 (0.631985s) +

    +     		+

    + 2.33312 (0.689662s) +

    +     		+

    + 1.57264 (0.791475s) +

    +     		+

    + 1.07795 (0.99014s) +

    +
    +

    + tommath_int +

    +     		+

    + 12.2393 (2.20868s) +

    +     		+

    + 10.1123 (2.98915s) +

    +     		+

    + 9.46676 (4.76442s) +

    +     		+

    + 12.1795 (11.1873s) +

    +
    +
    +
    +

    Table 1.26. Operator %(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.88485 (0.105552s) +

    +     		+

    + 2.00194 (0.203711s) +

    +     		+

    + 2.08202 (0.380096s) +

    +     		+

    + 2.12794 (0.752068s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1.7474 (0.0978544s) +

    +     		+

    + 1.88457 (0.191768s) +

    +     		+

    + 2.0306 (0.37071s) +

    +     		+

    + 2.0851 (0.736929s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (0.0560001s) +

    +     		+

    + 1 (0.101757s) +

    +     		+

    + 1 (0.182561s) +

    +     		+

    + 1 (0.353426s) +

    +
    +

    + tommath_int +

    +     		+

    + 30.4466 (1.70501s) +

    +     		+

    + 22.2997 (2.26915s) +

    +     		+

    + 19.6199 (3.58184s) +

    +     		+

    + 24.0694 (8.50676s) +

    +
    +
    +
    +

    Table 1.27. Operator <<

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.20362 (0.0224696s) +

    +     		+

    + 1.08555 (0.0294403s) +

    +     		+

    + 1 (0.0360516s) +

    +     		+

    + 1.07177 (0.0523935s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0186683s) +

    +     		+

    + 1 (0.0271201s) +

    +     		+

    + 1.02126 (0.036818s) +

    +     		+

    + 1 (0.0488848s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.36706 (0.0255207s) +

    +     		+

    + 1.12042 (0.0303858s) +

    +     		+

    + 1.24359 (0.0448335s) +

    +     		+

    + 1.40143 (0.0685085s) +

    +
    +

    + tommath_int +

    +     		+

    + 2.09357 (0.0390833s) +

    +     		+

    + 2.4569 (0.0666312s) +

    +     		+

    + 2.63592 (0.0950291s) +

    +     		+

    + 3.43638 (0.167987s) +

    +
    +
    +
    +

    Table 1.28. Operator >>

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.33649 (0.0210319s) +

    +     		+

    + 1.12919 (0.0266135s) +

    +     		+

    + 1.10413 (0.0307184s) +

    +     		+

    + 1.09267 (0.0399373s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0157367s) +

    +     		+

    + 1 (0.0235686s) +

    +     		+

    + 1 (0.0278214s) +

    +     		+

    + 1.05198 (0.0384501s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.72135 (0.0270884s) +

    +     		+

    + 1.2078 (0.0284661s) +

    +     		+

    + 1.16066 (0.0322912s) +

    +     		+

    + 1 (0.0365503s) +

    +
    +

    + tommath_int +

    +     		+

    + 15.4381 (0.242945s) +

    +     		+

    + 11.8797 (0.279987s) +

    +     		+

    + 10.9043 (0.303374s) +

    +     		+

    + 14.0762 (0.514491s) +

    +
    +
    +
    +

    Table 1.29. Operator &

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.65829 (0.0314059s) +

    +     		+

    + 1.42198 (0.0390384s) +

    +     		+

    + 1.48578 (0.0498903s) +

    +     		+

    + 1.51243 (0.0770342s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0189387s) +

    +     		+

    + 1 (0.0274536s) +

    +     		+

    + 1 (0.0335786s) +

    +     		+

    + 1 (0.0509341s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.80248 (0.0530755s) +

    +     		+

    + 2.39752 (0.0658206s) +

    +     		+

    + 2.66009 (0.089322s) +

    +     		+

    + 2.73942 (0.13953s) +

    +
    +

    + tommath_int +

    +     		+

    + 6.95432 (0.131706s) +

    +     		+

    + 5.4059 (0.148412s) +

    +     		+

    + 4.56887 (0.153417s) +

    +     		+

    + 6.5696 (0.334616s) +

    +
    +
    +
    +

    Table 1.30. Operator &(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.63285 (0.0472296s) +

    +     		+

    + 1.43344 (0.0588492s) +

    +     		+

    + 1.33141 (0.0724386s) +

    +     		+

    + 1.21353 (0.104144s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0289247s) +

    +     		+

    + 1 (0.0410546s) +

    +     		+

    + 1 (0.0544075s) +

    +     		+

    + 1 (0.0858187s) +

    +
    +

    + gmp_int +

    +     		+

    + 5.24478 (0.151704s) +

    +     		+

    + 3.81907 (0.15679s) +

    +     		+

    + 2.77979 (0.151242s) +

    +     		+

    + 1.84209 (0.158086s) +

    +
    +

    + tommath_int +

    +     		+

    + 11.7257 (0.339163s) +

    +     		+

    + 8.6379 (0.354625s) +

    +     		+

    + 6.90411 (0.375636s) +

    +     		+

    + 7.63253 (0.655013s) +

    +
    +
    +
    +

    Table 1.31. Operator ^

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.39325 (0.0297525s) +

    +     		+

    + 1.28821 (0.0385005s) +

    +     		+

    + 1.18843 (0.0492426s) +

    +     		+

    + 1.07724 (0.0758668s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0213547s) +

    +     		+

    + 1 (0.0298868s) +

    +     		+

    + 1 (0.041435s) +

    +     		+

    + 1 (0.070427s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.28582 (0.048813s) +

    +     		+

    + 2.03478 (0.0608129s) +

    +     		+

    + 2.05655 (0.0852131s) +

    +     		+

    + 1.92381 (0.135488s) +

    +
    +

    + tommath_int +

    +     		+

    + 6.17078 (0.131775s) +

    +     		+

    + 4.8567 (0.145151s) +

    +     		+

    + 3.64659 (0.151097s) +

    +     		+

    + 4.78192 (0.336776s) +

    +
    +
    +
    +

    Table 1.32. Operator ^(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.89396 (0.0383127s) +

    +     		+

    + 1.64269 (0.043417s) +

    +     		+

    + 1.5386 (0.0477162s) +

    +     		+

    + 1.32247 (0.0568053s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0202288s) +

    +     		+

    + 1 (0.0264305s) +

    +     		+

    + 1 (0.0310128s) +

    +     		+

    + 1 (0.0429539s) +

    +
    +

    + gmp_int +

    +     		+

    + 7.01953 (0.141997s) +

    +     		+

    + 5.47513 (0.14471s) +

    +     		+

    + 4.6627 (0.144603s) +

    +     		+

    + 3.59601 (0.154463s) +

    +
    +

    + tommath_int +

    +     		+

    + 16.2706 (0.329134s) +

    +     		+

    + 12.9494 (0.342258s) +

    +     		+

    + 11.3305 (0.35139s) +

    +     		+

    + 14.1712 (0.608709s) +

    +
    +
    +
    +

    Table 1.33. Operator |

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.34742 (0.0296944s) +

    +     		+

    + 1.25923 (0.0384846s) +

    +     		+

    + 1.20517 (0.0493908s) +

    +     		+

    + 1.10536 (0.0761343s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0220379s) +

    +     		+

    + 1 (0.030562s) +

    +     		+

    + 1 (0.0409823s) +

    +     		+

    + 1 (0.0688775s) +

    +
    +

    + gmp_int +

    +     		+

    + 2.14429 (0.0472558s) +

    +     		+

    + 1.95901 (0.0598712s) +

    +     		+

    + 2.07584 (0.0850728s) +

    +     		+

    + 1.94265 (0.133805s) +

    +
    +

    + tommath_int +

    +     		+

    + 5.98286 (0.13185s) +

    +     		+

    + 4.65705 (0.142329s) +

    +     		+

    + 3.85812 (0.158115s) +

    +     		+

    + 4.81524 (0.331662s) +

    +
    +
    +
    +

    Table 1.34. Operator |(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.40808 (0.0389721s) +

    +     		+

    + 1.65035 (0.0437872s) +

    +     		+

    + 1.51667 (0.0466144s) +

    +     		+

    + 1.37806 (0.0582842s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.0276775s) +

    +     		+

    + 1 (0.026532s) +

    +     		+

    + 1 (0.0307348s) +

    +     		+

    + 1 (0.0422945s) +

    +
    +

    + gmp_int +

    +     		+

    + 5.31451 (0.147092s) +

    +     		+

    + 5.37333 (0.142565s) +

    +     		+

    + 4.86508 (0.149527s) +

    +     		+

    + 3.74364 (0.158335s) +

    +
    +

    + tommath_int +

    +     		+

    + 11.9312 (0.330226s) +

    +     		+

    + 12.943 (0.343403s) +

    +     		+

    + 11.4457 (0.35178s) +

    +     		+

    + 14.4462 (0.610997s) +

    +
    +
    +
    +

    Table 1.35. Operator gcd

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.82514 (4.45586s) +

    +     		+

    + 1.75955 (10.1748s) +

    +     		+

    + 1.87025 (25.23s) +

    +     		+

    + 2.11453 (68.8556s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1.57965 (3.85654s) +

    +     		+

    + 1.67404 (9.68027s) +

    +     		+

    + 1.8405 (24.8287s) +

    +     		+

    + 2.27588 (74.1096s) +

    +
    +

    + gmp_int +

    +     		+

    + 1 (2.44138s) +

    +     		+

    + 1 (5.78259s) +

    +     		+

    + 1 (13.4902s) +

    +     		+

    + 1 (32.5631s) +

    +
    +

    + tommath_int +

    +     		+

    + 5.01357 (12.24s) +

    +     		+

    + 4.38161 (25.337s) +

    +     		+

    + 4.08681 (55.1319s) +

    +     		+

    + 4.01045 (130.593s) +

    +
    +
    +
    +

    Table 1.36. Operator str

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_int +

    +     		+

    + 1.46421 (0.00195137s) +

    +     		+

    + 1.21669 (0.00319216s) +

    +     		+

    + 1.25041 (0.00765237s) +

    +     		+

    + 1.53339 (0.0218096s) +

    +
    +

    + cpp_int(fixed) +

    +     		+

    + 1 (0.00133271s) +

    +     		+

    + 1 (0.00262366s) +

    +     		+

    + 1.0109 (0.00618661s) +

    +     		+

    + 1.24429 (0.0176978s) +

    +
    +

    + gmp_int +

    +     		+

    + 1.7777 (0.00236916s) +

    +     		+

    + 1.27408 (0.00334274s) +

    +     		+

    + 1 (0.00611991s) +

    +     		+

    + 1 (0.0142232s) +

    +
    +

    + tommath_int +

    +     		+

    + 11.9797 (0.0159654s) +

    +     		+

    + 18.3349 (0.0481046s) +

    +     		+

    + 18.3681 (0.112411s) +

    +     		+

    + 25.0355 (0.356085s) +

    +
    +
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/rational_performance.html b/doc/html/boost_multiprecision/perf/rational_performance.html new file mode 100644 index 00000000..6736d065 --- /dev/null +++ b/doc/html/boost_multiprecision/perf/rational_performance.html @@ -0,0 +1,905 @@ + + + +Rational Type Perfomance + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticism, and real-world + performance may vary widely depending upon the specifics of the program. + In each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. + The tests were run on 32-bit Windows Vista machine. +

    +
    +

    Table 1.37. Operator +

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.91758 (18.1263s) +

    +     		+

    + 6.60754 (44.1182s) +

    +     		+

    + 6.65334 (103.169s) +

    +     		+

    + 6.44717 (244.055s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (3.06312s) +

    +     		+

    + 1 (6.67695s) +

    +     		+

    + 1 (15.5064s) +

    +     		+

    + 1 (37.8546s) +

    +
    +
    +
    +

    Table 1.38. Operator +(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 3.98512 (2.67249s) +

    +     		+

    + 4.24335 (3.04309s) +

    +     		+

    + 4.65009 (3.83046s) +

    +     		+

    + 5.45832 (5.08346s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (0.670618s) +

    +     		+

    + 1 (0.717144s) +

    +     		+

    + 1 (0.823739s) +

    +     		+

    + 1 (0.931322s) +

    +
    +
    +
    +

    Table 1.39. Operator -

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.91504 (18.2374s) +

    +     		+

    + 6.55676 (43.8659s) +

    +     		+

    + 6.66239 (103.481s) +

    +     		+

    + 6.47224 (244.887s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (3.08322s) +

    +     		+

    + 1 (6.69018s) +

    +     		+

    + 1 (15.5321s) +

    +     		+

    + 1 (37.8365s) +

    +
    +
    +
    +

    Table 1.40. Operator -(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 3.96173 (2.66785s) +

    +     		+

    + 4.36532 (3.09023s) +

    +     		+

    + 4.59363 (3.74494s) +

    +     		+

    + 5.43075 (5.09156s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (0.673405s) +

    +     		+

    + 1 (0.707904s) +

    +     		+

    + 1 (0.815246s) +

    +     		+

    + 1 (0.937541s) +

    +
    +
    +
    +

    Table 1.41. Operator *

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.59286 (32.3559s) +

    +     		+

    + 6.54125 (82.4247s) +

    +     		+

    + 6.8815 (197.198s) +

    +     		+

    + 6.84066 (473.057s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (5.78521s) +

    +     		+

    + 1 (12.6008s) +

    +     		+

    + 1 (28.6562s) +

    +     		+

    + 1 (69.1537s) +

    +
    +
    +
    +

    Table 1.42. Operator *(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 2.70193 (3.1466s) +

    +     		+

    + 3.10134 (3.79056s) +

    +     		+

    + 3.659 (4.93935s) +

    +     		+

    + 4.61372 (6.89845s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (1.16457s) +

    +     		+

    + 1 (1.22223s) +

    +     		+

    + 1 (1.34992s) +

    +     		+

    + 1 (1.4952s) +

    +
    +
    +
    +

    Table 1.43. Operator /

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 4.36846 (63.9498s) +

    +     		+

    + 5.52565 (145.045s) +

    +     		+

    + 6.18331 (328.069s) +

    +     		+

    + 6.49822 (784.806s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (14.639s) +

    +     		+

    + 1 (26.2494s) +

    +     		+

    + 1 (53.0571s) +

    +     		+

    + 1 (120.772s) +

    +
    +
    +
    +

    Table 1.44. Operator /(int)

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 2.26643 (3.13785s) +

    +     		+

    + 2.57125 (3.76931s) +

    +     		+

    + 3.20872 (5.06758s) +

    +     		+

    + 4.02177 (7.17803s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (1.38449s) +

    +     		+

    + 1 (1.46594s) +

    +     		+

    + 1 (1.57931s) +

    +     		+

    + 1 (1.78479s) +

    +
    +
    +
    +

    Table 1.45. Operator str

    +
    +++++++ + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + 128 Bits +

    +     		+

    + 256 Bits +

    +     		+

    + 512 Bits +

    +     		+

    + 1024 Bits +

    +
    +

    + cpp_rational +

    +     		+

    + 5.40493 (0.0199393s) +

    +     		+

    + 8.55089 (0.0511907s) +

    +     		+

    + 9.91026 (0.118839s) +

    +     		+

    + 9.93546 (0.285367s) +

    +
    +

    + mpq_rational +

    +     		+

    + 1 (0.00368909s) +

    +     		+

    + 1 (0.00598659s) +

    +     		+

    + 1 (0.0119915s) +

    +     		+

    + 1 (0.028722s) +

    +
    +
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html new file mode 100644 index 00000000..4dd0d5ef --- /dev/null +++ b/doc/html/boost_multiprecision/perf/realworld.html @@ -0,0 +1,278 @@ + + + +Floating Point Real World Tests + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + These tests test the total time taken to execute all of Boost.Math's test + cases for these functions. In each case the best performing library gets + a relative score of 1, with the total execution time given in brackets. The + first three libraries listed are the various floating point types provided + by this library, while for comparison, two popular C++ front-ends to MPFR ( mpfr_class + and mpreal) are + also shown. +

    +

    + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. + The tests were run on 32-bit Windows Vista machine. +

    +
    +

    Table 1.6. Bessel Function Performance

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +
    +

    + mpfr_float +

    +     		+

    + 1.0 (6.472s) +

    +     		+

    + 1.193 (10.154s) +

    +
    +

    + mpf_float +

    +     		+

    + 1.801 (11.662s) +

    +     		+

    + 1.0(8.511s) +

    +
    +

    + cpp_dec_float +

    +     		+

    + 3.13 (20.285s) +

    +     		+

    + 2.46 (21.019s) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.001 (6.480s) +

    +     		+

    + 1.15(9.805s) +

    +
    +

    + mpreal +

    +     		+

    + 1.542 (9.981s) +

    +     		+

    + 1.61 (13.702s) +

    +
    +
    +
    +

    Table 1.7. Non-Central T Distribution Performance

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Library +

    +     		+

    + 50 Decimal Digits +

    +     		+

    + 100 Decimal Digits +

    +
    +

    + mpfr_float +

    +     		+

    + 1.308 (258.09s) +

    +     		+

    + 1.30 (516.74s) +

    +
    +

    + mpf_float +

    +     		+

    + 1.0 (197.30s) +

    +     		+

    + 1.0(397.30s) +

    +
    +

    + cpp_dec_float +

    +     		+

    + 1.695 (334.50s) +

    +     		+

    + 2.68 (1064.53s) +

    +
    +

    + mpfr_class +

    +     		+

    + 1.35 (266.39s) +

    +     		+

    + 1.323 (525.74s) +

    +
    +

    + mpreal +

    +     		+

    + 1.75 (346.64s) +

    +     		+

    + 1.635 (649.94s) +

    +
    +
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html new file mode 100644 index 00000000..35ad59f4 --- /dev/null +++ b/doc/html/boost_multiprecision/ref.html @@ -0,0 +1,44 @@ + + + +Reference + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    mp_number
    +
    cpp_int
    +
    gmp_int
    +
    tom_int
    +
    gmp_float
    +
    mpfr_float_backend
    +
    cpp_dec_float
    +
    Backend Requirements
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html new file mode 100644 index 00000000..3bf6b60f --- /dev/null +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -0,0 +1,2295 @@ + + + +Backend Requirements + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + The requirements on the Backend + template argument to mp_number + are split up into compulsory requirements, and optional requirements that + are either to improve performance or provide optional features. +

    +

    + In the following tables, type B is the Backend + template arument to mp_number, + b and b2 + are a variables of type B, cb + and cb2 are constant variables + of type B, a is a variable + of Arithmetic type, s is + a variable of type const char*, ui + is a variable of type unsigned, + bb is a variable of type + bool, pa + is a variable of type pointer-to-arithmetic-type, exp + is a variable of type B::exp_type, pexp + is a variable of type B::exp_type*, + B2 is another type that meets these requirements, b2 is a variable of type + B2. +

    +
    +

    Table 1.4. Compulsory Requirements on the Backend type.

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Expression +

    +     		+

    + Return Type +

    +     		+

    + Comments +

    +
    +

    + B::signed_types +

    +     		+

    + mpl::list<type-list> +

    +     		+

    + A list of signed integral types that can be assigned to type B. + The types shall be listed in order of size, smallest first, and + shall terminate in the type that is std::intmax_t. +

    +
    +

    + B::unsigned_types +

    +     		+

    + mpl::list<type-list> +

    +     		+

    + A list of unsigned integral types that can be assigned to type + B. The types shall be listed in order of size, smallest first, + and shall terminate in the type that is std::uintmax_t. +

    +
    +

    + B::float_types +

    +     		+

    + mpl::list<type-list> +

    +     		+

    + A list of floating-point types that can be assigned to type B.The + types shall be listed in order of size, smallest first, and shall + terminate in type long double. +

    +
    +

    + B::exponent_type +

    +     		+

    + A signed integral type. +

    +     		+

    + The type of the exponent of type B. +

    +
    +

    + B() +

    +     		+ +

    + Default constructor. +

    +
    +

    + B(cb) +

    +     		+ +

    + Copy Constructor. +

    +
    +

    + b = + b +

    +     		+

    + B& +

    +     		+

    + Assignment operator. +

    +
    +

    + b = + a +

    +     		+

    + B& +

    +     		+

    + Assignment from an Arithmetic type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + b = + s +

    +     		+

    + B& +

    +     		+

    + Assignment from a string. +

    +
    +

    + b.swap(b) +

    +     		+

    + void +

    +     		+

    + Swaps the contents of its arguments. +

    +
    +

    + cb.str(ui, + bb) +

    +     		+

    + std::string +

    +     		+

    + Returns the string representation of b + with ui digits + and in scientific format if bb + is true. If ui is zero, then returns as many + digits as are required to reconstruct the original value. +

    +
    +

    + b.negate() +

    +     		+

    + void +

    +     		+

    + Negates b. +

    +
    +

    + cb.compare(cb2) +

    +     		+

    + int +

    +     		+

    + Compares cb and + cb2, returns a + value less than zero if cb + < cb2, + a value greater than zero if cb + > cb2 + and zero if cb == cb2. +

    +
    +

    + cb.compare(a) +

    +     		+

    + int +

    +     		+

    + Compares cb and + a, returns a value + less than zero if cb + < a, + a value greater than zero if cb + > a + and zero if cb == a. + The type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_add(b, + cb) +

    +     		+

    + void +

    +     		+

    + Adds cb to b. +

    +
    +

    + eval_subtract(b, + cb) +

    +     		+

    + void +

    +     		+

    + Subtracts cb from + b. +

    +
    +

    + eval_multiply(b, + cb) +

    +     		+

    + void +

    +     		+

    + Multiplies b by + cb. +

    +
    +

    + eval_divide(b, + cb) +

    +     		+

    + void +

    +     		+

    + Divides b by cb. +

    +
    +

    + eval_modulus(b, + cb) +

    +     		+

    + void +

    +     		+

    + Computes b %= + cb, only required when + B is an integer + type. +

    +
    +

    + eval_bitwise_and(b, cb) +

    +     		+

    + void +

    +     		+

    + Computes b &= + cb, only required when + B is an integer + type. +

    +
    +

    + eval_bitwise_or(b, cb) +

    +     		+

    + void +

    +     		+

    + Computes b |= + cb, only required when + B is an integer + type. +

    +
    +

    + eval_bitwise_xor(b, cb) +

    +     		+

    + void +

    +     		+

    + Computes b ^= + cb, only required when + B is an integer + type. +

    +
    +

    + eval_complement(b, cb) +

    +     		+

    + void +

    +     		+

    + Computes the ones-complement of cb + and stores the result in b, + only required when B + is an integer type. +

    +
    +

    + eval_left_shift(b, ui) +

    +     		+

    + void +

    +     		+

    + Computes b <<= + ui, only required when + B is an integer + type. +

    +
    +

    + eval_right_shift(b, ui) +

    +     		+

    + void +

    +     		+

    + Computes b >>= + ui, only required when + B is an integer + type. +

    +
    +

    + eval_convert_to(pa, cb) +

    +     		+

    + void +

    +     		+

    + Converts cb to + the type of *pa + and store the result in *pa. Type B + shall support conversion to at least types std::intmax_t, + std::uintmax_t and long + long. Conversion to other + arithmetic types can then be synthesised using other operations. + Conversions to other types are entirely optional. +

    +
    +

    + eval_frexp(b, + cb, + pexp) +

    +     		+

    + void +

    +     		+

    + Stores values in b + and *pexp + such that the value of cb + is b * 2*pexp, only required when B + is a floating-point type. +

    +
    +

    + eval_ldexp(b, + cb, + exp) +

    +     		+

    + void +

    +     		+

    + Stores a value in b + that is cb * 2exp, only required when B + is a floating-point type. +

    +
    +

    + eval_floor(b, + cb) +

    +     		+

    + void +

    +     		+

    + Stores the floor of cb + in b, only required + when B is a floating-point + type. +

    +
    +

    + eval_ceil(b, + cb) +

    +     		+

    + void +

    +     		+

    + Stores the ceiling of cb + in b, only required + when B is a floating-point + type. +

    +
    +

    + eval_sqrt(b, + cb) +

    +     		+

    + void +

    +     		+

    + Stores the square root of cb + in b, only required + when B is a floating-point + type. +

    +
    +

    + boost::multiprecision::number_category<B>::type +

    +     		+

    + mpl::int_<N> +

    +     		+

    + N is one of the + values number_kind_integer, + number_kind_floating_point, + number_kind_rational + or number_kind_fixed_point. + Defaults to number_kind_floating_point. +

    +
    +
    +
    +

    Table 1.5. Optional Requirements on the Backend Type

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Expression +

    +     		+

    + Returns +

    +     		+

    + Comments +

    +
    +

    + B(b2) +

    +     		+

    + B +

    +     		+

    + Copy constructor from a different back-end type. +

    +
    +

    + b = + b2 +

    +     		+

    + b& +

    +     		+

    + Assignment operator from a different back-end type. +

    +
    +

    + assign_components(b, a, a) +

    +     		+

    + void +

    +     		+

    + Assigns to b the + two components in the following arguments. Only applies to rational + and complex number types. +

    +
    +

    + assign_components(b, b2, b2) +

    +     		+

    + void +

    +     		+

    + Assigns to b the + two components in the following arguments. Only applies to rational + and complex number types. +

    +
    +

    + eval_add(b, + a) +

    +     		+

    + void +

    +     		+

    + Adds a to b. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. +

    +
    +

    + eval_subtract(b, + a) +

    +     		+

    + void +

    +     		+

    + Subtracts a from + b. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_multiply(b, + a) +

    +     		+

    + void +

    +     		+

    + Multiplies b by + a. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_divide(b, + a) +

    +     		+

    + void +

    +     		+

    + Divides b by a. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. +

    +
    +

    + eval_modulus(b, + a) +

    +     		+

    + void +

    +     		+

    + Computes b %= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_and(b, a) +

    +     		+

    + void +

    +     		+

    + Computes b &= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_or(b, a) +

    +     		+

    + void +

    +     		+

    + Computes b |= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_xor(b, a) +

    +     		+

    + void +

    +     		+

    + Computes b ^= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_add(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Add cb to cb2 and stores the result in + b. +

    +
    +

    + eval_subtract(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Subtracts cb2 from + cb and stores the + result in b. +

    +
    +

    + eval_multiply(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Multiplies cb by + cb2 and stores + the result in b. +

    +
    +

    + eval_divide(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Divides cb by + cb2 and stores + the result in b. +

    +
    +

    + eval_add(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Add cb to a and stores the result in b. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. +

    +
    +

    + eval_subtract(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Subtracts a from + cb and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_multiply(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Multiplies cb by + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_divide(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Divides cb by + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_modulus(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb % + cb2 and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_bitwise_and(b, cb, cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb & + cb2 and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_bitwise_or(b, cb, cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb | + cb2 and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_bitwise_xor(b, cb, cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb ^ + cb2 and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_add(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Add a to cb and stores the result in + b. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_subtract(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Subtracts cb from + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_multiply(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Multiplies a by + cb and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_divide(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Divides a by cb and stores the result in + b. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_modulus(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Computes cb % + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_and(b, cb, a) +

    +     		+

    + void +

    +     		+

    + Computes cb & + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_or(b, cb, a) +

    +     		+

    + void +

    +     		+

    + Computes cb | + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_xor(b, cb, a) +

    +     		+

    + void +

    +     		+

    + Computes cb ^ + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_modulus(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Computes cb % + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_and(b, a, cb) +

    +     		+

    + void +

    +     		+

    + Computes cb & + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_or(b, a, cb) +

    +     		+

    + void +

    +     		+

    + Computes cb | + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_bitwise_xor(b, a, cb) +

    +     		+

    + void +

    +     		+

    + Computes a ^ + cb and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    +
    +

    + eval_left_shift(b, cb, ui) +

    +     		+

    + void +

    +     		+

    + Computes cb << + ui and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_right_shift(b, cb, ui) +

    +     		+

    + void +

    +     		+

    + Computes cb >> + ui and stores the result + in b, only required + when B is an integer + type. +

    +
    +

    + eval_increment(b) +

    +     		+

    + void +

    +     		+

    + Increments the value of b + by one. +

    +
    +

    + eval_decrement(b) +

    +     		+

    + void +

    +     		+

    + Decrements the value of b + by one. +

    +
    +

    + eval_is_zero(cb) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb is zero, otherwise false +

    +
    +

    + eval_get_sign(cb) +

    +     		+

    + int +

    +     		+

    + Returns a value < zero if cb + is negative, a value > zero if cb + is positive, and zero if cb + is zero. +

    +
    +

    + eval_abs(b, + cb) +

    +     		+

    + void +

    +     		+

    + Set b to the absolute + value of cb. +

    +
    +

    + eval_fabs(b, + cb) +

    +     		+

    + void +

    +     		+

    + Set b to the absolute + value of cb. +

    +
    +

    + eval_fpclassify(cb) +

    +     		+

    + int +

    +     		+

    + Returns one of the same values returned by std::fpclassify. + Only required when B + is an floating-point type. +

    +
    +

    + eval_trunc(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::trunc + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_round(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::round + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_exp(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::exp + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_log(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::log + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_log10(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::log10 + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_sin(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::sin + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_cos(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::cos + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_tan(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::exp + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_asin(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::asin + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_acos(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::acos + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_atan(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::atan + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_sinh(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::sinh + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_cosh(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::cosh + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_tanh(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::tanh + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_fmod(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::fmod + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_pow(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::pow + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_atan2(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::atan + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating-point type. +

    +
    +

    + eval_qr(cb, + cb2, + b, + b2) +

    +     		+

    + void +

    +     		+

    + Sets b to the result + of cb / + cb2 and b2 to the result of cb % + cb2. Only required when + B is an integer + type. +

    +
    +

    + eval_integer_modulus(cb, ui) +

    +     		+

    + unsigned +

    +     		+

    + Returns the result of cb + % ui. + Only required when B + is an integer type. +

    +
    +

    + eval_lsb(cb) +

    +     		+

    + unsigned +

    +     		+

    + Returns the index of the least significant bit that is set. Only + required when B + is an integer type. +

    +
    +

    + eval_bit_test(cb, + ui) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb + has bit ui set. + Only required when B + is an integer type. +

    +
    +

    + eval_bit_set(b, + ui) +

    +     		+

    + void +

    +     		+

    + Sets the bit at index ui + in b. Only required + when B is an integer + type. +

    +
    +

    + eval_bit_unset(b, ui) +

    +     		+

    + void +

    +     		+

    + Unsets the bit at index ui + in b. Only required + when B is an integer + type. +

    +
    +

    + eval_bit_flip(b, + ui) +

    +     		+

    + void +

    +     		+

    + Flips the bit at index ui + in b. Only required + when B is an integer + type. +

    +
    +

    + eval_gcd(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Sets b to the greatest + common divisor of cb + and cb2. Only required + when B is an integer + type. +

    +
    +

    + eval_lcm(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Sets b to the least + common multiple of cb + and cb2. Only required + when B is an integer + type. +

    +
    +
    +
    + + + + + +
    [Note]Note

    + The non-member functions are all named with an "eval_" prefix + to avoid conflicts with template classes of the same name - in point of + fact this naming convention shouldn't be necessary, but rather works around + some compiler bugs. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html new file mode 100644 index 00000000..9d34b1e6 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html @@ -0,0 +1,61 @@ + + + +cpp_dec_float + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class cpp_dec_float;
+
+typedef mp_number<cpp_dec_float<50> > cpp_dec_float_50;
+typedef mp_number<cpp_dec_float<100> > cpp_dec_float_100;
+
+}} // namespaces
+
    +

    + Class template cpp_dec_float + fulfills all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + The class takes a single template parameter - Digits10 + - which is the number of decimal digits precision the type should support. + Note that this type does not ever perform any dynamic memory allocation, + as a result the Digits10 + template argument should not be set too high or the classes size will grow + unreasonably large. +

    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html new file mode 100644 index 00000000..40530e86 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/cpp_int_ref.html @@ -0,0 +1,99 @@ + + + +cpp_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned MinBits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
+struct cpp_int_backend;
+
+typedef mp_number<cpp_int_backend<> >           cpp_int;    // arbitrary precision integer
+typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
+typedef mp_number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
+
+// Fixed precision unsigned types:
+typedef mp_number<cpp_int_backend<128, false, void>, false>   mp_uint128_t;
+typedef mp_number<cpp_int_backend<256, false, void>, false>   mp_uint256_t;
+typedef mp_number<cpp_int_backend<512, false, void>, false>   mp_uint512_t;
+typedef mp_number<cpp_int_backend<1024, false, void>, false>  mp_uint1024_t;
+
+// Fixed precision signed types:
+typedef mp_number<cpp_int_backend<128, true, void>, false>    mp_int128_t;
+typedef mp_number<cpp_int_backend<256, true, void>, false>    mp_int256_t;
+typedef mp_number<cpp_int_backend<512, true, void>, false>    mp_int512_t;
+typedef mp_number<cpp_int_backend<1024, true, void>, false>   mp_int1024_t;
+
+}} // namespaces
+
    +

    + Class template cpp_int_backend + fulfills all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + The template arguments are: +

    +
    +

    +
    +
    Argument
    +

    + Meaning +

    +
    MinBits
    +

    + The number of Bits to reserve inside the class's internal cache. When + constructing a value, the object will use this internal cache if possible + before resorting to dynamic memory allocation. When this value is zero, + then the size of the internal cache is 2*sizeof(void*)*CHAR_BIT. + When the Allocator argument is void, + then this parameter determines the precision of the type. +

    +
    Signed
    +

    + When true the type is + signed, otherwise unsigned. Note that unsigned types are currently + only supported when the Allocator parameter is void. +

    +
    Allocator
    +

    + The allocator used for dynamic memory allocation. This parameter can + be void, in which case + no dymanic memory will ever be allocated. +

    +
    +
    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/gmp_int_ref.html b/doc/html/boost_multiprecision/ref/gmp_int_ref.html new file mode 100644 index 00000000..71dfb0ae --- /dev/null +++ b/doc/html/boost_multiprecision/ref/gmp_int_ref.html @@ -0,0 +1,51 @@ + + + +gmp_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+class gmp_int;
+
+typedef mp_number<gmp_int >         mpz_int;
+
+}} // namespaces
+
    +

    + Class template gmp_int fulfills + all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html new file mode 100644 index 00000000..b883aa18 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -0,0 +1,695 @@ + + + +mp_number + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    + + Synopsis +
    +
    namespace boost{ namespace multiprecision{
+
+template <class Backend, bool ExpressionTemplates = true>
+class mp_number
+{
+   mp_number();
+   mp_number(see-below);
+   mp_number& operator=(see-below);
+
+   // Member operators
+   mp_number& operator+=(const see-below&);
+   mp_number& operator-=(const see-below&);
+   mp_number& operator*=(const see-below&);
+   mp_number& operator/=(const see-below&);
+   mp_number& operator++();
+   mp_number& operator--();
+   mp_number  operator++(int);
+   mp_number  operator--(int);
+
+   mp_number& operator%=(const see-below&);
+   mp_number& operator&=(const see-below&);
+   mp_number& operator|=(const see-below&);
+   mp_number& operator^=(const see-below&);
+   mp_number& operator<<=(const integer-type&);
+   mp_number& operator>>=(const integer-type&);
+
+   // Use in Boolean context:
+   operator convertible-to-bool-type()const;
+   // swap:
+   void swap(mp_number& other);
+   // Sign:
+   bool is_zero()const;
+   int sign()const;
+   // string conversion:
+   std::string str()const;
+   // Generic conversion mechanism
+   template <class T>
+   T convert_to()const;
+   // precision control:
+   static unsigned default_precision();
+   static void default_precision(unsigned digits10);
+   unsigned precision()const;
+   void precision(unsigned digits10);
+   // Comparison:
+   int compare(const mp_number<Backend>& o)const;
+   template <class V>
+   typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
+   // Access to the underlying implementation:
+   Backend& backend();
+   const Backend& backend()const;
+};
+
+// Non member operators:
+unmentionable-expression-template-type operator+(const see-below&, const see-below&);
+unmentionable-expression-template-type operator-(const see-below&, const see-below&);
+unmentionable-expression-template-type operator*(const see-below&, const see-below&);
+unmentionable-expression-template-type operator/(const see-below&, const see-below&);
+// Integer only operations:
+unmentionable-expression-template-type operator%(const see-below&, const see-below&);
+unmentionable-expression-template-type operator&(const see-below&, const see-below&);
+unmentionable-expression-template-type operator|(const see-below&, const see-below&);
+unmentionable-expression-template-type operator^(const see-below&, const see-below&);
+unmentionable-expression-template-type operator<<(const see-below&, const integer-type&);
+unmentionable-expression-template-type operator>>(const see-below&, const integer-type&);
+// Comparison operators:
+bool operator==(const see-below&, const see-below&);
+bool operator!=(const see-below&, const see-below&);
+bool operator< (const see-below&, const see-below&);
+bool operator> (const see-below&, const see-below&);
+bool operator<=(const see-below&, const see-below&);
+bool operator>=(const see-below&, const see-below&);
+
+// Swap:
+template <class Backend, bool ExpressionTemplates>
+void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
+
+// iostream support:
+template <class Backend, bool ExpressionTemplates>
+std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
+std::ostream& operator << (std::ostream& os, const unmentionable-expression-template-type& r);
+template <class Backend, bool ExpressionTemplates>
+std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r);
+
+// Non-member function standard library support:
+unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
+
+unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
+unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
+unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+
+// Traits support:
+template <class T>
+struct component_type;
+template <class T>
+struct number_category;
+
+// Integer specific functions:
+template <class Backend, bool ExpressionTemplates>
+bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
+               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
+template <class Integer>
+Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
+unsigned lsb(const mp_number-or-expression-template-type& x);
+template <class Backend, class ExpressionTemplates>
+bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+template <class Engine>
+bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
+bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
+
+// Rational number support:
+typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
+typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
+
+}} // namespaces
+
+namespace boost{ namespace math{
+
+// Boost.Math interoperability functions:
+int                                              fpclassify     (const mp_number-or-expression-template-type&, int);
+bool                                             isfinite       (const mp_number-or-expression-template-type&, int);
+bool                                             isnan          (const mp_number-or-expression-template-type&, int);
+bool                                             isinf          (const mp_number-or-expression-template-type&, int);
+bool                                             isnormal       (const mp_number-or-expression-template-type&, int);
+
+}} // namespaces
+
+// numeric_limits support:
+namespace std{
+
+template <class Backend, bool ExpressionTemplates>
+struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
+{
+   /* Usual members here */
+};
+
+}
+
    +
    + + Description +
    +
    template <class Backend, bool ExpressionTemplates = true>
+class mp_number;
+
    +

    + Class mp_number has two template + arguments: +

    +
    +

    +
    +
    Backend
    +

    + The actual arithmetic back-end that does all the work. +

    +
    ExpressionTemplates
    +

    + A Boolean value: when true, then expression templates are enabled, + otherwise they are disabled. +

    +
    +
    +
    mp_number();
+mp_number(see-below);
+mp_number& operator=(see-below);
+
    +

    + Type mp_number is default + constructible, and both copy constructible and assignable from: +

    +
      +
    • + Itself. +
      • +
    • + An expression template which is the result of one of the arithmetic operators. +
      • +
    • + Any builtin arithmetic type. +
      • +
    • + A std::string or any type which is convertible + to const char*. +
      • +
    • + Any type that the Backend is constructible or assignable from. +
      • +
    +

    + In addition, if the type has multiple components (for example rational or + complex number types), then there is a two argument constructor: +

    +
    mp_number(arg1, arg2);
+
    +

    + Where the two args must either be arithmetic types, or types that are convertible + to the two components of this. +

    +
    mp_number& operator+=(const see-below&);
+mp_number& operator-=(const see-below&);
+mp_number& operator*=(const see-below&);
+mp_number& operator/=(const see-below&);
+mp_number& operator++();
+mp_number& operator--();
+mp_number  operator++(int);
+mp_number  operator--(int);
+// Integer only operations:
+mp_number& operator%=(const see-below&);
+mp_number& operator&=(const see-below&);
+mp_number& operator|=(const see-below&);
+mp_number& operator^=(const see-below&);
+mp_number& operator<<=(const integer-type&);
+mp_number& operator>>=(const integer-type&);
+
    +

    + These operators all take their usual arithmetic meanings. +

    +

    + The arguments to these operators is either: +

    +
      +
    • + Another mp_number<Backend, + ExpressionTemplates>. +
      • +
    • + A builtin arithmetic type. +
      • +
    • + An expression template derived from mp_number<Backend>. +
      • +
    +

    + For the left and right shift operations, the argument must be a builtin integer + type with a positive value (negative values result in a std::runtime_error + being thrown). +

    +
    operator convertible-to-bool-type()const;
+
    +

    + Returns an unmentionable-type that is usable in Boolean + contexts (this allows mp_number + to be used in any Boolean context - if statements, conditional statements, + or as an argument to a logical operator - without type mp_number + being convertible to type bool. +

    +

    + This operator also enables the use of mp_number + with any of the following operators: !, + ||, && + and ?:. +

    +
    void swap(mp_number& other);
+
    +

    + Swaps *this + with other. +

    +
    bool is_zero()const;
+
    +

    + Returns true is *this is zero, + otherwise false. +

    +
    int sign()const;
+
    +

    + Returns a value less than zero if *this is negative, a value greater than zero + if *this + is positive, and zero if *this + is zero. +

    +
    std::string str(unsigned precision, bool scientific = true)const;
+
    +

    + Returns the number formatted as a string, with at least precision + digits, and in scientific format if scientific is true. +

    +
    template <class T>
+T convert_to()const;
+
    +

    + Provides a generic conversion mechanism to convert *this to type T. + Type T may be any arithmetic + type. Optionally other types may also be supported by specific Backend types. +

    +
    static unsigned default_precision();
+static void default_precision(unsigned digits10);
+unsigned precision()const;
+void precision(unsigned digits10);
+
    +

    + These functions are only available if the Backend template parameter supports + runtime changes to precision. They get and set the default precision and + the precision of *this + respectively. +

    +
    int compare(const mp_number<Backend, ExpressionTemplates>& o)const;
+template <class V>
+typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
+
    +

    + Returns: +

    +
      +
    • + A value less that 0 for *this < other +
      • +
    • + A value greater that 0 for *this > other +
      • +
    • + Zero for *this + == other +
      • +
    +
    Backend& backend();
+const Backend& backend()const;
+
    +

    + Returns the underlying back-end instance used by *this. +

    +
    + + Non-member + operators +
    +
    // Non member operators:
+unmentionable-expression-template-type operator+(const see-below&, const see-below&);
+unmentionable-expression-template-type operator-(const see-below&, const see-below&);
+unmentionable-expression-template-type operator*(const see-below&, const see-below&);
+unmentionable-expression-template-type operator/(const see-below&, const see-below&);
+// Integer only operations:
+unmentionable-expression-template-type operator%(const see-below&, const see-below&);
+unmentionable-expression-template-type operator&(const see-below&, const see-below&);
+unmentionable-expression-template-type operator|(const see-below&, const see-below&);
+unmentionable-expression-template-type operator^(const see-below&, const see-below&);
+unmentionable-expression-template-type operator<<(const see-below&, const integer-type&);
+unmentionable-expression-template-type operator>>(const see-below&, const integer-type&);
+// Comparison operators:
+bool operator==(const see-below&, const see-below&);
+bool operator!=(const see-below&, const see-below&);
+bool operator< (const see-below&, const see-below&);
+bool operator> (const see-below&, const see-below&);
+bool operator<=(const see-below&, const see-below&);
+bool operator>=(const see-below&, const see-below&);
+
    +

    + These operators all take their usual arithmetic meanings. +

    +

    + The arguments to these functions must contain at least one of the following: +

    +
      +
    • + An mp_number. +
      • +
    • + An expression template type derived from mp_number. +
      • +
    +

    + In addition, one of the two arguments may be a builtin arithmetic type. +

    +

    + The return type of these operators is either: +

    +
      +
    • + An unmentionable-type expression template type when + ExpressionTemplates is + true. +
      • +
    • + Type mp_number<Backend, + false> + when ExpressionTemplates + is false. +
      • +
    • + Type bool if the operator + is a comparison operator. +
      • +
    +

    + Finally note that the second argument to the left and right shift operations + must be a builtin integer type, and that the argument must be positive (negative + arguments result in a std::runtime_error + being thrown). +

    +
    + + swap +
    +
    template <class Backend, ExpressionTemplates>
+void swap(mp_number<Backend, ExpressionTemplates>& a, mp_number<Backend, ExpressionTemplates>& b);
+
    +

    + Swaps a and b. +

    +
    + + Iostream + Support +
    +
    template <class Backend, bool ExpressionTemplates>
+std::ostream& operator << (std::ostream& os, const mp_number<Backend, ExpressionTemplates>& r);
+template <class Unspecified...>
+std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r);
+template <class Backend, bool ExpressionTemplates>
+inline std::istream& operator >> (std::istream& is, mp_number<Backend, ExpressionTemplates>& r)
+
    +

    + These operators provided formatted input-output operations on mp_number types, and expression templates + derived from them. +

    +

    + It's down to the back-end type to actually implement string conversion. However, + the back-ends provided with this library support all of the iostream formatting + flags, field width and precision settings. +

    +
    + + Non-member + standard library function support +
    +
    unmentionable-expression-template-type    abs    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fabs   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sqrt   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    floor  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ceil   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    trunc  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    itrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    ltrunc (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lltrunc(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    round  (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    iround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    lround (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    llround(const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    exp    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    log10    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cos    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sin    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tan    (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    acos   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    asin   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    cosh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    sinh   (const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    tanh   (const mp_number-or-expression-template-type&);
+
+unmentionable-expression-template-type    ldexp (const mp_number-or-expression-template-type&, int);
+unmentionable-expression-template-type    frexp (const mp_number-or-expression-template-type&, int*);
+unmentionable-expression-template-type    pow   (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    fmod  (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+unmentionable-expression-template-type    atan2 (const mp_number-or-expression-template-type&, const mp_number-or-expression-template-type&);
+
    +

    + These functions all behave exactly as their standard library counterparts + do: their argument is either an instance of mp_number + or an expression template derived from it; If the argument is of type mp_number<Backend, false> + then that is also the return type, otherwise the return type is an expression + template. +

    +

    + These functions are normally implemented by the Backend type. However, default + versions are provided for Backend types that don't have native support for + these functions. Please note however, that this default support requires + the precision of the type to be a compile time constant - this means for + example that the GMP MPF Backend will + not work with these functions when that type is used at variable precision. +

    +

    + Also note that with the exception of abs + that these functions can only be used with floating-point Backend types. +

    +
    + + Traits + Class Support +
    +
    template <class T>
+struct component_type;
+
    +

    + If this is a type with mutiple components (for example rational or complex + types), then this trait has a single member type + that is the type of those components. +

    +
    template <class T>
+struct number_category;
+
    +

    + A traits class that inherits from mpl::int_<N> + where N is one of the enumerated + values number_kind_integer, + number_kind_floating_point, + number_kind_rational or + number_kind_fixed_point. +

    +
    + + Integer functions +
    +
    template <class Backend, bool ExpressionTemplates>
+bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
+               mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
+
    +

    + Divides x by y and returns both the quotient and remainder. After the call + q = + x / y and r + = x % y. +

    +
    template <class Integer>
+Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val);
+
    +

    + Returns the absolute value of x + % val. +

    +
    unsigned lsb(const mp_number-or-expression-template-type& x);
+
    +

    + Returns the index of the least significant bit that is set to 1. +

    +
    template <class Backend, class ExpressionTemplates>
+bool bit_test(const mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Returns true if the bit at + index in val is set. +

    +
    template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_set(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Sets the bit at index in val, and + returns val. +

    +
    template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_unset(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Unsets the bit at index in val, + and returns val. +

    +
    template <class Backend, class ExpressionTemplates>
+mp_number<Backend, ExpressionTemplates>& bit_flip(mp_number<Backend, ExpressionTemplates>& val, unsigned index);
+
    +

    + Flips the bit at index in val, + and returns val. +

    +
    template <class Engine>
+bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials, Engine& gen);
+bool miller_rabin_test(const mp_number-or-expression-template-type& n, unsigned trials);
+
    +

    + Tests to see if the number n is probably prime - the + test excludes the vast majority of composite numbers by excluding small prime + factors and performing a single Fermat test. Then performs trials + Miller-Rabin tests. Returns false + if n is definitely composite, or true + if n is probably prime with the probability of it being + composite less than 0.25^trials. +

    +
    + + Rational + Number Functions +
    +
    typename component_type<mp_number-or-expression-template-type>::type numerator  (const mp_number-or-expression-template-type&);
+typename component_type<mp_number-or-expression-template-type>::type denominator(const mp_number-or-expression-template-type&);
+
    +

    + These functions return the numerator and denominator of a rational number + respectively. +

    +
    + + Boost.Math + Interoperability Support +
    +
    namespace boost{ namespace math{
+
+int  fpclassify     (const mp_number-or-expression-template-type&, int);
+bool isfinite       (const mp_number-or-expression-template-type&, int);
+bool isnan          (const mp_number-or-expression-template-type&, int);
+bool isinf          (const mp_number-or-expression-template-type&, int);
+bool isnormal       (const mp_number-or-expression-template-type&, int);
+
+}} // namespaces
+
    +

    + These floating-point classification functions behave exactly as their Boost.Math + equivalents. +

    +

    + Other Boost.Math functions and templates may also be specialized or overloaded + to ensure interoperability. +

    +
    + + std::numeric_limits + support +
    +
    namespace std{
+
+template <class Backend, ExpressionTemplates>
+struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
+{
+   /* Usual members here */
+};
+
+}
+
    +

    + Class template std::numeric_limits is specialized for all instantiations + of mp_number whose precision + is known at compile time, plus those types whose precision is unlimited (though + it is much less useful in those cases). It is not specialized for types whose + precision can vary at compile time (such as mpf_float). +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/mpf_ref.html b/doc/html/boost_multiprecision/ref/mpf_ref.html new file mode 100644 index 00000000..fd2d8f50 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/mpf_ref.html @@ -0,0 +1,67 @@ + + + +gmp_float + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class gmp_float;
+
+typedef mp_number<gmp_float<50> >    mpf_float_50;
+typedef mp_number<gmp_float<100> >   mpf_float_100;
+typedef mp_number<gmp_float<500> >   mpf_float_500;
+typedef mp_number<gmp_float<1000> >  mpf_float_1000;
+typedef mp_number<gmp_float<0> >     mpf_float;
+
+}} // namespaces
+
    +

    + Class template gmp_float + fulfills all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + The class takes a single template parameter - Digits10 + - which is the number of decimal digits precision the type should support. + When this parameter is zero, then the precision can be set at runtime via + mp_number::default_precision and mp_number::precision. + Note that this type does not in any way change the GMP library's global state + (for example it does not change the default precision of the mpf_t data type), + therefore you can safely mix this type with existing code that uses GMP, + and also mix gmp_floats of + differing precision. +

    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/mpfr_ref.html b/doc/html/boost_multiprecision/ref/mpfr_ref.html new file mode 100644 index 00000000..7588f301 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/mpfr_ref.html @@ -0,0 +1,67 @@ + + + +mpfr_float_backend + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class mpfr_float_backend;
+
+typedef mp_number<mpfr_float_backend<50> >    mpfr_float_50;
+typedef mp_number<mpfr_float_backend<100> >   mpfr_float_100;
+typedef mp_number<mpfr_float_backend<500> >   mpfr_float_500;
+typedef mp_number<mpfr_float_backend<1000> >  mpfr_float_1000;
+typedef mp_number<mpfr_float_backend<0> >     mpfr_float;
+
+}} // namespaces
+
    +

    + Class template mpfr_float_backend + fulfills all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + The class takes a single template parameter - Digits10 + - which is the number of decimal digits precision the type should support. + When this parameter is zero, then the precision can be set at runtime via + mp_number::default_precision and mp_number::precision. + Note that this type does not in any way change the GMP or MPFR library's + global state (for example it does not change the default precision of the + mpfr_t data type), therefore you can safely mix this type with existing code + that uses GMP or MPFR, and also mix mpfr_float_backends + of differing precision. +

    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/tom_int_ref.html b/doc/html/boost_multiprecision/ref/tom_int_ref.html new file mode 100644 index 00000000..95abdcbe --- /dev/null +++ b/doc/html/boost_multiprecision/ref/tom_int_ref.html @@ -0,0 +1,51 @@ + + + +tom_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+class tommath_int;
+
+typedef mp_number<tommath_int >         tom_int;
+
+}} // namespaces
+
    +

    + Class template tommath_int + fulfills all of the requirements for a Backend + type. It's members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

    +

    + More information on this type can be found in the tutorial. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html new file mode 100644 index 00000000..8b64cd8e --- /dev/null +++ b/doc/html/boost_multiprecision/tut.html @@ -0,0 +1,82 @@ + + + +Tutorial + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    Integer Types
    +
    +
    cpp_int
    +
    gmp_int
    +
    tom_int
    +
    Examples
    +
    +
    Factorials
    +
    Bit Operations
    +
    +
    +
    Floating Point Numbers
    +
    +
    gmp_float
    +
    mpfr_float
    +
    cpp_dec_float
    +
    Examples
    +
    +
    Area of + Circle
    +
    Defining + a Lambda Function.
    +
    Calculating + a Derivative
    +
    Calculating + an Integral
    +
    Polynomial + Evaluation
    +
    +
    +
    Rational Number Types
    +
    +
    gmp_rational
    +
    cpp_rational
    +
    tommath_rational
    +
    Use With Boost.Rational
    +
    rational_adapter
    +
    +
    Constructing and + Interconverting Between Number Types
    +
    Generating Random Numbers
    +
    Primality Testing
    +
    +

    + In order to use this library you need to make two choices: what kind of number + do I want, and which back-end do I want to perform the actual arithmetic? +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/conversions.html b/doc/html/boost_multiprecision/tut/conversions.html new file mode 100644 index 00000000..b34da26c --- /dev/null +++ b/doc/html/boost_multiprecision/tut/conversions.html @@ -0,0 +1,106 @@ + + + +Constructing and Interconverting Between Number Types + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + All of the number types that are based on mp_number + have certain conversion rules in common. In particular: +

    +
    • + Any number type can be constructed (or assigned) from any builtin arithmetic + type: +
    +
    cpp_dec_float_50 df(0.5); // OK construction from double
+cpp_int          i(450);  // OK constructs from signed int
+
    +
    • + Any number type can be constructed (or assigned) from a const char* or a std::string: +
    +
    // pi to 50 places from a string:
+cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
+// Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly:
+cpp_int          i  = "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000";
+// Invalid input always results in a std::runtime_error being thrown:
+i = std::string("3.14");
+
    +
    • + Any number type will interoperate with the builtin type in arithmetic + expressions: +
    +
    // pi to 50 places from a string:
+cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
+// Multiply by 2 - using an integer literal here is usually more efficient
+// than constructing a temporary:
+df *= 2;
+
+// There is a need to be careful with integer types though:
+cpp_int i = 2;
+// Ooops, this really just multiplies by 3:
+i *= 3.14;
+
    +
    • + Any number type can be streamed to and from the C++ iostreams: +
    +
    cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
+// Now print at full precision:
+std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_50>::max_digits10)
+   << df << std::endl
+cpp_int i = 1;
+i <<= 256;
+// Now print in hex format with prefix:
+std::cout << std::hex << std::showbase << i << std::endl;
+
    +
    • + Some intercomnversions between number types are completely generic, and + are always available: +
    +
    cpp_int cppi(2);
+// We can always convert between numbers of the same category - 
+// int to int, rational to rational, or float to float, so this is OK:
+mpz_int z = cppi;
+// We can always promote from int to rational, int to float, or rational to float:
+cpp_rational     cppr = cppi;  // OK, int to rational
+cpp_dec_float_50 df =   cppi;  // OK, int to float
+df                  =   cppr;  // OK, rational to float
+// However narrowing conversions always fail:
+cppi                =   df;    // Compiler error, conversion not allowed
+
    +
    • + Other interconversions may be allowed as special cases, whenever the + backend allows it: +
    +
    mpf_t     m;           // Native GMP type.
+mpf_init_set_ui(m, 0); // set to a value;
+mpf_float i(m);        // copies the value of the native type.
+
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats.html b/doc/html/boost_multiprecision/tut/floats.html new file mode 100644 index 00000000..45d29397 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats.html @@ -0,0 +1,199 @@ + + + +Floating Point Numbers + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    gmp_float
    +
    mpfr_float
    +
    cpp_dec_float
    +
    Examples
    +
    +
    Area of + Circle
    +
    Defining + a Lambda Function.
    +
    Calculating + a Derivative
    +
    Calculating + an Integral
    +
    Polynomial + Evaluation
    +
    +
    +

    + The following back-ends provide floating point arithmetic: +

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend Type +

    +     		+

    + Header +

    +     		+

    + Radix +

    +     		+

    + Dependencies +

    +     		+

    + Pros +

    +     		+

    + Cons +

    +
    +

    + mpf_float<N> +

    +     		+

    + boost/multiprecision/gmp.hpp +

    +     		+

    + 2 +

    +     		+

    + GMP +

    +     		+

    + Very fast and efficient back-end. +

    +     		+

    + Dependency on GNU licensed GMP + library. +

    +
    +

    + mpfr_float<N> +

    +     		+

    + boost/multiprecision/mpfr.hpp +

    +     		+

    + 2 +

    +     		+

    + GMP and MPFR +

    +     		+

    + Very fast and efficient back-end, with its own standard library + implementation. +

    +     		+

    + Dependency on GNU licensed GMP + and MPFR libraries. +

    +
    +

    + cpp_dec_float<N> +

    +     		+

    + boost/multiprecision/cpp_dec_float.hpp +

    +     		+

    + 10 +

    +     		+

    + None +

    +     		+

    + Header only, all C++ implementation. Boost licence. +

    +     		+

    + Approximately 2x slower than the MPFR + or GMP libraries. +

    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html new file mode 100644 index 00000000..aea653f8 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html @@ -0,0 +1,117 @@ + + + +cpp_dec_float + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/cpp_dec_float.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class cpp_dec_float;
+
+typedef mp_number<cpp_dec_float<50> > cpp_dec_float_50;
+typedef mp_number<cpp_dec_float<100> > cpp_dec_float_100;
+
+}} // namespaces
+
    +

    + The cpp_dec_float back-end + is used in conjunction with mp_number: + It acts as an entirely C++ (header only and dependency free) real-number + type that is a drop-in replacement for the native C++ floating-point types, + but with much greater precision. +

    +

    + Type cpp_dec_float can + be used at fixed precision by specifying a non-zero Digits10 + template parameter. The typedefs cpp_dec_float_50 + and cpp_dec_float_100 provide + arithmetic types at 50 and 100 decimal digits precision respectively. +

    +

    + There is full standard library and numeric_limits + support available for this type. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed cpp_dec_floats + have a value of zero. +
      • +
    • + The radix of this type is 10. As a result it can behave subtly differently + from base-2 types. +
      • +
    • + It is not possible to round-trip this type to and from a string and + get back to exactly the same value (this is a result of the type having + some hidden internal guard digits). +
      • +
    • + The type has a number of internal guard digits over and above those + specified in the template argument. Normally these should not be visible + to the user. +
      • +
    +
    + + cpp_dec_float + example: +
    +

    +

    +
    #include <boost/multiprecision/cpp_dec_float.hpp>
+
+using namespace boost::multiprecision;
+
+// Operations at fixed precision and full numeric_limits support:
+cpp_dec_float_100 b = 2;
+std::cout << std::numeric_limits<cpp_dec_float_100>::digits << std::endl;
+// Note that digits10 is the same as digits, since we're base 10! :
+std::cout << std::numeric_limits<cpp_dec_float_100>::digits10 << std::endl;
+// We can use any C++ std lib function, lets print all the digits as well:
+std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_100>::max_digits10)
+   << log(b) << std::endl; // print log(2)
+// We can also use any function from Boost.Math:
+std::cout << boost::math::tgamma(b) << std::endl;
+// These even work when the argument is an expression template:
+std::cout << boost::math::tgamma(b * b) << std::endl;
+// And since we have an extended exponent range we can generate some really large 
+// numbers here (4.0238726007709377354370243e+2564):
+std::cout << boost::math::tgamma(cpp_dec_float_100(1000)) << std::endl;
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg.html new file mode 100644 index 00000000..90d9d20f --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg.html @@ -0,0 +1,46 @@ + + + +Examples + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    Area of + Circle
    +
    Defining + a Lambda Function.
    +
    Calculating + a Derivative
    +
    Calculating + an Integral
    +
    Polynomial + Evaluation
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html new file mode 100644 index 00000000..46500c20 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html @@ -0,0 +1,118 @@ + + + +Area of Circle + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Generic numeric programming employs templates to use the same code for + different floating-point types and functions. Consider the area of a + circle a of radius r, given by +

    +

    + a = π * r2 +

    +

    + The area of a circle can be computed in generic programming using Boost.Math + for the constant π as shown below: +

    +

    +

    +
    #include <boost/math/constants/constants.hpp>
+
+template<typename T>
+inline T area_of_a_circle(T r)
+{
+   using boost::math::constants::pi;
+   return pi<T>() * r * r;
+}
+
    +

    +

    +

    + It is possible to use area_of_a_circle() with built-in floating-point types + as well as floating-point types from Boost.Multiprecision. In particular, + consider a system with 4-byte single-precision float, 8-byte double-precision + double and also the cpp_dec_float_50 + data type from Boost.Multiprecision with 50 decimal digits of precision. +

    +

    + We can compute and print the approximate area of a circle with radius + 123/100 for float, double and cpp_dec_float_50 + with the program below. +

    +

    +

    +
    #include <iostream>
+#include <iomanip>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+
+using boost::multiprecision::cpp_dec_float_50;
+
+int main(int, char**)
+{
+   const float r_f(float(123) / 100);
+   const float a_f = area_of_a_circle(r_f);
+
+   const double r_d(double(123) / 100);
+   const double a_d = area_of_a_circle(r_d);
+
+   const cpp_dec_float_50 r_mp(cpp_dec_float_50(123) / 100);
+   const cpp_dec_float_50 a_mp = area_of_a_circle(r_mp);
+
+   // 4.75292
+   std::cout
+      << std::setprecision(std::numeric_limits<float>::digits10)
+      << a_f
+      << std::endl;
+
+   // 4.752915525616
+   std::cout
+      << std::setprecision(std::numeric_limits<double>::digits10)
+      << a_d
+      << std::endl;
+
+   // 4.7529155256159981904701331745635599135018975843146
+   std::cout
+      << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10)
+      << a_mp
+      << std::endl;
+}
+
    +

    +

    +

    + In the next example we'll look at calling both standard library and Boost.Math + functions from within generic code. We'll also show how to cope with + template arguments which are expression-templates rather than number + types. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html new file mode 100644 index 00000000..b7621a91 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html @@ -0,0 +1,161 @@ + + + +Calculating an Integral + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Similar to the generic derivative example, we can calculate integrals + in a similar manner: +

    +

    +

    +
    template<typename value_type, typename function_type>
+inline value_type integral(const value_type a,
+                           const value_type b,
+                           const value_type tol,
+                           function_type func)
+{
+   unsigned n = 1U;
+
+   value_type h = (b - a);
+   value_type I = (func(a) + func(b)) * (h / 2);
+
+   for(unsigned k = 0U; k < 8U; k++)
+   {
+      h /= 2;
+
+      value_type sum(0);
+      for(unsigned j = 1U; j <= n; j++)
+      {
+         sum += func(a + (value_type((j * 2) - 1) * h));
+      }
+
+      const value_type I0 = I;
+      I = (I / 2) + (h * sum);
+
+      const value_type ratio     = I0 / I;
+      const value_type delta     = ratio - 1;
+      const value_type delta_abs = ((delta < 0) ? -delta : delta);
+
+      if((k > 1U) && (delta_abs < tol))
+      {
+         break;
+      }
+
+      n *= 2U;
+   }
+
+   return I;
+}
+
    +

    +

    +

    + The following sample program shows how the function can be called, we + begin by defining a function object, which when integrated should yield + the Bessel J function: +

    +

    +

    +
    template<typename value_type>
+class cyl_bessel_j_integral_rep
+{
+public:
+   cyl_bessel_j_integral_rep(const unsigned N,
+      const value_type& X) : n(N), x(X) { }
+
+   value_type operator()(const value_type& t) const
+   {
+      // pi * Jn(x) = Int_0^pi [cos(x * sin(t) - n*t) dt]
+      return cos(x * sin(t) - (n * t));
+   }
+
+private:
+   const unsigned n;
+   const value_type x;
+};
+
    +

    +

    +

    +

    +
       /* The function can now be called as follows: */
+int main(int, char**)
+{
+   using boost::math::constants::pi;
+   typedef boost::multiprecision::cpp_dec_float_50 mp_type;
+
+   const float j2_f =
+      integral(0.0F,
+      pi<float>(),
+      0.01F,
+      cyl_bessel_j_integral_rep<float>(2U, 1.23F)) / pi<float>();
+
+   const double j2_d =
+      integral(0.0,
+      pi<double>(),
+      0.0001,
+      cyl_bessel_j_integral_rep<double>(2U, 1.23)) / pi<double>();
+
+   const mp_type j2_mp =
+      integral(mp_type(0),
+      pi<mp_type>(),
+      mp_type(1.0E-20),
+      cyl_bessel_j_integral_rep<mp_type>(2U, mp_type(123) / 100)) / pi<mp_type>();
+
+   // 0.166369
+   std::cout
+      << std::setprecision(std::numeric_limits<float>::digits10)
+      << j2_f
+      << std::endl;
+
+   // 0.166369383786814
+   std::cout
+      << std::setprecision(std::numeric_limits<double>::digits10)
+      << j2_d
+      << std::endl;
+
+   // 0.16636938378681407351267852431513159437103348245333
+   std::cout
+      << std::setprecision(std::numeric_limits<mp_type>::digits10)
+      << j2_mp
+      << std::endl;
+
+   //
+   // Print true value for comparison:
+   // 0.166369383786814073512678524315131594371033482453329
+   std::cout << boost::math::cyl_bessel_j(2, mp_type(123) / 100) << std::endl;
+}
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html new file mode 100644 index 00000000..981d684d --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html @@ -0,0 +1,222 @@ + + + +Defining a Lambda Function. + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + In this example we'll show several implementations of the Jahnke + and Emden Lambda function, each implementation a little more + sophisticated than the last. +

    +

    + The Jahnke-Emden Lambda function is defined by the equation: +

    +

    + JahnkeEmden(v, z) = Γ(v+1) * Jv(z) / (z / 2)v +

    +

    + If we were to implement this at double precision using Boost.Math's facilities + for the Gamma and Bessel function calls it would look like this: +

    +

    +

    +
    double JEL1(double v, double z)
+{
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / std::pow(z / 2, v);
+}
+
    +

    +

    +

    + Calling this function as: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10);
+std::cout << JEL1(2.5, 0.5) << std::endl;
+
    +

    + Yields the output: +

    +
    9.822663964796047e-001
    +

    + Now lets implement the function again, but this time using the multiprecision + type cpp_dec_float_50 + as the argument type: +

    +

    +

    +
    boost::multiprecision::cpp_dec_float_50
+   JEL2(boost::multiprecision::cpp_dec_float_50 v, boost::multiprecision::cpp_dec_float_50 z)
+{
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / boost::multiprecision::pow(z / 2, v);
+}
+
    +

    +

    +

    + The implementation is almost the same as before, but with one key difference + - we can no longer call std::pow, + instead we must call the version inside the boost::multiprecision + namespace. In point of fact, we could have omitted the namespace prefix + on the call to pow since + the right overload would have been found via argument + dependent lookup in any case. +

    +

    + Note also that the first argument to pow + along with the argument to tgamma + in the above code are actually expression templates. The pow and tgamma + functions will handle these arguments just fine. +

    +

    + Here's an example of how the function may be called: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10);
+std::cout << JEL2(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl;
+
    +

    + Which outputs: +

    +
    9.82266396479604757017335009796882833995903762577173e-01
    +

    + Now that we've seen some non-template examples, lets repeat the code + again, but this time as a template that can be called either with a builtin + type (float, double etc), or with a multiprecision + type: +

    +

    +

    +
    template <class Float>
+Float JEL3(Float v, Float z)
+{
+   using std::pow;
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
+}
+
    +

    +

    +

    + Once again the code is almost the same as before, but the call to pow has changed yet again. We need + the call to resolve to either std::pow + (when the argument is a builtin type), or to boost::multiprecision::pow + (when the argument is a multiprecision type). We do that by making the + call unqualified so that versions of pow + defined in the same namespace as type Float + are found via argument dependent lookup, while the using + std::pow directive makes the standard library + versions visible for builtin floating point types. +

    +

    + Let's call the function with both double + and multiprecision arguments: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10);
+std::cout << JEL3(2.5, 0.5) << std::endl;
+std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10);
+std::cout << JEL3(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl;
+
    +

    + Which outputs: +

    +
    9.822663964796047e-001
+9.82266396479604757017335009796882833995903762577173e-01
+
    +

    + Unfortunately there is a problem with this version: if we were to call + it like this: +

    +
    boost::multiprecision::cpp_dec_float_50 v(2), z(0.5);
+JEL3(v + 0.5, z);
+
    +

    + Then we would get a long and inscrutable error message from the compiler: + the problem here is that the first argument to JEL3 + is not a number type, but an expression template. We could obviously + add a typecast to fix the issue: +

    +
    JEL(cpp_dec_float_50(v + 0.5), z);
+
    +

    + However, if we want the function JEL to be truely reusable, then a better + solution might be preferred. To achieve this we can borrow some code + from Boost.Math which calculates the return type of mixed-argument functions, + here's how the new code looks now: +

    +

    +

    +
    template <class Float1, class Float2>
+typename boost::math::tools::promote_args<Float1, Float2>::type
+   JEL4(Float1 v, Float2 z)
+{
+   using std::pow;
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
+}
+
    +

    +

    +

    + As you can see the two arguments to the function are now separate template + types, and the return type is computed using the promote_args + metafunction from Boost.Math. +

    +

    + Now we can call: +

    +
    std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_100>::digits10);
+std::cout << JEL4(cpp_dec_float_100(2) + 0.5, cpp_dec_float_100(0.5)) << std::endl;
+
    +

    + And get 100 digits of output: +

    +
    9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01
    +

    + As a bonus, we can now call the function not just with expression templates, + but with other mixed types as well: for example float + and double or int and double, + and the correct return type will be computed in each case. +

    +

    + Note that while in this case we didn't have to change the body of the + function, in the general case any function like this which creates local + variables internally would have to use promote_args + to work out what type those variables should be, for example: +

    +
    template <class Float1, class Float2>
+typename boost::math::tools::promote_args<Float1, Float2>::type
+   JEL5(Float1 v, Float2 z)
+{
+   using std::pow;
+   typedef typename boost::math::tools::promote_args<Float1, Float2>::type variable_type;
+   variable_type t = pow(z / 2, v);
+   return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / t;
+}
+
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html new file mode 100644 index 00000000..70cdb83c --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html @@ -0,0 +1,202 @@ + + + +Calculating a Derivative + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + In this example we'll add even more power to generic numeric programming + using not only different floating-point types but also function objects + as template parameters. Consider some well-known central difference rules + for numerically computing the first derivative of a function f′(x) + with x ∈ ℜ: +

    +

    + +

    +

    + Where the difference terms mn are given by: +

    +

    + +

    +

    + and dx is the step-size of the derivative. +

    +

    + The third formula in Equation 1 is a three-point central difference rule. + It calculates the first derivative of f′(x) to O(dx6), + where dx is the given step-size. For example, if + the step-size is 0.01 this derivative calculation has about 6 decimal + digits of precision - just about right for the 7 decimal digits of single-precision + float. Let's make a generic template subroutine using this three-point + central difference rule. In particular: +

    +

    +

    +
    template<typename value_type, typename function_type>
+   value_type derivative(const value_type x, const value_type dx, function_type func)
+{
+   // Compute d/dx[func(*first)] using a three-point
+   // central difference rule of O(dx^6).
+
+   const value_type dx1 = dx;
+   const value_type dx2 = dx1 * 2;
+   const value_type dx3 = dx1 * 3;
+
+   const value_type m1 = (func(x + dx1) - func(x - dx1)) / 2;
+   const value_type m2 = (func(x + dx2) - func(x - dx2)) / 4;
+   const value_type m3 = (func(x + dx3) - func(x - dx3)) / 6;
+
+   const value_type fifteen_m1 = 15 * m1;
+   const value_type six_m2     =  6 * m2;
+   const value_type ten_dx1    = 10 * dx1;
+
+   return ((fifteen_m1 - six_m2) + m3) / ten_dx1;
+}
+
    +

    +

    +

    + The derivative() + template function can be used to compute the first derivative of any + function to O(dx6). For example, consider the first + derivative of sin(x) evaluated at x = + π/3. In other words, +

    +

    + +

    +

    + The code below computes the derivative in Equation 3 for float, double + and boost's multiple-precision type cpp_dec_float_50. +

    +

    +

    +
    #include <iostream>
+#include <iomanip>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+#include <boost/math/constants/constants.hpp>
+
+
+int main(int, char**)
+{
+   using boost::math::constants::pi;
+   using boost::multiprecision::cpp_dec_float_50;
+   //
+   // We'll pass a function pointer for the function object passed to derivative,
+   // the typecast is needed to select the correct overload of std::sin:
+   //
+   const float d_f = derivative(
+      pi<float>() / 3,
+      0.01F,
+      static_cast<float(*)(float)>(std::sin)
+   );
+
+   const double d_d = derivative(
+      pi<double>() / 3,
+      0.001,
+      static_cast<double(*)(double)>(std::sin)
+      );
+   //
+   // In the cpp_dec_float_50 case, the sin function is multiply overloaded
+   // to handle expression templates etc.  As a result it's hard to take it's
+   // address without knowing about its implementation details.  We'll use a 
+   // C++11 lambda expression to capture the call.
+   // We also need a typecast on the first argument so we don't accidently pass
+   // an expression template to a template function:
+   //
+   const cpp_dec_float_50 d_mp = derivative(
+      cpp_dec_float_50(pi<cpp_dec_float_50>() / 3),
+      cpp_dec_float_50(1.0E-9),
+      [](const cpp_dec_float_50& x) -> cpp_dec_float_50
+      {
+         return sin(x);
+      }
+      );
+
+   // 5.000029e-001
+   std::cout
+      << std::setprecision(std::numeric_limits<float>::digits10)
+      << d_f
+      << std::endl;
+
+   // 4.999999999998876e-001
+   std::cout
+      << std::setprecision(std::numeric_limits<double>::digits10)
+      << d_d
+      << std::endl;
+
+   // 4.99999999999999999999999999999999999999999999999999e-01
+   std::cout
+      << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10)
+      << d_mp
+      << std::endl;
+}
+
    +

    +

    +

    + The expected value of the derivative is 0.5. This central difference + rule in this example is ill-conditioned, meaning it suffers from slight + loss of precision. With that in mind, the results agree with the expected + value of 0.5. +

    +

    + We can take this a step further and use our derivative function to compute + a partial derivative. For example if we take the incomplete gamma function + P(a, z), and take the derivative with respect to + z at (2,2) then we can calculate + the result as shown below, for good measure we'll compare with the "correct" + result obtained from a call to gamma_p_derivative, + the results agree to approximately 44 digits: +

    +

    +

    +
    cpp_dec_float_50 gd = derivative(
+   cpp_dec_float_50(2),
+   cpp_dec_float_50(1.0E-9),
+   [](const cpp_dec_float_50& x) ->cpp_dec_float_50
+   {
+      return boost::math::gamma_p(2, x);
+   }
+);
+// 2.70670566473225383787998989944968806815263091819151e-01
+std::cout
+   << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10)
+   << gd
+   << std::endl;
+// 2.70670566473225383787998989944968806815253190143120e-01
+std::cout << boost::math::gamma_p_derivative(cpp_dec_float_50(2), cpp_dec_float_50(2)) << std::endl;
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html new file mode 100644 index 00000000..8acdc588 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html @@ -0,0 +1,146 @@ + + + +Polynomial Evaluation + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + In this example we'll look at polynomial evaluation, this is not only + an important use case, but it's one that mp_number + performs particularly well at because the expression templates completely + eliminate all temporaries from a Horner + polynomial evaluation scheme. +

    +

    + The following code evaluates sin(x) as a polynomial, accurate to at least + 64 decimal places: +

    +

    +

    +
    using boost::multiprecision::cpp_dec_float;
+typedef boost::multiprecision::mp_number<cpp_dec_float<64> > mp_type;
+
+mp_type mysin(const mp_type& x)
+{
+  // Approximation of sin(x * pi/2) for -1 <= x <= 1, using an order 63 polynomial.
+  static const std::array<mp_type, 32U> coefs =
+  {{
+    mp_type("+1.5707963267948966192313216916397514420985846996875529104874722961539082031431044993140174126711"), //"),
+    mp_type("-0.64596409750624625365575656389794573337969351178927307696134454382929989411386887578263960484"), // ^3
+    mp_type("+0.07969262624616704512050554949047802252091164235106119545663865720995702920146198554317279"), // ^5
+    mp_type("-0.0046817541353186881006854639339534378594950280185010575749538605102665157913157426229824"), // ^7
+    mp_type("+0.00016044118478735982187266087016347332970280754062061156858775174056686380286868007443"), // ^9
+    mp_type("-3.598843235212085340458540018208389404888495232432127661083907575106196374913134E-6"), // ^11
+    mp_type("+5.692172921967926811775255303592184372902829756054598109818158853197797542565E-8"), // ^13
+    mp_type("-6.688035109811467232478226335783138689956270985704278659373558497256423498E-10"), // ^15
+    mp_type("+6.066935731106195667101445665327140070166203261129845646380005577490472E-12"), // ^17
+    mp_type("-4.377065467313742277184271313776319094862897030084226361576452003432E-14"), // ^19
+    mp_type("+2.571422892860473866153865950420487369167895373255729246889168337E-16"), // ^21
+    mp_type("-1.253899540535457665340073300390626396596970180355253776711660E-18"), // ^23
+    mp_type("+5.15645517658028233395375998562329055050964428219501277474E-21"), // ^25
+    mp_type("-1.812399312848887477410034071087545686586497030654642705E-23"), // ^27
+    mp_type("+5.50728578652238583570585513920522536675023562254864E-26"), // ^29
+    mp_type("-1.461148710664467988723468673933026649943084902958E-28"), // ^31
+    mp_type("+3.41405297003316172502972039913417222912445427E-31"), // ^33
+    mp_type("-7.07885550810745570069916712806856538290251E-34"), // ^35
+    mp_type("+1.31128947968267628970845439024155655665E-36"), // ^37
+    mp_type("-2.18318293181145698535113946654065918E-39"), // ^39
+    mp_type("+3.28462680978498856345937578502923E-42"), // ^41
+    mp_type("-4.48753699028101089490067137298E-45"), // ^43
+    mp_type("+5.59219884208696457859353716E-48"), // ^45
+    mp_type("-6.38214503973500471720565E-51"), // ^47
+    mp_type("+6.69528558381794452556E-54"), // ^49
+    mp_type("-6.47841373182350206E-57"), // ^51
+    mp_type("+5.800016389666445E-60"), // ^53
+    mp_type("-4.818507347289E-63"), // ^55
+    mp_type("+3.724683686E-66"), // ^57
+    mp_type("-2.6856479E-69"), // ^59
+    mp_type("+1.81046E-72"), // ^61
+    mp_type("-1.133E-75"), // ^63
+  }};
+
+  const mp_type v = x * 2 / boost::math::constants::pi<mp_type>();
+  const mp_type x2 = (v * v);
+  //
+  // Polynomial evaluation follows, if mp_type allocates memory then
+  // just one such allocation occurs - to initialize the variable "sum" -
+  // and no temporaries are created at all.
+  //
+  const mp_type sum = (((((((((((((((((((((((((((((((     + coefs[31U]
+                                                     * x2 + coefs[30U])
+                                                     * x2 + coefs[29U])
+                                                     * x2 + coefs[28U])
+                                                     * x2 + coefs[27U])
+                                                     * x2 + coefs[26U])
+                                                     * x2 + coefs[25U])
+                                                     * x2 + coefs[24U])
+                                                     * x2 + coefs[23U])
+                                                     * x2 + coefs[22U])
+                                                     * x2 + coefs[21U])
+                                                     * x2 + coefs[20U])
+                                                     * x2 + coefs[19U])
+                                                     * x2 + coefs[18U])
+                                                     * x2 + coefs[17U])
+                                                     * x2 + coefs[16U])
+                                                     * x2 + coefs[15U])
+                                                     * x2 + coefs[14U])
+                                                     * x2 + coefs[13U])
+                                                     * x2 + coefs[12U])
+                                                     * x2 + coefs[11U])
+                                                     * x2 + coefs[10U])
+                                                     * x2 + coefs[9U])
+                                                     * x2 + coefs[8U])
+                                                     * x2 + coefs[7U])
+                                                     * x2 + coefs[6U])
+                                                     * x2 + coefs[5U])
+                                                     * x2 + coefs[4U])
+                                                     * x2 + coefs[3U])
+                                                     * x2 + coefs[2U])
+                                                     * x2 + coefs[1U])
+                                                     * x2 + coefs[0U])
+                                                     * v;
+
+  return sum;
+}
+
    +

    +

    +

    + Calling the function like so: +

    +
    std::cout << std::setprecision(std::numeric_limits<::mp_type>::digits10) << std::scientific;
+std::cout << mysin(mp_type(1)) << std::endl;
+
    +

    + Yields the expected output: +

    +
    7.0710678118654752440084436210484903928483593768847403658833986900e-01
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/gmp_float.html b/doc/html/boost_multiprecision/tut/floats/gmp_float.html new file mode 100644 index 00000000..3b104b2e --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/gmp_float.html @@ -0,0 +1,169 @@ + + + +gmp_float + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/gmp.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class gmp_float;
+
+typedef mp_number<gmp_float<50> >    mpf_float_50;
+typedef mp_number<gmp_float<100> >   mpf_float_100;
+typedef mp_number<gmp_float<500> >   mpf_float_500;
+typedef mp_number<gmp_float<1000> >  mpf_float_1000;
+typedef mp_number<gmp_float<0> >     mpf_float;
+
+}} // namespaces
+
    +

    + The gmp_float back-end + is used in conjunction with mp_number + : it acts as a thin wrapper around the GMP + mpf_t to provide an real-number + type that is a drop-in replacement for the native C++ floating-point types, + but with much greater precision. +

    +

    + Type gmp_float can be used + at fixed precision by specifying a non-zero Digits10 + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpf_float provides a variable precision type + whose precision can be controlled via the mp_numbers + member functions. +

    +
    + + + + + +
    [Note]Note

    + This type only provides standard library and numeric_limits + support when the precision is fixed at compile time. +

    +

    + As well as the usual conversions from arithmetic and string types, instances + of mp_number<mpf_float<N> > are copy constructible and assignable + from: +

    +
      +
    • + The GMP native types mpf_t, mpz_t, + mpq_t. +
      • +
    • + The mp_number wrappers + around those types: mp_number<mpf_float<M> >, + mp_number<gmp_int>, + mp_number<gmp_rational>. +
      • +
    +

    + It's also possible to access the underlying mpf_t + via the data() + member function of gmp_float. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed gmp_floats + have the value zero (this is the GMP + library's default behavior). +
      • +
    • + No changes are made to the GMP + library's global settings, so this type can be safely mixed with existing + GMP code. +
      • +
    • + It is not possible to round-trip objects of this type to and from a + string and get back exactly the same value. This appears to be a limitation + of GMP. +
      • +
    • + Since the underlying GMP types + have no notion of infinities or NaN's, care should be taken to avoid + numeric overflow or division by zero. That latter will trigger a hardware + exception, while generating excessively large exponents may result + in instability of the underlying GMP + library (in testing, converting a number with an excessively large + or small exponent to a string caused GMP + to segfault). +
      • +
    • + This type can equally be used with MPIR + as the underlying implementation - indeed that is the recommended option + on Win32. +
      • +
    +
    + + + GMP example: +
    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+
+using namespace boost::multiprecision;
+
+// Operations at variable precision and limited standard library support:
+mpf_float a = 2;
+mpf_float::default_precision(1000);
+std::cout << mpf_float::default_precision() << std::endl;
+std::cout << sqrt(a) << std::endl; // print root-2
+
+// Operations at fixed precision and full standard library support:
+mpf_float_100 b = 2;
+std::cout << std::numeric_limits<mpf_float_100>::digits << std::endl;
+// We can use any C++ std lib function:
+std::cout << log(b) << std::endl; // print log(2)
+// We can also use any function from Boost.Math:
+std::cout << boost::math::tgamma(b) << std::endl;
+// These even work when the argument is an expression template:
+std::cout << boost::math::tgamma(b * b) << std::endl;
+
+// Access the underlying representation:
+mpf_t f;
+mpf_init(f);
+mpf_set(f, a.backend().data());
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html new file mode 100644 index 00000000..595e9d2c --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html @@ -0,0 +1,159 @@ + + + +mpfr_float + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/mpfr_float.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+template <unsigned Digits10>
+class mpfr_float_backend;
+
+typedef mp_number<mpfr_float_backend<50> >    mpfr_float_50;
+typedef mp_number<mpfr_float_backend<100> >   mpfr_float_100;
+typedef mp_number<mpfr_float_backend<500> >   mpfr_float_500;
+typedef mp_number<mpfr_float_backend<1000> >  mpfr_float_1000;
+typedef mp_number<mpfr_float_backend<0> >     mpfr_float;
+
+}} // namespaces
+
    +

    + The mpfr_float_backend + type is used in conjunction with mp_number: + It acts as a thin wrapper around the MPFR + mpfr_t to provide an real-number + type that is a drop-in replacement for the native C++ floating-point types, + but with much greater precision. +

    +

    + Type mpfr_float_backend + can be used at fixed precision by specifying a non-zero Digits10 + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpfr_float provides a variable precision type + whose precision can be controlled via the mp_numbers + member functions. +

    +
    + + + + + +
    [Note]Note

    + This type only provides numeric_limits + support when the precision is fixed at compile time. +

    +

    + As well as the usual conversions from arithmetic and string types, instances + of mp_number<mpfr_float_backend<N> > are copy constructible and assignable + from: +

    +
      +
    • + The GMP native types mpf_t, mpz_t, + mpq_t. +
      • +
    • + The MPFR native type mpfr_t. +
      • +
    • + The mp_number wrappers + around those types: mp_number<mpfr_float_backend<M> >, + mp_number<mpf_float<M> >, mp_number<gmp_int>, mp_number<gmp_rational>. +
      • +
    +

    + It's also possible to access the underlying mpf_t + via the data() member function of gmp_float. +

    +

    + Things you should know when using this type: +

    +
      +
    • + A default constructed mpfr_float_backend + is set to a NaN (this is the default MPFR + behavior). +
      • +
    • + All operations use round to nearest. +
      • +
    • + No changes are made to GMP or + MPFR global settings, so this + type can coexist with existing MPFR + or GMP code. +
      • +
    • + The code can equally use MPIR + in place of GMP - indeed that + is the preferred option on Win32. +
      • +
    +
    + + + MPFR example: +
    +

    +

    +
    #include <boost/multiprecision/mpfr.hpp>
+
+using namespace boost::multiprecision;
+
+// Operations at variable precision and no numeric_limits support:
+mpfr_float a = 2;
+mpfr_float::default_precision(1000);
+std::cout << mpfr_float::default_precision() << std::endl;
+std::cout << sqrt(a) << std::endl; // print root-2
+
+// Operations at fixed precision and full numeric_limits support:
+mpfr_float_100 b = 2;
+std::cout << std::numeric_limits<mpfr_float_100>::digits << std::endl;
+// We can use any C++ std lib function:
+std::cout << log(b) << std::endl; // print log(2)
+// We can also use any function from Boost.Math:
+std::cout << boost::math::tgamma(b) << std::endl;
+// These even work when the argument is an expression template:
+std::cout << boost::math::tgamma(b * b) << std::endl;
+
+// Access the underlying data:
+mpfr_t r;
+mpfr_init(r);
+mpfr_set(r, b.backend().data(), GMP_RNDN);
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html new file mode 100644 index 00000000..754859f0 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints.html @@ -0,0 +1,191 @@ + + + +Integer Types + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    cpp_int
    +
    gmp_int
    +
    tom_int
    +
    Examples
    +
    +
    Factorials
    +
    Bit Operations
    +
    +
    +

    + The following back-ends provide integer arithmetic: +

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend Type +

    +     		+

    + Header +

    +     		+

    + Radix +

    +     		+

    + Dependencies +

    +     		+

    + Pros +

    +     		+

    + Cons +

    +
    +

    + cpp_int +

    +     		+

    + boost/multiprecision/cpp_int.hpp +

    +     		+

    + 2 +

    +     		+

    + None +

    +     		+

    + Very versatile, Boost licensed, all C++ integer type which support + both arbitrary + precision and fixed precision integer types. +

    +     		+

    + Slower than GMP, though + typically not as slow as libtommath +

    +
    +

    + gmp_int +

    +     		+

    + boost/multiprecision/gmp.hpp +

    +     		+

    + 2 +

    +     		+

    + GMP +

    +     		+

    + Very fast and efficient back-end. +

    +     		+

    + Dependency on GNU licensed GMP + library. +

    +
    +

    + tom_int +

    +     		+

    + boost/multiprecision/tommath.hpp +

    +     		+

    + 2 +

    +     		+

    + libtommath +

    +     		+

    + Public domain back-end with no licence restrictions. +

    +     		+

    + Slower than GMP. +

    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html new file mode 100644 index 00000000..98340475 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints/cpp_int.html @@ -0,0 +1,179 @@ + + + +cpp_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/cpp_int.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+typedef unspecified-type limb_type;
+
+template <unsigned MinDigits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
+class cpp_int_backend;
+
+typedef mp_number<cpp_int_backend<> >           cpp_int;    // arbitrary precision integer
+typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
+typedef mp_number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
+
+// Fixed precision unsigned types:
+typedef mp_number<cpp_int_backend<128, false, void>, false>   mp_uint128_t;
+typedef mp_number<cpp_int_backend<256, false, void>, false>   mp_uint256_t;
+typedef mp_number<cpp_int_backend<512, false, void>, false>   mp_uint512_t;
+typedef mp_number<cpp_int_backend<1024, false, void>, false>  mp_uint1024_t;
+
+// Fixed precision signed types:
+typedef mp_number<cpp_int_backend<128, true, void>, false>    mp_int128_t;
+typedef mp_number<cpp_int_backend<256, true, void>, false>    mp_int256_t;
+typedef mp_number<cpp_int_backend<512, true, void>, false>    mp_int512_t;
+typedef mp_number<cpp_int_backend<1024, true, void>, false>   mp_int1024_t;
+
+}} // namespaces
+
    +

    + The cpp_int_backend type + is used via one of the typedefs boost::multiprecision::cpp_int, + boost::multiprecision::mp_uint128_t, boost::multiprecision::mp_uint256_t, + boost::multiprecision::mp_uint512_t, boost::multiprecision::mp_int128_t, + boost::multiprecision::mp_int256_t or boost::multiprecision::mp_int512_t. +

    +

    + This back-end is the "Swiss Army Knife" of integer types as it + can represent both fixed and arbitrary + precision integer types, and both signed and unsigned types. There + are three template arguments: +

    +
    +

    +
    +
    MinBits
    +

    + Determines the number of Bits to store directly within the object + before resorting to dynamic memory allocation. When zero, this field + is determined automatically based on how many bits can be stored + in union with the dynamic storage header: setting a larger value + may improve performance as larger integer values will be stored internally + before memory allocation is required. When the Allocator parameter + is type void, then this + field determines the total number of bits in the resulting fixed + precision type. +

    +
    Signed
    +

    + Determines whether the resulting type is signed or not. Note that + for arbitrary + precision types (where the Allocator parameter is non-void), + then this parameter must be true. + For fixed precision types then this type may be either true (type is signed), or false (type is unsigned). +

    +
    Allocator
    +

    + The allocator to use for dynamic memory allocation, or type void if this is to be a fixed precision + type. +

    +
    +
    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed cpp_int_backends + have the value zero. +
      • +
    • + Division by zero results in a std::runtime_error + being thrown. +
      • +
    • + Construction from a string that contains invalid non-numeric characters + results in a std::runtime_error being thrown. +
      • +
    • + Since the precision of cpp_int_backend + is necessarily limited when the allocator parameter is void, care should + be taken to avoid numeric overflow when using this type unless you + actually want modulo-arithmetic behavior. +
      • +
    • + The type uses a sign-magnitude representation internally, so type + mp_int128_t has 128-bits + of precision plus an extra sign bit. In this respect the behaviour + of these types differs from built-in 2's complement types. In might + be tempting to use a 127-bit type instead, and indeed this does work, + but behaviour is still slightly different from a 2's complement built-in + type as the min and max values are identical (apart from the sign), + where as they differ by one for a true 2's complement type. That said + it should be noted that there's no requirement for built-in types to + be 2's complement either - it's simply that this is the most common + format by far. +
      • +
    • + Attempting to print negative values as either an Octal or Hexadecimal + string results in a std::runtime_error + being thrown, this is a direct consequence of the sign-magnitude representation. +
      • +
    • + The fixed precision types mp_[u]intXXX_t + have expression template support turned off - it seems to make little + difference to the performance of these types either way - so we may + as well have the faster compile times by turning the feature off. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+
+using namespace boost::multiprecision;
+
+mp_int128_t v = 1;
+
+// Do some fixed precision arithmetic:
+for(unsigned i = 1; i <= 20; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 20!
+
+// Repeat at arbitrary precision:
+cpp_int u = 1;
+for(unsigned i = 1; i <= 100; ++i)
+   u *= i;
+
+std::cout << u << std::endl; // prints 100!
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints/egs.html b/doc/html/boost_multiprecision/tut/ints/egs.html new file mode 100644 index 00000000..145a22b2 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints/egs.html @@ -0,0 +1,38 @@ + + + +Examples + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    Factorials
    +
    Bit Operations
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints/egs/bitops.html b/doc/html/boost_multiprecision/tut/ints/egs/bitops.html new file mode 100644 index 00000000..37b37e80 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints/egs/bitops.html @@ -0,0 +1,94 @@ + + + +Bit Operations + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + In this example we'll show how individual bits within an integer may + be manipulated, we'll start with an often needed calculation of 2n - + 1, which we could obviously implement like this: +

    +

    +

    +
    using boost::multiprecision::cpp_int;
+
+cpp_int b1(unsigned n)
+{
+   cpp_int r(1);
+   return (r << n) - 1;
+}
+
    +

    +

    +

    + Calling: +

    +
    std::cout << std::hex << std::showbase << b1(200) << std::endl;
+
    +

    + Yields as expected: +

    +
    0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
    +

    + However, we could equally just set the n'th bit in the result, like this: +

    +

    +

    +
    cpp_int b2(unsigned n)
+{
+   cpp_int r(0);
+   return --bit_set(r, n);
+}
+
    +

    +

    +

    + Note how the bit_set + function sets the specified bit in it's argument and then returns a reference + to the result - which we can then simply decrement. The result from a + call to b2 is the same + as that to b1. +

    +

    + We can equally test bits, so for example the n'th bit of the result returned + from b2 shouldn't be + set unless we increment it first: +

    +
    assert(!bit_test(b1(200), 200));     // OK
+assert(bit_test(++b1(200), 200));    // OK
+
    +

    + And of course if we flip the n'th bit after increment, then we should + get back to zero: +

    +
    assert(!bit_flip(++b1(200), 200));   // OK
+
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints/egs/factorials.html b/doc/html/boost_multiprecision/tut/ints/egs/factorials.html new file mode 100644 index 00000000..dfbfe6e5 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints/egs/factorials.html @@ -0,0 +1,145 @@ + + + +Factorials + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + In this simple example, we'll write a routine to print out all of the + factorials which will fit into a 128-bit integer. At the end of the routine + we do some fancy iostream formatting of the results: +

    +

    +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+#include <iostream>
+#include <iomanip>
+#include <vector>
+
+
+void print_factorials()
+{
+   using boost::multiprecision::cpp_int;
+   //
+   // Print all the factorials that will fit inside a 128-bit integer.
+   //
+   // Begin by building a big table of factorials, once we know just how 
+   // large the largest is, we'll be able to "pretty format" the results.
+   //
+   // Calculate the largest number that will fit inside 128 bits, we could
+   // also have used numeric_limits<mp_int128_t>::max() for this value:
+   cpp_int limit = (cpp_int(1) << 128) - 1;
+   // 
+   // Our table of values:
+   std::vector<cpp_int> results;
+   //
+   // Initial values:
+   unsigned i = 1;
+   cpp_int factorial = 1;
+   //
+   // Cycle through the factorials till we reach the limit:
+   while(factorial < limit)
+   {
+      results.push_back(factorial);
+      ++i;
+      factorial *= i;
+   }
+   //
+   // Lets see how many digits the largest factorial was:
+   unsigned digits = results.back().str().size();
+   //
+   // Now print them out, using right justification, while we're at it
+   // we'll indicate the limit of each integer type, so begin by defining
+   // the limits for 16, 32, 64 etc bit integers:
+   cpp_int limits[] = {
+      (cpp_int(1) << 16) - 1,
+      (cpp_int(1) << 32) - 1,
+      (cpp_int(1) << 64) - 1,
+      (cpp_int(1) << 128) - 1,
+   };
+   std::string bit_counts[] = { "16", "32", "64", "128" };
+   unsigned current_limit = 0;
+   for(unsigned j = 0; j < results.size(); ++j)
+   {
+      if(limits[current_limit] < results[j])
+      {
+         std::string message = "Limit of " + bit_counts[current_limit] + " bit integers";
+         std::cout << std::setfill('.') << std::setw(digits+1) << std::right << message << std::setfill(' ') << std::endl;
+         ++current_limit;
+      }
+      std::cout << std::setw(digits + 1) << std::right << results[j] << std::endl;
+   }
+}
+
    +

    +

    +

    + The output from this routine is: +

    +
    +                                       1
+                                       2
+                                       6
+                                      24
+                                     120
+                                     720
+                                    5040
+                                   40320
+................Limit of 16 bit integers
+                                  362880
+                                 3628800
+                                39916800
+                               479001600
+................Limit of 32 bit integers
+                              6227020800
+                             87178291200
+                           1307674368000
+                          20922789888000
+                         355687428096000
+                        6402373705728000
+                      121645100408832000
+                     2432902008176640000
+................Limit of 64 bit integers
+                    51090942171709440000
+                  1124000727777607680000
+                 25852016738884976640000
+                620448401733239439360000
+              15511210043330985984000000
+             403291461126605635584000000
+           10888869450418352160768000000
+          304888344611713860501504000000
+         8841761993739701954543616000000
+       265252859812191058636308480000000
+      8222838654177922817725562880000000
+    263130836933693530167218012160000000
+   8683317618811886495518194401280000000
+ 295232799039604140847618609643520000000
+
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints/gmp_int.html b/doc/html/boost_multiprecision/tut/ints/gmp_int.html new file mode 100644 index 00000000..1bf12605 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints/gmp_int.html @@ -0,0 +1,128 @@ + + + +gmp_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/gmp.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+class gmp_int;
+
+typedef mp_number<gmp_int >         mpz_int;
+
+}} // namespaces
+
    +

    + The gmp_int back-end is + used via the typedef boost::multiprecision::mpz_int. + It acts as a thin wrapper around the GMP + mpz_t to provide an integer + type that is a drop-in replacement for the native C++ integer types, but + with unlimited precision. +

    +

    + As well as the usual conversions from arithmetic and string types, type + mpz_int is copy constructible + and assignable from: +

    +
      +
    • + The GMP native types: mpf_t, mpz_t, + mpq_t. +
      • +
    • + Instances of mp_number<T> that are wrappers around those + types: mp_number<gmp_float<N> >, mp_number<gmp_rational>. +
      • +
    +

    + It's also possible to access the underlying mpz_t + via the data() + member function of gmp_int. +

    +

    + Things you should know when using this type: +

    +
      +
    • + No changes are made to the GMP library's global settings - so you can + safely mix this type with existing code that uses GMP. +
      • +
    • + Default constructed gmp_ints + have the value zero (this is GMP's default behavior). +
      • +
    • + Formatted IO for this type does not support octal or hexadecimal notation + for negative values, as a result performing formatted output on this + type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex + are set, will result in a std::runtime_error + will be thrown. +
      • +
    • + Division by zero is handled by the GMP + library - it will trigger a division by zero signal. +
      • +
    • + Although this type is a wrapper around GMP + it will work equally well with MPIR. + Indeed use of MPIR is recommended + on Win32. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+
+using namespace boost::multiprecision;
+
+mpz_int v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 1000!
+
+// Access the underlying representation:
+mpz_t z;
+mpz_init(z);
+mpz_set(z, v.backend().data());
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/ints/tom_int.html b/doc/html/boost_multiprecision/tut/ints/tom_int.html new file mode 100644 index 00000000..08ccad9d --- /dev/null +++ b/doc/html/boost_multiprecision/tut/ints/tom_int.html @@ -0,0 +1,119 @@ + + + +tom_int + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/tommath.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+class tommath_int;
+
+typedef mp_number<tommath_int >         tom_int;
+
+}} // namespaces
+
    +

    + The tommath_int back-end + is used via the typedef boost::multiprecision::tom_int. + It acts as a thin wrapper around the libtommath + tom_int to provide an integer + type that is a drop-in replacement for the native C++ integer types, but + with unlimited precision. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed objects have the value zero (this is libtommath's + default behavior). +
      • +
    • + Although tom_int is + mostly a drop in replacement for the builtin integer types, it should + be noted that it is a rather strange beast as it's a signed type that + is not a 2's complement type. As a result the bitwise operations | & ^ will throw a std::runtime_error + exception if either of the arguments is negative. Similarly the complement + operator~ is deliberately + not implemented for this type. +
      • +
    • + Formatted IO for this type does not support octal or hexadecimal notation + for negative values, as a result performing formatted output on this + type when the argument is negative and either of the flags std::ios_base::oct or std::ios_base::hex + are set, will result in a std::runtime_error + will be thrown. +
      • +
    • + Division by zero will result in a hardware signal being raised by + libtommath. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/tommath.hpp>
+
+boost::multiprecision::tom_int v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+
+std::cout << v << std::endl; // prints 1000!
+std::cout << std::hex << v << std::endl; // prints 1000! in hex format
+
+try{
+   std::cout << std::hex << -v << std::endl; // Ooops! can't print a negative value in hex format!
+}
+catch(const std::runtime_error& e)
+{
+   std::cout << e.what() << std::endl;
+}
+
+try{
+   // v is not a 2's complement type, bitwise operations are only supported
+   // on positive values:
+   v = -v & 2;
+}
+catch(const std::runtime_error& e)
+{
+   std::cout << e.what() << std::endl;
+}
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html new file mode 100644 index 00000000..8e83c166 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/primetest.html @@ -0,0 +1,109 @@ + + + +Primality Testing + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + The library implements a Miller-Rabin test for primality: +

    +
    #include <boost/multiprecision/miller_rabin.hpp>
+
+template <class Backend, bool ExpressionTemplates, class Engine>
+bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials, Engine& gen);
+
+template <class Backend, bool ExpressionTemplates, class Engine>
+bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials);
+
    +

    + These functions perform a Miller-Rabin test for primality, if the result + is false then n + is definitely composite, while if the result is true + then n is prime with probability 0.25^trials. + The algorithm used performs some trial divisions to exclude small prime factors, + does one Fermat test to exclude many more composites, and then uses the Miller-Rabin + algorithm straight out of Knuth Vol 2, which recomends 25 trials for a pretty + strong likelyhood that n is prime. +

    +

    + The third optional argument is for a Uniform Random Number Generator from + Boost.Random. When not provided the mt19937 + generator is used. Note that when producing random primes then you should + probably use a different random number generator to produce candidate prime + numbers for testing, than is used internally by miller_rabin_test + for determining whether the value is prime. It also helps of course to seed + the generators with some source of randomness. +

    +

    + The following example searches for a prime p + for which (p-1)/2 is also probably prime: +

    +

    +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+#include <boost/multiprecision/miller_rabin.hpp>
+#include <iostream>
+#include <iomanip>
+
+int main()
+{
+   using namespace boost::random;
+   using namespace boost::multiprecision;
+
+   typedef cpp_int int_type;
+   mt11213b base_gen(clock());
+   independent_bits_engine<mt11213b, 256, int_type> gen(base_gen);
+   //
+   // We must use a different generator for the tests and number generation, otherwise
+   // we get false positives.
+   //
+   mt19937 gen2(clock());
+
+   for(unsigned i = 0; i < 100000; ++i)
+   {
+      int_type n = gen();
+      if(miller_rabin_test(n, 25, gen2))
+      {
+         // Value n is probably prime, see if (n-1)/2 is also prime:
+         std::cout << "We have a probable prime with value: " << std::hex << std::showbase << n << std::endl;
+         if(miller_rabin_test((n-1)/2, 25, gen2))
+         {
+            std::cout << "We have a safe prime with value: " << std::hex << std::showbase << n << std::endl;
+            return 0;
+         }
+      }
+   }
+   std::cout << "Ooops, no safe primes were found" << std::endl;
+   return 1;
+}
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/random.html b/doc/html/boost_multiprecision/tut/random.html new file mode 100644 index 00000000..6f0d438b --- /dev/null +++ b/doc/html/boost_multiprecision/tut/random.html @@ -0,0 +1,157 @@ + + + +Generating Random Numbers + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + Random numbers are generated in conjunction with Boost.Random. However, since + Boost.Random is unaware of arbitrary + precision numbers, it's necessary to include the header: +

    +
    #include <boost/multiprecision/random.hpp>
+
    +

    + In order to act as a bridge between the two libraries. +

    +

    + Integers with N random bits are generated using independent_bits_engine: +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+
+//
+// Declare our random number generator type, the underlying generator
+// is the Mersenne twister mt19937 engine, and 256 bits are generated:
+//
+typedef independent_bits_engine<mt19937, 256, mpz_int> generator_type;
+generator_type gen;
+//
+// Generate some values:
+//
+std::cout << std::hex << std::showbase;
+for(unsigned i = 0; i < 10; ++i)
+   std::cout << gen() << std::endl;
+
    +

    +

    +

    + Alternatively we can generate integers in a given range using uniform_int_distribution, this will invoke + the underlying engine multiple times to build up the required number of bits + in the result: +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+
+//
+// Generate integers in a given range using uniform_int,
+// the underlying generator is invoked multiple times
+// to generate enough bits:
+//
+mt19937 mt;
+uniform_int_distribution<mpz_int> ui(0, mpz_int(1) << 256);
+//
+// Generate the numbers:
+//
+std::cout << std::hex << std::showbase;
+for(unsigned i = 0; i < 10; ++i)
+   std::cout << ui(mt) << std::endl;
+
    +

    +

    +

    + Floating point values in [0,1) are generated using uniform_01, + the trick here is to ensure that the underlying generator produces as many + random bits as there are digits in the floating point type. As above independent_bits_engine can be used for + this purpose, note that we also have to convert decimal digits (in the floating + point type) to bits (in the random number generator): +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+//
+// We need an underlying generator with at least as many bits as the
+// floating point type to generate numbers in [0, 1) with all the bits
+// in the floating point type randomly filled:
+//
+uniform_01<mpf_float_50> uf;
+independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen;
+//
+// Generate the values:
+//
+std::cout << std::setprecision(50);
+for(unsigned i = 0; i < 20; ++i)
+   std::cout << uf(gen) << std::endl;
+
    +

    +

    +

    + Finally, we can modify the above example to produce numbers distributed according + to some distribution: +

    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+#include <boost/multiprecision/random.hpp>
+
+using namespace boost::multiprecision;
+using namespace boost::random;
+//
+// We can repeat the above example, with other distributions:
+//
+uniform_real_distribution<mpf_float_50> ur(-20, 20);
+gamma_distribution<mpf_float_50> gd(20);
+independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen;
+//
+// Generate some values:
+//
+std::cout << std::setprecision(50);
+for(unsigned i = 0; i < 20; ++i)
+   std::cout << ur(gen) << std::endl;
+for(unsigned i = 0; i < 20; ++i)
+   std::cout << gd(gen) << std::endl;
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html new file mode 100644 index 00000000..0d05ef47 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -0,0 +1,252 @@ + + + +Rational Number Types + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +
    gmp_rational
    +
    cpp_rational
    +
    tommath_rational
    +
    Use With Boost.Rational
    +
    rational_adapter
    +
    +

    + The following back-ends provide rational number arithmetic: +

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend Type +

    +     		+

    + Header +

    +     		+

    + Radix +

    +     		+

    + Dependencies +

    +     		+

    + Pros +

    +     		+

    + Cons +

    +
    +

    + gmp_rational +

    +     		+

    + boost/multiprecision/gmp.hpp +

    +     		+

    + 2 +

    +     		+

    + GMP +

    +     		+

    + Very fast and efficient back-end. +

    +     		+

    + Dependency on GNU licensed GMP + library. +

    +
    +

    + cpp_rational +

    +     		+

    + boost/multiprecision/cpp_int.hpp +

    +     		+

    + 2 +

    +     		+

    + None +

    +     		+

    + An all C++ Boost-licensed implementation. +

    +     		+

    + Slower than GMP. +

    +
    +

    + tommath_rational +

    +     		+

    + boost/multiprecision/tommath.hpp +

    +     		+

    + 2 +

    +     		+

    + libtommath +

    +     		+

    + All C/C++ implementation that's Boost Software Licence compatible. +

    +     		+

    + Slower than GMP. +

    +
    +

    + rational_adapter +

    +     		+

    + boost/multiprecision/rational_adapter.hpp +

    +     		+

    + N/A +

    +     		+

    + none +

    +     		+

    + All C++ adapter that allows any inetger back-end type to be used + as a rational type. +

    +     		+

    + Requires an underlying integer back-end type. +

    +
    +

    + boost::rational +

    +     		+

    + boost/rational.hpp +

    +     		+

    + N/A +

    +     		+

    + None +

    +     		+

    + A C++ rational number type that can used with any mp_number integer type. +

    +     		+

    + The expression templates used by mp_number + end up being "hidden" inside boost::rational: + performance may well suffer as a result. +

    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational/br.html b/doc/html/boost_multiprecision/tut/rational/br.html new file mode 100644 index 00000000..a3efdfa6 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational/br.html @@ -0,0 +1,42 @@ + + + +Use With Boost.Rational + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + All of the integer types in this library can be used as template arguments + to boost::rational<IntType>. +

    +

    + Note that using the library in this way largely negates the effect of the + expression templates in mp_number. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html new file mode 100644 index 00000000..ea6b42a8 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html @@ -0,0 +1,108 @@ + + + +cpp_rational + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/cpp_int.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
+
+typedef mp_number<cpp_rational_backend>         cpp_rational;
+
+}} // namespaces
+
    +

    + The cpp_rational_backend + type is used via the typedef boost::multiprecision::cpp_rational. + It provides a rational number type that is a drop-in replacement for the + native C++ number types, but with unlimited precision. +

    +

    + As well as the usual conversions from arithmetic and string types, instances + of cpp_rational are copy + constructible and assignable from type cpp_int. +

    +

    + There is also a two argument constructor that accepts a numerator and denominator: + both of type cpp_int. +

    +

    + There are also non-member functions: +

    +
    cpp_int numerator(const cpp_rational&);
+cpp_int denominator(const cpp_rational&);
+
    +

    + which return the numerator and denominator of the number. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed cpp_rationals + have the value zero. +
      • +
    • + Division by zero results in a std::rumtime_error + being thrown. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+
+using namespace boost::multiprecision;
+
+cpp_rational v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+v /= 10;
+
+std::cout << v << std::endl; // prints 1000! / 10
+std::cout << numerator(v) << std::endl;
+std::cout << denominator(v) << std::endl;
+
+cpp_rational w(2, 3);  // component wise constructor
+std::cout << w << std::endl; // prints 2/3
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html new file mode 100644 index 00000000..8f1f28fe --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html @@ -0,0 +1,138 @@ + + + +gmp_rational + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/gmp.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+class gmp_rational;
+
+typedef mp_number<gmp_rational >         mpq_rational;
+
+}} // namespaces
+
    +

    + The gmp_rational back-end + is used via the typedef boost::multiprecision::mpq_rational. + It acts as a thin wrapper around the GMP + mpq_t to provide a rational + number type that is a drop-in replacement for the native C++ number types, + but with unlimited precision. +

    +

    + As well as the usual conversions from arithmetic and string types, instances + of mp_number<gmp_rational> + are copy constructible and assignable from: +

    +
      +
    • + The GMP native types: mpz_t, mpq_t. +
      • +
    • + mp_number<gmp_int>. +
      • +
    +

    + There is also a two-argument constructor that accepts a numerator and denominator + (both of type mp_number<gmp_int>). +

    +

    + There are also non-member functions: +

    +
    mpz_int numerator(const mpq_rational&);
+mpz_int denominator(const mpq_rational&);
+
    +

    + which return the numerator and denominator of the number. +

    +

    + It's also possible to access the underlying mpq_t + via the data() + member function of mpq_rational. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed mpq_rationals + have the value zero (this is the GMP + default behavior). +
      • +
    • + Division by zero results in a hardware exception inside the GMP library. +
      • +
    • + No changes are made to the GMP + library's global settings, so this type can coexist with existing + GMP code. +
      • +
    • + The code can equally be used with MPIR + as the underlying library - indeed that is the preferred option on + Win32. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/gmp.hpp>
+
+using namespace boost::multiprecision;
+
+mpq_rational v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+v /= 10;
+
+std::cout << v << std::endl; // prints 1000! / 10
+std::cout << numerator(v) << std::endl;
+std::cout << denominator(v) << std::endl;
+
+mpq_rational w(2, 3);  // component wise constructor
+std::cout << w << std::endl; // prints 2/3
+
+// Access the underlying data:
+mpq_t q;
+mpq_init(q);
+mpq_set(q, v.backend().data());
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational/rational_adapter.html b/doc/html/boost_multiprecision/tut/rational/rational_adapter.html new file mode 100644 index 00000000..6b4853f1 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational/rational_adapter.html @@ -0,0 +1,58 @@ + + + +rational_adapter + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    namespace boost{ namespace multiprecision{
+
+template <class IntBackend>
+class rational_adpater;
+
+}}
+
    +

    + The class template rational_adapter + is a back-end for mp_number + which converts any existing integer back-end into a rational-number back-end. +

    +

    + So for example, given an integer back-end type MyIntegerBackend, + the use would be something like: +

    +
    typedef mp_number<MyIntegerBackend>                    MyInt;
+typedef mp_number<rational_adapter<MyIntegerBackend> > MyRational;
+
+MyRational r = 2;
+r /= 3;
+MyInt i = numerator(r);
+assert(i == 2);
+
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html new file mode 100644 index 00000000..25520372 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html @@ -0,0 +1,115 @@ + + + +tommath_rational + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/tommath.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+typedef rational_adpater<tommath_int>        tommath_rational;
+typedef mp_number<tommath_rational >         tom_rational;
+
+}} // namespaces
+
    +

    + The tommath_rational back-end + is used via the typedef boost::multiprecision::tom_rational. + It acts as a thin wrapper around boost::rational<tom_int> to provide a rational number type that + is a drop-in replacement for the native C++ number types, but with unlimited + precision. +

    +

    + The advantage of using this type rather than boost::rational<tom_int> directly, is that it is expression-template + enabled, greatly reducing the number of temporaries created in complex + expressions. +

    +

    + There are also non-member functions: +

    +
    tom_int numerator(const tom_rational&);
+tom_int denominator(const tom_rational&);
+
    +

    + which return the numerator and denominator of the number. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed tom_rationals + have the value zero (this the inherited Boost.Rational behavior). +
      • +
    • + Division by zero results in a boost::bad_rational + exception being thrown (see the rational number library's docs for + more information). +
      • +
    • + No changes are made to libtommath's + global state, so this type can safely coexist with other libtommath + code. +
      • +
    • + Performance of this type has been found to be pretty poor - this need + further investigation - but it appears that Boost.Rational needs some + improvement in this area. +
      • +
    +
    + + Example: +
    +

    +

    +
    #include <boost/multiprecision/tommath.hpp>
+
+using namespace boost::multiprecision;
+
+tom_rational v = 1;
+
+// Do some arithmetic:
+for(unsigned i = 1; i <= 1000; ++i)
+   v *= i;
+v /= 10;
+
+std::cout << v << std::endl; // prints 1000! / 10
+std::cout << numerator(v) << std::endl;
+std::cout << denominator(v) << std::endl;
+
+tom_rational w(2, 3); // Component wise constructor
+std::cout << w << std::endl; // prints 2/3
+
    +

    +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/index.html b/doc/html/index.html new file mode 100644 index 00000000..91f25a9e --- /dev/null +++ b/doc/html/index.html @@ -0,0 +1,126 @@ + + + +Chapter 1. Boost.Multiprecision + + + + + + +
    Next
    +
    +
    +

    +Chapter 1. Boost.Multiprecision

    +

    +John Maddock +

    +

    +Christopher Kormanyos +

    +

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +
    +

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +

    Table of Contents

    +
    +
    Introduction
    +
    Tutorial
    +
    +
    Integer Types
    +
    +
    cpp_int
    +
    gmp_int
    +
    tom_int
    +
    Examples
    +
    +
    Factorials
    +
    Bit Operations
    +
    +
    +
    Floating Point Numbers
    +
    +
    gmp_float
    +
    mpfr_float
    +
    cpp_dec_float
    +
    Examples
    +
    +
    Area of + Circle
    +
    Defining + a Lambda Function.
    +
    Calculating + a Derivative
    +
    Calculating + an Integral
    +
    Polynomial + Evaluation
    +
    +
    +
    Rational Number Types
    +
    +
    gmp_rational
    +
    cpp_rational
    +
    tommath_rational
    +
    Use With Boost.Rational
    +
    rational_adapter
    +
    +
    Constructing and + Interconverting Between Number Types
    +
    Generating Random Numbers
    +
    Primality Testing
    +
    +
    Reference
    +
    +
    mp_number
    +
    cpp_int
    +
    gmp_int
    +
    tom_int
    +
    gmp_float
    +
    mpfr_float_backend
    +
    cpp_dec_float
    +
    Backend Requirements
    +
    +
    Performance Comparison
    +
    +
    Floating Point Real + World Tests
    +
    Integer Real + World Tests
    +
    Float Algorithm + Perfomance
    +
    Integer + Algorithm Perfomance
    +
    Rational + Type Perfomance
    +
    +
    Roadmap
    +
    +
    History
    +
    TODO
    +
    Acknowledgements
    +
    +
    Indexes
    +
    +
    Function Index
    +
    Class Index
    +
    Typedef Index
    +
    Index
    +
    +
    +
    +
    + + + +

    Last revised: April 13, 2012 at 15:27:12 GMT

    +
    +
    Next
    + + From 12fa743b47dc0877eb38bbd93d92af7309ef6fc3 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 13 Apr 2012 16:51:01 +0000 Subject: [PATCH 170/256] Improve class index. [SVN r77950] --- .../boost_multiprecision/indexes/s01.html | 16 ++-- .../boost_multiprecision/indexes/s02.html | 56 ++++++++++--- .../boost_multiprecision/indexes/s03.html | 16 ++-- .../boost_multiprecision/indexes/s04.html | 82 +++++++++++-------- doc/html/index.html | 2 +- doc/index.idx | 9 +- 6 files changed, 118 insertions(+), 63 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index e452e983..f9f2bbf8 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,10 +13,10 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    -

    A B C D E F I L M P R S T Z

    +Function Index
    +

    A B C D E F I L M P R S T Z

    A @@ -166,7 +166,7 @@
    -P +P

    • precision

      @@ -176,7 +176,7 @@
    -R +R
    • @@ -189,7 +189,7 @@
    -S +S
    • @@ -206,14 +206,14 @@
    -T +T
    -Z +Z

    • zero

      diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index 34f35429..b541c91b 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,27 +13,59 @@
      PrevUpHomeNext
      -
      +

      -Class Index

      -

      M T

      +Class Index
    +

    C G M N T

    -M +C +
    +
    +
    +G +
    +
    +
    +M +
    +
    +
    +N
    -T +T
    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index e3dfc498..34eeb3c1 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,13 +13,13 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    -

    C I L M T

    +Typedef Index
    +

    C I L M T

    -C +C
    • @@ -47,21 +47,21 @@
    -I +I
    -L +L
    -M +M
    • @@ -161,7 +161,7 @@
    -T +T

    • tommath_rational

      • diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 0c8231f2..08db6751 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,20 +12,20 @@
      PrevUpHome
      -
      +

      -Index

      -

      A B C D E F G I L M O P R S T Z

      +Index
    +

    A B C D E F G I L M N O P R S T Z

    -A +A
    -B +B
    • @@ -54,7 +54,7 @@
    -C +C
    -D +D
    -E +E
    -F +F
    -G +G
    -I +I
    -L +L
    • @@ -260,7 +266,7 @@
    -M +M
  • @@ -318,6 +324,7 @@

  • mpfr_float_1000

  • mpfr_float_50

  • mpfr_float_500

    • +

  • mpfr_float_backend

  • @@ -374,11 +381,11 @@

  • bit_test

  • bit_unset

  • compare

    • +

  • component_type

  • default_precision

  • divide_qr

  • fpclassify

  • integer_modulus

    • -

  • Introduction

  • iround

  • isfinite

  • isinf

    • @@ -392,6 +399,7 @@

  • ltrunc

  • miller_rabin_test

  • mp_number

    • +

  • number_category

  • precision

  • round

  • sign

    • @@ -418,14 +426,21 @@
    -O +N +
    +
    +
    +O
    -P +P
    • @@ -445,7 +460,7 @@
    -R +R
    • @@ -458,7 +473,7 @@
    -S +S
    • @@ -475,10 +490,14 @@
    -T +T
    -Z +Z

    • zero

      diff --git a/doc/html/index.html b/doc/html/index.html index 91f25a9e..07e5aa99 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -117,7 +117,7 @@
    - +

    Last revised: April 13, 2012 at 15:27:12 GMT

    Last revised: April 13, 2012 at 16:48:43 GMT
    diff --git a/doc/index.idx b/doc/index.idx index fc9adc82..629072a4 100644 --- a/doc/index.idx +++ b/doc/index.idx @@ -1,3 +1,11 @@ +# Copyright 2011 John Maddock. Distributed under the Boost +# Software License, Version 1.0. (See accompanying file +# LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +# +# Rewrite the class scanner to accept declarations, not just definitions, +# as the docs don't include full definitions. +# +!define-scanner class_name "^[[:space:]]*(template[[:space:]]*<[^;:{]+>[[:space:]]*)?(class|struct)[[:space:]]*(\<\w+\>([[:blank:]]*\([^)]*\))?[[:space:]]*)*(\<\w*\>)[[:space:]]*(<[^;:{]+>)?[[:space:]]*(\{|:[^;\{()]*\{)" "(?:class|struct)[^;{]+\\<\5\\>\\s*[;{]" \5 !scan-path boost/multiprecision .*\.hpp true @@ -8,4 +16,3 @@ - From 462bec3925a0391d18fce7948040d08f958289e8 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 14 Apr 2012 16:51:02 +0000 Subject: [PATCH 171/256] Fix ldexp/frexp in default_ops.hpp. Improve 64-bit platform detection in cpp_int_core.hpp. Get examples building with GCC [SVN r77971] --- example/floating_point_examples.cpp | 10 ++--- .../multiprecision/detail/cpp_int_core.hpp | 2 +- .../multiprecision/detail/default_ops.hpp | 37 ++++++++++++------- test/Jamfile.v2 | 2 +- 4 files changed, 30 insertions(+), 21 deletions(-) diff --git a/example/floating_point_examples.cpp b/example/floating_point_examples.cpp index 701d4b0b..6cb1f391 100644 --- a/example/floating_point_examples.cpp +++ b/example/floating_point_examples.cpp @@ -441,7 +441,7 @@ mp_type mysin(const mp_type& x) /*` Calling the function like so: - std::cout << std::setprecision(std::numeric_limits<::mp_type>::digits10) << std::scientific; + std::cout << std::setprecision(std::numeric_limits< ::mp_type>::digits10) << std::scientific; std::cout << mysin(mp_type(1)) << std::endl; Yields the expected output: @@ -657,9 +657,9 @@ int main(int, char**) //] - std::cout << std::setprecision(std::numeric_limits<::mp_type>::digits10) << std::scientific; - std::cout << mysin(boost::math::constants::pi<::mp_type>() / 4) << std::endl; - std::cout << boost::multiprecision::sin(boost::math::constants::pi<::mp_type>() / 4) << std::endl; + std::cout << std::setprecision(std::numeric_limits< ::mp_type>::digits10) << std::scientific; + std::cout << mysin(boost::math::constants::pi< ::mp_type>() / 4) << std::endl; + std::cout << boost::multiprecision::sin(boost::math::constants::pi< ::mp_type>() / 4) << std::endl; return 0; } @@ -683,4 +683,4 @@ Program output: 2.70670566473225383787998989944968806815253190143120e-01 7.0710678118654752440084436210484903928483593768847403658833986900e-01 7.0710678118654752440084436210484903928483593768847403658833986900e-01 -*/ \ No newline at end of file +*/ diff --git a/include/boost/multiprecision/detail/cpp_int_core.hpp b/include/boost/multiprecision/detail/cpp_int_core.hpp index 63d9efbf..e63fb2ed 100644 --- a/include/boost/multiprecision/detail/cpp_int_core.hpp +++ b/include/boost/multiprecision/detail/cpp_int_core.hpp @@ -8,7 +8,7 @@ namespace boost{ namespace multiprecision{ -#if defined(__GNUC__) && !defined(BOOST_INTEL) && defined(__x86_64__) +#if defined(__GNUC__) && !defined(BOOST_INTEL) && defined(__WORDSIZE) && (__WORDSIZE == 64) typedef boost::uint64_t limb_type; typedef boost::int64_t signed_limb_type; diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index ee90315a..2f6f1b5f 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -1153,20 +1153,7 @@ func(const Arithmetic& a, const mp_number& arg)\ }\ -#define HETERO_BINARY_OP_FUNCTOR(func, Arg2)\ -namespace detail{\ -template \ -struct BOOST_JOIN(func, _funct)\ -{\ - void operator()(Backend& result, Backend const& arg, Arg2 a)const\ - {\ - using default_ops:: BOOST_JOIN(eval_,func);\ - BOOST_JOIN(eval_,func)(result, arg, a);\ - }\ -};\ -\ -}\ -\ +#define HETERO_BINARY_OP_FUNCTOR_B(func, Arg2)\ template \ inline detail::mp_exp<\ detail::function\ @@ -1216,6 +1203,24 @@ func(const mp_number& arg, Arg2 const& a)\ return result;\ }\ +#define HETERO_BINARY_OP_FUNCTOR(func, Arg2)\ +namespace detail{\ +template \ +struct BOOST_JOIN(func, _funct)\ +{\ + template \ + void operator()(Backend& result, Backend const& arg, Arg a)const\ + {\ + using default_ops:: BOOST_JOIN(eval_,func);\ + BOOST_JOIN(eval_,func)(result, arg, a);\ + }\ +};\ +\ +}\ +\ +HETERO_BINARY_OP_FUNCTOR_B(func, Arg2) + + UNARY_OP_FUNCTOR(abs) UNARY_OP_FUNCTOR(fabs) UNARY_OP_FUNCTOR(sqrt) @@ -1238,6 +1243,10 @@ UNARY_OP_FUNCTOR(tanh) HETERO_BINARY_OP_FUNCTOR(ldexp, int) HETERO_BINARY_OP_FUNCTOR(frexp, int*) +HETERO_BINARY_OP_FUNCTOR_B(ldexp, long) +HETERO_BINARY_OP_FUNCTOR_B(frexp, long*) +HETERO_BINARY_OP_FUNCTOR_B(ldexp, long long) +HETERO_BINARY_OP_FUNCTOR_B(frexp, long long*) BINARY_OP_FUNCTOR(pow) BINARY_OP_FUNCTOR(fmod) BINARY_OP_FUNCTOR(atan2) diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 7087da06..8a064ad9 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -665,7 +665,7 @@ run ../example/tommath_snips.cpp $(TOMMATH) : # input files : # requirements [ check-target-builds ../config//has_tommath : : no ] ; -run ../example/floating_point_examples.cpp ; +run ../example/floating_point_examples.cpp : : : gcc:-std=c++0x ; if $(enable-specfun) { From a53f4f3fee66a0d449a49dd8ea10f157895f5c6c Mon Sep 17 00:00:00 2001 From: Christopher Kormanyos Date: Sun, 15 Apr 2012 09:27:55 +0000 Subject: [PATCH 172/256] - Re-factor constants in cpp_dec_float.hpp. - Tighten up tolerance on multiply, do trivial cleanup in cpp_dec_float. - Change digit progression in iteration in sqrt and atan. [SVN r77983] --- .../boost/multiprecision/cpp_dec_float.hpp | 74 +++++++++---------- .../multiprecision/detail/functions/trig.hpp | 4 +- 2 files changed, 39 insertions(+), 39 deletions(-) diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index cce91bc3..08c38f75 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -36,27 +36,32 @@ public: typedef long long exponent_type; - static const boost::int32_t mp_radix = 10; - static const boost::int32_t cpp_dec_float_digits = Digits10; + static const boost::int32_t mp_radix = 10; static const boost::int32_t cpp_dec_float_digits10_setting = Digits10; static const boost::int32_t cpp_dec_float_digits10_limit = boost::integer_traits::const_max - 100; - static const boost::int32_t cpp_dec_float_digits10 = ((cpp_dec_float_digits10_setting < static_cast(30)) ? static_cast(30) : ((cpp_dec_float_digits10_setting > cpp_dec_float_digits10_limit) ? cpp_dec_float_digits10_limit : cpp_dec_float_digits10_setting)); - static const boost::int32_t cpp_dec_float_digits10_extra = static_cast(((static_cast(cpp_dec_float_digits10) * 15LL) + 50LL) / 100LL); - static const boost::int32_t cpp_dec_float_max_digits10 = static_cast(cpp_dec_float_digits10 + ((cpp_dec_float_digits10_extra < static_cast(5)) ? static_cast(5) : ((cpp_dec_float_digits10_extra > static_cast(30)) ? static_cast(30) : cpp_dec_float_digits10_extra))); - static const boost::int64_t cpp_dec_float_max_exp10 = 2776234983093287512; + static const boost::int32_t cpp_dec_float_digits10 = ((Digits10 < 30) ? 30 : ((Digits10 > cpp_dec_float_digits10_limit) ? cpp_dec_float_digits10_limit : Digits10)); + static const boost::int64_t cpp_dec_float_max_exp10 = 2776234983093287512; static const boost::int64_t cpp_dec_float_min_exp10 = -2776234983093287512; static const boost::int64_t cpp_dec_float_max_exp = (cpp_dec_float_max_exp10 / 301LL) * 1000LL; static const boost::int64_t cpp_dec_float_min_exp = (cpp_dec_float_min_exp10 / 301LL) * 1000LL; - static const boost::int32_t mp_elem_digits10 = static_cast(8); + + static const boost::int32_t mp_elem_digits10 = static_cast(8); BOOST_STATIC_ASSERT(0 == cpp_dec_float_max_exp10 % mp_elem_digits10); BOOST_STATIC_ASSERT(cpp_dec_float_max_exp10 == -cpp_dec_float_min_exp10); private: - static const boost::int32_t cpp_dec_float_digits10_num_base = static_cast((cpp_dec_float_max_digits10 / mp_elem_digits10) + (((cpp_dec_float_max_digits10 % mp_elem_digits10) != 0) ? 1 : 0)); - static const boost::int32_t mp_elem_number = static_cast(cpp_dec_float_digits10_num_base + 2); - static const boost::int32_t mp_elem_mask = static_cast(100000000); + static const boost::int32_t cpp_dec_float_digits10_num_base = static_cast((cpp_dec_float_digits10 / mp_elem_digits10) + (((cpp_dec_float_digits10 % mp_elem_digits10) != 0) ? 1 : 0)); + + // There are three guard limbs. + // 1) The first limb has 'play' from 1...8 decimal digits. + // 2) The last limb also has 'play' from 1...8 decimal digits. + // 3) One limb can get lost when justifying after multiply, + // as only half of the triangle is multiplied and a carry + // from below is missing. + static const boost::int32_t mp_elem_number = static_cast(cpp_dec_float_digits10_num_base + 3); + static const boost::int32_t mp_elem_mask = static_cast(100000000); public: static const boost::int32_t cpp_dec_float_total_digits10 = mp_elem_number * mp_elem_digits10; @@ -181,8 +186,8 @@ public: prec_elem(mp_elem_number) { // TODO: this doesn't round! - std::copy(f.data.begin(), f.data.begin() + std::min(f.prec_elem, prec_elem), data.begin()); - precision(std::min(f.prec_elem, prec_elem)); + std::copy(f.data.begin(), f.data.begin() + (std::min)(f.prec_elem, prec_elem), data.begin()); + precision((std::min)(f.prec_elem, prec_elem)); } template @@ -215,7 +220,7 @@ public: { init.do_nothing(); static bool init = false; - static const std::string str_max = std::string("9." + std::string(static_cast(cpp_dec_float_max_digits10), static_cast('9'))) + static const std::string str_max = std::string("9." + std::string(static_cast(cpp_dec_float_total_digits10), static_cast('9'))) + std::string("e+" + boost::lexical_cast(cpp_dec_float_max_exp10)); static cpp_dec_float val_max; if(!init) @@ -327,8 +332,8 @@ public: exp = f.exp; neg = f.neg; fpclass = static_cast(static_cast(f.fpclass)); - std::copy(f.data.begin(), f.data.begin() + std::min(f.prec_elem, prec_elem), data.begin()); - precision(std::min(f.prec_elem, prec_elem)); + std::copy(f.data.begin(), f.data.begin() + (std::min)(f.prec_elem, prec_elem), data.begin()); + precision((std::min)(f.prec_elem, prec_elem)); return *this; } cpp_dec_float& operator= (long long v) @@ -431,10 +436,10 @@ public: signed long long extract_signed_long_long (void) const; unsigned long long extract_unsigned_long_long(void) const; void extract_parts (double& mantissa, boost::int64_t& exponent) const; - cpp_dec_float extract_integer_part (void) const; + cpp_dec_float extract_integer_part (void) const; void precision(const boost::int32_t prec_digits) { - if(prec_digits >= cpp_dec_float_digits10) + if(prec_digits >= cpp_dec_float_total_digits10) { prec_elem = mp_elem_number; } @@ -525,18 +530,12 @@ typename cpp_dec_float::initializer cpp_dec_float::init; template const boost::int32_t cpp_dec_float::mp_radix; template -const boost::int32_t cpp_dec_float::cpp_dec_float_digits; -template const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_setting; template const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_limit; template const boost::int32_t cpp_dec_float::cpp_dec_float_digits10; template -const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_extra; -template -const boost::int32_t cpp_dec_float::cpp_dec_float_max_digits10; -template const boost::int64_t cpp_dec_float::cpp_dec_float_max_exp; template const boost::int64_t cpp_dec_float::cpp_dec_float_min_exp; @@ -855,7 +854,8 @@ cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float boost::array(mp_elem_number + static_cast(1))> w = {{ 0u }}; - mul_loop_uv(data.data(), v.data.data(), w.data(), (std::min)(prec_elem, v.prec_elem)); + const boost::int32_t prec_mul = (std::min)(prec_elem, v.prec_elem); + mul_loop_uv(data.data(), v.data.data(), w.data(), prec_mul); // Copy the multiplication data into the result. // Shift the result and adjust the exponent if necessary. @@ -863,11 +863,11 @@ cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float { exp += static_cast(mp_elem_digits10); - std::copy(w.begin(), w.end() - 1u, data.begin()); + std::copy(w.begin(), w.begin() + prec_mul, data.begin()); } else { - std::copy(w.begin() + 1u, w.end(), data.begin()); + std::copy(w.begin() + 1u, w.begin() + (prec_mul + 1), data.begin()); } // Set the sign of the result. @@ -1146,13 +1146,13 @@ cpp_dec_float& cpp_dec_float::calculate_inv() // is used. During the iterative steps, the precision of the calculation is limited // to the minimum required in order to minimize the run-time. - static const boost::int32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; + static const boost::int32_t double_digits10_minus_a_few = std::numeric_limits::digits10 - 3; - for(boost::int32_t digits = double_digits10_minus_one; digits <= cpp_dec_float_max_digits10; digits *= static_cast(2)) + for(boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= static_cast(2)) { // Adjust precision of the terms. - precision(static_cast(digits * static_cast(2))); - x.precision(static_cast(digits * static_cast(2))); + precision(static_cast((digits + 10) * static_cast(2))); + x.precision(static_cast((digits + 10) * static_cast(2))); // Next iteration. cpp_dec_float t(*this); @@ -1221,13 +1221,13 @@ cpp_dec_float& cpp_dec_float::calculate_sqrt(void) // http://www.jjj.de/pibook/pibook.html // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846 - static const boost::uint32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; + static const boost::uint32_t double_digits10_minus_a_few = std::numeric_limits::digits10 - 3; - for(boost::int32_t digits = double_digits10_minus_one; digits <= cpp_dec_float_max_digits10; digits *= 2u) + for(boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= 2u) { // Adjust precision of the terms. - precision(digits * 2); - vi.precision(digits * 2); + precision((digits + 10) * 2); + vi.precision((digits + 10) * 2); // Next iteration of vi cpp_dec_float t(*this); @@ -1669,7 +1669,7 @@ std::string cpp_dec_float::str(boost::intmax_t number_of_digits, std:: boost::intmax_t org_digits(number_of_digits); boost::int64_t my_exp = order(); if(number_of_digits == 0) - number_of_digits = cpp_dec_float_max_digits10; + number_of_digits = cpp_dec_float_total_digits10; if(f & std::ios_base::fixed) { number_of_digits += my_exp + 1; @@ -2785,7 +2785,7 @@ inline void eval_frexp(cpp_dec_float& result, const cpp_dec_float r2; eval_frexp(r2, result, &e2); - // overflow prtection: + // overflow protection: if((t > 0) && (e2 > 0) && (t > (std::numeric_limits::max)() - e2)) BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2.")); if((t < 0) && (e2 < 0) && (t < (std::numeric_limits::min)() - e2)) @@ -2855,7 +2855,7 @@ namespace std static const bool is_iec559 = false; static const int digits = Digits10; static const int digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; - static const int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_digits10; + static const int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10 + 1; static const boost::int64_t min_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp; // Type differs from int. static const boost::int64_t min_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp10; // Type differs from int. static const boost::int64_t max_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp; // Type differs from int. diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index dbe134fd..73de53d4 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -653,10 +653,10 @@ void eval_atan(T& result, const T& x) result = fp_type(std::atan(d)); // Newton-Raphson iteration - static const boost::int32_t double_digits10_minus_one = std::numeric_limits::digits10 - 1; + static const boost::int32_t double_digits10_minus_a_few = std::numeric_limits::digits10 - 3; T s, c, t; - for(boost::int32_t digits = double_digits10_minus_one; digits <= std::numeric_limits >::digits10; digits *= 2) + for(boost::int32_t digits = double_digits10_minus_a_few; digits <= std::numeric_limits >::digits10; digits *= 2) { eval_sin(s, result); eval_cos(c, result); From 538415e0ef61285a3bfd2d170316a5532274fa29 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 15 Apr 2012 17:46:42 +0000 Subject: [PATCH 173/256] Correct wrong function-call argument in docs. Change max_digits10 in numeric_limits to include all the *possible* digits. [SVN r77996] --- doc/html/boost_multiprecision/indexes/s01.html | 4 ++-- doc/html/boost_multiprecision/indexes/s02.html | 4 ++-- doc/html/boost_multiprecision/indexes/s03.html | 4 ++-- doc/html/boost_multiprecision/indexes/s04.html | 4 ++-- doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html | 5 +++-- doc/html/index.html | 2 +- example/floating_point_examples.cpp | 3 ++- include/boost/multiprecision/cpp_dec_float.hpp | 2 +- 8 files changed, 15 insertions(+), 13 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index f9f2bbf8..87ffa2d8 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    +Function Index

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    diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index b541c91b..be58bd14 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

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    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 34eeb3c1..97dafaf5 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

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    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 08db6751..ac6db077 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

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    diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html index 8acdc588..c8f5fb7e 100644 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html @@ -122,8 +122,9 @@

    Calling the function like so:

    -
    std::cout << std::setprecision(std::numeric_limits<::mp_type>::digits10) << std::scientific;
-std::cout << mysin(mp_type(1)) << std::endl;
+
    mp_type pid4 = boost::math::constants::pi<mp_type>() / 4;
+std::cout << std::setprecision(std::numeric_limits< ::mp_type>::digits10) << std::scientific;
+std::cout << mysin(pid4) << std::endl;
 
    
 
    
             Yields the expected output:
diff --git a/doc/html/index.html b/doc/html/index.html
index 07e5aa99..444abace 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -117,7 +117,7 @@
    - +

    Last revised: April 13, 2012 at 16:48:43 GMT

    Last revised: April 15, 2012 at 17:36:47 GMT
    diff --git a/example/floating_point_examples.cpp b/example/floating_point_examples.cpp index 6cb1f391..7c391ddd 100644 --- a/example/floating_point_examples.cpp +++ b/example/floating_point_examples.cpp @@ -441,8 +441,9 @@ mp_type mysin(const mp_type& x) /*` Calling the function like so: + mp_type pid4 = boost::math::constants::pi() / 4; std::cout << std::setprecision(std::numeric_limits< ::mp_type>::digits10) << std::scientific; - std::cout << mysin(mp_type(1)) << std::endl; + std::cout << mysin(pid4) << std::endl; Yields the expected output: diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 08c38f75..417c0f81 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -2855,7 +2855,7 @@ namespace std static const bool is_iec559 = false; static const int digits = Digits10; static const int digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; - static const int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10 + 1; + static const int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_total_digits10; static const boost::int64_t min_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp; // Type differs from int. static const boost::int64_t min_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp10; // Type differs from int. static const boost::int64_t max_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp; // Type differs from int. From 1f15fc5ad9cbe2e5f07c0d6bd75f70f19557ddbd Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 16 Apr 2012 16:28:57 +0000 Subject: [PATCH 174/256] Deleted some dead files, moved some others around. [SVN r78014] --- .../generic_numerics/generic_numerics.pdf | Bin 98380 -> 0 bytes .../generic_area_of_a_circle.cpp | 45 -------- .../generic_derivative.cpp | 79 ------------- .../generic_numerics_src/generic_integral.cpp | 105 ------------------ .../{ => depricated}/arithmetic_backend.hpp | 0 .../{ => depricated}/fixed_int.hpp | 0 6 files changed, 229 deletions(-) delete mode 100644 example/generic_numerics_examples/generic_numerics/generic_numerics.pdf delete mode 100644 example/generic_numerics_examples/generic_numerics_src/generic_area_of_a_circle.cpp delete mode 100644 example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp delete mode 100644 example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp rename include/boost/multiprecision/{ => depricated}/arithmetic_backend.hpp (100%) rename include/boost/multiprecision/{ => depricated}/fixed_int.hpp (100%) diff --git a/example/generic_numerics_examples/generic_numerics/generic_numerics.pdf 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const float r_f(float(123) / 100); - const float a_f = area_of_a_circle(r_f); - - const double r_d(double(123) / 100); - const double a_d = area_of_a_circle(r_d); - - const cpp_dec_float_50 r_mp(cpp_dec_float_50(123) / 100); - const cpp_dec_float_50 a_mp = area_of_a_circle(r_mp); - - // 4.75292 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << a_f - << std::endl; - - // 4.752915525616 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << a_d - << std::endl; - - // 4.7529155256159981904701331745635599135018975843146 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << a_mp - << std::endl; -} diff --git a/example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp b/example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp deleted file mode 100644 index ccf0ad97..00000000 --- a/example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp +++ /dev/null @@ -1,79 +0,0 @@ -template -value_type derivative(const value_type x, - const value_type dx, - function_type func) -{ - // Compute d/dx[func(*first)] using a three-point - // central difference rule of O(dx^6). - - const value_type dx1 = dx; - const value_type dx2 = dx1 * 2; - const value_type dx3 = dx1 * 3; - - const value_type m1 = ( func(x + dx1) - - func(x - dx1)) / 2; - const value_type m2 = ( func(x + dx2) - - func(x - dx2)) / 4; - const value_type m3 = ( func(x + dx3) - - func(x - dx3)) / 6; - - const value_type fifteen_m1 = 15 * m1; - const value_type six_m2 = 6 * m2; - const value_type ten_dx1 = 10 * dx1; - - return ((fifteen_m1 - six_m2) + m3) / ten_dx1; -} - -#include -#include -#include -#include - -using boost::math::constants::pi; -using boost::multiprecision::cpp_dec_float_50; - -int main(int, char**) -{ - const float d_f = - derivative(float(pi() / 3), - 0.01F, - [](const float x) -> float - { - return ::sin(x); - }); - - const double d_d = - derivative(double(pi() / 3), - 0.001, - [](const double x) -> double - { - return ::sin(x); - }); - - const cpp_dec_float_50 d_mp = - derivative(cpp_dec_float_50(pi() / 3), - cpp_dec_float_50(1.0E-9), - [](const cpp_dec_float_50 x) -> cpp_dec_float_50 - { - return boost::multiprecision::sin(x); - }); - - // 0.500003 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << d_f - << std::endl; - - // 0.499999999999888 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << d_d - << std::endl; - - // 0.50000000000000000000000000000000000000000003925935 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << d_mp - << std::endl; -} diff --git a/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp b/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp deleted file mode 100644 index 787de062..00000000 --- a/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp +++ /dev/null @@ -1,105 +0,0 @@ -template -inline value_type integral(const value_type a, - const value_type b, - const value_type tol, - function_type func) -{ - unsigned n = 1U; - - value_type h = (b - a); - value_type I = (func(a) + func(b)) * (h / 2); - - for(unsigned k = 0U; k < 8U; k++) - { - h /= 2; - - value_type sum(0); - for(unsigned j = 1U; j <= n; j++) - { - sum += func(a + (value_type((j * 2) - 1) * h)); - } - - const value_type I0 = I; - I = (I / 2) + (h * sum); - - const value_type ratio = I0 / I; - const value_type delta = ratio - 1; - const value_type delta_abs = ((delta < 0) ? -delta : delta); - - if((k > 1U) && (delta_abs < tol)) - { - break; - } - - n *= 2U; - } - - return I; -} - -#include -#include -#include -#include - -template -class cyl_bessel_j_integral_rep -{ -public: - cyl_bessel_j_integral_rep(const unsigned N, - const value_type& X) : n(N), x(X) { } - - value_type operator()(const value_type& t) const - { - // pi * Jn(x) = Int_0^pi [cos(x * sin(t) - n*t) dt] - return cos(x * sin(t) - (n * t)); - } - -private: - const unsigned n; - const value_type x; -}; - - -int main(int, char**) -{ - using boost::math::constants::pi; - typedef boost::multiprecision::cpp_dec_float_50 mp_type; - - const float j2_f = - integral(0.0F, - pi(), - 0.01F, - cyl_bessel_j_integral_rep(2U, 1.23F)) / pi(); - - const double j2_d = - integral(0.0, - pi(), - 0.0001, - cyl_bessel_j_integral_rep(2U, 1.23)) / pi(); - - const mp_type j2_mp = - integral(mp_type(0), - pi(), - mp_type(1.0E-20), - cyl_bessel_j_integral_rep(2U, mp_type(123) / 100)) / pi(); - - // 0.166369 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << j2_f - << std::endl; - - // 0.166369383786814 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << j2_d - << std::endl; - - // 0.16636938378681407351267852431513159437103348245333 - std::cout - << std::setprecision(std::numeric_limits::digits10) - << j2_mp - << std::endl; -} diff --git a/include/boost/multiprecision/arithmetic_backend.hpp b/include/boost/multiprecision/depricated/arithmetic_backend.hpp similarity index 100% rename from include/boost/multiprecision/arithmetic_backend.hpp rename to include/boost/multiprecision/depricated/arithmetic_backend.hpp diff --git a/include/boost/multiprecision/fixed_int.hpp b/include/boost/multiprecision/depricated/fixed_int.hpp similarity index 100% rename from include/boost/multiprecision/fixed_int.hpp rename to include/boost/multiprecision/depricated/fixed_int.hpp From b6d6d5ea0131bdd9b8e293311bd1dd349ef0c3b4 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 17 Apr 2012 09:20:47 +0000 Subject: [PATCH 175/256] Fix __int128 selection logic [SVN r78034] --- include/boost/multiprecision/detail/cpp_int_core.hpp | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/include/boost/multiprecision/detail/cpp_int_core.hpp b/include/boost/multiprecision/detail/cpp_int_core.hpp index e63fb2ed..31ce2245 100644 --- a/include/boost/multiprecision/detail/cpp_int_core.hpp +++ b/include/boost/multiprecision/detail/cpp_int_core.hpp @@ -8,7 +8,8 @@ namespace boost{ namespace multiprecision{ -#if defined(__GNUC__) && !defined(BOOST_INTEL) && defined(__WORDSIZE) && (__WORDSIZE == 64) +#if defined(__GNUC__) && ((__GNUC__ > 4) || ((__GNUC__ == 4) && (__GNUC_MINOR__ >= 6))) \ + && !defined(BOOST_INTEL) && defined(__WORDSIZE) && (__WORDSIZE == 64) typedef boost::uint64_t limb_type; typedef boost::int64_t signed_limb_type; From 9ee0022c7720171b403789a5041387f6e4764c32 Mon Sep 17 00:00:00 2001 From: Christopher Kormanyos Date: Fri, 20 Apr 2012 20:05:49 +0000 Subject: [PATCH 176/256] Re-factor cpp_dec_float class constants. Extend cpp_dec_float low-digit range from 30 to 9. Removed temporary storage from cpp_dec_float multiply routine. Extended tests to 9, 18 and (sqrt test) to 1000 digits. [SVN r78097] --- .../boost/multiprecision/cpp_dec_float.hpp | 861 +++++++++--------- test/Jamfile.v2 | 7 + test/math/test_bessel_i.cpp | 2 + test/math/test_zeta.cpp | 2 + test/test_asin.cpp | 3 + test/test_atan.cpp | 3 + test/test_exp.cpp | 3 + test/test_log.cpp | 3 + test/test_pow.cpp | 3 + test/test_sin.cpp | 3 + test/test_sinh.cpp | 3 + test/test_sqrt.cpp | 208 +++-- 12 files changed, 573 insertions(+), 528 deletions(-) diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 417c0f81..74d3a3e5 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -9,8 +9,8 @@ // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 // -#ifndef BOOST_MP_EFX_BACKEND_HPP -#define BOOST_MP_EFX_BACKEND_HPP +#ifndef BOOST_MP_CPP_DEC_FLOAT_BACKEND_HPP +#define BOOST_MP_CPP_DEC_FLOAT_BACKEND_HPP #include #include @@ -29,30 +29,31 @@ namespace backends{ template class cpp_dec_float { -public: - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list float_types; - typedef long long exponent_type; - - - static const boost::int32_t mp_radix = 10; - +private: static const boost::int32_t cpp_dec_float_digits10_setting = Digits10; - static const boost::int32_t cpp_dec_float_digits10_limit = boost::integer_traits::const_max - 100; - static const boost::int32_t cpp_dec_float_digits10 = ((Digits10 < 30) ? 30 : ((Digits10 > cpp_dec_float_digits10_limit) ? cpp_dec_float_digits10_limit : Digits10)); - static const boost::int64_t cpp_dec_float_max_exp10 = 2776234983093287512; - static const boost::int64_t cpp_dec_float_min_exp10 = -2776234983093287512; - static const boost::int64_t cpp_dec_float_max_exp = (cpp_dec_float_max_exp10 / 301LL) * 1000LL; - static const boost::int64_t cpp_dec_float_min_exp = (cpp_dec_float_min_exp10 / 301LL) * 1000LL; - static const boost::int32_t mp_elem_digits10 = static_cast(8); +public: + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list float_types; + typedef long long exponent_type; + + static const boost::int32_t cpp_dec_float_radix = 10L; + static const boost::int32_t cpp_dec_float_digits10_limit_lo = 9L; + static const boost::int32_t cpp_dec_float_digits10_limit_hi = boost::integer_traits::const_max - 100; + static const boost::int32_t cpp_dec_float_digits10 = ((cpp_dec_float_digits10_setting < cpp_dec_float_digits10_limit_lo) ? cpp_dec_float_digits10_limit_lo : ((cpp_dec_float_digits10_setting > cpp_dec_float_digits10_limit_hi) ? cpp_dec_float_digits10_limit_hi : cpp_dec_float_digits10_setting)); + static const boost::int64_t cpp_dec_float_max_exp10 = static_cast( 2776234983093287512LL); + static const boost::int64_t cpp_dec_float_min_exp10 = static_cast(-2776234983093287512LL); + static const boost::int64_t cpp_dec_float_max_exp = static_cast((cpp_dec_float_max_exp10 / 301LL) * 1000LL); + static const boost::int64_t cpp_dec_float_min_exp = static_cast((cpp_dec_float_min_exp10 / 301LL) * 1000LL); - BOOST_STATIC_ASSERT(0 == cpp_dec_float_max_exp10 % mp_elem_digits10); BOOST_STATIC_ASSERT(cpp_dec_float_max_exp10 == -cpp_dec_float_min_exp10); private: - static const boost::int32_t cpp_dec_float_digits10_num_base = static_cast((cpp_dec_float_digits10 / mp_elem_digits10) + (((cpp_dec_float_digits10 % mp_elem_digits10) != 0) ? 1 : 0)); + static const boost::int32_t cpp_dec_float_elem_digits10 = 8L; + static const boost::int32_t cpp_dec_float_elem_mask = 100000000L; + + BOOST_STATIC_ASSERT(0 == cpp_dec_float_max_exp10 % cpp_dec_float_elem_digits10); // There are three guard limbs. // 1) The first limb has 'play' from 1...8 decimal digits. @@ -60,39 +61,41 @@ private: // 3) One limb can get lost when justifying after multiply, // as only half of the triangle is multiplied and a carry // from below is missing. - static const boost::int32_t mp_elem_number = static_cast(cpp_dec_float_digits10_num_base + 3); - static const boost::int32_t mp_elem_mask = static_cast(100000000); + static const boost::int32_t cpp_dec_float_elem_number_request = static_cast((cpp_dec_float_digits10 / cpp_dec_float_elem_digits10) + (((cpp_dec_float_digits10 % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)); + + // The number of elements needed (with a minimum of two) plus three added guard limbs. + static const boost::int32_t cpp_dec_float_elem_number = static_cast(((cpp_dec_float_elem_number_request < 2L) ? 2L : cpp_dec_float_elem_number_request) + 3L); public: - static const boost::int32_t cpp_dec_float_total_digits10 = mp_elem_number * mp_elem_digits10; + static const boost::int32_t cpp_dec_float_total_digits10 = static_cast(cpp_dec_float_elem_number * cpp_dec_float_elem_digits10); private: - typedef enum enum_fpclass + typedef enum enum_fpclass_type { - mp_finite, - mp_inf, - mp_NaN + cpp_dec_float_finite, + cpp_dec_float_inf, + cpp_dec_float_NaN } - t_fpclass; + fpclass_type; - typedef boost::array array_type; + typedef boost::array array_type; - array_type data; - boost::int64_t exp; - bool neg; - t_fpclass fpclass; - boost::int32_t prec_elem; + array_type data; + boost::int64_t exp; + bool neg; + fpclass_type fpclass; + boost::int32_t prec_elem; // // Special values constructor: // - cpp_dec_float(t_fpclass c) : + cpp_dec_float(fpclass_type c) : data(), exp (static_cast(0)), neg (false), fpclass (c), - prec_elem(mp_elem_number) { } + prec_elem(cpp_dec_float_elem_number) { } // // Static data initializer: @@ -130,15 +133,15 @@ public: data(), exp (static_cast(0)), neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) { } + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) { } cpp_dec_float(const char* s) : data(), exp (static_cast(0)), neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) { *this = s; } @@ -148,8 +151,8 @@ public: data(), exp (static_cast(0)), neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) { from_unsigned_long_long(i); } @@ -159,8 +162,8 @@ public: data(), exp (static_cast(0)), neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) { if(i < 0) { @@ -183,7 +186,7 @@ public: exp (f.exp), neg (f.neg), fpclass (static_cast(static_cast(f.fpclass))), - prec_elem(mp_elem_number) + prec_elem(cpp_dec_float_elem_number) { // TODO: this doesn't round! std::copy(f.data.begin(), f.data.begin() + (std::min)(f.prec_elem, prec_elem), data.begin()); @@ -195,8 +198,8 @@ public: data(), exp (static_cast(0)), neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) { *this = val; } @@ -206,13 +209,13 @@ public: // Specific special values. static const cpp_dec_float& nan() { - static const cpp_dec_float val(mp_NaN); + static const cpp_dec_float val(cpp_dec_float_NaN); init.do_nothing(); return val; } static const cpp_dec_float& inf() { - static const cpp_dec_float val(mp_inf); + static const cpp_dec_float val(cpp_dec_float_inf); init.do_nothing(); return val; } @@ -389,13 +392,13 @@ public: } // Comparison functions - bool isnan (void) const { return (fpclass == mp_NaN); } - bool isinf (void) const { return (fpclass == mp_inf); } - bool isfinite(void) const { return (fpclass == mp_finite); } + bool isnan (void) const { return (fpclass == cpp_dec_float_NaN); } + bool isinf (void) const { return (fpclass == cpp_dec_float_inf); } + bool isfinite(void) const { return (fpclass == cpp_dec_float_finite); } bool iszero (void) const { - return ((fpclass == mp_finite) && (data[0u] == 0u)); + return ((fpclass == cpp_dec_float_finite) && (data[0u] == 0u)); } bool isone (void) const; bool isint (void) const; @@ -441,14 +444,14 @@ public: { if(prec_digits >= cpp_dec_float_total_digits10) { - prec_elem = mp_elem_number; + prec_elem = cpp_dec_float_elem_number; } else { - const boost::int32_t elems = static_cast( static_cast( (prec_digits + (mp_elem_digits10 / 2)) / mp_elem_digits10) - + static_cast(((prec_digits % mp_elem_digits10) != 0) ? 1 : 0)); + const boost::int32_t elems = static_cast( static_cast( (prec_digits + (cpp_dec_float_elem_digits10 / 2)) / cpp_dec_float_elem_digits10) + + static_cast(((prec_digits % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)); - prec_elem = (std::min)(mp_elem_number, (std::max)(elems, static_cast(2))); + prec_elem = (std::min)(cpp_dec_float_elem_number, (std::max)(elems, static_cast(2))); } } static cpp_dec_float pow2(long long i); @@ -500,22 +503,22 @@ public: } } - return (bo_order_is_zero ? static_cast(0) - : static_cast(exp + prefix)); + return (bo_order_is_zero ? static_cast(0) : static_cast(exp + prefix)); } private: static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast(0u)); } - static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast(cpp_dec_float::mp_elem_mask - 1)); } + static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast(cpp_dec_float::cpp_dec_float_elem_mask - 1)); } static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast('0')); } void from_unsigned_long_long(const unsigned long long u); int cmp_data(const array_type& vd) const; - static void mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p); - static boost::uint32_t mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); - static boost::uint32_t div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); + + static boost::uint32_t mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p); + static boost::uint32_t mul_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); + static boost::uint32_t div_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); bool rd_string(const char* const s); @@ -528,11 +531,13 @@ template typename cpp_dec_float::initializer cpp_dec_float::init; template -const boost::int32_t cpp_dec_float::mp_radix; +const boost::int32_t cpp_dec_float::cpp_dec_float_radix; template const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_setting; template -const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_limit; +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_limit_lo; +template +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_limit_hi; template const boost::int32_t cpp_dec_float::cpp_dec_float_digits10; template @@ -544,13 +549,13 @@ const boost::int64_t cpp_dec_float::cpp_dec_float_max_exp10; template const boost::int64_t cpp_dec_float::cpp_dec_float_min_exp10; template -const boost::int32_t cpp_dec_float::mp_elem_digits10; +const boost::int32_t cpp_dec_float::cpp_dec_float_elem_digits10; template -const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_num_base; +const boost::int32_t cpp_dec_float::cpp_dec_float_elem_number_request; template -const boost::int32_t cpp_dec_float::mp_elem_number; +const boost::int32_t cpp_dec_float::cpp_dec_float_elem_number; template -const boost::int32_t cpp_dec_float::mp_elem_mask; +const boost::int32_t cpp_dec_float::cpp_dec_float_elem_mask; template @@ -576,7 +581,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float } // Get the offset for the add/sub operation. - static const boost::int64_t max_delta_exp = static_cast((mp_elem_number - 1) * mp_elem_digits10); + static const boost::int64_t max_delta_exp = static_cast((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); const boost::int64_t ofs_exp = static_cast(exp - v.exp); @@ -597,7 +602,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float typename array_type::iterator p_u = data.begin(); typename array_type::const_iterator p_v = v.data.begin(); bool b_copy = false; - const boost::int32_t ofs = static_cast(static_cast(ofs_exp) / mp_elem_digits10); + const boost::int32_t ofs = static_cast(static_cast(ofs_exp) / cpp_dec_float_elem_digits10); array_type n_data; if(neg == v.neg) @@ -623,11 +628,11 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float // Addition algorithm boost::uint32_t carry = static_cast(0u); - for(boost::int32_t j = static_cast(mp_elem_number - static_cast(1)); j >= static_cast(0); j--) + for(boost::int32_t j = static_cast(cpp_dec_float_elem_number - static_cast(1)); j >= static_cast(0); j--) { boost::uint32_t t = static_cast(static_cast(p_u[j] + p_v[j]) + carry); - carry = t / static_cast(mp_elem_mask); - p_u[j] = static_cast(t - static_cast(carry * static_cast(mp_elem_mask))); + carry = t / static_cast(cpp_dec_float_elem_mask); + p_u[j] = static_cast(t - static_cast(carry * static_cast(cpp_dec_float_elem_mask))); } if(b_copy) @@ -641,7 +646,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float { std::copy_backward(data.begin(), data.end() - static_cast(1u), data.end()); data[0] = carry; - exp += static_cast(mp_elem_digits10); + exp += static_cast(cpp_dec_float_elem_digits10); } } else @@ -686,7 +691,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float // Subtraction algorithm boost::int32_t borrow = static_cast(0); - for(j = static_cast(mp_elem_number - static_cast(1)); j >= static_cast(0); j--) + for(j = static_cast(cpp_dec_float_elem_number - static_cast(1)); j >= static_cast(0); j--) { boost::int32_t t = static_cast(static_cast( static_cast(p_u[j]) - static_cast(p_v[j])) - borrow); @@ -695,7 +700,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float if(t < static_cast(0)) { // Yes, underflow and borrow - t += static_cast(mp_elem_mask); + t += static_cast(cpp_dec_float_elem_mask); borrow = static_cast(1); } else @@ -703,7 +708,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float borrow = static_cast(0); } - p_u[j] = static_cast(static_cast(t) % static_cast(mp_elem_mask)); + p_u[j] = static_cast(static_cast(t) % static_cast(cpp_dec_float_elem_mask)); } if(b_copy) @@ -733,7 +738,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float std::copy(data.begin() + static_cast(sj), data.end(), data.begin()); std::fill(data.end() - sj, data.end(), static_cast(0u)); - exp -= static_cast(sj * static_cast(mp_elem_digits10)); + exp -= static_cast(sj * static_cast(cpp_dec_float_elem_digits10)); } } } @@ -852,22 +857,22 @@ cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float // Set the exponent of the result. exp += v.exp; - boost::array(mp_elem_number + static_cast(1))> w = {{ 0u }}; - const boost::int32_t prec_mul = (std::min)(prec_elem, v.prec_elem); - mul_loop_uv(data.data(), v.data.data(), w.data(), prec_mul); - // Copy the multiplication data into the result. - // Shift the result and adjust the exponent if necessary. - if(w[static_cast(0u)] != static_cast(0u)) - { - exp += static_cast(mp_elem_digits10); + const boost::uint32_t carry = mul_loop_uv(data.data(), v.data.data(), prec_mul); - std::copy(w.begin(), w.begin() + prec_mul, data.begin()); - } - else + // Handle a potential carry. + if(carry != static_cast(0u)) { - std::copy(w.begin() + 1u, w.begin() + (prec_mul + 1), data.begin()); + exp += cpp_dec_float_elem_digits10; + + // Shift the result of the multiplication one element to the right... + std::copy_backward(data.begin(), + data.begin() + static_cast(prec_elem - static_cast(1)), + data.begin() + static_cast(prec_elem)); + + // ... And insert the carry. + data.front() = carry; } // Set the sign of the result. @@ -945,7 +950,7 @@ cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const u return *this = zero(); } - if(n >= static_cast(mp_elem_mask)) + if(n >= static_cast(cpp_dec_float_elem_mask)) { neg = b_neg; cpp_dec_float t; @@ -966,7 +971,7 @@ cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const u // Handle the carry and adjust the exponent. if(carry != static_cast(0u)) { - exp += static_cast(mp_elem_digits10); + exp += static_cast(cpp_dec_float_elem_digits10); // Shift the result of the multiplication one element to the right. std::copy_backward(data.begin(), @@ -979,7 +984,7 @@ cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const u bool overflow = exp >= cpp_dec_float_max_exp10; if(exp == cpp_dec_float_max_exp10) { - // Check to see if we really truely have an overflow or not... + // Check to see if we really truly have an overflow or not... if(isneg()) { cpp_dec_float t(*this); @@ -1053,7 +1058,7 @@ cpp_dec_float& cpp_dec_float::div_unsigned_long_long(const u return *this; } - if(n >= static_cast(mp_elem_mask)) + if(n >= static_cast(cpp_dec_float_elem_mask)) { neg = b_neg; cpp_dec_float t; @@ -1072,14 +1077,14 @@ cpp_dec_float& cpp_dec_float::div_unsigned_long_long(const u if(data[0] == static_cast(0u)) { // Adjust the exponent - exp -= static_cast(mp_elem_digits10); + exp -= static_cast(cpp_dec_float_elem_digits10); // Shift result of the division one element to the left. std::copy(data.begin() + static_cast(1u), data.begin() + static_cast(prec_elem - static_cast(1)), data.begin()); - data[prec_elem - static_cast(1)] = static_cast(static_cast(prev * static_cast(mp_elem_mask)) / nn); + data[prec_elem - static_cast(1)] = static_cast(static_cast(prev * static_cast(cpp_dec_float_elem_mask)) / nn); } } @@ -1164,7 +1169,7 @@ cpp_dec_float& cpp_dec_float::calculate_inv() neg = b_neg; - prec_elem = mp_elem_number; + prec_elem = cpp_dec_float_elem_number; return *this; } @@ -1247,7 +1252,7 @@ cpp_dec_float& cpp_dec_float::calculate_sqrt(void) *this += t; } - prec_elem = mp_elem_number; + prec_elem = cpp_dec_float_elem_number; return *this; } @@ -1366,7 +1371,7 @@ bool cpp_dec_float::isone() const const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); return (it_non_zero == data.end()); } - else if((data[0u] == static_cast(mp_elem_mask - 1)) && (exp == static_cast(-mp_elem_digits10))) + else if((data[0u] == static_cast(cpp_dec_float_elem_mask - 1)) && (exp == static_cast(-cpp_dec_float_elem_digits10))) { const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate); return (it_non_nine == data.end()); @@ -1379,15 +1384,15 @@ bool cpp_dec_float::isone() const template bool cpp_dec_float::isint() const { - if(fpclass != mp_finite) { return false; } + if(fpclass != cpp_dec_float_finite) { return false; } if(iszero()) { return true; } if(exp < static_cast(0)) { return false; } // |*this| < 1. - const typename array_type::size_type offset_decimal_part = static_cast(exp / mp_elem_digits10) + 1u; + const typename array_type::size_type offset_decimal_part = static_cast(exp / cpp_dec_float_elem_digits10) + 1u; - if(offset_decimal_part >= static_cast(mp_elem_number)) + if(offset_decimal_part >= static_cast(cpp_dec_float_elem_number)) { // The number is too large to resolve the integer part. // It considered to be a pure integer. @@ -1424,8 +1429,8 @@ void cpp_dec_float::extract_parts(double& mantissa, boost::int64_t& ex } mantissa = static_cast(data[0]) - + (static_cast(data[1]) / static_cast(mp_elem_mask)) - + ((static_cast(data[2]) / static_cast(mp_elem_mask)) / static_cast(mp_elem_mask)); + + (static_cast(data[1]) / static_cast(cpp_dec_float_elem_mask)) + + ((static_cast(data[2]) / static_cast(cpp_dec_float_elem_mask)) / static_cast(cpp_dec_float_elem_mask)); mantissa /= static_cast(p10); @@ -1455,13 +1460,13 @@ double cpp_dec_float::extract_double(void) const if(xx.isneg()) xx.negate(); - // Check for zero cpp_dec_float. + // Check if *this cpp_dec_float is zero. if(iszero() || (xx.compare(double_min()) < 0)) { return 0.0; } - // Check if cpp_dec_float exceeds the maximum of double. + // Check if *this cpp_dec_float exceeds the maximum of double. if(xx.compare(double_max()) > 0) { return ((!neg) ? std::numeric_limits::infinity() @@ -1483,7 +1488,7 @@ long double cpp_dec_float::extract_long_double(void) const { // Returns the long double conversion of a cpp_dec_float. - // Check for non-normal cpp_dec_float. + // Check if *this cpp_dec_float is subnormal. if(!isfinite()) { if(isnan()) @@ -1501,13 +1506,13 @@ long double cpp_dec_float::extract_long_double(void) const if(xx.isneg()) xx.negate(); - // Check for zero cpp_dec_float. + // Check if *this cpp_dec_float is zero. if(iszero() || (xx.compare(long_double_min()) < 0)) { return static_cast(0.0); } - // Check if cpp_dec_float exceeds the maximum of double. + // Check if *this cpp_dec_float exceeds the maximum of double. if(xx.compare(long_double_max()) > 0) { return ((!neg) ? std::numeric_limits::infinity() @@ -1557,11 +1562,11 @@ signed long long cpp_dec_float::extract_signed_long_long(void) const val = static_cast(xn.data[0]); - const boost::int32_t imax = (std::min)(static_cast(static_cast(xn.exp) / mp_elem_digits10), static_cast(mp_elem_number - static_cast(1))); + const boost::int32_t imax = (std::min)(static_cast(static_cast(xn.exp) / cpp_dec_float_elem_digits10), static_cast(cpp_dec_float_elem_number - static_cast(1))); for(boost::int32_t i = static_cast(1); i <= imax; i++) { - val *= static_cast(mp_elem_mask); + val *= static_cast(cpp_dec_float_elem_mask); val += static_cast(xn.data[i]); } } @@ -1601,11 +1606,11 @@ unsigned long long cpp_dec_float::extract_unsigned_long_long(void) con // Extract the data into an unsigned long long value. val = static_cast(xn.data[0]); - const boost::int32_t imax = (std::min)(static_cast(static_cast(xn.exp) / mp_elem_digits10), static_cast(mp_elem_number - static_cast(1))); + const boost::int32_t imax = (std::min)(static_cast(static_cast(xn.exp) / cpp_dec_float_elem_digits10), static_cast(cpp_dec_float_elem_number - static_cast(1))); for(boost::int32_t i = static_cast(1); i <= imax; i++) { - val *= static_cast(mp_elem_mask); + val *= static_cast(cpp_dec_float_elem_mask); val += static_cast(xn.data[i]); } } @@ -1640,8 +1645,8 @@ cpp_dec_float cpp_dec_float::extract_integer_part(void) cons cpp_dec_float x = *this; // Clear out the decimal portion - const size_t first_clear = (static_cast(x.exp) / static_cast(mp_elem_digits10)) + 1u; - const size_t last_clear = static_cast(mp_elem_number); + const size_t first_clear = (static_cast(x.exp) / static_cast(cpp_dec_float_elem_digits10)) + 1u; + const size_t last_clear = static_cast(cpp_dec_float_elem_number); std::fill(x.data.begin() + first_clear, x.data.begin() + last_clear, static_cast(0u)); @@ -1677,8 +1682,8 @@ std::string cpp_dec_float::str(boost::intmax_t number_of_digits, std:: else if(f & std::ios_base::scientific) ++number_of_digits; // Determine the number of elements needed to provide the requested digits from cpp_dec_float. - const std::size_t number_of_elements = (std::min)(static_cast((number_of_digits / static_cast(mp_elem_digits10)) + 2u), - static_cast(mp_elem_number)); + const std::size_t number_of_elements = (std::min)(static_cast((number_of_digits / static_cast(cpp_dec_float_elem_digits10)) + 2u), + static_cast(cpp_dec_float_elem_number)); // Extract the remaining digits from cpp_dec_float after the decimal point. str = boost::lexical_cast(data[0]); @@ -1688,7 +1693,7 @@ std::string cpp_dec_float::str(boost::intmax_t number_of_digits, std:: { std::stringstream ss; - ss << std::setw(static_cast(mp_elem_digits10)) + ss << std::setw(static_cast(cpp_dec_float_elem_digits10)) << std::setfill(static_cast('0')) << data[i]; @@ -1808,6 +1813,9 @@ bool cpp_dec_float::rd_string(const char* const s) std::string str(s); + // TBD: Using several regular expressions may significantly reduce + // the code complexity (and perhaps the run-time) of rd_string(). + // Get a possible exponent and remove it. exp = static_cast(0); @@ -1857,8 +1865,7 @@ bool cpp_dec_float::rd_string(const char* const s) return true; } - - // Remove leading zeros for all input types. + // Remove the leading zeros for all input types. const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate); if(fwd_it_leading_zero != str.begin()) @@ -1877,10 +1884,10 @@ bool cpp_dec_float::rd_string(const char* const s) } // Put the input string into the standard cpp_dec_float input form - // aaa.bbbbE+/-n, where aa has 1...mp_elem_digits10, bbbb has an - // even multiple of mp_elem_digits10 which are possibly zero padded - // on the right-end, and n is a signed 32-bit integer which is an - // even multiple of mp_elem_digits10. + // aaa.bbbbE+/-n, where aaa has 1...cpp_dec_float_elem_digits10, bbbb has an + // even multiple of cpp_dec_float_elem_digits10 which are possibly zero padded + // on the right-end, and n is a signed 64-bit integer which is an + // even multiple of cpp_dec_float_elem_digits10. // Find a possible decimal point. pos = str.find(static_cast('.')); @@ -1918,7 +1925,7 @@ bool cpp_dec_float::rd_string(const char* const s) delta_exp = std::distance(str.begin() + 1u, it_non_zero); } - // Bring one single digit into the mantissa and adjust exponent accordingly. + // Bring one single digit into the mantissa and adjust the exponent accordingly. str.erase(str.begin(), it_non_zero); str.insert(static_cast(1u), "."); exp -= static_cast(delta_exp + 1u); @@ -1930,14 +1937,14 @@ bool cpp_dec_float::rd_string(const char* const s) str.append("."); } - // Shift the decimal point such that the exponent is an even multiple of mp_elem_digits10. + // Shift the decimal point such that the exponent is an even multiple of cpp_dec_float_elem_digits10. std::size_t n_shift = static_cast(0u); - const std::size_t n_exp_rem = static_cast(exp % static_cast(mp_elem_digits10)); + const std::size_t n_exp_rem = static_cast(exp % static_cast(cpp_dec_float_elem_digits10)); - if((exp % static_cast(mp_elem_digits10)) != static_cast(0)) + if((exp % static_cast(cpp_dec_float_elem_digits10)) != static_cast(0)) { n_shift = ((exp < static_cast(0)) - ? static_cast(n_exp_rem + static_cast(mp_elem_digits10)) + ? static_cast(n_exp_rem + static_cast(cpp_dec_float_elem_digits10)) : static_cast(n_exp_rem)); } @@ -1963,31 +1970,31 @@ bool cpp_dec_float::rd_string(const char* const s) exp -= static_cast(n_shift); } - // Cut the size of the mantissa to <= mp_elem_digits10. + // Cut the size of the mantissa to <= cpp_dec_float_elem_digits10. pos = str.find(static_cast('.')); pos_plus_one = static_cast(pos + 1u); - if(pos > static_cast(mp_elem_digits10)) + if(pos > static_cast(cpp_dec_float_elem_digits10)) { const boost::int32_t n_pos = static_cast(pos); - const boost::int32_t n_rem_is_zero = ((static_cast(n_pos % mp_elem_digits10) == static_cast(0)) ? static_cast(1) : static_cast(0)); - const boost::int32_t n = static_cast(static_cast(n_pos / mp_elem_digits10) - n_rem_is_zero); + const boost::int32_t n_rem_is_zero = ((static_cast(n_pos % cpp_dec_float_elem_digits10) == static_cast(0)) ? static_cast(1) : static_cast(0)); + const boost::int32_t n = static_cast(static_cast(n_pos / cpp_dec_float_elem_digits10) - n_rem_is_zero); - str.insert(static_cast(static_cast(n_pos - static_cast(n * mp_elem_digits10))), "."); + str.insert(static_cast(static_cast(n_pos - static_cast(n * cpp_dec_float_elem_digits10))), "."); str.erase(pos_plus_one, static_cast(1u)); - exp += static_cast(static_cast(n) * static_cast(mp_elem_digits10)); + exp += static_cast(static_cast(n) * static_cast(cpp_dec_float_elem_digits10)); } // Pad the decimal part such that its value is an even - // multiple of mp_elem_digits10. + // multiple of cpp_dec_float_elem_digits10. pos = str.find(static_cast('.')); pos_plus_one = static_cast(pos + 1u); const boost::int32_t n_dec = static_cast(static_cast(str.length() - 1u) - static_cast(pos)); - const boost::int32_t n_rem = static_cast(n_dec % mp_elem_digits10); - boost::int32_t n_cnt = ((n_rem != static_cast(0)) ? static_cast(mp_elem_digits10 - n_rem) + const boost::int32_t n_rem = static_cast(n_dec % cpp_dec_float_elem_digits10); + boost::int32_t n_cnt = ((n_rem != static_cast(0)) ? static_cast(cpp_dec_float_elem_digits10 - n_rem) : static_cast(0)); if(n_cnt != static_cast(0)) @@ -1996,7 +2003,7 @@ bool cpp_dec_float::rd_string(const char* const s) } // Truncate decimal part if it is too long. - const std::size_t max_dec = static_cast((mp_elem_number - 1) * mp_elem_digits10); + const std::size_t max_dec = static_cast((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); if(static_cast(str.length() - pos) > max_dec) { @@ -2016,15 +2023,15 @@ bool cpp_dec_float::rd_string(const char* const s) data[0u] = boost::lexical_cast(str.substr(static_cast(0u), pos)); // ...then get the remaining digits to the right of the decimal point. - const std::string::size_type i_end = ((str.length() - pos_plus_one) / static_cast(mp_elem_digits10)); + const std::string::size_type i_end = ((str.length() - pos_plus_one) / static_cast(cpp_dec_float_elem_digits10)); for(std::string::size_type i = static_cast(0u); i < i_end; i++) { const std::string::const_iterator it = str.begin() + pos_plus_one - + (i * static_cast(mp_elem_digits10)); + + (i * static_cast(cpp_dec_float_elem_digits10)); - data[i + 1u] = boost::lexical_cast(std::string(it, it + static_cast(mp_elem_digits10))); + data[i + 1u] = boost::lexical_cast(std::string(it, it + static_cast(cpp_dec_float_elem_digits10))); } // Check for overflow... @@ -2076,11 +2083,11 @@ cpp_dec_float::cpp_dec_float(const double mantissa, const long long ex : data (), exp (static_cast(0)), neg (false), - fpclass (mp_finite), - prec_elem(mp_elem_number) + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) { - // Create an cpp_dec_float from mantissa and exponent. - // This ctor does not maintain the full precision of double. + // Create *this cpp_dec_float from a given mantissa and exponent. + // Note: This constructor does not maintain the full precision of double. const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits::min)() * (1.0 + std::numeric_limits::epsilon()))); @@ -2098,9 +2105,9 @@ cpp_dec_float::cpp_dec_float(const double mantissa, const long long ex while(d > 10.0) { d /= 10.0; ++e; } while(d < 1.0) { d *= 10.0; --e; } - boost::int32_t shift = static_cast(e % static_cast(mp_elem_digits10)); + boost::int32_t shift = static_cast(e % static_cast(cpp_dec_float_elem_digits10)); - while(static_cast(shift-- % mp_elem_digits10) != static_cast(0)) + while(static_cast(shift-- % cpp_dec_float_elem_digits10) != static_cast(0)) { d *= 10.0; --e; @@ -2111,7 +2118,7 @@ cpp_dec_float::cpp_dec_float(const double mantissa, const long long ex std::fill(data.begin(), data.end(), static_cast(0u)); - static const boost::int32_t digit_ratio = static_cast(static_cast(std::numeric_limits::digits10) / static_cast(mp_elem_digits10)); + static const boost::int32_t digit_ratio = static_cast(static_cast(std::numeric_limits::digits10) / static_cast(cpp_dec_float_elem_digits10)); static const boost::int32_t digit_loops = static_cast(digit_ratio + static_cast(2)); for(boost::int32_t i = static_cast(0); i < digit_loops; i++) @@ -2119,7 +2126,7 @@ cpp_dec_float::cpp_dec_float(const double mantissa, const long long ex boost::uint32_t n = static_cast(static_cast(d)); data[i] = static_cast(n); d -= static_cast(n); - d *= static_cast(mp_elem_mask); + d *= static_cast(cpp_dec_float_elem_mask); } } @@ -2180,33 +2187,33 @@ void cpp_dec_float::from_unsigned_long_long(const unsigned long long u exp = static_cast(0); neg = false; - fpclass = mp_finite; - prec_elem = mp_elem_number; + fpclass = cpp_dec_float_finite; + prec_elem = cpp_dec_float_elem_number; std::size_t i =static_cast(0u); unsigned long long uu = u; - boost::uint32_t temp[(std::numeric_limits::digits10 / static_cast(mp_elem_digits10)) + 3] = { static_cast(0u) }; + boost::uint32_t temp[(std::numeric_limits::digits10 / static_cast(cpp_dec_float_elem_digits10)) + 3] = { static_cast(0u) }; while(uu != static_cast(0u)) { - temp[i] = static_cast(uu % static_cast(mp_elem_mask)); - uu = static_cast(uu / static_cast(mp_elem_mask)); + temp[i] = static_cast(uu % static_cast(cpp_dec_float_elem_mask)); + uu = static_cast(uu / static_cast(cpp_dec_float_elem_mask)); ++i; } if(i > static_cast(1u)) { - exp += static_cast((i - 1u) * static_cast(mp_elem_digits10)); + exp += static_cast((i - 1u) * static_cast(cpp_dec_float_elem_digits10)); } std::reverse(temp, temp + i); - std::copy(temp, temp + (std::min)(i, static_cast(mp_elem_number)), data.begin()); + std::copy(temp, temp + (std::min)(i, static_cast(cpp_dec_float_elem_number)), data.begin()); } template -void cpp_dec_float::mul_loop_uv(const boost::uint32_t* const u, const boost::uint32_t* const v, boost::uint32_t* const w, const boost::int32_t p) +boost::uint32_t cpp_dec_float::mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p) { // // There is a limit on how many limbs this algorithm can handle without dropping digits @@ -2214,24 +2221,24 @@ void cpp_dec_float::mul_loop_uv(const boost::uint32_t* const u, const // // FLOOR( (2^64 - 1) / (10^8 * 10^8) ) == 1844 // - BOOST_STATIC_ASSERT_MSG(mp_elem_number < 1800, "Too many limbs in the data type for the multiplication algorithm - unsupported precision in cpp_dec_float."); + BOOST_STATIC_ASSERT_MSG(cpp_dec_float_elem_number < 1800, "Too many limbs in the data type for the multiplication algorithm - unsupported precision in cpp_dec_float."); boost::uint64_t carry = static_cast(0u); for(boost::int32_t j = static_cast(p - 1u); j >= static_cast(0); j--) { - boost::uint64_t sum = carry; + boost::uint64_t sum = carry; - for(boost::int32_t i = j; i >= static_cast(0); i--) - { - sum += static_cast(u[i] * static_cast(v[j - i])); - } + for(boost::int32_t i = j; i >= static_cast(0); i--) + { + sum += static_cast(u[j - i] * static_cast(v[i])); + } - w[j + 1] = static_cast(sum % static_cast(mp_elem_mask)); - carry = static_cast(sum / static_cast(mp_elem_mask)); + u[j] = static_cast(sum % static_cast(cpp_dec_float_elem_mask)); + carry = static_cast(sum / static_cast(cpp_dec_float_elem_mask)); } - w[0u] = static_cast(carry); + return static_cast(carry); } template @@ -2243,8 +2250,8 @@ boost::uint32_t cpp_dec_float::mul_loop_n(boost::uint32_t* const u, bo for(boost::int32_t j = p - 1; j >= static_cast(0); j--) { const boost::uint64_t t = static_cast(carry + static_cast(u[j] * static_cast(n))); - carry = static_cast(t / static_cast(mp_elem_mask)); - u[j] = static_cast(t - static_cast(static_cast(mp_elem_mask) * static_cast(carry))); + carry = static_cast(t / static_cast(cpp_dec_float_elem_mask)); + u[j] = static_cast(t - static_cast(static_cast(cpp_dec_float_elem_mask) * static_cast(carry))); } return static_cast(carry); @@ -2257,7 +2264,7 @@ boost::uint32_t cpp_dec_float::div_loop_n(boost::uint32_t* const u, bo for(boost::int32_t j = static_cast(0); j < p; j++) { - const boost::uint64_t t = static_cast(u[j] + static_cast(prev * static_cast(mp_elem_mask))); + const boost::uint64_t t = static_cast(u[j] + static_cast(prev * static_cast(cpp_dec_float_elem_mask))); u[j] = static_cast(t / n); prev = static_cast(t - static_cast(n * static_cast(u[j]))); } @@ -2274,261 +2281,261 @@ cpp_dec_float cpp_dec_float::pow2(const long long p) init.do_nothing(); static const boost::array, 255u> p2_data = {{ - cpp_dec_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"), - cpp_dec_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"), - cpp_dec_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"), - cpp_dec_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"), - cpp_dec_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"), - cpp_dec_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"), - cpp_dec_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"), - cpp_dec_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"), - cpp_dec_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"), - cpp_dec_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"), - cpp_dec_float("6.018531076210112040799931070577897870431567650673088110124808736145496368408203125000000000000000000e-36"), - cpp_dec_float("1.203706215242022408159986214115579574086313530134617622024961747229099273681640625000000000000000000e-35"), - cpp_dec_float("2.407412430484044816319972428231159148172627060269235244049923494458198547363281250000000000000000000e-35"), - cpp_dec_float("4.814824860968089632639944856462318296345254120538470488099846988916397094726562500000000000000000000e-35"), - cpp_dec_float("9.629649721936179265279889712924636592690508241076940976199693977832794189453125000000000000000000000e-35"), - cpp_dec_float("1.925929944387235853055977942584927318538101648215388195239938795566558837890625000000000000000000000e-34"), - cpp_dec_float("3.851859888774471706111955885169854637076203296430776390479877591133117675781250000000000000000000000e-34"), - cpp_dec_float("7.703719777548943412223911770339709274152406592861552780959755182266235351562500000000000000000000000e-34"), - cpp_dec_float("1.540743955509788682444782354067941854830481318572310556191951036453247070312500000000000000000000000e-33"), - cpp_dec_float("3.081487911019577364889564708135883709660962637144621112383902072906494140625000000000000000000000000e-33"), - cpp_dec_float("6.162975822039154729779129416271767419321925274289242224767804145812988281250000000000000000000000000e-33"), - cpp_dec_float("1.232595164407830945955825883254353483864385054857848444953560829162597656250000000000000000000000000e-32"), - cpp_dec_float("2.465190328815661891911651766508706967728770109715696889907121658325195312500000000000000000000000000e-32"), - cpp_dec_float("4.930380657631323783823303533017413935457540219431393779814243316650390625000000000000000000000000000e-32"), - cpp_dec_float("9.860761315262647567646607066034827870915080438862787559628486633300781250000000000000000000000000000e-32"), - cpp_dec_float("1.972152263052529513529321413206965574183016087772557511925697326660156250000000000000000000000000000e-31"), - cpp_dec_float("3.944304526105059027058642826413931148366032175545115023851394653320312500000000000000000000000000000e-31"), - cpp_dec_float("7.888609052210118054117285652827862296732064351090230047702789306640625000000000000000000000000000000e-31"), - cpp_dec_float("1.577721810442023610823457130565572459346412870218046009540557861328125000000000000000000000000000000e-30"), - 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cpp_dec_float("5.169878828456422967946304325437267834786325693130493164062500000000000000000000000000000000000000000e-26"), + cpp_dec_float("1.033975765691284593589260865087453566957265138626098632812500000000000000000000000000000000000000000e-25"), + cpp_dec_float("2.067951531382569187178521730174907133914530277252197265625000000000000000000000000000000000000000000e-25"), + cpp_dec_float("4.135903062765138374357043460349814267829060554504394531250000000000000000000000000000000000000000000e-25"), + cpp_dec_float("8.271806125530276748714086920699628535658121109008789062500000000000000000000000000000000000000000000e-25"), + cpp_dec_float("1.654361225106055349742817384139925707131624221801757812500000000000000000000000000000000000000000000e-24"), + cpp_dec_float("3.308722450212110699485634768279851414263248443603515625000000000000000000000000000000000000000000000e-24"), + 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cpp_dec_float("2.273736754432320594787597656250000000000000000000000000000000000000000000000000000000000000000000000e-13"), + cpp_dec_float("4.547473508864641189575195312500000000000000000000000000000000000000000000000000000000000000000000000e-13"), + cpp_dec_float("9.094947017729282379150390625000000000000000000000000000000000000000000000000000000000000000000000000e-13"), + cpp_dec_float("1.818989403545856475830078125000000000000000000000000000000000000000000000000000000000000000000000000e-12"), + cpp_dec_float("3.637978807091712951660156250000000000000000000000000000000000000000000000000000000000000000000000000e-12"), + cpp_dec_float("7.275957614183425903320312500000000000000000000000000000000000000000000000000000000000000000000000000e-12"), + cpp_dec_float("1.455191522836685180664062500000000000000000000000000000000000000000000000000000000000000000000000000e-11"), + cpp_dec_float("2.910383045673370361328125000000000000000000000000000000000000000000000000000000000000000000000000000e-11"), + cpp_dec_float("5.820766091346740722656250000000000000000000000000000000000000000000000000000000000000000000000000000e-11"), + cpp_dec_float("1.164153218269348144531250000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), + cpp_dec_float("2.328306436538696289062500000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), + cpp_dec_float("4.656612873077392578125000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), + cpp_dec_float("9.313225746154785156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), + cpp_dec_float("1.862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), + cpp_dec_float("3.725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), + cpp_dec_float("7.450580596923828125000000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), + cpp_dec_float("1.490116119384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), + cpp_dec_float("2.980232238769531250000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), + cpp_dec_float("5.960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), + cpp_dec_float("1.192092895507812500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), + cpp_dec_float("2.384185791015625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), + cpp_dec_float("4.768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), + cpp_dec_float("9.536743164062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), + cpp_dec_float("1.907348632812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), + cpp_dec_float("3.814697265625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), + cpp_dec_float("7.629394531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), + cpp_dec_float("0.000015258789062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000030517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000061035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000122070312500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000244140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000488281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.001953125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.003906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.007812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.01562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.03125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.06250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.125"), + cpp_dec_float("0.25"), + cpp_dec_float("0.5"), + one(), + two(), + cpp_dec_float(static_cast(4)), + cpp_dec_float(static_cast(8)), + cpp_dec_float(static_cast(16)), + cpp_dec_float(static_cast(32)), + cpp_dec_float(static_cast(64)), + cpp_dec_float(static_cast(128)), + cpp_dec_float(static_cast(256)), + cpp_dec_float(static_cast(512)), + cpp_dec_float(static_cast(1024)), + cpp_dec_float(static_cast(2048)), + cpp_dec_float(static_cast(4096)), + cpp_dec_float(static_cast(8192)), + cpp_dec_float(static_cast(16384)), + cpp_dec_float(static_cast(32768)), + cpp_dec_float(static_cast(65536)), + cpp_dec_float(static_cast(131072)), + cpp_dec_float(static_cast(262144)), + cpp_dec_float(static_cast(524288)), + cpp_dec_float(static_cast(1uL << 20u)), + cpp_dec_float(static_cast(1uL << 21u)), + cpp_dec_float(static_cast(1uL << 22u)), + cpp_dec_float(static_cast(1uL << 23u)), + cpp_dec_float(static_cast(1uL << 24u)), + cpp_dec_float(static_cast(1uL << 25u)), + cpp_dec_float(static_cast(1uL << 26u)), + cpp_dec_float(static_cast(1uL << 27u)), + cpp_dec_float(static_cast(1uL << 28u)), + cpp_dec_float(static_cast(1uL << 29u)), + cpp_dec_float(static_cast(1uL << 30u)), + cpp_dec_float(static_cast(1uL << 31u)), + cpp_dec_float(static_cast(1uLL << 32u)), + cpp_dec_float(static_cast(1uLL << 33u)), + cpp_dec_float(static_cast(1uLL << 34u)), + cpp_dec_float(static_cast(1uLL << 35u)), + cpp_dec_float(static_cast(1uLL << 36u)), + cpp_dec_float(static_cast(1uLL << 37u)), + cpp_dec_float(static_cast(1uLL << 38u)), + cpp_dec_float(static_cast(1uLL << 39u)), + cpp_dec_float(static_cast(1uLL << 40u)), + cpp_dec_float(static_cast(1uLL << 41u)), + cpp_dec_float(static_cast(1uLL << 42u)), + cpp_dec_float(static_cast(1uLL << 43u)), + cpp_dec_float(static_cast(1uLL << 44u)), + cpp_dec_float(static_cast(1uLL << 45u)), + cpp_dec_float(static_cast(1uLL << 46u)), + cpp_dec_float(static_cast(1uLL << 47u)), + cpp_dec_float(static_cast(1uLL << 48u)), + cpp_dec_float(static_cast(1uLL << 49u)), + cpp_dec_float(static_cast(1uLL << 50u)), + cpp_dec_float(static_cast(1uLL << 51u)), + cpp_dec_float(static_cast(1uLL << 52u)), + cpp_dec_float(static_cast(1uLL << 53u)), + cpp_dec_float(static_cast(1uLL << 54u)), + cpp_dec_float(static_cast(1uLL << 55u)), + cpp_dec_float(static_cast(1uLL << 56u)), + cpp_dec_float(static_cast(1uLL << 57u)), + cpp_dec_float(static_cast(1uLL << 58u)), + cpp_dec_float(static_cast(1uLL << 59u)), + cpp_dec_float(static_cast(1uLL << 60u)), + cpp_dec_float(static_cast(1uLL << 61u)), + cpp_dec_float(static_cast(1uLL << 62u)), + cpp_dec_float(static_cast(1uLL << 63u)), + cpp_dec_float("1.844674407370955161600000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), + cpp_dec_float("3.689348814741910323200000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), + cpp_dec_float("7.378697629483820646400000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), + cpp_dec_float("1.475739525896764129280000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), + cpp_dec_float("2.951479051793528258560000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), + cpp_dec_float("5.902958103587056517120000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), + cpp_dec_float("1.180591620717411303424000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), + cpp_dec_float("2.361183241434822606848000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), + cpp_dec_float("4.722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), + cpp_dec_float("9.444732965739290427392000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), + cpp_dec_float("1.888946593147858085478400000000000000000000000000000000000000000000000000000000000000000000000000000e22"), + cpp_dec_float("3.777893186295716170956800000000000000000000000000000000000000000000000000000000000000000000000000000e22"), + cpp_dec_float("7.555786372591432341913600000000000000000000000000000000000000000000000000000000000000000000000000000e22"), + cpp_dec_float("1.511157274518286468382720000000000000000000000000000000000000000000000000000000000000000000000000000e23"), + cpp_dec_float("3.022314549036572936765440000000000000000000000000000000000000000000000000000000000000000000000000000e23"), + cpp_dec_float("6.044629098073145873530880000000000000000000000000000000000000000000000000000000000000000000000000000e23"), + cpp_dec_float("1.208925819614629174706176000000000000000000000000000000000000000000000000000000000000000000000000000e24"), + cpp_dec_float("2.417851639229258349412352000000000000000000000000000000000000000000000000000000000000000000000000000e24"), + cpp_dec_float("4.835703278458516698824704000000000000000000000000000000000000000000000000000000000000000000000000000e24"), + cpp_dec_float("9.671406556917033397649408000000000000000000000000000000000000000000000000000000000000000000000000000e24"), + cpp_dec_float("1.934281311383406679529881600000000000000000000000000000000000000000000000000000000000000000000000000e25"), + cpp_dec_float("3.868562622766813359059763200000000000000000000000000000000000000000000000000000000000000000000000000e25"), + cpp_dec_float("7.737125245533626718119526400000000000000000000000000000000000000000000000000000000000000000000000000e25"), + cpp_dec_float("1.547425049106725343623905280000000000000000000000000000000000000000000000000000000000000000000000000e26"), + cpp_dec_float("3.094850098213450687247810560000000000000000000000000000000000000000000000000000000000000000000000000e26"), + cpp_dec_float("6.189700196426901374495621120000000000000000000000000000000000000000000000000000000000000000000000000e26"), + cpp_dec_float("1.237940039285380274899124224000000000000000000000000000000000000000000000000000000000000000000000000e27"), + cpp_dec_float("2.475880078570760549798248448000000000000000000000000000000000000000000000000000000000000000000000000e27"), + cpp_dec_float("4.951760157141521099596496896000000000000000000000000000000000000000000000000000000000000000000000000e27"), + cpp_dec_float("9.903520314283042199192993792000000000000000000000000000000000000000000000000000000000000000000000000e27"), + cpp_dec_float("1.980704062856608439838598758400000000000000000000000000000000000000000000000000000000000000000000000e28"), + cpp_dec_float("3.961408125713216879677197516800000000000000000000000000000000000000000000000000000000000000000000000e28"), + cpp_dec_float("7.922816251426433759354395033600000000000000000000000000000000000000000000000000000000000000000000000e28"), + cpp_dec_float("1.584563250285286751870879006720000000000000000000000000000000000000000000000000000000000000000000000e29"), + cpp_dec_float("3.169126500570573503741758013440000000000000000000000000000000000000000000000000000000000000000000000e29"), + cpp_dec_float("6.338253001141147007483516026880000000000000000000000000000000000000000000000000000000000000000000000e29"), + cpp_dec_float("1.267650600228229401496703205376000000000000000000000000000000000000000000000000000000000000000000000e30"), + cpp_dec_float("2.535301200456458802993406410752000000000000000000000000000000000000000000000000000000000000000000000e30"), + cpp_dec_float("5.070602400912917605986812821504000000000000000000000000000000000000000000000000000000000000000000000e30"), + cpp_dec_float("1.014120480182583521197362564300800000000000000000000000000000000000000000000000000000000000000000000e31"), + cpp_dec_float("2.028240960365167042394725128601600000000000000000000000000000000000000000000000000000000000000000000e31"), + cpp_dec_float("4.056481920730334084789450257203200000000000000000000000000000000000000000000000000000000000000000000e31"), + cpp_dec_float("8.112963841460668169578900514406400000000000000000000000000000000000000000000000000000000000000000000e31"), + cpp_dec_float("1.622592768292133633915780102881280000000000000000000000000000000000000000000000000000000000000000000e32"), + cpp_dec_float("3.245185536584267267831560205762560000000000000000000000000000000000000000000000000000000000000000000e32"), + cpp_dec_float("6.490371073168534535663120411525120000000000000000000000000000000000000000000000000000000000000000000e32"), + cpp_dec_float("1.298074214633706907132624082305024000000000000000000000000000000000000000000000000000000000000000000e33"), + cpp_dec_float("2.596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000e33"), + cpp_dec_float("5.192296858534827628530496329220096000000000000000000000000000000000000000000000000000000000000000000e33"), + cpp_dec_float("1.038459371706965525706099265844019200000000000000000000000000000000000000000000000000000000000000000e34"), + cpp_dec_float("2.076918743413931051412198531688038400000000000000000000000000000000000000000000000000000000000000000e34"), + cpp_dec_float("4.153837486827862102824397063376076800000000000000000000000000000000000000000000000000000000000000000e34"), + cpp_dec_float("8.307674973655724205648794126752153600000000000000000000000000000000000000000000000000000000000000000e34"), + cpp_dec_float("1.661534994731144841129758825350430720000000000000000000000000000000000000000000000000000000000000000e35"), + cpp_dec_float("3.323069989462289682259517650700861440000000000000000000000000000000000000000000000000000000000000000e35"), + cpp_dec_float("6.646139978924579364519035301401722880000000000000000000000000000000000000000000000000000000000000000e35"), + cpp_dec_float("1.329227995784915872903807060280344576000000000000000000000000000000000000000000000000000000000000000e36"), + cpp_dec_float("2.658455991569831745807614120560689152000000000000000000000000000000000000000000000000000000000000000e36"), + cpp_dec_float("5.316911983139663491615228241121378304000000000000000000000000000000000000000000000000000000000000000e36"), + cpp_dec_float("1.063382396627932698323045648224275660800000000000000000000000000000000000000000000000000000000000000e37"), + cpp_dec_float("2.126764793255865396646091296448551321600000000000000000000000000000000000000000000000000000000000000e37"), + cpp_dec_float("4.253529586511730793292182592897102643200000000000000000000000000000000000000000000000000000000000000e37"), + cpp_dec_float("8.507059173023461586584365185794205286400000000000000000000000000000000000000000000000000000000000000e37"), + cpp_dec_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38") }}; if((p > static_cast(-128)) && (p < static_cast(+128))) @@ -2860,7 +2867,7 @@ namespace std static const boost::int64_t min_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp10; // Type differs from int. static const boost::int64_t max_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp; // Type differs from int. static const boost::int64_t max_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp10; // Type differs from int. - static const int radix = boost::multiprecision::cpp_dec_float::mp_radix; + static const int radix = boost::multiprecision::cpp_dec_float::cpp_dec_float_radix; static const std::float_round_style round_style = std::round_to_nearest; static const bool has_infinity = true; static const bool has_quiet_NaN = true; diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 8a064ad9..006df7b0 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -322,6 +322,13 @@ run test_exp.cpp TEST_CPP_DEC_FLOAT : test_exp_cpp_dec_float ; +run test_sqrt.cpp + : # command line + : # input files + : # requirements + TEST_CPP_DEC_FLOAT + : test_sqrt_cpp_dec_float ; + run test_log.cpp : # command line : # input files diff --git a/test/math/test_bessel_i.cpp b/test/math/test_bessel_i.cpp index e9d09955..0b59d0b9 100644 --- a/test/math/test_bessel_i.cpp +++ b/test/math/test_bessel_i.cpp @@ -81,6 +81,7 @@ int test_main(int, char* []) expected_results(); // // Test at: + // 9 decimal digits: tests the least wide arbitrary precision code // 18 decimal digits: tests 80-bit long double approximations // 30 decimal digits: tests 128-bit long double approximations // 35 decimal digits: tests arbitrary precision code @@ -97,6 +98,7 @@ int test_main(int, char* []) test_bessel(mp_number >(), "mp_number >"); #endif #ifdef TEST_CPP_DEC_FLOAT + test_bessel(mp_number >(), "mp_number >"); test_bessel(mp_number >(), "mp_number >"); test_bessel(mp_number >(), "mp_number >"); test_bessel(mp_number >(), "mp_number >"); diff --git a/test/math/test_zeta.cpp b/test/math/test_zeta.cpp index e9db0af5..bc3d773a 100644 --- a/test/math/test_zeta.cpp +++ b/test/math/test_zeta.cpp @@ -77,6 +77,7 @@ int test_main(int, char* []) expected_results(); // // Test at: + // 9 decimal digits: tests the least wide arbitrary precision code // 18 decimal digits: tests 80-bit long double approximations // 30 decimal digits: tests 128-bit long double approximations // 35 decimal digits: tests arbitrary precision code @@ -92,6 +93,7 @@ int test_main(int, char* []) test_zeta(mp_number >(), "mp_number >"); #endif #ifdef TEST_CPP_DEC_FLOAT + test_zeta(mp_number >(), "mp_number >"); test_zeta(mp_number >(), "mp_number >"); test_zeta(mp_number >(), "mp_number >"); test_zeta(mp_number >(), "mp_number >"); diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 64178d58..7adb1afa 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -107,6 +107,9 @@ int main() test > >(); test > >(); test > >(); + // Check low multiprecision digit counts. + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_atan.cpp b/test/test_atan.cpp index d1ee181c..2061afa9 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -253,6 +253,9 @@ int main() test > >(); test > >(); test > >(); + // Check low multiprecision digit counts. + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_exp.cpp b/test/test_exp.cpp index 7bd32666..6644b750 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -189,6 +189,9 @@ int main() test > >(); test > >(); test > >(); + // Check low multiprecision digit counts. + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_log.cpp b/test/test_log.cpp index fcd628f6..084c50c2 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -217,6 +217,9 @@ int main() test > >(); test > >(); test > >(); + // Check low multiprecision digit counts. + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_pow.cpp b/test/test_pow.cpp index e98be847..315ad995 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -592,6 +592,9 @@ int main() test > >(); test > >(); test > >(); + // Check low multiprecision digit counts. + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_sin.cpp b/test/test_sin.cpp index 708fe5e8..06f035d1 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -301,6 +301,9 @@ int main() test > >(); test > >(); test > >(); + // Check low multiprecision digit counts. + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index 8ba7078b..7f6c6320 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -225,6 +225,9 @@ int main() test > >(); test > >(); test > >(); + // Check low multiprecision digit counts. + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp index df50cf9f..3f01cbbd 100644 --- a/test/test_sqrt.cpp +++ b/test/test_sqrt.cpp @@ -50,109 +50,109 @@ void test() static const boost::array data = {{ "0", - "1.7724538509055160272981674833411451827975494561223871282138077898529112845910321813749506567385446654162268236242825706662361528657244226025250937096027870684620376986531051228499251730289508262289320953792679628001746390153514797205167001901852340185854469744949126403139217755259062164054193325009063984076137334774751534336679897893658518364087954511651617387600590673934317913328098548462481849021", - "2.506628274631000502415765284811045253006986740609938316629923576342293654607841974946595838378057266116009972665203879644866323618126736180957855655966147931913435480458123731137327804313019938802647150234465504898425802329413862779668683613033675823844181156078490095600041375150275291651461225843861864920699060926664091188015739697252377702538748247848633488642597506589513095738763427251926880402", - 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"4.6894720998347514072224884956178300284641581320824106981633983758453256799744598320502835518976559264849872655758786968460389643339445673551269229241587961003379434250163073293499620997874074698516457801989721178630024470871191608919926005831108426583129390228179129584616970283973090935125037470398636450816554023533350528106738423929159432353981681442386558251657700009494385592281294126884159744657", - "5.0132565492620010048315305696220905060139734812198766332598471526845873092156839498931916767561145322320199453304077592897326472362534723619157113119322958638268709609162474622746556086260398776052943004689310097968516046588277255593373672260673516476883623121569801912000827503005505833029224516877237298413981218533281823760314793945047554050774964956972669772851950131790261914775268545038537608041", - 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}}; - T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"; + T pi = "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913152"; unsigned max_err = 0; for(unsigned k = 0; k < data.size(); k++) @@ -195,6 +195,12 @@ int main() test > >(); test > >(); test > >(); + // Check low multiprecision digit counts. + test > >(); + test > >(); + // Check up to 1000 multiprecision digits. + test > >(); + test > >(); #endif return boost::report_errors(); } From 101137773525a0c784919aabc078ad866c667a1e Mon Sep 17 00:00:00 2001 From: Christopher Kormanyos Date: Fri, 20 Apr 2012 20:48:32 +0000 Subject: [PATCH 177/256] - Added generic examples LaTeX source documentation. [SVN r78102] --- .../generic_numerics/generic_numerics.pdf | Bin 0 -> 98380 bytes .../generic_numerics/generic_numerics.tcp | 12 + .../generic_numerics/generic_numerics.tex | 314 ++++++++++++++++++ .../generic_area_of_a_circle.cpp | 45 +++ .../generic_derivative.cpp | 79 +++++ .../generic_numerics_src/generic_integral.cpp | 105 ++++++ 6 files changed, 555 insertions(+) create mode 100644 example/generic_numerics_examples/generic_numerics/generic_numerics.pdf create mode 100644 example/generic_numerics_examples/generic_numerics/generic_numerics.tcp create mode 100644 example/generic_numerics_examples/generic_numerics/generic_numerics.tex create mode 100644 example/generic_numerics_examples/generic_numerics_src/generic_area_of_a_circle.cpp create mode 100644 example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp create mode 100644 example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp diff --git 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zqCDFlk?g&A0sZsEn16#JqbV*SsR2My)&3I}Vu!oDvJ(pNGRv<3{S4*rWP$Fy1MWa%?@Sir!!IoSdjdp!{v|W_zd^YwEh8$e#H~sI)*h^_ zv8uC`Jg=%H7EdsMqJV2Fd-52$FL$836Pft*D|>!M_qU^VYT*5E;Qmc7aCd9XKgu;Fo1^n-6{b#Vms`>wArj+OvZ3Pu>d3z@_1#7(ZzFb7?TT|gX*D+va z|Lx14dW`?#OX&VBTnT#vX9pZ~tnGpI9XP|tnHdvzaAL)Qpg+0I!;)7N3;8rKKSjk0(M>Gc~gV0pCBN@&1Gcg7IMha7Y-4^A||2 z9UH5YEzX1-0zyH^0Y%Thzkss@638DD(BC#F1_L;f_yxlMW8>!sJiglofe<%=T{a97 zg8`~yw+#?*1y-ItHaHxJ*=`#WL5$-b8$WU9-fcr6A^XRL@$Y*t3bk)s2m<~G8;qFA zyT*XPps>9*3=)X~_TydcFh~?;Z#xJI1$b_EI|vHFzZWwEfrReEjD#Zg+8}6t^u96B z=>79Rp^53f3m*i7!0hV}14jc3%kFk)3~j|~XsKFk;tbRQNB3b8LYFqr*uL!kDL zi^1%h8x(@vHwIuMo|<-Hh60Y>I}a!zRJ#`+6p94oTlc&dMy!xMHVlNg6YU-Y14HiZ z4~Bxn_Rbdul+fNW;Bd^o`T(?aQG3TlK>7EzL%@Kj@4q4(wnKMb+2KYkehz8u0J_VVH1b{z!@g~+FVz`LMNLdMxt`Hg_j*>z^ zAmZY1xC9C&iUHCRA|` + +using boost::math::constants::pi; + +template +inline T area_of_a_circle(T r) +{ + return pi() * (r * r); +} +\end{lstlisting} + +It is possible to use {\lstinline|area_of_a_circle()|} +with built-in floating-point types as well as floating-point +types from {\lstinline|Boost|}.{\lstinline|Multiprecision|}. +In particular, consider a system with $4$--byte single-precision +{\lstinline|float|}, $8$--byte double-precision {\lstinline|double|} +and also the {\lstinline|cpp_dec_float_50|} data type +from {\lstinline|Boost|}.{\lstinline|Multiprecision|} +with $50$~decimal digits of precision. + +We can compute and print the approximate area of a circle with +radius~$123/\,100$ for {\lstinline|float|}, {\lstinline|double|} +and {\lstinline|cpp_dec_float_50|} with the program below. + +\begin{lstlisting} +#include +#include +#include + +using boost::multiprecision::cpp_dec_float_50; + +int main(int, char**) +{ + const float r_f(float(123) / 100); + const float a_f = area_of_a_circle(r_f); + + const double r_d(double(123) / 100); + const double a_d = area_of_a_circle(r_d); + + const cpp_dec_float_50 r_mp(cpp_dec_float_50(123) / 100); + const cpp_dec_float_50 a_mp = area_of_a_circle(r_mp); + + // 4.75292 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_f + << std::endl; + + // 4.752915525616 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_d + << std::endl; + + // 4.7529155256159981904701331745635599135018975843146 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_mp + << std::endl; +} +\end{lstlisting} + +Let's add even more power to generic numeric programming +using not only different floating-point types +but also function objects as template parameters. +Consider some well-known central difference rules for +numerically computing the first derivative of a +function~$f^{\prime}(x)$ with $x\in\mathbb{R}$. + +\begin{eqnarray} +f^{\prime}\left(x\right) &\,\approx\,& m_{1} + \,+\, O(dx^{2}) \nonumber \\[3pt] +f^{\prime}\left(x\right) &\,\approx\,& \frac{4}{3}m_{1} + \,-\, \frac{1}{3}m_{2} + \,+\, O(dx^{4}) \nonumber \\[3pt] +f^{\prime}\left(x\right) &\,\approx\,& \frac{3}{2}m_{1} + \,-\, \frac{3}{5}m_{2} + \,+\, \frac{1}{10}m_{3} + \,+\, O(dx^{6})\,{\text{,}} +\label{equation:centraldiffderiv} +\end{eqnarray} + +\noindent where the difference terms $m_{n}$ are given by + +\begin{eqnarray} +m_{1} &\,=\,& \dfrac{f\left(x+ dx\right) + \,-\, f\left(x- dx\right)}{2\,dx} \nonumber \\[3pt] +m_{2} &\,=\,& \dfrac{f\left(x+2dx\right) + \,-\, f\left(x-2dx\right)}{4\,dx} \nonumber \\[3pt] +m_{3} &\,=\,& \dfrac{f\left(x+3dx\right) + \,-\, f\left(x-3dx\right)}{6\,dx}\,\,{\text{,}} +\end{eqnarray} + +\noindent and $dx$ is the step-size of the derivative. + +The third formula in Equation~\ref{equation:centraldiffderiv} +is a three-point central difference rule. It calculates +the first derivative of $f(x)$~to $O(dx^{6})$, where~$dx$ +is the given step-size. For example, if the step-size is~$0.01$ +this derivative calculation has about $6$~decimal digits +of precision---just about right for the $7$~decimal digits +of single-precision {\lstinline|float|}. + +Let's make a generic template subroutine using this +three-point central difference rule. In particular, + +\begin{lstlisting} +template +value_type derivative(const value_type x, + const value_type dx, + function_type func) +{ + // Compute d/dx[func(*first)] using a three-point + // central difference rule of O(dx^6). + + const value_type dx1 = dx; + const value_type dx2 = dx1 * 2; + const value_type dx3 = dx1 * 3; + + const value_type m1 = ( func(x + dx1) + - func(x - dx1)) / 2; + const value_type m2 = ( func(x + dx2) + - func(x - dx2)) / 4; + const value_type m3 = ( func(x + dx3) + - func(x - dx3)) / 6; + + const value_type fifteen_m1 = 15 * m1; + const value_type six_m2 = 6 * m2; + const value_type ten_dx1 = 10 * dx1; + + return ((fifteen_m1 - six_m2) + m3) / ten_dx1; +} +\end{lstlisting} + +The {\lstinline|derivative()|} template function can be used to compute +the first derivative of any function to $O(dx^{6})$. For example, +consider the first derivative of $\sin{x}$ evaluated at $x\,=\,\pi/\,3$. +In other words, + +\begin{equation} +\dfrac{d}{dx}\,\sin{x} +\biggr\vert_{x=\frac{\pi}{3}} +\,=\, \cos{\dfrac{\pi}{3}} +\,=\, \dfrac{1}{2}\,{\text{.}} +\label{equation:SinDerivative} +\end{equation} + +The code below computes the derivative in +Equation~\ref{equation:SinDerivative} for +{\lstinline|float|}, {\lstinline|double|} +and boost's multiple-precision type +{\lstinline|cpp_dec_float_50|}. The code uses the +{\lstinline|derivative()|} function in combination with +a lambda expression. + +\begin{lstlisting} +#include +#include +#include +#include + +using boost::math::constants::pi; +using boost::multiprecision::cpp_dec_float_50; + +int main(int, char**) +{ + const float d_f = + derivative(float(pi() / 3), + 0.01F, + [](const float x) -> float + { + return ::sin(x); + }); + + const double d_d = + derivative(double(pi() / 3), + 0.001, + [](const double x) -> double + { + return ::sin(x); + }); + + const cpp_dec_float_50 d_mp = + derivative(cpp_dec_float_50(pi() / 3), + cpp_dec_float_50(1.0E-9), + [](const cpp_dec_float_50 x) -> cpp_dec_float_50 + { + return boost::multiprecision::sin(x); + }); + + // 0.500003 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_f + << std::endl; + + // 0.499999999999888 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_d + << std::endl; + + // 0.50000000000000000000000000000000000000000003925935 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_mp + << std::endl; +} +\end{lstlisting} + +The expected value of the derivative is $0.5$. +This central difference rule in this example +is ill-conditioned, meaning it suffers from slight +loss of precision. With that in mind, the results agree +with the expected value of~$0.5$. + +A generic numerical integration template similar to the +{\lstinline|derivative()|} template is shown below. + +\begin{lstlisting} +template +inline value_type integral(const value_type a, + const value_type b, + const value_type tol, + function_type func) +{ + unsigned n = 1U; + + value_type h = (b - a); + value_type I = (func(a) + func(b)) * (h / 2); + + for(unsigned k = 0U; k < 8U; k++) + { + h /= 2; + + value_type sum(0); + for(unsigned j = 1U; j <= n; j++) + { + sum += func(a + (value_type((j * 2) - 1) * h)); + } + + const value_type I0 = I; + I = (I / 2) + (h * sum); + + const value_type ratio = I0 / I; + const value_type delta = ratio - 1; + const value_type delta_abs = ((delta < 0) ? -delta : delta); + + if((k > 1U) && (delta_abs < tol)) + { + break; + } + + n *= 2U; + } + + return I; +} +\end{lstlisting} + +\end{document} diff --git a/example/generic_numerics_examples/generic_numerics_src/generic_area_of_a_circle.cpp b/example/generic_numerics_examples/generic_numerics_src/generic_area_of_a_circle.cpp new file mode 100644 index 00000000..e2d25b9f --- /dev/null +++ b/example/generic_numerics_examples/generic_numerics_src/generic_area_of_a_circle.cpp @@ -0,0 +1,45 @@ +#include + +using boost::math::constants::pi; + +template +inline T area_of_a_circle(T r) +{ + return pi() * (r * r); +} + +#include +#include +#include + +using boost::multiprecision::cpp_dec_float_50; + +int main(int, char**) +{ + const float r_f(float(123) / 100); + const float a_f = area_of_a_circle(r_f); + + const double r_d(double(123) / 100); + const double a_d = area_of_a_circle(r_d); + + const cpp_dec_float_50 r_mp(cpp_dec_float_50(123) / 100); + const cpp_dec_float_50 a_mp = area_of_a_circle(r_mp); + + // 4.75292 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_f + << std::endl; + + // 4.752915525616 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_d + << std::endl; + + // 4.7529155256159981904701331745635599135018975843146 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << a_mp + << std::endl; +} diff --git a/example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp b/example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp new file mode 100644 index 00000000..ccf0ad97 --- /dev/null +++ b/example/generic_numerics_examples/generic_numerics_src/generic_derivative.cpp @@ -0,0 +1,79 @@ +template +value_type derivative(const value_type x, + const value_type dx, + function_type func) +{ + // Compute d/dx[func(*first)] using a three-point + // central difference rule of O(dx^6). + + const value_type dx1 = dx; + const value_type dx2 = dx1 * 2; + const value_type dx3 = dx1 * 3; + + const value_type m1 = ( func(x + dx1) + - func(x - dx1)) / 2; + const value_type m2 = ( func(x + dx2) + - func(x - dx2)) / 4; + const value_type m3 = ( func(x + dx3) + - func(x - dx3)) / 6; + + const value_type fifteen_m1 = 15 * m1; + const value_type six_m2 = 6 * m2; + const value_type ten_dx1 = 10 * dx1; + + return ((fifteen_m1 - six_m2) + m3) / ten_dx1; +} + +#include +#include +#include +#include + +using boost::math::constants::pi; +using boost::multiprecision::cpp_dec_float_50; + +int main(int, char**) +{ + const float d_f = + derivative(float(pi() / 3), + 0.01F, + [](const float x) -> float + { + return ::sin(x); + }); + + const double d_d = + derivative(double(pi() / 3), + 0.001, + [](const double x) -> double + { + return ::sin(x); + }); + + const cpp_dec_float_50 d_mp = + derivative(cpp_dec_float_50(pi() / 3), + cpp_dec_float_50(1.0E-9), + [](const cpp_dec_float_50 x) -> cpp_dec_float_50 + { + return boost::multiprecision::sin(x); + }); + + // 0.500003 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_f + << std::endl; + + // 0.499999999999888 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_d + << std::endl; + + // 0.50000000000000000000000000000000000000000003925935 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << d_mp + << std::endl; +} diff --git a/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp b/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp new file mode 100644 index 00000000..787de062 --- /dev/null +++ b/example/generic_numerics_examples/generic_numerics_src/generic_integral.cpp @@ -0,0 +1,105 @@ +template +inline value_type integral(const value_type a, + const value_type b, + const value_type tol, + function_type func) +{ + unsigned n = 1U; + + value_type h = (b - a); + value_type I = (func(a) + func(b)) * (h / 2); + + for(unsigned k = 0U; k < 8U; k++) + { + h /= 2; + + value_type sum(0); + for(unsigned j = 1U; j <= n; j++) + { + sum += func(a + (value_type((j * 2) - 1) * h)); + } + + const value_type I0 = I; + I = (I / 2) + (h * sum); + + const value_type ratio = I0 / I; + const value_type delta = ratio - 1; + const value_type delta_abs = ((delta < 0) ? -delta : delta); + + if((k > 1U) && (delta_abs < tol)) + { + break; + } + + n *= 2U; + } + + return I; +} + +#include +#include +#include +#include + +template +class cyl_bessel_j_integral_rep +{ +public: + cyl_bessel_j_integral_rep(const unsigned N, + const value_type& X) : n(N), x(X) { } + + value_type operator()(const value_type& t) const + { + // pi * Jn(x) = Int_0^pi [cos(x * sin(t) - n*t) dt] + return cos(x * sin(t) - (n * t)); + } + +private: + const unsigned n; + const value_type x; +}; + + +int main(int, char**) +{ + using boost::math::constants::pi; + typedef boost::multiprecision::cpp_dec_float_50 mp_type; + + const float j2_f = + integral(0.0F, + pi(), + 0.01F, + cyl_bessel_j_integral_rep(2U, 1.23F)) / pi(); + + const double j2_d = + integral(0.0, + pi(), + 0.0001, + cyl_bessel_j_integral_rep(2U, 1.23)) / pi(); + + const mp_type j2_mp = + integral(mp_type(0), + pi(), + mp_type(1.0E-20), + cyl_bessel_j_integral_rep(2U, mp_type(123) / 100)) / pi(); + + // 0.166369 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_f + << std::endl; + + // 0.166369383786814 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_d + << std::endl; + + // 0.16636938378681407351267852431513159437103348245333 + std::cout + << std::setprecision(std::numeric_limits::digits10) + << j2_mp + << std::endl; +} From 0279459351a64e72d28285d11fd270f1947512fd Mon Sep 17 00:00:00 2001 From: Christopher Kormanyos Date: Fri, 20 Apr 2012 23:17:48 +0000 Subject: [PATCH 178/256] Ensure that potentially truncated digit counts in cpp_dec_float are properly used. [SVN r78105] --- include/boost/multiprecision/cpp_dec_float.hpp | 12 ++++++++---- 1 file changed, 8 insertions(+), 4 deletions(-) diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 74d3a3e5..499c50d3 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -1,6 +1,6 @@ /////////////////////////////////////////////////////////////////////////////// -// Copyright Christopher Kormanyos 2002 - 2011. -// Copyright 2011 John Maddock. Distributed under the Boost +// Copyright Christopher Kormanyos 2002 - 2012. +// Copyright 2012 John Maddock. Distributed under the Boost // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) // @@ -2860,7 +2860,7 @@ namespace std static const bool is_bounded = true; static const bool is_modulo = false; static const bool is_iec559 = false; - static const int digits = Digits10; + static const int digits = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; static const int digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; static const int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_total_digits10; static const boost::int64_t min_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp; // Type differs from int. @@ -2896,8 +2896,12 @@ namespace policies{ template struct precision< boost::multiprecision::mp_number, ExpressionTemplates>, Policy> { + // Define a local copy of cpp_dec_float_digits10 because it might differ + // from the template parameter Digits10 for small or large digit counts. + static const boost::int32_t cpp_dec_float_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; + typedef typename Policy::precision_type precision_type; - typedef digits2<((Digits10 + 1) * 1000L) / 301L> digits_2; + typedef digits2<((cpp_dec_float_digits10 + 1LL) * 1000LL) / 301LL> digits_2; typedef typename mpl::if_c< ((digits_2::value <= precision_type::value) || (Policy::precision_type::value <= 0)), From d2bc0f90f7da3fb47597f93ec71497253729aa70 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 4 May 2012 08:20:33 +0000 Subject: [PATCH 179/256] Change non-member functions to use enable_if so they're restricted to the number type to which they apply (better error messages). Enhance concept checks to check things which weren't previously tested. [SVN r78321] --- .../multiprecision/detail/default_ops.hpp | 281 +++++++++++++----- .../multiprecision/detail/functions/pow.hpp | 6 +- .../multiprecision/detail/functions/trig.hpp | 4 +- test/mp_number_concept_check.cpp | 114 +++++++ 4 files changed, 325 insertions(+), 80 deletions(-) diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 2f6f1b5f..8c58cc8d 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -484,6 +484,68 @@ inline void eval_round(T& result, const T& a) } } +template +inline typename enable_if, void>::type eval_pow(T& result, const T& x, const A& a) +{ + // Note this one is resticted to float arguments since pow.hpp already has a version for + // integer powers.... + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = a; + eval_pow(result, x, c); +} + +template +inline typename enable_if, void>::type eval_pow(T& result, const A& x, const T& a) +{ + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = x; + eval_pow(result, c, a); +} + +template +inline typename enable_if, void>::type eval_fmod(T& result, const T& x, const A& a) +{ + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = a; + eval_fmod(result, x, c); +} + +template +inline typename enable_if, void>::type eval_fmod(T& result, const A& x, const T& a) +{ + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = x; + eval_fmod(result, c, a); +} + +template +inline typename enable_if, void>::type eval_atan2(T& result, const T& x, const A& a) +{ + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = a; + eval_atan2(result, x, c); +} + +template +inline typename enable_if, void>::type eval_atan2(T& result, const A& x, const T& a) +{ + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = x; + eval_atan2(result, c, a); +} + template inline typename enable_if >::type eval_gcd(T& result, const T& a, const Arithmetic& b) { @@ -861,7 +923,7 @@ inline long long llround(const mp_number& v) } #endif -#define UNARY_OP_FUNCTOR(func)\ +#define UNARY_OP_FUNCTOR(func, category)\ namespace detail{\ template \ struct BOOST_JOIN(func, _funct)\ @@ -876,11 +938,12 @@ struct BOOST_JOIN(func, _funct)\ }\ \ template \ -inline detail::mp_exp<\ +inline typename enable_if_c >::value == category,\ + detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ -> \ + , detail::mp_exp >\ +>::type \ func(const detail::mp_exp& arg)\ {\ return detail::mp_exp<\ @@ -893,11 +956,12 @@ func(const detail::mp_exp& arg)\ );\ }\ template \ -inline detail::mp_exp<\ +inline typename enable_if_c::value == category,\ + detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ -> \ + , mp_number >\ +>::type \ func(const mp_number& arg)\ {\ return detail::mp_exp<\ @@ -910,7 +974,9 @@ func(const mp_number& arg)\ );\ }\ template \ -inline mp_number \ +inline typename boost::enable_if_c<\ + boost::multiprecision::number_category::value == category,\ + mp_number >::type \ func(const mp_number& arg)\ {\ mp_number result;\ @@ -919,7 +985,7 @@ func(const mp_number& arg)\ return result;\ } -#define BINARY_OP_FUNCTOR(func)\ +#define BINARY_OP_FUNCTOR(func, category)\ namespace detail{\ template \ struct BOOST_JOIN(func, _funct)\ @@ -945,12 +1011,13 @@ struct BOOST_JOIN(func, _funct)\ \ }\ template \ -inline detail::mp_exp<\ +inline typename enable_if_c::value == category,\ + detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , mp_number \ - , mp_number \ -> \ + , mp_number > \ +>::type \ func(const mp_number& arg, const mp_number& a)\ {\ return detail::mp_exp<\ @@ -965,12 +1032,14 @@ func(const mp_number& arg, const mp_number& a)\ );\ }\ template \ -inline detail::mp_exp<\ +inline typename enable_if_c<\ + (number_category::value == category) && (number_category >::value == category),\ + detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , mp_number \ - , detail::mp_exp \ -> \ + , detail::mp_exp > \ +>::type \ func(const mp_number& arg, const detail::mp_exp& a)\ {\ return detail::mp_exp<\ @@ -985,12 +1054,14 @@ func(const mp_number& arg, const detail::mp_exp& a)\ );\ }\ template \ -inline detail::mp_exp<\ +inline typename enable_if_c<\ + (number_category::value == category) && (number_category >::value == category),\ + detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , detail::mp_exp \ - , mp_number \ -> \ + , mp_number > \ +>::type \ func(const detail::mp_exp& arg, const mp_number& a)\ {\ return detail::mp_exp<\ @@ -1005,12 +1076,14 @@ func(const detail::mp_exp& arg, const mp_number& a)\ );\ }\ template \ -inline detail::mp_exp<\ +inline typename enable_if_c<\ + (number_category >::value == category) && (number_category >::value == category),\ + detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) >::type> \ , detail::mp_exp \ - , detail::mp_exp \ -> \ + , detail::mp_exp > \ +>::type \ func(const detail::mp_exp& arg, const detail::mp_exp& a)\ {\ return detail::mp_exp<\ @@ -1025,8 +1098,8 @@ func(const detail::mp_exp& arg, const detail::mp_exp \ -inline typename enable_if<\ - is_arithmetic,\ +inline typename enable_if_c<\ + is_arithmetic::value && (number_category::value == category),\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ @@ -1048,8 +1121,8 @@ func(const mp_number& arg, const Arithmetic& a)\ );\ }\ template \ -inline typename enable_if<\ - is_arithmetic,\ +inline typename enable_if_c<\ + is_arithmetic::value && (number_category >::value == category),\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) >::type> \ @@ -1071,8 +1144,8 @@ func(const detail::mp_exp& arg, const Arithmetic& a)\ );\ }\ template \ -inline typename enable_if<\ - is_arithmetic,\ +inline typename enable_if_c<\ + is_arithmetic::value && (number_category::value == category),\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ @@ -1094,8 +1167,8 @@ func(const Arithmetic& arg, const mp_number& a)\ );\ }\ template \ -inline typename enable_if<\ - is_arithmetic,\ +inline typename enable_if_c<\ + is_arithmetic::value && (number_category >::value == category),\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) >::type> \ @@ -1117,7 +1190,8 @@ func(const Arithmetic& arg, const detail::mp_exp& a)\ );\ }\ template \ -inline mp_number \ +inline typename enable_if_c<(number_category::value == category),\ + mp_number >::type \ func(const mp_number& arg, const mp_number& a)\ {\ mp_number result;\ @@ -1126,8 +1200,8 @@ func(const mp_number& arg, const mp_number& a)\ return result;\ }\ template \ -inline typename enable_if<\ - is_arithmetic,\ +inline typename enable_if_c<\ + is_arithmetic::value && (number_category::value == category),\ mp_number \ >::type \ func(const mp_number& arg, const Arithmetic& a)\ @@ -1139,8 +1213,8 @@ func(const mp_number& arg, const Arithmetic& a)\ return result;\ }\ template \ -inline typename enable_if<\ - is_arithmetic,\ +inline typename enable_if_c<\ + is_arithmetic::value && (number_category::value == category),\ mp_number \ >::type \ func(const Arithmetic& a, const mp_number& arg)\ @@ -1153,14 +1227,16 @@ func(const Arithmetic& a, const mp_number& arg)\ }\ -#define HETERO_BINARY_OP_FUNCTOR_B(func, Arg2)\ +#define HETERO_BINARY_OP_FUNCTOR_B(func, Arg2, category)\ template \ -inline detail::mp_exp<\ +inline typename enable_if_c<\ + (number_category >::value == category),\ + detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) >::type> \ , detail::mp_exp \ - , Arg2\ -> \ + , Arg2> \ +>::type \ func(const detail::mp_exp& arg, Arg2 const& a)\ {\ return detail::mp_exp<\ @@ -1174,12 +1250,14 @@ func(const detail::mp_exp& arg, Arg2 const& a)\ );\ }\ template \ -inline detail::mp_exp<\ +inline typename enable_if_c<\ + (number_category::value == category),\ + detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , mp_number \ - , Arg2\ -> \ + , Arg2> \ +>::type \ func(const mp_number& arg, Arg2 const& a)\ {\ return detail::mp_exp<\ @@ -1194,7 +1272,9 @@ func(const mp_number& arg, Arg2 const& a)\ );\ }\ template \ -inline mp_number \ +inline typename enable_if_c<\ + (number_category::value == category),\ + mp_number >::type \ func(const mp_number& arg, Arg2 const& a)\ {\ mp_number result;\ @@ -1203,7 +1283,7 @@ func(const mp_number& arg, Arg2 const& a)\ return result;\ }\ -#define HETERO_BINARY_OP_FUNCTOR(func, Arg2)\ +#define HETERO_BINARY_OP_FUNCTOR(func, Arg2, category)\ namespace detail{\ template \ struct BOOST_JOIN(func, _funct)\ @@ -1218,44 +1298,97 @@ struct BOOST_JOIN(func, _funct)\ \ }\ \ -HETERO_BINARY_OP_FUNCTOR_B(func, Arg2) +HETERO_BINARY_OP_FUNCTOR_B(func, Arg2, category) +namespace detail{ +template +struct abs_funct +{ + void operator()(Backend& result, const Backend& arg)const + { + using default_ops::eval_abs; + eval_abs(result, arg); + } +}; -UNARY_OP_FUNCTOR(abs) -UNARY_OP_FUNCTOR(fabs) -UNARY_OP_FUNCTOR(sqrt) -UNARY_OP_FUNCTOR(floor) -UNARY_OP_FUNCTOR(ceil) -UNARY_OP_FUNCTOR(trunc) -UNARY_OP_FUNCTOR(round) -UNARY_OP_FUNCTOR(exp) -UNARY_OP_FUNCTOR(log) -UNARY_OP_FUNCTOR(log10) -UNARY_OP_FUNCTOR(cos) -UNARY_OP_FUNCTOR(sin) -UNARY_OP_FUNCTOR(tan) -UNARY_OP_FUNCTOR(asin) -UNARY_OP_FUNCTOR(acos) -UNARY_OP_FUNCTOR(atan) -UNARY_OP_FUNCTOR(cosh) -UNARY_OP_FUNCTOR(sinh) -UNARY_OP_FUNCTOR(tanh) +} -HETERO_BINARY_OP_FUNCTOR(ldexp, int) -HETERO_BINARY_OP_FUNCTOR(frexp, int*) -HETERO_BINARY_OP_FUNCTOR_B(ldexp, long) -HETERO_BINARY_OP_FUNCTOR_B(frexp, long*) -HETERO_BINARY_OP_FUNCTOR_B(ldexp, long long) -HETERO_BINARY_OP_FUNCTOR_B(frexp, long long*) -BINARY_OP_FUNCTOR(pow) -BINARY_OP_FUNCTOR(fmod) -BINARY_OP_FUNCTOR(atan2) +template +inline detail::mp_exp< + detail::function + , detail::abs_funct >::type> + , detail::mp_exp > +abs(const detail::mp_exp& arg) +{ + return detail::mp_exp< + detail::function + , detail::abs_funct >::type> + , detail::mp_exp +> ( + detail::abs_funct >::type>() + , arg + ); +} +template +inline detail::mp_exp< + detail::function + , detail::abs_funct + , mp_number > +abs(const mp_number& arg) +{ + return detail::mp_exp< + detail::function + , detail::abs_funct + , mp_number + >( + detail::abs_funct() + , arg + ); +} +template +inline mp_number +abs(const mp_number& arg) +{ + mp_number result; + using default_ops::eval_abs; + eval_abs(result.backend(), arg.backend()); + return result; +} + +UNARY_OP_FUNCTOR(fabs, number_kind_floating_point) +UNARY_OP_FUNCTOR(sqrt, number_kind_floating_point) +UNARY_OP_FUNCTOR(floor, number_kind_floating_point) +UNARY_OP_FUNCTOR(ceil, number_kind_floating_point) +UNARY_OP_FUNCTOR(trunc, number_kind_floating_point) +UNARY_OP_FUNCTOR(round, number_kind_floating_point) +UNARY_OP_FUNCTOR(exp, number_kind_floating_point) +UNARY_OP_FUNCTOR(log, number_kind_floating_point) +UNARY_OP_FUNCTOR(log10, number_kind_floating_point) +UNARY_OP_FUNCTOR(cos, number_kind_floating_point) +UNARY_OP_FUNCTOR(sin, number_kind_floating_point) +UNARY_OP_FUNCTOR(tan, number_kind_floating_point) +UNARY_OP_FUNCTOR(asin, number_kind_floating_point) +UNARY_OP_FUNCTOR(acos, number_kind_floating_point) +UNARY_OP_FUNCTOR(atan, number_kind_floating_point) +UNARY_OP_FUNCTOR(cosh, number_kind_floating_point) +UNARY_OP_FUNCTOR(sinh, number_kind_floating_point) +UNARY_OP_FUNCTOR(tanh, number_kind_floating_point) + +HETERO_BINARY_OP_FUNCTOR(ldexp, int, number_kind_floating_point) +HETERO_BINARY_OP_FUNCTOR(frexp, int*, number_kind_floating_point) +HETERO_BINARY_OP_FUNCTOR_B(ldexp, long, number_kind_floating_point) +HETERO_BINARY_OP_FUNCTOR_B(frexp, long*, number_kind_floating_point) +HETERO_BINARY_OP_FUNCTOR_B(ldexp, long long, number_kind_floating_point) +HETERO_BINARY_OP_FUNCTOR_B(frexp, long long*, number_kind_floating_point) +BINARY_OP_FUNCTOR(pow, number_kind_floating_point) +BINARY_OP_FUNCTOR(fmod, number_kind_floating_point) +BINARY_OP_FUNCTOR(atan2, number_kind_floating_point) // // Integer functions: // -BINARY_OP_FUNCTOR(gcd) -BINARY_OP_FUNCTOR(lcm) +BINARY_OP_FUNCTOR(gcd, number_kind_integer) +BINARY_OP_FUNCTOR(lcm, number_kind_integer) #undef BINARY_OP_FUNCTOR diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index f9f2e37b..76312f66 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -84,11 +84,9 @@ inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) } // namespace detail template -inline void eval_pow(T& result, const T& t, const U& p) +inline typename enable_if >::type eval_pow(T& result, const T& t, const U& p) { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_floating_point, "The pow function is only valid for floating point types."); - typedef typename is_integral::type tag_type; - detail::pow_imp(result, t, p, tag_type()); + detail::pow_imp(result, t, p, mpl::true_()); } template diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index 73de53d4..d03d6cd2 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -766,7 +766,7 @@ void eval_atan2(T& result, const T& y, const T& x) eval_add(result, get_constant_pi()); } } - +/* template typename disable_if >::type eval_atan2(T& result, const T& a, const Arithmetic& b) { @@ -775,4 +775,4 @@ typename disable_if >::type eval_atan2(T& result, const T x = static_cast::type>(b); eval_atan2(result, a, x); } - +*/ diff --git a/test/mp_number_concept_check.cpp b/test/mp_number_concept_check.cpp index 07c6861a..3e051ff5 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -59,34 +59,148 @@ #include #include "libs/math/test/compile_test/instantiate.hpp" +template +void test_extra(T) +{ + T t = 1; + t = abs(t); + t = abs(t*t); + + t = fabs(t); + t = fabs(t*t); + + t = sqrt(t); + t = sqrt(t*t); + + t = floor(t); + t = floor(t*t); + + t = ceil(t); + t = ceil(t*t); + + t = trunc(t); + t = trunc(t*t); + + t = round(t); + t = round(t*t); + + t = exp(t); + t = exp(t*t); + + t = log(t); + t = log(t*t); + + t = log10(t); + t = log10(t*t); + + t = cos(t); + t = cos(t*t); + + t = sin(t); + t = sin(t*t); + + t = tan(t); + t = tan(t*t); + + t = asin(t); + t = asin(t*t); + + t = atan(t); + t = atan(t*t); + + t = acos(t); + t = acos(t*t); + + t = cosh(t); + t = cosh(t*t); + + t = sinh(t); + t = sinh(t*t); + + t = tanh(t); + t = tanh(t*t); + + double dval = 2; + t = pow(t, t); + t = pow(t, t*t); + t = pow(t, dval); + t = pow(t*t, t); + t = pow(t*t, t*t); + t = pow(t*t, dval); + t = pow(dval, t); + t = pow(dval, t*t); + + t = atan2(t, t); + t = atan2(t, t*t); + t = atan2(t, dval); + t = atan2(t*t, t); + t = atan2(t*t, t*t); + t = atan2(t*t, dval); + t = atan2(dval, t); + t = atan2(dval, t*t); + + t = fmod(t, t); + t = fmod(t, t*t); + t = fmod(t, dval); + t = fmod(t*t, t); + t = fmod(t*t, t*t); + t = fmod(t*t, dval); + t = fmod(dval, t); + t = fmod(dval, t*t); + + typedef typename T::backend_type backend_type; + typedef typename backend_type::exponent_type exp_type; + exp_type e = 0; + int i = 0; + + t = ldexp(t, i); + t = ldexp(t*t, i); + t = ldexp(t, e); + t = ldexp(t*t, e); + + t = frexp(t, &i); + t = frexp(t*t, &i); + t = frexp(t, &e); + t = frexp(t*t, &e); +} + void foo() { #ifdef TEST_BACKEND instantiate(boost::multiprecision::concepts::mp_number_float_architype()); + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); #endif #ifdef TEST_MPF_50 instantiate(boost::multiprecision::mpf_float_50()); + test_extra(boost::multiprecision::mpf_float_50()); #endif #ifdef TEST_MPFR_50 instantiate(boost::multiprecision::mpfr_float_50()); + test_extra(boost::multiprecision::mpfr_float_50()); #endif #ifdef TEST_MPFR_6 instantiate(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::mp_number >()); #endif #ifdef TEST_MPFR_15 instantiate(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::mp_number >()); #endif #ifdef TEST_MPFR_17 instantiate(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::mp_number >()); #endif #ifdef TEST_MPFR_30 instantiate(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::mp_number >()); #endif #ifdef TEST_CPP_DEC_FLOAT instantiate(boost::multiprecision::cpp_dec_float_50()); + test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET instantiate(boost::multiprecision::mp_number, false>()); + test_extra(boost::multiprecision::mp_number, false>()); #endif } From 62c5ef6ca0c11d2b10912de6966d000338dd61c1 Mon Sep 17 00:00:00 2001 From: Christopher Kormanyos Date: Sun, 6 May 2012 20:42:55 +0000 Subject: [PATCH 180/256] Switched erroneous use of old enum_fpclass to correct new fpclass_type. [SVN r78363] --- include/boost/multiprecision/cpp_dec_float.hpp | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 499c50d3..d09a0b75 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -185,9 +185,9 @@ public: cpp_dec_float(const cpp_dec_float& f) : exp (f.exp), neg (f.neg), - fpclass (static_cast(static_cast(f.fpclass))), + fpclass (static_cast(static_cast(f.fpclass))), prec_elem(cpp_dec_float_elem_number) - { + { // TODO: this doesn't round! std::copy(f.data.begin(), f.data.begin() + (std::min)(f.prec_elem, prec_elem), data.begin()); precision((std::min)(f.prec_elem, prec_elem)); @@ -334,7 +334,7 @@ public: { exp = f.exp; neg = f.neg; - fpclass = static_cast(static_cast(f.fpclass)); + fpclass = static_cast(static_cast(f.fpclass)); std::copy(f.data.begin(), f.data.begin() + (std::min)(f.prec_elem, prec_elem), data.begin()); precision((std::min)(f.prec_elem, prec_elem)); return *this; From a8c73aea66ce94bdb5ddb1a821c45e3af82b307f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 10 May 2012 09:20:26 +0000 Subject: [PATCH 181/256] Change non-member functions to be protected by enable_if based on the type of the number. Extend expression templates to 4 arguments. Add pow and powm functions for integer types. Update docs to match. [SVN r78401] --- .../boost_multiprecision/indexes/s01.html | 14 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 9 +- .../boost_multiprecision/ref/mp_number.html | 17 +- doc/html/index.html | 2 +- doc/multiprecision.qbk | 13 +- .../boost/multiprecision/cpp_dec_float.hpp | 2 +- include/boost/multiprecision/cpp_int.hpp | 7 + .../multiprecision/detail/default_ops.hpp | 306 +++++----- .../multiprecision/detail/functions/pow.hpp | 67 ++- .../multiprecision/detail/functions/trig.hpp | 26 +- .../multiprecision/detail/mp_number_base.hpp | 539 ++++++++++-------- include/boost/multiprecision/gmp.hpp | 23 + include/boost/multiprecision/integer_ops.hpp | 180 +++++- include/boost/multiprecision/miller_rabin.hpp | 12 +- include/boost/multiprecision/mp_number.hpp | 117 ++-- include/boost/multiprecision/mpfr.hpp | 17 +- test/test_cpp_int.cpp | 27 + 19 files changed, 873 insertions(+), 513 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 87ffa2d8..ddb95fbb 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@ -
    +

    -Function Index

    +Function Index

    A B C D E F I L M P R S T Z

    @@ -168,13 +168,19 @@
    P
    -
    R
    diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index be58bd14..738fe63f 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

    C G M N T

    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 97dafaf5..23a657a4 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    C I L M T

    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index ac6db077..fd084d6d 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G I L M N O P R S T Z

    @@ -400,6 +400,7 @@

  • miller_rabin_test

  • mp_number

  • number_category

    • +

  • powm

  • precision

  • round

  • sign

    • @@ -444,6 +445,10 @@
    • +

      powm

      +
      +
      • +

    • precision

      • Introduction

        • diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html index b883aa18..75a54542 100644 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -144,8 +144,10 @@ struct number_category; // Integer specific functions: +unmentionable-expression-template-type pow(const mp_number-or-expression-template-type&, unsigned); +unmentionable-expression-template-type powm(const mp_number-or-expression-template-type& b, const mp_number-or-expression-template-type& p, const mp_number-or-expression-template-type& m); template <class Backend, bool ExpressionTemplates> -bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y, +void divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y, mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r); template <class Integer> Integer integer_modulus(const mp_number-or-expression-template-type& x, Integer val); @@ -558,6 +560,19 @@ Integer functions +
        unmentionable-expression-template-type    pow(const mp_number-or-expression-template-type& b, unsigned p);
+
        +

        + Returns bp as an expression template. Note that this + function should be used with extreme care as the result can grow so large + as to take "effectively forever" to compute, or else simply run + the host machine out of memory. +

        +
        unmentionable-expression-template-type    powm(const mp_number-or-expression-template-type& b, const mp_number-or-expression-template-type& p, const mp_number-or-expression-template-type& m);
+
        +

        + Returns bp mod m as an expression template. + 

        template <class Backend, bool ExpressionTemplates>
 bool divide_qr(const mp_number-or-expression-template-type& x, const mp_number-or-expression-template-type& y,
                mp_number<Backend, ExpressionTemplates>& q, mp_number<Backend, ExpressionTemplates>& r);
diff --git a/doc/html/index.html b/doc/html/index.html
index 444abace..c699fb31 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -117,7 +117,7 @@
    - +

    Last revised: April 15, 2012 at 17:36:47 GMT

    Last revised: May 09, 2012 at 18:07:25 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 4804fd6d..f7819bc6 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -1052,8 +1052,10 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba struct number_category; // Integer specific functions: + ``['unmentionable-expression-template-type]`` pow(const ``['mp_number-or-expression-template-type]``&, unsigned); + ``['unmentionable-expression-template-type]`` powm(const ``['mp_number-or-expression-template-type]``& b, const ``['mp_number-or-expression-template-type]``& p, const ``['mp_number-or-expression-template-type]``& m); template - bool divide_qr(const ``['mp_number-or-expression-template-type]``& x, const ``['mp_number-or-expression-template-type]``& y, + void divide_qr(const ``['mp_number-or-expression-template-type]``& x, const ``['mp_number-or-expression-template-type]``& y, mp_number& q, mp_number& r); template Integer integer_modulus(const ``['mp_number-or-expression-template-type]``& x, Integer val); @@ -1336,6 +1338,15 @@ A traits class that inherits from `mpl::int_` where `N` is one of the enumera [h4 Integer functions] + ``['unmentionable-expression-template-type]`` pow(const ``['mp_number-or-expression-template-type]``& b, unsigned p); + +Returns ['b[super p]] as an expression template. Note that this function should be used with extreme care as the result can grow so +large as to take "effectively forever" to compute, or else simply run the host machine out of memory. + + ``['unmentionable-expression-template-type]`` powm(const ``['mp_number-or-expression-template-type]``& b, const ``['mp_number-or-expression-template-type]``& p, const ``['mp_number-or-expression-template-type]``& m); + +Returns ['b[super p] mod m] as an expression template. + template bool divide_qr(const ``['mp_number-or-expression-template-type]``& x, const ``['mp_number-or-expression-template-type]``& y, mp_number& q, mp_number& r); diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index d09a0b75..d276e12e 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -334,7 +334,7 @@ public: { exp = f.exp; neg = f.neg; - fpclass = static_cast(static_cast(f.fpclass)); + fpclass = static_cast(static_cast(f.fpclass)); std::copy(f.data.begin(), f.data.begin() + (std::min)(f.prec_elem, prec_elem), data.begin()); precision((std::min)(f.prec_elem, prec_elem)); return *this; diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index a72008c4..1474a6f0 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1082,10 +1082,13 @@ inline void eval_multiply(cpp_int_backend& result, c for(unsigned j = 0; j < inner_limit; ++j) { BOOST_ASSERT(i+j < result.size()); + BOOST_ASSERT((std::numeric_limits::max)() - carry > static_cast(cpp_int_backend::max_limb_value) * static_cast(cpp_int_backend::max_limb_value)); carry += static_cast(pa[i]) * static_cast(pb[j]); + BOOST_ASSERT((std::numeric_limits::max)() - carry >= pr[i+j]); carry += pr[i + j]; pr[i + j] = static_cast(carry); carry >>= cpp_int_backend::limb_bits; + BOOST_ASSERT(carry <= (cpp_int_backend::max_limb_value)); } if(cpp_int_backend::variable || (i + bs < result.size())) pr[i + bs] = static_cast(carry); @@ -1529,6 +1532,8 @@ void divide_unsigned_helper(cpp_int_backend* result, { --r_order; // No remainder, division was exact. r.resize(r.size() - 1); + if(result) + pres[r_order] = static_cast(0u); } } else @@ -1540,6 +1545,8 @@ void divide_unsigned_helper(cpp_int_backend* result, { --r_order; // No remainder, division was exact. r.resize(r.size() - 1); + if(result) + pres[r_order] = static_cast(0u); } } } diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 8c58cc8d..e5511ffc 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -445,6 +445,26 @@ inline void eval_fmod(T& result, const T& a, const T& b) eval_multiply(n, b); eval_subtract(result, a, n); } +template +inline typename enable_if, void>::type eval_fmod(T& result, const T& x, const A& a) +{ + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = a; + eval_fmod(result, x, c); +} + +template +inline typename enable_if, void>::type eval_fmod(T& result, const A& x, const T& a) +{ + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = x; + eval_fmod(result, c, a); +} + template inline void eval_trunc(T& result, const T& a) { @@ -484,68 +504,6 @@ inline void eval_round(T& result, const T& a) } } -template -inline typename enable_if, void>::type eval_pow(T& result, const T& x, const A& a) -{ - // Note this one is resticted to float arguments since pow.hpp already has a version for - // integer powers.... - typedef typename boost::multiprecision::detail::canonical::type canonical_type; - typedef typename mpl::if_, T, canonical_type>::type cast_type; - cast_type c; - c = a; - eval_pow(result, x, c); -} - -template -inline typename enable_if, void>::type eval_pow(T& result, const A& x, const T& a) -{ - typedef typename boost::multiprecision::detail::canonical::type canonical_type; - typedef typename mpl::if_, T, canonical_type>::type cast_type; - cast_type c; - c = x; - eval_pow(result, c, a); -} - -template -inline typename enable_if, void>::type eval_fmod(T& result, const T& x, const A& a) -{ - typedef typename boost::multiprecision::detail::canonical::type canonical_type; - typedef typename mpl::if_, T, canonical_type>::type cast_type; - cast_type c; - c = a; - eval_fmod(result, x, c); -} - -template -inline typename enable_if, void>::type eval_fmod(T& result, const A& x, const T& a) -{ - typedef typename boost::multiprecision::detail::canonical::type canonical_type; - typedef typename mpl::if_, T, canonical_type>::type cast_type; - cast_type c; - c = x; - eval_fmod(result, c, a); -} - -template -inline typename enable_if, void>::type eval_atan2(T& result, const T& x, const A& a) -{ - typedef typename boost::multiprecision::detail::canonical::type canonical_type; - typedef typename mpl::if_, T, canonical_type>::type cast_type; - cast_type c; - c = a; - eval_atan2(result, x, c); -} - -template -inline typename enable_if, void>::type eval_atan2(T& result, const A& x, const T& a) -{ - typedef typename boost::multiprecision::detail::canonical::type canonical_type; - typedef typename mpl::if_, T, canonical_type>::type cast_type; - cast_type c; - c = x; - eval_atan2(result, c, a); -} - template inline typename enable_if >::type eval_gcd(T& result, const T& a, const Arithmetic& b) { @@ -670,10 +628,10 @@ inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_ using multiprecision::default_ops::eval_fpclassify; return eval_fpclassify(arg.backend()); } -template -inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) +template +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) { - typedef typename multiprecision::detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::mp_exp::result_type value_type; return fpclassify(value_type(arg)); } template @@ -682,10 +640,10 @@ inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_n int v = fpclassify(arg); return (v != FP_INFINITE) && (v != FP_NAN); } -template -inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) +template +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) { - typedef typename multiprecision::detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::mp_exp::result_type value_type; return isfinite(value_type(arg)); } template @@ -693,10 +651,10 @@ inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_numb { return fpclassify(arg) == FP_NAN; } -template -inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) +template +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) { - typedef typename multiprecision::detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::mp_exp::result_type value_type; return isnan(value_type(arg)); } template @@ -704,10 +662,10 @@ inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_numb { return fpclassify(arg) == FP_INFINITE; } -template -inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) +template +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) { - typedef typename multiprecision::detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::mp_exp::result_type value_type; return isinf(value_type(arg)); } template @@ -715,20 +673,20 @@ inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_n { return fpclassify(arg) == FP_NORMAL; } -template -inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) +template +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) { - typedef typename multiprecision::detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::mp_exp::result_type value_type; return isnormal(value_type(arg)); } } // namespace math namespace multiprecision{ -template -inline typename detail::mp_exp::result_type trunc(const detail::mp_exp& v, const Policy& pol) +template +inline typename detail::mp_exp::result_type trunc(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::mp_exp::result_type number_type; return trunc(number_type(v), pol); } @@ -741,17 +699,17 @@ inline mp_number trunc(const mp_number -inline int itrunc(const detail::mp_exp& v, const Policy& pol) +template +inline int itrunc(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, number_type(v), 0, pol).template convert_to(); return r.template convert_to(); } -template -inline int itrunc(const detail::mp_exp& v) +template +inline int itrunc(const detail::mp_exp& v) { return itrunc(v, boost::math::policies::policy<>()); } @@ -768,17 +726,17 @@ inline int itrunc(const mp_number& v) { return itrunc(v, boost::math::policies::policy<>()); } -template -inline long ltrunc(const detail::mp_exp& v, const Policy& pol) +template +inline long ltrunc(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, number_type(v), 0L, pol).template convert_to(); return r.template convert_to(); } -template -inline long ltrunc(const detail::mp_exp& v) +template +inline long ltrunc(const detail::mp_exp& v) { return ltrunc(v, boost::math::policies::policy<>()); } @@ -796,17 +754,17 @@ inline long ltrunc(const mp_number& v) return ltrunc(v, boost::math::policies::policy<>()); } #ifndef BOOST_NO_LONG_LONG -template -inline long long lltrunc(const detail::mp_exp& v, const Policy& pol) +template +inline long long lltrunc(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, number_type(v), 0LL, pol).template convert_to(); return r.template convert_to(); } -template -inline long long lltrunc(const detail::mp_exp& v) +template +inline long long lltrunc(const detail::mp_exp& v) { return lltrunc(v, boost::math::policies::policy<>()); } @@ -824,10 +782,10 @@ inline long long lltrunc(const mp_number& v) return lltrunc(v, boost::math::policies::policy<>()); } #endif -template -inline typename detail::mp_exp::result_type round(const detail::mp_exp& v, const Policy& pol) +template +inline typename detail::mp_exp::result_type round(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::mp_exp::result_type number_type; return round(static_cast(v), pol); } template @@ -839,17 +797,17 @@ inline mp_number round(const mp_number -inline int iround(const detail::mp_exp& v, const Policy& pol) +template +inline int iround(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, number_type(v), 0, pol).template convert_to(); return r.template convert_to(); } -template -inline int iround(const detail::mp_exp& v) +template +inline int iround(const detail::mp_exp& v) { return iround(v, boost::math::policies::policy<>()); } @@ -866,17 +824,17 @@ inline int iround(const mp_number& v) { return iround(v, boost::math::policies::policy<>()); } -template -inline long lround(const detail::mp_exp& v, const Policy& pol) +template +inline long lround(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, number_type(v), 0L, pol).template convert_to(); return r.template convert_to(); } -template -inline long lround(const detail::mp_exp& v) +template +inline long lround(const detail::mp_exp& v) { return lround(v, boost::math::policies::policy<>()); } @@ -894,17 +852,17 @@ inline long lround(const mp_number& v) return lround(v, boost::math::policies::policy<>()); } #ifndef BOOST_NO_LONG_LONG -template -inline long long llround(const detail::mp_exp& v, const Policy& pol) +template +inline long long llround(const detail::mp_exp& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::mp_exp::result_type number_type; number_type r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, number_type(v), 0LL, pol).template convert_to(); return r.template convert_to(); } -template -inline long long llround(const detail::mp_exp& v) +template +inline long long llround(const detail::mp_exp& v) { return llround(v, boost::math::policies::policy<>()); } @@ -937,21 +895,21 @@ struct BOOST_JOIN(func, _funct)\ \ }\ \ -template \ -inline typename enable_if_c >::value == category,\ +template \ +inline typename enable_if_c >::value == category,\ detail::mp_exp<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp >\ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp > \ >::type \ -func(const detail::mp_exp& arg)\ +func(const detail::mp_exp& arg)\ {\ return detail::mp_exp<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ > (\ - detail::BOOST_JOIN(func, _funct) >::type>() \ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg \ );\ }\ @@ -960,7 +918,7 @@ inline typename enable_if_c::value == category,\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number >\ + , mp_number > \ >::type \ func(const mp_number& arg)\ {\ @@ -1031,43 +989,43 @@ func(const mp_number& arg, const mp_number& a)\ a\ );\ }\ -template \ +template \ inline typename enable_if_c<\ - (number_category::value == category) && (number_category >::value == category),\ + (number_category::value == category) && (number_category >::value == category),\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , mp_number \ - , detail::mp_exp > \ + , detail::mp_exp > \ >::type \ -func(const mp_number& arg, const detail::mp_exp& a)\ +func(const mp_number& arg, const detail::mp_exp& a)\ {\ return detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , mp_number \ - , detail::mp_exp \ + , detail::mp_exp \ >(\ detail::BOOST_JOIN(func, _funct)() \ , arg,\ a\ );\ }\ -template \ +template \ inline typename enable_if_c<\ - (number_category::value == category) && (number_category >::value == category),\ + (number_category::value == category) && (number_category >::value == category),\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , detail::mp_exp \ + , detail::mp_exp \ , mp_number > \ >::type \ -func(const detail::mp_exp& arg, const mp_number& a)\ +func(const detail::mp_exp& arg, const mp_number& a)\ {\ return detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , detail::mp_exp \ + , detail::mp_exp \ , mp_number \ >(\ detail::BOOST_JOIN(func, _funct)() \ @@ -1075,24 +1033,24 @@ func(const detail::mp_exp& arg, const mp_number& a)\ a\ );\ }\ -template \ +template \ inline typename enable_if_c<\ - (number_category >::value == category) && (number_category >::value == category),\ + (number_category >::value == category) && (number_category >::value == category),\ detail::mp_exp<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ - , detail::mp_exp > \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ + , detail::mp_exp > \ >::type \ -func(const detail::mp_exp& arg, const detail::mp_exp& a)\ +func(const detail::mp_exp& arg, const detail::mp_exp& a)\ {\ return detail::mp_exp<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ + , detail::mp_exp \ >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg,\ a\ );\ @@ -1120,25 +1078,25 @@ func(const mp_number& arg, const Arithmetic& a)\ a\ );\ }\ -template \ +template \ inline typename enable_if_c<\ - is_arithmetic::value && (number_category >::value == category),\ + is_arithmetic::value && (number_category >::value == category),\ detail::mp_exp<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ , Arithmetic\ > \ >::type \ -func(const detail::mp_exp& arg, const Arithmetic& a)\ +func(const detail::mp_exp& arg, const Arithmetic& a)\ {\ return detail::mp_exp<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ , Arithmetic\ >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg,\ a\ );\ @@ -1166,25 +1124,25 @@ func(const Arithmetic& arg, const mp_number& a)\ a\ );\ }\ -template \ +template \ inline typename enable_if_c<\ - is_arithmetic::value && (number_category >::value == category),\ + is_arithmetic::value && (number_category >::value == category),\ detail::mp_exp<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::BOOST_JOIN(func, _funct) >::type> \ , Arithmetic \ - , detail::mp_exp \ + , detail::mp_exp \ > \ >::type \ -func(const Arithmetic& arg, const detail::mp_exp& a)\ +func(const Arithmetic& arg, const detail::mp_exp& a)\ {\ return detail::mp_exp<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::BOOST_JOIN(func, _funct) >::type> \ , Arithmetic \ - , detail::mp_exp \ + , detail::mp_exp \ >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg,\ a\ );\ @@ -1228,24 +1186,24 @@ func(const Arithmetic& a, const mp_number& arg)\ #define HETERO_BINARY_OP_FUNCTOR_B(func, Arg2, category)\ -template \ +template \ inline typename enable_if_c<\ - (number_category >::value == category),\ + (number_category >::value == category),\ detail::mp_exp<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ , Arg2> \ >::type \ -func(const detail::mp_exp& arg, Arg2 const& a)\ +func(const detail::mp_exp& arg, Arg2 const& a)\ {\ return detail::mp_exp<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::mp_exp \ , Arg2\ >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg, a \ );\ }\ @@ -1313,19 +1271,19 @@ struct abs_funct } -template +template inline detail::mp_exp< detail::function - , detail::abs_funct >::type> - , detail::mp_exp > -abs(const detail::mp_exp& arg) + , detail::abs_funct >::type> + , detail::mp_exp > +abs(const detail::mp_exp& arg) { return detail::mp_exp< detail::function - , detail::abs_funct >::type> - , detail::mp_exp + , detail::abs_funct >::type> + , detail::mp_exp > ( - detail::abs_funct >::type>() + detail::abs_funct >::type>() , arg ); } @@ -1389,7 +1347,7 @@ BINARY_OP_FUNCTOR(atan2, number_kind_floating_point) // BINARY_OP_FUNCTOR(gcd, number_kind_integer) BINARY_OP_FUNCTOR(lcm, number_kind_integer) - +HETERO_BINARY_OP_FUNCTOR_B(pow, unsigned, number_kind_integer) #undef BINARY_OP_FUNCTOR #undef UNARY_OP_FUNCTOR diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 76312f66..bbb6b537 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -15,30 +15,11 @@ namespace detail{ template -inline T pow_imp(T& result, const T& t, const U& p, const mpl::false_&) -{ - T temp(p); - eval_pow(result, t, p); -} - -template -inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) +inline void pow_imp(T& result, const T& t, const U& p, const mpl::false_&) { // Compute the pure power of typename T t^p. Binary splitting of the power is // used. The resulting computational complexity has the order of log2[abs(p)]. - - typedef typename mpl::front::type int_type; - - if(p < 0) - { - T temp; - temp = static_cast(1); - T denom; - pow_imp(denom, t, -p, mpl::true_()); - eval_divide(result, temp, denom); - return; - } - + typedef typename boost::multiprecision::detail::canonical::type int_type; switch(p) { case 0: @@ -74,19 +55,37 @@ inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) if(p_minus_n) { T temp; - pow_imp(temp, t, p_minus_n, mpl::true_()); + pow_imp(temp, t, p_minus_n, mpl::false_()); eval_multiply(result, temp); } } } } +template +inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) +{ + // Signed integer power, just take care of the sign then call the unsigned version: + typedef typename boost::multiprecision::detail::canonical::type int_type; + + if(p < 0) + { + T temp; + temp = static_cast(1); + T denom; + pow_imp(denom, t, -p, mpl::false_()); + eval_divide(result, temp, denom); + return; + } + pow_imp(result, t, p, mpl::false_()); +} + } // namespace detail template inline typename enable_if >::type eval_pow(T& result, const T& t, const U& p) { - detail::pow_imp(result, t, p, mpl::true_()); + detail::pow_imp(result, t, p, boost::is_signed()); } template @@ -545,6 +544,28 @@ inline void eval_pow(T& result, const T& x, const T& a) } } +template +inline typename enable_if, void>::type eval_pow(T& result, const T& x, const A& a) +{ + // Note this one is resticted to float arguments since pow.hpp already has a version for + // integer powers.... + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = a; + eval_pow(result, x, c); +} + +template +inline typename enable_if, void>::type eval_pow(T& result, const A& x, const T& a) +{ + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = x; + eval_pow(result, c, a); +} + namespace detail{ template diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index d03d6cd2..b60722f5 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -766,13 +766,23 @@ void eval_atan2(T& result, const T& y, const T& x) eval_add(result, get_constant_pi()); } } -/* -template -typename disable_if >::type eval_atan2(T& result, const T& a, const Arithmetic& b) +template +inline typename enable_if, void>::type eval_atan2(T& result, const T& x, const A& a) { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_floating_point, "The atan2 function is only valid for floating point types."); - T x; - x = static_cast::type>(b); - eval_atan2(result, a, x); + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = a; + eval_atan2(result, x, c); } -*/ + +template +inline typename enable_if, void>::type eval_atan2(T& result, const A& x, const T& a) +{ + typedef typename boost::multiprecision::detail::canonical::type canonical_type; + typedef typename mpl::if_, T, canonical_type>::type cast_type; + cast_type c; + c = x; + eval_atan2(result, c, a); +} + diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 317462dd..d57d30dd 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -22,12 +22,28 @@ namespace boost{ namespace multiprecision{ template class mp_number; +template +struct is_mp_number : public mpl::false_ {}; + +template +struct is_mp_number > : public mpl::true_ {}; + namespace detail{ // Forward-declare an expression wrapper -template +template struct mp_exp; +} // namespace detail + +template +struct is_mp_number_expression : public mpl::false_ {}; + +template +struct is_mp_number_expression > : public mpl::true_ {}; + +namespace detail{ + template typename boost::enable_if, T>::type abs(const T& t) { @@ -144,10 +160,10 @@ struct backend_type > typedef T type; }; -template -struct backend_type > +template +struct backend_type > { - typedef typename backend_type::result_type>::type type; + typedef typename backend_type::result_type>::type type; }; @@ -157,8 +173,8 @@ template struct is_mp_number > : public mpl::true_{}; template struct is_mp_number_exp : public mpl::false_{}; -template -struct is_mp_number_exp > : public mpl::true_{}; +template +struct is_mp_number_exp > : public mpl::true_{}; template struct combine_expression; @@ -187,10 +203,10 @@ struct arg_type typedef mp_exp type; }; -template -struct arg_type > +template +struct arg_type > { - typedef mp_exp type; + typedef mp_exp type; }; template @@ -219,14 +235,14 @@ struct mp_exp_storage typedef const T* type; }; -template -struct mp_exp_storage > +template +struct mp_exp_storage > { - typedef mp_exp type; + typedef mp_exp type; }; template -struct mp_exp +struct mp_exp { typedef mpl::int_<1> arity; typedef typename arg_type::type left_type; @@ -253,7 +269,7 @@ private: }; template -struct mp_exp +struct mp_exp { typedef mpl::int_<0> arity; typedef Arg1 result_type; @@ -276,7 +292,7 @@ private: }; template -struct mp_exp +struct mp_exp { typedef mpl::int_<2> arity; typedef typename arg_type::type left_type; @@ -309,7 +325,7 @@ private: }; template -struct mp_exp +struct mp_exp { typedef mpl::int_<3> arity; typedef typename arg_type::type left_type; @@ -350,6 +366,61 @@ private: mp_exp& operator=(const mp_exp&); }; +template +struct mp_exp +{ + typedef mpl::int_<4> arity; + typedef typename arg_type::type left_type; + typedef typename arg_type::type left_middle_type; + typedef typename arg_type::type right_middle_type; + typedef typename arg_type::type right_type; + typedef typename left_type::result_type left_result_type; + typedef typename left_middle_type::result_type left_middle_result_type; + typedef typename right_middle_type::result_type right_middle_result_type; + typedef typename right_type::result_type right_result_type; + typedef typename combine_expression< + typename combine_expression< + typename combine_expression::type, + right_middle_result_type + >::type, + right_result_type + >::type result_type; + typedef tag tag_type; + + mp_exp(const Arg1& a1, const Arg2& a2, const Arg3& a3, const Arg4& a4) : arg1(a1), arg2(a2), arg3(a3), arg4(a4) {} + + left_type left()const { return left_type(arg1); } + left_middle_type left_middle()const { return left_middle_type(arg2); } + right_middle_type right_middle()const { return right_middle_type(arg3); } + right_type right()const { return right_type(arg4); } + const Arg1& left_ref()const{ return arg1; } + const Arg2& left_middle_ref()const{ return arg2; } + const Arg3& right_middle_ref()const{ return arg3; } + const Arg4& right_ref()const{ return arg4; } + + operator unmentionable_type()const + { + result_type r(*this); + return r ? &unmentionable::proc : 0; + } + + static const unsigned left_depth = left_type::depth + 1; + static const unsigned left_middle_depth = left_middle_type::depth + 1; + static const unsigned right_middle_depth = right_middle_type::depth + 1; + static const unsigned right_depth = right_type::depth + 1; + + static const unsigned left_max_depth = left_depth > left_middle_depth ? left_depth : left_middle_depth; + static const unsigned right_max_depth = right_depth > right_middle_depth ? right_depth : right_middle_depth; + + static const unsigned depth = left_max_depth > right_max_depth ? left_max_depth : right_max_depth; +private: + typename mp_exp_storage::type arg1; + typename mp_exp_storage::type arg2; + typename mp_exp_storage::type arg3; + typename mp_exp_storage::type arg4; + mp_exp& operator=(const mp_exp&); +}; + template struct digits2 { @@ -506,16 +577,16 @@ void format_float_string(S& str, boost::intmax_t my_exp, boost::intmax_t digits, // template inline const mp_number& operator + (const mp_number& v) { return v; } -template -inline const detail::mp_exp& operator + (const detail::mp_exp& v) { return v; } +template +inline const detail::mp_exp& operator + (const detail::mp_exp& v) { return v; } template inline detail::mp_exp > operator - (const mp_number& v) { return detail::mp_exp >(v); } -template -inline detail::mp_exp > operator - (const detail::mp_exp& v) { return detail::mp_exp >(v); } +template +inline detail::mp_exp > operator - (const detail::mp_exp& v) { return detail::mp_exp >(v); } template inline detail::mp_exp > operator ~ (const mp_number& v) { return detail::mp_exp >(v); } -template -inline detail::mp_exp > operator ~ (const detail::mp_exp& v) { return detail::mp_exp >(v); } +template +inline detail::mp_exp > operator ~ (const detail::mp_exp& v) { return detail::mp_exp >(v); } // // Then addition: // @@ -537,50 +608,50 @@ inline typename enable_if, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator + (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator + (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, mp_number > - operator + (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, mp_number > + operator + (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator + (const detail::mp_exp& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator + (const detail::mp_exp& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline typename enable_if, detail::mp_exp, V > >::type - operator + (const detail::mp_exp& a, const V& b) +template +inline typename enable_if, detail::mp_exp, V > >::type + operator + (const detail::mp_exp& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } -template -inline typename enable_if, detail::mp_exp > >::type - operator + (const V& a, const detail::mp_exp& b) +template +inline typename enable_if, detail::mp_exp > >::type + operator + (const V& a, const detail::mp_exp& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } // // Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: // -template -inline detail::mp_exp, typename detail::mp_exp::left_type > - operator + (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, typename detail::mp_exp::left_type > + operator + (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); + return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); } -template -inline detail::mp_exp, typename detail::mp_exp::left_type > - operator + (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, typename detail::mp_exp::left_type > + operator + (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref()); + return detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref()); } template inline detail::mp_exp, mp_number > @@ -627,51 +698,51 @@ inline typename enable_if, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator - (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator - (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, mp_number > - operator - (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, mp_number > + operator - (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator - (const detail::mp_exp& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator - (const detail::mp_exp& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline typename enable_if, detail::mp_exp, V > >::type - operator - (const detail::mp_exp& a, const V& b) +template +inline typename enable_if, detail::mp_exp, V > >::type + operator - (const detail::mp_exp& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } -template -inline typename enable_if, detail::mp_exp > >::type - operator - (const V& a, const detail::mp_exp& b) +template +inline typename enable_if, detail::mp_exp > >::type + operator - (const V& a, const detail::mp_exp& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } // // Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: // -template -inline detail::mp_exp, typename detail::mp_exp::left_type > - operator - (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, typename detail::mp_exp::left_type > + operator - (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); + return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); } -template -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator - (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator - (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); } template inline detail::mp_exp, mp_number > @@ -719,52 +790,52 @@ inline typename enable_if, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator * (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator * (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, mp_number > - operator * (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, mp_number > + operator * (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator * (const detail::mp_exp& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator * (const detail::mp_exp& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline typename enable_if, detail::mp_exp, V > >::type - operator * (const detail::mp_exp& a, const V& b) +template +inline typename enable_if, detail::mp_exp, V > >::type + operator * (const detail::mp_exp& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } -template -inline typename enable_if, detail::mp_exp > >::type - operator * (const V& a, const detail::mp_exp& b) +template +inline typename enable_if, detail::mp_exp > >::type + operator * (const V& a, const detail::mp_exp& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } // // Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: // -template -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator * (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator * (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type > (a, b.left_ref())); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type > (a, b.left_ref())); } -template -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator * (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator * (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); } template inline detail::mp_exp, mp_number > > @@ -815,52 +886,52 @@ inline typename enable_if, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator / (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator / (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, mp_number > - operator / (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, mp_number > + operator / (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator / (const detail::mp_exp& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator / (const detail::mp_exp& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline typename enable_if, detail::mp_exp, V > >::type - operator / (const detail::mp_exp& a, const V& b) +template +inline typename enable_if, detail::mp_exp, V > >::type + operator / (const detail::mp_exp& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } -template -inline typename enable_if, detail::mp_exp > >::type - operator / (const V& a, const detail::mp_exp& b) +template +inline typename enable_if, detail::mp_exp > >::type + operator / (const V& a, const detail::mp_exp& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } // // Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: // -template -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator / (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, typename detail::mp_exp::left_type > > + operator / (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref())); + return detail::mp_exp, typename detail::mp_exp::left_type > >( + detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref())); } -template -inline detail::mp_exp::left_type, mp_number > > - operator / (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp::left_type, mp_number > > + operator / (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp::left_type, mp_number > >( - detail::mp_exp::left_type, mp_number >(a.left_ref(), b)); + return detail::mp_exp::left_type, mp_number > >( + detail::mp_exp::left_type, mp_number >(a.left_ref(), b)); } template inline detail::mp_exp, mp_number > > @@ -911,35 +982,35 @@ inline typename enable_if, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator % (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator % (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, mp_number > - operator % (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, mp_number > + operator % (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator % (const detail::mp_exp& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator % (const detail::mp_exp& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline typename enable_if, detail::mp_exp, V > >::type - operator % (const detail::mp_exp& a, const V& b) +template +inline typename enable_if, detail::mp_exp, V > >::type + operator % (const detail::mp_exp& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } -template -inline typename enable_if, detail::mp_exp > >::type - operator % (const V& a, const detail::mp_exp& b) +template +inline typename enable_if, detail::mp_exp > >::type + operator % (const V& a, const detail::mp_exp& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } // // Left shift: @@ -950,11 +1021,11 @@ inline typename enable_if, detail::mp_exp, I>(a, b); } -template -inline typename enable_if, detail::mp_exp, I> >::type - operator << (const detail::mp_exp& a, const I& b) +template +inline typename enable_if, detail::mp_exp, I> >::type + operator << (const detail::mp_exp& a, const I& b) { - return detail::mp_exp, I>(a, b); + return detail::mp_exp, I>(a, b); } // // Right shift: @@ -965,11 +1036,11 @@ inline typename enable_if, detail::mp_exp, I>(a, b); } -template -inline typename enable_if, detail::mp_exp, I> >::type - operator >> (const detail::mp_exp& a, const I& b) +template +inline typename enable_if, detail::mp_exp, I> >::type + operator >> (const detail::mp_exp& a, const I& b) { - return detail::mp_exp, I>(a, b); + return detail::mp_exp, I>(a, b); } // // Bitwise AND: @@ -992,35 +1063,35 @@ inline typename enable_if, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator & (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator & (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, mp_number > - operator & (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, mp_number > + operator & (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator & (const detail::mp_exp& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator & (const detail::mp_exp& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline typename enable_if, detail::mp_exp, V > >::type - operator & (const detail::mp_exp& a, const V& b) +template +inline typename enable_if, detail::mp_exp, V > >::type + operator & (const detail::mp_exp& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } -template -inline typename enable_if, detail::mp_exp > >::type - operator & (const V& a, const detail::mp_exp& b) +template +inline typename enable_if, detail::mp_exp > >::type + operator & (const V& a, const detail::mp_exp& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } // // Bitwise OR: @@ -1043,35 +1114,35 @@ inline typename enable_if, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator| (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator| (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, mp_number > - operator| (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, mp_number > + operator| (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator| (const detail::mp_exp& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator| (const detail::mp_exp& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline typename enable_if, detail::mp_exp, V > >::type - operator| (const detail::mp_exp& a, const V& b) +template +inline typename enable_if, detail::mp_exp, V > >::type + operator| (const detail::mp_exp& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } -template -inline typename enable_if, detail::mp_exp > >::type - operator| (const V& a, const detail::mp_exp& b) +template +inline typename enable_if, detail::mp_exp > >::type + operator| (const V& a, const detail::mp_exp& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } // // Bitwise XOR: @@ -1094,35 +1165,35 @@ inline typename enable_if, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator^ (const mp_number& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator^ (const mp_number& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline detail::mp_exp, mp_number > - operator^ (const detail::mp_exp& a, const mp_number& b) +template +inline detail::mp_exp, mp_number > + operator^ (const detail::mp_exp& a, const mp_number& b) { - return detail::mp_exp, mp_number >(a, b); + return detail::mp_exp, mp_number >(a, b); } -template -inline detail::mp_exp, detail::mp_exp > - operator^ (const detail::mp_exp& a, const detail::mp_exp& b) +template +inline detail::mp_exp, detail::mp_exp > + operator^ (const detail::mp_exp& a, const detail::mp_exp& b) { - return detail::mp_exp, detail::mp_exp >(a, b); + return detail::mp_exp, detail::mp_exp >(a, b); } -template -inline typename enable_if, detail::mp_exp, V > >::type - operator^ (const detail::mp_exp& a, const V& b) +template +inline typename enable_if, detail::mp_exp, V > >::type + operator^ (const detail::mp_exp& a, const V& b) { - return detail::mp_exp, V >(a, b); + return detail::mp_exp, V >(a, b); } -template -inline typename enable_if, detail::mp_exp > >::type - operator^ (const V& a, const detail::mp_exp& b) +template +inline typename enable_if, detail::mp_exp > >::type + operator^ (const V& a, const detail::mp_exp& b) { - return detail::mp_exp >(a, b); + return detail::mp_exp >(a, b); } // @@ -1140,15 +1211,15 @@ template struct number_category : public mpl::int_ {}; template struct number_category > : public number_category{}; -template -struct number_category > : public number_category::result_type>{}; +template +struct number_category > : public number_category::result_type>{}; template struct component_type; template struct component_type > : public component_type{}; -template -struct component_type > : public component_type::result_type>{}; +template +struct component_type > : public component_type::result_type>{}; }} // namespaces @@ -1157,10 +1228,10 @@ namespace boost{ namespace math{ namespace tools{ template struct promote_arg; -template -struct promote_arg > +template +struct promote_arg > { - typedef typename boost::multiprecision::detail::mp_exp::result_type type; + typedef typename boost::multiprecision::detail::mp_exp::result_type type; }; }}} diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index a4014cdd..02f11216 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1412,6 +1412,29 @@ inline typename enable_if, Integer>::type eval_integer_modulu typedef typename make_unsigned::type unsigned_type; return eval_integer_modulus(x, static_cast(std::abs(val))); } +inline void eval_powm(gmp_int& result, const gmp_int& base, const gmp_int& p, const gmp_int& m) +{ + if(eval_get_sign(p) < 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); + } + mpz_powm(result.data(), base.data(), p.data(), m.data()); +} + +template +inline typename enable_if< + mpl::and_< + is_unsigned, + mpl::bool_ + > +>::type eval_powm(gmp_int& result, const gmp_int& base, Integer p, const gmp_int& m) +{ + if(p < 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); + } + mpz_powm_ui(result.data(), base.data(), p, m.data()); +} struct gmp_rational; void eval_add(gmp_rational& t, const gmp_rational& o); diff --git a/include/boost/multiprecision/integer_ops.hpp b/include/boost/multiprecision/integer_ops.hpp index 6a83b2a6..fa4f6976 100644 --- a/include/boost/multiprecision/integer_ops.hpp +++ b/include/boost/multiprecision/integer_ops.hpp @@ -49,25 +49,25 @@ inline typename enable_if_c::value == number_kind_integ eval_qr(x.backend(), y.backend(), q.backend(), r.backend()); } -template +template inline typename enable_if_c::value == number_kind_integer>::type - divide_qr(const mp_number& x, const multiprecision::detail::mp_exp& y, + divide_qr(const mp_number& x, const multiprecision::detail::mp_exp& y, mp_number& q, mp_number& r) { divide_qr(x, mp_number(y), q, r); } -template +template inline typename enable_if_c::value == number_kind_integer>::type - divide_qr(const multiprecision::detail::mp_exp& x, const mp_number& y, + divide_qr(const multiprecision::detail::mp_exp& x, const mp_number& y, mp_number& q, mp_number& r) { divide_qr(mp_number(x), y, q, r); } -template +template inline typename enable_if_c::value == number_kind_integer>::type - divide_qr(const multiprecision::detail::mp_exp& x, const multiprecision::detail::mp_exp& y, + divide_qr(const multiprecision::detail::mp_exp& x, const multiprecision::detail::mp_exp& y, mp_number& q, mp_number& r) { divide_qr(mp_number(x), mp_number(y), q, r); @@ -81,11 +81,11 @@ inline typename enable_if, mpl::bool_ -inline typename enable_if, mpl::bool_::result_type>::value == number_kind_integer> >, Integer>::type - integer_modulus(const multiprecision::detail::mp_exp& x, Integer val) +template +inline typename enable_if, mpl::bool_::result_type>::value == number_kind_integer> >, Integer>::type + integer_modulus(const multiprecision::detail::mp_exp& x, Integer val) { - typedef typename multiprecision::detail::mp_exp::result_type result_type; + typedef typename multiprecision::detail::mp_exp::result_type result_type; return integer_modulus(result_type(x), val); } @@ -97,11 +97,11 @@ inline typename enable_if_c::value == number_kind_integ return eval_lsb(x.backend()); } -template -inline typename enable_if_c::result_type>::value == number_kind_integer, unsigned>::type - lsb(const multiprecision::detail::mp_exp& x) +template +inline typename enable_if_c::result_type>::value == number_kind_integer, unsigned>::type + lsb(const multiprecision::detail::mp_exp& x) { - typedef typename multiprecision::detail::mp_exp::result_type number_type; + typedef typename multiprecision::detail::mp_exp::result_type number_type; number_type n(x); using default_ops::eval_lsb; return eval_lsb(n.backend()); @@ -115,11 +115,11 @@ inline typename enable_if_c::value == number_kind_integ return eval_bit_test(x.backend(), index); } -template -inline typename enable_if_c::result_type>::value == number_kind_integer, bool>::type - bit_test(const multiprecision::detail::mp_exp& x, unsigned index) +template +inline typename enable_if_c::result_type>::value == number_kind_integer, bool>::type + bit_test(const multiprecision::detail::mp_exp& x, unsigned index) { - typedef typename multiprecision::detail::mp_exp::result_type number_type; + typedef typename multiprecision::detail::mp_exp::result_type number_type; number_type n(x); using default_ops::eval_bit_test; return eval_bit_test(n.backend(), index); @@ -152,6 +152,150 @@ inline typename enable_if_c::value == number_kind_integ return x; } +namespace detail{ + +// +// Calculate (a^p)%c: +// +template +void eval_powm(Backend& result, const Backend& a, const Backend& p, const Backend& c) +{ + typedef typename canonical::type ui_type; + Backend x, y(a), b(p); + x = ui_type(1u); + while(eval_get_sign(b) > 0) + { + if(eval_bit_test(b, 0)) + { + eval_multiply(result, x, y); + eval_modulus(x, result, c); + } + eval_multiply(result, y, y); + eval_modulus(y, result, c); + eval_right_shift(b, ui_type(1)); + } + eval_modulus(result, x, c); +} + +template +void eval_powm(Backend& result, const Backend& a, const Backend& p, Integer c) +{ + typedef typename canonical::type ui_type; + typedef typename canonical::type i_type; + + if(eval_get_sign(p) < 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); + } + + Backend x, y(a), b(p); + x = ui_type(1u); + while(eval_get_sign(b) > 0) + { + if(eval_bit_test(b, 0)) + { + eval_multiply(result, x, y); + eval_modulus(x, result, static_cast(c)); + } + eval_multiply(result, y, y); + eval_modulus(y, result, static_cast(c)); + eval_right_shift(b, ui_type(1)); + } + eval_modulus(result, x, static_cast(c)); +} + +template +void eval_powm(Backend& result, const Backend& a, Integer b, const Backend& c) +{ + typedef typename canonical::type ui_type; + typedef typename canonical::type i_type; + + if(b < 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); + } + + Backend x, y(a); + x = ui_type(1u); + while(b > 0) + { + if(b & 1) + { + eval_multiply(result, x, y); + eval_modulus(x, result, c); + } + eval_multiply(result, y, y); + eval_modulus(y, result, c); + b >>= 1; + } + eval_modulus(result, x, c); +} + +template +void eval_powm(Backend& result, const Backend& a, Integer1 b, Integer2 c) +{ + typedef typename canonical::type ui_type; + typedef typename canonical::type i1_type; + typedef typename canonical::type i2_type; + + if(b < 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); + } + + Backend x, y(a); + x = ui_type(1u); + while(b > 0) + { + if(b & 1) + { + eval_multiply(result, x, y); + eval_modulus(x, result, static_cast(c)); + } + eval_multiply(result, y, y); + eval_modulus(y, result, static_cast(c)); + b >>= 1; + } + eval_modulus(result, x, static_cast(c)); +} + +struct powm_func +{ + template + void operator()(T& result, const T& b, const U& p, const V& m)const + { + eval_powm(result, b, p, m); + } +}; + +} + +template +inline typename enable_if< + mpl::and_< + mpl::bool_::value == number_kind_integer>, + mpl::or_< + is_mp_number, + is_mp_number_expression + >, + mpl::or_< + is_mp_number, + is_mp_number_expression, + is_integral + >, + mpl::or_< + is_mp_number, + is_mp_number_expression, + is_integral + > + >, + detail::mp_exp >::type + powm(const T& b, const U& p, const V& mod) +{ + return detail::mp_exp( + detail::powm_func(), b, p, mod); +} + }} //namespaces #endif diff --git a/include/boost/multiprecision/miller_rabin.hpp b/include/boost/multiprecision/miller_rabin.hpp index 1e6bbe98..03f21b53 100644 --- a/include/boost/multiprecision/miller_rabin.hpp +++ b/include/boost/multiprecision/miller_rabin.hpp @@ -197,17 +197,17 @@ bool miller_rabin_test(const mp_number& x, unsigne return miller_rabin_test(x, trials, gen); } -template -bool miller_rabin_test(const detail::mp_exp & n, unsigned trials, Engine& gen) +template +bool miller_rabin_test(const detail::mp_exp & n, unsigned trials, Engine& gen) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::mp_exp::result_type number_type; return miller_rabin_test(number_type(n), trials, gen); } -template -bool miller_rabin_test(const detail::mp_exp & n, unsigned trials) +template +bool miller_rabin_test(const detail::mp_exp & n, unsigned trials) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::mp_exp::result_type number_type; return miller_rabin_test(number_type(n), trials); } diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 41f9106c..c75af312 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -88,10 +88,10 @@ public: mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) : m_backend(v){} - template - mp_number& operator=(const detail::mp_exp& e) + template + mp_number& operator=(const detail::mp_exp& e) { - typedef typename is_same::result_type>::type tag_type; + typedef typename is_same::result_type>::type tag_type; do_assign(e, tag_type()); return *this; } @@ -144,8 +144,8 @@ public: return *this; } - template - mp_number(const detail::mp_exp& e) + template + mp_number(const detail::mp_exp& e) { *this = e; } @@ -165,8 +165,8 @@ public: return *this; } - template - mp_number& operator+=(const detail::mp_exp& e) + template + mp_number& operator+=(const detail::mp_exp& e) { // Create a copy if e contains this, but not if we're just doing a // x *= x @@ -564,17 +564,17 @@ public: return m_backend; } private: - template - void do_assign(const detail::mp_exp& e, const mpl::true_&) + template + void do_assign(const detail::mp_exp& e, const mpl::true_&) { do_assign(e, tag()); } - template - void do_assign(const detail::mp_exp& e, const mpl::false_&) + template + void do_assign(const detail::mp_exp& e, const mpl::false_&) { // The result of the expression isn't the same type as this - // create a temporary result and assign it to *this: - typedef typename detail::mp_exp::result_type temp_type; + typedef typename detail::mp_exp::result_type temp_type; temp_type t(e); *this = t; } @@ -1061,12 +1061,12 @@ private: { typedef typename Exp::right_type right_type; typedef typename right_type::tag_type tag_type; - do_assign_function_1(e.left().value(), e.right(), tag_type()); + do_assign_function_1(e.left().value(), e.right_ref(), tag_type()); } template void do_assign_function_1(const F& f, const Exp& val, const detail::terminal&) { - f(m_backend, function_arg_value(val.value())); + f(m_backend, function_arg_value(val)); } template void do_assign_function_1(const F& f, const Exp& val, const Tag&) @@ -1081,24 +1081,24 @@ private: typedef typename middle_type::tag_type tag_type; typedef typename Exp::right_type end_type; typedef typename end_type::tag_type end_tag; - do_assign_function_2(e.left().value(), e.middle(), e.right(), tag_type(), end_tag()); + do_assign_function_2(e.left().value(), e.middle_ref(), e.right_ref(), tag_type(), end_tag()); } template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const detail::terminal&) { - f(m_backend, function_arg_value(val1.value()), function_arg_value(val2.value())); + f(m_backend, function_arg_value(val1), function_arg_value(val2)); } template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const detail::terminal&) { self_type temp1(val1); - f(m_backend, temp1.backend(), function_arg_value(val2.value())); + f(m_backend, temp1.backend(), function_arg_value(val2)); } template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const Tag2&) { self_type temp2(val2); - f(m_backend, function_arg_value(val1.value()), temp2.backend()); + f(m_backend, function_arg_value(val1), temp2.backend()); } template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const Tag2&) @@ -1108,6 +1108,51 @@ private: f(m_backend, temp1.backend(), temp2.backend()); } + template + void do_assign_function(const Exp& e, const mpl::int_<4>&) + { + typedef typename Exp::left_middle_type left_type; + typedef typename left_type::tag_type left_tag_type; + typedef typename Exp::right_middle_type middle_type; + typedef typename middle_type::tag_type middle_tag_type; + typedef typename Exp::right_type right_type; + typedef typename right_type::tag_type right_tag_type; + do_assign_function_3a(e.left().value(), e.left_middle_ref(), e.right_middle_ref(), e.right_ref(), left_tag_type(), middle_tag_type(), right_tag_type()); + } + template + void do_assign_function_3a(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const detail::terminal&, const Tag2& t2, const Tag3& t3) + { + do_assign_function_3b(f, val1, val2, val3, t2, t3); + } + template + void do_assign_function_3a(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag1&, const Tag2& t2, const Tag3& t3) + { + mp_number t(val1); + do_assign_function_3b(f, t, val2, val3, t2, t3); + } + template + void do_assign_function_3b(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const detail::terminal&, const Tag3& t3) + { + do_assign_function_3c(f, val1, val2, val3, t3); + } + template + void do_assign_function_3b(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag2& t2, const Tag3& t3) + { + mp_number t(val2); + do_assign_function_3c(f, val1, t, val3, t3); + } + template + void do_assign_function_3c(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const detail::terminal&) + { + f(m_backend, function_arg_value(val1), function_arg_value(val2), function_arg_value(val3)); + } + template + void do_assign_function_3c(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag3& t3) + { + mp_number t(val3); + do_assign_function_3c(f, val1, val2, t, detail::terminal()); + } + template void do_add(const Exp& e, const detail::terminal&) { @@ -1485,6 +1530,10 @@ private: static const Backend& function_arg_value(const self_type& v) { return v.backend(); } template static const V& function_arg_value(const V& v) { return v; } + template + static const A1& function_arg_value(const detail::mp_exp& exp) { return exp.value(); } + template + static const Backend& function_arg_value(const detail::mp_exp, A2, A3, A4>& exp) { return exp.value().backend(); } Backend m_backend; }; @@ -1497,14 +1546,14 @@ inline int mp_number_compare(const mp_number& a, c return a.compare(b); } -template -inline int mp_number_compare(const mp_number& a, const mp_exp& b) +template +inline int mp_number_compare(const mp_number& a, const mp_exp& b) { return a.compare(mp_number(b)); } -template -inline int mp_number_compare(const mp_exp& a, const mp_number& b) +template +inline int mp_number_compare(const mp_exp& a, const mp_number& b) { return -b.compare(mp_number(a)); } @@ -1521,26 +1570,26 @@ inline int mp_number_compare(const Val a, const mp_number -inline int mp_number_compare(const mp_exp& a, const mp_exp& b) +template +inline int mp_number_compare(const mp_exp& a, const mp_exp& b) { - typedef typename mp_exp::result_type real1; + typedef typename mp_exp::result_type real1; typedef typename mp_exp::result_type real2; return real1(a).compare(real2(b)); } -template -inline typename enable_if, int>::type mp_number_compare(const mp_exp& a, const Val b) +template +inline typename enable_if, int>::type mp_number_compare(const mp_exp& a, const Val b) { - typedef typename mp_exp::result_type real; + typedef typename mp_exp::result_type real; real t(a); return t.compare(b); } -template -inline typename enable_if, int>::type mp_number_compare(const Val a, const mp_exp& b) +template +inline typename enable_if, int>::type mp_number_compare(const Val a, const mp_exp& b) { - typedef typename mp_exp::result_type real; + typedef typename mp_exp::result_type real; return -real(b).compare(a); } @@ -1640,10 +1689,10 @@ inline std::ostream& operator << (std::ostream& os, const mp_number -inline std::ostream& operator << (std::ostream& os, const mp_exp& r) +template +inline std::ostream& operator << (std::ostream& os, const mp_exp& r) { - typedef typename mp_exp::result_type value_type; + typedef typename mp_exp::result_type value_type; value_type temp(r); return os << temp; } diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index cdb38d26..e72d320a 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -900,18 +900,31 @@ inline void eval_pow(mpfr_float_backend& result, const mpfr_float_back mpfr_pow(result.data(), b.data(), e.data(), GMP_RNDN); } +#ifdef BOOST_MSVC +// +// The enable_if usage below doesn't work with msvc - but only when +// certain other enable_if usages are defined first. It's a capricious +// and rather annoying compiler bug in other words.... +// +# define BOOST_MP_ENABLE_IF_WORKAROUND (Digits10 || !Digits10) && +#else +#define BOOST_MP_ENABLE_IF_WORKAROUND +#endif + template -inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) { mpfr_pow_si(result.data(), b.data(), e, GMP_RNDN); } template -inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) { mpfr_pow_ui(result.data(), b.data(), e, GMP_RNDN); } +#undef BOOST_MP_ENABLE_IF_WORKAROUND + template inline void eval_exp(mpfr_float_backend& result, const mpfr_float_backend& arg) { diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp index fb836463..aba0d58a 100644 --- a/test/test_cpp_int.cpp +++ b/test/test_cpp_int.cpp @@ -257,6 +257,33 @@ void test() BOOST_CHECK_EQUAL(t.str(), t1.str()); } + // + // Now integer functions: + // + mpz_int z1, z2; + test_type t1, t2; + divide_qr(a, b, z1, z2); + divide_qr(a1, b1, t1, t2); + BOOST_CHECK_EQUAL(z1.str(), t1.str()); + BOOST_CHECK_EQUAL(z2.str(), t2.str()); + BOOST_CHECK_EQUAL(integer_modulus(a, si), integer_modulus(a1, si)); + BOOST_CHECK_EQUAL(lsb(a), lsb(a1)); + + for(unsigned i = 0; i < 1000; i += 13) + { + BOOST_CHECK_EQUAL(bit_test(a, i), bit_test(a1, i)); + } + if(!std::numeric_limits::is_modulo) + { + // We have to take care that our powers don't grow too large, otherwise this takes "forever", + // also don't test for modulo types, as these may give a diffferent result from arbitrary + // precision types: + BOOST_CHECK_EQUAL(mpz_int(pow(d, ui % 19)).str(), test_type(pow(d1, ui % 19)).str()); + BOOST_CHECK_EQUAL(mpz_int(powm(a, b, c)).str(), test_type(powm(a, b, c)).str()); + BOOST_CHECK_EQUAL(mpz_int(powm(a, b, ui)).str(), test_type(powm(a, b, ui)).str()); + BOOST_CHECK_EQUAL(mpz_int(powm(a, ui, c)).str(), test_type(powm(a, ui, c)).str()); + } + if(last_error_count != boost::detail::test_errors()) { last_error_count = boost::detail::test_errors(); From ebd7502fdceb08ab4606755d7b0849803c2b660b Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 11 May 2012 17:19:13 +0000 Subject: [PATCH 182/256] Enhance pow and powm tests. Quash some warnings. Fix the IO tests on GCC. [SVN r78423] --- include/boost/multiprecision/cpp_int.hpp | 5 ++-- .../detail/generic_interconvert.hpp | 7 +++++ include/boost/multiprecision/integer_ops.hpp | 25 ++++++++++++++++ include/boost/multiprecision/miller_rabin.hpp | 30 ++++++------------- include/boost/multiprecision/mp_number.hpp | 16 +++++----- test/Jamfile.v2 | 3 ++ test/test_arithmetic.cpp | 25 +++++++++++++++- test/test_cpp_int.cpp | 2 +- test/test_float_io.cpp | 29 +++++++++++++++++- 9 files changed, 108 insertions(+), 34 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 1474a6f0..e57e10d6 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -119,14 +119,14 @@ public: { *limbs() = 0; } - cpp_int_base(const cpp_int_base& o) : m_limbs(0), m_internal(true) + cpp_int_base(const cpp_int_base& o) : allocator_type(o), m_limbs(0), m_internal(true) { resize(o.size()); std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); m_sign = o.m_sign; } #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_base(cpp_int_base&& o) : m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) + cpp_int_base(cpp_int_base&& o) : allocator_type(o), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) { if(m_internal) { @@ -149,6 +149,7 @@ public: { if(this != &o) { + static_cast(*this) = static_cast(o); m_limbs = 0; resize(o.size()); std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); diff --git a/include/boost/multiprecision/detail/generic_interconvert.hpp b/include/boost/multiprecision/detail/generic_interconvert.hpp index 4356e522..caf83869 100644 --- a/include/boost/multiprecision/detail/generic_interconvert.hpp +++ b/include/boost/multiprecision/detail/generic_interconvert.hpp @@ -107,6 +107,10 @@ void generic_interconvert(To& to, const From& from, const mpl::int_ void generic_interconvert(To& to, const From& from, const mpl::int_& /*to_type*/, const mpl::int_& /*from_type*/) { +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4127) +#endif // // The code here only works when the radix of "From" is 2, we could try shifting by other // radixes but it would complicate things.... use a string convertion when the radix is other @@ -178,6 +182,9 @@ void generic_interconvert(To& to, const From& from, const mpl::int_(e)); +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif } template diff --git a/include/boost/multiprecision/integer_ops.hpp b/include/boost/multiprecision/integer_ops.hpp index fa4f6976..ccdbbe8b 100644 --- a/include/boost/multiprecision/integer_ops.hpp +++ b/include/boost/multiprecision/integer_ops.hpp @@ -160,7 +160,14 @@ namespace detail{ template void eval_powm(Backend& result, const Backend& a, const Backend& p, const Backend& c) { + using default_ops::eval_bit_test; + using default_ops::eval_get_sign; + using default_ops::eval_multiply; + using default_ops::eval_modulus; + using default_ops::eval_right_shift; + typedef typename canonical::type ui_type; + Backend x, y(a), b(p); x = ui_type(1u); while(eval_get_sign(b) > 0) @@ -183,6 +190,12 @@ void eval_powm(Backend& result, const Backend& a, const Backend& p, Integer c) typedef typename canonical::type ui_type; typedef typename canonical::type i_type; + using default_ops::eval_bit_test; + using default_ops::eval_get_sign; + using default_ops::eval_multiply; + using default_ops::eval_modulus; + using default_ops::eval_right_shift; + if(eval_get_sign(p) < 0) { BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); @@ -210,6 +223,12 @@ void eval_powm(Backend& result, const Backend& a, Integer b, const Backend& c) typedef typename canonical::type ui_type; typedef typename canonical::type i_type; + using default_ops::eval_bit_test; + using default_ops::eval_get_sign; + using default_ops::eval_multiply; + using default_ops::eval_modulus; + using default_ops::eval_right_shift; + if(b < 0) { BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); @@ -238,6 +257,12 @@ void eval_powm(Backend& result, const Backend& a, Integer1 b, Integer2 c) typedef typename canonical::type i1_type; typedef typename canonical::type i2_type; + using default_ops::eval_bit_test; + using default_ops::eval_get_sign; + using default_ops::eval_multiply; + using default_ops::eval_modulus; + using default_ops::eval_right_shift; + if(b < 0) { BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); diff --git a/include/boost/multiprecision/miller_rabin.hpp b/include/boost/multiprecision/miller_rabin.hpp index 03f21b53..557114cd 100644 --- a/include/boost/multiprecision/miller_rabin.hpp +++ b/include/boost/multiprecision/miller_rabin.hpp @@ -10,25 +10,6 @@ namespace boost{ namespace multiprecision{ -// -// Calculate (a^b)%c: -// -template -void expmod(const mp_number& a, mp_number b, const mp_number& c, mp_number& result) -{ - typedef mp_number number_type; - number_type x(1), y(a); - while(b > 0) - { - if(b & 1) - { - x = (x * y) % c; - } - y = (y * y) % c; - b /= 2; - } - result = x % c; -} template bool check_small_factors(const mp_number& n) @@ -140,6 +121,10 @@ template typename enable_if_c::value == number_kind_integer, bool>::type miller_rabin_test(const mp_number& n, unsigned trials, Engine& gen) { +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4127) +#endif typedef mp_number number_type; if(n <= 227) @@ -155,7 +140,7 @@ typename enable_if_c::value == number_kind_integer, boo // Begin with a single Fermat test - it excludes a lot of candidates: // number_type q(228), x, y; // We know n is greater than this, as we've excluded small factors - expmod(q, nm1, n, x); + x = powm(q, nm1, n); if(x != 1u) return false; @@ -174,7 +159,7 @@ typename enable_if_c::value == number_kind_integer, boo for(unsigned i = 0; i < trials; ++i) { x = dist(gen); - expmod(x, q, n, y); + y = powm(x, q, n); unsigned j = 0; while(true) { @@ -188,6 +173,9 @@ typename enable_if_c::value == number_kind_integer, boo } } return true; // Yeheh! probably prime. +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif } template diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index c75af312..84a5feae 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -59,12 +59,12 @@ public: mp_number(const mp_number& val) : m_backend(val.m_backend) {} template - mp_number(const mp_number& val, typename enable_if >::type* dummy1 = 0) + mp_number(const mp_number& val, typename enable_if >::type* = 0) { m_backend = val.backend(); } template - mp_number(const mp_number& val, typename disable_if >::type* dummy1 = 0) + mp_number(const mp_number& val, typename disable_if >::type* = 0) { // // Attempt a generic interconvertion: @@ -72,13 +72,13 @@ public: detail::generic_interconvert(backend(), val.backend(), number_category(), number_category()); } template - mp_number(V v1, V v2, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) + mp_number(V v1, V v2, typename enable_if, is_same, is_convertible > >::type* = 0) { using default_ops::assign_components; assign_components(m_backend, canonical_value(v1), canonical_value(v2)); } template - mp_number(const mp_number& v1, const mp_number& v2, typename enable_if >::type* dummy1 = 0) + mp_number(const mp_number& v1, const mp_number& v2, typename enable_if >::type* = 0) { using default_ops::assign_components; assign_components(m_backend, v1.backend(), v2.backend()); @@ -1136,7 +1136,7 @@ private: do_assign_function_3c(f, val1, val2, val3, t3); } template - void do_assign_function_3b(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag2& t2, const Tag3& t3) + void do_assign_function_3b(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag2& /*t2*/, const Tag3& t3) { mp_number t(val2); do_assign_function_3c(f, val1, t, val3, t3); @@ -1147,7 +1147,7 @@ private: f(m_backend, function_arg_value(val1), function_arg_value(val2), function_arg_value(val3)); } template - void do_assign_function_3c(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag3& t3) + void do_assign_function_3c(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag3& /*t3*/) { mp_number t(val3); do_assign_function_3c(f, val1, val2, t, detail::terminal()); @@ -1727,7 +1727,7 @@ inline std::istream& operator >> (std::istream& is, rational= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F')))) + while((EOF != (c = static_cast(is.peek()))) && (c == 'x' || c == 'X' || c == '-' || c == '+' || (c >= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F')))) { if(c == 'x' || c == 'X') have_hex = true; @@ -1739,7 +1739,7 @@ inline std::istream& operator >> (std::istream& is, rational= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F')))) + while((EOF != (c = static_cast(is.peek()))) && (c == 'x' || c == 'X' || c == '-' || c == '+' || (c >= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F')))) { if(c == 'x' || c == 'X') have_hex = true; diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 006df7b0..31c52fc0 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -23,6 +23,9 @@ project : requirements $(mpfr_path)/build.vc10/lib/Win32/Debug $(tommath_path) msvc:static + msvc:all + gcc:-Wall + gcc:-Wextra ; local enable-specfun = [ MATCH (--enable-specfun) : [ modules.peek : ARGV ] ] ; diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index c230a9cd..00b70f4f 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -412,7 +412,7 @@ void test_integer_ops(const boost::mpl::int_::is_specialized && (!std::numeric_limits::is_bounded || (i * 17 < std::numeric_limits::digits))) + if(std::numeric_limits::is_specialized && (!std::numeric_limits::is_bounded || ((int)i * 17 < std::numeric_limits::digits))) { BOOST_TEST(lsb(Real(1) << (i * 17)) == i * 17); BOOST_TEST(bit_test(Real(1) << (i * 17), i * 17)); @@ -428,6 +428,29 @@ void test_integer_ops(const boost::mpl::int_ diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp index aba0d58a..52b4102a 100644 --- a/test/test_cpp_int.cpp +++ b/test/test_cpp_int.cpp @@ -284,7 +284,7 @@ void test() BOOST_CHECK_EQUAL(mpz_int(powm(a, ui, c)).str(), test_type(powm(a, ui, c)).str()); } - if(last_error_count != boost::detail::test_errors()) + if(last_error_count != (unsigned)boost::detail::test_errors()) { last_error_count = boost::detail::test_errors(); std::cout << std::hex << std::showbase; diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp index 17bc33d5..fb51eede 100644 --- a/test/test_float_io.cpp +++ b/test/test_float_io.cpp @@ -208,6 +208,33 @@ T generate_random() return ldexp(val, ui(gen)); } +template +struct max_digits10_proxy +{ + static const unsigned value = std::numeric_limits::digits10 + 5; +}; +#ifdef TEST_CPP_DEC_FLOAT +template +struct max_digits10_proxy, ET> > +{ + static const unsigned value = std::numeric_limits, ET> >::max_digits10; +}; +#endif +#ifdef TEST_MPF_50 +template +struct max_digits10_proxy, ET> > +{ + static const unsigned value = std::numeric_limits, ET> >::max_digits10; +}; +#endif +#ifdef TEST_MPFR_50 +template +struct max_digits10_proxy, ET> > +{ + static const unsigned value = std::numeric_limits, ET> >::max_digits10; +}; +#endif + template void do_round_trip(const T& val, std::ios_base::fmtflags f) { @@ -215,7 +242,7 @@ void do_round_trip(const T& val, std::ios_base::fmtflags f) #ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST ss << std::setprecision(std::numeric_limits::max_digits10); #else - ss << std::setprecision(std::numeric_limits::digits10 + 5); + ss << std::setprecision(max_digits10_proxy::value); #endif ss.flags(f); ss << val; From cd741c1249d0f727bb68fbf1a9f4fe452d410b1a Mon Sep 17 00:00:00 2001 From: "Vicente J. Botet Escriba" Date: Sun, 3 Jun 2012 20:51:41 +0000 Subject: [PATCH 183/256] Multiprecision: added error log [SVN r78803] --- test/error.txt | 93662 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 93662 insertions(+) create mode 100644 test/error.txt diff --git a/test/error.txt b/test/error.txt new file mode 100644 index 00000000..7c949f7a --- /dev/null +++ b/test/error.txt @@ -0,0 +1,93662 @@ +warning: mismatched versions of Boost.Build engine and core +warning: Boost.Build engine (bjam) is 2011.04.00 +warning: Boost.Build core (at /Users/viboes/boost/trunk/tools/build/v2) is 2011.12-svn +...patience... +...found 905 targets... +...updating 4 targets... +testing.capture-output bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9/release/test_float_io_cpp_dec_float.run +====== BEGIN OUTPUT ====== +Testing value 123456789 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 1e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 1.e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +1e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.2e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +123456789.0 +Testing value 123456789 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.2e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.23e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +123456789.00 +Testing value 123456789 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.23e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.235e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +123456789.000 +Testing value 123456789 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.235e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +123456789.0000 +Testing value 123456789 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 123456789.00000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 123456789.00000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +123456789.00000 +Testing value 123456789 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 123456789.000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 123456789.000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +123456789.000000 +Testing value 123456789 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 123456789.0000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 123456789.0000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +123456789.0000000 +Testing value 123456789 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.23456789e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.23456789e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.23456789e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 123456789.00000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 123456789.00000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +123456789.00000000 +Testing value 123456789 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 123456789. +Testing value 123456789 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.234567890e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.234567890e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.234567890e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 123456789.000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 123456789.000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +123456789.000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.2345678900e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.2345678900e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.2345678900e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 123456789.0000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 123456789.0000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +123456789.0000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.23456789000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.23456789000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.23456789000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 123456789.00000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 123456789.00000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +123456789.00000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.234567890000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.234567890000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.234567890000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 123456789.000000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 123456789.000000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +123456789.000000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 123456789.0000000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 123456789.0000000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +123456789.0000000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -1e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -1.e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -1e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -123456789. +Testing value -123456789 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +15432098.6 +Testing value 15432098.625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +15432098.62 +Testing value 15432098.625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +15432098.6250 +Testing value 15432098.625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +15432098.62500 +Testing value 15432098.625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.543210e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 15432098.625000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 15432098.625000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +15432098.625000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 15432098.6250000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 15432098.6250000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +15432098.6250000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 15432099 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 15432099. +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +15432099 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 15432098.62500000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 15432098.62500000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +15432098.62500000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +15432098.6 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 15432098.625000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 15432098.625000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +15432098.625000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +15432098.62 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 15432098.6250000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 15432098.6250000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099. +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +1929012.3 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +1929012.33 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +1929012.328 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +1929012.3281 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +1929012.32812 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +1929012.328125 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1929012 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1929012. +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1929012 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +1929012.3 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +1929012.33 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +1929012.328 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +1929012.3281 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +1929012.32812 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +1929012.328125 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 1929012.3281250000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 1929012.3281250000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012. +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +241126.5 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +241126.54 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +241126.5410 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +241126.54102 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 241127 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 241127. +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +241127 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +241126.541016 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +241126.5 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +241126.5410156 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +241126.54 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 241126.54101562 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 241126.54101562 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +241126.54101562 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 241126.541015625 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 241126.541015625 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +241126.541015625 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +241126.54102 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +241126.541016 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +241126.5410156 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 241126.5410156250000 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 241126.5410156250000 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127. +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 3e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 3.e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +3e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +30140.8 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +30140.82 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +30140.818 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +30140.8176 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 30141 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 30141. +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +30141 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +30140.81763 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +30140.8 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +30140.82 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +30140.818 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +30140.8176 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +30140.81763 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 30140.8176269531250 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 30140.8176269531250 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -3.e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141. +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +3767.60 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +3767.602 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3768 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3768. +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3768 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +3767.602 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 3767.6022033691406 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 3767.6022033691406 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3768 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3768. +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3768 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 5e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 5.e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +5e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +471.0 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 471 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 471. +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +471 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +470.950 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 471 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +471 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +470.9503 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +470.95028 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +470.950275 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +470.9503 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +470.95028 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +470.950275 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 470.9502754211426 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 470.9502754211426 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -5e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -5.e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -5e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -471. +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 6e+01 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 6.e+01 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +6e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +58.9 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 59 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 59. +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +59 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +58.87 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +58.9 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +58.869 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +58.87 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +58.8688 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +58.869 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +58.86878 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +58.8688 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +58.868784 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +58.86878 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +58.868784 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 58.8687844276428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 58.8687844276428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -6e+01 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -6.e+01 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -6e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -59 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -59. +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -59 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 7 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 7. +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +7 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +7.4 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +7.4 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +7.36 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +7.36 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +7.359 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +7.359 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 7.3585980534554 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 7.3585980534554 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -7 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -7. +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -7 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.9 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.9 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.920 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.1 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.1 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.11 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.11 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.01 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.014 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.01 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.014 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 3e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 3.e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +3e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000280708239 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000280708239 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -3e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -3.e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -3e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000035088530 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000035088530 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000004386066 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000004386066 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 5.e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000548258 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000548258 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -5.e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 7e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 7.e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +7e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000068532 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000068532 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -7e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -7.e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -7e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 9e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 9.e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +9e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000008567 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000008567 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -9e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -9.e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -9e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +Testing value 123456789 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 1e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 1.e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +1e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.2e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +123456789.0 +Testing value 123456789 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.2e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.23e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +123456789.00 +Testing value 123456789 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.23e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.235e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +123456789.000 +Testing value 123456789 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.235e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +123456789.0000 +Testing value 123456789 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 123456789.00000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 123456789.00000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +123456789.00000 +Testing value 123456789 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 123456789.000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 123456789.000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +123456789.000000 +Testing value 123456789 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 123456789.0000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 123456789.0000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +123456789.0000000 +Testing value 123456789 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.23456789e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.23456789e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.23456789e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 123456789.00000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 123456789.00000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +123456789.00000000 +Testing value 123456789 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 123456789. +Testing value 123456789 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.234567890e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.234567890e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.234567890e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 123456789.000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 123456789.000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +123456789.000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.2345678900e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.2345678900e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.2345678900e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 123456789.0000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 123456789.0000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +123456789.0000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.23456789000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.23456789000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.23456789000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 123456789.00000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 123456789.00000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +123456789.00000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.234567890000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.234567890000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.234567890000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 123456789.000000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 123456789.000000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +123456789.000000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 123456789.0000000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 123456789.0000000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +123456789.0000000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -1e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -1.e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -1e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -123456789. +Testing value -123456789 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +15432098.6 +Testing value 15432098.625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +15432098.62 +Testing value 15432098.625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +15432098.6250 +Testing value 15432098.625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +15432098.62500 +Testing value 15432098.625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.543210e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 15432098.625000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 15432098.625000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +15432098.625000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 15432098.6250000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 15432098.6250000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +15432098.6250000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 15432099 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 15432099. +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +15432099 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 15432098.62500000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 15432098.62500000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +15432098.62500000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +15432098.6 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 15432098.625000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 15432098.625000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +15432098.625000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +15432098.62 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 15432098.6250000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 15432098.6250000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099. +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +1929012.3 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +1929012.33 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +1929012.328 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +1929012.3281 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +1929012.32812 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +1929012.328125 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1929012 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1929012. +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1929012 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +1929012.3 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +1929012.33 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +1929012.328 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +1929012.3281 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +1929012.32812 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +1929012.328125 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 1929012.3281250000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 1929012.3281250000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012. +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +241126.5 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +241126.54 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +241126.5410 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +241126.54102 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 241127 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 241127. +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +241127 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +241126.541016 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +241126.5 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +241126.5410156 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +241126.54 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 241126.54101562 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 241126.54101562 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +241126.54101562 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 241126.541015625 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 241126.541015625 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +241126.541015625 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +241126.54102 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +241126.541016 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +241126.5410156 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 241126.5410156250000 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 241126.5410156250000 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127. +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 3e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 3.e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +3e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +30140.8 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +30140.82 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +30140.818 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +30140.8176 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 30141 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 30141. +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +30141 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +30140.81763 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +30140.8 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +30140.82 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +30140.818 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +30140.8176 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +30140.81763 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 30140.8176269531250 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 30140.8176269531250 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -3.e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141. +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +3767.60 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +3767.602 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3768 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3768. +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3768 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +3767.602 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 3767.6022033691406 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 3767.6022033691406 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3768 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3768. +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3768 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 5e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 5.e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +5e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +471.0 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 471 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 471. +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +471 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +470.950 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 471 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +471 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +470.9503 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +470.95028 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +470.950275 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +470.9503 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +470.95028 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +470.950275 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 470.9502754211426 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 470.9502754211426 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -5e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -5.e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -5e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -471. +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 6e+01 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 6.e+01 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +6e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +58.9 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 59 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 59. +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +59 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +58.87 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +58.9 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +58.869 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +58.87 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +58.8688 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +58.869 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +58.86878 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +58.8688 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +58.868784 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +58.86878 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +58.868784 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 58.8687844276428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 58.8687844276428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -6e+01 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -6.e+01 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -6e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -59 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -59. +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -59 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 7 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 7. +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +7 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +7.4 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +7.4 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +7.36 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +7.36 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +7.359 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +7.359 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 7.3585980534554 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 7.3585980534554 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -7 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -7. +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -7 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.9 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.9 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.920 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.1 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.1 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.11 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.11 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.01 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.014 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.01 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.014 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 3e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 3.e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +3e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000280708239 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000280708239 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -3e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -3.e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -3e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000035088530 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000035088530 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000004386066 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000004386066 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 5.e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000548258 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000548258 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -5.e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 7e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 7.e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +7e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000068532 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000068532 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -7e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -7.e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -7e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 9e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 9.e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +9e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000008567 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000008567 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -9e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -9.e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -9e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +9360 errors detected. + +EXIT STATUS: 1 +====== END OUTPUT ====== + + + "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9/release/test_float_io_cpp_dec_float" > "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9/release/test_float_io_cpp_dec_float.output" 2>&1 + status=$? + echo >> "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9/release/test_float_io_cpp_dec_float.output" + echo EXIT STATUS: $status >> "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9/release/test_float_io_cpp_dec_float.output" + if test $status -eq 0 ; then + cp "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9/release/test_float_io_cpp_dec_float.output" "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9/release/test_float_io_cpp_dec_float.run" + fi + verbose=0 + if test $status -ne 0 ; then + verbose=1 + fi + if test $verbose -eq 1 ; then + echo ====== BEGIN OUTPUT ====== + cat "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9/release/test_float_io_cpp_dec_float.output" + echo ====== END OUTPUT ====== + fi + exit $status + +...failed testing.capture-output bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9/release/test_float_io_cpp_dec_float.run... +testing.capture-output bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9x/release/test_float_io_cpp_dec_float.run +====== BEGIN OUTPUT ====== +Testing value 123456789 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 1e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 1.e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +1e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.2e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +123456789.0 +Testing value 123456789 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.2e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.23e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +123456789.00 +Testing value 123456789 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.23e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.235e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +123456789.000 +Testing value 123456789 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.235e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +123456789.0000 +Testing value 123456789 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 123456789.00000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 123456789.00000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +123456789.00000 +Testing value 123456789 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 123456789.000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 123456789.000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +123456789.000000 +Testing value 123456789 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 123456789.0000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 123456789.0000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +123456789.0000000 +Testing value 123456789 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.23456789e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.23456789e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.23456789e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 123456789.00000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 123456789.00000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +123456789.00000000 +Testing value 123456789 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 123456789. +Testing value 123456789 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.234567890e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.234567890e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.234567890e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 123456789.000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 123456789.000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +123456789.000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.2345678900e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.2345678900e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.2345678900e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 123456789.0000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 123456789.0000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +123456789.0000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.23456789000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.23456789000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.23456789000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 123456789.00000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 123456789.00000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +123456789.00000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.234567890000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.234567890000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.234567890000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 123456789.000000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 123456789.000000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +123456789.000000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 123456789.0000000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 123456789.0000000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +123456789.0000000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -1e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -1.e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -1e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -123456789. +Testing value -123456789 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +15432098.6 +Testing value 15432098.625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +15432098.62 +Testing value 15432098.625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +15432098.6250 +Testing value 15432098.625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +15432098.62500 +Testing value 15432098.625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.543210e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 15432098.625000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 15432098.625000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +15432098.625000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 15432098.6250000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 15432098.6250000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +15432098.6250000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 15432099 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 15432099. +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +15432099 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 15432098.62500000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 15432098.62500000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +15432098.62500000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +15432098.6 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 15432098.625000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 15432098.625000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +15432098.625000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +15432098.62 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 15432098.6250000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 15432098.6250000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099. +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +1929012.3 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +1929012.33 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +1929012.328 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +1929012.3281 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +1929012.32812 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +1929012.328125 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1929012 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1929012. +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1929012 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +1929012.3 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +1929012.33 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +1929012.328 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +1929012.3281 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +1929012.32812 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +1929012.328125 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 1929012.3281250000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 1929012.3281250000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012. +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +241126.5 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +241126.54 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +241126.5410 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +241126.54102 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 241127 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 241127. +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +241127 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +241126.541016 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +241126.5 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +241126.5410156 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +241126.54 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 241126.54101562 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 241126.54101562 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +241126.54101562 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 241126.541015625 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 241126.541015625 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +241126.541015625 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +241126.54102 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +241126.541016 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +241126.5410156 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 241126.5410156250000 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 241126.5410156250000 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127. +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 3e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 3.e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +3e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +30140.8 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +30140.82 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +30140.818 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +30140.8176 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 30141 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 30141. +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +30141 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +30140.81763 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +30140.8 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +30140.82 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +30140.818 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +30140.8176 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +30140.81763 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 30140.8176269531250 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 30140.8176269531250 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -3.e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141. +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +3767.60 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +3767.602 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3768 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3768. +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3768 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +3767.602 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 3767.6022033691406 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 3767.6022033691406 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3768 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3768. +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3768 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 5e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 5.e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +5e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +471.0 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 471 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 471. +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +471 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +470.950 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 471 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +471 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +470.9503 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +470.95028 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +470.950275 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +470.9503 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +470.95028 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +470.950275 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 470.9502754211426 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 470.9502754211426 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -5e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -5.e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -5e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -471. +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 6e+01 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 6.e+01 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +6e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +58.9 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 59 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 59. +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +59 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +58.87 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +58.9 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +58.869 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +58.87 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +58.8688 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +58.869 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +58.86878 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +58.8688 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +58.868784 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +58.86878 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +58.868784 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 58.8687844276428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 58.8687844276428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -6e+01 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -6.e+01 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -6e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -59 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -59. +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -59 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 7 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 7. +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +7 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +7.4 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +7.4 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +7.36 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +7.36 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +7.359 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +7.359 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 7.3585980534554 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 7.3585980534554 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -7 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -7. +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -7 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.9 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.9 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.920 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.1 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.1 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.11 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.11 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.01 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.014 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.01 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.014 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 3e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 3.e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +3e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000280708239 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000280708239 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -3e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -3.e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -3e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000035088530 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000035088530 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000004386066 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000004386066 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 5.e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000548258 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000548258 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -5.e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 7e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 7.e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +7e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000068532 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000068532 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -7e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -7.e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -7e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 9e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 9.e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +9e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000008567 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000008567 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -9e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -9.e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -9e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +Testing value 123456789 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 1e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 1.e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +1e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.2e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +123456789.0 +Testing value 123456789 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.2e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.2e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.23e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +123456789.00 +Testing value 123456789 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.23e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.23e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.235e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +123456789.000 +Testing value 123456789 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.235e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.235e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +123456789.0000 +Testing value 123456789 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.2346e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.2346e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 123456789.00000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 123456789.00000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +123456789.00000 +Testing value 123456789 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.23457e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.23457e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 123456789.000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 123456789.000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +123456789.000000 +Testing value 123456789 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.234568e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1.234568e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 123456789.0000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 123456789.0000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +123456789.0000000 +Testing value 123456789 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1.2345679e+08 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +1.2345679e+08 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.23456789e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.23456789e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.23456789e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 123456789.00000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 123456789.00000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +123456789.00000000 +Testing value 123456789 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 123456789. +Testing value 123456789 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.234567890e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.234567890e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.234567890e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 123456789.000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 123456789.000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +123456789.000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 123456789.0 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.2345678900e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.2345678900e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.2345678900e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 123456789.0000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 123456789.0000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +123456789.0000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 123456789.00 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.23456789000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.23456789000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.23456789000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 123456789.00000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 123456789.00000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +123456789.00000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 123456789.000 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.234567890000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.234567890000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.234567890000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 123456789.000000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 123456789.000000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +123456789.000000000000 +Testing value 123456789 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 123456789 +Testing value 123456789 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 123456789.0000 +Testing value 123456789 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +123456789 +Testing value 123456789 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.2345678900000e+08 +Testing value 123456789 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 123456789.0000000000000 +Testing value 123456789 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 123456789.0000000000000 +Testing value 123456789 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +123456789.0000000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -1e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -1.e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -1e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.2e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.23e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.235e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.2346e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -123456789.00000 +Testing value -123456789 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.23457e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -123456789.000000 +Testing value -123456789 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.234568e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -123456789.0000000 +Testing value -123456789 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1.2345679e+08 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.23456789e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -123456789.00000000 +Testing value -123456789 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -123456789. +Testing value -123456789 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.234567890e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -123456789.000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -123456789.0 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.2345678900e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -123456789.0000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -123456789.00 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.23456789000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -123456789.00000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -123456789.000 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.234567890000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -123456789.000000000000 +Testing value -123456789 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -123456789.0000 +Testing value -123456789 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -123456789 +Testing value -123456789 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.2345678900000e+08 +Testing value -123456789 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value -123456789 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value -123456789 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -123456789.0000000000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +15432098.6 +Testing value 15432098.625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.5e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.5e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +15432098.62 +Testing value 15432098.625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.54e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.54e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.543e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.543e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +15432098.6250 +Testing value 15432098.625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.5432e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.5432e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +15432098.62500 +Testing value 15432098.625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.543210e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 15432098.625000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 15432098.625000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +15432098.625000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.54321e+07 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1.543210e+07 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1.54321e+07 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.5432099e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 15432098.6250000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 15432098.6250000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +15432098.6250000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 15432099 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 15432099. +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +15432099 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.54320986e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 15432098.62500000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 15432098.62500000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +15432098.62500000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 15432098.6 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +15432098.6 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.543209862e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 15432098.625000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 15432098.625000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +15432098.625000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 15432098.62 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +15432098.62 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.5432098625e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +15432098.6250000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.54320986250e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +15432098.62500000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 15432098.6250 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.543209862500e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +15432098.625000000000 +Testing value 15432098.625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 15432098.625 +Testing value 15432098.625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 15432098.62500 +Testing value 15432098.625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +15432098.625 +Testing value 15432098.625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.5432098625000e+07 +Testing value 15432098.625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 15432098.6250000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 15432098.6250000000000 +Testing value 15432098.625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.5e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.54e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.543e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.5432e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -15432098.625000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.543210e+07 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1.54321e+07 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.5432099e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -15432098.6250000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099. +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -15432099 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.54320986e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -15432098.62500000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -15432098.6 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.543209862e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -15432098.625000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -15432098.62 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.5432098625e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -15432098.6250000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.54320986250e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -15432098.62500000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -15432098.6250 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.543209862500e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -15432098.625000000000 +Testing value -15432098.625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -15432098.62500 +Testing value -15432098.625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -15432098.625 +Testing value -15432098.625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.5432098625000e+07 +Testing value -15432098.625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value -15432098.625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -15432098.6250000000000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +1929012.3 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 1.9e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +1.9e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +1929012.33 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 1.93e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +1.93e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +1929012.328 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +1929012.3281 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.929e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 1.9290e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +1.929e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +1929012.32812 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +1.92901e+06 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.929012e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +1929012.328125 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 1929012 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 1929012. +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +1929012 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.9290123e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +1929012.3281250 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 1929012.3 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +1929012.3 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.92901233e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +1929012.32812500 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 1929012.33 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +1929012.33 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.929012328e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +1929012.328125000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 1929012.328 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +1929012.328 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.9290123281e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +1929012.3281250000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 1929012.3281 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +1929012.3281 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.92901232812e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +1929012.32812500000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 1929012.32812 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +1929012.32812 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.929012328125e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +1929012.328125000000 +Testing value 1929012.328125 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 1929012.328125 +Testing value 1929012.328125 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +1929012.328125 +Testing value 1929012.328125 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.9290123281250e+06 +Testing value 1929012.328125 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 1929012.3281250000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 1929012.3281250000000 +Testing value 1929012.328125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -1.9e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -1.93e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.9290e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -1.929e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -1.92901e+06 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.929012e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012. +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -1929012 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.9290123e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -1929012.3281250 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -1929012.3 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.92901233e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -1929012.32812500 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -1929012.33 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.929012328e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -1929012.328125000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -1929012.328 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.9290123281e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -1929012.3281250000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -1929012.3281 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.92901232812e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -1929012.32812500000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -1929012.32812 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.929012328125e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -1929012.328125000000 +Testing value -1929012.328125 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -1929012.328125 +Testing value -1929012.328125 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.9290123281250e+06 +Testing value -1929012.328125 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value -1929012.328125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -1929012.3281250000000 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 2e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 2.e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +2e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +241126.5 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 2.4e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +2.4e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +241126.54 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 2.41e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +2.41e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 2.411e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +2.411e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +241126.5410 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +2.4113e+05 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.41127e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +241126.54102 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 241127 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 241127. +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +241127 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.411265e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +241126.541016 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 241126.5 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +241126.5 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.4112654e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +241126.5410156 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 241126.54 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +241126.54 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.41126541e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 241126.54101562 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 241126.54101562 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +241126.54101562 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.411265410e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 241126.541015625 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 241126.541015625 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +241126.541015625 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 241126.541 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 241126.5410 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +241126.541 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.4112654102e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +241126.5410156250 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 241126.54102 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +241126.54102 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.41126541016e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +241126.54101562500 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 241126.541016 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +241126.541016 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.411265410156e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +241126.541015625000 +Testing value 241126.541015625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 241126.5410156 +Testing value 241126.541015625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +241126.5410156 +Testing value 241126.541015625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.4112654101562e+05 +Testing value 241126.541015625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 241126.5410156250000 +Testing value 241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 241126.5410156250000 +Testing value 241126.541015625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -2e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -2.e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -2e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -2.4e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -2.41e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -2.411e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.4113e+05 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.41127e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127. +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -241127 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.411265e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -241126.5 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.4112654e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -241126.54 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.41126541e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -241126.54101562 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.411265410e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -241126.541015625 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -241126.5410 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -241126.541 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.4112654102e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -241126.5410156250 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -241126.54102 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.41126541016e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -241126.54101562500 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -241126.541016 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.411265410156e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -241126.541015625000 +Testing value -241126.541015625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -241126.5410156 +Testing value -241126.541015625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.4112654101562e+05 +Testing value -241126.541015625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value -241126.541015625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -241126.5410156250000 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 3e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 3.e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +3e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +30140.8 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.0e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +30140.82 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.01e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +30140.818 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3.014e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.0141e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +30140.8176 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 30141 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 30141. +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +30141 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.01408e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +30140.81763 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 30140.8 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +30140.8 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.014082e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 30140.82 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +30140.82 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.0140818e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 30140.818 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +30140.818 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.01408176e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 30140.8176 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +30140.8176 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.014081763e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +30140.817626953 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 30140.81763 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +30140.81763 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.0140817627e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +30140.8176269531 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.01408176270e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +30140.81762695312 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 30140.817627 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 30140.8176270 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +30140.817627 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.014081762695e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +30140.817626953125 +Testing value 30140.817626953125 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +30140.81762695 +Testing value 30140.817626953125 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.0140817626953e+04 +Testing value 30140.817626953125 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 30140.8176269531250 +Testing value 30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 30140.8176269531250 +Testing value 30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -3.e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.0e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.01e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3.014e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.0141e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141. +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -30141 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.01408e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -30140.8 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.014082e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -30140.82 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.0140818e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -30140.818 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.01408176e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -30140.8176 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.014081763e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -30140.817626953 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -30140.81763 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.0140817627e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -30140.8176269531 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.01408176270e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -30140.81762695312 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -30140.8176270 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -30140.817627 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.014081762695e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -30140.817626953125 +Testing value -30140.817626953125 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -30140.81762695 +Testing value -30140.817626953125 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.0140817626953e+04 +Testing value -30140.817626953125 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value -30140.817626953125 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -30140.8176269531250 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3.8e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +3767.60 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.77e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.768e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +3767.602 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3768 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3768. +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3768 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.7676e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.76760e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 3767.6 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 3767.60 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +3767.6 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.767602e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 3767.602 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +3767.602 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.7676022e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.76760220e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 3767.60220 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +3767.6022 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.767602203e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +3767.602203 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.7676022034e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +3767.6022033691 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +3767.6022034 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.76760220337e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +3767.60220336914 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +3767.60220337 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.767602203369e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +3767.602203369141 +Testing value 3767.602203369140625 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +3767.602203369 +Testing value 3767.602203369140625 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.7676022033691e+03 +Testing value 3767.602203369140625 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 3767.6022033691406 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 3767.6022033691406 +Testing value 3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3.8e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.77e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.768e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3768 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3768. +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3768 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.7676e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.76760e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.60 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -3767.6 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.767602e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -3767.602 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.7676022e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.76760220e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -3767.60220 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -3767.6022 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.767602203e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -3767.602203 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.7676022034e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -3767.6022033691 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -3767.6022034 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.76760220337e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -3767.60220336914 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -3767.60220337 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.767602203369e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -3767.602203369141 +Testing value -3767.602203369140625 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -3767.602203369 +Testing value -3767.602203369140625 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.7676022033691e+03 +Testing value -3767.602203369140625 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value -3767.602203369140625 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -3767.6022033691406 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 5e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 5.e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +5e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +471.0 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +4.7e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 4.71e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 471 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 471. +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +471 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 4.710e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +470.950 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 471 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 471.0 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +471 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.7095e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +470.9503 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.70950e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +470.95028 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 470.95 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 470.950 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +470.95 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.709503e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +470.950275 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 470.9503 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +470.9503 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.7095028e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 470.95028 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +470.95028 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.70950275e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 470.950275 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +470.950275 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.709502754e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +470.9502754 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.7095027542e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +470.95027542 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.70950275421e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +470.95027542114 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +470.950275421 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.709502754211e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +470.950275421143 +Testing value 470.95027542114257812 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +470.9502754211 +Testing value 470.95027542114257812 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.7095027542114e+02 +Testing value 470.95027542114257812 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 470.9502754211426 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 470.9502754211426 +Testing value 470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -5e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -5.e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -5e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -4.7e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -4.71e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -471. +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -4.710e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -471.0 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -471 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.7095e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.70950e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.950 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -470.95 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.709503e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -470.9503 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.7095028e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -470.95028 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.70950275e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -470.950275 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.709502754e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -470.9502754 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.7095027542e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -470.95027542 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.70950275421e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -470.95027542114 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -470.950275421 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.709502754211e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -470.950275421143 +Testing value -470.95027542114257812 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -470.9502754211 +Testing value -470.95027542114257812 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.7095027542114e+02 +Testing value -470.95027542114257812 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value -470.95027542114257812 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -470.9502754211426 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 6e+01 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 6.e+01 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +6e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 5.9e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +58.9 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 59 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 59. +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +59 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 5.89e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +58.87 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 58.9 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +58.9 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 5.887e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +58.869 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 58.87 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +58.87 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.8869e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +58.8688 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 58.869 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +58.869 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.88688e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +58.86878 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 58.8688 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +58.8688 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.886878e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +58.868784 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 58.86878 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +58.86878 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.8868784e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 58.868784 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +58.868784 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.88687844e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +58.8687844 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.886878443e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +58.86878443 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.8868784428e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +58.868784428 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.88687844276e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +58.8687844276 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.886878442764e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +58.868784427643 +Testing value 58.868784427642822266 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +58.86878442764 +Testing value 58.868784427642822266 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.8868784427643e+01 +Testing value 58.868784427642822266 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 58.8687844276428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 58.8687844276428 +Testing value 58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -6e+01 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -6.e+01 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -6e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -5.9e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -59 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -59. +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -59 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -5.89e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -58.9 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -5.887e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -58.87 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.8869e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -58.869 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.88688e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -58.8688 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.886878e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -58.86878 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.8868784e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -58.868784 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.88687844e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -58.8687844 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.886878443e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -58.86878443 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.8868784428e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -58.868784428 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.88687844276e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -58.8687844276 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.886878442764e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -58.868784427643 +Testing value -58.868784427642822266 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -58.86878442764 +Testing value -58.868784427642822266 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.8868784427643e+01 +Testing value -58.868784427642822266 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value -58.868784427642822266 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -58.8687844276428 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 7 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 7. +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +7 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 7.4e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +7.4 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 7.4 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +7.4 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 7.36e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +7.36 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 7.36 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +7.36 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 7.359e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +7.359 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 7.359 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +7.359 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 7.3586e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 7.35860e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 7.35860 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +7.3586 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 7.358598e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +7.358598 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 7.3585981e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +7.3585981 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 7.35859805e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +7.35859805 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 7.358598053e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +7.358598053 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 7.3585980535e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +7.3585980535 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 7.35859805346e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +7.35859805346 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 7.358598053455e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +7.358598053455 +Testing value 7.3585980534553527832 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 7.3585980534554e+00 +Testing value 7.3585980534553527832 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 7.3585980534554 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 7.3585980534554 +Testing value 7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -7 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -7. +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -7 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -7.4e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -7.4 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -7.36e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -7.36 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -7.359e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -7.359 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -7.3586e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -7.35860e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.35860 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -7.3586 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -7.358598e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -7.358598 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -7.3585981e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -7.3585981 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -7.35859805e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -7.35859805 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -7.358598053e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -7.358598053 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -7.3585980535e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -7.3585980535 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -7.35859805346e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -7.35859805346 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -7.358598053455e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -7.358598053455 +Testing value -7.3585980534553527832 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -7.3585980534554e+00 +Testing value -7.3585980534553527832 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value -7.3585980534553527832 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -7.3585980534554 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.9 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 9.2e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.9 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.9 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 9.20e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.92 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.92 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 9.198e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.920 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.920 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 9.1982e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.9198 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 9.19825e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.91982 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 9.198248e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.919825 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 9.1982476e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.9198248 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 9.19824757e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.91982476 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 9.198247567e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.919824757 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 9.1982475668e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.9198247567 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 9.19824756682e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.91982475668 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 9.198247566819e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.919824756682 +Testing value 0.9198247566819190979 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 9.1982475668192e-01 +Testing value 0.9198247566819190979 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.9198247566819 +Testing value 0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -9.2e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.9 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -9.20e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.92 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -9.198e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.920 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -9.1982e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.9198 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -9.19825e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.91982 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -9.198248e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.919825 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -9.1982476e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.9198248 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -9.19824757e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.91982476 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -9.198247567e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.919824757 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -9.1982475668e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.9198247567 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -9.19824756682e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.91982475668 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -9.198247566819e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.919824756682 +Testing value -0.9198247566819190979 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -9.1982475668192e-01 +Testing value -0.9198247566819190979 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value -0.9198247566819190979 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.9198247566819 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.1 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.1e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.1 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.1 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.11 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.15e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.11 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.11 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.150e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.115 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.115 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.1498e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.1150 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.14978e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.11498 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.149781e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.114978 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.1497809e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.1149781 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.14978095e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.11497809 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.149780946e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.114978095 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.1497809459e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.1149780946 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.14978094585e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.11497809459 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.149780945852e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.114978094585 +Testing value 0.11497809458523988724 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.1497809458524e-01 +Testing value 0.11497809458523988724 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.1149780945852 +Testing value 0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.1e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.1 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.15e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.11 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.150e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.115 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.1498e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.1150 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.14978e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.11498 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.149781e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.114978 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.1497809e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.1149781 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.14978095e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.11497809 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.149780946e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.114978095 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.1497809459e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.1149780946 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.14978094585e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.11497809459 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.149780945852e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.114978094585 +Testing value -0.11497809458523988724 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.1497809458524e-01 +Testing value -0.11497809458523988724 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value -0.11497809458523988724 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.1149780945852 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.01 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.4e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.014 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.44e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.01 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.01 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.437e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.014 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.014 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.4372e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0144 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.43723e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.01437 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.437226e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.014372 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.4372262e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0143723 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.43722618e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.01437226 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.437226182e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.014372262 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.4372261823e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0143722618 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.43722618232e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.01437226182 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.437226182315e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.014372261823 +Testing value 0.014372261823154985905 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.01437226182315 +Testing value 0.014372261823154985905 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.4372261823155e-02 +Testing value 0.014372261823154985905 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0143722618232 +Testing value 0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.4e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.44e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.01 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.437e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.014 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.4372e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0144 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.43723e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.01437 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.437226e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.014372 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.4372262e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0143723 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.43722618e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.01437226 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.437226182e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.014372262 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.4372261823e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0143722618 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.43722618232e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.01437226182 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.437226182315e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.014372261823 +Testing value -0.014372261823154985905 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.01437226182315 +Testing value -0.014372261823154985905 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.4372261823155e-02 +Testing value -0.014372261823154985905 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value -0.014372261823154985905 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0143722618232 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 1.8e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 1.80e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 1.797e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.002 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 1.7965e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0018 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 1.79653e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00180 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 1.796533e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.001797 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 1.7965327e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0017965 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 1.79653273e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00179653 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 1.796532728e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.001796533 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 1.7965327279e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0017965327 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 1.79653272789e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00179653273 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.00179653272789 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 1.796532727894e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.001796532728 +Testing value 0.0017965327278943732381 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.001796532727894 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 1.7965327278944e-03 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0017965327279 +Testing value 0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -1.8e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -1.80e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -1.797e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.002 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -1.7965e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0018 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -1.79653e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00180 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -1.796533e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.001797 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -1.7965327e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0017965 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -1.79653273e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00179653 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -1.796532728e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.001796533 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -1.7965327279e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0017965327 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -1.79653272789e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00179653273 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.00179653272789 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -1.796532727894e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.001796532728 +Testing value -0.0017965327278943732381 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.001796532727894 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -1.7965327278944e-03 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value -0.0017965327278943732381 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0017965327279 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.2e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.25e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.246e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.2457e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0002 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.24567e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00022 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.245666e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000225 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.2456659e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0002246 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.24566591e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00022457 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.245665910e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000224567 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.2456659099e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0002245666 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +0.00022456659099 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.24566590987e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00022456659 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +0.000224566590987 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.245665909868e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000224566591 +Testing value 0.00022456659098679665476 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +0.0002245665909868 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.2456659098680e-04 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0002245665910 +Testing value 0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.2e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.25e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.246e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.2457e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0002 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.24567e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00022 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.245666e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000225 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.2456659e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0002246 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.24566591e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00022457 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.245665910e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000224567 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.2456659099e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0002245666 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -0.00022456659099 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.24566590987e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00022456659 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -0.000224566590987 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.245665909868e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000224566591 +Testing value -0.00022456659098679665476 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -0.0002245665909868 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.2456659098680e-04 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value -0.00022456659098679665476 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0002245665910 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 3e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 3.e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +3e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +2.8e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +2.81e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +2.807e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +2.8071e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00003 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +2.80708e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000028 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +2.807082e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000281 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +2.8070824e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00002807 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +2.80708239e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000028071 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +2.807082387e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000280708 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +2.8070823873e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00002807082 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +2.80708238733e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000028070824 +Testing value 2.8070823873349581845e-05 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +2.807082387335e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 2.8070823873350e-05 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000280708239 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000280708239 +Testing value 2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -3e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -3.e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -3e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -2.8e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -2.81e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -2.807e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -2.8071e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00003 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -2.80708e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000028 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -2.807082e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000281 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -2.8070824e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00002807 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -2.80708239e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000028071 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -2.807082387e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000280708 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -2.8070823873e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00002807082 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -2.80708238733e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000028070824 +Testing value -2.8070823873349581845e-05 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -2.807082387335e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -2.8070823873350e-05 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value -2.8070823873349581845e-05 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000280708239 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +3.5e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +3.51e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +3.509e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +3.5089e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +3.50885e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000004 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000035 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 3.5088530e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +3.508853e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000351 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +3.50885298e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000003509 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +3.508852984e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000035089 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +3.5088529842e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000350885 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +3.50885298417e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000003508853 +Testing value 3.5088529841686977306e-06 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +3.508852984169e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 3.5088529841687e-06 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000035088530 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000035088530 +Testing value 3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -3.5e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -3.51e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -3.509e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -3.5089e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -3.50885e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000004 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000035 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.5088530e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -3.508853e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000351 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -3.50885298e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000003509 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -3.508852984e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000035089 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -3.5088529842e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000350885 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -3.50885298417e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000003508853 +Testing value -3.5088529841686977306e-06 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -3.508852984169e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -3.5088529841687e-06 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value -3.5088529841686977306e-06 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000035088530 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 4.e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +4.4e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +4.39e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +4.386e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +4.3861e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +4.38607e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +4.386066e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000004 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +4.3860662e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000044 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000439 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 4.386066230e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +4.38606623e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000004386 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +4.3860662302e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000043861 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +4.38606623021e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000438607 +Testing value 4.3860662302108721633e-07 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +4.386066230211e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 4.3860662302109e-07 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000004386066 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000004386066 +Testing value 4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -4.e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -4.4e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -4.39e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -4.386e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -4.3861e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -4.38607e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -4.386066e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000004 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -4.3860662e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000044 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000439 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -4.386066230e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -4.38606623e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000004386 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -4.3860662302e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000043861 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -4.38606623021e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000438607 +Testing value -4.3860662302108721633e-07 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -4.386066230211e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -4.3860662302109e-07 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value -4.3860662302108721633e-07 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000004386066 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 5.e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +5.5e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +5.48e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +5.483e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +5.4826e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +5.48258e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +5.482583e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000001 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +5.4825828e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000005 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +5.48258279e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000055 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +5.482582788e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000548 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +5.4825827878e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000005483 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +5.48258278776e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000054826 +Testing value 5.4825827877635902041e-08 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +5.482582787764e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 5.4825827877636e-08 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000548258 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000548258 +Testing value 5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -5.e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -5.5e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -5.48e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -5.483e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -5.4826e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -5.48258e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -5.482583e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000001 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -5.4825828e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000005 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -5.48258279e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000055 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -5.482582788e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000548 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -5.4825827878e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000005483 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -5.48258278776e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000054826 +Testing value -5.4825827877635902041e-08 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -5.482582787764e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -5.4825827877636e-08 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value -5.4825827877635902041e-08 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000548258 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 7e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 7.e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +7e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +6.9e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +6.85e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +6.853e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +6.8532e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +6.85323e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +6.853228e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000000 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +6.8532285e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000001 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +6.85322848e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000007 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +6.853228485e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000069 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000000685 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 6.85322848470e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +6.8532284847e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000006853 +Testing value 6.8532284847044877552e-09 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +6.853228484704e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 6.8532284847045e-09 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000068532 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000068532 +Testing value 6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -7e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -7.e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -7e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -6.9e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -6.85e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -6.853e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -6.8532e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -6.85323e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -6.853228e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -6.8532285e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000001 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -6.85322848e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000007 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -6.853228485e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000069 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000685 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -6.85322848470e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -6.8532284847e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000006853 +Testing value -6.8532284847044877552e-09 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -6.853228484704e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -6.8532284847045e-09 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value -6.8532284847044877552e-09 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000068532 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 1 +Got: 1e+09 +Expected: 9e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 1 +Got: 1.e+09 +Expected: 9.e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 1 +Got: +1e+09 +Expected: +9e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 1 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 1 +Got: +9.9e+08 +Expected: +8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: 987654312.0 +Expected: 0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 1 +Got: +987654312.0 +Expected: +0.0 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 2 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 2 +Got: 9.9e+08 +Expected: 8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 2 +Got: +9.9e+08 +Expected: +8.6e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 2 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 2 +Got: +9.88e+08 +Expected: +8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: 987654312.00 +Expected: 0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 2 +Got: +987654312.00 +Expected: +0.00 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 3 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 3 +Got: 9.88e+08 +Expected: 8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 3 +Got: +9.88e+08 +Expected: +8.57e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 3 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 3 +Got: +9.877e+08 +Expected: +8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: 987654312.000 +Expected: 0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 3 +Got: +987654312.000 +Expected: +0.000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 4 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 4 +Got: 9.877e+08 +Expected: 8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 4 +Got: +9.877e+08 +Expected: +8.567e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 4 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 4 +Got: +9.8765e+08 +Expected: +8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: 987654312.0000 +Expected: 0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 4 +Got: +987654312.0000 +Expected: +0.0000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 5 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 5 +Got: 9.8765e+08 +Expected: 8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 5 +Got: +9.8765e+08 +Expected: +8.5665e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 5 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 5 +Got: +9.87654e+08 +Expected: +8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: 987654312.00000 +Expected: 0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 5 +Got: +987654312.00000 +Expected: +0.00000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 6 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 6 +Got: 9.87654e+08 +Expected: 8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 6 +Got: +9.87654e+08 +Expected: +8.56654e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 6 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 6 +Got: +9.876543e+08 +Expected: +8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: 987654312.000000 +Expected: 0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 6 +Got: +987654312.000000 +Expected: +0.000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 7 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 7 +Got: 9.876543e+08 +Expected: 8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 7 +Got: +9.876543e+08 +Expected: +8.566536e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 7 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 7 +Got: +9.8765431e+08 +Expected: +8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: 987654312.0000000 +Expected: 0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 7 +Got: +987654312.0000000 +Expected: +0.0000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 8 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 8 +Got: 9.8765431e+08 +Expected: 8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 8 +Got: +9.8765431e+08 +Expected: +8.5665356e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 8 +Got: 9.87654312e+08 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 8 +Got: +9.87654312e+08 +Expected: +8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: 9.87654312e+08 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: 987654312.00000000 +Expected: 0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 8 +Got: +987654312.00000000 +Expected: +0.00000000 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 9 +Got: 987654312 +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 9 +Got: 987654312. +Expected: 8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 9 +Got: +987654312 +Expected: +8.56653561e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 9 +Got: 9.876543120e+08 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 9 +Got: +9.876543120e+08 +Expected: +8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: 9.876543120e+08 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: 987654312.000000000 +Expected: 0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 9 +Got: +987654312.000000000 +Expected: +0.000000001 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 10 +Got: 987654312 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 10 +Got: 987654312.0 +Expected: 8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 10 +Got: +987654312 +Expected: +8.566535606e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 10 +Got: +9.8765431200e+08 +Expected: +8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: 9.8765431200e+08 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: 987654312.0000000000 +Expected: 0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 10 +Got: +987654312.0000000000 +Expected: +0.0000000009 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 11 +Got: 987654312 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 11 +Got: 987654312.00 +Expected: 8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 11 +Got: +987654312 +Expected: +8.5665356059e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 11 +Got: +9.87654312000e+08 +Expected: +8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: 9.87654312000e+08 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: 987654312.00000000000 +Expected: 0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 11 +Got: +987654312.00000000000 +Expected: +0.00000000086 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 12 +Got: 987654312 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 12 +Got: 987654312.000 +Expected: 8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 12 +Got: +987654312 +Expected: +8.56653560588e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 12 +Got: +9.876543120000e+08 +Expected: +8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: 9.876543120000e+08 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: 987654312.000000000000 +Expected: 0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 12 +Got: +987654312.000000000000 +Expected: +0.000000000857 +Testing value 8.5665356058806096939e-10 +Formatting flags were: +Precision is: 13 +Got: 987654312 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 13 +Got: 987654312.0000 +Expected: 8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 13 +Got: +987654312 +Expected: +8.566535605881e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 13 +Got: +9.8765431200000e+08 +Expected: +8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: 9.8765431200000e+08 +Expected: 8.5665356058806e-10 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000008567 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: 987654312.0000000000000 +Expected: 0.0000000008567 +Testing value 8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 13 +Got: +987654312.0000000000000 +Expected: +0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 1 +Got: -1e+09 +Expected: -9e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 1 +Got: -1.e+09 +Expected: -9.e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 1 +Got: -1e+09 +Expected: -9e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 1 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 1 +Got: -987654312.0 +Expected: -0.0 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 2 +Got: -9.9e+08 +Expected: -8.6e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 2 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 2 +Got: -987654312.00 +Expected: -0.00 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 3 +Got: -9.88e+08 +Expected: -8.57e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 3 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 3 +Got: -987654312.000 +Expected: -0.000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 4 +Got: -9.877e+08 +Expected: -8.567e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 4 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 4 +Got: -987654312.0000 +Expected: -0.0000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 5 +Got: -9.8765e+08 +Expected: -8.5665e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 5 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 5 +Got: -987654312.00000 +Expected: -0.00000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 6 +Got: -9.87654e+08 +Expected: -8.56654e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 6 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 6 +Got: -987654312.000000 +Expected: -0.000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 7 +Got: -9.876543e+08 +Expected: -8.566536e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 7 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 7 +Got: -987654312.0000000 +Expected: -0.0000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 8 +Got: -9.8765431e+08 +Expected: -8.5665356e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 8 +Got: -9.87654312e+08 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 8 +Got: -987654312.00000000 +Expected: -0.00000000 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 9 +Got: -987654312 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 9 +Got: -987654312. +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 9 +Got: -987654312 +Expected: -8.56653561e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 9 +Got: -9.876543120e+08 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 9 +Got: -987654312.000000000 +Expected: -0.000000001 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 10 +Got: -987654312 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 10 +Got: -987654312.0 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 10 +Got: -987654312 +Expected: -8.566535606e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 10 +Got: -9.8765431200e+08 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 10 +Got: -987654312.0000000000 +Expected: -0.0000000009 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 11 +Got: -987654312 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 11 +Got: -987654312.00 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 11 +Got: -987654312 +Expected: -8.5665356059e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 11 +Got: -9.87654312000e+08 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 11 +Got: -987654312.00000000000 +Expected: -0.00000000086 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 12 +Got: -987654312 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 12 +Got: -987654312.000 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 12 +Got: -987654312 +Expected: -8.56653560588e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 12 +Got: -9.876543120000e+08 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 12 +Got: -987654312.000000000000 +Expected: -0.000000000857 +Testing value -8.5665356058806096939e-10 +Formatting flags were: +Precision is: 13 +Got: -987654312 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpoint +Precision is: 13 +Got: -987654312.0000 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: showpos +Precision is: 13 +Got: -987654312 +Expected: -8.566535605881e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpos +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: scientific showpoint +Precision is: 13 +Got: -9.8765431200000e+08 +Expected: -8.5665356058806e-10 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpoint +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +Testing value -8.5665356058806096939e-10 +Formatting flags were: fixed showpos +Precision is: 13 +Got: -987654312.0000000000000 +Expected: -0.0000000008567 +9360 errors detected. + +EXIT STATUS: 1 +====== END OUTPUT ====== + + + "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9x/release/test_float_io_cpp_dec_float" > "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9x/release/test_float_io_cpp_dec_float.output" 2>&1 + status=$? + echo >> "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9x/release/test_float_io_cpp_dec_float.output" + echo EXIT STATUS: $status >> "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9x/release/test_float_io_cpp_dec_float.output" + if test $status -eq 0 ; then + cp "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9x/release/test_float_io_cpp_dec_float.output" "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9x/release/test_float_io_cpp_dec_float.run" + fi + verbose=0 + if test $status -ne 0 ; then + verbose=1 + fi + if test $verbose -eq 1 ; then + echo ====== BEGIN OUTPUT ====== + cat "bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9x/release/test_float_io_cpp_dec_float.output" + echo ====== END OUTPUT ====== + fi + exit $status + +...failed testing.capture-output bin/test_float_io_cpp_dec_float.test/clang-darwin-2.9x/release/test_float_io_cpp_dec_float.run... +...failed updating 2 targets... +...skipped 2 targets... From 1b33ece7f87bbb07374297e96c4ba569c576ea56 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 4 Jun 2012 15:25:22 +0000 Subject: [PATCH 184/256] Documentation update - address Marc Glisse's comments on the overview section. [SVN r78806] --- .../boost_multiprecision/indexes/s01.html | 4 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 4 +- doc/html/boost_multiprecision/intro.html | 37 +++++++++++++------ doc/html/index.html | 2 +- doc/multiprecision.qbk | 20 +++++++--- performance/sf_performance.cpp | 11 +++++- 8 files changed, 59 insertions(+), 27 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index ddb95fbb..0ae96943 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
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    diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index 738fe63f..d7ff7db4 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,9 +13,9 @@
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    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 23a657a4..15f2b2a6 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
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    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index fd084d6d..2fe2796a 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
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    diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index 724a4e3a..af4854f1 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -132,16 +132,19 @@

    If type T is an mp_number, then this expression is evaluated without creating a single temporary value. In contrast, - if we were using the C++ wrapper that ships with GMP - - mpfr_class - - then this expression would result in no less than 11 temporaries (this is - true even though mpfr_class - does use expression templates to reduce the number of temporaries somewhat). - Had we used an even simpler wrapper around GMP - or MPFR like mpclass - things would have been even worse and no less that 24 temporaries are created - for this simple expression (note - we actually measure the number of memory - allocations performed rather than the number of temporaries directly). + if we were using the mpfr_class + C++ wrapper for MPFR - then this expression + would result in no less than 11 temporaries (this is true even though mpfr_class does + use expression templates to reduce the number of temporaries somewhat). Had + we used an even simpler wrapper around MPFR + like mpreal things + would have been even worse and no less that 24 temporaries are created for + this simple expression (note - we actually measure the number of memory allocations + performed rather than the number of temporaries directly, note also that the + mpf_class + wrapper that will be supplied with GMP-5.1 reduces the number of temporaries + to pretty much zero). Finally if we use this library with expression templates + disabled, we still only generate 11 temporaries [1] [2].

    This library also extends expression template support to standard library functions @@ -504,7 +507,19 @@

    PrevUpHomeNext
    -
    +
    +
    +

    [1] + The actual number generated will depend on the compiler, how well it optimises + the code, and whether it supports rvalue references. The number of 11 temporaries + was generated with Visual C++ 10 +

    +

    [2] + Marc Glisse suggested pre-review that this could be reduced still further + by careful use of rvalue-references and move semantics in the operator overloads. + This will be investigated further at a later date. +

    +
    diff --git a/doc/html/index.html b/doc/html/index.html index c699fb31..3984146c 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -117,7 +117,7 @@
    - +

    Last revised: May 09, 2012 at 18:07:25 GMT

    Last revised: June 04, 2012 at 15:17:54 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index f7819bc6..4299d633 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -29,7 +29,7 @@ [template mpfr[] [@http://www.mpfr.org MPFR]] [template gmp[] [@http://gmplib.org GMP]] -[template mpf_class[] [@http://gmplib.org/manual/C_002b_002b-Interface-Floats.html#C_002b_002b-Interface-Floats mpfr_class]] +[template mpf_class[] [@http://gmplib.org/manual/C_002b_002b-Interface-Floats.html#C_002b_002b-Interface-Floats mpf_class]] [template mpfr_class[] [@http://math.berkeley.edu/~wilken/code/gmpfrxx/ mpfr_class]] [template mpreal[] [@http://www.holoborodko.com/pavel/mpfr/ mpreal]] [template mpir[] [@http://mpir.org/ MPIR]] @@ -133,11 +133,17 @@ lets suppose we're evaluating a polynomial via Horners method, something like th y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; If type `T` is an `mp_number`, then this expression is evaluated ['without creating a single temporary value]. In contrast, -if we were using the C++ wrapper that ships with [gmp] - [mpf_class] - then this expression would result in no less than 11 -temporaries (this is true even though [mpf_class] does use expression templates to reduce the number of temporaries somewhat). Had -we used an even simpler wrapper around [gmp] or [mpfr] like `mpclass` things would have been even worse and no less that 24 temporaries +if we were using the [mpfr_class] C++ wrapper for [mpfr] - then this expression would result in no less than 11 +temporaries (this is true even though [mpfr_class] does use expression templates to reduce the number of temporaries somewhat). Had +we used an even simpler wrapper around [mpfr] like [mpreal] things would have been even worse and no less that 24 temporaries are created for this simple expression (note - we actually measure the number of memory allocations performed rather than -the number of temporaries directly). +the number of temporaries directly, note also that the [mpf_class] wrapper that will be supplied with GMP-5.1 reduces the number of +temporaries to pretty much zero). Finally if we use this library with expression templates disabled, we still only generate 11 +temporaries +[footnote The actual number generated will depend on the compiler, how well it optimises the code, and whether it supports +rvalue references. The number of 11 temporaries was generated with Visual C++ 10] +[footnote Marc Glisse suggested pre-review that this could be reduced still further by careful use of rvalue-references +and move semantics in the operator overloads. This will be investigated further at a later date.]. This library also extends expression template support to standard library functions like `abs` or `sin` with `mp_number` arguments. This means that an expression such as: @@ -982,6 +988,8 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba }; // Non member operators: + ``['unmentionable-expression-template-type]`` operator+(const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator-(const ``['see-below]``&); ``['unmentionable-expression-template-type]`` operator+(const ``['see-below]``&, const ``['see-below]``&); ``['unmentionable-expression-template-type]`` operator-(const ``['see-below]``&, const ``['see-below]``&); ``['unmentionable-expression-template-type]`` operator*(const ``['see-below]``&, const ``['see-below]``&); @@ -1218,6 +1226,8 @@ Returns the underlying back-end instance used by `*this`. [h4 Non-member operators] // Non member operators: + ``['unmentionable-expression-template-type]`` operator+(const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator-(const ``['see-below]``&); ``['unmentionable-expression-template-type]`` operator+(const ``['see-below]``&, const ``['see-below]``&); ``['unmentionable-expression-template-type]`` operator-(const ``['see-below]``&, const ``['see-below]``&); ``['unmentionable-expression-template-type]`` operator*(const ``['see-below]``&, const ``['see-below]``&); diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index e2183f7f..5bd20871 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -228,6 +228,7 @@ int main() std::cout << "Allocation Counts for Horner Evaluation:\n"; #ifdef TEST_MPFR basic_allocation_test("mpfr_float_50", mpfr_float_50(2)); + basic_allocation_test("mpfr_float_50 - no expression templates", mp_number, false>(2)); #endif #ifdef TEST_MPFR_CLASS basic_allocation_test("mpfr_class", mpfr_class(2)); @@ -239,6 +240,7 @@ int main() std::cout << "Allocation Counts for boost::math::tools::evaluate_polynomial:\n"; #ifdef TEST_MPFR poly_allocation_test("mpfr_float_50", mpfr_float_50(2)); + poly_allocation_test("mpfr_float_50 - no expression templates", mp_number, false>(2)); #endif #ifdef TEST_MPFR_CLASS poly_allocation_test("mpfr_class", mpfr_class(2)); @@ -270,7 +272,7 @@ int main() #ifdef TEST_MPFR_CLASS time_proc("mpfr_class", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); #endif -#ifdef TEST_MP_REAL +#ifdef TEST_MPREAL time_proc("mpfr::mpreal", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); #endif // @@ -288,6 +290,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_100", test_bessel); + time_proc("mpf_float_100 (no expression templates", test_bessel, false> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_bessel); @@ -314,6 +317,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_50", test_polynomial); + time_proc("mpf_float_50 (no expression templates", test_polynomial, false> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_polynomial); @@ -339,6 +343,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_100", test_polynomial); + time_proc("mpf_float_100 (no expression templates", test_polynomial, false> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_polynomial); @@ -364,6 +369,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_50", test_nct); + time_proc("mpf_float_50 (no expression templates", test_nct, false> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_nct); @@ -371,7 +377,7 @@ int main() #ifdef TEST_MPFR_CLASS time_proc("mpfr_class", test_nct); #endif -#ifdef TEST_MP_REAL +#ifdef TEST_MPREAL time_proc("mpfr::mpreal", test_nct); #endif // @@ -389,6 +395,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_100", test_nct); + time_proc("mpf_float_100 (no expression templates", test_nct, false> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_nct); From f543ec2639dbbc506d64018cee50d1d518f3f3cb Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 4 Jun 2012 17:50:57 +0000 Subject: [PATCH 185/256] Address doc concerns of Vincente Botet Escriba in pre-review comments. Rebuild docs. [SVN r78807] --- .../boost_multiprecision/indexes/s01.html | 4 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 4 +- doc/html/boost_multiprecision/intro.html | 20 ++ doc/html/boost_multiprecision/perf.html | 6 +- .../perf/float_performance.html | 18 +- .../perf/integer_performance.html | 40 +-- .../perf/rational_performance.html | 18 +- .../boost_multiprecision/perf/realworld.html | 4 +- doc/html/boost_multiprecision/ref.html | 1 + .../boost_multiprecision/ref/backendconc.html | 17 +- .../boost_multiprecision/ref/cpp_dec_ref.html | 3 + .../boost_multiprecision/ref/cpp_int_ref.html | 3 + .../boost_multiprecision/ref/gmp_int_ref.html | 3 + .../boost_multiprecision/ref/headers.html | 331 ++++++++++++++++++ .../boost_multiprecision/ref/mp_number.html | 24 +- .../boost_multiprecision/ref/mpf_ref.html | 3 + .../boost_multiprecision/ref/mpfr_ref.html | 3 + .../boost_multiprecision/ref/tom_int_ref.html | 3 + .../boost_multiprecision/tut/conversions.html | 15 + .../tut/floats/cpp_dec_float.html | 15 + .../tut/floats/mpfr_float.html | 5 + .../tut/ints/cpp_int.html | 14 + .../tut/ints/gmp_int.html | 5 + doc/html/index.html | 3 +- doc/multiprecision.qbk | 101 +++++- .../multiprecision/detail/mp_number_base.hpp | 14 + include/boost/multiprecision/mpfr.hpp | 2 +- 29 files changed, 628 insertions(+), 59 deletions(-) create mode 100644 doc/html/boost_multiprecision/ref/headers.html diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 0ae96943..3f5d4981 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
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    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 15f2b2a6..f078a0ef 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
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    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 2fe2796a..5c34b04c 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
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    diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index af4854f1..e13b16a1 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -86,6 +86,26 @@ my_float a, b, c; // These variables have 300 decimal digits precision +

    + Note that mixing arithmetic operations using types of different precision is + strictly forbidden: +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+
+namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
+
+mp::mp_int128_t a(3), b(2);
+mp::mp_int512_t c(50), d;
+
+d = c * a;   // Compiler error
+
    +

    + However, conversions are allowed: +

    +
    d = a; // OK, widening conversion.
+d = a * b;  // OK, can convert from an expression template too.
+d = mp::mp_int512_t(a) * c; // OK, all the types in the expression are the same now.
+
    Expression diff --git a/doc/html/boost_multiprecision/perf.html b/doc/html/boost_multiprecision/perf.html index 7460f077..7a2b730a 100644 --- a/doc/html/boost_multiprecision/perf.html +++ b/doc/html/boost_multiprecision/perf.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -40,7 +40,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html index 9e9b8217..d34ab87c 100644 --- a/doc/html/boost_multiprecision/perf/float_performance.html +++ b/doc/html/boost_multiprecision/perf/float_performance.html @@ -33,7 +33,7 @@ The tests were run on 32-bit Windows Vista machine.

    -

    Table 1.8. Operator +

    +

    Table 1.10. Operator +

    @@ -134,7 +134,7 @@

    -

    Table 1.9. Operator +(int)

    +

    Table 1.11. Operator +(int)

    @@ -235,7 +235,7 @@

    -

    Table 1.10. Operator -

    +

    Table 1.12. Operator -

    @@ -336,7 +336,7 @@

    -

    Table 1.11. Operator -(int)

    +

    Table 1.13. Operator -(int)

    @@ -437,7 +437,7 @@

    -

    Table 1.12. Operator *

    +

    Table 1.14. Operator *

    @@ -538,7 +538,7 @@

    -

    Table 1.13. Operator *(int)

    +

    Table 1.15. Operator *(int)

    @@ -639,7 +639,7 @@

    -

    Table 1.14. Operator /

    +

    Table 1.16. Operator /

    @@ -740,7 +740,7 @@

    -

    Table 1.15. Operator /(int)

    +

    Table 1.17. Operator /(int)

    @@ -841,7 +841,7 @@

    -

    Table 1.16. Operator str

    +

    Table 1.18. Operator str

    diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html index b7bbe0e7..56ea5b0e 100644 --- a/doc/html/boost_multiprecision/perf/integer_performance.html +++ b/doc/html/boost_multiprecision/perf/integer_performance.html @@ -37,7 +37,7 @@ much better there.

    -

    Table 1.17. Operator +

    +

    Table 1.19. Operator +

    @@ -186,7 +186,7 @@

    -

    Table 1.18. Operator +(int)

    +

    Table 1.20. Operator +(int)

    @@ -335,7 +335,7 @@

    -

    Table 1.19. Operator -

    +

    Table 1.21. Operator -

    @@ -484,7 +484,7 @@

    -

    Table 1.20. Operator -(int)

    +

    Table 1.22. Operator -(int)

    @@ -633,7 +633,7 @@

    -

    Table 1.21. Operator *

    +

    Table 1.23. Operator *

    @@ -782,7 +782,7 @@

    -

    Table 1.22. Operator *(int)

    +

    Table 1.24. Operator *(int)

    @@ -931,7 +931,7 @@

    -

    Table 1.23. Operator /

    +

    Table 1.25. Operator /

    @@ -1080,7 +1080,7 @@

    -

    Table 1.24. Operator /(int)

    +

    Table 1.26. Operator /(int)

    @@ -1229,7 +1229,7 @@

    -

    Table 1.25. Operator %

    +

    Table 1.27. Operator %

    @@ -1378,7 +1378,7 @@

    -

    Table 1.26. Operator %(int)

    +

    Table 1.28. Operator %(int)

    @@ -1527,7 +1527,7 @@

    -

    Table 1.27. Operator <<

    +

    Table 1.29. Operator <<

    @@ -1676,7 +1676,7 @@

    -

    Table 1.28. Operator >>

    +

    Table 1.30. Operator >>

    @@ -1825,7 +1825,7 @@

    -

    Table 1.29. Operator &

    +

    Table 1.31. Operator &

    @@ -1974,7 +1974,7 @@

    -

    Table 1.30. Operator &(int)

    +

    Table 1.32. Operator &(int)

    @@ -2123,7 +2123,7 @@

    -

    Table 1.31. Operator ^

    +

    Table 1.33. Operator ^

    @@ -2272,7 +2272,7 @@

    -

    Table 1.32. Operator ^(int)

    +

    Table 1.34. Operator ^(int)

    @@ -2421,7 +2421,7 @@

    -

    Table 1.33. Operator |

    +

    Table 1.35. Operator |

    @@ -2570,7 +2570,7 @@

    -

    Table 1.34. Operator |(int)

    +

    Table 1.36. Operator |(int)

    @@ -2719,7 +2719,7 @@

    -

    Table 1.35. Operator gcd

    +

    Table 1.37. Operator gcd

    @@ -2868,7 +2868,7 @@

    -

    Table 1.36. Operator str

    +

    Table 1.38. Operator str

    diff --git a/doc/html/boost_multiprecision/perf/rational_performance.html b/doc/html/boost_multiprecision/perf/rational_performance.html index 6736d065..98fb8836 100644 --- a/doc/html/boost_multiprecision/perf/rational_performance.html +++ b/doc/html/boost_multiprecision/perf/rational_performance.html @@ -33,7 +33,7 @@ The tests were run on 32-bit Windows Vista machine.

    -

    Table 1.37. Operator +

    +

    Table 1.39. Operator +

    @@ -128,7 +128,7 @@

    -

    Table 1.38. Operator +(int)

    +

    Table 1.40. Operator +(int)

    @@ -223,7 +223,7 @@

    -

    Table 1.39. Operator -

    +

    Table 1.41. Operator -

    @@ -318,7 +318,7 @@

    -

    Table 1.40. Operator -(int)

    +

    Table 1.42. Operator -(int)

    @@ -413,7 +413,7 @@

    -

    Table 1.41. Operator *

    +

    Table 1.43. Operator *

    @@ -508,7 +508,7 @@

    -

    Table 1.42. Operator *(int)

    +

    Table 1.44. Operator *(int)

    @@ -603,7 +603,7 @@

    -

    Table 1.43. Operator /

    +

    Table 1.45. Operator /

    @@ -698,7 +698,7 @@

    -

    Table 1.44. Operator /(int)

    +

    Table 1.46. Operator /(int)

    @@ -793,7 +793,7 @@

    -

    Table 1.45. Operator str

    +

    Table 1.47. Operator str

    diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html index 4dd0d5ef..a084ecc1 100644 --- a/doc/html/boost_multiprecision/perf/realworld.html +++ b/doc/html/boost_multiprecision/perf/realworld.html @@ -33,7 +33,7 @@ The tests were run on 32-bit Windows Vista machine.

    -

    Table 1.6. Bessel Function Performance

    +

    Table 1.8. Bessel Function Performance

    @@ -147,7 +147,7 @@

    -

    Table 1.7. Non-Central T Distribution Performance

    +

    Table 1.9. Non-Central T Distribution Performance

    diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html index 35ad59f4..4f869c43 100644 --- a/doc/html/boost_multiprecision/ref.html +++ b/doc/html/boost_multiprecision/ref.html @@ -26,6 +26,7 @@
    mpfr_float_backend
    cpp_dec_float
    Backend Requirements
    +
    Header File Structure
    diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index 3bf6b60f..c2465281 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -7,11 +7,11 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -2266,7 +2266,16 @@

    -
    +

    + The tables above place no throws requirements on any + of the operations. It is up to each type modelling this concept to decide + when or whether throwing an exception is desirable. However, thrown exceptions + should always either be the type, or inherit from the type std::runtime_error. + For example, a floating point type might choose to throw std::overflow_error + whenever the result of an operation would be infinite, and std::underflow_error + whenever it would round to zero. +

    +
    @@ -2289,7 +2298,7 @@
    [Note] Note
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html index 9d34b1e6..48ce9b5b 100644 --- a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html @@ -41,6 +41,9 @@ template argument should not be set too high or the classes size will grow unreasonably large.

    +

    + The type of number_category<cpp_int<Args...> >::type is mpl::int_<number_kind_floating_point>. +

    More information on this type can be found in the tutorial.

    diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html index 40530e86..43160fed 100644 --- a/doc/html/boost_multiprecision/ref/cpp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_int_ref.html @@ -79,6 +79,9 @@

    +

    + The type of number_category<cpp_int<Args...> >::type is mpl::int_<number_kind_integer>. +

    More information on this type can be found in the tutorial.

    diff --git a/doc/html/boost_multiprecision/ref/gmp_int_ref.html b/doc/html/boost_multiprecision/ref/gmp_int_ref.html index 71dfb0ae..6d536179 100644 --- a/doc/html/boost_multiprecision/ref/gmp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/gmp_int_ref.html @@ -31,6 +31,9 @@ type. It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change.

    +

    + The type of number_category<cpp_int<Args...> >::type is mpl::int_<number_kind_integer>. +

    More information on this type can be found in the tutorial.

    diff --git a/doc/html/boost_multiprecision/ref/headers.html b/doc/html/boost_multiprecision/ref/headers.html new file mode 100644 index 00000000..010807eb --- /dev/null +++ b/doc/html/boost_multiprecision/ref/headers.html @@ -0,0 +1,331 @@ + + + +Header File Structure + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +
    +

    Table 1.6. Top level headers

    +
    ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Header +

    +     		+

    + Contains +

    +
    +

    + cpp_int.hpp +

    +     		+

    + The cpp_int backend + type. +

    +
    +

    + gmp.hpp +

    +     		+

    + Defines all GMP related + backends. +

    +
    +

    + integer_ops.hpp +

    +     		+

    + Integer specific non-member functions. +

    +
    +

    + miller_rabin.hpp +

    +     		+

    + Miller Rabin primality testing code. +

    +
    +

    + mp_number.hpp +

    +     		+

    + Defines the mp_number + backend, is included by all the backend headers. +

    +
    +

    + mpfr.hpp +

    +     		+

    + Defines the mpfr_float_backend backend. +

    +
    +

    + random.hpp +

    +     		+

    + Defines code to interoperate with Boost.Random. +

    +
    +

    + rational_adapter.hpp +

    +     		+

    + Defines the rational_adapter + backend. +

    +
    +

    + cpp_dec_float.hpp +

    +     		+

    + Defines the cpp_dec_float + backend. +

    +
    +

    + tommath.hpp +

    +     		+

    + Defines the tommath_int + backend. +

    +
    +

    + concepts/mp_number_architypes.hpp +

    +     		+

    + Defines a backend concept architypes for testing use. +

    +
    +
    +
    +

    Table 1.7. Implementation Headers]

    +
    ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Header +

    +     		+

    + Contains +

    +
    +

    + detail/big_lanczos.hpp +

    +     		+

    + Lanczos support for Boost.Math integration. +

    +
    +

    + detail/cpp_int_core.hpp +

    +     		+

    + Platform and peformance tuning for the cpp_int + backend. +

    +
    +

    + detail/default_ops.hpp +

    +     		+

    + Default versions of the optional backend non-member functions. +

    +
    +

    + detail/generic_interconvert.hpp +

    +     		+

    + Generic interconversion routines. +

    +
    +

    + detail/mp_number_base.hpp +

    +     		+

    + All the expression template code, metaprogramming, and operator + overloads for mp_number. +

    +
    +

    + detail/no_et_ops.hpp +

    +     		+

    + The non-expression template operators. +

    +
    +

    + defail/functions/constants.hpp +

    +     		+

    + Defines constants used by the floating point functions. +

    +
    +

    + detail/functions/pow.hpp +

    +     		+

    + Defines default versions of the power and exponential related floating + point functions. +

    +
    +

    + detail/functions/trig.hpp +

    +     		+

    + Defines default versions of the trigonometric related floating + point functions. +

    +
    +
    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/mp_number.html b/doc/html/boost_multiprecision/ref/mp_number.html index 75a54542..5f2605b4 100644 --- a/doc/html/boost_multiprecision/ref/mp_number.html +++ b/doc/html/boost_multiprecision/ref/mp_number.html @@ -74,6 +74,8 @@ }; // Non member operators: +unmentionable-expression-template-type operator+(const see-below&); +unmentionable-expression-template-type operator-(const see-below&); unmentionable-expression-template-type operator+(const see-below&, const see-below&); unmentionable-expression-template-type operator-(const see-below&, const see-below&); unmentionable-expression-template-type operator*(const see-below&, const see-below&); @@ -242,6 +244,13 @@
  • Any type that the Backend is constructible or assignable from.
    • +
  • + An rvalue reference to another mp_number. + Move-semantics are used for construction if the backend also supports + rvalue reference construction. In the case of assignment, move semantics + are always supported when the argument is an rvalue reference irrespective + of the backend. +

    • In addition, if the type has multiple components (for example rational or @@ -292,6 +301,10 @@ type with a positive value (negative values result in a std::runtime_error being thrown).

    +

    + Note that all the types involved in the expression must evaluate to the same + type - which is to say we cannot mix an mp_number<B1> with an mp_number<B2> where B1 and B2 are different types. + 

    operator convertible-to-bool-type()const;

    @@ -383,6 +396,8 @@ operators 

    // Non member operators:
+unmentionable-expression-template-type operator+(const see-below&);
+unmentionable-expression-template-type operator-(const see-below&);
 unmentionable-expression-template-type operator+(const see-below&, const see-below&);
 unmentionable-expression-template-type operator-(const see-below&, const see-below&);
 unmentionable-expression-template-type operator*(const see-below&, const see-below&);
@@ -439,6 +454,10 @@
             is a comparison operator.
           
 
+
    
+        Note that all the types involved in the expression must evaluate to the same
+        type - which is to say we cannot mix an mp_number<B1> with an mp_number<B2> where B1 and B2 are different types.
+      
    
 
    
         Finally note that the second argument to the left and right shift operations
         must be a builtin integer type, and that the argument must be positive (negative
@@ -530,7 +549,10 @@
       
    
 
    
         Also note that with the exception of abs
-        that these functions can only be used with floating-point Backend types.
+        that these functions can only be used with floating-point Backend types (if
+        any other types such as fixed precision or complex types are added to the
+        library later, then these functions may be extended to support those number
+        types).
       
    
 
    
 
diff --git a/doc/html/boost_multiprecision/ref/mpf_ref.html b/doc/html/boost_multiprecision/ref/mpf_ref.html
index fd2d8f50..9481059c 100644
--- a/doc/html/boost_multiprecision/ref/mpf_ref.html
+++ b/doc/html/boost_multiprecision/ref/mpf_ref.html
@@ -47,6 +47,9 @@
         and also mix gmp_floats of
         differing precision.
       
    
+
    
+        The type of number_category<cpp_int<Args...> >::type is mpl::int_<number_kind_floating_point>.
+      
    
 
    
         More information on this type can be found in the tutorial.
       
    
diff --git a/doc/html/boost_multiprecision/ref/mpfr_ref.html b/doc/html/boost_multiprecision/ref/mpfr_ref.html
index 7588f301..eb96296a 100644
--- a/doc/html/boost_multiprecision/ref/mpfr_ref.html
+++ b/doc/html/boost_multiprecision/ref/mpfr_ref.html
@@ -47,6 +47,9 @@
         that uses GMP or MPFR, and also mix mpfr_float_backends
         of differing precision.
       
    
+
    
+        The type of number_category<cpp_int<Args...> >::type is mpl::int_<number_kind_floating_point>.
+      
    
 
    
         More information on this type can be found in the tutorial.
       
    
diff --git a/doc/html/boost_multiprecision/ref/tom_int_ref.html b/doc/html/boost_multiprecision/ref/tom_int_ref.html
index 95abdcbe..9855b80a 100644
--- a/doc/html/boost_multiprecision/ref/tom_int_ref.html
+++ b/doc/html/boost_multiprecision/ref/tom_int_ref.html
@@ -31,6 +31,9 @@
         type. It's members and non-member functions are deliberately not documented:
         these are considered implementation details that are subject to change.
       
    
+
    
+        The type of number_category<cpp_int<Args...> >::type is mpl::int_<number_kind_integer>.
+      
    
 
    
         More information on this type can be found in the tutorial.
       
    
diff --git a/doc/html/boost_multiprecision/tut/conversions.html b/doc/html/boost_multiprecision/tut/conversions.html
index b34da26c..dd36b344 100644
--- a/doc/html/boost_multiprecision/tut/conversions.html
+++ b/doc/html/boost_multiprecision/tut/conversions.html
@@ -89,6 +89,21 @@
 mpf_init_set_ui(m, 0); // set to a value;
 mpf_float i(m);        // copies the value of the native type.
    +

    + More information on what additional types a backend supports conversions + from are given in the tutorial for each backend. +

    +
    • + An mp_number can be converted + to any built in type, via the convert_to + member function: +
    +
    mpz_int z(2);
+int i = z.template convert_to<int>(); // sets i to 2
+
    +

    + Additional conversions may be supported by particular backends. +

    diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html index aea653f8..a109f6fc 100644 --- a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html +++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html @@ -70,6 +70,21 @@ specified in the template argument. Normally these should not be visible to the user. +
  • + The type supports both infinities and NaN's. An infinity is generated + whenever the result would overflow, and a NaN is generated for any + mathematically undefined operation. +
    • +
  • + There is a std::numeric_limits specialisation for + this type. +
    • +
  • + Any mp_number instantiated + on this type, is convertible to any other mp_number + instantiated on this type - for example you can convert from mp_number<cpp_dec_float<50> > to mp_number<cpp_dec_float<SomeOtherValue> >. + Narrowing conversions are truncating. +
    • diff --git a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html index 595e9d2c..8d42e7ac 100644 --- a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html +++ b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html @@ -107,6 +107,11 @@ in place of GMP - indeed that is the preferred option on Win32. +
  • + This backend supports rvalue-references and is move-aware, making instantiations + of mp_number on this + backend move aware. +
    • diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html index 98340475..021c5d0c 100644 --- a/doc/html/boost_multiprecision/tut/ints/cpp_int.html +++ b/doc/html/boost_multiprecision/tut/ints/cpp_int.html @@ -134,6 +134,20 @@ difference to the performance of these types either way - so we may as well have the faster compile times by turning the feature off. +
  • + Unsigned types support subtraction, and unary negation - the result + is "as if" a 2's complement operation had been performed + - in other words they behave pretty much as a built in integer type + would in this situation. So for example if we were using mp_uint128_t then both mp_uint128_t(1)-4 + and -mp_uint128(3) + would result in the value 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD + of type mp_uint128_t. +
    • +
  • + This backend supports rvalue-references and is move-aware, making instantiations + of mp_number on this + backend move aware. +
    • diff --git a/doc/html/boost_multiprecision/tut/ints/gmp_int.html b/doc/html/boost_multiprecision/tut/ints/gmp_int.html index 1bf12605..1b7c9282 100644 --- a/doc/html/boost_multiprecision/tut/ints/gmp_int.html +++ b/doc/html/boost_multiprecision/tut/ints/gmp_int.html @@ -85,6 +85,11 @@ Indeed use of MPIR is recommended on Win32. +
  • + This backend supports rvalue-references and is move-aware, making instantiations + of mp_number on this + backend move aware. +
    • diff --git a/doc/html/index.html b/doc/html/index.html index 3984146c..284440fb 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -86,6 +86,7 @@
    mpfr_float_backend
    cpp_dec_float
    Backend Requirements
    +
    Header File Structure
    Performance Comparison
    @@ -117,7 +118,7 @@
    - +

    Last revised: June 04, 2012 at 15:17:54 GMT

    Last revised: June 04, 2012 at 17:33:32 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 4299d633..144abd36 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -100,6 +100,23 @@ by passing a second template argument to `mp_number`: my_float a, b, c; // These variables have 300 decimal digits precision +Note that mixing arithmetic operations using types of different precision is strictly forbidden: + + #include + + namespace mp = boost::multiprecision; // Reduce the typing a bit later... + + mp::mp_int128_t a(3), b(2); + mp::mp_int512_t c(50), d; + + d = c * a; // Compiler error + +However, conversions are allowed: + + d = a; // OK, widening conversion. + d = a * b; // OK, can convert from an expression template too. + d = mp::mp_int512_t(a) * c; // OK, all the types in the expression are the same now. + [h4 Expression Templates] Class `mp_number` is expression-template-enabled: that means that rather than having a multiplication @@ -333,6 +350,12 @@ this is a direct consequence of the sign-magnitude representation. * The fixed precision types `mp_[u]intXXX_t` have expression template support turned off - it seems to make little difference to the performance of these types either way - so we may as well have the faster compile times by turning the feature off. +* Unsigned types support subtraction, and unary negation - the result is "as if" a 2's complement operation had been performed + - in other words they behave pretty much as a built in integer type would in this situation. So for example if we were using + `mp_uint128_t` then both `mp_uint128_t(1)-4` and `-mp_uint128(3)` would result in the value `0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD` + of type `mp_uint128_t`. +* This backend supports rvalue-references and is move-aware, making instantiations of `mp_number` on this backend move aware. + [h5 Example:] @@ -373,6 +396,7 @@ as a result performing formatted output on this type when the argument is negati * Division by zero is handled by the [gmp] library - it will trigger a division by zero signal. * Although this type is a wrapper around [gmp] it will work equally well with [mpir]. Indeed use of [mpir] is recommended on Win32. +* This backend supports rvalue-references and is move-aware, making instantiations of `mp_number` on this backend move aware. [h5 Example:] @@ -543,6 +567,7 @@ Things you should know when using this type: * No changes are made to [gmp] or [mpfr] global settings, so this type can coexist with existing [mpfr] or [gmp] code. * The code can equally use [mpir] in place of [gmp] - indeed that is the preferred option on Win32. +* This backend supports rvalue-references and is move-aware, making instantiations of `mp_number` on this backend move aware. [h5 [mpfr] example:] @@ -582,6 +607,12 @@ Things you should know when using this type: (this is a result of the type having some hidden internal guard digits). * The type has a number of internal guard digits over and above those specified in the template argument. Normally these should not be visible to the user. +* The type supports both infinities and NaN's. An infinity is generated whenever the result would overflow, +and a NaN is generated for any mathematically undefined operation. +* There is a `std::numeric_limits` specialisation for this type. +* Any `mp_number` instantiated on this type, is convertible to any other `mp_number` instantiated on this type - +for example you can convert from `mp_number >` to `mp_number >`. +Narrowing conversions are truncating. [h5 cpp_dec_float example:] @@ -865,6 +896,15 @@ In particular: mpf_init_set_ui(m, 0); // set to a value; mpf_float i(m); // copies the value of the native type. +More information on what additional types a backend supports conversions from are given in the tutorial for each backend. + +* An `mp_number` can be converted to any built in type, via the `convert_to` member function: + + mpz_int z(2); + int i = z.template convert_to(); // sets i to 2 + +Additional conversions may be supported by particular backends. + [endsect] [section:random Generating Random Numbers] @@ -1131,6 +1171,9 @@ Type `mp_number` is default constructible, and both copy constructible and assig * Any builtin arithmetic type. * A `std::string` or any type which is convertible to `const char*`. * Any type that the Backend is constructible or assignable from. +* An rvalue reference to another `mp_number`. Move-semantics are used for construction if the backend also +supports rvalue reference construction. In the case of assignment, move semantics are always supported +when the argument is an rvalue reference irrespective of the backend. In addition, if the type has multiple components (for example rational or complex number types), then there is a two argument constructor: @@ -1166,6 +1209,9 @@ The arguments to these operators is either: For the left and right shift operations, the argument must be a builtin integer type with a positive value (negative values result in a `std::runtime_error` being thrown). +Note that all the types involved in the expression must evaluate to the same type - which is to say +we cannot mix an `mp_number` with an `mp_number` where B1 and B2 are different types. + operator ``['convertible-to-bool-type]``()const; Returns an ['unmentionable-type] that is usable in Boolean contexts (this allows `mp_number` to be used in any @@ -1262,6 +1308,9 @@ The return type of these operators is either: * Type `mp_number` when `ExpressionTemplates` is `false`. * Type `bool` if the operator is a comparison operator. +Note that all the types involved in the expression must evaluate to the same type - which is to say +we cannot mix an `mp_number` with an `mp_number` where B1 and B2 are different types. + Finally note that the second argument to the left and right shift operations must be a builtin integer type, and that the argument must be positive (negative arguments result in a `std::runtime_error` being thrown). @@ -1329,7 +1378,8 @@ don't have native support for these functions. Please note however, that this d to be a compile time constant - this means for example that the [gmp] MPF Backend will not work with these functions when that type is used at variable precision. -Also note that with the exception of `abs` that these functions can only be used with floating-point Backend types. +Also note that with the exception of `abs` that these functions can only be used with floating-point Backend types (if any other types +such as fixed precision or complex types are added to the library later, then these functions may be extended to support those number types). [h4 Traits Class Support] @@ -1487,6 +1537,8 @@ The template arguments are: no dymanic memory will ever be allocated.]] ] +The type of `number_category >::type` is `mpl::int_`. + More information on this type can be found in the [link boost_multiprecision.tut.ints.cpp_int tutorial]. [endsect] @@ -1505,6 +1557,8 @@ Class template `gmp_int` fulfills all of the requirements for a [link boost_mult It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. +The type of `number_category >::type` is `mpl::int_`. + More information on this type can be found in the [link boost_multiprecision.tut.ints.gmp_int tutorial]. [endsect] @@ -1523,6 +1577,8 @@ Class template `tommath_int` fulfills all of the requirements for a [link boost_ It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. +The type of `number_category >::type` is `mpl::int_`. + More information on this type can be found in the [link boost_multiprecision.tut.ints.tom_int tutorial]. [endsect] @@ -1552,6 +1608,8 @@ and `mp_number::precision`. Note that this type does not in any way change the it does not change the default precision of the mpf_t data type), therefore you can safely mix this type with existing code that uses GMP, and also mix `gmp_float`s of differing precision. +The type of `number_category >::type` is `mpl::int_`. + More information on this type can be found in the [link boost_multiprecision.tut.floats.gmp_float tutorial]. [endsect] @@ -1581,6 +1639,8 @@ and `mp_number::precision`. Note that this type does not in any way change the it does not change the default precision of the mpfr_t data type), therefore you can safely mix this type with existing code that uses GMP or MPFR, and also mix `mpfr_float_backend`s of differing precision. +The type of `number_category >::type` is `mpl::int_`. + More information on this type can be found in the [link boost_multiprecision.tut.floats.mpfr_float tutorial]. [endsect] @@ -1605,6 +1665,8 @@ The class takes a single template parameter - `Digits10` - which is the number o should support. Note that this type does not ever perform any dynamic memory allocation, as a result the `Digits10` template argument should not be set too high or the classes size will grow unreasonably large. +The type of `number_category >::type` is `mpl::int_`. + More information on this type can be found in the [link boost_multiprecision.tut.floats.cpp_dec_float tutorial]. [endsect] @@ -1771,12 +1833,49 @@ of type B2. [[`eval_lcm(b, cb, cb2)`][`void`][Sets `b` to the least common multiple of `cb` and `cb2`. Only required when `B` is an integer type.]] ] +The tables above place no ['throws] requirements on any of the operations. It is up to each type modelling this concept to +decide when or whether throwing an exception is desirable. However, thrown exceptions should always either be the type, or +inherit from the type `std::runtime_error`. For example, a floating point type might choose to throw `std::overflow_error` +whenever the result of an operation would be infinite, and `std::underflow_error` whenever it would round to zero. + [note The non-member functions are all named with an "eval_" prefix to avoid conflicts with template classes of the same name - in point of fact this naming convention shouldn't be necessary, but rather works around some compiler bugs.] [endsect] +[section:headers Header File Structure] + +[table Top level headers +[[Header][Contains]] +[[cpp_int.hpp][The `cpp_int` backend type.]] +[[gmp.hpp][Defines all [gmp] related backends.]] +[[integer_ops.hpp][Integer specific non-member functions.]] +[[miller_rabin.hpp][Miller Rabin primality testing code.]] +[[mp_number.hpp][Defines the `mp_number` backend, is included by all the backend headers.]] +[[mpfr.hpp][Defines the mpfr_float_backend backend.]] +[[random.hpp][Defines code to interoperate with Boost.Random.]] +[[rational_adapter.hpp][Defines the `rational_adapter` backend.]] +[[cpp_dec_float.hpp][Defines the `cpp_dec_float` backend.]] +[[tommath.hpp][Defines the `tommath_int` backend.]] +[[concepts/mp_number_architypes.hpp][Defines a backend concept architypes for testing use.]] +] + +[table Implementation Headers] +[[Header][Contains]] +[[detail/big_lanczos.hpp][Lanczos support for Boost.Math integration.]] +[[detail/cpp_int_core.hpp][Platform and peformance tuning for the `cpp_int` backend.]] +[[detail/default_ops.hpp][Default versions of the optional backend non-member functions.]] +[[detail/generic_interconvert.hpp][Generic interconversion routines.]] +[[detail/mp_number_base.hpp][All the expression template code, metaprogramming, and operator overloads for `mp_number`.]] +[[detail/no_et_ops.hpp][The non-expression template operators.]] +[[defail/functions/constants.hpp][Defines constants used by the floating point functions.]] +[[detail/functions/pow.hpp][Defines default versions of the power and exponential related floating point functions.]] +[[detail/functions/trig.hpp][Defines default versions of the trigonometric related floating point functions.]] +] + +[endsect] + [endsect] [section:perf Performance Comparison] diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index d57d30dd..cc24dfbd 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -1234,6 +1234,20 @@ struct promote_arg > typedef typename boost::multiprecision::detail::mp_exp::result_type type; }; +template +inline R real_cast(const boost::multiprecision::mp_number& val) +{ + return val.template convert_to(); +} + +template +inline R real_cast(const boost::multiprecision::detail::mp_exp& val) +{ + typedef typename boost::multiprecision::detail::mp_exp::result_type val_type; + return val_type(val).template convert_to(); +} + + }}} #endif // BOOST_MATH_BIG_NUM_BASE_HPP diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index e72d320a..58039d23 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -25,7 +25,7 @@ struct mpfr_float_backend; namespace detail{ -long get_default_precision() { return 50; } +inline long get_default_precision() { return 50; } template struct mpfr_float_imp From e299171d07132581031cdcdd759618288276b847 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 5 Jun 2012 10:40:56 +0000 Subject: [PATCH 186/256] Add performance test comparing double to mp_number>. Fix typo in docs and regenerate. [SVN r78811] --- .../boost_multiprecision/indexes/s01.html | 4 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 4 +- .../boost_multiprecision/ref/backendconc.html | 3 +- doc/html/index.html | 2 +- doc/multiprecision.qbk | 2 +- performance/float_backend.hpp | 437 ++++++++++++++++++ performance/sf_performance.cpp | 13 + 9 files changed, 461 insertions(+), 12 deletions(-) create mode 100644 performance/float_backend.hpp diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 3f5d4981..c4563d74 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
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    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 5c34b04c..02a9f039 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
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    diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index c2465281..f901dcde 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -1715,8 +1715,7 @@

    eval_round(b, - cb, - cb2) + cb)

    		diff --git a/doc/html/index.html b/doc/html/index.html index 284440fb..00bd89b8 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -118,7 +118,7 @@ - +

    Last revised: June 04, 2012 at 17:33:32 GMT

    Last revised: June 05, 2012 at 10:39:20 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 144abd36..92c2c9b1 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -1806,7 +1806,7 @@ of type B2. [[`eval_fabs(b, cb)`][`void`][Set `b` to the absolute value of `cb`.]] [[`eval_fpclassify(cb)`][`int`][Returns one of the same values returned by `std::fpclassify`. Only required when `B` is an floating-point type.]] [[`eval_trunc(b, cb)`][`void`][Performs the equivalent operation to `std::trunc` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_round(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::round` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] +[[`eval_round(b, cb)`][`void`][Performs the equivalent operation to `std::round` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] [[`eval_exp(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] [[`eval_log(b, cb)`][`void`][Performs the equivalent operation to `std::log` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] [[`eval_log10(b, cb)`][`void`][Performs the equivalent operation to `std::log10` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] diff --git a/performance/float_backend.hpp b/performance/float_backend.hpp new file mode 100644 index 00000000..59b88c2f --- /dev/null +++ b/performance/float_backend.hpp @@ -0,0 +1,437 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MATH_FLOAT_BACKEND_HPP +#define BOOST_MATH_FLOAT_BACKEND_HPP + +#include +#include +#include +#include +#include +#include +#include + +namespace boost{ +namespace multiprecision{ +namespace backends{ + +template +struct float_backend +{ + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list float_types; + typedef int exponent_type; + + float_backend(){} + float_backend(const float_backend& o) + { + m_value = o.m_value; + } + float_backend(const Arithmetic& o) : m_value(o) {} +#ifndef BOOST_NO_RVALUE_REFERENCES + float_backend(float_backend&& o) : m_value(o.m_value) {} + float_backend(Arithmetic&& o) : m_value(o) {} +#endif + float_backend& operator = (const float_backend& o) + { + m_value = o.m_value; + return *this; + } + float_backend& operator = (unsigned long long i) + { + m_value = i; + return *this; + } + float_backend& operator = (unsigned i) + { + m_value = i; + return *this; + } + float_backend& operator = (long long i) + { + m_value = i; + return *this; + } + float_backend& operator = (int i) + { + m_value = i; + return *this; + } + float_backend& operator = (long double d) + { + m_value = d; + return *this; + } + float_backend& operator = (double d) + { + m_value = d; + return *this; + } + float_backend& operator = (const char* s) + { + m_value = boost::lexical_cast(s); + return *this; + } + void swap(float_backend& o) + { + std::swap(m_value, o.m_value); + } + std::string str(std::streamsize digits, std::ios_base::fmtflags f)const + { + std::stringstream ss; + ss.flags(f); + ss << std::setprecision(digits) << m_value; + return ss.str(); + } + void negate() + { + m_value = -m_value; + } + int compare(const float_backend& o)const + { + return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); + } + int compare(long long i)const + { + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(int i)const + { + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(unsigned long long i)const + { + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(unsigned i)const + { + return m_value > i ? 1 : (m_value < i ? -1 : 0); + } + int compare(long double d)const + { + return m_value > d ? 1 : (m_value < d ? -1 : 0); + } + int compare(double d)const + { + return m_value > d ? 1 : (m_value < d ? -1 : 0); + } + Arithmetic& data() { return m_value; } + const Arithmetic& data()const { return m_value; } +private: + Arithmetic m_value; +}; + +template +inline void eval_add(float_backend& result, const float_backend& o) +{ + result.data() += o.data(); +} +template +inline void eval_subtract(float_backend& result, const float_backend& o) +{ + result.data() -= o.data(); +} +template +inline void eval_multiply(float_backend& result, const float_backend& o) +{ + result.data() *= o.data(); +} +template +inline void eval_divide(float_backend& result, const float_backend& o) +{ + result.data() /= o.data(); +} + +template +inline typename enable_if >::type eval_add(float_backend& result, const A2& o) +{ + result.data() += o; +} +template +inline typename enable_if >::type eval_subtract(float_backend& result, const A2& o) +{ + result.data() -= o; +} +template +inline typename enable_if >::type eval_multiply(float_backend& result, const A2& o) +{ + result.data() *= o; +} +template +inline typename enable_if >::type eval_divide(float_backend& result, const A2& o) +{ + result.data() /= o; +} + +template +inline void eval_add(float_backend& result, const float_backend& a, const float_backend& b) +{ + result.data() = a.data() + b.data(); +} +template +inline void eval_subtract(float_backend& result, const float_backend& a, const float_backend& b) +{ + result.data() = a.data() - b.data(); +} +template +inline void eval_multiply(float_backend& result, const float_backend& a, const float_backend& b) +{ + result.data() = a.data() * b.data(); +} +template +inline void eval_divide(float_backend& result, const float_backend& a, const float_backend& b) +{ + result.data() = a.data() / b.data(); +} + +template +inline typename enable_if>::type eval_add(float_backend& result, const A2& a, const float_backend& b) +{ + result.data() = a + b.data(); +} +template +inline typename enable_if>::type eval_subtract(float_backend& result, const A2& a, const float_backend& b) +{ + result.data() = a - b.data(); +} +template +inline typename enable_if>::type eval_multiply(float_backend& result, const A2& a, const float_backend& b) +{ + result.data() = a * b.data(); +} +template +inline typename enable_if>::type eval_divide(float_backend& result, const A2& a, const float_backend& b) +{ + result.data() = a / b.data(); +} + +template +inline bool eval_is_zero(const float_backend& val) +{ + return val.data() == 0; +} + +template +inline int eval_get_sign(const float_backend& val) +{ + return val.data() == 0 ? 0 : val.data() < 0 ? -1 : 1; +} + +template +inline void eval_abs(float_backend& result, const float_backend& o) +{ + result.data() = std::abs(o.data()); +} + +template +inline void eval_fabs(float_backend& result, const float_backend& o) +{ + result.data() = std::abs(o.data()); +} + +template +inline void eval_floor(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = floor(o.data()); +} + +template +inline void eval_ceil(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = ceil(o.data()); +} + +template +inline void eval_sqrt(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = sqrt(o.data()); +} + +template +inline int eval_fpclassify(const float_backend& o) +{ + return (boost::math::fpclassify)(o.data()); +} + +template +inline void eval_trunc(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = trunc(o.data()); +} + +template +inline void eval_round(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = round(o.data()); +} + +template +inline void eval_exp(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = exp(o.data()); +} + +template +inline void eval_log(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = log(o.data()); +} + +template +inline void eval_log10(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = log10(o.data()); +} + +template +inline void eval_sin(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = sin(o.data()); +} + +template +inline void eval_cos(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = cos(o.data()); +} + +template +inline void eval_tan(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = tan(o.data()); +} + +template +inline void eval_acos(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = acos(o.data()); +} + +template +inline void eval_asin(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = asin(o.data()); +} + +template +inline void eval_atan(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = atan(o.data()); +} + +template +inline void eval_sinh(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = sinh(o.data()); +} + +template +inline void eval_cosh(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = cosh(o.data()); +} + +template +inline void eval_tanh(float_backend& result, const float_backend& o) +{ + BOOST_MATH_STD_USING + result.data() = tanh(o.data()); +} + +template +inline void eval_fmod(float_backend& result, const float_backend& a, const float_backend& b) +{ + BOOST_MATH_STD_USING + result.data() = fmod(a.data(), b.data()); +} + +template +inline void eval_pow(float_backend& result, const float_backend& a, const float_backend& b) +{ + BOOST_MATH_STD_USING + result.data() = pow(a.data(), b.data()); +} + +template +inline void eval_atan2(float_backend& result, const float_backend& a, const float_backend& b) +{ + BOOST_MATH_STD_USING + result.data() = atan2(a.data(), b.data()); +} + +} // namespace backends + +using boost::multiprecision::backends::float_backend; + +}} // namespaces + +namespace boost{ namespace math{ namespace tools{ + +template <> +inline double real_cast(concepts::real_concept r) +{ + return static_cast(r.value()); +} + +}}} + + +namespace std{ + +template +class numeric_limits, ExpressionTemplates > > : public std::numeric_limits +{ + typedef std::numeric_limits base_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; +public: + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } +}; + +template<> +class numeric_limits : public std::numeric_limits +{ + typedef std::numeric_limits base_type; + typedef boost::math::concepts::real_concept number_type; +public: + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } +}; + +} + +#endif diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index 5bd20871..f748a5a9 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -14,6 +14,9 @@ # define TEST_MPREAL #endif +#ifdef TEST_FLOAT +#include "float_backend.hpp" +#endif #ifdef TEST_MPFR_CLASS #include #endif @@ -249,6 +252,16 @@ int main() poly_allocation_test("mpfr::mpreal", mpfr::mpreal(2)); #endif + // + // Comparison for builtin floats: + // +#ifdef TEST_FLOAT + time_proc("double", test_bessel); + time_proc("real_concept", test_bessel); + time_proc("float_backend", test_bessel > >); + time_proc("float_backend - no expression templates", test_bessel, false> >); +#endif + // // 50 digits first: // From 3fc6a3f67ccf8af93c1c3005906d1202b76f3d8a Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 5 Jun 2012 17:19:56 +0000 Subject: [PATCH 187/256] Update TODO list. [SVN r78815] --- doc/html/boost_multiprecision/indexes/s01.html | 4 ++-- doc/html/boost_multiprecision/indexes/s02.html | 4 ++-- doc/html/boost_multiprecision/indexes/s03.html | 4 ++-- doc/html/boost_multiprecision/indexes/s04.html | 4 ++-- doc/html/boost_multiprecision/map/todo.html | 15 +++++++++++++++ doc/html/index.html | 2 +- doc/multiprecision.qbk | 4 ++++ 7 files changed, 28 insertions(+), 9 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index c4563d74..c51f2f47 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
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    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index f8981198..80fb897d 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
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    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 02a9f039..fd536361 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
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    diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index 00d93f94..9b6465df 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -47,6 +47,21 @@ Comments
      +
    • + Can the non-expression template operators be further optimised with rvalue + reference support? +
      • +
    • + Can any functions - in particular value initialization - be made constexp? +
      • +
    • + Can we differentiate between explicit and implicit conversions in the + mp_number constructor (may need some new type traits)? +
      • +
    • + Can ring types (exact floating point types) be supported? The answer + should be yes, but someone needs to write it. +
    • Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents. Open question - what should diff --git a/doc/html/index.html b/doc/html/index.html index 00bd89b8..4e0ab81c 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -118,7 +118,7 @@
    - +

    Last revised: June 05, 2012 at 10:39:20 GMT

    Last revised: June 05, 2012 at 17:15:21 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 92c2c9b1..1be60a64 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -2262,6 +2262,10 @@ More a list of what ['could] be done, rather than what ['should] be done (which [h4 Pre-Review Comments] +* Can the non-expression template operators be further optimised with rvalue reference support? +* Can any functions - in particular value initialization - be made `constexp`? +* Can we differentiate between explicit and implicit conversions in the mp_number constructor (may need some new type traits)? +* Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it. * Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents. Open question - what should be the default - int32_t or int64_t? * Document the size requirements of fixed precision ints. From 5ce96a14597ea6be84feee3799d2fc29cf70e2b3 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 7 Jun 2012 10:06:56 +0000 Subject: [PATCH 188/256] Fix some doc typos and regenerate docs. [SVN r78843] --- doc/html/boost_multiprecision/indexes/s01.html | 4 ++-- doc/html/boost_multiprecision/indexes/s02.html | 4 ++-- doc/html/boost_multiprecision/indexes/s03.html | 4 ++-- doc/html/boost_multiprecision/indexes/s04.html | 4 ++-- .../boost_multiprecision/ref/cpp_dec_ref.html | 4 ++-- .../boost_multiprecision/ref/cpp_int_ref.html | 2 +- .../boost_multiprecision/ref/gmp_int_ref.html | 2 +- doc/html/boost_multiprecision/ref/mpf_ref.html | 2 +- .../boost_multiprecision/ref/mpfr_ref.html | 2 +- .../boost_multiprecision/ref/tom_int_ref.html | 2 +- .../boost_multiprecision/tut/conversions.html | 2 +- .../tut/floats/fp_eg/nd.html | 2 +- .../tut/ints/egs/bitops.html | 2 +- .../boost_multiprecision/tut/rational.html | 2 +- doc/html/index.html | 2 +- doc/multiprecision.qbk | 18 +++++++++--------- example/floating_point_examples.cpp | 2 +- example/integer_examples.cpp | 2 +- 18 files changed, 31 insertions(+), 31 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index c51f2f47..717f0ba7 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
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    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 80fb897d..607ffea8 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
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    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index fd536361..0881eae2 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
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    diff --git a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html index 48ce9b5b..031f0575 100644 --- a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html @@ -30,7 +30,7 @@

    Class template cpp_dec_float fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: + type. Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change.

    @@ -38,7 +38,7 @@ - which is the number of decimal digits precision the type should support. Note that this type does not ever perform any dynamic memory allocation, as a result the Digits10 - template argument should not be set too high or the classes size will grow + template argument should not be set too high or the class's size will grow unreasonably large.

    diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html index 43160fed..e0c9f368 100644 --- a/doc/html/boost_multiprecision/ref/cpp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_int_ref.html @@ -43,7 +43,7 @@

    Class template cpp_int_backend fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: + type. Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change.

    diff --git a/doc/html/boost_multiprecision/ref/gmp_int_ref.html b/doc/html/boost_multiprecision/ref/gmp_int_ref.html index 6d536179..ff5fb3ca 100644 --- a/doc/html/boost_multiprecision/ref/gmp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/gmp_int_ref.html @@ -28,7 +28,7 @@

    Class template gmp_int fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: + type. Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change.

    diff --git a/doc/html/boost_multiprecision/ref/mpf_ref.html b/doc/html/boost_multiprecision/ref/mpf_ref.html index 9481059c..1eb8aad6 100644 --- a/doc/html/boost_multiprecision/ref/mpf_ref.html +++ b/doc/html/boost_multiprecision/ref/mpf_ref.html @@ -33,7 +33,7 @@

    Class template gmp_float fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: + type. Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change.

    diff --git a/doc/html/boost_multiprecision/ref/mpfr_ref.html b/doc/html/boost_multiprecision/ref/mpfr_ref.html index eb96296a..a60f9563 100644 --- a/doc/html/boost_multiprecision/ref/mpfr_ref.html +++ b/doc/html/boost_multiprecision/ref/mpfr_ref.html @@ -33,7 +33,7 @@

    Class template mpfr_float_backend fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: + type. Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change.

    diff --git a/doc/html/boost_multiprecision/ref/tom_int_ref.html b/doc/html/boost_multiprecision/ref/tom_int_ref.html index 9855b80a..c95e2112 100644 --- a/doc/html/boost_multiprecision/ref/tom_int_ref.html +++ b/doc/html/boost_multiprecision/ref/tom_int_ref.html @@ -28,7 +28,7 @@

    Class template tommath_int fulfills all of the requirements for a Backend - type. It's members and non-member functions are deliberately not documented: + type. Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change.

    diff --git a/doc/html/boost_multiprecision/tut/conversions.html b/doc/html/boost_multiprecision/tut/conversions.html index dd36b344..81632bc8 100644 --- a/doc/html/boost_multiprecision/tut/conversions.html +++ b/doc/html/boost_multiprecision/tut/conversions.html @@ -67,7 +67,7 @@ std::cout << std::hex << std::showbase << i << std::endl;

    • - Some intercomnversions between number types are completely generic, and + Some interconversions between number types are completely generic, and are always available: 
    cpp_int cppi(2);
diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html
index 70cdb83c..71e7e9a9 100644
--- a/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html
+++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html
@@ -114,7 +114,7 @@
       );
    //
    // In the cpp_dec_float_50 case, the sin function is multiply overloaded
-   // to handle expression templates etc.  As a result it's hard to take it's
+   // to handle expression templates etc.  As a result it's hard to take its
    // address without knowing about its implementation details.  We'll use a 
    // C++11 lambda expression to capture the call.
    // We also need a typecast on the first argument so we don't accidently pass
diff --git a/doc/html/boost_multiprecision/tut/ints/egs/bitops.html b/doc/html/boost_multiprecision/tut/ints/egs/bitops.html
index 37b37e80..cd9dbdc3 100644
--- a/doc/html/boost_multiprecision/tut/ints/egs/bitops.html
+++ b/doc/html/boost_multiprecision/tut/ints/egs/bitops.html
@@ -58,7 +58,7 @@
           
    
 
    
             Note how the bit_set
-            function sets the specified bit in it's argument and then returns a reference
+            function sets the specified bit in its argument and then returns a reference
             to the result - which we can then simply decrement. The result from a
             call to b2 is the same
             as that to b1.
diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html
index 0d05ef47..2571ebe6 100644
--- a/doc/html/boost_multiprecision/tut/rational.html
+++ b/doc/html/boost_multiprecision/tut/rational.html
@@ -189,7 +189,7 @@

    - All C++ adapter that allows any inetger back-end type to be used + All C++ adapter that allows any integer back-end type to be used as a rational type.

    - +

    Last revised: June 05, 2012 at 17:15:21 GMT

    Last revised: June 07, 2012 at 09:33:02 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 1be60a64..c83d197f 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -672,7 +672,7 @@ The following back-ends provide rational number arithmetic: [[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] [[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licensed implementation.][Slower than [gmp].]] [[`tommath_rational`][boost/multiprecision/tommath.hpp][2][[tommath]][All C/C++ implementation that's Boost Software Licence compatible.][Slower than [gmp].]] -[[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any inetger back-end type to be used as a rational type.][Requires an underlying integer back-end type.]] +[[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any integer back-end type to be used as a rational type.][Requires an underlying integer back-end type.]] [[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `mp_number` integer type.][The expression templates used by `mp_number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]] ] @@ -877,7 +877,7 @@ In particular: // Now print in hex format with prefix: std::cout << std::hex << std::showbase << i << std::endl; -* Some intercomnversions between number types are completely generic, and are always available: +* Some interconversions between number types are completely generic, and are always available: cpp_int cppi(2); // We can always convert between numbers of the same category - @@ -1519,7 +1519,7 @@ whose precision can vary at compile time (such as `mpf_float`). }} // namespaces Class template `cpp_int_backend` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The template arguments are: @@ -1554,7 +1554,7 @@ More information on this type can be found in the [link boost_multiprecision.tut }} // namespaces Class template `gmp_int` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The type of `number_category >::type` is `mpl::int_`. @@ -1574,7 +1574,7 @@ More information on this type can be found in the [link boost_multiprecision.tut }} // namespaces Class template `tommath_int` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The type of `number_category >::type` is `mpl::int_`. @@ -1599,7 +1599,7 @@ More information on this type can be found in the [link boost_multiprecision.tut }} // namespaces Class template `gmp_float` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type @@ -1630,7 +1630,7 @@ More information on this type can be found in the [link boost_multiprecision.tut }} // namespaces Class template `mpfr_float_backend` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type @@ -1658,12 +1658,12 @@ More information on this type can be found in the [link boost_multiprecision.tut }} // namespaces Class template `cpp_dec_float` fulfills all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -It's members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type should support. Note that this type does not ever perform any dynamic memory allocation, as a result the `Digits10` -template argument should not be set too high or the classes size will grow unreasonably large. +template argument should not be set too high or the class's size will grow unreasonably large. The type of `number_category >::type` is `mpl::int_`. diff --git a/example/floating_point_examples.cpp b/example/floating_point_examples.cpp index 7c391ddd..e1c9b97a 100644 --- a/example/floating_point_examples.cpp +++ b/example/floating_point_examples.cpp @@ -537,7 +537,7 @@ int main(int, char**) ); // // In the cpp_dec_float_50 case, the sin function is multiply overloaded - // to handle expression templates etc. As a result it's hard to take it's + // to handle expression templates etc. As a result it's hard to take its // address without knowing about its implementation details. We'll use a // C++11 lambda expression to capture the call. // We also need a typecast on the first argument so we don't accidently pass diff --git a/example/integer_examples.cpp b/example/integer_examples.cpp index 68cb0653..f57e76e8 100644 --- a/example/integer_examples.cpp +++ b/example/integer_examples.cpp @@ -157,7 +157,7 @@ cpp_int b2(unsigned n) } /*` -Note how the `bit_set` function sets the specified bit in it's argument and then returns a reference to the result - +Note how the `bit_set` function sets the specified bit in its argument and then returns a reference to the result - which we can then simply decrement. The result from a call to `b2` is the same as that to `b1`. We can equally test bits, so for example the n'th bit of the result returned from `b2` shouldn't be set From e0a8f821c52f5384ff317cb2ec8db0dacbbb2f2d Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 14 Jun 2012 10:26:15 +0000 Subject: [PATCH 189/256] Change BOOST_MP_NOEXCEPT to BOOST_NOEXCEPT. Add some missing #includes. [SVN r78943] --- .../concepts/mp_number_architypes.hpp | 18 ++--- include/boost/multiprecision/cpp_int.hpp | 54 +++++++------- .../depricated/arithmetic_backend.hpp | 18 ++--- .../multiprecision/depricated/fixed_int.hpp | 18 ++--- .../multiprecision/detail/mp_number_base.hpp | 6 -- include/boost/multiprecision/gmp.hpp | 72 +++++++++---------- include/boost/multiprecision/mp_number.hpp | 2 + include/boost/multiprecision/mpfr.hpp | 36 +++++----- .../boost/multiprecision/rational_adapter.hpp | 18 ++--- include/boost/multiprecision/tommath.hpp | 18 ++--- 10 files changed, 128 insertions(+), 132 deletions(-) diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_architypes.hpp index ea29ecde..bc281b4f 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_architypes.hpp @@ -198,15 +198,15 @@ class numeric_limits base_type; typedef boost::multiprecision::mp_number number_type; public: - static number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } - static number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } - static number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } - static number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); } - static number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; } - static number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); } - static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); } - static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); } - static number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } + static number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } + static number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } + static number_type lowest() BOOST_NOEXCEPT { return -(max)(); } + static number_type epsilon() BOOST_NOEXCEPT { return base_type::epsilon(); } + static number_type round_error() BOOST_NOEXCEPT { return epsilon() / 2; } + static number_type infinity() BOOST_NOEXCEPT { return base_type::infinity(); } + static number_type quiet_NaN() BOOST_NOEXCEPT { return base_type::quiet_NaN(); } + static number_type signaling_NaN() BOOST_NOEXCEPT { return base_type::signaling_NaN(); } + static number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } }; } diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index e57e10d6..b3ba4475 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -2316,15 +2316,15 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - static number_type (min)() BOOST_MP_NOEXCEPT + static number_type (min)() BOOST_NOEXCEPT { return number_type(0); } - static number_type (max)() BOOST_MP_NOEXCEPT + static number_type (max)() BOOST_NOEXCEPT { return number_type(0); } - static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + static number_type lowest() BOOST_NOEXCEPT { return (min)(); } BOOST_STATIC_CONSTEXPR int digits = 0; BOOST_STATIC_CONSTEXPR int digits10 = 0; BOOST_STATIC_CONSTEXPR int max_digits10 = 0; @@ -2332,8 +2332,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = true; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - static number_type epsilon() BOOST_MP_NOEXCEPT { return 0; } - static number_type round_error() BOOST_MP_NOEXCEPT { return 0; } + static number_type epsilon() BOOST_NOEXCEPT { return 0; } + static number_type round_error() BOOST_NOEXCEPT { return 0; } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -2343,10 +2343,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - static number_type infinity() BOOST_MP_NOEXCEPT { return 0; } - static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return 0; } - static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return 0; } - static number_type denorm_min() BOOST_MP_NOEXCEPT { return 0; } + static number_type infinity() BOOST_NOEXCEPT { return 0; } + static number_type quiet_NaN() BOOST_NOEXCEPT { return 0; } + static number_type signaling_NaN() BOOST_NOEXCEPT { return 0; } + static number_type denorm_min() BOOST_NOEXCEPT { return 0; } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -2378,11 +2378,11 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - static number_type (min)() BOOST_MP_NOEXCEPT + static number_type (min)() BOOST_NOEXCEPT { return -(max)(); } - static number_type (max)() BOOST_MP_NOEXCEPT + static number_type (max)() BOOST_NOEXCEPT { typedef typename number_type::backend_type backend_type; init.do_nothing(); @@ -2401,7 +2401,7 @@ public: } return val; } - static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + static number_type lowest() BOOST_NOEXCEPT { return (min)(); } BOOST_STATIC_CONSTEXPR int digits = MinBits; BOOST_STATIC_CONSTEXPR int digits10 = static_cast(MinBits * 301L / 1000L); BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; @@ -2409,8 +2409,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = true; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - static number_type epsilon() BOOST_MP_NOEXCEPT { return 0; } - static number_type round_error() BOOST_MP_NOEXCEPT { return 0; } + static number_type epsilon() BOOST_NOEXCEPT { return 0; } + static number_type round_error() BOOST_NOEXCEPT { return 0; } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -2420,10 +2420,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - static number_type infinity() BOOST_MP_NOEXCEPT { return 0; } - static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return 0; } - static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return 0; } - static number_type denorm_min() BOOST_MP_NOEXCEPT { return 0; } + static number_type infinity() BOOST_NOEXCEPT { return 0; } + static number_type quiet_NaN() BOOST_NOEXCEPT { return 0; } + static number_type signaling_NaN() BOOST_NOEXCEPT { return 0; } + static number_type denorm_min() BOOST_NOEXCEPT { return 0; } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = true; BOOST_STATIC_CONSTEXPR bool is_modulo = true; @@ -2457,11 +2457,11 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - static number_type (min)() BOOST_MP_NOEXCEPT + static number_type (min)() BOOST_NOEXCEPT { return number_type(0); } - static number_type (max)() BOOST_MP_NOEXCEPT + static number_type (max)() BOOST_NOEXCEPT { typedef typename number_type::backend_type backend_type; init.do_nothing(); @@ -2480,7 +2480,7 @@ public: } return val; } - static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + static number_type lowest() BOOST_NOEXCEPT { return (min)(); } BOOST_STATIC_CONSTEXPR int digits = MinBits; BOOST_STATIC_CONSTEXPR int digits10 = static_cast(MinBits * 301L / 1000L); BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; @@ -2488,8 +2488,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = true; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - static number_type epsilon() BOOST_MP_NOEXCEPT { return 0; } - static number_type round_error() BOOST_MP_NOEXCEPT { return 0; } + static number_type epsilon() BOOST_NOEXCEPT { return 0; } + static number_type round_error() BOOST_NOEXCEPT { return 0; } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -2499,10 +2499,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - static number_type infinity() BOOST_MP_NOEXCEPT { return 0; } - static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return 0; } - static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return 0; } - static number_type denorm_min() BOOST_MP_NOEXCEPT { return 0; } + static number_type infinity() BOOST_NOEXCEPT { return 0; } + static number_type quiet_NaN() BOOST_NOEXCEPT { return 0; } + static number_type signaling_NaN() BOOST_NOEXCEPT { return 0; } + static number_type denorm_min() BOOST_NOEXCEPT { return 0; } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = true; BOOST_STATIC_CONSTEXPR bool is_modulo = true; diff --git a/include/boost/multiprecision/depricated/arithmetic_backend.hpp b/include/boost/multiprecision/depricated/arithmetic_backend.hpp index af26b1ca..9925d3f8 100644 --- a/include/boost/multiprecision/depricated/arithmetic_backend.hpp +++ b/include/boost/multiprecision/depricated/arithmetic_backend.hpp @@ -133,15 +133,15 @@ class numeric_limits base_type; typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; public: - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; } - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_NOEXCEPT { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } }; } diff --git a/include/boost/multiprecision/depricated/fixed_int.hpp b/include/boost/multiprecision/depricated/fixed_int.hpp index ff59dbef..80be2036 100644 --- a/include/boost/multiprecision/depricated/fixed_int.hpp +++ b/include/boost/multiprecision/depricated/fixed_int.hpp @@ -1538,7 +1538,7 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { static bool init = false; static number_type val; @@ -1549,7 +1549,7 @@ public: } return val; } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { static bool init = false; static number_type val; @@ -1560,7 +1560,7 @@ public: } return val; } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_NOEXCEPT { return (min)(); } BOOST_STATIC_CONSTEXPR int digits = Bits; BOOST_STATIC_CONSTEXPR int digits10 = (digits * 301L) / 1000; BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; @@ -1568,8 +1568,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = true; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return 0; } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT { return 0; } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -1579,10 +1579,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return 0; } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return 0; } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return 0; } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT { return 0; } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return 0; } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = true; BOOST_STATIC_CONSTEXPR bool is_modulo = true; diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index cc24dfbd..103ad9fe 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -11,12 +11,6 @@ #include #include -#ifdef BOOST_NO_NOEXCEPT -#define BOOST_MP_NOEXCEPT -#else -#define BOOST_MP_NOEXCEPT noexcept -#endif - namespace boost{ namespace multiprecision{ template diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 02f11216..08b93a07 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1844,7 +1844,7 @@ public: // mpf_get_str on 64-bit Linux builds. Possibly we could use larger // exponent values elsewhere. // - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1856,7 +1856,7 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1868,7 +1868,7 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_NOEXCEPT { return -(max)(); } @@ -1880,7 +1880,7 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1893,7 +1893,7 @@ public: return value.second; } // What value should this be???? - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT { // returns epsilon/2 initializer.do_nothing(); @@ -1915,10 +1915,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT { return number_type(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = true; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -1950,9 +1950,9 @@ class numeric_limits, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; - static number_type (min)() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type (max)() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type lowest() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type (min)() BOOST_NOEXCEPT { return number_type(); } + static number_type (max)() BOOST_NOEXCEPT { return number_type(); } + static number_type lowest() BOOST_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int digits = 0; BOOST_STATIC_CONSTEXPR int digits10 = 0; BOOST_STATIC_CONSTEXPR int max_digits10 = 0; @@ -1960,8 +1960,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 0; - static number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type epsilon() BOOST_NOEXCEPT { return number_type(); } + static number_type round_error() BOOST_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -1971,10 +1971,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - static number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type infinity() BOOST_NOEXCEPT { return number_type(); } + static number_type quiet_NaN() BOOST_NOEXCEPT { return number_type(); } + static number_type signaling_NaN() BOOST_NOEXCEPT { return number_type(); } + static number_type denorm_min() BOOST_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -1993,15 +1993,15 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - static number_type (min)() BOOST_MP_NOEXCEPT + static number_type (min)() BOOST_NOEXCEPT { return number_type(); } - static number_type (max)() BOOST_MP_NOEXCEPT + static number_type (max)() BOOST_NOEXCEPT { return number_type(); } - static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + static number_type lowest() BOOST_NOEXCEPT { return (min)(); } BOOST_STATIC_CONSTEXPR int digits = INT_MAX; BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L; BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; @@ -2009,8 +2009,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = true; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - static number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type epsilon() BOOST_NOEXCEPT { return number_type(); } + static number_type round_error() BOOST_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -2020,10 +2020,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - static number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type infinity() BOOST_NOEXCEPT { return number_type(); } + static number_type quiet_NaN() BOOST_NOEXCEPT { return number_type(); } + static number_type signaling_NaN() BOOST_NOEXCEPT { return number_type(); } + static number_type denorm_min() BOOST_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -2042,15 +2042,15 @@ public: // Largest and smallest numbers are bounded only by available memory, set // to zero: // - static number_type (min)() BOOST_MP_NOEXCEPT + static number_type (min)() BOOST_NOEXCEPT { return number_type(); } - static number_type (max)() BOOST_MP_NOEXCEPT + static number_type (max)() BOOST_NOEXCEPT { return number_type(); } - static number_type lowest() BOOST_MP_NOEXCEPT { return (min)(); } + static number_type lowest() BOOST_NOEXCEPT { return (min)(); } // Digits are unbounded, use zero for now: BOOST_STATIC_CONSTEXPR int digits = 0; BOOST_STATIC_CONSTEXPR int digits10 = 0; @@ -2059,8 +2059,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = true; BOOST_STATIC_CONSTEXPR int radix = 2; - static number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type round_error() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type epsilon() BOOST_NOEXCEPT { return number_type(); } + static number_type round_error() BOOST_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -2070,10 +2070,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - static number_type infinity() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(); } - static number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(); } + static number_type infinity() BOOST_NOEXCEPT { return number_type(); } + static number_type quiet_NaN() BOOST_NOEXCEPT { return number_type(); } + static number_type signaling_NaN() BOOST_NOEXCEPT { return number_type(); } + static number_type denorm_min() BOOST_NOEXCEPT { return number_type(); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 84a5feae..a8928cfe 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -20,6 +20,8 @@ #include #include #include +#include // stream operators +#include // EOF namespace boost{ namespace multiprecision{ diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 58039d23..1ea8f782 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -1045,7 +1045,7 @@ class numeric_limits, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1057,7 +1057,7 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1069,7 +1069,7 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_NOEXCEPT { return -(max)(); } @@ -1081,7 +1081,7 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT { initializer.do_nothing(); static std::pair value; @@ -1094,7 +1094,7 @@ public: return value.second; } // What value should this be???? - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT { // returns epsilon/2 initializer.do_nothing(); @@ -1116,7 +1116,7 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT { // returns epsilon/2 initializer.do_nothing(); @@ -1129,7 +1129,7 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT { // returns epsilon/2 initializer.do_nothing(); @@ -1142,11 +1142,11 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT { return number_type(0); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(0); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = true; BOOST_STATIC_CONSTEXPR bool is_modulo = false; @@ -1180,9 +1180,9 @@ class numeric_limits, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; - static number_type (min)() BOOST_MP_NOEXCEPT { return number_type(0); } - static number_type (max)() BOOST_MP_NOEXCEPT { return number_type(0); } - static number_type lowest() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type (min)() BOOST_NOEXCEPT { return number_type(0); } + static number_type (max)() BOOST_NOEXCEPT { return number_type(0); } + static number_type lowest() BOOST_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR int digits = 0; BOOST_STATIC_CONSTEXPR int digits10 = 0; BOOST_STATIC_CONSTEXPR int max_digits10 = 0; @@ -1190,8 +1190,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 0; - static number_type epsilon() BOOST_MP_NOEXCEPT { return number_type(0); } - static number_type round_error() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type epsilon() BOOST_NOEXCEPT { return number_type(0); } + static number_type round_error() BOOST_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR int min_exponent = 0; BOOST_STATIC_CONSTEXPR int min_exponent10 = 0; BOOST_STATIC_CONSTEXPR int max_exponent = 0; @@ -1201,10 +1201,10 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - static number_type infinity() BOOST_MP_NOEXCEPT { return number_type(0); } - static number_type quiet_NaN() BOOST_MP_NOEXCEPT { return number_type(0); } - static number_type signaling_NaN() BOOST_MP_NOEXCEPT { return number_type(0); } - static number_type denorm_min() BOOST_MP_NOEXCEPT { return number_type(0); } + static number_type infinity() BOOST_NOEXCEPT { return number_type(0); } + static number_type quiet_NaN() BOOST_NOEXCEPT { return number_type(0); } + static number_type signaling_NaN() BOOST_NOEXCEPT { return number_type(0); } + static number_type denorm_min() BOOST_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR bool is_bounded = false; BOOST_STATIC_CONSTEXPR bool is_modulo = false; diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index c01af0fd..0aa4ec70 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -205,15 +205,15 @@ class numeric_limits Date: Fri, 15 Jun 2012 09:10:47 +0000 Subject: [PATCH 190/256] Fix valgrind spotted bug in cpp_int subtraction routine. Add missing numeric_limits members. Fix GCC warning in gmp.hpp. [SVN r78953] --- include/boost/multiprecision/cpp_int.hpp | 153 ++++++++++++++++++++++- include/boost/multiprecision/gmp.hpp | 10 ++ 2 files changed, 162 insertions(+), 1 deletion(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index b3ba4475..c6e4864d 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -964,12 +964,16 @@ inline void subtract_unsigned(cpp_int_backend& resul result.sign(s); return; } + // This isn't used till later, but comparison has to occur before we resize the result, + // as that may also resize a or b if this is an inplace operation: + int c = a.compare_unsigned(b); + // Set up the result vector: result.resize(x); + // Now that a, b, and result are stable, get pointers to their limbs: typename cpp_int_backend::const_limb_pointer pa = a.limbs(); typename cpp_int_backend::const_limb_pointer pb = b.limbs(); typename cpp_int_backend::limb_pointer pr = result.limbs(); bool swapped = false; - int c = a.compare_unsigned(b); if(c < 0) { swap(pa, pb); @@ -2355,6 +2359,55 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +const int numeric_limits, ExpressionTemplates> >::digits; +template +const int numeric_limits, ExpressionTemplates> >::digits10; +template +const int numeric_limits, ExpressionTemplates> >::max_digits10; +template +const bool numeric_limits, ExpressionTemplates> >::is_signed; +template +const bool numeric_limits, ExpressionTemplates> >::is_integer; +template +const bool numeric_limits, ExpressionTemplates> >::is_exact; +template +const int numeric_limits, ExpressionTemplates> >::radix; +template +const int numeric_limits, ExpressionTemplates> >::min_exponent; +template +const int numeric_limits, ExpressionTemplates> >::min_exponent10; +template +const int numeric_limits, ExpressionTemplates> >::max_exponent; +template +const int numeric_limits, ExpressionTemplates> >::max_exponent10; +template +const bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +const bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +const bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +const float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +const bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +const bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +const bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +const bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +const bool numeric_limits, ExpressionTemplates> >::traps; +template +const bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +const float_round_style numeric_limits, ExpressionTemplates> >::round_style; + +#endif + template class numeric_limits, ExpressionTemplates> > { @@ -2435,6 +2488,55 @@ public: template const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +const int numeric_limits, ExpressionTemplates> >::digits; +template +const int numeric_limits, ExpressionTemplates> >::digits10; +template +const int numeric_limits, ExpressionTemplates> >::max_digits10; +template +const bool numeric_limits, ExpressionTemplates> >::is_signed; +template +const bool numeric_limits, ExpressionTemplates> >::is_integer; +template +const bool numeric_limits, ExpressionTemplates> >::is_exact; +template +const int numeric_limits, ExpressionTemplates> >::radix; +template +const int numeric_limits, ExpressionTemplates> >::min_exponent; +template +const int numeric_limits, ExpressionTemplates> >::min_exponent10; +template +const int numeric_limits, ExpressionTemplates> >::max_exponent; +template +const int numeric_limits, ExpressionTemplates> >::max_exponent10; +template +const bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +const bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +const bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +const float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +const bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +const bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +const bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +const bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +const bool numeric_limits, ExpressionTemplates> >::traps; +template +const bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +const float_round_style numeric_limits, ExpressionTemplates> >::round_style; + +#endif + template class numeric_limits, ExpressionTemplates> > { @@ -2514,6 +2616,55 @@ public: template const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +const int numeric_limits, ExpressionTemplates> >::digits; +template +const int numeric_limits, ExpressionTemplates> >::digits10; +template +const int numeric_limits, ExpressionTemplates> >::max_digits10; +template +const bool numeric_limits, ExpressionTemplates> >::is_signed; +template +const bool numeric_limits, ExpressionTemplates> >::is_integer; +template +const bool numeric_limits, ExpressionTemplates> >::is_exact; +template +const int numeric_limits, ExpressionTemplates> >::radix; +template +const int numeric_limits, ExpressionTemplates> >::min_exponent; +template +const int numeric_limits, ExpressionTemplates> >::min_exponent10; +template +const int numeric_limits, ExpressionTemplates> >::max_exponent; +template +const int numeric_limits, ExpressionTemplates> >::max_exponent10; +template +const bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +const bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +const bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +const float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +const bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +const bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +const bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +const bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +const bool numeric_limits, ExpressionTemplates> >::traps; +template +const bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +const float_round_style numeric_limits, ExpressionTemplates> >::round_style; + +#endif + } #endif diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 08b93a07..fef98b76 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1428,6 +1428,16 @@ inline typename enable_if< mpl::bool_ > >::type eval_powm(gmp_int& result, const gmp_int& base, Integer p, const gmp_int& m) +{ + mpz_powm_ui(result.data(), base.data(), p, m.data()); +} +template +inline typename enable_if< + mpl::and_< + is_signed, + mpl::bool_ + > +>::type eval_powm(gmp_int& result, const gmp_int& base, Integer p, const gmp_int& m) { if(p < 0) { From a6a4ff0c5e2c7de600506924d739bced9d7d3cf2 Mon Sep 17 00:00:00 2001 From: Christopher Kormanyos Date: Mon, 25 Jun 2012 21:17:27 +0000 Subject: [PATCH 191/256] Improve the pow_imp function with the S-and-X binary method (Knuth, Vol 2, 4.6.3). [SVN r79092] --- .../multiprecision/detail/functions/pow.hpp | 62 +++++++------------ 1 file changed, 23 insertions(+), 39 deletions(-) diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index bbb6b537..109937cd 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -17,47 +17,31 @@ namespace detail{ template inline void pow_imp(T& result, const T& t, const U& p, const mpl::false_&) { - // Compute the pure power of typename T t^p. Binary splitting of the power is - // used. The resulting computational complexity has the order of log2[abs(p)]. - typedef typename boost::multiprecision::detail::canonical::type int_type; - switch(p) + // Compute the pure power of typename T t^p. + // Use the S-and-X binary method, as described in + // D. E. Knuth, "The Art of Computer Programming", Vol. 2, + // Section 4.6.3 . The resulting computational complexity + // is order log2[abs(p)]. + + // This will store the result. + result = ((U(p % U(2)) != U(0)) ? t : T(1)); + + U p2(p); + + // The variable x stores the binary powers of t. + T x(t); + + while(U(p2 /= 2) != U(0)) { - case 0: - result = static_cast(1); - break; - case 1: - result = t; - break; - case 2: - eval_multiply(result, t, t); - break; - case 3: - eval_multiply(result, t, t); - eval_multiply(result, t); - break; - case 4: - eval_multiply(result, t, t); - eval_multiply(result, result); - break; - default: + // Square x for each binary power. + eval_multiply(x, x); + + const bool has_binary_power = (U(p2 % U(2)) != U(0)); + + if(has_binary_power) { - result = t; - U n; - - for(n = static_cast(1); n <= static_cast(p / static_cast(2)); n *= static_cast(2)) - { - eval_multiply(result, result); - } - - const U p_minus_n = static_cast(p - n); - - // Call the function recursively for computing the remaining power of n. - if(p_minus_n) - { - T temp; - pow_imp(temp, t, p_minus_n, mpl::false_()); - eval_multiply(result, temp); - } + // Multiply the result with each binary power contained in the exponent. + eval_multiply(result, x); } } } From f09ead8e3782d99415aaf029747246aa6c1fb10b Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 27 Jun 2012 18:25:10 +0000 Subject: [PATCH 192/256] Some file renaming and fixes from Steven Watanabe's comments. [SVN r79141] --- doc/multiprecision.qbk | 7 +- ...rchitypes.hpp => mp_number_archetypes.hpp} | 4 +- .../multiprecision/detail/default_ops.hpp | 1 + .../detail/functions/constants.hpp | 58 +++-- .../multiprecision/detail/functions/pow.hpp | 123 +++++------ .../detail/generic_interconvert.hpp | 4 +- .../multiprecision/detail/mp_number_base.hpp | 2 + test/Jamfile.v2 | 24 ++- test/math/log1p_expm1_test.cpp | 2 +- test/math/powm1_sqrtp1m1_test.cpp | 2 +- test/math/test_bessel_i.cpp | 2 +- test/math/test_bessel_j.cpp | 2 +- test/math/test_bessel_k.cpp | 2 +- test/math/test_bessel_y.cpp | 2 +- test/math/test_beta.cpp | 2 +- test/math/test_binomial_coeff.cpp | 2 +- test/math/test_carlson.cpp | 2 +- test/math/test_cbrt.cpp | 2 +- test/math/test_digamma.cpp | 2 +- test/math/test_ellint_1.cpp | 2 +- test/math/test_ellint_2.cpp | 2 +- test/math/test_ellint_3.cpp | 2 +- test/math/test_erf.cpp | 2 +- test/math/test_expint.cpp | 2 +- test/math/test_gamma.cpp | 2 +- test/math/test_hermite.cpp | 2 +- test/math/test_ibeta.cpp | 2 +- test/math/test_ibeta_2.cpp | 2 +- test/math/test_ibeta_3.cpp | 2 +- test/math/test_ibeta_4.cpp | 2 +- test/math/test_ibeta_inv_1.cpp | 2 +- test/math/test_ibeta_inv_ab_4.cpp | 2 +- test/math/test_igamma.cpp | 2 +- test/math/test_igamma_inv.cpp | 2 +- test/math/test_igamma_inva.cpp | 2 +- test/math/test_laguerre.cpp | 2 +- test/math/test_legendre.cpp | 2 +- test/math/test_tgamma_ratio.cpp | 2 +- test/math/test_zeta.cpp | 2 +- test/mp_number_concept_check.cpp | 2 +- test/test_acos.cpp | 2 +- test/test_arithmetic.cpp | 2 +- test/test_asin.cpp | 2 +- test/test_atan.cpp | 2 +- test/test_constants.cpp | 198 ++++++++++++++++++ test/test_cos.cpp | 2 +- test/test_cosh.cpp | 2 +- test/test_exp.cpp | 2 +- test/test_fpclassify.cpp | 2 +- test/test_log.cpp | 2 +- test/test_numeric_limits.cpp | 2 +- test/test_pow.cpp | 2 +- test/test_round.cpp | 2 +- test/test_sin.cpp | 2 +- test/test_sinh.cpp | 2 +- test/test_sqrt.cpp | 2 +- test/test_tanh.cpp | 2 +- 57 files changed, 388 insertions(+), 129 deletions(-) rename include/boost/multiprecision/concepts/{mp_number_architypes.hpp => mp_number_archetypes.hpp} (98%) create mode 100644 test/test_constants.cpp diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index c83d197f..97064c3d 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -1681,7 +1681,8 @@ In the following tables, type B is the `Backend` template arument to `mp_number` a variables of type B, `cb` and `cb2` are constant variables of type B, `a` is a variable of Arithmetic type, `s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`, `pa` is a variable of type pointer-to-arithmetic-type, `exp` is a variable of type `B::exp_type`, -`pexp` is a variable of type `B::exp_type*`, B2 is another type that meets these requirements, b2 is a variable +`pexp` is a variable of type `B::exp_type*`, `i` is a variable of type `int`, `pi` pointer to a variable of type `int`, +B2 is another type that meets these requirements, b2 is a variable of type B2. [table Compulsory Requirements on the Backend type. @@ -1725,6 +1726,8 @@ of type B2. Conversions to other types are entirely optional.]] [[`eval_frexp(b, cb, pexp)`][`void`][Stores values in `b` and `*pexp` such that the value of `cb` is b * 2[super *pexp], only required when `B` is a floating-point type.]] [[`eval_ldexp(b, cb, exp)`][`void`][Stores a value in `b` that is cb * 2[super exp], only required when `B` is a floating-point type.]] +[[`eval_frexp(b, cb, pi)`][`void`][Stores values in `b` and `*pi` such that the value of `cb` is b * 2[super *pi], only required when `B` is a floating-point type.]] +[[`eval_ldexp(b, cb, i)`][`void`][Stores a value in `b` that is cb * 2[super i], only required when `B` is a floating-point type.]] [[`eval_floor(b, cb)`][`void`][Stores the floor of `cb` in `b`, only required when `B` is a floating-point type.]] [[`eval_ceil(b, cb)`][`void`][Stores the ceiling of `cb` in `b`, only required when `B` is a floating-point type.]] [[`eval_sqrt(b, cb)`][`void`][Stores the square root of `cb` in `b`, only required when `B` is a floating-point type.]] @@ -1858,7 +1861,7 @@ in point of fact this naming convention shouldn't be necessary, but rather works [[rational_adapter.hpp][Defines the `rational_adapter` backend.]] [[cpp_dec_float.hpp][Defines the `cpp_dec_float` backend.]] [[tommath.hpp][Defines the `tommath_int` backend.]] -[[concepts/mp_number_architypes.hpp][Defines a backend concept architypes for testing use.]] +[[concepts/mp_number_archetypes.hpp][Defines a backend concept architypes for testing use.]] ] [table Implementation Headers] diff --git a/include/boost/multiprecision/concepts/mp_number_architypes.hpp b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp similarity index 98% rename from include/boost/multiprecision/concepts/mp_number_architypes.hpp rename to include/boost/multiprecision/concepts/mp_number_archetypes.hpp index bc281b4f..e82f69ac 100644 --- a/include/boost/multiprecision/concepts/mp_number_architypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp @@ -7,12 +7,14 @@ #define BOOST_MATH_CONCEPTS_ER_HPP #include +#include #include #include #include #include #include -#include +#include +#include namespace boost{ namespace multiprecision{ diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index e5511ffc..7462bcba 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -13,6 +13,7 @@ #include #include #include +#include #ifndef INSTRUMENT_BACKEND #ifndef BOOST_MP_INSTRUMENT diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp index 685b04e0..4946ccf5 100644 --- a/include/boost/multiprecision/detail/functions/constants.hpp +++ b/include/boost/multiprecision/detail/functions/constants.hpp @@ -9,12 +9,7 @@ template void calc_log2(T& num, unsigned digits) { - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - typename T::unsigned_types, - pred_type - >::type iter_type; - typedef typename mpl::deref::type ui_type; + typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename mpl::front::type si_type; // @@ -35,15 +30,27 @@ void calc_log2(T& num, unsigned digits) // // Check if we can just construct from string: // - if(digits < 3640) + if(digits < 3640) // 3640 binary digits ~ 1100 decimal digits { num = string_val; return; } - num = static_cast(1180509120u); + // + // We calculate log2 from using the formula: + // + // ln(2) = 3/4 SUM[n>=0] ((-1)^n * N!^2 / (2^n(2n+1)!)) + // + // Numerator and denominator are calculated separately and then + // divided at the end, we also precalculate the terms up to n = 5 + // since these fit in a 32-bit integer anyway. + // + // See Gourdon, X., and Sebah, P. The logarithmic constant: log 2, Jan. 2004. + // Also http://www.mpfr.org/algorithms.pdf. + // + num = static_cast(1180509120uL); T denom, next_term, temp; - denom = static_cast(1277337600u); - next_term = static_cast(120u); + denom = static_cast(1277337600uL); + next_term = static_cast(120uL); si_type sign = -1; ui_type limit = digits / 3 + 1; @@ -58,7 +65,8 @@ void calc_log2(T& num, unsigned digits) sign = -sign; eval_multiply(next_term, n); eval_multiply(temp, next_term, next_term); - eval_multiply(temp, sign); + if(sign < 0) + temp.negate(); eval_add(num, temp); } eval_multiply(denom, ui_type(4)); @@ -92,7 +100,7 @@ void calc_e(T& result, unsigned digits) // // Check if we can just construct from string: // - if(digits < 3640) + if(digits < 3640) // 3640 binary digits ~ 1100 decimal digits { result = string_val; return; @@ -102,6 +110,9 @@ void calc_e(T& result, unsigned digits) lim = ui_type(1); eval_ldexp(lim, lim, digits); + // + // Standard evaluation from the definition of e: http://functions.wolfram.com/Constants/E/02/ + // result = ui_type(2); T denom; denom = ui_type(1); @@ -138,7 +149,7 @@ void calc_pi(T& result, unsigned digits) // // Check if we can just construct from string: // - if(digits < 3640) + if(digits < 3640) // 3640 binary digits ~ 1100 decimal digits { result = string_val; return; @@ -157,6 +168,25 @@ void calc_pi(T& result, unsigned digits) lim = ui_type(1); eval_ldexp(lim, lim, -(int)digits); + // + // This algorithm is from: + // Schonhage, A., Grotefeld, A. F. W., and Vetter, E. Fast Algorithms: A Multitape Turing + // Machine Implementation. BI Wissenschaftverlag, 1994. + // Also described in MPFR's algorithm guide: http://www.mpfr.org/algorithms.pdf. + // + // Let: + // a[0] = A[0] = 1 + // B[0] = 1/2 + // D[0] = 1/4 + // Then: + // S[k+1] = (A[k]+B[k]) / 4 + // b[k] = sqrt(B[k]) + // a[k+1] = a[k]^2 + // B[k+1] = 2(A[k+1]-S[k+1]) + // D[k+1] = D[k] - 2^k(A[k+1]-B[k+1]) + // Stop when |A[k]-B[k]| <= 2^(k-p) + // and PI = B[k]/D[k] + unsigned k = 1; do @@ -248,7 +278,7 @@ const T& get_constant_pi() static bool b = false; if(!b) { - calc_pi(result, boost::multiprecision::detail::digits2 >::value + 10); + calc_pi(result, boost::multiprecision::detail::digits2 >::value); b = true; } diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index 109937cd..b7cc9e26 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -23,8 +23,15 @@ inline void pow_imp(T& result, const T& t, const U& p, const mpl::false_&) // Section 4.6.3 . The resulting computational complexity // is order log2[abs(p)]. + typedef typename boost::multiprecision::detail::canonical::type int_type; + // This will store the result. - result = ((U(p % U(2)) != U(0)) ? t : T(1)); + if(U(p % U(2)) != U(0)) + { + result = t; + } + else + result = int_type(1); U p2(p); @@ -51,17 +58,18 @@ inline void pow_imp(T& result, const T& t, const U& p, const mpl::true_&) { // Signed integer power, just take care of the sign then call the unsigned version: typedef typename boost::multiprecision::detail::canonical::type int_type; + typedef typename make_unsigned::type ui_type; if(p < 0) { T temp; temp = static_cast(1); T denom; - pow_imp(denom, t, -p, mpl::false_()); + pow_imp(denom, t, static_cast(-p), mpl::false_()); eval_divide(result, temp, denom); return; } - pow_imp(result, t, p, mpl::false_()); + pow_imp(result, t, static_cast(p), mpl::false_()); } } // namespace detail @@ -166,7 +174,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x) template void eval_exp(T& result, const T& x) { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_floating_point, "The ldexp function is only valid for floating point types."); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_floating_point, "The exp function is only valid for floating point types."); if(&x == &result) { T temp; @@ -251,7 +259,7 @@ void eval_exp(T& result, const T& x) } // Check for pure-integer arguments which can be either signed or unsigned. - long long ll; + boost::intmax_t ll; eval_trunc(exp_series, x); eval_convert_to(&ll, exp_series); if(x.compare(ll) == 0) @@ -268,34 +276,25 @@ void eval_exp(T& result, const T& x) // implemented as a hypergeometric function, |r| is bounded by // ln2 / p2. For small arguments, no scaling is done. - const bool b_scale = (xx.compare(float_type(1e-4)) > 0); - // Compute the exponential series of the (possibly) scaled argument. - if(b_scale) - { - eval_divide(result, xx, get_constant_ln2()); - exp_type n; - eval_convert_to(&n, result); + eval_divide(result, xx, get_constant_ln2()); + exp_type n; + eval_convert_to(&n, result); - // The scaling is 2^11 = 2048. - static const si_type p2 = static_cast(si_type(1) << 11); + // The scaling is 2^11 = 2048. + static const si_type p2 = static_cast(si_type(1) << 11); - eval_multiply(exp_series, get_constant_ln2(), static_cast(n)); - eval_subtract(exp_series, xx); - eval_divide(exp_series, p2); - exp_series.negate(); - hyp0F0(result, exp_series); + eval_multiply(exp_series, get_constant_ln2(), static_cast(n)); + eval_subtract(exp_series, xx); + eval_divide(exp_series, p2); + exp_series.negate(); + hyp0F0(result, exp_series); - detail::pow_imp(exp_series, result, p2, mpl::true_()); - result = ui_type(1); - eval_ldexp(result, result, n); - eval_multiply(exp_series, result); - } - else - { - hyp0F0(exp_series, xx); - } + detail::pow_imp(exp_series, result, p2, mpl::true_()); + result = ui_type(1); + eval_ldexp(result, result, n); + eval_multiply(exp_series, result); if(isneg) eval_divide(result, ui_type(1), exp_series); @@ -313,14 +312,6 @@ void eval_log(T& result, const T& arg) // then let y = x - 1 and compute: // log(x) = log(2) * n + log1p(1 + y) // - if(&arg == &result) - { - T temp; - eval_log(temp, arg); - result = temp; - return; - } - typedef typename boost::multiprecision::detail::canonical::type si_type; typedef typename boost::multiprecision::detail::canonical::type ui_type; typedef typename T::exponent_type exp_type; @@ -394,7 +385,7 @@ const T& get_constant_log10() template void eval_log10(T& result, const T& arg) { - BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_floating_point, "The fabs function is only valid for floating point types."); + BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_floating_point, "The log10 function is only valid for floating point types."); eval_log(result, arg); eval_divide(result, get_constant_log10()); } @@ -444,21 +435,9 @@ inline void eval_pow(T& result, const T& x, const T& a) return; } - long long an; - eval_convert_to(&an, a); - const bool bo_a_isint = a.compare(an) == 0; - - if((eval_get_sign(x) < 0) && !bo_a_isint) - { - result = std::numeric_limits >::quiet_NaN().backend(); - } - - T t; - T da(a); - eval_subtract(da, an); - if(a.compare(si_type(-1)) < 0) { + T t, da; t = a; t.negate(); eval_pow(da, x, t); @@ -466,15 +445,34 @@ inline void eval_pow(T& result, const T& x, const T& a) return; } - eval_subtract(da, a, an); - - if(bo_a_isint) + bool bo_a_isint = false; + boost::intmax_t an; + T fa; + try { - detail::pow_imp(result, x, an, mpl::true_()); - return; + eval_convert_to(&an, a); + if(a.compare(an) == 0) + { + detail::pow_imp(result, x, an, mpl::true_()); + return; + } + } + catch(const std::exception&) + { + // conversion failed, just fall through, value is not an integer. + an = (std::numeric_limits::max)(); } - if((eval_get_sign(x) > 0) && (x.compare(fp_type(0.5)) >= 0) && (x.compare(fp_type(0.9)) < 0)) + if((eval_get_sign(x) < 0) && !bo_a_isint) + { + result = std::numeric_limits >::quiet_NaN().backend(); + } + + T t, da; + + eval_subtract(da, a, an); + + if((x.compare(fp_type(0.5)) >= 0) && (x.compare(fp_type(0.9)) < 0)) { if(a.compare(fp_type(1e-5f)) <= 0) { @@ -595,7 +593,11 @@ namespace detail{ if(p_sinh) *p_sinh = x; if(p_cosh) + { *p_cosh = x; + if(eval_get_sign(x) < 0) + p_cosh->negate(); + } return; case FP_ZERO: if(p_sinh) @@ -606,12 +608,11 @@ namespace detail{ default: ; } - T e_px, e_mx; - - bool small_sinh = eval_get_sign(x) < 0 ? e_px.compare(fp_type(-0.5)) > 0 : e_px.compare(fp_type(0.5)) < 0; + bool small_sinh = eval_get_sign(x) < 0 ? x.compare(fp_type(-0.5)) > 0 : x.compare(fp_type(0.5)) < 0; if(p_cosh || !small_sinh) { + T e_px, e_mx; eval_exp(e_px, x); eval_divide(e_mx, ui_type(1), e_px); @@ -624,13 +625,13 @@ namespace detail{ else { eval_subtract(*p_sinh, e_px, e_mx); - eval_divide(*p_sinh, ui_type(2)); + eval_ldexp(*p_sinh, *p_sinh, -1); } } if(p_cosh) { eval_add(*p_cosh, e_px, e_mx); - eval_divide(*p_cosh, ui_type(2)); + eval_ldexp(*p_cosh, *p_cosh, -1); } } else diff --git a/include/boost/multiprecision/detail/generic_interconvert.hpp b/include/boost/multiprecision/detail/generic_interconvert.hpp index caf83869..fe837873 100644 --- a/include/boost/multiprecision/detail/generic_interconvert.hpp +++ b/include/boost/multiprecision/detail/generic_interconvert.hpp @@ -159,7 +159,7 @@ void generic_interconvert(To& to, const From& from, const mpl::int_::digits - 1; + static const int shift = std::numeric_limits::digits - 1; while(!eval_is_zero(f)) { @@ -168,7 +168,7 @@ void generic_interconvert(To& to, const From& from, const mpl::int_::is_specialized); BOOST_STATIC_ASSERT((std::numeric_limits::radix == 2) || (std::numeric_limits::radix == 10)); + // If we really have so many digits that this fails, then we're probably going to hit other problems anyway: + BOOST_STATIC_ASSERT(LONG_MAX / 1000 > (std::numeric_limits::digits + 1)); static const long value = std::numeric_limits::radix == 10 ? (((std::numeric_limits::digits + 1) * 1000L) / 301L) : std::numeric_limits::digits; }; diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 31c52fc0..30a59b3b 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -522,7 +522,6 @@ run test_round.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - [ check-target-builds ../config//has_mpfr : : no ] : test_round_cpp_dec_float ; run test_fpclassify.cpp @@ -555,6 +554,29 @@ run test_fpclassify.cpp TEST_CPP_DEC_FLOAT : test_fpclassify_cpp_dec_float ; +run test_constants.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : no ] + : test_constants_mpf50 ; + +run test_constants.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_constants_mpfr_50 ; + +run test_constants.cpp + : # command line + : # input files + : # requirements + TEST_CPP_DEC_FLOAT + : test_constants_cpp_dec_float ; + run test_test.cpp ; diff --git a/test/math/log1p_expm1_test.cpp b/test/math/log1p_expm1_test.cpp index 87a69406..9b9867aa 100644 --- a/test/math/log1p_expm1_test.cpp +++ b/test/math/log1p_expm1_test.cpp @@ -35,7 +35,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/powm1_sqrtp1m1_test.cpp b/test/math/powm1_sqrtp1m1_test.cpp index c84ee860..56bdd600 100644 --- a/test/math/powm1_sqrtp1m1_test.cpp +++ b/test/math/powm1_sqrtp1m1_test.cpp @@ -35,7 +35,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_bessel_i.cpp b/test/math/test_bessel_i.cpp index 0b59d0b9..e4db9ff8 100644 --- a/test/math/test_bessel_i.cpp +++ b/test/math/test_bessel_i.cpp @@ -35,7 +35,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_bessel_j.cpp b/test/math/test_bessel_j.cpp index f5b70f1c..951a6821 100644 --- a/test/math/test_bessel_j.cpp +++ b/test/math/test_bessel_j.cpp @@ -35,7 +35,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_bessel_k.cpp b/test/math/test_bessel_k.cpp index 6d3a4816..044fc49a 100644 --- a/test/math/test_bessel_k.cpp +++ b/test/math/test_bessel_k.cpp @@ -36,7 +36,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp index 68a94851..43cd9501 100644 --- a/test/math/test_bessel_y.cpp +++ b/test/math/test_bessel_y.cpp @@ -35,7 +35,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_beta.cpp b/test/math/test_beta.cpp index 73e33f04..cf363b4e 100644 --- a/test/math/test_beta.cpp +++ b/test/math/test_beta.cpp @@ -35,7 +35,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_binomial_coeff.cpp b/test/math/test_binomial_coeff.cpp index 291361e3..3b6882d9 100644 --- a/test/math/test_binomial_coeff.cpp +++ b/test/math/test_binomial_coeff.cpp @@ -35,7 +35,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_carlson.cpp b/test/math/test_carlson.cpp index 46efabee..e0a9e3c8 100644 --- a/test/math/test_carlson.cpp +++ b/test/math/test_carlson.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_cbrt.cpp b/test/math/test_cbrt.cpp index ca647216..e7bee00c 100644 --- a/test/math/test_cbrt.cpp +++ b/test/math/test_cbrt.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_digamma.cpp b/test/math/test_digamma.cpp index 7767b46c..8da4bd53 100644 --- a/test/math/test_digamma.cpp +++ b/test/math/test_digamma.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_ellint_1.cpp b/test/math/test_ellint_1.cpp index 7ba717cf..356653d0 100644 --- a/test/math/test_ellint_1.cpp +++ b/test/math/test_ellint_1.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_ellint_2.cpp b/test/math/test_ellint_2.cpp index 534cbd84..a8cbfca5 100644 --- a/test/math/test_ellint_2.cpp +++ b/test/math/test_ellint_2.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_ellint_3.cpp b/test/math/test_ellint_3.cpp index 95fe73e1..c57ddfec 100644 --- a/test/math/test_ellint_3.cpp +++ b/test/math/test_ellint_3.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_erf.cpp b/test/math/test_erf.cpp index d2fda9fb..b185c3cd 100644 --- a/test/math/test_erf.cpp +++ b/test/math/test_erf.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_expint.cpp b/test/math/test_expint.cpp index fbacc55b..71961792 100644 --- a/test/math/test_expint.cpp +++ b/test/math/test_expint.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_gamma.cpp b/test/math/test_gamma.cpp index 42c2cb02..c29d6aa6 100644 --- a/test/math/test_gamma.cpp +++ b/test/math/test_gamma.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_hermite.cpp b/test/math/test_hermite.cpp index 02d88f1c..be956ce1 100644 --- a/test/math/test_hermite.cpp +++ b/test/math/test_hermite.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_ibeta.cpp b/test/math/test_ibeta.cpp index 167b8f31..15ca1bc6 100644 --- a/test/math/test_ibeta.cpp +++ b/test/math/test_ibeta.cpp @@ -31,7 +31,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_ibeta_2.cpp b/test/math/test_ibeta_2.cpp index d8e3f09a..c7cb04fc 100644 --- a/test/math/test_ibeta_2.cpp +++ b/test/math/test_ibeta_2.cpp @@ -31,7 +31,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_ibeta_3.cpp b/test/math/test_ibeta_3.cpp index 101cca1b..77b69d78 100644 --- a/test/math/test_ibeta_3.cpp +++ b/test/math/test_ibeta_3.cpp @@ -31,7 +31,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_ibeta_4.cpp b/test/math/test_ibeta_4.cpp index 9f78fef9..5f3246fd 100644 --- a/test/math/test_ibeta_4.cpp +++ b/test/math/test_ibeta_4.cpp @@ -31,7 +31,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_ibeta_inv_1.cpp b/test/math/test_ibeta_inv_1.cpp index fd2b3e5f..21a3ea35 100644 --- a/test/math/test_ibeta_inv_1.cpp +++ b/test/math/test_ibeta_inv_1.cpp @@ -31,7 +31,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_ibeta_inv_ab_4.cpp b/test/math/test_ibeta_inv_ab_4.cpp index eb91e02d..f0149957 100644 --- a/test/math/test_ibeta_inv_ab_4.cpp +++ b/test/math/test_ibeta_inv_ab_4.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_igamma.cpp b/test/math/test_igamma.cpp index 517b0e81..66aa9011 100644 --- a/test/math/test_igamma.cpp +++ b/test/math/test_igamma.cpp @@ -31,7 +31,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_igamma_inv.cpp b/test/math/test_igamma_inv.cpp index 010c3762..e7f8775a 100644 --- a/test/math/test_igamma_inv.cpp +++ b/test/math/test_igamma_inv.cpp @@ -31,7 +31,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_igamma_inva.cpp b/test/math/test_igamma_inva.cpp index f380c3b3..026694c8 100644 --- a/test/math/test_igamma_inva.cpp +++ b/test/math/test_igamma_inva.cpp @@ -31,7 +31,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_laguerre.cpp b/test/math/test_laguerre.cpp index aabb836d..f3cded2a 100644 --- a/test/math/test_laguerre.cpp +++ b/test/math/test_laguerre.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_legendre.cpp b/test/math/test_legendre.cpp index 25a1f7a8..e392365f 100644 --- a/test/math/test_legendre.cpp +++ b/test/math/test_legendre.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_tgamma_ratio.cpp b/test/math/test_tgamma_ratio.cpp index 1084d843..982546bd 100644 --- a/test/math/test_tgamma_ratio.cpp +++ b/test/math/test_tgamma_ratio.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/math/test_zeta.cpp b/test/math/test_zeta.cpp index bc3d773a..4484a7d3 100644 --- a/test/math/test_zeta.cpp +++ b/test/math/test_zeta.cpp @@ -30,7 +30,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/mp_number_concept_check.cpp b/test/mp_number_concept_check.cpp index 3e051ff5..45831f29 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/mp_number_concept_check.cpp @@ -47,7 +47,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) #include diff --git a/test/test_acos.cpp b/test/test_acos.cpp index a827fc48..6e81985f 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 00b70f4f..afd0784c 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -45,7 +45,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 7adb1afa..61ab5d12 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_atan.cpp b/test/test_atan.cpp index 2061afa9..de426780 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_constants.cpp b/test/test_constants.cpp new file mode 100644 index 00000000..5e9ad8e7 --- /dev/null +++ b/test/test_constants.cpp @@ -0,0 +1,198 @@ +// Copyright John Maddock 2012. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#if !defined(TEST_MPF_50) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50) +# define TEST_MPF_50 +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFR_50 + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include +#endif +#if defined(TEST_MPFR_50) +#include +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include +#endif + +#include "test.hpp" + +static const char* ln2 = +"0.693147180559945309417232121458176568075500134360255254120680009493393621969694" +"71560586332699641868754200148102057068573368552023575813055703267075163507596193" +"07275708283714351903070386238916734711233501153644979552391204751726815749320651" +"55524734139525882950453007095326366642654104239157814952043740430385500801944170" +"64167151864471283996817178454695702627163106454615025720740248163777338963855069" +"52606683411372738737229289564935470257626520988596932019650585547647033067936544" +"32547632744951250406069438147104689946506220167720424524529612687946546193165174" +"68139267250410380254625965686914419287160829380317271436778265487756648508567407" +"76484514644399404614226031930967354025744460703080960850474866385231381816767514" +"38667476647890881437141985494231519973548803751658612753529166100071053558249879" +"41472950929311389715599820565439287170007218085761025236889213244971389320378439" +"35308877482597017155910708823683627589842589185353024363421436706118923678919237" +"23146723217205340164925687274778234453534764811494186423867767744060695626573796" +"00867076257199184734022651462837904883062033061144630073719489002743643965002580" +"93651944304119115060809487930678651588709006052034684297361938412896525565396860" +"22194122924207574321757489097706752687115817051137009158942665478595964890653058" +"46025866838294002283300538207400567705304678700184162404418833232798386349001563" +"12188956065055315127219939833203075140842609147900126516824344389357247278820548" +"62715527418772430024897945401961872339808608316648114909306675193393128904316413" +"70681397776498176974868903887789991296503619270710889264105230924783917373501229" +"84242049956893599220660220465494151061391878857442455775102068370308666194808964" +"12186807790208181588580001688115973056186676199187395200766719214592236720602539" +"59543654165531129517598994005600036651356756905124592682574394648316833262490180" +"38242408242314523061409638057007025513877026817851630690255137032340538021450190" +"15374029509942262995779647427138157363801729873940704242179972266962979939312706" +"93574724049338653087975872169964512944649188377115670167859880498183889678413493" +"83140140731664727653276359192335112333893387095132090592721854713289754707978913" +"84445466676192702885533423429899321803769154973340267546758873236778342916191810" +"43011609169526554785973289176354555674286387746398710191243175425588830120677921" +"02803412068797591430812833072303008834947057924965910058600123415617574132724659" +"43068435465211135021544341539955381856522750221424566440006276183303206472725721" +"97515290827856842132079598863896727711955221881904660395700977470651261950527893" +"22960889314056254334425523920620303439417773579455921259019925591148440242390125" +"54259003129537051922061506434583787873002035414421785758013236451660709914383145" +"00498589668857722214865288216941812704886075897220321666312837832915676307498729" +"85746389282693735098407780493950049339987626475507031622161390348452994249172483" +"73406136622638349368111684167056925214751383930638455371862687797328895558871634" +"429756244755392366369488877823890174981027"; +static const char* pi = +"3.141592653589793238462643383279502884197169399375105820974944592307816406286208" +"99862803482534211706798214808651328230664709384460955058223172535940812848111745" +"02841027019385211055596446229489549303819644288109756659334461284756482337867831" +"65271201909145648566923460348610454326648213393607260249141273724587006606315588" +"17488152092096282925409171536436789259036001133053054882046652138414695194151160" +"94330572703657595919530921861173819326117931051185480744623799627495673518857527" +"24891227938183011949129833673362440656643086021394946395224737190702179860943702" +"77053921717629317675238467481846766940513200056812714526356082778577134275778960" +"91736371787214684409012249534301465495853710507922796892589235420199561121290219" +"60864034418159813629774771309960518707211349999998372978049951059731732816096318" +"59502445945534690830264252230825334468503526193118817101000313783875288658753320" +"83814206171776691473035982534904287554687311595628638823537875937519577818577805" +"32171226806613001927876611195909216420198938095257201065485863278865936153381827" +"96823030195203530185296899577362259941389124972177528347913151557485724245415069" +"59508295331168617278558890750983817546374649393192550604009277016711390098488240" +"12858361603563707660104710181942955596198946767837449448255379774726847104047534" +"64620804668425906949129331367702898915210475216205696602405803815019351125338243" +"00355876402474964732639141992726042699227967823547816360093417216412199245863150" +"30286182974555706749838505494588586926995690927210797509302955321165344987202755" +"96023648066549911988183479775356636980742654252786255181841757467289097777279380" +"00816470600161452491921732172147723501414419735685481613611573525521334757418494" +"68438523323907394143334547762416862518983569485562099219222184272550254256887671" +"79049460165346680498862723279178608578438382796797668145410095388378636095068006" +"42251252051173929848960841284886269456042419652850222106611863067442786220391949" +"45047123713786960956364371917287467764657573962413890865832645995813390478027590" +"09946576407895126946839835259570982582262052248940772671947826848260147699090264" +"01363944374553050682034962524517493996514314298091906592509372216964615157098583" +"87410597885959772975498930161753928468138268683868942774155991855925245953959431" +"04997252468084598727364469584865383673622262609912460805124388439045124413654976" +"27807977156914359977001296160894416948685558484063534220722258284886481584560285" +"06016842739452267467678895252138522549954666727823986456596116354886230577456498" +"03559363456817432411251507606947945109659609402522887971089314566913686722874894" +"05601015033086179286809208747609178249385890097149096759852613655497818931297848" +"21682998948722658804857564014270477555132379641451523746234364542858444795265867" +"82105114135473573952311342716610213596953623144295248493718711014576540359027993" +"44037420073105785390621983874478084784896833214457138687519435064302184531910484" +"81005370614680674919278191197939952061419663428754440643745123718192179998391015" +"91956181467514269123974894090718649423196"; +static const char* e = +"2.718281828459045235360287471352662497757247093699959574966967627724076630353547" +"59457138217852516642742746639193200305992181741359662904357290033429526059563073" +"81323286279434907632338298807531952510190115738341879307021540891499348841675092" +"44761460668082264800168477411853742345442437107539077744992069551702761838606261" +"33138458300075204493382656029760673711320070932870912744374704723069697720931014" +"16928368190255151086574637721112523897844250569536967707854499699679468644549059" +"87931636889230098793127736178215424999229576351482208269895193668033182528869398" +"49646510582093923982948879332036250944311730123819706841614039701983767932068328" +"23764648042953118023287825098194558153017567173613320698112509961818815930416903" +"51598888519345807273866738589422879228499892086805825749279610484198444363463244" +"96848756023362482704197862320900216099023530436994184914631409343173814364054625" +"31520961836908887070167683964243781405927145635490613031072085103837505101157477" +"04171898610687396965521267154688957035035402123407849819334321068170121005627880" +"23519303322474501585390473041995777709350366041699732972508868769664035557071622" +"68447162560798826517871341951246652010305921236677194325278675398558944896970964" +"09754591856956380236370162112047742722836489613422516445078182442352948636372141" +"74023889344124796357437026375529444833799801612549227850925778256209262264832627" +"79333865664816277251640191059004916449982893150566047258027786318641551956532442" +"58698294695930801915298721172556347546396447910145904090586298496791287406870504" +"89585867174798546677575732056812884592054133405392200011378630094556068816674001" +"69842055804033637953764520304024322566135278369511778838638744396625322498506549" +"95886234281899707733276171783928034946501434558897071942586398772754710962953741" +"52111513683506275260232648472870392076431005958411661205452970302364725492966693" +"81151373227536450988890313602057248176585118063036442812314965507047510254465011" +"72721155519486685080036853228183152196003735625279449515828418829478761085263981" +"39559900673764829224437528718462457803619298197139914756448826260390338144182326" +"25150974827987779964373089970388867782271383605772978824125611907176639465070633" +"04527954661855096666185664709711344474016070462621568071748187784437143698821855" +"96709591025968620023537185887485696522000503117343920732113908032936344797273559" +"55277349071783793421637012050054513263835440001863239914907054797780566978533580" +"48966906295119432473099587655236812859041383241160722602998330535370876138939639" +"17795745401613722361878936526053815584158718692553860616477983402543512843961294" +"60352913325942794904337299085731580290958631382683291477116396337092400316894586" +"36060645845925126994655724839186564209752685082307544254599376917041977780085362" +"73094171016343490769642372229435236612557250881477922315197477806056967253801718" +"07763603462459278778465850656050780844211529697521890874019660906651803516501792" +"50461950136658543663271254963990854914420001457476081930221206602433009641270489" +"43903971771951806990869986066365832322787"; + +template +inline bool is_mpfr(const T&) +{ + return false; +} +#if defined(TEST_MPFR_50) +template +inline bool is_mpfr(const boost::multiprecision::mp_number >&) +{ + return true; +} +#endif + +template +void test() +{ + typedef typename T::backend_type backend_type; + T num, expect; + num.backend() = boost::multiprecision::default_ops::get_constant_pi(); + expect = pi; + BOOST_CHECK_CLOSE_FRACTION(num, expect, std::numeric_limits::epsilon() * (is_mpfr(num) ? 1200 : 2)); + num.backend() = boost::multiprecision::default_ops::get_constant_ln2(); + expect = ln2; + BOOST_CHECK_CLOSE_FRACTION(num, expect, std::numeric_limits::epsilon() * (is_mpfr(num) ? 30 : 1)); + num.backend() = boost::multiprecision::default_ops::get_constant_e(); + expect = e; + BOOST_CHECK_CLOSE_FRACTION(num, expect, std::numeric_limits::epsilon() * (is_mpfr(num) ? 2 : 1)); +} + +int main() +{ +#ifdef TEST_MPFR_50 + test > >(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test > >(); +#endif +#ifdef TEST_MPF_50 + test > >(); +#endif + return boost::report_errors(); +} + diff --git a/test/test_cos.cpp b/test/test_cos.cpp index 71c0c9b3..b31528bf 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index ad609a88..ada92a21 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_exp.cpp b/test/test_exp.cpp index 6644b750..da5cceff 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_fpclassify.cpp b/test/test_fpclassify.cpp index 732a2069..063ba8a9 100644 --- a/test/test_fpclassify.cpp +++ b/test/test_fpclassify.cpp @@ -36,7 +36,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_log.cpp b/test/test_log.cpp index 084c50c2..35714bc0 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index da557a47..20ad2dad 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -36,7 +36,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_pow.cpp b/test/test_pow.cpp index 315ad995..4c55ab07 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -39,7 +39,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_round.cpp b/test/test_round.cpp index f6058668..1fb4822d 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -37,7 +37,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_sin.cpp b/test/test_sin.cpp index 06f035d1..f8ad7830 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index 7f6c6320..b4fc7194 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp index 3f01cbbd..da17ea4c 100644 --- a/test/test_sqrt.cpp +++ b/test/test_sqrt.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index 93052dd7..d4f57038 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -38,7 +38,7 @@ #include #endif #ifdef TEST_BACKEND -#include +#include #endif #ifdef TEST_CPP_DEC_FLOAT #include From 1a4e3af5c8a50c026fe13285275c5656777aaf1d Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 29 Jun 2012 11:53:25 +0000 Subject: [PATCH 193/256] Fix Linux x64 errors [SVN r79165] --- include/boost/multiprecision/detail/functions/pow.hpp | 4 ++-- .../boost/multiprecision/detail/generic_interconvert.hpp | 2 +- test/Jamfile.v2 | 2 +- test/math/test_bessel_i.cpp | 2 +- test/math/test_bessel_y.cpp | 2 +- test/math/test_beta.cpp | 6 +++--- test/math/test_binomial_coeff.cpp | 2 +- test/math/test_gamma.cpp | 2 +- test/math/test_ibeta.cpp | 2 +- test/math/test_ibeta_inv_1.cpp | 2 +- test/math/test_ibeta_inv_ab_4.cpp | 2 +- test/math/test_igamma_inv.cpp | 2 +- 12 files changed, 15 insertions(+), 15 deletions(-) diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index b7cc9e26..dbae9aac 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -259,7 +259,7 @@ void eval_exp(T& result, const T& x) } // Check for pure-integer arguments which can be either signed or unsigned. - boost::intmax_t ll; + typename boost::multiprecision::detail::canonical::type ll; eval_trunc(exp_series, x); eval_convert_to(&ll, exp_series); if(x.compare(ll) == 0) @@ -446,7 +446,7 @@ inline void eval_pow(T& result, const T& x, const T& a) } bool bo_a_isint = false; - boost::intmax_t an; + typename boost::multiprecision::detail::canonical::type an; T fa; try { diff --git a/include/boost/multiprecision/detail/generic_interconvert.hpp b/include/boost/multiprecision/detail/generic_interconvert.hpp index fe837873..adb1eea8 100644 --- a/include/boost/multiprecision/detail/generic_interconvert.hpp +++ b/include/boost/multiprecision/detail/generic_interconvert.hpp @@ -168,7 +168,7 @@ void generic_interconvert(To& to, const From& from, const mpl::int_::type ll; eval_convert_to(&ll, term); eval_add(to, ll); eval_subtract(f, term); diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 30a59b3b..75686515 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -585,7 +585,7 @@ run test_float_io.cpp : # input files : # requirements TEST_CPP_DEC_FLOAT - release # Otherwise runtime is slow + #release # Otherwise runtime is slow : test_float_io_cpp_dec_float ; run test_float_io.cpp gmp diff --git a/test/math/test_bessel_i.cpp b/test/math/test_bessel_i.cpp index e4db9ff8..4e94c24a 100644 --- a/test/math/test_bessel_i.cpp +++ b/test/math/test_bessel_i.cpp @@ -63,7 +63,7 @@ void expected_results() ".*", // test type(s) ".*", // test data group ".*", // test function - 300, // Max Peek error + 500, // Max Peek error 200); // Max mean error // diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp index 43cd9501..44d23126 100644 --- a/test/math/test_bessel_y.cpp +++ b/test/math/test_bessel_y.cpp @@ -100,7 +100,7 @@ void expected_results() ".*", // platform ".*mpfr_float_backend<18>.*", // test type(s) ".*", // test data group - ".*", 10000, 4000); // test function + ".*", 15000, 4000); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_beta.cpp b/test/math/test_beta.cpp index cf363b4e..49541cd8 100644 --- a/test/math/test_beta.cpp +++ b/test/math/test_beta.cpp @@ -72,7 +72,7 @@ void expected_results() ".*", // platform ".*mpfr_float_backend<18>.*", // test type(s) "Beta Function: Small.*", // test data group - "boost::math::beta", 200, 200); // test function + "boost::math::beta", 1000, 750); // test function add_expected_result( ".*", // compiler ".*", // stdlib @@ -86,14 +86,14 @@ void expected_results() ".*", // platform ".*", // test type(s) "Beta Function: Medium.*", // test data group - "boost::math::beta", 260, 200); // test function + "boost::math::beta", 1000, 750); // test function add_expected_result( ".*", // compiler ".*", // stdlib ".*", // platform ".*", // test type(s) "Beta Function: Divergent.*", // test data group - "boost::math::beta", 200, 200); // test function + "boost::math::beta", 1000, 700); // test function // // Finish off by printing out the compiler/stdlib/platform names, // we do this to make it easier to mark up expected error rates. diff --git a/test/math/test_binomial_coeff.cpp b/test/math/test_binomial_coeff.cpp index 3b6882d9..0d9bf414 100644 --- a/test/math/test_binomial_coeff.cpp +++ b/test/math/test_binomial_coeff.cpp @@ -65,7 +65,7 @@ void expected_results() ".*", // platform ".*mpfr_float_backend<18>.*", // test type(s) ".*", // test data group - ".*", 500, 150); // test function + ".*", 750, 150); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_gamma.cpp b/test/math/test_gamma.cpp index c29d6aa6..c7511413 100644 --- a/test/math/test_gamma.cpp +++ b/test/math/test_gamma.cpp @@ -61,7 +61,7 @@ void expected_results() ".*", // platform ".*", // test type(s) "factorials", // test data group - "boost::math::tgamma", 70, 25); // test function + "boost::math::tgamma", 140, 70); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_ibeta.cpp b/test/math/test_ibeta.cpp index 15ca1bc6..dde145f8 100644 --- a/test/math/test_ibeta.cpp +++ b/test/math/test_ibeta.cpp @@ -64,7 +64,7 @@ void expected_results() "[^|]*", // platform ".*mpfr_float_backend<18>.*", // test type(s) "(?i).*small.*", // test data group - ".*", 400, 200); // test function + ".*", 2000, 500); // test function add_expected_result( "[^|]*", // compiler "[^|]*", // stdlib diff --git a/test/math/test_ibeta_inv_1.cpp b/test/math/test_ibeta_inv_1.cpp index 21a3ea35..2492b7ac 100644 --- a/test/math/test_ibeta_inv_1.cpp +++ b/test/math/test_ibeta_inv_1.cpp @@ -57,7 +57,7 @@ void expected_results() ".*", // platform ".*mpfr_float_backend<18>.*", // test type(s) ".*", // test data group - ".*", 20000000, 2000000); // test function + ".*", 50000000, 7000000); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_ibeta_inv_ab_4.cpp b/test/math/test_ibeta_inv_ab_4.cpp index f0149957..67c4c588 100644 --- a/test/math/test_ibeta_inv_ab_4.cpp +++ b/test/math/test_ibeta_inv_ab_4.cpp @@ -57,7 +57,7 @@ void expected_results() ".*", // platform ".*", // test type(s) ".*", // test data group - ".*", 2000, 200); // test function + ".*", 10000, 1000); // test function // // Finish off by printing out the compiler/stdlib/platform names, // we do this to make it easier to mark up expected error rates. diff --git a/test/math/test_igamma_inv.cpp b/test/math/test_igamma_inv.cpp index e7f8775a..3a0d76cc 100644 --- a/test/math/test_igamma_inv.cpp +++ b/test/math/test_igamma_inv.cpp @@ -62,7 +62,7 @@ void expected_results() ".*", // platform ".*mpfr_float_backend<18>.*", // test type(s) ".*small.*", // test data group - ".*", 30000000L, 5000000L); // test function + ".*", 30000000L, 20000000L); // test function add_expected_result( ".*", // compiler ".*", // stdlib From 2ea2ab8a2b099528a9455b60cfff2a1e4f8db541 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 30 Jun 2012 16:48:17 +0000 Subject: [PATCH 194/256] Add better rvalue reference support to the non-expression template operators. Add numeric_limits member definitions. [SVN r79187] --- .../boost/multiprecision/cpp_dec_float.hpp | 113 ++++-- include/boost/multiprecision/cpp_int.hpp | 132 +++---- .../boost/multiprecision/detail/no_et_ops.hpp | 330 ++++++++++++++++++ include/boost/multiprecision/gmp.hpp | 147 ++++++++ include/boost/multiprecision/mpfr.hpp | 98 ++++++ .../boost/multiprecision/rational_adapter.hpp | 14 +- include/boost/multiprecision/tommath.hpp | 48 +++ performance/float_backend.hpp | 36 +- 8 files changed, 800 insertions(+), 118 deletions(-) diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index d276e12e..5b6233fa 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -2853,40 +2853,89 @@ namespace std class numeric_limits, ExpressionTemplates> > { public: - static const bool is_specialized = true; - static const bool is_signed = true; - static const bool is_integer = false; - static const bool is_exact = false; - static const bool is_bounded = true; - static const bool is_modulo = false; - static const bool is_iec559 = false; - static const int digits = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; - static const int digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; - static const int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_total_digits10; - static const boost::int64_t min_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp; // Type differs from int. - static const boost::int64_t min_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp10; // Type differs from int. - static const boost::int64_t max_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp; // Type differs from int. - static const boost::int64_t max_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp10; // Type differs from int. - static const int radix = boost::multiprecision::cpp_dec_float::cpp_dec_float_radix; - static const std::float_round_style round_style = std::round_to_nearest; - static const bool has_infinity = true; - static const bool has_quiet_NaN = true; - static const bool has_signaling_NaN = false; - static const std::float_denorm_style has_denorm = std::denorm_absent; - static const bool has_denorm_loss = false; - static const bool traps = false; - static const bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = true; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; + BOOST_STATIC_CONSTEXPR int digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; + BOOST_STATIC_CONSTEXPR int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_total_digits10; + BOOST_STATIC_CONSTEXPR boost::int64_t min_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp; // Type differs from int. + BOOST_STATIC_CONSTEXPR boost::int64_t min_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp10; // Type differs from int. + BOOST_STATIC_CONSTEXPR boost::int64_t max_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp; // Type differs from int. + BOOST_STATIC_CONSTEXPR boost::int64_t max_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp10; // Type differs from int. + BOOST_STATIC_CONSTEXPR int radix = boost::multiprecision::cpp_dec_float::cpp_dec_float_radix; + BOOST_STATIC_CONSTEXPR std::float_round_style round_style = std::round_to_nearest; + BOOST_STATIC_CONSTEXPR bool has_infinity = true; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR std::float_denorm_style has_denorm = std::denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; - static const boost::multiprecision::mp_number, ExpressionTemplates> (min) (void) { return (boost::multiprecision::cpp_dec_float::min)(); } - static const boost::multiprecision::mp_number, ExpressionTemplates> (max) (void) { return (boost::multiprecision::cpp_dec_float::max)(); } - static const boost::multiprecision::mp_number, ExpressionTemplates> lowest (void) { return boost::multiprecision::cpp_dec_float::zero(); } - static const boost::multiprecision::mp_number, ExpressionTemplates> epsilon (void) { return boost::multiprecision::cpp_dec_float::eps(); } - static const boost::multiprecision::mp_number, ExpressionTemplates> round_error (void) { return 0.5L; } - static const boost::multiprecision::mp_number, ExpressionTemplates> infinity (void) { return boost::multiprecision::cpp_dec_float::inf(); } - static const boost::multiprecision::mp_number, ExpressionTemplates> quiet_NaN (void) { return boost::multiprecision::cpp_dec_float::nan(); } - static const boost::multiprecision::mp_number, ExpressionTemplates> signaling_NaN(void) { return boost::multiprecision::cpp_dec_float::zero(); } - static const boost::multiprecision::mp_number, ExpressionTemplates> denorm_min (void) { return boost::multiprecision::cpp_dec_float::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> (min) (void) { return (boost::multiprecision::cpp_dec_float::min)(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> (max) (void) { return (boost::multiprecision::cpp_dec_float::max)(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> lowest (void) { return boost::multiprecision::cpp_dec_float::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> epsilon (void) { return boost::multiprecision::cpp_dec_float::eps(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> round_error (void) { return 0.5L; } + BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> infinity (void) { return boost::multiprecision::cpp_dec_float::inf(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> quiet_NaN (void) { return boost::multiprecision::cpp_dec_float::nan(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> signaling_NaN(void) { return boost::multiprecision::cpp_dec_float::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> denorm_min (void) { return boost::multiprecision::cpp_dec_float::zero(); } }; + +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +template +BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; + +#endif } namespace boost{ namespace math{ diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index c6e4864d..ed6a318d 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -2362,49 +2362,49 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -const int numeric_limits, ExpressionTemplates> >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; template -const int numeric_limits, ExpressionTemplates> >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; template -const int numeric_limits, ExpressionTemplates> >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; template -const bool numeric_limits, ExpressionTemplates> >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; template -const bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -const bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; template -const int numeric_limits, ExpressionTemplates> >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; template -const int numeric_limits, ExpressionTemplates> >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; template -const int numeric_limits, ExpressionTemplates> >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; template -const int numeric_limits, ExpressionTemplates> >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; template -const int numeric_limits, ExpressionTemplates> >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; template -const bool numeric_limits, ExpressionTemplates> >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; template -const bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; template -const bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; template -const float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; template -const bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; template -const bool numeric_limits, ExpressionTemplates> >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; template -const bool numeric_limits, ExpressionTemplates> >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; template -const bool numeric_limits, ExpressionTemplates> >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; template -const bool numeric_limits, ExpressionTemplates> >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; template -const bool numeric_limits, ExpressionTemplates> >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; template -const float_round_style numeric_limits, ExpressionTemplates> >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif @@ -2491,49 +2491,49 @@ const typename numeric_limits -const int numeric_limits, ExpressionTemplates> >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; template -const int numeric_limits, ExpressionTemplates> >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; template -const int numeric_limits, ExpressionTemplates> >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; template -const bool numeric_limits, ExpressionTemplates> >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; template -const bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -const bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; template -const int numeric_limits, ExpressionTemplates> >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; template -const int numeric_limits, ExpressionTemplates> >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; template -const int numeric_limits, ExpressionTemplates> >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; template -const int numeric_limits, ExpressionTemplates> >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; template -const int numeric_limits, ExpressionTemplates> >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; template -const bool numeric_limits, ExpressionTemplates> >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; template -const bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; template -const bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; template -const float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; template -const bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; template -const bool numeric_limits, ExpressionTemplates> >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; template -const bool numeric_limits, ExpressionTemplates> >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; template -const bool numeric_limits, ExpressionTemplates> >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; template -const bool numeric_limits, ExpressionTemplates> >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; template -const bool numeric_limits, ExpressionTemplates> >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; template -const float_round_style numeric_limits, ExpressionTemplates> >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif @@ -2619,49 +2619,49 @@ const typename numeric_limits -const int numeric_limits, ExpressionTemplates> >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; template -const int numeric_limits, ExpressionTemplates> >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; template -const int numeric_limits, ExpressionTemplates> >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; template -const bool numeric_limits, ExpressionTemplates> >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; template -const bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -const bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; template -const int numeric_limits, ExpressionTemplates> >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; template -const int numeric_limits, ExpressionTemplates> >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; template -const int numeric_limits, ExpressionTemplates> >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; template -const int numeric_limits, ExpressionTemplates> >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; template -const int numeric_limits, ExpressionTemplates> >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; template -const bool numeric_limits, ExpressionTemplates> >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; template -const bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; template -const bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; template -const float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; template -const bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; template -const bool numeric_limits, ExpressionTemplates> >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; template -const bool numeric_limits, ExpressionTemplates> >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; template -const bool numeric_limits, ExpressionTemplates> >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; template -const bool numeric_limits, ExpressionTemplates> >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; template -const bool numeric_limits, ExpressionTemplates> >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; template -const float_round_style numeric_limits, ExpressionTemplates> >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif diff --git a/include/boost/multiprecision/detail/no_et_ops.hpp b/include/boost/multiprecision/detail/no_et_ops.hpp index 3710c644..c57d7b00 100644 --- a/include/boost/multiprecision/detail/no_et_ops.hpp +++ b/include/boost/multiprecision/detail/no_et_ops.hpp @@ -298,6 +298,336 @@ inline typename enable_if, mp_number >::type return result; } +#ifndef BOOST_NO_RVALUE_REFERENCES +// +// If we have rvalue references go all over again with rvalue ref overloads and move semantics: +// +template +inline mp_number&& operator - (mp_number&& v) +{ + v.backend().negate(); + return static_cast&&>(v); +} +template +inline mp_number&& operator ~ (mp_number&& v) +{ + eval_complement(v.backend(), v.backend()); + return static_cast&&>(v); +} +// +// Addition: +// +template +inline mp_number&& operator + (mp_number&& a, const mp_number& b) +{ + using default_ops::eval_add; + eval_add(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline mp_number&& operator + (const mp_number& a, mp_number&& b) +{ + using default_ops::eval_add; + eval_add(b.backend(), a.backend()); + return static_cast&&>(b); +} +template +inline mp_number&& operator + (mp_number&& a, mp_number&& b) +{ + using default_ops::eval_add; + eval_add(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator + (mp_number&& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_add; + eval_add(a.backend(), static_cast(b)); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator + (const V& a, mp_number&& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_add; + eval_add(b.backend(), static_cast(a)); + return static_cast&&>(b); +} +// +// Subtraction: +// +template +inline mp_number&& operator - (mp_number&& a, const mp_number& b) +{ + using default_ops::eval_subtract; + eval_subtract(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline mp_number&& operator - (const mp_number& a, mp_number&& b) +{ + using default_ops::eval_subtract; + eval_subtract(b.backend(), a.backend()); + b.backend().negate(); + return static_cast&&>(b); +} +template +inline mp_number&& operator - (mp_number&& a, mp_number&& b) +{ + using default_ops::eval_subtract; + eval_subtract(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator - (mp_number&& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_subtract; + eval_subtract(a.backend(), static_cast(b)); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator - (const V& a, mp_number&& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_subtract; + eval_subtract(b.backend(), static_cast(a)); + b.backend().negate(); + return static_cast&&>(b); +} +// +// Multiply: +// +template +inline mp_number&& operator * (mp_number&& a, const mp_number& b) +{ + using default_ops::eval_multiply; + eval_multiply(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline mp_number&& operator * (const mp_number& a, mp_number&& b) +{ + using default_ops::eval_multiply; + eval_multiply(b.backend(), a.backend()); + return static_cast&&>(b); +} +template +inline mp_number&& operator * (mp_number&& a, mp_number&& b) +{ + using default_ops::eval_multiply; + eval_multiply(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator * (mp_number&& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_multiply; + eval_multiply(a.backend(), static_cast(b)); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator * (const V& a, mp_number&& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_multiply; + eval_multiply(b.backend(), static_cast(a)); + return static_cast&&>(b); +} +// +// divide: +// +template +inline mp_number&& operator / (mp_number&& a, const mp_number& b) +{ + using default_ops::eval_divide; + eval_divide(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator / (mp_number&& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_divide; + eval_divide(a.backend(), static_cast(b)); + return static_cast&&>(a); +} +// +// modulus: +// +template +inline mp_number&& operator % (mp_number&& a, const mp_number& b) +{ + using default_ops::eval_modulus; + eval_modulus(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator % (mp_number&& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_modulus; + eval_modulus(a.backend(), static_cast(b)); + return static_cast&&>(a); +} +// +// Bitwise or: +// +template +inline mp_number&& operator | (mp_number&& a, const mp_number& b) +{ + using default_ops::eval_bitwise_or; + eval_bitwise_or(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline mp_number&& operator | (const mp_number& a, mp_number&& b) +{ + using default_ops::eval_bitwise_or; + eval_bitwise_or(b.backend(), a.backend()); + return static_cast&&>(b); +} +template +inline mp_number&& operator | (mp_number&& a, mp_number&& b) +{ + using default_ops::eval_bitwise_or; + eval_bitwise_or(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator | (mp_number&& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_bitwise_or; + eval_bitwise_or(a.backend(), static_cast(b)); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator | (const V& a, mp_number&& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_bitwise_or; + eval_bitwise_or(b.backend(), static_cast(a)); + return static_cast&&>(b); +} +// +// Bitwise xor: +// +template +inline mp_number&& operator ^ (mp_number&& a, const mp_number& b) +{ + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline mp_number&& operator ^ (const mp_number& a, mp_number&& b) +{ + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(b.backend(), a.backend()); + return static_cast&&>(b); +} +template +inline mp_number&& operator ^ (mp_number&& a, mp_number&& b) +{ + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator ^ (mp_number&& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(a.backend(), static_cast(b)); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator ^ (const V& a, mp_number&& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_bitwise_xor; + eval_bitwise_xor(b.backend(), static_cast(a)); + return static_cast&&>(b); +} +// +// Bitwise and: +// +template +inline mp_number&& operator & (mp_number&& a, const mp_number& b) +{ + using default_ops::eval_bitwise_and; + eval_bitwise_and(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline mp_number&& operator & (const mp_number& a, mp_number&& b) +{ + using default_ops::eval_bitwise_and; + eval_bitwise_and(b.backend(), a.backend()); + return static_cast&&>(b); +} +template +inline mp_number&& operator & (mp_number&& a, mp_number&& b) +{ + using default_ops::eval_bitwise_and; + eval_bitwise_and(a.backend(), b.backend()); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator & (mp_number&& a, const V& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_bitwise_and; + eval_bitwise_and(a.backend(), static_cast(b)); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator & (const V& a, mp_number&& b) +{ + typedef typename detail::canonical::type canonical_type; + using default_ops::eval_bitwise_and; + eval_bitwise_and(b.backend(), static_cast(a)); + return static_cast&&>(b); +} +// +// shifts: +// +template +inline typename enable_if, mp_number&& >::type + operator << (mp_number&& a, const I& b) +{ + using default_ops::eval_left_shift; + eval_left_shift(a.backend(), b); + return static_cast&&>(a); +} +template +inline typename enable_if, mp_number&& >::type + operator >> (mp_number&& a, const I& b) +{ + using default_ops::eval_right_shift; + eval_right_shift(a.backend(), b); + return static_cast&&>(a); +} + +#endif + }} // namespaces #endif // BOOST_MP_NO_ET_OPS_HPP diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index fef98b76..396ba558 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1993,6 +1993,55 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; + +#endif + template class numeric_limits > { @@ -2042,6 +2091,55 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; + +#endif + template class numeric_limits > { @@ -2092,6 +2190,55 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; + +#endif + #ifdef BOOST_MSVC #pragma warning(pop) #endif diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 1ea8f782..98f82825 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -1174,6 +1174,56 @@ private: template const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +template +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; + +#endif + + template class numeric_limits, ExpressionTemplates> > { @@ -1213,5 +1263,53 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; + +#endif } // namespace std #endif diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index 0aa4ec70..c6a53aa7 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -197,8 +197,8 @@ struct component_type > namespace std{ -template -class numeric_limits > > : public std::numeric_limits > +template +class numeric_limits, ExpressionTemplates> > : public std::numeric_limits > { typedef std::numeric_limits > base_type; typedef boost::multiprecision::mp_number > number_type; @@ -216,6 +216,16 @@ public: BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } }; +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; + +#endif + + } #endif diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 6eaa6c4f..e67cf8fe 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -540,6 +540,54 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; + +#endif } #endif diff --git a/performance/float_backend.hpp b/performance/float_backend.hpp index 59b88c2f..8b2f2c9b 100644 --- a/performance/float_backend.hpp +++ b/performance/float_backend.hpp @@ -404,15 +404,15 @@ class numeric_limits base_type; typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; public: - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; } - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_NOEXCEPT { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } }; template<> @@ -421,15 +421,15 @@ class numeric_limits : public std::numeric_ typedef std::numeric_limits base_type; typedef boost::math::concepts::real_concept number_type; public: - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_MP_NOEXCEPT { return (base_type::min)(); } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_MP_NOEXCEPT { return (base_type::max)(); } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_MP_NOEXCEPT { return -(max)(); } - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_MP_NOEXCEPT { return base_type::epsilon(); } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_MP_NOEXCEPT { return epsilon() / 2; } - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_MP_NOEXCEPT { return base_type::infinity(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_MP_NOEXCEPT { return base_type::quiet_NaN(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_MP_NOEXCEPT { return base_type::signaling_NaN(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_MP_NOEXCEPT { return base_type::denorm_min(); } + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_NOEXCEPT { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } }; } From 26905dc5ead68a845e67fa9fbe84855882051320 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 2 Jul 2012 08:08:28 +0000 Subject: [PATCH 195/256] Fix non ET operators to return by value (not rvalue refs as that's unsafe - thanks to Howard Hinnant for the test case). Fix move constructors to actually move! Add move test case. Add better move support throughout the lib. [SVN r79224] --- include/boost/multiprecision/cpp_int.hpp | 2 +- .../multiprecision/detail/default_ops.hpp | 68 ++--- .../multiprecision/detail/mp_number_base.hpp | 13 +- .../boost/multiprecision/detail/no_et_ops.hpp | 142 ++++++----- include/boost/multiprecision/gmp.hpp | 26 +- include/boost/multiprecision/mp_number.hpp | 54 ++-- include/boost/multiprecision/mpfr.hpp | 9 +- include/boost/multiprecision/tommath.hpp | 10 +- test/Jamfile.v2 | 31 +++ test/test_move.cpp | 241 ++++++++++++++++++ 10 files changed, 458 insertions(+), 138 deletions(-) create mode 100644 test/test_move.cpp diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index ed6a318d..ca80fd2f 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -411,7 +411,7 @@ public: cpp_int_backend(){} cpp_int_backend(const cpp_int_backend& o) : base_type(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_backend(cpp_int_backend&& o) : base_type(o) {} + cpp_int_backend(cpp_int_backend&& o) : base_type(static_cast(o)) {} #endif cpp_int_backend& operator = (const cpp_int_backend& o) { diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 7462bcba..74c245cb 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -111,10 +111,10 @@ inline typename enable_if, is_convertible -inline bool is_same_object(const T& u, const T&v) +inline bool is_same_object(const T& u, const T&v) BOOST_NOEXCEPT { return &u == &v; } template -inline bool is_same_object(const T&, const U&) +BOOST_CONSTEXPR inline bool is_same_object(const T&, const U&) BOOST_NOEXCEPT { return false; } // @@ -688,7 +688,7 @@ template inline typename detail::mp_exp::result_type trunc(const detail::mp_exp& v, const Policy& pol) { typedef typename detail::mp_exp::result_type number_type; - return trunc(number_type(v), pol); + return BOOST_MP_MOVE(trunc(number_type(v), pol)); } template @@ -697,7 +697,7 @@ inline mp_number trunc(const mp_number result; eval_trunc(result.backend(), v.backend()); - return result; + return BOOST_MP_MOVE(result); } template @@ -787,7 +787,7 @@ template inline typename detail::mp_exp::result_type round(const detail::mp_exp& v, const Policy& pol) { typedef typename detail::mp_exp::result_type number_type; - return round(static_cast(v), pol); + return BOOST_MP_MOVE(round(static_cast(v), pol)); } template inline mp_number round(const mp_number& v, const Policy&) @@ -795,7 +795,7 @@ inline mp_number round(const mp_number result; eval_round(result.backend(), v.backend()); - return result; + return BOOST_MP_MOVE(result); } template @@ -919,9 +919,9 @@ inline typename enable_if_c::value == category,\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number > \ + , mp_number > \ >::type \ -func(const mp_number& arg)\ +func(const mp_number& arg)\ {\ return detail::mp_exp<\ detail::function\ @@ -941,7 +941,7 @@ func(const mp_number& arg)\ mp_number result;\ using default_ops::BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend());\ - return result;\ + return BOOST_MP_MOVE(result);\ } #define BINARY_OP_FUNCTOR(func, category)\ @@ -974,10 +974,10 @@ inline typename enable_if_c::value == category,\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ - , mp_number > \ + , mp_number \ + , mp_number > \ >::type \ -func(const mp_number& arg, const mp_number& a)\ +func(const mp_number& arg, const mp_number& a)\ {\ return detail::mp_exp<\ detail::function\ @@ -996,10 +996,10 @@ inline typename enable_if_c<\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ + , mp_number \ , detail::mp_exp > \ >::type \ -func(const mp_number& arg, const detail::mp_exp& a)\ +func(const mp_number& arg, const detail::mp_exp& a)\ {\ return detail::mp_exp<\ detail::function\ @@ -1019,9 +1019,9 @@ inline typename enable_if_c<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , detail::mp_exp \ - , mp_number > \ + , mp_number > \ >::type \ -func(const detail::mp_exp& arg, const mp_number& a)\ +func(const detail::mp_exp& arg, const mp_number& a)\ {\ return detail::mp_exp<\ detail::function\ @@ -1062,11 +1062,11 @@ inline typename enable_if_c<\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ + , mp_number \ , Arithmetic\ > \ >::type \ -func(const mp_number& arg, const Arithmetic& a)\ +func(const mp_number& arg, const Arithmetic& a)\ {\ return detail::mp_exp<\ detail::function\ @@ -1109,10 +1109,10 @@ inline typename enable_if_c<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , Arithmetic \ - , mp_number \ + , mp_number \ > \ >::type \ -func(const Arithmetic& arg, const mp_number& a)\ +func(const Arithmetic& arg, const mp_number& a)\ {\ return detail::mp_exp<\ detail::function\ @@ -1156,7 +1156,7 @@ func(const mp_number& arg, const mp_number& a)\ mp_number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), a.backend());\ - return result;\ + return BOOST_MP_MOVE(result);\ }\ template \ inline typename enable_if_c<\ @@ -1169,7 +1169,7 @@ func(const mp_number& arg, const Arithmetic& a)\ mp_number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), static_cast(a));\ - return result;\ + return BOOST_MP_MOVE(result);\ }\ template \ inline typename enable_if_c<\ @@ -1182,7 +1182,7 @@ func(const Arithmetic& a, const mp_number& arg)\ mp_number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), static_cast(a), arg.backend());\ - return result;\ + return BOOST_MP_MOVE(result);\ }\ @@ -1214,10 +1214,10 @@ inline typename enable_if_c<\ detail::mp_exp<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ + , mp_number \ , Arg2> \ >::type \ -func(const mp_number& arg, Arg2 const& a)\ +func(const mp_number& arg, Arg2 const& a)\ {\ return detail::mp_exp<\ detail::function\ @@ -1239,7 +1239,7 @@ func(const mp_number& arg, Arg2 const& a)\ mp_number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), a);\ - return result;\ + return BOOST_MP_MOVE(result);\ }\ #define HETERO_BINARY_OP_FUNCTOR(func, Arg2, category)\ @@ -1292,13 +1292,13 @@ template inline detail::mp_exp< detail::function , detail::abs_funct - , mp_number > -abs(const mp_number& arg) + , mp_number > +abs(const mp_number& arg) { return detail::mp_exp< detail::function , detail::abs_funct - , mp_number + , mp_number >( detail::abs_funct() , arg @@ -1311,7 +1311,7 @@ abs(const mp_number& arg) mp_number result; using default_ops::eval_abs; eval_abs(result.backend(), arg.backend()); - return result; + return BOOST_MP_MOVE(result); } UNARY_OP_FUNCTOR(fabs, number_kind_floating_point) @@ -1366,25 +1366,25 @@ namespace detail{ template inline multiprecision::mp_number sinc_pi(const multiprecision::mp_number& x) { - return detail::sinc_pi_imp(x); + return BOOST_MP_MOVE(detail::sinc_pi_imp(x)); } template inline multiprecision::mp_number sinc_pi(const multiprecision::mp_number& x, const Policy&) { - return detail::sinc_pi_imp(x); + return BOOST_MP_MOVE(detail::sinc_pi_imp(x)); } template inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x) { - return detail::sinhc_pi_imp(x); + return BOOST_MP_MOVE(detail::sinhc_pi_imp(x)); } template inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x, const Policy&) { - return boost::math::sinhc_pi(x); + return BOOST_MP_MOVE(boost::math::sinhc_pi(x)); } #ifdef BOOST_MSVC diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index ae8b1abc..92f0b691 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -37,7 +37,9 @@ template struct is_mp_number_expression > : public mpl::true_ {}; namespace detail{ - +// +// Workaround for missing abs(long long) on some compilers: +// template typename boost::enable_if, T>::type abs(const T& t) { @@ -46,6 +48,15 @@ typename boost::enable_if, T>::type abs(const T& t) #define BOOST_MP_USING_ABS using std::abs; using boost::multiprecision::detail::abs; +// +// Move support: +// +#ifndef BOOST_NO_RVALUE_REFERENCES +# define BOOST_MP_MOVE(x) std::move(x) +#else +# define BOOST_MP_MOVE(x) x +#endif + template struct has_enough_bits { diff --git a/include/boost/multiprecision/detail/no_et_ops.hpp b/include/boost/multiprecision/detail/no_et_ops.hpp index c57d7b00..aa1ea7e6 100644 --- a/include/boost/multiprecision/detail/no_et_ops.hpp +++ b/include/boost/multiprecision/detail/no_et_ops.hpp @@ -19,14 +19,14 @@ inline mp_number operator - (const mp_number& v) { mp_number result(v); result.backend().negate(); - return result; + return BOOST_MP_MOVE(result); } template inline mp_number operator ~ (const mp_number& v) { mp_number result; eval_complement(result.backend(), v.backend()); - return result; + return BOOST_MP_MOVE(result); } // // Addition: @@ -37,7 +37,7 @@ inline mp_number operator + (const mp_number& a, const mp_nu mp_number result; using default_ops::eval_add; eval_add(result.backend(), a.backend(), b.backend()); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -47,7 +47,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_add; eval_add(result.backend(), a.backend(), static_cast(b)); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -57,7 +57,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_add; eval_add(result.backend(), b.backend(), static_cast(a)); - return result; + return BOOST_MP_MOVE(result); } // // Subtraction: @@ -68,7 +68,7 @@ inline mp_number operator - (const mp_number& a, const mp_nu mp_number result; using default_ops::eval_subtract; eval_subtract(result.backend(), a.backend(), b.backend()); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -78,7 +78,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_subtract; eval_subtract(result.backend(), a.backend(), static_cast(b)); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -88,7 +88,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_subtract; eval_subtract(result.backend(), static_cast(a), b.backend()); - return result; + return BOOST_MP_MOVE(result); } // // Multiply: @@ -99,7 +99,7 @@ inline mp_number operator * (const mp_number& a, const mp_nu mp_number result; using default_ops::eval_multiply; eval_multiply(result.backend(), a.backend(), b.backend()); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -109,7 +109,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_multiply; eval_multiply(result.backend(), a.backend(), static_cast(b)); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -119,7 +119,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_multiply; eval_multiply(result.backend(), b.backend(), static_cast(a)); - return result; + return BOOST_MP_MOVE(result); } // // divide: @@ -130,7 +130,7 @@ inline mp_number operator / (const mp_number& a, const mp_nu mp_number result; using default_ops::eval_divide; eval_divide(result.backend(), a.backend(), b.backend()); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -140,7 +140,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_divide; eval_divide(result.backend(), a.backend(), static_cast(b)); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -150,7 +150,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_divide; eval_divide(result.backend(), static_cast(a), b.backend()); - return result; + return BOOST_MP_MOVE(result); } // // modulus: @@ -161,7 +161,7 @@ inline mp_number operator % (const mp_number& a, const mp_nu mp_number result; using default_ops::eval_modulus; eval_modulus(result.backend(), a.backend(), b.backend()); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -171,7 +171,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_modulus; eval_modulus(result.backend(), a.backend(), static_cast(b)); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -181,7 +181,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_modulus; eval_modulus(result.backend(), static_cast(a), b.backend()); - return result; + return BOOST_MP_MOVE(result); } // // Bitwise or: @@ -192,7 +192,7 @@ inline mp_number operator | (const mp_number& a, const mp_nu mp_number result; using default_ops::eval_bitwise_or; eval_bitwise_or(result.backend(), a.backend(), b.backend()); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -202,7 +202,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_bitwise_or; eval_bitwise_or(result.backend(), a.backend(), static_cast(b)); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -212,7 +212,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_bitwise_or; eval_bitwise_or(result.backend(), b.backend(), static_cast(a)); - return result; + return BOOST_MP_MOVE(result); } // // Bitwise xor: @@ -223,7 +223,7 @@ inline mp_number operator ^ (const mp_number& a, const mp_nu mp_number result; using default_ops::eval_bitwise_xor; eval_bitwise_xor(result.backend(), a.backend(), b.backend()); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -233,7 +233,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_bitwise_xor; eval_bitwise_xor(result.backend(), a.backend(), static_cast(b)); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -243,7 +243,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_bitwise_xor; eval_bitwise_xor(result.backend(), b.backend(), static_cast(a)); - return result; + return BOOST_MP_MOVE(result); } // // Bitwise and: @@ -254,7 +254,7 @@ inline mp_number operator & (const mp_number& a, const mp_nu mp_number result; using default_ops::eval_bitwise_and; eval_bitwise_and(result.backend(), a.backend(), b.backend()); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -264,7 +264,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_bitwise_and; eval_bitwise_and(result.backend(), a.backend(), static_cast(b)); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -274,7 +274,7 @@ inline typename enable_if, mp_number >::type mp_number result; using default_ops::eval_bitwise_and; eval_bitwise_and(result.backend(), b.backend(), static_cast(a)); - return result; + return BOOST_MP_MOVE(result); } // // shifts: @@ -286,7 +286,7 @@ inline typename enable_if, mp_number >::type mp_number result(a); using default_ops::eval_left_shift; eval_left_shift(result.backend(), b); - return result; + return BOOST_MP_MOVE(result); } template inline typename enable_if, mp_number >::type @@ -295,21 +295,29 @@ inline typename enable_if, mp_number >::type mp_number result(a); using default_ops::eval_right_shift; eval_right_shift(result.backend(), b); - return result; + return BOOST_MP_MOVE(result); } #ifndef BOOST_NO_RVALUE_REFERENCES // -// If we have rvalue references go all over again with rvalue ref overloads and move semantics: +// If we have rvalue references go all over again with rvalue ref overloads and move semantics. +// Note that while it would be tempting to implement these so they return an rvalue reference +// (and indeed this would be optimally efficient), this is unsafe due to users propensity to +// write: +// +// const T& t = a * b; +// +// which would lead to a dangling reference if we didn't return by value. Of course move +// semantics help a great deal in return by value, so performance is still pretty good... // template -inline mp_number&& operator - (mp_number&& v) +inline mp_number operator - (mp_number&& v) { v.backend().negate(); return static_cast&&>(v); } template -inline mp_number&& operator ~ (mp_number&& v) +inline mp_number operator ~ (mp_number&& v) { eval_complement(v.backend(), v.backend()); return static_cast&&>(v); @@ -318,28 +326,28 @@ inline mp_number&& operator ~ (mp_number&& v) // Addition: // template -inline mp_number&& operator + (mp_number&& a, const mp_number& b) +inline mp_number operator + (mp_number&& a, const mp_number& b) { using default_ops::eval_add; eval_add(a.backend(), b.backend()); return static_cast&&>(a); } template -inline mp_number&& operator + (const mp_number& a, mp_number&& b) +inline mp_number operator + (const mp_number& a, mp_number&& b) { using default_ops::eval_add; eval_add(b.backend(), a.backend()); return static_cast&&>(b); } template -inline mp_number&& operator + (mp_number&& a, mp_number&& b) +inline mp_number operator + (mp_number&& a, mp_number&& b) { using default_ops::eval_add; eval_add(a.backend(), b.backend()); return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator + (mp_number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -348,7 +356,7 @@ inline typename enable_if, mp_number&& >::type return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator + (const V& a, mp_number&& b) { typedef typename detail::canonical::type canonical_type; @@ -360,14 +368,14 @@ inline typename enable_if, mp_number&& >::type // Subtraction: // template -inline mp_number&& operator - (mp_number&& a, const mp_number& b) +inline mp_number operator - (mp_number&& a, const mp_number& b) { using default_ops::eval_subtract; eval_subtract(a.backend(), b.backend()); return static_cast&&>(a); } template -inline mp_number&& operator - (const mp_number& a, mp_number&& b) +inline mp_number operator - (const mp_number& a, mp_number&& b) { using default_ops::eval_subtract; eval_subtract(b.backend(), a.backend()); @@ -375,14 +383,14 @@ inline mp_number&& operator - (const mp_number& a, mp_number return static_cast&&>(b); } template -inline mp_number&& operator - (mp_number&& a, mp_number&& b) +inline mp_number operator - (mp_number&& a, mp_number&& b) { using default_ops::eval_subtract; eval_subtract(a.backend(), b.backend()); return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator - (mp_number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -391,7 +399,7 @@ inline typename enable_if, mp_number&& >::type return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator - (const V& a, mp_number&& b) { typedef typename detail::canonical::type canonical_type; @@ -404,28 +412,28 @@ inline typename enable_if, mp_number&& >::type // Multiply: // template -inline mp_number&& operator * (mp_number&& a, const mp_number& b) +inline mp_number operator * (mp_number&& a, const mp_number& b) { using default_ops::eval_multiply; eval_multiply(a.backend(), b.backend()); return static_cast&&>(a); } template -inline mp_number&& operator * (const mp_number& a, mp_number&& b) +inline mp_number operator * (const mp_number& a, mp_number&& b) { using default_ops::eval_multiply; eval_multiply(b.backend(), a.backend()); return static_cast&&>(b); } template -inline mp_number&& operator * (mp_number&& a, mp_number&& b) +inline mp_number operator * (mp_number&& a, mp_number&& b) { using default_ops::eval_multiply; eval_multiply(a.backend(), b.backend()); return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator * (mp_number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -434,7 +442,7 @@ inline typename enable_if, mp_number&& >::type return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator * (const V& a, mp_number&& b) { typedef typename detail::canonical::type canonical_type; @@ -446,14 +454,14 @@ inline typename enable_if, mp_number&& >::type // divide: // template -inline mp_number&& operator / (mp_number&& a, const mp_number& b) +inline mp_number operator / (mp_number&& a, const mp_number& b) { using default_ops::eval_divide; eval_divide(a.backend(), b.backend()); return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator / (mp_number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -465,14 +473,14 @@ inline typename enable_if, mp_number&& >::type // modulus: // template -inline mp_number&& operator % (mp_number&& a, const mp_number& b) +inline mp_number operator % (mp_number&& a, const mp_number& b) { using default_ops::eval_modulus; eval_modulus(a.backend(), b.backend()); return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator % (mp_number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -484,28 +492,28 @@ inline typename enable_if, mp_number&& >::type // Bitwise or: // template -inline mp_number&& operator | (mp_number&& a, const mp_number& b) +inline mp_number operator | (mp_number&& a, const mp_number& b) { using default_ops::eval_bitwise_or; eval_bitwise_or(a.backend(), b.backend()); return static_cast&&>(a); } template -inline mp_number&& operator | (const mp_number& a, mp_number&& b) +inline mp_number operator | (const mp_number& a, mp_number&& b) { using default_ops::eval_bitwise_or; eval_bitwise_or(b.backend(), a.backend()); return static_cast&&>(b); } template -inline mp_number&& operator | (mp_number&& a, mp_number&& b) +inline mp_number operator | (mp_number&& a, mp_number&& b) { using default_ops::eval_bitwise_or; eval_bitwise_or(a.backend(), b.backend()); return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator | (mp_number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -514,7 +522,7 @@ inline typename enable_if, mp_number&& >::type return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator | (const V& a, mp_number&& b) { typedef typename detail::canonical::type canonical_type; @@ -526,28 +534,28 @@ inline typename enable_if, mp_number&& >::type // Bitwise xor: // template -inline mp_number&& operator ^ (mp_number&& a, const mp_number& b) +inline mp_number operator ^ (mp_number&& a, const mp_number& b) { using default_ops::eval_bitwise_xor; eval_bitwise_xor(a.backend(), b.backend()); return static_cast&&>(a); } template -inline mp_number&& operator ^ (const mp_number& a, mp_number&& b) +inline mp_number operator ^ (const mp_number& a, mp_number&& b) { using default_ops::eval_bitwise_xor; eval_bitwise_xor(b.backend(), a.backend()); return static_cast&&>(b); } template -inline mp_number&& operator ^ (mp_number&& a, mp_number&& b) +inline mp_number operator ^ (mp_number&& a, mp_number&& b) { using default_ops::eval_bitwise_xor; eval_bitwise_xor(a.backend(), b.backend()); return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator ^ (mp_number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -556,7 +564,7 @@ inline typename enable_if, mp_number&& >::type return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator ^ (const V& a, mp_number&& b) { typedef typename detail::canonical::type canonical_type; @@ -568,28 +576,28 @@ inline typename enable_if, mp_number&& >::type // Bitwise and: // template -inline mp_number&& operator & (mp_number&& a, const mp_number& b) +inline mp_number operator & (mp_number&& a, const mp_number& b) { using default_ops::eval_bitwise_and; eval_bitwise_and(a.backend(), b.backend()); return static_cast&&>(a); } template -inline mp_number&& operator & (const mp_number& a, mp_number&& b) +inline mp_number operator & (const mp_number& a, mp_number&& b) { using default_ops::eval_bitwise_and; eval_bitwise_and(b.backend(), a.backend()); return static_cast&&>(b); } template -inline mp_number&& operator & (mp_number&& a, mp_number&& b) +inline mp_number operator & (mp_number&& a, mp_number&& b) { using default_ops::eval_bitwise_and; eval_bitwise_and(a.backend(), b.backend()); return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator & (mp_number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -598,7 +606,7 @@ inline typename enable_if, mp_number&& >::type return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator & (const V& a, mp_number&& b) { typedef typename detail::canonical::type canonical_type; @@ -610,7 +618,7 @@ inline typename enable_if, mp_number&& >::type // shifts: // template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator << (mp_number&& a, const I& b) { using default_ops::eval_left_shift; @@ -618,7 +626,7 @@ inline typename enable_if, mp_number&& >::type return static_cast&&>(a); } template -inline typename enable_if, mp_number&& >::type +inline typename enable_if, mp_number >::type operator >> (mp_number&& a, const I& b) { using default_ops::eval_right_shift; diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 396ba558..a4b0a33d 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -337,7 +337,7 @@ struct gmp_float : public detail::gmp_float_imp mpf_set_q(this->m_data, val); } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_float(gmp_float&& o) : detail::gmp_float_imp(o) {} + gmp_float(gmp_float&& o) : detail::gmp_float_imp(static_cast&&>(o)) {} #endif gmp_float& operator=(const gmp_float& o) { @@ -412,7 +412,7 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> mpf_set(this->m_data, o.data()); } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_float(gmp_float&& o) : detail::gmp_float_imp<0>(o) {} + gmp_float(gmp_float&& o) : detail::gmp_float_imp<0>(static_cast&&>(o)) {} #endif gmp_float(const gmp_int& o); gmp_float(const gmp_rational& o); @@ -874,6 +874,13 @@ struct gmp_int { mpz_init_set(m_data, o.m_data); } +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_int(gmp_int&& o) + { + m_data[0] = o.m_data[0]; + o.m_data[0]._mp_d = 0; + } +#endif gmp_int(mpf_t val) { mpz_init(this->m_data); @@ -1072,7 +1079,8 @@ struct gmp_int } ~gmp_int() { - mpz_clear(m_data); + if(m_data[0]._mp_d) + mpz_clear(m_data); } void negate() { @@ -1469,6 +1477,15 @@ struct gmp_rational mpq_init(m_data); mpq_set_z(m_data, o.data()); } +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_rational(gmp_rational&& o) + { + m_data[0]._mp_num = o.data()[0]._mp_num; + m_data[0]._mp_den = o.data()[0]._mp_den; + o.data()[0]._mp_num._mp_d = 0; + o.data()[0]._mp_den._mp_d = 0; + } +#endif gmp_rational(mpq_t o) { mpq_init(m_data); @@ -1613,7 +1630,8 @@ struct gmp_rational } ~gmp_rational() { - mpq_clear(m_data); + if(m_data[0]._mp_num._mp_d || m_data[0]._mp_den._mp_d) + mpq_clear(m_data); } void negate() { diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index a8928cfe..db19d5a7 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -153,7 +153,7 @@ public: } #ifndef BOOST_NO_RVALUE_REFERENCES - mp_number(mp_number&& r) : m_backend(r.m_backend){} + mp_number(mp_number&& r) : m_backend(static_cast(r.m_backend)){} mp_number& operator=(mp_number&& r) { m_backend.swap(r.m_backend); @@ -171,7 +171,7 @@ public: mp_number& operator+=(const detail::mp_exp& e) { // Create a copy if e contains this, but not if we're just doing a - // x *= x + // x += x if(contains_self(e) && !is_self(e)) { self_type temp(e); @@ -202,7 +202,7 @@ public: template mp_number& operator-=(const detail::mp_exp& e) { - // Create a copy if e contains this, but not if we're just doing a + // Create a copy if e contains this: if(contains_self(e)) { self_type temp(e); @@ -235,7 +235,7 @@ public: mp_number& operator*=(const detail::mp_exp& e) { // Create a temporary if the RHS references *this, but not - // if we're just doing an x += x; + // if we're just doing an x *= x; if(contains_self(e) && !is_self(e)) { self_type temp(e); @@ -1094,20 +1094,20 @@ private: void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const detail::terminal&) { self_type temp1(val1); - f(m_backend, temp1.backend(), function_arg_value(val2)); + f(m_backend, BOOST_MP_MOVE(temp1.backend()), function_arg_value(val2)); } template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const Tag2&) { self_type temp2(val2); - f(m_backend, function_arg_value(val1), temp2.backend()); + f(m_backend, function_arg_value(val1), BOOST_MP_MOVE(temp2.backend())); } template void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const Tag2&) { self_type temp1(val1); self_type temp2(val2); - f(m_backend, temp1.backend(), temp2.backend()); + f(m_backend, BOOST_MP_MOVE(temp1.backend()), BOOST_MP_MOVE(temp2.backend())); } template @@ -1130,7 +1130,7 @@ private: void do_assign_function_3a(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag1&, const Tag2& t2, const Tag3& t3) { mp_number t(val1); - do_assign_function_3b(f, t, val2, val3, t2, t3); + do_assign_function_3b(f, BOOST_MP_MOVE(t), val2, val3, t2, t3); } template void do_assign_function_3b(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const detail::terminal&, const Tag3& t3) @@ -1141,7 +1141,7 @@ private: void do_assign_function_3b(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag2& /*t2*/, const Tag3& t3) { mp_number t(val2); - do_assign_function_3c(f, val1, t, val3, t3); + do_assign_function_3c(f, val1, BOOST_MP_MOVE(t), val3, t3); } template void do_assign_function_3c(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const detail::terminal&) @@ -1152,7 +1152,7 @@ private: void do_assign_function_3c(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag3& /*t3*/) { mp_number t(val3); - do_assign_function_3c(f, val1, val2, t, detail::terminal()); + do_assign_function_3c(f, val1, val2, BOOST_MP_MOVE(t), detail::terminal()); } template @@ -1469,23 +1469,23 @@ private: // Tests if the expression contains a reference to *this: template - bool contains_self(const Exp& e)const + bool contains_self(const Exp& e)const BOOST_NOEXCEPT { return contains_self(e, typename Exp::arity()); } template - bool contains_self(const Exp& e, mpl::int_<0> const&)const + bool contains_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT { return is_realy_self(e.value()); } template - bool contains_self(const Exp& e, mpl::int_<1> const&)const + bool contains_self(const Exp& e, mpl::int_<1> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child_type; return contains_self(e.left(), typename child_type::arity()); } template - bool contains_self(const Exp& e, mpl::int_<2> const&)const + bool contains_self(const Exp& e, mpl::int_<2> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child0_type; typedef typename Exp::right_type child1_type; @@ -1493,7 +1493,7 @@ private: || contains_self(e.right(), typename child1_type::arity()); } template - bool contains_self(const Exp& e, mpl::int_<3> const&)const + bool contains_self(const Exp& e, mpl::int_<3> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child0_type; typedef typename Exp::middle_type child1_type; @@ -1505,37 +1505,37 @@ private: // Test if the expression is a reference to *this: template - bool is_self(const Exp& e)const + bool is_self(const Exp& e)const BOOST_NOEXCEPT { return is_self(e, typename Exp::arity()); } template - bool is_self(const Exp& e, mpl::int_<0> const&)const + bool is_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT { return is_realy_self(e.value()); } template - bool is_self(const Exp&, mpl::int_ const&)const + BOOST_CONSTEXPR bool is_self(const Exp&, mpl::int_ const&)const BOOST_NOEXCEPT { return false; } template - bool is_realy_self(const Val&)const { return false; } - bool is_realy_self(const self_type& v)const { return &v == this; } + BOOST_CONSTEXPR bool is_realy_self(const Val&)const BOOST_NOEXCEPT{ return false; } + BOOST_CONSTEXPR bool is_realy_self(const self_type& v)const BOOST_NOEXCEPT{ return &v == this; } - static const Backend& canonical_value(const self_type& v){ return v.m_backend; } + static const Backend& canonical_value(const self_type& v) BOOST_NOEXCEPT { return v.m_backend; } template - static typename detail::canonical::type canonical_value(const V& v){ return static_cast::type>(v); } - static typename detail::canonical::type canonical_value(const std::string& v){ return v.c_str(); } + static typename detail::canonical::type canonical_value(const V& v) BOOST_NOEXCEPT { return static_cast::type>(v); } + static typename detail::canonical::type canonical_value(const std::string& v) BOOST_NOEXCEPT { return v.c_str(); } - static const Backend& function_arg_value(const self_type& v) { return v.backend(); } + static const Backend& function_arg_value(const self_type& v) BOOST_NOEXCEPT { return v.backend(); } template - static const V& function_arg_value(const V& v) { return v; } + static const V& function_arg_value(const V& v) BOOST_NOEXCEPT { return v; } template - static const A1& function_arg_value(const detail::mp_exp& exp) { return exp.value(); } + static const A1& function_arg_value(const detail::mp_exp& exp) BOOST_NOEXCEPT { return exp.value(); } template - static const Backend& function_arg_value(const detail::mp_exp, A2, A3, A4>& exp) { return exp.value().backend(); } + static const Backend& function_arg_value(const detail::mp_exp, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value().backend(); } Backend m_backend; }; diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 98f82825..43604382 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -152,7 +152,10 @@ struct mpfr_float_imp } mpfr_float_imp& operator = (const char* s) { - mpfr_set_str(m_data, s, 10, GMP_RNDN); + if(mpfr_set_str(m_data, s, 10, GMP_RNDN) != 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Unable to parse string as a valid floating point number.")); + } return *this; } void swap(mpfr_float_imp& o) @@ -314,7 +317,7 @@ struct mpfr_float_backend : public detail::mpfr_float_imp } mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp(o) {} + mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp(static_cast&&>(o)) {} #endif template mpfr_float_backend(const mpfr_float_backend& val) @@ -453,7 +456,7 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> } mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp<0>(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp<0>(o) {} + mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp<0>(static_cast&&>(o)) {} #endif mpfr_float_backend(const mpfr_float_backend& o, unsigned digits10) { diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index e67cf8fe..d7456fd0 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -46,6 +46,13 @@ struct tommath_int { detail::check_tommath_result(mp_init_copy(&m_data, const_cast< ::mp_int*>(&o.m_data))); } +#ifndef BOOST_NO_RVALUE_REFERENCES + tommath_int(tommath_int&& o) + { + m_data = o.m_data; + o.m_data.dp = 0; + } +#endif tommath_int& operator = (const tommath_int& o) { detail::check_tommath_result(mp_copy(const_cast< ::mp_int*>(&o.m_data), &m_data)); @@ -209,7 +216,8 @@ struct tommath_int } ~tommath_int() { - mp_clear(&m_data); + if(m_data.dp) + mp_clear(&m_data); } void negate() { diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 75686515..deec7251 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -578,6 +578,37 @@ run test_constants.cpp : test_constants_cpp_dec_float ; +run test_move.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR + [ check-target-builds ../config//has_mpfr : : no ] + : test_move_mpfr ; + +run test_move.cpp gmp + : # command line + : # input files + : # requirements + TEST_GMP + [ check-target-builds ../config//has_gmp : : no ] + : test_move_gmp ; + +run test_move.cpp $(TOMMATH) + : # command line + : # input files + : # requirements + TEST_TOMMATH + [ check-target-builds ../config//has_tommath : : no ] + : test_move_tommath ; + +run test_move.cpp + : # command line + : # input files + : # requirements + TEST_CPP_INT + : test_move_cpp_int ; + run test_test.cpp ; run test_float_io.cpp diff --git a/test/test_move.cpp b/test/test_move.cpp new file mode 100644 index 00000000..f67e497b --- /dev/null +++ b/test/test_move.cpp @@ -0,0 +1,241 @@ +// Copyright John Maddock 2012. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include + +#ifndef BOOST_NO_RVALUE_REFERENCES + +#if !defined(TEST_GMP) && !defined(TEST_MPFR) && !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) +# define TEST_GMP +# define TEST_MPFR +# define TEST_TOMMATH +# define TEST_CPP_INT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_GMP) +#include +#endif +#if defined(TEST_MPFR) +#include +#endif +#ifdef TEST_TOMMATH +#include +#endif +#ifdef TEST_CPP_INT +#include +#endif + +#include "test.hpp" + +unsigned allocation_count = 0; + +void *(*alloc_func_ptr) (size_t); +void *(*realloc_func_ptr) (void *, size_t, size_t); +void (*free_func_ptr) (void *, size_t); + +void *alloc_func(size_t n) +{ + ++allocation_count; + return (*alloc_func_ptr)(n); +} + +void free_func(void * p, size_t n) +{ + (*free_func_ptr)(p, n); +} + +void * realloc_func(void * p, size_t old, size_t n) +{ + ++allocation_count; + return (*realloc_func_ptr)(p, old, n); +} + +template +void do_something(const T&) +{ +} + + +int main() +{ +#if defined(TEST_MPFR) || defined(TEST_GMP) + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + mp_set_memory_functions(&alloc_func, &realloc_func, &free_func); +#endif + + using namespace boost::multiprecision; + +#ifdef TEST_MPFR + { + mpfr_float_50 a = 2; + BOOST_TEST(allocation_count); // sanity check that we are tracking allocations + allocation_count = 0; + mpfr_float_50 b = std::move(a); + BOOST_TEST(allocation_count == 0); + // + // Move assign - we rely on knowledge of the internals to make this test work!! + // + mpfr_float_50 c(3); + do_something(b); + do_something(c); + const void* p = b.backend().data()[0]._mpfr_d; + BOOST_TEST(c.backend().data()[0]._mpfr_d != p); + c = std::move(b); + BOOST_TEST(c.backend().data()[0]._mpfr_d == p); + BOOST_TEST(b.backend().data()[0]._mpfr_d != p); + // + // Again with variable precision, this we can test more easily: + // + mpfr_float d, e; + d.precision(100); + e.precision(1000); + d = 2; + e = 3; + allocation_count = 0; + BOOST_TEST(d == 2); + d = std::move(e); + BOOST_TEST(allocation_count == 0); + BOOST_TEST(d == 3); + } +#endif +#ifdef TEST_GMP + { + mpf_float_50 a = 2; + BOOST_TEST(allocation_count); // sanity check that we are tracking allocations + allocation_count = 0; + mpf_float_50 b = std::move(a); + BOOST_TEST(allocation_count == 0); + // + // Move assign: this requires knowledge of the internals to test!! + // + mpf_float_50 c(3); + do_something(b); + do_something(c); + const void* p = b.backend().data()[0]._mp_d; + BOOST_TEST(c.backend().data()[0]._mp_d != p); + c = std::move(b); + BOOST_TEST(c.backend().data()[0]._mp_d == p); + BOOST_TEST(b.backend().data()[0]._mp_d != p); + // + // Again with variable precision, this we can test more easily: + // + mpf_float d, e; + d.precision(100); + e.precision(1000); + d = 2; + e = 3; + allocation_count = 0; + BOOST_TEST(d == 2); + d = std::move(e); + BOOST_TEST(allocation_count == 0); + BOOST_TEST(d == 3); + } + { + mpz_int a = 2; + BOOST_TEST(allocation_count); // sanity check that we are tracking allocations + allocation_count = 0; + mpz_int b = std::move(a); + BOOST_TEST(allocation_count == 0); + + // + // Move assign: + // + mpz_int d, e; + d = 2; + d <<= 1000; + e = 3; + allocation_count = 0; + e = std::move(d); + BOOST_TEST(allocation_count == 0); + } + { + mpq_rational a = 2; + BOOST_TEST(allocation_count); // sanity check that we are tracking allocations + allocation_count = 0; + mpq_rational b = std::move(a); + BOOST_TEST(allocation_count == 0); + + // + // Move assign: + // + mpq_rational d, e; + d = mpz_int(2) << 1000; + e = 3; + allocation_count = 0; + e = std::move(d); + BOOST_TEST(allocation_count == 0); + } +#endif +#ifdef TEST_TOMMATH + { + tom_int a = 2; + void const* p = a.backend().data().dp; + tom_int b = std::move(a); + BOOST_TEST(b.backend().data().dp == p); + BOOST_TEST(a.backend().data().dp == 0); + + // + // Move assign: + // + tom_int d, e; + d = 2; + d <<= 1000; + e = 3; + p = d.backend().data().dp; + BOOST_TEST(p != e.backend().data().dp); + e = std::move(d); + BOOST_TEST(e.backend().data().dp == p); + } +#endif +#ifdef TEST_CPP_INT + { + cpp_int a = 2; + a <<= 1000; // Force dynamic allocation. + void const* p = a.backend().limbs(); + cpp_int b = std::move(a); + BOOST_TEST(b.backend().limbs() == p); + + // + // Move assign: + // + cpp_int d, e; + d = 2; + d <<= 1000; + e = 3; + e <<= 1000; + p = d.backend().limbs(); + BOOST_TEST(p != e.backend().limbs()); + e = std::move(d); + BOOST_TEST(e.backend().limbs() == p); + } +#endif + return boost::report_errors(); +} + +#else +// +// No rvalue refs, nothing to test: +// +int main() +{ + return 0; +} + +#endif + From ccf276db86ebcaf7ab3aeb3cf30f8d77ebb04825 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 3 Jul 2012 12:32:17 +0000 Subject: [PATCH 196/256] Add tentative noexcept support. [SVN r79243] --- include/boost/multiprecision/cpp_int.hpp | 290 +++++++++------------ include/boost/multiprecision/mp_number.hpp | 76 +++--- performance/Jamfile.v2 | 16 +- performance/miller_rabin_performance.cpp | 9 +- performance/sf_performance.cpp | 4 + 5 files changed, 177 insertions(+), 218 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index ca80fd2f..d50bf068 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -71,14 +71,14 @@ public: // // Helper functions for getting at our internal data, and manipulating storage: // - allocator_type& allocator(){ return *this; } - const allocator_type& allocator()const{ return *this; } - unsigned size()const { return m_limbs; } - limb_pointer limbs() { return m_internal ? m_data.la : m_data.ld.data; } - const_limb_pointer limbs()const { return m_internal ? m_data.la : m_data.ld.data; } - unsigned capacity()const { return m_internal ? internal_limb_count : m_data.ld.capacity; } - bool sign()const { return m_sign; } - void sign(bool b) + allocator_type& allocator() BOOST_NOEXCEPT { return *this; } + const allocator_type& allocator()const BOOST_NOEXCEPT { return *this; } + unsigned size()const BOOST_NOEXCEPT { return m_limbs; } + limb_pointer limbs() BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; } + const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; } + unsigned capacity()const BOOST_NOEXCEPT { return m_internal ? internal_limb_count : m_data.ld.capacity; } + bool sign()const BOOST_NOEXCEPT { return m_sign; } + void sign(bool b) BOOST_NOEXCEPT { m_sign = b; // Check for zero value: @@ -109,15 +109,14 @@ public: m_limbs = new_size; } } - void normalize() + void normalize() BOOST_NOEXCEPT { limb_pointer p = limbs(); while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; } - cpp_int_base() : m_limbs(1), m_sign(false), m_internal(true) + BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1), m_sign(false), m_internal(true) { - *limbs() = 0; } cpp_int_base(const cpp_int_base& o) : allocator_type(o), m_limbs(0), m_internal(true) { @@ -126,7 +125,7 @@ public: m_sign = o.m_sign; } #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_base(cpp_int_base&& o) : allocator_type(o), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) + cpp_int_base(cpp_int_base&& o) BOOST_NOEXCEPT : allocator_type(o), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) { if(m_internal) { @@ -140,7 +139,7 @@ public: } } #endif - ~cpp_int_base() + ~cpp_int_base() BOOST_NOEXCEPT { if(!m_internal) allocator().deallocate(limbs(), capacity()); @@ -156,7 +155,7 @@ public: m_sign = o.m_sign; } } - void negate() + void negate() BOOST_NOEXCEPT { m_sign = !m_sign; // Check for zero value: @@ -166,11 +165,11 @@ public: m_sign = false; } } - bool isneg()const + bool isneg()const BOOST_NOEXCEPT { return m_sign; } - void do_swap(cpp_int_base& o) + void do_swap(cpp_int_base& o) BOOST_NOEXCEPT { std::swap(m_data, o.m_data); std::swap(m_sign, o.m_sign); @@ -203,11 +202,11 @@ public: // // Helper functions for getting at our internal data, and manipulating storage: // - unsigned size()const { return m_limbs; } - limb_pointer limbs() { return m_data; } - const_limb_pointer limbs()const { return m_data; } - bool sign()const { return m_sign; } - void sign(bool b) + unsigned size()const BOOST_NOEXCEPT { return m_limbs; } + limb_pointer limbs() BOOST_NOEXCEPT { return m_data; } + const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_data; } + bool sign()const BOOST_NOEXCEPT { return m_sign; } + void sign(bool b) BOOST_NOEXCEPT { m_sign = b; // Check for zero value: @@ -217,11 +216,11 @@ public: m_sign = false; } } - void resize(unsigned new_size) + void resize(unsigned new_size) BOOST_NOEXCEPT { m_limbs = static_cast((std::min)(new_size, internal_limb_count)); } - void normalize() + void normalize() BOOST_NOEXCEPT { limb_pointer p = limbs(); p[internal_limb_count-1] &= upper_limb_mask; @@ -229,24 +228,21 @@ public: if((m_limbs == 1) && (!*p)) m_sign = false; // zero is always unsigned } - cpp_int_base() : m_limbs(1), m_sign(false) - { - *limbs() = 0; - } - cpp_int_base(const cpp_int_base& o) : m_limbs(0) + BOOST_CONSTEXPR cpp_int_base() : m_data(), m_limbs(1), m_sign(false) {} + cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(0) { resize(o.size()); std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); m_sign = o.m_sign; } #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_base(cpp_int_base&& o) : m_limbs(o.m_limbs), m_sign(o.m_sign) + cpp_int_base(cpp_int_base&& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs), m_sign(o.m_sign) { std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); } #endif - ~cpp_int_base() {} - void assign(const cpp_int_base& o) + ~cpp_int_base() BOOST_NOEXCEPT {} + void assign(const cpp_int_base& o) BOOST_NOEXCEPT { if(this != &o) { @@ -255,7 +251,7 @@ public: m_sign = o.m_sign; } } - void negate() + void negate() BOOST_NOEXCEPT { m_sign = !m_sign; // Check for zero value: @@ -265,11 +261,11 @@ public: m_sign = false; } } - bool isneg()const + bool isneg()const BOOST_NOEXCEPT { return m_sign; } - void do_swap(cpp_int_base& o) + void do_swap(cpp_int_base& o) BOOST_NOEXCEPT { for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i) std::swap(m_data[i], o.m_data[i]); @@ -301,39 +297,36 @@ public: // // Helper functions for getting at our internal data, and manipulating storage: // - unsigned size()const { return m_limbs; } - limb_pointer limbs() { return m_data; } - const_limb_pointer limbs()const { return m_data; } - bool sign()const { return false; } - void sign(bool b) { if(b) negate(); } - void resize(unsigned new_size) + unsigned size()const BOOST_NOEXCEPT { return m_limbs; } + limb_pointer limbs() BOOST_NOEXCEPT { return m_data; } + const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_data; } + BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; } + void sign(bool b) BOOST_NOEXCEPT { if(b) negate(); } + void resize(unsigned new_size) BOOST_NOEXCEPT { m_limbs = (std::min)(new_size, internal_limb_count); } - void normalize() + void normalize() BOOST_NOEXCEPT { limb_pointer p = limbs(); p[internal_limb_count-1] &= upper_limb_mask; while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; } - cpp_int_base() : m_limbs(1) - { - *limbs() = 0; - } - cpp_int_base(const cpp_int_base& o) : m_limbs(0) + BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1) {} + cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(0) { resize(o.size()); std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); } #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_base(cpp_int_base&& o) : m_limbs(o.m_limbs) + cpp_int_base(cpp_int_base&& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs) { std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); } #endif - ~cpp_int_base() {} - void assign(const cpp_int_base& o) + ~cpp_int_base() BOOST_NOEXCEPT {} + void assign(const cpp_int_base& o) BOOST_NOEXCEPT { if(this != &o) { @@ -341,7 +334,7 @@ public: std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); } } - void negate() + void negate() BOOST_NOEXCEPT { // Not so much a negate as a complement - this gets called when subtraction // would result in a "negative" number: @@ -354,11 +347,11 @@ public: normalize(); eval_increment(static_cast& >(*this)); } - bool isneg()const + BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT { return false; } - void do_swap(cpp_int_base& o) + void do_swap(cpp_int_base& o) BOOST_NOEXCEPT { for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i) std::swap(m_data[i], o.m_data[i]); @@ -408,31 +401,31 @@ public: typedef mpl::list unsigned_types; typedef mpl::list float_types; - cpp_int_backend(){} - cpp_int_backend(const cpp_int_backend& o) : base_type(o) {} + BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{} + cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) : base_type(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_backend(cpp_int_backend&& o) : base_type(static_cast(o)) {} + cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT : base_type(static_cast(o)) {} #endif - cpp_int_backend& operator = (const cpp_int_backend& o) + cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { this->assign(o); return *this; } - cpp_int_backend& operator = (limb_type i) + cpp_int_backend& operator = (limb_type i) BOOST_NOEXCEPT { this->resize(1); *this->limbs() = i; this->sign(false); return *this; } - cpp_int_backend& operator = (signed_limb_type i) + cpp_int_backend& operator = (signed_limb_type i) BOOST_NOEXCEPT { this->resize(1); *this->limbs() = static_cast(std::abs(i)); this->sign(i < 0); return *this; } - cpp_int_backend& operator = (double_limb_type i) + cpp_int_backend& operator = (double_limb_type i) BOOST_NOEXCEPT_IF(MinBits <= sizeof(double_limb_type) * CHAR_BIT) { BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type)); BOOST_STATIC_ASSERT(base_type::internal_limb_count >= 2); @@ -443,7 +436,7 @@ public: this->sign(false); return *this; } - cpp_int_backend& operator = (signed_double_limb_type i) + cpp_int_backend& operator = (signed_double_limb_type i) BOOST_NOEXCEPT_IF(MinBits <= sizeof(signed_double_limb_type) * CHAR_BIT) { BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type)); BOOST_STATIC_ASSERT(base_type::internal_limb_count >= 2); @@ -463,7 +456,7 @@ public: return *this; } - cpp_int_backend& operator = (long double a) + cpp_int_backend& operator = (long double a) BOOST_NOEXCEPT_IF(MinBits <= sizeof(long double) * CHAR_BIT) { using default_ops::eval_add; using default_ops::eval_subtract; @@ -607,7 +600,7 @@ public: this->negate(); return *this; } - void swap(cpp_int_backend& o) + void swap(cpp_int_backend& o) BOOST_NOEXCEPT { this->do_swap(o); } @@ -707,7 +700,7 @@ public: } return result; } - int compare(const cpp_int_backend& o)const + int compare(const cpp_int_backend& o)const BOOST_NOEXCEPT { if(this->sign() != o.sign()) return this->sign() ? -1 : 1; @@ -719,7 +712,7 @@ public: result = -result; return result; } - int compare_unsigned(const cpp_int_backend& o)const + int compare_unsigned(const cpp_int_backend& o)const BOOST_NOEXCEPT { if(this->size() != o.size()) { @@ -735,7 +728,7 @@ public: return 0; } template - typename enable_if, int>::type compare(Arithmatic i)const + typename enable_if, int>::type compare(Arithmatic i)const BOOST_NOEXCEPT { // braindead version: cpp_int_backend t; @@ -746,12 +739,12 @@ public: template -inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_add(result, result, o); } template -inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { using std::swap; @@ -811,7 +804,7 @@ inline void add_unsigned(cpp_int_backend& result, co result.sign(a.sign()); } template -inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign() != b.sign()) { @@ -822,7 +815,7 @@ inline void eval_add(cpp_int_backend& result, const } template -inline void add_unsigned(cpp_int_backend& result, const limb_type& o) +inline void add_unsigned(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Addition using modular arithmatic. // Nothing fancy, just let uintmax_t take the strain: @@ -845,7 +838,7 @@ inline void add_unsigned(cpp_int_backend& result, co result.normalize(); } template -inline void eval_add(cpp_int_backend& result, const limb_type& o) +inline void eval_add(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(result.sign()) { @@ -855,7 +848,7 @@ inline void eval_add(cpp_int_backend& result, const add_unsigned(result, o); } template -inline void eval_add(cpp_int_backend& result, const signed_limb_type& o) +inline void eval_add(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o < 0) eval_subtract(result, static_cast(-o)); @@ -864,7 +857,7 @@ inline void eval_add(cpp_int_backend& result, const } template -inline void subtract_unsigned(cpp_int_backend& result, const limb_type& o) +inline void subtract_unsigned(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Subtract one limb. // Nothing fancy, just let uintmax_t take the strain: @@ -893,7 +886,7 @@ inline void subtract_unsigned(cpp_int_backend& resul } } template -inline void eval_subtract(cpp_int_backend& result, const limb_type& o) +inline void eval_subtract(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(result.sign()) add_unsigned(result, o); @@ -901,7 +894,7 @@ inline void eval_subtract(cpp_int_backend& result, c subtract_unsigned(result, o); } template -inline void eval_subtract(cpp_int_backend& result, const signed_limb_type& o) +inline void eval_subtract(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o) { @@ -912,7 +905,7 @@ inline void eval_subtract(cpp_int_backend& result, c } } template -inline void eval_increment(cpp_int_backend& result) +inline void eval_increment(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) { static const limb_type one = 1; if(!result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) @@ -923,7 +916,7 @@ inline void eval_increment(cpp_int_backend& result) eval_add(result, one); } template -inline void eval_decrement(cpp_int_backend& result) +inline void eval_decrement(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) { static const limb_type one = 1; if(!result.sign() && result.limbs()[0]) @@ -934,12 +927,12 @@ inline void eval_decrement(cpp_int_backend& result) eval_subtract(result, one); } template -inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_subtract(result, result, o); } template -inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { using std::swap; @@ -1016,7 +1009,7 @@ inline void subtract_unsigned(cpp_int_backend& resul result.negate(); } template -inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign() != b.sign()) { @@ -1026,7 +1019,7 @@ inline void eval_subtract(cpp_int_backend& result, c subtract_unsigned(result, a, b); } template -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Very simple long multiplication, only usable for small numbers of limb_type's // but that's the typical use case for this type anyway: @@ -1106,12 +1099,12 @@ inline void eval_multiply(cpp_int_backend& result, c result.sign(a.sign() != b.sign()); } template -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a) +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, a); } template -inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const limb_type& val) +inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(!val) { @@ -1140,12 +1133,12 @@ inline void eval_multiply(cpp_int_backend& result, c result.normalize(); } template -inline void eval_multiply(cpp_int_backend& result, const limb_type& val) +inline void eval_multiply(cpp_int_backend& result, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, val); } template -inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const signed_limb_type& val) +inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(val > 0) eval_multiply(result, a, static_cast(val)); @@ -1156,12 +1149,12 @@ inline void eval_multiply(cpp_int_backend& result, c } } template -inline void eval_multiply(cpp_int_backend& result, const signed_limb_type& val) +inline void eval_multiply(cpp_int_backend& result, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, val); } template -void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) +void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) BOOST_NOEXCEPT_IF(boost::is_void::value) { if((result == &x) || (&r == &x)) { @@ -1428,7 +1421,7 @@ void divide_unsigned_helper(cpp_int_backend* result, } template -void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) +void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) BOOST_NOEXCEPT_IF(boost::is_void::value) { if((result == &x) || (&r == &x)) { @@ -1571,20 +1564,20 @@ void divide_unsigned_helper(cpp_int_backend* result, } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { cpp_int_backend r; divide_unsigned_helper(&result, a, b, r); result.sign(a.sign() != b.sign()); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { cpp_int_backend r; divide_unsigned_helper(&result, a, b, r); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { cpp_int_backend r; divide_unsigned_helper(&result, a, std::abs(b), r); @@ -1592,65 +1585,65 @@ inline void eval_divide(cpp_int_backend& result, con result.negate(); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { // There is no in place divide: cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_divide(cpp_int_backend& result, limb_type b) +inline void eval_divide(cpp_int_backend& result, limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) { // There is no in place divide: cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_divide(cpp_int_backend& result, signed_limb_type b) +inline void eval_divide(cpp_int_backend& result, signed_limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) { // There is no in place divide: cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { divide_unsigned_helper(static_cast* >(0), a, b, result); result.sign(a.sign()); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) { divide_unsigned_helper(static_cast* >(0), a, b, result); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) { divide_unsigned_helper(static_cast* >(0), a, static_cast(std::abs(b)), result); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { // There is no in place divide: cpp_int_backend a(result); eval_modulus(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, limb_type b) +inline void eval_modulus(cpp_int_backend& result, limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) { // There is no in place divide: cpp_int_backend a(result); eval_modulus(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, signed_limb_type b) +inline void eval_modulus(cpp_int_backend& result, signed_limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) { // There is no in place divide: cpp_int_backend a(result); eval_modulus(result, a, b); } template -void bitwise_op(cpp_int_backend& result, const cpp_int_backend& o, Op op) +void bitwise_op(cpp_int_backend& result, const cpp_int_backend& o, Op op) BOOST_NOEXCEPT { // // There are 4 cases: @@ -1775,70 +1768,27 @@ void bitwise_op(cpp_int_backend& result, const cpp_i result.normalize(); } -struct bit_and{ limb_type operator()(limb_type a, limb_type b)const{ return a & b; } }; -struct bit_or{ limb_type operator()(limb_type a, limb_type b)const{ return a | b; } }; -struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const{ return a ^ b; } }; +struct bit_and{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a & b; } }; +struct bit_or { limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a | b; } }; +struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a ^ b; } }; template -inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o)BOOST_NOEXCEPT { bitwise_op(result, o, bit_and()); } -#if 0 template -inline void eval_bitwise_and(cpp_int_backend& result, limb_type o) -{ - result.data()[cpp_int_backend::limb_count - 1] &= o; - for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) - result.data()[i] = 0; -} -template -inline void eval_bitwise_and(cpp_int_backend& result, signed_limb_type o) -{ - result.data()[cpp_int_backend::limb_count - 1] &= o; - limb_type mask = o < 0 ? cpp_int_backend::max_limb_value : 0; - for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) - result.data()[i] &= mask; -} -template -inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) -{ - for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count; ++i) - result.data()[i] |= o.data()[i]; -} -template -inline void eval_bitwise_or(cpp_int_backend& result, limb_type o) -{ - result.data()[cpp_int_backend::limb_count - 1] |= o; -} -#endif -template -inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { bitwise_op(result, o, bit_or()); } template -inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { bitwise_op(result, o, bit_xor()); } -#if 0 template -inline void eval_bitwise_xor(cpp_int_backend& result, limb_type o) -{ - result.data()[cpp_int_backend::limb_count - 1] ^= o; -} -template -inline void eval_bitwise_xor(cpp_int_backend& result, signed_limb_type o) -{ - result.data()[cpp_int_backend::limb_count - 1] ^= o; - limb_type mask = o < 0 ? cpp_int_backend::max_limb_value : 0; - for(typename cpp_int_backend::data_type::size_type i = 0; i < cpp_int_backend::limb_count - 1; ++i) - result.data()[i] ^= mask; -} -#endif -template -inline void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) +inline void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Increment and negate: result = o; @@ -1846,7 +1796,7 @@ inline void eval_complement(cpp_int_backend& result, result.negate(); } template -inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) +inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT { if(!s) return; @@ -1922,7 +1872,7 @@ inline void eval_left_shift(cpp_int_backend& result, doub } } template -inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) +inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(!s) return; @@ -1979,7 +1929,7 @@ inline void eval_left_shift(cpp_int_backend& result, } } template -inline void eval_right_shift(cpp_int_backend& result, double_limb_type s) +inline void eval_right_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(!s) return; @@ -2022,18 +1972,18 @@ inline void eval_right_shift(cpp_int_backend& result } template -inline Integer negate_integer(Integer i, const mpl::true_&) +inline Integer negate_integer(Integer i, const mpl::true_&) BOOST_NOEXCEPT { return -i; } template -inline Integer negate_integer(Integer i, const mpl::false_&) +inline Integer negate_integer(Integer i, const mpl::false_&) BOOST_NOEXCEPT { return ~--i; } template -inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) +inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) BOOST_NOEXCEPT { *result = static_cast(backend.limbs()[0]); unsigned shift = cpp_int_backend::limb_bits; @@ -2049,7 +1999,7 @@ inline typename enable_if, void>::type eval_convert_to(R* result, } template -inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) +inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) BOOST_NOEXCEPT { typename cpp_int_backend::const_limb_pointer p = backend.limbs(); unsigned shift = cpp_int_backend::limb_bits; @@ -2064,17 +2014,17 @@ inline typename enable_if, void>::type eval_convert_to(R* r } template -inline bool eval_is_zero(const cpp_int_backend& val) +inline bool eval_is_zero(const cpp_int_backend& val) BOOST_NOEXCEPT { return (val.size() == 1) && (val.limbs()[0] == 0); } template -inline int eval_get_sign(const cpp_int_backend& val) +inline int eval_get_sign(const cpp_int_backend& val) BOOST_NOEXCEPT { return eval_is_zero(val) ? 0 : val.sign() ? -1 : 1; } template -inline void eval_abs(cpp_int_backend& result, const cpp_int_backend& val) +inline void eval_abs(cpp_int_backend& result, const cpp_int_backend& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { result = val; result.sign(false); @@ -2084,7 +2034,7 @@ inline void eval_abs(cpp_int_backend& result, const // Get the location of the least-significant-bit: // template -inline unsigned eval_lsb(const cpp_int_backend& a) +inline unsigned eval_lsb(const cpp_int_backend& a) BOOST_NOEXCEPT { BOOST_ASSERT(eval_get_sign(a) != 0); @@ -2109,7 +2059,7 @@ inline unsigned eval_lsb(const cpp_int_backend& a) } template -inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { int shift; @@ -2169,7 +2119,7 @@ inline void eval_gcd(cpp_int_backend& result, const } template -inline bool eval_bit_test(const cpp_int_backend& val, unsigned index) +inline bool eval_bit_test(const cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT { unsigned offset = index / cpp_int_backend::limb_bits; unsigned shift = index % cpp_int_backend::limb_bits; @@ -2180,7 +2130,7 @@ inline bool eval_bit_test(const cpp_int_backend& val } template -inline void eval_bit_set(cpp_int_backend& val, unsigned index) +inline void eval_bit_set(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT_IF(boost::is_void::value) { unsigned offset = index / cpp_int_backend::limb_bits; unsigned shift = index % cpp_int_backend::limb_bits; @@ -2198,7 +2148,7 @@ inline void eval_bit_set(cpp_int_backend& val, unsig } template -inline void eval_bit_unset(cpp_int_backend& val, unsigned index) +inline void eval_bit_unset(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT { unsigned offset = index / cpp_int_backend::limb_bits; unsigned shift = index % cpp_int_backend::limb_bits; @@ -2210,7 +2160,7 @@ inline void eval_bit_unset(cpp_int_backend& val, uns } template -inline void eval_bit_flip(cpp_int_backend& val, unsigned index) +inline void eval_bit_flip(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT_IF(boost::is_void::value) { unsigned offset = index / cpp_int_backend::limb_bits; unsigned shift = index % cpp_int_backend::limb_bits; @@ -2229,7 +2179,7 @@ inline void eval_bit_flip(cpp_int_backend& val, unsi } template -inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { cpp_int_backend t; eval_gcd(t, a, b); @@ -2249,7 +2199,7 @@ inline void eval_lcm(cpp_int_backend& result, const template inline void eval_qr(const cpp_int_backend& x, const cpp_int_backend& y, - cpp_int_backend& q, cpp_int_backend& r) + cpp_int_backend& q, cpp_int_backend& r) BOOST_NOEXCEPT_IF(boost::is_void::value) { divide_unsigned_helper(&q, x, y, r); q.sign(x.sign() != y.sign()); @@ -2257,7 +2207,7 @@ inline void eval_qr(const cpp_int_backend& x, const } template -inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) +inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if((sizeof(Integer) <= sizeof(limb_type)) || (val <= (std::numeric_limits::max)())) { @@ -2271,7 +2221,7 @@ inline typename enable_if, Integer>::type eval_integer_modu } } template -inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) +inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) BOOST_NOEXCEPT_IF(boost::is_void::value) { typedef typename make_unsigned::type unsigned_type; return eval_integer_modulus(x, static_cast(std::abs(val))); diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index db19d5a7..54950bc1 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -37,14 +37,15 @@ class mp_number typedef mp_number self_type; public: typedef Backend backend_type; - mp_number(){} - mp_number(const mp_number& e) : m_backend(e.m_backend){} + BOOST_CONSTEXPR mp_number() BOOST_NOEXCEPT_IF(noexcept(Backend())) {} + mp_number(const mp_number& e) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(e.m_backend){} template mp_number(V v, typename enable_if, is_same, is_convertible > >::type* = 0) { m_backend = canonical_value(v); } - mp_number(const mp_number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} + mp_number(const mp_number& e, unsigned digits10) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval()), 0u))) + : m_backend(e.m_backend, digits10){} /* // // This conflicts with component based initialization (for rational and complex types) @@ -58,10 +59,10 @@ public: } */ template - mp_number(const mp_number& val) : m_backend(val.m_backend) {} + mp_number(const mp_number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} template - mp_number(const mp_number& val, typename enable_if >::type* = 0) + mp_number(const mp_number& val, typename enable_if >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) { m_backend = val.backend(); } @@ -88,6 +89,7 @@ public: template mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) + BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(v){} template @@ -98,7 +100,7 @@ public: return *this; } - mp_number& operator=(const mp_number& e) + mp_number& operator=(const mp_number& e) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = e.m_backend; return *this; @@ -106,7 +108,7 @@ public: template typename enable_if, is_same, is_convertible >, mp_number& >::type - operator=(const V& v) + operator=(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval::type>())) { m_backend = canonical_value(v); return *this; @@ -114,14 +116,14 @@ public: template typename enable_if, mpl::not_, is_same, is_convertible > > >, mp_number& >::type - operator=(const V& v) + operator=(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = v; return *this; } template - mp_number& operator=(const mp_number& v) + mp_number& operator=(const mp_number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = v.backend(); return *this; @@ -129,7 +131,7 @@ public: template typename enable_if, mp_number& >::type - operator=(const mp_number& v) + operator=(const mp_number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = v.backend(); return *this; @@ -153,8 +155,8 @@ public: } #ifndef BOOST_NO_RVALUE_REFERENCES - mp_number(mp_number&& r) : m_backend(static_cast(r.m_backend)){} - mp_number& operator=(mp_number&& r) + mp_number(mp_number&& r) BOOST_NOEXCEPT : m_backend(static_cast(r.m_backend)){} + mp_number& operator=(mp_number&& r) BOOST_NOEXCEPT { m_backend.swap(r.m_backend); return *this; @@ -316,7 +318,7 @@ public: using default_ops::eval_increment; self_type temp(*this); eval_increment(m_backend); - return temp; + return BOOST_MP_MOVE(temp); } mp_number operator--(int) @@ -324,7 +326,7 @@ public: using default_ops::eval_decrement; self_type temp(*this); eval_decrement(m_backend); - return temp; + return BOOST_MP_MOVE(temp); } template @@ -491,7 +493,7 @@ public: // // swap: // - void swap(self_type& other) + void swap(self_type& other) BOOST_NOEXCEPT { m_backend.swap(other.backend()); } @@ -526,7 +528,7 @@ public: // // Default precision: // - static unsigned default_precision() + static unsigned default_precision() BOOST_NOEXCEPT { return Backend::default_precision(); } @@ -534,7 +536,7 @@ public: { Backend::default_precision(digits10); } - unsigned precision()const + unsigned precision()const BOOST_NOEXCEPT { return m_backend.precision(); } @@ -546,6 +548,7 @@ public: // Comparison: // int compare(const mp_number& o)const + BOOST_NOEXCEPT_IF(noexcept(std::declval().compare(std::declval()))) { return m_backend.compare(o.m_backend); } @@ -557,11 +560,11 @@ public: return eval_get_sign(m_backend); return m_backend.compare(canonical_value(o)); } - Backend& backend() + Backend& backend() BOOST_NOEXCEPT { return m_backend; } - const Backend& backend()const + const Backend& backend()const BOOST_NOEXCEPT { return m_backend; } @@ -603,7 +606,7 @@ private: BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); } template - void check_shift_range(V, const mpl::false_&, const mpl::false_&){} + void check_shift_range(V, const mpl::false_&, const mpl::false_&) BOOST_NOEXCEPT{} template void do_assign(const Exp& e, const detail::add_immediates&) @@ -611,15 +614,6 @@ private: using default_ops::eval_add; eval_add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } -/* - template - void do_assign(const Exp& e, const detail::add_and_negate_immediates&) - { - using default_ops::eval_add; - eval_add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); - m_backend.negate(); - } -*/ template void do_assign(const Exp& e, const detail::subtract_immediates&) { @@ -1469,23 +1463,23 @@ private: // Tests if the expression contains a reference to *this: template - bool contains_self(const Exp& e)const BOOST_NOEXCEPT + BOOST_CONSTEXPR bool contains_self(const Exp& e)const BOOST_NOEXCEPT { return contains_self(e, typename Exp::arity()); } template - bool contains_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT + BOOST_CONSTEXPR bool contains_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT { return is_realy_self(e.value()); } template - bool contains_self(const Exp& e, mpl::int_<1> const&)const BOOST_NOEXCEPT + BOOST_CONSTEXPR bool contains_self(const Exp& e, mpl::int_<1> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child_type; return contains_self(e.left(), typename child_type::arity()); } template - bool contains_self(const Exp& e, mpl::int_<2> const&)const BOOST_NOEXCEPT + BOOST_CONSTEXPR bool contains_self(const Exp& e, mpl::int_<2> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child0_type; typedef typename Exp::right_type child1_type; @@ -1493,7 +1487,7 @@ private: || contains_self(e.right(), typename child1_type::arity()); } template - bool contains_self(const Exp& e, mpl::int_<3> const&)const BOOST_NOEXCEPT + BOOST_CONSTEXPR bool contains_self(const Exp& e, mpl::int_<3> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child0_type; typedef typename Exp::middle_type child1_type; @@ -1505,12 +1499,12 @@ private: // Test if the expression is a reference to *this: template - bool is_self(const Exp& e)const BOOST_NOEXCEPT + BOOST_CONSTEXPR bool is_self(const Exp& e)const BOOST_NOEXCEPT { return is_self(e, typename Exp::arity()); } template - bool is_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT + BOOST_CONSTEXPR bool is_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT { return is_realy_self(e.value()); } @@ -1524,18 +1518,18 @@ private: BOOST_CONSTEXPR bool is_realy_self(const Val&)const BOOST_NOEXCEPT{ return false; } BOOST_CONSTEXPR bool is_realy_self(const self_type& v)const BOOST_NOEXCEPT{ return &v == this; } - static const Backend& canonical_value(const self_type& v) BOOST_NOEXCEPT { return v.m_backend; } + static BOOST_CONSTEXPR const Backend& canonical_value(const self_type& v) BOOST_NOEXCEPT { return v.m_backend; } template - static typename detail::canonical::type canonical_value(const V& v) BOOST_NOEXCEPT { return static_cast::type>(v); } + static BOOST_CONSTEXPR typename detail::canonical::type canonical_value(const V& v) BOOST_NOEXCEPT { return static_cast::type>(v); } static typename detail::canonical::type canonical_value(const std::string& v) BOOST_NOEXCEPT { return v.c_str(); } - static const Backend& function_arg_value(const self_type& v) BOOST_NOEXCEPT { return v.backend(); } + static BOOST_CONSTEXPR const Backend& function_arg_value(const self_type& v) BOOST_NOEXCEPT { return v.backend(); } template - static const V& function_arg_value(const V& v) BOOST_NOEXCEPT { return v; } + static BOOST_CONSTEXPR const V& function_arg_value(const V& v) BOOST_NOEXCEPT { return v; } template static const A1& function_arg_value(const detail::mp_exp& exp) BOOST_NOEXCEPT { return exp.value(); } template - static const Backend& function_arg_value(const detail::mp_exp, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value().backend(); } + static BOOST_CONSTEXPR const Backend& function_arg_value(const detail::mp_exp, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value().backend(); } Backend m_backend; }; diff --git a/performance/Jamfile.v2 b/performance/Jamfile.v2 index be2cc779..66d35e7f 100644 --- a/performance/Jamfile.v2 +++ b/performance/Jamfile.v2 @@ -53,7 +53,16 @@ exe performance_test : performance_test.cpp /boost/system//boost_system TEST_CPP_INT ; -exe sf_performance : sf_performance.cpp /boost/system//boost_system /boost/system//boost_chrono /boost/system//boost_thread +exe miller_rabin_performance : miller_rabin_performance.cpp /boost/system//boost_system /boost/chrono//boost_chrono + : release + [ check-target-builds ../config//has_gmp : TEST_MPF TEST_MPZ gmp : ] + [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr : ] + #[ check-target-builds ../config//has_tommath : TEST_TOMMATH $(TOMMATH) : ] + TEST_CPP_DEC_FLOAT + TEST_CPP_INT + ; + +exe sf_performance : sf_performance.cpp /boost/system//boost_system /boost/chrono//boost_chrono /boost/thread//boost_thread : release [ check-target-builds ../config//has_gmp : TEST_MPF TEST_MPZ gmp : ] [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr : ] @@ -105,5 +114,8 @@ exe linpack_benchmark_double : obj_linpack_benchmark_double f2c : release ; -install . : performance_test sf_performance linpack_benchmark_double linpack_benchmark_cpp_float linpack_benchmark_mpf linpack_benchmark_mpfr ; +install miller_rabin_install : miller_rabin_performance : . ; +install performance_test_install : performance_test : . ; +install sf_performance_install : sf_performance : . ; +install . : linpack_benchmark_double linpack_benchmark_cpp_float linpack_benchmark_mpf linpack_benchmark_mpfr ; diff --git a/performance/miller_rabin_performance.cpp b/performance/miller_rabin_performance.cpp index e0c32dc3..458c14b2 100644 --- a/performance/miller_rabin_performance.cpp +++ b/performance/miller_rabin_performance.cpp @@ -138,11 +138,10 @@ int main() #ifdef TEST_CPP_INT test_miller_rabin, false> >("cpp_int (no Expression templates)"); test_miller_rabin("cpp_int"); - test_miller_rabin, false> >("cpp_int (64-bit cache)"); - test_miller_rabin, false> >("cpp_int (256-bit cache)"); - test_miller_rabin, false> >("cpp_int (512-bit cache)"); - test_miller_rabin, false> >("cpp_int (1024-bit cache)"); - test_miller_rabin, false> >("mp_int1024_t (no Expression templates)"); + test_miller_rabin > >("cpp_int (64-bit cache)"); + test_miller_rabin > >("cpp_int (256-bit cache)"); + test_miller_rabin > >("cpp_int (512-bit cache)"); + test_miller_rabin > >("cpp_int (1024-bit cache)"); test_miller_rabin("mp_int1024_t"); #endif #ifdef TEST_MPZ diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index f748a5a9..2e66acd9 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -273,8 +273,12 @@ int main() mpfr::mpreal::set_default_prec(50 * 1000L / 301L); #endif #ifdef TEST_MPFR +#if MPFR_VERSION, 1); +#else time_proc("mpfr_float_50", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); #endif +#endif #ifdef TEST_MPF time_proc("mpf_float_50", test_bessel, 3); time_proc("mpf_float_50 (no expression templates", test_bessel, false> >, 3); From f4a922e32563bde9c977d89c8569ea391a67052e Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 3 Jul 2012 18:18:08 +0000 Subject: [PATCH 197/256] Fix some asserts and comments, plus one C++11 issue. [SVN r79250] --- example/floating_point_examples.cpp | 2 +- include/boost/multiprecision/cpp_int.hpp | 8 ++++++-- include/boost/multiprecision/mp_number.hpp | 2 +- 3 files changed, 8 insertions(+), 4 deletions(-) diff --git a/example/floating_point_examples.cpp b/example/floating_point_examples.cpp index e1c9b97a..37761d94 100644 --- a/example/floating_point_examples.cpp +++ b/example/floating_point_examples.cpp @@ -83,7 +83,7 @@ Yields the output: [pre 9.822663964796047e-001] -Now lets implement the function again, but this time using the multiprecision type +Now let's implement the function again, but this time using the multiprecision type `cpp_dec_float_50` as the argument type: */ diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index d50bf068..bb4afa86 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1072,6 +1072,10 @@ inline void eval_multiply(cpp_int_backend& result, c result.resize(as + bs); typename cpp_int_backend::limb_pointer pr = result.limbs(); + static const double_limb_type limb_max = ~static_cast(0u); + static const double_limb_type double_limb_max = ~static_cast(0u); + BOOST_STATIC_ASSERT(double_limb_max - 2 * limb_max >= limb_max * limb_max); + double_limb_type carry = 0; std::memset(pr, 0, result.size() * sizeof(limb_type)); for(unsigned i = 0; i < as; ++i) @@ -1080,9 +1084,9 @@ inline void eval_multiply(cpp_int_backend& result, c for(unsigned j = 0; j < inner_limit; ++j) { BOOST_ASSERT(i+j < result.size()); - BOOST_ASSERT((std::numeric_limits::max)() - carry > static_cast(cpp_int_backend::max_limb_value) * static_cast(cpp_int_backend::max_limb_value)); + BOOST_ASSERT(!std::numeric_limits::is_specialized || ((std::numeric_limits::max)() - carry > static_cast(cpp_int_backend::max_limb_value) * static_cast(cpp_int_backend::max_limb_value))); carry += static_cast(pa[i]) * static_cast(pb[j]); - BOOST_ASSERT((std::numeric_limits::max)() - carry >= pr[i+j]); + BOOST_ASSERT(!std::numeric_limits::is_specialized || ((std::numeric_limits::max)() - carry >= pr[i+j])); carry += pr[i + j]; pr[i + j] = static_cast(carry); carry >>= cpp_int_backend::limb_bits; diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 54950bc1..8c84a319 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -44,7 +44,7 @@ public: { m_backend = canonical_value(v); } - mp_number(const mp_number& e, unsigned digits10) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval()), 0u))) + mp_number(const mp_number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} /* // From 19ee491c558006eb102adb08dde3e6967497bac8 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 7 Jul 2012 11:16:28 +0000 Subject: [PATCH 198/256] Add noexcept support/markup where possible. [SVN r79331] --- doc/multiprecision.qbk | 27 +- .../concepts/mp_number_archetypes.hpp | 9 +- .../boost/multiprecision/cpp_dec_float.hpp | 236 ++++++++-------- include/boost/multiprecision/cpp_int.hpp | 37 ++- .../multiprecision/detail/mp_number_base.hpp | 24 +- include/boost/multiprecision/gmp.hpp | 204 ++++++++------ include/boost/multiprecision/mpfr.hpp | 266 +++++++++--------- .../boost/multiprecision/rational_adapter.hpp | 10 + include/boost/multiprecision/tommath.hpp | 94 ++++++- test/test.hpp | 6 +- test/test_arithmetic.cpp | 54 +++- test/test_cpp_int.cpp | 2 + 12 files changed, 586 insertions(+), 383 deletions(-) diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 97064c3d..284b2451 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -393,7 +393,9 @@ existing code that uses [gmp]. * Formatted IO for this type does not support octal or hexadecimal notation for negative values, as a result performing formatted output on this type when the argument is negative and either of the flags `std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. -* Division by zero is handled by the [gmp] library - it will trigger a division by zero signal. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid integer. +* Division by zero results in a `std::runtime_error` being thrown. * Although this type is a wrapper around [gmp] it will work equally well with [mpir]. Indeed use of [mpir] is recommended on Win32. * This backend supports rvalue-references and is move-aware, making instantiations of `mp_number` on this backend move aware. @@ -429,7 +431,9 @@ operator`~` is deliberately not implemented for this type. * Formatted IO for this type does not support octal or hexadecimal notation for negative values, as a result performing formatted output on this type when the argument is negative and either of the flags `std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. -* Division by zero will result in a hardware signal being raised by [tommath]. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid integer. +* Division by zero results in a `std::runtime_error` being thrown. [h5 Example:] @@ -506,6 +510,7 @@ Things you should know when using this type: * Default constructed `gmp_float`s have the value zero (this is the [gmp] library's default behavior). * No changes are made to the [gmp] library's global settings, so this type can be safely mixed with existing [gmp] code. +* This backend supports rvalue-references and is move-aware, making instantiations of `mp_number` on this backend move aware. * It is not possible to round-trip objects of this type to and from a string and get back exactly the same value. This appears to be a limitation of [gmp]. * Since the underlying [gmp] types have no notion of infinities or NaN's, care should be taken @@ -515,6 +520,9 @@ library (in testing, converting a number with an excessively large or small expo to a string caused [gmp] to segfault). * This type can equally be used with [mpir] as the underlying implementation - indeed that is the recommended option on Win32. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. +* Division by zero results in a `std::runtime_error` being thrown. [h5 [gmp] example:] @@ -568,6 +576,9 @@ Things you should know when using this type: [mpfr] or [gmp] code. * The code can equally use [mpir] in place of [gmp] - indeed that is the preferred option on Win32. * This backend supports rvalue-references and is move-aware, making instantiations of `mp_number` on this backend move aware. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. +* Division by zero results in an infinity. [h5 [mpfr] example:] @@ -613,6 +624,8 @@ and a NaN is generated for any mathematically undefined operation. * Any `mp_number` instantiated on this type, is convertible to any other `mp_number` instantiated on this type - for example you can convert from `mp_number >` to `mp_number >`. Narrowing conversions are truncating. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. [h5 cpp_dec_float example:] @@ -711,7 +724,9 @@ It's also possible to access the underlying `mpq_t` via the `data()` member func Things you should know when using this type: * Default constructed `mpq_rational`s have the value zero (this is the [gmp] default behavior). -* Division by zero results in a hardware exception inside the [gmp] library. +* Division by zero results in a `std::runtime_error` being thrown. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be +interpreted as a valid rational number. * No changes are made to the [gmp] library's global settings, so this type can coexist with existing [gmp] code. * The code can equally be used with [mpir] as the underlying library - indeed that is the preferred option on Win32. @@ -753,6 +768,8 @@ Things you should know when using this type: * Default constructed `cpp_rational`s have the value zero. * Division by zero results in a `std::rumtime_error` being thrown. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be +interpreted as a valid rational number. [h5 Example:] @@ -788,7 +805,9 @@ which return the numerator and denominator of the number. Things you should know when using this type: * Default constructed `tom_rational`s have the value zero (this the inherited Boost.Rational behavior). -* Division by zero results in a `boost::bad_rational` exception being thrown (see the rational number library's docs for more information). +* Division by zero results in a `std::runtime_error` being thrown. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be +interpreted as a valid rational number. * No changes are made to [tommath]'s global state, so this type can safely coexist with other [tommath] code. * Performance of this type has been found to be pretty poor - this need further investigation - but it appears that Boost.Rational needs some improvement in this area. diff --git a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp index e82f69ac..d10449cc 100644 --- a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp @@ -67,7 +67,14 @@ struct mp_number_backend_float_architype } mp_number_backend_float_architype& operator = (const char* s) { - m_value = boost::lexical_cast(s); + try + { + m_value = boost::lexical_cast(s); + } + catch(const std::exception&) + { + BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Unable to parse input string: \"") + s + std::string("\" as a valid floating point number."))); + } std::cout << "const char* Assignment (" << s << ")" << std::endl; return *this; } diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 5b6233fa..3110088a 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -90,7 +90,7 @@ private: // // Special values constructor: // - cpp_dec_float(fpclass_type c) : + cpp_dec_float(fpclass_type c) BOOST_NOEXCEPT : data(), exp (static_cast(0)), neg (false), @@ -129,7 +129,7 @@ private: public: // Constructors - cpp_dec_float() : + cpp_dec_float() BOOST_NOEXCEPT : data(), exp (static_cast(0)), neg (false), @@ -147,7 +147,7 @@ public: } template - cpp_dec_float(I i, typename enable_if >::type* = 0) : + cpp_dec_float(I i, typename enable_if >::type* = 0) BOOST_NOEXCEPT : data(), exp (static_cast(0)), neg (false), @@ -158,7 +158,7 @@ public: } template - cpp_dec_float(I i, typename enable_if >::type* = 0) : + cpp_dec_float(I i, typename enable_if >::type* = 0) BOOST_NOEXCEPT : data(), exp (static_cast(0)), neg (false), @@ -174,7 +174,7 @@ public: from_unsigned_long_long(i); } - cpp_dec_float(const cpp_dec_float& f) : + cpp_dec_float(const cpp_dec_float& f) BOOST_NOEXCEPT : data (f.data), exp (f.exp), neg (f.neg), @@ -182,7 +182,7 @@ public: prec_elem(f.prec_elem) { } template - cpp_dec_float(const cpp_dec_float& f) : + cpp_dec_float(const cpp_dec_float& f) BOOST_NOEXCEPT : exp (f.exp), neg (f.neg), fpclass (static_cast(static_cast(f.fpclass))), @@ -194,7 +194,7 @@ public: } template - cpp_dec_float(const F val, typename enable_if >::type* = 0): + cpp_dec_float(const F val, typename enable_if >::type* = 0) BOOST_NOEXCEPT : data(), exp (static_cast(0)), neg (false), @@ -204,22 +204,22 @@ public: *this = val; } - cpp_dec_float(const double val, long long exponent); + cpp_dec_float(const double val, long long exponent) BOOST_NOEXCEPT; // Specific special values. - static const cpp_dec_float& nan() + static const cpp_dec_float& nan() BOOST_NOEXCEPT { static const cpp_dec_float val(cpp_dec_float_NaN); init.do_nothing(); return val; } - static const cpp_dec_float& inf() + static const cpp_dec_float& inf() BOOST_NOEXCEPT { static const cpp_dec_float val(cpp_dec_float_inf); init.do_nothing(); return val; } - static const cpp_dec_float& (max)() + static const cpp_dec_float& (max)() BOOST_NOEXCEPT { init.do_nothing(); static bool init = false; @@ -234,7 +234,7 @@ public: return val_max; } - static const cpp_dec_float& (min)() + static const cpp_dec_float& (min)() BOOST_NOEXCEPT { init.do_nothing(); static bool init = false; @@ -246,73 +246,73 @@ public: } return val_min; } - static const cpp_dec_float& zero() + static const cpp_dec_float& zero() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val(static_cast(0u)); return val; } - static const cpp_dec_float& one() + static const cpp_dec_float& one() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val(static_cast(1u)); return val; } - static const cpp_dec_float& two() + static const cpp_dec_float& two() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val(static_cast(2u)); return val; } - static const cpp_dec_float& half() + static const cpp_dec_float& half() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val(0.5L); return val; } - static const cpp_dec_float& double_min() + static const cpp_dec_float& double_min() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val(static_cast((std::numeric_limits::min)())); return val; } - static const cpp_dec_float& double_max() + static const cpp_dec_float& double_max() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val(static_cast((std::numeric_limits::max)())); return val; } - static const cpp_dec_float& long_double_min() + static const cpp_dec_float& long_double_min() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val((std::numeric_limits::min)()); return val; } - static const cpp_dec_float& long_double_max() + static const cpp_dec_float& long_double_max() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val((std::numeric_limits::max)()); return val; } - static const cpp_dec_float& long_long_max() + static const cpp_dec_float& long_long_max() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val((std::numeric_limits::max)()); return val; } - static const cpp_dec_float& long_long_min() + static const cpp_dec_float& long_long_min() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val((std::numeric_limits::min)()); return val; } - static const cpp_dec_float& ulong_long_max() + static const cpp_dec_float& ulong_long_max() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val((std::numeric_limits::max)()); return val; } - static const cpp_dec_float& eps() + static const cpp_dec_float& eps() BOOST_NOEXCEPT { init.do_nothing(); static cpp_dec_float val(1.0, 1 - (int)Digits10); @@ -320,7 +320,7 @@ public: } // Basic operations. - cpp_dec_float& operator= (const cpp_dec_float& v) + cpp_dec_float& operator= (const cpp_dec_float& v) BOOST_NOEXCEPT { data = v.data; exp = v.exp; @@ -330,7 +330,7 @@ public: return *this; } template - cpp_dec_float& operator=(const cpp_dec_float& f) + cpp_dec_float& operator=(const cpp_dec_float& f) BOOST_NOEXCEPT { exp = f.exp; neg = f.neg; @@ -339,7 +339,7 @@ public: precision((std::min)(f.prec_elem, prec_elem)); return *this; } - cpp_dec_float& operator= (long long v) + cpp_dec_float& operator= (long long v) BOOST_NOEXCEPT { if(v < 0) { @@ -350,82 +350,82 @@ public: from_unsigned_long_long(v); return *this; } - cpp_dec_float& operator= (unsigned long long v) + cpp_dec_float& operator= (unsigned long long v) BOOST_NOEXCEPT { from_unsigned_long_long(v); return *this; } - cpp_dec_float& operator= (long double v); + cpp_dec_float& operator= (long double v) BOOST_NOEXCEPT; cpp_dec_float& operator= (const char* v) { rd_string(v); return *this; } - cpp_dec_float& operator+=(const cpp_dec_float& v); - cpp_dec_float& operator-=(const cpp_dec_float& v); - cpp_dec_float& operator*=(const cpp_dec_float& v); - cpp_dec_float& operator/=(const cpp_dec_float& v); + cpp_dec_float& operator+=(const cpp_dec_float& v) BOOST_NOEXCEPT; + cpp_dec_float& operator-=(const cpp_dec_float& v) BOOST_NOEXCEPT; + cpp_dec_float& operator*=(const cpp_dec_float& v) BOOST_NOEXCEPT; + cpp_dec_float& operator/=(const cpp_dec_float& v) BOOST_NOEXCEPT; - cpp_dec_float& add_unsigned_long_long(const unsigned long long n) + cpp_dec_float& add_unsigned_long_long(const unsigned long long n) BOOST_NOEXCEPT { cpp_dec_float t; t.from_unsigned_long_long(n); return *this += t; } - cpp_dec_float& sub_unsigned_long_long(const unsigned long long n) + cpp_dec_float& sub_unsigned_long_long(const unsigned long long n) BOOST_NOEXCEPT { cpp_dec_float t; t.from_unsigned_long_long(n); return *this -= t; } - cpp_dec_float& mul_unsigned_long_long(const unsigned long long n); - cpp_dec_float& div_unsigned_long_long(const unsigned long long n); + cpp_dec_float& mul_unsigned_long_long(const unsigned long long n) BOOST_NOEXCEPT; + cpp_dec_float& div_unsigned_long_long(const unsigned long long n) BOOST_NOEXCEPT; // Elementary primitives. - cpp_dec_float& calculate_inv (void); - cpp_dec_float& calculate_sqrt(void); - void negate() + cpp_dec_float& calculate_inv (void) BOOST_NOEXCEPT; + cpp_dec_float& calculate_sqrt(void) BOOST_NOEXCEPT; + void negate() BOOST_NOEXCEPT { if(!iszero()) neg = !neg; } // Comparison functions - bool isnan (void) const { return (fpclass == cpp_dec_float_NaN); } - bool isinf (void) const { return (fpclass == cpp_dec_float_inf); } - bool isfinite(void) const { return (fpclass == cpp_dec_float_finite); } + bool isnan (void) const BOOST_NOEXCEPT { return (fpclass == cpp_dec_float_NaN); } + bool isinf (void) const BOOST_NOEXCEPT { return (fpclass == cpp_dec_float_inf); } + bool isfinite(void) const BOOST_NOEXCEPT { return (fpclass == cpp_dec_float_finite); } - bool iszero (void) const + bool iszero (void) const BOOST_NOEXCEPT { return ((fpclass == cpp_dec_float_finite) && (data[0u] == 0u)); } - bool isone (void) const; - bool isint (void) const; - bool isneg (void) const { return neg; } + bool isone (void) const BOOST_NOEXCEPT; + bool isint (void) const BOOST_NOEXCEPT; + bool isneg (void) const BOOST_NOEXCEPT { return neg; } // Operators pre-increment and pre-decrement - cpp_dec_float& operator++(void) + cpp_dec_float& operator++(void) BOOST_NOEXCEPT { return *this += one(); } - cpp_dec_float& operator--(void) + cpp_dec_float& operator--(void) BOOST_NOEXCEPT { return *this -= one(); } std::string str(boost::intmax_t digits, std::ios_base::fmtflags f)const; - int compare(const cpp_dec_float& v)const; + int compare(const cpp_dec_float& v)const BOOST_NOEXCEPT; template - int compare(const V& v)const + int compare(const V& v)const BOOST_NOEXCEPT { cpp_dec_float t; t = v; return compare(t); } - void swap(cpp_dec_float& v) + void swap(cpp_dec_float& v) BOOST_NOEXCEPT { data.swap(v.data); std::swap(exp, v.exp); @@ -434,13 +434,13 @@ public: std::swap(prec_elem, v.prec_elem); } - double extract_double (void) const; - long double extract_long_double (void) const; - signed long long extract_signed_long_long (void) const; - unsigned long long extract_unsigned_long_long(void) const; - void extract_parts (double& mantissa, boost::int64_t& exponent) const; - cpp_dec_float extract_integer_part (void) const; - void precision(const boost::int32_t prec_digits) + double extract_double (void) const BOOST_NOEXCEPT; + long double extract_long_double (void) const BOOST_NOEXCEPT; + signed long long extract_signed_long_long (void) const BOOST_NOEXCEPT; + unsigned long long extract_unsigned_long_long(void) const BOOST_NOEXCEPT; + void extract_parts (double& mantissa, boost::int64_t& exponent) const BOOST_NOEXCEPT; + cpp_dec_float extract_integer_part (void) const BOOST_NOEXCEPT; + void precision(const boost::int32_t prec_digits) BOOST_NOEXCEPT { if(prec_digits >= cpp_dec_float_total_digits10) { @@ -454,8 +454,8 @@ public: prec_elem = (std::min)(cpp_dec_float_elem_number, (std::max)(elems, static_cast(2))); } } - static cpp_dec_float pow2(long long i); - long long order()const + static cpp_dec_float pow2(long long i) BOOST_NOEXCEPT; + long long order()const BOOST_NOEXCEPT { const bool bo_order_is_zero = ((!isfinite()) || (data[0] == static_cast(0u))); // @@ -507,18 +507,18 @@ public: } private: - static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast(0u)); } - static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast(cpp_dec_float::cpp_dec_float_elem_mask - 1)); } - static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast('0')); } + static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) BOOST_NOEXCEPT { return (d != static_cast(0u)); } + static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) BOOST_NOEXCEPT { return (d != static_cast(cpp_dec_float::cpp_dec_float_elem_mask - 1)); } + static bool char_is_nonzero_predicate(const char& c) BOOST_NOEXCEPT { return (c != static_cast('0')); } - void from_unsigned_long_long(const unsigned long long u); + void from_unsigned_long_long(const unsigned long long u) BOOST_NOEXCEPT; - int cmp_data(const array_type& vd) const; + int cmp_data(const array_type& vd) const BOOST_NOEXCEPT; - static boost::uint32_t mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p); - static boost::uint32_t mul_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); - static boost::uint32_t div_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); + static boost::uint32_t mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p) BOOST_NOEXCEPT; + static boost::uint32_t mul_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) BOOST_NOEXCEPT; + static boost::uint32_t div_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) BOOST_NOEXCEPT; bool rd_string(const char* const s); @@ -559,7 +559,7 @@ const boost::int32_t cpp_dec_float::cpp_dec_float_elem_mask; template -cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float& v) +cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float& v) BOOST_NOEXCEPT { if(isnan()) { @@ -779,7 +779,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float } template -cpp_dec_float& cpp_dec_float::operator-=(const cpp_dec_float& v) +cpp_dec_float& cpp_dec_float::operator-=(const cpp_dec_float& v) BOOST_NOEXCEPT { // Use *this - v = -(-*this + v). negate(); @@ -789,7 +789,7 @@ cpp_dec_float& cpp_dec_float::operator-=(const cpp_dec_float } template -cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float& v) +cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float& v) BOOST_NOEXCEPT { // Evaluate the sign of the result. const bool b_result_is_neg = (neg != v.neg); @@ -882,7 +882,7 @@ cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float } template -cpp_dec_float& cpp_dec_float::operator/=(const cpp_dec_float& v) +cpp_dec_float& cpp_dec_float::operator/=(const cpp_dec_float& v) BOOST_NOEXCEPT { const bool u_and_v_are_finite_and_identical = ( isfinite() && (fpclass == v.fpclass) @@ -917,7 +917,7 @@ cpp_dec_float& cpp_dec_float::operator/=(const cpp_dec_float } template -cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const unsigned long long n) +cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const unsigned long long n) BOOST_NOEXCEPT { // Multiply *this with a constant unsigned long long. @@ -1012,7 +1012,7 @@ cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const u } template -cpp_dec_float& cpp_dec_float::div_unsigned_long_long(const unsigned long long n) +cpp_dec_float& cpp_dec_float::div_unsigned_long_long(const unsigned long long n) BOOST_NOEXCEPT { // Divide *this by a constant unsigned long long. @@ -1101,7 +1101,7 @@ cpp_dec_float& cpp_dec_float::div_unsigned_long_long(const u } template -cpp_dec_float& cpp_dec_float::calculate_inv() +cpp_dec_float& cpp_dec_float::calculate_inv() BOOST_NOEXCEPT { // Compute the inverse of *this. const bool b_neg = neg; @@ -1175,7 +1175,7 @@ cpp_dec_float& cpp_dec_float::calculate_inv() } template -cpp_dec_float& cpp_dec_float::calculate_sqrt(void) +cpp_dec_float& cpp_dec_float::calculate_sqrt(void) BOOST_NOEXCEPT { // Compute the square root of *this. @@ -1258,7 +1258,7 @@ cpp_dec_float& cpp_dec_float::calculate_sqrt(void) } template -int cpp_dec_float::cmp_data(const array_type& vd) const +int cpp_dec_float::cmp_data(const array_type& vd) const BOOST_NOEXCEPT { // Compare the data of *this with those of v. // Return +1 for *this > v @@ -1280,7 +1280,7 @@ int cpp_dec_float::cmp_data(const array_type& vd) const } template -int cpp_dec_float::compare(const cpp_dec_float& v) const +int cpp_dec_float::compare(const cpp_dec_float& v) const BOOST_NOEXCEPT { // Compare v with *this. // Return +1 for *this > v @@ -1358,7 +1358,7 @@ int cpp_dec_float::compare(const cpp_dec_float& v) const } template -bool cpp_dec_float::isone() const +bool cpp_dec_float::isone() const BOOST_NOEXCEPT { // Check if the value of *this is identically 1 or very close to 1. @@ -1382,7 +1382,7 @@ bool cpp_dec_float::isone() const } template -bool cpp_dec_float::isint() const +bool cpp_dec_float::isint() const BOOST_NOEXCEPT { if(fpclass != cpp_dec_float_finite) { return false; } @@ -1405,7 +1405,7 @@ bool cpp_dec_float::isint() const } template -void cpp_dec_float::extract_parts(double& mantissa, boost::int64_t& exponent) const +void cpp_dec_float::extract_parts(double& mantissa, boost::int64_t& exponent) const BOOST_NOEXCEPT { // Extract the approximate parts mantissa and base-10 exponent from the input cpp_dec_float value x. @@ -1438,7 +1438,7 @@ void cpp_dec_float::extract_parts(double& mantissa, boost::int64_t& ex } template -double cpp_dec_float::extract_double(void) const +double cpp_dec_float::extract_double(void) const BOOST_NOEXCEPT { // Returns the double conversion of a cpp_dec_float. @@ -1484,7 +1484,7 @@ double cpp_dec_float::extract_double(void) const } template -long double cpp_dec_float::extract_long_double(void) const +long double cpp_dec_float::extract_long_double(void) const BOOST_NOEXCEPT { // Returns the long double conversion of a cpp_dec_float. @@ -1530,7 +1530,7 @@ long double cpp_dec_float::extract_long_double(void) const } template -signed long long cpp_dec_float::extract_signed_long_long(void) const +signed long long cpp_dec_float::extract_signed_long_long(void) const BOOST_NOEXCEPT { // Extracts a signed long long from *this. // If (x > maximum of signed long long) or (x < minimum of signed long long), @@ -1575,7 +1575,7 @@ signed long long cpp_dec_float::extract_signed_long_long(void) const } template -unsigned long long cpp_dec_float::extract_unsigned_long_long(void) const +unsigned long long cpp_dec_float::extract_unsigned_long_long(void) const BOOST_NOEXCEPT { // Extracts an unsigned long long from *this. // If x exceeds the maximum of unsigned long long, @@ -1619,7 +1619,7 @@ unsigned long long cpp_dec_float::extract_unsigned_long_long(void) con } template -cpp_dec_float cpp_dec_float::extract_integer_part(void) const +cpp_dec_float cpp_dec_float::extract_integer_part(void) const BOOST_NOEXCEPT { // Compute the signed integer part of x. @@ -2079,7 +2079,7 @@ bool cpp_dec_float::rd_string(const char* const s) } template -cpp_dec_float::cpp_dec_float(const double mantissa, const long long exponent) +cpp_dec_float::cpp_dec_float(const double mantissa, const long long exponent) BOOST_NOEXCEPT : data (), exp (static_cast(0)), neg (false), @@ -2131,7 +2131,7 @@ cpp_dec_float::cpp_dec_float(const double mantissa, const long long ex } template -cpp_dec_float& cpp_dec_float::operator = (long double a) +cpp_dec_float& cpp_dec_float::operator = (long double a) BOOST_NOEXCEPT { // Christopher Kormanyos's original code used a cast to long long here, but that fails // when long double has more digits than a long long. @@ -2181,7 +2181,7 @@ cpp_dec_float& cpp_dec_float::operator = (long double a) } template -void cpp_dec_float::from_unsigned_long_long(const unsigned long long u) +void cpp_dec_float::from_unsigned_long_long(const unsigned long long u) BOOST_NOEXCEPT { std::fill(data.begin(), data.end(), static_cast(0u)); @@ -2213,7 +2213,7 @@ void cpp_dec_float::from_unsigned_long_long(const unsigned long long u } template -boost::uint32_t cpp_dec_float::mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p) +boost::uint32_t cpp_dec_float::mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p) BOOST_NOEXCEPT { // // There is a limit on how many limbs this algorithm can handle without dropping digits @@ -2242,7 +2242,7 @@ boost::uint32_t cpp_dec_float::mul_loop_uv(boost::uint32_t* const u, c } template -boost::uint32_t cpp_dec_float::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) +boost::uint32_t cpp_dec_float::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) BOOST_NOEXCEPT { boost::uint64_t carry = static_cast(0u); @@ -2258,7 +2258,7 @@ boost::uint32_t cpp_dec_float::mul_loop_n(boost::uint32_t* const u, bo } template -boost::uint32_t cpp_dec_float::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) +boost::uint32_t cpp_dec_float::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) BOOST_NOEXCEPT { boost::uint64_t prev = static_cast(0u); @@ -2273,7 +2273,7 @@ boost::uint32_t cpp_dec_float::div_loop_n(boost::uint32_t* const u, bo } template -cpp_dec_float cpp_dec_float::pow2(const long long p) +cpp_dec_float cpp_dec_float::pow2(const long long p) BOOST_NOEXCEPT { // Create a static const table of p^2 for -128 < p < +128. // Note: The size of this table must be odd-numbered and @@ -2563,49 +2563,49 @@ cpp_dec_float cpp_dec_float::pow2(const long long p) template -inline void eval_add(cpp_dec_float& result, const cpp_dec_float& o) +inline void eval_add(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT { result += o; } template -inline void eval_subtract(cpp_dec_float& result, const cpp_dec_float& o) +inline void eval_subtract(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT { result -= o; } template -inline void eval_multiply(cpp_dec_float& result, const cpp_dec_float& o) +inline void eval_multiply(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT { result *= o; } template -inline void eval_divide(cpp_dec_float& result, const cpp_dec_float& o) +inline void eval_divide(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT { result /= o; } template -inline void eval_add(cpp_dec_float& result, const unsigned long long& o) +inline void eval_add(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT { result.add_unsigned_long_long(o); } template -inline void eval_subtract(cpp_dec_float& result, const unsigned long long& o) +inline void eval_subtract(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT { result.sub_unsigned_long_long(o); } template -inline void eval_multiply(cpp_dec_float& result, const unsigned long long& o) +inline void eval_multiply(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT { result.mul_unsigned_long_long(o); } template -inline void eval_divide(cpp_dec_float& result, const unsigned long long& o) +inline void eval_divide(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT { result.div_unsigned_long_long(o); } template -inline void eval_add(cpp_dec_float& result, long long o) +inline void eval_add(cpp_dec_float& result, long long o) BOOST_NOEXCEPT { if(o < 0) result.sub_unsigned_long_long(-o); @@ -2613,7 +2613,7 @@ inline void eval_add(cpp_dec_float& result, long long o) result.add_unsigned_long_long(o); } template -inline void eval_subtract(cpp_dec_float& result, long long o) +inline void eval_subtract(cpp_dec_float& result, long long o) BOOST_NOEXCEPT { if(o < 0) result.add_unsigned_long_long(-o); @@ -2621,7 +2621,7 @@ inline void eval_subtract(cpp_dec_float& result, long long o) result.sub_unsigned_long_long(o); } template -inline void eval_multiply(cpp_dec_float& result, long long o) +inline void eval_multiply(cpp_dec_float& result, long long o) BOOST_NOEXCEPT { if(o < 0) { @@ -2632,7 +2632,7 @@ inline void eval_multiply(cpp_dec_float& result, long long o) result.mul_unsigned_long_long(o); } template -inline void eval_divide(cpp_dec_float& result, long long o) +inline void eval_divide(cpp_dec_float& result, long long o) BOOST_NOEXCEPT { if(o < 0) { @@ -2644,17 +2644,17 @@ inline void eval_divide(cpp_dec_float& result, long long o) } template -inline void eval_convert_to(unsigned long long* result, const cpp_dec_float& val) +inline void eval_convert_to(unsigned long long* result, const cpp_dec_float& val) BOOST_NOEXCEPT { *result = val.extract_unsigned_long_long(); } template -inline void eval_convert_to(long long* result, const cpp_dec_float& val) +inline void eval_convert_to(long long* result, const cpp_dec_float& val) BOOST_NOEXCEPT { *result = val.extract_signed_long_long(); } template -inline void eval_convert_to(long double* result, cpp_dec_float& val) +inline void eval_convert_to(long double* result, cpp_dec_float& val) BOOST_NOEXCEPT { *result = val.extract_long_double(); } @@ -2663,7 +2663,7 @@ inline void eval_convert_to(long double* result, cpp_dec_float& val) // Non member function support: // template -inline int eval_fpclassify(const cpp_dec_float& x) +inline int eval_fpclassify(const cpp_dec_float& x) BOOST_NOEXCEPT { if(x.isinf()) return FP_INFINITE; @@ -2675,7 +2675,7 @@ inline int eval_fpclassify(const cpp_dec_float& x) } template -inline void eval_abs(cpp_dec_float& result, const cpp_dec_float& x) +inline void eval_abs(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT { result = x; if(x.isneg()) @@ -2683,7 +2683,7 @@ inline void eval_abs(cpp_dec_float& result, const cpp_dec_float -inline void eval_fabs(cpp_dec_float& result, const cpp_dec_float& x) +inline void eval_fabs(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT { result = x; if(x.isneg()) @@ -2691,14 +2691,14 @@ inline void eval_fabs(cpp_dec_float& result, const cpp_dec_float -inline void eval_sqrt(cpp_dec_float& result, const cpp_dec_float& x) +inline void eval_sqrt(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT { result = x; result.calculate_sqrt(); } template -inline void eval_floor(cpp_dec_float& result, const cpp_dec_float& x) +inline void eval_floor(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT { result = x; if(!x.isfinite() || x.isint()) @@ -2712,7 +2712,7 @@ inline void eval_floor(cpp_dec_float& result, const cpp_dec_float -inline void eval_ceil(cpp_dec_float& result, const cpp_dec_float& x) +inline void eval_ceil(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT { result = x; if(!x.isfinite() || x.isint()) @@ -2742,7 +2742,7 @@ inline void eval_trunc(cpp_dec_float& result, const cpp_dec_float -inline void eval_ldexp(cpp_dec_float& result, const cpp_dec_float& x, long long e) +inline void eval_ldexp(cpp_dec_float& result, const cpp_dec_float& x, long long e) BOOST_NOEXCEPT { result = x; result *= cpp_dec_float::pow2(e); @@ -2827,12 +2827,12 @@ inline void eval_frexp(cpp_dec_float& result, const cpp_dec_float -inline bool eval_is_zero(const cpp_dec_float& val) +inline bool eval_is_zero(const cpp_dec_float& val) BOOST_NOEXCEPT { return val.iszero(); } template -inline int eval_get_sign(const cpp_dec_float& val) +inline int eval_get_sign(const cpp_dec_float& val) BOOST_NOEXCEPT { return val.iszero() ? 0 : val.isneg() ? -1 : 1; } diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index bb4afa86..de26540f 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -24,7 +24,7 @@ namespace backends{ #ifdef BOOST_MSVC // warning C4127: conditional expression is constant #pragma warning(push) -#pragma warning(disable:4127) +#pragma warning(disable:4127 4351) #endif template > @@ -114,7 +114,6 @@ public: limb_pointer p = limbs(); while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; } - BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1), m_sign(false), m_internal(true) { } @@ -1158,7 +1157,7 @@ inline void eval_multiply(cpp_int_backend& result, c eval_multiply(result, result, val); } template -void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) BOOST_NOEXCEPT_IF(boost::is_void::value) +void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) { if((result == &x) || (&r == &x)) { @@ -1425,7 +1424,7 @@ void divide_unsigned_helper(cpp_int_backend* result, } template -void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) BOOST_NOEXCEPT_IF(boost::is_void::value) +void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) { if((result == &x) || (&r == &x)) { @@ -1568,20 +1567,20 @@ void divide_unsigned_helper(cpp_int_backend* result, } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { cpp_int_backend r; divide_unsigned_helper(&result, a, b, r); result.sign(a.sign() != b.sign()); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) { cpp_int_backend r; divide_unsigned_helper(&result, a, b, r); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) { cpp_int_backend r; divide_unsigned_helper(&result, a, std::abs(b), r); @@ -1589,58 +1588,58 @@ inline void eval_divide(cpp_int_backend& result, con result.negate(); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& b) { // There is no in place divide: cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_divide(cpp_int_backend& result, limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_divide(cpp_int_backend& result, limb_type b) { // There is no in place divide: cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_divide(cpp_int_backend& result, signed_limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_divide(cpp_int_backend& result, signed_limb_type b) { // There is no in place divide: cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { divide_unsigned_helper(static_cast* >(0), a, b, result); result.sign(a.sign()); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) { divide_unsigned_helper(static_cast* >(0), a, b, result); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) { divide_unsigned_helper(static_cast* >(0), a, static_cast(std::abs(b)), result); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) { // There is no in place divide: cpp_int_backend a(result); eval_modulus(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_modulus(cpp_int_backend& result, limb_type b) { // There is no in place divide: cpp_int_backend a(result); eval_modulus(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, signed_limb_type b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_modulus(cpp_int_backend& result, signed_limb_type b) { // There is no in place divide: cpp_int_backend a(result); @@ -1777,17 +1776,17 @@ struct bit_or { limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCE struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a ^ b; } }; template -inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o)BOOST_NOEXCEPT +inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o)BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_and()); } template -inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_or()); } template -inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_xor()); } diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp index 92f0b691..2d3e0b89 100644 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ b/include/boost/multiprecision/detail/mp_number_base.hpp @@ -41,7 +41,7 @@ namespace detail{ // Workaround for missing abs(long long) on some compilers: // template -typename boost::enable_if, T>::type abs(const T& t) +typename boost::enable_if, T>::type abs(const T& t) BOOST_NOEXCEPT { return t < 0 ? -t : t; } @@ -258,7 +258,7 @@ struct mp_exp left_type left()const { return left_type(arg); } - const Arg1& left_ref()const{ return arg; } + const Arg1& left_ref()const BOOST_NOEXCEPT { return arg; } static const unsigned depth = left_type::depth + 1; @@ -282,7 +282,7 @@ struct mp_exp explicit mp_exp(const Arg1& a) : arg(a) {} - const Arg1& value()const { return arg; } + const Arg1& value()const BOOST_NOEXCEPT { return arg; } static const unsigned depth = 0; @@ -311,8 +311,8 @@ struct mp_exp left_type left()const { return left_type(arg1); } right_type right()const { return right_type(arg2); } - const Arg1& left_ref()const{ return arg1; } - const Arg2& right_ref()const{ return arg2; } + const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; } + const Arg2& right_ref()const BOOST_NOEXCEPT { return arg2; } operator unmentionable_type()const { @@ -350,9 +350,9 @@ struct mp_exp left_type left()const { return left_type(arg1); } middle_type middle()const { return middle_type(arg2); } right_type right()const { return right_type(arg3); } - const Arg1& left_ref()const{ return arg1; } - const Arg2& middle_ref()const{ return arg2; } - const Arg3& right_ref()const{ return arg3; } + const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; } + const Arg2& middle_ref()const BOOST_NOEXCEPT { return arg2; } + const Arg3& right_ref()const BOOST_NOEXCEPT { return arg3; } operator unmentionable_type()const { @@ -398,10 +398,10 @@ struct mp_exp left_middle_type left_middle()const { return left_middle_type(arg2); } right_middle_type right_middle()const { return right_middle_type(arg3); } right_type right()const { return right_type(arg4); } - const Arg1& left_ref()const{ return arg1; } - const Arg2& left_middle_ref()const{ return arg2; } - const Arg3& right_middle_ref()const{ return arg3; } - const Arg4& right_ref()const{ return arg4; } + const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; } + const Arg2& left_middle_ref()const BOOST_NOEXCEPT { return arg2; } + const Arg3& right_middle_ref()const BOOST_NOEXCEPT { return arg3; } + const Arg4& right_ref()const BOOST_NOEXCEPT { return arg4; } operator unmentionable_type()const { diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index a4b0a33d..9a46792c 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -30,6 +30,11 @@ namespace backends{ template struct gmp_float; +// +// Within this file, the only functions we mark as noexcept are those that manipulate +// (but don't create) an mpf_t. All other types may allocate at pretty much any time +// via a user-supplied allocator, and therefore throw. +// namespace detail{ template @@ -40,7 +45,7 @@ struct gmp_float_imp typedef mpl::list float_types; typedef long exponent_type; - gmp_float_imp(){} + gmp_float_imp() BOOST_NOEXCEPT {} gmp_float_imp(const gmp_float_imp& o) { @@ -54,7 +59,7 @@ struct gmp_float_imp mpf_set(m_data, o.m_data); } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_float_imp(gmp_float_imp&& o) + gmp_float_imp(gmp_float_imp&& o) BOOST_NOEXCEPT { m_data[0] = o.m_data[0]; o.m_data[0]._mp_d = 0; @@ -66,7 +71,7 @@ struct gmp_float_imp return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_float_imp& operator = (gmp_float_imp&& o) + gmp_float_imp& operator = (gmp_float_imp&& o) BOOST_NOEXCEPT { mpf_swap(m_data, o.m_data); return *this; @@ -100,17 +105,17 @@ struct gmp_float_imp mpf_neg(m_data, m_data); return *this; } - gmp_float_imp& operator = (unsigned long i) + gmp_float_imp& operator = (unsigned long i) BOOST_NOEXCEPT { mpf_set_ui(m_data, i); return *this; } - gmp_float_imp& operator = (long i) + gmp_float_imp& operator = (long i) BOOST_NOEXCEPT { mpf_set_si(m_data, i); return *this; } - gmp_float_imp& operator = (double d) + gmp_float_imp& operator = (double d) BOOST_NOEXCEPT { mpf_set_d(m_data, d); return *this; @@ -163,10 +168,11 @@ struct gmp_float_imp } gmp_float_imp& operator = (const char* s) { - mpf_set_str(m_data, s, 10); + if(0 != mpf_set_str(m_data, s, 10)) + BOOST_THROW_EXCEPTION(std::runtime_error(std::string("The string \"") + s + std::string("\"could not be interpreted as a valid floating point number."))); return *this; } - void swap(gmp_float_imp& o) + void swap(gmp_float_imp& o) BOOST_NOEXCEPT { mpf_swap(m_data, o.m_data); } @@ -265,24 +271,24 @@ struct gmp_float_imp boost::multiprecision::detail::format_float_string(result, e, org_digits, f, mpf_sgn(m_data) == 0); return result; } - ~gmp_float_imp() + ~gmp_float_imp() BOOST_NOEXCEPT { if(m_data[0]._mp_d) mpf_clear(m_data); } - void negate() + void negate() BOOST_NOEXCEPT { mpf_neg(m_data, m_data); } - int compare(const gmp_float& o)const + int compare(const gmp_float& o)const BOOST_NOEXCEPT { return mpf_cmp(m_data, o.m_data); } - int compare(long i)const + int compare(long i)const BOOST_NOEXCEPT { return mpf_cmp_si(m_data, i); } - int compare(unsigned long i)const + int compare(unsigned long i)const BOOST_NOEXCEPT { return mpf_cmp_ui(m_data, i); } @@ -293,11 +299,11 @@ struct gmp_float_imp d = v; return compare(d); } - mpf_t& data() { return m_data; } - const mpf_t& data()const { return m_data; } + mpf_t& data() BOOST_NOEXCEPT { return m_data; } + const mpf_t& data()const BOOST_NOEXCEPT { return m_data; } protected: mpf_t m_data; - static unsigned& get_default_precision() + static unsigned& get_default_precision() BOOST_NOEXCEPT { static unsigned val = 50; return val; @@ -337,7 +343,7 @@ struct gmp_float : public detail::gmp_float_imp mpf_set_q(this->m_data, val); } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_float(gmp_float&& o) : detail::gmp_float_imp(static_cast&&>(o)) {} + gmp_float(gmp_float&& o) BOOST_NOEXCEPT : detail::gmp_float_imp(static_cast&&>(o)) {} #endif gmp_float& operator=(const gmp_float& o) { @@ -345,7 +351,7 @@ struct gmp_float : public detail::gmp_float_imp return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_float& operator=(gmp_float&& o) + gmp_float& operator=(gmp_float&& o) BOOST_NOEXCEPT { *static_cast*>(this) = static_cast&&>(o); return *this; @@ -355,17 +361,17 @@ struct gmp_float : public detail::gmp_float_imp gmp_float& operator=(const gmp_float& o); gmp_float& operator=(const gmp_int& o); gmp_float& operator=(const gmp_rational& o); - gmp_float& operator=(const mpf_t& val) + gmp_float& operator=(const mpf_t& val) BOOST_NOEXCEPT { mpf_set(this->m_data, val); return *this; } - gmp_float& operator=(const mpz_t& val) + gmp_float& operator=(const mpz_t& val) BOOST_NOEXCEPT { mpf_set_z(this->m_data, val); return *this; } - gmp_float& operator=(const mpq_t& val) + gmp_float& operator=(const mpq_t& val) BOOST_NOEXCEPT { mpf_set_q(this->m_data, val); return *this; @@ -412,7 +418,7 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> mpf_set(this->m_data, o.data()); } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_float(gmp_float&& o) : detail::gmp_float_imp<0>(static_cast&&>(o)) {} + gmp_float(gmp_float&& o) BOOST_NOEXCEPT : detail::gmp_float_imp<0>(static_cast&&>(o)) {} #endif gmp_float(const gmp_int& o); gmp_float(const gmp_rational& o); @@ -428,7 +434,7 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_float& operator=(gmp_float&& o) + gmp_float& operator=(gmp_float&& o) BOOST_NOEXCEPT { *static_cast*>(this) = static_cast &&>(o); return *this; @@ -463,66 +469,75 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> *static_cast*>(this) = v; return *this; } - static unsigned default_precision() + static unsigned default_precision() BOOST_NOEXCEPT { return get_default_precision(); } - static void default_precision(unsigned v) + static void default_precision(unsigned v) BOOST_NOEXCEPT { get_default_precision() = v; } - unsigned precision()const + unsigned precision()const BOOST_NOEXCEPT { return mpf_get_prec(this->m_data) * 301L / 1000 - 1; } - void precision(unsigned digits10) + void precision(unsigned digits10) BOOST_NOEXCEPT { mpf_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); } }; template -inline void eval_add(gmp_float& result, const gmp_float& o) +inline void eval_add(gmp_float& result, const gmp_float& o) BOOST_NOEXCEPT { mpf_add(result.data(), result.data(), o.data()); } template -inline void eval_subtract(gmp_float& result, const gmp_float& o) +inline void eval_subtract(gmp_float& result, const gmp_float& o) BOOST_NOEXCEPT { mpf_sub(result.data(), result.data(), o.data()); } template -inline void eval_multiply(gmp_float& result, const gmp_float& o) +inline void eval_multiply(gmp_float& result, const gmp_float& o) BOOST_NOEXCEPT { mpf_mul(result.data(), result.data(), o.data()); } template +inline bool eval_is_zero(const gmp_float& val) BOOST_NOEXCEPT +{ + return mpf_sgn(val.data()) == 0; +} +template inline void eval_divide(gmp_float& result, const gmp_float& o) { + if(eval_is_zero(o)) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpf_div(result.data(), result.data(), o.data()); } template -inline void eval_add(gmp_float& result, unsigned long i) +inline void eval_add(gmp_float& result, unsigned long i) BOOST_NOEXCEPT { mpf_add_ui(result.data(), result.data(), i); } template -inline void eval_subtract(gmp_float& result, unsigned long i) +inline void eval_subtract(gmp_float& result, unsigned long i) BOOST_NOEXCEPT { mpf_sub_ui(result.data(), result.data(), i); } template -inline void eval_multiply(gmp_float& result, unsigned long i) +inline void eval_multiply(gmp_float& result, unsigned long i) BOOST_NOEXCEPT { mpf_mul_ui(result.data(), result.data(), i); } template inline void eval_divide(gmp_float& result, unsigned long i) { + if(i == 0) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpf_div_ui(result.data(), result.data(), i); } template -inline void eval_add(gmp_float& result, long i) +inline void eval_add(gmp_float& result, long i) BOOST_NOEXCEPT { if(i > 0) mpf_add_ui(result.data(), result.data(), i); @@ -530,7 +545,7 @@ inline void eval_add(gmp_float& result, long i) mpf_sub_ui(result.data(), result.data(), std::abs(i)); } template -inline void eval_subtract(gmp_float& result, long i) +inline void eval_subtract(gmp_float& result, long i) BOOST_NOEXCEPT { if(i > 0) mpf_sub_ui(result.data(), result.data(), i); @@ -538,7 +553,7 @@ inline void eval_subtract(gmp_float& result, long i) mpf_add_ui(result.data(), result.data(), std::abs(i)); } template -inline void eval_multiply(gmp_float& result, long i) +inline void eval_multiply(gmp_float& result, long i) BOOST_NOEXCEPT { mpf_mul_ui(result.data(), result.data(), std::abs(i)); if(i < 0) @@ -547,6 +562,8 @@ inline void eval_multiply(gmp_float& result, long i) template inline void eval_divide(gmp_float& result, long i) { + if(i == 0) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpf_div_ui(result.data(), result.data(), std::abs(i)); if(i < 0) mpf_neg(result.data(), result.data()); @@ -555,17 +572,17 @@ inline void eval_divide(gmp_float& result, long i) // Specialised 3 arg versions of the basic operators: // template -inline void eval_add(gmp_float& a, const gmp_float& x, const gmp_float& y) +inline void eval_add(gmp_float& a, const gmp_float& x, const gmp_float& y) BOOST_NOEXCEPT { mpf_add(a.data(), x.data(), y.data()); } template -inline void eval_add(gmp_float& a, const gmp_float& x, unsigned long y) +inline void eval_add(gmp_float& a, const gmp_float& x, unsigned long y) BOOST_NOEXCEPT { mpf_add_ui(a.data(), x.data(), y); } template -inline void eval_add(gmp_float& a, const gmp_float& x, long y) +inline void eval_add(gmp_float& a, const gmp_float& x, long y) BOOST_NOEXCEPT { if(y < 0) mpf_sub_ui(a.data(), x.data(), -y); @@ -573,12 +590,12 @@ inline void eval_add(gmp_float& a, const gmp_float& x, long mpf_add_ui(a.data(), x.data(), y); } template -inline void eval_add(gmp_float& a, unsigned long x, const gmp_float& y) +inline void eval_add(gmp_float& a, unsigned long x, const gmp_float& y) BOOST_NOEXCEPT { mpf_add_ui(a.data(), y.data(), x); } template -inline void eval_add(gmp_float& a, long x, const gmp_float& y) +inline void eval_add(gmp_float& a, long x, const gmp_float& y) BOOST_NOEXCEPT { if(x < 0) { @@ -589,17 +606,17 @@ inline void eval_add(gmp_float& a, long x, const gmp_float& mpf_add_ui(a.data(), y.data(), x); } template -inline void eval_subtract(gmp_float& a, const gmp_float& x, const gmp_float& y) +inline void eval_subtract(gmp_float& a, const gmp_float& x, const gmp_float& y) BOOST_NOEXCEPT { mpf_sub(a.data(), x.data(), y.data()); } template -inline void eval_subtract(gmp_float& a, const gmp_float& x, unsigned long y) +inline void eval_subtract(gmp_float& a, const gmp_float& x, unsigned long y) BOOST_NOEXCEPT { mpf_sub_ui(a.data(), x.data(), y); } template -inline void eval_subtract(gmp_float& a, const gmp_float& x, long y) +inline void eval_subtract(gmp_float& a, const gmp_float& x, long y) BOOST_NOEXCEPT { if(y < 0) mpf_add_ui(a.data(), x.data(), -y); @@ -607,12 +624,12 @@ inline void eval_subtract(gmp_float& a, const gmp_float& x, mpf_sub_ui(a.data(), x.data(), y); } template -inline void eval_subtract(gmp_float& a, unsigned long x, const gmp_float& y) +inline void eval_subtract(gmp_float& a, unsigned long x, const gmp_float& y) BOOST_NOEXCEPT { mpf_ui_sub(a.data(), x, y.data()); } template -inline void eval_subtract(gmp_float& a, long x, const gmp_float& y) +inline void eval_subtract(gmp_float& a, long x, const gmp_float& y) BOOST_NOEXCEPT { if(x < 0) { @@ -624,17 +641,17 @@ inline void eval_subtract(gmp_float& a, long x, const gmp_float -inline void eval_multiply(gmp_float& a, const gmp_float& x, const gmp_float& y) +inline void eval_multiply(gmp_float& a, const gmp_float& x, const gmp_float& y) BOOST_NOEXCEPT { mpf_mul(a.data(), x.data(), y.data()); } template -inline void eval_multiply(gmp_float& a, const gmp_float& x, unsigned long y) +inline void eval_multiply(gmp_float& a, const gmp_float& x, unsigned long y) BOOST_NOEXCEPT { mpf_mul_ui(a.data(), x.data(), y); } template -inline void eval_multiply(gmp_float& a, const gmp_float& x, long y) +inline void eval_multiply(gmp_float& a, const gmp_float& x, long y) BOOST_NOEXCEPT { if(y < 0) { @@ -645,12 +662,12 @@ inline void eval_multiply(gmp_float& a, const gmp_float& x, mpf_mul_ui(a.data(), x.data(), y); } template -inline void eval_multiply(gmp_float& a, unsigned long x, const gmp_float& y) +inline void eval_multiply(gmp_float& a, unsigned long x, const gmp_float& y) BOOST_NOEXCEPT { mpf_mul_ui(a.data(), y.data(), x); } template -inline void eval_multiply(gmp_float& a, long x, const gmp_float& y) +inline void eval_multiply(gmp_float& a, long x, const gmp_float& y) BOOST_NOEXCEPT { if(x < 0) { @@ -664,16 +681,22 @@ inline void eval_multiply(gmp_float& a, long x, const gmp_float inline void eval_divide(gmp_float& a, const gmp_float& x, const gmp_float& y) { + if(eval_is_zero(y)) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpf_div(a.data(), x.data(), y.data()); } template inline void eval_divide(gmp_float& a, const gmp_float& x, unsigned long y) { + if(y == 0) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpf_div_ui(a.data(), x.data(), y); } template inline void eval_divide(gmp_float& a, const gmp_float& x, long y) { + if(y == 0) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); if(y < 0) { mpf_div_ui(a.data(), x.data(), -y); @@ -685,11 +708,15 @@ inline void eval_divide(gmp_float& a, const gmp_float& x, lo template inline void eval_divide(gmp_float& a, unsigned long x, const gmp_float& y) { + if(eval_is_zero(y)) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpf_ui_div(a.data(), x, y.data()); } template inline void eval_divide(gmp_float& a, long x, const gmp_float& y) { + if(eval_is_zero(y)) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); if(x < 0) { mpf_ui_div(a.data(), -x, y.data()); @@ -700,18 +727,13 @@ inline void eval_divide(gmp_float& a, long x, const gmp_float -inline bool eval_is_zero(const gmp_float& val) -{ - return mpf_sgn(val.data()) == 0; -} -template -inline int eval_get_sign(const gmp_float& val) +inline int eval_get_sign(const gmp_float& val) BOOST_NOEXCEPT { return mpf_sgn(val.data()); } template -inline void eval_convert_to(unsigned long* result, const gmp_float& val) +inline void eval_convert_to(unsigned long* result, const gmp_float& val) BOOST_NOEXCEPT { if(0 == mpf_fits_ulong_p(val.data())) *result = (std::numeric_limits::max)(); @@ -719,7 +741,7 @@ inline void eval_convert_to(unsigned long* result, const gmp_float& va *result = mpf_get_ui(val.data()); } template -inline void eval_convert_to(long* result, const gmp_float& val) +inline void eval_convert_to(long* result, const gmp_float& val) BOOST_NOEXCEPT { if(0 == mpf_fits_slong_p(val.data())) { @@ -730,7 +752,7 @@ inline void eval_convert_to(long* result, const gmp_float& val) *result = mpf_get_si(val.data()); } template -inline void eval_convert_to(double* result, const gmp_float& val) +inline void eval_convert_to(double* result, const gmp_float& val) BOOST_NOEXCEPT { *result = mpf_get_d(val.data()); } @@ -804,39 +826,39 @@ inline void eval_convert_to(unsigned long long* result, const gmp_float -inline void eval_sqrt(gmp_float& result, const gmp_float& val) +inline void eval_sqrt(gmp_float& result, const gmp_float& val) BOOST_NOEXCEPT { mpf_sqrt(result.data(), val.data()); } template -inline void eval_abs(gmp_float& result, const gmp_float& val) +inline void eval_abs(gmp_float& result, const gmp_float& val) BOOST_NOEXCEPT { mpf_abs(result.data(), val.data()); } template -inline void eval_fabs(gmp_float& result, const gmp_float& val) +inline void eval_fabs(gmp_float& result, const gmp_float& val) BOOST_NOEXCEPT { mpf_abs(result.data(), val.data()); } template -inline void eval_ceil(gmp_float& result, const gmp_float& val) +inline void eval_ceil(gmp_float& result, const gmp_float& val) BOOST_NOEXCEPT { mpf_ceil(result.data(), val.data()); } template -inline void eval_floor(gmp_float& result, const gmp_float& val) +inline void eval_floor(gmp_float& result, const gmp_float& val) BOOST_NOEXCEPT { mpf_floor(result.data(), val.data()); } template -inline void eval_trunc(gmp_float& result, const gmp_float& val) +inline void eval_trunc(gmp_float& result, const gmp_float& val) BOOST_NOEXCEPT { mpf_trunc(result.data(), val.data()); } template -inline void eval_ldexp(gmp_float& result, const gmp_float& val, long e) +inline void eval_ldexp(gmp_float& result, const gmp_float& val, long e) BOOST_NOEXCEPT { if(e > 0) mpf_mul_2exp(result.data(), val.data(), e); @@ -846,7 +868,7 @@ inline void eval_ldexp(gmp_float& result, const gmp_float& v result = val; } template -inline void eval_frexp(gmp_float& result, const gmp_float& val, int* e) +inline void eval_frexp(gmp_float& result, const gmp_float& val, int* e) BOOST_NOEXCEPT { long v; mpf_get_d_2exp(&v, val.data()); @@ -854,7 +876,7 @@ inline void eval_frexp(gmp_float& result, const gmp_float& v eval_ldexp(result, val, -v); } template -inline void eval_frexp(gmp_float& result, const gmp_float& val, long* e) +inline void eval_frexp(gmp_float& result, const gmp_float& val, long* e) BOOST_NOEXCEPT { mpf_get_d_2exp(e, val.data()); eval_ldexp(result, val, -*e); @@ -875,7 +897,7 @@ struct gmp_int mpz_init_set(m_data, o.m_data); } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_int(gmp_int&& o) + gmp_int(gmp_int&& o) BOOST_NOEXCEPT { m_data[0] = o.m_data[0]; o.m_data[0]._mp_d = 0; @@ -1015,7 +1037,10 @@ struct gmp_int } } if(n) - mpz_set_str(m_data, s, radix); + { + if(0 != mpz_set_str(m_data, s, radix)) + BOOST_THROW_EXCEPTION(std::runtime_error(std::string("The string \"") + s + std::string("\"could not be interpreted as a valid integer."))); + } else mpz_set_ui(m_data, 0); return *this; @@ -1111,6 +1136,10 @@ protected: mpz_t m_data; }; +inline bool eval_is_zero(const gmp_int& val) +{ + return mpz_sgn(val.data()) == 0; +} inline void eval_add(gmp_int& t, const gmp_int& o) { mpz_add(t.data(), t.data(), o.data()); @@ -1125,6 +1154,8 @@ inline void eval_multiply(gmp_int& t, const gmp_int& o) } inline void eval_divide(gmp_int& t, const gmp_int& o) { + if(eval_is_zero(o)) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpz_tdiv_q(t.data(), t.data(), o.data()); } inline void eval_modulus(gmp_int& t, const gmp_int& o) @@ -1149,6 +1180,8 @@ inline void eval_modulus(gmp_int& t, unsigned long i) } inline void eval_divide(gmp_int& t, unsigned long i) { + if(i == 0) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpz_tdiv_q_ui(t.data(), t.data(), i); } inline void eval_add(gmp_int& t, long i) @@ -1177,6 +1210,8 @@ inline void eval_modulus(gmp_int& t, long i) } inline void eval_divide(gmp_int& t, long i) { + if(i == 0) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpz_tdiv_q_ui(t.data(), t.data(), std::abs(i)); if(i < 0) mpz_neg(t.data(), t.data()); @@ -1231,6 +1266,8 @@ inline void eval_multiply(gmp_int& t, const gmp_int& p, const gmp_int& o) } inline void eval_divide(gmp_int& t, const gmp_int& p, const gmp_int& o) { + if(eval_is_zero(o)) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpz_tdiv_q(t.data(), p.data(), o.data()); } inline void eval_modulus(gmp_int& t, const gmp_int& p, const gmp_int& o) @@ -1255,6 +1292,8 @@ inline void eval_modulus(gmp_int& t, const gmp_int& p, unsigned long i) } inline void eval_divide(gmp_int& t, const gmp_int& p, unsigned long i) { + if(i == 0) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpz_tdiv_q_ui(t.data(), p.data(), i); } inline void eval_add(gmp_int& t, const gmp_int& p, long i) @@ -1283,6 +1322,8 @@ inline void eval_modulus(gmp_int& t, const gmp_int& p, long i) } inline void eval_divide(gmp_int& t, const gmp_int& p, long i) { + if(i == 0) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpz_tdiv_q_ui(t.data(), p.data(), std::abs(i)); if(i < 0) mpz_neg(t.data(), t.data()); @@ -1308,10 +1349,6 @@ inline void eval_complement(gmp_int& result, const gmp_int& u) mpz_com(result.data(), u.data()); } -inline bool eval_is_zero(const gmp_int& val) -{ - return mpz_sgn(val.data()) == 0; -} inline int eval_get_sign(const gmp_int& val) { return mpz_sgn(val.data()); @@ -1478,7 +1515,7 @@ struct gmp_rational mpq_set_z(m_data, o.data()); } #ifndef BOOST_NO_RVALUE_REFERENCES - gmp_rational(gmp_rational&& o) + gmp_rational(gmp_rational&& o) BOOST_NOEXCEPT { m_data[0]._mp_num = o.data()[0]._mp_num; m_data[0]._mp_den = o.data()[0]._mp_den; @@ -1594,7 +1631,8 @@ struct gmp_rational } gmp_rational& operator = (const char* s) { - mpq_set_str(m_data, s, 10); + if(0 != mpq_set_str(m_data, s, 10)) + BOOST_THROW_EXCEPTION(std::runtime_error(std::string("The string \"") + s + std::string("\"could not be interpreted as a valid rational number."))); return *this; } gmp_rational& operator=(const gmp_int& o) @@ -1662,6 +1700,10 @@ protected: mpq_t m_data; }; +inline bool eval_is_zero(const gmp_rational& val) +{ + return mpq_sgn(val.data()) == 0; +} inline mp_number numerator(const mp_number& val) { mp_number result; @@ -1689,6 +1731,8 @@ inline void eval_multiply(gmp_rational& t, const gmp_rational& o) } inline void eval_divide(gmp_rational& t, const gmp_rational& o) { + if(eval_is_zero(o)) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpq_div(t.data(), t.data(), o.data()); } inline void eval_add(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) @@ -1705,13 +1749,11 @@ inline void eval_multiply(gmp_rational& t, const gmp_rational& p, const gmp_rati } inline void eval_divide(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) { + if(eval_is_zero(o)) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); mpq_div(t.data(), p.data(), o.data()); } -inline bool eval_is_zero(const gmp_rational& val) -{ - return mpq_sgn(val.data()) == 0; -} inline int eval_get_sign(const gmp_rational& val) { return mpq_sgn(val.data()); diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 43604382..174deb08 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -35,7 +35,7 @@ struct mpfr_float_imp typedef mpl::list float_types; typedef long exponent_type; - mpfr_float_imp(){} + mpfr_float_imp() BOOST_NOEXCEPT {} mpfr_float_imp(const mpfr_float_imp& o) { @@ -43,24 +43,36 @@ struct mpfr_float_imp mpfr_set(m_data, o.m_data, GMP_RNDN); } #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_float_imp(mpfr_float_imp&& o) + mpfr_float_imp(mpfr_float_imp&& o) BOOST_NOEXCEPT { m_data[0] = o.m_data[0]; o.m_data[0]._mpfr_d = 0; } #endif - mpfr_float_imp& operator = (const mpfr_float_imp& o) + mpfr_float_imp& operator = (const mpfr_float_imp& o) BOOST_NOEXCEPT { mpfr_set(m_data, o.m_data, GMP_RNDN); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_float_imp& operator = (mpfr_float_imp&& o) + mpfr_float_imp& operator = (mpfr_float_imp&& o) BOOST_NOEXCEPT { mpfr_swap(m_data, o.m_data); return *this; } #endif +#ifdef _MPFR_H_HAVE_INTMAX_T + mpfr_float_imp& operator = (unsigned long long i) BOOST_NOEXCEPT + { + mpfr_set_uj(m_data, i, GMP_RNDN); + return *this; + } + mpfr_float_imp& operator = (long long i) BOOST_NOEXCEPT + { + mpfr_set_sj(m_data, i, GMP_RNDN); + return *this; + } +#else mpfr_float_imp& operator = (unsigned long long i) { unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); @@ -89,76 +101,36 @@ struct mpfr_float_imp mpfr_neg(m_data, m_data, GMP_RNDN); return *this; } - mpfr_float_imp& operator = (unsigned long i) +#endif + mpfr_float_imp& operator = (unsigned long i) BOOST_NOEXCEPT { mpfr_set_ui(m_data, i, GMP_RNDN); return *this; } - mpfr_float_imp& operator = (long i) + mpfr_float_imp& operator = (long i) BOOST_NOEXCEPT { mpfr_set_si(m_data, i, GMP_RNDN); return *this; } - mpfr_float_imp& operator = (double d) + mpfr_float_imp& operator = (double d) BOOST_NOEXCEPT { mpfr_set_d(m_data, d, GMP_RNDN); return *this; } - mpfr_float_imp& operator = (long double a) + mpfr_float_imp& operator = (long double a) BOOST_NOEXCEPT { - using std::frexp; - using std::ldexp; - using std::floor; - - if (a == 0) { - mpfr_set_si(m_data, 0, GMP_RNDN); - return *this; - } - - if (a == 1) { - mpfr_set_si(m_data, 1, GMP_RNDN); - return *this; - } - - BOOST_ASSERT(!(boost::math::isinf)(a)); - BOOST_ASSERT(!(boost::math::isnan)(a)); - - int e; - long double f, term; - mpfr_init_set_ui(m_data, 0u, GMP_RNDN); - - f = frexp(a, &e); - - static const int shift = std::numeric_limits::digits - 1; - - while(f) - { - // extract int sized bits from f: - f = ldexp(f, shift); - term = floor(f); - e -= shift; - mpfr_mul_2exp(m_data, m_data, shift, GMP_RNDN); - if(term > 0) - mpfr_add_ui(m_data, m_data, static_cast(term), GMP_RNDN); - else - mpfr_sub_ui(m_data, m_data, static_cast(-term), GMP_RNDN); - f -= term; - } - if(e > 0) - mpfr_mul_2exp(m_data, m_data, e, GMP_RNDN); - else if(e < 0) - mpfr_div_2exp(m_data, m_data, -e, GMP_RNDN); + mpfr_set_ld(m_data, a, GMP_RNDN); return *this; } mpfr_float_imp& operator = (const char* s) { if(mpfr_set_str(m_data, s, 10, GMP_RNDN) != 0) { - BOOST_THROW_EXCEPTION(std::runtime_error("Unable to parse string as a valid floating point number.")); + BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Unable to parse string \"") + s + std::string("\"as a valid floating point number."))); } return *this; } - void swap(mpfr_float_imp& o) + void swap(mpfr_float_imp& o) BOOST_NOEXCEPT { mpfr_swap(m_data, o.m_data); } @@ -267,39 +239,39 @@ struct mpfr_float_imp boost::multiprecision::detail::format_float_string(result, e, org_digits, f, 0 != mpfr_zero_p(m_data)); return result; } - ~mpfr_float_imp() + ~mpfr_float_imp() BOOST_NOEXCEPT { if(m_data[0]._mpfr_d) mpfr_clear(m_data); } - void negate() + void negate() BOOST_NOEXCEPT { mpfr_neg(m_data, m_data, GMP_RNDN); } - int compare(const mpfr_float_backend& o)const + int compare(const mpfr_float_backend& o)const BOOST_NOEXCEPT { return mpfr_cmp(m_data, o.m_data); } - int compare(long i)const + int compare(long i)const BOOST_NOEXCEPT { return mpfr_cmp_si(m_data, i); } - int compare(unsigned long i)const + int compare(unsigned long i)const BOOST_NOEXCEPT { return mpfr_cmp_ui(m_data, i); } template - int compare(V v)const + int compare(V v)const BOOST_NOEXCEPT { mpfr_float_backend d; d = v; return compare(d); } - mpfr_t& data() { return m_data; } - const mpfr_t& data()const { return m_data; } + mpfr_t& data() BOOST_NOEXCEPT { return m_data; } + const mpfr_t& data()const BOOST_NOEXCEPT { return m_data; } protected: mpfr_t m_data; - static unsigned& get_default_precision() + static unsigned& get_default_precision() BOOST_NOEXCEPT { static unsigned val = 50; return val; @@ -367,7 +339,7 @@ struct mpfr_float_backend : public detail::mpfr_float_imp return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_float_backend& operator=(mpfr_float_backend&& o) + mpfr_float_backend& operator=(mpfr_float_backend&& o) BOOST_NOEXCEPT { *static_cast*>(this) = static_cast&&>(o); return *this; @@ -379,44 +351,44 @@ struct mpfr_float_backend : public detail::mpfr_float_imp *static_cast*>(this) = v; return *this; } - mpfr_float_backend& operator=(const mpfr_t& val) + mpfr_float_backend& operator=(const mpfr_t& val)BOOST_NOEXCEPT { mpfr_set(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpf_t& val) + mpfr_float_backend& operator=(const mpf_t& val)BOOST_NOEXCEPT { mpfr_set_f(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpz_t& val) + mpfr_float_backend& operator=(const mpz_t& val)BOOST_NOEXCEPT { mpfr_set_z(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpq_t& val) + mpfr_float_backend& operator=(const mpq_t& val)BOOST_NOEXCEPT { mpfr_set_q(this->m_data, val, GMP_RNDN); return *this; } template - mpfr_float_backend& operator=(const mpfr_float_backend& val) + mpfr_float_backend& operator=(const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_set(this->m_data, val.data(), GMP_RNDN); return *this; } template - mpfr_float_backend& operator=(const gmp_float& val) + mpfr_float_backend& operator=(const gmp_float& val) BOOST_NOEXCEPT { mpfr_set_f(this->m_data, val.data(), GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const gmp_int& val) + mpfr_float_backend& operator=(const gmp_int& val) BOOST_NOEXCEPT { mpfr_set_z(this->m_data, val.data(), GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const gmp_rational& val) + mpfr_float_backend& operator=(const gmp_rational& val) BOOST_NOEXCEPT { mpfr_set_q(this->m_data, val.data(), GMP_RNDN); return *this; @@ -456,7 +428,7 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> } mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp<0>(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp<0>(static_cast&&>(o)) {} + mpfr_float_backend(mpfr_float_backend&& o) BOOST_NOEXCEPT : detail::mpfr_float_imp<0>(static_cast&&>(o)) {} #endif mpfr_float_backend(const mpfr_float_backend& o, unsigned digits10) { @@ -492,7 +464,7 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_float_backend& operator=(mpfr_float_backend&& o) + mpfr_float_backend& operator=(mpfr_float_backend&& o) BOOST_NOEXCEPT { *static_cast*>(this) = static_cast &&>(o); return *this; @@ -504,78 +476,78 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> *static_cast*>(this) = v; return *this; } - mpfr_float_backend& operator=(const mpfr_t& val) + mpfr_float_backend& operator=(const mpfr_t& val) BOOST_NOEXCEPT { mpfr_set(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpf_t& val) + mpfr_float_backend& operator=(const mpf_t& val) BOOST_NOEXCEPT { mpfr_set_f(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpz_t& val) + mpfr_float_backend& operator=(const mpz_t& val) BOOST_NOEXCEPT { mpfr_set_z(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpq_t& val) + mpfr_float_backend& operator=(const mpq_t& val) BOOST_NOEXCEPT { mpfr_set_q(this->m_data, val, GMP_RNDN); return *this; } template - mpfr_float_backend& operator=(const mpfr_float_backend& val) + mpfr_float_backend& operator=(const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_set(this->m_data, val.data(), GMP_RNDN); return *this; } template - mpfr_float_backend& operator=(const gmp_float& val) + mpfr_float_backend& operator=(const gmp_float& val) BOOST_NOEXCEPT { mpfr_set_f(this->m_data, val.data(), GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const gmp_int& val) + mpfr_float_backend& operator=(const gmp_int& val) BOOST_NOEXCEPT { mpfr_set_z(this->m_data, val.data(), GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const gmp_rational& val) + mpfr_float_backend& operator=(const gmp_rational& val) BOOST_NOEXCEPT { mpfr_set_q(this->m_data, val.data(), GMP_RNDN); return *this; } - static unsigned default_precision() + static unsigned default_precision() BOOST_NOEXCEPT { return get_default_precision(); } - static void default_precision(unsigned v) + static void default_precision(unsigned v) BOOST_NOEXCEPT { get_default_precision() = v; } - unsigned precision()const + unsigned precision()const BOOST_NOEXCEPT { return mpfr_get_prec(this->m_data) * 301L / 1000 - 1; } - void precision(unsigned digits10) + void precision(unsigned digits10) BOOST_NOEXCEPT { mpfr_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); } }; template -inline void eval_add(mpfr_float_backend& result, const mpfr_float_backend& o) +inline void eval_add(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT { mpfr_add(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void eval_subtract(mpfr_float_backend& result, const mpfr_float_backend& o) +inline void eval_subtract(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT { mpfr_sub(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void eval_multiply(mpfr_float_backend& result, const mpfr_float_backend& o) +inline void eval_multiply(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT { mpfr_mul(result.data(), result.data(), o.data(), GMP_RNDN); } @@ -585,17 +557,17 @@ inline void eval_divide(mpfr_float_backend& result, const mpfr_float_b mpfr_div(result.data(), result.data(), o.data(), GMP_RNDN); } template -inline void eval_add(mpfr_float_backend& result, unsigned long i) +inline void eval_add(mpfr_float_backend& result, unsigned long i) BOOST_NOEXCEPT { mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void eval_subtract(mpfr_float_backend& result, unsigned long i) +inline void eval_subtract(mpfr_float_backend& result, unsigned long i) BOOST_NOEXCEPT { mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void eval_multiply(mpfr_float_backend& result, unsigned long i) +inline void eval_multiply(mpfr_float_backend& result, unsigned long i) BOOST_NOEXCEPT { mpfr_mul_ui(result.data(), result.data(), i, GMP_RNDN); } @@ -605,7 +577,7 @@ inline void eval_divide(mpfr_float_backend& result, unsigned long i) mpfr_div_ui(result.data(), result.data(), i, GMP_RNDN); } template -inline void eval_add(mpfr_float_backend& result, long i) +inline void eval_add(mpfr_float_backend& result, long i) BOOST_NOEXCEPT { if(i > 0) mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); @@ -613,7 +585,7 @@ inline void eval_add(mpfr_float_backend& result, long i) mpfr_sub_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); } template -inline void eval_subtract(mpfr_float_backend& result, long i) +inline void eval_subtract(mpfr_float_backend& result, long i) BOOST_NOEXCEPT { if(i > 0) mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); @@ -621,7 +593,7 @@ inline void eval_subtract(mpfr_float_backend& result, long i) mpfr_add_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); } template -inline void eval_multiply(mpfr_float_backend& result, long i) +inline void eval_multiply(mpfr_float_backend& result, long i) BOOST_NOEXCEPT { mpfr_mul_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); if(i < 0) @@ -638,17 +610,17 @@ inline void eval_divide(mpfr_float_backend& result, long i) // Specialised 3 arg versions of the basic operators: // template -inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_add(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT { mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, long y) +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT { if(y < 0) mpfr_sub_ui(a.data(), x.data(), -y, GMP_RNDN); @@ -656,12 +628,12 @@ inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend -inline void eval_add(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) +inline void eval_add(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } template -inline void eval_add(mpfr_float_backend& a, long x, const mpfr_float_backend& y) +inline void eval_add(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { if(x < 0) { @@ -672,17 +644,17 @@ inline void eval_add(mpfr_float_backend& a, long x, const mpfr_float_b mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } template -inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_sub(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT { mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, long y) +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT { if(y < 0) mpfr_add_ui(a.data(), x.data(), -y, GMP_RNDN); @@ -690,12 +662,12 @@ inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_back mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void eval_subtract(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) +inline void eval_subtract(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); } template -inline void eval_subtract(mpfr_float_backend& a, long x, const mpfr_float_backend& y) +inline void eval_subtract(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { if(x < 0) { @@ -707,17 +679,17 @@ inline void eval_subtract(mpfr_float_backend& a, long x, const mpfr_fl } template -inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_mul(a.data(), x.data(), y.data(), GMP_RNDN); } template -inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT { mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, long y) +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT { if(y < 0) { @@ -728,12 +700,12 @@ inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_back mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); } template -inline void eval_multiply(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) +inline void eval_multiply(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); } template -inline void eval_multiply(mpfr_float_backend& a, long x, const mpfr_float_backend& y) +inline void eval_multiply(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { if(x < 0) { @@ -783,12 +755,12 @@ inline void eval_divide(mpfr_float_backend& a, long x, const mpfr_floa } template -inline bool eval_is_zero(const mpfr_float_backend& val) +inline bool eval_is_zero(const mpfr_float_backend& val) BOOST_NOEXCEPT { return 0 != mpfr_zero_p(val.data()); } template -inline int eval_get_sign(const mpfr_float_backend& val) +inline int eval_get_sign(const mpfr_float_backend& val) BOOST_NOEXCEPT { return mpfr_sgn(val.data()); } @@ -796,32 +768,48 @@ inline int eval_get_sign(const mpfr_float_backend& val) template inline void eval_convert_to(unsigned long* result, const mpfr_float_backend& val) { + if(mpfr_nan_p(val.data())) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer.")); + } *result = mpfr_get_ui(val.data(), GMP_RNDN); } template inline void eval_convert_to(long* result, const mpfr_float_backend& val) { + if(mpfr_nan_p(val.data())) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer.")); + } *result = mpfr_get_si(val.data(), GMP_RNDN); } #ifdef _MPFR_H_HAVE_INTMAX_T template inline void eval_convert_to(unsigned long long* result, const mpfr_float_backend& val) { + if(mpfr_nan_p(val.data())) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer.")); + } *result = mpfr_get_uj(val.data(), GMP_RNDN); } template inline void eval_convert_to(long long* result, const mpfr_float_backend& val) { + if(mpfr_nan_p(val.data())) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer.")); + } *result = mpfr_get_sj(val.data(), GMP_RNDN); } #endif template -inline void eval_convert_to(double* result, const mpfr_float_backend& val) +inline void eval_convert_to(double* result, const mpfr_float_backend& val) BOOST_NOEXCEPT { *result = mpfr_get_d(val.data(), GMP_RNDN); } template -inline void eval_convert_to(long double* result, const mpfr_float_backend& val) +inline void eval_convert_to(long double* result, const mpfr_float_backend& val) BOOST_NOEXCEPT { *result = mpfr_get_ld(val.data(), GMP_RNDN); } @@ -830,29 +818,29 @@ inline void eval_convert_to(long double* result, const mpfr_float_backend -inline void eval_sqrt(mpfr_float_backend& result, const mpfr_float_backend& val) +inline void eval_sqrt(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_sqrt(result.data(), val.data(), GMP_RNDN); } template -inline void eval_abs(mpfr_float_backend& result, const mpfr_float_backend& val) +inline void eval_abs(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_abs(result.data(), val.data(), GMP_RNDN); } template -inline void eval_fabs(mpfr_float_backend& result, const mpfr_float_backend& val) +inline void eval_fabs(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_abs(result.data(), val.data(), GMP_RNDN); } template -inline void eval_ceil(mpfr_float_backend& result, const mpfr_float_backend& val) +inline void eval_ceil(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_ceil(result.data(), val.data()); } template -inline void eval_floor(mpfr_float_backend& result, const mpfr_float_backend& val) +inline void eval_floor(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_floor(result.data(), val.data()); } @@ -867,7 +855,7 @@ inline void eval_trunc(mpfr_float_backend& result, const mpfr_float_ba mpfr_trunc(result.data(), val.data()); } template -inline void eval_ldexp(mpfr_float_backend& result, const mpfr_float_backend& val, long e) +inline void eval_ldexp(mpfr_float_backend& result, const mpfr_float_backend& val, long e) BOOST_NOEXCEPT { if(e > 0) mpfr_mul_2exp(result.data(), val.data(), e, GMP_RNDN); @@ -877,7 +865,7 @@ inline void eval_ldexp(mpfr_float_backend& result, const mpfr_float_ba result = val; } template -inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_backend& val, int* e) +inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_backend& val, int* e) BOOST_NOEXCEPT { long v; mpfr_get_d_2exp(&v, val.data(), GMP_RNDN); @@ -885,20 +873,20 @@ inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_ba eval_ldexp(result, val, -v); } template -inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_backend& val, long* e) +inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_backend& val, long* e) BOOST_NOEXCEPT { mpfr_get_d_2exp(e, val.data(), GMP_RNDN); return eval_ldexp(result, val, -*e); } template -inline int eval_fpclassify(const mpfr_float_backend& val) +inline int eval_fpclassify(const mpfr_float_backend& val) BOOST_NOEXCEPT { return mpfr_inf_p(val.data()) ? FP_INFINITE : mpfr_nan_p(val.data()) ? FP_NAN : mpfr_zero_p(val.data()) ? FP_ZERO : FP_NORMAL; } template -inline void eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const mpfr_float_backend& e) +inline void eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const mpfr_float_backend& e) BOOST_NOEXCEPT { mpfr_pow(result.data(), b.data(), e.data(), GMP_RNDN); } @@ -915,13 +903,13 @@ inline void eval_pow(mpfr_float_backend& result, const mpfr_float_back #endif template -inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) BOOST_NOEXCEPT { mpfr_pow_si(result.data(), b.data(), e, GMP_RNDN); } template -inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) BOOST_NOEXCEPT { mpfr_pow_ui(result.data(), b.data(), e, GMP_RNDN); } @@ -929,79 +917,79 @@ inline typename enable_if, mpl::bool_ -inline void eval_exp(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_exp(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_exp(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_log(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_log(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_log(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_log10(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_log10(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_log10(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_sin(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_sin(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_sin(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_cos(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_cos(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_cos(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_tan(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_tan(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_tan(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_asin(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_asin(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_asin(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_acos(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_acos(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_acos(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_atan(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_atan(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_atan(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_atan2(mpfr_float_backend& result, const mpfr_float_backend& arg1, const mpfr_float_backend& arg2) +inline void eval_atan2(mpfr_float_backend& result, const mpfr_float_backend& arg1, const mpfr_float_backend& arg2) BOOST_NOEXCEPT { mpfr_atan2(result.data(), arg1.data(), arg2.data(), GMP_RNDN); } template -inline void eval_sinh(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_sinh(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_sinh(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_cosh(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_cosh(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_cosh(result.data(), arg.data(), GMP_RNDN); } template -inline void eval_tanh(mpfr_float_backend& result, const mpfr_float_backend& arg) +inline void eval_tanh(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_tanh(result.data(), arg.data(), GMP_RNDN); } @@ -1023,12 +1011,12 @@ namespace math{ namespace tools{ template <> -inline int digits() +inline int digits() BOOST_NOEXCEPT { return boost::multiprecision::backends::detail::get_default_precision(); } template <> -inline int digits, false> >() +inline int digits, false> >() BOOST_NOEXCEPT { return boost::multiprecision::backends::detail::get_default_precision(); } diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index c6a53aa7..a7192b1d 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -60,6 +60,7 @@ struct rational_adapter multiprecision::mp_number v1, v2; char c; bool have_hex = false; + const char* p = s; // saved for later while((0 != (c = *s)) && (c == 'x' || c == 'X' || c == '-' || c == '+' || (c >= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F')))) { @@ -84,6 +85,10 @@ struct rational_adapter } else v2 = 1; + if(*s) + { + BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Could parse the string \"") + p + std::string("\" as a valid rational number."))); + } data().assign(v1, v2); return *this; } @@ -141,6 +146,11 @@ inline void eval_multiply(rational_adapter& result, const rational_a template inline void eval_divide(rational_adapter& result, const rational_adapter& o) { + using default_ops::eval_is_zero; + if(eval_is_zero(o)) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Divide by zero.")); + } result.data() /= o.data(); } diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index d7456fd0..cc32fcd9 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -47,7 +47,7 @@ struct tommath_int detail::check_tommath_result(mp_init_copy(&m_data, const_cast< ::mp_int*>(&o.m_data))); } #ifndef BOOST_NO_RVALUE_REFERENCES - tommath_int(tommath_int&& o) + tommath_int(tommath_int&& o) BOOST_NOEXCEPT { m_data = o.m_data; o.m_data.dp = 0; @@ -164,8 +164,21 @@ struct tommath_int } tommath_int& operator = (const char* s) { + // + // We don't use libtommath's own routine because it doesn't error check the input :-( + // + using default_ops::eval_multiply; + using default_ops::eval_add; std::size_t n = s ? std::strlen(s) : 0; - int radix = 10; + *this = static_cast(0u); + unsigned radix = 10; + bool isneg = false; + if(n && (*s == '-')) + { + --n; + ++s; + isneg = true; + } if(n && (*s == '0')) { if((n > 1) && ((s[1] == 'x') || (s[1] == 'X'))) @@ -178,13 +191,80 @@ struct tommath_int { radix = 8; n -= 1; - s += 1; } } if(n) - detail::check_tommath_result(mp_read_radix(&m_data, s, radix)); - else - detail::check_tommath_result(mp_set_int(&m_data, 0)); + { + if(radix == 8 || radix == 16) + { + unsigned shift = radix == 8 ? 3 : 4; + unsigned block_count = DIGIT_BIT / shift; + unsigned block_shift = shift * block_count; + boost::uint32_t val, block; + while(*s) + { + block = 0; + for(unsigned i = 0; (i < block_count); ++i) + { + if(*s >= '0' && *s <= '9') + val = *s - '0'; + else if(*s >= 'a' && *s <= 'f') + val = 10 + *s - 'a'; + else if(*s >= 'A' && *s <= 'F') + val = 10 + *s - 'A'; + else + val = 400; + if(val > radix) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string.")); + } + block <<= shift; + block |= val; + if(!*++s) + { + // final shift is different: + block_shift = (i + 1) * shift; + break; + } + } + detail::check_tommath_result(mp_mul_2d(&data(), block_shift, &data())); + if(data().used) + data().dp[0] |= block; + else + *this = block; + } + } + else + { + // Base 10, we extract blocks of size 10^9 at a time, that way + // the number of multiplications is kept to a minimum: + boost::uint32_t block_mult = 1000000000; + while(*s) + { + boost::uint32_t block = 0; + for(unsigned i = 0; i < 9; ++i) + { + boost::uint32_t val; + if(*s >= '0' && *s <= '9') + val = *s - '0'; + else + BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected character encountered in input.")); + block *= 10; + block += val; + if(!*++s) + { + static const boost::uint32_t block_multiplier[9] = { 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 }; + block_mult = block_multiplier[i]; + break; + } + } + eval_multiply(*this, block_mult); + eval_add(*this, block); + } + } + } + if(isneg) + this->negate(); return *this; } std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const @@ -238,7 +318,7 @@ struct tommath_int } ::mp_int& data() { return m_data; } const ::mp_int& data()const { return m_data; } - void swap(tommath_int& o) + void swap(tommath_int& o)BOOST_NOEXCEPT { mp_exch(&m_data, &o.data()); } diff --git a/test/test.hpp b/test/test.hpp index 2214491f..6e83d762 100644 --- a/test/test.hpp +++ b/test/test.hpp @@ -102,7 +102,11 @@ void report_unexpected_exception(const E& e, int severity, const char* file, int BOOST_MP_REPORT_SEVERITY(severity); } -#define BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) catch(const std::exception& e) { report_unexpected_exception(e, severity, __FILE__, __LINE__, BOOST_CURRENT_FUNCTION); } +#define BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) \ + catch(const std::exception& e) \ + { report_unexpected_exception(e, severity, __FILE__, __LINE__, BOOST_CURRENT_FUNCTION); }\ + catch(...)\ + { std::cout << "Exception of unknown type was thrown" << std::endl; report_severity(severity); } #define BOOST_CHECK_IMP(x, severity)\ diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index afd0784c..e1bba8ba 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -11,9 +11,9 @@ #include #endif -#include #include #include +#include "test.hpp" #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \ !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) \ @@ -65,6 +65,12 @@ #define NO_MIXED_OPS +template +bool is_boost_rational(const boost::rational&) +{ + return true; +} + namespace boost{ namespace multiprecision{ #ifdef TEST_TOMMATH_BOOST_RATIONAL @@ -146,6 +152,12 @@ void test_complement(Real, Real, Real, const boost::mpl::false_&) template void test_integer_ops(const T&){} +template +bool is_boost_rational(const T&) +{ + return false; +} + template void test_integer_ops(const boost::mpl::int_&) { @@ -156,6 +168,25 @@ void test_integer_ops(const boost::mpl::int_> b; + BOOST_CHECK_EQUAL(a, b); } template @@ -451,6 +482,12 @@ void test_integer_ops(const boost::mpl::int_ @@ -517,6 +554,21 @@ void test_float_ops(const boost::mpl::int_(3.25)); r = pow(v, 25); BOOST_TEST(r == boost::math::pow<25>(Real(3.25))); + // + // Things that are expected errors: + // + BOOST_CHECK_THROW(Real("3.14L"), std::runtime_error); + if(std::numeric_limits::is_specialized) + { + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK(boost::math::isinf(Real(20) / 0u)); + } + else + { + BOOST_CHECK_THROW(Real(Real(20) / 0u), std::runtime_error); + } + } } template diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp index 52b4102a..a21f2a8b 100644 --- a/test/test_cpp_int.cpp +++ b/test/test_cpp_int.cpp @@ -60,6 +60,8 @@ void test() unsigned last_error_count = 0; boost::timer tim; + BOOST_CHECK_EQUAL(Number(), 0); + for(int i = 0; i < 10000; ++i) { mpz_int a = generate_random(1000); From 08ee67ccc201e74c1907329698a7dbc0a4a462c4 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 8 Jul 2012 17:54:35 +0000 Subject: [PATCH 199/256] Fix some 64-bit compilation issues. [SVN r79362] --- include/boost/multiprecision/cpp_int.hpp | 3 ++- include/boost/multiprecision/tommath.hpp | 2 +- performance/miller_rabin_performance.cpp | 2 +- 3 files changed, 4 insertions(+), 3 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index de26540f..a9ebeac7 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1511,7 +1511,8 @@ void divide_unsigned_helper(cpp_int_backend* result, { result->resize(r_order + 1); pres = result->limbs(); - pres[r_order] = 0; // just in case we don't set the most significant limb below. + if(result->size() > r_order) + pres[r_order] = 0; // just in case we don't set the most significant limb below. } do diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index cc32fcd9..5f2c3db6 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -200,7 +200,7 @@ struct tommath_int unsigned shift = radix == 8 ? 3 : 4; unsigned block_count = DIGIT_BIT / shift; unsigned block_shift = shift * block_count; - boost::uint32_t val, block; + unsigned long long val, block; while(*s) { block = 0; diff --git a/performance/miller_rabin_performance.cpp b/performance/miller_rabin_performance.cpp index 458c14b2..9667aa51 100644 --- a/performance/miller_rabin_performance.cpp +++ b/performance/miller_rabin_performance.cpp @@ -138,7 +138,7 @@ int main() #ifdef TEST_CPP_INT test_miller_rabin, false> >("cpp_int (no Expression templates)"); test_miller_rabin("cpp_int"); - test_miller_rabin > >("cpp_int (64-bit cache)"); + test_miller_rabin > >("cpp_int (128-bit cache)"); test_miller_rabin > >("cpp_int (256-bit cache)"); test_miller_rabin > >("cpp_int (512-bit cache)"); test_miller_rabin > >("cpp_int (1024-bit cache)"); From 281c667b71890db51f3b8fb8156d787977656862 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 23 Jul 2012 08:57:44 +0000 Subject: [PATCH 200/256] Update frontend to allow direct construction of backend. Improve construction times for cpp_int from integers. Allow constexpr construction. Allow fixed precision cpp_int's with small bit counts. [SVN r79692] --- doc/multiprecision.qbk | 6 + include/boost/multiprecision/cpp_int.hpp | 1137 +++++++++++------ .../multiprecision/detail/cpp_int_core.hpp | 58 +- .../detail/cpp_int_trivial_ops.hpp | 284 ++++ include/boost/multiprecision/gmp.hpp | 4 - include/boost/multiprecision/mp_number.hpp | 19 +- include/boost/multiprecision/mpfr.hpp | 4 - performance/performance_test.cpp | 87 +- test/test_arithmetic.cpp | 4 + 9 files changed, 1189 insertions(+), 414 deletions(-) create mode 100644 include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 284b2451..71b6a134 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -119,6 +119,8 @@ However, conversions are allowed: [h4 Expression Templates] +TODO: compare to rvalue refs. + Class `mp_number` is expression-template-enabled: that means that rather than having a multiplication operator that looks like this: @@ -246,6 +248,8 @@ We'll conclude this section by providing some more performance comparisons betwe again, all are using [mpfr] to carry out the underlying arithmetic, and all are operating at the same precision (50 decimal digits): +TODO: Update, compare to rvalue refs but no ET's as well. + [table Evaluation of Boost.Math's Bessel function test data [[Library][Relative Time][Relative Number of Memory Allocations]] [[mp_number][1.0 (6.21s)][1.0 (2685469)]] @@ -1696,6 +1700,8 @@ The requirements on the `Backend` template argument to `mp_number` are split up compulsory requirements, and optional requirements that are either to improve performance or provide optional features. +TODO: Add optional construction support, add throws specification, clarify what compulsory means. + In the following tables, type B is the `Backend` template arument to `mp_number`, `b` and `b2` are a variables of type B, `cb` and `cb2` are constant variables of type B, `a` is a variable of Arithmetic type, `s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`, diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index a9ebeac7..0edba4aa 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -16,6 +16,7 @@ #include #include #include +#include namespace boost{ namespace multiprecision{ @@ -27,16 +28,32 @@ namespace backends{ #pragma warning(disable:4127 4351) #endif -template > +template , bool trivial = is_void::value && (MinBits <= sizeof(double_limb_type) * CHAR_BIT) > struct cpp_int_backend; -template > -struct cpp_int_base : private Allocator::template rebind::other +template , bool trivial = false> +struct cpp_int_base; + +template +struct is_trivial_cpp_int; +template +struct is_trivial_cpp_int > +{ + typedef mpl::bool_ type; +}; + +template +struct cpp_int_base : private Allocator::template rebind::other { typedef typename Allocator::template rebind::other allocator_type; typedef typename allocator_type::pointer limb_pointer; typedef typename allocator_type::const_pointer const_limb_pointer; + // + // Interface invariants: + // + BOOST_STATIC_ASSERT(!is_void::value); + private: struct limb_data { @@ -61,6 +78,16 @@ private: { limb_data ld; limb_type la[internal_limb_count]; + limb_type first; + double_limb_type double_first; + + BOOST_CONSTEXPR data_type() : first(0) {} + BOOST_CONSTEXPR data_type(limb_type i) : first(i) {} + BOOST_CONSTEXPR data_type(signed_limb_type i) : first(i < 0 ? -i : i) {} +#ifdef BOOST_LITTLE_ENDIAN + BOOST_CONSTEXPR data_type(double_limb_type i) : double_first(i) {} + BOOST_CONSTEXPR data_type(signed_double_limb_type i) : double_first(i < 0 ? -i : i) {} +#endif }; data_type m_data; @@ -68,6 +95,19 @@ private: bool m_sign, m_internal; public: + // + // Direct construction: + // + BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT + : m_data(i), m_limbs(1), m_sign(false), m_internal(true) { } + BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT + : m_data(i), m_limbs(1), m_sign(i < 0), m_internal(true) { } +#if defined(BOOST_LITTLE_ENDIAN) + BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT + : m_data(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false), m_internal(true) { } + BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT + : m_data(i), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), m_sign(i < 0), m_internal(true) { } +#endif // // Helper functions for getting at our internal data, and manipulating storage: // @@ -114,13 +154,11 @@ public: limb_pointer p = limbs(); while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; } - BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1), m_sign(false), m_internal(true) - { - } + BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1), m_sign(false), m_internal(true) {} cpp_int_base(const cpp_int_base& o) : allocator_type(o), m_limbs(0), m_internal(true) { resize(o.size()); - std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + std::copy(o.limbs(), o.limbs() + o.size(), limbs()); m_sign = o.m_sign; } #ifndef BOOST_NO_RVALUE_REFERENCES @@ -128,7 +166,7 @@ public: { if(m_internal) { - std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + std::copy(o.limbs(), o.limbs() + o.size(), limbs()); } else { @@ -178,11 +216,16 @@ public: }; template -struct cpp_int_base +struct cpp_int_base { typedef limb_type* limb_pointer; typedef const limb_type* const_limb_pointer; + // + // Interface invariants: + // + BOOST_STATIC_ASSERT_MSG(MinBits > sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?"); + public: BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT); BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u)); @@ -193,11 +236,28 @@ public: BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs"); private: - limb_type m_data[internal_limb_count]; + union{ + limb_type m_data[internal_limb_count]; + limb_type m_first_limb; + double_limb_type m_double_first_limb; + }; boost::uint16_t m_limbs; bool m_sign; public: + // + // Direct construction: + // + BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT + : m_first_limb(i), m_limbs(1), m_sign(false) {} + BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT + : m_first_limb(std::abs(i)), m_limbs(1), m_sign(i < 0) {} +#if defined(BOOST_LITTLE_ENDIAN) + BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT + : m_double_first_limb(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false) {} + BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT + : m_double_first_limb(i < 0 ? -i : i), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), m_sign(i < 0) {} +#endif // // Helper functions for getting at our internal data, and manipulating storage: // @@ -227,20 +287,12 @@ public: if((m_limbs == 1) && (!*p)) m_sign = false; // zero is always unsigned } - BOOST_CONSTEXPR cpp_int_base() : m_data(), m_limbs(1), m_sign(false) {} - cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(0) + BOOST_CONSTEXPR cpp_int_base() : m_first_limb(0), m_limbs(1), m_sign(false) {} + cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs), m_sign(o.m_sign) { - resize(o.size()); - std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); - m_sign = o.m_sign; + std::copy(o.limbs(), o.limbs() + o.size(), limbs()); } -#ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_base(cpp_int_base&& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs), m_sign(o.m_sign) - { - std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); - } -#endif - ~cpp_int_base() BOOST_NOEXCEPT {} + //~cpp_int_base() BOOST_NOEXCEPT {} void assign(const cpp_int_base& o) BOOST_NOEXCEPT { if(this != &o) @@ -274,11 +326,16 @@ public: }; template -struct cpp_int_base +struct cpp_int_base { typedef limb_type* limb_pointer; typedef const limb_type* const_limb_pointer; + // + // Interface invariants: + // + BOOST_STATIC_ASSERT_MSG(MinBits > sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?"); + public: BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT); BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u)); @@ -289,10 +346,27 @@ public: BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs"); private: - limb_type m_data[internal_limb_count]; + union{ + limb_type m_data[internal_limb_count]; + limb_type m_first_limb; + double_limb_type m_double_first_limb; + }; limb_type m_limbs; public: + // + // Direct construction: + // + BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT + : m_first_limb(i), m_limbs(1) {} + cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT + : m_first_limb(i < 0 ? -i : i), m_limbs(1) { if(i < 0) negate(); } +#ifdef BOOST_LITTLE_ENDIAN + BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT + : m_double_first_limb(i), m_limbs(i > max_limb_value ? 2 : 1) {} + cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT + : m_double_first_limb(i < 0 ? -i : i), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)) { if(i < 0) negate(); } +#endif // // Helper functions for getting at our internal data, and manipulating storage: // @@ -312,19 +386,12 @@ public: while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; } - BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1) {} - cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(0) + BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_first_limb(0), m_limbs(1) {} + cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs) { - resize(o.size()); - std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + std::copy(o.limbs(), o.limbs() + o.size(), limbs()); } -#ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_base(cpp_int_base&& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs) - { - std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); - } -#endif - ~cpp_int_base() BOOST_NOEXCEPT {} + //~cpp_int_base() BOOST_NOEXCEPT {} void assign(const cpp_int_base& o) BOOST_NOEXCEPT { if(this != &o) @@ -358,52 +425,244 @@ public: } }; -template -const unsigned cpp_int_base::limb_bits; -template -const limb_type cpp_int_base::max_limb_value; -template -const limb_type cpp_int_base::sign_bit_mask; -template -const unsigned cpp_int_base::internal_limb_count; -template -const bool cpp_int_base::variable; - -template -const unsigned cpp_int_base::limb_bits; -template -const limb_type cpp_int_base::max_limb_value; -template -const limb_type cpp_int_base::sign_bit_mask; -template -const unsigned cpp_int_base::internal_limb_count; -template -const bool cpp_int_base::variable; - -template -const unsigned cpp_int_base::limb_bits; -template -const limb_type cpp_int_base::max_limb_value; -template -const limb_type cpp_int_base::sign_bit_mask; -template -const unsigned cpp_int_base::internal_limb_count; -template -const bool cpp_int_base::variable; - -template -struct cpp_int_backend : public cpp_int_base +template +struct trivial_limb_type { - typedef cpp_int_base base_type; + typedef typename mpl::if_c< + N <= sizeof(long long) * CHAR_BIT, + typename boost::uint_t::least, + double_limb_type + >::type type; +}; + +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4244) // loss of data in initialization +#endif + +template +struct cpp_int_base +{ + typedef typename trivial_limb_type::type local_limb_type; + typedef local_limb_type* limb_pointer; + typedef const local_limb_type* const_limb_pointer; +private: + BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(local_limb_type) * CHAR_BIT); + BOOST_STATIC_CONSTANT(local_limb_type, limb_mask = MinBits < limb_bits ? (local_limb_type(1) << MinBits) -1 : (~local_limb_type(0))); + + local_limb_type m_data; + bool m_sign; + + // + // Interface invariants: + // + BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?"); + +public: + // + // Direct construction: + // + template + BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + : m_data(i < 0 ? -i : i), m_sign(i < 0) {} + template + BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + : m_data(i), m_sign(false) {} + template + cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + : m_data(std::fabs(i)), m_sign(i < 0) {} + // + // Helper functions for getting at our internal data, and manipulating storage: + // + BOOST_CONSTEXPR unsigned size()const BOOST_NOEXCEPT { return 1; } + limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; } + const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; } + bool sign()const BOOST_NOEXCEPT { return m_sign; } + void sign(bool b) BOOST_NOEXCEPT + { + m_sign = b; + // Check for zero value: + if(m_sign && !m_data) + { + m_sign = false; + } + } + void resize(unsigned new_size) BOOST_NOEXCEPT {} + void normalize() BOOST_NOEXCEPT + { + if(!m_data) + m_sign = false; // zero is always unsigned + m_data &= limb_mask; + } + + BOOST_CONSTEXPR cpp_int_base() : m_data(0), m_sign(false) {} + BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_data(o.m_data), m_sign(o.m_sign) {} + //~cpp_int_base() BOOST_NOEXCEPT {} + void assign(const cpp_int_base& o) BOOST_NOEXCEPT + { + m_data = o.m_data; + m_sign = o.m_sign; + } + void negate() BOOST_NOEXCEPT + { + m_sign = !m_sign; + // Check for zero value: + if(m_data == 0) + { + m_sign = false; + } + } + bool isneg()const BOOST_NOEXCEPT + { + return m_sign; + } + void do_swap(cpp_int_base& o) BOOST_NOEXCEPT + { + std::swap(m_sign, o.m_sign); + std::swap(m_data, o.m_data); + } +}; + +template +struct cpp_int_base +{ + typedef typename trivial_limb_type::type local_limb_type; + typedef local_limb_type* limb_pointer; + typedef const local_limb_type* const_limb_pointer; +private: + BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(local_limb_type) * CHAR_BIT); + BOOST_STATIC_CONSTANT(local_limb_type, limb_mask = MinBits < limb_bits ? (local_limb_type(1) << MinBits) -1 : (~local_limb_type(0))); + + local_limb_type m_data; + + // + // Interface invariants: + // + BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?"); + +public: + // + // Direct construction: + // + template + BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + : m_data(i < 0 ? 1 + ~static_cast(-i) : static_cast(i)) {} + template + BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + : m_data(i) {} + template + cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + : m_data(std::fabs(i)) + { + if(i < 0) + negate(); + } + // + // Helper functions for getting at our internal data, and manipulating storage: + // + BOOST_CONSTEXPR unsigned size()const BOOST_NOEXCEPT { return 1; } + limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; } + const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; } + BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; } + void sign(bool b) BOOST_NOEXCEPT + { + if(b) + negate(); + } + void resize(unsigned new_size) BOOST_NOEXCEPT {} + void normalize() BOOST_NOEXCEPT + { + m_data &= limb_mask; + } + + BOOST_CONSTEXPR cpp_int_base() : m_data(0) {} + BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_data(o.m_data) {} + //~cpp_int_base() BOOST_NOEXCEPT {} + void assign(const cpp_int_base& o) BOOST_NOEXCEPT + { + m_data = o.m_data; + } + void negate() BOOST_NOEXCEPT + { + m_data = ~m_data; + ++m_data; + } + BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT + { + return false; + } + void do_swap(cpp_int_base& o) BOOST_NOEXCEPT + { + std::swap(m_data, o.m_data); + } +}; + +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + +template +const unsigned cpp_int_base::limb_bits; +template +const limb_type cpp_int_base::max_limb_value; +template +const limb_type cpp_int_base::sign_bit_mask; +template +const unsigned cpp_int_base::internal_limb_count; +template +const bool cpp_int_base::variable; + +template +const unsigned cpp_int_base::limb_bits; +template +const limb_type cpp_int_base::max_limb_value; +template +const limb_type cpp_int_base::sign_bit_mask; +template +const unsigned cpp_int_base::internal_limb_count; +template +const bool cpp_int_base::variable; + +template +const unsigned cpp_int_base::limb_bits; +template +const limb_type cpp_int_base::max_limb_value; +template +const limb_type cpp_int_base::sign_bit_mask; +template +const unsigned cpp_int_base::internal_limb_count; +template +const bool cpp_int_base::variable; + +template +struct cpp_int_backend : public cpp_int_base +{ + typedef cpp_int_backend self_type; + typedef cpp_int_base base_type; + typedef typename is_trivial_cpp_int::type trivial_tag; public: typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list float_types; BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{} - cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) : base_type(o) {} + BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) : base_type(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT : base_type(static_cast(o)) {} + BOOST_CONSTEXPR cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT : base_type(static_cast(o)) {} +#endif + template + BOOST_CONSTEXPR cpp_int_backend(LT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT + : base_type(i) {} + template + BOOST_CONSTEXPR cpp_int_backend(SLT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT + : base_type(i) {} +#if defined(BOOST_LITTLE_ENDIAN) + template + BOOST_CONSTEXPR cpp_int_backend(LT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT + : base_type(i) {} + template + BOOST_CONSTEXPR cpp_int_backend(SLT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT + : base_type(i) {} #endif cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { @@ -736,14 +995,110 @@ public: } }; +template +struct cpp_int_backend : public cpp_int_base +{ +public: + typedef cpp_int_backend self_type; + typedef cpp_int_base base_type; + typedef typename is_trivial_cpp_int::type trivial_tag; + typedef mpl::list< + signed char, short, int, long, + long long, signed_double_limb_type> signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list float_types; + + BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(typename base_type::local_limb_type) * CHAR_BIT); + + BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{} + BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT : base_type(o) {} + cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_NOEXCEPT + { + this->assign(o); + return *this; + } + + template + BOOST_CONSTEXPR cpp_int_backend(A i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + : base_type(i) {} + + template + typename enable_if, cpp_int_backend&>::type operator = (SI i) BOOST_NOEXCEPT + { + *this->limbs() = static_cast(std::abs(i)); + this->sign(i < 0); + return *this; + } + template + typename enable_if, cpp_int_backend&>::type operator = (UI i) BOOST_NOEXCEPT + { + *this->limbs() = static_cast(i); + return *this; + } + template + typename enable_if, cpp_int_backend&>::type operator = (F i) BOOST_NOEXCEPT + { + *this->limbs() = static_cast(std::abs(i)); + this->sign(i < 0); + return *this; + } + cpp_int_backend& operator = (const char* s) + { + try{ + *this->limbs() = boost::lexical_cast(s); + } + catch(const std::exception&) + { + BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Could not interpret the string \"") + s + std::string("\" as a valid integer value."))); + } + return *this; + } + void swap(cpp_int_backend& o) BOOST_NOEXCEPT + { + this->do_swap(o); + } + std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const + { + std::stringstream ss; + ss.flags(f); + ss << *this->limbs(); + std::string result; + if(this->sign()) + result += '-'; + result += ss.str(); + return result; + } + int compare(const cpp_int_backend& o)const BOOST_NOEXCEPT + { + if(this->sign() != o.sign()) + return this->sign() ? -1 : 1; + int result = 0; + // Only do the compare if the same sign: + result = *this->limbs() == *o.limbs() ? 0 : *this->limbs() < *o.limbs() ? -1 : 1; + + if(this->sign()) + result = -result; + return result; + } + template + typename enable_if, int>::type compare(Arithmatic i)const BOOST_NOEXCEPT + { + // braindead version: + cpp_int_backend t; + t = i; + return compare(t); + } +}; + template -inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_add(result, result, o); } template -inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { using std::swap; @@ -761,10 +1116,10 @@ inline void add_unsigned(cpp_int_backend& result, co return; } result.resize(x); - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); - typename cpp_int_backend::const_limb_pointer pb = b.limbs(); - typename cpp_int_backend::limb_pointer pr = result.limbs(); - typename cpp_int_backend::limb_pointer pr_end = pr + m; + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr_end = pr + m; if(as < bs) swap(pa, pb); @@ -774,7 +1129,7 @@ inline void add_unsigned(cpp_int_backend& result, co { carry += static_cast(*pa) + static_cast(*pb); *pr = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; ++pr, ++pa, ++pb; } pr_end += x - m; @@ -789,21 +1144,21 @@ inline void add_unsigned(cpp_int_backend& result, co } carry += static_cast(*pa); *pr = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; ++pr, ++pa; } if(carry) { result.resize(x + 1); // We overflowed, need to add one more limb: - if(cpp_int_backend::variable || (result.size() > x)) + if(cpp_int_backend::variable || (result.size() > x)) result.limbs()[x] = static_cast(carry); } result.normalize(); result.sign(a.sign()); } template -inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign() != b.sign()) { @@ -814,30 +1169,30 @@ inline void eval_add(cpp_int_backend& result, const } template -inline void add_unsigned(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void add_unsigned(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Addition using modular arithmatic. // Nothing fancy, just let uintmax_t take the strain: double_limb_type carry = o; - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); for(unsigned i = 0; carry && (i < result.size()); ++i) { carry += static_cast(pr[i]); pr[i] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } if(carry) { unsigned x = result.size(); result.resize(x + 1); // We overflowed, need to add one more limb: - if(cpp_int_backend::variable || (result.size() > x)) + if(cpp_int_backend::variable || (result.size() > x)) result.limbs()[x] = static_cast(carry); } result.normalize(); } template -inline void eval_add(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_add(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(result.sign()) { @@ -847,7 +1202,7 @@ inline void eval_add(cpp_int_backend& result, const add_unsigned(result, o); } template -inline void eval_add(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_add(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o < 0) eval_subtract(result, static_cast(-o)); @@ -856,12 +1211,12 @@ inline void eval_add(cpp_int_backend& result, const } template -inline void subtract_unsigned(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void subtract_unsigned(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Subtract one limb. // Nothing fancy, just let uintmax_t take the strain: - BOOST_STATIC_CONSTANT(double_limb_type, borrow = static_cast(cpp_int_backend::max_limb_value) + 1); - typename cpp_int_backend::limb_pointer p = result.limbs(); + BOOST_STATIC_CONSTANT(double_limb_type, borrow = static_cast(cpp_int_backend::max_limb_value) + 1); + typename cpp_int_backend::limb_pointer p = result.limbs(); if(*p > o) { *p -= o; @@ -877,7 +1232,7 @@ inline void subtract_unsigned(cpp_int_backend& resul ++p; while(!*p) { - *p = cpp_int_backend::max_limb_value; + *p = cpp_int_backend::max_limb_value; ++p; } --*p; @@ -885,7 +1240,7 @@ inline void subtract_unsigned(cpp_int_backend& resul } } template -inline void eval_subtract(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_subtract(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(result.sign()) add_unsigned(result, o); @@ -893,7 +1248,7 @@ inline void eval_subtract(cpp_int_backend& result, c subtract_unsigned(result, o); } template -inline void eval_subtract(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_subtract(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o) { @@ -904,10 +1259,10 @@ inline void eval_subtract(cpp_int_backend& result, c } } template -inline void eval_increment(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_increment(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) { static const limb_type one = 1; - if(!result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) + if(!result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) ++result.limbs()[0]; else if(result.sign() && result.limbs()[0]) --result.limbs()[0]; @@ -915,23 +1270,23 @@ inline void eval_increment(cpp_int_backend& result) eval_add(result, one); } template -inline void eval_decrement(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_decrement(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) { static const limb_type one = 1; if(!result.sign() && result.limbs()[0]) --result.limbs()[0]; - else if(result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) + else if(result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) ++result.limbs()[0]; else eval_subtract(result, one); } template -inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_subtract(result, result, o); } template -inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { using std::swap; @@ -962,9 +1317,9 @@ inline void subtract_unsigned(cpp_int_backend& resul // Set up the result vector: result.resize(x); // Now that a, b, and result are stable, get pointers to their limbs: - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); - typename cpp_int_backend::const_limb_pointer pb = b.limbs(); - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); bool swapped = false; if(c < 0) { @@ -983,7 +1338,7 @@ inline void subtract_unsigned(cpp_int_backend& resul { borrow = static_cast(pa[i]) - static_cast(pb[i]) - borrow; pr[i] = static_cast(borrow); - borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; + borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; ++i; } // Now where only a has digits, only as long as we've borrowed: @@ -991,7 +1346,7 @@ inline void subtract_unsigned(cpp_int_backend& resul { borrow = static_cast(pa[i]) - borrow; pr[i] = static_cast(borrow); - borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; + borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; ++i; } // Any remaining digits are the same as those in pa: @@ -1008,7 +1363,7 @@ inline void subtract_unsigned(cpp_int_backend& resul result.negate(); } template -inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign() != b.sign()) { @@ -1018,7 +1373,7 @@ inline void eval_subtract(cpp_int_backend& result, c subtract_unsigned(result, a, b); } template -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Very simple long multiplication, only usable for small numbers of limb_type's // but that's the typical use case for this type anyway: @@ -1027,8 +1382,8 @@ inline void eval_multiply(cpp_int_backend& result, c // unsigned as = a.size(); unsigned bs = b.size(); - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); - typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); if(as == 1) { bool s = b.sign() != a.sign(); @@ -1057,19 +1412,19 @@ inline void eval_multiply(cpp_int_backend& result, c if(&result == &a) { - cpp_int_backend t(a); + cpp_int_backend t(a); eval_multiply(result, t, b); return; } if(&result == &b) { - cpp_int_backend t(b); + cpp_int_backend t(b); eval_multiply(result, a, t); return; } result.resize(as + bs); - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); static const double_limb_type limb_max = ~static_cast(0u); static const double_limb_type double_limb_max = ~static_cast(0u); @@ -1079,19 +1434,19 @@ inline void eval_multiply(cpp_int_backend& result, c std::memset(pr, 0, result.size() * sizeof(limb_type)); for(unsigned i = 0; i < as; ++i) { - unsigned inner_limit = cpp_int_backend::variable ? bs : (std::min)(result.size() - i, bs); + unsigned inner_limit = cpp_int_backend::variable ? bs : (std::min)(result.size() - i, bs); for(unsigned j = 0; j < inner_limit; ++j) { BOOST_ASSERT(i+j < result.size()); - BOOST_ASSERT(!std::numeric_limits::is_specialized || ((std::numeric_limits::max)() - carry > static_cast(cpp_int_backend::max_limb_value) * static_cast(cpp_int_backend::max_limb_value))); + BOOST_ASSERT(!std::numeric_limits::is_specialized || ((std::numeric_limits::max)() - carry > static_cast(cpp_int_backend::max_limb_value) * static_cast(cpp_int_backend::max_limb_value))); carry += static_cast(pa[i]) * static_cast(pb[j]); BOOST_ASSERT(!std::numeric_limits::is_specialized || ((std::numeric_limits::max)() - carry >= pr[i+j])); carry += pr[i + j]; pr[i + j] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; - BOOST_ASSERT(carry <= (cpp_int_backend::max_limb_value)); + carry >>= cpp_int_backend::limb_bits; + BOOST_ASSERT(carry <= (cpp_int_backend::max_limb_value)); } - if(cpp_int_backend::variable || (i + bs < result.size())) + if(cpp_int_backend::variable || (i + bs < result.size())) pr[i + bs] = static_cast(carry); carry = 0; } @@ -1102,12 +1457,12 @@ inline void eval_multiply(cpp_int_backend& result, c result.sign(a.sign() != b.sign()); } template -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, a); } template -inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(!val) { @@ -1115,33 +1470,33 @@ inline void eval_multiply(cpp_int_backend& result, c return; } double_limb_type carry = 0; - typename cpp_int_backend::limb_pointer p = result.limbs(); - typename cpp_int_backend::limb_pointer pe = result.limbs() + result.size(); - typename cpp_int_backend::limb_pointer pa = a.limbs(); + typename cpp_int_backend::limb_pointer p = result.limbs(); + typename cpp_int_backend::limb_pointer pe = result.limbs() + result.size(); + typename cpp_int_backend::limb_pointer pa = a.limbs(); while(p != pe) { carry += static_cast(*pa) * static_cast(val); *p = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; ++p, ++pa; } if(carry) { unsigned i = result.size(); result.resize(i + 1); - if(cpp_int_backend::variable || (result.size() > i)) + if(cpp_int_backend::variable || (result.size() > i)) result.limbs()[i] = static_cast(carry); } - if(!cpp_int_backend::variable) + if(!cpp_int_backend::variable) result.normalize(); } template -inline void eval_multiply(cpp_int_backend& result, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_multiply(cpp_int_backend& result, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, val); } template -inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(val > 0) eval_multiply(result, a, static_cast(val)); @@ -1152,22 +1507,22 @@ inline void eval_multiply(cpp_int_backend& result, c } } template -inline void eval_multiply(cpp_int_backend& result, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_multiply(cpp_int_backend& result, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, val); } template -void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) +void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) { if((result == &x) || (&r == &x)) { - cpp_int_backend t(x); + cpp_int_backend t(x); divide_unsigned_helper(result, t, y, r); return; } if((result == &y) || (&r == &y)) { - cpp_int_backend t(y); + cpp_int_backend t(y); divide_unsigned_helper(result, x, t, r); return; } @@ -1195,7 +1550,7 @@ void divide_unsigned_helper(cpp_int_backend* result, if(result == &r) { - cpp_int_backend rem; + cpp_int_backend rem; divide_unsigned_helper(result, x, y, rem); r = rem; return; @@ -1217,8 +1572,8 @@ void divide_unsigned_helper(cpp_int_backend* result, return; } - typename cpp_int_backend::const_limb_pointer px = x.limbs(); - typename cpp_int_backend::const_limb_pointer py = y.limbs(); + typename cpp_int_backend::const_limb_pointer px = x.limbs(); + typename cpp_int_backend::const_limb_pointer py = y.limbs(); limb_type r_order = x.size() - 1; if((r_order == 0) && (*px == 0)) @@ -1247,7 +1602,7 @@ void divide_unsigned_helper(cpp_int_backend* result, } } - cpp_int_backend t; + cpp_int_backend t; bool r_neg = false; // @@ -1263,9 +1618,9 @@ void divide_unsigned_helper(cpp_int_backend* result, else if(r_order == 1) { double_limb_type a, b; - a = (static_cast(px[1]) << cpp_int_backend::limb_bits) | px[0]; + a = (static_cast(px[1]) << cpp_int_backend::limb_bits) | px[0]; b = y_order ? - (static_cast(py[1]) << cpp_int_backend::limb_bits) | py[0] + (static_cast(py[1]) << cpp_int_backend::limb_bits) | py[0] : py[0]; if(result) *result = a / b; @@ -1277,9 +1632,9 @@ void divide_unsigned_helper(cpp_int_backend* result, // if(result) result->resize(1 + r_order - y_order); - typename cpp_int_backend::const_limb_pointer prem = r.limbs(); + typename cpp_int_backend::const_limb_pointer prem = r.limbs(); // This is initialised just to keep the compiler from emitting useless warnings later on: - typename cpp_int_backend::limb_pointer pr = typename cpp_int_backend::limb_pointer(); + typename cpp_int_backend::limb_pointer pr = typename cpp_int_backend::limb_pointer(); if(result) { pr = result->limbs(); @@ -1297,10 +1652,10 @@ void divide_unsigned_helper(cpp_int_backend* result, if((prem[r_order] <= py[y_order]) && (r_order > 0)) { double_limb_type a, b, v; - a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; + a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; b = py[y_order]; v = a / b; - if(v > cpp_int_backend::max_limb_value) + if(v > cpp_int_backend::max_limb_value) guess = 1; else { @@ -1315,8 +1670,8 @@ void divide_unsigned_helper(cpp_int_backend* result, else { double_limb_type a, b, v; - a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; - b = (y_order > 0) ? (static_cast(py[y_order]) << cpp_int_backend::limb_bits) | py[y_order - 1] : (static_cast(py[y_order]) << cpp_int_backend::limb_bits); + a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; + b = (y_order > 0) ? (static_cast(py[y_order]) << cpp_int_backend::limb_bits) | py[y_order - 1] : (static_cast(py[y_order]) << cpp_int_backend::limb_bits); v = a / b; guess = static_cast(v); } @@ -1340,7 +1695,7 @@ void divide_unsigned_helper(cpp_int_backend* result, eval_subtract(*result, t); } } - else if(cpp_int_backend::max_limb_value - pr[shift] > guess) + else if(cpp_int_backend::max_limb_value - pr[shift] > guess) pr[shift] += guess; else { @@ -1357,15 +1712,15 @@ void divide_unsigned_helper(cpp_int_backend* result, // double_limb_type carry = 0; t.resize(y.size() + shift + 1); - bool truncated_t = !cpp_int_backend::variable && (t.size() != y.size() + shift + 1); - typename cpp_int_backend::limb_pointer pt = t.limbs(); + bool truncated_t = !cpp_int_backend::variable && (t.size() != y.size() + shift + 1); + typename cpp_int_backend::limb_pointer pt = t.limbs(); for(unsigned i = 0; i < shift; ++i) pt[i] = 0; for(unsigned i = 0; i < y.size(); ++i) { carry += static_cast(py[i]) * static_cast(guess); pt[i + shift] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } if(carry && !truncated_t) { @@ -1424,18 +1779,18 @@ void divide_unsigned_helper(cpp_int_backend* result, } template -void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) +void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) { if((result == &x) || (&r == &x)) { - cpp_int_backend t(x); + cpp_int_backend t(x); divide_unsigned_helper(result, t, y, r); return; } if(result == &r) { - cpp_int_backend rem; + cpp_int_backend rem; divide_unsigned_helper(result, x, y, rem); r = rem; return; @@ -1459,7 +1814,7 @@ void divide_unsigned_helper(cpp_int_backend* result, // r = x; r.sign(false); - typename cpp_int_backend::limb_pointer pr = r.limbs(); + typename cpp_int_backend::limb_pointer pr = r.limbs(); if((r_order == 0) && (*pr == 0)) { @@ -1494,7 +1849,7 @@ void divide_unsigned_helper(cpp_int_backend* result, else if(r_order == 1) { double_limb_type a; - a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[0]; + a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[0]; if(result) { *result = a / y; @@ -1506,7 +1861,7 @@ void divide_unsigned_helper(cpp_int_backend* result, } // This is initialised just to keep the compiler from emitting useless warnings later on: - typename cpp_int_backend::limb_pointer pres = typename cpp_int_backend::limb_pointer(); + typename cpp_int_backend::limb_pointer pres = typename cpp_int_backend::limb_pointer(); if(result) { result->resize(r_order + 1); @@ -1523,7 +1878,7 @@ void divide_unsigned_helper(cpp_int_backend* result, if((pr[r_order] < y) && r_order) { double_limb_type a, b; - a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[r_order - 1]; + a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[r_order - 1]; b = a % y; r.resize(r.size() - 1); --r_order; @@ -1568,86 +1923,86 @@ void divide_unsigned_helper(cpp_int_backend* result, } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(&result, a, b, r); result.sign(a.sign() != b.sign()); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(&result, a, b, r); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(&result, a, std::abs(b), r); if(b < 0) result.negate(); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& b) +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_divide(cpp_int_backend& result, limb_type b) +inline void eval_divide(cpp_int_backend& result, limb_type b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_divide(cpp_int_backend& result, signed_limb_type b) +inline void eval_divide(cpp_int_backend& result, signed_limb_type b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { - divide_unsigned_helper(static_cast* >(0), a, b, result); + divide_unsigned_helper(static_cast* >(0), a, b, result); result.sign(a.sign()); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) { - divide_unsigned_helper(static_cast* >(0), a, b, result); + divide_unsigned_helper(static_cast* >(0), a, b, result); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) { - divide_unsigned_helper(static_cast* >(0), a, static_cast(std::abs(b)), result); + divide_unsigned_helper(static_cast* >(0), a, static_cast(std::abs(b)), result); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); eval_modulus(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, limb_type b) +inline void eval_modulus(cpp_int_backend& result, limb_type b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); eval_modulus(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, signed_limb_type b) +inline void eval_modulus(cpp_int_backend& result, signed_limb_type b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); eval_modulus(result, a, b); } template -void bitwise_op(cpp_int_backend& result, const cpp_int_backend& o, Op op) BOOST_NOEXCEPT +void bitwise_op(cpp_int_backend& result, const cpp_int_backend& o, Op op) BOOST_NOEXCEPT { // // There are 4 cases: @@ -1666,8 +2021,8 @@ void bitwise_op(cpp_int_backend& result, const cpp_i unsigned m, x; minmax(rs, os, m, x); result.resize(x); - typename cpp_int_backend::limb_pointer pr = result.limbs(); - typename cpp_int_backend::const_limb_pointer po = o.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::const_limb_pointer po = o.limbs(); for(unsigned i = rs; i < x; ++i) pr[i] = 0; @@ -1690,13 +2045,13 @@ void bitwise_op(cpp_int_backend& result, const cpp_i { carry += static_cast(~po[i]); pr[i] = op(pr[i], static_cast(carry)); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } for(unsigned i = os; i < x; ++i) { carry += static_cast(~limb_type(0)); pr[i] = op(pr[i], static_cast(carry)); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } // Set the overflow into the "extra" limb: carry += static_cast(~limb_type(0)); @@ -1713,13 +2068,13 @@ void bitwise_op(cpp_int_backend& result, const cpp_i { carry += static_cast(~pr[i]); pr[i] = op(static_cast(carry), po[i]); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } for(unsigned i = os; i < x; ++i) { carry += static_cast(~pr[i]); pr[i] = op(static_cast(carry), limb_type(0)); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } // Set the overflow into the "extra" limb: carry += static_cast(~limb_type(0)); @@ -1735,16 +2090,16 @@ void bitwise_op(cpp_int_backend& result, const cpp_i r_carry += static_cast(~pr[i]); o_carry += static_cast(~po[i]); pr[i] = op(static_cast(r_carry), static_cast(o_carry)); - r_carry >>= cpp_int_backend::limb_bits; - o_carry >>= cpp_int_backend::limb_bits; + r_carry >>= cpp_int_backend::limb_bits; + o_carry >>= cpp_int_backend::limb_bits; } for(unsigned i = os; i < x; ++i) { r_carry += static_cast(~pr[i]); o_carry += static_cast(~limb_type(0)); pr[i] = op(static_cast(r_carry), static_cast(o_carry)); - r_carry >>= cpp_int_backend::limb_bits; - o_carry >>= cpp_int_backend::limb_bits; + r_carry >>= cpp_int_backend::limb_bits; + o_carry >>= cpp_int_backend::limb_bits; } // Set the overflow into the "extra" limb: r_carry += static_cast(~limb_type(0)); @@ -1763,7 +2118,7 @@ void bitwise_op(cpp_int_backend& result, const cpp_i { carry += static_cast(~pr[i]); pr[i] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } } else @@ -1777,22 +2132,22 @@ struct bit_or { limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCE struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a ^ b; } }; template -inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o)BOOST_NOEXCEPT_IF(is_void::value) +inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o)BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_and()); } template -inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) +inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_or()); } template -inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) +inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_xor()); } template -inline void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Increment and negate: result = o; @@ -1800,7 +2155,7 @@ inline void eval_complement(cpp_int_backend& result, result.negate(); } template -inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT +inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT { if(!s) return; @@ -1876,23 +2231,23 @@ inline void eval_left_shift(cpp_int_backend& result, doub } } template -inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(!s) return; - limb_type offset = static_cast(s / cpp_int_backend::limb_bits); - limb_type shift = static_cast(s % cpp_int_backend::limb_bits); + limb_type offset = static_cast(s / cpp_int_backend::limb_bits); + limb_type shift = static_cast(s % cpp_int_backend::limb_bits); unsigned ors = result.size(); if((ors == 1) && (!*result.limbs())) return; // shifting zero yields zero. unsigned rs = ors; - if(shift && (result.limbs()[rs - 1] >> (cpp_int_backend::limb_bits - shift))) + if(shift && (result.limbs()[rs - 1] >> (cpp_int_backend::limb_bits - shift))) ++rs; // Most significant limb will overflow when shifted rs += offset; result.resize(rs); - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); unsigned i = 0; if(shift) @@ -1901,20 +2256,20 @@ inline void eval_left_shift(cpp_int_backend& result, i = 0; if(rs > ors + offset) { - pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift); + pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift); --rs; } else { pr[rs - 1 - i] = pr[ors - 1 - i] << shift; if(ors > 1) - pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); + pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); ++i; } for(; ors > 1 + i; ++i) { pr[rs - 1 - i] = pr[ors - 1 - i] << shift; - pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); + pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift); } if(ors >= 1 + i) { @@ -1933,13 +2288,13 @@ inline void eval_left_shift(cpp_int_backend& result, } } template -inline void eval_right_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_right_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(!s) return; - limb_type offset = static_cast(s / cpp_int_backend::limb_bits); - limb_type shift = static_cast(s % cpp_int_backend::limb_bits); + limb_type offset = static_cast(s / cpp_int_backend::limb_bits); + limb_type shift = static_cast(s % cpp_int_backend::limb_bits); unsigned ors = result.size(); unsigned rs = ors; if(offset >= rs) @@ -1948,7 +2303,7 @@ inline void eval_right_shift(cpp_int_backend& result return; } rs -= offset; - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); if((pr[ors - 1] >> shift) == 0) --rs; if(rs == 0) @@ -1963,7 +2318,7 @@ inline void eval_right_shift(cpp_int_backend& result for(; i + offset + 1 < ors; ++i) { pr[i] = pr[i + offset] >> shift; - pr[i] |= pr[i + offset + 1] << (cpp_int_backend::limb_bits - shift); + pr[i] |= pr[i + offset + 1] << (cpp_int_backend::limb_bits - shift); } pr[i] = pr[i + offset] >> shift; } @@ -1987,14 +2342,14 @@ inline Integer negate_integer(Integer i, const mpl::false_&) BOOST_NOEXCEPT } template -inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) BOOST_NOEXCEPT +inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) BOOST_NOEXCEPT { *result = static_cast(backend.limbs()[0]); - unsigned shift = cpp_int_backend::limb_bits; + unsigned shift = cpp_int_backend::limb_bits; for(unsigned i = 1; (i < backend.size()) && (shift < static_cast(std::numeric_limits::digits)); ++i) { *result += static_cast(backend.limbs()[i]) << shift; - shift += cpp_int_backend::limb_bits; + shift += cpp_int_backend::limb_bits; } if(backend.sign()) { @@ -2003,32 +2358,32 @@ inline typename enable_if, void>::type eval_convert_to(R* result, } template -inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) BOOST_NOEXCEPT +inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) BOOST_NOEXCEPT { - typename cpp_int_backend::const_limb_pointer p = backend.limbs(); - unsigned shift = cpp_int_backend::limb_bits; + typename cpp_int_backend::const_limb_pointer p = backend.limbs(); + unsigned shift = cpp_int_backend::limb_bits; *result = static_cast(*p); for(unsigned i = 1; i < backend.size(); ++i) { *result += static_cast(std::ldexp(static_cast(p[i]), shift)); - shift += cpp_int_backend::limb_bits; + shift += cpp_int_backend::limb_bits; } if(backend.sign()) *result = -*result; } template -inline bool eval_is_zero(const cpp_int_backend& val) BOOST_NOEXCEPT +inline bool eval_is_zero(const cpp_int_backend& val) BOOST_NOEXCEPT { return (val.size() == 1) && (val.limbs()[0] == 0); } template -inline int eval_get_sign(const cpp_int_backend& val) BOOST_NOEXCEPT +inline int eval_get_sign(const cpp_int_backend& val) BOOST_NOEXCEPT { return eval_is_zero(val) ? 0 : val.sign() ? -1 : 1; } template -inline void eval_abs(cpp_int_backend& result, const cpp_int_backend& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_abs(cpp_int_backend& result, const cpp_int_backend& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { result = val; result.sign(false); @@ -2038,7 +2393,7 @@ inline void eval_abs(cpp_int_backend& result, const // Get the location of the least-significant-bit: // template -inline unsigned eval_lsb(const cpp_int_backend& a) BOOST_NOEXCEPT +inline unsigned eval_lsb(const cpp_int_backend& a) BOOST_NOEXCEPT { BOOST_ASSERT(eval_get_sign(a) != 0); @@ -2059,15 +2414,15 @@ inline unsigned eval_lsb(const cpp_int_backend& a) B ++result; } - return result + index * cpp_int_backend::limb_bits; + return result + index * cpp_int_backend::limb_bits; } template -inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { int shift; - cpp_int_backend u(a), v(b); + cpp_int_backend u(a), v(b); int s = eval_get_sign(u); @@ -2123,10 +2478,10 @@ inline void eval_gcd(cpp_int_backend& result, const } template -inline bool eval_bit_test(const cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT +inline bool eval_bit_test(const cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT { - unsigned offset = index / cpp_int_backend::limb_bits; - unsigned shift = index % cpp_int_backend::limb_bits; + unsigned offset = index / cpp_int_backend::limb_bits; + unsigned shift = index % cpp_int_backend::limb_bits; limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u); if(offset >= val.size()) return false; @@ -2134,10 +2489,10 @@ inline bool eval_bit_test(const cpp_int_backend& val } template -inline void eval_bit_set(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_bit_set(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT_IF(boost::is_void::value) { - unsigned offset = index / cpp_int_backend::limb_bits; - unsigned shift = index % cpp_int_backend::limb_bits; + unsigned offset = index / cpp_int_backend::limb_bits; + unsigned shift = index % cpp_int_backend::limb_bits; limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u); if(offset >= val.size()) { @@ -2152,10 +2507,10 @@ inline void eval_bit_set(cpp_int_backend& val, unsig } template -inline void eval_bit_unset(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT +inline void eval_bit_unset(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT { - unsigned offset = index / cpp_int_backend::limb_bits; - unsigned shift = index % cpp_int_backend::limb_bits; + unsigned offset = index / cpp_int_backend::limb_bits; + unsigned shift = index % cpp_int_backend::limb_bits; limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u); if(offset >= val.size()) return; @@ -2164,10 +2519,10 @@ inline void eval_bit_unset(cpp_int_backend& val, uns } template -inline void eval_bit_flip(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_bit_flip(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT_IF(boost::is_void::value) { - unsigned offset = index / cpp_int_backend::limb_bits; - unsigned shift = index % cpp_int_backend::limb_bits; + unsigned offset = index / cpp_int_backend::limb_bits; + unsigned shift = index % cpp_int_backend::limb_bits; limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u); if(offset >= val.size()) { @@ -2183,9 +2538,9 @@ inline void eval_bit_flip(cpp_int_backend& val, unsi } template -inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { - cpp_int_backend t; + cpp_int_backend t; eval_gcd(t, a, b); if(eval_is_zero(t)) @@ -2202,8 +2557,8 @@ inline void eval_lcm(cpp_int_backend& result, const } template -inline void eval_qr(const cpp_int_backend& x, const cpp_int_backend& y, - cpp_int_backend& q, cpp_int_backend& r) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_qr(const cpp_int_backend& x, const cpp_int_backend& y, + cpp_int_backend& q, cpp_int_backend& r) BOOST_NOEXCEPT_IF(boost::is_void::value) { divide_unsigned_helper(&q, x, y, r); q.sign(x.sign() != y.sign()); @@ -2211,12 +2566,12 @@ inline void eval_qr(const cpp_int_backend& x, const } template -inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if((sizeof(Integer) <= sizeof(limb_type)) || (val <= (std::numeric_limits::max)())) { - cpp_int_backend d; - divide_unsigned_helper(static_cast*>(0), x, val, d); + cpp_int_backend d; + divide_unsigned_helper(static_cast*>(0), x, val, d); return d.limbs()[0]; } else @@ -2225,7 +2580,7 @@ inline typename enable_if, Integer>::type eval_integer_modu } } template -inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) BOOST_NOEXCEPT_IF(boost::is_void::value) { typedef typename make_unsigned::type unsigned_type; return eval_integer_modulus(x, static_cast(std::abs(val))); @@ -2235,8 +2590,8 @@ inline typename enable_if, Integer>::type eval_integer_modulu using boost::multiprecision::backends::cpp_int_backend; -template -struct number_category > : public mpl::int_{}; +template +struct number_category > : public mpl::int_{}; typedef mp_number > cpp_int; typedef rational_adapter > cpp_rational_backend; @@ -2260,13 +2615,15 @@ typedef mp_number, false> mp_int1024_t; }} // namespaces +#include + namespace std{ -template -class numeric_limits, ExpressionTemplates> > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; @@ -2315,57 +2672,57 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif -template -class numeric_limits, ExpressionTemplates> > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; struct inititializer { @@ -2439,62 +2796,62 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template -const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; +template +const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif -template -class numeric_limits, ExpressionTemplates> > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; struct inititializer { @@ -2567,55 +2924,55 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template -const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; +template +const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif diff --git a/include/boost/multiprecision/detail/cpp_int_core.hpp b/include/boost/multiprecision/detail/cpp_int_core.hpp index 31ce2245..773a3790 100644 --- a/include/boost/multiprecision/detail/cpp_int_core.hpp +++ b/include/boost/multiprecision/detail/cpp_int_core.hpp @@ -6,13 +6,63 @@ #ifndef BOOST_MP_CPP_INT_CORE_HPP #define BOOST_MP_CPP_INT_CORE_HPP +#include + namespace boost{ namespace multiprecision{ +namespace detail{ + +// +// These traits calculate the largest type in the list +// [unsigned] ong long, long, int, which has the specified number +// of bits. Note that intN_t and boost::int_t find the first +// member of the above list, not the last. We want the last in the +// list to ensure that mixed arithmetic operations are as efficient +// as possible. +// +template +struct largest_signed_type +{ + typedef typename mpl::if_c< + 1 + std::numeric_limits::digits == N, + long long, + typename mpl::if_c< + 1 + std::numeric_limits::digits == N, + long, + typename mpl::if_c< + 1 + std::numeric_limits::digits == N, + int, + typename boost::int_t::exact + >::type + >::type + >::type type; +}; + +template +struct largest_unsigned_type +{ + typedef typename mpl::if_c< + std::numeric_limits::digits == N, + unsigned long long, + typename mpl::if_c< + std::numeric_limits::digits == N, + unsigned long, + typename mpl::if_c< + std::numeric_limits::digits == N, + unsigned int, + typename boost::uint_t::exact + >::type + >::type + >::type type; +}; + +} + #if defined(__GNUC__) && ((__GNUC__ > 4) || ((__GNUC__ == 4) && (__GNUC_MINOR__ >= 6))) \ && !defined(BOOST_INTEL) && defined(__WORDSIZE) && (__WORDSIZE == 64) -typedef boost::uint64_t limb_type; -typedef boost::int64_t signed_limb_type; +typedef detail::largest_unsigned_type<64>::type limb_type; +typedef detail::largest_signed_type<64>::type signed_limb_type; typedef unsigned __int128 double_limb_type; typedef __int128 signed_double_limb_type; static const limb_type max_block_10 = 1000000000000000000uLL; @@ -28,8 +78,8 @@ inline limb_type block_multiplier(unsigned count) #else -typedef boost::uint32_t limb_type; -typedef boost::int32_t signed_limb_type; +typedef detail::largest_unsigned_type<32>::type limb_type; +typedef detail::largest_signed_type<32>::type signed_limb_type; typedef boost::uint64_t double_limb_type; typedef boost::int64_t signed_double_limb_type; static const limb_type max_block_10 = 1000000000; diff --git a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp new file mode 100644 index 00000000..199bcb90 --- /dev/null +++ b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp @@ -0,0 +1,284 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_CPP_INT_TRIVIAL_OPS_HPP +#define BOOST_MP_CPP_INT_TRIVIAL_OPS_HPP + +#include + +namespace boost{ namespace multiprecision{ namespace backends{ + +template +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + if(result.sign() != o.sign()) + { + if(*o.limbs() > *result.limbs()) + { + *result.limbs() = *o.limbs() - *result.limbs(); + result.negate(); + } + else + *result.limbs() -= *o.limbs(); + } + else + *result.limbs() += *o.limbs(); +} + +template +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + *result.limbs() += *o.limbs(); +} + +template +inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + if(result.sign() != o.sign()) + { + *result.limbs() += *o.limbs(); + } + else if(*result.limbs() < *o.limbs()) + { + *result.limbs() = *o.limbs() - *result.limbs(); + result.negate(); + } + else + *result.limbs() -= *o.limbs(); +} + +template +inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + *result.limbs() -= *o.limbs(); +} + +template +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + *result.limbs() *= *o.limbs(); + result.sign(result.sign() != o.sign()); +} + +template +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + *result.limbs() *= *o.limbs(); +} + +template +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& o) +{ + if(!*o.limbs()) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + *result.limbs() /= *o.limbs(); + result.sign(result.sign() != o.sign()); +} + +template +inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& o) +{ + if(!*o.limbs()) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + *result.limbs() /= *o.limbs(); +} + +template +inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& o) +{ + if(!*o.limbs()) + BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + *result.limbs() %= *o.limbs(); + result.sign(result.sign()); +} + +template +inline void eval_left_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT +{ + *result.limbs() <<= s; +} + +template +inline void eval_right_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT +{ + *result.limbs() >>= s; +} + +template +inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + typename cpp_int_backend::local_limb_type a, b; + a = *result.limbs(); + if(result.isneg()) + { + a = ~a; + ++a; + } + b = *o.limbs(); + if(o.isneg()) + { + b = ~b; + ++b; + } + a &= b; + bool isneg = false; + static const typename cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1); + if(a & mask) + { + a = ~a; + ++a; + isneg = true; + } + *result.limbs() = a; + result.sign(isneg); +} + +template +inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + *result.limbs() &= *o.limbs(); +} + +template +inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + typename cpp_int_backend::local_limb_type a, b; + a = *result.limbs(); + if(result.isneg()) + { + a = ~a; + ++a; + } + b = *o.limbs(); + if(o.isneg()) + { + b = ~b; + ++b; + } + a |= b; + bool isneg = false; + static const typename cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1); + if(a & mask) + { + a = ~a; + ++a; + isneg = true; + } + *result.limbs() = a; + result.sign(isneg); +} + +template +inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + *result.limbs() |= *o.limbs(); +} + +template +inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + typename cpp_int_backend::local_limb_type a, b; + a = *result.limbs(); + if(result.isneg()) + { + a = ~a; + ++a; + } + b = *o.limbs(); + if(o.isneg()) + { + b = ~b; + ++b; + } + a ^= b; + bool isneg = false; + static const typename cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1); + if(a & mask) + { + a = ~a; + ++a; + isneg = true; + } + *result.limbs() = a; + result.sign(isneg); +} + +template +inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + *result.limbs() ^= *o.limbs(); +} + +template +inline void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + typename cpp_int_backend::local_limb_type a; + a = *o.limbs(); + if(o.isneg()) + { + a = ~a; + ++a; + } + a = ~a; + bool isneg = false; + static const typename cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1); + if(a & mask) + { + a = ~a; + ++a; + isneg = true; + } + *result.limbs() = a; + result.sign(isneg); +} + +template +inline void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +{ + *result.limbs() = ~*o.limbs(); +} + +template +inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +{ + *result.limbs() = boost::math::gcd(*a.limbs(), *b.limbs()); +} + +template +inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +{ + *result.limbs() = boost::math::lcm(*a.limbs(), *b.limbs()); +} + +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4127 4018) +#endif +template +inline void eval_convert_to(R* result, const cpp_int_backend& val) +{ + if(std::numeric_limits::is_specialized && (*val.limbs() > (std::numeric_limits::max)())) + *result = (std::numeric_limits::max)(); + else + *result = static_cast(*val.limbs()); + if(val.isneg()) + *result = negate_integer(*result, mpl::bool_::value || boost::is_floating_point::value>()); +} + +template +inline void eval_convert_to(R* result, const cpp_int_backend& val) +{ + if(std::numeric_limits::is_specialized && (*val.limbs() > (std::numeric_limits::max)())) + *result = (std::numeric_limits::max)(); + else + *result = static_cast(*val.limbs()); +} +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + +}}} // namespaces + +#endif diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 9a46792c..0782839d 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -391,10 +391,6 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> { mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); } - gmp_float(unsigned digits10) - { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - } gmp_float(mpf_t val) { mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 8c84a319..c81f691d 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -38,13 +38,20 @@ class mp_number public: typedef Backend backend_type; BOOST_CONSTEXPR mp_number() BOOST_NOEXCEPT_IF(noexcept(Backend())) {} - mp_number(const mp_number& e) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(e.m_backend){} + BOOST_CONSTEXPR mp_number(const mp_number& e) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(e.m_backend){} template - mp_number(V v, typename enable_if, is_same, is_convertible > >::type* = 0) + mp_number(V v, typename enable_if_c< + (boost::is_arithmetic::value || is_same::value || is_convertible::value) + && !is_convertible::type, Backend>::value >::type* = 0) { m_backend = canonical_value(v); } - mp_number(const mp_number& e, unsigned digits10) + template + BOOST_CONSTEXPR mp_number(V v, typename enable_if_c< + (boost::is_arithmetic::value || is_same::value || is_convertible::value) + && is_convertible::type, Backend>::value >::type* = 0) + : m_backend(canonical_value(v)) {} + BOOST_CONSTEXPR mp_number(const mp_number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} /* // @@ -59,7 +66,7 @@ public: } */ template - mp_number(const mp_number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} + BOOST_CONSTEXPR mp_number(const mp_number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} template mp_number(const mp_number& val, typename enable_if >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) @@ -88,7 +95,7 @@ public: } template - mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) + BOOST_CONSTEXPR mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(v){} @@ -155,7 +162,7 @@ public: } #ifndef BOOST_NO_RVALUE_REFERENCES - mp_number(mp_number&& r) BOOST_NOEXCEPT : m_backend(static_cast(r.m_backend)){} + BOOST_CONSTEXPR mp_number(mp_number&& r) BOOST_NOEXCEPT : m_backend(static_cast(r.m_backend)){} mp_number& operator=(mp_number&& r) BOOST_NOEXCEPT { m_backend.swap(r.m_backend); diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 174deb08..3c1301e5 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -402,10 +402,6 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> { mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); } - mpfr_float_backend(unsigned digits10) - { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); - } mpfr_float_backend(mpfr_t val) { mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index da143eb9..e94ed3fd 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -84,6 +84,13 @@ private: unsigned bits_wanted; // for integer types +namespace boost{ namespace multiprecision{ + +template<> +class number_category : public mpl::int_{}; + +}} + template struct tester { @@ -177,13 +184,24 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } - double test_str() + double test_str(const boost::mpl::false_&) + { + stopwatch w; + for(unsigned i = 0; i < b.size(); ++i) + a[i] = boost::lexical_cast(boost::lexical_cast(b[i])); + return boost::chrono::duration_cast >(w.elapsed()).count(); + } + double test_str(const boost::mpl::true_&) { stopwatch w; for(unsigned i = 0; i < b.size(); ++i) a[i] = b[i].str(); return boost::chrono::duration_cast >(w.elapsed()).count(); } + double test_str() + { + return test_str(boost::is_class()); + } // // The following tests only work for integer types: // @@ -303,6 +321,7 @@ struct tester } double test_gcd() { + using boost::math::gcd; stopwatch w; for(unsigned i = 0; i < 1000; ++i) { @@ -311,6 +330,54 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } + double test_construct() + { + std::allocator a; + T* pt = a.allocate(1000); + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < 1000; ++i) + new(pt+i) T(); + for(unsigned i = 0; i < 1000; ++i) + a.destroy(pt+i); + } + double result = boost::chrono::duration_cast >(w.elapsed()).count(); + a.deallocate(pt, 1000); + return result; + } + double test_construct_unsigned() + { + std::allocator a; + T* pt = a.allocate(1000); + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < 1000; ++i) + new(pt+i) T(i); + for(unsigned i = 0; i < 1000; ++i) + a.destroy(pt+i); + } + double result = boost::chrono::duration_cast >(w.elapsed()).count(); + a.deallocate(pt, 1000); + return result; + } + double test_construct_unsigned_ll() + { + std::allocator a; + T* pt = a.allocate(1000); + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned long long j = 0; j < 1000; ++j) + new(pt+j) T(j); + for(unsigned j = 0; j < 1000; ++j) + a.destroy(pt+j); + } + double result = boost::chrono::duration_cast >(w.elapsed()).count(); + a.deallocate(pt, 1000); + return result; + } private: T generate_random() { @@ -489,6 +556,10 @@ void test(const char* type, unsigned precision) report_result(cat, type, "-(int)", precision, t.test_subtract_int()); report_result(cat, type, "*(int)", precision, t.test_multiply_int()); report_result(cat, type, "/(int)", precision, t.test_divide_int()); + // construction and destruction: + report_result(cat, type, "construct", precision, t.test_construct()); + report_result(cat, type, "construct(unsigned)", precision, t.test_construct_unsigned()); + report_result(cat, type, "construct(unsigned long long)", precision, t.test_construct_unsigned_ll()); test_int_ops(t, type, precision, typename boost::multiprecision::number_category::type()); } @@ -566,6 +637,9 @@ void quickbook_results() int main() { +#ifdef TEST_INT64 + test("boost::int64_t", 64); +#endif #ifdef TEST_MPF test("gmp_float", 50); test("gmp_float", 100); @@ -578,15 +652,16 @@ int main() test("gmp_int", 1024); #endif #ifdef TEST_CPP_INT + test, false > >("cpp_int(fixed)", 64); + test, false > >("cpp_int(fixed)", 128); + test, false > >("cpp_int(fixed)", 256); + test, false > >("cpp_int(fixed)", 512); + test, false > >("cpp_int(fixed)", 1024); + test("cpp_int", 128); test("cpp_int", 256); test("cpp_int", 512); test("cpp_int", 1024); - - test > >("cpp_int(fixed)", 128); - test > >("cpp_int(fixed)", 256); - test > >("cpp_int(fixed)", 512); - test > >("cpp_int(fixed)", 1024); #endif #ifdef TEST_CPP_INT_RATIONAL test("cpp_rational", 128); diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index e1bba8ba..352aee53 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -1171,6 +1171,10 @@ int main() test(); test, false> >(); test > >(); + + // Again with "trivial" backends: + test, false > >(); + test, false > >(); #endif #ifdef TEST_CPP_INT_BR test(); From 7b353cb29610ce8cc9fb0f5e2ab9a0b0b031f072 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 23 Jul 2012 17:47:44 +0000 Subject: [PATCH 201/256] Fix Linux x64 failures. [SVN r79700] --- include/boost/multiprecision/cpp_int.hpp | 112 ++++++++++++++++-- .../multiprecision/detail/cpp_int_core.hpp | 3 + .../detail/cpp_int_trivial_ops.hpp | 2 +- 3 files changed, 106 insertions(+), 11 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 0edba4aa..40643feb 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -425,16 +425,21 @@ public: } }; -template -struct trivial_limb_type +template +struct trivial_limb_type_imp { - typedef typename mpl::if_c< - N <= sizeof(long long) * CHAR_BIT, - typename boost::uint_t::least, - double_limb_type - >::type type; + typedef double_limb_type type; }; +template +struct trivial_limb_type_imp +{ + typedef typename boost::uint_t::least type; +}; + +template +struct trivial_limb_type : public trivial_limb_type_imp {}; + #ifdef BOOST_MSVC #pragma warning(push) #pragma warning(disable:4244) // loss of data in initialization @@ -446,10 +451,10 @@ struct cpp_int_base typedef typename trivial_limb_type::type local_limb_type; typedef local_limb_type* limb_pointer; typedef const local_limb_type* const_limb_pointer; -private: +protected: BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(local_limb_type) * CHAR_BIT); BOOST_STATIC_CONSTANT(local_limb_type, limb_mask = MinBits < limb_bits ? (local_limb_type(1) << MinBits) -1 : (~local_limb_type(0))); - +private: local_limb_type m_data; bool m_sign; @@ -1058,7 +1063,8 @@ public: { this->do_swap(o); } - std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const +private: + std::string str(std::ios_base::fmtflags f, const mpl::false_&)const { std::stringstream ss; ss.flags(f); @@ -1069,6 +1075,92 @@ public: result += ss.str(); return result; } + std::string str(std::ios_base::fmtflags f, const mpl::true_&)const + { + // Even though we have only one limb, we can't do IO on it :-( + int base = 10; + if((f & std::ios_base::oct) == std::ios_base::oct) + base = 8; + else if((f & std::ios_base::hex) == std::ios_base::hex) + base = 16; + std::string result; + + unsigned Bits = base_type::limb_bits; + + if(base == 8 || base == 16) + { + if(this->sign()) + BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported.")); + limb_type shift = base == 8 ? 3 : 4; + limb_type mask = static_cast((1u << shift) - 1); + typename base_type::local_limb_type v = *this->limbs(); + result.assign(Bits / shift + (Bits % shift ? 1 : 0), '0'); + int pos = result.size() - 1; + for(unsigned i = 0; i < Bits / shift; ++i) + { + char c = '0' + static_cast(v & mask); + if(c > '9') + c += 'A' - '9' - 1; + result[pos--] = c; + v >>= shift; + } + if(Bits % shift) + { + mask = static_cast((1u << (Bits % shift)) - 1); + char c = '0' + static_cast(v & mask); + if(c > '9') + c += 'A' - '9'; + result[pos] = c; + } + // + // Get rid of leading zeros: + // + std::string::size_type n = result.find_first_not_of('0'); + if(!result.empty() && (n == std::string::npos)) + n = result.size() - 1; + result.erase(0, n); + if(f & std::ios_base::showbase) + { + const char* pp = base == 8 ? "0" : "0x"; + result.insert(0, pp); + } + } + else + { + result.assign(Bits / 3 + 1, '0'); + int pos = result.size() - 1; + typename base_type::local_limb_type v(*this->limbs()); + bool neg = false; + if(this->sign()) + { + neg = true; + } + while(v) + { + result[pos] = (v % 10) + '0'; + --pos; + v /= 10; + } + unsigned n = result.find_first_not_of('0'); + result.erase(0, n); + if(result.empty()) + result = "0"; + if(neg) + result.insert(0, 1, '-'); + else if(f & std::ios_base::showpos) + result.insert(0, 1, '+'); + } + return result; + } +public: + std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const + { +#ifdef BOOST_MP_NO_DOUBLE_LIMB_TYPE_IO + return str(f, mpl::bool_::value>()); +#else + return str(f, mpl::bool_()); +#endif + } int compare(const cpp_int_backend& o)const BOOST_NOEXCEPT { if(this->sign() != o.sign()) diff --git a/include/boost/multiprecision/detail/cpp_int_core.hpp b/include/boost/multiprecision/detail/cpp_int_core.hpp index 773a3790..f2e86cf1 100644 --- a/include/boost/multiprecision/detail/cpp_int_core.hpp +++ b/include/boost/multiprecision/detail/cpp_int_core.hpp @@ -76,6 +76,9 @@ inline limb_type block_multiplier(unsigned count) return values[count]; } +// Can't do formatted IO on an __int128 +#define BOOST_MP_NO_DOUBLE_LIMB_TYPE_IO + #else typedef detail::largest_unsigned_type<32>::type limb_type; diff --git a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp index 199bcb90..22e7d197 100644 --- a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp +++ b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp @@ -159,7 +159,7 @@ inline void eval_bitwise_or(cpp_int_backend& result, } a |= b; bool isneg = false; - static const typename cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1); + static const typename cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (sizeof(typename cpp_int_backend::local_limb_type) * CHAR_BIT - 1); if(a & mask) { a = ~a; From 64fe0089d30b7cb28fda103ad32fd84b456ba584 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 24 Jul 2012 18:03:54 +0000 Subject: [PATCH 202/256] Refactor concept checks for faster compilers. Add constexpr construction test. [SVN r79724] --- include/boost/multiprecision/cpp_int.hpp | 58 ++++--- performance/performance_test.cpp | 5 +- test/Jamfile.v2 | 107 ++++++------- .../mp_number_concept_check.cpp | 18 +-- test/concepts/sf_concept_check_basic.cpp | 149 ++++++++++++++++++ test/concepts/sf_concept_check_bessel.cpp | 114 ++++++++++++++ test/concepts/sf_concept_check_elliptic.cpp | 120 ++++++++++++++ test/concepts/sf_concept_check_gamma.cpp | 136 ++++++++++++++++ test/concepts/sf_concept_check_poly.cpp | 111 +++++++++++++ test/test_constexpr.cpp | 39 +++++ 10 files changed, 755 insertions(+), 102 deletions(-) rename test/{ => concepts}/mp_number_concept_check.cpp (84%) create mode 100644 test/concepts/sf_concept_check_basic.cpp create mode 100644 test/concepts/sf_concept_check_bessel.cpp create mode 100644 test/concepts/sf_concept_check_elliptic.cpp create mode 100644 test/concepts/sf_concept_check_gamma.cpp create mode 100644 test/concepts/sf_concept_check_poly.cpp create mode 100644 test/test_constexpr.cpp diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 40643feb..94e428d7 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -236,11 +236,15 @@ public: BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs"); private: - union{ + union data_type{ limb_type m_data[internal_limb_count]; limb_type m_first_limb; double_limb_type m_double_first_limb; - }; + + BOOST_CONSTEXPR data_type(){} + BOOST_CONSTEXPR data_type(limb_type i) : m_first_limb(i) {} + BOOST_CONSTEXPR data_type(double_limb_type i) : m_double_first_limb(i) {} + } m_wrapper; boost::uint16_t m_limbs; bool m_sign; @@ -249,21 +253,21 @@ public: // Direct construction: // BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT - : m_first_limb(i), m_limbs(1), m_sign(false) {} + : m_wrapper(i), m_limbs(1), m_sign(false) {} BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT - : m_first_limb(std::abs(i)), m_limbs(1), m_sign(i < 0) {} + : m_wrapper(limb_type(i < 0 ? -i : i)), m_limbs(1), m_sign(i < 0) {} #if defined(BOOST_LITTLE_ENDIAN) BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT - : m_double_first_limb(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false) {} + : m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false) {} BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT - : m_double_first_limb(i < 0 ? -i : i), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), m_sign(i < 0) {} + : m_wrapper(double_limb_type(i < 0 ? -i : i)), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), m_sign(i < 0) {} #endif // // Helper functions for getting at our internal data, and manipulating storage: // unsigned size()const BOOST_NOEXCEPT { return m_limbs; } - limb_pointer limbs() BOOST_NOEXCEPT { return m_data; } - const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_data; } + limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; } + const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; } bool sign()const BOOST_NOEXCEPT { return m_sign; } void sign(bool b) BOOST_NOEXCEPT { @@ -287,7 +291,7 @@ public: if((m_limbs == 1) && (!*p)) m_sign = false; // zero is always unsigned } - BOOST_CONSTEXPR cpp_int_base() : m_first_limb(0), m_limbs(1), m_sign(false) {} + BOOST_CONSTEXPR cpp_int_base() : m_wrapper(limb_type(0u)), m_limbs(1), m_sign(false) {} cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs), m_sign(o.m_sign) { std::copy(o.limbs(), o.limbs() + o.size(), limbs()); @@ -298,7 +302,7 @@ public: if(this != &o) { resize(o.size()); - std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + std::copy(o.limbs(), o.limbs() + o.size(), limbs()); m_sign = o.m_sign; } } @@ -319,7 +323,7 @@ public: void do_swap(cpp_int_base& o) BOOST_NOEXCEPT { for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i) - std::swap(m_data[i], o.m_data[i]); + std::swap(m_wrapper.m_data[i], o.m_wrapper.m_data[i]); std::swap(m_sign, o.m_sign); std::swap(m_limbs, o.m_limbs); } @@ -346,11 +350,15 @@ public: BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs"); private: - union{ + union data_type{ limb_type m_data[internal_limb_count]; limb_type m_first_limb; double_limb_type m_double_first_limb; - }; + + BOOST_CONSTEXPR data_type() {} + BOOST_CONSTEXPR data_type(limb_type i) : m_first_limb(i) {} + BOOST_CONSTEXPR data_type(double_limb_type i) : m_double_first_limb(i) {} + } m_wrapper; limb_type m_limbs; public: @@ -358,21 +366,21 @@ public: // Direct construction: // BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT - : m_first_limb(i), m_limbs(1) {} + : m_wrapper(i), m_limbs(1) {} cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT - : m_first_limb(i < 0 ? -i : i), m_limbs(1) { if(i < 0) negate(); } + : m_wrapper(limb_type(i < 0 ? -i : i)), m_limbs(1) { if(i < 0) negate(); } #ifdef BOOST_LITTLE_ENDIAN BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT - : m_double_first_limb(i), m_limbs(i > max_limb_value ? 2 : 1) {} + : m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1) {} cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT - : m_double_first_limb(i < 0 ? -i : i), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)) { if(i < 0) negate(); } + : m_wrapper(double_limb_type(i < 0 ? -i : i)), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)) { if(i < 0) negate(); } #endif // // Helper functions for getting at our internal data, and manipulating storage: // unsigned size()const BOOST_NOEXCEPT { return m_limbs; } - limb_pointer limbs() BOOST_NOEXCEPT { return m_data; } - const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_data; } + limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; } + const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; } BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; } void sign(bool b) BOOST_NOEXCEPT { if(b) negate(); } void resize(unsigned new_size) BOOST_NOEXCEPT @@ -386,7 +394,7 @@ public: while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; } - BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_first_limb(0), m_limbs(1) {} + BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_wrapper(limb_type(0u)), m_limbs(1) {} cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs) { std::copy(o.limbs(), o.limbs() + o.size(), limbs()); @@ -397,7 +405,7 @@ public: if(this != &o) { resize(o.size()); - std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + std::copy(o.limbs(), o.limbs() + o.size(), limbs()); } } void negate() BOOST_NOEXCEPT @@ -406,10 +414,10 @@ public: // would result in a "negative" number: unsigned i; for(i = m_limbs; i < internal_limb_count; ++i) - m_data[i] = 0; + m_wrapper.m_data[i] = 0; m_limbs = internal_limb_count; for(i = 0; i < internal_limb_count; ++i) - m_data[i] = ~m_data[i]; + m_wrapper.m_data[i] = ~m_wrapper.m_data[i]; normalize(); eval_increment(static_cast& >(*this)); } @@ -420,7 +428,7 @@ public: void do_swap(cpp_int_base& o) BOOST_NOEXCEPT { for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i) - std::swap(m_data[i], o.m_data[i]); + std::swap(m_wrapper.m_data[i], o.m_wrapper.m_data[i]); std::swap(m_limbs, o.m_limbs); } }; @@ -442,7 +450,7 @@ struct trivial_limb_type : public trivial_limb_type_imp diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index e94ed3fd..8dd0b3ed 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -88,6 +88,8 @@ namespace boost{ namespace multiprecision{ template<> class number_category : public mpl::int_{}; +template<> +class number_category : public mpl::int_{}; }} @@ -638,7 +640,7 @@ void quickbook_results() int main() { #ifdef TEST_INT64 - test("boost::int64_t", 64); + test("boost::uint64_t", 64); #endif #ifdef TEST_MPF test("gmp_float", 50); @@ -652,6 +654,7 @@ int main() test("gmp_int", 1024); #endif #ifdef TEST_CPP_INT + test, false > >("cpp_int(unsigned, fixed)", 64); test, false > >("cpp_int(fixed)", 64); test, false > >("cpp_int(fixed)", 128); test, false > >("cpp_int(fixed)", 256); diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index deec7251..a10e4f59 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -610,6 +610,7 @@ run test_move.cpp : test_move_cpp_int ; run test_test.cpp ; +compile test_constexpr.cpp ; run test_float_io.cpp : # command line @@ -772,73 +773,59 @@ if $(enable-specfun) if ! $(disable-concepts) { - run mp_number_concept_check.cpp mpfr - : # command line - : # input files - : # requirements - TEST_MPFR_50 - [ check-target-builds ../config//has_mpfr : : no ] - : mp_number_concept_check_mpfr_50 ; - run mp_number_concept_check.cpp mpfr - : # command line - : # input files - : # requirements - TEST_MPFR_6 - [ check-target-builds ../config//has_mpfr : : no ] - : mp_number_concept_check_mpfr_6 ; + for local source in [ glob concepts/*.cpp ] + { - run mp_number_concept_check.cpp mpfr - : # command line - : # input files - : # requirements - TEST_MPFR_15 - [ check-target-builds ../config//has_mpfr : : no ] - : mp_number_concept_check_mpfr_15 ; + compile $(source) mpfr + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : $(source:B)_mpfr_50 ; - run mp_number_concept_check.cpp mpfr - : # command line - : # input files - : # requirements - TEST_MPFR_17 - [ check-target-builds ../config//has_mpfr : : no ] - : mp_number_concept_check_mpfr_17 ; + compile $(source) mpfr + : # requirements + TEST_MPFR_6 + [ check-target-builds ../config//has_mpfr : : no ] + : $(source:B)_mpfr_6 ; - run mp_number_concept_check.cpp mpfr - : # command line - : # input files - : # requirements - TEST_MPFR_30 - [ check-target-builds ../config//has_mpfr : : no ] - : mp_number_concept_check_mpfr_30 ; + compile $(source) mpfr + : # requirements + TEST_MPFR_15 + [ check-target-builds ../config//has_mpfr : : no ] + : $(source:B)_mpfr_15 ; - run mp_number_concept_check.cpp gmp - : # command line - : # input files - : # requirements - TEST_MPF_50 - [ check-target-builds ../config//has_gmp : : no ] - : mp_number_concept_check_mpf50 ; + compile $(source) mpfr + : # requirements + TEST_MPFR_17 + [ check-target-builds ../config//has_mpfr : : no ] + : $(source:B)_mpfr_17 ; - run mp_number_concept_check.cpp - : # command line - : # input files - : # requirements - TEST_CPP_DEC_FLOAT - : mp_number_concept_check_cpp_dec_float ; + compile $(source) mpfr + : # requirements + TEST_MPFR_30 + [ check-target-builds ../config//has_mpfr : : no ] + : $(source:B)_mpfr_30 ; - run mp_number_concept_check.cpp - : # command line - : # input files - : # requirements - TEST_CPP_DEC_FLOAT_NO_ET - : mp_number_concept_check_cpp_dec_float_no_et ; + compile $(source) gmp + : # requirements + TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : no ] + : $(source:B)_mpf50 ; - run mp_number_concept_check.cpp - : # command line - : # input files - : # requirements - TEST_BACKEND - : mp_number_concept_check_backend_concept ; + compile $(source) + : # requirements + TEST_CPP_DEC_FLOAT + : $(source:B)_cpp_dec_float ; + compile $(source) + : # requirements + TEST_CPP_DEC_FLOAT_NO_ET + : $(source:B)_cpp_dec_float_no_et ; + + compile $(source) + : # requirements + TEST_BACKEND + : $(source:B)_backend_concept ; + } } diff --git a/test/mp_number_concept_check.cpp b/test/concepts/mp_number_concept_check.cpp similarity index 84% rename from test/mp_number_concept_check.cpp rename to test/concepts/mp_number_concept_check.cpp index 45831f29..d921dce7 100644 --- a/test/mp_number_concept_check.cpp +++ b/test/concepts/mp_number_concept_check.cpp @@ -4,13 +4,9 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) // -// This tests two things: that cpp_dec_float_50 meets our -// conceptual requirements, and that we can instantiate -// all our distributions and special functions on this type. +// This tests that cpp_dec_float_50 meets our +// conceptual requirements. // -#define BOOST_MATH_ASSERT_UNDEFINED_POLICY false -#define BOOST_MATH_INSTANTIATE_MINIMUM - #ifdef _MSC_VER # define _SCL_SECURE_NO_WARNINGS # pragma warning(disable:4800) @@ -57,7 +53,6 @@ #endif #include -#include "libs/math/test/compile_test/instantiate.hpp" template void test_extra(T) @@ -167,39 +162,30 @@ void test_extra(T) void foo() { #ifdef TEST_BACKEND - instantiate(boost::multiprecision::concepts::mp_number_float_architype()); test_extra(boost::multiprecision::concepts::mp_number_float_architype()); #endif #ifdef TEST_MPF_50 - instantiate(boost::multiprecision::mpf_float_50()); test_extra(boost::multiprecision::mpf_float_50()); #endif #ifdef TEST_MPFR_50 - instantiate(boost::multiprecision::mpfr_float_50()); test_extra(boost::multiprecision::mpfr_float_50()); #endif #ifdef TEST_MPFR_6 - instantiate(boost::multiprecision::mp_number >()); test_extra(boost::multiprecision::mp_number >()); #endif #ifdef TEST_MPFR_15 - instantiate(boost::multiprecision::mp_number >()); test_extra(boost::multiprecision::mp_number >()); #endif #ifdef TEST_MPFR_17 - instantiate(boost::multiprecision::mp_number >()); test_extra(boost::multiprecision::mp_number >()); #endif #ifdef TEST_MPFR_30 - instantiate(boost::multiprecision::mp_number >()); test_extra(boost::multiprecision::mp_number >()); #endif #ifdef TEST_CPP_DEC_FLOAT - instantiate(boost::multiprecision::cpp_dec_float_50()); test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - instantiate(boost::multiprecision::mp_number, false>()); test_extra(boost::multiprecision::mp_number, false>()); #endif } diff --git a/test/concepts/sf_concept_check_basic.cpp b/test/concepts/sf_concept_check_basic.cpp new file mode 100644 index 00000000..75c35b08 --- /dev/null +++ b/test/concepts/sf_concept_check_basic.cpp @@ -0,0 +1,149 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements when used with Boost.Math. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) +#include +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include +#endif + +#include + +template +void test_extra(T) +{ + T v1, v2, v3; + int i; + (boost::math::fpclassify)(v1); + (boost::math::isfinite)(v1); + (boost::math::isnormal)(v1); + (boost::math::isnan)(v1); + (boost::math::isinf)(v1); + (boost::math::signbit)(v1); + (boost::math::copysign)(v1, v2); + (boost::math::changesign)(v1); + (boost::math::sign)(v1); + boost::math::log1p(v1); + boost::math::expm1(v1); + boost::math::cbrt(v1); + boost::math::sqrt1pm1(v1); + boost::math::powm1(v1, v2); + boost::math::hypot(v1, v2); + boost::math::sinc_pi(v1); + boost::math::sinhc_pi(v1); + boost::math::asinh(v1); + boost::math::acosh(v1); + boost::math::atanh(v1); + boost::math::sin_pi(v1); + boost::math::cos_pi(v1); + boost::math::trunc(v1); + boost::math::itrunc(v1); + boost::math::ltrunc(v1); + boost::math::round(v1); + boost::math::iround(v1); + boost::math::lround(v1); + boost::math::modf(v1, &v1); + boost::math::modf(v1, &i); + long l; + boost::math::modf(v1, &l); +#ifdef BOOST_HAS_LONG_LONG + boost::math::lltrunc(v1); + boost::math::llround(v1); + boost::long_long_type ll; + boost::math::modf(v1, &ll); +#endif + boost::math::pow<2>(v1); + boost::math::nextafter(v1, v1); + boost::math::float_next(v1); + boost::math::float_prior(v1); + boost::math::float_distance(v1, v1); + // Misc functions that don't fit elsewhere: + boost::math::expint(v1); + boost::math::expint(i); + boost::math::expint(i, v2); + boost::math::expint(i, i); + boost::math::zeta(v1); + boost::math::zeta(i); + boost::math::owens_t(v1, v2); +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::mp_number, false>()); +#endif +} + +int main() +{ + foo(); +} diff --git a/test/concepts/sf_concept_check_bessel.cpp b/test/concepts/sf_concept_check_bessel.cpp new file mode 100644 index 00000000..12a40a13 --- /dev/null +++ b/test/concepts/sf_concept_check_bessel.cpp @@ -0,0 +1,114 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements when used with Boost.Math. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) +#include +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include +#endif + +#include + +template +void test_extra(T) +{ + T v1, v2, v3; + int i(0); + boost::math::cyl_neumann(v1, v2); + boost::math::cyl_neumann(i, v2); + boost::math::cyl_bessel_j(v1, v2); + boost::math::cyl_bessel_j(i, v2); + boost::math::cyl_bessel_i(v1, v2); + boost::math::cyl_bessel_i(i, v2); + boost::math::cyl_bessel_k(v1, v2); + boost::math::cyl_bessel_k(i, v2); + boost::math::sph_bessel(i, v2); + boost::math::sph_bessel(i, 1); + boost::math::sph_neumann(i, v2); + boost::math::sph_neumann(i, i); + boost::math::airy_ai(v1); + boost::math::airy_bi(v1); + boost::math::airy_ai_prime(v1); + boost::math::airy_bi_prime(v1); +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::mp_number, false>()); +#endif +} + +int main() +{ + foo(); +} diff --git a/test/concepts/sf_concept_check_elliptic.cpp b/test/concepts/sf_concept_check_elliptic.cpp new file mode 100644 index 00000000..e754f53e --- /dev/null +++ b/test/concepts/sf_concept_check_elliptic.cpp @@ -0,0 +1,120 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements when used with Boost.Math. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) +#include +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include +#endif + +#include + +template +void test_extra(T) +{ + T v1, v2, v3; + boost::math::ellint_1(v1); + boost::math::ellint_1(v1, v2); + boost::math::ellint_2(v1); + boost::math::ellint_2(v1, v2); + boost::math::ellint_3(v1, v2); + boost::math::ellint_3(v1, v2, v3); + boost::math::ellint_rc(v1, v2); + boost::math::ellint_rd(v1, v2, v3); + boost::math::ellint_rf(v1, v2, v3); + boost::math::ellint_rj(v1, v2, v3, v1); + boost::math::jacobi_elliptic(v1, v2, &v1, &v2); + boost::math::jacobi_cd(v1, v2); + boost::math::jacobi_cn(v1, v2); + boost::math::jacobi_cs(v1, v2); + boost::math::jacobi_dc(v1, v2); + boost::math::jacobi_dn(v1, v2); + boost::math::jacobi_ds(v1, v2); + boost::math::jacobi_nc(v1, v2); + boost::math::jacobi_nd(v1, v2); + boost::math::jacobi_ns(v1, v2); + boost::math::jacobi_sc(v1, v2); + boost::math::jacobi_sd(v1, v2); + boost::math::jacobi_sn(v1, v2); +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::mp_number, false>()); +#endif +} + +int main() +{ + foo(); +} diff --git a/test/concepts/sf_concept_check_gamma.cpp b/test/concepts/sf_concept_check_gamma.cpp new file mode 100644 index 00000000..bd108e9a --- /dev/null +++ b/test/concepts/sf_concept_check_gamma.cpp @@ -0,0 +1,136 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements when used with Boost.Math. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) +#include +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include +#endif + +#include + +template +void test_extra(T) +{ + T v1, v2, v3; + int i; + boost::math::tgamma(v1); + boost::math::tgamma1pm1(v1); + boost::math::lgamma(v1); + boost::math::lgamma(v1, &i); + boost::math::digamma(v1); + boost::math::tgamma_ratio(v1, v2); + boost::math::tgamma_delta_ratio(v1, v2); + boost::math::factorial(i); + boost::math::unchecked_factorial(i); + i = boost::math::max_factorial::value; + boost::math::double_factorial(i); + boost::math::rising_factorial(v1, i); + boost::math::falling_factorial(v1, i); + boost::math::tgamma(v1, v2); + boost::math::tgamma_lower(v1, v2); + boost::math::gamma_p(v1, v2); + boost::math::gamma_q(v1, v2); + boost::math::gamma_p_inv(v1, v2); + boost::math::gamma_q_inv(v1, v2); + boost::math::gamma_p_inva(v1, v2); + boost::math::gamma_q_inva(v1, v2); + boost::math::erf(v1); + boost::math::erfc(v1); + boost::math::erf_inv(v1); + boost::math::erfc_inv(v1); + boost::math::beta(v1, v2); + boost::math::beta(v1, v2, v3); + boost::math::betac(v1, v2, v3); + boost::math::ibeta(v1, v2, v3); + boost::math::ibetac(v1, v2, v3); + boost::math::ibeta_inv(v1, v2, v3); + boost::math::ibetac_inv(v1, v2, v3); + boost::math::ibeta_inva(v1, v2, v3); + boost::math::ibetac_inva(v1, v2, v3); + boost::math::ibeta_invb(v1, v2, v3); + boost::math::ibetac_invb(v1, v2, v3); + boost::math::gamma_p_derivative(v2, v3); + boost::math::ibeta_derivative(v1, v2, v3); +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::mp_number, false>()); +#endif +} + +int main() +{ + foo(); +} diff --git a/test/concepts/sf_concept_check_poly.cpp b/test/concepts/sf_concept_check_poly.cpp new file mode 100644 index 00000000..d8e855e2 --- /dev/null +++ b/test/concepts/sf_concept_check_poly.cpp @@ -0,0 +1,111 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements when used with Boost.Math. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) +#include +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include +#endif + +#include + +template +void test_extra(T) +{ + T v1, v2, v3; + boost::math::legendre_p(1, v1); + boost::math::legendre_p(1, 0, v1); + boost::math::legendre_q(1, v1); + boost::math::legendre_next(2, v1, v2, v3); + boost::math::legendre_next(2, 2, v1, v2, v3); + boost::math::laguerre(1, v1); + boost::math::laguerre(2, 1, v1); + boost::math::laguerre(2u, 1u, v1); + boost::math::laguerre_next(2, v1, v2, v3); + boost::math::laguerre_next(2, 1, v1, v2, v3); + boost::math::hermite(1, v1); + boost::math::hermite_next(2, v1, v2, v3); + boost::math::spherical_harmonic_r(2, 1, v1, v2); + boost::math::spherical_harmonic_i(2, 1, v1, v2); +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::mp_number >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::mp_number, false>()); +#endif +} + +int main() +{ + foo(); +} diff --git a/test/test_constexpr.cpp b/test/test_constexpr.cpp new file mode 100644 index 00000000..6e97e2ae --- /dev/null +++ b/test/test_constexpr.cpp @@ -0,0 +1,39 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +#ifndef BOOST_NO_CONSTEXPR + +template +void test1() +{ + constexpr T i1 = 2u; + constexpr T i2; + constexpr T i3 = -3; + constexpr T i4(i1); +} +template +void test2() +{ + constexpr T i1 = 2u; + constexpr T i2; + constexpr T i3 = -3; +} +template +void test3() +{ + constexpr T i1 = 2u; + constexpr T i2; +} + +using namespace boost::multiprecision; + +template void test1, false> >(); +template void test1, false> >(); +template void test3, false> >(); +template void test2, false> >(); + +#endif \ No newline at end of file From 36847e4e0b39e7b0d3f971b6ad403c040cd63d04 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 30 Jul 2012 15:23:51 +0000 Subject: [PATCH 203/256] Add delaunay performance test case. Rework rvalue reference support for better performance. Rework default operators for better performance. [SVN r79802] --- include/boost/multiprecision/cpp_int.hpp | 162 +- .../multiprecision/detail/default_ops.hpp | 341 +- include/boost/multiprecision/gmp.hpp | 18 + include/boost/multiprecision/mp_number.hpp | 2 +- .../boost/multiprecision/rational_adapter.hpp | 5 + include/boost/multiprecision/tommath.hpp | 6 + ...oat_backend.hpp => arithmetic_backend.hpp} | 182 +- performance/delaunay_data.txt | 100000 +++++++++++++++ performance/delaunay_test.cpp | 279 + performance/performance_test.cpp | 132 + performance/sf_performance.cpp | 9 +- 11 files changed, 100939 insertions(+), 197 deletions(-) rename performance/{float_backend.hpp => arithmetic_backend.hpp} (55%) create mode 100644 performance/delaunay_data.txt create mode 100644 performance/delaunay_test.cpp diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 94e428d7..2391a0d4 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -135,7 +135,7 @@ public: { cap = (std::max)(cap * 4, new_size); limb_pointer pl = allocator().allocate(cap); - std::memcpy(pl, limbs(), size() * sizeof(limb_type)); + std::copy(limbs(), limbs() + size(), pl); if(!m_internal) allocator().deallocate(limbs(), capacity()); else @@ -162,7 +162,7 @@ public: m_sign = o.m_sign; } #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_base(cpp_int_base&& o) BOOST_NOEXCEPT : allocator_type(o), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) + cpp_int_base(cpp_int_base&& o) BOOST_NOEXCEPT : allocator_type(static_cast(o)), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) { if(m_internal) { @@ -175,6 +175,26 @@ public: o.m_internal = true; } } + cpp_int_base& operator = (cpp_int_base&& o) BOOST_NOEXCEPT + { + if(!m_internal) + allocator().deallocate(m_data.ld.data, m_data.ld.capacity); + *static_cast(this) = static_cast(o); + m_limbs = o.m_limbs; + m_sign = o.m_sign; + m_internal = o.m_internal; + if(m_internal) + { + std::copy(o.limbs(), o.limbs() + o.size(), limbs()); + } + else + { + m_data.ld = o.m_data.ld; + o.m_limbs = 0; + o.m_internal = true; + } + return *this; + } #endif ~cpp_int_base() BOOST_NOEXCEPT { @@ -188,7 +208,7 @@ public: static_cast(*this) = static_cast(o); m_limbs = 0; resize(o.size()); - std::memcpy(limbs(), o.limbs(), size() * sizeof(limb_type)); + std::copy(o.limbs(), o.limbs() + o.size(), limbs()); m_sign = o.m_sign; } } @@ -682,6 +702,13 @@ public: this->assign(o); return *this; } +#ifndef BOOST_NO_RVALUE_REFERENCES + cpp_int_backend& operator = (cpp_int_backend&& o) BOOST_NOEXCEPT_IF(boost::is_void::value) + { + *static_cast(this) = static_cast(o); + return *this; + } +#endif cpp_int_backend& operator = (limb_type i) BOOST_NOEXCEPT { this->resize(1); @@ -1239,7 +1266,7 @@ inline void add_unsigned(cpp_int_backend& res if(!carry) { if(pa != pr) - std::memcpy(pr, pa, (pr_end - pr) * sizeof(limb_type)); + std::copy(pa, pa + (pr_end - pr), pr); break; } carry += static_cast(*pa); @@ -1269,18 +1296,27 @@ inline void eval_add(cpp_int_backend& result, } template -inline void add_unsigned(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Addition using modular arithmatic. // Nothing fancy, just let uintmax_t take the strain: + if(&result != &a) + result.resize(a.size()); double_limb_type carry = o; typename cpp_int_backend::limb_pointer pr = result.limbs(); - for(unsigned i = 0; carry && (i < result.size()); ++i) + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + unsigned i = 0; + for(; carry && (i < result.size()); ++i) { - carry += static_cast(pr[i]); + carry += static_cast(pa[i]); pr[i] = static_cast(carry); carry >>= cpp_int_backend::limb_bits; } + if(&a != &result) + { + for(; i < result.size(); ++i) + pr[i] = pa[i]; + } if(carry) { unsigned x = result.size(); @@ -1299,7 +1335,18 @@ inline void eval_add(cpp_int_backend& result, subtract_unsigned(result, o); } else - add_unsigned(result, o); + add_unsigned(result, result, o); +} +template +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +{ + if(a.sign()) + { + result = a; + subtract_unsigned(result, o); + } + else + add_unsigned(result, a, o); } template inline void eval_add(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) @@ -1309,6 +1356,16 @@ inline void eval_add(cpp_int_backend& result, else if(o > 0) eval_add(result, static_cast(o)); } +template +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +{ + if(o < 0) + eval_subtract(result, a, static_cast(-o)); + else if(o > 0) + eval_add(result, a, static_cast(o)); + else if(&result != &a) + result = a; +} template inline void subtract_unsigned(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) @@ -1343,11 +1400,22 @@ template inline void eval_subtract(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(result.sign()) - add_unsigned(result, o); + add_unsigned(result, result, o); else subtract_unsigned(result, o); } template +inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +{ + if(a.sign()) + add_unsigned(result, a, o); + else + { + result = a; + subtract_unsigned(result, o); + } +} +template inline void eval_subtract(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o) @@ -1359,6 +1427,19 @@ inline void eval_subtract(cpp_int_backend& re } } template +inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +{ + if(o) + { + if(o < 0) + eval_add(result, a, static_cast(-o)); + else + eval_subtract(result, a, static_cast(o)); + } + else if(&result != &a) + result = a; +} +template inline void eval_increment(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) { static const limb_type one = 1; @@ -1451,7 +1532,7 @@ inline void subtract_unsigned(cpp_int_backend } // Any remaining digits are the same as those in pa: if((x != i) && (pa != pr)) - std::memcpy(pr + i, pa + i, (x - i) * sizeof(limb_type)); + std::copy(pa + i, pa + x, pr + i); BOOST_ASSERT(0 == borrow); // @@ -1494,18 +1575,16 @@ inline void eval_multiply(cpp_int_backend& re else { limb_type l = *pa; - result = b; - eval_multiply(result, l); + eval_multiply(result, b, l); } result.sign(s); return; } if(bs == 1) { - limb_type l = *pb; bool s = b.sign() != a.sign(); - result = a; - eval_multiply(result, l); + limb_type l = *pb; + eval_multiply(result, a, l); result.sign(s); return; } @@ -1562,17 +1641,19 @@ inline void eval_multiply(cpp_int_backend& re eval_multiply(result, result, a); } template -inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(!val) { result = static_cast(0); return; } + if(&a != &result) + result.resize(a.size()); double_limb_type carry = 0; typename cpp_int_backend::limb_pointer p = result.limbs(); typename cpp_int_backend::limb_pointer pe = result.limbs() + result.size(); - typename cpp_int_backend::limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); while(p != pe) { carry += static_cast(*pa) * static_cast(val); @@ -1587,6 +1668,7 @@ inline void eval_multiply(cpp_int_backend& re if(cpp_int_backend::variable || (result.size() > i)) result.limbs()[i] = static_cast(carry); } + result.sign(a.sign()); if(!cpp_int_backend::variable) result.normalize(); } @@ -1596,7 +1678,25 @@ inline void eval_multiply(cpp_int_backend& re eval_multiply(result, result, val); } template -inline void eval_multiply(cpp_int_backend& result, cpp_int_backend& a, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +{ + if(val <= (std::numeric_limits::max)()) + { + eval_multiply(result, a, static_cast(val)); + } + else + { + cpp_int_backend t(val); + eval_multiply(result, a, t); + } +} +template +inline void eval_multiply(cpp_int_backend& result, const double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +{ + eval_multiply(result, result, val); +} +template +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(val > 0) eval_multiply(result, a, static_cast(val)); @@ -1611,6 +1711,32 @@ inline void eval_multiply(cpp_int_backend& re { eval_multiply(result, result, val); } +template +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const signed_double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +{ + if(val > 0) + { + if(val <= (std::numeric_limits::max)()) + { + eval_multiply(result, a, static_cast(val)); + return; + } + } + else if(val >= -static_cast((std::numeric_limits::max)())) + { + eval_multiply(result, a, static_cast(-val)); + result.negate(); + return; + } + cpp_int_backend t(val); + eval_multiply(result, a, t); +} +template +inline void eval_multiply(cpp_int_backend& result, const signed_double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +{ + eval_multiply(result, result, val); +} + template void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) { diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 74c245cb..e0e621d6 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -34,10 +34,11 @@ namespace boost{ namespace multiprecision{ namespace default_ops{ #endif // // Default versions of mixed arithmetic, these just construct a temporary -// from the arithmetic value and then do the arithmetic on that: +// from the arithmetic value and then do the arithmetic on that, two versions +// of each depending on whether the backend can be directly constructed from type V: // template -inline typename enable_if, is_convertible, is_same > >::type +inline typename enable_if_c::value && !is_convertible::value >::type eval_add(T& result, V const& v) { T t; @@ -45,7 +46,14 @@ inline typename enable_if, is_convertible -inline typename enable_if, is_convertible, is_same > >::type +inline typename enable_if_c::value && is_convertible::value >::type + eval_add(T& result, V const& v) +{ + T t(v); + eval_add(result, t); +} +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_subtract(T& result, V const& v) { T t; @@ -53,7 +61,14 @@ inline typename enable_if, is_convertible -inline typename enable_if, is_convertible, is_same > >::type +inline typename enable_if_c::value && is_convertible::value>::type + eval_subtract(T& result, V const& v) +{ + T t(v); + eval_subtract(result, t); +} +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_multiply(T& result, V const& v) { T t; @@ -61,7 +76,14 @@ inline typename enable_if, is_convertible -inline typename enable_if, is_convertible, is_same > >::type +inline typename enable_if_c::value && is_convertible::value>::type + eval_multiply(T& result, V const& v) +{ + T t(v); + eval_multiply(result, t); +} +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_divide(T& result, V const& v) { T t; @@ -69,7 +91,14 @@ inline typename enable_if, is_convertible -inline typename enable_if, is_convertible, is_same > >::type +inline typename enable_if_c::value && is_convertible::value>::type + eval_divide(T& result, V const& v) +{ + T t(v); + eval_divide(result, t); +} +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_modulus(T& result, V const& v) { T t; @@ -77,7 +106,14 @@ inline typename enable_if, is_convertible -inline typename enable_if, is_convertible, is_same > >::type +inline typename enable_if_c::value && is_convertible::value>::type + eval_modulus(T& result, V const& v) +{ + T t(v); + eval_modulus(result, t); +} +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_bitwise_and(T& result, V const& v) { T t; @@ -85,7 +121,14 @@ inline typename enable_if, is_convertible -inline typename enable_if, is_convertible, is_same > >::type +inline typename enable_if_c::value && is_convertible::value>::type + eval_bitwise_and(T& result, V const& v) +{ + T t(v); + eval_bitwise_and(result, t); +} +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_bitwise_or(T& result, V const& v) { T t; @@ -93,22 +136,43 @@ inline typename enable_if, is_convertible -inline typename enable_if, is_convertible, is_same > >::type +inline typename enable_if_c::value && is_convertible::value>::type + eval_bitwise_or(T& result, V const& v) +{ + T t(v); + eval_bitwise_or(result, t); +} +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_bitwise_xor(T& result, V const& v) { T t; t = v; eval_bitwise_xor(result, t); } +template +inline typename enable_if_c::value && is_convertible::value>::type + eval_bitwise_xor(T& result, V const& v) +{ + T t(v); + eval_bitwise_xor(result, t); +} template -inline typename enable_if, is_convertible, is_same > >::type +inline typename enable_if_c::value && !is_convertible::value>::type eval_complement(T& result, V const& v) { T t; t = v; eval_complement(result, t); } +template +inline typename enable_if_c::value && is_convertible::value>::type + eval_complement(T& result, V const& v) +{ + T t(v); + eval_complement(result, t); +} template inline bool is_same_object(const T& u, const T&v) BOOST_NOEXCEPT @@ -118,16 +182,16 @@ BOOST_CONSTEXPR inline bool is_same_object(const T&, const U&) BOOST_NOEXCEPT { return false; } // -// Default versions of 3-arg arithmetic functions, these just forward to the 2 arg versions: +// Default versions of 3-arg arithmetic functions, these mostly just forward to the 2 arg versions: // -template -inline void eval_add(T& t, const U& u, const V& v) +template +inline void eval_add(T& t, const T& u, const T& v) { - if(is_same_object(t, v)) + if(&t == &v) { eval_add(t, u); } - else if(is_same_object(t, u)) + else if(&t == &u) { eval_add(t, v); } @@ -137,22 +201,37 @@ inline void eval_add(T& t, const U& u, const V& v) eval_add(t, v); } } -template -inline typename disable_if >::type eval_add(T& t, const U& a, const T& b) +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_add(T& t, const T& u, const U& v) { - return eval_add(t, b, a); + T vv; + vv = v; + eval_add(t, u, vv); +} +template +inline typename enable_if_c::value && is_convertible::value>::type eval_add(T& t, const T& u, const U& v) +{ + T vv(v); + eval_add(t, u, vv); +} +template +inline typename enable_if_c::value>::type eval_add(T& t, const U& u, const T& v) +{ + eval_add(t, v, u); } -template -inline void eval_subtract(T& t, const U& u, const V& v) +template +inline void eval_subtract(T& t, const T& u, const T& v) { - if(is_same_object(t, u)) - eval_subtract(t, v); - else if(is_same_object(t, v)) + if(&t == &v) { eval_subtract(t, u); t.negate(); } + else if(&t == &u) + { + eval_subtract(t, v); + } else { t = u; @@ -160,19 +239,36 @@ inline void eval_subtract(T& t, const U& u, const V& v) } } template -inline typename disable_if >::type eval_subtract(T& t, const U& a, const T& b) +inline typename enable_if_c::value && !is_convertible::value>::type eval_subtract(T& t, const T& u, const U& v) { - eval_subtract(t, b, a); + T vv; + vv = v; + eval_subtract(t, u, vv); +} +template +inline typename enable_if_c::value && is_convertible::value>::type eval_subtract(T& t, const T& u, const U& v) +{ + T vv(v); + eval_subtract(t, u, vv); +} +template +inline typename enable_if_c::value>::type eval_subtract(T& t, const U& u, const T& v) +{ + eval_subtract(t, v, u); t.negate(); } -template -inline void eval_multiply(T& t, const U& u, const V& v) +template +inline void eval_multiply(T& t, const T& u, const T& v) { - if(is_same_object(t, u)) - eval_multiply(t, v); - else if(is_same_object(t, v)) + if(&t == &v) + { eval_multiply(t, u); + } + else if(&t == &u) + { + eval_multiply(t, v); + } else { t = u; @@ -180,18 +276,32 @@ inline void eval_multiply(T& t, const U& u, const V& v) } } template -inline typename disable_if >::type eval_multiply(T& t, const U& a, const T& b) +inline typename enable_if_c::value && !is_convertible::value>::type eval_multiply(T& t, const T& u, const U& v) { - eval_multiply(t, b, a); + T vv; + vv = v; + eval_multiply(t, u, vv); } -template -inline void eval_divide(T& t, const U& u, const V& v) +template +inline typename enable_if_c::value && is_convertible::value>::type eval_multiply(T& t, const T& u, const U& v) { - if(is_same_object(t, u)) + T vv(v); + eval_multiply(t, u, vv); +} +template +inline typename enable_if_c::value>::type eval_multiply(T& t, const U& u, const T& v) +{ + eval_multiply(t, v, u); +} + +template +inline void eval_divide(T& t, const T& u, const T& v) +{ + if(&t == &u) eval_divide(t, v); - else if(is_same_object(t, v)) + else if(&t == &v) { - T temp = t; + T temp; eval_divide(temp, u, v); temp.swap(t); } @@ -201,12 +311,40 @@ inline void eval_divide(T& t, const U& u, const V& v) eval_divide(t, v); } } -template -inline void eval_modulus(T& t, const U& u, const V& v) +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_divide(T& t, const T& u, const U& v) { - if(is_same_object(t, u)) + T vv; + vv = v; + eval_divide(t, u, vv); +} +template +inline typename enable_if_c::value && is_convertible::value>::type eval_divide(T& t, const T& u, const U& v) +{ + T vv(v); + eval_divide(t, u, vv); +} +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_divide(T& t, const U& u, const T& v) +{ + T uu; + uu = u; + eval_divide(t, uu, v); +} +template +inline typename enable_if_c::value && is_convertible::value>::type eval_divide(T& t, const U& u, const T& v) +{ + T uu(u); + eval_divide(t, uu, v); +} + + +template +inline void eval_modulus(T& t, const T& u, const T& v) +{ + if(&t == &u) eval_modulus(t, v); - else if(is_same_object(t, v)) + else if(&t == &v) { T temp; eval_modulus(temp, u, v); @@ -218,13 +356,44 @@ inline void eval_modulus(T& t, const U& u, const V& v) eval_modulus(t, v); } } -template -inline void eval_bitwise_and(T& t, const U& u, const V& v) +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_modulus(T& t, const T& u, const U& v) { - if(is_same_object(t, u)) - eval_bitwise_and(t, v); - else if(is_same_object(t, v)) + T vv; + vv = v; + eval_modulus(t, u, vv); +} +template +inline typename enable_if_c::value && is_convertible::value>::type eval_modulus(T& t, const T& u, const U& v) +{ + T vv(v); + eval_modulus(t, u, vv); +} +template +inline typename enable_if_c::value && !is_convertible::value>::type eval_modulus(T& t, const U& u, const T& v) +{ + T uu; + uu = u; + eval_modulus(t, uu, v); +} +template +inline typename enable_if_c::value && is_convertible::value>::type eval_modulus(T& t, const U& u, const T& v) +{ + T uu(u); + eval_modulus(t, uu, v); +} + +template +inline void eval_bitwise_and(T& t, const T& u, const T& v) +{ + if(&t == &v) + { eval_bitwise_and(t, u); + } + else if(&t == &u) + { + eval_bitwise_and(t, v); + } else { t = u; @@ -232,18 +401,35 @@ inline void eval_bitwise_and(T& t, const U& u, const V& v) } } template -inline typename disable_if >::type eval_bitwise_and(T& t, const U& a, const T& b) +inline typename enable_if_c::value && !is_convertible::value>::type eval_bitwise_and(T& t, const T& u, const U& v) { - eval_bitwise_and(t, b, a); + T vv; + vv = v; + eval_bitwise_and(t, u, vv); +} +template +inline typename enable_if_c::value && is_convertible::value>::type eval_bitwise_and(T& t, const T& u, const U& v) +{ + T vv(v); + eval_bitwise_and(t, u, vv); +} +template +inline typename enable_if_c::value>::type eval_bitwise_and(T& t, const U& u, const T& v) +{ + eval_bitwise_and(t, v, u); } -template -inline void eval_bitwise_or(T& t, const U& u, const V& v) +template +inline void eval_bitwise_or(T& t, const T& u, const T& v) { - if(is_same_object(t, u)) - eval_bitwise_or(t, v); - else if(is_same_object(t, v)) + if(&t == &v) + { eval_bitwise_or(t, u); + } + else if(&t == &u) + { + eval_bitwise_or(t, v); + } else { t = u; @@ -251,18 +437,35 @@ inline void eval_bitwise_or(T& t, const U& u, const V& v) } } template -inline typename disable_if >::type eval_bitwise_or(T& t, const U& a, const T& b) +inline typename enable_if_c::value && !is_convertible::value>::type eval_bitwise_or(T& t, const T& u, const U& v) { - eval_bitwise_or(t, b, a); + T vv; + vv = v; + eval_bitwise_or(t, u, vv); +} +template +inline typename enable_if_c::value && is_convertible::value>::type eval_bitwise_or(T& t, const T& u, const U& v) +{ + T vv(v); + eval_bitwise_or(t, u, vv); +} +template +inline typename enable_if_c::value>::type eval_bitwise_or(T& t, const U& u, const T& v) +{ + eval_bitwise_or(t, v, u); } -template -inline void eval_bitwise_xor(T& t, const U& u, const V& v) +template +inline void eval_bitwise_xor(T& t, const T& u, const T& v) { - if(is_same_object(t, u)) - eval_bitwise_xor(t, v); - else if(is_same_object(t, v)) + if(&t == &v) + { eval_bitwise_xor(t, u); + } + else if(&t == &u) + { + eval_bitwise_xor(t, v); + } else { t = u; @@ -270,9 +473,22 @@ inline void eval_bitwise_xor(T& t, const U& u, const V& v) } } template -inline typename disable_if >::type eval_bitwise_xor(T& t, const U& a, const T& b) +inline typename enable_if_c::value && !is_convertible::value>::type eval_bitwise_xor(T& t, const T& u, const U& v) { - eval_bitwise_xor(t, b, a); + T vv; + vv = v; + eval_bitwise_xor(t, u, vv); +} +template +inline typename enable_if_c::value && is_convertible::value>::type eval_bitwise_xor(T& t, const T& u, const U& v) +{ + T vv(v); + eval_bitwise_xor(t, u, vv); +} +template +inline typename enable_if_c::value>::type eval_bitwise_xor(T& t, const U& u, const T& v) +{ + eval_bitwise_xor(t, v, u); } template @@ -281,7 +497,6 @@ inline void eval_increment(T& val) typedef typename mpl::front::type ui_type; eval_add(val, static_cast(1u)); } - template inline void eval_decrement(T& val) { diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 0782839d..fa3b10ca 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -925,6 +925,14 @@ struct gmp_int mpz_set(m_data, o.m_data); return *this; } +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_int& operator = (gmp_int&& o) BOOST_NOEXCEPT + { + m_data[0] = o.m_data[0]; + o.m_data[0]._mp_d = 0; + return *this; + } +#endif gmp_int& operator = (unsigned long long i) { unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); @@ -1534,6 +1542,16 @@ struct gmp_rational mpq_set(m_data, o.m_data); return *this; } +#ifndef BOOST_NO_RVALUE_REFERENCES + gmp_rational& operator = (gmp_rational&& o) BOOST_NOEXCEPT + { + m_data[0]._mp_num = o.data()[0]._mp_num; + m_data[0]._mp_den = o.data()[0]._mp_den; + o.data()[0]._mp_num._mp_d = 0; + o.data()[0]._mp_den._mp_d = 0; + return *this; + } +#endif gmp_rational& operator = (unsigned long long i) { unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index c81f691d..3d93418e 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -165,7 +165,7 @@ public: BOOST_CONSTEXPR mp_number(mp_number&& r) BOOST_NOEXCEPT : m_backend(static_cast(r.m_backend)){} mp_number& operator=(mp_number&& r) BOOST_NOEXCEPT { - m_backend.swap(r.m_backend); + m_backend = static_cast(r.m_backend); return *this; } #endif diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index a7192b1d..f3e4cd47 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -37,6 +37,11 @@ struct rational_adapter #ifndef BOOST_NO_RVALUE_REFERENCES rational_adapter(rational_adapter&& o) : m_value(o.m_value) {} rational_adapter(IntBackend&& o) : m_value(o) {} + rational_adapter& operator = (rational_adapter&& o) + { + m_value = static_cast(o.m_value); + return *this; + } #endif rational_adapter& operator = (const rational_adapter& o) { diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 5f2c3db6..21525be5 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -52,6 +52,12 @@ struct tommath_int m_data = o.m_data; o.m_data.dp = 0; } + tommath_int& operator = (tommath_int&& o) + { + m_data = o.m_data; + o.m_data.dp = 0; + return *this; + } #endif tommath_int& operator = (const tommath_int& o) { diff --git a/performance/float_backend.hpp b/performance/arithmetic_backend.hpp similarity index 55% rename from performance/float_backend.hpp rename to performance/arithmetic_backend.hpp index 8b2f2c9b..69176f3c 100644 --- a/performance/float_backend.hpp +++ b/performance/arithmetic_backend.hpp @@ -19,64 +19,37 @@ namespace multiprecision{ namespace backends{ template -struct float_backend +struct arithmetic_backend { - typedef mpl::list signed_types; - typedef mpl::list unsigned_types; - typedef mpl::list float_types; - typedef int exponent_type; + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list float_types; + typedef int exponent_type; - float_backend(){} - float_backend(const float_backend& o) + arithmetic_backend(){} + arithmetic_backend(const arithmetic_backend& o) { m_value = o.m_value; } - float_backend(const Arithmetic& o) : m_value(o) {} -#ifndef BOOST_NO_RVALUE_REFERENCES - float_backend(float_backend&& o) : m_value(o.m_value) {} - float_backend(Arithmetic&& o) : m_value(o) {} -#endif - float_backend& operator = (const float_backend& o) + template + arithmetic_backend(const A& o, const typename enable_if >::type* = 0) : m_value(o) {} + arithmetic_backend& operator = (const arithmetic_backend& o) { m_value = o.m_value; return *this; } - float_backend& operator = (unsigned long long i) + template + typename enable_if, arithmetic_backend&>::type operator = (A i) { m_value = i; return *this; } - float_backend& operator = (unsigned i) - { - m_value = i; - return *this; - } - float_backend& operator = (long long i) - { - m_value = i; - return *this; - } - float_backend& operator = (int i) - { - m_value = i; - return *this; - } - float_backend& operator = (long double d) - { - m_value = d; - return *this; - } - float_backend& operator = (double d) - { - m_value = d; - return *this; - } - float_backend& operator = (const char* s) + arithmetic_backend& operator = (const char* s) { m_value = boost::lexical_cast(s); return *this; } - void swap(float_backend& o) + void swap(arithmetic_backend& o) { std::swap(m_value, o.m_value); } @@ -91,289 +64,276 @@ struct float_backend { m_value = -m_value; } - int compare(const float_backend& o)const + int compare(const arithmetic_backend& o)const { return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); } - int compare(long long i)const + template + typename enable_if, int>::type compare(A i)const { return m_value > i ? 1 : (m_value < i ? -1 : 0); } - int compare(int i)const - { - return m_value > i ? 1 : (m_value < i ? -1 : 0); - } - int compare(unsigned long long i)const - { - return m_value > i ? 1 : (m_value < i ? -1 : 0); - } - int compare(unsigned i)const - { - return m_value > i ? 1 : (m_value < i ? -1 : 0); - } - int compare(long double d)const - { - return m_value > d ? 1 : (m_value < d ? -1 : 0); - } - int compare(double d)const - { - return m_value > d ? 1 : (m_value < d ? -1 : 0); - } Arithmetic& data() { return m_value; } const Arithmetic& data()const { return m_value; } private: Arithmetic m_value; }; +template +inline void eval_convert_to(R* result, const arithmetic_backend& backend) +{ + *result = backend.data(); +} + template -inline void eval_add(float_backend& result, const float_backend& o) +inline void eval_add(arithmetic_backend& result, const arithmetic_backend& o) { result.data() += o.data(); } template -inline void eval_subtract(float_backend& result, const float_backend& o) +inline void eval_subtract(arithmetic_backend& result, const arithmetic_backend& o) { result.data() -= o.data(); } template -inline void eval_multiply(float_backend& result, const float_backend& o) +inline void eval_multiply(arithmetic_backend& result, const arithmetic_backend& o) { result.data() *= o.data(); } template -inline void eval_divide(float_backend& result, const float_backend& o) +inline void eval_divide(arithmetic_backend& result, const arithmetic_backend& o) { result.data() /= o.data(); } template -inline typename enable_if >::type eval_add(float_backend& result, const A2& o) +inline typename enable_if >::type eval_add(arithmetic_backend& result, const A2& o) { result.data() += o; } template -inline typename enable_if >::type eval_subtract(float_backend& result, const A2& o) +inline typename enable_if >::type eval_subtract(arithmetic_backend& result, const A2& o) { result.data() -= o; } template -inline typename enable_if >::type eval_multiply(float_backend& result, const A2& o) +inline typename enable_if >::type eval_multiply(arithmetic_backend& result, const A2& o) { result.data() *= o; } template -inline typename enable_if >::type eval_divide(float_backend& result, const A2& o) +inline typename enable_if >::type eval_divide(arithmetic_backend& result, const A2& o) { result.data() /= o; } template -inline void eval_add(float_backend& result, const float_backend& a, const float_backend& b) +inline void eval_add(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) { result.data() = a.data() + b.data(); } template -inline void eval_subtract(float_backend& result, const float_backend& a, const float_backend& b) +inline void eval_subtract(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) { result.data() = a.data() - b.data(); } template -inline void eval_multiply(float_backend& result, const float_backend& a, const float_backend& b) +inline void eval_multiply(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) { result.data() = a.data() * b.data(); } template -inline void eval_divide(float_backend& result, const float_backend& a, const float_backend& b) +inline void eval_divide(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) { result.data() = a.data() / b.data(); } template -inline typename enable_if>::type eval_add(float_backend& result, const A2& a, const float_backend& b) +inline typename enable_if>::type eval_add(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) { - result.data() = a + b.data(); + result.data() = a.data() + b; } template -inline typename enable_if>::type eval_subtract(float_backend& result, const A2& a, const float_backend& b) +inline typename enable_if>::type eval_subtract(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) { - result.data() = a - b.data(); + result.data() = a.data() - b; } template -inline typename enable_if>::type eval_multiply(float_backend& result, const A2& a, const float_backend& b) +inline typename enable_if>::type eval_multiply(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) { - result.data() = a * b.data(); + result.data() = a.data() * b; } template -inline typename enable_if>::type eval_divide(float_backend& result, const A2& a, const float_backend& b) +inline typename enable_if>::type eval_divide(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) { - result.data() = a / b.data(); + result.data() = a.data() / b; } template -inline bool eval_is_zero(const float_backend& val) +inline bool eval_is_zero(const arithmetic_backend& val) { return val.data() == 0; } template -inline int eval_get_sign(const float_backend& val) +inline int eval_get_sign(const arithmetic_backend& val) { return val.data() == 0 ? 0 : val.data() < 0 ? -1 : 1; } template -inline void eval_abs(float_backend& result, const float_backend& o) +inline void eval_abs(arithmetic_backend& result, const arithmetic_backend& o) { result.data() = std::abs(o.data()); } template -inline void eval_fabs(float_backend& result, const float_backend& o) +inline void eval_fabs(arithmetic_backend& result, const arithmetic_backend& o) { result.data() = std::abs(o.data()); } template -inline void eval_floor(float_backend& result, const float_backend& o) +inline void eval_floor(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = floor(o.data()); } template -inline void eval_ceil(float_backend& result, const float_backend& o) +inline void eval_ceil(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = ceil(o.data()); } template -inline void eval_sqrt(float_backend& result, const float_backend& o) +inline void eval_sqrt(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = sqrt(o.data()); } template -inline int eval_fpclassify(const float_backend& o) +inline int eval_fpclassify(const arithmetic_backend& o) { return (boost::math::fpclassify)(o.data()); } template -inline void eval_trunc(float_backend& result, const float_backend& o) +inline void eval_trunc(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = trunc(o.data()); } template -inline void eval_round(float_backend& result, const float_backend& o) +inline void eval_round(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = round(o.data()); } template -inline void eval_exp(float_backend& result, const float_backend& o) +inline void eval_exp(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = exp(o.data()); } template -inline void eval_log(float_backend& result, const float_backend& o) +inline void eval_log(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = log(o.data()); } template -inline void eval_log10(float_backend& result, const float_backend& o) +inline void eval_log10(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = log10(o.data()); } template -inline void eval_sin(float_backend& result, const float_backend& o) +inline void eval_sin(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = sin(o.data()); } template -inline void eval_cos(float_backend& result, const float_backend& o) +inline void eval_cos(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = cos(o.data()); } template -inline void eval_tan(float_backend& result, const float_backend& o) +inline void eval_tan(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = tan(o.data()); } template -inline void eval_acos(float_backend& result, const float_backend& o) +inline void eval_acos(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = acos(o.data()); } template -inline void eval_asin(float_backend& result, const float_backend& o) +inline void eval_asin(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = asin(o.data()); } template -inline void eval_atan(float_backend& result, const float_backend& o) +inline void eval_atan(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = atan(o.data()); } template -inline void eval_sinh(float_backend& result, const float_backend& o) +inline void eval_sinh(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = sinh(o.data()); } template -inline void eval_cosh(float_backend& result, const float_backend& o) +inline void eval_cosh(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = cosh(o.data()); } template -inline void eval_tanh(float_backend& result, const float_backend& o) +inline void eval_tanh(arithmetic_backend& result, const arithmetic_backend& o) { BOOST_MATH_STD_USING result.data() = tanh(o.data()); } template -inline void eval_fmod(float_backend& result, const float_backend& a, const float_backend& b) +inline void eval_fmod(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) { BOOST_MATH_STD_USING result.data() = fmod(a.data(), b.data()); } template -inline void eval_pow(float_backend& result, const float_backend& a, const float_backend& b) +inline void eval_pow(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) { BOOST_MATH_STD_USING result.data() = pow(a.data(), b.data()); } template -inline void eval_atan2(float_backend& result, const float_backend& a, const float_backend& b) +inline void eval_atan2(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) { BOOST_MATH_STD_USING result.data() = atan2(a.data(), b.data()); @@ -381,7 +341,7 @@ inline void eval_atan2(float_backend& result, const float_backend(concepts::real_concept r namespace std{ template -class numeric_limits, ExpressionTemplates > > : public std::numeric_limits +class numeric_limits, ExpressionTemplates > > : public std::numeric_limits { typedef std::numeric_limits base_type; - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } diff --git a/performance/delaunay_data.txt b/performance/delaunay_data.txt new file mode 100644 index 00000000..20932f78 --- /dev/null +++ b/performance/delaunay_data.txt @@ -0,0 +1,100000 @@ +1760125 5599875 1663688 5645904 1599875 5760125 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1626168 5682784 diff --git a/performance/delaunay_test.cpp b/performance/delaunay_test.cpp new file mode 100644 index 00000000..bc8db005 --- /dev/null +++ b/performance/delaunay_test.cpp @@ -0,0 +1,279 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. +// Copyright 2012 Phil Endecott +// Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include "arithmetic_backend.hpp" +#include + +#include +#include + +template +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + +// Custom 128-bit maths used for exact calculation of the Delaunay test. +// Only the few operators actually needed here are implemented. + +struct int128_t { + int64_t high; + uint64_t low; + + int128_t() {} + int128_t(int32_t i): high(i>>31), low(static_cast(i)) {} + int128_t(uint32_t i): high(0), low(i) {} + int128_t(int64_t i): high(i>>63), low(i) {} + int128_t(uint64_t i): high(0), low(i) {} +}; + +inline int128_t operator<<(int128_t val, int amt) +{ + int128_t r; + r.low = val.low << amt; + r.high = val.low >> (64-amt); + r.high |= val.high << amt; + return r; +} + +inline int128_t& operator+=(int128_t& l, int128_t r) +{ + l.low += r.low; + bool carry = l.low < r.low; + l.high += r.high; + if (carry) ++l.high; + return l; +} + +inline int128_t operator-(int128_t val) +{ + val.low = ~val.low; + val.high = ~val.high; + val.low += 1; + if (val.low == 0) val.high += 1; + return val; +} + +inline int128_t operator+(int128_t l, int128_t r) +{ + l += r; + return l; +} + +inline bool operator<(int128_t l, int128_t r) +{ + if (l.high != r.high) return l.high < r.high; + return l.low < r.low; +} + + +inline int128_t mult_64x64_to_128(int64_t a, int64_t b) +{ + // Make life simple by dealing only with positive numbers: + bool neg = false; + if (a<0) { neg = !neg; a = -a; } + if (b<0) { neg = !neg; b = -b; } + + // Divide input into 32-bit halves: + uint32_t ah = a >> 32; + uint32_t al = a & 0xffffffff; + uint32_t bh = b >> 32; + uint32_t bl = b & 0xffffffff; + + // Long multiplication, with 64-bit temporaries: + + // ah al + // * bh bl + // ---------------- + // al*bl (t1) + // + ah*bl (t2) + // + al*bh (t3) + // + ah*bh (t4) + // ---------------- + + uint64_t t1 = static_cast(al)*bl; + uint64_t t2 = static_cast(ah)*bl; + uint64_t t3 = static_cast(al)*bh; + uint64_t t4 = static_cast(ah)*bh; + + int128_t r(t1); + r.high = t4; + r += int128_t(t2) << 32; + r += int128_t(t3) << 32; + + if (neg) r = -r; + + return r; +} + +template +__forceinline void mul_2n(R& r, const T& a, const T& b) +{ + r = R(a) * b; +} + +__forceinline void mul_2n(int128_t& r, const boost::int64_t& a, const boost::int64_t& b) +{ + r = mult_64x64_to_128(a, b); +} + +template +inline bool delaunay_test(int32_t ax, int32_t ay, int32_t bx, int32_t by, + int32_t cx, int32_t cy, int32_t dx, int32_t dy) +{ + // Test whether the quadrilateral ABCD's diagonal AC should be flipped to BD. + // This is the Cline & Renka method. + // Flip if the sum of the angles ABC and CDA is greater than 180 degrees. + // Equivalently, flip if sin(ABC + CDA) < 0. + // Trig identity: cos(ABC) * sin(CDA) + sin(ABC) * cos(CDA) < 0 + // We can use scalar and vector products to find sin and cos, and simplify + // to the following code. + // Numerical robustness is important. This code addresses it by performing + // exact calculations with large integer types. + + typedef typename Traits::i64_t i64; + typedef typename Traits::i128_t i128; + + i64 ax64 = ax, ay64 = ay, bx64 = bx, by64 = by, + cx64 = cx, cy64 = cy, dx64 = dx, dy64 = dy; + + i64 cos_abc, t; + mul_2n(cos_abc, (ax-bx), (cx-bx)); + mul_2n(t, (ay-by), (cy-by)); + cos_abc += t; + + i64 cos_cda; + mul_2n(cos_cda, (cx-dx), (ax-dx)); + mul_2n(t, (cy-dy), (ay-dy)); + cos_cda += t; + + if (cos_abc >= 0 && cos_cda >= 0) return false; + if (cos_abc < 0 && cos_cda < 0) return true; + + i64 sin_abc; + mul_2n(sin_abc, (ax-bx), (cy-by)); + mul_2n(t, (cx-bx), (ay-by)); + sin_abc -= t; + + i64 sin_cda; + mul_2n(sin_cda, (cx-dx), (ay-dy)); + mul_2n(t, (ax-dx), (cy-dy)); + sin_cda -= t; + + i128 sin_sum, t128; + mul_2n(sin_sum, sin_abc, cos_cda); + mul_2n(t128, cos_abc, sin_cda); + sin_sum += t128; + + return sin_sum < 0; +} + + +struct dt_dat { + int32_t ax, ay, bx, by, cx, cy, dx, dy; +}; + +typedef std::vector data_t; +data_t data; + +static void load_data() +{ + std::ifstream is("delaunay_data.txt"); + + while (is.good()) + { + dt_dat d; + is >> d.ax >> d.ay >> d.bx >> d.by >> d.cx >> d.cy >> d.dx >> d.dy; + if (is.good()) + { + data.push_back(d); + d.ax >>= 10; + d.ay >>= 10; + d.bx >>= 10; + d.by >>= 10; + d.cx >>= 10; + d.cy >>= 10; + d.dx >>= 10; + d.dy >>= 10; + data.push_back(d); + } + } +} + +template +void do_calc(const char* name) +{ + std::cout << "Running calculations for: " << name << std::endl; + + stopwatch w; + + boost::uint64_t flips = 0; + boost::uint64_t calcs = 0; + + for(int j = 0; j < 1000; ++j) + { + for(data_t::const_iterator i = data.begin(); i != data.end(); ++i) + { + const dt_dat& d = *i; + bool flip = delaunay_test(d.ax,d.ay, d.bx,d.by, d.cx,d.cy, d.dx,d.dy); + if (flip) ++flips; + ++calcs; + } + } + double t = boost::chrono::duration_cast >(w.elapsed()).count(); + + std::cout << "Number of calculations = " << calcs << std::endl; + std::cout << "Number of flips = " << flips << std::endl; + std::cout << "Total execution time = " << t << std::endl; + std::cout << "Time per calculation = " << t / calcs << std::endl << std::endl; +} + +template +struct test_traits +{ + typedef I64 i64_t; + typedef I128 i128_t; +}; + + +int main() +{ + using namespace boost::multiprecision; + std::cout << "loading data...\n"; + load_data(); + + std::cout << "calculating...\n"; + + do_calc >("int64_t, int64_t"); + do_calc >, mp_number > > >("arithmetic_backend"); + do_calc >("int64_t, int128_t"); + do_calc >("int64_t, mp_int128_t"); + do_calc, true> > >("int64_t, mp_int128_t (ET)"); + do_calc >("int64_t, cpp_int"); + do_calc, false> > >("int64_t, cpp_int (no ET's)"); + do_calc > > >("int64_t, cpp_int(128-bit cache)"); + do_calc, false> > >("int64_t, cpp_int (128-bit Cache no ET's)"); + + return 0; +} + diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index 8dd0b3ed..61116348 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -380,6 +380,129 @@ struct tester a.deallocate(pt, 1000); return result; } + + // + // Hetero operations: + // + template + static T get_hetero_test_value(boost::mpl::false_ const&) + { + return T(2) / 3; + } + template + static T get_hetero_test_value(boost::mpl::true_ const&) + { + return (std::numeric_limits::max)() >> 4; + } + template + static T get_hetero_test_value() + { + return get_hetero_test_value(boost::is_integral()); + } + template + double test_multiply_hetero() + { + static const T val = get_hetero_test_value(); + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] * val; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } + template + double test_inplace_multiply_hetero() + { + static const T val = get_hetero_test_value(); + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i]; + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] *= val; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } + template + double test_add_hetero() + { + static const T val = get_hetero_test_value(); + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] + val; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } + template + double test_inplace_add_hetero() + { + static const T val = get_hetero_test_value(); + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i]; + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] += val; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } + template + double test_subtract_hetero() + { + static const T val = get_hetero_test_value(); + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] - val; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } + template + double test_inplace_subtract_hetero() + { + static const T val = get_hetero_test_value(); + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i]; + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] -= val; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } + template + double test_divide_hetero() + { + static const T val = get_hetero_test_value(); + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] / val; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } + template + double test_inplace_divide_hetero() + { + static const T val = get_hetero_test_value(); + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i]; + stopwatch w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] /= val; + } + return boost::chrono::duration_cast >(w.elapsed()).count(); + } private: T generate_random() { @@ -563,6 +686,15 @@ void test(const char* type, unsigned precision) report_result(cat, type, "construct(unsigned)", precision, t.test_construct_unsigned()); report_result(cat, type, "construct(unsigned long long)", precision, t.test_construct_unsigned_ll()); test_int_ops(t, type, precision, typename boost::multiprecision::number_category::type()); + // Hetero ops: + report_result(cat, type, "+", precision, t.template test_add_hetero()); + report_result(cat, type, "-", precision, t.template test_subtract_hetero()); + report_result(cat, type, "*", precision, t.template test_multiply_hetero()); + report_result(cat, type, "/", precision, t.template test_divide_hetero()); + report_result(cat, type, "+", precision, t.template test_inplace_add_hetero()); + report_result(cat, type, "-", precision, t.template test_inplace_subtract_hetero()); + report_result(cat, type, "*", precision, t.template test_inplace_multiply_hetero()); + report_result(cat, type, "/", precision, t.template test_inplace_divide_hetero()); } void quickbook_results() diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index 2e66acd9..2277fd35 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -6,16 +6,17 @@ #define BOOST_MATH_MAX_ROOT_ITERATION_POLICY 500 #if !defined(TEST_MPFR) && !defined(TEST_MPREAL) && !defined(TEST_MPF) && !defined(TEST_MPREAL) \ - && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_CLASS) + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_CLASS) && !defined(TEST_FLOAT) # define TEST_MPFR # define TEST_MPF # define TEST_CPP_DEC_FLOAT # define TEST_MPFR_CLASS # define TEST_MPREAL +# define TEST_FLOAT #endif #ifdef TEST_FLOAT -#include "float_backend.hpp" +#include "arithmetic_backend.hpp" #endif #ifdef TEST_MPFR_CLASS #include @@ -258,8 +259,8 @@ int main() #ifdef TEST_FLOAT time_proc("double", test_bessel); time_proc("real_concept", test_bessel); - time_proc("float_backend", test_bessel > >); - time_proc("float_backend - no expression templates", test_bessel, false> >); + time_proc("arithmetic_backend", test_bessel > >); + time_proc("arithmetic_backend - no expression templates", test_bessel, false> >); #endif // From 5711748ee1bbe48641f3897ebe131dfc3bfd30af Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 30 Jul 2012 17:51:47 +0000 Subject: [PATCH 204/256] Fix misc bugs introduced in last commit. [SVN r79804] --- include/boost/multiprecision/cpp_int.hpp | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 2391a0d4..cc6295b5 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1326,6 +1326,7 @@ inline void add_unsigned(cpp_int_backend& res result.limbs()[x] = static_cast(carry); } result.normalize(); + result.sign(a.sign()); } template inline void eval_add(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) @@ -1400,7 +1401,9 @@ template inline void eval_subtract(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(result.sign()) + { add_unsigned(result, result, o); + } else subtract_unsigned(result, o); } @@ -1408,7 +1411,9 @@ template inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign()) + { add_unsigned(result, a, o); + } else { result = a; @@ -2068,8 +2073,8 @@ void divide_unsigned_helper(cpp_int_backend* *result = *pr / y; result->sign(x.sign()); } - r.sign(x.sign()); *pr %= y; + r.sign(x.sign()); return; } else if(r_order == 1) From c79fb415268c643bf3a46fb744589fa5804705a6 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 31 Jul 2012 18:14:14 +0000 Subject: [PATCH 205/256] Rework comparison operators - note that existing backends are made less efficient by this at present. [SVN r79823] --- .../detail/mp_number_compare.hpp | 488 ++++++++++++++++++ include/boost/multiprecision/mp_number.hpp | 6 +- performance/Jamfile.v2 | 4 + performance/arithmetic_backend.hpp | 149 +++++- performance/sf_performance.cpp | 13 +- test/test_arithmetic.cpp | 25 +- 6 files changed, 671 insertions(+), 14 deletions(-) create mode 100644 include/boost/multiprecision/detail/mp_number_compare.hpp diff --git a/include/boost/multiprecision/detail/mp_number_compare.hpp b/include/boost/multiprecision/detail/mp_number_compare.hpp new file mode 100644 index 00000000..909d4af8 --- /dev/null +++ b/include/boost/multiprecision/detail/mp_number_compare.hpp @@ -0,0 +1,488 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MP_COMPARE_HPP +#define BOOST_MP_COMPARE_HPP + +// +// Comparison operators for mp_number. +// + +namespace boost{ namespace multiprecision{ + +namespace default_ops{ + +template +inline bool eval_eq(const B& a, const B& b) +{ + return a.compare(b) == 0; +} +template +inline typename enable_if_c<(is_arithmetic::value && is_convertible::value), bool>::type eval_eq(const B& a, const A& b) +{ + B t(b); + return eval_eq(a, t); +} +template +inline typename enable_if_c<(is_arithmetic::value && !is_convertible::value), bool>::type eval_eq(const B& a, const A& b) +{ + B t; + t = b; + return eval_eq(a, t); +} + +template +inline bool eval_lt(const B& a, const B& b) +{ + return a.compare(b) < 0; +} +template +inline typename enable_if_c<(is_arithmetic::value && is_convertible::value), bool>::type eval_lt(const B& a, const A& b) +{ + B t(b); + return eval_lt(a, t); +} +template +inline typename enable_if_c<(is_arithmetic::value && !is_convertible::value), bool>::type eval_lt(const B& a, const A& b) +{ + B t; + t = b; + return eval_lt(a, t); +} + +template +inline bool eval_gt(const B& a, const B& b) +{ + return a.compare(b) > 0; +} +template +inline typename enable_if_c<(is_arithmetic::value && is_convertible::value), bool>::type eval_gt(const B& a, const A& b) +{ + B t(b); + return eval_gt(a, t); +} +template +inline typename enable_if_c<(is_arithmetic::value && !is_convertible::value), bool>::type eval_gt(const B& a, const A& b) +{ + B t; + t = b; + return eval_gt(a, t); +} + +} + +template +inline bool operator == (const mp_number& a, const mp_number& b) +{ + using default_ops::eval_eq; + return eval_eq(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator == (const mp_number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + return eval_eq(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator == (const mp_number& a, const detail::mp_exp& b) +{ + using default_ops::eval_eq; + typename detail::mp_exp::result_type t(b); + return eval_eq(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator == (const Arithmetic& a, const mp_number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + return eval_eq(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator == (const Arithmetic& a, const detail::mp_exp& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + result_type t(b); + return eval_eq(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator == (const detail::mp_exp& a, const mp_number& b) +{ + using default_ops::eval_eq; + typename detail::mp_exp::result_type t(a); + return eval_eq(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator == (const detail::mp_exp& a, const Arithmetic& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + result_type t(a); + return eval_eq(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type + operator == (const detail::mp_exp& a, const detail::mp_exp& b) +{ + using default_ops::eval_eq; + typename detail::mp_exp::result_type t(a); + typename detail::mp_exp::result_type t2(b); + return eval_eq(t.backend(), t2.backend()); +} + +template +inline bool operator != (const mp_number& a, const mp_number& b) +{ + using default_ops::eval_eq; + return !eval_eq(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator != (const mp_number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + return !eval_eq(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator != (const mp_number& a, const detail::mp_exp& b) +{ + using default_ops::eval_eq; + typename detail::mp_exp::result_type t(b); + return !eval_eq(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator != (const Arithmetic& a, const mp_number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + return !eval_eq(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator != (const Arithmetic& a, const detail::mp_exp& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + result_type t(b); + return !eval_eq(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator != (const detail::mp_exp& a, const mp_number& b) +{ + using default_ops::eval_eq; + typename detail::mp_exp::result_type t(a); + return !eval_eq(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator != (const detail::mp_exp& a, const Arithmetic& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + result_type t(a); + return !eval_eq(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type + operator != (const detail::mp_exp& a, const detail::mp_exp& b) +{ + using default_ops::eval_eq; + typename detail::mp_exp::result_type t(a); + typename detail::mp_exp::result_type t2(b); + return !eval_eq(t.backend(), t2.backend()); +} + +template +inline bool operator < (const mp_number& a, const mp_number& b) +{ + using default_ops::eval_lt; + return eval_lt(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator < (const mp_number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + return eval_lt(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator < (const mp_number& a, const detail::mp_exp& b) +{ + using default_ops::eval_lt; + typename detail::mp_exp::result_type t(b); + return eval_lt(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator < (const Arithmetic& a, const mp_number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + return eval_gt(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator < (const Arithmetic& a, const detail::mp_exp& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + result_type t(b); + return eval_gt(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator < (const detail::mp_exp& a, const mp_number& b) +{ + using default_ops::eval_lt; + typename detail::mp_exp::result_type t(a); + return eval_lt(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator < (const detail::mp_exp& a, const Arithmetic& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + result_type t(a); + return eval_lt(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type + operator < (const detail::mp_exp& a, const detail::mp_exp& b) +{ + using default_ops::eval_lt; + typename detail::mp_exp::result_type t(a); + typename detail::mp_exp::result_type t2(b); + return eval_lt(t.backend(), t2.backend()); +} + +template +inline bool operator > (const mp_number& a, const mp_number& b) +{ + using default_ops::eval_gt; + return eval_gt(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator > (const mp_number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + return eval_gt(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator > (const mp_number& a, const detail::mp_exp& b) +{ + using default_ops::eval_gt; + typename detail::mp_exp::result_type t(b); + return eval_gt(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator > (const Arithmetic& a, const mp_number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + return eval_lt(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator > (const Arithmetic& a, const detail::mp_exp& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + result_type t(b); + return eval_lt(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator > (const detail::mp_exp& a, const mp_number& b) +{ + using default_ops::eval_gt; + typename detail::mp_exp::result_type t(a); + return eval_gt(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator > (const detail::mp_exp& a, const Arithmetic& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + result_type t(a); + return eval_gt(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type + operator > (const detail::mp_exp& a, const detail::mp_exp& b) +{ + using default_ops::eval_gt; + typename detail::mp_exp::result_type t(a); + typename detail::mp_exp::result_type t2(b); + return eval_gt(t.backend(), t2.backend()); +} + +template +inline bool operator <= (const mp_number& a, const mp_number& b) +{ + using default_ops::eval_gt; + return !eval_gt(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator <= (const mp_number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + return !eval_gt(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator <= (const mp_number& a, const detail::mp_exp& b) +{ + using default_ops::eval_gt; + typename detail::mp_exp::result_type t(b); + return !eval_gt(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator <= (const Arithmetic& a, const mp_number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + return !eval_lt(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator <= (const Arithmetic& a, const detail::mp_exp& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + result_type t(b); + return !eval_lt(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator <= (const detail::mp_exp& a, const mp_number& b) +{ + using default_ops::eval_gt; + typename detail::mp_exp::result_type t(a); + return !eval_gt(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator <= (const detail::mp_exp& a, const Arithmetic& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + result_type t(a); + return !eval_gt(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type + operator <= (const detail::mp_exp& a, const detail::mp_exp& b) +{ + using default_ops::eval_gt; + typename detail::mp_exp::result_type t(a); + typename detail::mp_exp::result_type t2(b); + return !eval_gt(t.backend(), t2.backend()); +} + +template +inline bool operator >= (const mp_number& a, const mp_number& b) +{ + using default_ops::eval_lt; + return !eval_lt(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator >= (const mp_number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + return !eval_lt(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator >= (const mp_number& a, const detail::mp_exp& b) +{ + using default_ops::eval_lt; + typename detail::mp_exp::result_type t(b); + return !eval_lt(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator >= (const Arithmetic& a, const mp_number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + return !eval_gt(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator >= (const Arithmetic& a, const detail::mp_exp& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + result_type t(b); + return !eval_gt(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type + operator >= (const detail::mp_exp& a, const mp_number& b) +{ + using default_ops::eval_lt; + typename detail::mp_exp::result_type t(a); + return !eval_lt(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator >= (const detail::mp_exp& a, const Arithmetic& b) +{ + typedef typename detail::mp_exp::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + result_type t(a); + return !eval_lt(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type + operator >= (const detail::mp_exp& a, const detail::mp_exp& b) +{ + using default_ops::eval_lt; + typename detail::mp_exp::result_type t(a); + typename detail::mp_exp::result_type t2(b); + return !eval_lt(t.backend(), t2.backend()); +} + + +}} // namespaces + +#endif // BOOST_MP_COMPARE_HPP + diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 3d93418e..4a8ee16d 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -20,6 +20,7 @@ #include #include #include +#include #include // stream operators #include // EOF @@ -1630,14 +1631,13 @@ struct is_valid_comparison : public boost::multiprecision::detail::is_valid_comp } - +/* template inline typename boost::enable_if, bool>::type operator == (const Exp1& a, const Exp2& b) { return 0 == detail::mp_number_compare(a, b); } - template inline typename boost::enable_if, bool>::type operator != (const Exp1& a, const Exp2& b) @@ -1672,7 +1672,7 @@ inline typename boost::enable_if, bool>: { return 0 < detail::mp_number_compare(a, b); } - +*/ template inline std::ostream& operator << (std::ostream& os, const mp_number& r) { diff --git a/performance/Jamfile.v2 b/performance/Jamfile.v2 index 66d35e7f..eb349c69 100644 --- a/performance/Jamfile.v2 +++ b/performance/Jamfile.v2 @@ -69,6 +69,8 @@ exe sf_performance : sf_performance.cpp /boost/system//boost_system /boost/chron TEST_CPP_DEC_FLOAT msvc:-bigobj ; + +exe delaunay_test : delaunay_test.cpp /boost/system//boost_system /boost/chrono//boost_chrono ; obj obj_linpack_benchmark_mpfr : linpack-benchmark.cpp : release @@ -118,4 +120,6 @@ install miller_rabin_install : miller_rabin_performance : . ; install performance_test_install : performance_test : . ; install sf_performance_install : sf_performance : . ; install . : linpack_benchmark_double linpack_benchmark_cpp_float linpack_benchmark_mpf linpack_benchmark_mpfr ; +install delaunay_install : delaunay_test : . ; + diff --git a/performance/arithmetic_backend.hpp b/performance/arithmetic_backend.hpp index 69176f3c..e3d5f4d1 100644 --- a/performance/arithmetic_backend.hpp +++ b/performance/arithmetic_backend.hpp @@ -18,6 +18,11 @@ namespace boost{ namespace multiprecision{ namespace backends{ +#ifdef BOOST_MSVC +# pragma warning(push) +# pragma warning(disable:4389 4244 4018 4244 4127) +#endif + template struct arithmetic_backend { @@ -46,7 +51,14 @@ struct arithmetic_backend } arithmetic_backend& operator = (const char* s) { - m_value = boost::lexical_cast(s); + try + { + m_value = boost::lexical_cast(s); + } + catch(const bad_lexical_cast&) + { + throw std::runtime_error(std::string("Unable to interpret the string provided: \"") + s + std::string("\" as a compatible number type.")); + } return *this; } void swap(arithmetic_backend& o) @@ -57,12 +69,20 @@ struct arithmetic_backend { std::stringstream ss; ss.flags(f); - ss << std::setprecision(digits) << m_value; + ss << std::setprecision(digits ? digits : std::numeric_limits::digits10 + 4) << m_value; return ss.str(); } + void do_negate(const mpl::true_&) + { + m_value = 1 + ~m_value; + } + void do_negate(const mpl::false_&) + { + m_value = -m_value; + } void negate() { - m_value = -m_value; + do_negate(is_unsigned()); } int compare(const arithmetic_backend& o)const { @@ -85,6 +105,37 @@ inline void eval_convert_to(R* result, const arithmetic_backend& bac *result = backend.data(); } +template +inline bool eval_eq(const arithmetic_backend& a, const arithmetic_backend& b) +{ + return a.data() == b.data(); +} +template +inline bool eval_eq(const arithmetic_backend& a, const A2& b) +{ + return a.data() == b; +} +template +inline bool eval_lt(const arithmetic_backend& a, const arithmetic_backend& b) +{ + return a.data() < b.data(); +} +template +inline bool eval_lt(const arithmetic_backend& a, const A2& b) +{ + return a.data() < b; +} +template +inline bool eval_gt(const arithmetic_backend& a, const arithmetic_backend& b) +{ + return a.data() > b.data(); +} +template +inline bool eval_gt(const arithmetic_backend& a, const A2& b) +{ + return a.data() > b; +} + template inline void eval_add(arithmetic_backend& result, const arithmetic_backend& o) { @@ -103,6 +154,8 @@ inline void eval_multiply(arithmetic_backend& result, const arithmet template inline void eval_divide(arithmetic_backend& result, const arithmetic_backend& o) { + if(!std::numeric_limits::has_infinity && !o.data()) + BOOST_THROW_EXCEPTION(std::runtime_error("Divide by zero")); result.data() /= o.data(); } @@ -124,6 +177,8 @@ inline typename enable_if >::type eval_multiply(arithmetic_bac template inline typename enable_if >::type eval_divide(arithmetic_backend& result, const A2& o) { + if(!std::numeric_limits::has_infinity && !o) + BOOST_THROW_EXCEPTION(std::runtime_error("Divide by zero")); result.data() /= o; } @@ -145,6 +200,8 @@ inline void eval_multiply(arithmetic_backend& result, const arithmet template inline void eval_divide(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) { + if(!std::numeric_limits::has_infinity && !b.data()) + BOOST_THROW_EXCEPTION(std::runtime_error("Divide by zero")); result.data() = a.data() / b.data(); } @@ -166,6 +223,8 @@ inline typename enable_if>::type eval_multiply(arithmetic_back template inline typename enable_if>::type eval_divide(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) { + if(!std::numeric_limits::has_infinity && !b) + BOOST_THROW_EXCEPTION(std::runtime_error("Divide by zero")); result.data() = a.data() / b; } @@ -181,10 +240,15 @@ inline int eval_get_sign(const arithmetic_backend& val) return val.data() == 0 ? 0 : val.data() < 0 ? -1 : 1; } +template +inline typename enable_if, T>::type abs(T v) { return v; } + template inline void eval_abs(arithmetic_backend& result, const arithmetic_backend& o) { - result.data() = std::abs(o.data()); + using std::abs; + using boost::multiprecision::backends::abs; + result.data() = abs(o.data()); } template @@ -234,6 +298,20 @@ inline void eval_round(arithmetic_backend& result, const arithmetic_ result.data() = round(o.data()); } +template +inline void eval_frexp(arithmetic_backend& result, const arithmetic_backend& a, int* v) +{ + BOOST_MATH_STD_USING + result.data() = frexp(a.data(), v); +} + +template +inline void eval_ldexp(arithmetic_backend& result, const arithmetic_backend& a, int v) +{ + BOOST_MATH_STD_USING + result.data() = ldexp(a.data(), v); +} + template inline void eval_exp(arithmetic_backend& result, const arithmetic_backend& o) { @@ -339,10 +417,71 @@ inline void eval_atan2(arithmetic_backend& result, const arithmetic_ result.data() = atan2(a.data(), b.data()); } +template +inline void eval_left_shift(arithmetic_backend& result, I val) +{ + result.data() <<= val; +} + +template +inline void eval_right_shift(arithmetic_backend& result, I val) +{ + result.data() >>= val; +} + +template +inline void eval_modulus(arithmetic_backend& result, const arithmetic_backend& a) +{ + result.data() %= a.data(); +} + +template +inline void eval_bitwise_and(arithmetic_backend& result, const arithmetic_backend& a) +{ + result.data() &= a.data(); +} + +template +inline void eval_bitwise_or(arithmetic_backend& result, const arithmetic_backend& a) +{ + result.data() |= a.data(); +} + +template +inline void eval_bitwise_xor(arithmetic_backend& result, const arithmetic_backend& a) +{ + result.data() ^= a.data(); +} + +template +inline void eval_complement(arithmetic_backend& result, const arithmetic_backend& a) +{ + result.data() = ~a.data(); +} + +template +inline void eval_gcd(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) +{ + result.data() = boost::math::gcd(a.data(), b.data()); +} + +template +inline void eval_lcm(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) +{ + result.data() = boost::math::lcm(a.data(), b.data()); +} + +#ifdef BOOST_MSVC +# pragma warning(pop) +#endif + } // namespace backends using boost::multiprecision::backends::arithmetic_backend; +template +struct number_category > : public mpl::int_::value ? number_kind_integer : number_kind_floating_point>{}; + }} // namespaces namespace boost{ namespace math{ namespace tools{ @@ -394,4 +533,6 @@ public: } +#include + #endif diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index 2277fd35..b6b056bf 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -257,10 +257,15 @@ int main() // Comparison for builtin floats: // #ifdef TEST_FLOAT - time_proc("double", test_bessel); - time_proc("real_concept", test_bessel); - time_proc("arithmetic_backend", test_bessel > >); - time_proc("arithmetic_backend - no expression templates", test_bessel, false> >); + time_proc("Bessel Functions - double", test_bessel); + time_proc("Bessel Functions - real_concept", test_bessel); + time_proc("Bessel Functions - arithmetic_backend", test_bessel > >); + time_proc("Bessel Functions - arithmetic_backend - no expression templates", test_bessel, false> >); + + time_proc("Non-central T - double", test_nct); + time_proc("Non-central T - real_concept", test_nct); + time_proc("Non-central T - arithmetic_backend", test_nct > >); + time_proc("Non-central T - arithmetic_backend - no expression templates", test_nct, false> >); #endif // diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 352aee53..c85ae630 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -18,7 +18,7 @@ #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \ !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) \ && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\ - && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_BR) + && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_BR) && !defined(TEST_ARITHMETIC_BACKEND) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND @@ -30,6 +30,7 @@ # define TEST_TOMMATH # define TEST_CPP_INT # define TEST_CPP_INT_BR +# define TEST_ARITHMETIC_BACKEND #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -40,6 +41,9 @@ #endif +#if defined(TEST_ARITHMETIC_BACKEND) +# include "../performance/arithmetic_backend.hpp" +#endif #if defined(TEST_MPF_50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) || defined(TEST_MPZ_BOOST_RATIONAL) #include #include @@ -628,7 +632,10 @@ void test_negative_mixed(boost::mpl::true_ const&) Num tol = 0; #endif std::ios_base::fmtflags f = boost::is_floating_point::value ? std::ios_base::scientific : std::ios_base::fmtflags(0); - BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, f)), tol); + if(std::numeric_limits::digits <= std::numeric_limits::digits) + { + BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, f)), tol); + } BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, f)), 0); BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, f)), 0); BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, f)), 0); @@ -693,6 +700,10 @@ template void test_mixed() { typedef typename lexical_cast_target_type::type target_type; + + if(std::numeric_limits::digits < std::numeric_limits::digits) + return; + std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; Num n1 = static_cast(1uLL << (std::numeric_limits::digits - 1)); Num n2 = 1; @@ -730,7 +741,10 @@ void test_mixed() Num tol = 0; #endif std::ios_base::fmtflags f = boost::is_floating_point::value ? std::ios_base::scientific : std::ios_base::fmtflags(0); - BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, f)), tol); + if(std::numeric_limits::digits <= std::numeric_limits::digits) + { + BOOST_TEST_CLOSE(n1, boost::lexical_cast(Real(n1).str(0, f)), tol); + } BOOST_TEST_CLOSE(n2, boost::lexical_cast(Real(n2).str(0, f)), 0); BOOST_TEST_CLOSE(n3, boost::lexical_cast(Real(n3).str(0, f)), 0); BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, f)), 0); @@ -1126,6 +1140,11 @@ void test() int main() { +#ifdef TEST_ARITHMETIC_BACKEND + test > >(); + test > >(); + test > >(); +#endif #ifdef TEST_BACKEND test >(); #endif From 8a54889f3592b34fd01080a8e41221e97d7b47b8 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 2 Aug 2012 12:27:00 +0000 Subject: [PATCH 206/256] Update comparison operators for better efficiency. Rework delaunay performance test to use less disk space. [SVN r79848] --- include/boost/multiprecision/cpp_int.hpp | 116 + .../detail/cpp_int_trivial_ops.hpp | 105 + include/boost/multiprecision/gmp.hpp | 54 +- include/boost/multiprecision/mpfr.hpp | 16 + performance/arithmetic_backend.hpp | 40 +- performance/delaunay_data.txt | 100000 --------------- performance/delaunay_test.cpp | 52 +- test/test_arithmetic.cpp | 106 +- 8 files changed, 431 insertions(+), 100058 deletions(-) delete mode 100644 performance/delaunay_data.txt diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index cc6295b5..c8e56196 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1218,6 +1218,122 @@ public: } }; +template +inline bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +{ + return (a.sign() == b.sign()) + && (a.size() == b.size()) + && std::equal(a.limbs(), a.limbs() + a.size(), b.limbs()); +} +template +inline bool eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +{ + return (a.sign() == false) + && (a.size() == 1) + && (*a.limbs() == b); +} +template +inline bool eval_eq(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT +{ + return (a.sign() == (b < 0)) + && (a.size() == 1) + && (*a.limbs() == static_cast(std::abs(b))); +} +template +inline bool eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +{ + return (a.size() == 1) + && (*a.limbs() == b); +} +template +inline bool eval_eq(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT +{ + return (b < 0) ? eval_eq(a, cpp_int_backend(b)) : eval_eq(a, static_cast(b)); // Use bit pattern of b for comparison +} + +template +inline bool eval_lt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +{ + if(a.sign()) + return true; + if(a.size() > 1) + return false; + return *a.limbs() < b; +} +template +inline bool eval_lt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT +{ + if((b == 0) || (a.sign() != (b < 0))) + return a.sign(); + if(a.sign()) + { + if(a.size() > 1) + return true; + return *a.limbs() > static_cast(std::abs(b)); + } + else + { + if(a.size() > 1) + return false; + return *a.limbs() < static_cast(b); + } +} + +template +inline bool eval_lt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +{ + if(a.size() > 1) + return false; + return *a.limbs() < b; +} +template +inline bool eval_lt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT +{ + return (b < 0) ? a.compare(b) < 0 : eval_lt(a, static_cast(b)); // Use bit pattern of b for comparison +} + +template +inline bool eval_gt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +{ + if(a.sign()) + return false; + if(a.size() > 1) + return true; + return *a.limbs() > b; +} +template +inline bool eval_gt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT +{ + if(b == 0) + return !a.sign() && ((a.size() > 1) || *a.limbs()); + if(a.sign() != (b < 0)) + return !a.sign(); + if(a.sign()) + { + if(a.size() > 1) + return false; + return *a.limbs() < static_cast(std::abs(b)); + } + else + { + if(a.size() > 1) + return true; + return *a.limbs() > static_cast(b); + } +} + +template +inline bool eval_gt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +{ + if(a.size() > 1) + return true; + return *a.limbs() > b; +} +template +inline bool eval_gt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT +{ + return (b < 0) ? a.compare(b) > 0 : eval_gt(a, static_cast(b)); // Use bit pattern of b for comparison. +} template inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) diff --git a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp index 22e7d197..056c7adb 100644 --- a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp +++ b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp @@ -10,6 +10,111 @@ namespace boost{ namespace multiprecision{ namespace backends{ +template +inline bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +{ + return (a.sign() == b.sign()) && (*a.limbs() == *b.limbs()); +} +template +inline bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +{ + return *a.limbs() == *b.limbs(); +} +template +inline typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +{ + return !a.sign() && (*a.limbs() == b); +} +template +inline typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +{ + return (a.sign() == (b < 0)) && (*a.limbs() == std::abs(b)); +} +template +inline typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +{ + return *a.limbs() == b; +} +template +inline typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +{ + return *a.limbs() == b; +} + +template +inline bool eval_lt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +{ + if(a.sign() != b.sign()) + return a.sign(); + return a.sign() ? *a.limbs() > *b.limbs() : *a.limbs() < *b.limbs(); +} +template +inline bool eval_lt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +{ + return *a.limbs() < *b.limbs(); +} +template +inline typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +{ + if(a.sign()) + return true; + return *a.limbs() < b; +} +template +inline typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +{ + if(a.sign() != (b < 0)) + return a.sign(); + return a.sign() ? (*a.limbs() > std::abs(b)) : (*a.limbs() < std::abs(b)); +} +template +inline typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +{ + return *a.limbs() < b; +} +template +inline typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +{ + return *a.limbs() < b; +} + +template +inline bool eval_gt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +{ + if(a.sign() != b.sign()) + return !a.sign(); + return a.sign() ? *a.limbs() < *b.limbs() : *a.limbs() > *b.limbs(); +} +template +inline bool eval_gt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +{ + return *a.limbs() > *b.limbs(); +} +template +inline typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +{ + if(a.sign()) + return false; + return *a.limbs() > b; +} +template +inline typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +{ + if(a.sign() != (b < 0)) + return !a.sign(); + return a.sign() ? (*a.limbs() < std::abs(b)) : (*a.limbs() > std::abs(b)); +} +template +inline typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +{ + return *a.limbs() > b; +} +template +inline typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +{ + return *a.limbs() > b; +} + template inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index fa3b10ca..4cf0aa42 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -483,6 +483,22 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> } }; +template +inline typename disable_if, T>, bool>::type eval_eq(const gmp_float& a, const T& b) BOOST_NOEXCEPT +{ + return a.compare(b) == 0; +} +template +inline typename disable_if, T>, bool>::type eval_lt(const gmp_float& a, const T& b) BOOST_NOEXCEPT +{ + return a.compare(b) < 0; +} +template +inline typename disable_if, T>, bool>::type eval_gt(const gmp_float& a, const T& b) BOOST_NOEXCEPT +{ + return a.compare(b) > 0; +} + template inline void eval_add(gmp_float& result, const gmp_float& o) BOOST_NOEXCEPT { @@ -928,6 +944,8 @@ struct gmp_int #ifndef BOOST_NO_RVALUE_REFERENCES gmp_int& operator = (gmp_int&& o) BOOST_NOEXCEPT { + if(m_data[0]._mp_d) + mpz_clear(m_data); m_data[0] = o.m_data[0]; o.m_data[0]._mp_d = 0; return *this; @@ -1140,6 +1158,22 @@ protected: mpz_t m_data; }; +template +inline typename disable_if, bool>::type eval_eq(const gmp_int& a, const T& b) +{ + return a.compare(b) == 0; +} +template +inline typename disable_if, bool>::type eval_lt(const gmp_int& a, const T& b) +{ + return a.compare(b) < 0; +} +template +inline typename disable_if, bool>::type eval_gt(const gmp_int& a, const T& b) +{ + return a.compare(b) > 0; +} + inline bool eval_is_zero(const gmp_int& val) { return mpz_sgn(val.data()) == 0; @@ -1700,11 +1734,11 @@ struct gmp_rational d = v; return compare(d); } - int compare(unsigned long v) + int compare(unsigned long v)const { return mpq_cmp_ui(m_data, v, 1); } - int compare(long v) + int compare(long v)const { return mpq_cmp_si(m_data, v, 1); } @@ -1731,6 +1765,22 @@ inline mp_number denominator(const mp_number& val) return result; } +template +inline bool eval_eq(gmp_rational& a, const T& b) +{ + return a.compare(b) == 0; +} +template +inline bool eval_lt(gmp_rational& a, const T& b) +{ + return a.compare(b) < 0; +} +template +inline bool eval_gt(gmp_rational& a, const T& b) +{ + return a.compare(b) > 0; +} + inline void eval_add(gmp_rational& t, const gmp_rational& o) { mpq_add(t.data(), t.data(), o.data()); diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 3c1301e5..a847c5d1 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -532,6 +532,22 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> } }; +template +inline typename disable_if, T>, bool>::type eval_eq(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT +{ + return a.compare(b) == 0; +} +template +inline typename disable_if, T>, bool>::type eval_lt(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT +{ + return a.compare(b) < 0; +} +template +inline typename disable_if, T>, bool>::type eval_gt(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT +{ + return a.compare(b) > 0; +} + template inline void eval_add(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT { diff --git a/performance/arithmetic_backend.hpp b/performance/arithmetic_backend.hpp index e3d5f4d1..e7170c1f 100644 --- a/performance/arithmetic_backend.hpp +++ b/performance/arithmetic_backend.hpp @@ -152,9 +152,14 @@ inline void eval_multiply(arithmetic_backend& result, const arithmet result.data() *= o.data(); } template -inline void eval_divide(arithmetic_backend& result, const arithmetic_backend& o) +inline typename enable_if_c::has_infinity>::type eval_divide(arithmetic_backend& result, const arithmetic_backend& o) { - if(!std::numeric_limits::has_infinity && !o.data()) + result.data() /= o.data(); +} +template +inline typename disable_if_c::has_infinity>::type eval_divide(arithmetic_backend& result, const arithmetic_backend& o) +{ + if(!o.data()) BOOST_THROW_EXCEPTION(std::runtime_error("Divide by zero")); result.data() /= o.data(); } @@ -175,12 +180,19 @@ inline typename enable_if >::type eval_multiply(arithmetic_bac result.data() *= o; } template -inline typename enable_if >::type eval_divide(arithmetic_backend& result, const A2& o) +inline typename enable_if_c<(is_arithmetic::value && !std::numeric_limits::has_infinity)>::type + eval_divide(arithmetic_backend& result, const A2& o) { - if(!std::numeric_limits::has_infinity && !o) + if(!o) BOOST_THROW_EXCEPTION(std::runtime_error("Divide by zero")); result.data() /= o; } +template +inline typename enable_if_c<(is_arithmetic::value && std::numeric_limits::has_infinity)>::type + eval_divide(arithmetic_backend& result, const A2& o) +{ + result.data() /= o; +} template inline void eval_add(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) @@ -198,9 +210,14 @@ inline void eval_multiply(arithmetic_backend& result, const arithmet result.data() = a.data() * b.data(); } template -inline void eval_divide(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) +inline typename enable_if_c::has_infinity>::type eval_divide(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) { - if(!std::numeric_limits::has_infinity && !b.data()) + result.data() = a.data() / b.data(); +} +template +inline typename disable_if_c::has_infinity>::type eval_divide(arithmetic_backend& result, const arithmetic_backend& a, const arithmetic_backend& b) +{ + if(!b.data()) BOOST_THROW_EXCEPTION(std::runtime_error("Divide by zero")); result.data() = a.data() / b.data(); } @@ -221,12 +238,19 @@ inline typename enable_if>::type eval_multiply(arithmetic_back result.data() = a.data() * b; } template -inline typename enable_if>::type eval_divide(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) +inline typename enable_if_c<(is_arithmetic::value && !std::numeric_limits::has_infinity)>::type + eval_divide(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) { - if(!std::numeric_limits::has_infinity && !b) + if(!b) BOOST_THROW_EXCEPTION(std::runtime_error("Divide by zero")); result.data() = a.data() / b; } +template +inline typename enable_if_c<(is_arithmetic::value && std::numeric_limits::has_infinity)>::type + eval_divide(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) +{ + result.data() = a.data() / b; +} template inline bool eval_is_zero(const arithmetic_backend& val) diff --git a/performance/delaunay_data.txt b/performance/delaunay_data.txt deleted 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1625424 5682296 1625336 5682248 1626168 5682784 -1626224 5682776 1626952 5680672 1625424 5682296 1626168 5682784 -1625424 5682296 1626744 5680528 1625336 5682248 1626168 5682784 diff --git a/performance/delaunay_test.cpp b/performance/delaunay_test.cpp index bc8db005..7aa6170b 100644 --- a/performance/delaunay_test.cpp +++ b/performance/delaunay_test.cpp @@ -8,6 +8,8 @@ #include #include "arithmetic_backend.hpp" #include +#include +#include #include #include @@ -196,30 +198,6 @@ struct dt_dat { typedef std::vector data_t; data_t data; -static void load_data() -{ - std::ifstream is("delaunay_data.txt"); - - while (is.good()) - { - dt_dat d; - is >> d.ax >> d.ay >> d.bx >> d.by >> d.cx >> d.cy >> d.dx >> d.dy; - if (is.good()) - { - data.push_back(d); - d.ax >>= 10; - d.ay >>= 10; - d.bx >>= 10; - d.by >>= 10; - d.cx >>= 10; - d.cy >>= 10; - d.dx >>= 10; - d.dy >>= 10; - data.push_back(d); - } - } -} - template void do_calc(const char* name) { @@ -256,6 +234,32 @@ struct test_traits }; +dt_dat generate_quadrilateral() +{ + static boost::random::mt19937 gen; + static boost::random::uniform_int_distribution<> dist(INT_MIN/2, INT_MAX/2); + + dt_dat result; + + result.ax = dist(gen); + result.ay = dist(gen); + result.bx = boost::random::uniform_int_distribution<>(result.ax, INT_MAX/2)(gen); // bx is to the right of ax. + result.by = dist(gen); + result.cx = dist(gen); + result.cy = boost::random::uniform_int_distribution<>(result.cx > result.bx ? result.by : result.ay, INT_MAX/2)(gen); // cy is below at least one of ay and by. + result.dx = boost::random::uniform_int_distribution<>(result.cx, INT_MAX/2)(gen); // dx is to the right of cx. + result.dy = boost::random::uniform_int_distribution<>(result.cx > result.bx ? result.by : result.ay, INT_MAX/2)(gen); // cy is below at least one of ay and by. + + return result; +} + +static void load_data() +{ + for(unsigned i = 0; i < 100000; ++i) + data.push_back(generate_quadrilateral()); +} + + int main() { using namespace boost::multiprecision; diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index c85ae630..85b3c9da 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -135,6 +135,72 @@ template <> struct is_twos_complement_integer : public boost::mpl::false_ {}; #endif +#define BOOST_TEST_EQUAL(a, b) BOOST_TEST((a) == (b)) + +template +void test_comparisons(Val a, Val b) +{ + Real r1(a); + Real r2(b); + Real z(1); + + BOOST_TEST_EQUAL(r1 == r2, a == b); + BOOST_TEST_EQUAL(r1 != r2, a != b); + BOOST_TEST_EQUAL(r1 <= r2, a <= b); + BOOST_TEST_EQUAL(r1 < r2, a < b); + BOOST_TEST_EQUAL(r1 >= r2, a >= b); + BOOST_TEST_EQUAL(r1 > r2, a > b); + + BOOST_TEST_EQUAL(r1 == b, a == b); + BOOST_TEST_EQUAL(r1 != b, a != b); + BOOST_TEST_EQUAL(r1 <= b, a <= b); + BOOST_TEST_EQUAL(r1 < b, a < b); + BOOST_TEST_EQUAL(r1 >= b, a >= b); + BOOST_TEST_EQUAL(r1 > b, a > b); + + BOOST_TEST_EQUAL(a == r2, a == b); + BOOST_TEST_EQUAL(a != r2, a != b); + BOOST_TEST_EQUAL(a <= r2, a <= b); + BOOST_TEST_EQUAL(a < r2, a < b); + BOOST_TEST_EQUAL(a >= r2, a >= b); + BOOST_TEST_EQUAL(a > r2, a > b); + + BOOST_TEST_EQUAL(r1*z == r2, a == b); + BOOST_TEST_EQUAL(r1*z != r2, a != b); + BOOST_TEST_EQUAL(r1*z <= r2, a <= b); + BOOST_TEST_EQUAL(r1*z < r2, a < b); + BOOST_TEST_EQUAL(r1*z >= r2, a >= b); + BOOST_TEST_EQUAL(r1*z > r2, a > b); + + BOOST_TEST_EQUAL(r1 == r2*z, a == b); + BOOST_TEST_EQUAL(r1 != r2*z, a != b); + BOOST_TEST_EQUAL(r1 <= r2*z, a <= b); + BOOST_TEST_EQUAL(r1 < r2*z, a < b); + BOOST_TEST_EQUAL(r1 >= r2*z, a >= b); + BOOST_TEST_EQUAL(r1 > r2*z, a > b); + + BOOST_TEST_EQUAL(r1*z == r2*z, a == b); + BOOST_TEST_EQUAL(r1*z != r2*z, a != b); + BOOST_TEST_EQUAL(r1*z <= r2*z, a <= b); + BOOST_TEST_EQUAL(r1*z < r2*z, a < b); + BOOST_TEST_EQUAL(r1*z >= r2*z, a >= b); + BOOST_TEST_EQUAL(r1*z > r2*z, a > b); + + BOOST_TEST_EQUAL(r1*z == b, a == b); + BOOST_TEST_EQUAL(r1*z != b, a != b); + BOOST_TEST_EQUAL(r1*z <= b, a <= b); + BOOST_TEST_EQUAL(r1*z < b, a < b); + BOOST_TEST_EQUAL(r1*z >= b, a >= b); + BOOST_TEST_EQUAL(r1*z > b, a > b); + + BOOST_TEST_EQUAL(a == r2*z, a == b); + BOOST_TEST_EQUAL(a != r2*z, a != b); + BOOST_TEST_EQUAL(a <= r2*z, a <= b); + BOOST_TEST_EQUAL(a < r2*z, a < b); + BOOST_TEST_EQUAL(a >= r2*z, a >= b); + BOOST_TEST_EQUAL(a > r2*z, a > b); +} + template void test_complement(Real a, Real b, Real c, const boost::mpl::true_&) { @@ -601,18 +667,14 @@ void test_negative_mixed(boost::mpl::true_ const&) Num n3 = 0; Num n4 = -20; Num n5 = -8; - BOOST_TEST((Real(n2) < 0) == true); - BOOST_TEST((Real(n2) <= 0) == true); - BOOST_TEST((Real(n2) > 0) == false); - BOOST_TEST((Real(n2) >= 0) == false); - BOOST_TEST((Real(n2) == 0) == false); - BOOST_TEST((Real(n2) != 0) == true); - BOOST_TEST((Real(n2) == n2) == true); - BOOST_TEST((Real(n2) != n2) == false); - BOOST_TEST((Real(n2) >= n2) == true); - BOOST_TEST((Real(n2) <= n2) == true); - BOOST_TEST((Real(n2) > n2) == false); - BOOST_TEST((Real(n2) < n2) == false); + + test_comparisons(n1, n2); + test_comparisons(n1, n3); + test_comparisons(n3, n1); + test_comparisons(n2, n1); + test_comparisons(n1, n1); + test_comparisons(n3, n3); + // Default construct: BOOST_TEST(Real(n1) == n1); BOOST_TEST(Real(n2) == n2); @@ -710,18 +772,14 @@ void test_mixed() Num n3 = 0; Num n4 = 20; Num n5 = 8; - BOOST_TEST((Real(n2) < 0) == false); - BOOST_TEST((Real(n2) <= 0) == false); - BOOST_TEST((Real(n2) > 0) == true); - BOOST_TEST((Real(n2) >= 0) == true); - BOOST_TEST((Real(n2) == 0) == false); - BOOST_TEST((Real(n2) != 0) == true); - BOOST_TEST((Real(n2) == n2) == true); - BOOST_TEST((Real(n2) != n2) == false); - BOOST_TEST((Real(n2) >= n2) == true); - BOOST_TEST((Real(n2) <= n2) == true); - BOOST_TEST((Real(n2) > n2) == false); - BOOST_TEST((Real(n2) < n2) == false); + + test_comparisons(n1, n2); + test_comparisons(n1, n3); + test_comparisons(n1, n1); + test_comparisons(n3, n1); + test_comparisons(n2, n1); + test_comparisons(n3, n3); + // Default construct: BOOST_TEST(Real(n1) == n1); BOOST_TEST(Real(n2) == n2); From 2fb7c1a0449b1230f584be9c259d773444666b1e Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 2 Aug 2012 17:14:17 +0000 Subject: [PATCH 207/256] Fix Linux x64 C++0x build issues. [SVN r79854] --- include/boost/multiprecision/mp_number.hpp | 10 +++++----- performance/arithmetic_backend.hpp | 7 ++++--- performance/delaunay_test.cpp | 7 ++----- test/Jamfile.v2 | 2 +- 4 files changed, 12 insertions(+), 14 deletions(-) diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 4a8ee16d..7fb7fed7 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -1471,23 +1471,23 @@ private: // Tests if the expression contains a reference to *this: template - BOOST_CONSTEXPR bool contains_self(const Exp& e)const BOOST_NOEXCEPT + bool contains_self(const Exp& e)const BOOST_NOEXCEPT { return contains_self(e, typename Exp::arity()); } template - BOOST_CONSTEXPR bool contains_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT + bool contains_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT { return is_realy_self(e.value()); } template - BOOST_CONSTEXPR bool contains_self(const Exp& e, mpl::int_<1> const&)const BOOST_NOEXCEPT + bool contains_self(const Exp& e, mpl::int_<1> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child_type; return contains_self(e.left(), typename child_type::arity()); } template - BOOST_CONSTEXPR bool contains_self(const Exp& e, mpl::int_<2> const&)const BOOST_NOEXCEPT + bool contains_self(const Exp& e, mpl::int_<2> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child0_type; typedef typename Exp::right_type child1_type; @@ -1495,7 +1495,7 @@ private: || contains_self(e.right(), typename child1_type::arity()); } template - BOOST_CONSTEXPR bool contains_self(const Exp& e, mpl::int_<3> const&)const BOOST_NOEXCEPT + bool contains_self(const Exp& e, mpl::int_<3> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child0_type; typedef typename Exp::middle_type child1_type; diff --git a/performance/arithmetic_backend.hpp b/performance/arithmetic_backend.hpp index e7170c1f..a4d59f36 100644 --- a/performance/arithmetic_backend.hpp +++ b/performance/arithmetic_backend.hpp @@ -13,6 +13,7 @@ #include #include #include +#include namespace boost{ namespace multiprecision{ @@ -223,17 +224,17 @@ inline typename disable_if_c::has_infinity>::typ } template -inline typename enable_if>::type eval_add(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) +inline typename enable_if >::type eval_add(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) { result.data() = a.data() + b; } template -inline typename enable_if>::type eval_subtract(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) +inline typename enable_if >::type eval_subtract(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) { result.data() = a.data() - b; } template -inline typename enable_if>::type eval_multiply(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) +inline typename enable_if >::type eval_multiply(arithmetic_backend& result, const arithmetic_backend& a, const A2& b) { result.data() = a.data() * b; } diff --git a/performance/delaunay_test.cpp b/performance/delaunay_test.cpp index 7aa6170b..f9921c46 100644 --- a/performance/delaunay_test.cpp +++ b/performance/delaunay_test.cpp @@ -129,12 +129,12 @@ inline int128_t mult_64x64_to_128(int64_t a, int64_t b) } template -__forceinline void mul_2n(R& r, const T& a, const T& b) +inline void mul_2n(R& r, const T& a, const T& b) { r = R(a) * b; } -__forceinline void mul_2n(int128_t& r, const boost::int64_t& a, const boost::int64_t& b) +inline void mul_2n(int128_t& r, const boost::int64_t& a, const boost::int64_t& b) { r = mult_64x64_to_128(a, b); } @@ -156,9 +156,6 @@ inline bool delaunay_test(int32_t ax, int32_t ay, int32_t bx, int32_t by, typedef typename Traits::i64_t i64; typedef typename Traits::i128_t i128; - i64 ax64 = ax, ay64 = ay, bx64 = bx, by64 = by, - cx64 = cx, cy64 = cy, dx64 = dx, dy64 = dy; - i64 cos_abc, t; mul_2n(cos_abc, (ax-bx), (cx-bx)); mul_2n(t, (ay-by), (cy-by)); diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index a10e4f59..3c47c6d2 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -578,7 +578,7 @@ run test_constants.cpp : test_constants_cpp_dec_float ; -run test_move.cpp mpfr +run test_move.cpp mpfr gmp : # command line : # input files : # requirements From 7111ca4216c91c51e884af590ff5881d44b499e3 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 3 Aug 2012 12:18:10 +0000 Subject: [PATCH 208/256] Fix buglets in performance test code. Explain delaunay code digit usage better. [SVN r79857] --- performance/delaunay_test.cpp | 17 ++++++++++------- performance/sf_performance.cpp | 1 + 2 files changed, 11 insertions(+), 7 deletions(-) diff --git a/performance/delaunay_test.cpp b/performance/delaunay_test.cpp index f9921c46..34d6a5da 100644 --- a/performance/delaunay_test.cpp +++ b/performance/delaunay_test.cpp @@ -129,12 +129,12 @@ inline int128_t mult_64x64_to_128(int64_t a, int64_t b) } template -inline void mul_2n(R& r, const T& a, const T& b) +__forceinline void mul_2n(R& r, const T& a, const T& b) { r = R(a) * b; } -inline void mul_2n(int128_t& r, const boost::int64_t& a, const boost::int64_t& b) +__forceinline void mul_2n(int128_t& r, const boost::int64_t& a, const boost::int64_t& b) { r = mult_64x64_to_128(a, b); } @@ -152,14 +152,17 @@ inline bool delaunay_test(int32_t ax, int32_t ay, int32_t bx, int32_t by, // to the following code. // Numerical robustness is important. This code addresses it by performing // exact calculations with large integer types. + // + // NOTE: This routine is limited to inputs with up to 30 BIT PRECISION, which + // is to say all inputs must be in the range [INT_MIN/2, INT_MAX/2]. typedef typename Traits::i64_t i64; typedef typename Traits::i128_t i128; i64 cos_abc, t; - mul_2n(cos_abc, (ax-bx), (cx-bx)); + mul_2n(cos_abc, (ax-bx), (cx-bx)); // subtraction yields 31-bit values, multiplied to give 62-bit values mul_2n(t, (ay-by), (cy-by)); - cos_abc += t; + cos_abc += t; // addition yields 63 bit value, leaving one left for the sign i64 cos_cda; mul_2n(cos_cda, (cx-dx), (ax-dx)); @@ -180,9 +183,9 @@ inline bool delaunay_test(int32_t ax, int32_t ay, int32_t bx, int32_t by, sin_cda -= t; i128 sin_sum, t128; - mul_2n(sin_sum, sin_abc, cos_cda); + mul_2n(sin_sum, sin_abc, cos_cda); // 63-bit inputs multiplied to 126-bit output mul_2n(t128, cos_abc, sin_cda); - sin_sum += t128; + sin_sum += t128; // Addition yields 127 bit result, leaving one bit for the sign return sin_sum < 0; } @@ -266,7 +269,7 @@ int main() std::cout << "calculating...\n"; do_calc >("int64_t, int64_t"); - do_calc >, mp_number > > >("arithmetic_backend"); + do_calc, false>, mp_number, false> > >("arithmetic_backend"); do_calc >("int64_t, int128_t"); do_calc >("int64_t, mp_int128_t"); do_calc, true> > >("int64_t, mp_int128_t (ET)"); diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index b6b056bf..0c10a841 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -4,6 +4,7 @@ // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ #define BOOST_MATH_MAX_ROOT_ITERATION_POLICY 500 +#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false #if !defined(TEST_MPFR) && !defined(TEST_MPREAL) && !defined(TEST_MPF) && !defined(TEST_MPREAL) \ && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_CLASS) && !defined(TEST_FLOAT) From bb2ac1a969be7607c9e5972628dd72c9ab6471b5 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 3 Aug 2012 18:24:53 +0000 Subject: [PATCH 209/256] Mark up some functions as being forced inline. [SVN r79859] --- include/boost/multiprecision/cpp_int.hpp | 310 +++++++++--------- .../detail/cpp_int_trivial_ops.hpp | 66 ++-- include/boost/multiprecision/mp_number.hpp | 120 +++---- performance/delaunay_test.cpp | 7 +- 4 files changed, 252 insertions(+), 251 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index c8e56196..92672f52 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -98,26 +98,26 @@ public: // // Direct construction: // - BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT : m_data(i), m_limbs(1), m_sign(false), m_internal(true) { } - BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT : m_data(i), m_limbs(1), m_sign(i < 0), m_internal(true) { } #if defined(BOOST_LITTLE_ENDIAN) - BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT : m_data(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false), m_internal(true) { } - BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT : m_data(i), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), m_sign(i < 0), m_internal(true) { } #endif // // Helper functions for getting at our internal data, and manipulating storage: // - allocator_type& allocator() BOOST_NOEXCEPT { return *this; } - const allocator_type& allocator()const BOOST_NOEXCEPT { return *this; } - unsigned size()const BOOST_NOEXCEPT { return m_limbs; } - limb_pointer limbs() BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; } - const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; } - unsigned capacity()const BOOST_NOEXCEPT { return m_internal ? internal_limb_count : m_data.ld.capacity; } - bool sign()const BOOST_NOEXCEPT { return m_sign; } + BOOST_FORCEINLINE allocator_type& allocator() BOOST_NOEXCEPT { return *this; } + BOOST_FORCEINLINE const allocator_type& allocator()const BOOST_NOEXCEPT { return *this; } + BOOST_FORCEINLINE unsigned size()const BOOST_NOEXCEPT { return m_limbs; } + BOOST_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; } + BOOST_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; } + BOOST_FORCEINLINE unsigned capacity()const BOOST_NOEXCEPT { return m_internal ? internal_limb_count : m_data.ld.capacity; } + BOOST_FORCEINLINE bool sign()const BOOST_NOEXCEPT { return m_sign; } void sign(bool b) BOOST_NOEXCEPT { m_sign = b; @@ -149,13 +149,13 @@ public: m_limbs = new_size; } } - void normalize() BOOST_NOEXCEPT + BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT { limb_pointer p = limbs(); while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; } - BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1), m_sign(false), m_internal(true) {} - cpp_int_base(const cpp_int_base& o) : allocator_type(o), m_limbs(0), m_internal(true) + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1), m_sign(false), m_internal(true) {} + BOOST_FORCEINLINE cpp_int_base(const cpp_int_base& o) : allocator_type(o), m_limbs(0), m_internal(true) { resize(o.size()); std::copy(o.limbs(), o.limbs() + o.size(), limbs()); @@ -196,7 +196,7 @@ public: return *this; } #endif - ~cpp_int_base() BOOST_NOEXCEPT + BOOST_FORCEINLINE ~cpp_int_base() BOOST_NOEXCEPT { if(!m_internal) allocator().deallocate(limbs(), capacity()); @@ -212,7 +212,7 @@ public: m_sign = o.m_sign; } } - void negate() BOOST_NOEXCEPT + BOOST_FORCEINLINE void negate() BOOST_NOEXCEPT { m_sign = !m_sign; // Check for zero value: @@ -222,11 +222,11 @@ public: m_sign = false; } } - bool isneg()const BOOST_NOEXCEPT + BOOST_FORCEINLINE bool isneg()const BOOST_NOEXCEPT { return m_sign; } - void do_swap(cpp_int_base& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT { std::swap(m_data, o.m_data); std::swap(m_sign, o.m_sign); @@ -272,24 +272,24 @@ public: // // Direct construction: // - BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT : m_wrapper(i), m_limbs(1), m_sign(false) {} - BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT : m_wrapper(limb_type(i < 0 ? -i : i)), m_limbs(1), m_sign(i < 0) {} #if defined(BOOST_LITTLE_ENDIAN) - BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT : m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false) {} - BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT : m_wrapper(double_limb_type(i < 0 ? -i : i)), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), m_sign(i < 0) {} #endif // // Helper functions for getting at our internal data, and manipulating storage: // - unsigned size()const BOOST_NOEXCEPT { return m_limbs; } - limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; } - const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; } - bool sign()const BOOST_NOEXCEPT { return m_sign; } - void sign(bool b) BOOST_NOEXCEPT + BOOST_FORCEINLINE unsigned size()const BOOST_NOEXCEPT { return m_limbs; } + BOOST_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; } + BOOST_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; } + BOOST_FORCEINLINE bool sign()const BOOST_NOEXCEPT { return m_sign; } + BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT { m_sign = b; // Check for zero value: @@ -299,11 +299,11 @@ public: m_sign = false; } } - void resize(unsigned new_size) BOOST_NOEXCEPT + BOOST_FORCEINLINE void resize(unsigned new_size) BOOST_NOEXCEPT { m_limbs = static_cast((std::min)(new_size, internal_limb_count)); } - void normalize() BOOST_NOEXCEPT + BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT { limb_pointer p = limbs(); p[internal_limb_count-1] &= upper_limb_mask; @@ -311,8 +311,8 @@ public: if((m_limbs == 1) && (!*p)) m_sign = false; // zero is always unsigned } - BOOST_CONSTEXPR cpp_int_base() : m_wrapper(limb_type(0u)), m_limbs(1), m_sign(false) {} - cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs), m_sign(o.m_sign) + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() : m_wrapper(limb_type(0u)), m_limbs(1), m_sign(false) {} + BOOST_FORCEINLINE cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs), m_sign(o.m_sign) { std::copy(o.limbs(), o.limbs() + o.size(), limbs()); } @@ -326,7 +326,7 @@ public: m_sign = o.m_sign; } } - void negate() BOOST_NOEXCEPT + BOOST_FORCEINLINE void negate() BOOST_NOEXCEPT { m_sign = !m_sign; // Check for zero value: @@ -336,11 +336,11 @@ public: m_sign = false; } } - bool isneg()const BOOST_NOEXCEPT + BOOST_FORCEINLINE bool isneg()const BOOST_NOEXCEPT { return m_sign; } - void do_swap(cpp_int_base& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT { for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i) std::swap(m_wrapper.m_data[i], o.m_wrapper.m_data[i]); @@ -385,42 +385,42 @@ public: // // Direct construction: // - BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT : m_wrapper(i), m_limbs(1) {} - cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT : m_wrapper(limb_type(i < 0 ? -i : i)), m_limbs(1) { if(i < 0) negate(); } #ifdef BOOST_LITTLE_ENDIAN - BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT : m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1) {} - cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT : m_wrapper(double_limb_type(i < 0 ? -i : i)), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)) { if(i < 0) negate(); } #endif // // Helper functions for getting at our internal data, and manipulating storage: // - unsigned size()const BOOST_NOEXCEPT { return m_limbs; } - limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; } - const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; } - BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; } - void sign(bool b) BOOST_NOEXCEPT { if(b) negate(); } - void resize(unsigned new_size) BOOST_NOEXCEPT + BOOST_FORCEINLINE unsigned size()const BOOST_NOEXCEPT { return m_limbs; } + BOOST_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; } + BOOST_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; } + BOOST_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; } + BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT { if(b) negate(); } + BOOST_FORCEINLINE void resize(unsigned new_size) BOOST_NOEXCEPT { m_limbs = (std::min)(new_size, internal_limb_count); } - void normalize() BOOST_NOEXCEPT + BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT { limb_pointer p = limbs(); p[internal_limb_count-1] &= upper_limb_mask; while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; } - BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_wrapper(limb_type(0u)), m_limbs(1) {} - cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs) + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_wrapper(limb_type(0u)), m_limbs(1) {} + BOOST_FORCEINLINE cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs) { std::copy(o.limbs(), o.limbs() + o.size(), limbs()); } //~cpp_int_base() BOOST_NOEXCEPT {} - void assign(const cpp_int_base& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT { if(this != &o) { @@ -441,11 +441,11 @@ public: normalize(); eval_increment(static_cast& >(*this)); } - BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT { return false; } - void do_swap(cpp_int_base& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT { for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i) std::swap(m_wrapper.m_data[i], o.m_wrapper.m_data[i]); @@ -496,22 +496,22 @@ public: // Direct construction: // template - BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT : m_data(i < 0 ? -i : i), m_sign(i < 0) {} template - BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT : m_data(i), m_sign(false) {} template - cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + BOOST_FORCEINLINE cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT : m_data(std::fabs(i)), m_sign(i < 0) {} // // Helper functions for getting at our internal data, and manipulating storage: // - BOOST_CONSTEXPR unsigned size()const BOOST_NOEXCEPT { return 1; } - limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; } - const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; } - bool sign()const BOOST_NOEXCEPT { return m_sign; } - void sign(bool b) BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR unsigned size()const BOOST_NOEXCEPT { return 1; } + BOOST_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; } + BOOST_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; } + BOOST_FORCEINLINE bool sign()const BOOST_NOEXCEPT { return m_sign; } + BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT { m_sign = b; // Check for zero value: @@ -520,23 +520,23 @@ public: m_sign = false; } } - void resize(unsigned new_size) BOOST_NOEXCEPT {} - void normalize() BOOST_NOEXCEPT + BOOST_FORCEINLINE void resize(unsigned new_size) BOOST_NOEXCEPT {} + BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT { if(!m_data) m_sign = false; // zero is always unsigned m_data &= limb_mask; } - BOOST_CONSTEXPR cpp_int_base() : m_data(0), m_sign(false) {} - BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_data(o.m_data), m_sign(o.m_sign) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() : m_data(0), m_sign(false) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_data(o.m_data), m_sign(o.m_sign) {} //~cpp_int_base() BOOST_NOEXCEPT {} - void assign(const cpp_int_base& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT { m_data = o.m_data; m_sign = o.m_sign; } - void negate() BOOST_NOEXCEPT + BOOST_FORCEINLINE void negate() BOOST_NOEXCEPT { m_sign = !m_sign; // Check for zero value: @@ -545,11 +545,11 @@ public: m_sign = false; } } - bool isneg()const BOOST_NOEXCEPT + BOOST_FORCEINLINE bool isneg()const BOOST_NOEXCEPT { return m_sign; } - void do_swap(cpp_int_base& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT { std::swap(m_sign, o.m_sign); std::swap(m_data, o.m_data); @@ -578,13 +578,13 @@ public: // Direct construction: // template - BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT : m_data(i < 0 ? 1 + ~static_cast(-i) : static_cast(i)) {} template - BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT : m_data(i) {} template - cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + BOOST_FORCEINLINE cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT : m_data(std::fabs(i)) { if(i < 0) @@ -593,38 +593,38 @@ public: // // Helper functions for getting at our internal data, and manipulating storage: // - BOOST_CONSTEXPR unsigned size()const BOOST_NOEXCEPT { return 1; } - limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; } - const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; } - BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; } - void sign(bool b) BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR unsigned size()const BOOST_NOEXCEPT { return 1; } + BOOST_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; } + BOOST_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; } + BOOST_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; } + BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT { if(b) negate(); } - void resize(unsigned new_size) BOOST_NOEXCEPT {} - void normalize() BOOST_NOEXCEPT + BOOST_FORCEINLINE void resize(unsigned new_size) BOOST_NOEXCEPT {} + BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT { m_data &= limb_mask; } - BOOST_CONSTEXPR cpp_int_base() : m_data(0) {} - BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_data(o.m_data) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() : m_data(0) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_data(o.m_data) {} //~cpp_int_base() BOOST_NOEXCEPT {} - void assign(const cpp_int_base& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT { m_data = o.m_data; } - void negate() BOOST_NOEXCEPT + BOOST_FORCEINLINE void negate() BOOST_NOEXCEPT { m_data = ~m_data; ++m_data; } - BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT { return false; } - void do_swap(cpp_int_base& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT { std::swap(m_data, o.m_data); } @@ -678,45 +678,45 @@ public: typedef mpl::list unsigned_types; typedef mpl::list float_types; - BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{} - BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) : base_type(o) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) : base_type(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - BOOST_CONSTEXPR cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT : base_type(static_cast(o)) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT : base_type(static_cast(o)) {} #endif template - BOOST_CONSTEXPR cpp_int_backend(LT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(LT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT : base_type(i) {} template - BOOST_CONSTEXPR cpp_int_backend(SLT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(SLT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT : base_type(i) {} #if defined(BOOST_LITTLE_ENDIAN) template - BOOST_CONSTEXPR cpp_int_backend(LT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(LT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT : base_type(i) {} template - BOOST_CONSTEXPR cpp_int_backend(SLT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(SLT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT : base_type(i) {} #endif - cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) + BOOST_FORCEINLINE cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { this->assign(o); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_backend& operator = (cpp_int_backend&& o) BOOST_NOEXCEPT_IF(boost::is_void::value) + BOOST_FORCEINLINE cpp_int_backend& operator = (cpp_int_backend&& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { *static_cast(this) = static_cast(o); return *this; } #endif - cpp_int_backend& operator = (limb_type i) BOOST_NOEXCEPT + BOOST_FORCEINLINE cpp_int_backend& operator = (limb_type i) BOOST_NOEXCEPT { this->resize(1); *this->limbs() = i; this->sign(false); return *this; } - cpp_int_backend& operator = (signed_limb_type i) BOOST_NOEXCEPT + BOOST_FORCEINLINE cpp_int_backend& operator = (signed_limb_type i) BOOST_NOEXCEPT { this->resize(1); *this->limbs() = static_cast(std::abs(i)); @@ -898,7 +898,7 @@ public: this->negate(); return *this; } - void swap(cpp_int_backend& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE void swap(cpp_int_backend& o) BOOST_NOEXCEPT { this->do_swap(o); } @@ -1026,7 +1026,7 @@ public: return 0; } template - typename enable_if, int>::type compare(Arithmatic i)const BOOST_NOEXCEPT + BOOST_FORCEINLINE typename enable_if, int>::type compare(Arithmatic i)const BOOST_NOEXCEPT { // braindead version: cpp_int_backend t; @@ -1051,33 +1051,33 @@ public: BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(typename base_type::local_limb_type) * CHAR_BIT); - BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{} - BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT : base_type(o) {} - cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT : base_type(o) {} + BOOST_FORCEINLINE cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_NOEXCEPT { this->assign(o); return *this; } template - BOOST_CONSTEXPR cpp_int_backend(A i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(A i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT : base_type(i) {} template - typename enable_if, cpp_int_backend&>::type operator = (SI i) BOOST_NOEXCEPT + BOOST_FORCEINLINE typename enable_if, cpp_int_backend&>::type operator = (SI i) BOOST_NOEXCEPT { *this->limbs() = static_cast(std::abs(i)); this->sign(i < 0); return *this; } template - typename enable_if, cpp_int_backend&>::type operator = (UI i) BOOST_NOEXCEPT + BOOST_FORCEINLINE typename enable_if, cpp_int_backend&>::type operator = (UI i) BOOST_NOEXCEPT { *this->limbs() = static_cast(i); return *this; } template - typename enable_if, cpp_int_backend&>::type operator = (F i) BOOST_NOEXCEPT + BOOST_FORCEINLINE typename enable_if, cpp_int_backend&>::type operator = (F i) BOOST_NOEXCEPT { *this->limbs() = static_cast(std::abs(i)); this->sign(i < 0); @@ -1094,7 +1094,7 @@ public: } return *this; } - void swap(cpp_int_backend& o) BOOST_NOEXCEPT + BOOST_FORCEINLINE void swap(cpp_int_backend& o) BOOST_NOEXCEPT { this->do_swap(o); } @@ -1209,7 +1209,7 @@ public: return result; } template - typename enable_if, int>::type compare(Arithmatic i)const BOOST_NOEXCEPT + BOOST_FORCEINLINE typename enable_if, int>::type compare(Arithmatic i)const BOOST_NOEXCEPT { // braindead version: cpp_int_backend t; @@ -1219,40 +1219,40 @@ public: }; template -inline bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT { return (a.sign() == b.sign()) && (a.size() == b.size()) && std::equal(a.limbs(), a.limbs() + a.size(), b.limbs()); } template -inline bool eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT { return (a.sign() == false) && (a.size() == 1) && (*a.limbs() == b); } template -inline bool eval_eq(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT { return (a.sign() == (b < 0)) && (a.size() == 1) && (*a.limbs() == static_cast(std::abs(b))); } template -inline bool eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT { return (a.size() == 1) && (*a.limbs() == b); } template -inline bool eval_eq(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT { return (b < 0) ? eval_eq(a, cpp_int_backend(b)) : eval_eq(a, static_cast(b)); // Use bit pattern of b for comparison } template -inline bool eval_lt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_lt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT { if(a.sign()) return true; @@ -1280,20 +1280,20 @@ inline bool eval_lt(const cpp_int_backend& a, s } template -inline bool eval_lt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_lt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT { if(a.size() > 1) return false; return *a.limbs() < b; } template -inline bool eval_lt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_lt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT { return (b < 0) ? a.compare(b) < 0 : eval_lt(a, static_cast(b)); // Use bit pattern of b for comparison } template -inline bool eval_gt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT { if(a.sign()) return false; @@ -1323,20 +1323,20 @@ inline bool eval_gt(const cpp_int_backend& a, s } template -inline bool eval_gt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT { if(a.size() > 1) return true; return *a.limbs() > b; } template -inline bool eval_gt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT { return (b < 0) ? a.compare(b) > 0 : eval_gt(a, static_cast(b)); // Use bit pattern of b for comparison. } template -inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_add(result, result, o); } @@ -1445,7 +1445,7 @@ inline void add_unsigned(cpp_int_backend& res result.sign(a.sign()); } template -inline void eval_add(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(result.sign()) { @@ -1455,7 +1455,7 @@ inline void eval_add(cpp_int_backend& result, add_unsigned(result, result, o); } template -inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign()) { @@ -1466,7 +1466,7 @@ inline void eval_add(cpp_int_backend& result, add_unsigned(result, a, o); } template -inline void eval_add(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o < 0) eval_subtract(result, static_cast(-o)); @@ -1474,7 +1474,7 @@ inline void eval_add(cpp_int_backend& result, eval_add(result, static_cast(o)); } template -inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o < 0) eval_subtract(result, a, static_cast(-o)); @@ -1514,7 +1514,7 @@ inline void subtract_unsigned(cpp_int_backend } } template -inline void eval_subtract(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(result.sign()) { @@ -1524,7 +1524,7 @@ inline void eval_subtract(cpp_int_backend& re subtract_unsigned(result, o); } template -inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign()) { @@ -1537,7 +1537,7 @@ inline void eval_subtract(cpp_int_backend& re } } template -inline void eval_subtract(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o) { @@ -1548,7 +1548,7 @@ inline void eval_subtract(cpp_int_backend& re } } template -inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o) { @@ -1561,7 +1561,7 @@ inline void eval_subtract(cpp_int_backend& re result = a; } template -inline void eval_increment(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_increment(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) { static const limb_type one = 1; if(!result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value)) @@ -1572,7 +1572,7 @@ inline void eval_increment(cpp_int_backend& r eval_add(result, one); } template -inline void eval_decrement(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_decrement(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value) { static const limb_type one = 1; if(!result.sign() && result.limbs()[0]) @@ -1583,7 +1583,7 @@ inline void eval_decrement(cpp_int_backend& r eval_subtract(result, one); } template -inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_subtract(result, result, o); } @@ -1665,7 +1665,7 @@ inline void subtract_unsigned(cpp_int_backend result.negate(); } template -inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign() != b.sign()) { @@ -1757,7 +1757,7 @@ inline void eval_multiply(cpp_int_backend& re result.sign(a.sign() != b.sign()); } template -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, a); } @@ -1794,12 +1794,12 @@ inline void eval_multiply(cpp_int_backend& re result.normalize(); } template -inline void eval_multiply(cpp_int_backend& result, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, val); } template -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(val <= (std::numeric_limits::max)()) { @@ -1812,12 +1812,12 @@ inline void eval_multiply(cpp_int_backend& re } } template -inline void eval_multiply(cpp_int_backend& result, const double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, val); } template -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(val > 0) eval_multiply(result, a, static_cast(val)); @@ -1828,7 +1828,7 @@ inline void eval_multiply(cpp_int_backend& re } } template -inline void eval_multiply(cpp_int_backend& result, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, val); } @@ -1853,7 +1853,7 @@ inline void eval_multiply(cpp_int_backend& re eval_multiply(result, a, t); } template -inline void eval_multiply(cpp_int_backend& result, const signed_double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const signed_double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, val); } @@ -2270,20 +2270,20 @@ void divide_unsigned_helper(cpp_int_backend* } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { cpp_int_backend r; divide_unsigned_helper(&result, a, b, r); result.sign(a.sign() != b.sign()); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) { cpp_int_backend r; divide_unsigned_helper(&result, a, b, r); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) { cpp_int_backend r; divide_unsigned_helper(&result, a, std::abs(b), r); @@ -2291,58 +2291,58 @@ inline void eval_divide(cpp_int_backend& resu result.negate(); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& b) +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& b) { // There is no in place divide: cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_divide(cpp_int_backend& result, limb_type b) +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, limb_type b) { // There is no in place divide: cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_divide(cpp_int_backend& result, signed_limb_type b) +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, signed_limb_type b) { // There is no in place divide: cpp_int_backend a(result); eval_divide(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) { divide_unsigned_helper(static_cast* >(0), a, b, result); result.sign(a.sign()); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) { divide_unsigned_helper(static_cast* >(0), a, b, result); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) { divide_unsigned_helper(static_cast* >(0), a, static_cast(std::abs(b)), result); } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) { // There is no in place divide: cpp_int_backend a(result); eval_modulus(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, limb_type b) +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, limb_type b) { // There is no in place divide: cpp_int_backend a(result); eval_modulus(result, a, b); } template -inline void eval_modulus(cpp_int_backend& result, signed_limb_type b) +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, signed_limb_type b) { // There is no in place divide: cpp_int_backend a(result); @@ -2479,22 +2479,22 @@ struct bit_or { limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCE struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a ^ b; } }; template -inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o)BOOST_NOEXCEPT_IF(is_void::value) +BOOST_FORCEINLINE void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o)BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_and()); } template -inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) +BOOST_FORCEINLINE void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_or()); } template -inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) +BOOST_FORCEINLINE void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_xor()); } template -inline void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Increment and negate: result = o; @@ -2720,17 +2720,17 @@ inline typename enable_if, void>::type eval_convert_to(R* r } template -inline bool eval_is_zero(const cpp_int_backend& val) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_is_zero(const cpp_int_backend& val) BOOST_NOEXCEPT { return (val.size() == 1) && (val.limbs()[0] == 0); } template -inline int eval_get_sign(const cpp_int_backend& val) BOOST_NOEXCEPT +BOOST_FORCEINLINE int eval_get_sign(const cpp_int_backend& val) BOOST_NOEXCEPT { return eval_is_zero(val) ? 0 : val.sign() ? -1 : 1; } template -inline void eval_abs(cpp_int_backend& result, const cpp_int_backend& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_abs(cpp_int_backend& result, const cpp_int_backend& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { result = val; result.sign(false); @@ -2927,7 +2927,7 @@ inline typename enable_if, Integer>::type eval_integer_modu } } template -inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) BOOST_NOEXCEPT_IF(boost::is_void::value) { typedef typename make_unsigned::type unsigned_type; return eval_integer_modulus(x, static_cast(std::abs(val))); diff --git a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp index 056c7adb..f2700c5e 100644 --- a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp +++ b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp @@ -11,106 +11,106 @@ namespace boost{ namespace multiprecision{ namespace backends{ template -inline bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT { return (a.sign() == b.sign()) && (*a.limbs() == *b.limbs()); } template -inline bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT { return *a.limbs() == *b.limbs(); } template -inline typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, U b) BOOST_NOEXCEPT { return !a.sign() && (*a.limbs() == b); } template -inline typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, S b) BOOST_NOEXCEPT { return (a.sign() == (b < 0)) && (*a.limbs() == std::abs(b)); } template -inline typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, U b) BOOST_NOEXCEPT { return *a.limbs() == b; } template -inline typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, S b) BOOST_NOEXCEPT { return *a.limbs() == b; } template -inline bool eval_lt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_lt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT { if(a.sign() != b.sign()) return a.sign(); return a.sign() ? *a.limbs() > *b.limbs() : *a.limbs() < *b.limbs(); } template -inline bool eval_lt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_lt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT { return *a.limbs() < *b.limbs(); } template -inline typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT { if(a.sign()) return true; return *a.limbs() < b; } template -inline typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT { if(a.sign() != (b < 0)) return a.sign(); return a.sign() ? (*a.limbs() > std::abs(b)) : (*a.limbs() < std::abs(b)); } template -inline typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT { return *a.limbs() < b; } template -inline typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT { return *a.limbs() < b; } template -inline bool eval_gt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT { if(a.sign() != b.sign()) return !a.sign(); return a.sign() ? *a.limbs() < *b.limbs() : *a.limbs() > *b.limbs(); } template -inline bool eval_gt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT { return *a.limbs() > *b.limbs(); } template -inline typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT { if(a.sign()) return false; return *a.limbs() > b; } template -inline typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT { if(a.sign() != (b < 0)) return !a.sign(); return a.sign() ? (*a.limbs() < std::abs(b)) : (*a.limbs() > std::abs(b)); } template -inline typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT { return *a.limbs() > b; } template -inline typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT +BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT { return *a.limbs() > b; } @@ -133,7 +133,7 @@ inline void eval_add(cpp_int_backend& result, const c } template -inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { *result.limbs() += *o.limbs(); } @@ -155,26 +155,26 @@ inline void eval_subtract(cpp_int_backend& result, co } template -inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { *result.limbs() -= *o.limbs(); } template -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { *result.limbs() *= *o.limbs(); result.sign(result.sign() != o.sign()); } template -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { *result.limbs() *= *o.limbs(); } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& o) +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& o) { if(!*o.limbs()) BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); @@ -183,7 +183,7 @@ inline void eval_divide(cpp_int_backend& result, cons } template -inline void eval_divide(cpp_int_backend& result, const cpp_int_backend& o) +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& o) { if(!*o.limbs()) BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); @@ -191,7 +191,7 @@ inline void eval_divide(cpp_int_backend& result, con } template -inline void eval_modulus(cpp_int_backend& result, const cpp_int_backend& o) +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& o) { if(!*o.limbs()) BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); @@ -200,13 +200,13 @@ inline void eval_modulus(cpp_int_backend& result, c } template -inline void eval_left_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_left_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT { *result.limbs() <<= s; } template -inline void eval_right_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_right_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT { *result.limbs() >>= s; } @@ -241,7 +241,7 @@ inline void eval_bitwise_and(cpp_int_backend& result, } template -inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { *result.limbs() &= *o.limbs(); } @@ -276,7 +276,7 @@ inline void eval_bitwise_or(cpp_int_backend& result, } template -inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { *result.limbs() |= *o.limbs(); } @@ -311,7 +311,7 @@ inline void eval_bitwise_xor(cpp_int_backend& result, } template -inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { *result.limbs() ^= *o.limbs(); } @@ -340,19 +340,19 @@ inline void eval_complement(cpp_int_backend& result, } template -inline void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT { *result.limbs() = ~*o.limbs(); } template -inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT { *result.limbs() = boost::math::gcd(*a.limbs(), *b.limbs()); } template -inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +BOOST_FORCEINLINE void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT { *result.limbs() = boost::math::lcm(*a.limbs(), *b.limbs()); } diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 7fb7fed7..a4ab00b7 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -38,21 +38,21 @@ class mp_number typedef mp_number self_type; public: typedef Backend backend_type; - BOOST_CONSTEXPR mp_number() BOOST_NOEXCEPT_IF(noexcept(Backend())) {} - BOOST_CONSTEXPR mp_number(const mp_number& e) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(e.m_backend){} + BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number() BOOST_NOEXCEPT_IF(noexcept(Backend())) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(const mp_number& e) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(e.m_backend){} template - mp_number(V v, typename enable_if_c< + BOOST_FORCEINLINE mp_number(V v, typename enable_if_c< (boost::is_arithmetic::value || is_same::value || is_convertible::value) && !is_convertible::type, Backend>::value >::type* = 0) { m_backend = canonical_value(v); } template - BOOST_CONSTEXPR mp_number(V v, typename enable_if_c< + BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(V v, typename enable_if_c< (boost::is_arithmetic::value || is_same::value || is_convertible::value) && is_convertible::type, Backend>::value >::type* = 0) : m_backend(canonical_value(v)) {} - BOOST_CONSTEXPR mp_number(const mp_number& e, unsigned digits10) + BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(const mp_number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} /* // @@ -67,10 +67,10 @@ public: } */ template - BOOST_CONSTEXPR mp_number(const mp_number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(const mp_number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} template - mp_number(const mp_number& val, typename enable_if >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) + BOOST_FORCEINLINE mp_number(const mp_number& val, typename enable_if >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) { m_backend = val.backend(); } @@ -83,20 +83,20 @@ public: detail::generic_interconvert(backend(), val.backend(), number_category(), number_category()); } template - mp_number(V v1, V v2, typename enable_if, is_same, is_convertible > >::type* = 0) + BOOST_FORCEINLINE mp_number(V v1, V v2, typename enable_if, is_same, is_convertible > >::type* = 0) { using default_ops::assign_components; assign_components(m_backend, canonical_value(v1), canonical_value(v2)); } template - mp_number(const mp_number& v1, const mp_number& v2, typename enable_if >::type* = 0) + BOOST_FORCEINLINE mp_number(const mp_number& v1, const mp_number& v2, typename enable_if >::type* = 0) { using default_ops::assign_components; assign_components(m_backend, v1.backend(), v2.backend()); } template - BOOST_CONSTEXPR mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) + BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(v){} @@ -108,14 +108,14 @@ public: return *this; } - mp_number& operator=(const mp_number& e) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) + BOOST_FORCEINLINE mp_number& operator=(const mp_number& e) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = e.m_backend; return *this; } template - typename enable_if, is_same, is_convertible >, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, is_same, is_convertible >, mp_number& >::type operator=(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval::type>())) { m_backend = canonical_value(v); @@ -123,7 +123,7 @@ public: } template - typename enable_if, mpl::not_, is_same, is_convertible > > >, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, mpl::not_, is_same, is_convertible > > >, mp_number& >::type operator=(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = v; @@ -131,14 +131,14 @@ public: } template - mp_number& operator=(const mp_number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) + BOOST_FORCEINLINE mp_number& operator=(const mp_number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = v.backend(); return *this; } template - typename enable_if, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, mp_number& >::type operator=(const mp_number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = v.backend(); @@ -163,8 +163,8 @@ public: } #ifndef BOOST_NO_RVALUE_REFERENCES - BOOST_CONSTEXPR mp_number(mp_number&& r) BOOST_NOEXCEPT : m_backend(static_cast(r.m_backend)){} - mp_number& operator=(mp_number&& r) BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(mp_number&& r) BOOST_NOEXCEPT : m_backend(static_cast(r.m_backend)){} + BOOST_FORCEINLINE mp_number& operator=(mp_number&& r) BOOST_NOEXCEPT { m_backend = static_cast(r.m_backend); return *this; @@ -307,21 +307,21 @@ public: // execute the increment/decrement on destruction, but // correct implemetation will be tricky, so defered for now... // - mp_number& operator++() + BOOST_FORCEINLINE mp_number& operator++() { using default_ops::eval_increment; eval_increment(m_backend); return *this; } - mp_number& operator--() + BOOST_FORCEINLINE mp_number& operator--() { using default_ops::eval_decrement; eval_decrement(m_backend); return *this; } - mp_number operator++(int) + BOOST_FORCEINLINE mp_number operator++(int) { using default_ops::eval_increment; self_type temp(*this); @@ -329,7 +329,7 @@ public: return BOOST_MP_MOVE(temp); } - mp_number operator--(int) + BOOST_FORCEINLINE mp_number operator--(int) { using default_ops::eval_decrement; self_type temp(*this); @@ -338,7 +338,7 @@ public: } template - typename enable_if, mp_number&>::type operator <<= (V val) + BOOST_FORCEINLINE typename enable_if, mp_number&>::type operator <<= (V val) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left-shift operation is only valid for integer types"); check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); @@ -347,7 +347,7 @@ public: } template - typename enable_if, mp_number&>::type operator >>= (V val) + BOOST_FORCEINLINE typename enable_if, mp_number&>::type operator >>= (V val) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right-shift operation is only valid for integer types"); check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); @@ -355,7 +355,7 @@ public: return *this; } - mp_number& operator /= (const self_type& e) + BOOST_FORCEINLINE mp_number& operator /= (const self_type& e) { do_divide(detail::mp_exp(e), detail::terminal()); return *this; @@ -378,7 +378,7 @@ public: } template - typename enable_if, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, mp_number& >::type operator/=(const V& v) { using default_ops::eval_divide; @@ -386,7 +386,7 @@ public: return *this; } - mp_number& operator&=(const self_type& e) + BOOST_FORCEINLINE mp_number& operator&=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); do_bitwise_and(detail::mp_exp(e), detail::terminal()); @@ -412,7 +412,7 @@ public: } template - typename enable_if, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, mp_number& >::type operator&=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); @@ -421,7 +421,7 @@ public: return *this; } - mp_number& operator|=(const self_type& e) + BOOST_FORCEINLINE mp_number& operator|=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); do_bitwise_or(detail::mp_exp(e), detail::terminal()); @@ -447,7 +447,7 @@ public: } template - typename enable_if, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, mp_number& >::type operator|=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); @@ -456,7 +456,7 @@ public: return *this; } - mp_number& operator^=(const self_type& e) + BOOST_FORCEINLINE mp_number& operator^=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); do_bitwise_xor(detail::mp_exp(e), detail::terminal()); @@ -480,7 +480,7 @@ public: } template - typename enable_if, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, mp_number& >::type operator^=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); @@ -493,7 +493,7 @@ public: // typedef bool (self_type::*unmentionable_type)()const; - operator unmentionable_type()const + BOOST_FORCEINLINE operator unmentionable_type()const { return is_zero() ? 0 : &self_type::is_zero; } @@ -501,19 +501,19 @@ public: // // swap: // - void swap(self_type& other) BOOST_NOEXCEPT + BOOST_FORCEINLINE void swap(self_type& other) BOOST_NOEXCEPT { m_backend.swap(other.backend()); } // // Zero and sign: // - bool is_zero()const + BOOST_FORCEINLINE bool is_zero()const { using default_ops::eval_is_zero; return eval_is_zero(m_backend); } - int sign()const + BOOST_FORCEINLINE int sign()const { using default_ops::eval_get_sign; return eval_get_sign(m_backend); @@ -555,24 +555,24 @@ public: // // Comparison: // - int compare(const mp_number& o)const + BOOST_FORCEINLINE int compare(const mp_number& o)const BOOST_NOEXCEPT_IF(noexcept(std::declval().compare(std::declval()))) { return m_backend.compare(o.m_backend); } template - typename enable_if, int>::type compare(const V& o)const + BOOST_FORCEINLINE typename enable_if, int>::type compare(const V& o)const { using default_ops::eval_get_sign; if(o == 0) return eval_get_sign(m_backend); return m_backend.compare(canonical_value(o)); } - Backend& backend() BOOST_NOEXCEPT + BOOST_FORCEINLINE Backend& backend() BOOST_NOEXCEPT { return m_backend; } - const Backend& backend()const BOOST_NOEXCEPT + BOOST_FORCEINLINE const Backend& backend()const BOOST_NOEXCEPT { return m_backend; } @@ -1471,23 +1471,23 @@ private: // Tests if the expression contains a reference to *this: template - bool contains_self(const Exp& e)const BOOST_NOEXCEPT + BOOST_FORCEINLINE bool contains_self(const Exp& e)const BOOST_NOEXCEPT { return contains_self(e, typename Exp::arity()); } template - bool contains_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT + BOOST_FORCEINLINE bool contains_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT { return is_realy_self(e.value()); } template - bool contains_self(const Exp& e, mpl::int_<1> const&)const BOOST_NOEXCEPT + BOOST_FORCEINLINE bool contains_self(const Exp& e, mpl::int_<1> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child_type; return contains_self(e.left(), typename child_type::arity()); } template - bool contains_self(const Exp& e, mpl::int_<2> const&)const BOOST_NOEXCEPT + BOOST_FORCEINLINE bool contains_self(const Exp& e, mpl::int_<2> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child0_type; typedef typename Exp::right_type child1_type; @@ -1495,7 +1495,7 @@ private: || contains_self(e.right(), typename child1_type::arity()); } template - bool contains_self(const Exp& e, mpl::int_<3> const&)const BOOST_NOEXCEPT + BOOST_FORCEINLINE bool contains_self(const Exp& e, mpl::int_<3> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child0_type; typedef typename Exp::middle_type child1_type; @@ -1507,51 +1507,52 @@ private: // Test if the expression is a reference to *this: template - BOOST_CONSTEXPR bool is_self(const Exp& e)const BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR bool is_self(const Exp& e)const BOOST_NOEXCEPT { return is_self(e, typename Exp::arity()); } template - BOOST_CONSTEXPR bool is_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR bool is_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT { return is_realy_self(e.value()); } template - BOOST_CONSTEXPR bool is_self(const Exp&, mpl::int_ const&)const BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR bool is_self(const Exp&, mpl::int_ const&)const BOOST_NOEXCEPT { return false; } template - BOOST_CONSTEXPR bool is_realy_self(const Val&)const BOOST_NOEXCEPT{ return false; } - BOOST_CONSTEXPR bool is_realy_self(const self_type& v)const BOOST_NOEXCEPT{ return &v == this; } + BOOST_FORCEINLINE BOOST_CONSTEXPR bool is_realy_self(const Val&)const BOOST_NOEXCEPT{ return false; } + BOOST_FORCEINLINE BOOST_CONSTEXPR bool is_realy_self(const self_type& v)const BOOST_NOEXCEPT{ return &v == this; } - static BOOST_CONSTEXPR const Backend& canonical_value(const self_type& v) BOOST_NOEXCEPT { return v.m_backend; } + static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& canonical_value(const self_type& v) BOOST_NOEXCEPT { return v.m_backend; } template - static BOOST_CONSTEXPR typename detail::canonical::type canonical_value(const V& v) BOOST_NOEXCEPT { return static_cast::type>(v); } - static typename detail::canonical::type canonical_value(const std::string& v) BOOST_NOEXCEPT { return v.c_str(); } + static BOOST_FORCEINLINE BOOST_CONSTEXPR typename detail::canonical::type canonical_value(const V& v) BOOST_NOEXCEPT { return static_cast::type>(v); } + static BOOST_FORCEINLINE typename detail::canonical::type canonical_value(const std::string& v) BOOST_NOEXCEPT { return v.c_str(); } - static BOOST_CONSTEXPR const Backend& function_arg_value(const self_type& v) BOOST_NOEXCEPT { return v.backend(); } + static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const self_type& v) BOOST_NOEXCEPT { return v.backend(); } template - static BOOST_CONSTEXPR const V& function_arg_value(const V& v) BOOST_NOEXCEPT { return v; } + static BOOST_FORCEINLINE BOOST_CONSTEXPR const V& function_arg_value(const V& v) BOOST_NOEXCEPT { return v; } template - static const A1& function_arg_value(const detail::mp_exp& exp) BOOST_NOEXCEPT { return exp.value(); } + static BOOST_FORCEINLINE const A1& function_arg_value(const detail::mp_exp& exp) BOOST_NOEXCEPT { return exp.value(); } template - static BOOST_CONSTEXPR const Backend& function_arg_value(const detail::mp_exp, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value().backend(); } + static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const detail::mp_exp, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value().backend(); } Backend m_backend; }; +/* namespace detail { template -inline int mp_number_compare(const mp_number& a, const mp_number& b) +BOOST_FORCEINLINE int mp_number_compare(const mp_number& a, const mp_number& b) { return a.compare(b); } template -inline int mp_number_compare(const mp_number& a, const mp_exp& b) +BOOST_FORCEINLINE int mp_number_compare(const mp_number& a, const mp_exp& b) { return a.compare(mp_number(b)); } @@ -1631,7 +1632,6 @@ struct is_valid_comparison : public boost::multiprecision::detail::is_valid_comp } -/* template inline typename boost::enable_if, bool>::type operator == (const Exp1& a, const Exp2& b) @@ -1712,7 +1712,7 @@ inline std::istream& operator >> (std::istream& is, mp_number -inline void swap(mp_number& a, mp_number& b) +BOOST_FORCEINLINE void swap(mp_number& a, mp_number& b) { a.swap(b); } diff --git a/performance/delaunay_test.cpp b/performance/delaunay_test.cpp index 34d6a5da..62a03981 100644 --- a/performance/delaunay_test.cpp +++ b/performance/delaunay_test.cpp @@ -129,12 +129,13 @@ inline int128_t mult_64x64_to_128(int64_t a, int64_t b) } template -__forceinline void mul_2n(R& r, const T& a, const T& b) +BOOST_FORCEINLINE void mul_2n(R& r, const T& a, const T& b) { - r = R(a) * b; + r = a; + r *= b; } -__forceinline void mul_2n(int128_t& r, const boost::int64_t& a, const boost::int64_t& b) +BOOST_FORCEINLINE void mul_2n(int128_t& r, const boost::int64_t& a, const boost::int64_t& b) { r = mult_64x64_to_128(a, b); } From 7a7a287def426407c25316d7600460a56d3496f9 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 4 Aug 2012 10:59:56 +0000 Subject: [PATCH 210/256] Fix C++11 compiler issues [SVN r79861] --- performance/arithmetic_backend.hpp | 18 +++++------ performance/performance_test.cpp | 50 +++++++++++++++--------------- 2 files changed, 34 insertions(+), 34 deletions(-) diff --git a/performance/arithmetic_backend.hpp b/performance/arithmetic_backend.hpp index a4d59f36..acff30cd 100644 --- a/performance/arithmetic_backend.hpp +++ b/performance/arithmetic_backend.hpp @@ -545,15 +545,15 @@ class numeric_limits : public std::numeric_ typedef std::numeric_limits base_type; typedef boost::math::concepts::real_concept number_type; public: - BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } - BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } - BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_NOEXCEPT { return -(max)(); } - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT { return base_type::epsilon(); } - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT { return epsilon() / 2; } - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT { return base_type::infinity(); } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT { return base_type::quiet_NaN(); } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT { return base_type::signaling_NaN(); } - BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } + static const number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } + static const number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } + static const number_type lowest() BOOST_NOEXCEPT { return -(max)(); } + static const number_type epsilon() BOOST_NOEXCEPT { return base_type::epsilon(); } + static const number_type round_error() BOOST_NOEXCEPT { return epsilon() / 2; } + static const number_type infinity() BOOST_NOEXCEPT { return base_type::infinity(); } + static const number_type quiet_NaN() BOOST_NOEXCEPT { return base_type::quiet_NaN(); } + static const number_type signaling_NaN() BOOST_NOEXCEPT { return base_type::signaling_NaN(); } + static const number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } }; } diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index 61116348..dcc93932 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -384,25 +384,25 @@ struct tester // // Hetero operations: // - template - static T get_hetero_test_value(boost::mpl::false_ const&) + template + static U get_hetero_test_value(boost::mpl::false_ const&) { - return T(2) / 3; + return U(2) / 3; } - template - static T get_hetero_test_value(boost::mpl::true_ const&) + template + static U get_hetero_test_value(boost::mpl::true_ const&) { - return (std::numeric_limits::max)() >> 4; + return (std::numeric_limits::max)() >> 4; } - template - static T get_hetero_test_value() + template + static U get_hetero_test_value() { - return get_hetero_test_value(boost::is_integral()); + return get_hetero_test_value(boost::is_integral()); } - template + template double test_multiply_hetero() { - static const T val = get_hetero_test_value(); + static const U val = get_hetero_test_value(); stopwatch w; for(unsigned i = 0; i < 1000; ++i) { @@ -411,10 +411,10 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } - template + template double test_inplace_multiply_hetero() { - static const T val = get_hetero_test_value(); + static const U val = get_hetero_test_value(); for(unsigned i = 0; i < b.size(); ++i) a[i] = b[i]; stopwatch w; @@ -425,10 +425,10 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } - template + template double test_add_hetero() { - static const T val = get_hetero_test_value(); + static const U val = get_hetero_test_value(); stopwatch w; for(unsigned i = 0; i < 1000; ++i) { @@ -437,10 +437,10 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } - template + template double test_inplace_add_hetero() { - static const T val = get_hetero_test_value(); + static const U val = get_hetero_test_value(); for(unsigned i = 0; i < b.size(); ++i) a[i] = b[i]; stopwatch w; @@ -451,10 +451,10 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } - template + template double test_subtract_hetero() { - static const T val = get_hetero_test_value(); + static const U val = get_hetero_test_value(); stopwatch w; for(unsigned i = 0; i < 1000; ++i) { @@ -463,10 +463,10 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } - template + template double test_inplace_subtract_hetero() { - static const T val = get_hetero_test_value(); + static const U val = get_hetero_test_value(); for(unsigned i = 0; i < b.size(); ++i) a[i] = b[i]; stopwatch w; @@ -477,10 +477,10 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } - template + template double test_divide_hetero() { - static const T val = get_hetero_test_value(); + static const U val = get_hetero_test_value(); stopwatch w; for(unsigned i = 0; i < 1000; ++i) { @@ -489,10 +489,10 @@ struct tester } return boost::chrono::duration_cast >(w.elapsed()).count(); } - template + template double test_inplace_divide_hetero() { - static const T val = get_hetero_test_value(); + static const U val = get_hetero_test_value(); for(unsigned i = 0; i < b.size(); ++i) a[i] = b[i]; stopwatch w; From 821afe64fbe8345785f041b45b023805fad659e8 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 7 Aug 2012 08:10:07 +0000 Subject: [PATCH 211/256] Add uBlas interoperability tests. Add file include tests. [SVN r79894] --- include/boost/multiprecision/mp_number.hpp | 148 +------ performance/sf_performance.cpp | 2 +- test/Jamfile.v2 | 22 ++ .../cpp_dec_float_include_test.cpp | 12 + test/include_test/cpp_int_include_test.cpp | 16 + test/include_test/gmp_include_test.cpp | 14 + test/include_test/mpfr_include_test.cpp | 12 + test/include_test/tommath_include_test.cpp | 12 + test/ublas_interop/common/init.hpp | 100 +++++ test/ublas_interop/common/testhelper.hpp | 74 ++++ test/ublas_interop/test1.cpp | 20 + test/ublas_interop/test1.hpp | 45 +++ test/ublas_interop/test11.cpp | 182 +++++++++ test/ublas_interop/test12.cpp | 102 +++++ test/ublas_interop/test13.cpp | 167 ++++++++ test/ublas_interop/test2.cpp | 87 +++++ test/ublas_interop/test2.hpp | 69 ++++ test/ublas_interop/test21.cpp | 95 +++++ test/ublas_interop/test22.cpp | 147 +++++++ test/ublas_interop/test23.cpp | 208 ++++++++++ test/ublas_interop/test3.cpp | 20 + test/ublas_interop/test3.hpp | 63 +++ test/ublas_interop/test31.cpp | 248 ++++++++++++ test/ublas_interop/test32.cpp | 324 ++++++++++++++++ test/ublas_interop/test33.cpp | 347 +++++++++++++++++ test/ublas_interop/test4.cpp | 19 + test/ublas_interop/test4.hpp | 39 ++ test/ublas_interop/test42.cpp | 361 ++++++++++++++++++ test/ublas_interop/test43.cpp | 326 ++++++++++++++++ test/ublas_interop/test5.cpp | 19 + test/ublas_interop/test5.hpp | 35 ++ test/ublas_interop/test52.cpp | 214 +++++++++++ test/ublas_interop/test53.cpp | 223 +++++++++++ test/ublas_interop/test6.cpp | 19 + test/ublas_interop/test6.hpp | 32 ++ test/ublas_interop/test62.cpp | 218 +++++++++++ test/ublas_interop/test63.cpp | 223 +++++++++++ test/ublas_interop/test7.cpp | 31 ++ test/ublas_interop/test7.hpp | 36 ++ test/ublas_interop/test71.cpp | 170 +++++++++ test/ublas_interop/test72.cpp | 165 ++++++++ test/ublas_interop/test73.cpp | 202 ++++++++++ 42 files changed, 4735 insertions(+), 133 deletions(-) create mode 100644 test/include_test/cpp_dec_float_include_test.cpp create mode 100644 test/include_test/cpp_int_include_test.cpp create mode 100644 test/include_test/gmp_include_test.cpp create mode 100644 test/include_test/mpfr_include_test.cpp create mode 100644 test/include_test/tommath_include_test.cpp create mode 100644 test/ublas_interop/common/init.hpp create mode 100644 test/ublas_interop/common/testhelper.hpp create mode 100644 test/ublas_interop/test1.cpp create mode 100644 test/ublas_interop/test1.hpp create mode 100644 test/ublas_interop/test11.cpp create mode 100644 test/ublas_interop/test12.cpp create mode 100644 test/ublas_interop/test13.cpp create mode 100644 test/ublas_interop/test2.cpp create mode 100644 test/ublas_interop/test2.hpp create mode 100644 test/ublas_interop/test21.cpp create mode 100644 test/ublas_interop/test22.cpp create mode 100644 test/ublas_interop/test23.cpp create mode 100644 test/ublas_interop/test3.cpp create mode 100644 test/ublas_interop/test3.hpp create mode 100644 test/ublas_interop/test31.cpp create mode 100644 test/ublas_interop/test32.cpp create mode 100644 test/ublas_interop/test33.cpp create mode 100644 test/ublas_interop/test4.cpp create mode 100644 test/ublas_interop/test4.hpp create mode 100644 test/ublas_interop/test42.cpp create mode 100644 test/ublas_interop/test43.cpp create mode 100644 test/ublas_interop/test5.cpp create mode 100644 test/ublas_interop/test5.hpp create mode 100644 test/ublas_interop/test52.cpp create mode 100644 test/ublas_interop/test53.cpp create mode 100644 test/ublas_interop/test6.cpp create mode 100644 test/ublas_interop/test6.hpp create mode 100644 test/ublas_interop/test62.cpp create mode 100644 test/ublas_interop/test63.cpp create mode 100644 test/ublas_interop/test7.cpp create mode 100644 test/ublas_interop/test7.hpp create mode 100644 test/ublas_interop/test71.cpp create mode 100644 test/ublas_interop/test72.cpp create mode 100644 test/ublas_interop/test73.cpp diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index a4ab00b7..f788940c 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -1541,138 +1541,6 @@ private: Backend m_backend; }; -/* -namespace detail -{ - -template -BOOST_FORCEINLINE int mp_number_compare(const mp_number& a, const mp_number& b) -{ - return a.compare(b); -} - -template -BOOST_FORCEINLINE int mp_number_compare(const mp_number& a, const mp_exp& b) -{ - return a.compare(mp_number(b)); -} - -template -inline int mp_number_compare(const mp_exp& a, const mp_number& b) -{ - return -b.compare(mp_number(a)); -} - -template -inline int mp_number_compare(const mp_number& a, const Val b) -{ - return a.compare(b); -} - -template -inline int mp_number_compare(const Val a, const mp_number& b) -{ - return -b.compare(a); -} - -template -inline int mp_number_compare(const mp_exp& a, const mp_exp& b) -{ - typedef typename mp_exp::result_type real1; - typedef typename mp_exp::result_type real2; - return real1(a).compare(real2(b)); -} - -template -inline typename enable_if, int>::type mp_number_compare(const mp_exp& a, const Val b) -{ - typedef typename mp_exp::result_type real; - real t(a); - return t.compare(b); -} - -template -inline typename enable_if, int>::type mp_number_compare(const Val a, const mp_exp& b) -{ - typedef typename mp_exp::result_type real; - return -real(b).compare(a); -} - -template -struct is_valid_comparison_imp -{ - typedef typename mpl::or_< - is_mp_number, - is_mp_number_exp - >::type is1; - typedef typename mpl::or_< - is_mp_number, - is_mp_number_exp - >::type is2; - typedef typename mpl::or_< - mpl::and_< - is1, - mpl::or_< - is2, - is_arithmetic - > - >, - mpl::and_< - is2, - mpl::or_< - is1, - is_arithmetic - > - > - >::type type; -}; - -template -struct is_valid_comparison : public boost::multiprecision::detail::is_valid_comparison_imp::type {}; - -} - -template -inline typename boost::enable_if, bool>::type - operator == (const Exp1& a, const Exp2& b) -{ - return 0 == detail::mp_number_compare(a, b); -} -template -inline typename boost::enable_if, bool>::type - operator != (const Exp1& a, const Exp2& b) -{ - return 0 != detail::mp_number_compare(a, b); -} - -template -inline typename boost::enable_if, bool>::type - operator <= (const Exp1& a, const Exp2& b) -{ - return 0 >= detail::mp_number_compare(a, b); -} - -template -inline typename boost::enable_if, bool>::type - operator < (const Exp1& a, const Exp2& b) -{ - return 0 > detail::mp_number_compare(a, b); -} - -template -inline typename boost::enable_if, bool>::type - operator >= (const Exp1& a, const Exp2& b) -{ - return 0 <= detail::mp_number_compare(a, b); -} - -template -inline typename boost::enable_if, bool>::type - operator > (const Exp1& a, const Exp2& b) -{ - return 0 < detail::mp_number_compare(a, b); -} -*/ template inline std::ostream& operator << (std::ostream& os, const mp_number& r) { @@ -1793,6 +1661,22 @@ inline multiprecision::mp_number denominator(const ratio return a.denominator(); } +namespace numeric { namespace ublas { +// +// uBlas interoperability: +// +template +class sparse_vector_element; + +template +inline bool operator == (const sparse_vector_element& a, const ::boost::multiprecision::mp_number& b) +{ +typedef typename sparse_vector_element::const_reference ref_type; + return static_cast(a) == b; +} + +}} // namespaces + #ifdef BOOST_MSVC #pragma warning(pop) #endif diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index 0c10a841..3646e1b3 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -225,7 +225,7 @@ void time_proc(const char* name, Real (*proc)(), unsigned threads = 1) int main() { using namespace boost::multiprecision; -#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) || defined(TEST_MPREAL) +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) || defined(TEST_MPREAL) || defined(TEST_MPF) mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); mp_set_memory_functions(&alloc_func, &realloc_func, &free_func); #endif diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 3c47c6d2..a8879efd 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -731,6 +731,27 @@ run ../example/tommath_snips.cpp $(TOMMATH) [ check-target-builds ../config//has_tommath : : no ] ; run ../example/floating_point_examples.cpp : : : gcc:-std=c++0x ; +compile include_test/mpfr_include_test.cpp + : # requirements + [ check-target-builds ../config//has_mpfr : : no ] ; +compile include_test/gmp_include_test.cpp + : # requirements + [ check-target-builds ../config//has_gmp : : no ] ; +compile include_test/tommath_include_test.cpp + : # requirements + [ check-target-builds ../config//has_tommath : : no ] ; +compile include_test/cpp_int_include_test.cpp ; +compile include_test/cpp_dec_float_include_test.cpp ; + +run ublas_interop/test1.cpp ublas_interop/test11.cpp ublas_interop/test12.cpp ublas_interop/test13.cpp ; +run ublas_interop/test2.cpp ublas_interop/test21.cpp ublas_interop/test22.cpp ublas_interop/test23.cpp ; +#run ublas_interop/test3.cpp ublas_interop/test31.cpp ublas_interop/test32.cpp ublas_interop/test33.cpp ; +run ublas_interop/test4.cpp ublas_interop/test42.cpp ublas_interop/test43.cpp ; +run ublas_interop/test5.cpp ublas_interop/test52.cpp ublas_interop/test53.cpp ; +run ublas_interop/test6.cpp ublas_interop/test62.cpp ublas_interop/test63.cpp ; +run ublas_interop/test7.cpp ublas_interop/test71.cpp ublas_interop/test72.cpp ublas_interop/test73.cpp ; + + if $(enable-specfun) { @@ -771,6 +792,7 @@ if $(enable-specfun) } } + if ! $(disable-concepts) { diff --git a/test/include_test/cpp_dec_float_include_test.cpp b/test/include_test/cpp_dec_float_include_test.cpp new file mode 100644 index 00000000..bdf09e83 --- /dev/null +++ b/test/include_test/cpp_dec_float_include_test.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include + +using namespace boost::multiprecision; + +cpp_dec_float<50> a; + + diff --git a/test/include_test/cpp_int_include_test.cpp b/test/include_test/cpp_int_include_test.cpp new file mode 100644 index 00000000..f193178c --- /dev/null +++ b/test/include_test/cpp_int_include_test.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include + +using namespace boost::multiprecision; + +mp_number > a; +mp_number, false> b; +mp_number, false> c; +mp_number, false> d; +mp_number, false> e; + + diff --git a/test/include_test/gmp_include_test.cpp b/test/include_test/gmp_include_test.cpp new file mode 100644 index 00000000..4b07266f --- /dev/null +++ b/test/include_test/gmp_include_test.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include + +using namespace boost::multiprecision; + +mpf_float a; +mpz_int b; +mpq_rational c; + + diff --git a/test/include_test/mpfr_include_test.cpp b/test/include_test/mpfr_include_test.cpp new file mode 100644 index 00000000..f84cbb95 --- /dev/null +++ b/test/include_test/mpfr_include_test.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include + +using namespace boost::multiprecision; + +mpfr_float a; + + diff --git a/test/include_test/tommath_include_test.cpp b/test/include_test/tommath_include_test.cpp new file mode 100644 index 00000000..bc000fef --- /dev/null +++ b/test/include_test/tommath_include_test.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include + +using namespace boost::multiprecision; + +tom_int a; + + diff --git a/test/ublas_interop/common/init.hpp b/test/ublas_interop/common/init.hpp new file mode 100644 index 00000000..a9691b4e --- /dev/null +++ b/test/ublas_interop/common/init.hpp @@ -0,0 +1,100 @@ +/* + * Copyright (c) 2004 Michael Stevens + * Use, modification and distribution are subject to the + * Boost Software License, Version 1.0. (See accompanying file + * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + */ + +/* + * Default construct test when possible + */ + +template +struct default_construct +{ + static void test() {} +}; +template +struct default_construct > +{ + static void test () + { + VC default_constuct; + initialize_vector (default_constuct); + std::cout << "default construct = " << default_constuct << std::endl; + } +}; +template +struct default_construct > +{ + static void test () + { + MC default_constuct; + initialize_vector (default_constuct); + std::cout << "default construct = " << default_constuct << std::endl; + } +}; + +/* + * Initialise test values in vector/matrix + */ + +template +void initialize_vector (V &v) { + typename V::size_type size = v.size (); + for (typename V::size_type i = 0; i < size; ++ i) + v [i] = typename V::value_type ( i + 1.f ); +} + +template +void initialize_matrix_impl (M &m, ublas::packed_proxy_tag) { + typename M::size_type size1 = m.size1 (); +#ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION + for (typename M::iterator1 i = m.begin1(); i != m.end1(); ++ i) + for (typename M::iterator2 j = i.begin(); j != i.end(); ++ j) + *j = typename M::value_type ( i.index1() * size1 + j.index2() + 1.f ); +#else + for (typename M::iterator1 i = m.begin1(); i != m.end1(); ++ i) + for (typename M::iterator2 j = ublas::begin (i, ublas::iterator1_tag ()); j != ublas::end (i, ublas::iterator1_tag ()); ++ j) + *j = typename M::value_type ( i.index1() * size1 + j.index2() + 1.f ); +#endif +} + +template +void initialize_matrix_impl (M &m, ublas::sparse_proxy_tag) { + typename M::size_type size1 = m.size1 (); + typename M::size_type size2 = m.size2 (); + for (typename M::size_type i = 0; i < size1; ++ i) + for (typename M::size_type j = 0; j < size2; ++ j) + m (i, j) = typename M::value_type (i * size1 + j + 1.f); +} + +template +void initialize_matrix (M &m) { + initialize_matrix_impl (m, typename M::storage_category()); +} + +template +void initialize_matrix (M &m, ublas::lower_tag) { + typename M::size_type size1 = m.size1 (); + typename M::size_type size2 = m.size2 (); + for (typename M::size_type i = 0; i < size1; ++ i) { + typename M::size_type j = 0; + for (; j <= i; ++ j) + m (i, j) = i * size1 + j + 1.f; + for (; j < size2; ++ j) + m (i, j) = 0.f; + } +} +template +void initialize_matrix (M &m, ublas::upper_tag) { + typename M::size_type size1 = m.size1 (); + typename M::size_type size2 = m.size2 (); + for (typename M::size_type i = 0; i < size1; ++ i) { + typename M::size_type j = 0; + for (; j < i; ++ j) + m (i, j) = 0.f; + for (; j < size2; ++ j) + m (i, j) = i * size1 + j + 1.f; + } +} diff --git a/test/ublas_interop/common/testhelper.hpp b/test/ublas_interop/common/testhelper.hpp new file mode 100644 index 00000000..4fbf9c4d --- /dev/null +++ b/test/ublas_interop/common/testhelper.hpp @@ -0,0 +1,74 @@ +// Copyright 2008 Gunter Winkler +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) + + +#ifndef _HPP_TESTHELPER_ +#define _HPP_TESTHELPER_ + +#include + +static unsigned _success_counter = 0; +static unsigned _fail_counter = 0; + +static inline +void assertTrue(const char* message, bool condition) { +#ifndef NOMESSAGES + std::cout << message; +#endif + if ( condition ) { + ++ _success_counter; + std::cout << "1\n"; // success + } else { + ++ _fail_counter; + std::cout << "0\n"; // failed + } +} + +template < class T > +void assertEquals(const char* message, T expected, T actual) { +#ifndef NOMESSAGES + std::cout << message; +#endif + if ( expected == actual ) { + ++ _success_counter; + std::cout << "1\n"; // success + } else { + #ifndef NOMESSAGES + std::cout << " expected " << expected << " actual " << actual << " "; + #endif + ++ _fail_counter; + std::cout << "0\n"; // failed + } +} + +static +std::pair getResults() { + return std::make_pair(_success_counter, _fail_counter); +} + +template < class M1, class M2 > +bool compare( const boost::numeric::ublas::matrix_expression & m1, + const boost::numeric::ublas::matrix_expression & m2 ) { + size_t size1 = (std::min)(m1().size1(), m2().size1()); + size_t size2 = (std::min)(m1().size2(), m2().size2()); + for (size_t i=0; i < size1; ++i) { + for (size_t j=0; j < size2; ++j) { + if ( m1()(i,j) != m2()(i,j) ) return false; + } + } + return true; +} + +template < class M1, class M2 > +bool compare( const boost::numeric::ublas::vector_expression & m1, + const boost::numeric::ublas::vector_expression & m2 ) { + size_t size = (std::min)(m1().size(), m2().size()); + for (size_t i=0; i < size; ++i) { + if ( m1()(i) != m2()(i) ) return false; + } + return true; +} + +#endif diff --git a/test/ublas_interop/test1.cpp b/test/ublas_interop/test1.cpp new file mode 100644 index 00000000..53de7901 --- /dev/null +++ b/test/ublas_interop/test1.cpp @@ -0,0 +1,20 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test1.hpp" + +int main () { + test_vector (); + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/test/ublas_interop/test1.hpp b/test/ublas_interop/test1.hpp new file mode 100644 index 00000000..f6627dce --- /dev/null +++ b/test/ublas_interop/test1.hpp @@ -0,0 +1,45 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST1_H +#define TEST1_H + +#include + +#ifdef _MSC_VER +# pragma warning(disable:4800 4996) +#endif + +#include + +typedef boost::multiprecision::mp_number, false> mp_test_type; +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE + + +#include +#include +#include +#include +#include + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +void test_vector (); +void test_matrix_vector (); +void test_matrix (); + +#endif diff --git a/test/ublas_interop/test11.cpp b/test/ublas_interop/test11.cpp new file mode 100644 index 00000000..70e77611 --- /dev/null +++ b/test/ublas_interop/test11.cpp @@ -0,0 +1,182 @@ +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. + +#include "test1.hpp" + +// Test vector expression templates +template +struct test_my_vector { + typedef typename V::value_type value_type; + typedef typename V::size_type size_type; + typedef typename ublas::type_traits::real_type real_type; + + template + void test_container_with (VP &v1) const { + // Container type tests in addition to expression types + // Insert and erase + v1.insert_element (0, 55); + v1.erase_element (1); + v1.clear (); + } + + template + void test_expression_with (VP &v1, VP &v2, VP &v3) const { + // Expression type tests + value_type t; + size_type i; + real_type n; + + // Default Construct + default_construct::test (); + + // Copy and swap + initialize_vector (v1); + initialize_vector (v2); + v1 = v2; + std::cout << "v1 = v2 = " << v1 << std::endl; + v1.assign_temporary (v2); + std::cout << "v1.assign_temporary (v2) = " << v1 << std::endl; + v1.swap (v2); + std::cout << "v1.swap (v2) = " << v1 << " " << v2 << std::endl; + + // Zero assignment + v1 = ublas::zero_vector<> (v1.size ()); + std::cout << "v1.zero_vector = " << v1 << std::endl; + v1 = v2; + +#ifndef BOOST_NO_FUNCTION_TEMPLATE_ORDERING + // Project range and slice + initialize_vector (v1); + initialize_vector (v2); + project (v1, ublas::range(0,1)) = project (v2, ublas::range(0,1)); + project (v1, ublas::range(0,1)) = project (v2, ublas::slice(0,1,1)); + project (v1, ublas::slice(2,-1,2)) = project (v2, ublas::slice(0,1,2)); + project (v1, ublas::slice(2,-1,2)) = project (v2, ublas::range(0,2)); + std::cout << "v1 = range/slice " << v1 << std::endl; +#endif + + // Unary vector operations resulting in a vector + initialize_vector (v1); + v2 = - v1; + std::cout << "- v1 = " << v2 << std::endl; + v2 = ublas::conj (v1); + std::cout << "conj (v1) = " << v2 << std::endl; + + // Binary vector operations resulting in a vector + initialize_vector (v1); + initialize_vector (v2); + v3 = v1 + v2; + std::cout << "v1 + v2 = " << v3 << std::endl; + v3 = v1 - v2; + std::cout << "v1 - v2 = " << v3 << std::endl; + v3 = ublas::element_prod (v1, v2); + std::cout << "element_prod (v1, v2) = " << v3 << std::endl; + + // Scaling a vector + t = N; + initialize_vector (v1); + v2 = value_type (1.) * v1; + std::cout << "1. * v1 = " << v2 << std::endl; + v2 = t * v1; + std::cout << "N * v1 = " << v2 << std::endl; + initialize_vector (v1); + v2 = v1 * value_type (1.); + std::cout << "v1 * 1. = " << v2 << std::endl; + v2 = v1 * t; + std::cout << "v1 * value_type(N) = " << v2 << std::endl; + // test interop with integer + v2 = v1 * N; + + std::cout << "v1 * N = " << v2 << std::endl; + + // Some assignments + initialize_vector (v1); + initialize_vector (v2); + v2 += v1; + std::cout << "v2 += v1 = " << v2 << std::endl; + v2 -= v1; + std::cout << "v2 -= v1 = " << v2 << std::endl; + v2 = v2 + v1; + std::cout << "v2 = v2 + v1 = " << v2 << std::endl; + v2 = v2 - v1; + std::cout << "v2 = v2 - v1 = " << v2 << std::endl; + v1 *= value_type (1.); + std::cout << "v1 *= 1. = " << v1 << std::endl; + v1 *= t; + std::cout << "v1 *= value_type(N) = " << v1 << std::endl; + // test interop with integer + v1 *= N; + std::cout << "v1 *= N = " << v1 << std::endl; + + // Unary vector operations resulting in a scalar + initialize_vector (v1); + t = ublas::sum (v1); + std::cout << "sum (v1) = " << t << std::endl; + n = ublas::norm_1 (v1); + std::cout << "norm_1 (v1) = " << n << std::endl; + n = ublas::norm_2 (v1); + std::cout << "norm_2 (v1) = " << n << std::endl; + n = ublas::norm_inf (v1); + std::cout << "norm_inf (v1) = " << n << std::endl; + + i = ublas::index_norm_inf (v1); + std::cout << "index_norm_inf (v1) = " << i << std::endl; + + // Binary vector operations resulting in a scalar + initialize_vector (v1); + initialize_vector (v2); + t = ublas::inner_prod (v1, v2); + std::cout << "inner_prod (v1, v2) = " << t << std::endl; + + // Scalar and Binary vector expression resulting in a vector + initialize_vector (v1); + initialize_vector (v2); + v1 = v1 * ublas::inner_prod (v1, v2); + std::cout << "v1 * inner_prod (v1, v2) = " << v1 << std::endl; + } + + void operator () () const { + V v1 (N), v2 (N), v3 (N); + test_expression_with (v1, v2, v3); + test_container_with (v1); + +#ifdef USE_RANGE + ublas::vector_range vr1 (v1, ublas::range (0, N)), + vr2 (v2, ublas::range (0, N)), + vr3 (v3, ublas::range (0, N)); + test_expression_with (vr1, vr2, vr3); +#endif + +#ifdef USE_SLICE + ublas::vector_slice vs1 (v1, ublas::slice (0, 1, N)), + vs2 (v2, ublas::slice (0, 1, N)), + vs3 (v3, ublas::slice (0, 1, N)); + test_expression_with (vs1, vs2, vs3); +#endif + } +}; + +// Test vector +void test_vector () { + std::cout << "test_vector" << std::endl; + + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_vector >, 3 > () (); + + + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_vector >, 3 > () (); + + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_vector >, 3 > () (); + + std::cout << "mp_test_type, bounded" << std::endl; + test_my_vector, 3> () (); +} diff --git a/test/ublas_interop/test12.cpp b/test/ublas_interop/test12.cpp new file mode 100644 index 00000000..fac3634f --- /dev/null +++ b/test/ublas_interop/test12.cpp @@ -0,0 +1,102 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test1.hpp" + +// Test matrix & vector expression templates +template +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template + void test_with (VP &v1, VP &v2, MP &m1) const { + { + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v1 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v1 << std::endl; + v1 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v1 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; + } + } + void operator () () const { + { + V v1 (N), v2 (N); + M m1 (N, N); + test_with (v1, v2, m1); + + ublas::matrix_row mr1 (m1, 0), mr2 (m1, 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column mc1 (m1, 0), mc2 (m1, 1); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::matrix >, 3> () (); + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::matrix >, 3> () (); + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::matrix >, 3> () (); + std::cout << "mp_test_type, bounded" << std::endl; + test_my_matrix_vector, + ublas::bounded_matrix, 3> () (); + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::vector_of_vector, 3 + 1> >, 3> () (); + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::vector_of_vector > >, 3> () (); + std::cout << "mp_test_type, std::vector" << std::endl; + /* + // This fails with an internal std lib assersion, even when mp_test_type is double, + // looks like a bug in the uBlas test code... + test_my_matrix_vector >, + ublas::vector_of_vector > >, 3> () ();*/ +} diff --git a/test/ublas_interop/test13.cpp b/test/ublas_interop/test13.cpp new file mode 100644 index 00000000..2e8432a5 --- /dev/null +++ b/test/ublas_interop/test13.cpp @@ -0,0 +1,167 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test1.hpp" + +// Test matrix expression templates +template +struct test_my_matrix { + typedef typename M::value_type value_type; + + template + void test_container_with (VP &v1) const { + // Container type tests in addition to expression types + // Insert and erase + v1.insert_element (0,0, 55); + v1.erase_element (1,1); + v1.clear (); + } + + template + void test_expression_with (MP &m1, MP &m2, MP &m3) const { + value_type t; + + // Default Construct + default_construct::test (); + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + +#ifndef BOOST_NO_FUNCTION_TEMPLATE_ORDERING + // Project range and slice + initialize_matrix (m1); + initialize_matrix (m2); + project (m1, ublas::range(0,1),ublas::range(0,1)) = project (m2, ublas::range(0,1),ublas::range(0,1)); + project (m1, ublas::range(0,1),ublas::range(0,1)) = project (m2, ublas::slice(0,1,1),ublas::slice(0,1,1)); + project (m1, ublas::slice(2,-1,2),ublas::slice(2,-1,2)) = project (m2, ublas::slice(0,1,2),ublas::slice(0,1,2)); + project (m1, ublas::slice(2,-1,2),ublas::slice(2,-1,2)) = project (m2, ublas::range(0,2),ublas::range(0,2)); + std::cout << "m1 = range/slice " << m1 << std::endl; +#endif + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + m3 = ublas::element_prod (m1, m2); + std::cout << "element_prod (m1, m2) = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m2 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + m2 = ublas::trans (m1); + std::cout << "trans (m1) = " << m2 << std::endl; + + // Hermitean + initialize_matrix (m1); + m2 = ublas::herm (m1); + std::cout << "herm (m1) = " << m2 << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + m3 = ublas::prod (m1, m2); + std::cout << "prod (m1, m2) = " << m3 << std::endl; + } + + void operator () () const { + M m1 (N, N), m2 (N, N), m3 (N, N); + test_expression_with (m1, m2, m3); + test_container_with (m1); + +#ifdef USE_RANGE + ublas::matrix_range mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_expression_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_expression_with (ms1, ms2, ms3); +#endif + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix >, 3> () (); + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix >, 3> () (); + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix >, 3> () (); + std::cout << "mp_test_type, bounded" << std::endl; + test_my_matrix, 3> () (); + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix, 3 + 1> >, 3> () (); + /* + // This fails with an internal std lib assersion, even when mp_test_type is double, + // looks like a bug in the uBlas test code... + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix > >, 3> () (); + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix > >, 3> () ();*/ +} diff --git a/test/ublas_interop/test2.cpp b/test/ublas_interop/test2.cpp new file mode 100644 index 00000000..0550dc80 --- /dev/null +++ b/test/ublas_interop/test2.cpp @@ -0,0 +1,87 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test2.hpp" + +int main () { +#ifdef USE_FLOAT + std::cout << "mp_test_type" << std::endl; + test_blas_1, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double" << std::endl; + test_blas_1, 3> ().test (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex" << std::endl; + test_blas_1 >, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex" << std::endl; + test_blas_1 >, 3> ().test (); +#endif +#endif + + std::cout << "test_blas_2" << std::endl; + +#ifdef USE_FLOAT + std::cout << "mp_test_type" << std::endl; + test_blas_2, ublas::matrix, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double" << std::endl; + test_blas_2, ublas::matrix, 3> ().test (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex" << std::endl; + test_blas_2 >, ublas::matrix >, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex" << std::endl; + test_blas_2 >, ublas::matrix >, 3> ().test (); +#endif +#endif + + std::cout << "test_blas_3" << std::endl; + +#ifdef USE_FLOAT + std::cout << "mp_test_type" << std::endl; + test_blas_3, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double" << std::endl; + test_blas_3, 3> ().test (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex" << std::endl; + test_blas_3 >, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex" << std::endl; + test_blas_3 >, 3> ().test (); +#endif +#endif + + return 0; +} diff --git a/test/ublas_interop/test2.hpp b/test/ublas_interop/test2.hpp new file mode 100644 index 00000000..0009b832 --- /dev/null +++ b/test/ublas_interop/test2.hpp @@ -0,0 +1,69 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST2_H +#define TEST2_H + +#ifdef _MSC_VER +# pragma warning(disable:4800 4996) +#endif + +#include + +typedef boost::multiprecision::mp_number, false> mp_test_type; +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_RANGE +#define USE_SLICE +#define USE_UNBOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX + +#include + +#include +#include +#include +#include +#include + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +template +struct test_blas_1 { + typedef typename V::value_type value_type; + typedef typename ublas::type_traits::real_type real_type; + + void test (); +}; + +template +struct test_blas_2 { + typedef typename V::value_type value_type; + + void test (); +}; + +template +struct test_blas_3 { + typedef typename M::value_type value_type; + + void test (); +}; + + +#endif diff --git a/test/ublas_interop/test21.cpp b/test/ublas_interop/test21.cpp new file mode 100644 index 00000000..252d1f1c --- /dev/null +++ b/test/ublas_interop/test21.cpp @@ -0,0 +1,95 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test2.hpp" + +template +void test_blas_1::test () { + { + value_type t; + real_type n; + V v1 (N), v2 (N); + + // _asum + initialize_vector (v1); + n = ublas::blas_1::asum (v1); + std::cout << "asum (v1) = " << n << std::endl; + + // _amax + initialize_vector (v1); + n = ublas::blas_1::amax (v1); + std::cout << "amax (v1) = " << n << std::endl; + + // _nrm2 + initialize_vector (v1); + n = ublas::blas_1::nrm2 (v1); + std::cout << "nrm2 (v1) = " << n << std::endl; + + // _dot + // _dotu + // _dotc + initialize_vector (v1); + initialize_vector (v2); + t = ublas::blas_1::dot (v1, v2); + std::cout << "dot (v1, v2) = " << t << std::endl; + t = ublas::blas_1::dot (ublas::conj (v1), v2); + std::cout << "dot (conj (v1), v2) = " << t << std::endl; + + // _copy + initialize_vector (v2); + ublas::blas_1::copy (v1, v2); + std::cout << "copy (v1, v2) = " << v1 << std::endl; + + // _swap + initialize_vector (v1); + initialize_vector (v2); + ublas::blas_1::swap (v1, v2); + std::cout << "swap (v1, v2) = " << v1 << " " << v2 << std::endl; + + // _scal + // csscal + // zdscal + initialize_vector (v1); + ublas::blas_1::scal (v1, value_type (1)); + std::cout << "scal (v1, 1) = " << v1 << std::endl; + + // _axpy + initialize_vector (v1); + initialize_vector (v2); + ublas::blas_1::axpy (v1, value_type (1), v2); + std::cout << "axpy (v1, 1, v2) = " << v1 << std::endl; + + // _rot + initialize_vector (v1); + initialize_vector (v2); + ublas::blas_1::rot (value_type (1), v1, value_type (1), v2); + std::cout << "rot (1, v1, 1, v2) = " << v1 << " " << v2 << std::endl; + } +} + +#ifdef USE_FLOAT +template struct test_blas_1, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_1, 3>; +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT +template struct test_blas_1 >, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_1 >, 3>; +#endif +#endif diff --git a/test/ublas_interop/test22.cpp b/test/ublas_interop/test22.cpp new file mode 100644 index 00000000..297bb06a --- /dev/null +++ b/test/ublas_interop/test22.cpp @@ -0,0 +1,147 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test2.hpp" + +template +void test_blas_2::test () { + { + V v1 (N), v2 (N); + M m (N, N); + + // _t_mv + initialize_vector (v1); + initialize_matrix (m); + ublas::blas_2::tmv (v1, m); + std::cout << "tmv (v1, m) = " << v1 << std::endl; + initialize_vector (v1); + initialize_matrix (m); + ublas::blas_2::tmv (v1, ublas::trans (m)); + std::cout << "tmv (v1, trans (m)) = " << v1 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_vector (v1); + initialize_matrix (m); + ublas::blas_2::tmv (v1, ublas::herm (m)); + std::cout << "tmv (v1, herm (m)) = " << v1 << std::endl; +#endif + + // _t_sv + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::lower_tag ()); + ublas::blas_2::tsv (v1, m, ublas::lower_tag ()); + std::cout << "tsv (v1, m) = " << v1 << " " << ublas::prod (m, v1) - v2 << std::endl; + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::upper_tag ()); + ublas::blas_2::tsv (v1, ublas::trans (m), ublas::lower_tag ()); + std::cout << "tsv (v1, trans (m)) = " << v1 << " " << ublas::prod (ublas::trans (m), v1) - v2 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::upper_tag ()); + ublas::blas_2::tsv (v1, ublas::herm (m), ublas::lower_tag ()); + std::cout << "tsv (v1, herm (m)) = " << v1 << " " << ublas::prod (ublas::herm (m), v1) - v2 << std::endl; +#endif + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::upper_tag ()); + ublas::blas_2::tsv (v1, m, ublas::upper_tag ()); + std::cout << "tsv (v1, m) = " << v1 << " " << ublas::prod (m, v1) - v2 << std::endl; + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::lower_tag ()); + ublas::blas_2::tsv (v1, ublas::trans (m), ublas::upper_tag ()); + std::cout << "tsv (v1, trans (m)) = " << v1 << " " << ublas::prod (ublas::trans (m), v1) - v2 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::lower_tag ()); + ublas::blas_2::tsv (v1, ublas::herm (m), ublas::upper_tag ()); + std::cout << "tsv (v1, herm (m)) = " << v1 << " " << ublas::prod (ublas::herm (m), v1) - v2 << std::endl; +#endif + + // _g_mv + // _s_mv + // _h_mv + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m); + ublas::blas_2::gmv (v1, value_type (1), value_type (1), m, v2); + std::cout << "gmv (v1, 1, 1, m, v2) = " << v1 << std::endl; + ublas::blas_2::gmv (v1, value_type (1), value_type (1), ublas::trans (m), v2); + std::cout << "gmv (v1, 1, 1, trans (m), v2) = " << v1 << std::endl; +#ifdef USE_STD_COMPLEX + ublas::blas_2::gmv (v1, value_type (1), value_type (1), ublas::herm (m), v2); + std::cout << "gmv (v1, 1, 1, herm (m), v2) = " << v1 << std::endl; +#endif + + // _g_r + // _g_ru + // _g_rc + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m); + ublas::blas_2::gr (m, value_type (1), v1, v2); + std::cout << "gr (m, 1, v1, v2) = " << m << std::endl; + ublas::blas_2::gr (m, value_type (1), v1, ublas::conj (v2)); + std::cout << "gr (m, 1, v1, conj (v2)) = " << m << std::endl; + + // _s_r + initialize_vector (v1); + initialize_matrix (m); + ublas::blas_2::sr (m, value_type (1), v1); + std::cout << "sr (m, 1, v1) = " << m << std::endl; + +#ifdef USE_STD_COMPLEX + // _h_r + initialize_vector (v1); + initialize_matrix (m); + ublas::blas_2::hr (m, value_type (1), v1); + std::cout << "hr (m, 1, v1) = " << m << std::endl; +#endif + + // _s_r2 + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m); + ublas::blas_2::sr2 (m, value_type (1), v1, v2); + std::cout << "sr2 (m, 1, v1, v2) = " << m << std::endl; + +#ifdef USE_STD_COMPLEX + // _h_r2 + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m); + ublas::blas_2::hr2 (m, value_type (1), v1, v2); + std::cout << "hr2 (m, 1, v1, v2) = " << m << std::endl; +#endif + } +} + +#ifdef USE_FLOAT +template struct test_blas_2, ublas::matrix, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_2, ublas::matrix, 3>; +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT +template struct test_blas_2 >, ublas::matrix >, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_2 >, ublas::matrix >, 3>; +#endif +#endif diff --git a/test/ublas_interop/test23.cpp b/test/ublas_interop/test23.cpp new file mode 100644 index 00000000..d56771c2 --- /dev/null +++ b/test/ublas_interop/test23.cpp @@ -0,0 +1,208 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test2.hpp" + +template +void test_blas_3::test () { + { + M m1 (N, N), m2 (N, N), m3 (N, N); + + // _t_mm + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), m2, m1); + std::cout << "tmm (m1, 1, m2, m1) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), m2, ublas::trans (m1)); + std::cout << "tmm (m1, 1, m2, trans (m1)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::trans (m2), m1); + std::cout << "tmm (m1, 1, trans (m2), m1) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::trans (m2), ublas::trans (m1)); + std::cout << "tmm (m1, 1, trans (m2), trans (m1)) = " << m1 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), m2, ublas::herm (m1)); + std::cout << "tmm (m1, 1, m2, herm (m1)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::herm (m2), m1); + std::cout << "tmm (m1, 1, herm (m2), m1) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::trans (m2), ublas::herm (m1)); + std::cout << "tmm (m1, 1, trans (m2), herm (m1)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::herm (m2), ublas::trans (m1)); + std::cout << "tmm (m1, 1, herm (m2), trans (m1)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::herm (m2), ublas::herm (m1)); + std::cout << "tmm (m1, 1, herm (m2), herm (m1)) = " << m1 << std::endl; +#endif + + // _t_sm + initialize_matrix (m1); + initialize_matrix (m2, ublas::lower_tag ()); + initialize_matrix (m3); + ublas::blas_3::tsm (m1, value_type (1), m2, ublas::lower_tag ()); + std::cout << "tsm (m1, 1, m2) = " << m1 << " " << ublas::prod (m2, m1) - value_type (1) * m3 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2, ublas::upper_tag ()); + ublas::blas_3::tsm (m1, value_type (1), ublas::trans (m2), ublas::lower_tag ()); + std::cout << "tsm (m1, 1, trans (m2)) = " << m1 << " " << ublas::prod (ublas::trans (m2), m1) - value_type (1) * m3 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_matrix (m1); + initialize_matrix (m2, ublas::upper_tag ()); + ublas::blas_3::tsm (m1, value_type (1), ublas::herm (m2), ublas::lower_tag ()); + std::cout << "tsm (m1, 1, herm (m2)) = " << m1 << " " << ublas::prod (ublas::herm (m2), m1) - value_type (1) * m3 << std::endl; +#endif + initialize_matrix (m1); + initialize_matrix (m2, ublas::upper_tag ()); + ublas::blas_3::tsm (m1, value_type (1), m2, ublas::upper_tag ()); + std::cout << "tsm (m1, 1, m2) = " << m1 << " " << ublas::prod (m2, m1) - value_type (1) * m3 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2, ublas::lower_tag ()); + ublas::blas_3::tsm (m1, value_type (1), ublas::trans (m2), ublas::upper_tag ()); + std::cout << "tsm (m1, 1, trans (m2)) = " << m1 << " " << ublas::prod (ublas::trans (m2), m1) - value_type (1) * m3 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_matrix (m1); + initialize_matrix (m2, ublas::lower_tag ()); + ublas::blas_3::tsm (m1, value_type (1), ublas::herm (m2), ublas::upper_tag ()); + std::cout << "tsm (m1, 1, herm (m2)) = " << m1 << " " << ublas::prod (ublas::herm (m2), m1) - value_type (1) * m3 << std::endl; +#endif + + // _g_mm + // _s_mm + // _h_mm + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), m2, m3); + std::cout << "gmm (m1, 1, 1, m2, m3) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::trans (m2), m3); + std::cout << "gmm (m1, 1, 1, trans (m2), m3) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), m2, ublas::trans (m3)); + std::cout << "gmm (m1, 1, 1, m2, trans (m3)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::trans (m2), ublas::trans (m3)); + std::cout << "gmm (m1, 1, 1, trans (m2), trans (m3)) = " << m1 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::herm (m2), m3); + std::cout << "gmm (m1, 1, 1, herm (m2), m3) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), m2, ublas::herm (m3)); + std::cout << "gmm (m1, 1, 1, m2, herm (m3)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::herm (m2), ublas::trans (m3)); + std::cout << "gmm (m1, 1, 1, herm (m2), trans (m3)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::trans (m2), ublas::herm (m3)); + std::cout << "gmm (m1, 1, 1, trans (m2), herm (m3)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::herm (m2), ublas::herm (m3)); + std::cout << "gmm (m1, 1, 1, herm (m2), herm (m3)) = " << m1 << std::endl; +#endif + + // s_rk + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::srk (m1, value_type (1), value_type (1), m2); + std::cout << "srk (m1, 1, 1, m2) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::srk (m1, value_type (1), value_type (1), ublas::trans (m2)); + std::cout << "srk (m1, 1, 1, trans (m2)) = " << m1 << std::endl; + +#ifdef USE_STD_COMPLEX + // h_rk + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::hrk (m1, value_type (1), value_type (1), m2); + std::cout << "hrk (m1, 1, 1, m2) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::hrk (m1, value_type (1), value_type (1), ublas::herm (m2)); + std::cout << "hrk (m1, 1, 1, herm (m2)) = " << m1 << std::endl; +#endif + + // s_r2k + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::sr2k (m1, value_type (1), value_type (1), m2, m3); + std::cout << "sr2k (m1, 1, 1, m2, m3) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::sr2k (m1, value_type (1), value_type (1), ublas::trans (m2), ublas::trans (m3)); + std::cout << "sr2k (m1, 1, 1, trans (m2), trans (m3)) = " << m1 << std::endl; + +#ifdef USE_STD_COMPLEX + // h_r2k + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::hr2k (m1, value_type (1), value_type (1), m2, m3); + std::cout << "hr2k (m1, 1, 1, m2, m3) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::hr2k (m1, value_type (1), value_type (1), ublas::herm (m2), ublas::herm (m3)); + std::cout << "hr2k (m1, 1, 1, herm (m2), herm (m3)) = " << m1 << std::endl; +#endif + } +} + +#ifdef USE_FLOAT +template struct test_blas_3, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_3, 3>; +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT +template struct test_blas_3 >, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_3 >, 3>; +#endif +#endif diff --git a/test/ublas_interop/test3.cpp b/test/ublas_interop/test3.cpp new file mode 100644 index 00000000..fb2b94da --- /dev/null +++ b/test/ublas_interop/test3.cpp @@ -0,0 +1,20 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test3.hpp" + +int main () { + test_vector (); + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/test/ublas_interop/test3.hpp b/test/ublas_interop/test3.hpp new file mode 100644 index 00000000..032b029c --- /dev/null +++ b/test/ublas_interop/test3.hpp @@ -0,0 +1,63 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST3_H +#define TEST3_H + +#ifdef _MSC_VER +# pragma warning(disable:4800 4996) +#endif + +#include + +typedef boost::multiprecision::mp_number, false> mp_test_type; +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + +#include + +#include +#include +#include +#include +#include +#include +#include +#ifdef USE_GENERALIZED_VECTOR_OF_VECTOR +#include +#endif +#include + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +void test_vector (); +void test_matrix_vector (); +void test_matrix (); + +#endif diff --git a/test/ublas_interop/test31.cpp b/test/ublas_interop/test31.cpp new file mode 100644 index 00000000..a1484cfd --- /dev/null +++ b/test/ublas_interop/test31.cpp @@ -0,0 +1,248 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test3.hpp" + +// Test vector expression templates +template +struct test_my_vector { + typedef typename V::value_type value_type; + typedef typename V::size_type size_type; + typedef typename ublas::type_traits::real_type real_type; + + template + void test_with (VP &v1, VP &v2, VP &v3) const { + { + value_type t; + size_type i; + real_type n; + + // Default Construct + default_construct::test (); + + // Copy and swap + initialize_vector (v1); + initialize_vector (v2); + v1 = v2; + std::cout << "v1 = v2 = " << v1 << std::endl; + v1.assign_temporary (v2); + std::cout << "v1.assign_temporary (v2) = " << v1 << std::endl; + v1.swap (v2); + std::cout << "v1.swap (v2) = " << v1 << " " << v2 << std::endl; + + // Zero assignment + v1 = ublas::zero_vector<> (v1.size ()); + std::cout << "v1.zero_vector = " << v1 << std::endl; + v1 = v2; + +#ifndef BOOST_NO_FUNCTION_TEMPLATE_ORDERING + // Project range and slice + initialize_vector (v1); + initialize_vector (v2); + project (v1, ublas::range(0,1)) = project (v2, ublas::range(0,1)); + project (v1, ublas::range(0,1)) = project (v2, ublas::slice(0,1,1)); + project (v1, ublas::slice(2,-1,2)) = project (v2, ublas::slice(0,1,2)); + project (v1, ublas::slice(2,-1,2)) = project (v2, ublas::range(0,2)); + std::cout << "v1 = range/slice " << v1 << std::endl; +#endif + + // Unary vector operations resulting in a vector + initialize_vector (v1); + v2 = - v1; + std::cout << "- v1 = " << v2 << std::endl; + v2 = ublas::conj (v1); + std::cout << "conj (v1) = " << v2 << std::endl; + + // Binary vector operations resulting in a vector + initialize_vector (v1); + initialize_vector (v2); + initialize_vector (v3); + v3 = v1 + v2; + std::cout << "v1 + v2 = " << v3 << std::endl; + + v3 = v1 - v2; + std::cout << "v1 - v2 = " << v3 << std::endl; + + // Scaling a vector + t = N; + initialize_vector (v1); + v2 = value_type (1.) * v1; + std::cout << "1. * v1 = " << v2 << std::endl; + v2 = t * v1; + std::cout << "N * v1 = " << v2 << std::endl; + initialize_vector (v1); + v2 = v1 * value_type (1.); + std::cout << "v1 * 1. = " << v2 << std::endl; + v2 = v1 * t; + std::cout << "v1 * N = " << v2 << std::endl; + + // Some assignments + initialize_vector (v1); + initialize_vector (v2); + v2 += v1; + std::cout << "v2 += v1 = " << v2 << std::endl; + v2 -= v1; + std::cout << "v2 -= v1 = " << v2 << std::endl; + v2 = v2 + v1; + std::cout << "v2 = v2 + v1 = " << v2 << std::endl; + v2 = v2 - v1; + std::cout << "v2 = v2 - v1 = " << v2 << std::endl; + v1 *= value_type (1.); + std::cout << "v1 *= 1. = " << v1 << std::endl; + v1 *= t; + std::cout << "v1 *= N = " << v1 << std::endl; + + // Unary vector operations resulting in a scalar + initialize_vector (v1); + t = ublas::sum (v1); + std::cout << "sum (v1) = " << t << std::endl; + n = ublas::norm_1 (v1); + std::cout << "norm_1 (v1) = " << n << std::endl; + n = ublas::norm_2 (v1); + std::cout << "norm_2 (v1) = " << n << std::endl; + n = ublas::norm_inf (v1); + std::cout << "norm_inf (v1) = " << n << std::endl; + + i = ublas::index_norm_inf (v1); + std::cout << "index_norm_inf (v1) = " << i << std::endl; + + // Binary vector operations resulting in a scalar + initialize_vector (v1); + initialize_vector (v2); + t = ublas::inner_prod (v1, v2); + std::cout << "inner_prod (v1, v2) = " << t << std::endl; + } + } + void operator () () const { + { + V v1 (N, N), v2 (N, N), v3 (N, N); + test_with (v1, v2, v3); + +#ifdef USE_RANGE + ublas::vector_range vr1 (v1, ublas::range (0, N)), + vr2 (v2, ublas::range (0, N)), + vr3 (v3, ublas::range (0, N)); + test_with (vr1, vr2, vr3); +#endif + +#ifdef USE_SLICE + ublas::vector_slice vs1 (v1, ublas::slice (0, 1, N)), + vs2 (v2, ublas::slice (0, 1, N)), + vs3 (v3, ublas::slice (0, 1, N)); + test_with (vs1, vs2, vs3); +#endif + } + } +}; + +// Test vector +void test_vector () { + std::cout << "test_vector" << std::endl; + +#ifdef USE_SPARSE_VECTOR +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, map_array" << std::endl; + test_my_vector >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, map_array" << std::endl; + test_my_vector >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, map_array" << std::endl; + test_my_vector, ublas::map_array > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, map_array" << std::endl; + test_my_vector, ublas::map_array > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::map" << std::endl; + test_my_vector >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::map" << std::endl; + test_my_vector >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::map" << std::endl; + test_my_vector, std::map > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::map" << std::endl; + test_my_vector, std::map > > , 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_COMPRESSED_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type compressed" << std::endl; + test_my_vector, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double compressed" << std::endl; + test_my_vector, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex compressed" << std::endl; + test_my_vector >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex compressed" << std::endl; + test_my_vector >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_COORDINATE_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type coordinate" << std::endl; + test_my_vector, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double coordinate" << std::endl; + test_my_vector, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex coordinate" << std::endl; + test_my_vector >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex coordinate" << std::endl; + test_my_vector >, 3 > () (); +#endif +#endif +#endif +} diff --git a/test/ublas_interop/test32.cpp b/test/ublas_interop/test32.cpp new file mode 100644 index 00000000..7240b4ce --- /dev/null +++ b/test/ublas_interop/test32.cpp @@ -0,0 +1,324 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test3.hpp" + +// Test matrix & vector expression templates +template +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template + void test_with (VP &v1, VP &v2, MP &m1) const { + { + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v1 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v1 << std::endl; + v1 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v1 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; + } + } + void operator () () const { + { + V v1 (N, N), v2 (N, N); + M m1 (N, N, N * N); + + test_with (v1, v2, m1); + + ublas::matrix_row mr1 (m1, 0), mr2 (m1, N - 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column mc1 (m1, 0), mc2 (m1, N - 1); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_SPARSE_MATRIX +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, map_array" << std::endl; + test_my_matrix_vector >, + ublas::mapped_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, map_array" << std::endl; + test_my_matrix_vector >, + ublas::mapped_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, map_array" << std::endl; + test_my_matrix_vector, ublas::map_array > >, + ublas::mapped_matrix, ublas::row_major, ublas::map_array > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, map_array" << std::endl; + test_my_matrix_vector, ublas::map_array > >, + ublas::mapped_matrix, ublas::row_major, ublas::map_array > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::map" << std::endl; + test_my_matrix_vector >, + ublas::mapped_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::map" << std::endl; + test_my_matrix_vector >, + ublas::mapped_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::map" << std::endl; + test_my_matrix_vector, std::map > >, + ublas::mapped_matrix, ublas::row_major, std::map > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::map" << std::endl; + test_my_matrix_vector, std::map > >, + ublas::mapped_matrix, ublas::row_major, std::map > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_SPARSE_VECTOR_OF_SPARSE_VECTOR +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_vector map_array" << std::endl; + test_my_matrix_vector >, + ublas::mapped_vector > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_vector map_array" << std::endl; + test_my_matrix_vector >, + ublas::mapped_vector > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, mapped_vector map_array" << std::endl; + test_my_matrix_vector, ublas::map_array > >, + ublas::mapped_vector, ublas::row_major, ublas::map_array > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex,mapped_vector map_array" << std::endl; + test_my_matrix_vector, ublas::map_array > >, + ublas::mapped_vector, ublas::row_major, ublas::map_array > > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_vector std::map" << std::endl; + test_my_matrix_vector >, + ublas::mapped_vector > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_vector std::map" << std::endl; + test_my_matrix_vector >, + ublas::mapped_vector > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, mapped_vector std::map" << std::endl; + test_my_matrix_vector, std::map > >, + ublas::mapped_vector, ublas::row_major, std::map > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, mapped_vector std::map" << std::endl; + test_my_matrix_vector, std::map > >, + ublas::mapped_vector, ublas::row_major, std::map > > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_GENERALIZED_VECTOR_OF_VECTOR +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix_vector >, + ublas::generalized_vector_of_vector > > >, 3 > () (); + test_my_matrix_vector >, + ublas::generalized_vector_of_vector >, ublas::map_array > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix_vector >, + ublas::generalized_vector_of_vector > > >, 3 > () (); + test_my_matrix_vector >, + ublas::generalized_vector_of_vector >, ublas::map_array > > > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix_vector, ublas::map_array > >, + ublas::generalized_vector_of_vector, ublas::row_major, ublas::vector, ublas::map_array > > > >, 3 > () (); + test_my_matrix_vector, ublas::map_array > >, + ublas::generalized_vector_of_vector, ublas::row_major, ublas::mapped_vector, ublas::map_array > >, ublas::map_array, ublas::map_array > > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix_vector, ublas::map_array > >, + ublas::generalized_vector_of_vector, ublas::row_major, ublas::vector, ublas::map_array > > > >, 3 > () (); + test_my_matrix_vector, ublas::map_array > >, + ublas::generalized_vector_of_vector, ublas::row_major, ublas::mapped_vector, ublas::map_array > >, ublas::map_array, ublas::map_array > > > > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix_vector >, + ublas::generalized_vector_of_vector > > >, 3 > () (); + test_my_matrix_vector >, + ublas::generalized_vector_of_vector >, std::map > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix_vector >, + ublas::generalized_vector_of_vector > > >, 3 > () (); + test_my_matrix_vector >, + ublas::generalized_vector_of_vector >, std::map > > > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix_vector, std::map > >, + ublas::generalized_vector_of_vector, ublas::row_major, ublas::vector, std::map > > > >, 3 > () (); + test_my_matrix_vector, std::map > >, + ublas::generalized_vector_of_vector, ublas::row_major, ublas::mapped_vector, std::map > >, std::map, std::map > > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix_vector, std::map > >, + ublas::generalized_vector_of_vector, ublas::row_major, ublas::vector, std::map > > > >, 3 > () (); + test_my_matrix_vector, std::map > >, + ublas::generalized_vector_of_vector, ublas::row_major, ublas::mapped_vector, std::map > >, std::map, std::map > > > > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_COMPRESSED_MATRIX +#ifdef USE_FLOAT + std::cout << "mp_test_type compressed" << std::endl; + test_my_matrix_vector, + ublas::compressed_matrix, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double compressed" << std::endl; + test_my_matrix_vector, + ublas::compressed_matrix, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex compressed" << std::endl; + test_my_matrix_vector >, + ublas::compressed_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex compressed" << std::endl; + test_my_matrix_vector >, + ublas::compressed_matrix >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_COORDINATE_MATRIX +#ifdef USE_FLOAT + std::cout << "mp_test_type coordinate" << std::endl; + test_my_matrix_vector, + ublas::coordinate_matrix, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double coordinate" << std::endl; + test_my_matrix_vector, + ublas::coordinate_matrix, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex coordinate" << std::endl; + test_my_matrix_vector >, + ublas::coordinate_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex coordinate" << std::endl; + test_my_matrix_vector >, + ublas::coordinate_matrix >, 3 > () (); +#endif +#endif +#endif +} diff --git a/test/ublas_interop/test33.cpp b/test/ublas_interop/test33.cpp new file mode 100644 index 00000000..46d73519 --- /dev/null +++ b/test/ublas_interop/test33.cpp @@ -0,0 +1,347 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test3.hpp" + +// Test matrix expression templates +template +struct test_my_matrix { + typedef typename M::value_type value_type; + + template + void test_with (MP &m1, MP &m2, MP &m3) const { + { + value_type t; + + // Default Construct + default_construct::test (); + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + +#ifndef BOOST_NO_FUNCTION_TEMPLATE_ORDERING + // Project range and slice + initialize_matrix (m1); + initialize_matrix (m2); + project (m1, ublas::range(0,1),ublas::range(0,1)) = project (m2, ublas::range(0,1),ublas::range(0,1)); + project (m1, ublas::range(0,1),ublas::range(0,1)) = project (m2, ublas::slice(0,1,1),ublas::slice(0,1,1)); + project (m1, ublas::slice(2,-1,2),ublas::slice(2,-1,2)) = project (m2, ublas::slice(0,1,2),ublas::slice(0,1,2)); + project (m1, ublas::slice(2,-1,2),ublas::slice(2,-1,2)) = project (m2, ublas::range(0,2),ublas::range(0,2)); + std::cout << "m1 = range/slice " << m1 << std::endl; +#endif + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m2 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + m2 = ublas::trans (m1); + std::cout << "trans (m1) = " << m2 << std::endl; + + // Hermitean + initialize_matrix (m1); + m2 = ublas::herm (m1); + std::cout << "herm (m1) = " << m2 << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + m3 = ublas::prod (m1, m2); + std::cout << "prod (m1, m2) = " << m3 << std::endl; + } + } + void operator () () const { + { + M m1 (N, N, N * N), m2 (N, N, N * N), m3 (N, N, N * N); + test_with (m1, m2, m3); + +#ifdef USE_RANGE + ublas::matrix_range mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_SPARSE_MATRIX +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_matrix map_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_matrix map_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, mapped_matrix map_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::map_array > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, mapped_matrix map_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::map_array > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_matrix std::map" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_matrix std::map" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, mapped_matrix std::map" << std::endl; + test_my_matrix, ublas::row_major, std::map > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, mapped_matrix std::map" << std::endl; + test_my_matrix, ublas::row_major, std::map > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_SPARSE_VECTOR_OF_SPARSE_VECTOR +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_vector_of_mapped_vector map_array" << std::endl; + test_my_matrix > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_vector_of_mapped_vector map_array" << std::endl; + test_my_matrix > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, mapped_vector_of_mapped_vector map_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::map_array > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, mapped_vector_of_mapped_vectormap_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::map_array > > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_vector_of_mapped_vector std::map" << std::endl; + test_my_matrix > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_vector_of_mapped_vector std::map" << std::endl; + test_my_matrix > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, mapped_vector_of_mapped_vector std::map" << std::endl; + test_my_matrix, ublas::row_major, std::map > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, mapped_vector_of_mapped_vector std::map" << std::endl; + test_my_matrix, ublas::row_major, std::map > > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_GENERALIZED_VECTOR_OF_VECTOR +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type,generalized_vector_of_vector map_array" << std::endl; + test_my_matrix > > >, 3 > () (); + test_my_matrix >, ublas::map_array > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix > > >, 3 > () (); + test_my_matrix >, ublas::map_array > > > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::vector, ublas::map_array > > > >, 3 > () (); + test_my_matrix, ublas::row_major, ublas::mapped_vector, ublas::map_array > >, ublas::map_array, ublas::map_array > > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::vector, ublas::map_array > > > >, 3 > () (); + test_my_matrix, ublas::row_major, ublas::mapped_vector, ublas::map_array > >, ublas::map_array, ublas::map_array > > > > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix > > >, 3 > () (); + test_my_matrix >, std::map > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix > > >, 3 > () (); + test_my_matrix >, std::map > > > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix, ublas::row_major, ublas::vector, std::map > > > >, 3 > () (); + test_my_matrix, ublas::row_major, ublas::mapped_vector, std::map > >, std::map, std::map > > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix, ublas::row_major, ublas::vector, std::map > > > >, 3 > () (); + test_my_matrix, ublas::row_major, ublas::mapped_vector, std::map > >, std::map, std::map > > > > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_COMPRESSED_MATRIX +#ifdef USE_FLOAT + std::cout << "mp_test_type compressed_matrix" << std::endl; + test_my_matrix, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double compressed_matrix" << std::endl; + test_my_matrix, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex compressed_matrix" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex compressed_matrix" << std::endl; + test_my_matrix >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_COORDINATE_MATRIX +#ifdef USE_FLOAT + std::cout << "mp_test_type coordinate_matrix" << std::endl; + test_my_matrix, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double coordinate_matrix" << std::endl; + test_my_matrix, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex coordinate_matrix" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex coordinate_matrix" << std::endl; + test_my_matrix >, 3 > () (); +#endif +#endif +#endif +} diff --git a/test/ublas_interop/test4.cpp b/test/ublas_interop/test4.cpp new file mode 100644 index 00000000..bf5816f5 --- /dev/null +++ b/test/ublas_interop/test4.cpp @@ -0,0 +1,19 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test4.hpp" + +int main () { + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/test/ublas_interop/test4.hpp b/test/ublas_interop/test4.hpp new file mode 100644 index 00000000..fc5b48cb --- /dev/null +++ b/test/ublas_interop/test4.hpp @@ -0,0 +1,39 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST4_H +#define TEST4_H + +#include + +#include +#include +#include +#include +#include + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +//#define USE_BANDED +#define USE_DIAGONAL + + +void test_matrix_vector (); +void test_matrix (); + + +// FIXME slice are failing in assignment to zero elements +#undef USE_SLICE + +#endif diff --git a/test/ublas_interop/test42.cpp b/test/ublas_interop/test42.cpp new file mode 100644 index 00000000..325d8094 --- /dev/null +++ b/test/ublas_interop/test42.cpp @@ -0,0 +1,361 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test4.hpp" + +// Test matrix & vector expression templates +template +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template + void test_with (VP &v1, VP &v2, MP &m1) const { + { +#ifndef USE_DIAGONAL + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v2 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v2 << std::endl; + v2 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v2 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + v1 (0) = 0; + v1 (N - 1) = 0; + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; +#endif + } + } + void operator () () const { + { + V v1 (N), v2 (N); +#ifdef USE_BANDED + M m1 (N, N, 1, 1); +#endif +#ifdef USE_DIAGONAL + M m1 (N, N); +#endif + test_with (v1, v2, m1); + + ublas::matrix_row mr1 (m1, 1), mr2 (m1, 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column mc1 (m1, 1), mc2 (m1, 1); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } + + void operator () (int) const { +#ifdef USE_ADAPTOR + { +#ifdef USE_BANDED + V v1 (N), v2 (N); + M m1 (N, N, 1, 1); + ublas::banded_adaptor bam1 (m1, 1, 1); + test_with (v1, v2, bam1); + + ublas::matrix_row > mr1 (bam1, 1), mr2 (bam1, 1); + test_with (mr1, mr2, bam1); + + ublas::matrix_column > mc1 (bam1, 1), mc2 (bam1, 1); + test_with (mc1, mc2, bam1); + +#ifdef USE_RANGE + ublas::matrix_vector_range > mvr1 (bam1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (bam1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, bam1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice > mvs1 (bam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (bam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, bam1); +#endif +#endif +#ifdef USE_DIAGONAL + V v1 (N), v2 (N); + M m1 (N, N); + ublas::diagonal_adaptor dam1 (m1); + test_with (v1, v2, dam1); + + ublas::matrix_row > mr1 (dam1, 1), mr2 (dam1, 1); + test_with (mr1, mr2, dam1); + + ublas::matrix_column > mc1 (dam1, 1), mc2 (dam1, 1); + test_with (mc1, mc2, dam1); + +#ifdef USE_RANGE + ublas::matrix_vector_range > mvr1 (dam1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (dam1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, dam1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice > mvs1 (dam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (dam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, dam1); +#endif +#endif + } +#endif + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_BANDED +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::banded_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::banded_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::banded_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::banded_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::banded_matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (); + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::banded_matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::banded_matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (); + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::banded_matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::banded_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::banded_matrix, ublas::row_major, std::vector > >, 3> () (); + test_my_matrix_vector, std::vector > >, + ublas::banded_matrix, ublas::row_major, std::vector > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::banded_matrix, ublas::row_major, std::vector > >, 3> () (); + test_my_matrix_vector, std::vector > >, + ublas::banded_matrix, ublas::row_major, std::vector > >, 3> () (0); +#endif +#endif +#endif +#endif + +#ifdef USE_DIAGONAL +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::diagonal_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::diagonal_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::diagonal_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::diagonal_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::diagonal_matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (); + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::diagonal_matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::diagonal_matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (); + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::diagonal_matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::diagonal_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::diagonal_matrix, ublas::row_major, std::vector > >, 3> () (); + test_my_matrix_vector, std::vector > >, + ublas::diagonal_matrix, ublas::row_major, std::vector > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::diagonal_matrix, ublas::row_major, std::vector > >, 3> () (); + test_my_matrix_vector, std::vector > >, + ublas::diagonal_matrix, ublas::row_major, std::vector > >, 3> () (0); +#endif +#endif +#endif +#endif +} diff --git a/test/ublas_interop/test43.cpp b/test/ublas_interop/test43.cpp new file mode 100644 index 00000000..82682c97 --- /dev/null +++ b/test/ublas_interop/test43.cpp @@ -0,0 +1,326 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test4.hpp" + +// Test matrix expression templates +template +struct test_my_matrix { + typedef typename M::value_type value_type; + + template + void test_with (MP &m1, MP &m2, MP &m3) const { + { + value_type t; + + // Default Construct + default_construct::test (); + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m2 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + m2 = ublas::trans (m1); + std::cout << "trans (m1) = " << m2 << std::endl; + + // Hermitean + initialize_matrix (m1); + m2 = ublas::herm (m1); + std::cout << "herm (m1) = " << m2 << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + // Banded times banded isn't banded + std::cout << "prod (m1, m2) = " << ublas::prod (m1, m2) << std::endl; + } + } + void operator () () const { + { +#ifdef USE_BANDED + M m1 (N, N, 1, 1), m2 (N, N, 1, 1), m3 (N, N, 1, 1); +#endif +#ifdef USE_DIAGONAL + M m1 (N, N), m2 (N, N), m3 (N, N); +#endif + test_with (m1, m2, m3); + +#ifdef USE_RANGE + ublas::matrix_range mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } + +#ifdef USE_ADAPTOR + { +#ifdef USE_BANDED + M m1 (N, N, 1, 1), m2 (N, N, 1, 1), m3 (N, N, 1, 1); + ublas::banded_adaptor bam1 (m1, 1, 1), bam2 (m2, 1, 1), bam3 (m3, 1, 1); + test_with (bam1, bam2, bam3); + +#ifdef USE_RANGE + ublas::matrix_range > mr1 (bam1, ublas::range (0, N), ublas::range (0, N)), + mr2 (bam2, ublas::range (0, N), ublas::range (0, N)), + mr3 (bam3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice > ms1 (bam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (bam2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (bam3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif +#endif +#ifdef USE_DIAGONAL + M m1 (N, N), m2 (N, N), m3 (N, N); + ublas::diagonal_adaptor dam1 (m1), dam2 (m2), dam3 (m3); + test_with (dam1, dam2, dam3); + +#ifdef USE_RANGE + ublas::matrix_range > mr1 (dam1, ublas::range (0, N), ublas::range (0, N)), + mr2 (dam2, ublas::range (0, N), ublas::range (0, N)), + mr3 (dam3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice > ms1 (dam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (dam2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (dam3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif +#endif + } +#endif + + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_BANDED +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_DIAGONAL +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > >, 3 > () (); +#endif +#endif +#endif +#endif +} diff --git a/test/ublas_interop/test5.cpp b/test/ublas_interop/test5.cpp new file mode 100644 index 00000000..548cd603 --- /dev/null +++ b/test/ublas_interop/test5.cpp @@ -0,0 +1,19 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test5.hpp" + +int main () { + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/test/ublas_interop/test5.hpp b/test/ublas_interop/test5.hpp new file mode 100644 index 00000000..a13dfa2e --- /dev/null +++ b/test/ublas_interop/test5.hpp @@ -0,0 +1,35 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST5_H +#define TEST5_H + +#include + +#include +#include +#include +#include +#include + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +void test_matrix_vector (); +void test_matrix (); + + +// FIXME slice are failing in assignment to zero elements +#undef USE_SLICE + +#endif diff --git a/test/ublas_interop/test52.cpp b/test/ublas_interop/test52.cpp new file mode 100644 index 00000000..9e13dfde --- /dev/null +++ b/test/ublas_interop/test52.cpp @@ -0,0 +1,214 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test5.hpp" + +// Test matrix & vector expression templates +template +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template + void test_with (VP &v1, VP &v2, MP &m1) const { + { + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v2 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v2 << std::endl; + v2 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v2 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + v1 (0) = 0; + v2 (N - 1) = 0; + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; + } + } + void operator () () const { + { + V v1 (N), v2 (N); + M m1 (N, N); + test_with (v1, v2, m1); + + ublas::matrix_row mr1 (m1, N - 1), mr2 (m1, N - 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column mc1 (m1, 0), mc2 (m1, 0); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } + + void operator () (int) const { +#ifdef USE_ADAPTOR + { + V v1 (N), v2 (N); + M m1 (N, N); + ublas::triangular_adaptor tam1 (m1); + test_with (v1, v2, tam1); + + ublas::matrix_row > mr1 (tam1, N - 1), mr2 (tam1, N - 1); + test_with (mr1, mr2, tam1); + + ublas::matrix_column > mc1 (tam1, 0), mc2 (tam1, 0); + test_with (mc1, mc2, tam1); + +#ifdef USE_RANGE + ublas::matrix_vector_range > mvr1 (tam1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (tam1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, tam1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice > mvs1 (tam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (tam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, tam1); +#endif + } +#endif + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3> () (); + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3> () (); + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::triangular_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, std::vector > >, 3> () (); + test_my_matrix_vector, std::vector > >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, std::vector > >, 3> () (0); + + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, std::vector > >, 3> () (); + test_my_matrix_vector, std::vector > >, + ublas::triangular_matrix, ublas::lower, ublas::row_major, std::vector > >, 3> () (0); +#endif +#endif +#endif +} diff --git a/test/ublas_interop/test53.cpp b/test/ublas_interop/test53.cpp new file mode 100644 index 00000000..041be1f5 --- /dev/null +++ b/test/ublas_interop/test53.cpp @@ -0,0 +1,223 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test5.hpp" + +// Test matrix expression templates +template +struct test_my_matrix { + typedef typename M::value_type value_type; + + template + void test_with (MP &m1, MP &m2, MP &m3) const { + { + value_type t; + + // Default Construct + default_construct::test (); + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m2 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + // Transpose of a triangular isn't triangular of the same kind + std::cout << "trans (m1) = " << ublas::trans (m1) << std::endl; + + // Hermitian + initialize_matrix (m1); + // Hermitian of a triangular isn't hermitian of the same kind + std::cout << "herm (m1) = " << ublas::herm (m1) << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + m3 = ublas::prod (m1, m2); + std::cout << "prod (m1, m2) = " << m3 << std::endl; + } + } + void operator () () const { + { + M m1 (N, N), m2 (N, N), m3 (N, N); + test_with (m1, m2, m3); + +#ifdef USE_RANGE + ublas::matrix_range mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } + +#ifdef USE_ADAPTOR + { + M m1 (N, N), m2 (N, N), m3 (N, N); + ublas::triangular_adaptor tam1 (m1), tam2 (m2), tam3 (m3); + test_with (tam1, tam2, tam3); + +#ifdef USE_RANGE + ublas::matrix_range > mr1 (tam1, ublas::range (0, N), ublas::range (0, N)), + mr2 (tam2, ublas::range (0, N), ublas::range (0, N)), + mr3 (tam3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice > ms1 (tam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (tam2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (tam3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } +#endif + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, std::vector > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE +std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, std::vector > >, 3 > () (); +#endif +#endif +#endif +} diff --git a/test/ublas_interop/test6.cpp b/test/ublas_interop/test6.cpp new file mode 100644 index 00000000..61a5c310 --- /dev/null +++ b/test/ublas_interop/test6.cpp @@ -0,0 +1,19 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test6.hpp" + +int main () { + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/test/ublas_interop/test6.hpp b/test/ublas_interop/test6.hpp new file mode 100644 index 00000000..766d6b92 --- /dev/null +++ b/test/ublas_interop/test6.hpp @@ -0,0 +1,32 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST6_H +#define TEST6_H + +#include + +#include +#include +#include +#include +#include + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +void test_matrix_vector (); +void test_matrix (); + + +#endif diff --git a/test/ublas_interop/test62.cpp b/test/ublas_interop/test62.cpp new file mode 100644 index 00000000..a7529d29 --- /dev/null +++ b/test/ublas_interop/test62.cpp @@ -0,0 +1,218 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test6.hpp" + +// Test matrix & vector expression templates +template +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template + void test_with (VP &v1, VP &v2, MP &m1) const { + { + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v2 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v2 << std::endl; + v2 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v2 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + v1 (0) = 0; + v1 (N - 1) = 0; + v2 (0) = 0; + v2 (N - 1) = 0; + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; + } + } + void operator () () const { + { + V v1 (N), v2 (N); + M m1 (N, N); + test_with (v1, v2, m1); + + ublas::matrix_row mr1 (m1, N - 1), mr2 (m1, N - 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column mc1 (m1, 0), mc2 (m1, 0); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } + + void operator () (int) const { +#ifdef USE_ADAPTOR + { + V v1 (N), v2 (N); + M m1 (N, N); + ublas::symmetric_adaptor tam1 (m1); + test_with (v1, v2, tam1); + + ublas::matrix_row > mr1 (tam1, N - 1), mr2 (tam1, N - 1); + test_with (mr1, mr2, tam1); + + ublas::matrix_column > mc1 (tam1, 0), mc2 (tam1, 0); + test_with (mc1, mc2, tam1); + +#ifdef USE_RANGE + ublas::matrix_vector_range > mvr1 (tam1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (tam1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, tam1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice > mvs1 (tam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (tam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, tam1); +#endif + } +#endif + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3> () (); + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3> () (); + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (); + test_my_matrix_vector >, + ublas::symmetric_matrix >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, std::vector > >, 3> () (); + test_my_matrix_vector, std::vector > >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, std::vector > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, std::vector > >, 3> () (); + test_my_matrix_vector, std::vector > >, + ublas::symmetric_matrix, ublas::lower, ublas::row_major, std::vector > >, 3> () (0); +#endif +#endif +#endif +} diff --git a/test/ublas_interop/test63.cpp b/test/ublas_interop/test63.cpp new file mode 100644 index 00000000..d36f09c1 --- /dev/null +++ b/test/ublas_interop/test63.cpp @@ -0,0 +1,223 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test6.hpp" + +// Test matrix expression templates +template +struct test_my_matrix { + typedef typename M::value_type value_type; + + template + void test_with (MP &m1, MP &m2, MP &m3) const { + { + value_type t; + + // Default Construct + default_construct::test (); + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m1 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + m2 = ublas::trans (m1); + std::cout << "trans (m1) = " << m2 << std::endl; + + // Hermitean + initialize_matrix (m1); + m2 = ublas::herm (m1); + std::cout << "herm (m1) = " << m2 << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + m3 = ublas::prod (m1, m2); + std::cout << "prod (m1, m2) = " << m3 << std::endl; + } + } + void operator () () const { + { + M m1 (N, N), m2 (N, N), m3 (N, N); + test_with (m1, m2, m3); + +#ifdef USE_RANGE + ublas::matrix_range mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } + +#ifdef USE_ADAPTOR + { + M m1 (N, N), m2 (N, N), m3 (N, N); + ublas::symmetric_adaptor sam1 (m1), sam2 (m2), sam3 (m3); + test_with (sam1, sam2, sam3); + +#ifdef USE_RANGE + ublas::matrix_range > mr1 (sam1, ublas::range (0, N), ublas::range (0, N)), + mr2 (sam2, ublas::range (0, N), ublas::range (0, N)), + mr3 (sam3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice > ms1 (sam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (sam2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (sam3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } +#endif + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, ublas::unbounded_array > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, std::vector > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::lower, ublas::row_major, std::vector > >, 3 > () (); +#endif +#endif +#endif +} diff --git a/test/ublas_interop/test7.cpp b/test/ublas_interop/test7.cpp new file mode 100644 index 00000000..f564031c --- /dev/null +++ b/test/ublas_interop/test7.cpp @@ -0,0 +1,31 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include + +#include +#include + +#include +#include +#include + +#include "test7.hpp" + +// this testcase requires fix of task #2473 + +int main () { + test_vector (); + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/test/ublas_interop/test7.hpp b/test/ublas_interop/test7.hpp new file mode 100644 index 00000000..5dbae1fc --- /dev/null +++ b/test/ublas_interop/test7.hpp @@ -0,0 +1,36 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST7_H +#define TEST7_H + +#include + +#include +#include + +#include +#include +#include +#include +#include + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +void test_vector (); +void test_matrix_vector (); +void test_matrix (); + + +#endif diff --git a/test/ublas_interop/test71.cpp b/test/ublas_interop/test71.cpp new file mode 100644 index 00000000..4639b139 --- /dev/null +++ b/test/ublas_interop/test71.cpp @@ -0,0 +1,170 @@ +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test7.hpp" + +// Test vector expression templates +template +struct test_my_vector { + typedef typename V::value_type value_type; + typedef typename V::size_type size_type; + typedef typename ublas::type_traits::real_type real_type; + + template + void test_with (VP &v1, VP &v2, VP &v3) const { + { + value_type t; + size_type i; + real_type n; + + // Copy and swap + initialize_vector (v1); + initialize_vector (v2); + v1 = v2; + std::cout << "v1 = v2 = " << v1 << std::endl; + v1.assign_temporary (v2); + std::cout << "v1.assign_temporary (v2) = " << v1 << std::endl; + v1.swap (v2); + std::cout << "v1.swap (v2) = " << v1 << " " << v2 << std::endl; + + // Zero assignment + v1 = ublas::zero_vector (v1.size ()); + std::cout << "v1.zero_vector = " << v1 << std::endl; + v1 = v2; + + // Unary vector operations resulting in a vector + initialize_vector (v1); + v2 = - v1; + std::cout << "- v1 = " << v2 << std::endl; + v2 = ublas::conj (v1); + std::cout << "conj (v1) = " << v2 << std::endl; + + // Binary vector operations resulting in a vector + initialize_vector (v1); + initialize_vector (v2); + v3 = v1 + v2; + std::cout << "v1 + v2 = " << v3 << std::endl; + + v3 = v1 - v2; + std::cout << "v1 - v2 = " << v3 << std::endl; + + // Scaling a vector + t = value_type (N); + initialize_vector (v1); + v2 = value_type (1.) * v1; + std::cout << "1. * v1 = " << v2 << std::endl; +// v2 = t * v1; + std::cout << "N * v1 = " << v2 << std::endl; + initialize_vector (v1); +// v2 = v1 * value_type (1.); + std::cout << "v1 * 1. = " << v2 << std::endl; +// v2 = v1 * t; + std::cout << "v1 * N = " << v2 << std::endl; + + // Some assignments + initialize_vector (v1); + initialize_vector (v2); + v2 += v1; + std::cout << "v2 += v1 = " << v2 << std::endl; + v2 -= v1; + std::cout << "v2 -= v1 = " << v2 << std::endl; + v2 = v2 + v1; + std::cout << "v2 = v2 + v1 = " << v2 << std::endl; + v2 = v2 - v1; + std::cout << "v2 = v2 - v1 = " << v2 << std::endl; + v1 *= value_type (1.); + std::cout << "v1 *= 1. = " << v1 << std::endl; + v1 *= t; + std::cout << "v1 *= N = " << v1 << std::endl; + + // Unary vector operations resulting in a scalar + initialize_vector (v1); + t = ublas::sum (v1); + std::cout << "sum (v1) = " << t << std::endl; + n = ublas::norm_1 (v1); + std::cout << "norm_1 (v1) = " << n << std::endl; + n = ublas::norm_2 (v1); + std::cout << "norm_2 (v1) = " << n << std::endl; + n = ublas::norm_inf (v1); + std::cout << "norm_inf (v1) = " << n << std::endl; + + i = ublas::index_norm_inf (v1); + std::cout << "index_norm_inf (v1) = " << i << std::endl; + + // Binary vector operations resulting in a scalar + initialize_vector (v1); + initialize_vector (v2); + t = ublas::inner_prod (v1, v2); + std::cout << "inner_prod (v1, v2) = " << t << std::endl; + } + } + void operator () () const { + { + V v1 (N), v2 (N), v3 (N); + test_with (v1, v2, v3); + +#ifdef USE_RANGE + ublas::vector_range vr1 (v1, ublas::range (0, N)), + vr2 (v2, ublas::range (0, N)), + vr3 (v3, ublas::range (0, N)); + test_with (vr1, vr2, vr3); +#endif + +#ifdef USE_SLICE + ublas::vector_slice vs1 (v1, ublas::slice (0, 1, N)), + vs2 (v2, ublas::slice (0, 1, N)), + vs3 (v3, ublas::slice (0, 1, N)); + test_with (vs1, vs2, vs3); +#endif + } + } +}; + +// Test vector +void test_vector () { + std::cout << "test_vector" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, bounded_array" << std::endl; + test_my_vector, ublas::bounded_array, 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, bounded_array" << std::endl; + test_my_vector, ublas::bounded_array, 3> >, 3 > () (); +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, unbounded_array" << std::endl; + test_my_vector, ublas::unbounded_array > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, unbounded_array" << std::endl; + test_my_vector, ublas::unbounded_array > >, 3 > () (); +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, std::vector" << std::endl; + test_my_vector, std::vector > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, std::vector" << std::endl; + test_my_vector, std::vector > >, 3 > () (); +#endif +#endif +} diff --git a/test/ublas_interop/test72.cpp b/test/ublas_interop/test72.cpp new file mode 100644 index 00000000..07b1d8a0 --- /dev/null +++ b/test/ublas_interop/test72.cpp @@ -0,0 +1,165 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test7.hpp" + +// Test matrix & vector expression templates +template +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template + void test_with (VP &v1, VP &v2, MP &m1) const { + { + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v1 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v1 << std::endl; + v1 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v1 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; + } + } + void operator () () const { + { + V v1 (N), v2 (N); + M m1 (N, N); + test_with (v1, v2, m1); + + ublas::matrix_row mr1 (m1, 0), mr2 (m1, 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column mc1 (m1, 0), mc2 (m1, 1); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_MATRIX +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (); +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::matrix, ublas::row_major, std::vector > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::matrix, ublas::row_major, std::vector > >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_VECTOR_OF_VECTOR +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::vector_of_vector, ublas::row_major, ublas::bounded_array, 3>, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::vector_of_vector, ublas::row_major, ublas::bounded_array, 3>, 3 + 1> >, 3> () (); +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::vector_of_vector, ublas::row_major, ublas::unbounded_array > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::vector_of_vector, ublas::row_major, ublas::unbounded_array > > >, 3> () (); +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::vector_of_vector, ublas::row_major, std::vector > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::vector_of_vector, ublas::row_major, std::vector > > >, 3> () (); +#endif +#endif +#endif +} diff --git a/test/ublas_interop/test73.cpp b/test/ublas_interop/test73.cpp new file mode 100644 index 00000000..60b10bb7 --- /dev/null +++ b/test/ublas_interop/test73.cpp @@ -0,0 +1,202 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test7.hpp" + +// Test matrix expression templates +template +struct test_my_matrix { + typedef typename M::value_type value_type; + + template + void test_with (MP &m1, MP &m2, MP &m3) const { + { + value_type t; + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m1 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + m2 = ublas::trans (m1); + std::cout << "trans (m1) = " << m2 << std::endl; + + // Hermitean + initialize_matrix (m1); + m2 = ublas::herm (m1); + std::cout << "herm (m1) = " << m2 << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + m3 = ublas::prod (m1, m2); + std::cout << "prod (m1, m2) = " << m3 << std::endl; + } + } + void operator () () const { + { + M m1 (N, N), m2 (N, N), m3 (N, N); + test_with (m1, m2, m3); + +#ifdef USE_RANGE + ublas::matrix_range mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_MATRIX +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3 > () (); +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > >, 3 > () (); +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_VECTOR_OF_VECTOR +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3>, 3 + 1> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3>, 3 + 1> >, 3 > () (); +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > > >, 3 > () (); +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > > >, 3 > () (); +#endif +#endif +#endif +} From c8c3610cdcde9265b2d3de43224d6296e4b61c52 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 7 Aug 2012 11:47:25 +0000 Subject: [PATCH 212/256] Fix uBlas tests and failures resulting from them. [SVN r79902] --- .../detail/mp_number_compare.hpp | 54 +++--- test/Jamfile.v2 | 2 +- test/ublas_interop/test1.hpp | 17 +- test/ublas_interop/test11.cpp | 83 ++++++++ test/ublas_interop/test12.cpp | 183 +++++++++++++++++- test/ublas_interop/test13.cpp | 162 +++++++++++++++- test/ublas_interop/test2.hpp | 12 +- test/ublas_interop/test4.hpp | 25 +++ test/ublas_interop/test5.hpp | 25 +++ test/ublas_interop/test7.hpp | 25 +++ 10 files changed, 544 insertions(+), 44 deletions(-) diff --git a/include/boost/multiprecision/detail/mp_number_compare.hpp b/include/boost/multiprecision/detail/mp_number_compare.hpp index 909d4af8..e8d53b9d 100644 --- a/include/boost/multiprecision/detail/mp_number_compare.hpp +++ b/include/boost/multiprecision/detail/mp_number_compare.hpp @@ -20,17 +20,15 @@ inline bool eval_eq(const B& a, const B& b) return a.compare(b) == 0; } template -inline typename enable_if_c<(is_arithmetic::value && is_convertible::value), bool>::type eval_eq(const B& a, const A& b) +inline bool eval_eq(const B& a, const A& b) { - B t(b); - return eval_eq(a, t); -} -template -inline typename enable_if_c<(is_arithmetic::value && !is_convertible::value), bool>::type eval_eq(const B& a, const A& b) -{ - B t; - t = b; - return eval_eq(a, t); + typedef typename mpl::if_< + is_convertible >, + mp_number, + mp_number + >::type mp_type; + mp_type t(b); + return eval_eq(a, t.backend()); } template @@ -39,17 +37,15 @@ inline bool eval_lt(const B& a, const B& b) return a.compare(b) < 0; } template -inline typename enable_if_c<(is_arithmetic::value && is_convertible::value), bool>::type eval_lt(const B& a, const A& b) +inline bool eval_lt(const B& a, const A& b) { - B t(b); - return eval_lt(a, t); -} -template -inline typename enable_if_c<(is_arithmetic::value && !is_convertible::value), bool>::type eval_lt(const B& a, const A& b) -{ - B t; - t = b; - return eval_lt(a, t); + typedef typename mpl::if_< + is_convertible >, + mp_number, + mp_number + >::type mp_type; + mp_type t(b); + return eval_lt(a, t.backend()); } template @@ -58,17 +54,15 @@ inline bool eval_gt(const B& a, const B& b) return a.compare(b) > 0; } template -inline typename enable_if_c<(is_arithmetic::value && is_convertible::value), bool>::type eval_gt(const B& a, const A& b) +inline bool eval_gt(const B& a, const A& b) { - B t(b); - return eval_gt(a, t); -} -template -inline typename enable_if_c<(is_arithmetic::value && !is_convertible::value), bool>::type eval_gt(const B& a, const A& b) -{ - B t; - t = b; - return eval_gt(a, t); + typedef typename mpl::if_< + is_convertible >, + mp_number, + mp_number + >::type mp_type; + mp_type t(b); + return eval_gt(a, t.backend()); } } diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index a8879efd..abb83aa9 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -749,7 +749,7 @@ run ublas_interop/test2.cpp ublas_interop/test21.cpp ublas_interop/test22.cpp ub run ublas_interop/test4.cpp ublas_interop/test42.cpp ublas_interop/test43.cpp ; run ublas_interop/test5.cpp ublas_interop/test52.cpp ublas_interop/test53.cpp ; run ublas_interop/test6.cpp ublas_interop/test62.cpp ublas_interop/test63.cpp ; -run ublas_interop/test7.cpp ublas_interop/test71.cpp ublas_interop/test72.cpp ublas_interop/test73.cpp ; +#run ublas_interop/test7.cpp ublas_interop/test71.cpp ublas_interop/test72.cpp ublas_interop/test73.cpp ; if $(enable-specfun) diff --git a/test/ublas_interop/test1.hpp b/test/ublas_interop/test1.hpp index f6627dce..9d0731cb 100644 --- a/test/ublas_interop/test1.hpp +++ b/test/ublas_interop/test1.hpp @@ -13,8 +13,6 @@ #ifndef TEST1_H #define TEST1_H -#include - #ifdef _MSC_VER # pragma warning(disable:4800 4996) #endif @@ -26,7 +24,21 @@ typedef boost::multiprecision::mp_number #include #include @@ -42,4 +54,5 @@ void test_vector (); void test_matrix_vector (); void test_matrix (); + #endif diff --git a/test/ublas_interop/test11.cpp b/test/ublas_interop/test11.cpp index 70e77611..e874d65e 100644 --- a/test/ublas_interop/test11.cpp +++ b/test/ublas_interop/test11.cpp @@ -167,16 +167,99 @@ struct test_my_vector { void test_vector () { std::cout << "test_vector" << std::endl; +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT std::cout << "mp_test_type, bounded_array" << std::endl; test_my_vector >, 3 > () (); +#endif +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_vector >, 3 > () (); +#endif +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_vector, ublas::bounded_array, 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_vector, ublas::bounded_array, 3> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT std::cout << "mp_test_type, unbounded_array" << std::endl; test_my_vector >, 3 > () (); +#endif +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_vector >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_vector, ublas::unbounded_array > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_vector, ublas::unbounded_array > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT std::cout << "mp_test_type, std::vector" << std::endl; test_my_vector >, 3 > () (); +#endif +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_vector >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_vector, std::vector > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_vector, std::vector > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_BOUNDED_VECTOR +#ifdef USE_FLOAT std::cout << "mp_test_type, bounded" << std::endl; test_my_vector, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded" << std::endl; + test_my_vector, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded" << std::endl; + test_my_vector, 3>, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded" << std::endl; + test_my_vector, 3>, 3> () (); +#endif +#endif +#endif } diff --git a/test/ublas_interop/test12.cpp b/test/ublas_interop/test12.cpp index fac3634f..7059fb9e 100644 --- a/test/ublas_interop/test12.cpp +++ b/test/ublas_interop/test12.cpp @@ -75,28 +75,203 @@ struct test_my_matrix_vector { void test_matrix_vector () { std::cout << "test_matrix_vector" << std::endl; +#ifdef USE_MATRIX +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT std::cout << "mp_test_type, bounded_array" << std::endl; test_my_matrix_vector >, ublas::matrix >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::matrix >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT std::cout << "mp_test_type, unbounded_array" << std::endl; test_my_matrix_vector >, ublas::matrix >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::matrix >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT std::cout << "mp_test_type, std::vector" << std::endl; test_my_matrix_vector >, ublas::matrix >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::matrix >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::matrix, ublas::row_major, std::vector > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::matrix, ublas::row_major, std::vector > >, 3> () (); +#endif +#endif +#endif +#endif + +#ifdef USE_BOUNDED_MATRIX +#ifdef USE_FLOAT std::cout << "mp_test_type, bounded" << std::endl; test_my_matrix_vector, ublas::bounded_matrix, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded" << std::endl; + test_my_matrix_vector, + ublas::bounded_matrix, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded" << std::endl; + test_my_matrix_vector, 3>, + ublas::bounded_matrix, 3, 3>, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded" << std::endl; + test_my_matrix_vector, 3>, + ublas::bounded_matrix, 3, 3>, 3> () (); +#endif +#endif +#endif + +#ifdef USE_VECTOR_OF_VECTOR +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT std::cout << "mp_test_type, bounded_array" << std::endl; test_my_matrix_vector >, ublas::vector_of_vector, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector >, + ublas::vector_of_vector, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::vector_of_vector, ublas::row_major, ublas::bounded_array, 3>, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix_vector, ublas::bounded_array, 3> >, + ublas::vector_of_vector, ublas::row_major, ublas::bounded_array, 3>, 3 + 1> >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT std::cout << "mp_test_type, unbounded_array" << std::endl; test_my_matrix_vector >, ublas::vector_of_vector > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector >, + ublas::vector_of_vector > >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::vector_of_vector, ublas::row_major, ublas::unbounded_array > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix_vector, ublas::unbounded_array > >, + ublas::vector_of_vector, ublas::row_major, ublas::unbounded_array > > >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT std::cout << "mp_test_type, std::vector" << std::endl; - /* - // This fails with an internal std lib assersion, even when mp_test_type is double, - // looks like a bug in the uBlas test code... test_my_matrix_vector >, - ublas::vector_of_vector > >, 3> () ();*/ + ublas::vector_of_vector > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector >, + ublas::vector_of_vector > >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::vector_of_vector, ublas::row_major, std::vector > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix_vector, std::vector > >, + ublas::vector_of_vector, ublas::row_major, std::vector > > >, 3> () (); +#endif +#endif +#endif +#endif } diff --git a/test/ublas_interop/test13.cpp b/test/ublas_interop/test13.cpp index 2e8432a5..d2f80377 100644 --- a/test/ublas_interop/test13.cpp +++ b/test/ublas_interop/test13.cpp @@ -147,21 +147,175 @@ struct test_my_matrix { void test_matrix () { std::cout << "test_matrix" << std::endl; +#ifdef USE_MATRIX +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT std::cout << "mp_test_type, bounded_array" << std::endl; test_my_matrix >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3 * 3> >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT std::cout << "mp_test_type, unbounded_array" << std::endl; test_my_matrix >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT std::cout << "mp_test_type, std::vector" << std::endl; test_my_matrix >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > >, 3> () (); +#endif +#endif +#endif +#endif + +#ifdef USE_BOUNDED_MATRIX +#ifdef USE_FLOAT std::cout << "mp_test_type, bounded" << std::endl; test_my_matrix, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded" << std::endl; + test_my_matrix, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded" << std::endl; + test_my_matrix, 3, 3>, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded" << std::endl; + test_my_matrix, 3, 3>, 3> () (); +#endif +#endif +#endif + +#ifdef USE_VECTOR_OF_VECTOR +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT std::cout << "mp_test_type, bounded_array" << std::endl; test_my_matrix, 3 + 1> >, 3> () (); - /* - // This fails with an internal std lib assersion, even when mp_test_type is double, - // looks like a bug in the uBlas test code... +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3>, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, bounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::bounded_array, 3>, 3 + 1> >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT std::cout << "mp_test_type, unbounded_array" << std::endl; test_my_matrix > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix > >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, unbounded_array" << std::endl; + test_my_matrix, ublas::row_major, ublas::unbounded_array > > >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT std::cout << "mp_test_type, std::vector" << std::endl; - test_my_matrix > >, 3> () ();*/ + test_my_matrix > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix > >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex, std::vector" << std::endl; + test_my_matrix, ublas::row_major, std::vector > > >, 3> () (); +#endif +#endif +#endif +#endif } diff --git a/test/ublas_interop/test2.hpp b/test/ublas_interop/test2.hpp index 0009b832..b58c6177 100644 --- a/test/ublas_interop/test2.hpp +++ b/test/ublas_interop/test2.hpp @@ -12,7 +12,6 @@ #ifndef TEST2_H #define TEST2_H - #ifdef _MSC_VER # pragma warning(disable:4800 4996) #endif @@ -25,11 +24,18 @@ typedef boost::multiprecision::mp_number diff --git a/test/ublas_interop/test4.hpp b/test/ublas_interop/test4.hpp index fc5b48cb..20194f7a 100644 --- a/test/ublas_interop/test4.hpp +++ b/test/ublas_interop/test4.hpp @@ -13,6 +13,31 @@ #ifndef TEST4_H #define TEST4_H +#ifdef _MSC_VER +# pragma warning(disable:4800 4996) +#endif + +#include + +typedef boost::multiprecision::mp_number, false> mp_test_type; +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + #include #include diff --git a/test/ublas_interop/test5.hpp b/test/ublas_interop/test5.hpp index a13dfa2e..cd98e665 100644 --- a/test/ublas_interop/test5.hpp +++ b/test/ublas_interop/test5.hpp @@ -13,6 +13,31 @@ #ifndef TEST5_H #define TEST5_H +#ifdef _MSC_VER +# pragma warning(disable:4800 4996) +#endif + +#include + +typedef boost::multiprecision::mp_number, false> mp_test_type; +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + #include #include diff --git a/test/ublas_interop/test7.hpp b/test/ublas_interop/test7.hpp index 5dbae1fc..4990642f 100644 --- a/test/ublas_interop/test7.hpp +++ b/test/ublas_interop/test7.hpp @@ -13,6 +13,31 @@ #ifndef TEST7_H #define TEST7_H +#ifdef _MSC_VER +# pragma warning(disable:4800 4996) +#endif + +#include + +typedef boost::multiprecision::mp_number, false> mp_test_type; +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + #include #include From 3bcbb056e7b708e043360413ef3de178f102190d Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 7 Aug 2012 17:55:32 +0000 Subject: [PATCH 213/256] Add better error checking for moved-from types. [SVN r79913] --- include/boost/multiprecision/gmp.hpp | 180 ++++++++++++++++++--- include/boost/multiprecision/mp_number.hpp | 3 +- include/boost/multiprecision/mpfr.hpp | 44 ++++- include/boost/multiprecision/tommath.hpp | 36 ++++- test/test_move.cpp | 52 +++++- 5 files changed, 279 insertions(+), 36 deletions(-) diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 4cf0aa42..8baab295 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -56,7 +56,8 @@ struct gmp_float_imp // things go badly wrong!! // mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); - mpf_set(m_data, o.m_data); + if(o.m_data[0]._mp_d) + mpf_set(m_data, o.m_data); } #ifndef BOOST_NO_RVALUE_REFERENCES gmp_float_imp(gmp_float_imp&& o) BOOST_NOEXCEPT @@ -67,7 +68,10 @@ struct gmp_float_imp #endif gmp_float_imp& operator = (const gmp_float_imp& o) { - mpf_set(m_data, o.m_data); + if(m_data[0]._mp_d == 0) + mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + if(o.m_data[0]._mp_d) + mpf_set(m_data, o.m_data); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES @@ -79,6 +83,8 @@ struct gmp_float_imp #endif gmp_float_imp& operator = (unsigned long long i) { + if(m_data[0]._mp_d == 0) + mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpf_t t; @@ -99,6 +105,8 @@ struct gmp_float_imp gmp_float_imp& operator = (long long i) { BOOST_MP_USING_ABS + if(m_data[0]._mp_d == 0) + mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); bool neg = i < 0; *this = static_cast(abs(i)); if(neg) @@ -107,16 +115,22 @@ struct gmp_float_imp } gmp_float_imp& operator = (unsigned long i) BOOST_NOEXCEPT { + if(m_data[0]._mp_d == 0) + mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpf_set_ui(m_data, i); return *this; } gmp_float_imp& operator = (long i) BOOST_NOEXCEPT { + if(m_data[0]._mp_d == 0) + mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpf_set_si(m_data, i); return *this; } gmp_float_imp& operator = (double d) BOOST_NOEXCEPT { + if(m_data[0]._mp_d == 0) + mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpf_set_d(m_data, d); return *this; } @@ -126,6 +140,9 @@ struct gmp_float_imp using std::ldexp; using std::floor; + if(m_data[0]._mp_d == 0) + mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + if (a == 0) { mpf_set_si(m_data, 0); return *this; @@ -168,6 +185,8 @@ struct gmp_float_imp } gmp_float_imp& operator = (const char* s) { + if(m_data[0]._mp_d == 0) + mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); if(0 != mpf_set_str(m_data, s, 10)) BOOST_THROW_EXCEPTION(std::runtime_error(std::string("The string \"") + s + std::string("\"could not be interpreted as a valid floating point number."))); return *this; @@ -178,6 +197,8 @@ struct gmp_float_imp } std::string str(std::streamsize digits, std::ios_base::fmtflags f)const { + BOOST_ASSERT(m_data[0]._mp_d); + bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; std::streamsize org_digits(digits); @@ -278,18 +299,22 @@ struct gmp_float_imp } void negate() BOOST_NOEXCEPT { + BOOST_ASSERT(m_data[0]._mp_d); mpf_neg(m_data, m_data); } int compare(const gmp_float& o)const BOOST_NOEXCEPT { + BOOST_ASSERT(m_data[0]._mp_d && o.m_data[0]._mp_d); return mpf_cmp(m_data, o.m_data); } int compare(long i)const BOOST_NOEXCEPT { + BOOST_ASSERT(m_data[0]._mp_d); return mpf_cmp_si(m_data, i); } int compare(unsigned long i)const BOOST_NOEXCEPT { + BOOST_ASSERT(m_data[0]._mp_d); return mpf_cmp_ui(m_data, i); } template @@ -299,8 +324,16 @@ struct gmp_float_imp d = v; return compare(d); } - mpf_t& data() BOOST_NOEXCEPT { return m_data; } - const mpf_t& data()const BOOST_NOEXCEPT { return m_data; } + mpf_t& data() BOOST_NOEXCEPT + { + BOOST_ASSERT(m_data[0]._mp_d); + return m_data; + } + const mpf_t& data()const BOOST_NOEXCEPT + { + BOOST_ASSERT(m_data[0]._mp_d); + return m_data; + } protected: mpf_t m_data; static unsigned& get_default_precision() BOOST_NOEXCEPT @@ -363,16 +396,22 @@ struct gmp_float : public detail::gmp_float_imp gmp_float& operator=(const gmp_rational& o); gmp_float& operator=(const mpf_t& val) BOOST_NOEXCEPT { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); mpf_set(this->m_data, val); return *this; } gmp_float& operator=(const mpz_t& val) BOOST_NOEXCEPT { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); mpf_set_z(this->m_data, val); return *this; } gmp_float& operator=(const mpq_t& val) BOOST_NOEXCEPT { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); mpf_set_q(this->m_data, val); return *this; } @@ -439,6 +478,8 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> template gmp_float& operator=(const gmp_float& o) { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); mpf_set(this->m_data, o.data()); return *this; } @@ -446,16 +487,22 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> gmp_float& operator=(const gmp_rational& o); gmp_float& operator=(const mpf_t& val) { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); mpf_set(this->m_data, val); return *this; } gmp_float& operator=(const mpz_t& val) { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); mpf_set_z(this->m_data, val); return *this; } gmp_float& operator=(const mpq_t& val) { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); mpf_set_q(this->m_data, val); return *this; } @@ -906,7 +953,10 @@ struct gmp_int } gmp_int(const gmp_int& o) { - mpz_init_set(m_data, o.m_data); + if(o.m_data[0]._mp_d) + mpz_init_set(m_data, o.m_data); + else + mpz_init(this->m_data); } #ifndef BOOST_NO_RVALUE_REFERENCES gmp_int(gmp_int&& o) BOOST_NOEXCEPT @@ -938,21 +988,21 @@ struct gmp_int gmp_int(const gmp_rational& o); gmp_int& operator = (const gmp_int& o) { - mpz_set(m_data, o.m_data); + if(o.m_data[0]._mp_d) + mpz_set(m_data, o.m_data); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES gmp_int& operator = (gmp_int&& o) BOOST_NOEXCEPT { - if(m_data[0]._mp_d) - mpz_clear(m_data); - m_data[0] = o.m_data[0]; - o.m_data[0]._mp_d = 0; + mpz_swap(m_data, o.m_data); return *this; } #endif gmp_int& operator = (unsigned long long i) { + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpz_t t; @@ -973,6 +1023,8 @@ struct gmp_int gmp_int& operator = (long long i) { BOOST_MP_USING_ABS + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); bool neg = i < 0; *this = static_cast(abs(i)); if(neg) @@ -981,16 +1033,22 @@ struct gmp_int } gmp_int& operator = (unsigned long i) { + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); mpz_set_ui(m_data, i); return *this; } gmp_int& operator = (long i) { + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); mpz_set_si(m_data, i); return *this; } gmp_int& operator = (double d) { + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); mpz_set_d(m_data, d); return *this; } @@ -1000,6 +1058,9 @@ struct gmp_int using std::ldexp; using std::floor; + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); + if (a == 0) { mpz_set_si(m_data, 0); return *this; @@ -1042,6 +1103,8 @@ struct gmp_int } gmp_int& operator = (const char* s) { + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); std::size_t n = s ? std::strlen(s) : 0; int radix = 10; if(n && (*s == '0')) @@ -1069,22 +1132,30 @@ struct gmp_int } gmp_int& operator=(const mpf_t& val) { + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); mpz_set_f(this->m_data, val); return *this; } gmp_int& operator=(const mpz_t& val) { + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); mpz_set(this->m_data, val); return *this; } gmp_int& operator=(const mpq_t& val) { + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); mpz_set_q(this->m_data, val); return *this; } template gmp_int& operator=(const gmp_float& o) { + if(m_data[0]._mp_d == 0) + mpz_init(this->m_data); mpz_set_f(this->m_data, o.data()); return *this; } @@ -1095,6 +1166,8 @@ struct gmp_int } std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const { + BOOST_ASSERT(m_data[0]._mp_d); + int base = 10; if((f & std::ios_base::oct) == std::ios_base::oct) base = 8; @@ -1131,18 +1204,22 @@ struct gmp_int } void negate() { + BOOST_ASSERT(m_data[0]._mp_d); mpz_neg(m_data, m_data); } int compare(const gmp_int& o)const { + BOOST_ASSERT(m_data[0]._mp_d && o.m_data[0]._mp_d); return mpz_cmp(m_data, o.m_data); } int compare(long i)const { + BOOST_ASSERT(m_data[0]._mp_d); return mpz_cmp_si(m_data, i); } int compare(unsigned long i)const { + BOOST_ASSERT(m_data[0]._mp_d); return mpz_cmp_ui(m_data, i); } template @@ -1152,8 +1229,16 @@ struct gmp_int d = v; return compare(d); } - mpz_t& data() { return m_data; } - const mpz_t& data()const { return m_data; } + mpz_t& data() + { + BOOST_ASSERT(m_data[0]._mp_d); + return m_data; + } + const mpz_t& data()const + { + BOOST_ASSERT(m_data[0]._mp_d); + return m_data; + } protected: mpz_t m_data; }; @@ -1545,7 +1630,8 @@ struct gmp_rational gmp_rational(const gmp_rational& o) { mpq_init(m_data); - mpq_set(m_data, o.m_data); + if(o.m_data[0]._mp_num._mp_d) + mpq_set(m_data, o.m_data); } gmp_rational(const gmp_int& o) { @@ -1557,8 +1643,8 @@ struct gmp_rational { m_data[0]._mp_num = o.data()[0]._mp_num; m_data[0]._mp_den = o.data()[0]._mp_den; - o.data()[0]._mp_num._mp_d = 0; - o.data()[0]._mp_den._mp_d = 0; + o.m_data[0]._mp_num._mp_d = 0; + o.m_data[0]._mp_den._mp_d = 0; } #endif gmp_rational(mpq_t o) @@ -1573,21 +1659,21 @@ struct gmp_rational } gmp_rational& operator = (const gmp_rational& o) { - mpq_set(m_data, o.m_data); + if(o.m_data[0]._mp_num._mp_d) + mpq_set(m_data, o.m_data); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES gmp_rational& operator = (gmp_rational&& o) BOOST_NOEXCEPT { - m_data[0]._mp_num = o.data()[0]._mp_num; - m_data[0]._mp_den = o.data()[0]._mp_den; - o.data()[0]._mp_num._mp_d = 0; - o.data()[0]._mp_den._mp_d = 0; + mpq_swap(m_data, o.m_data); return *this; } #endif gmp_rational& operator = (unsigned long long i) { + if(m_data[0]._mp_den._mp_d == 0) + mpq_init(m_data); unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpq_t t; @@ -1608,6 +1694,8 @@ struct gmp_rational gmp_rational& operator = (long long i) { BOOST_MP_USING_ABS + if(m_data[0]._mp_den._mp_d == 0) + mpq_init(m_data); bool neg = i < 0; *this = static_cast(abs(i)); if(neg) @@ -1616,16 +1704,22 @@ struct gmp_rational } gmp_rational& operator = (unsigned long i) { + if(m_data[0]._mp_den._mp_d == 0) + mpq_init(m_data); mpq_set_ui(m_data, i, 1); return *this; } gmp_rational& operator = (long i) { + if(m_data[0]._mp_den._mp_d == 0) + mpq_init(m_data); mpq_set_si(m_data, i, 1); return *this; } gmp_rational& operator = (double d) { + if(m_data[0]._mp_den._mp_d == 0) + mpq_init(m_data); mpq_set_d(m_data, d); return *this; } @@ -1637,6 +1731,9 @@ struct gmp_rational using default_ops::eval_add; using default_ops::eval_subtract; + if(m_data[0]._mp_den._mp_d == 0) + mpq_init(m_data); + if (a == 0) { mpq_set_si(m_data, 0, 1); return *this; @@ -1679,22 +1776,30 @@ struct gmp_rational } gmp_rational& operator = (const char* s) { + if(m_data[0]._mp_den._mp_d == 0) + mpq_init(m_data); if(0 != mpq_set_str(m_data, s, 10)) BOOST_THROW_EXCEPTION(std::runtime_error(std::string("The string \"") + s + std::string("\"could not be interpreted as a valid rational number."))); return *this; } gmp_rational& operator=(const gmp_int& o) { + if(m_data[0]._mp_den._mp_d == 0) + mpq_init(m_data); mpq_set_z(m_data, o.data()); return *this; } gmp_rational& operator=(const mpq_t& o) { + if(m_data[0]._mp_den._mp_d == 0) + mpq_init(m_data); mpq_set(m_data, o); return *this; } gmp_rational& operator=(const mpz_t& o) { + if(m_data[0]._mp_den._mp_d == 0) + mpq_init(m_data); mpq_set_z(m_data, o); return *this; } @@ -1704,6 +1809,7 @@ struct gmp_rational } std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags /*f*/)const { + BOOST_ASSERT(m_data[0]._mp_num._mp_d); // TODO make a better job of this including handling of f!! void *(*alloc_func_ptr) (size_t); void *(*realloc_func_ptr) (void *, size_t, size_t); @@ -1721,10 +1827,12 @@ struct gmp_rational } void negate() { + BOOST_ASSERT(m_data[0]._mp_num._mp_d); mpq_neg(m_data, m_data); } int compare(const gmp_rational& o)const { + BOOST_ASSERT(m_data[0]._mp_num._mp_d && o.m_data[0]._mp_num._mp_d); return mpq_cmp(m_data, o.m_data); } template @@ -1736,14 +1844,24 @@ struct gmp_rational } int compare(unsigned long v)const { + BOOST_ASSERT(m_data[0]._mp_num._mp_d); return mpq_cmp_ui(m_data, v, 1); } int compare(long v)const { + BOOST_ASSERT(m_data[0]._mp_num._mp_d); return mpq_cmp_si(m_data, v, 1); } - mpq_t& data() { return m_data; } - const mpq_t& data()const { return m_data; } + mpq_t& data() + { + BOOST_ASSERT(m_data[0]._mp_num._mp_d); + return m_data; + } + const mpq_t& data()const + { + BOOST_ASSERT(m_data[0]._mp_num._mp_d); + return m_data; + } protected: mpq_t m_data; }; @@ -1870,37 +1988,43 @@ template template inline gmp_float::gmp_float(const gmp_float& o) { - mpf_init2(this->m_data, ((Digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); mpf_set(this->m_data, o.data()); } template inline gmp_float::gmp_float(const gmp_int& o) { - mpf_init2(this->m_data, ((Digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); mpf_set_z(this->data(), o.data()); } template inline gmp_float::gmp_float(const gmp_rational& o) { - mpf_init2(this->m_data, ((Digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); mpf_set_q(this->data(), o.data()); } template template inline gmp_float& gmp_float::operator=(const gmp_float& o) { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); mpf_set(this->m_data, o.data()); return *this; } template inline gmp_float& gmp_float::operator=(const gmp_int& o) { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); mpf_set_z(this->data(), o.data()); return *this; } template inline gmp_float& gmp_float::operator=(const gmp_rational& o) { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); mpf_set_q(this->data(), o.data()); return *this; } @@ -1916,11 +2040,15 @@ inline gmp_float<0>::gmp_float(const gmp_rational& o) } inline gmp_float<0>& gmp_float<0>::operator=(const gmp_int& o) { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, ((this->get_default_precision() + 1) * 1000L) / 301L); mpf_set_z(this->data(), o.data()); return *this; } inline gmp_float<0>& gmp_float<0>::operator=(const gmp_rational& o) { + if(this->m_data[0]._mp_d == 0) + mpf_init2(this->m_data, ((this->get_default_precision() + 1) * 1000L) / 301L); mpf_set_q(this->data(), o.data()); return *this; } @@ -1931,6 +2059,8 @@ inline gmp_int::gmp_int(const gmp_rational& o) } inline gmp_int& gmp_int::operator=(const gmp_rational& o) { + if(this->m_data[0]._mp_d == 0) + mpz_init(this->m_data); mpz_set_q(this->m_data, o.data()); return *this; } diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index f788940c..8b6df37f 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -28,8 +28,9 @@ namespace boost{ namespace multiprecision{ #ifdef BOOST_MSVC // warning C4127: conditional expression is constant +// warning C4714: function marked as __forceinline not inlined #pragma warning(push) -#pragma warning(disable:4127) +#pragma warning(disable:4127 4714) #endif template diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index a847c5d1..63f98959 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -40,7 +40,8 @@ struct mpfr_float_imp mpfr_float_imp(const mpfr_float_imp& o) { mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); - mpfr_set(m_data, o.m_data, GMP_RNDN); + if(o.m_data[0]._mpfr_d) + mpfr_set(m_data, o.m_data, GMP_RNDN); } #ifndef BOOST_NO_RVALUE_REFERENCES mpfr_float_imp(mpfr_float_imp&& o) BOOST_NOEXCEPT @@ -51,7 +52,10 @@ struct mpfr_float_imp #endif mpfr_float_imp& operator = (const mpfr_float_imp& o) BOOST_NOEXCEPT { - mpfr_set(m_data, o.m_data, GMP_RNDN); + if(m_data[0]._mpfr_d == 0) + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + if(o.m_data[0]._mpfr_d) + mpfr_set(m_data, o.m_data, GMP_RNDN); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES @@ -64,17 +68,23 @@ struct mpfr_float_imp #ifdef _MPFR_H_HAVE_INTMAX_T mpfr_float_imp& operator = (unsigned long long i) BOOST_NOEXCEPT { + if(m_data[0]._mpfr_d == 0) + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpfr_set_uj(m_data, i, GMP_RNDN); return *this; } mpfr_float_imp& operator = (long long i) BOOST_NOEXCEPT { + if(m_data[0]._mpfr_d == 0) + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpfr_set_sj(m_data, i, GMP_RNDN); return *this; } #else mpfr_float_imp& operator = (unsigned long long i) { + if(m_data[0]._mpfr_d == 0) + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpfr_t t; @@ -95,6 +105,8 @@ struct mpfr_float_imp mpfr_float_imp& operator = (long long i) { BOOST_MP_USING_ABS + if(m_data[0]._mpfr_d == 0) + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); bool neg = i < 0; *this = static_cast(abs(i)); if(neg) @@ -104,26 +116,36 @@ struct mpfr_float_imp #endif mpfr_float_imp& operator = (unsigned long i) BOOST_NOEXCEPT { + if(m_data[0]._mpfr_d == 0) + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpfr_set_ui(m_data, i, GMP_RNDN); return *this; } mpfr_float_imp& operator = (long i) BOOST_NOEXCEPT { + if(m_data[0]._mpfr_d == 0) + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpfr_set_si(m_data, i, GMP_RNDN); return *this; } mpfr_float_imp& operator = (double d) BOOST_NOEXCEPT { + if(m_data[0]._mpfr_d == 0) + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpfr_set_d(m_data, d, GMP_RNDN); return *this; } mpfr_float_imp& operator = (long double a) BOOST_NOEXCEPT { + if(m_data[0]._mpfr_d == 0) + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); mpfr_set_ld(m_data, a, GMP_RNDN); return *this; } mpfr_float_imp& operator = (const char* s) { + if(m_data[0]._mpfr_d == 0) + mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); if(mpfr_set_str(m_data, s, 10, GMP_RNDN) != 0) { BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Unable to parse string \"") + s + std::string("\"as a valid floating point number."))); @@ -136,6 +158,8 @@ struct mpfr_float_imp } std::string str(std::streamsize digits, std::ios_base::fmtflags f)const { + BOOST_ASSERT(m_data[0]._mpfr_d); + bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; @@ -246,18 +270,22 @@ struct mpfr_float_imp } void negate() BOOST_NOEXCEPT { + BOOST_ASSERT(m_data[0]._mpfr_d); mpfr_neg(m_data, m_data, GMP_RNDN); } int compare(const mpfr_float_backend& o)const BOOST_NOEXCEPT { + BOOST_ASSERT(m_data[0]._mpfr_d && o.m_data[0]._mpfr_d); return mpfr_cmp(m_data, o.m_data); } int compare(long i)const BOOST_NOEXCEPT { + BOOST_ASSERT(m_data[0]._mpfr_d); return mpfr_cmp_si(m_data, i); } int compare(unsigned long i)const BOOST_NOEXCEPT { + BOOST_ASSERT(m_data[0]._mpfr_d); return mpfr_cmp_ui(m_data, i); } template @@ -267,8 +295,16 @@ struct mpfr_float_imp d = v; return compare(d); } - mpfr_t& data() BOOST_NOEXCEPT { return m_data; } - const mpfr_t& data()const BOOST_NOEXCEPT { return m_data; } + mpfr_t& data() BOOST_NOEXCEPT + { + BOOST_ASSERT(m_data[0]._mpfr_d); + return m_data; + } + const mpfr_t& data()const BOOST_NOEXCEPT + { + BOOST_ASSERT(m_data[0]._mpfr_d); + return m_data; + } protected: mpfr_t m_data; static unsigned& get_default_precision() BOOST_NOEXCEPT diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 21525be5..6f137936 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -54,18 +54,22 @@ struct tommath_int } tommath_int& operator = (tommath_int&& o) { - m_data = o.m_data; - o.m_data.dp = 0; + mp_exch(&m_data, &o.data()); return *this; } #endif tommath_int& operator = (const tommath_int& o) { - detail::check_tommath_result(mp_copy(const_cast< ::mp_int*>(&o.m_data), &m_data)); + if(m_data.dp == 0) + detail::check_tommath_result(mp_init(&m_data)); + if(o.m_data.dp) + detail::check_tommath_result(mp_copy(const_cast< ::mp_int*>(&o.m_data), &m_data)); return *this; } tommath_int& operator = (unsigned long long i) { + if(m_data.dp == 0) + detail::check_tommath_result(mp_init(&m_data)); unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; ::mp_int t; @@ -86,6 +90,8 @@ struct tommath_int tommath_int& operator = (long long i) { BOOST_MP_USING_ABS + if(m_data.dp == 0) + detail::check_tommath_result(mp_init(&m_data)); bool neg = i < 0; *this = static_cast(abs(i)); if(neg) @@ -99,11 +105,15 @@ struct tommath_int // tommath_int& operator = (boost::uint32_t i) { + if(m_data.dp == 0) + detail::check_tommath_result(mp_init(&m_data)); detail::check_tommath_result((mp_set_int(&m_data, i))); return *this; } tommath_int& operator = (boost::int32_t i) { + if(m_data.dp == 0) + detail::check_tommath_result(mp_init(&m_data)); bool neg = i < 0; *this = static_cast(std::abs(i)); if(neg) @@ -116,6 +126,9 @@ struct tommath_int using std::ldexp; using std::floor; + if(m_data.dp == 0) + detail::check_tommath_result(mp_init(&m_data)); + if (a == 0) { detail::check_tommath_result(mp_set_int(&m_data, 0)); return *this; @@ -175,6 +188,8 @@ struct tommath_int // using default_ops::eval_multiply; using default_ops::eval_add; + if(m_data.dp == 0) + detail::check_tommath_result(mp_init(&m_data)); std::size_t n = s ? std::strlen(s) : 0; *this = static_cast(0u); unsigned radix = 10; @@ -275,6 +290,7 @@ struct tommath_int } std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const { + BOOST_ASSERT(m_data.dp); int base = 10; if((f & std::ios_base::oct) == std::ios_base::oct) base = 8; @@ -307,10 +323,12 @@ struct tommath_int } void negate() { + BOOST_ASSERT(m_data.dp); mp_neg(&m_data, &m_data); } int compare(const tommath_int& o)const { + BOOST_ASSERT(m_data.dp && o.m_data.dp); return mp_cmp(const_cast< ::mp_int*>(&m_data), const_cast< ::mp_int*>(&o.m_data)); } template @@ -322,8 +340,16 @@ struct tommath_int d = v; return t.compare(d); } - ::mp_int& data() { return m_data; } - const ::mp_int& data()const { return m_data; } + ::mp_int& data() + { + BOOST_ASSERT(m_data.dp); + return m_data; + } + const ::mp_int& data()const + { + BOOST_ASSERT(m_data.dp); + return m_data; + } void swap(tommath_int& o)BOOST_NOEXCEPT { mp_exch(&m_data, &o.data()); diff --git a/test/test_move.cpp b/test/test_move.cpp index f67e497b..1ce4a4cf 100644 --- a/test/test_move.cpp +++ b/test/test_move.cpp @@ -71,6 +71,19 @@ void do_something(const T&) { } +template +void test_std_lib() +{ + std::vector v; + for(unsigned i = 0; i < 100; ++i) + v.insert(v.begin(), i); + + T a(2), b(3); + std::swap(a, b); + BOOST_TEST(a == 3); + BOOST_TEST(b == 2); +} + int main() { @@ -83,6 +96,7 @@ int main() #ifdef TEST_MPFR { + test_std_lib(); mpfr_float_50 a = 2; BOOST_TEST(allocation_count); // sanity check that we are tracking allocations allocation_count = 0; @@ -112,10 +126,16 @@ int main() d = std::move(e); BOOST_TEST(allocation_count == 0); BOOST_TEST(d == 3); + e = 2; + BOOST_TEST(e == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); } #endif #ifdef TEST_GMP { + test_std_lib(); mpf_float_50 a = 2; BOOST_TEST(allocation_count); // sanity check that we are tracking allocations allocation_count = 0; @@ -145,8 +165,14 @@ int main() d = std::move(e); BOOST_TEST(allocation_count == 0); BOOST_TEST(d == 3); + e = 2; + BOOST_TEST(e == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); } { + test_std_lib(); mpz_int a = 2; BOOST_TEST(allocation_count); // sanity check that we are tracking allocations allocation_count = 0; @@ -163,8 +189,14 @@ int main() allocation_count = 0; e = std::move(d); BOOST_TEST(allocation_count == 0); + e = 2; + BOOST_TEST(e == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); } { + test_std_lib(); mpq_rational a = 2; BOOST_TEST(allocation_count); // sanity check that we are tracking allocations allocation_count = 0; @@ -180,15 +212,22 @@ int main() allocation_count = 0; e = std::move(d); BOOST_TEST(allocation_count == 0); + d = 2; + BOOST_TEST(d == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); } #endif #ifdef TEST_TOMMATH { + test_std_lib(); tom_int a = 2; void const* p = a.backend().data().dp; tom_int b = std::move(a); BOOST_TEST(b.backend().data().dp == p); - BOOST_TEST(a.backend().data().dp == 0); + // We can't test this, as it will assert inside data(): + //BOOST_TEST(a.backend().data().dp == 0); // // Move assign: @@ -201,10 +240,16 @@ int main() BOOST_TEST(p != e.backend().data().dp); e = std::move(d); BOOST_TEST(e.backend().data().dp == p); + d = 2; + BOOST_TEST(d == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); } #endif #ifdef TEST_CPP_INT { + test_std_lib(); cpp_int a = 2; a <<= 1000; // Force dynamic allocation. void const* p = a.backend().limbs(); @@ -223,6 +268,11 @@ int main() BOOST_TEST(p != e.backend().limbs()); e = std::move(d); BOOST_TEST(e.backend().limbs() == p); + d = 2; + BOOST_TEST(d == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); } #endif return boost::report_errors(); From 8807532ee456d022216e574d0a2abe2077d8b137 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 8 Aug 2012 16:12:33 +0000 Subject: [PATCH 214/256] Added explicit conversion operators. Moved some files into /detail/ [SVN r79926] --- include/boost/multiprecision/cpp_int.hpp | 2 +- include/boost/multiprecision/detail/default_ops.hpp | 5 +++++ .../multiprecision/{ => detail}/integer_ops.hpp | 0 include/boost/multiprecision/gmp.hpp | 2 +- include/boost/multiprecision/mp_number.hpp | 7 +++++++ include/boost/multiprecision/tommath.hpp | 2 +- performance/arithmetic_backend.hpp | 2 +- test/test_arithmetic.cpp | 12 ++++++++++++ 8 files changed, 28 insertions(+), 4 deletions(-) rename include/boost/multiprecision/{ => detail}/integer_ops.hpp (100%) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 92672f52..3873720b 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -10,7 +10,7 @@ #include #include #include -#include +#include #include #include #include diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index e0e621d6..bf56825b 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -611,6 +611,11 @@ inline void eval_convert_to(terminal* result, const B& backend) result->value = boost::lexical_cast(backend.str(0, std::ios_base::fmtflags(0))); } +template +inline void eval_convert_to(std::string* result, const B& backend) +{ + *result = backend.str(0, std::ios_base::fmtflags(0)); +} // // Functions: // diff --git a/include/boost/multiprecision/integer_ops.hpp b/include/boost/multiprecision/detail/integer_ops.hpp similarity index 100% rename from include/boost/multiprecision/integer_ops.hpp rename to include/boost/multiprecision/detail/integer_ops.hpp diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 8baab295..bc5549e2 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -7,7 +7,7 @@ #define BOOST_MATH_ER_GMP_BACKEND_HPP #include -#include +#include #include #include #include diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/mp_number.hpp index 8b6df37f..704cec15 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/mp_number.hpp @@ -534,6 +534,13 @@ public: eval_convert_to(&result, m_backend); return result; } +#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS +template +explicit operator T()const +{ + return this->template convert_to(); +} +#endif // // Default precision: // diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 6f137936..eee4b341 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -8,7 +8,7 @@ #include #include -#include +#include #include #include #include diff --git a/performance/arithmetic_backend.hpp b/performance/arithmetic_backend.hpp index acff30cd..676c82d2 100644 --- a/performance/arithmetic_backend.hpp +++ b/performance/arithmetic_backend.hpp @@ -558,6 +558,6 @@ public: } -#include +#include #endif diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 85b3c9da..fad3dbb3 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -688,6 +688,12 @@ void test_negative_mixed(boost::mpl::true_ const&) BOOST_TEST(Real(n2).template convert_to() == n2); BOOST_TEST(Real(n3).template convert_to() == n3); BOOST_TEST(Real(n4).template convert_to() == n4); +#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS + BOOST_TEST(static_cast(Real(n1)) == n1); + BOOST_TEST(static_cast(Real(n2)) == n2); + BOOST_TEST(static_cast(Real(n3)) == n3); + BOOST_TEST(static_cast(Real(n4)) == n4); +#endif #if defined(TEST_MPFR) || defined(TEST_MPFR_50) Num tol = 10 * std::numeric_limits::epsilon(); #else @@ -789,6 +795,12 @@ void test_mixed() BOOST_TEST(Real(n2).template convert_to() == n2); BOOST_TEST(Real(n3).template convert_to() == n3); BOOST_TEST(Real(n4).template convert_to() == n4); +#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS + BOOST_TEST(static_cast(Real(n1)) == n1); + BOOST_TEST(static_cast(Real(n2)) == n2); + BOOST_TEST(static_cast(Real(n3)) == n3); + BOOST_TEST(static_cast(Real(n4)) == n4); +#endif BOOST_TEST(n1 == Real(n1)); BOOST_TEST(n2 == Real(n2)); BOOST_TEST(n3 == Real(n3)); From e2ef393c232c4c3deaf81c0b7279b5040c195566 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 8 Aug 2012 18:14:50 +0000 Subject: [PATCH 215/256] Big search and replace rename, removing mp_ prefix. [SVN r79932] --- doc/multiprecision.qbk | 556 ++++---- example/cpp_int_snips.cpp | 2 +- example/floating_point_examples.cpp | 4 +- example/integer_examples.cpp | 2 +- .../concepts/mp_number_archetypes.hpp | 8 +- .../boost/multiprecision/cpp_dec_float.hpp | 78 +- include/boost/multiprecision/cpp_int.hpp | 170 +-- .../depricated/arithmetic_backend.hpp | 6 +- .../multiprecision/depricated/fixed_int.hpp | 26 +- .../multiprecision/detail/big_lanczos.hpp | 4 +- .../detail/cpp_int_trivial_ops.hpp | 12 +- .../multiprecision/detail/default_ops.hpp | 376 ++--- .../detail/functions/constants.hpp | 6 +- .../multiprecision/detail/functions/pow.hpp | 22 +- .../multiprecision/detail/functions/trig.hpp | 24 +- .../detail/generic_interconvert.hpp | 18 +- .../multiprecision/detail/integer_ops.hpp | 64 +- .../multiprecision/detail/mp_number_base.hpp | 1262 ----------------- .../detail/mp_number_compare.hpp | 482 ------- .../boost/multiprecision/detail/no_et_ops.hpp | 334 ++--- .../multiprecision/detail/number_base.hpp | 1262 +++++++++++++++++ .../multiprecision/detail/number_compare.hpp | 482 +++++++ include/boost/multiprecision/gmp.hpp | 186 +-- include/boost/multiprecision/miller_rabin.hpp | 16 +- include/boost/multiprecision/mpfr.hpp | 126 +- .../{mp_number.hpp => number.hpp} | 198 +-- include/boost/multiprecision/random.hpp | 34 +- .../boost/multiprecision/rational_adapter.hpp | 22 +- include/boost/multiprecision/tommath.hpp | 54 +- performance/arithmetic_backend.hpp | 6 +- performance/delaunay_test.cpp | 12 +- performance/linpack-benchmark.cpp | 8 +- performance/miller_rabin_performance.cpp | 16 +- performance/performance_test.cpp | 14 +- performance/sf_performance.cpp | 24 +- ...ept_check.cpp => number_concept_check.cpp} | 18 +- test/concepts/sf_concept_check_basic.cpp | 10 +- test/concepts/sf_concept_check_bessel.cpp | 10 +- test/concepts/sf_concept_check_elliptic.cpp | 10 +- test/concepts/sf_concept_check_gamma.cpp | 10 +- test/concepts/sf_concept_check_poly.cpp | 10 +- test/include_test/cpp_int_include_test.cpp | 10 +- test/math/log1p_expm1_test.cpp | 18 +- test/math/powm1_sqrtp1m1_test.cpp | 18 +- test/math/test_bessel_i.cpp | 20 +- test/math/test_bessel_j.cpp | 18 +- test/math/test_bessel_k.cpp | 18 +- test/math/test_bessel_y.cpp | 18 +- test/math/test_beta.cpp | 18 +- test/math/test_binomial_coeff.cpp | 18 +- test/math/test_carlson.cpp | 18 +- test/math/test_cbrt.cpp | 18 +- test/math/test_digamma.cpp | 18 +- test/math/test_ellint_1.cpp | 18 +- test/math/test_ellint_2.cpp | 18 +- test/math/test_ellint_3.cpp | 18 +- test/math/test_erf.cpp | 18 +- test/math/test_expint.cpp | 18 +- test/math/test_gamma.cpp | 18 +- test/math/test_hermite.cpp | 18 +- test/math/test_ibeta.cpp | 18 +- test/math/test_ibeta_2.cpp | 18 +- test/math/test_ibeta_3.cpp | 18 +- test/math/test_ibeta_4.cpp | 18 +- test/math/test_ibeta_inv_1.cpp | 18 +- test/math/test_ibeta_inv_ab_4.cpp | 18 +- test/math/test_igamma.cpp | 18 +- test/math/test_igamma_inv.cpp | 18 +- test/math/test_igamma_inva.cpp | 18 +- test/math/test_laguerre.cpp | 18 +- test/math/test_legendre.cpp | 18 +- test/math/test_tgamma_ratio.cpp | 18 +- test/math/test_zeta.cpp | 20 +- test/test_acos.cpp | 18 +- test/test_arithmetic.cpp | 26 +- test/test_asin.cpp | 22 +- test/test_atan.cpp | 24 +- test/test_constants.cpp | 8 +- test/test_constexpr.cpp | 8 +- test/test_cos.cpp | 18 +- test/test_cosh.cpp | 18 +- test/test_cpp_int.cpp | 2 +- test/test_exp.cpp | 22 +- test/test_fixed_int.cpp | 2 +- test/test_float_io.cpp | 14 +- test/test_fpclassify.cpp | 2 +- test/test_generic_conv.cpp | 6 +- test/test_int_io.cpp | 6 +- test/test_log.cpp | 22 +- test/test_numeric_limits.cpp | 10 +- test/test_pow.cpp | 22 +- test/test_rational_io.cpp | 4 +- test/test_round.cpp | 18 +- test/test_sin.cpp | 22 +- test/test_sinh.cpp | 22 +- test/test_sqrt.cpp | 26 +- test/test_tanh.cpp | 18 +- test/ublas_interop/test1.hpp | 2 +- test/ublas_interop/test2.hpp | 2 +- test/ublas_interop/test3.hpp | 2 +- test/ublas_interop/test4.hpp | 2 +- test/ublas_interop/test5.hpp | 2 +- test/ublas_interop/test7.hpp | 2 +- 103 files changed, 3466 insertions(+), 3462 deletions(-) delete mode 100644 include/boost/multiprecision/detail/mp_number_base.hpp delete mode 100644 include/boost/multiprecision/detail/mp_number_compare.hpp create mode 100644 include/boost/multiprecision/detail/number_base.hpp create mode 100644 include/boost/multiprecision/detail/number_compare.hpp rename include/boost/multiprecision/{mp_number.hpp => number.hpp} (86%) rename test/concepts/{mp_number_concept_check.cpp => number_concept_check.cpp} (85%) diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 71b6a134..46679178 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -59,7 +59,7 @@ expression-template-enabled for better performance than naive user-defined types The Multiprecision library comes in two distinct parts: -* An expression-template-enabled front-end `mp_number` +* An expression-template-enabled front-end `number` that handles all the operator overloading, expression evaluation optimization, and code reduction. * A selection of back-ends that implement the actual arithmetic operations, and need conform only to the reduced interface requirements of the front-end. @@ -76,7 +76,7 @@ integer type using [gmp] as the underlying implementation then you could use: boost::multiprecision::mpz_int myint; // Arbitrary precision integer type. -Alternatively, you can compose your own multiprecision type, by combining `mp_number` with one of the +Alternatively, you can compose your own multiprecision type, by combining `number` with one of the predefined back-end types. For example, suppose you wanted a 300 decimal digit floating-point type based on the [mpfr] library. In this case, there's no predefined typedef with that level of precision, so instead we compose our own: @@ -85,18 +85,18 @@ so instead we compose our own: namespace mp = boost::multiprecision; // Reduce the typing a bit later... - typedef mp::mp_number > my_float; + typedef mp::number > my_float; my_float a, b, c; // These variables have 300 decimal digits precision We can repeat the above example, but with the expression templates disabled (for faster compile times, but slower runtimes) -by passing a second template argument to `mp_number`: +by passing a second template argument to `number`: #include // Defines the Backend type that wraps MPFR namespace mp = boost::multiprecision; // Reduce the typing a bit later... - typedef mp::mp_number, false> my_float; + typedef mp::number, false> my_float; my_float a, b, c; // These variables have 300 decimal digits precision @@ -106,8 +106,8 @@ Note that mixing arithmetic operations using types of different precision is str namespace mp = boost::multiprecision; // Reduce the typing a bit later... - mp::mp_int128_t a(3), b(2); - mp::mp_int512_t c(50), d; + mp::int128_t a(3), b(2); + mp::int512_t c(50), d; d = c * a; // Compiler error @@ -115,19 +115,19 @@ However, conversions are allowed: d = a; // OK, widening conversion. d = a * b; // OK, can convert from an expression template too. - d = mp::mp_int512_t(a) * c; // OK, all the types in the expression are the same now. + d = mp::int512_t(a) * c; // OK, all the types in the expression are the same now. [h4 Expression Templates] TODO: compare to rvalue refs. -Class `mp_number` is expression-template-enabled: that means that rather than having a multiplication +Class `number` is expression-template-enabled: that means that rather than having a multiplication operator that looks like this: template - mp_number operator * (const mp_number& a, const mp_number& b) + number operator * (const number& a, const number& b) { - mp_number result(a); + number result(a); result *= b; return result; } @@ -135,7 +135,7 @@ operator that looks like this: Instead the operator looks more like this: template - ``['unmentionable-type]`` operator * (const mp_number& a, const mp_number& b); + ``['unmentionable-type]`` operator * (const number& a, const number& b); Where the "unmentionable" return type is an implementation detail that, rather than containing the result of the multiplication, contains instructions on how to compute the result. In effect it's just a pair @@ -151,7 +151,7 @@ lets suppose we're evaluating a polynomial via Horners method, something like th //.... y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; -If type `T` is an `mp_number`, then this expression is evaluated ['without creating a single temporary value]. In contrast, +If type `T` is an `number`, then this expression is evaluated ['without creating a single temporary value]. In contrast, if we were using the [mpfr_class] C++ wrapper for [mpfr] - then this expression would result in no less than 11 temporaries (this is true even though [mpfr_class] does use expression templates to reduce the number of temporaries somewhat). Had we used an even simpler wrapper around [mpfr] like [mpreal] things would have been even worse and no less that 24 temporaries @@ -164,7 +164,7 @@ rvalue references. The number of 11 temporaries was generated with Visual C++ 1 [footnote Marc Glisse suggested pre-review that this could be reduced still further by careful use of rvalue-references and move semantics in the operator overloads. This will be investigated further at a later date.]. -This library also extends expression template support to standard library functions like `abs` or `sin` with `mp_number` +This library also extends expression template support to standard library functions like `abs` or `sin` with `number` arguments. This means that an expression such as: y = abs(x); @@ -185,7 +185,7 @@ Given the comments above, you might be forgiven for thinking that expression-tem sadly though, all tricks like this have their downsides. For one thing, expression template libraries like this one, tend to be slower to compile than their simpler cousins, they're also harder to debug (should you actually want to step through our code!), and rely on compiler optimizations being turned -on to give really good performance. Also, since the return type from expressions involving `mp_number`s +on to give really good performance. Also, since the return type from expressions involving `number`s is an "unmentionable implementation detail", you have to be careful to cast the result of an expression to the actual number type when passing an expression to a template function. For example, given: @@ -224,7 +224,7 @@ we see the following typical results for polynomial execution: [table Evaluation of Order 6 Polynomial. [[Library][Relative Time][Relative number of memory allocations]] -[[mp_number][1.0 (0.00793s)][1.0 (2996 total)]] +[[number][1.0 (0.00793s)][1.0 (2996 total)]] [[[mpfr_class]][1.2 (0.00931s)][4.3 (12976 total)]] [[[mpreal]][1.9 (0.0148s)][9.3 (27947 total)]] ] @@ -241,7 +241,7 @@ magic by converting out-of-place operators to in-place ones, we necessarily take transformation is more efficient than creating the extra temporary variable, just not by as much as one would hope. -Finally, note that `mp_number` takes a second template argument, which, when set to `false` disables all +Finally, note that `number` takes a second template argument, which, when set to `false` disables all the expression template machinery. The result is much faster to compile, but slower at runtime. We'll conclude this section by providing some more performance comparisons between these three libraries, @@ -252,14 +252,14 @@ TODO: Update, compare to rvalue refs but no ET's as well. [table Evaluation of Boost.Math's Bessel function test data [[Library][Relative Time][Relative Number of Memory Allocations]] -[[mp_number][1.0 (6.21s)][1.0 (2685469)]] +[[number][1.0 (6.21s)][1.0 (2685469)]] [[[mpfr_class]][1.04 (6.45s)][1.47 (3946007)]] [[[mpreal]][1.53 (9.52s)][4.92 (13222940)]] ] [table Evaluation of Boost.Math's Non-Central T distribution test data [[Library][Relative Time][Relative Number of Memory Allocations]] -[[mp_number][1.0 (269s)][1.0 (139082551)]] +[[number][1.0 (269s)][1.0 (139082551)]] [[[mpfr_class]][1.04 (278s)][1.81 (252400791)]] [[[mpreal]][1.49 (401s)][3.22 (447009280)]] ] @@ -294,28 +294,28 @@ The following back-ends provide integer arithmetic: template > class cpp_int_backend; - typedef mp_number > cpp_int; // arbitrary precision integer + typedef number > cpp_int; // arbitrary precision integer typedef rational_adapter > cpp_rational_backend; - typedef mp_number cpp_rational; // arbitrary precision rational number + typedef number cpp_rational; // arbitrary precision rational number // Fixed precision unsigned types: - typedef mp_number, false> mp_uint128_t; - typedef mp_number, false> mp_uint256_t; - typedef mp_number, false> mp_uint512_t; - typedef mp_number, false> mp_uint1024_t; + typedef number, false> uint128_t; + typedef number, false> uint256_t; + typedef number, false> uint512_t; + typedef number, false> uint1024_t; // Fixed precision signed types: - typedef mp_number, false> mp_int128_t; - typedef mp_number, false> mp_int256_t; - typedef mp_number, false> mp_int512_t; - typedef mp_number, false> mp_int1024_t; + typedef number, false> int128_t; + typedef number, false> int256_t; + typedef number, false> int512_t; + typedef number, false> int1024_t; }} // namespaces The `cpp_int_backend` type is used via one of the typedefs `boost::multiprecision::cpp_int`, -`boost::multiprecision::mp_uint128_t`, `boost::multiprecision::mp_uint256_t`, -`boost::multiprecision::mp_uint512_t`, `boost::multiprecision::mp_int128_t`, `boost::multiprecision::mp_int256_t` -or `boost::multiprecision::mp_int512_t`. +`boost::multiprecision::uint128_t`, `boost::multiprecision::uint256_t`, +`boost::multiprecision::uint512_t`, `boost::multiprecision::int128_t`, `boost::multiprecision::int256_t` +or `boost::multiprecision::int512_t`. This back-end is the "Swiss Army Knife" of integer types as it can represent both fixed and [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] @@ -343,7 +343,7 @@ Things you should know when using this type: * Since the precision of `cpp_int_backend` is necessarily limited when the allocator parameter is void, care should be taken to avoid numeric overflow when using this type unless you actually want modulo-arithmetic behavior. -* The type uses a sign-magnitude representation internally, so type `mp_int128_t` has 128-bits of precision plus an extra sign bit. +* The type uses a sign-magnitude representation internally, so type `int128_t` has 128-bits of precision plus an extra sign bit. In this respect the behaviour of these types differs from built-in 2's complement types. In might be tempting to use a 127-bit type instead, and indeed this does work, but behaviour is still slightly different from a 2's complement built-in type as the min and max values are identical (apart from the sign), where as they differ by one for a true 2's complement type. @@ -356,9 +356,9 @@ difference to the performance of these types either way - so we may as well have the feature off. * Unsigned types support subtraction, and unary negation - the result is "as if" a 2's complement operation had been performed - in other words they behave pretty much as a built in integer type would in this situation. So for example if we were using - `mp_uint128_t` then both `mp_uint128_t(1)-4` and `-mp_uint128(3)` would result in the value `0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD` - of type `mp_uint128_t`. -* This backend supports rvalue-references and is move-aware, making instantiations of `mp_number` on this backend move aware. + `uint128_t` then both `uint128_t(1)-4` and `-uint128(3)` would result in the value `0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD` + of type `uint128_t`. +* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. [h5 Example:] @@ -375,7 +375,7 @@ the feature off. class gmp_int; - typedef mp_number mpz_int; + typedef number mpz_int; }} // namespaces @@ -385,7 +385,7 @@ to provide an integer type that is a drop-in replacement for the native C++ inte As well as the usual conversions from arithmetic and string types, type `mpz_int` is copy constructible and assignable from: * The [gmp] native types: `mpf_t`, `mpz_t`, `mpq_t`. -* Instances of `mp_number` that are wrappers around those types: `mp_number >`, `mp_number`. +* Instances of `number` that are wrappers around those types: `number >`, `number`. It's also possible to access the underlying `mpz_t` via the `data()` member function of `gmp_int`. @@ -402,7 +402,7 @@ as a valid integer. * Division by zero results in a `std::runtime_error` being thrown. * Although this type is a wrapper around [gmp] it will work equally well with [mpir]. Indeed use of [mpir] is recommended on Win32. -* This backend supports rvalue-references and is move-aware, making instantiations of `mp_number` on this backend move aware. +* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. [h5 Example:] @@ -418,7 +418,7 @@ is recommended on Win32. class tommath_int; - typedef mp_number tom_int; + typedef number tom_int; }} // namespaces @@ -481,15 +481,15 @@ The following back-ends provide floating point arithmetic: template class gmp_float; - typedef mp_number > mpf_float_50; - typedef mp_number > mpf_float_100; - typedef mp_number > mpf_float_500; - typedef mp_number > mpf_float_1000; - typedef mp_number > mpf_float; + typedef number > mpf_float_50; + typedef number > mpf_float_100; + typedef number > mpf_float_500; + typedef number > mpf_float_1000; + typedef number > mpf_float; }} // namespaces -The `gmp_float` back-end is used in conjunction with `mp_number` : it acts as a thin wrapper around the [gmp] `mpf_t` +The `gmp_float` back-end is used in conjunction with `number` : it acts as a thin wrapper around the [gmp] `mpf_t` to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. @@ -497,15 +497,15 @@ Type `gmp_float` can be used at fixed precision by specifying a non-zero `Digits at variable precision by setting the template argument to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision respectively. The typedef mpf_float provides a variable precision type whose precision can be controlled via the -`mp_number`s member functions. +`number`s member functions. [note This type only provides standard library and `numeric_limits` support when the precision is fixed at compile time.] -As well as the usual conversions from arithmetic and string types, instances of `mp_number >` are +As well as the usual conversions from arithmetic and string types, instances of `number >` are copy constructible and assignable from: * The [gmp] native types `mpf_t`, `mpz_t`, `mpq_t`. -* The `mp_number` wrappers around those types: `mp_number >`, `mp_number`, `mp_number`. +* The `number` wrappers around those types: `number >`, `number`, `number`. It's also possible to access the underlying `mpf_t` via the `data()` member function of `gmp_float`. @@ -514,7 +514,7 @@ Things you should know when using this type: * Default constructed `gmp_float`s have the value zero (this is the [gmp] library's default behavior). * No changes are made to the [gmp] library's global settings, so this type can be safely mixed with existing [gmp] code. -* This backend supports rvalue-references and is move-aware, making instantiations of `mp_number` on this backend move aware. +* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. * It is not possible to round-trip objects of this type to and from a string and get back exactly the same value. This appears to be a limitation of [gmp]. * Since the underlying [gmp] types have no notion of infinities or NaN's, care should be taken @@ -543,15 +543,15 @@ as a valid floating point number. template class mpfr_float_backend; - typedef mp_number > mpfr_float_50; - typedef mp_number > mpfr_float_100; - typedef mp_number > mpfr_float_500; - typedef mp_number > mpfr_float_1000; - typedef mp_number > mpfr_float; + typedef number > mpfr_float_50; + typedef number > mpfr_float_100; + typedef number > mpfr_float_500; + typedef number > mpfr_float_1000; + typedef number > mpfr_float; }} // namespaces -The `mpfr_float_backend` type is used in conjunction with `mp_number`: It acts as a thin wrapper around the [mpfr] `mpfr_t` +The `mpfr_float_backend` type is used in conjunction with `number`: It acts as a thin wrapper around the [mpfr] `mpfr_t` to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. @@ -559,16 +559,16 @@ Type `mpfr_float_backend` can be used at fixed precision by specifying a non-zer at variable precision by setting the template argument to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision respectively. The typedef mpfr_float provides a variable precision type whose precision can be controlled via the -`mp_number`s member functions. +`number`s member functions. [note This type only provides `numeric_limits` support when the precision is fixed at compile time.] -As well as the usual conversions from arithmetic and string types, instances of `mp_number >` are +As well as the usual conversions from arithmetic and string types, instances of `number >` are copy constructible and assignable from: * The [gmp] native types `mpf_t`, `mpz_t`, `mpq_t`. * The [mpfr] native type `mpfr_t`. -* The `mp_number` wrappers around those types: `mp_number >`, `mp_number >`, `mp_number`, `mp_number`. +* The `number` wrappers around those types: `number >`, `number >`, `number`, `number`. It's also possible to access the underlying `mpf_t` via the data() member function of `gmp_float`. @@ -579,7 +579,7 @@ Things you should know when using this type: * No changes are made to [gmp] or [mpfr] global settings, so this type can coexist with existing [mpfr] or [gmp] code. * The code can equally use [mpir] in place of [gmp] - indeed that is the preferred option on Win32. -* This backend supports rvalue-references and is move-aware, making instantiations of `mp_number` on this backend move aware. +* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. * Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted as a valid floating point number. * Division by zero results in an infinity. @@ -599,12 +599,12 @@ as a valid floating point number. template class cpp_dec_float; - typedef mp_number > cpp_dec_float_50; - typedef mp_number > cpp_dec_float_100; + typedef number > cpp_dec_float_50; + typedef number > cpp_dec_float_100; }} // namespaces -The `cpp_dec_float` back-end is used in conjunction with `mp_number`: It acts as an entirely C++ (header only and dependency free) +The `cpp_dec_float` back-end is used in conjunction with `number`: It acts as an entirely C++ (header only and dependency free) real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. @@ -625,8 +625,8 @@ Normally these should not be visible to the user. * The type supports both infinities and NaN's. An infinity is generated whenever the result would overflow, and a NaN is generated for any mathematically undefined operation. * There is a `std::numeric_limits` specialisation for this type. -* Any `mp_number` instantiated on this type, is convertible to any other `mp_number` instantiated on this type - -for example you can convert from `mp_number >` to `mp_number >`. +* Any `number` instantiated on this type, is convertible to any other `number` instantiated on this type - +for example you can convert from `number >` to `number >`. Narrowing conversions are truncating. * Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted as a valid floating point number. @@ -690,7 +690,7 @@ The following back-ends provide rational number arithmetic: [[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licensed implementation.][Slower than [gmp].]] [[`tommath_rational`][boost/multiprecision/tommath.hpp][2][[tommath]][All C/C++ implementation that's Boost Software Licence compatible.][Slower than [gmp].]] [[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any integer back-end type to be used as a rational type.][Requires an underlying integer back-end type.]] -[[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `mp_number` integer type.][The expression templates used by `mp_number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]] +[[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `number` integer type.][The expression templates used by `number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]] ] [section:gmp_rational gmp_rational] @@ -701,20 +701,20 @@ The following back-ends provide rational number arithmetic: class gmp_rational; - typedef mp_number mpq_rational; + typedef number mpq_rational; }} // namespaces The `gmp_rational` back-end is used via the typedef `boost::multiprecision::mpq_rational`. It acts as a thin wrapper around the [gmp] `mpq_t` to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. -As well as the usual conversions from arithmetic and string types, instances of `mp_number` are copy constructible +As well as the usual conversions from arithmetic and string types, instances of `number` are copy constructible and assignable from: * The [gmp] native types: `mpz_t`, `mpq_t`. -* `mp_number`. +* `number`. -There is also a two-argument constructor that accepts a numerator and denominator (both of type `mp_number`). +There is also a two-argument constructor that accepts a numerator and denominator (both of type `number`). There are also non-member functions: @@ -749,7 +749,7 @@ interpreted as a valid rational number. typedef rational_adapter > cpp_rational_backend; - typedef mp_number cpp_rational; + typedef number cpp_rational; }} // namespaces @@ -788,7 +788,7 @@ interpreted as a valid rational number. namespace boost{ namespace multiprecision{ typedef rational_adpater tommath_rational; - typedef mp_number tom_rational; + typedef number tom_rational; }} // namespaces @@ -826,7 +826,7 @@ needs some improvement in this area. All of the integer types in this library can be used as template arguments to `boost::rational`. -Note that using the library in this way largely negates the effect of the expression templates in `mp_number`. +Note that using the library in this way largely negates the effect of the expression templates in `number`. [endsect] @@ -839,13 +839,13 @@ Note that using the library in this way largely negates the effect of the expres }} -The class template `rational_adapter` is a back-end for `mp_number` which converts any existing integer back-end +The class template `rational_adapter` is a back-end for `number` which converts any existing integer back-end into a rational-number back-end. So for example, given an integer back-end type `MyIntegerBackend`, the use would be something like: - typedef mp_number MyInt; - typedef mp_number > MyRational; + typedef number MyInt; + typedef number > MyRational; MyRational r = 2; r /= 3; @@ -858,7 +858,7 @@ So for example, given an integer back-end type `MyIntegerBackend`, the use would [section:conversions Constructing and Interconverting Between Number Types] -All of the number types that are based on `mp_number` have certain conversion rules in common. +All of the number types that are based on `number` have certain conversion rules in common. In particular: * Any number type can be constructed (or assigned) from any builtin arithmetic type: @@ -921,7 +921,7 @@ In particular: More information on what additional types a backend supports conversions from are given in the tutorial for each backend. -* An `mp_number` can be converted to any built in type, via the `convert_to` member function: +* An `number` can be converted to any built in type, via the `convert_to` member function: mpz_int z(2); int i = z.template convert_to(); // sets i to 2 @@ -968,10 +968,10 @@ The library implements a Miller-Rabin test for primality: #include template - bool miller_rabin_test(const mp_number& n, unsigned trials, Engine& gen); + bool miller_rabin_test(const number& n, unsigned trials, Engine& gen); template - bool miller_rabin_test(const mp_number& n, unsigned trials); + bool miller_rabin_test(const number& n, unsigned trials); These functions perform a Miller-Rabin test for primality, if the result is `false` then /n/ is definitely composite, while if the result is `true` then /n/ is prime with probability ['0.25^trials]. The algorithm used performs some @@ -994,40 +994,40 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba [section:ref Reference] -[section:mp_number mp_number] +[section:number number] [h4 Synopsis] namespace boost{ namespace multiprecision{ template - class mp_number + class number { - mp_number(); - mp_number(see-below); - mp_number& operator=(see-below); + number(); + number(see-below); + number& operator=(see-below); // Member operators - mp_number& operator+=(const ``['see-below]``&); - mp_number& operator-=(const ``['see-below]``&); - mp_number& operator*=(const ``['see-below]``&); - mp_number& operator/=(const ``['see-below]``&); - mp_number& operator++(); - mp_number& operator--(); - mp_number operator++(int); - mp_number operator--(int); + number& operator+=(const ``['see-below]``&); + number& operator-=(const ``['see-below]``&); + number& operator*=(const ``['see-below]``&); + number& operator/=(const ``['see-below]``&); + number& operator++(); + number& operator--(); + number operator++(int); + number operator--(int); - mp_number& operator%=(const ``['see-below]``&); - mp_number& operator&=(const ``['see-below]``&); - mp_number& operator|=(const ``['see-below]``&); - mp_number& operator^=(const ``['see-below]``&); - mp_number& operator<<=(const ``['integer-type]``&); - mp_number& operator>>=(const ``['integer-type]``&); + number& operator%=(const ``['see-below]``&); + number& operator&=(const ``['see-below]``&); + number& operator|=(const ``['see-below]``&); + number& operator^=(const ``['see-below]``&); + number& operator<<=(const ``['integer-type]``&); + number& operator>>=(const ``['integer-type]``&); // Use in Boolean context: operator ``['convertible-to-bool-type]``()const; // swap: - void swap(mp_number& other); + void swap(number& other); // Sign: bool is_zero()const; int sign()const; @@ -1042,7 +1042,7 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba unsigned precision()const; void precision(unsigned digits10); // Comparison: - int compare(const mp_number& o)const; + int compare(const number& o)const; template typename enable_if, int>::type compare(const V& o)const; // Access to the underlying implementation: @@ -1074,47 +1074,47 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba // Swap: template - void swap(mp_number& a, mp_number& b); + void swap(number& a, number& b); // iostream support: template - std::ostream& operator << (std::ostream& os, const mp_number& r); + std::ostream& operator << (std::ostream& os, const number& r); std::ostream& operator << (std::ostream& os, const ``['unmentionable-expression-template-type]``& r); template - std::istream& operator >> (std::istream& is, mp_number& r); + std::istream& operator >> (std::istream& is, number& r); // Non-member function standard library support: - ``['unmentionable-expression-template-type]`` abs (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` fabs (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sqrt (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` floor (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` ceil (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` trunc (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` itrunc (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` ltrunc (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` lltrunc(const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` round (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` iround (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` lround (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` llround(const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` exp (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` log (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` log10 (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` cos (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sin (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` tan (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` acos (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` asin (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` atan (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` cosh (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sinh (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` tanh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` abs (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fabs (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sqrt (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` floor (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ceil (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` trunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` itrunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ltrunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lltrunc(const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` round (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` iround (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lround (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` llround(const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` exp (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log10 (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cos (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sin (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tan (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` acos (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` asin (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cosh (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sinh (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tanh (const ``['number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` ldexp (const ``['mp_number-or-expression-template-type]``&, int); - ``['unmentionable-expression-template-type]`` frexp (const ``['mp_number-or-expression-template-type]``&, int*); - ``['unmentionable-expression-template-type]`` pow (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` fmod (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` atan2 (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ldexp (const ``['number-or-expression-template-type]``&, int); + ``['unmentionable-expression-template-type]`` frexp (const ``['number-or-expression-template-type]``&, int*); + ``['unmentionable-expression-template-type]`` pow (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fmod (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan2 (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); // Traits support: template @@ -1123,40 +1123,40 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba struct number_category; // Integer specific functions: - ``['unmentionable-expression-template-type]`` pow(const ``['mp_number-or-expression-template-type]``&, unsigned); - ``['unmentionable-expression-template-type]`` powm(const ``['mp_number-or-expression-template-type]``& b, const ``['mp_number-or-expression-template-type]``& p, const ``['mp_number-or-expression-template-type]``& m); + ``['unmentionable-expression-template-type]`` pow(const ``['number-or-expression-template-type]``&, unsigned); + ``['unmentionable-expression-template-type]`` powm(const ``['number-or-expression-template-type]``& b, const ``['number-or-expression-template-type]``& p, const ``['number-or-expression-template-type]``& m); template - void divide_qr(const ``['mp_number-or-expression-template-type]``& x, const ``['mp_number-or-expression-template-type]``& y, - mp_number& q, mp_number& r); + void divide_qr(const ``['number-or-expression-template-type]``& x, const ``['number-or-expression-template-type]``& y, + number& q, number& r); template - Integer integer_modulus(const ``['mp_number-or-expression-template-type]``& x, Integer val); - unsigned lsb(const ``['mp_number-or-expression-template-type]``& x); + Integer integer_modulus(const ``['number-or-expression-template-type]``& x, Integer val); + unsigned lsb(const ``['number-or-expression-template-type]``& x); template - bool bit_test(const mp_number& val, unsigned index); + bool bit_test(const number& val, unsigned index); template - mp_number& bit_set(mp_number& val, unsigned index); + number& bit_set(number& val, unsigned index); template - mp_number& bit_unset(mp_number& val, unsigned index); + number& bit_unset(number& val, unsigned index); template - mp_number& bit_flip(mp_number& val, unsigned index); + number& bit_flip(number& val, unsigned index); template - bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials, Engine& gen); - bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials); + bool miller_rabin_test(const ``['number-or-expression-template-type]``& n, unsigned trials, Engine& gen); + bool miller_rabin_test(const ``['number-or-expression-template-type]``& n, unsigned trials); // Rational number support: - typename component_type<``['mp_number-or-expression-template-type]``>::type numerator (const ``['mp_number-or-expression-template-type]``&); - typename component_type<``['mp_number-or-expression-template-type]``>::type denominator(const ``['mp_number-or-expression-template-type]``&); + typename component_type<``['number-or-expression-template-type]``>::type numerator (const ``['number-or-expression-template-type]``&); + typename component_type<``['number-or-expression-template-type]``>::type denominator(const ``['number-or-expression-template-type]``&); }} // namespaces namespace boost{ namespace math{ // Boost.Math interoperability functions: - int fpclassify (const ``['mp_number-or-expression-template-type]``&, int); - bool isfinite (const ``['mp_number-or-expression-template-type]``&, int); - bool isnan (const ``['mp_number-or-expression-template-type]``&, int); - bool isinf (const ``['mp_number-or-expression-template-type]``&, int); - bool isnormal (const ``['mp_number-or-expression-template-type]``&, int); + int fpclassify (const ``['number-or-expression-template-type]``&, int); + bool isfinite (const ``['number-or-expression-template-type]``&, int); + bool isnan (const ``['number-or-expression-template-type]``&, int); + bool isinf (const ``['number-or-expression-template-type]``&, int); + bool isnormal (const ``['number-or-expression-template-type]``&, int); }} // namespaces @@ -1174,77 +1174,77 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba [h4 Description] template - class mp_number; + class number; -Class `mp_number` has two template arguments: +Class `number` has two template arguments: [variablelist [[Backend][The actual arithmetic back-end that does all the work.]] [[ExpressionTemplates][A Boolean value: when true, then expression templates are enabled, otherwise they are disabled.]] ] - mp_number(); - mp_number(see-below); - mp_number& operator=(see-below); + number(); + number(see-below); + number& operator=(see-below); -Type `mp_number` is default constructible, and both copy constructible and assignable from: +Type `number` is default constructible, and both copy constructible and assignable from: * Itself. * An expression template which is the result of one of the arithmetic operators. * Any builtin arithmetic type. * A `std::string` or any type which is convertible to `const char*`. * Any type that the Backend is constructible or assignable from. -* An rvalue reference to another `mp_number`. Move-semantics are used for construction if the backend also +* An rvalue reference to another `number`. Move-semantics are used for construction if the backend also supports rvalue reference construction. In the case of assignment, move semantics are always supported when the argument is an rvalue reference irrespective of the backend. In addition, if the type has multiple components (for example rational or complex number types), then there is a two argument constructor: - mp_number(arg1, arg2); + number(arg1, arg2); Where the two args must either be arithmetic types, or types that are convertible to the two components of `this`. - mp_number& operator+=(const ``['see-below]``&); - mp_number& operator-=(const ``['see-below]``&); - mp_number& operator*=(const ``['see-below]``&); - mp_number& operator/=(const ``['see-below]``&); - mp_number& operator++(); - mp_number& operator--(); - mp_number operator++(int); - mp_number operator--(int); + number& operator+=(const ``['see-below]``&); + number& operator-=(const ``['see-below]``&); + number& operator*=(const ``['see-below]``&); + number& operator/=(const ``['see-below]``&); + number& operator++(); + number& operator--(); + number operator++(int); + number operator--(int); // Integer only operations: - mp_number& operator%=(const ``['see-below]``&); - mp_number& operator&=(const ``['see-below]``&); - mp_number& operator|=(const ``['see-below]``&); - mp_number& operator^=(const ``['see-below]``&); - mp_number& operator<<=(const ``['integer-type]``&); - mp_number& operator>>=(const ``['integer-type]``&); + number& operator%=(const ``['see-below]``&); + number& operator&=(const ``['see-below]``&); + number& operator|=(const ``['see-below]``&); + number& operator^=(const ``['see-below]``&); + number& operator<<=(const ``['integer-type]``&); + number& operator>>=(const ``['integer-type]``&); These operators all take their usual arithmetic meanings. The arguments to these operators is either: -* Another `mp_number`. +* Another `number`. * A builtin arithmetic type. -* An expression template derived from `mp_number`. +* An expression template derived from `number`. For the left and right shift operations, the argument must be a builtin integer type with a positive value (negative values result in a `std::runtime_error` being thrown). Note that all the types involved in the expression must evaluate to the same type - which is to say -we cannot mix an `mp_number` with an `mp_number` where B1 and B2 are different types. +we cannot mix an `number` with an `number` where B1 and B2 are different types. operator ``['convertible-to-bool-type]``()const; -Returns an ['unmentionable-type] that is usable in Boolean contexts (this allows `mp_number` to be used in any +Returns an ['unmentionable-type] that is usable in Boolean contexts (this allows `number` to be used in any Boolean context - if statements, conditional statements, or as an argument to a logical operator - without -type `mp_number` being convertible to type `bool`. +type `number` being convertible to type `bool`. -This operator also enables the use of `mp_number` with any of the following operators: +This operator also enables the use of `number` with any of the following operators: `!`, `||`, `&&` and `?:`. - void swap(mp_number& other); + void swap(number& other); Swaps `*this` with `other`. @@ -1277,7 +1277,7 @@ Optionally other types may also be supported by specific `Backend` types. These functions are only available if the Backend template parameter supports runtime changes to precision. They get and set the default precision and the precision of `*this` respectively. - int compare(const mp_number& o)const; + int compare(const number& o)const; template typename enable_if, int>::type compare(const V& other)const; @@ -1320,19 +1320,19 @@ These operators all take their usual arithmetic meanings. The arguments to these functions must contain at least one of the following: -* An `mp_number`. -* An expression template type derived from `mp_number`. +* An `number`. +* An expression template type derived from `number`. In addition, one of the two arguments may be a builtin arithmetic type. The return type of these operators is either: * An ['unmentionable-type] expression template type when `ExpressionTemplates` is `true`. -* Type `mp_number` when `ExpressionTemplates` is `false`. +* Type `number` when `ExpressionTemplates` is `false`. * Type `bool` if the operator is a comparison operator. Note that all the types involved in the expression must evaluate to the same type - which is to say -we cannot mix an `mp_number` with an `mp_number` where B1 and B2 are different types. +we cannot mix an `number` with an `number` where B1 and B2 are different types. Finally note that the second argument to the left and right shift operations must be a builtin integer type, and that the argument must be positive (negative arguments result in a `std::runtime_error` being thrown). @@ -1340,60 +1340,60 @@ and that the argument must be positive (negative arguments result in a `std::run [h4 swap] template - void swap(mp_number& a, mp_number& b); + void swap(number& a, number& b); Swaps `a` and `b`. [h4 Iostream Support] template - std::ostream& operator << (std::ostream& os, const mp_number& r); + std::ostream& operator << (std::ostream& os, const number& r); template std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r); template - inline std::istream& operator >> (std::istream& is, mp_number& r) + inline std::istream& operator >> (std::istream& is, number& r) -These operators provided formatted input-output operations on `mp_number` types, and expression templates derived from them. +These operators provided formatted input-output operations on `number` types, and expression templates derived from them. It's down to the back-end type to actually implement string conversion. However, the back-ends provided with this library support all of the iostream formatting flags, field width and precision settings. [h4 Non-member standard library function support] - ``['unmentionable-expression-template-type]`` abs (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` fabs (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sqrt (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` floor (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` ceil (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` trunc (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` itrunc (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` ltrunc (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` lltrunc(const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` round (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` iround (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` lround (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` llround(const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` exp (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` log (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` log10 (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` cos (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sin (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` tan (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` acos (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` asin (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` atan (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` cosh (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` sinh (const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` tanh (const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` abs (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fabs (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sqrt (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` floor (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ceil (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` trunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` itrunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ltrunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lltrunc(const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` round (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` iround (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lround (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` llround(const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` exp (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log10 (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cos (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sin (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tan (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` acos (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` asin (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cosh (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sinh (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tanh (const ``['number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` ldexp (const ``['mp_number-or-expression-template-type]``&, int); - ``['unmentionable-expression-template-type]`` frexp (const ``['mp_number-or-expression-template-type]``&, int*); - ``['unmentionable-expression-template-type]`` pow (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` fmod (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); - ``['unmentionable-expression-template-type]`` atan2 (const ``['mp_number-or-expression-template-type]``&, const ``['mp_number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ldexp (const ``['number-or-expression-template-type]``&, int); + ``['unmentionable-expression-template-type]`` frexp (const ``['number-or-expression-template-type]``&, int*); + ``['unmentionable-expression-template-type]`` pow (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fmod (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan2 (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); -These functions all behave exactly as their standard library counterparts do: their argument is either an instance of `mp_number` or -an expression template derived from it; If the argument is of type `mp_number` then that is also the return type, +These functions all behave exactly as their standard library counterparts do: their argument is either an instance of `number` or +an expression template derived from it; If the argument is of type `number` then that is also the return type, otherwise the return type is an expression template. These functions are normally implemented by the Backend type. However, default versions are provided for Backend types that @@ -1421,53 +1421,53 @@ A traits class that inherits from `mpl::int_` where `N` is one of the enumera [h4 Integer functions] - ``['unmentionable-expression-template-type]`` pow(const ``['mp_number-or-expression-template-type]``& b, unsigned p); + ``['unmentionable-expression-template-type]`` pow(const ``['number-or-expression-template-type]``& b, unsigned p); Returns ['b[super p]] as an expression template. Note that this function should be used with extreme care as the result can grow so large as to take "effectively forever" to compute, or else simply run the host machine out of memory. - ``['unmentionable-expression-template-type]`` powm(const ``['mp_number-or-expression-template-type]``& b, const ``['mp_number-or-expression-template-type]``& p, const ``['mp_number-or-expression-template-type]``& m); + ``['unmentionable-expression-template-type]`` powm(const ``['number-or-expression-template-type]``& b, const ``['number-or-expression-template-type]``& p, const ``['number-or-expression-template-type]``& m); Returns ['b[super p] mod m] as an expression template. template - bool divide_qr(const ``['mp_number-or-expression-template-type]``& x, const ``['mp_number-or-expression-template-type]``& y, - mp_number& q, mp_number& r); + bool divide_qr(const ``['number-or-expression-template-type]``& x, const ``['number-or-expression-template-type]``& y, + number& q, number& r); Divides x by y and returns both the quotient and remainder. After the call `q = x / y` and `r = x % y`. template - Integer integer_modulus(const ``['mp_number-or-expression-template-type]``& x, Integer val); + Integer integer_modulus(const ``['number-or-expression-template-type]``& x, Integer val); Returns the absolute value of `x % val`. - unsigned lsb(const ``['mp_number-or-expression-template-type]``& x); + unsigned lsb(const ``['number-or-expression-template-type]``& x); Returns the index of the least significant bit that is set to 1. template - bool bit_test(const mp_number& val, unsigned index); + bool bit_test(const number& val, unsigned index); Returns `true` if the bit at /index/ in /val/ is set. template - mp_number& bit_set(mp_number& val, unsigned index); + number& bit_set(number& val, unsigned index); Sets the bit at /index/ in /val/, and returns /val/. template - mp_number& bit_unset(mp_number& val, unsigned index); + number& bit_unset(number& val, unsigned index); Unsets the bit at /index/ in /val/, and returns /val/. template - mp_number& bit_flip(mp_number& val, unsigned index); + number& bit_flip(number& val, unsigned index); Flips the bit at /index/ in /val/, and returns /val/. template - bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials, Engine& gen); - bool miller_rabin_test(const ``['mp_number-or-expression-template-type]``& n, unsigned trials); + bool miller_rabin_test(const ``['number-or-expression-template-type]``& n, unsigned trials, Engine& gen); + bool miller_rabin_test(const ``['number-or-expression-template-type]``& n, unsigned trials); Tests to see if the number /n/ is probably prime - the test excludes the vast majority of composite numbers by excluding small prime factors and performing a single Fermat test. Then performs /trials/ Miller-Rabin @@ -1476,8 +1476,8 @@ probability of it being composite less than 0.25^trials. [h4 Rational Number Functions] - typename component_type<``['mp_number-or-expression-template-type]``>::type numerator (const ``['mp_number-or-expression-template-type]``&); - typename component_type<``['mp_number-or-expression-template-type]``>::type denominator(const ``['mp_number-or-expression-template-type]``&); + typename component_type<``['number-or-expression-template-type]``>::type numerator (const ``['number-or-expression-template-type]``&); + typename component_type<``['number-or-expression-template-type]``>::type denominator(const ``['number-or-expression-template-type]``&); These functions return the numerator and denominator of a rational number respectively. @@ -1485,11 +1485,11 @@ These functions return the numerator and denominator of a rational number respec namespace boost{ namespace math{ - int fpclassify (const ``['mp_number-or-expression-template-type]``&, int); - bool isfinite (const ``['mp_number-or-expression-template-type]``&, int); - bool isnan (const ``['mp_number-or-expression-template-type]``&, int); - bool isinf (const ``['mp_number-or-expression-template-type]``&, int); - bool isnormal (const ``['mp_number-or-expression-template-type]``&, int); + int fpclassify (const ``['number-or-expression-template-type]``&, int); + bool isfinite (const ``['number-or-expression-template-type]``&, int); + bool isnan (const ``['number-or-expression-template-type]``&, int); + bool isinf (const ``['number-or-expression-template-type]``&, int); + bool isnormal (const ``['number-or-expression-template-type]``&, int); }} // namespaces @@ -1510,7 +1510,7 @@ specialized or overloaded to ensure interoperability. } -Class template `std::numeric_limits` is specialized for all instantiations of `mp_number` whose precision is known at compile time, plus those +Class template `std::numeric_limits` is specialized for all instantiations of `number` whose precision is known at compile time, plus those types whose precision is unlimited (though it is much less useful in those cases). It is not specialized for types whose precision can vary at compile time (such as `mpf_float`). @@ -1523,21 +1523,21 @@ whose precision can vary at compile time (such as `mpf_float`). template > struct cpp_int_backend; - typedef mp_number > cpp_int; // arbitrary precision integer + typedef number > cpp_int; // arbitrary precision integer typedef rational_adapter > cpp_rational_backend; - typedef mp_number cpp_rational; // arbitrary precision rational number + typedef number cpp_rational; // arbitrary precision rational number // Fixed precision unsigned types: - typedef mp_number, false> mp_uint128_t; - typedef mp_number, false> mp_uint256_t; - typedef mp_number, false> mp_uint512_t; - typedef mp_number, false> mp_uint1024_t; + typedef number, false> uint128_t; + typedef number, false> uint256_t; + typedef number, false> uint512_t; + typedef number, false> uint1024_t; // Fixed precision signed types: - typedef mp_number, false> mp_int128_t; - typedef mp_number, false> mp_int256_t; - typedef mp_number, false> mp_int512_t; - typedef mp_number, false> mp_int1024_t; + typedef number, false> int128_t; + typedef number, false> int256_t; + typedef number, false> int512_t; + typedef number, false> int1024_t; }} // namespaces @@ -1572,7 +1572,7 @@ More information on this type can be found in the [link boost_multiprecision.tut class gmp_int; - typedef mp_number mpz_int; + typedef number mpz_int; }} // namespaces @@ -1592,7 +1592,7 @@ More information on this type can be found in the [link boost_multiprecision.tut class tommath_int; - typedef mp_number tom_int; + typedef number tom_int; }} // namespaces @@ -1613,11 +1613,11 @@ More information on this type can be found in the [link boost_multiprecision.tut template class gmp_float; - typedef mp_number > mpf_float_50; - typedef mp_number > mpf_float_100; - typedef mp_number > mpf_float_500; - typedef mp_number > mpf_float_1000; - typedef mp_number > mpf_float; + typedef number > mpf_float_50; + typedef number > mpf_float_100; + typedef number > mpf_float_500; + typedef number > mpf_float_1000; + typedef number > mpf_float; }} // namespaces @@ -1626,8 +1626,8 @@ Its members and non-member functions are deliberately not documented: these are to change. The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type -should support. When this parameter is zero, then the precision can be set at runtime via `mp_number::default_precision` -and `mp_number::precision`. Note that this type does not in any way change the GMP library's global state (for example +should support. When this parameter is zero, then the precision can be set at runtime via `number::default_precision` +and `number::precision`. Note that this type does not in any way change the GMP library's global state (for example it does not change the default precision of the mpf_t data type), therefore you can safely mix this type with existing code that uses GMP, and also mix `gmp_float`s of differing precision. @@ -1644,11 +1644,11 @@ More information on this type can be found in the [link boost_multiprecision.tut template class mpfr_float_backend; - typedef mp_number > mpfr_float_50; - typedef mp_number > mpfr_float_100; - typedef mp_number > mpfr_float_500; - typedef mp_number > mpfr_float_1000; - typedef mp_number > mpfr_float; + typedef number > mpfr_float_50; + typedef number > mpfr_float_100; + typedef number > mpfr_float_500; + typedef number > mpfr_float_1000; + typedef number > mpfr_float; }} // namespaces @@ -1657,8 +1657,8 @@ Its members and non-member functions are deliberately not documented: these are to change. The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type -should support. When this parameter is zero, then the precision can be set at runtime via `mp_number::default_precision` -and `mp_number::precision`. Note that this type does not in any way change the GMP or MPFR library's global state (for example +should support. When this parameter is zero, then the precision can be set at runtime via `number::default_precision` +and `number::precision`. Note that this type does not in any way change the GMP or MPFR library's global state (for example it does not change the default precision of the mpfr_t data type), therefore you can safely mix this type with existing code that uses GMP or MPFR, and also mix `mpfr_float_backend`s of differing precision. @@ -1675,8 +1675,8 @@ More information on this type can be found in the [link boost_multiprecision.tut template class cpp_dec_float; - typedef mp_number > cpp_dec_float_50; - typedef mp_number > cpp_dec_float_100; + typedef number > cpp_dec_float_50; + typedef number > cpp_dec_float_100; }} // namespaces @@ -1696,13 +1696,13 @@ More information on this type can be found in the [link boost_multiprecision.tut [section:backendconc Backend Requirements] -The requirements on the `Backend` template argument to `mp_number` are split up into +The requirements on the `Backend` template argument to `number` are split up into compulsory requirements, and optional requirements that are either to improve performance or provide optional features. TODO: Add optional construction support, add throws specification, clarify what compulsory means. -In the following tables, type B is the `Backend` template arument to `mp_number`, `b` and `b2` are +In the following tables, type B is the `Backend` template arument to `number`, `b` and `b2` are a variables of type B, `cb` and `cb2` are constant variables of type B, `a` is a variable of Arithmetic type, `s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`, `pa` is a variable of type pointer-to-arithmetic-type, `exp` is a variable of type `B::exp_type`, @@ -1880,7 +1880,7 @@ in point of fact this naming convention shouldn't be necessary, but rather works [[gmp.hpp][Defines all [gmp] related backends.]] [[integer_ops.hpp][Integer specific non-member functions.]] [[miller_rabin.hpp][Miller Rabin primality testing code.]] -[[mp_number.hpp][Defines the `mp_number` backend, is included by all the backend headers.]] +[[number.hpp][Defines the `number` backend, is included by all the backend headers.]] [[mpfr.hpp][Defines the mpfr_float_backend backend.]] [[random.hpp][Defines code to interoperate with Boost.Random.]] [[rational_adapter.hpp][Defines the `rational_adapter` backend.]] @@ -1895,7 +1895,7 @@ in point of fact this naming convention shouldn't be necessary, but rather works [[detail/cpp_int_core.hpp][Platform and peformance tuning for the `cpp_int` backend.]] [[detail/default_ops.hpp][Default versions of the optional backend non-member functions.]] [[detail/generic_interconvert.hpp][Generic interconversion routines.]] -[[detail/mp_number_base.hpp][All the expression template code, metaprogramming, and operator overloads for `mp_number`.]] +[[detail/number_base.hpp][All the expression template code, metaprogramming, and operator overloads for `number`.]] [[detail/no_et_ops.hpp][The non-expression template operators.]] [[defail/functions/constants.hpp][Defines constants used by the floating point functions.]] [[detail/functions/pow.hpp][Defines default versions of the power and exponential related floating point functions.]] @@ -1959,8 +1959,8 @@ Windows Vista machine. [[cpp_int (256-bit cache)][1.29367(0.442451s)]] [[cpp_int (512-bit cache)][1.08821(0.37218s)]] [[cpp_int (1024-bit cache)][1.07902(0.369037s)]] -[[mp_int1024_t][1.02616(0.35096s)]] -[[mp_int1024_t (no Expression templates)][1(0.342011s)]] +[[int1024_t][1.02616(0.35096s)]] +[[int1024_t (no Expression templates)][1(0.342011s)]] [[tom_int][3.74233(1.27992s)]] [[tom_int (no Expression templates)][3.97646(1.35999s)]] ] @@ -2292,7 +2292,7 @@ More a list of what ['could] be done, rather than what ['should] be done (which * Can the non-expression template operators be further optimised with rvalue reference support? * Can any functions - in particular value initialization - be made `constexp`? -* Can we differentiate between explicit and implicit conversions in the mp_number constructor (may need some new type traits)? +* Can we differentiate between explicit and implicit conversions in the number constructor (may need some new type traits)? * Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it. * Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents. Open question - what should be the default - int32_t or int64_t? diff --git a/example/cpp_int_snips.cpp b/example/cpp_int_snips.cpp index 191fcecb..a2818740 100644 --- a/example/cpp_int_snips.cpp +++ b/example/cpp_int_snips.cpp @@ -13,7 +13,7 @@ void t1() using namespace boost::multiprecision; - mp_int128_t v = 1; + int128_t v = 1; // Do some fixed precision arithmetic: for(unsigned i = 1; i <= 20; ++i) diff --git a/example/floating_point_examples.cpp b/example/floating_point_examples.cpp index 37761d94..2200b73d 100644 --- a/example/floating_point_examples.cpp +++ b/example/floating_point_examples.cpp @@ -343,7 +343,7 @@ private: /*` In this example we'll look at polynomial evaluation, this is not only an important -use case, but it's one that `mp_number` performs particularly well at because the +use case, but it's one that `number` performs particularly well at because the expression templates ['completely eliminate all temporaries] from a [@http://en.wikipedia.org/wiki/Horner%27s_method Horner polynomial evaluation scheme]. @@ -353,7 +353,7 @@ The following code evaluates `sin(x)` as a polynomial, accurate to at least 64 d */ using boost::multiprecision::cpp_dec_float; -typedef boost::multiprecision::mp_number > mp_type; +typedef boost::multiprecision::number > mp_type; mp_type mysin(const mp_type& x) { diff --git a/example/integer_examples.cpp b/example/integer_examples.cpp index f57e76e8..0b2edbbd 100644 --- a/example/integer_examples.cpp +++ b/example/integer_examples.cpp @@ -32,7 +32,7 @@ void print_factorials() // large the largest is, we'll be able to "pretty format" the results. // // Calculate the largest number that will fit inside 128 bits, we could - // also have used numeric_limits::max() for this value: + // also have used numeric_limits::max() for this value: cpp_int limit = (cpp_int(1) << 128) - 1; // // Our table of values: diff --git a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp index d10449cc..bb2c8678 100644 --- a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp @@ -12,7 +12,7 @@ #include #include #include -#include +#include #include #include @@ -195,17 +195,17 @@ inline int eval_fpclassify(const mp_number_backend_float_architype& arg) return (boost::math::fpclassify)(arg.m_value); } -typedef boost::multiprecision::mp_number mp_number_float_architype; +typedef boost::multiprecision::number mp_number_float_architype; }}} // namespaces namespace std{ template -class numeric_limits > : public std::numeric_limits +class numeric_limits > : public std::numeric_limits { typedef std::numeric_limits base_type; - typedef boost::multiprecision::mp_number number_type; + typedef boost::multiprecision::number number_type; public: static number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } static number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 3110088a..f8115b4a 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -14,7 +14,7 @@ #include #include -#include +#include #include // @@ -1342,9 +1342,9 @@ int cpp_dec_float::compare(const cpp_dec_float& v) const BOOST_NOEXCEP else if(exp != v.exp) { // The signs are the same and the exponents are different. - const int val_cmp_exp = ((exp < v.exp) ? 1 : -1); + const int val_cexpression = ((exp < v.exp) ? 1 : -1); - return (neg ? val_cmp_exp : -val_cmp_exp); + return (neg ? val_cexpression : -val_cexpression); } else { @@ -2730,7 +2730,7 @@ inline void eval_trunc(cpp_dec_float& result, const cpp_dec_float(%1%)", 0, mp_number >(x), 0, boost::math::policies::policy<>()).backend(); + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, number >(x), 0, boost::math::policies::policy<>()).backend(); return; } else if(x.isint()) @@ -2842,15 +2842,15 @@ inline int eval_get_sign(const cpp_dec_float& val) BOOST_NOEXCEPT using boost::multiprecision::backends::cpp_dec_float; -typedef mp_number > cpp_dec_float_50; -typedef mp_number > cpp_dec_float_100; +typedef number > cpp_dec_float_50; +typedef number > cpp_dec_float_100; }} namespace std { template - class numeric_limits, ExpressionTemplates> > + class numeric_limits, ExpressionTemplates> > { public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; @@ -2877,63 +2877,63 @@ namespace std BOOST_STATIC_CONSTEXPR bool traps = false; BOOST_STATIC_CONSTEXPR bool tinyness_before = false; - BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> (min) (void) { return (boost::multiprecision::cpp_dec_float::min)(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> (max) (void) { return (boost::multiprecision::cpp_dec_float::max)(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> lowest (void) { return boost::multiprecision::cpp_dec_float::zero(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> epsilon (void) { return boost::multiprecision::cpp_dec_float::eps(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> round_error (void) { return 0.5L; } - BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> infinity (void) { return boost::multiprecision::cpp_dec_float::inf(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> quiet_NaN (void) { return boost::multiprecision::cpp_dec_float::nan(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> signaling_NaN(void) { return boost::multiprecision::cpp_dec_float::zero(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::mp_number, ExpressionTemplates> denorm_min (void) { return boost::multiprecision::cpp_dec_float::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> (min) (void) { return (boost::multiprecision::cpp_dec_float::min)(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> (max) (void) { return (boost::multiprecision::cpp_dec_float::max)(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> lowest (void) { return boost::multiprecision::cpp_dec_float::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> epsilon (void) { return boost::multiprecision::cpp_dec_float::eps(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> round_error (void) { return 0.5L; } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> infinity (void) { return boost::multiprecision::cpp_dec_float::inf(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> quiet_NaN (void) { return boost::multiprecision::cpp_dec_float::nan(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> signaling_NaN(void) { return boost::multiprecision::cpp_dec_float::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> denorm_min (void) { return boost::multiprecision::cpp_dec_float::zero(); } }; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; template -BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::min_exponent; +BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::min_exponent; template -BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::min_exponent10; template -BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::max_exponent; +BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::max_exponent; template -BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::max_exponent10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif } @@ -2943,7 +2943,7 @@ namespace boost{ namespace math{ namespace policies{ template -struct precision< boost::multiprecision::mp_number, ExpressionTemplates>, Policy> +struct precision< boost::multiprecision::number, ExpressionTemplates>, Policy> { // Define a local copy of cpp_dec_float_digits10 because it might differ // from the template parameter Digits10 for small or large digit counts. diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 3873720b..9a4e771b 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -9,7 +9,7 @@ #include #include #include -#include +#include #include #include #include @@ -2940,21 +2940,21 @@ using boost::multiprecision::backends::cpp_int_backend; template struct number_category > : public mpl::int_{}; -typedef mp_number > cpp_int; +typedef number > cpp_int; typedef rational_adapter > cpp_rational_backend; -typedef mp_number cpp_rational; +typedef number cpp_rational; // Fixed precision unsigned types: -typedef mp_number, false> mp_uint128_t; -typedef mp_number, false> mp_uint256_t; -typedef mp_number, false> mp_uint512_t; -typedef mp_number, false> mp_uint1024_t; +typedef number, false> uint128_t; +typedef number, false> uint256_t; +typedef number, false> uint512_t; +typedef number, false> uint1024_t; // Fixed precision signed types: -typedef mp_number, false> mp_int128_t; -typedef mp_number, false> mp_int256_t; -typedef mp_number, false> mp_int512_t; -typedef mp_number, false> mp_int1024_t; +typedef number, false> int128_t; +typedef number, false> int256_t; +typedef number, false> int512_t; +typedef number, false> int1024_t; #ifdef BOOST_MSVC #pragma warning(pop) @@ -2968,9 +2968,9 @@ typedef mp_number, false> mp_int1024_t; namespace std{ template -class numeric_limits, ExpressionTemplates> > +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; @@ -3020,56 +3020,56 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif template -class numeric_limits, ExpressionTemplates> > +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; struct inititializer { @@ -3144,61 +3144,61 @@ public: }; template -const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; +const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif template -class numeric_limits, ExpressionTemplates> > +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; struct inititializer { @@ -3272,54 +3272,54 @@ public: }; template -const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; +const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif diff --git a/include/boost/multiprecision/depricated/arithmetic_backend.hpp b/include/boost/multiprecision/depricated/arithmetic_backend.hpp index 9925d3f8..0f6e4c02 100644 --- a/include/boost/multiprecision/depricated/arithmetic_backend.hpp +++ b/include/boost/multiprecision/depricated/arithmetic_backend.hpp @@ -11,7 +11,7 @@ #include #include #include -#include +#include namespace boost{ namespace multiprecision{ @@ -128,10 +128,10 @@ using boost::multiprecision::backends::arithmetic_backend; namespace std{ template -class numeric_limits, ExpressionTemplates > > : public std::numeric_limits +class numeric_limits, ExpressionTemplates > > : public std::numeric_limits { typedef std::numeric_limits base_type; - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } diff --git a/include/boost/multiprecision/depricated/fixed_int.hpp b/include/boost/multiprecision/depricated/fixed_int.hpp index 80be2036..c12fa3a8 100644 --- a/include/boost/multiprecision/depricated/fixed_int.hpp +++ b/include/boost/multiprecision/depricated/fixed_int.hpp @@ -9,7 +9,7 @@ #include #include #include -#include +#include #include #include #include @@ -1504,13 +1504,13 @@ inline void eval_lcm(fixed_int& result, const fixed_int struct number_category > : public mpl::int_{}; -typedef mp_number > mp_uint128_t; -typedef mp_number > mp_uint256_t; -typedef mp_number > mp_uint512_t; +typedef number > uint128_t; +typedef number > uint256_t; +typedef number > uint512_t; -typedef mp_number > mp_int128_t; -typedef mp_number > mp_int256_t; -typedef mp_number > mp_int512_t; +typedef number > int128_t; +typedef number > int256_t; +typedef number > int512_t; }} // namespaces @@ -1518,16 +1518,16 @@ typedef mp_number > mp_int512_t; namespace std{ template -class numeric_limits, ExpressionTemplates> > +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; struct initializer { initializer() { - (std::numeric_limits > >::min)(); - (std::numeric_limits > >::max)(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); } void do_nothing()const{} }; @@ -1592,8 +1592,8 @@ public: }; template -typename numeric_limits, ExpressionTemplates> >::initializer const - numeric_limits, ExpressionTemplates> >::init; +typename numeric_limits, ExpressionTemplates> >::initializer const + numeric_limits, ExpressionTemplates> >::init; } #endif diff --git a/include/boost/multiprecision/detail/big_lanczos.hpp b/include/boost/multiprecision/detail/big_lanczos.hpp index 998d5dca..c3cb1461 100644 --- a/include/boost/multiprecision/detail/big_lanczos.hpp +++ b/include/boost/multiprecision/detail/big_lanczos.hpp @@ -17,9 +17,9 @@ template struct lanczos; template -struct lanczos, Policy> +struct lanczos, Policy> { - typedef typename boost::math::policies::precision, Policy>::type precision_type; + typedef typename boost::math::policies::precision, Policy>::type precision_type; typedef typename mpl::if_c< precision_type::value <= 73, lanczos13UDT, diff --git a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp index f2700c5e..47f9147a 100644 --- a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp +++ b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp @@ -10,6 +10,14 @@ namespace boost{ namespace multiprecision{ namespace backends{ +#ifdef BOOST_MSVC +#pragma warning(push) + // C4389: signed/unsigned mismatch + // C4127: conditional expression is constant + // C4018: signed/unsigned mismatch +#pragma warning(disable:4127 4018 4389) +#endif + template BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT { @@ -357,10 +365,6 @@ BOOST_FORCEINLINE void eval_lcm(cpp_int_backend& re *result.limbs() = boost::math::lcm(*a.limbs(), *b.limbs()); } -#ifdef BOOST_MSVC -#pragma warning(push) -#pragma warning(disable:4127 4018) -#endif template inline void eval_convert_to(R* result, const cpp_int_backend& val) { diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index bf56825b..becb7cb4 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -7,7 +7,7 @@ #define BOOST_MATH_BIG_NUM_DEF_OPS #include -#include +#include #include #include #include @@ -693,7 +693,7 @@ inline void eval_trunc(T& result, const T& a) int c = eval_fpclassify(a); if(c == FP_NAN || c == FP_INFINITE) { - result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number(a), 0, boost::math::policies::policy<>()).backend(); + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, number(a), 0, boost::math::policies::policy<>()).backend(); return; } if(eval_get_sign(a) < 0) @@ -710,7 +710,7 @@ inline void eval_round(T& result, const T& a) int c = eval_fpclassify(a); if(c == FP_NAN || c == FP_INFINITE) { - result = boost::math::policies::raise_rounding_error("boost::multiprecision::round<%1%>(%1%)", 0, mp_number(a), 0, boost::math::policies::policy<>()).backend(); + result = boost::math::policies::raise_rounding_error("boost::multiprecision::round<%1%>(%1%)", 0, number(a), 0, boost::math::policies::policy<>()).backend(); return; } if(eval_get_sign(a) < 0) @@ -844,60 +844,60 @@ namespace math{ // Default versions of floating point classification routines: // template -inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number& arg) { using multiprecision::default_ops::eval_fpclassify; return eval_fpclassify(arg.backend()); } template -inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) +inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression& arg) { - typedef typename multiprecision::detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::expression::result_type value_type; return fpclassify(value_type(arg)); } template -inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number& arg) { int v = fpclassify(arg); return (v != FP_INFINITE) && (v != FP_NAN); } template -inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) +inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression& arg) { - typedef typename multiprecision::detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::expression::result_type value_type; return isfinite(value_type(arg)); } template -inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number& arg) { return fpclassify(arg) == FP_NAN; } template -inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) +inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression& arg) { - typedef typename multiprecision::detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::expression::result_type value_type; return isnan(value_type(arg)); } template -inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number& arg) { return fpclassify(arg) == FP_INFINITE; } template -inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) +inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression& arg) { - typedef typename multiprecision::detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::expression::result_type value_type; return isinf(value_type(arg)); } template -inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::mp_number& arg) +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number& arg) { return fpclassify(arg) == FP_NORMAL; } template -inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::mp_exp& arg) +inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression& arg) { - typedef typename multiprecision::detail::mp_exp::result_type value_type; + typedef typename multiprecision::detail::expression::result_type value_type; return isnormal(value_type(arg)); } @@ -905,198 +905,198 @@ inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::deta namespace multiprecision{ template -inline typename detail::mp_exp::result_type trunc(const detail::mp_exp& v, const Policy& pol) +inline typename detail::expression::result_type trunc(const detail::expression& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::expression::result_type number_type; return BOOST_MP_MOVE(trunc(number_type(v), pol)); } template -inline mp_number trunc(const mp_number& v, const Policy&) +inline number trunc(const number& v, const Policy&) { using default_ops::eval_trunc; - mp_number result; + number result; eval_trunc(result.backend(), v.backend()); return BOOST_MP_MOVE(result); } template -inline int itrunc(const detail::mp_exp& v, const Policy& pol) +inline int itrunc(const detail::expression& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::expression::result_type number_type; number_type r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, number_type(v), 0, pol).template convert_to(); return r.template convert_to(); } template -inline int itrunc(const detail::mp_exp& v) +inline int itrunc(const detail::expression& v) { return itrunc(v, boost::math::policies::policy<>()); } template -inline int itrunc(const mp_number& v, const Policy& pol) +inline int itrunc(const number& v, const Policy& pol) { - mp_number r = trunc(v, pol); + number r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } template -inline int itrunc(const mp_number& v) +inline int itrunc(const number& v) { return itrunc(v, boost::math::policies::policy<>()); } template -inline long ltrunc(const detail::mp_exp& v, const Policy& pol) +inline long ltrunc(const detail::expression& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::expression::result_type number_type; number_type r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, number_type(v), 0L, pol).template convert_to(); return r.template convert_to(); } template -inline long ltrunc(const detail::mp_exp& v) +inline long ltrunc(const detail::expression& v) { return ltrunc(v, boost::math::policies::policy<>()); } template -inline long ltrunc(const mp_number& v, const Policy& pol) +inline long ltrunc(const number& v, const Policy& pol) { - mp_number r = trunc(v, pol); + number r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } template -inline long ltrunc(const mp_number& v) +inline long ltrunc(const number& v) { return ltrunc(v, boost::math::policies::policy<>()); } #ifndef BOOST_NO_LONG_LONG template -inline long long lltrunc(const detail::mp_exp& v, const Policy& pol) +inline long long lltrunc(const detail::expression& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::expression::result_type number_type; number_type r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, number_type(v), 0LL, pol).template convert_to(); return r.template convert_to(); } template -inline long long lltrunc(const detail::mp_exp& v) +inline long long lltrunc(const detail::expression& v) { return lltrunc(v, boost::math::policies::policy<>()); } template -inline long long lltrunc(const mp_number& v, const Policy& pol) +inline long long lltrunc(const number& v, const Policy& pol) { - mp_number r = trunc(v, pol); + number r = trunc(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } template -inline long long lltrunc(const mp_number& v) +inline long long lltrunc(const number& v) { return lltrunc(v, boost::math::policies::policy<>()); } #endif template -inline typename detail::mp_exp::result_type round(const detail::mp_exp& v, const Policy& pol) +inline typename detail::expression::result_type round(const detail::expression& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::expression::result_type number_type; return BOOST_MP_MOVE(round(static_cast(v), pol)); } template -inline mp_number round(const mp_number& v, const Policy&) +inline number round(const number& v, const Policy&) { using default_ops::eval_round; - mp_number result; + number result; eval_round(result.backend(), v.backend()); return BOOST_MP_MOVE(result); } template -inline int iround(const detail::mp_exp& v, const Policy& pol) +inline int iround(const detail::expression& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::expression::result_type number_type; number_type r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, number_type(v), 0, pol).template convert_to(); return r.template convert_to(); } template -inline int iround(const detail::mp_exp& v) +inline int iround(const detail::expression& v) { return iround(v, boost::math::policies::policy<>()); } template -inline int iround(const mp_number& v, const Policy& pol) +inline int iround(const number& v, const Policy& pol) { - mp_number r = round(v, pol); + number r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } template -inline int iround(const mp_number& v) +inline int iround(const number& v) { return iround(v, boost::math::policies::policy<>()); } template -inline long lround(const detail::mp_exp& v, const Policy& pol) +inline long lround(const detail::expression& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::expression::result_type number_type; number_type r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, number_type(v), 0L, pol).template convert_to(); return r.template convert_to(); } template -inline long lround(const detail::mp_exp& v) +inline long lround(const detail::expression& v) { return lround(v, boost::math::policies::policy<>()); } template -inline long lround(const mp_number& v, const Policy& pol) +inline long lround(const number& v, const Policy& pol) { - mp_number r = round(v, pol); + number r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } template -inline long lround(const mp_number& v) +inline long lround(const number& v) { return lround(v, boost::math::policies::policy<>()); } #ifndef BOOST_NO_LONG_LONG template -inline long long llround(const detail::mp_exp& v, const Policy& pol) +inline long long llround(const detail::expression& v, const Policy& pol) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::expression::result_type number_type; number_type r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, number_type(v), 0LL, pol).template convert_to(); return r.template convert_to(); } template -inline long long llround(const detail::mp_exp& v) +inline long long llround(const detail::expression& v) { return llround(v, boost::math::policies::policy<>()); } template -inline long long llround(const mp_number& v, const Policy& pol) +inline long long llround(const number& v, const Policy& pol) { - mp_number r = round(v, pol); + number r = round(v, pol); if((r > (std::numeric_limits::max)()) || r < (std::numeric_limits::min)() || !boost::math::isfinite(v)) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } template -inline long long llround(const mp_number& v) +inline long long llround(const number& v) { return llround(v, boost::math::policies::policy<>()); } @@ -1117,36 +1117,36 @@ struct BOOST_JOIN(func, _funct)\ }\ \ template \ -inline typename enable_if_c >::value == category,\ - detail::mp_exp<\ +inline typename enable_if_c >::value == category,\ + detail::expression<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp > \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::expression > \ >::type \ -func(const detail::mp_exp& arg)\ +func(const detail::expression& arg)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::expression \ > (\ - detail::BOOST_JOIN(func, _funct) >::type>() \ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg \ );\ }\ template \ inline typename enable_if_c::value == category,\ - detail::mp_exp<\ + detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number > \ + , number > \ >::type \ -func(const mp_number& arg)\ +func(const number& arg)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ + , number \ >(\ detail::BOOST_JOIN(func, _funct)() \ , arg \ @@ -1155,10 +1155,10 @@ func(const mp_number& arg)\ template \ inline typename boost::enable_if_c<\ boost::multiprecision::number_category::value == category,\ - mp_number >::type \ -func(const mp_number& arg)\ + number >::type \ +func(const number& arg)\ {\ - mp_number result;\ + number result;\ using default_ops::BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend());\ return BOOST_MP_MOVE(result);\ @@ -1191,19 +1191,19 @@ struct BOOST_JOIN(func, _funct)\ }\ template \ inline typename enable_if_c::value == category,\ - detail::mp_exp<\ + detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ - , mp_number > \ + , number \ + , number > \ >::type \ -func(const mp_number& arg, const mp_number& a)\ +func(const number& arg, const number& a)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ - , mp_number \ + , number \ + , number \ >(\ detail::BOOST_JOIN(func, _funct)() \ , arg,\ @@ -1212,20 +1212,20 @@ func(const mp_number& arg, const mp_number& a)\ }\ template \ inline typename enable_if_c<\ - (number_category::value == category) && (number_category >::value == category),\ - detail::mp_exp<\ + (number_category::value == category) && (number_category >::value == category),\ + detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ - , detail::mp_exp > \ + , number \ + , detail::expression > \ >::type \ -func(const mp_number& arg, const detail::mp_exp& a)\ +func(const number& arg, const detail::expression& a)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ - , detail::mp_exp \ + , number \ + , detail::expression \ >(\ detail::BOOST_JOIN(func, _funct)() \ , arg,\ @@ -1234,20 +1234,20 @@ func(const mp_number& arg, const detail::mp_exp \ inline typename enable_if_c<\ - (number_category::value == category) && (number_category >::value == category),\ - detail::mp_exp<\ + (number_category::value == category) && (number_category >::value == category),\ + detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , detail::mp_exp \ - , mp_number > \ + , detail::expression \ + , number > \ >::type \ -func(const detail::mp_exp& arg, const mp_number& a)\ +func(const detail::expression& arg, const number& a)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , detail::mp_exp \ - , mp_number \ + , detail::expression \ + , number \ >(\ detail::BOOST_JOIN(func, _funct)() \ , arg,\ @@ -1256,22 +1256,22 @@ func(const detail::mp_exp& arg, const mp_number \ inline typename enable_if_c<\ - (number_category >::value == category) && (number_category >::value == category),\ - detail::mp_exp<\ + (number_category >::value == category) && (number_category >::value == category),\ + detail::expression<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ - , detail::mp_exp > \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::expression \ + , detail::expression > \ >::type \ -func(const detail::mp_exp& arg, const detail::mp_exp& a)\ +func(const detail::expression& arg, const detail::expression& a)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::expression \ + , detail::expression \ >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg,\ a\ );\ @@ -1279,19 +1279,19 @@ func(const detail::mp_exp& arg, const detail::mp_exp \ inline typename enable_if_c<\ is_arithmetic::value && (number_category::value == category),\ - detail::mp_exp<\ + detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ + , number \ , Arithmetic\ > \ >::type \ -func(const mp_number& arg, const Arithmetic& a)\ +func(const number& arg, const Arithmetic& a)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ + , number \ , Arithmetic\ >(\ detail::BOOST_JOIN(func, _funct)() \ @@ -1301,23 +1301,23 @@ func(const mp_number& arg, const Arithmetic& a)\ }\ template \ inline typename enable_if_c<\ - is_arithmetic::value && (number_category >::value == category),\ - detail::mp_exp<\ + is_arithmetic::value && (number_category >::value == category),\ + detail::expression<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::expression \ , Arithmetic\ > \ >::type \ -func(const detail::mp_exp& arg, const Arithmetic& a)\ +func(const detail::expression& arg, const Arithmetic& a)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::expression \ , Arithmetic\ >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg,\ a\ );\ @@ -1325,20 +1325,20 @@ func(const detail::mp_exp& arg, const Arithmetic& a)\ template \ inline typename enable_if_c<\ is_arithmetic::value && (number_category::value == category),\ - detail::mp_exp<\ + detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , Arithmetic \ - , mp_number \ + , number \ > \ >::type \ -func(const Arithmetic& arg, const mp_number& a)\ +func(const Arithmetic& arg, const number& a)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , Arithmetic \ - , mp_number \ + , number \ >(\ detail::BOOST_JOIN(func, _funct)() \ , arg,\ @@ -1347,33 +1347,33 @@ func(const Arithmetic& arg, const mp_number& a)\ }\ template \ inline typename enable_if_c<\ - is_arithmetic::value && (number_category >::value == category),\ - detail::mp_exp<\ + is_arithmetic::value && (number_category >::value == category),\ + detail::expression<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::BOOST_JOIN(func, _funct) >::type> \ , Arithmetic \ - , detail::mp_exp \ + , detail::expression \ > \ >::type \ -func(const Arithmetic& arg, const detail::mp_exp& a)\ +func(const Arithmetic& arg, const detail::expression& a)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::BOOST_JOIN(func, _funct) >::type> \ , Arithmetic \ - , detail::mp_exp \ + , detail::expression \ >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg,\ a\ );\ }\ template \ inline typename enable_if_c<(number_category::value == category),\ - mp_number >::type \ -func(const mp_number& arg, const mp_number& a)\ + number >::type \ +func(const number& arg, const number& a)\ {\ - mp_number result;\ + number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), a.backend());\ return BOOST_MP_MOVE(result);\ @@ -1381,12 +1381,12 @@ func(const mp_number& arg, const mp_number& a)\ template \ inline typename enable_if_c<\ is_arithmetic::value && (number_category::value == category),\ - mp_number \ + number \ >::type \ -func(const mp_number& arg, const Arithmetic& a)\ +func(const number& arg, const Arithmetic& a)\ {\ typedef typename detail::canonical::type canonical_type;\ - mp_number result;\ + number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), static_cast(a));\ return BOOST_MP_MOVE(result);\ @@ -1394,12 +1394,12 @@ func(const mp_number& arg, const Arithmetic& a)\ template \ inline typename enable_if_c<\ is_arithmetic::value && (number_category::value == category),\ - mp_number \ + number \ >::type \ -func(const Arithmetic& a, const mp_number& arg)\ +func(const Arithmetic& a, const number& arg)\ {\ typedef typename detail::canonical::type canonical_type;\ - mp_number result;\ + number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), static_cast(a), arg.backend());\ return BOOST_MP_MOVE(result);\ @@ -1409,40 +1409,40 @@ func(const Arithmetic& a, const mp_number& arg)\ #define HETERO_BINARY_OP_FUNCTOR_B(func, Arg2, category)\ template \ inline typename enable_if_c<\ - (number_category >::value == category),\ - detail::mp_exp<\ + (number_category >::value == category),\ + detail::expression<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::expression \ , Arg2> \ >::type \ -func(const detail::mp_exp& arg, Arg2 const& a)\ +func(const detail::expression& arg, Arg2 const& a)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ - , detail::BOOST_JOIN(func, _funct) >::type> \ - , detail::mp_exp \ + , detail::BOOST_JOIN(func, _funct) >::type> \ + , detail::expression \ , Arg2\ >(\ - detail::BOOST_JOIN(func, _funct) >::type>() \ + detail::BOOST_JOIN(func, _funct) >::type>() \ , arg, a \ );\ }\ template \ inline typename enable_if_c<\ (number_category::value == category),\ - detail::mp_exp<\ + detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ + , number \ , Arg2> \ >::type \ -func(const mp_number& arg, Arg2 const& a)\ +func(const number& arg, Arg2 const& a)\ {\ - return detail::mp_exp<\ + return detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , mp_number \ + , number \ , Arg2\ >(\ detail::BOOST_JOIN(func, _funct)() \ @@ -1453,10 +1453,10 @@ func(const mp_number& arg, Arg2 const& a)\ template \ inline typename enable_if_c<\ (number_category::value == category),\ - mp_number >::type \ -func(const mp_number& arg, Arg2 const& a)\ + number >::type \ +func(const number& arg, Arg2 const& a)\ {\ - mp_number result;\ + number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), a);\ return BOOST_MP_MOVE(result);\ @@ -1493,42 +1493,42 @@ struct abs_funct } template -inline detail::mp_exp< +inline detail::expression< detail::function - , detail::abs_funct >::type> - , detail::mp_exp > -abs(const detail::mp_exp& arg) + , detail::abs_funct >::type> + , detail::expression > +abs(const detail::expression& arg) { - return detail::mp_exp< + return detail::expression< detail::function - , detail::abs_funct >::type> - , detail::mp_exp + , detail::abs_funct >::type> + , detail::expression > ( - detail::abs_funct >::type>() + detail::abs_funct >::type>() , arg ); } template -inline detail::mp_exp< +inline detail::expression< detail::function , detail::abs_funct - , mp_number > -abs(const mp_number& arg) + , number > +abs(const number& arg) { - return detail::mp_exp< + return detail::expression< detail::function , detail::abs_funct - , mp_number + , number >( detail::abs_funct() , arg ); } template -inline mp_number -abs(const mp_number& arg) +inline number +abs(const number& arg) { - mp_number result; + number result; using default_ops::eval_abs; eval_abs(result.backend(), arg.backend()); return BOOST_MP_MOVE(result); @@ -1577,32 +1577,32 @@ HETERO_BINARY_OP_FUNCTOR_B(pow, unsigned, number_kind_integer) namespace math{ // -// Overload of Boost.Math functions that find the wrong overload when used with mp_number: +// Overload of Boost.Math functions that find the wrong overload when used with number: // namespace detail{ template T sinc_pi_imp(T); template T sinhc_pi_imp(T); } template -inline multiprecision::mp_number sinc_pi(const multiprecision::mp_number& x) +inline multiprecision::number sinc_pi(const multiprecision::number& x) { return BOOST_MP_MOVE(detail::sinc_pi_imp(x)); } template -inline multiprecision::mp_number sinc_pi(const multiprecision::mp_number& x, const Policy&) +inline multiprecision::number sinc_pi(const multiprecision::number& x, const Policy&) { return BOOST_MP_MOVE(detail::sinc_pi_imp(x)); } template -inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x) +inline multiprecision::number sinhc_pi(const multiprecision::number& x) { return BOOST_MP_MOVE(detail::sinhc_pi_imp(x)); } template -inline multiprecision::mp_number sinhc_pi(const multiprecision::mp_number& x, const Policy&) +inline multiprecision::number sinhc_pi(const multiprecision::number& x, const Policy&) { return BOOST_MP_MOVE(boost::math::sinhc_pi(x)); } diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp index 4946ccf5..537b7bd1 100644 --- a/include/boost/multiprecision/detail/functions/constants.hpp +++ b/include/boost/multiprecision/detail/functions/constants.hpp @@ -246,7 +246,7 @@ const T& get_constant_ln2() static bool b = false; if(!b) { - calc_log2(result, boost::multiprecision::detail::digits2 >::value); + calc_log2(result, boost::multiprecision::detail::digits2 >::value); b = true; } @@ -262,7 +262,7 @@ const T& get_constant_e() static bool b = false; if(!b) { - calc_e(result, boost::multiprecision::detail::digits2 >::value); + calc_e(result, boost::multiprecision::detail::digits2 >::value); b = true; } @@ -278,7 +278,7 @@ const T& get_constant_pi() static bool b = false; if(!b) { - calc_pi(result, boost::multiprecision::detail::digits2 >::value); + calc_pi(result, boost::multiprecision::detail::digits2 >::value); b = true; } diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp index dbae9aac..c0c2abc8 100644 --- a/include/boost/multiprecision/detail/functions/pow.hpp +++ b/include/boost/multiprecision/detail/functions/pow.hpp @@ -90,7 +90,7 @@ void hyp0F0(T& H0F0, const T& x) typedef typename mpl::front::type ui_type; BOOST_ASSERT(&H0F0 != &x); - long tol = boost::multiprecision::detail::digits2 >::value; + long tol = boost::multiprecision::detail::digits2 >::value; T t; T x_pow_n_div_n_fact(x); @@ -146,7 +146,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x) eval_multiply(H1F0, pochham_a, x_pow_n_div_n_fact); eval_add(H1F0, si_type(1)); T lim; - eval_ldexp(lim, H1F0, 1 - boost::multiprecision::detail::digits2 >::value); + eval_ldexp(lim, H1F0, 1 - boost::multiprecision::detail::digits2 >::value); if(eval_get_sign(lim) < 0) lim.negate(); @@ -154,7 +154,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x) T term, part; // Series expansion of hyperg_1f0(a; ; x). - for(n = 2; n < boost::multiprecision::detail::digits2 >::value + 10; n++) + for(n = 2; n < boost::multiprecision::detail::digits2 >::value + 10; n++) { eval_multiply(x_pow_n_div_n_fact, x); eval_divide(x_pow_n_div_n_fact, n); @@ -167,7 +167,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x) if(lim.compare(term) >= 0) break; } - if(n >= boost::multiprecision::detail::digits2 >::value + 10) + if(n >= boost::multiprecision::detail::digits2 >::value + 10) BOOST_THROW_EXCEPTION(std::runtime_error("H1F0 failed to converge")); } @@ -193,7 +193,7 @@ void eval_exp(T& result, const T& x) bool isneg = eval_get_sign(x) < 0; if(type == FP_NAN) { - result = std::numeric_limits >::quiet_NaN().backend(); + result = std::numeric_limits >::quiet_NaN().backend(); return; } else if(type == FP_INFINITE) @@ -218,7 +218,7 @@ void eval_exp(T& result, const T& x) xx.negate(); // Check the range of the argument. - static const canonical_exp_type maximum_arg_for_exp = std::numeric_limits >::max_exponent == 0 ? (std::numeric_limits::max)() : std::numeric_limits >::max_exponent; + static const canonical_exp_type maximum_arg_for_exp = std::numeric_limits >::max_exponent == 0 ? (std::numeric_limits::max)() : std::numeric_limits >::max_exponent; if(xx.compare(maximum_arg_for_exp) >= 0) { @@ -226,7 +226,7 @@ void eval_exp(T& result, const T& x) if(isneg) result = ui_type(0); else - result = std::numeric_limits >::has_infinity ? std::numeric_limits >::infinity().backend() : (std::numeric_limits >::max)().backend(); + result = std::numeric_limits >::has_infinity ? std::numeric_limits >::infinity().backend() : (std::numeric_limits >::max)().backend(); return; } if(xx.compare(si_type(1)) <= 0) @@ -234,7 +234,7 @@ void eval_exp(T& result, const T& x) // // Use series for exp(x) - 1: // - T lim = std::numeric_limits >::epsilon().backend(); + T lim = std::numeric_limits >::epsilon().backend(); unsigned k = 2; exp_series = xx; result = si_type(1); @@ -344,7 +344,7 @@ void eval_log(T& result, const T& arg) else eval_subtract(result, t); - eval_multiply(lim, result, std::numeric_limits >::epsilon().backend()); + eval_multiply(lim, result, std::numeric_limits >::epsilon().backend()); if(eval_get_sign(lim) < 0) lim.negate(); INSTRUMENT_BACKEND(lim); @@ -465,7 +465,7 @@ inline void eval_pow(T& result, const T& x, const T& a) if((eval_get_sign(x) < 0) && !bo_a_isint) { - result = std::numeric_limits >::quiet_NaN().backend(); + result = std::numeric_limits >::quiet_NaN().backend(); } T t, da; @@ -564,7 +564,7 @@ namespace detail{ ui_type k = 1; T lim(x); - eval_ldexp(lim, lim, 1 - boost::multiprecision::detail::digits2 >::value); + eval_ldexp(lim, lim, 1 - boost::multiprecision::detail::digits2 >::value); do { diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp index b60722f5..4e57b070 100644 --- a/include/boost/multiprecision/detail/functions/trig.hpp +++ b/include/boost/multiprecision/detail/functions/trig.hpp @@ -36,7 +36,7 @@ void hyp0F1(T& result, const T& b, const T& x) T tol; tol = ui_type(1); - eval_ldexp(tol, tol, 1 - boost::multiprecision::detail::digits2 >::value); + eval_ldexp(tol, tol, 1 - boost::multiprecision::detail::digits2 >::value); eval_multiply(tol, result); if(eval_get_sign(tol) < 0) tol.negate(); @@ -87,7 +87,7 @@ void eval_sin(T& result, const T& x) { case FP_INFINITE: case FP_NAN: - result = std::numeric_limits >::quiet_NaN().backend(); + result = std::numeric_limits >::quiet_NaN().backend(); return; case FP_ZERO: result = ui_type(0); @@ -233,7 +233,7 @@ void eval_cos(T& result, const T& x) { case FP_INFINITE: case FP_NAN: - result = std::numeric_limits >::quiet_NaN().backend(); + result = std::numeric_limits >::quiet_NaN().backend(); return; case FP_ZERO: result = ui_type(1); @@ -391,7 +391,7 @@ void hyp2F1(T& result, const T& a, const T& b, const T& c, const T& x) eval_add(result, ui_type(1)); T lim; - eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value); + eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value); if(eval_get_sign(lim) < 0) lim.negate(); @@ -447,7 +447,7 @@ void eval_asin(T& result, const T& x) { case FP_NAN: case FP_INFINITE: - result = std::numeric_limits >::quiet_NaN().backend(); + result = std::numeric_limits >::quiet_NaN().backend(); return; case FP_ZERO: result = ui_type(0); @@ -464,7 +464,7 @@ void eval_asin(T& result, const T& x) int c = xx.compare(ui_type(1)); if(c > 0) { - result = std::numeric_limits >::quiet_NaN().backend(); + result = std::numeric_limits >::quiet_NaN().backend(); return; } else if(c == 0) @@ -524,7 +524,7 @@ void eval_asin(T& result, const T& x) eval_subtract(result, s); T lim; - eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value); + eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value); if(eval_get_sign(s) < 0) s.negate(); if(eval_get_sign(lim) < 0) @@ -546,7 +546,7 @@ inline void eval_acos(T& result, const T& x) { case FP_NAN: case FP_INFINITE: - result = std::numeric_limits >::quiet_NaN().backend(); + result = std::numeric_limits >::quiet_NaN().backend(); return; case FP_ZERO: result = get_constant_pi(); @@ -559,7 +559,7 @@ inline void eval_acos(T& result, const T& x) if(c > 0) { - result = std::numeric_limits >::quiet_NaN().backend(); + result = std::numeric_limits >::quiet_NaN().backend(); return; } else if(c == 0) @@ -591,7 +591,7 @@ void eval_atan(T& result, const T& x) switch(eval_fpclassify(x)) { case FP_NAN: - result = std::numeric_limits >::quiet_NaN().backend(); + result = std::numeric_limits >::quiet_NaN().backend(); return; case FP_ZERO: result = ui_type(0); @@ -656,7 +656,7 @@ void eval_atan(T& result, const T& x) static const boost::int32_t double_digits10_minus_a_few = std::numeric_limits::digits10 - 3; T s, c, t; - for(boost::int32_t digits = double_digits10_minus_a_few; digits <= std::numeric_limits >::digits10; digits *= 2) + for(boost::int32_t digits = double_digits10_minus_a_few; digits <= std::numeric_limits >::digits10; digits *= 2) { eval_sin(s, result); eval_cos(c, result); @@ -710,7 +710,7 @@ void eval_atan2(T& result, const T& y, const T& x) { if(eval_fpclassify(x) == FP_INFINITE) { - result = std::numeric_limits >::quiet_NaN().backend(); + result = std::numeric_limits >::quiet_NaN().backend(); } else { diff --git a/include/boost/multiprecision/detail/generic_interconvert.hpp b/include/boost/multiprecision/detail/generic_interconvert.hpp index adb1eea8..2cda6a6e 100644 --- a/include/boost/multiprecision/detail/generic_interconvert.hpp +++ b/include/boost/multiprecision/detail/generic_interconvert.hpp @@ -116,7 +116,7 @@ void generic_interconvert(To& to, const From& from, const mpl::int_ >::radix != 2) + if(std::numeric_limits >::radix != 2) { to = from.str(0, std::ios_base::fmtflags()).c_str(); return; @@ -190,10 +190,10 @@ void generic_interconvert(To& to, const From& from, const mpl::int_ void generic_interconvert(To& to, const From& from, const mpl::int_& /*to_type*/, const mpl::int_& /*from_type*/) { - typedef typename component_type >::type from_component_type; - typedef typename component_type >::type to_component_type; + typedef typename component_type >::type from_component_type; + typedef typename component_type >::type to_component_type; - mp_number t(from); + number t(from); to_component_type n(numerator(t)), d(denominator(t)); using default_ops::assign_components; assign_components(to, n.backend(), d.backend()); @@ -202,9 +202,9 @@ void generic_interconvert(To& to, const From& from, const mpl::int_ void generic_interconvert(To& to, const From& from, const mpl::int_& /*to_type*/, const mpl::int_& /*from_type*/) { - typedef typename component_type >::type to_component_type; + typedef typename component_type >::type to_component_type; - mp_number t(from); + number t(from); to_component_type n(t), d(1); using default_ops::assign_components; assign_components(to, n.backend(), d.backend()); @@ -213,12 +213,12 @@ void generic_interconvert(To& to, const From& from, const mpl::int_ void generic_interconvert(To& to, const From& from, const mpl::int_& /*to_type*/, const mpl::int_& /*from_type*/) { - typedef typename component_type >::type from_component_type; + typedef typename component_type >::type from_component_type; using default_ops::eval_divide; - mp_number t(from); + number t(from); from_component_type n(numerator(t)), d(denominator(t)); - mp_number fn(n), fd(d); + number fn(n), fd(d); eval_divide(to, fn.backend(), fd.backend()); } diff --git a/include/boost/multiprecision/detail/integer_ops.hpp b/include/boost/multiprecision/detail/integer_ops.hpp index ccdbbe8b..4103d81b 100644 --- a/include/boost/multiprecision/detail/integer_ops.hpp +++ b/include/boost/multiprecision/detail/integer_ops.hpp @@ -6,7 +6,7 @@ #ifndef BOOST_MP_INT_FUNC_HPP #define BOOST_MP_INT_FUNC_HPP -#include +#include namespace boost{ namespace multiprecision{ @@ -42,8 +42,8 @@ inline Integer eval_integer_modulus(const Backend& x, Integer val) template inline typename enable_if_c::value == number_kind_integer>::type - divide_qr(const mp_number& x, const mp_number& y, - mp_number& q, mp_number& r) + divide_qr(const number& x, const number& y, + number& q, number& r) { using default_ops::eval_qr; eval_qr(x.backend(), y.backend(), q.backend(), r.backend()); @@ -51,57 +51,57 @@ inline typename enable_if_c::value == number_kind_integ template inline typename enable_if_c::value == number_kind_integer>::type - divide_qr(const mp_number& x, const multiprecision::detail::mp_exp& y, - mp_number& q, mp_number& r) + divide_qr(const number& x, const multiprecision::detail::expression& y, + number& q, number& r) { - divide_qr(x, mp_number(y), q, r); + divide_qr(x, number(y), q, r); } template inline typename enable_if_c::value == number_kind_integer>::type - divide_qr(const multiprecision::detail::mp_exp& x, const mp_number& y, - mp_number& q, mp_number& r) + divide_qr(const multiprecision::detail::expression& x, const number& y, + number& q, number& r) { - divide_qr(mp_number(x), y, q, r); + divide_qr(number(x), y, q, r); } template inline typename enable_if_c::value == number_kind_integer>::type - divide_qr(const multiprecision::detail::mp_exp& x, const multiprecision::detail::mp_exp& y, - mp_number& q, mp_number& r) + divide_qr(const multiprecision::detail::expression& x, const multiprecision::detail::expression& y, + number& q, number& r) { - divide_qr(mp_number(x), mp_number(y), q, r); + divide_qr(number(x), number(y), q, r); } template inline typename enable_if, mpl::bool_::value == number_kind_integer> >, Integer>::type - integer_modulus(const mp_number& x, Integer val) + integer_modulus(const number& x, Integer val) { using default_ops::eval_integer_modulus; return eval_integer_modulus(x.backend(), val); } template -inline typename enable_if, mpl::bool_::result_type>::value == number_kind_integer> >, Integer>::type - integer_modulus(const multiprecision::detail::mp_exp& x, Integer val) +inline typename enable_if, mpl::bool_::result_type>::value == number_kind_integer> >, Integer>::type + integer_modulus(const multiprecision::detail::expression& x, Integer val) { - typedef typename multiprecision::detail::mp_exp::result_type result_type; + typedef typename multiprecision::detail::expression::result_type result_type; return integer_modulus(result_type(x), val); } template inline typename enable_if_c::value == number_kind_integer, unsigned>::type - lsb(const mp_number& x) + lsb(const number& x) { using default_ops::eval_lsb; return eval_lsb(x.backend()); } template -inline typename enable_if_c::result_type>::value == number_kind_integer, unsigned>::type - lsb(const multiprecision::detail::mp_exp& x) +inline typename enable_if_c::result_type>::value == number_kind_integer, unsigned>::type + lsb(const multiprecision::detail::expression& x) { - typedef typename multiprecision::detail::mp_exp::result_type number_type; + typedef typename multiprecision::detail::expression::result_type number_type; number_type n(x); using default_ops::eval_lsb; return eval_lsb(n.backend()); @@ -109,25 +109,25 @@ inline typename enable_if_c inline typename enable_if_c::value == number_kind_integer, bool>::type - bit_test(const mp_number& x, unsigned index) + bit_test(const number& x, unsigned index) { using default_ops::eval_bit_test; return eval_bit_test(x.backend(), index); } template -inline typename enable_if_c::result_type>::value == number_kind_integer, bool>::type - bit_test(const multiprecision::detail::mp_exp& x, unsigned index) +inline typename enable_if_c::result_type>::value == number_kind_integer, bool>::type + bit_test(const multiprecision::detail::expression& x, unsigned index) { - typedef typename multiprecision::detail::mp_exp::result_type number_type; + typedef typename multiprecision::detail::expression::result_type number_type; number_type n(x); using default_ops::eval_bit_test; return eval_bit_test(n.backend(), index); } template -inline typename enable_if_c::value == number_kind_integer, mp_number&>::type - bit_set(mp_number& x, unsigned index) +inline typename enable_if_c::value == number_kind_integer, number&>::type + bit_set(number& x, unsigned index) { using default_ops::eval_bit_set; eval_bit_set(x.backend(), index); @@ -135,8 +135,8 @@ inline typename enable_if_c::value == number_kind_integ } template -inline typename enable_if_c::value == number_kind_integer, mp_number&>::type - bit_unset(mp_number& x, unsigned index) +inline typename enable_if_c::value == number_kind_integer, number&>::type + bit_unset(number& x, unsigned index) { using default_ops::eval_bit_unset; eval_bit_unset(x.backend(), index); @@ -144,8 +144,8 @@ inline typename enable_if_c::value == number_kind_integ } template -inline typename enable_if_c::value == number_kind_integer, mp_number&>::type - bit_flip(mp_number& x, unsigned index) +inline typename enable_if_c::value == number_kind_integer, number&>::type + bit_flip(number& x, unsigned index) { using default_ops::eval_bit_flip; eval_bit_flip(x.backend(), index); @@ -314,10 +314,10 @@ inline typename enable_if< is_integral > >, - detail::mp_exp >::type + detail::expression >::type powm(const T& b, const U& p, const V& mod) { - return detail::mp_exp( + return detail::expression( detail::powm_func(), b, p, mod); } diff --git a/include/boost/multiprecision/detail/mp_number_base.hpp b/include/boost/multiprecision/detail/mp_number_base.hpp deleted file mode 100644 index 2d3e0b89..00000000 --- a/include/boost/multiprecision/detail/mp_number_base.hpp +++ /dev/null @@ -1,1262 +0,0 @@ -/////////////////////////////////////////////////////////////////////////////// -// Copyright 2011 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_BIG_NUM_BASE_HPP -#define BOOST_MATH_BIG_NUM_BASE_HPP - -#include -#include -#include -#include - -namespace boost{ namespace multiprecision{ - -template -class mp_number; - -template -struct is_mp_number : public mpl::false_ {}; - -template -struct is_mp_number > : public mpl::true_ {}; - -namespace detail{ - -// Forward-declare an expression wrapper -template -struct mp_exp; - -} // namespace detail - -template -struct is_mp_number_expression : public mpl::false_ {}; - -template -struct is_mp_number_expression > : public mpl::true_ {}; - -namespace detail{ -// -// Workaround for missing abs(long long) on some compilers: -// -template -typename boost::enable_if, T>::type abs(const T& t) BOOST_NOEXCEPT -{ - return t < 0 ? -t : t; -} - -#define BOOST_MP_USING_ABS using std::abs; using boost::multiprecision::detail::abs; - -// -// Move support: -// -#ifndef BOOST_NO_RVALUE_REFERENCES -# define BOOST_MP_MOVE(x) std::move(x) -#else -# define BOOST_MP_MOVE(x) x -#endif - -template -struct has_enough_bits -{ - template - struct type : public mpl::bool_::digits >= b>{}; -}; - -template -struct canonical_imp -{ - typedef Val type; -}; -template -struct canonical_imp > -{ - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - typename Backend::signed_types, - pred_type - >::type iter_type; - typedef typename mpl::deref::type type; -}; -template -struct canonical_imp > -{ - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - typename Backend::unsigned_types, - pred_type - >::type iter_type; - typedef typename mpl::deref::type type; -}; -template -struct canonical_imp > -{ - typedef typename has_enough_bits::digits>::template type pred_type; - typedef typename mpl::find_if< - typename Backend::float_types, - pred_type - >::type iter_type; - typedef typename mpl::deref::type type; -}; -template -struct canonical_imp > -{ - typedef const char* type; -}; - -template -struct canonical -{ - typedef typename mpl::if_< - is_signed, - mpl::int_<0>, - typename mpl::if_< - is_unsigned, - mpl::int_<1>, - typename mpl::if_< - is_floating_point, - mpl::int_<2>, - typename mpl::if_< - mpl::or_< - is_convertible, - is_same - >, - mpl::int_<3>, - mpl::int_<4> - >::type - >::type - >::type - >::type tag_type; - - typedef typename canonical_imp::type type; -}; - -struct terminal{}; -struct negate{}; -struct plus{}; -struct minus{}; -struct multiplies{}; -struct divides{}; -struct modulus{}; -struct shift_left{}; -struct shift_right{}; -struct bitwise_and{}; -struct bitwise_or{}; -struct bitwise_xor{}; -struct bitwise_complement{}; -struct add_immediates{}; -struct subtract_immediates{}; -struct multiply_immediates{}; -struct divide_immediates{}; -struct modulus_immediates{}; -struct bitwise_and_immediates{}; -struct bitwise_or_immediates{}; -struct bitwise_xor_immediates{}; -struct complement_immediates{}; -struct function{}; - -template -struct backend_type; - -template -struct backend_type > -{ - typedef T type; -}; - -template -struct backend_type > -{ - typedef typename backend_type::result_type>::type type; -}; - - -template -struct is_mp_number : public mpl::false_{}; -template -struct is_mp_number > : public mpl::true_{}; -template -struct is_mp_number_exp : public mpl::false_{}; -template -struct is_mp_number_exp > : public mpl::true_{}; - -template -struct combine_expression; - -template -struct combine_expression, T2> -{ - typedef mp_number type; -}; - -template -struct combine_expression > -{ - typedef mp_number type; -}; - -template -struct combine_expression, mp_number > -{ - typedef mp_number type; -}; - -template -struct arg_type -{ - typedef mp_exp type; -}; - -template -struct arg_type > -{ - typedef mp_exp type; -}; - -template -struct unmentionable -{ - static void proc(){} -}; - -typedef void (*unmentionable_type)(); - -template -struct mp_exp_storage -{ - typedef const T& type; -}; - -template -struct mp_exp_storage -{ - typedef T* type; -}; - -template -struct mp_exp_storage -{ - typedef const T* type; -}; - -template -struct mp_exp_storage > -{ - typedef mp_exp type; -}; - -template -struct mp_exp -{ - typedef mpl::int_<1> arity; - typedef typename arg_type::type left_type; - typedef typename left_type::result_type result_type; - typedef tag tag_type; - - explicit mp_exp(const Arg1& a) : arg(a) {} - - left_type left()const { return left_type(arg); } - - const Arg1& left_ref()const BOOST_NOEXCEPT { return arg; } - - static const unsigned depth = left_type::depth + 1; - - operator unmentionable_type()const - { - result_type r(*this); - return r ? &unmentionable::proc : 0; - } - -private: - typename mp_exp_storage::type arg; - mp_exp& operator=(const mp_exp&); -}; - -template -struct mp_exp -{ - typedef mpl::int_<0> arity; - typedef Arg1 result_type; - typedef terminal tag_type; - - explicit mp_exp(const Arg1& a) : arg(a) {} - - const Arg1& value()const BOOST_NOEXCEPT { return arg; } - - static const unsigned depth = 0; - - operator unmentionable_type()const - { - return arg ? &unmentionable::proc : 0; - } - -private: - typename mp_exp_storage::type arg; - mp_exp& operator=(const mp_exp&); -}; - -template -struct mp_exp -{ - typedef mpl::int_<2> arity; - typedef typename arg_type::type left_type; - typedef typename arg_type::type right_type; - typedef typename left_type::result_type left_result_type; - typedef typename right_type::result_type right_result_type; - typedef typename combine_expression::type result_type; - typedef tag tag_type; - - mp_exp(const Arg1& a1, const Arg2& a2) : arg1(a1), arg2(a2) {} - - left_type left()const { return left_type(arg1); } - right_type right()const { return right_type(arg2); } - const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; } - const Arg2& right_ref()const BOOST_NOEXCEPT { return arg2; } - - operator unmentionable_type()const - { - result_type r(*this); - return r ? &unmentionable::proc : 0; - } - - static const unsigned left_depth = left_type::depth + 1; - static const unsigned right_depth = right_type::depth + 1; - static const unsigned depth = left_depth > right_depth ? left_depth : right_depth; -private: - typename mp_exp_storage::type arg1; - typename mp_exp_storage::type arg2; - mp_exp& operator=(const mp_exp&); -}; - -template -struct mp_exp -{ - typedef mpl::int_<3> arity; - typedef typename arg_type::type left_type; - typedef typename arg_type::type middle_type; - typedef typename arg_type::type right_type; - typedef typename left_type::result_type left_result_type; - typedef typename middle_type::result_type middle_result_type; - typedef typename right_type::result_type right_result_type; - typedef typename combine_expression< - left_result_type, - typename combine_expression::type - >::type result_type; - typedef tag tag_type; - - mp_exp(const Arg1& a1, const Arg2& a2, const Arg3& a3) : arg1(a1), arg2(a2), arg3(a3) {} - - left_type left()const { return left_type(arg1); } - middle_type middle()const { return middle_type(arg2); } - right_type right()const { return right_type(arg3); } - const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; } - const Arg2& middle_ref()const BOOST_NOEXCEPT { return arg2; } - const Arg3& right_ref()const BOOST_NOEXCEPT { return arg3; } - - operator unmentionable_type()const - { - result_type r(*this); - return r ? &unmentionable::proc : 0; - } - - static const unsigned left_depth = left_type::depth + 1; - static const unsigned middle_depth = middle_type::depth + 1; - static const unsigned right_depth = right_type::depth + 1; - static const unsigned depth = left_depth > right_depth ? (left_depth > middle_depth ? left_depth : middle_depth) : (right_depth > middle_depth ? right_depth : middle_depth); -private: - typename mp_exp_storage::type arg1; - typename mp_exp_storage::type arg2; - typename mp_exp_storage::type arg3; - mp_exp& operator=(const mp_exp&); -}; - -template -struct mp_exp -{ - typedef mpl::int_<4> arity; - typedef typename arg_type::type left_type; - typedef typename arg_type::type left_middle_type; - typedef typename arg_type::type right_middle_type; - typedef typename arg_type::type right_type; - typedef typename left_type::result_type left_result_type; - typedef typename left_middle_type::result_type left_middle_result_type; - typedef typename right_middle_type::result_type right_middle_result_type; - typedef typename right_type::result_type right_result_type; - typedef typename combine_expression< - typename combine_expression< - typename combine_expression::type, - right_middle_result_type - >::type, - right_result_type - >::type result_type; - typedef tag tag_type; - - mp_exp(const Arg1& a1, const Arg2& a2, const Arg3& a3, const Arg4& a4) : arg1(a1), arg2(a2), arg3(a3), arg4(a4) {} - - left_type left()const { return left_type(arg1); } - left_middle_type left_middle()const { return left_middle_type(arg2); } - right_middle_type right_middle()const { return right_middle_type(arg3); } - right_type right()const { return right_type(arg4); } - const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; } - const Arg2& left_middle_ref()const BOOST_NOEXCEPT { return arg2; } - const Arg3& right_middle_ref()const BOOST_NOEXCEPT { return arg3; } - const Arg4& right_ref()const BOOST_NOEXCEPT { return arg4; } - - operator unmentionable_type()const - { - result_type r(*this); - return r ? &unmentionable::proc : 0; - } - - static const unsigned left_depth = left_type::depth + 1; - static const unsigned left_middle_depth = left_middle_type::depth + 1; - static const unsigned right_middle_depth = right_middle_type::depth + 1; - static const unsigned right_depth = right_type::depth + 1; - - static const unsigned left_max_depth = left_depth > left_middle_depth ? left_depth : left_middle_depth; - static const unsigned right_max_depth = right_depth > right_middle_depth ? right_depth : right_middle_depth; - - static const unsigned depth = left_max_depth > right_max_depth ? left_max_depth : right_max_depth; -private: - typename mp_exp_storage::type arg1; - typename mp_exp_storage::type arg2; - typename mp_exp_storage::type arg3; - typename mp_exp_storage::type arg4; - mp_exp& operator=(const mp_exp&); -}; - -template -struct digits2 -{ - BOOST_STATIC_ASSERT(std::numeric_limits::is_specialized); - BOOST_STATIC_ASSERT((std::numeric_limits::radix == 2) || (std::numeric_limits::radix == 10)); - // If we really have so many digits that this fails, then we're probably going to hit other problems anyway: - BOOST_STATIC_ASSERT(LONG_MAX / 1000 > (std::numeric_limits::digits + 1)); - static const long value = std::numeric_limits::radix == 10 ? (((std::numeric_limits::digits + 1) * 1000L) / 301L) : std::numeric_limits::digits; -}; - -#ifndef BOOST_MP_MIN_EXPONENT_DIGITS -#ifdef _MSC_VER -# define BOOST_MP_MIN_EXPONENT_DIGITS 2 -#else -# define BOOST_MP_MIN_EXPONENT_DIGITS 2 -#endif -#endif - -template -void format_float_string(S& str, boost::intmax_t my_exp, boost::intmax_t digits, std::ios_base::fmtflags f, bool iszero) -{ - typedef typename S::size_type size_type; - bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; - bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; - bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; - bool showpos = (f & std::ios_base::showpos) == std::ios_base::showpos; - - bool neg = str.size() && (str[0] == '-'); - - if(neg) - str.erase(0, 1); - - if(digits == 0) - { - digits = (std::max)(str.size(), size_type(16)); - } - - if(iszero || str.empty() || (str.find_first_not_of('0') == S::npos)) - { - // We will be printing zero, even though the value might not - // actually be zero (it just may have been rounded to zero). - str = "0"; - if(scientific || fixed) - { - str.append(1, '.'); - str.append(size_type(digits), '0'); - if(scientific) - str.append("e+00"); - } - else - { - if(showpoint) - { - str.append(1, '.'); - if(digits > 1) - str.append(size_type(digits - 1), '0'); - } - } - if(neg) - str.insert(0, 1, '-'); - else if(showpos) - str.insert(0, 1, '+'); - return; - } - - if(!fixed && !scientific && !showpoint) - { - // - // Suppress trailing zeros: - // - std::string::iterator pos = str.end(); - while(pos != str.begin() && *--pos == '0'){} - if(pos != str.end()) - ++pos; - str.erase(pos, str.end()); - if(str.empty()) - str = '0'; - } - else if(!fixed || (my_exp >= 0)) - { - // - // Pad out the end with zero's if we need to: - // - boost::intmax_t chars = str.size(); - chars = digits - chars; - if(scientific) - ++chars; - if(chars > 0) - { - str.append(static_cast(chars), '0'); - } - } - - if(fixed || (!scientific && (my_exp >= -4) && (my_exp < digits))) - { - if(1 + my_exp > static_cast(str.size())) - { - // Just pad out the end with zeros: - str.append(static_cast(1 + my_exp - str.size()), '0'); - if(showpoint || fixed) - str.append("."); - } - else if(my_exp + 1 < static_cast(str.size())) - { - if(my_exp < 0) - { - str.insert(0, static_cast(-1 - my_exp), '0'); - str.insert(0, "0."); - } - else - { - // Insert the decimal point: - str.insert(static_cast(my_exp + 1), 1, '.'); - } - } - else if(showpoint || fixed) // we have exactly the digits we require to left of the point - str += "."; - - if(fixed) - { - // We may need to add trailing zeros: - boost::intmax_t l = str.find('.') + 1; - l = digits - (str.size() - l); - if(l > 0) - str.append(size_type(l), '0'); - } - } - else - { - BOOST_MP_USING_ABS - // Scientific format: - if(showpoint || (str.size() > 1)) - str.insert(1, 1, '.'); - str.append(1, 'e'); - S e = boost::lexical_cast(abs(my_exp)); - if(e.size() < BOOST_MP_MIN_EXPONENT_DIGITS) - e.insert(0, BOOST_MP_MIN_EXPONENT_DIGITS-e.size(), '0'); - if(my_exp < 0) - e.insert(0, 1, '-'); - else - e.insert(0, 1, '+'); - str.append(e); - } - if(neg) - str.insert(0, 1, '-'); - else if(showpos) - str.insert(0, 1, '+'); -} - -} // namespace detail - -// -// Non-member operators for mp_number: -// -// Unary operators first: -// -template -inline const mp_number& operator + (const mp_number& v) { return v; } -template -inline const detail::mp_exp& operator + (const detail::mp_exp& v) { return v; } -template -inline detail::mp_exp > operator - (const mp_number& v) { return detail::mp_exp >(v); } -template -inline detail::mp_exp > operator - (const detail::mp_exp& v) { return detail::mp_exp >(v); } -template -inline detail::mp_exp > operator ~ (const mp_number& v) { return detail::mp_exp >(v); } -template -inline detail::mp_exp > operator ~ (const detail::mp_exp& v) { return detail::mp_exp >(v); } -// -// Then addition: -// -template -inline detail::mp_exp, mp_number > - operator + (const mp_number& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator + (const mp_number& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator + (const V& a, const mp_number& b) -{ - return detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator + (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, mp_number > - operator + (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator + (const detail::mp_exp& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator + (const detail::mp_exp& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator + (const V& a, const detail::mp_exp& b) -{ - return detail::mp_exp >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::mp_exp, typename detail::mp_exp::left_type > - operator + (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); -} -template -inline detail::mp_exp, typename detail::mp_exp::left_type > - operator + (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref()); -} -template -inline detail::mp_exp, mp_number > - operator + (const mp_number& a, const detail::mp_exp >& b) -{ - return detail::mp_exp, mp_number >(a, b.left_ref()); -} -template -inline detail::mp_exp, mp_number > - operator + (const detail::mp_exp >& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(b, a.left_ref()); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator + (const detail::mp_exp >& a, const V& b) -{ - return detail::mp_exp >(b, a.left_ref()); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator + (const V& a, const detail::mp_exp >& b) -{ - return detail::mp_exp, mp_number >(a, b.left_ref()); -} -// -// Subtraction: -// -template -inline detail::mp_exp, mp_number > - operator - (const mp_number& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator - (const mp_number& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator - (const V& a, const mp_number& b) -{ - return detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator - (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, mp_number > - operator - (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator - (const detail::mp_exp& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator - (const detail::mp_exp& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator - (const V& a, const detail::mp_exp& b) -{ - return detail::mp_exp >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::mp_exp, typename detail::mp_exp::left_type > - operator - (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref()); -} -template -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator - (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); -} -template -inline detail::mp_exp, mp_number > - operator - (const mp_number& a, const detail::mp_exp >& b) -{ - return detail::mp_exp, mp_number >(a, b.left_ref()); -} -template -inline detail::mp_exp, mp_number > > - operator - (const detail::mp_exp >& a, const mp_number& b) -{ - return detail::mp_exp, mp_number > >( - detail::mp_exp, mp_number >(b, a.left_ref())); -} -template -inline typename enable_if, detail::mp_exp, V > > >::type - operator - (const detail::mp_exp >& a, const V& b) -{ - return detail::mp_exp, V > >(detail::mp_exp, V >(a.left_ref(), b)); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator - (const V& a, const detail::mp_exp >& b) -{ - return detail::mp_exp >(a, b.left_ref()); -} -// -// Multiplication: -// -template -inline detail::mp_exp, mp_number > - operator * (const mp_number& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator * (const mp_number& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator * (const V& a, const mp_number& b) -{ - return detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator * (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, mp_number > - operator * (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator * (const detail::mp_exp& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator * (const detail::mp_exp& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator * (const V& a, const detail::mp_exp& b) -{ - return detail::mp_exp >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator * (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type > (a, b.left_ref())); -} -template -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator * (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type >(b, a.left_ref())); -} -template -inline detail::mp_exp, mp_number > > - operator * (const mp_number& a, const detail::mp_exp >& b) -{ - return detail::mp_exp, mp_number > >( - detail::mp_exp, mp_number >(a, b.left_ref())); -} -template -inline detail::mp_exp, mp_number > > - operator * (const detail::mp_exp >& a, const mp_number& b) -{ - return detail::mp_exp, mp_number > >( - detail::mp_exp, mp_number >(b, a.left_ref())); -} -template -inline typename enable_if, detail::mp_exp, V > > >::type - operator * (const detail::mp_exp >& a, const V& b) -{ - return detail::mp_exp, V > > ( - detail::mp_exp, V >(a.left_ref(), b)); -} -template -inline typename enable_if, detail::mp_exp, V > > >::type - operator * (const V& a, const detail::mp_exp >& b) -{ - return detail::mp_exp, V > >( - detail::mp_exp, V >(b.left_ref(), a)); -} -// -// Division: -// -template -inline detail::mp_exp, mp_number > - operator / (const mp_number& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator / (const mp_number& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator / (const V& a, const mp_number& b) -{ - return detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator / (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, mp_number > - operator / (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator / (const detail::mp_exp& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator / (const detail::mp_exp& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator / (const V& a, const detail::mp_exp& b) -{ - return detail::mp_exp >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::mp_exp, typename detail::mp_exp::left_type > > - operator / (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, typename detail::mp_exp::left_type > >( - detail::mp_exp, typename detail::mp_exp::left_type >(a, b.left_ref())); -} -template -inline detail::mp_exp::left_type, mp_number > > - operator / (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp::left_type, mp_number > >( - detail::mp_exp::left_type, mp_number >(a.left_ref(), b)); -} -template -inline detail::mp_exp, mp_number > > - operator / (const mp_number& a, const detail::mp_exp >& b) -{ - return detail::mp_exp, mp_number > >( - detail::mp_exp, mp_number >(a, b.left_ref())); -} -template -inline detail::mp_exp, mp_number > > - operator / (const detail::mp_exp >& a, const mp_number& b) -{ - return detail::mp_exp, mp_number > >( - detail::mp_exp, mp_number >(a.left_ref(), b)); -} -template -inline typename enable_if, detail::mp_exp, V > > >::type - operator / (const detail::mp_exp >& a, const V& b) -{ - return detail::mp_exp, V > >( - detail::mp_exp, V>(a.left_ref(), b)); -} -template -inline typename enable_if, detail::mp_exp > > >::type - operator / (const V& a, const detail::mp_exp >& b) -{ - return detail::mp_exp > >( - detail::mp_exp >(a, b.left_ref())); -} -// -// Modulus: -// -template -inline detail::mp_exp, mp_number > - operator % (const mp_number& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator % (const mp_number& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator % (const V& a, const mp_number& b) -{ - return detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator % (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, mp_number > - operator % (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator % (const detail::mp_exp& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator % (const detail::mp_exp& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator % (const V& a, const detail::mp_exp& b) -{ - return detail::mp_exp >(a, b); -} -// -// Left shift: -// -template -inline typename enable_if, detail::mp_exp, I > >::type - operator << (const mp_number& a, const I& b) -{ - return detail::mp_exp, I>(a, b); -} -template -inline typename enable_if, detail::mp_exp, I> >::type - operator << (const detail::mp_exp& a, const I& b) -{ - return detail::mp_exp, I>(a, b); -} -// -// Right shift: -// -template -inline typename enable_if, detail::mp_exp, I > >::type - operator >> (const mp_number& a, const I& b) -{ - return detail::mp_exp, I>(a, b); -} -template -inline typename enable_if, detail::mp_exp, I> >::type - operator >> (const detail::mp_exp& a, const I& b) -{ - return detail::mp_exp, I>(a, b); -} -// -// Bitwise AND: -// -template -inline detail::mp_exp, mp_number > - operator & (const mp_number& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator & (const mp_number& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator & (const V& a, const mp_number& b) -{ - return detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator & (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, mp_number > - operator & (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator & (const detail::mp_exp& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator & (const detail::mp_exp& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator & (const V& a, const detail::mp_exp& b) -{ - return detail::mp_exp >(a, b); -} -// -// Bitwise OR: -// -template -inline detail::mp_exp, mp_number > - operator| (const mp_number& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator| (const mp_number& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator| (const V& a, const mp_number& b) -{ - return detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator| (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, mp_number > - operator| (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator| (const detail::mp_exp& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator| (const detail::mp_exp& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator| (const V& a, const detail::mp_exp& b) -{ - return detail::mp_exp >(a, b); -} -// -// Bitwise XOR: -// -template -inline detail::mp_exp, mp_number > - operator^ (const mp_number& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator^ (const mp_number& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator^ (const V& a, const mp_number& b) -{ - return detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator^ (const mp_number& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline detail::mp_exp, mp_number > - operator^ (const detail::mp_exp& a, const mp_number& b) -{ - return detail::mp_exp, mp_number >(a, b); -} -template -inline detail::mp_exp, detail::mp_exp > - operator^ (const detail::mp_exp& a, const detail::mp_exp& b) -{ - return detail::mp_exp, detail::mp_exp >(a, b); -} -template -inline typename enable_if, detail::mp_exp, V > >::type - operator^ (const detail::mp_exp& a, const V& b) -{ - return detail::mp_exp, V >(a, b); -} -template -inline typename enable_if, detail::mp_exp > >::type - operator^ (const V& a, const detail::mp_exp& b) -{ - return detail::mp_exp >(a, b); -} - -// -// Traits class, lets us know what kind of number we have, defaults to a floating point type: -// -enum number_category_type -{ - number_kind_integer = 0, - number_kind_floating_point = 1, - number_kind_rational = 2, - number_kind_fixed_point = 3 -}; - -template -struct number_category : public mpl::int_ {}; -template -struct number_category > : public number_category{}; -template -struct number_category > : public number_category::result_type>{}; - -template -struct component_type; -template -struct component_type > : public component_type{}; -template -struct component_type > : public component_type::result_type>{}; - -}} // namespaces - -namespace boost{ namespace math{ namespace tools{ - -template -struct promote_arg; - -template -struct promote_arg > -{ - typedef typename boost::multiprecision::detail::mp_exp::result_type type; -}; - -template -inline R real_cast(const boost::multiprecision::mp_number& val) -{ - return val.template convert_to(); -} - -template -inline R real_cast(const boost::multiprecision::detail::mp_exp& val) -{ - typedef typename boost::multiprecision::detail::mp_exp::result_type val_type; - return val_type(val).template convert_to(); -} - - -}}} - -#endif // BOOST_MATH_BIG_NUM_BASE_HPP - - diff --git a/include/boost/multiprecision/detail/mp_number_compare.hpp b/include/boost/multiprecision/detail/mp_number_compare.hpp deleted file mode 100644 index e8d53b9d..00000000 --- a/include/boost/multiprecision/detail/mp_number_compare.hpp +++ /dev/null @@ -1,482 +0,0 @@ -/////////////////////////////////////////////////////////////////////////////// -// Copyright 2012 John Maddock. Distributed under the Boost -// Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MP_COMPARE_HPP -#define BOOST_MP_COMPARE_HPP - -// -// Comparison operators for mp_number. -// - -namespace boost{ namespace multiprecision{ - -namespace default_ops{ - -template -inline bool eval_eq(const B& a, const B& b) -{ - return a.compare(b) == 0; -} -template -inline bool eval_eq(const B& a, const A& b) -{ - typedef typename mpl::if_< - is_convertible >, - mp_number, - mp_number - >::type mp_type; - mp_type t(b); - return eval_eq(a, t.backend()); -} - -template -inline bool eval_lt(const B& a, const B& b) -{ - return a.compare(b) < 0; -} -template -inline bool eval_lt(const B& a, const A& b) -{ - typedef typename mpl::if_< - is_convertible >, - mp_number, - mp_number - >::type mp_type; - mp_type t(b); - return eval_lt(a, t.backend()); -} - -template -inline bool eval_gt(const B& a, const B& b) -{ - return a.compare(b) > 0; -} -template -inline bool eval_gt(const B& a, const A& b) -{ - typedef typename mpl::if_< - is_convertible >, - mp_number, - mp_number - >::type mp_type; - mp_type t(b); - return eval_gt(a, t.backend()); -} - -} - -template -inline bool operator == (const mp_number& a, const mp_number& b) -{ - using default_ops::eval_eq; - return eval_eq(a.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator == (const mp_number& a, const Arithmetic& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_eq; - return eval_eq(a.backend(), ct(b)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator == (const mp_number& a, const detail::mp_exp& b) -{ - using default_ops::eval_eq; - typename detail::mp_exp::result_type t(b); - return eval_eq(a.backend(), t.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator == (const Arithmetic& a, const mp_number& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_eq; - return eval_eq(b.backend(), ct(a)); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator == (const Arithmetic& a, const detail::mp_exp& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_eq; - result_type t(b); - return eval_eq(t.backend(), ct(a)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator == (const detail::mp_exp& a, const mp_number& b) -{ - using default_ops::eval_eq; - typename detail::mp_exp::result_type t(a); - return eval_eq(t.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator == (const detail::mp_exp& a, const Arithmetic& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_eq; - result_type t(a); - return eval_eq(t.backend(), ct(b)); -} -template -inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type - operator == (const detail::mp_exp& a, const detail::mp_exp& b) -{ - using default_ops::eval_eq; - typename detail::mp_exp::result_type t(a); - typename detail::mp_exp::result_type t2(b); - return eval_eq(t.backend(), t2.backend()); -} - -template -inline bool operator != (const mp_number& a, const mp_number& b) -{ - using default_ops::eval_eq; - return !eval_eq(a.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator != (const mp_number& a, const Arithmetic& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_eq; - return !eval_eq(a.backend(), ct(b)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator != (const mp_number& a, const detail::mp_exp& b) -{ - using default_ops::eval_eq; - typename detail::mp_exp::result_type t(b); - return !eval_eq(a.backend(), t.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator != (const Arithmetic& a, const mp_number& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_eq; - return !eval_eq(b.backend(), ct(a)); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator != (const Arithmetic& a, const detail::mp_exp& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_eq; - result_type t(b); - return !eval_eq(t.backend(), ct(a)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator != (const detail::mp_exp& a, const mp_number& b) -{ - using default_ops::eval_eq; - typename detail::mp_exp::result_type t(a); - return !eval_eq(t.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator != (const detail::mp_exp& a, const Arithmetic& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_eq; - result_type t(a); - return !eval_eq(t.backend(), ct(b)); -} -template -inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type - operator != (const detail::mp_exp& a, const detail::mp_exp& b) -{ - using default_ops::eval_eq; - typename detail::mp_exp::result_type t(a); - typename detail::mp_exp::result_type t2(b); - return !eval_eq(t.backend(), t2.backend()); -} - -template -inline bool operator < (const mp_number& a, const mp_number& b) -{ - using default_ops::eval_lt; - return eval_lt(a.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator < (const mp_number& a, const Arithmetic& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_lt; - return eval_lt(a.backend(), ct(b)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator < (const mp_number& a, const detail::mp_exp& b) -{ - using default_ops::eval_lt; - typename detail::mp_exp::result_type t(b); - return eval_lt(a.backend(), t.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator < (const Arithmetic& a, const mp_number& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_gt; - return eval_gt(b.backend(), ct(a)); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator < (const Arithmetic& a, const detail::mp_exp& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_gt; - result_type t(b); - return eval_gt(t.backend(), ct(a)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator < (const detail::mp_exp& a, const mp_number& b) -{ - using default_ops::eval_lt; - typename detail::mp_exp::result_type t(a); - return eval_lt(t.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator < (const detail::mp_exp& a, const Arithmetic& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_lt; - result_type t(a); - return eval_lt(t.backend(), ct(b)); -} -template -inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type - operator < (const detail::mp_exp& a, const detail::mp_exp& b) -{ - using default_ops::eval_lt; - typename detail::mp_exp::result_type t(a); - typename detail::mp_exp::result_type t2(b); - return eval_lt(t.backend(), t2.backend()); -} - -template -inline bool operator > (const mp_number& a, const mp_number& b) -{ - using default_ops::eval_gt; - return eval_gt(a.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator > (const mp_number& a, const Arithmetic& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_gt; - return eval_gt(a.backend(), ct(b)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator > (const mp_number& a, const detail::mp_exp& b) -{ - using default_ops::eval_gt; - typename detail::mp_exp::result_type t(b); - return eval_gt(a.backend(), t.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator > (const Arithmetic& a, const mp_number& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_lt; - return eval_lt(b.backend(), ct(a)); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator > (const Arithmetic& a, const detail::mp_exp& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_lt; - result_type t(b); - return eval_lt(t.backend(), ct(a)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator > (const detail::mp_exp& a, const mp_number& b) -{ - using default_ops::eval_gt; - typename detail::mp_exp::result_type t(a); - return eval_gt(t.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator > (const detail::mp_exp& a, const Arithmetic& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_gt; - result_type t(a); - return eval_gt(t.backend(), ct(b)); -} -template -inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type - operator > (const detail::mp_exp& a, const detail::mp_exp& b) -{ - using default_ops::eval_gt; - typename detail::mp_exp::result_type t(a); - typename detail::mp_exp::result_type t2(b); - return eval_gt(t.backend(), t2.backend()); -} - -template -inline bool operator <= (const mp_number& a, const mp_number& b) -{ - using default_ops::eval_gt; - return !eval_gt(a.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator <= (const mp_number& a, const Arithmetic& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_gt; - return !eval_gt(a.backend(), ct(b)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator <= (const mp_number& a, const detail::mp_exp& b) -{ - using default_ops::eval_gt; - typename detail::mp_exp::result_type t(b); - return !eval_gt(a.backend(), t.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator <= (const Arithmetic& a, const mp_number& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_lt; - return !eval_lt(b.backend(), ct(a)); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator <= (const Arithmetic& a, const detail::mp_exp& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_lt; - result_type t(b); - return !eval_lt(t.backend(), ct(a)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator <= (const detail::mp_exp& a, const mp_number& b) -{ - using default_ops::eval_gt; - typename detail::mp_exp::result_type t(a); - return !eval_gt(t.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator <= (const detail::mp_exp& a, const Arithmetic& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_gt; - result_type t(a); - return !eval_gt(t.backend(), ct(b)); -} -template -inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type - operator <= (const detail::mp_exp& a, const detail::mp_exp& b) -{ - using default_ops::eval_gt; - typename detail::mp_exp::result_type t(a); - typename detail::mp_exp::result_type t2(b); - return !eval_gt(t.backend(), t2.backend()); -} - -template -inline bool operator >= (const mp_number& a, const mp_number& b) -{ - using default_ops::eval_lt; - return !eval_lt(a.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator >= (const mp_number& a, const Arithmetic& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_lt; - return !eval_lt(a.backend(), ct(b)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator >= (const mp_number& a, const detail::mp_exp& b) -{ - using default_ops::eval_lt; - typename detail::mp_exp::result_type t(b); - return !eval_lt(a.backend(), t.backend()); -} -template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator >= (const Arithmetic& a, const mp_number& b) -{ - typedef typename detail::canonical::type ct; - using default_ops::eval_gt; - return !eval_gt(b.backend(), ct(a)); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator >= (const Arithmetic& a, const detail::mp_exp& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_gt; - result_type t(b); - return !eval_gt(t.backend(), ct(a)); -} -template -inline typename enable_if, typename detail::mp_exp::result_type>, bool>::type - operator >= (const detail::mp_exp& a, const mp_number& b) -{ - using default_ops::eval_lt; - typename detail::mp_exp::result_type t(a); - return !eval_lt(t.backend(), b.backend()); -} -template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type - operator >= (const detail::mp_exp& a, const Arithmetic& b) -{ - typedef typename detail::mp_exp::result_type result_type; - typedef typename detail::canonical::type ct; - using default_ops::eval_lt; - result_type t(a); - return !eval_lt(t.backend(), ct(b)); -} -template -inline typename enable_if::result_type, typename detail::mp_exp::result_type>, bool>::type - operator >= (const detail::mp_exp& a, const detail::mp_exp& b) -{ - using default_ops::eval_lt; - typename detail::mp_exp::result_type t(a); - typename detail::mp_exp::result_type t2(b); - return !eval_lt(t.backend(), t2.backend()); -} - - -}} // namespaces - -#endif // BOOST_MP_COMPARE_HPP - diff --git a/include/boost/multiprecision/detail/no_et_ops.hpp b/include/boost/multiprecision/detail/no_et_ops.hpp index aa1ea7e6..28c7c6d4 100644 --- a/include/boost/multiprecision/detail/no_et_ops.hpp +++ b/include/boost/multiprecision/detail/no_et_ops.hpp @@ -10,21 +10,21 @@ namespace boost{ namespace multiprecision{ // -// Operators for non-expression template enabled mp_number. +// Operators for non-expression template enabled number. // NOTE: this is not a complete header - really just a suffix to default_ops.hpp. // NOTE: these operators have to be defined after the methods in default_ops.hpp. // template -inline mp_number operator - (const mp_number& v) +inline number operator - (const number& v) { - mp_number result(v); + number result(v); result.backend().negate(); return BOOST_MP_MOVE(result); } template -inline mp_number operator ~ (const mp_number& v) +inline number operator ~ (const number& v) { - mp_number result; + number result; eval_complement(result.backend(), v.backend()); return BOOST_MP_MOVE(result); } @@ -32,29 +32,29 @@ inline mp_number operator ~ (const mp_number& v) // Addition: // template -inline mp_number operator + (const mp_number& a, const mp_number& b) +inline number operator + (const number& a, const number& b) { - mp_number result; + number result; using default_ops::eval_add; eval_add(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator + (const mp_number& a, const V& b) +inline typename enable_if, number >::type + operator + (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_add; eval_add(result.backend(), a.backend(), static_cast(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator + (const V& a, const mp_number& b) +inline typename enable_if, number >::type + operator + (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_add; eval_add(result.backend(), b.backend(), static_cast(a)); return BOOST_MP_MOVE(result); @@ -63,29 +63,29 @@ inline typename enable_if, mp_number >::type // Subtraction: // template -inline mp_number operator - (const mp_number& a, const mp_number& b) +inline number operator - (const number& a, const number& b) { - mp_number result; + number result; using default_ops::eval_subtract; eval_subtract(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator - (const mp_number& a, const V& b) +inline typename enable_if, number >::type + operator - (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_subtract; eval_subtract(result.backend(), a.backend(), static_cast(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator - (const V& a, const mp_number& b) +inline typename enable_if, number >::type + operator - (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_subtract; eval_subtract(result.backend(), static_cast(a), b.backend()); return BOOST_MP_MOVE(result); @@ -94,29 +94,29 @@ inline typename enable_if, mp_number >::type // Multiply: // template -inline mp_number operator * (const mp_number& a, const mp_number& b) +inline number operator * (const number& a, const number& b) { - mp_number result; + number result; using default_ops::eval_multiply; eval_multiply(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator * (const mp_number& a, const V& b) +inline typename enable_if, number >::type + operator * (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_multiply; eval_multiply(result.backend(), a.backend(), static_cast(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator * (const V& a, const mp_number& b) +inline typename enable_if, number >::type + operator * (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_multiply; eval_multiply(result.backend(), b.backend(), static_cast(a)); return BOOST_MP_MOVE(result); @@ -125,29 +125,29 @@ inline typename enable_if, mp_number >::type // divide: // template -inline mp_number operator / (const mp_number& a, const mp_number& b) +inline number operator / (const number& a, const number& b) { - mp_number result; + number result; using default_ops::eval_divide; eval_divide(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator / (const mp_number& a, const V& b) +inline typename enable_if, number >::type + operator / (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_divide; eval_divide(result.backend(), a.backend(), static_cast(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator / (const V& a, const mp_number& b) +inline typename enable_if, number >::type + operator / (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_divide; eval_divide(result.backend(), static_cast(a), b.backend()); return BOOST_MP_MOVE(result); @@ -156,29 +156,29 @@ inline typename enable_if, mp_number >::type // modulus: // template -inline mp_number operator % (const mp_number& a, const mp_number& b) +inline number operator % (const number& a, const number& b) { - mp_number result; + number result; using default_ops::eval_modulus; eval_modulus(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator % (const mp_number& a, const V& b) +inline typename enable_if, number >::type + operator % (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_modulus; eval_modulus(result.backend(), a.backend(), static_cast(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator % (const V& a, const mp_number& b) +inline typename enable_if, number >::type + operator % (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_modulus; eval_modulus(result.backend(), static_cast(a), b.backend()); return BOOST_MP_MOVE(result); @@ -187,29 +187,29 @@ inline typename enable_if, mp_number >::type // Bitwise or: // template -inline mp_number operator | (const mp_number& a, const mp_number& b) +inline number operator | (const number& a, const number& b) { - mp_number result; + number result; using default_ops::eval_bitwise_or; eval_bitwise_or(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator | (const mp_number& a, const V& b) +inline typename enable_if, number >::type + operator | (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_bitwise_or; eval_bitwise_or(result.backend(), a.backend(), static_cast(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator | (const V& a, const mp_number& b) +inline typename enable_if, number >::type + operator | (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_bitwise_or; eval_bitwise_or(result.backend(), b.backend(), static_cast(a)); return BOOST_MP_MOVE(result); @@ -218,29 +218,29 @@ inline typename enable_if, mp_number >::type // Bitwise xor: // template -inline mp_number operator ^ (const mp_number& a, const mp_number& b) +inline number operator ^ (const number& a, const number& b) { - mp_number result; + number result; using default_ops::eval_bitwise_xor; eval_bitwise_xor(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator ^ (const mp_number& a, const V& b) +inline typename enable_if, number >::type + operator ^ (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_bitwise_xor; eval_bitwise_xor(result.backend(), a.backend(), static_cast(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator ^ (const V& a, const mp_number& b) +inline typename enable_if, number >::type + operator ^ (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_bitwise_xor; eval_bitwise_xor(result.backend(), b.backend(), static_cast(a)); return BOOST_MP_MOVE(result); @@ -249,29 +249,29 @@ inline typename enable_if, mp_number >::type // Bitwise and: // template -inline mp_number operator & (const mp_number& a, const mp_number& b) +inline number operator & (const number& a, const number& b) { - mp_number result; + number result; using default_ops::eval_bitwise_and; eval_bitwise_and(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator & (const mp_number& a, const V& b) +inline typename enable_if, number >::type + operator & (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_bitwise_and; eval_bitwise_and(result.backend(), a.backend(), static_cast(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator & (const V& a, const mp_number& b) +inline typename enable_if, number >::type + operator & (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; - mp_number result; + number result; using default_ops::eval_bitwise_and; eval_bitwise_and(result.backend(), b.backend(), static_cast(a)); return BOOST_MP_MOVE(result); @@ -280,19 +280,19 @@ inline typename enable_if, mp_number >::type // shifts: // template -inline typename enable_if, mp_number >::type - operator << (const mp_number& a, const I& b) +inline typename enable_if, number >::type + operator << (const number& a, const I& b) { - mp_number result(a); + number result(a); using default_ops::eval_left_shift; eval_left_shift(result.backend(), b); return BOOST_MP_MOVE(result); } template -inline typename enable_if, mp_number >::type - operator >> (const mp_number& a, const I& b) +inline typename enable_if, number >::type + operator >> (const number& a, const I& b) { - mp_number result(a); + number result(a); using default_ops::eval_right_shift; eval_right_shift(result.backend(), b); return BOOST_MP_MOVE(result); @@ -311,327 +311,327 @@ inline typename enable_if, mp_number >::type // semantics help a great deal in return by value, so performance is still pretty good... // template -inline mp_number operator - (mp_number&& v) +inline number operator - (number&& v) { v.backend().negate(); - return static_cast&&>(v); + return static_cast&&>(v); } template -inline mp_number operator ~ (mp_number&& v) +inline number operator ~ (number&& v) { eval_complement(v.backend(), v.backend()); - return static_cast&&>(v); + return static_cast&&>(v); } // // Addition: // template -inline mp_number operator + (mp_number&& a, const mp_number& b) +inline number operator + (number&& a, const number& b) { using default_ops::eval_add; eval_add(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline mp_number operator + (const mp_number& a, mp_number&& b) +inline number operator + (const number& a, number&& b) { using default_ops::eval_add; eval_add(b.backend(), a.backend()); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline mp_number operator + (mp_number&& a, mp_number&& b) +inline number operator + (number&& a, number&& b) { using default_ops::eval_add; eval_add(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator + (mp_number&& a, const V& b) +inline typename enable_if, number >::type + operator + (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_add; eval_add(a.backend(), static_cast(b)); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator + (const V& a, mp_number&& b) +inline typename enable_if, number >::type + operator + (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_add; eval_add(b.backend(), static_cast(a)); - return static_cast&&>(b); + return static_cast&&>(b); } // // Subtraction: // template -inline mp_number operator - (mp_number&& a, const mp_number& b) +inline number operator - (number&& a, const number& b) { using default_ops::eval_subtract; eval_subtract(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline mp_number operator - (const mp_number& a, mp_number&& b) +inline number operator - (const number& a, number&& b) { using default_ops::eval_subtract; eval_subtract(b.backend(), a.backend()); b.backend().negate(); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline mp_number operator - (mp_number&& a, mp_number&& b) +inline number operator - (number&& a, number&& b) { using default_ops::eval_subtract; eval_subtract(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator - (mp_number&& a, const V& b) +inline typename enable_if, number >::type + operator - (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_subtract; eval_subtract(a.backend(), static_cast(b)); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator - (const V& a, mp_number&& b) +inline typename enable_if, number >::type + operator - (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_subtract; eval_subtract(b.backend(), static_cast(a)); b.backend().negate(); - return static_cast&&>(b); + return static_cast&&>(b); } // // Multiply: // template -inline mp_number operator * (mp_number&& a, const mp_number& b) +inline number operator * (number&& a, const number& b) { using default_ops::eval_multiply; eval_multiply(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline mp_number operator * (const mp_number& a, mp_number&& b) +inline number operator * (const number& a, number&& b) { using default_ops::eval_multiply; eval_multiply(b.backend(), a.backend()); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline mp_number operator * (mp_number&& a, mp_number&& b) +inline number operator * (number&& a, number&& b) { using default_ops::eval_multiply; eval_multiply(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator * (mp_number&& a, const V& b) +inline typename enable_if, number >::type + operator * (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_multiply; eval_multiply(a.backend(), static_cast(b)); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator * (const V& a, mp_number&& b) +inline typename enable_if, number >::type + operator * (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_multiply; eval_multiply(b.backend(), static_cast(a)); - return static_cast&&>(b); + return static_cast&&>(b); } // // divide: // template -inline mp_number operator / (mp_number&& a, const mp_number& b) +inline number operator / (number&& a, const number& b) { using default_ops::eval_divide; eval_divide(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator / (mp_number&& a, const V& b) +inline typename enable_if, number >::type + operator / (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_divide; eval_divide(a.backend(), static_cast(b)); - return static_cast&&>(a); + return static_cast&&>(a); } // // modulus: // template -inline mp_number operator % (mp_number&& a, const mp_number& b) +inline number operator % (number&& a, const number& b) { using default_ops::eval_modulus; eval_modulus(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator % (mp_number&& a, const V& b) +inline typename enable_if, number >::type + operator % (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_modulus; eval_modulus(a.backend(), static_cast(b)); - return static_cast&&>(a); + return static_cast&&>(a); } // // Bitwise or: // template -inline mp_number operator | (mp_number&& a, const mp_number& b) +inline number operator | (number&& a, const number& b) { using default_ops::eval_bitwise_or; eval_bitwise_or(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline mp_number operator | (const mp_number& a, mp_number&& b) +inline number operator | (const number& a, number&& b) { using default_ops::eval_bitwise_or; eval_bitwise_or(b.backend(), a.backend()); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline mp_number operator | (mp_number&& a, mp_number&& b) +inline number operator | (number&& a, number&& b) { using default_ops::eval_bitwise_or; eval_bitwise_or(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator | (mp_number&& a, const V& b) +inline typename enable_if, number >::type + operator | (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_or; eval_bitwise_or(a.backend(), static_cast(b)); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator | (const V& a, mp_number&& b) +inline typename enable_if, number >::type + operator | (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_or; eval_bitwise_or(b.backend(), static_cast(a)); - return static_cast&&>(b); + return static_cast&&>(b); } // // Bitwise xor: // template -inline mp_number operator ^ (mp_number&& a, const mp_number& b) +inline number operator ^ (number&& a, const number& b) { using default_ops::eval_bitwise_xor; eval_bitwise_xor(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline mp_number operator ^ (const mp_number& a, mp_number&& b) +inline number operator ^ (const number& a, number&& b) { using default_ops::eval_bitwise_xor; eval_bitwise_xor(b.backend(), a.backend()); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline mp_number operator ^ (mp_number&& a, mp_number&& b) +inline number operator ^ (number&& a, number&& b) { using default_ops::eval_bitwise_xor; eval_bitwise_xor(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator ^ (mp_number&& a, const V& b) +inline typename enable_if, number >::type + operator ^ (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_xor; eval_bitwise_xor(a.backend(), static_cast(b)); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator ^ (const V& a, mp_number&& b) +inline typename enable_if, number >::type + operator ^ (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_xor; eval_bitwise_xor(b.backend(), static_cast(a)); - return static_cast&&>(b); + return static_cast&&>(b); } // // Bitwise and: // template -inline mp_number operator & (mp_number&& a, const mp_number& b) +inline number operator & (number&& a, const number& b) { using default_ops::eval_bitwise_and; eval_bitwise_and(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline mp_number operator & (const mp_number& a, mp_number&& b) +inline number operator & (const number& a, number&& b) { using default_ops::eval_bitwise_and; eval_bitwise_and(b.backend(), a.backend()); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline mp_number operator & (mp_number&& a, mp_number&& b) +inline number operator & (number&& a, number&& b) { using default_ops::eval_bitwise_and; eval_bitwise_and(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator & (mp_number&& a, const V& b) +inline typename enable_if, number >::type + operator & (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_and; eval_bitwise_and(a.backend(), static_cast(b)); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator & (const V& a, mp_number&& b) +inline typename enable_if, number >::type + operator & (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_and; eval_bitwise_and(b.backend(), static_cast(a)); - return static_cast&&>(b); + return static_cast&&>(b); } // // shifts: // template -inline typename enable_if, mp_number >::type - operator << (mp_number&& a, const I& b) +inline typename enable_if, number >::type + operator << (number&& a, const I& b) { using default_ops::eval_left_shift; eval_left_shift(a.backend(), b); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, mp_number >::type - operator >> (mp_number&& a, const I& b) +inline typename enable_if, number >::type + operator >> (number&& a, const I& b) { using default_ops::eval_right_shift; eval_right_shift(a.backend(), b); - return static_cast&&>(a); + return static_cast&&>(a); } #endif diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp new file mode 100644 index 00000000..29f5379a --- /dev/null +++ b/include/boost/multiprecision/detail/number_base.hpp @@ -0,0 +1,1262 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_BIG_NUM_BASE_HPP +#define BOOST_MATH_BIG_NUM_BASE_HPP + +#include +#include +#include +#include + +namespace boost{ namespace multiprecision{ + +template +class number; + +template +struct is_mp_number : public mpl::false_ {}; + +template +struct is_mp_number > : public mpl::true_ {}; + +namespace detail{ + +// Forward-declare an expression wrapper +template +struct expression; + +} // namespace detail + +template +struct is_mp_number_expression : public mpl::false_ {}; + +template +struct is_mp_number_expression > : public mpl::true_ {}; + +namespace detail{ +// +// Workaround for missing abs(long long) on some compilers: +// +template +typename boost::enable_if, T>::type abs(const T& t) BOOST_NOEXCEPT +{ + return t < 0 ? -t : t; +} + +#define BOOST_MP_USING_ABS using std::abs; using boost::multiprecision::detail::abs; + +// +// Move support: +// +#ifndef BOOST_NO_RVALUE_REFERENCES +# define BOOST_MP_MOVE(x) std::move(x) +#else +# define BOOST_MP_MOVE(x) x +#endif + +template +struct has_enough_bits +{ + template + struct type : public mpl::bool_::digits >= b>{}; +}; + +template +struct canonical_imp +{ + typedef Val type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::signed_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::unsigned_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename mpl::find_if< + typename Backend::float_types, + pred_type + >::type iter_type; + typedef typename mpl::deref::type type; +}; +template +struct canonical_imp > +{ + typedef const char* type; +}; + +template +struct canonical +{ + typedef typename mpl::if_< + is_signed, + mpl::int_<0>, + typename mpl::if_< + is_unsigned, + mpl::int_<1>, + typename mpl::if_< + is_floating_point, + mpl::int_<2>, + typename mpl::if_< + mpl::or_< + is_convertible, + is_same + >, + mpl::int_<3>, + mpl::int_<4> + >::type + >::type + >::type + >::type tag_type; + + typedef typename canonical_imp::type type; +}; + +struct terminal{}; +struct negate{}; +struct plus{}; +struct minus{}; +struct multiplies{}; +struct divides{}; +struct modulus{}; +struct shift_left{}; +struct shift_right{}; +struct bitwise_and{}; +struct bitwise_or{}; +struct bitwise_xor{}; +struct bitwise_complement{}; +struct add_immediates{}; +struct subtract_immediates{}; +struct multiply_immediates{}; +struct divide_immediates{}; +struct modulus_immediates{}; +struct bitwise_and_immediates{}; +struct bitwise_or_immediates{}; +struct bitwise_xor_immediates{}; +struct complement_immediates{}; +struct function{}; + +template +struct backend_type; + +template +struct backend_type > +{ + typedef T type; +}; + +template +struct backend_type > +{ + typedef typename backend_type::result_type>::type type; +}; + + +template +struct is_mp_number : public mpl::false_{}; +template +struct is_mp_number > : public mpl::true_{}; +template +struct is_mp_number_exp : public mpl::false_{}; +template +struct is_mp_number_exp > : public mpl::true_{}; + +template +struct combine_expression; + +template +struct combine_expression, T2> +{ + typedef number type; +}; + +template +struct combine_expression > +{ + typedef number type; +}; + +template +struct combine_expression, number > +{ + typedef number type; +}; + +template +struct arg_type +{ + typedef expression type; +}; + +template +struct arg_type > +{ + typedef expression type; +}; + +template +struct unmentionable +{ + static void proc(){} +}; + +typedef void (*unmentionable_type)(); + +template +struct expression_storage +{ + typedef const T& type; +}; + +template +struct expression_storage +{ + typedef T* type; +}; + +template +struct expression_storage +{ + typedef const T* type; +}; + +template +struct expression_storage > +{ + typedef expression type; +}; + +template +struct expression +{ + typedef mpl::int_<1> arity; + typedef typename arg_type::type left_type; + typedef typename left_type::result_type result_type; + typedef tag tag_type; + + explicit expression(const Arg1& a) : arg(a) {} + + left_type left()const { return left_type(arg); } + + const Arg1& left_ref()const BOOST_NOEXCEPT { return arg; } + + static const unsigned depth = left_type::depth + 1; + + operator unmentionable_type()const + { + result_type r(*this); + return r ? &unmentionable::proc : 0; + } + +private: + typename expression_storage::type arg; + expression& operator=(const expression&); +}; + +template +struct expression +{ + typedef mpl::int_<0> arity; + typedef Arg1 result_type; + typedef terminal tag_type; + + explicit expression(const Arg1& a) : arg(a) {} + + const Arg1& value()const BOOST_NOEXCEPT { return arg; } + + static const unsigned depth = 0; + + operator unmentionable_type()const + { + return arg ? &unmentionable::proc : 0; + } + +private: + typename expression_storage::type arg; + expression& operator=(const expression&); +}; + +template +struct expression +{ + typedef mpl::int_<2> arity; + typedef typename arg_type::type left_type; + typedef typename arg_type::type right_type; + typedef typename left_type::result_type left_result_type; + typedef typename right_type::result_type right_result_type; + typedef typename combine_expression::type result_type; + typedef tag tag_type; + + expression(const Arg1& a1, const Arg2& a2) : arg1(a1), arg2(a2) {} + + left_type left()const { return left_type(arg1); } + right_type right()const { return right_type(arg2); } + const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; } + const Arg2& right_ref()const BOOST_NOEXCEPT { return arg2; } + + operator unmentionable_type()const + { + result_type r(*this); + return r ? &unmentionable::proc : 0; + } + + static const unsigned left_depth = left_type::depth + 1; + static const unsigned right_depth = right_type::depth + 1; + static const unsigned depth = left_depth > right_depth ? left_depth : right_depth; +private: + typename expression_storage::type arg1; + typename expression_storage::type arg2; + expression& operator=(const expression&); +}; + +template +struct expression +{ + typedef mpl::int_<3> arity; + typedef typename arg_type::type left_type; + typedef typename arg_type::type middle_type; + typedef typename arg_type::type right_type; + typedef typename left_type::result_type left_result_type; + typedef typename middle_type::result_type middle_result_type; + typedef typename right_type::result_type right_result_type; + typedef typename combine_expression< + left_result_type, + typename combine_expression::type + >::type result_type; + typedef tag tag_type; + + expression(const Arg1& a1, const Arg2& a2, const Arg3& a3) : arg1(a1), arg2(a2), arg3(a3) {} + + left_type left()const { return left_type(arg1); } + middle_type middle()const { return middle_type(arg2); } + right_type right()const { return right_type(arg3); } + const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; } + const Arg2& middle_ref()const BOOST_NOEXCEPT { return arg2; } + const Arg3& right_ref()const BOOST_NOEXCEPT { return arg3; } + + operator unmentionable_type()const + { + result_type r(*this); + return r ? &unmentionable::proc : 0; + } + + static const unsigned left_depth = left_type::depth + 1; + static const unsigned middle_depth = middle_type::depth + 1; + static const unsigned right_depth = right_type::depth + 1; + static const unsigned depth = left_depth > right_depth ? (left_depth > middle_depth ? left_depth : middle_depth) : (right_depth > middle_depth ? right_depth : middle_depth); +private: + typename expression_storage::type arg1; + typename expression_storage::type arg2; + typename expression_storage::type arg3; + expression& operator=(const expression&); +}; + +template +struct expression +{ + typedef mpl::int_<4> arity; + typedef typename arg_type::type left_type; + typedef typename arg_type::type left_middle_type; + typedef typename arg_type::type right_middle_type; + typedef typename arg_type::type right_type; + typedef typename left_type::result_type left_result_type; + typedef typename left_middle_type::result_type left_middle_result_type; + typedef typename right_middle_type::result_type right_middle_result_type; + typedef typename right_type::result_type right_result_type; + typedef typename combine_expression< + typename combine_expression< + typename combine_expression::type, + right_middle_result_type + >::type, + right_result_type + >::type result_type; + typedef tag tag_type; + + expression(const Arg1& a1, const Arg2& a2, const Arg3& a3, const Arg4& a4) : arg1(a1), arg2(a2), arg3(a3), arg4(a4) {} + + left_type left()const { return left_type(arg1); } + left_middle_type left_middle()const { return left_middle_type(arg2); } + right_middle_type right_middle()const { return right_middle_type(arg3); } + right_type right()const { return right_type(arg4); } + const Arg1& left_ref()const BOOST_NOEXCEPT { return arg1; } + const Arg2& left_middle_ref()const BOOST_NOEXCEPT { return arg2; } + const Arg3& right_middle_ref()const BOOST_NOEXCEPT { return arg3; } + const Arg4& right_ref()const BOOST_NOEXCEPT { return arg4; } + + operator unmentionable_type()const + { + result_type r(*this); + return r ? &unmentionable::proc : 0; + } + + static const unsigned left_depth = left_type::depth + 1; + static const unsigned left_middle_depth = left_middle_type::depth + 1; + static const unsigned right_middle_depth = right_middle_type::depth + 1; + static const unsigned right_depth = right_type::depth + 1; + + static const unsigned left_max_depth = left_depth > left_middle_depth ? left_depth : left_middle_depth; + static const unsigned right_max_depth = right_depth > right_middle_depth ? right_depth : right_middle_depth; + + static const unsigned depth = left_max_depth > right_max_depth ? left_max_depth : right_max_depth; +private: + typename expression_storage::type arg1; + typename expression_storage::type arg2; + typename expression_storage::type arg3; + typename expression_storage::type arg4; + expression& operator=(const expression&); +}; + +template +struct digits2 +{ + BOOST_STATIC_ASSERT(std::numeric_limits::is_specialized); + BOOST_STATIC_ASSERT((std::numeric_limits::radix == 2) || (std::numeric_limits::radix == 10)); + // If we really have so many digits that this fails, then we're probably going to hit other problems anyway: + BOOST_STATIC_ASSERT(LONG_MAX / 1000 > (std::numeric_limits::digits + 1)); + static const long value = std::numeric_limits::radix == 10 ? (((std::numeric_limits::digits + 1) * 1000L) / 301L) : std::numeric_limits::digits; +}; + +#ifndef BOOST_MP_MIN_EXPONENT_DIGITS +#ifdef _MSC_VER +# define BOOST_MP_MIN_EXPONENT_DIGITS 2 +#else +# define BOOST_MP_MIN_EXPONENT_DIGITS 2 +#endif +#endif + +template +void format_float_string(S& str, boost::intmax_t my_exp, boost::intmax_t digits, std::ios_base::fmtflags f, bool iszero) +{ + typedef typename S::size_type size_type; + bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; + bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; + bool showpoint = (f & std::ios_base::showpoint) == std::ios_base::showpoint; + bool showpos = (f & std::ios_base::showpos) == std::ios_base::showpos; + + bool neg = str.size() && (str[0] == '-'); + + if(neg) + str.erase(0, 1); + + if(digits == 0) + { + digits = (std::max)(str.size(), size_type(16)); + } + + if(iszero || str.empty() || (str.find_first_not_of('0') == S::npos)) + { + // We will be printing zero, even though the value might not + // actually be zero (it just may have been rounded to zero). + str = "0"; + if(scientific || fixed) + { + str.append(1, '.'); + str.append(size_type(digits), '0'); + if(scientific) + str.append("e+00"); + } + else + { + if(showpoint) + { + str.append(1, '.'); + if(digits > 1) + str.append(size_type(digits - 1), '0'); + } + } + if(neg) + str.insert(0, 1, '-'); + else if(showpos) + str.insert(0, 1, '+'); + return; + } + + if(!fixed && !scientific && !showpoint) + { + // + // Suppress trailing zeros: + // + std::string::iterator pos = str.end(); + while(pos != str.begin() && *--pos == '0'){} + if(pos != str.end()) + ++pos; + str.erase(pos, str.end()); + if(str.empty()) + str = '0'; + } + else if(!fixed || (my_exp >= 0)) + { + // + // Pad out the end with zero's if we need to: + // + boost::intmax_t chars = str.size(); + chars = digits - chars; + if(scientific) + ++chars; + if(chars > 0) + { + str.append(static_cast(chars), '0'); + } + } + + if(fixed || (!scientific && (my_exp >= -4) && (my_exp < digits))) + { + if(1 + my_exp > static_cast(str.size())) + { + // Just pad out the end with zeros: + str.append(static_cast(1 + my_exp - str.size()), '0'); + if(showpoint || fixed) + str.append("."); + } + else if(my_exp + 1 < static_cast(str.size())) + { + if(my_exp < 0) + { + str.insert(0, static_cast(-1 - my_exp), '0'); + str.insert(0, "0."); + } + else + { + // Insert the decimal point: + str.insert(static_cast(my_exp + 1), 1, '.'); + } + } + else if(showpoint || fixed) // we have exactly the digits we require to left of the point + str += "."; + + if(fixed) + { + // We may need to add trailing zeros: + boost::intmax_t l = str.find('.') + 1; + l = digits - (str.size() - l); + if(l > 0) + str.append(size_type(l), '0'); + } + } + else + { + BOOST_MP_USING_ABS + // Scientific format: + if(showpoint || (str.size() > 1)) + str.insert(1, 1, '.'); + str.append(1, 'e'); + S e = boost::lexical_cast(abs(my_exp)); + if(e.size() < BOOST_MP_MIN_EXPONENT_DIGITS) + e.insert(0, BOOST_MP_MIN_EXPONENT_DIGITS-e.size(), '0'); + if(my_exp < 0) + e.insert(0, 1, '-'); + else + e.insert(0, 1, '+'); + str.append(e); + } + if(neg) + str.insert(0, 1, '-'); + else if(showpos) + str.insert(0, 1, '+'); +} + +} // namespace detail + +// +// Non-member operators for number: +// +// Unary operators first: +// +template +inline const number& operator + (const number& v) { return v; } +template +inline const detail::expression& operator + (const detail::expression& v) { return v; } +template +inline detail::expression > operator - (const number& v) { return detail::expression >(v); } +template +inline detail::expression > operator - (const detail::expression& v) { return detail::expression >(v); } +template +inline detail::expression > operator ~ (const number& v) { return detail::expression >(v); } +template +inline detail::expression > operator ~ (const detail::expression& v) { return detail::expression >(v); } +// +// Then addition: +// +template +inline detail::expression, number > + operator + (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator + (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator + (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator + (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator + (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator + (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator + (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator + (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::expression, typename detail::expression::left_type > + operator + (const number& a, const detail::expression& b) +{ + return detail::expression, typename detail::expression::left_type >(a, b.left_ref()); +} +template +inline detail::expression, typename detail::expression::left_type > + operator + (const detail::expression& a, const number& b) +{ + return detail::expression, typename detail::expression::left_type >(b, a.left_ref()); +} +template +inline detail::expression, number > + operator + (const number& a, const detail::expression >& b) +{ + return detail::expression, number >(a, b.left_ref()); +} +template +inline detail::expression, number > + operator + (const detail::expression >& a, const number& b) +{ + return detail::expression, number >(b, a.left_ref()); +} +template +inline typename enable_if, detail::expression > >::type + operator + (const detail::expression >& a, const V& b) +{ + return detail::expression >(b, a.left_ref()); +} +template +inline typename enable_if, detail::expression > >::type + operator + (const V& a, const detail::expression >& b) +{ + return detail::expression, number >(a, b.left_ref()); +} +// +// Subtraction: +// +template +inline detail::expression, number > + operator - (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator - (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator - (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator - (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator - (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator - (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator - (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator - (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::expression, typename detail::expression::left_type > + operator - (const number& a, const detail::expression& b) +{ + return detail::expression, typename detail::expression::left_type >(a, b.left_ref()); +} +template +inline detail::expression, typename detail::expression::left_type > > + operator - (const detail::expression& a, const number& b) +{ + return detail::expression, typename detail::expression::left_type > >( + detail::expression, typename detail::expression::left_type >(b, a.left_ref())); +} +template +inline detail::expression, number > + operator - (const number& a, const detail::expression >& b) +{ + return detail::expression, number >(a, b.left_ref()); +} +template +inline detail::expression, number > > + operator - (const detail::expression >& a, const number& b) +{ + return detail::expression, number > >( + detail::expression, number >(b, a.left_ref())); +} +template +inline typename enable_if, detail::expression, V > > >::type + operator - (const detail::expression >& a, const V& b) +{ + return detail::expression, V > >(detail::expression, V >(a.left_ref(), b)); +} +template +inline typename enable_if, detail::expression > >::type + operator - (const V& a, const detail::expression >& b) +{ + return detail::expression >(a, b.left_ref()); +} +// +// Multiplication: +// +template +inline detail::expression, number > + operator * (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator * (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator * (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator * (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator * (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator * (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator * (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator * (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::expression, typename detail::expression::left_type > > + operator * (const number& a, const detail::expression& b) +{ + return detail::expression, typename detail::expression::left_type > >( + detail::expression, typename detail::expression::left_type > (a, b.left_ref())); +} +template +inline detail::expression, typename detail::expression::left_type > > + operator * (const detail::expression& a, const number& b) +{ + return detail::expression, typename detail::expression::left_type > >( + detail::expression, typename detail::expression::left_type >(b, a.left_ref())); +} +template +inline detail::expression, number > > + operator * (const number& a, const detail::expression >& b) +{ + return detail::expression, number > >( + detail::expression, number >(a, b.left_ref())); +} +template +inline detail::expression, number > > + operator * (const detail::expression >& a, const number& b) +{ + return detail::expression, number > >( + detail::expression, number >(b, a.left_ref())); +} +template +inline typename enable_if, detail::expression, V > > >::type + operator * (const detail::expression >& a, const V& b) +{ + return detail::expression, V > > ( + detail::expression, V >(a.left_ref(), b)); +} +template +inline typename enable_if, detail::expression, V > > >::type + operator * (const V& a, const detail::expression >& b) +{ + return detail::expression, V > >( + detail::expression, V >(b.left_ref(), a)); +} +// +// Division: +// +template +inline detail::expression, number > + operator / (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator / (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator / (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator / (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator / (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator / (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator / (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator / (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::expression, typename detail::expression::left_type > > + operator / (const number& a, const detail::expression& b) +{ + return detail::expression, typename detail::expression::left_type > >( + detail::expression, typename detail::expression::left_type >(a, b.left_ref())); +} +template +inline detail::expression::left_type, number > > + operator / (const detail::expression& a, const number& b) +{ + return detail::expression::left_type, number > >( + detail::expression::left_type, number >(a.left_ref(), b)); +} +template +inline detail::expression, number > > + operator / (const number& a, const detail::expression >& b) +{ + return detail::expression, number > >( + detail::expression, number >(a, b.left_ref())); +} +template +inline detail::expression, number > > + operator / (const detail::expression >& a, const number& b) +{ + return detail::expression, number > >( + detail::expression, number >(a.left_ref(), b)); +} +template +inline typename enable_if, detail::expression, V > > >::type + operator / (const detail::expression >& a, const V& b) +{ + return detail::expression, V > >( + detail::expression, V>(a.left_ref(), b)); +} +template +inline typename enable_if, detail::expression > > >::type + operator / (const V& a, const detail::expression >& b) +{ + return detail::expression > >( + detail::expression >(a, b.left_ref())); +} +// +// Modulus: +// +template +inline detail::expression, number > + operator % (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator % (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator % (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator % (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator % (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator % (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator % (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator % (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Left shift: +// +template +inline typename enable_if, detail::expression, I > >::type + operator << (const number& a, const I& b) +{ + return detail::expression, I>(a, b); +} +template +inline typename enable_if, detail::expression, I> >::type + operator << (const detail::expression& a, const I& b) +{ + return detail::expression, I>(a, b); +} +// +// Right shift: +// +template +inline typename enable_if, detail::expression, I > >::type + operator >> (const number& a, const I& b) +{ + return detail::expression, I>(a, b); +} +template +inline typename enable_if, detail::expression, I> >::type + operator >> (const detail::expression& a, const I& b) +{ + return detail::expression, I>(a, b); +} +// +// Bitwise AND: +// +template +inline detail::expression, number > + operator & (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator & (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator & (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator & (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator & (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator & (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator & (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator & (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Bitwise OR: +// +template +inline detail::expression, number > + operator| (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator| (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator| (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator| (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator| (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator| (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator| (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator| (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Bitwise XOR: +// +template +inline detail::expression, number > + operator^ (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator^ (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator^ (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator^ (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator^ (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator^ (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if, detail::expression, V > >::type + operator^ (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if, detail::expression > >::type + operator^ (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} + +// +// Traits class, lets us know what kind of number we have, defaults to a floating point type: +// +enum number_category_type +{ + number_kind_integer = 0, + number_kind_floating_point = 1, + number_kind_rational = 2, + number_kind_fixed_point = 3 +}; + +template +struct number_category : public mpl::int_ {}; +template +struct number_category > : public number_category{}; +template +struct number_category > : public number_category::result_type>{}; + +template +struct component_type; +template +struct component_type > : public component_type{}; +template +struct component_type > : public component_type::result_type>{}; + +}} // namespaces + +namespace boost{ namespace math{ namespace tools{ + +template +struct promote_arg; + +template +struct promote_arg > +{ + typedef typename boost::multiprecision::detail::expression::result_type type; +}; + +template +inline R real_cast(const boost::multiprecision::number& val) +{ + return val.template convert_to(); +} + +template +inline R real_cast(const boost::multiprecision::detail::expression& val) +{ + typedef typename boost::multiprecision::detail::expression::result_type val_type; + return val_type(val).template convert_to(); +} + + +}}} + +#endif // BOOST_MATH_BIG_NUM_BASE_HPP + + diff --git a/include/boost/multiprecision/detail/number_compare.hpp b/include/boost/multiprecision/detail/number_compare.hpp new file mode 100644 index 00000000..7b881d73 --- /dev/null +++ b/include/boost/multiprecision/detail/number_compare.hpp @@ -0,0 +1,482 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MP_COMPARE_HPP +#define BOOST_MP_COMPARE_HPP + +// +// Comparison operators for number. +// + +namespace boost{ namespace multiprecision{ + +namespace default_ops{ + +template +inline bool eval_eq(const B& a, const B& b) +{ + return a.compare(b) == 0; +} +template +inline bool eval_eq(const B& a, const A& b) +{ + typedef typename mpl::if_< + is_convertible >, + number, + number + >::type mp_type; + mp_type t(b); + return eval_eq(a, t.backend()); +} + +template +inline bool eval_lt(const B& a, const B& b) +{ + return a.compare(b) < 0; +} +template +inline bool eval_lt(const B& a, const A& b) +{ + typedef typename mpl::if_< + is_convertible >, + number, + number + >::type mp_type; + mp_type t(b); + return eval_lt(a, t.backend()); +} + +template +inline bool eval_gt(const B& a, const B& b) +{ + return a.compare(b) > 0; +} +template +inline bool eval_gt(const B& a, const A& b) +{ + typedef typename mpl::if_< + is_convertible >, + number, + number + >::type mp_type; + mp_type t(b); + return eval_gt(a, t.backend()); +} + +} + +template +inline bool operator == (const number& a, const number& b) +{ + using default_ops::eval_eq; + return eval_eq(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator == (const number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + return eval_eq(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator == (const number& a, const detail::expression& b) +{ + using default_ops::eval_eq; + typename detail::expression::result_type t(b); + return eval_eq(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator == (const Arithmetic& a, const number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + return eval_eq(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator == (const Arithmetic& a, const detail::expression& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + result_type t(b); + return eval_eq(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator == (const detail::expression& a, const number& b) +{ + using default_ops::eval_eq; + typename detail::expression::result_type t(a); + return eval_eq(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator == (const detail::expression& a, const Arithmetic& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + result_type t(a); + return eval_eq(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type + operator == (const detail::expression& a, const detail::expression& b) +{ + using default_ops::eval_eq; + typename detail::expression::result_type t(a); + typename detail::expression::result_type t2(b); + return eval_eq(t.backend(), t2.backend()); +} + +template +inline bool operator != (const number& a, const number& b) +{ + using default_ops::eval_eq; + return !eval_eq(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator != (const number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + return !eval_eq(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator != (const number& a, const detail::expression& b) +{ + using default_ops::eval_eq; + typename detail::expression::result_type t(b); + return !eval_eq(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator != (const Arithmetic& a, const number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + return !eval_eq(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator != (const Arithmetic& a, const detail::expression& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + result_type t(b); + return !eval_eq(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator != (const detail::expression& a, const number& b) +{ + using default_ops::eval_eq; + typename detail::expression::result_type t(a); + return !eval_eq(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator != (const detail::expression& a, const Arithmetic& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_eq; + result_type t(a); + return !eval_eq(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type + operator != (const detail::expression& a, const detail::expression& b) +{ + using default_ops::eval_eq; + typename detail::expression::result_type t(a); + typename detail::expression::result_type t2(b); + return !eval_eq(t.backend(), t2.backend()); +} + +template +inline bool operator < (const number& a, const number& b) +{ + using default_ops::eval_lt; + return eval_lt(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator < (const number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + return eval_lt(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator < (const number& a, const detail::expression& b) +{ + using default_ops::eval_lt; + typename detail::expression::result_type t(b); + return eval_lt(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator < (const Arithmetic& a, const number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + return eval_gt(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator < (const Arithmetic& a, const detail::expression& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + result_type t(b); + return eval_gt(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator < (const detail::expression& a, const number& b) +{ + using default_ops::eval_lt; + typename detail::expression::result_type t(a); + return eval_lt(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator < (const detail::expression& a, const Arithmetic& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + result_type t(a); + return eval_lt(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type + operator < (const detail::expression& a, const detail::expression& b) +{ + using default_ops::eval_lt; + typename detail::expression::result_type t(a); + typename detail::expression::result_type t2(b); + return eval_lt(t.backend(), t2.backend()); +} + +template +inline bool operator > (const number& a, const number& b) +{ + using default_ops::eval_gt; + return eval_gt(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator > (const number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + return eval_gt(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator > (const number& a, const detail::expression& b) +{ + using default_ops::eval_gt; + typename detail::expression::result_type t(b); + return eval_gt(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator > (const Arithmetic& a, const number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + return eval_lt(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator > (const Arithmetic& a, const detail::expression& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + result_type t(b); + return eval_lt(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator > (const detail::expression& a, const number& b) +{ + using default_ops::eval_gt; + typename detail::expression::result_type t(a); + return eval_gt(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator > (const detail::expression& a, const Arithmetic& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + result_type t(a); + return eval_gt(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type + operator > (const detail::expression& a, const detail::expression& b) +{ + using default_ops::eval_gt; + typename detail::expression::result_type t(a); + typename detail::expression::result_type t2(b); + return eval_gt(t.backend(), t2.backend()); +} + +template +inline bool operator <= (const number& a, const number& b) +{ + using default_ops::eval_gt; + return !eval_gt(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator <= (const number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + return !eval_gt(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator <= (const number& a, const detail::expression& b) +{ + using default_ops::eval_gt; + typename detail::expression::result_type t(b); + return !eval_gt(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator <= (const Arithmetic& a, const number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + return !eval_lt(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator <= (const Arithmetic& a, const detail::expression& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + result_type t(b); + return !eval_lt(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator <= (const detail::expression& a, const number& b) +{ + using default_ops::eval_gt; + typename detail::expression::result_type t(a); + return !eval_gt(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator <= (const detail::expression& a, const Arithmetic& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + result_type t(a); + return !eval_gt(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type + operator <= (const detail::expression& a, const detail::expression& b) +{ + using default_ops::eval_gt; + typename detail::expression::result_type t(a); + typename detail::expression::result_type t2(b); + return !eval_gt(t.backend(), t2.backend()); +} + +template +inline bool operator >= (const number& a, const number& b) +{ + using default_ops::eval_lt; + return !eval_lt(a.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator >= (const number& a, const Arithmetic& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + return !eval_lt(a.backend(), ct(b)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator >= (const number& a, const detail::expression& b) +{ + using default_ops::eval_lt; + typename detail::expression::result_type t(b); + return !eval_lt(a.backend(), t.backend()); +} +template +inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator >= (const Arithmetic& a, const number& b) +{ + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + return !eval_gt(b.backend(), ct(a)); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator >= (const Arithmetic& a, const detail::expression& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_gt; + result_type t(b); + return !eval_gt(t.backend(), ct(a)); +} +template +inline typename enable_if, typename detail::expression::result_type>, bool>::type + operator >= (const detail::expression& a, const number& b) +{ + using default_ops::eval_lt; + typename detail::expression::result_type t(a); + return !eval_lt(t.backend(), b.backend()); +} +template +inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type + operator >= (const detail::expression& a, const Arithmetic& b) +{ + typedef typename detail::expression::result_type result_type; + typedef typename detail::canonical::type ct; + using default_ops::eval_lt; + result_type t(a); + return !eval_lt(t.backend(), ct(b)); +} +template +inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type + operator >= (const detail::expression& a, const detail::expression& b) +{ + using default_ops::eval_lt; + typename detail::expression::result_type t(a); + typename detail::expression::result_type t2(b); + return !eval_lt(t.backend(), t2.backend()); +} + + +}} // namespaces + +#endif // BOOST_MP_COMPARE_HPP + diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index bc5549e2..b8d290f9 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -6,7 +6,7 @@ #ifndef BOOST_MATH_ER_GMP_BACKEND_HPP #define BOOST_MATH_ER_GMP_BACKEND_HPP -#include +#include #include #include #include @@ -1870,15 +1870,15 @@ inline bool eval_is_zero(const gmp_rational& val) { return mpq_sgn(val.data()) == 0; } -inline mp_number numerator(const mp_number& val) +inline number numerator(const number& val) { - mp_number result; + number result; mpz_set(result.backend().data(), (mpq_numref(val.backend().data()))); return result; } -inline mp_number denominator(const mp_number& val) +inline number denominator(const number& val) { - mp_number result; + number result; mpz_set(result.backend().data(), (mpq_denref(val.backend().data()))); return result; } @@ -2072,9 +2072,9 @@ using boost::multiprecision::backends::gmp_rational; using boost::multiprecision::backends::gmp_float; template <> -struct component_type > +struct component_type > { - typedef mp_number type; + typedef number type; }; template<> @@ -2082,13 +2082,13 @@ struct number_category : public mpl::int_{}; template<> struct number_category : public mpl::int_{}; -typedef mp_number > mpf_float_50; -typedef mp_number > mpf_float_100; -typedef mp_number > mpf_float_500; -typedef mp_number > mpf_float_1000; -typedef mp_number > mpf_float; -typedef mp_number mpz_int; -typedef mp_number mpq_rational; +typedef number > mpf_float_50; +typedef number > mpf_float_100; +typedef number > mpf_float_500; +typedef number > mpf_float_1000; +typedef number > mpf_float; +typedef number mpz_int; +typedef number mpq_rational; }} // namespaces @@ -2098,9 +2098,9 @@ namespace std{ // numeric_limits [partial] specializations for the types declared in this header: // template -class numeric_limits, ExpressionTemplates> > +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; // @@ -2195,10 +2195,10 @@ private: { data_initializer() { - std::numeric_limits > >::epsilon(); - std::numeric_limits > >::round_error(); - (std::numeric_limits > >::min)(); - (std::numeric_limits > >::max)(); + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); } void do_nothing()const{} }; @@ -2206,12 +2206,12 @@ private: }; template -const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; +const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; template -class numeric_limits, ExpressionTemplates> > +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; static number_type (min)() BOOST_NOEXCEPT { return number_type(); } @@ -2250,56 +2250,56 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif template -class numeric_limits > +class numeric_limits > { - typedef boost::multiprecision::mp_number number_type; + typedef boost::multiprecision::number number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; // @@ -2348,56 +2348,56 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; #endif template -class numeric_limits > +class numeric_limits > { - typedef boost::multiprecision::mp_number number_type; + typedef boost::multiprecision::number number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; // @@ -2447,49 +2447,49 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; #endif diff --git a/include/boost/multiprecision/miller_rabin.hpp b/include/boost/multiprecision/miller_rabin.hpp index 557114cd..f1961bf2 100644 --- a/include/boost/multiprecision/miller_rabin.hpp +++ b/include/boost/multiprecision/miller_rabin.hpp @@ -12,7 +12,7 @@ namespace boost{ namespace multiprecision{ template -bool check_small_factors(const mp_number& n) +bool check_small_factors(const number& n) { static const boost::uint32_t small_factors1[] = { 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u }; @@ -119,13 +119,13 @@ inline bool is_small_prime(unsigned n) template typename enable_if_c::value == number_kind_integer, bool>::type - miller_rabin_test(const mp_number& n, unsigned trials, Engine& gen) + miller_rabin_test(const number& n, unsigned trials, Engine& gen) { #ifdef BOOST_MSVC #pragma warning(push) #pragma warning(disable:4127) #endif - typedef mp_number number_type; + typedef number number_type; if(n <= 227) return is_small_prime(n.template convert_to()); @@ -179,23 +179,23 @@ typename enable_if_c::value == number_kind_integer, boo } template -bool miller_rabin_test(const mp_number& x, unsigned trials) +bool miller_rabin_test(const number& x, unsigned trials) { static mt19937 gen; return miller_rabin_test(x, trials, gen); } template -bool miller_rabin_test(const detail::mp_exp & n, unsigned trials, Engine& gen) +bool miller_rabin_test(const detail::expression & n, unsigned trials, Engine& gen) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::expression::result_type number_type; return miller_rabin_test(number_type(n), trials, gen); } template -bool miller_rabin_test(const detail::mp_exp & n, unsigned trials) +bool miller_rabin_test(const detail::expression & n, unsigned trials) { - typedef typename detail::mp_exp::result_type number_type; + typedef typename detail::expression::result_type number_type; return miller_rabin_test(number_type(n), trials); } diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 63f98959..859e51b3 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -6,7 +6,7 @@ #ifndef BOOST_MATH_BN_MPFR_HPP #define BOOST_MATH_BN_MPFR_HPP -#include +#include #include #include #include @@ -897,7 +897,7 @@ inline void eval_trunc(mpfr_float_backend& result, const mpfr_float_ba { if(0 == mpfr_number_p(val.data())) { - result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, mp_number >(val), 0, boost::math::policies::policy<>()).backend(); + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, number >(val), 0, boost::math::policies::policy<>()).backend(); return; } mpfr_trunc(result.data(), val.data()); @@ -1046,11 +1046,11 @@ inline void eval_tanh(mpfr_float_backend& result, const mpfr_float_bac using boost::multiprecision::backends::mpfr_float_backend; -typedef mp_number > mpfr_float_50; -typedef mp_number > mpfr_float_100; -typedef mp_number > mpfr_float_500; -typedef mp_number > mpfr_float_1000; -typedef mp_number > mpfr_float; +typedef number > mpfr_float_50; +typedef number > mpfr_float_100; +typedef number > mpfr_float_500; +typedef number > mpfr_float_1000; +typedef number > mpfr_float; } // namespace multiprecision @@ -1064,7 +1064,7 @@ inline int digits() BOOST_NOEXCEPT return boost::multiprecision::backends::detail::get_default_precision(); } template <> -inline int digits, false> >() BOOST_NOEXCEPT +inline int digits, false> >() BOOST_NOEXCEPT { return boost::multiprecision::backends::detail::get_default_precision(); } @@ -1079,9 +1079,9 @@ namespace std{ // numeric_limits [partial] specializations for the types declared in this header: // template -class numeric_limits, ExpressionTemplates> > +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT @@ -1198,12 +1198,12 @@ private: { data_initializer() { - std::numeric_limits > >::epsilon(); - std::numeric_limits > >::round_error(); - (std::numeric_limits > >::min)(); - (std::numeric_limits > >::max)(); - std::numeric_limits > >::infinity(); - std::numeric_limits > >::quiet_NaN(); + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); + std::numeric_limits > >::infinity(); + std::numeric_limits > >::quiet_NaN(); } void do_nothing()const{} }; @@ -1211,62 +1211,62 @@ private: }; template -const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; +const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; template -BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent; +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent; template -BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent10; template -BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent; +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent; template -BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif template -class numeric_limits, ExpressionTemplates> > +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = false; static number_type (min)() BOOST_NOEXCEPT { return number_type(0); } @@ -1305,49 +1305,49 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif } // namespace std diff --git a/include/boost/multiprecision/mp_number.hpp b/include/boost/multiprecision/number.hpp similarity index 86% rename from include/boost/multiprecision/mp_number.hpp rename to include/boost/multiprecision/number.hpp index 704cec15..15096180 100644 --- a/include/boost/multiprecision/mp_number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -20,7 +20,7 @@ #include #include #include -#include +#include #include // stream operators #include // EOF @@ -34,26 +34,26 @@ namespace boost{ namespace multiprecision{ #endif template -class mp_number +class number { - typedef mp_number self_type; + typedef number self_type; public: typedef Backend backend_type; - BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number() BOOST_NOEXCEPT_IF(noexcept(Backend())) {} - BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(const mp_number& e) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(e.m_backend){} + BOOST_FORCEINLINE BOOST_CONSTEXPR number() BOOST_NOEXCEPT_IF(noexcept(Backend())) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& e) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(e.m_backend){} template - BOOST_FORCEINLINE mp_number(V v, typename enable_if_c< + BOOST_FORCEINLINE number(V v, typename enable_if_c< (boost::is_arithmetic::value || is_same::value || is_convertible::value) && !is_convertible::type, Backend>::value >::type* = 0) { m_backend = canonical_value(v); } template - BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(V v, typename enable_if_c< + BOOST_FORCEINLINE BOOST_CONSTEXPR number(V v, typename enable_if_c< (boost::is_arithmetic::value || is_same::value || is_convertible::value) && is_convertible::type, Backend>::value >::type* = 0) : m_backend(canonical_value(v)) {} - BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(const mp_number& e, unsigned digits10) + BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} /* // @@ -61,22 +61,22 @@ public: // which is arguably more useful. Disabled for now. // template - mp_number(V v, unsigned digits10, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) + number(V v, unsigned digits10, typename enable_if, is_same, is_convertible > >::type* dummy1 = 0) { m_backend.precision(digits10); m_backend = canonical_value(v); } */ template - BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(const mp_number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} template - BOOST_FORCEINLINE mp_number(const mp_number& val, typename enable_if >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) + BOOST_FORCEINLINE number(const number& val, typename enable_if >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) { m_backend = val.backend(); } template - mp_number(const mp_number& val, typename disable_if >::type* = 0) + number(const number& val, typename disable_if >::type* = 0) { // // Attempt a generic interconvertion: @@ -84,39 +84,39 @@ public: detail::generic_interconvert(backend(), val.backend(), number_category(), number_category()); } template - BOOST_FORCEINLINE mp_number(V v1, V v2, typename enable_if, is_same, is_convertible > >::type* = 0) + BOOST_FORCEINLINE number(V v1, V v2, typename enable_if, is_same, is_convertible > >::type* = 0) { using default_ops::assign_components; assign_components(m_backend, canonical_value(v1), canonical_value(v2)); } template - BOOST_FORCEINLINE mp_number(const mp_number& v1, const mp_number& v2, typename enable_if >::type* = 0) + BOOST_FORCEINLINE number(const number& v1, const number& v2, typename enable_if >::type* = 0) { using default_ops::assign_components; assign_components(m_backend, v1.backend(), v2.backend()); } template - BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) + BOOST_FORCEINLINE BOOST_CONSTEXPR number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(v){} template - mp_number& operator=(const detail::mp_exp& e) + number& operator=(const detail::expression& e) { - typedef typename is_same::result_type>::type tag_type; + typedef typename is_same::result_type>::type tag_type; do_assign(e, tag_type()); return *this; } - BOOST_FORCEINLINE mp_number& operator=(const mp_number& e) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) + BOOST_FORCEINLINE number& operator=(const number& e) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = e.m_backend; return *this; } template - BOOST_FORCEINLINE typename enable_if, is_same, is_convertible >, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, is_same, is_convertible >, number& >::type operator=(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval::type>())) { m_backend = canonical_value(v); @@ -124,7 +124,7 @@ public: } template - BOOST_FORCEINLINE typename enable_if, mpl::not_, is_same, is_convertible > > >, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, mpl::not_, is_same, is_convertible > > >, number& >::type operator=(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = v; @@ -132,23 +132,23 @@ public: } template - BOOST_FORCEINLINE mp_number& operator=(const mp_number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) + BOOST_FORCEINLINE number& operator=(const number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = v.backend(); return *this; } template - BOOST_FORCEINLINE typename enable_if, mp_number& >::type - operator=(const mp_number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) + BOOST_FORCEINLINE typename enable_if, number& >::type + operator=(const number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = v.backend(); return *this; } template - typename disable_if, mp_number& >::type - operator=(const mp_number& v) + typename disable_if, number& >::type + operator=(const number& v) { // // Attempt a generic interconvertion: @@ -158,35 +158,35 @@ public: } template - mp_number(const detail::mp_exp& e) + number(const detail::expression& e) { *this = e; } #ifndef BOOST_NO_RVALUE_REFERENCES - BOOST_FORCEINLINE BOOST_CONSTEXPR mp_number(mp_number&& r) BOOST_NOEXCEPT : m_backend(static_cast(r.m_backend)){} - BOOST_FORCEINLINE mp_number& operator=(mp_number&& r) BOOST_NOEXCEPT + BOOST_FORCEINLINE BOOST_CONSTEXPR number(number&& r) BOOST_NOEXCEPT : m_backend(static_cast(r.m_backend)){} + BOOST_FORCEINLINE number& operator=(number&& r) BOOST_NOEXCEPT { m_backend = static_cast(r.m_backend); return *this; } #endif - mp_number& operator+=(const self_type& val) + number& operator+=(const self_type& val) { - do_add(detail::mp_exp(val), detail::terminal()); + do_add(detail::expression(val), detail::terminal()); return *this; } template - mp_number& operator+=(const detail::mp_exp& e) + number& operator+=(const detail::expression& e) { // Create a copy if e contains this, but not if we're just doing a // x += x if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_add(detail::mp_exp(temp), detail::terminal()); + do_add(detail::expression(temp), detail::terminal()); } else { @@ -196,7 +196,7 @@ public: } template - typename enable_if, mp_number& >::type + typename enable_if, number& >::type operator+=(const V& v) { using default_ops::eval_add; @@ -204,14 +204,14 @@ public: return *this; } - mp_number& operator-=(const self_type& val) + number& operator-=(const self_type& val) { - do_subtract(detail::mp_exp(val), detail::terminal()); + do_subtract(detail::expression(val), detail::terminal()); return *this; } template - mp_number& operator-=(const detail::mp_exp& e) + number& operator-=(const detail::expression& e) { // Create a copy if e contains this: if(contains_self(e)) @@ -227,7 +227,7 @@ public: } template - typename enable_if, mp_number& >::type + typename enable_if, number& >::type operator-=(const V& v) { using default_ops::eval_subtract; @@ -236,21 +236,21 @@ public: } - mp_number& operator *= (const self_type& e) + number& operator *= (const self_type& e) { - do_multiplies(detail::mp_exp(e), detail::terminal()); + do_multiplies(detail::expression(e), detail::terminal()); return *this; } template - mp_number& operator*=(const detail::mp_exp& e) + number& operator*=(const detail::expression& e) { // Create a temporary if the RHS references *this, but not // if we're just doing an x *= x; if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_multiplies(detail::mp_exp(temp), detail::terminal()); + do_multiplies(detail::expression(temp), detail::terminal()); } else { @@ -260,7 +260,7 @@ public: } template - typename enable_if, mp_number& >::type + typename enable_if, number& >::type operator*=(const V& v) { using default_ops::eval_multiply; @@ -268,14 +268,14 @@ public: return *this; } - mp_number& operator%=(const self_type& e) + number& operator%=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); - do_modulus(detail::mp_exp(e), detail::terminal()); + do_modulus(detail::expression(e), detail::terminal()); return *this; } template - mp_number& operator%=(const detail::mp_exp& e) + number& operator%=(const detail::expression& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); // Create a temporary if the RHS references *this: @@ -291,7 +291,7 @@ public: return *this; } template - typename enable_if, mp_number& >::type + typename enable_if, number& >::type operator%=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); @@ -308,21 +308,21 @@ public: // execute the increment/decrement on destruction, but // correct implemetation will be tricky, so defered for now... // - BOOST_FORCEINLINE mp_number& operator++() + BOOST_FORCEINLINE number& operator++() { using default_ops::eval_increment; eval_increment(m_backend); return *this; } - BOOST_FORCEINLINE mp_number& operator--() + BOOST_FORCEINLINE number& operator--() { using default_ops::eval_decrement; eval_decrement(m_backend); return *this; } - BOOST_FORCEINLINE mp_number operator++(int) + inline number operator++(int) { using default_ops::eval_increment; self_type temp(*this); @@ -330,7 +330,7 @@ public: return BOOST_MP_MOVE(temp); } - BOOST_FORCEINLINE mp_number operator--(int) + inline number operator--(int) { using default_ops::eval_decrement; self_type temp(*this); @@ -339,7 +339,7 @@ public: } template - BOOST_FORCEINLINE typename enable_if, mp_number&>::type operator <<= (V val) + BOOST_FORCEINLINE typename enable_if, number&>::type operator <<= (V val) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left-shift operation is only valid for integer types"); check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); @@ -348,7 +348,7 @@ public: } template - BOOST_FORCEINLINE typename enable_if, mp_number&>::type operator >>= (V val) + BOOST_FORCEINLINE typename enable_if, number&>::type operator >>= (V val) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right-shift operation is only valid for integer types"); check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); @@ -356,20 +356,20 @@ public: return *this; } - BOOST_FORCEINLINE mp_number& operator /= (const self_type& e) + BOOST_FORCEINLINE number& operator /= (const self_type& e) { - do_divide(detail::mp_exp(e), detail::terminal()); + do_divide(detail::expression(e), detail::terminal()); return *this; } template - mp_number& operator/=(const detail::mp_exp& e) + number& operator/=(const detail::expression& e) { // Create a temporary if the RHS references *this: if(contains_self(e)) { self_type temp(e); - do_divide(detail::mp_exp(temp), detail::terminal()); + do_divide(detail::expression(temp), detail::terminal()); } else { @@ -379,7 +379,7 @@ public: } template - BOOST_FORCEINLINE typename enable_if, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, number& >::type operator/=(const V& v) { using default_ops::eval_divide; @@ -387,15 +387,15 @@ public: return *this; } - BOOST_FORCEINLINE mp_number& operator&=(const self_type& e) + BOOST_FORCEINLINE number& operator&=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); - do_bitwise_and(detail::mp_exp(e), detail::terminal()); + do_bitwise_and(detail::expression(e), detail::terminal()); return *this; } template - mp_number& operator&=(const detail::mp_exp& e) + number& operator&=(const detail::expression& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); // Create a temporary if the RHS references *this, but not @@ -413,7 +413,7 @@ public: } template - BOOST_FORCEINLINE typename enable_if, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, number& >::type operator&=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); @@ -422,15 +422,15 @@ public: return *this; } - BOOST_FORCEINLINE mp_number& operator|=(const self_type& e) + BOOST_FORCEINLINE number& operator|=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); - do_bitwise_or(detail::mp_exp(e), detail::terminal()); + do_bitwise_or(detail::expression(e), detail::terminal()); return *this; } template - mp_number& operator|=(const detail::mp_exp& e) + number& operator|=(const detail::expression& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); // Create a temporary if the RHS references *this, but not @@ -448,7 +448,7 @@ public: } template - BOOST_FORCEINLINE typename enable_if, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, number& >::type operator|=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); @@ -457,15 +457,15 @@ public: return *this; } - BOOST_FORCEINLINE mp_number& operator^=(const self_type& e) + BOOST_FORCEINLINE number& operator^=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); - do_bitwise_xor(detail::mp_exp(e), detail::terminal()); + do_bitwise_xor(detail::expression(e), detail::terminal()); return *this; } template - mp_number& operator^=(const detail::mp_exp& e) + number& operator^=(const detail::expression& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); if(contains_self(e)) @@ -481,7 +481,7 @@ public: } template - BOOST_FORCEINLINE typename enable_if, mp_number& >::type + BOOST_FORCEINLINE typename enable_if, number& >::type operator^=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); @@ -563,7 +563,7 @@ explicit operator T()const // // Comparison: // - BOOST_FORCEINLINE int compare(const mp_number& o)const + BOOST_FORCEINLINE int compare(const number& o)const BOOST_NOEXCEPT_IF(noexcept(std::declval().compare(std::declval()))) { return m_backend.compare(o.m_backend); @@ -586,16 +586,16 @@ explicit operator T()const } private: template - void do_assign(const detail::mp_exp& e, const mpl::true_&) + void do_assign(const detail::expression& e, const mpl::true_&) { do_assign(e, tag()); } template - void do_assign(const detail::mp_exp& e, const mpl::false_&) + void do_assign(const detail::expression& e, const mpl::false_&) { // The result of the expression isn't the same type as this - // create a temporary result and assign it to *this: - typedef typename detail::mp_exp::result_type temp_type; + typedef typename detail::expression::result_type temp_type; temp_type t(e); *this = t; } @@ -1083,7 +1083,7 @@ private: template void do_assign_function_1(const F& f, const Exp& val, const Tag&) { - mp_number t(val); + number t(val); f(m_backend, t.backend()); } template @@ -1139,7 +1139,7 @@ private: template void do_assign_function_3a(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag1&, const Tag2& t2, const Tag3& t3) { - mp_number t(val1); + number t(val1); do_assign_function_3b(f, BOOST_MP_MOVE(t), val2, val3, t2, t3); } template @@ -1150,7 +1150,7 @@ private: template void do_assign_function_3b(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag2& /*t2*/, const Tag3& t3) { - mp_number t(val2); + number t(val2); do_assign_function_3c(f, val1, BOOST_MP_MOVE(t), val3, t3); } template @@ -1161,7 +1161,7 @@ private: template void do_assign_function_3c(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag3& /*t3*/) { - mp_number t(val3); + number t(val3); do_assign_function_3c(f, val1, val2, BOOST_MP_MOVE(t), detail::terminal()); } @@ -1201,7 +1201,7 @@ private: void do_add(const Exp& e, const unknown&) { self_type temp(e); - do_add(detail::mp_exp(temp), detail::terminal()); + do_add(detail::expression(temp), detail::terminal()); } template @@ -1269,7 +1269,7 @@ private: void do_subtract(const Exp& e, const unknown&) { self_type temp(e); - do_subtract(detail::mp_exp(temp), detail::terminal()); + do_subtract(detail::expression(temp), detail::terminal()); } template @@ -1543,14 +1543,14 @@ private: template static BOOST_FORCEINLINE BOOST_CONSTEXPR const V& function_arg_value(const V& v) BOOST_NOEXCEPT { return v; } template - static BOOST_FORCEINLINE const A1& function_arg_value(const detail::mp_exp& exp) BOOST_NOEXCEPT { return exp.value(); } + static BOOST_FORCEINLINE const A1& function_arg_value(const detail::expression& exp) BOOST_NOEXCEPT { return exp.value(); } template - static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const detail::mp_exp, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value().backend(); } + static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const detail::expression, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value().backend(); } Backend m_backend; }; template -inline std::ostream& operator << (std::ostream& os, const mp_number& r) +inline std::ostream& operator << (std::ostream& os, const number& r) { std::streamsize d = os.precision(); std::string s = r.str(d, os.flags()); @@ -1569,9 +1569,9 @@ inline std::ostream& operator << (std::ostream& os, const mp_number -inline std::ostream& operator << (std::ostream& os, const mp_exp& r) +inline std::ostream& operator << (std::ostream& os, const expression& r) { - typedef typename mp_exp::result_type value_type; + typedef typename expression::result_type value_type; value_type temp(r); return os << temp; } @@ -1579,7 +1579,7 @@ inline std::ostream& operator << (std::ostream& os, const mp_exp -inline std::istream& operator >> (std::istream& is, mp_number& r) +inline std::istream& operator >> (std::istream& is, number& r) { std::string s; is >> s; @@ -1588,7 +1588,7 @@ inline std::istream& operator >> (std::istream& is, mp_number -BOOST_FORCEINLINE void swap(mp_number& a, mp_number& b) +BOOST_FORCEINLINE void swap(number& a, number& b) { a.swap(b); } @@ -1599,10 +1599,10 @@ template class rational; template -inline std::istream& operator >> (std::istream& is, rational >& r) +inline std::istream& operator >> (std::istream& is, rational >& r) { std::string s1; - multiprecision::mp_number v1, v2; + multiprecision::number v1, v2; char c; bool have_hex = false; @@ -1634,37 +1634,37 @@ inline std::istream& operator >> (std::istream& is, rational -typename enable_if, bool>::type operator == (const rational >& a, const Arithmetic& b) +typename enable_if, bool>::type operator == (const rational >& a, const Arithmetic& b) { - return a == multiprecision::mp_number(b); + return a == multiprecision::number(b); } template -typename enable_if, bool>::type operator == (const Arithmetic& b, const rational >& a) +typename enable_if, bool>::type operator == (const Arithmetic& b, const rational >& a) { - return a == multiprecision::mp_number(b); + return a == multiprecision::number(b); } template -typename enable_if, bool>::type operator != (const rational >& a, const Arithmetic& b) +typename enable_if, bool>::type operator != (const rational >& a, const Arithmetic& b) { - return a != multiprecision::mp_number(b); + return a != multiprecision::number(b); } template -typename enable_if, bool>::type operator != (const Arithmetic& b, const rational >& a) +typename enable_if, bool>::type operator != (const Arithmetic& b, const rational >& a) { - return a != multiprecision::mp_number(b); + return a != multiprecision::number(b); } template -inline multiprecision::mp_number numerator(const rational >& a) +inline multiprecision::number numerator(const rational >& a) { return a.numerator(); } template -inline multiprecision::mp_number denominator(const rational >& a) +inline multiprecision::number denominator(const rational >& a) { return a.denominator(); } @@ -1677,7 +1677,7 @@ template class sparse_vector_element; template -inline bool operator == (const sparse_vector_element& a, const ::boost::multiprecision::mp_number& b) +inline bool operator == (const sparse_vector_element& a, const ::boost::multiprecision::number& b) { typedef typename sparse_vector_element::const_reference ref_type; return static_cast(a) == b; diff --git a/include/boost/multiprecision/random.hpp b/include/boost/multiprecision/random.hpp index a76372a5..d60cfb72 100644 --- a/include/boost/multiprecision/random.hpp +++ b/include/boost/multiprecision/random.hpp @@ -8,7 +8,7 @@ #ifndef BOOST_MP_RANDOM_HPP #define BOOST_MP_RANDOM_HPP -#include +#include namespace boost{ namespace random{ namespace detail{ // @@ -18,8 +18,8 @@ namespace boost{ namespace random{ namespace detail{ // UDT's and depricate/remove this header altogether. // template -boost::multiprecision::mp_number - generate_uniform_int(Engine& eng, const boost::multiprecision::mp_number& min_value, const boost::multiprecision::mp_number& max_value); +boost::multiprecision::number + generate_uniform_int(Engine& eng, const boost::multiprecision::number& min_value, const boost::multiprecision::number& max_value); }}} @@ -31,20 +31,20 @@ namespace random{ namespace detail{ template -struct subtract, true> +struct subtract, true> { - typedef boost::multiprecision::mp_number result_type; + typedef boost::multiprecision::number result_type; result_type operator()(result_type const& x, result_type const& y) { return x - y; } }; } template -class independent_bits_engine > +class independent_bits_engine > { public: typedef Engine base_type; - typedef boost::multiprecision::mp_number result_type; + typedef boost::multiprecision::number result_type; static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; } @@ -199,11 +199,11 @@ private: }; template -class uniform_smallint > +class uniform_smallint > { public: - typedef boost::multiprecision::mp_number input_type; - typedef boost::multiprecision::mp_number result_type; + typedef boost::multiprecision::number input_type; + typedef boost::multiprecision::number result_type; class param_type { @@ -382,22 +382,22 @@ private: namespace detail{ template -struct select_uniform_01 > +struct select_uniform_01 > { template struct apply { - typedef new_uniform_01 > type; + typedef new_uniform_01 > type; }; }; template -boost::multiprecision::mp_number +boost::multiprecision::number generate_uniform_int( - Engine& eng, const boost::multiprecision::mp_number& min_value, const boost::multiprecision::mp_number& max_value, + Engine& eng, const boost::multiprecision::number& min_value, const boost::multiprecision::number& max_value, boost::mpl::true_ /** is_integral */) { - typedef boost::multiprecision::mp_number result_type; + typedef boost::multiprecision::number result_type; // Since we're using big-numbers, use the result type for all internal calculations: typedef result_type range_type; typedef result_type base_result; @@ -558,8 +558,8 @@ boost::multiprecision::mp_number } template -inline boost::multiprecision::mp_number - generate_uniform_int(Engine& eng, const boost::multiprecision::mp_number& min_value, const boost::multiprecision::mp_number& max_value) +inline boost::multiprecision::number + generate_uniform_int(Engine& eng, const boost::multiprecision::number& min_value, const boost::multiprecision::number& max_value) { typedef typename Engine::result_type base_result; typedef typename mpl::or_, mpl::bool_::value == boost::multiprecision::number_kind_integer> >::type tag_type; diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index f3e4cd47..06fe7eb1 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -11,7 +11,7 @@ #include #include #include -#include +#include #include namespace boost{ @@ -21,7 +21,7 @@ namespace backends{ template struct rational_adapter { - typedef mp_number integer_type; + typedef number integer_type; typedef boost::rational rational_type; typedef typename IntBackend::signed_types signed_types; @@ -62,7 +62,7 @@ struct rational_adapter rational_adapter& operator = (const char* s) { std::string s1; - multiprecision::mp_number v1, v2; + multiprecision::number v1, v2; char c; bool have_hex = false; const char* p = s; // saved for later @@ -178,12 +178,12 @@ inline int eval_get_sign(const rational_adapter& val) } template -inline mp_number numerator(const mp_number >& val) +inline number numerator(const number >& val) { return val.backend().data().numerator(); } template -inline mp_number denominator(const mp_number >& val) +inline number denominator(const number >& val) { return val.backend().data().denominator(); } @@ -204,7 +204,7 @@ using boost::multiprecision::backends::rational_adapter; template struct component_type > { - typedef mp_number type; + typedef number type; }; }} // namespaces @@ -213,10 +213,10 @@ struct component_type > namespace std{ template -class numeric_limits, ExpressionTemplates> > : public std::numeric_limits > +class numeric_limits, ExpressionTemplates> > : public std::numeric_limits > { - typedef std::numeric_limits > base_type; - typedef boost::multiprecision::mp_number > number_type; + typedef std::numeric_limits > base_type; + typedef boost::multiprecision::number > number_type; public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = true; @@ -234,9 +234,9 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; #endif diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index eee4b341..0068ffde 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -6,7 +6,7 @@ #ifndef BOOST_MATH_MP_TOMMATH_BACKEND_HPP #define BOOST_MATH_MP_TOMMATH_BACKEND_HPP -#include +#include #include #include #include @@ -603,18 +603,18 @@ using boost::multiprecision::backends::tommath_int; template<> struct number_category : public mpl::int_{}; -typedef mp_number tom_int; +typedef number tom_int; typedef rational_adapter tommath_rational; -typedef mp_number tom_rational; +typedef number tom_rational; }} // namespaces namespace std{ template -class numeric_limits > +class numeric_limits > { - typedef boost::multiprecision::mp_number number_type; + typedef boost::multiprecision::number number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; // @@ -663,49 +663,49 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; template -BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; +BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; +BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; #endif } diff --git a/performance/arithmetic_backend.hpp b/performance/arithmetic_backend.hpp index 676c82d2..3e9028a2 100644 --- a/performance/arithmetic_backend.hpp +++ b/performance/arithmetic_backend.hpp @@ -12,7 +12,7 @@ #include #include #include -#include +#include #include namespace boost{ @@ -523,10 +523,10 @@ inline double real_cast(concepts::real_concept r namespace std{ template -class numeric_limits, ExpressionTemplates > > : public std::numeric_limits +class numeric_limits, ExpressionTemplates > > : public std::numeric_limits { typedef std::numeric_limits base_type; - typedef boost::multiprecision::mp_number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } diff --git a/performance/delaunay_test.cpp b/performance/delaunay_test.cpp index 62a03981..cb4ba42c 100644 --- a/performance/delaunay_test.cpp +++ b/performance/delaunay_test.cpp @@ -270,14 +270,14 @@ int main() std::cout << "calculating...\n"; do_calc >("int64_t, int64_t"); - do_calc, false>, mp_number, false> > >("arithmetic_backend"); + do_calc, false>, number, false> > >("arithmetic_backend"); do_calc >("int64_t, int128_t"); - do_calc >("int64_t, mp_int128_t"); - do_calc, true> > >("int64_t, mp_int128_t (ET)"); + do_calc >("int64_t, int128_t"); + do_calc, true> > >("int64_t, int128_t (ET)"); do_calc >("int64_t, cpp_int"); - do_calc, false> > >("int64_t, cpp_int (no ET's)"); - do_calc > > >("int64_t, cpp_int(128-bit cache)"); - do_calc, false> > >("int64_t, cpp_int (128-bit Cache no ET's)"); + do_calc, false> > >("int64_t, cpp_int (no ET's)"); + do_calc > > >("int64_t, cpp_int(128-bit cache)"); + do_calc, false> > >("int64_t, cpp_int (128-bit Cache no ET's)"); return 0; } diff --git a/performance/linpack-benchmark.cpp b/performance/linpack-benchmark.cpp index 8db9b096..ec21f437 100644 --- a/performance/linpack-benchmark.cpp +++ b/performance/linpack-benchmark.cpp @@ -93,9 +93,9 @@ int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type extern "C" int MAIN__() { #ifdef TEST_MPF_50 - std::cout << "Testing mp_number >" << std::endl; + std::cout << "Testing number >" << std::endl; #elif defined(TEST_MPFR_50) - std::cout << "Testing mp_number >" << std::endl; + std::cout << "Testing number >" << std::endl; #elif defined(TEST_GMPXX) std::cout << "Testing mpf_class at 50 decimal degits" << std::endl; mpf_set_default_prec(((50 + 1) * 1000L) / 301L); @@ -103,7 +103,7 @@ extern "C" int MAIN__() std::cout << "Testing mpfr_class at 50 decimal degits" << std::endl; mpfr_set_default_prec(((50 + 1) * 1000L) / 301L); #elif defined(TEST_CPP_DEC_FLOAT) - std::cout << "Testing mp_number >" << std::endl; + std::cout << "Testing number >" << std::endl; #else std::cout << "Testing double" << std::endl; #endif @@ -1221,7 +1221,7 @@ times for array with leading dimension of1001 266.45 0.798 267.24 2.5021 0.79933 4772.2 -mp_number >: +number >: ~~~~~~~~~~~~~~~~~~~~~~~~~~~ norm. resid resid machep x(1) x(n) diff --git a/performance/miller_rabin_performance.cpp b/performance/miller_rabin_performance.cpp index 9667aa51..fe202391 100644 --- a/performance/miller_rabin_performance.cpp +++ b/performance/miller_rabin_performance.cpp @@ -136,21 +136,21 @@ int main() { using namespace boost::multiprecision; #ifdef TEST_CPP_INT - test_miller_rabin, false> >("cpp_int (no Expression templates)"); + test_miller_rabin, false> >("cpp_int (no Expression templates)"); test_miller_rabin("cpp_int"); - test_miller_rabin > >("cpp_int (128-bit cache)"); - test_miller_rabin > >("cpp_int (256-bit cache)"); - test_miller_rabin > >("cpp_int (512-bit cache)"); - test_miller_rabin > >("cpp_int (1024-bit cache)"); - test_miller_rabin("mp_int1024_t"); + test_miller_rabin > >("cpp_int (128-bit cache)"); + test_miller_rabin > >("cpp_int (256-bit cache)"); + test_miller_rabin > >("cpp_int (512-bit cache)"); + test_miller_rabin > >("cpp_int (1024-bit cache)"); + test_miller_rabin("int1024_t"); #endif #ifdef TEST_MPZ - test_miller_rabin >("mpz_int (no Expression templates)"); + test_miller_rabin >("mpz_int (no Expression templates)"); test_miller_rabin("mpz_int"); std::cout << "Time for mpz_int (native Miller Rabin Test) = " << test_miller_rabin_gmp() << std::endl; #endif #ifdef TEST_TOMMATH - test_miller_rabin >("tom_int (no Expression templates)"); + test_miller_rabin >("tom_int (no Expression templates)"); test_miller_rabin("tom_int"); #endif mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index dcc93932..4c58e672 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -786,12 +786,12 @@ int main() test("gmp_int", 1024); #endif #ifdef TEST_CPP_INT - test, false > >("cpp_int(unsigned, fixed)", 64); - test, false > >("cpp_int(fixed)", 64); - test, false > >("cpp_int(fixed)", 128); - test, false > >("cpp_int(fixed)", 256); - test, false > >("cpp_int(fixed)", 512); - test, false > >("cpp_int(fixed)", 1024); + test, false > >("cpp_int(unsigned, fixed)", 64); + test, false > >("cpp_int(fixed)", 64); + test, false > >("cpp_int(fixed)", 128); + test, false > >("cpp_int(fixed)", 256); + test, false > >("cpp_int(fixed)", 512); + test, false > >("cpp_int(fixed)", 1024); test("cpp_int", 128); test("cpp_int", 256); @@ -828,7 +828,7 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test("cpp_dec_float", 50); test("cpp_dec_float", 100); - test > >("cpp_dec_float", 500); + test > >("cpp_dec_float", 500); #endif #ifdef TEST_MPFR test("mpfr_float", 50); diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index 3646e1b3..d2f95d07 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -233,7 +233,7 @@ int main() std::cout << "Allocation Counts for Horner Evaluation:\n"; #ifdef TEST_MPFR basic_allocation_test("mpfr_float_50", mpfr_float_50(2)); - basic_allocation_test("mpfr_float_50 - no expression templates", mp_number, false>(2)); + basic_allocation_test("mpfr_float_50 - no expression templates", number, false>(2)); #endif #ifdef TEST_MPFR_CLASS basic_allocation_test("mpfr_class", mpfr_class(2)); @@ -245,7 +245,7 @@ int main() std::cout << "Allocation Counts for boost::math::tools::evaluate_polynomial:\n"; #ifdef TEST_MPFR poly_allocation_test("mpfr_float_50", mpfr_float_50(2)); - poly_allocation_test("mpfr_float_50 - no expression templates", mp_number, false>(2)); + poly_allocation_test("mpfr_float_50 - no expression templates", number, false>(2)); #endif #ifdef TEST_MPFR_CLASS poly_allocation_test("mpfr_class", mpfr_class(2)); @@ -260,13 +260,13 @@ int main() #ifdef TEST_FLOAT time_proc("Bessel Functions - double", test_bessel); time_proc("Bessel Functions - real_concept", test_bessel); - time_proc("Bessel Functions - arithmetic_backend", test_bessel > >); - time_proc("Bessel Functions - arithmetic_backend - no expression templates", test_bessel, false> >); + time_proc("Bessel Functions - arithmetic_backend", test_bessel > >); + time_proc("Bessel Functions - arithmetic_backend - no expression templates", test_bessel, false> >); time_proc("Non-central T - double", test_nct); time_proc("Non-central T - real_concept", test_nct); - time_proc("Non-central T - arithmetic_backend", test_nct > >); - time_proc("Non-central T - arithmetic_backend - no expression templates", test_nct, false> >); + time_proc("Non-central T - arithmetic_backend", test_nct > >); + time_proc("Non-central T - arithmetic_backend - no expression templates", test_nct, false> >); #endif // @@ -288,7 +288,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_50", test_bessel, 3); - time_proc("mpf_float_50 (no expression templates", test_bessel, false> >, 3); + time_proc("mpf_float_50 (no expression templates", test_bessel, false> >, 3); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_bessel, 3); @@ -314,7 +314,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_100", test_bessel); - time_proc("mpf_float_100 (no expression templates", test_bessel, false> >); + time_proc("mpf_float_100 (no expression templates", test_bessel, false> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_bessel); @@ -341,7 +341,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_50", test_polynomial); - time_proc("mpf_float_50 (no expression templates", test_polynomial, false> >); + time_proc("mpf_float_50 (no expression templates", test_polynomial, false> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_polynomial); @@ -367,7 +367,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_100", test_polynomial); - time_proc("mpf_float_100 (no expression templates", test_polynomial, false> >); + time_proc("mpf_float_100 (no expression templates", test_polynomial, false> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_polynomial); @@ -393,7 +393,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_50", test_nct); - time_proc("mpf_float_50 (no expression templates", test_nct, false> >); + time_proc("mpf_float_50 (no expression templates", test_nct, false> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_nct); @@ -419,7 +419,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_100", test_nct); - time_proc("mpf_float_100 (no expression templates", test_nct, false> >); + time_proc("mpf_float_100 (no expression templates", test_nct, false> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_nct); diff --git a/test/concepts/mp_number_concept_check.cpp b/test/concepts/number_concept_check.cpp similarity index 85% rename from test/concepts/mp_number_concept_check.cpp rename to test/concepts/number_concept_check.cpp index d921dce7..106fbe5a 100644 --- a/test/concepts/mp_number_concept_check.cpp +++ b/test/concepts/number_concept_check.cpp @@ -171,22 +171,22 @@ void foo() test_extra(boost::multiprecision::mpfr_float_50()); #endif #ifdef TEST_MPFR_6 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_15 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_17 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_30 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::mp_number, false>()); + test_extra(boost::multiprecision::number, false>()); #endif } @@ -202,16 +202,16 @@ int main() BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif #ifdef TEST_MPFR_6 - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); #endif #ifdef TEST_MPFR_15 - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); #endif #ifdef TEST_MPFR_17 - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); #endif #ifdef TEST_MPFR_30 - BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept > >)); #endif #ifdef TEST_MPFR_50 BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); diff --git a/test/concepts/sf_concept_check_basic.cpp b/test/concepts/sf_concept_check_basic.cpp index 75c35b08..16cecfce 100644 --- a/test/concepts/sf_concept_check_basic.cpp +++ b/test/concepts/sf_concept_check_basic.cpp @@ -124,22 +124,22 @@ void foo() test_extra(boost::multiprecision::mpfr_float_50()); #endif #ifdef TEST_MPFR_6 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_15 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_17 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_30 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::mp_number, false>()); + test_extra(boost::multiprecision::number, false>()); #endif } diff --git a/test/concepts/sf_concept_check_bessel.cpp b/test/concepts/sf_concept_check_bessel.cpp index 12a40a13..0c3c3935 100644 --- a/test/concepts/sf_concept_check_bessel.cpp +++ b/test/concepts/sf_concept_check_bessel.cpp @@ -89,22 +89,22 @@ void foo() test_extra(boost::multiprecision::mpfr_float_50()); #endif #ifdef TEST_MPFR_6 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_15 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_17 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_30 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::mp_number, false>()); + test_extra(boost::multiprecision::number, false>()); #endif } diff --git a/test/concepts/sf_concept_check_elliptic.cpp b/test/concepts/sf_concept_check_elliptic.cpp index e754f53e..e55cace4 100644 --- a/test/concepts/sf_concept_check_elliptic.cpp +++ b/test/concepts/sf_concept_check_elliptic.cpp @@ -95,22 +95,22 @@ void foo() test_extra(boost::multiprecision::mpfr_float_50()); #endif #ifdef TEST_MPFR_6 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_15 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_17 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_30 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::mp_number, false>()); + test_extra(boost::multiprecision::number, false>()); #endif } diff --git a/test/concepts/sf_concept_check_gamma.cpp b/test/concepts/sf_concept_check_gamma.cpp index bd108e9a..2dcdcaf8 100644 --- a/test/concepts/sf_concept_check_gamma.cpp +++ b/test/concepts/sf_concept_check_gamma.cpp @@ -111,22 +111,22 @@ void foo() test_extra(boost::multiprecision::mpfr_float_50()); #endif #ifdef TEST_MPFR_6 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_15 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_17 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_30 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::mp_number, false>()); + test_extra(boost::multiprecision::number, false>()); #endif } diff --git a/test/concepts/sf_concept_check_poly.cpp b/test/concepts/sf_concept_check_poly.cpp index d8e855e2..fff337e9 100644 --- a/test/concepts/sf_concept_check_poly.cpp +++ b/test/concepts/sf_concept_check_poly.cpp @@ -86,22 +86,22 @@ void foo() test_extra(boost::multiprecision::mpfr_float_50()); #endif #ifdef TEST_MPFR_6 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_15 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_17 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_MPFR_30 - test_extra(boost::multiprecision::mp_number >()); + test_extra(boost::multiprecision::number >()); #endif #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::mp_number, false>()); + test_extra(boost::multiprecision::number, false>()); #endif } diff --git a/test/include_test/cpp_int_include_test.cpp b/test/include_test/cpp_int_include_test.cpp index f193178c..7e665657 100644 --- a/test/include_test/cpp_int_include_test.cpp +++ b/test/include_test/cpp_int_include_test.cpp @@ -7,10 +7,10 @@ using namespace boost::multiprecision; -mp_number > a; -mp_number, false> b; -mp_number, false> c; -mp_number, false> d; -mp_number, false> e; +number > a; +number, false> b; +number, false> c; +number, false> d; +number, false> e; diff --git a/test/math/log1p_expm1_test.cpp b/test/math/log1p_expm1_test.cpp index 9b9867aa..1754094c 100644 --- a/test/math/log1p_expm1_test.cpp +++ b/test/math/log1p_expm1_test.cpp @@ -128,19 +128,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test(mp_number >(), "mp_number >"); - test(mp_number >(), "mp_number >"); - test(mp_number >(), "mp_number >"); + test(number >(), "number >"); + test(number >(), "number >"); + test(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test(mp_number >(), "mp_number >"); - test(mp_number >(), "mp_number >"); - test(mp_number >(), "mp_number >"); + test(number >(), "number >"); + test(number >(), "number >"); + test(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test(mp_number >(), "mp_number >"); - test(mp_number >(), "mp_number >"); - test(mp_number >(), "mp_number >"); + test(number >(), "number >"); + test(number >(), "number >"); + test(number >(), "number >"); #endif return 0; } diff --git a/test/math/powm1_sqrtp1m1_test.cpp b/test/math/powm1_sqrtp1m1_test.cpp index 56bdd600..c3853651 100644 --- a/test/math/powm1_sqrtp1m1_test.cpp +++ b/test/math/powm1_sqrtp1m1_test.cpp @@ -120,19 +120,19 @@ int test_main(int, char* []) // #ifdef TEST_MPF_50 // We have accuracy issues with gmp_float<18> - maybe in std::exp?? Disabled for now. - //test_powm1_sqrtp1m1(mp_number >(), "mp_number >"); - test_powm1_sqrtp1m1(mp_number >(), "mp_number >"); - test_powm1_sqrtp1m1(mp_number >(), "mp_number >"); + //test_powm1_sqrtp1m1(number >(), "number >"); + test_powm1_sqrtp1m1(number >(), "number >"); + test_powm1_sqrtp1m1(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_powm1_sqrtp1m1(mp_number >(), "mp_number >"); - test_powm1_sqrtp1m1(mp_number >(), "mp_number >"); - test_powm1_sqrtp1m1(mp_number >(), "mp_number >"); + test_powm1_sqrtp1m1(number >(), "number >"); + test_powm1_sqrtp1m1(number >(), "number >"); + test_powm1_sqrtp1m1(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_powm1_sqrtp1m1(mp_number >(), "mp_number >"); - test_powm1_sqrtp1m1(mp_number >(), "mp_number >"); - test_powm1_sqrtp1m1(mp_number >(), "mp_number >"); + test_powm1_sqrtp1m1(number >(), "number >"); + test_powm1_sqrtp1m1(number >(), "number >"); + test_powm1_sqrtp1m1(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_bessel_i.cpp b/test/math/test_bessel_i.cpp index 4e94c24a..3532f397 100644 --- a/test/math/test_bessel_i.cpp +++ b/test/math/test_bessel_i.cpp @@ -88,20 +88,20 @@ int test_main(int, char* []) // #ifdef TEST_MPF_50 // We have accuracy issues with gmp_float<18> - maybe in std::exp?? Disabled for now. - //test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + //test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_bessel_j.cpp b/test/math/test_bessel_j.cpp index 951a6821..931422aa 100644 --- a/test/math/test_bessel_j.cpp +++ b/test/math/test_bessel_j.cpp @@ -130,19 +130,19 @@ int test_main(int, char* []) // #ifdef TEST_MPF_50 // We have accuracy issues with gmp_float<18> - maybe in std::exp?? Disabled for now. - //test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + //test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_bessel_k.cpp b/test/math/test_bessel_k.cpp index 044fc49a..856180e9 100644 --- a/test/math/test_bessel_k.cpp +++ b/test/math/test_bessel_k.cpp @@ -103,19 +103,19 @@ int test_main(int, char* []) // #ifdef TEST_MPF_50 // We have accuracy issues with gmp_float<18> - maybe in std::exp?? Disabled for now. - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp index 44d23126..dd9c99dd 100644 --- a/test/math/test_bessel_y.cpp +++ b/test/math/test_bessel_y.cpp @@ -129,19 +129,19 @@ int test_main(int, char* []) // #ifdef TEST_MPF_50 // We have accuracy issues with gmp_float<18> - our argument reduction in std::sin isn't accurate enough: - //test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + //test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); - test_bessel(mp_number >(), "mp_number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); + test_bessel(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_beta.cpp b/test/math/test_beta.cpp index 49541cd8..b69c1808 100644 --- a/test/math/test_beta.cpp +++ b/test/math/test_beta.cpp @@ -115,19 +115,19 @@ int test_main(int, char* []) // #ifdef TEST_MPF_50 // We have accuracy issues with gmp_float<18> - our argument reduction in std::sin isn't accurate enough: - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_binomial_coeff.cpp b/test/math/test_binomial_coeff.cpp index 0d9bf414..146b1af2 100644 --- a/test/math/test_binomial_coeff.cpp +++ b/test/math/test_binomial_coeff.cpp @@ -94,19 +94,19 @@ int test_main(int, char* []) // #ifdef TEST_MPF_50 // We have accuracy issues with gmp_float<18> - our argument reduction in std::sin isn't accurate enough: - test_binomial(mp_number >(), "mp_number >"); - test_binomial(mp_number >(), "mp_number >"); - test_binomial(mp_number >(), "mp_number >"); + test_binomial(number >(), "number >"); + test_binomial(number >(), "number >"); + test_binomial(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_binomial(mp_number >(), "mp_number >"); - test_binomial(mp_number >(), "mp_number >"); - test_binomial(mp_number >(), "mp_number >"); + test_binomial(number >(), "number >"); + test_binomial(number >(), "number >"); + test_binomial(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_binomial(mp_number >(), "mp_number >"); - test_binomial(mp_number >(), "mp_number >"); - test_binomial(mp_number >(), "mp_number >"); + test_binomial(number >(), "number >"); + test_binomial(number >(), "number >"); + test_binomial(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_carlson.cpp b/test/math/test_carlson.cpp index e0a9e3c8..1aacc108 100644 --- a/test/math/test_carlson.cpp +++ b/test/math/test_carlson.cpp @@ -86,19 +86,19 @@ int test_main(int, char* []) // #ifdef TEST_MPF_50 // We have accuracy issues with gmp_float<18> - our argument reduction in std::sin isn't accurate enough: - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_cbrt.cpp b/test/math/test_cbrt.cpp index e7bee00c..b896d6d7 100644 --- a/test/math/test_cbrt.cpp +++ b/test/math/test_cbrt.cpp @@ -75,19 +75,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_cbrt(mp_number >(), "mp_number >"); - test_cbrt(mp_number >(), "mp_number >"); - test_cbrt(mp_number >(), "mp_number >"); + test_cbrt(number >(), "number >"); + test_cbrt(number >(), "number >"); + test_cbrt(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_cbrt(mp_number >(), "mp_number >"); - test_cbrt(mp_number >(), "mp_number >"); - test_cbrt(mp_number >(), "mp_number >"); + test_cbrt(number >(), "number >"); + test_cbrt(number >(), "number >"); + test_cbrt(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_cbrt(mp_number >(), "mp_number >"); - test_cbrt(mp_number >(), "mp_number >"); - test_cbrt(mp_number >(), "mp_number >"); + test_cbrt(number >(), "number >"); + test_cbrt(number >(), "number >"); + test_cbrt(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_digamma.cpp b/test/math/test_digamma.cpp index 8da4bd53..2d18eaa6 100644 --- a/test/math/test_digamma.cpp +++ b/test/math/test_digamma.cpp @@ -89,19 +89,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_digamma(mp_number >(), "mp_number >"); - test_digamma(mp_number >(), "mp_number >"); - test_digamma(mp_number >(), "mp_number >"); + test_digamma(number >(), "number >"); + test_digamma(number >(), "number >"); + test_digamma(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_digamma(mp_number >(), "mp_number >"); - test_digamma(mp_number >(), "mp_number >"); - test_digamma(mp_number >(), "mp_number >"); + test_digamma(number >(), "number >"); + test_digamma(number >(), "number >"); + test_digamma(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_digamma(mp_number >(), "mp_number >"); - test_digamma(mp_number >(), "mp_number >"); - test_digamma(mp_number >(), "mp_number >"); + test_digamma(number >(), "number >"); + test_digamma(number >(), "number >"); + test_digamma(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_ellint_1.cpp b/test/math/test_ellint_1.cpp index 356653d0..c7da569a 100644 --- a/test/math/test_ellint_1.cpp +++ b/test/math/test_ellint_1.cpp @@ -82,19 +82,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_ellint_2.cpp b/test/math/test_ellint_2.cpp index a8cbfca5..c07bddac 100644 --- a/test/math/test_ellint_2.cpp +++ b/test/math/test_ellint_2.cpp @@ -75,19 +75,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_ellint_3.cpp b/test/math/test_ellint_3.cpp index c57ddfec..9d3d6904 100644 --- a/test/math/test_ellint_3.cpp +++ b/test/math/test_ellint_3.cpp @@ -96,19 +96,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); - test_spots(mp_number >(), "mp_number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); + test_spots(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_erf.cpp b/test/math/test_erf.cpp index b185c3cd..1b77e3a4 100644 --- a/test/math/test_erf.cpp +++ b/test/math/test_erf.cpp @@ -96,19 +96,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_erf(mp_number >(), "mp_number >"); - test_erf(mp_number >(), "mp_number >"); - test_erf(mp_number >(), "mp_number >"); + test_erf(number >(), "number >"); + test_erf(number >(), "number >"); + test_erf(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_erf(mp_number >(), "mp_number >"); - test_erf(mp_number >(), "mp_number >"); - test_erf(mp_number >(), "mp_number >"); + test_erf(number >(), "number >"); + test_erf(number >(), "number >"); + test_erf(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_erf(mp_number >(), "mp_number >"); - test_erf(mp_number >(), "mp_number >"); - test_erf(mp_number >(), "mp_number >"); + test_erf(number >(), "number >"); + test_erf(number >(), "number >"); + test_erf(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_expint.cpp b/test/math/test_expint.cpp index 71961792..0dbffc58 100644 --- a/test/math/test_expint.cpp +++ b/test/math/test_expint.cpp @@ -96,19 +96,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_expint(mp_number >(), "mp_number >"); - test_expint(mp_number >(), "mp_number >"); - test_expint(mp_number >(), "mp_number >"); + test_expint(number >(), "number >"); + test_expint(number >(), "number >"); + test_expint(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_expint(mp_number >(), "mp_number >"); - test_expint(mp_number >(), "mp_number >"); - test_expint(mp_number >(), "mp_number >"); + test_expint(number >(), "number >"); + test_expint(number >(), "number >"); + test_expint(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_expint(mp_number >(), "mp_number >"); - test_expint(mp_number >(), "mp_number >"); - test_expint(mp_number >(), "mp_number >"); + test_expint(number >(), "number >"); + test_expint(number >(), "number >"); + test_expint(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_gamma.cpp b/test/math/test_gamma.cpp index c7511413..44ca68be 100644 --- a/test/math/test_gamma.cpp +++ b/test/math/test_gamma.cpp @@ -110,19 +110,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_hermite.cpp b/test/math/test_hermite.cpp index be956ce1..271b8138 100644 --- a/test/math/test_hermite.cpp +++ b/test/math/test_hermite.cpp @@ -75,19 +75,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_hermite(mp_number >(), "mp_number >"); - test_hermite(mp_number >(), "mp_number >"); - test_hermite(mp_number >(), "mp_number >"); + test_hermite(number >(), "number >"); + test_hermite(number >(), "number >"); + test_hermite(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_hermite(mp_number >(), "mp_number >"); - test_hermite(mp_number >(), "mp_number >"); - test_hermite(mp_number >(), "mp_number >"); + test_hermite(number >(), "number >"); + test_hermite(number >(), "number >"); + test_hermite(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_hermite(mp_number >(), "mp_number >"); - test_hermite(mp_number >(), "mp_number >"); - test_hermite(mp_number >(), "mp_number >"); + test_hermite(number >(), "number >"); + test_hermite(number >(), "number >"); + test_hermite(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_ibeta.cpp b/test/math/test_ibeta.cpp index dde145f8..b78358f2 100644 --- a/test/math/test_ibeta.cpp +++ b/test/math/test_ibeta.cpp @@ -106,19 +106,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_ibeta_2.cpp b/test/math/test_ibeta_2.cpp index c7cb04fc..7dcc2fd8 100644 --- a/test/math/test_ibeta_2.cpp +++ b/test/math/test_ibeta_2.cpp @@ -106,19 +106,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_ibeta_3.cpp b/test/math/test_ibeta_3.cpp index 77b69d78..d1f0d132 100644 --- a/test/math/test_ibeta_3.cpp +++ b/test/math/test_ibeta_3.cpp @@ -92,19 +92,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_ibeta_4.cpp b/test/math/test_ibeta_4.cpp index 5f3246fd..f71c117f 100644 --- a/test/math/test_ibeta_4.cpp +++ b/test/math/test_ibeta_4.cpp @@ -99,19 +99,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_ibeta_inv_1.cpp b/test/math/test_ibeta_inv_1.cpp index 2492b7ac..88fc6184 100644 --- a/test/math/test_ibeta_inv_1.cpp +++ b/test/math/test_ibeta_inv_1.cpp @@ -85,19 +85,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - //test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + //test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_ibeta_inv_ab_4.cpp b/test/math/test_ibeta_inv_ab_4.cpp index 67c4c588..e00fb612 100644 --- a/test/math/test_ibeta_inv_ab_4.cpp +++ b/test/math/test_ibeta_inv_ab_4.cpp @@ -78,19 +78,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - //test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + //test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); - test_beta(mp_number >(), "mp_number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); + test_beta(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_igamma.cpp b/test/math/test_igamma.cpp index 66aa9011..429f1f40 100644 --- a/test/math/test_igamma.cpp +++ b/test/math/test_igamma.cpp @@ -82,19 +82,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_igamma_inv.cpp b/test/math/test_igamma_inv.cpp index 3a0d76cc..1bf31054 100644 --- a/test/math/test_igamma_inv.cpp +++ b/test/math/test_igamma_inv.cpp @@ -97,19 +97,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_igamma_inva.cpp b/test/math/test_igamma_inva.cpp index 026694c8..09633434 100644 --- a/test/math/test_igamma_inva.cpp +++ b/test/math/test_igamma_inva.cpp @@ -76,19 +76,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); - test_gamma(mp_number >(), "mp_number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); + test_gamma(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_laguerre.cpp b/test/math/test_laguerre.cpp index f3cded2a..fe309c88 100644 --- a/test/math/test_laguerre.cpp +++ b/test/math/test_laguerre.cpp @@ -75,19 +75,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_laguerre(mp_number >(), "mp_number >"); - test_laguerre(mp_number >(), "mp_number >"); - test_laguerre(mp_number >(), "mp_number >"); + test_laguerre(number >(), "number >"); + test_laguerre(number >(), "number >"); + test_laguerre(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_laguerre(mp_number >(), "mp_number >"); - test_laguerre(mp_number >(), "mp_number >"); - test_laguerre(mp_number >(), "mp_number >"); + test_laguerre(number >(), "number >"); + test_laguerre(number >(), "number >"); + test_laguerre(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_laguerre(mp_number >(), "mp_number >"); - test_laguerre(mp_number >(), "mp_number >"); - test_laguerre(mp_number >(), "mp_number >"); + test_laguerre(number >(), "number >"); + test_laguerre(number >(), "number >"); + test_laguerre(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_legendre.cpp b/test/math/test_legendre.cpp index e392365f..e3b26c51 100644 --- a/test/math/test_legendre.cpp +++ b/test/math/test_legendre.cpp @@ -75,19 +75,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_legendre_p(mp_number >(), "mp_number >"); - test_legendre_p(mp_number >(), "mp_number >"); - test_legendre_p(mp_number >(), "mp_number >"); + test_legendre_p(number >(), "number >"); + test_legendre_p(number >(), "number >"); + test_legendre_p(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_legendre_p(mp_number >(), "mp_number >"); - test_legendre_p(mp_number >(), "mp_number >"); - test_legendre_p(mp_number >(), "mp_number >"); + test_legendre_p(number >(), "number >"); + test_legendre_p(number >(), "number >"); + test_legendre_p(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_legendre_p(mp_number >(), "mp_number >"); - test_legendre_p(mp_number >(), "mp_number >"); - test_legendre_p(mp_number >(), "mp_number >"); + test_legendre_p(number >(), "number >"); + test_legendre_p(number >(), "number >"); + test_legendre_p(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_tgamma_ratio.cpp b/test/math/test_tgamma_ratio.cpp index 982546bd..7657e325 100644 --- a/test/math/test_tgamma_ratio.cpp +++ b/test/math/test_tgamma_ratio.cpp @@ -89,19 +89,19 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_tgamma_ratio(mp_number >(), "mp_number >"); - test_tgamma_ratio(mp_number >(), "mp_number >"); - test_tgamma_ratio(mp_number >(), "mp_number >"); + test_tgamma_ratio(number >(), "number >"); + test_tgamma_ratio(number >(), "number >"); + test_tgamma_ratio(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_tgamma_ratio(mp_number >(), "mp_number >"); - test_tgamma_ratio(mp_number >(), "mp_number >"); - test_tgamma_ratio(mp_number >(), "mp_number >"); + test_tgamma_ratio(number >(), "number >"); + test_tgamma_ratio(number >(), "number >"); + test_tgamma_ratio(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_tgamma_ratio(mp_number >(), "mp_number >"); - test_tgamma_ratio(mp_number >(), "mp_number >"); - test_tgamma_ratio(mp_number >(), "mp_number >"); + test_tgamma_ratio(number >(), "number >"); + test_tgamma_ratio(number >(), "number >"); + test_tgamma_ratio(number >(), "number >"); #endif return 0; } diff --git a/test/math/test_zeta.cpp b/test/math/test_zeta.cpp index 4484a7d3..0c7976cd 100644 --- a/test/math/test_zeta.cpp +++ b/test/math/test_zeta.cpp @@ -83,20 +83,20 @@ int test_main(int, char* []) // 35 decimal digits: tests arbitrary precision code // #ifdef TEST_MPF_50 - test_zeta(mp_number >(), "mp_number >"); - test_zeta(mp_number >(), "mp_number >"); - test_zeta(mp_number >(), "mp_number >"); + test_zeta(number >(), "number >"); + test_zeta(number >(), "number >"); + test_zeta(number >(), "number >"); #endif #ifdef TEST_MPFR_50 - test_zeta(mp_number >(), "mp_number >"); - test_zeta(mp_number >(), "mp_number >"); - test_zeta(mp_number >(), "mp_number >"); + test_zeta(number >(), "number >"); + test_zeta(number >(), "number >"); + test_zeta(number >(), "number >"); #endif #ifdef TEST_CPP_DEC_FLOAT - test_zeta(mp_number >(), "mp_number >"); - test_zeta(mp_number >(), "mp_number >"); - test_zeta(mp_number >(), "mp_number >"); - test_zeta(mp_number >(), "mp_number >"); + test_zeta(number >(), "number >"); + test_zeta(number >(), "number >"); + test_zeta(number >(), "number >"); + test_zeta(number >(), "number >"); #endif return 0; } diff --git a/test/test_acos.cpp b/test/test_acos.cpp index 6e81985f..b4dcc828 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -89,7 +89,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -103,14 +103,14 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index fad3dbb3..71e49d19 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -1211,12 +1211,12 @@ void test() int main() { #ifdef TEST_ARITHMETIC_BACKEND - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); #endif #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -1228,14 +1228,14 @@ int main() #endif #ifdef TEST_MPZ test(); - test > >(); + test > >(); #endif #ifdef TEST_MPQ test(); #endif #ifdef TEST_CPP_DEC_FLOAT test(); - test, false> >(); + test, false> >(); #endif #ifdef TEST_MPFR test(); @@ -1245,7 +1245,7 @@ int main() #endif #ifdef TEST_TOMMATH test(); - test > >(); + test > >(); #endif #ifdef TEST_TOMMATH_BOOST_RATIONAL test >(); @@ -1255,15 +1255,15 @@ int main() #endif #ifdef TEST_CPP_INT test(); - test(); - test(); + test(); + test(); test(); - test, false> >(); - test > >(); + test, false> >(); + test > >(); // Again with "trivial" backends: - test, false > >(); - test, false > >(); + test, false > >(); + test, false > >(); #endif #ifdef TEST_CPP_INT_BR test(); diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 61ab5d12..271172fe 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -85,7 +85,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -99,17 +99,17 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); // Check low multiprecision digit counts. - test > >(); - test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_atan.cpp b/test/test_atan.cpp index de426780..1b28a395 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -62,7 +62,7 @@ struct is_mpfr_type : public boost::mpl::false_ {}; #ifdef TEST_MPFR_50 template -struct is_mpfr_type > > : public boost::mpl::true_{}; +struct is_mpfr_type > > : public boost::mpl::true_{}; #endif template @@ -231,7 +231,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -245,17 +245,17 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); // Check low multiprecision digit counts. - test > >(); - test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_constants.cpp b/test/test_constants.cpp index 5e9ad8e7..4e72ca11 100644 --- a/test/test_constants.cpp +++ b/test/test_constants.cpp @@ -160,7 +160,7 @@ inline bool is_mpfr(const T&) } #if defined(TEST_MPFR_50) template -inline bool is_mpfr(const boost::multiprecision::mp_number >&) +inline bool is_mpfr(const boost::multiprecision::number >&) { return true; } @@ -185,13 +185,13 @@ void test() int main() { #ifdef TEST_MPFR_50 - test > >(); + test > >(); #endif #ifdef TEST_CPP_DEC_FLOAT - test > >(); + test > >(); #endif #ifdef TEST_MPF_50 - test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_constexpr.cpp b/test/test_constexpr.cpp index 6e97e2ae..66e601b1 100644 --- a/test/test_constexpr.cpp +++ b/test/test_constexpr.cpp @@ -31,9 +31,9 @@ void test3() using namespace boost::multiprecision; -template void test1, false> >(); -template void test1, false> >(); -template void test3, false> >(); -template void test2, false> >(); +template void test1, false> >(); +template void test1, false> >(); +template void test3, false> >(); +template void test2, false> >(); #endif \ No newline at end of file diff --git a/test/test_cos.cpp b/test/test_cos.cpp index b31528bf..36488b1b 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -285,7 +285,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -299,14 +299,14 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index ada92a21..46900c40 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -127,7 +127,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -141,14 +141,14 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp index a21f2a8b..9efa78a3 100644 --- a/test/test_cpp_int.cpp +++ b/test/test_cpp_int.cpp @@ -340,7 +340,7 @@ int main() { using namespace boost::multiprecision; test(); - test > >(); + test > >(); return boost::report_errors(); } diff --git a/test/test_exp.cpp b/test/test_exp.cpp index da5cceff..4167d4c7 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -167,7 +167,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -181,17 +181,17 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); // Check low multiprecision digit counts. - test > >(); - test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_fixed_int.cpp b/test/test_fixed_int.cpp index e69e2e29..87a72399 100644 --- a/test/test_fixed_int.cpp +++ b/test/test_fixed_int.cpp @@ -54,7 +54,7 @@ T generate_random(unsigned bits_wanted) int main() { using namespace boost::multiprecision; - typedef mp_number > packed_type; + typedef number > packed_type; unsigned last_error_count = 0; for(int i = 0; i < 1000; ++i) { diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp index fb51eede..410b531a 100644 --- a/test/test_float_io.cpp +++ b/test/test_float_io.cpp @@ -42,7 +42,7 @@ #if defined(TEST_MPF_50) template -bool is_mpf(const boost::multiprecision::mp_number >&) +bool is_mpf(const boost::multiprecision::number >&) { return true; } #endif template @@ -215,23 +215,23 @@ struct max_digits10_proxy }; #ifdef TEST_CPP_DEC_FLOAT template -struct max_digits10_proxy, ET> > +struct max_digits10_proxy, ET> > { - static const unsigned value = std::numeric_limits, ET> >::max_digits10; + static const unsigned value = std::numeric_limits, ET> >::max_digits10; }; #endif #ifdef TEST_MPF_50 template -struct max_digits10_proxy, ET> > +struct max_digits10_proxy, ET> > { - static const unsigned value = std::numeric_limits, ET> >::max_digits10; + static const unsigned value = std::numeric_limits, ET> >::max_digits10; }; #endif #ifdef TEST_MPFR_50 template -struct max_digits10_proxy, ET> > +struct max_digits10_proxy, ET> > { - static const unsigned value = std::numeric_limits, ET> >::max_digits10; + static const unsigned value = std::numeric_limits, ET> >::max_digits10; }; #endif diff --git a/test/test_fpclassify.cpp b/test/test_fpclassify.cpp index 063ba8a9..b579daca 100644 --- a/test/test_fpclassify.cpp +++ b/test/test_fpclassify.cpp @@ -314,7 +314,7 @@ int main() test(); #endif #ifdef TEST_BACKEND - test >(); + test >(); #endif return boost::report_errors(); } diff --git a/test/test_generic_conv.cpp b/test/test_generic_conv.cpp index df033f83..a552a3cd 100644 --- a/test/test_generic_conv.cpp +++ b/test/test_generic_conv.cpp @@ -58,7 +58,7 @@ int main() // // Now integer to float: // - typedef mp_number > dec_float_500; + typedef number > dec_float_500; dec_float_500 df(c); dec_float_500 df2(c.str()); BOOST_CHECK_EQUAL(df, df2); @@ -66,7 +66,7 @@ int main() df2 = -df2; BOOST_CHECK_EQUAL(df, df2); #ifdef TEST_GMP - typedef mp_number > mpf_type; + typedef number > mpf_type; mpf_type mpf(c); mpf_type mpf2(c.str()); BOOST_CHECK_EQUAL(mpf, mpf2); @@ -75,7 +75,7 @@ int main() BOOST_CHECK_EQUAL(mpf, mpf2); #endif #ifdef TEST_MPFR - typedef mp_number > mpfr_type; + typedef number > mpfr_type; mpfr_type mpfr(c); mpfr_type mpfr2(c.str()); BOOST_CHECK_EQUAL(mpfr, mpfr2); diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp index 87c79ec7..1f87a88c 100644 --- a/test/test_int_io.cpp +++ b/test/test_int_io.cpp @@ -123,9 +123,9 @@ int main() test_round_trip(); #endif #ifdef TEST_CPP_INT - test_round_trip > >(); - test_round_trip > >(); - test_round_trip > >(); + test_round_trip > >(); + test_round_trip > >(); + test_round_trip > >(); #endif return boost::report_errors(); } diff --git a/test/test_log.cpp b/test/test_log.cpp index 35714bc0..1d5f0342 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -195,7 +195,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -209,17 +209,17 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); // Check low multiprecision digit counts. - test > >(); - test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index 20ad2dad..6d5c376d 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -201,7 +201,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -237,10 +237,10 @@ int main() #endif #ifdef TEST_CPP_INT test(); - test(); - test(); - test > >(); - test > >(); + test(); + test(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_pow.cpp b/test/test_pow.cpp index 4c55ab07..49762f90 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -570,7 +570,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -584,17 +584,17 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); // Check low multiprecision digit counts. - test > >(); - test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_rational_io.cpp b/test/test_rational_io.cpp index 4d629fb7..8003d4f3 100644 --- a/test/test_rational_io.cpp +++ b/test/test_rational_io.cpp @@ -92,7 +92,7 @@ void do_round_trip(const T& val, std::ios_base::fmtflags f, const boost::mpl::fa template struct is_mp_number : public boost::mpl::false_{}; template -struct is_mp_number > : public boost::mpl::true_{}; +struct is_mp_number > : public boost::mpl::true_{}; template void do_round_trip(const T& val, std::ios_base::fmtflags f) @@ -127,7 +127,7 @@ int main() #ifdef TEST_MPQ test_round_trip(); test_round_trip >(); - test_round_trip > >(); + test_round_trip > >(); #endif #ifdef TEST_TOMMATH test_round_trip >(); diff --git a/test/test_round.cpp b/test/test_round.cpp index 1fb4822d..d77f24be 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -390,17 +390,17 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif #ifdef TEST_BACKEND - test >(); + test >(); #endif return boost::report_errors(); } diff --git a/test/test_sin.cpp b/test/test_sin.cpp index f8ad7830..fef86827 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -279,7 +279,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -293,17 +293,17 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); // Check low multiprecision digit counts. - test > >(); - test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index b4fc7194..2a18c8b5 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -203,7 +203,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -217,17 +217,17 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); // Check low multiprecision digit counts. - test > >(); - test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp index da17ea4c..57b84206 100644 --- a/test/test_sqrt.cpp +++ b/test/test_sqrt.cpp @@ -173,7 +173,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -187,20 +187,20 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); // Check low multiprecision digit counts. - test > >(); - test > >(); + test > >(); + test > >(); // Check up to 1000 multiprecision digits. - test > >(); - test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index d4f57038..a76fbe48 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -122,7 +122,7 @@ void test() int main() { #ifdef TEST_BACKEND - test >(); + test >(); #endif #ifdef TEST_MPF_50 test(); @@ -136,14 +136,14 @@ int main() test(); test(); // Some "peculiar" digit counts which stress our code: - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); #endif return boost::report_errors(); } diff --git a/test/ublas_interop/test1.hpp b/test/ublas_interop/test1.hpp index 9d0731cb..db44c15f 100644 --- a/test/ublas_interop/test1.hpp +++ b/test/ublas_interop/test1.hpp @@ -19,7 +19,7 @@ #include -typedef boost::multiprecision::mp_number, false> mp_test_type; +typedef boost::multiprecision::number, false> mp_test_type; //typedef double mp_test_type; #define USE_RANGE diff --git a/test/ublas_interop/test2.hpp b/test/ublas_interop/test2.hpp index b58c6177..8dfc0a61 100644 --- a/test/ublas_interop/test2.hpp +++ b/test/ublas_interop/test2.hpp @@ -18,7 +18,7 @@ #include -typedef boost::multiprecision::mp_number, false> mp_test_type; +typedef boost::multiprecision::number, false> mp_test_type; //typedef double mp_test_type; #define USE_RANGE diff --git a/test/ublas_interop/test3.hpp b/test/ublas_interop/test3.hpp index 032b029c..e884d80c 100644 --- a/test/ublas_interop/test3.hpp +++ b/test/ublas_interop/test3.hpp @@ -19,7 +19,7 @@ #include -typedef boost::multiprecision::mp_number, false> mp_test_type; +typedef boost::multiprecision::number, false> mp_test_type; //typedef double mp_test_type; #define USE_RANGE diff --git a/test/ublas_interop/test4.hpp b/test/ublas_interop/test4.hpp index 20194f7a..6001e9c4 100644 --- a/test/ublas_interop/test4.hpp +++ b/test/ublas_interop/test4.hpp @@ -19,7 +19,7 @@ #include -typedef boost::multiprecision::mp_number, false> mp_test_type; +typedef boost::multiprecision::number, false> mp_test_type; //typedef double mp_test_type; #define USE_RANGE diff --git a/test/ublas_interop/test5.hpp b/test/ublas_interop/test5.hpp index cd98e665..639cecaf 100644 --- a/test/ublas_interop/test5.hpp +++ b/test/ublas_interop/test5.hpp @@ -19,7 +19,7 @@ #include -typedef boost::multiprecision::mp_number, false> mp_test_type; +typedef boost::multiprecision::number, false> mp_test_type; //typedef double mp_test_type; #define USE_RANGE diff --git a/test/ublas_interop/test7.hpp b/test/ublas_interop/test7.hpp index 4990642f..40546991 100644 --- a/test/ublas_interop/test7.hpp +++ b/test/ublas_interop/test7.hpp @@ -19,7 +19,7 @@ #include -typedef boost::multiprecision::mp_number, false> mp_test_type; +typedef boost::multiprecision::number, false> mp_test_type; //typedef double mp_test_type; #define USE_RANGE From 6f317ee809ccfa0e1a726e1ac523de307ad73261 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 8 Aug 2012 18:25:27 +0000 Subject: [PATCH 216/256] Rebuild docs. [SVN r79933] --- .../boost_multiprecision/indexes/s01.html | 99 ++--- .../boost_multiprecision/indexes/s02.html | 38 +- .../boost_multiprecision/indexes/s03.html | 94 +++-- .../boost_multiprecision/indexes/s04.html | 280 ++++++------- doc/html/boost_multiprecision/intro.html | 76 +++- doc/html/boost_multiprecision/map/todo.html | 2 +- .../perf/int_real_world.html | 4 +- doc/html/boost_multiprecision/ref.html | 8 +- .../boost_multiprecision/ref/backendconc.html | 55 ++- .../boost_multiprecision/ref/cpp_dec_ref.html | 4 +- .../boost_multiprecision/ref/cpp_int_ref.html | 26 +- .../boost_multiprecision/ref/gmp_int_ref.html | 2 +- .../boost_multiprecision/ref/headers.html | 10 +- .../boost_multiprecision/ref/mpf_ref.html | 12 +- .../boost_multiprecision/ref/mpfr_ref.html | 12 +- .../ref/{mp_number.html => number.html} | 384 +++++++++--------- .../boost_multiprecision/ref/tom_int_ref.html | 2 +- .../boost_multiprecision/tut/conversions.html | 34 +- .../tut/floats/cpp_dec_float.html | 17 +- .../tut/floats/fp_eg/jel.html | 2 +- .../tut/floats/fp_eg/poly_eg.html | 4 +- .../tut/floats/gmp_float.html | 38 +- .../tut/floats/mpfr_float.html | 34 +- .../tut/ints/cpp_int.html | 40 +- .../tut/ints/egs/factorials.html | 2 +- .../tut/ints/gmp_int.html | 18 +- .../tut/ints/tom_int.html | 10 +- .../boost_multiprecision/tut/primetest.html | 4 +- .../boost_multiprecision/tut/rational.html | 4 +- .../boost_multiprecision/tut/rational/br.html | 2 +- .../tut/rational/cpp_rational.html | 7 +- .../tut/rational/gmp_rational.html | 16 +- .../tut/rational/rational_adapter.html | 6 +- .../tut/rational/tommath_rational.html | 12 +- doc/html/index.html | 4 +- doc/multiprecision.qbk | 55 ++- 36 files changed, 803 insertions(+), 614 deletions(-) rename doc/html/boost_multiprecision/ref/{mp_number.html => number.html} (67%) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 717f0ba7..b8cec282 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,52 +13,41 @@ -
    +

    -Function Index

    -

    A B C D E F I L M P R S T Z

    +Function Index
    +

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    Z diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index 863536e0..f03f6b35 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,18 +13,18 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    -

    C G M N T

    +Class Index
    +

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    -C +C
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    -
    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 0881eae2..7d33939b 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,58 +12,51 @@
    PrevUpHome
    -
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    -

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    +Index
    +

    B C D E F G I L M N O P R S T U Z

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  • @@ -120,7 +113,7 @@
    • -D +D
    -E +E
    -F +F
    -G +G
    • @@ -192,7 +185,7 @@
    -I +I
    -L +L
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    diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index e13b16a1..f1b934dc 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -31,7 +31,7 @@

    • - An expression-template-enabled front-end mp_number + An expression-template-enabled front-end number that handles all the operator overloading, expression evaluation optimization, and code reduction.
      • @@ -59,7 +59,7 @@

      Alternatively, you can compose your own multiprecision type, by combining - mp_number with one of the predefined + number with one of the predefined back-end types. For example, suppose you wanted a 300 decimal digit floating-point type based on the MPFR library. In this case, there's no predefined typedef with that level of precision, so instead @@ -69,20 +69,20 @@ namespace mp = boost::multiprecision; // Reduce the typing a bit later... -typedef mp::mp_number<mp::mpfr_float_backend<300> > my_float; +typedef mp::number<mp::mpfr_float_backend<300> > my_float; my_float a, b, c; // These variables have 300 decimal digits precision

      We can repeat the above example, but with the expression templates disabled (for faster compile times, but slower runtimes) by passing a second template - argument to mp_number: + argument to number: 

      #include <boost/multiprecision/mpfr.hpp>  // Defines the Backend type that wraps MPFR
 
 namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
 
-typedef mp::mp_number<mp::mpfr_float_backend<300>, false>  my_float;
+typedef mp::number<mp::mpfr_float_backend<300>, false>  my_float;
 
 my_float a, b, c; // These variables have 300 decimal digits precision
      @@ -94,8 +94,8 @@ namespace mp = boost::multiprecision; // Reduce the typing a bit later... -mp::mp_int128_t a(3), b(2); -mp::mp_int512_t c(50), d; +mp::int128_t a(3), b(2); +mp::int512_t c(50), d; d = c * a; // Compiler error @@ -104,22 +104,55 @@ 

      d = a; // OK, widening conversion.
 d = a * b;  // OK, can convert from an expression template too.
-d = mp::mp_int512_t(a) * c; // OK, all the types in the expression are the same now.
+d = mp::int512_t(a) * c; // OK, all the types in the expression are the same now.
      + Move + Semantics +
      +

      + On compilers that support rvalue-references, class number + is move-enabled if the underlying backend is. +

      +

      + In addition the non-expression template operator overloads (see below) are + move aware and have overloads that look something like: +

      +
      template <class B>
+number<B, false> operator + (number&& a, const number& b)
+{
+    return std::move(a += b);
+}
+
      +

      + These operator overloads ensure that many expressions can be evaluated without + actually generating any temporaries. However, there are still many simple expressions + such as: +

      +
      a = b * c;
+
      +

      + Which don't noticably benefit from move support. Therefore, optimal performance + comes from having both move-support, and expression templates enabled. +

      +
      + Expression Templates

      - Class mp_number is expression-template-enabled: + TODO: compare to rvalue refs. +

      +

      + Class number is expression-template-enabled: that means that rather than having a multiplication operator that looks like this: 

      template <class Backend>
-mp_number<Backend> operator * (const mp_number<Backend>& a, const mp_number<Backend>& b)
+number<Backend> operator * (const number<Backend>& a, const number<Backend>& b)
 {
-   mp_number<Backend> result(a);
+   number<Backend> result(a);
    result *= b;
    return result;
 }
@@ -128,7 +161,7 @@
       Instead the operator looks more like this:
     
      
 
      template <class Backend>
-unmentionable-type operator * (const mp_number<Backend>& a, const mp_number<Backend>& b);
+unmentionable-type operator * (const number<Backend>& a, const number<Backend>& b);
 
      
 
      
       Where the "unmentionable" return type is an implementation detail
@@ -150,7 +183,7 @@
 y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0];

      - If type T is an mp_number, then this expression is evaluated + If type T is a number, then this expression is evaluated without creating a single temporary value. In contrast, if we were using the mpfr_class C++ wrapper for MPFR - then this expression @@ -169,7 +202,7 @@

      This library also extends expression template support to standard library functions like abs or sin - with mp_number arguments. This + with number arguments. This means that an expression such as: 

      y = abs(x);
@@ -200,7 +233,7 @@
       tend to be slower to compile than their simpler cousins, they're also harder
       to debug (should you actually want to step through our code!), and rely on
       compiler optimizations being turned on to give really good performance. Also,
-      since the return type from expressions involving mp_numbers
+      since the return type from expressions involving numbers
       is an "unmentionable implementation detail", you have to be careful
       to cast the result of an expression to the actual number type when passing
       an expression to a template function. For example, given:
@@ -282,7 +315,7 @@
    + + + + + + + + + +

    - mp_number + number

    		@@ -356,8 +389,8 @@

    - Finally, note that mp_number - takes a second template argument, which, when set to false + Finally, note that number takes + a second template argument, which, when set to false disables all the expression template machinery. The result is much faster to compile, but slower at runtime.

    @@ -367,6 +400,9 @@ to carry out the underlying arithmetic, and all are operating at the same precision (50 decimal digits):

    +

    + TODO: Update, compare to rvalue refs but no ET's as well. +

    Table 1.2. Evaluation of Boost.Math's Bessel function test data

    @@ -396,7 +432,7 @@

    - mp_number + number

    		@@ -476,7 +512,7 @@

    - mp_number + number

    		diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index 9b6465df..2877ef6c 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -56,7 +56,7 @@
  • Can we differentiate between explicit and implicit conversions in the - mp_number constructor (may need some new type traits)? + number constructor (may need some new type traits)?
  • Can ring types (exact floating point types) be supported? The answer diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html index 89278b58..353ab9ee 100644 --- a/doc/html/boost_multiprecision/perf/int_real_world.html +++ b/doc/html/boost_multiprecision/perf/int_real_world.html @@ -145,7 +145,7 @@

    • - mp_int1024_t + int1024_t

    		@@ -157,7 +157,7 @@

    - mp_int1024_t (no Expression templates) + int1024_t (no Expression templates)

    		diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html index 4f869c43..0516caf6 100644 --- a/doc/html/boost_multiprecision/ref.html +++ b/doc/html/boost_multiprecision/ref.html @@ -7,18 +7,18 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext
    -
    mp_number
    +
    number
    cpp_int
    gmp_int
    tom_int
    @@ -39,7 +39,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index f901dcde..32100789 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -19,13 +19,17 @@

    The requirements on the Backend - template argument to mp_number + template argument to number are split up into compulsory requirements, and optional requirements that are either to improve performance or provide optional features.

    +

    + TODO: Add optional construction support, add throws specification, clarify + what compulsory means. +

    In the following tables, type B is the Backend - template arument to mp_number, + template arument to number, b and b2 are a variables of type B, cb and cb2 are constant variables @@ -38,6 +42,9 @@ is a variable of type pointer-to-arithmetic-type, exp is a variable of type B::exp_type, pexp is a variable of type B::exp_type*, + i is a variable of type + int, pi + pointer to a variable of type int, B2 is another type that meets these requirements, b2 is a variable of type B2.

    @@ -614,6 +621,50 @@
    +

    + eval_frexp(b, + cb, + pi) +

    +     		+

    + void +

    +     		+

    + Stores values in b + and *pi + such that the value of cb + is b * 2*pi, only required when B + is a floating-point type. +

    +
    +

    + eval_ldexp(b, + cb, + i) +

    +     		+

    + void +

    +     		+

    + Stores a value in b + that is cb * 2i, only required when B + is a floating-point type. +

    +

    eval_floor(b, diff --git a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html index 031f0575..8d84ad3d 100644 --- a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html @@ -22,8 +22,8 @@ template <unsigned Digits10> class cpp_dec_float; -typedef mp_number<cpp_dec_float<50> > cpp_dec_float_50; -typedef mp_number<cpp_dec_float<100> > cpp_dec_float_100; +typedef number<cpp_dec_float<50> > cpp_dec_float_50; +typedef number<cpp_dec_float<100> > cpp_dec_float_100; }} // namespaces diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html index e0c9f368..a302ef80 100644 --- a/doc/html/boost_multiprecision/ref/cpp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_int_ref.html @@ -6,12 +6,12 @@ - +

    -PrevUpHomeNext +PrevUpHomeNext

    @@ -22,21 +22,21 @@ template <unsigned MinBits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> > struct cpp_int_backend; -typedef mp_number<cpp_int_backend<> > cpp_int; // arbitrary precision integer +typedef number<cpp_int_backend<> > cpp_int; // arbitrary precision integer typedef rational_adapter<cpp_int_backend<> > cpp_rational_backend; -typedef mp_number<cpp_rational_backend> cpp_rational; // arbitrary precision rational number +typedef number<cpp_rational_backend> cpp_rational; // arbitrary precision rational number // Fixed precision unsigned types: -typedef mp_number<cpp_int_backend<128, false, void>, false> mp_uint128_t; -typedef mp_number<cpp_int_backend<256, false, void>, false> mp_uint256_t; -typedef mp_number<cpp_int_backend<512, false, void>, false> mp_uint512_t; -typedef mp_number<cpp_int_backend<1024, false, void>, false> mp_uint1024_t; +typedef number<cpp_int_backend<128, false, void>, false> uint128_t; +typedef number<cpp_int_backend<256, false, void>, false> uint256_t; +typedef number<cpp_int_backend<512, false, void>, false> uint512_t; +typedef number<cpp_int_backend<1024, false, void>, false> uint1024_t; // Fixed precision signed types: -typedef mp_number<cpp_int_backend<128, true, void>, false> mp_int128_t; -typedef mp_number<cpp_int_backend<256, true, void>, false> mp_int256_t; -typedef mp_number<cpp_int_backend<512, true, void>, false> mp_int512_t; -typedef mp_number<cpp_int_backend<1024, true, void>, false> mp_int1024_t; +typedef number<cpp_int_backend<128, true, void>, false> int128_t; +typedef number<cpp_int_backend<256, true, void>, false> int256_t; +typedef number<cpp_int_backend<512, true, void>, false> int512_t; +typedef number<cpp_int_backend<1024, true, void>, false> int1024_t; }} // namespaces @@ -96,7 +96,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/ref/gmp_int_ref.html b/doc/html/boost_multiprecision/ref/gmp_int_ref.html index ff5fb3ca..2f2655e7 100644 --- a/doc/html/boost_multiprecision/ref/gmp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/gmp_int_ref.html @@ -21,7 +21,7 @@ class gmp_int; -typedef mp_number<gmp_int > mpz_int; +typedef number<gmp_int > mpz_int; }} // namespaces diff --git a/doc/html/boost_multiprecision/ref/headers.html b/doc/html/boost_multiprecision/ref/headers.html index 010807eb..87b88f8a 100644 --- a/doc/html/boost_multiprecision/ref/headers.html +++ b/doc/html/boost_multiprecision/ref/headers.html @@ -90,12 +90,12 @@
    PrevUpHomeNext

    - mp_number.hpp + number.hpp

    - Defines the mp_number + Defines the number backend, is included by all the backend headers.

    - concepts/mp_number_architypes.hpp + concepts/mp_number_archetypes.hpp

    		@@ -250,13 +250,13 @@

    - detail/mp_number_base.hpp + detail/number_base.hpp

    All the expression template code, metaprogramming, and operator - overloads for mp_number. + overloads for number.

    diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html index a109f6fc..268d472b 100644 --- a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html +++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html @@ -25,14 +25,14 @@ template <unsigned Digits10> class cpp_dec_float; -typedef mp_number<cpp_dec_float<50> > cpp_dec_float_50; -typedef mp_number<cpp_dec_float<100> > cpp_dec_float_100; +typedef number<cpp_dec_float<50> > cpp_dec_float_50; +typedef number<cpp_dec_float<100> > cpp_dec_float_100; }} // namespaces

    The cpp_dec_float back-end - is used in conjunction with mp_number: + is used in conjunction with number: It acts as an entirely C++ (header only and dependency free) real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. @@ -80,11 +80,16 @@ this type.

  • - Any mp_number instantiated - on this type, is convertible to any other mp_number - instantiated on this type - for example you can convert from mp_number<cpp_dec_float<50> > to mp_number<cpp_dec_float<SomeOtherValue> >. + Any number instantiated + on this type, is convertible to any other number + instantiated on this type - for example you can convert from number<cpp_dec_float<50> > to number<cpp_dec_float<SomeOtherValue> >. Narrowing conversions are truncating.
    • +
  • + Conversion from a string results in a std::runtime_error + being thrown if the string can not be interpreted as a valid floating + point number. +
    • diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html index 981d684d..e3e4c8e0 100644 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html @@ -53,7 +53,7 @@ 

    9.822663964796047e-001

    - Now lets implement the function again, but this time using the multiprecision + Now let's implement the function again, but this time using the multiprecision type cpp_dec_float_50 as the argument type:

    diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html index c8f5fb7e..2c28c3be 100644 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html @@ -20,7 +20,7 @@

    In this example we'll look at polynomial evaluation, this is not only - an important use case, but it's one that mp_number + an important use case, but it's one that number performs particularly well at because the expression templates completely eliminate all temporaries from a Horner polynomial evaluation scheme. @@ -32,7 +32,7 @@ 

    using boost::multiprecision::cpp_dec_float;
-typedef boost::multiprecision::mp_number<cpp_dec_float<64> > mp_type;
+typedef boost::multiprecision::number<cpp_dec_float<64> > mp_type;
 
 mp_type mysin(const mp_type& x)
 {
diff --git a/doc/html/boost_multiprecision/tut/floats/gmp_float.html b/doc/html/boost_multiprecision/tut/floats/gmp_float.html
index 3b104b2e..e60bb835 100644
--- a/doc/html/boost_multiprecision/tut/floats/gmp_float.html
+++ b/doc/html/boost_multiprecision/tut/floats/gmp_float.html
@@ -25,17 +25,17 @@
 template <unsigned Digits10>
 class gmp_float;
 
-typedef mp_number<gmp_float<50> >    mpf_float_50;
-typedef mp_number<gmp_float<100> >   mpf_float_100;
-typedef mp_number<gmp_float<500> >   mpf_float_500;
-typedef mp_number<gmp_float<1000> >  mpf_float_1000;
-typedef mp_number<gmp_float<0> >     mpf_float;
+typedef number<gmp_float<50> >    mpf_float_50;
+typedef number<gmp_float<100> >   mpf_float_100;
+typedef number<gmp_float<500> >   mpf_float_500;
+typedef number<gmp_float<1000> >  mpf_float_1000;
+typedef number<gmp_float<0> >     mpf_float;
 
 }} // namespaces

    The gmp_float back-end - is used in conjunction with mp_number + is used in conjunction with number : it acts as a thin wrapper around the GMP mpf_t to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, @@ -48,7 +48,7 @@ to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision respectively. The typedef mpf_float provides a variable precision type - whose precision can be controlled via the mp_numbers + whose precision can be controlled via the numbers member functions.

    @@ -63,7 +63,7 @@

    As well as the usual conversions from arithmetic and string types, instances - of mp_number<mpf_float<N> > are copy constructible and assignable + of number<mpf_float<N> > are copy constructible and assignable from:

      @@ -72,10 +72,10 @@ mpq_t.
    • - The mp_number wrappers - around those types: mp_number<mpf_float<M> >, - mp_number<gmp_int>, - mp_number<gmp_rational>. + The number wrappers + around those types: number<mpf_float<M> >, + number<gmp_int>, + number<gmp_rational>.

    @@ -97,6 +97,11 @@ library's global settings, so this type can be safely mixed with existing GMP code. +

  • + This backend supports rvalue-references and is move-aware, making instantiations + of number on this backend + move aware. +
  • It is not possible to round-trip objects of this type to and from a string and get back exactly the same value. This appears to be a limitation @@ -117,6 +122,15 @@ as the underlying implementation - indeed that is the recommended option on Win32.
    • +
  • + Conversion from a string results in a std::runtime_error + being thrown if the string can not be interpreted as a valid floating + point number. +
    • +
  • + Division by zero results in a std::runtime_error + being thrown. +
    • diff --git a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html index 8d42e7ac..183ccfdc 100644 --- a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html +++ b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html @@ -25,17 +25,17 @@ template <unsigned Digits10> class mpfr_float_backend; -typedef mp_number<mpfr_float_backend<50> > mpfr_float_50; -typedef mp_number<mpfr_float_backend<100> > mpfr_float_100; -typedef mp_number<mpfr_float_backend<500> > mpfr_float_500; -typedef mp_number<mpfr_float_backend<1000> > mpfr_float_1000; -typedef mp_number<mpfr_float_backend<0> > mpfr_float; +typedef number<mpfr_float_backend<50> > mpfr_float_50; +typedef number<mpfr_float_backend<100> > mpfr_float_100; +typedef number<mpfr_float_backend<500> > mpfr_float_500; +typedef number<mpfr_float_backend<1000> > mpfr_float_1000; +typedef number<mpfr_float_backend<0> > mpfr_float; }} // namespaces

    The mpfr_float_backend - type is used in conjunction with mp_number: + type is used in conjunction with number: It acts as a thin wrapper around the MPFR mpfr_t to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, @@ -48,7 +48,7 @@ to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision respectively. The typedef mpfr_float provides a variable precision type - whose precision can be controlled via the mp_numbers + whose precision can be controlled via the numbers member functions.

    @@ -63,7 +63,7 @@

    As well as the usual conversions from arithmetic and string types, instances - of mp_number<mpfr_float_backend<N> > are copy constructible and assignable + of number<mpfr_float_backend<N> > are copy constructible and assignable from:

      @@ -75,9 +75,9 @@ The MPFR native type mpfr_t.
    • - The mp_number wrappers - around those types: mp_number<mpfr_float_backend<M> >, - mp_number<mpf_float<M> >, mp_number<gmp_int>, mp_number<gmp_rational>. + The number wrappers + around those types: number<mpfr_float_backend<M> >, + number<mpf_float<M> >, number<gmp_int>, number<gmp_rational>.

    @@ -109,8 +109,16 @@

  • This backend supports rvalue-references and is move-aware, making instantiations - of mp_number on this - backend move aware. + of number on this backend + move aware. +
    • +
  • + Conversion from a string results in a std::runtime_error + being thrown if the string can not be interpreted as a valid floating + point number. +
    • +
  • + Division by zero results in an infinity.
    • diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html index 021c5d0c..65301980 100644 --- a/doc/html/boost_multiprecision/tut/ints/cpp_int.html +++ b/doc/html/boost_multiprecision/tut/ints/cpp_int.html @@ -27,30 +27,30 @@ template <unsigned MinDigits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> > class cpp_int_backend; -typedef mp_number<cpp_int_backend<> > cpp_int; // arbitrary precision integer +typedef number<cpp_int_backend<> > cpp_int; // arbitrary precision integer typedef rational_adapter<cpp_int_backend<> > cpp_rational_backend; -typedef mp_number<cpp_rational_backend> cpp_rational; // arbitrary precision rational number +typedef number<cpp_rational_backend> cpp_rational; // arbitrary precision rational number // Fixed precision unsigned types: -typedef mp_number<cpp_int_backend<128, false, void>, false> mp_uint128_t; -typedef mp_number<cpp_int_backend<256, false, void>, false> mp_uint256_t; -typedef mp_number<cpp_int_backend<512, false, void>, false> mp_uint512_t; -typedef mp_number<cpp_int_backend<1024, false, void>, false> mp_uint1024_t; +typedef number<cpp_int_backend<128, false, void>, false> uint128_t; +typedef number<cpp_int_backend<256, false, void>, false> uint256_t; +typedef number<cpp_int_backend<512, false, void>, false> uint512_t; +typedef number<cpp_int_backend<1024, false, void>, false> uint1024_t; // Fixed precision signed types: -typedef mp_number<cpp_int_backend<128, true, void>, false> mp_int128_t; -typedef mp_number<cpp_int_backend<256, true, void>, false> mp_int256_t; -typedef mp_number<cpp_int_backend<512, true, void>, false> mp_int512_t; -typedef mp_number<cpp_int_backend<1024, true, void>, false> mp_int1024_t; +typedef number<cpp_int_backend<128, true, void>, false> int128_t; +typedef number<cpp_int_backend<256, true, void>, false> int256_t; +typedef number<cpp_int_backend<512, true, void>, false> int512_t; +typedef number<cpp_int_backend<1024, true, void>, false> int1024_t; }} // namespaces

    The cpp_int_backend type is used via one of the typedefs boost::multiprecision::cpp_int, - boost::multiprecision::mp_uint128_t, boost::multiprecision::mp_uint256_t, - boost::multiprecision::mp_uint512_t, boost::multiprecision::mp_int128_t, - boost::multiprecision::mp_int256_t or boost::multiprecision::mp_int512_t. + boost::multiprecision::uint128_t, boost::multiprecision::uint256_t, + boost::multiprecision::uint512_t, boost::multiprecision::int128_t, + boost::multiprecision::int256_t or boost::multiprecision::int512_t.

    This back-end is the "Swiss Army Knife" of integer types as it @@ -112,7 +112,7 @@

  • The type uses a sign-magnitude representation internally, so type - mp_int128_t has 128-bits + int128_t has 128-bits of precision plus an extra sign bit. In this respect the behaviour of these types differs from built-in 2's complement types. In might be tempting to use a 127-bit type instead, and indeed this does work, @@ -138,15 +138,15 @@ Unsigned types support subtraction, and unary negation - the result is "as if" a 2's complement operation had been performed - in other words they behave pretty much as a built in integer type - would in this situation. So for example if we were using mp_uint128_t then both mp_uint128_t(1)-4 - and -mp_uint128(3) + would in this situation. So for example if we were using uint128_t then both uint128_t(1)-4 + and -uint128(3) would result in the value 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD - of type mp_uint128_t. + of type uint128_t.
  • This backend supports rvalue-references and is move-aware, making instantiations - of mp_number on this - backend move aware. + of number on this backend + move aware.
    • @@ -159,7 +159,7 @@ using namespace boost::multiprecision; -mp_int128_t v = 1; +int128_t v = 1; // Do some fixed precision arithmetic: for(unsigned i = 1; i <= 20; ++i) diff --git a/doc/html/boost_multiprecision/tut/ints/egs/factorials.html b/doc/html/boost_multiprecision/tut/ints/egs/factorials.html index dfbfe6e5..bc812cd7 100644 --- a/doc/html/boost_multiprecision/tut/ints/egs/factorials.html +++ b/doc/html/boost_multiprecision/tut/ints/egs/factorials.html @@ -40,7 +40,7 @@ // large the largest is, we'll be able to "pretty format" the results. // // Calculate the largest number that will fit inside 128 bits, we could - // also have used numeric_limits<mp_int128_t>::max() for this value: + // also have used numeric_limits<int128_t>::max() for this value: cpp_int limit = (cpp_int(1) << 128) - 1; // // Our table of values: diff --git a/doc/html/boost_multiprecision/tut/ints/gmp_int.html b/doc/html/boost_multiprecision/tut/ints/gmp_int.html index 1b7c9282..75dfcbf9 100644 --- a/doc/html/boost_multiprecision/tut/ints/gmp_int.html +++ b/doc/html/boost_multiprecision/tut/ints/gmp_int.html @@ -24,7 +24,7 @@ class gmp_int; -typedef mp_number<gmp_int > mpz_int; +typedef number<gmp_int > mpz_int; }} // namespaces @@ -47,8 +47,8 @@ mpq_t.
  • - Instances of mp_number<T> that are wrappers around those - types: mp_number<gmp_float<N> >, mp_number<gmp_rational>. + Instances of number<T> that are wrappers around those + types: number<gmp_float<N> >, number<gmp_rational>.

    • @@ -76,8 +76,12 @@ will be thrown.

  • - Division by zero is handled by the GMP - library - it will trigger a division by zero signal. + Conversion from a string results in a std::runtime_error + being thrown if the string can not be interpreted as a valid integer. +
    • +
  • + Division by zero results in a std::runtime_error + being thrown.
  • Although this type is a wrapper around GMP @@ -87,8 +91,8 @@
  • This backend supports rvalue-references and is move-aware, making instantiations - of mp_number on this - backend move aware. + of number on this backend + move aware.
    • diff --git a/doc/html/boost_multiprecision/tut/ints/tom_int.html b/doc/html/boost_multiprecision/tut/ints/tom_int.html index 08ccad9d..b242c3f1 100644 --- a/doc/html/boost_multiprecision/tut/ints/tom_int.html +++ b/doc/html/boost_multiprecision/tut/ints/tom_int.html @@ -24,7 +24,7 @@ class tommath_int; -typedef mp_number<tommath_int > tom_int; +typedef number<tommath_int > tom_int; }} // namespaces @@ -61,8 +61,12 @@ will be thrown.
  • - Division by zero will result in a hardware signal being raised by - libtommath. + Conversion from a string results in a std::runtime_error + being thrown if the string can not be interpreted as a valid integer. +
    • +
  • + Division by zero results in a std::runtime_error + being thrown.
    • diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html index 8e83c166..ae6e1e3f 100644 --- a/doc/html/boost_multiprecision/tut/primetest.html +++ b/doc/html/boost_multiprecision/tut/primetest.html @@ -23,10 +23,10 @@ 
    #include <boost/multiprecision/miller_rabin.hpp>
 
 template <class Backend, bool ExpressionTemplates, class Engine>
-bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials, Engine& gen);
+bool miller_rabin_test(const number<Backend, ExpressionTemplates>& n, unsigned trials, Engine& gen);
 
 template <class Backend, bool ExpressionTemplates, class Engine>
-bool miller_rabin_test(const mp_number<Backend, ExpressionTemplates>& n, unsigned trials);
+bool miller_rabin_test(const number<Backend, ExpressionTemplates>& n, unsigned trials);

    These functions perform a Miller-Rabin test for primality, if the result diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 2571ebe6..2f156532 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -222,12 +222,12 @@

    - A C++ rational number type that can used with any mp_number integer type. + A C++ rational number type that can used with any number integer type.

    - The expression templates used by mp_number + The expression templates used by number end up being "hidden" inside boost::rational: performance may well suffer as a result.

    diff --git a/doc/html/boost_multiprecision/tut/rational/br.html b/doc/html/boost_multiprecision/tut/rational/br.html index a3efdfa6..0f6c0044 100644 --- a/doc/html/boost_multiprecision/tut/rational/br.html +++ b/doc/html/boost_multiprecision/tut/rational/br.html @@ -23,7 +23,7 @@

    Note that using the library in this way largely negates the effect of the - expression templates in mp_number. + expression templates in number.

    diff --git a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html index ea6b42a8..9c07ed72 100644 --- a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html +++ b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html @@ -24,7 +24,7 @@ typedefrational_adapter<cpp_int_backend<>>cpp_rational_backend; -typedefmp_number<cpp_rational_backend>cpp_rational; +typedefnumber<cpp_rational_backend>cpp_rational;}}// namespaces @@ -64,6 +64,11 @@ Division by zero results in a std::rumtime_error being thrown. +
  • + Conversion from a string results in a std::runtime_error + being thrown if the string can not be interpreted as a valid rational + number. +
    • diff --git a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html index 8f1f28fe..f8e6dfc5 100644 --- a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html +++ b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html @@ -24,7 +24,7 @@ class gmp_rational; -typedef mp_number<gmp_rational > mpq_rational; +typedef number<gmp_rational > mpq_rational; }} // namespaces @@ -38,7 +38,7 @@

    As well as the usual conversions from arithmetic and string types, instances - of mp_number<gmp_rational> + of number<gmp_rational> are copy constructible and assignable from:

      @@ -46,12 +46,12 @@ The GMP native types: mpz_t, mpq_t.
    • - mp_number<gmp_int>. + number<gmp_int>.

    There is also a two-argument constructor that accepts a numerator and denominator - (both of type mp_number<gmp_int>). + (both of type number<gmp_int>).

    There are also non-member functions: @@ -77,7 +77,13 @@ default behavior).

  • - Division by zero results in a hardware exception inside the GMP library. + Division by zero results in a std::runtime_error + being thrown. +
    • +
  • + Conversion from a string results in a std::runtime_error + being thrown if the string can not be interpreted as a valid rational + number.
  • No changes are made to the GMP diff --git a/doc/html/boost_multiprecision/tut/rational/rational_adapter.html b/doc/html/boost_multiprecision/tut/rational/rational_adapter.html index 6b4853f1..e377fe2e 100644 --- a/doc/html/boost_multiprecision/tut/rational/rational_adapter.html +++ b/doc/html/boost_multiprecision/tut/rational/rational_adapter.html @@ -26,15 +26,15 @@

    The class template rational_adapter - is a back-end for mp_number + is a back-end for number which converts any existing integer back-end into a rational-number back-end.

    So for example, given an integer back-end type MyIntegerBackend, the use would be something like:

    -
    typedef mp_number<MyIntegerBackend>                    MyInt;
-typedef mp_number<rational_adapter<MyIntegerBackend> > MyRational;
+
    typedef number<MyIntegerBackend>                    MyInt;
+typedef number<rational_adapter<MyIntegerBackend> > MyRational;
 
 MyRational r = 2;
 r /= 3;
diff --git a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html
index 25520372..11982c13 100644
--- a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html
+++ b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html
@@ -23,7 +23,7 @@
 
    namespace boost{ namespace multiprecision{
 
 typedef rational_adpater<tommath_int>        tommath_rational;
-typedef mp_number<tommath_rational >         tom_rational;
+typedef number<tommath_rational >         tom_rational;
 
 }} // namespaces
 
    
@@ -57,9 +57,13 @@
               have the value zero (this the inherited Boost.Rational behavior).
  • - Division by zero results in a boost::bad_rational - exception being thrown (see the rational number library's docs for - more information). + Division by zero results in a std::runtime_error + being thrown. +
    • +
  • + Conversion from a string results in a std::runtime_error + being thrown if the string can not be interpreted as a valid rational + number.
  • No changes are made to libtommath's diff --git a/doc/html/index.html b/doc/html/index.html index 55b45c32..ba6104dd 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -78,7 +78,7 @@
    Reference
    -
    mp_number
    +
    number
    cpp_int
    gmp_int
    tom_int
    @@ -118,7 +118,7 @@
    • - +

    Last revised: June 07, 2012 at 09:33:02 GMT

    Last revised: August 08, 2012 at 18:23:03 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 46679178..ca42b29c 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -117,6 +117,27 @@ However, conversions are allowed: d = a * b; // OK, can convert from an expression template too. d = mp::int512_t(a) * c; // OK, all the types in the expression are the same now. +[h4 Move Semantics] + +On compilers that support rvalue-references, class `number` is move-enabled if the underlying backend is. + +In addition the non-expression template operator overloads (see below) are move aware and have overloads +that look something like: + + template + number operator + (number&& a, const number& b) + { + return std::move(a += b); + } + +These operator overloads ensure that many expressions can be evaluated without actually generating any temporaries. +However, there are still many simple expressions such as: + + a = b * c; + +Which don't noticably benefit from move support. Therefore, optimal performance comes from having both +move-support, and expression templates enabled. + [h4 Expression Templates] TODO: compare to rvalue refs. @@ -151,7 +172,7 @@ lets suppose we're evaluating a polynomial via Horners method, something like th //.... y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; -If type `T` is an `number`, then this expression is evaluated ['without creating a single temporary value]. In contrast, +If type `T` is a `number`, then this expression is evaluated ['without creating a single temporary value]. In contrast, if we were using the [mpfr_class] C++ wrapper for [mpfr] - then this expression would result in no less than 11 temporaries (this is true even though [mpfr_class] does use expression templates to reduce the number of temporaries somewhat). Had we used an even simpler wrapper around [mpfr] like [mpreal] things would have been even worse and no less that 24 temporaries @@ -866,6 +887,20 @@ In particular: cpp_dec_float_50 df(0.5); // OK construction from double cpp_int i(450); // OK constructs from signed int +* A `number` can be converted to any built in type, via the `convert_to` member function: + + mpz_int z(2); + int i = z.template convert_to(); // sets i to 2 + +Additional conversions may be supported by particular backends. + +* A `number` can be converted to any built in type, via an explicit conversion operator: +this functionality is only available on compilers supporting C++11's explicit conversion syntax. + + mpz_int z(2); + int i = z; // Error, implicit conversion not allowed. + int j = static_cast(z); // OK explicit conversion. + * Any number type can be constructed (or assigned) from a `const char*` or a `std::string`: // pi to 50 places from a string: @@ -921,13 +956,6 @@ In particular: More information on what additional types a backend supports conversions from are given in the tutorial for each backend. -* An `number` can be converted to any built in type, via the `convert_to` member function: - - mpz_int z(2); - int i = z.template convert_to(); // sets i to 2 - -Additional conversions may be supported by particular backends. - [endsect] [section:random Generating Random Numbers] @@ -1036,6 +1064,8 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba // Generic conversion mechanism template T convert_to()const; + template + explicit operator T ()const; // precision control: static unsigned default_precision(); static void default_precision(unsigned digits10); @@ -1233,7 +1263,7 @@ For the left and right shift operations, the argument must be a builtin integer type with a positive value (negative values result in a `std::runtime_error` being thrown). Note that all the types involved in the expression must evaluate to the same type - which is to say -we cannot mix an `number` with an `number` where B1 and B2 are different types. +we cannot mix a `number` with a `number` where B1 and B2 are different types. operator ``['convertible-to-bool-type]``()const; @@ -1265,6 +1295,9 @@ if /scientific/ is true. template T convert_to()const; + template + explicit operator T ()const; + Provides a generic conversion mechanism to convert `*this` to type `T`. Type `T` may be any arithmetic type. Optionally other types may also be supported by specific `Backend` types. @@ -1320,7 +1353,7 @@ These operators all take their usual arithmetic meanings. The arguments to these functions must contain at least one of the following: -* An `number`. +* A `number`. * An expression template type derived from `number`. In addition, one of the two arguments may be a builtin arithmetic type. @@ -1332,7 +1365,7 @@ The return type of these operators is either: * Type `bool` if the operator is a comparison operator. Note that all the types involved in the expression must evaluate to the same type - which is to say -we cannot mix an `number` with an `number` where B1 and B2 are different types. +we cannot mix a `number` with a `number` where B1 and B2 are different types. Finally note that the second argument to the left and right shift operations must be a builtin integer type, and that the argument must be positive (negative arguments result in a `std::runtime_error` being thrown). From 6fe80f07dee7401b086803aab828b70d265df284 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 10 Aug 2012 08:37:37 +0000 Subject: [PATCH 217/256] Much improved concept docs. Regenerate docs. Make some cpp_int specific routines generic instead. Changed divide-by-zero to be an overflow error. [SVN r79952] --- .../boost_multiprecision/indexes/s01.html | 268 +- .../boost_multiprecision/indexes/s02.html | 16 +- .../boost_multiprecision/indexes/s03.html | 18 +- .../boost_multiprecision/indexes/s04.html | 344 +- doc/html/boost_multiprecision/intro.html | 9 + .../boost_multiprecision/ref/backendconc.html | 3204 ++++++++++++----- doc/html/index.html | 2 +- doc/multiprecision.qbk | 429 ++- include/boost/multiprecision/cpp_int.hpp | 81 +- .../multiprecision/depricated/fixed_int.hpp | 2 +- .../detail/cpp_int_trivial_ops.hpp | 6 +- .../multiprecision/detail/integer_ops.hpp | 82 + include/boost/multiprecision/gmp.hpp | 32 +- .../boost/multiprecision/rational_adapter.hpp | 2 +- include/boost/multiprecision/tommath.hpp | 12 + test/test_arithmetic.cpp | 6 +- 16 files changed, 3254 insertions(+), 1259 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index b8cec282..d414d97f 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,13 +13,20 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    -

    B C D E F I L M P R S T Z

    +Function Index
    +

    A B C D E F I L M P R S T Z

    -B +A +
    +
    +
    +B
    • @@ -40,14 +47,14 @@
    -C +C
    -D +D
    • @@ -69,21 +76,246 @@
    -E +E
    -
    -F +F
    -I +I
    • @@ -120,7 +352,7 @@
    -L +L
    • @@ -145,7 +377,7 @@
    -M +M

    • miller_rabin_test

      @@ -155,7 +387,7 @@
    -P +P
    • @@ -171,7 +403,7 @@
    -R +R
    • @@ -184,7 +416,7 @@
    -S +S
    • @@ -197,14 +429,14 @@
    -T +T
    -Z +Z

    • zero

      diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index f03f6b35..d1ecfc4b 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,13 +13,13 @@
      PrevUpHomeNext
      -
      +

      -Class Index

      -

      C G M N T

      +Class Index
    +

    C G M N T

    -C +C
    • @@ -33,7 +33,7 @@
    -G +G
    -M +M

    • mpfr_float_backend

      @@ -51,7 +51,7 @@
    -N +N
    -T +T

    • tommath_int

      diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 3c80e3ca..14438ba0 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,13 +13,13 @@
      PrevUpHomeNext
      -
      +

      -Typedef Index

      -

      C I L M T U

      +Typedef Index
    +

    C I L M T U

    -C +C
    • @@ -47,7 +47,7 @@
    -I +I
    • @@ -72,14 +72,14 @@
    -L +L
    -M +M
    • @@ -154,7 +154,7 @@
    -T +T
    -U +U
    • diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 7d33939b..50d6b336 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,13 +12,20 @@
      PrevUpHome
      -
      +

      -Index

      -

      B C D E F G I L M N O P R S T U Z

      +Index
    +

    A B C D E F G I L M N O P R S T U Z

    -B +A +
    +
    +
    +B
    • @@ -43,7 +50,7 @@
    -C +C
    -D +D
    • @@ -135,21 +163,246 @@
    -E +E
    -
    -F +F
    -G +G
    • @@ -185,7 +438,7 @@
    -I +I
    • @@ -246,7 +499,7 @@
    -L +L
    • @@ -275,7 +528,7 @@
    -M +M
    • @@ -373,7 +626,7 @@
    -N +N
    • @@ -417,14 +670,59 @@
    -O +O
    -P +P
    • @@ -452,7 +750,7 @@
    -R +R
    • @@ -465,7 +763,7 @@
    -S +S
    • @@ -478,7 +776,7 @@
    -T +T
    • @@ -511,7 +809,7 @@
    -U +U
    • @@ -532,7 +830,7 @@
    -Z +Z
    @@ -72,6 +81,11 @@ Comments

    		+

    + Throws +

    +
    +

    +   +

    +
    @@ -111,6 +130,11 @@ and shall terminate in the type that is std::uintmax_t.

    		+

    +   +

    +
    @@ -130,6 +154,11 @@ terminate in type long double.

    		+

    +   +

    +
    @@ -144,7 +173,13 @@

    - The type of the exponent of type B. + The type of the exponent of type B. This type is required only + for floating point types. +

    +     		+

    +  

    +

    +   +

    +
    @@ -175,6 +215,11 @@ Copy Constructor.

    		+

    +   +

    +
    @@ -193,6 +238,11 @@ Assignment operator.

    		+

    +   +

    +
    @@ -213,6 +263,11 @@ B::unsigned_types or B::float_types.

    		+

    +   +

    +
    @@ -231,6 +286,12 @@ Assignment from a string.

    		+

    + Throws a std::runtime_error if the string could + not be interpretted as a valid number. +

    +
    @@ -248,6 +309,11 @@ Swaps the contents of its arguments.

    		+

    + noexcept +

    +
    @@ -270,6 +336,11 @@ digits as are required to reconstruct the original value.

    		+

    +   +

    +
    @@ -287,6 +358,11 @@ Negates b.

    		+

    +   +

    +
    @@ -310,6 +386,11 @@ and zero if cb == cb2.

    		+

    + noexcept +

    +
    @@ -336,6 +417,11 @@ B::unsigned_types or B::float_types.

    		+

    +   +

    +
    @@ -354,6 +440,11 @@ Adds cb to b.

    		+

    +   +

    +
    @@ -373,6 +464,11 @@ b.

    		+

    +   +

    +
    @@ -392,6 +488,11 @@ cb.

    		+

    +   +

    +
    @@ -410,6 +511,13 @@ Divides b by cb.

    		+

    + std::overflow_error if cb has the + value zero, and std::numeric_limits<number<B> >::has_infinity == + false +

    +
    @@ -431,6 +539,12 @@ type.

    		+

    + std::overflow_error if cb has the + value zero. +

    +
    @@ -451,6 +565,11 @@ type.

    		+

    +   +

    +
    @@ -471,6 +590,11 @@ type.

    		+

    +   +

    +
    @@ -491,6 +615,11 @@ type.

    		+

    +   +

    +
    @@ -511,6 +640,11 @@ is an integer type.

    		+

    +   +

    +
    @@ -531,6 +665,11 @@ type.

    		+

    +   +

    +
    @@ -551,6 +690,11 @@ type.

    		+

    +   +

    +
    @@ -575,6 +719,11 @@ Conversions to other types are entirely optional.

    		+

    +   +

    +
    @@ -598,6 +747,11 @@ is a floating-point type.

    		+

    +   +

    +
    @@ -619,6 +773,11 @@ is a floating-point type.

    		+

    +   +

    +
    @@ -642,6 +801,12 @@ is a floating-point type.

    		+

    + std::runtime_error if the exponent + of cb is too large to be stored in an int. +

    +
    @@ -663,6 +828,11 @@ is a floating-point type.

    		+

    +   +

    +
    @@ -684,6 +854,11 @@ type.

    		+

    +   +

    +
    @@ -705,6 +880,11 @@ type.

    		+

    +   +

    +
    @@ -726,6 +906,11 @@ type.

    		+

    +   +

    +
    @@ -748,6 +933,11 @@ Defaults to number_kind_floating_point.

    		+

    +   +

    +
    @@ -759,6 +949,7 @@
    @@ -776,9 +967,101 @@ Comments

    		+

    + Throws +

    +
    +

    + Construct and assign: +

    +     		   
    +

    + B(rb) +

    +     		+

    + B +

    +     		+

    + Move constructor. Afterwards variable rb + shall be in sane state, albeit with unspecified value. Only destruction + and assignment to the moved-from variable rb + need be supported after the operation. +

    +     		+

    + noexcept +

    +
    +

    + b = + rb +

    +     		+

    + B& +

    +     		+

    + Move-assign. Afterwards variable rb + shall be in sane state, albeit with unspecified value. Only destruction + and assignment to the moved-from variable rb + need be supported after the operation. +

    +     		+

    + noexcept +

    +
    +

    + B(a) +

    +     		+

    + B +

    +     		+

    + Direct construction from an arithmetic type. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. When not provided, + this operation is simulated using default-construction followed + by assignment. +

    +     		+

    +   +

    +

    B(b2) @@ -791,7 +1074,13 @@

    - Copy constructor from a different back-end type. + Copy constructor from a different back-end type. When not provided, + a generic interconversion routine is used. +

    +     		+

    +  

    - Assignment operator from a different back-end type. + Assignment operator from a different back-end type. When not provided, + a generic interconversion routine is used. +

    +     		+

    +  

    +

    +  

    +

    +   +

    +
    +

    + Comparisons: +

    +     		   
    +

    + eval_eq(cb, + cb2) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb and cb2 + are equal in value. When not provided, the default implementation + returns cb.compare(cb2) + == 0. +

    +     		+

    + noexcept +

    +
    +

    + eval_eq(cb, + a) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb and a + are equal in value. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + return the equivalent of eval_eq(cb, B(a)). +

    +     		+

    +   +

    +
    +

    + eval_eq(a, + cb) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb and a + are equal in value. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + the default version returns eval_eq(cb, a). +

    +     		+

    +   +

    +
    +

    + eval_lt(cb, + cb2) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb is less than cb2 in value. When not provided, + the default implementation returns cb.compare(cb2) < + 0. +

    +     		+

    + noexcept +

    +
    +

    + eval_lt(cb, + a) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb is less than a in value. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. When not provided, + the default implementation returns eval_lt(cb, B(a)). +

    +     		+

    +   +

    +
    +

    + eval_lt(a, + cb) +

    +     		+

    + bool +

    +     		+

    + Returns true if a is less than cb in value. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. When not provided, + the default implementation returns eval_gt(cb, a). +

    +     		+

    +   +

    +
    +

    + eval_gt(cb, + cb2) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb is greater than cb2 in value. When not provided, + the default implementation returns cb.compare(cb2) > + 0. +

    +     		+

    + noexcept +

    +
    +

    + eval_gt(cb, + a) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb is greater than a in value. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. When not provided, + the default implementation returns eval_gt(cb, B(a)). +

    +     		+

    +   +

    +
    +

    + eval_gt(a, + cb) +

    +     		+

    + bool +

    +     		+

    + Returns true if a is greater than cb in value. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. When not provided, + the default implementation returns eval_lt(cb, a). +

    +     		+

    +   +

    +
    +

    + eval_is_zero(cb) +

    +     		+

    + bool +

    +     		+

    + Returns true if cb is zero, otherwise false. The default version of this + function returns cb.compare(ui_type(0)) == + 0, where ui_type + is ui_type is + typename mpl::front<typename + B::unsigned_types>::type. +

    +     		+

    +   +

    +
    +

    + eval_get_sign(cb) +

    +     		+

    + int +

    +     		+

    + Returns a value < zero if cb + is negative, a value > zero if cb + is positive, and zero if cb + is zero. The default version of this function returns cb.compare(ui_type(0)), + where ui_type is + ui_type is typename mpl::front<typename + B::unsigned_types>::type. +

    +     		+

    +   +

    +
    +

    + Basic arithmetic: +

    +     		   
    @@ -867,160 +1483,13 @@

    Adds a to b. The type of a shall be listed in one of the type lists B::signed_types, B::unsigned_types - or B::float_types. -

    -
    -

    - eval_subtract(b, - a) + or B::float_types. When not provided, + the default version calls eval_add(b, B(a))

    - void -

    -     		-

    - Subtracts a from - b. The type of - a shall be listed - in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_multiply(b, - a) -

    -     		-

    - void -

    -     		-

    - Multiplies b by - a. The type of - a shall be listed - in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_divide(b, - a) -

    -     		-

    - void -

    -     		-

    - Divides b by a. The type of a shall be listed in one of the - type lists B::signed_types, B::unsigned_types - or B::float_types. -

    -
    -

    - eval_modulus(b, - a) -

    -     		-

    - void -

    -     		-

    - Computes b %= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_and(b, a) -

    -     		-

    - void -

    -     		-

    - Computes b &= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_or(b, a) -

    -     		-

    - void -

    -     		-

    - Computes b |= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_xor(b, a) -

    -     		-

    - void -

    -     		-

    - Computes b ^= - cb, only required when - B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. +  

    Add cb to cb2 and stores the result in - b. -

    -
    -

    - eval_subtract(b, - cb, - cb2) + b. When not provided, + does the equivalent of b + = cb; eval_add(b, cb2).

    - void -

    -     		-

    - Subtracts cb2 from - cb and stores the - result in b. -

    -
    -

    - eval_multiply(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Multiplies cb by - cb2 and stores - the result in b. -

    -
    -

    - eval_divide(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Divides cb by - cb2 and stores - the result in b. +  

    -

    - eval_subtract(b, - cb, - a) + or B::float_types. When not provided, + does the equivalent of eval_add(b, cb, B(a)).

    - void -

    -     		-

    - Subtracts a from - cb and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_multiply(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Multiplies cb by - a and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_divide(b, - cb, - a) -

    -     		-

    - void -

    -     		-

    - Divides cb by - a and stores the - result in b. The - type of a shall - be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_modulus(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb % - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_bitwise_and(b, cb, cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb & - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_bitwise_or(b, cb, cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb | - cb2 and stores the result - in b, only required - when B is an integer - type. -

    -
    -

    - eval_bitwise_xor(b, cb, cb2) -

    -     		-

    - void -

    -     		-

    - Computes cb ^ - cb2 and stores the result - in b, only required - when B is an integer - type. +  

    +

    +   +

    +
    +

    + eval_subtract(b, + a) +

    +     		+

    + void +

    +     		+

    + Subtracts a from + b. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + the default version calls eval_subtract(b, B(a)) +

    +     		+

    +   +

    +
    +

    + eval_subtract(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Subtracts cb2 from + cb and stores the + result in b. When + not provided, does the equivalent of b + = cb; eval_subtract(b, cb2). +

    +     		+

    +   +

    +
    +

    + eval_subtract(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Subtracts a from + cb and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_subtract(b, cb, B(a)). +

    +     		+

    +  

    +

    +   +

    +
    +

    + eval_multiply(b, + a) +

    +     		+

    + void +

    +     		+

    + Multiplies b by + a. The type of + a shall be listed + in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + the default version calls eval_multiply(b, B(a)) +

    +     		+

    +   +

    +
    +

    + eval_multiply(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Multiplies cb by + cb2 and stores + the result in b. + When not provided, does the equivalent of b + = cb; eval_multiply(b, cb2). +

    +     		+

    +   +

    +
    +

    + eval_multiply(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Multiplies cb by + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_multiply(b, cb, B(a)). +

    +     		+

    +  

    +

    +   +

    +
    +

    + eval_divide(b, + a) +

    +     		+

    + void +

    +     		+

    + Divides b by a. The type of a shall be listed in one of the + type lists B::signed_types, B::unsigned_types + or B::float_types. When not provided, + the default version calls eval_divide(b, B(a)) +

    +     		+

    + std::overflow_error if a has the value zero, and std::numeric_limits<number<B> + >::has_infinity + == false +

    +
    +

    + eval_divide(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Divides cb by + cb2 and stores + the result in b. + When not provided, does the equivalent of b + = cb; eval_divide(b, cb2). +

    +     		+

    + std::overflow_error if cb2 has the value zero, and + std::numeric_limits<number<B> + >::has_infinity + == false +

    +
    +

    + eval_divide(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Divides cb by + a and stores the + result in b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_divide(b, cb, B(a)). +

    +     		+

    + std::overflow_error if a has the value zero, and std::numeric_limits<number<B> + >::has_infinity + == false

    +

    + std::overflow_error if cb has the + value zero, and std::numeric_limits<number<B> >::has_infinity == + false +

    +
    +

    + eval_increment(b) +

    +     		+

    + void +

    +     		+

    + Increments the value of b + by one. When not provided, does the equivalent of eval_add(b, + static_cast<ui_type>(1u)). + Where ui_type is + typename mpl::front<typename + B::unsigned_types>::type. +

    +     		+

    +   +

    +
    +

    + eval_decrement(b) +

    +     		+

    + void +

    +     		+

    + Decrements the value of b + by one. When not provided, does the equivalent of eval_subtract(b, + static_cast<ui_type>(1u)). + Where ui_type is + typename mpl::front<typename + B::unsigned_types>::type. +

    +     		+

    +   +

    +
    +

    + Integer specific operations: +

    +     		   
    +

    + eval_modulus(b, + a) +

    +     		+

    + void +

    +     		+

    + Computes b %= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + the default version calls eval_modulus(b, B(a)) +

    +     		+

    + std::overflow_error if a has the value zero. +

    +
    +

    + eval_modulus(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb % + cb2 and stores the result + in b, only required + when B is an integer + type. When not provided, does the equivalent of b + = cb; eval_modulus(b, cb2). +

    +     		+

    + std::overflow_error if a has the value zero.

    -

    - eval_bitwise_and(b, cb, a) + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_modulus(b, cb, B(a)).

    - void -

    -     		-

    - Computes cb & - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_or(b, cb, a) -

    -     		-

    - void -

    -     		-

    - Computes cb | - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. -

    -
    -

    - eval_bitwise_xor(b, cb, a) -

    -     		-

    - void -

    -     		-

    - Computes cb ^ - a and stores the result - in b, only required - when B is an integer - type. The type of a - shall be listed in one of the type lists B::signed_types, - B::unsigned_types or B::float_types. + std::overflow_error if a has the value zero.

    +

    + std::overflow_error if a has the value zero. +

    +
    +

    + eval_bitwise_and(b, a) +

    +     		+

    + void +

    +     		+

    + Computes b &= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + the default version calls eval_bitwise_and(b, B(a)) +

    +     		+

    +   +

    +
    +

    + eval_bitwise_and(b, cb, cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb & + cb2 and stores the result + in b, only required + when B is an integer + type. When not provided, does the equivalent of b + = cb; eval_bitwise_and(b, cb2). +

    +     		+

    +   +

    +
    +

    + eval_bitwise_and(b, cb, a) +

    +     		+

    + void +

    +     		+

    + Computes cb & + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_bitwise_and(b, cb, B(a)). +

    +     		+

    +  

    +

    +   +

    +
    +

    + eval_bitwise_or(b, a) +

    +     		+

    + void +

    +     		+

    + Computes b |= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + the default version calls eval_bitwise_or(b, B(a)) +

    +     		+

    +   +

    +
    +

    + eval_bitwise_or(b, cb, cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb | + cb2 and stores the result + in b, only required + when B is an integer + type. When not provided, does the equivalent of b + = cb; eval_bitwise_or(b, cb2). +

    +     		+

    +   +

    +
    +

    + eval_bitwise_or(b, cb, a) +

    +     		+

    + void +

    +     		+

    + Computes cb | + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_bitwise_or(b, cb, B(a)). +

    +     		+

    +  

    +

    +   +

    +
    +

    + eval_bitwise_xor(b, a) +

    +     		+

    + void +

    +     		+

    + Computes b ^= + cb, only required when + B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + the default version calls eval_bitwise_xor(b, B(a)) +

    +     		+

    +   +

    +
    +

    + eval_bitwise_xor(b, cb, cb2) +

    +     		+

    + void +

    +     		+

    + Computes cb ^ + cb2 and stores the result + in b, only required + when B is an integer + type. When not provided, does the equivalent of b + = cb; eval_bitwise_xor(b, cb2). +

    +     		+

    +   +

    +
    +

    + eval_bitwise_xor(b, cb, a) +

    +     		+

    + void +

    +     		+

    + Computes cb ^ + a and stores the result + in b, only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided, + does the equivalent of eval_bitwise_xor(b, cb, B(a)). +

    +     		+

    +  

    +

    +  

    +

    +  

    - eval_increment(b) -

    -     		-

    - void -

    -     		-

    - Increments the value of b - by one. -

    -
    -

    - eval_decrement(b) -

    -     		-

    - void -

    -     		-

    - Decrements the value of b - by one. -

    -
    -

    - eval_is_zero(cb) -

    -     		-

    - bool -

    -     		-

    - Returns true if cb is zero, otherwise false -

    -
    -

    - eval_get_sign(cb) -

    -     		-

    - int -

    -     		-

    - Returns a value < zero if cb - is negative, a value > zero if cb - is positive, and zero if cb - is zero. -

    -
    -

    - eval_abs(b, - cb) -

    -     		-

    - void -

    -     		-

    - Set b to the absolute - value of cb. -

    -
    -

    - eval_fabs(b, - cb) -

    -     		-

    - void -

    -     		-

    - Set b to the absolute - value of cb. -

    -
    -

    - eval_fpclassify(cb) -

    -     		-

    - int -

    -     		-

    - Returns one of the same values returned by std::fpclassify. - Only required when B - is an floating-point type. -

    -
    -

    - eval_trunc(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::trunc - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_round(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::round - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_exp(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::exp - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_log(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::log - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_log10(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::log10 - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_sin(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::sin - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_cos(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::cos - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_tan(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::exp - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_asin(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::asin - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_acos(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::acos - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_atan(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::atan - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_sinh(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::sinh - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_cosh(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::cosh - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_tanh(b, - cb) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::tanh - on argument cb - and stores the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_fmod(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::fmod - on arguments cb - and cb2, and store - the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_pow(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::pow - on arguments cb - and cb2, and store - the result in b. - Only required when B - is an floating-point type. -

    -
    -

    - eval_atan2(b, - cb, - cb2) -

    -     		-

    - void -

    -     		-

    - Performs the equivalent operation to std::atan - on arguments cb - and cb2, and store - the result in b. - Only required when B - is an floating-point type. +  

    +

    + std::overflow_error if a has the value zero.

    +

    + std::overflow_error if a has the value zero.

    +

    +  

    +

    +  

    +

    +  

    +

    +  

    +

    +  

    +

    +  

    +

    +   +

    +
    +

    + eval_gcd(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Sets b to the greatest + common divisor of cb + and cb2. Only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. The default version + of this function calls eval_gcd(b, cb, B(a)). +

    +     		+

    +   +

    +
    +

    + eval_lcm(b, + cb, + a) +

    +     		+

    + void +

    +     		+

    + Sets b to the least + common multiple of cb + and cb2. Only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. The default version + of this function calls eval_lcm(b, cb, B(a)). +

    +     		+

    +   +

    +
    +

    + eval_gcd(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Sets b to the greatest + common divisor of cb + and a. Only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. The default version + of this function calls eval_gcd(b, cb, a). +

    +     		+

    +   +

    +
    +

    + eval_lcm(b, + a, + cb) +

    +     		+

    + void +

    +     		+

    + Sets b to the least + common multiple of cb + and a. Only required + when B is an integer + type. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. The default version + of this function calls eval_lcm(b, cb, a). +

    +     		+

    +   +

    +
    +

    + eval_powm(b, + cb, + cb2, + cb3) +

    +     		+

    + void +

    +     		+

    + Sets b to the result + of (cb^cb2)%cb3. The default version of this + function is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_powm(b, + cb, + cb2, + a) +

    +     		+

    + void +

    +     		+

    + Sets b to the result + of (cb^cb2)%a. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types. The default version + of this function is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_powm(b, + cb, + a, + cb2) +

    +     		+

    + void +

    +     		+

    + Sets b to the result + of (cb^a)%cb2. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types. The default version + of this function is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_powm(b, + cb, + a, + a) +

    +     		+

    + void +

    +     		+

    + Sets b to the result + of (cb^a)%a. The type of a + shall be listed in one of the type lists B::signed_types, + B::unsigned_types. The default version + of this function is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + Sign manipulation: +

    +     		   
    +

    + eval_abs(b, + cb) +

    +     		+

    + void +

    +     		+

    + Set b to the absolute + value of cb. The + default version of this functions assigns cb + to b, and then + calls b.negate() + if eval_get_sign(cb) < + 0. +

    +     		+

    +   +

    +
    +

    + eval_fabs(b, + cb) +

    +     		+

    + void +

    +     		+

    + Set b to the absolute + value of cb. The + default version of this functions assigns cb + to b, and then + calls b.negate() + if eval_get_sign(cb) < + 0. +

    +     		+

    +   +

    +
    +

    + Floating point functions: +

    +     		   
    +

    + eval_fpclassify(cb) +

    +     		+

    + int +

    +     		+

    + Returns one of the same values returned by std::fpclassify. + Only required when B + is an floating-point type. The default version of this function + will only test for zero cb. +

    +     		+

    +   +

    +
    +

    + eval_trunc(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::trunc + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_round(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::round + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_exp(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::exp + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_log(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::log + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_log10(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::log10 + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_sin(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::sin + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_cos(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::cos + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_tan(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::exp + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_asin(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::asin + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_acos(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::acos + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_atan(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::atan + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_sinh(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::sinh + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_cosh(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::cosh + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_tanh(b, + cb) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::tanh + on argument cb + and stores the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_fmod(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::fmod + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_pow(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::pow + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +   +

    +
    +

    + eval_atan2(b, + cb, + cb2) +

    +     		+

    + void +

    +     		+

    + Performs the equivalent operation to std::atan + on arguments cb + and cb2, and store + the result in b. + Only required when B + is an floating-point type. The default version of this function + is synthesised from other operations above. +

    +     		+

    +  


    - The tables above place no throws requirements on any - of the operations. It is up to each type modelling this concept to decide + When the tables above place no throws requirements on + an operation, then it is up to each type modelling this concept to decide when or whether throwing an exception is desirable. However, thrown exceptions should always either be the type, or inherit from the type std::runtime_error. For example, a floating point type might choose to throw std::overflow_error diff --git a/doc/html/index.html b/doc/html/index.html index ba6104dd..bb9676a2 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -118,7 +118,7 @@ - +

    Last revised: August 08, 2012 at 18:23:03 GMT

    Last revised: August 09, 2012 at 17:32:59 GMT

    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index ca42b29c..c05e6e9a 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -47,7 +47,6 @@ '''] - [section:intro Introduction] The Multiprecision Library provides ['User-defined] integer, rational and floating-point C++ types which @@ -138,6 +137,12 @@ However, there are still many simple expressions such as: Which don't noticably benefit from move support. Therefore, optimal performance comes from having both move-support, and expression templates enabled. +Note that while "moved-from" objects are left in a sane state, they have an unspecified value, and the only permitted +operations on them are destruction or the assignment of a new value. Any other operation should be considered +a programming error and many backends will trigger an assertion if any other operation is attempted. This behavior +allows for optimal performance on move-construction (i.e. no allocation required, we just take ownership of the existing +object's internal state), while maintaining usability in the standard library containers. + [h4 Expression Templates] TODO: compare to rvalue refs. @@ -1730,13 +1735,17 @@ More information on this type can be found in the [link boost_multiprecision.tut [section:backendconc Backend Requirements] The requirements on the `Backend` template argument to `number` are split up into -compulsory requirements, and optional requirements that are either to improve performance -or provide optional features. +sections: compulsary and optional. -TODO: Add optional construction support, add throws specification, clarify what compulsory means. +Compulsary requirements have no default implementation in the library, therefore if the feature +they implement is to be supported at all, then they must be implemented by the backend. + +Optional requirements have default implementations that are called if the backend doesn't provide +it's own. Typically the backend will implement these to improve performance. In the following tables, type B is the `Backend` template arument to `number`, `b` and `b2` are -a variables of type B, `cb` and `cb2` are constant variables of type B, `a` is a variable of Arithmetic type, +a variables of type B, `cb`, `cb2` and `cb3` are constant variables of type `const B`, +`rb` is a variable of type `B&&`, `a` and `a2` are variables of Arithmetic type, `s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`, `pa` is a variable of type pointer-to-arithmetic-type, `exp` is a variable of type `B::exp_type`, `pexp` is a variable of type `B::exp_type*`, `i` is a variable of type `int`, `pi` pointer to a variable of type `int`, @@ -1744,157 +1753,325 @@ B2 is another type that meets these requirements, b2 is a variable of type B2. [table Compulsory Requirements on the Backend type. -[[Expression][Return Type][Comments]] +[[Expression][Return Type][Comments][Throws]] [[`B::signed_types`][`mpl::list`][A list of signed integral types that can be assigned to type B. The types shall be - listed in order of size, smallest first, and shall terminate in the type that is `std::intmax_t`.]] + listed in order of size, smallest first, and shall terminate in the type that is `std::intmax_t`.][[space]]] [[`B::unsigned_types`][`mpl::list`][A list of unsigned integral types that can be assigned to type B. The types shall be - listed in order of size, smallest first, and shall terminate in the type that is `std::uintmax_t`.]] + listed in order of size, smallest first, and shall terminate in the type that is `std::uintmax_t`.][[space]]] [[`B::float_types`][`mpl::list`][A list of floating-point types that can be assigned to type B.The types shall be - listed in order of size, smallest first, and shall terminate in type `long double`.]] -[[`B::exponent_type`][A signed integral type.][The type of the exponent of type B.]] -[[`B()`][ ][Default constructor.]] -[[`B(cb)`][ ][Copy Constructor.]] -[[`b = b`][`B&`][Assignment operator.]] + listed in order of size, smallest first, and shall terminate in type `long double`.][[space]]] +[[`B::exponent_type`][A signed integral type.][The type of the exponent of type B. This type is required only for floating point types.][[space]]] +[[`B()`][ ][Default constructor.][[space]]] +[[`B(cb)`][ ][Copy Constructor.][[space]]] +[[`b = b`][`B&`][Assignment operator.][[space]]] [[`b = a`][`B&`][Assignment from an Arithmetic type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`b = s`][`B&`][Assignment from a string.]] -[[`b.swap(b)`][`void`][Swaps the contents of its arguments.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.][[space]]] +[[`b = s`][`B&`][Assignment from a string.][Throws a `std::runtime_error` if the string could not be interpretted as a valid number.]] +[[`b.swap(b)`][`void`][Swaps the contents of its arguments.][`noexcept`]] [[`cb.str(ui, bb)`][`std::string`][Returns the string representation of `b` with `ui` digits and in scientific format if `bb` is `true`. - If `ui` is zero, then returns as many digits as are required to reconstruct the original value.]] -[[`b.negate()`][`void`][Negates `b`.]] + If `ui` is zero, then returns as many digits as are required to reconstruct the original value.][[space]]] +[[`b.negate()`][`void`][Negates `b`.][[space]]] [[`cb.compare(cb2)`][`int`][Compares `cb` and `cb2`, returns a value less than zero if `cb < cb2`, a value greater than zero if `cb > cb2` and zero - if `cb == cb2`.]] + if `cb == cb2`.][`noexcept`]] [[`cb.compare(a)`][`int`][Compares `cb` and `a`, returns a value less than zero if `cb < a`, a value greater than zero if `cb > a` and zero if `cb == a`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_add(b, cb)`][`void`][Adds `cb` to `b`.]] -[[`eval_subtract(b, cb)`][`void`][Subtracts `cb` from `b`.]] -[[`eval_multiply(b, cb)`][`void`][Multiplies `b` by `cb`.]] -[[`eval_divide(b, cb)`][`void`][Divides `b` by `cb`.]] -[[`eval_modulus(b, cb)`][`void`][Computes `b %= cb`, only required when `B` is an integer type.]] -[[`eval_bitwise_and(b, cb)`][`void`][Computes `b &= cb`, only required when `B` is an integer type.]] -[[`eval_bitwise_or(b, cb)`][`void`][Computes `b |= cb`, only required when `B` is an integer type.]] -[[`eval_bitwise_xor(b, cb)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type.]] -[[`eval_complement(b, cb)`][`void`][Computes the ones-complement of `cb` and stores the result in `b`, only required when `B` is an integer type.]] -[[`eval_left_shift(b, ui)`][`void`][Computes `b <<= ui`, only required when `B` is an integer type.]] -[[`eval_right_shift(b, ui)`][`void`][Computes `b >>= ui`, only required when `B` is an integer type.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`.][[space]]] +[[`eval_add(b, cb)`][`void`][Adds `cb` to `b`.][[space]]] +[[`eval_subtract(b, cb)`][`void`][Subtracts `cb` from `b`.][[space]]] +[[`eval_multiply(b, cb)`][`void`][Multiplies `b` by `cb`.][[space]]] +[[`eval_divide(b, cb)`][`void`][Divides `b` by `cb`.] + [`std::overflow_error` if cb has the value zero, and `std::numeric_limits >::has_infinity == false`]] +[[`eval_modulus(b, cb)`][`void`][Computes `b %= cb`, only required when `B` is an integer type.] + [`std::overflow_error` if cb has the value zero.]] +[[`eval_bitwise_and(b, cb)`][`void`][Computes `b &= cb`, only required when `B` is an integer type.][[space]]] +[[`eval_bitwise_or(b, cb)`][`void`][Computes `b |= cb`, only required when `B` is an integer type.][[space]]] +[[`eval_bitwise_xor(b, cb)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type.][[space]]] +[[`eval_complement(b, cb)`][`void`][Computes the ones-complement of `cb` and stores the result in `b`, only required when `B` is an integer type.][[space]]] +[[`eval_left_shift(b, ui)`][`void`][Computes `b <<= ui`, only required when `B` is an integer type.][[space]]] +[[`eval_right_shift(b, ui)`][`void`][Computes `b >>= ui`, only required when `B` is an integer type.][[space]]] [[`eval_convert_to(pa, cb)`][`void`][Converts `cb` to the type of `*pa` and store the result in `*pa`. Type `B` shall support conversion to at least types `std::intmax_t`, `std::uintmax_t` and `long long`. Conversion to other arithmetic types can then be synthesised using other operations. - Conversions to other types are entirely optional.]] -[[`eval_frexp(b, cb, pexp)`][`void`][Stores values in `b` and `*pexp` such that the value of `cb` is b * 2[super *pexp], only required when `B` is a floating-point type.]] -[[`eval_ldexp(b, cb, exp)`][`void`][Stores a value in `b` that is cb * 2[super exp], only required when `B` is a floating-point type.]] -[[`eval_frexp(b, cb, pi)`][`void`][Stores values in `b` and `*pi` such that the value of `cb` is b * 2[super *pi], only required when `B` is a floating-point type.]] -[[`eval_ldexp(b, cb, i)`][`void`][Stores a value in `b` that is cb * 2[super i], only required when `B` is a floating-point type.]] -[[`eval_floor(b, cb)`][`void`][Stores the floor of `cb` in `b`, only required when `B` is a floating-point type.]] -[[`eval_ceil(b, cb)`][`void`][Stores the ceiling of `cb` in `b`, only required when `B` is a floating-point type.]] -[[`eval_sqrt(b, cb)`][`void`][Stores the square root of `cb` in `b`, only required when `B` is a floating-point type.]] + Conversions to other types are entirely optional.][[space]]] +[[`eval_frexp(b, cb, pexp)`][`void`][Stores values in `b` and `*pexp` such that the value of `cb` is b * 2[super *pexp], only required when `B` is a floating-point type.][[space]]] +[[`eval_ldexp(b, cb, exp)`][`void`][Stores a value in `b` that is cb * 2[super exp], only required when `B` is a floating-point type.][[space]]] +[[`eval_frexp(b, cb, pi)`][`void`][Stores values in `b` and `*pi` such that the value of `cb` is b * 2[super *pi], only required when `B` is a floating-point type.] + [`std::runtime_error` if the exponent of cb is too large to be stored in an `int`.]] +[[`eval_ldexp(b, cb, i)`][`void`][Stores a value in `b` that is cb * 2[super i], only required when `B` is a floating-point type.][[space]]] +[[`eval_floor(b, cb)`][`void`][Stores the floor of `cb` in `b`, only required when `B` is a floating-point type.][[space]]] +[[`eval_ceil(b, cb)`][`void`][Stores the ceiling of `cb` in `b`, only required when `B` is a floating-point type.][[space]]] +[[`eval_sqrt(b, cb)`][`void`][Stores the square root of `cb` in `b`, only required when `B` is a floating-point type.][[space]]] [[`boost::multiprecision::number_category::type`][`mpl::int_`][`N` is one of the values `number_kind_integer`, `number_kind_floating_point`, `number_kind_rational` or `number_kind_fixed_point`. - Defaults to `number_kind_floating_point`.]] + Defaults to `number_kind_floating_point`.][[space]]] ] [table Optional Requirements on the Backend Type -[[Expression][Returns][Comments]] -[[`B(b2)`][`B`][Copy constructor from a different back-end type.]] -[[`b = b2`][`b&`][Assignment operator from a different back-end type.]] +[[Expression][Returns][Comments][Throws]] + +[[['Construct and assign:]]] +[[`B(rb)`][`B`][Move constructor. Afterwards variable `rb` shall be in sane state, albeit with unspecified value. + Only destruction and assignment to the moved-from variable `rb` need be supported after the operation.][`noexcept`]] +[[`b = rb`][`B&`][Move-assign. Afterwards variable `rb` shall be in sane state, albeit with unspecified value. + Only destruction and assignment to the moved-from variable `rb` need be supported after the operation.][`noexcept`]] +[[`B(a)`][`B`][Direct construction from an arithmetic type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, this operation is simulated using default-construction followed by assignment.][[space]]] +[[`B(b2)`][`B`][Copy constructor from a different back-end type. When not provided, a generic interconversion routine is used.][[space]]] +[[`b = b2`][`b&`][Assignment operator from a different back-end type. When not provided, a generic interconversion routine is used.][[space]]] [[`assign_components(b, a, a)`][`void`][Assigns to `b` the two components in the following arguments. - Only applies to rational and complex number types.]] + Only applies to rational and complex number types. + When not provided, arithmetic operations are used to synthesise the result from the two values.][[space]]] [[`assign_components(b, b2, b2)`][`void`][Assigns to `b` the two components in the following arguments. - Only applies to rational and complex number types.]] + Only applies to rational and complex number types. + When not provided, arithmetic operations are used to synthesise the result from the two values.][[space]]] + +[[['Comparisons:]]] +[[`eval_eq(cb, cb2)`][`bool`][Returns `true` if `cb` and `cb2` are equal in value. + When not provided, the default implementation returns `cb.compare(cb2) == 0`.][`noexcept`]] +[[`eval_eq(cb, a)`][`bool`][Returns `true` if `cb` and `a` are equal in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, return the equivalent of `eval_eq(cb, B(a))`.][[space]]] +[[`eval_eq(a, cb)`][`bool`][Returns `true` if `cb` and `a` are equal in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version returns `eval_eq(cb, a)`.][[space]]] +[[`eval_lt(cb, cb2)`][`bool`][Returns `true` if `cb` is less than `cb2` in value. + When not provided, the default implementation returns `cb.compare(cb2) < 0`.][`noexcept`]] +[[`eval_lt(cb, a)`][`bool`][Returns `true` if `cb` is less than `a` in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default implementation returns `eval_lt(cb, B(a))`.][[space]]] +[[`eval_lt(a, cb)`][`bool`][Returns `true` if `a` is less than `cb` in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default implementation returns `eval_gt(cb, a)`.][[space]]] +[[`eval_gt(cb, cb2)`][`bool`][Returns `true` if `cb` is greater than `cb2` in value. + When not provided, the default implementation returns `cb.compare(cb2) > 0`.][`noexcept`]] +[[`eval_gt(cb, a)`][`bool`][Returns `true` if `cb` is greater than `a` in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default implementation returns `eval_gt(cb, B(a))`.][[space]]] +[[`eval_gt(a, cb)`][`bool`][Returns `true` if `a` is greater than `cb` in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default implementation returns `eval_lt(cb, a)`.][[space]]] +[[`eval_is_zero(cb)`][`bool`][Returns `true` if `cb` is zero, otherwise `false`. The default version of this function + returns `cb.compare(ui_type(0)) == 0`, where `ui_type` is `ui_type` is + `typename mpl::front::type`.][[space]]] +[[`eval_get_sign(cb)`][`int`][Returns a value < zero if `cb` is negative, a value > zero if `cb` is positive, and zero if `cb` is zero. + The default version of this function + returns `cb.compare(ui_type(0))`, where `ui_type` is `ui_type` is + `typename mpl::front::type`.][[space]]] + +[[['Basic arithmetic:]]] [[`eval_add(b, a)`][`void`][Adds `a` to `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_subtract(b, a)`][`void`][Subtracts `a` from `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_multiply(b, a)`][`void`][Multiplies `b` by `a`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_divide(b, a)`][`void`][Divides `b` by `a`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_modulus(b, a)`][`void`][Computes `b %= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_bitwise_and(b, a)`][`void`][Computes `b &= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_bitwise_or(b, a)`][`void`][Computes `b |= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_bitwise_xor(b, a)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_add(b, cb, cb2)`][`void`][Add `cb` to `cb2` and stores the result in `b`.]] -[[`eval_subtract(b, cb, cb2)`][`void`][Subtracts `cb2` from `cb` and stores the result in `b`.]] -[[`eval_multiply(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and stores the result in `b`.]] -[[`eval_divide(b, cb, cb2)`][`void`][Divides `cb` by `cb2` and stores the result in `b`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_add(b, B(a))`][[space]]] +[[`eval_add(b, cb, cb2)`][`void`][Add `cb` to `cb2` and stores the result in `b`. + When not provided, does the equivalent of `b = cb; eval_add(b, cb2)`.][[space]]] [[`eval_add(b, cb, a)`][`void`][Add `cb` to `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_subtract(b, cb, a)`][`void`][Subtracts `a` from `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_multiply(b, cb, a)`][`void`][Multiplies `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_divide(b, cb, a)`][`void`][Divides `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_modulus(b, cb, cb2)`][`void`][Computes `cb % cb2` and stores the result in `b`, only required when `B` is an integer type.]] -[[`eval_bitwise_and(b, cb, cb2)`][`void`][Computes `cb & cb2` and stores the result in `b`, only required when `B` is an integer type.]] -[[`eval_bitwise_or(b, cb, cb2)`][`void`][Computes `cb | cb2` and stores the result in `b`, only required when `B` is an integer type.]] -[[`eval_bitwise_xor(b, cb, cb2)`][`void`][Computes `cb ^ cb2` and stores the result in `b`, only required when `B` is an integer type.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_add(b, cb, B(a))`.][[space]]] [[`eval_add(b, a, cb)`][`void`][Add `a` to `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_add(b, cb, a)`.][[space]]] +[[`eval_subtract(b, a)`][`void`][Subtracts `a` from `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_subtract(b, B(a))`][[space]]] +[[`eval_subtract(b, cb, cb2)`][`void`][Subtracts `cb2` from `cb` and stores the result in `b`. + When not provided, does the equivalent of `b = cb; eval_subtract(b, cb2)`.][[space]]] +[[`eval_subtract(b, cb, a)`][`void`][Subtracts `a` from `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_subtract(b, cb, B(a))`.][[space]]] [[`eval_subtract(b, a, cb)`][`void`][Subtracts `cb` from `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_subtract(b, cb, a); b.negate();`.][[space]]] +[[`eval_multiply(b, a)`][`void`][Multiplies `b` by `a`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_multiply(b, B(a))`][[space]]] +[[`eval_multiply(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and stores the result in `b`. + When not provided, does the equivalent of `b = cb; eval_multiply(b, cb2)`.][[space]]] +[[`eval_multiply(b, cb, a)`][`void`][Multiplies `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_multiply(b, cb, B(a))`.][[space]]] [[`eval_multiply(b, a, cb)`][`void`][Multiplies `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_multiply(b, cb, a)`.][[space]]] +[[`eval_divide(b, a)`][`void`][Divides `b` by `a`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_divide(b, B(a))`] + [`std::overflow_error` if `a` has the value zero, and `std::numeric_limits >::has_infinity == false`]] +[[`eval_divide(b, cb, cb2)`][`void`][Divides `cb` by `cb2` and stores the result in `b`. + When not provided, does the equivalent of `b = cb; eval_divide(b, cb2)`.] + [`std::overflow_error` if `cb2` has the value zero, and `std::numeric_limits >::has_infinity == false`]] +[[`eval_divide(b, cb, a)`][`void`][Divides `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_divide(b, cb, B(a))`.] + [`std::overflow_error` if `a` has the value zero, and `std::numeric_limits >::has_infinity == false`]] [[`eval_divide(b, a, cb)`][`void`][Divides `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_divide(b, B(a), cb)`.] + [`std::overflow_error` if cb has the value zero, and `std::numeric_limits >::has_infinity == false`]] +[[`eval_increment(b)`][void][Increments the value of `b` by one. + When not provided, does the equivalent of `eval_add(b, static_cast(1u))`. + Where `ui_type` is `typename mpl::front::type`.][[space]]] +[[`eval_decrement(b)`][void][Decrements the value of `b` by one. + When not provided, does the equivalent of `eval_subtract(b, static_cast(1u))`. + Where `ui_type` is `typename mpl::front::type`.][[space]]] + +[[['Integer specific operations:]]] +[[`eval_modulus(b, a)`][`void`][Computes `b %= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_modulus(b, B(a))`] + [`std::overflow_error` if `a` has the value zero.]] +[[`eval_modulus(b, cb, cb2)`][`void`][Computes `cb % cb2` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_modulus(b, cb2)`.] + [`std::overflow_error` if `a` has the value zero.]] [[`eval_modulus(b, cb, a)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_bitwise_and(b, cb, a)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_bitwise_or(b, cb, a)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_bitwise_xor(b, cb, a)`][`void`][Computes `cb ^ a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_modulus(b, cb, B(a))`.] + [`std::overflow_error` if `a` has the value zero.]] [[`eval_modulus(b, a, cb)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_modulus(b, B(a), cb)`.] + [`std::overflow_error` if `a` has the value zero.]] +[[`eval_bitwise_and(b, a)`][`void`][Computes `b &= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_bitwise_and(b, B(a))`][[space]]] +[[`eval_bitwise_and(b, cb, cb2)`][`void`][Computes `cb & cb2` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_bitwise_and(b, cb2)`.][[space]]] +[[`eval_bitwise_and(b, cb, a)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_and(b, cb, B(a))`.][[space]]] [[`eval_bitwise_and(b, a, cb)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_and(b, cb, a)`.][[space]]] +[[`eval_bitwise_or(b, a)`][`void`][Computes `b |= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_bitwise_or(b, B(a))`][[space]]] +[[`eval_bitwise_or(b, cb, cb2)`][`void`][Computes `cb | cb2` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_bitwise_or(b, cb2)`.][[space]]] +[[`eval_bitwise_or(b, cb, a)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_or(b, cb, B(a))`.][[space]]] [[`eval_bitwise_or(b, a, cb)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_or(b, cb, a)`.][[space]]] +[[`eval_bitwise_xor(b, a)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_bitwise_xor(b, B(a))`][[space]]] +[[`eval_bitwise_xor(b, cb, cb2)`][`void`][Computes `cb ^ cb2` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_bitwise_xor(b, cb2)`.][[space]]] +[[`eval_bitwise_xor(b, cb, a)`][`void`][Computes `cb ^ a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_xor(b, cb, B(a))`.][[space]]] [[`eval_bitwise_xor(b, a, cb)`][`void`][Computes `a ^ cb` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists - `B::signed_types`, `B::unsigned_types` or `B::float_types`.]] -[[`eval_left_shift(b, cb, ui)`][`void`][Computes `cb << ui` and stores the result in `b`, only required when `B` is an integer type.]] -[[`eval_right_shift(b, cb, ui)`][`void`][Computes `cb >> ui` and stores the result in `b`, only required when `B` is an integer type.]] -[[`eval_increment(b)`][void][Increments the value of `b` by one.]] -[[`eval_decrement(b)`][void][Decrements the value of `b` by one.]] -[[`eval_is_zero(cb)`][`bool`][Returns `true` if `cb` is zero, otherwise `false`]] -[[`eval_get_sign(cb)`][`int`][Returns a value < zero if `cb` is negative, a value > zero if `cb` is positive, and zero if `cb` is zero.]] -[[`eval_abs(b, cb)`][`void`][Set `b` to the absolute value of `cb`.]] -[[`eval_fabs(b, cb)`][`void`][Set `b` to the absolute value of `cb`.]] -[[`eval_fpclassify(cb)`][`int`][Returns one of the same values returned by `std::fpclassify`. Only required when `B` is an floating-point type.]] -[[`eval_trunc(b, cb)`][`void`][Performs the equivalent operation to `std::trunc` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_round(b, cb)`][`void`][Performs the equivalent operation to `std::round` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_exp(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_log(b, cb)`][`void`][Performs the equivalent operation to `std::log` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_log10(b, cb)`][`void`][Performs the equivalent operation to `std::log10` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_sin(b, cb)`][`void`][Performs the equivalent operation to `std::sin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_cos(b, cb)`][`void`][Performs the equivalent operation to `std::cos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_tan(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_asin(b, cb)`][`void`][Performs the equivalent operation to `std::asin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_acos(b, cb)`][`void`][Performs the equivalent operation to `std::acos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_atan(b, cb)`][`void`][Performs the equivalent operation to `std::atan` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_sinh(b, cb)`][`void`][Performs the equivalent operation to `std::sinh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_cosh(b, cb)`][`void`][Performs the equivalent operation to `std::cosh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_tanh(b, cb)`][`void`][Performs the equivalent operation to `std::tanh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_fmod(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::fmod` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_pow(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::pow` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_atan2(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::atan` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type.]] -[[`eval_qr(cb, cb2, b, b2)`][`void`][Sets `b` to the result of `cb / cb2` and `b2` to the result of `cb % cb2`. Only required when `B` is an integer type.]] -[[`eval_integer_modulus(cb, ui)`][`unsigned`][Returns the result of `cb % ui`. Only required when `B` is an integer type.]] -[[`eval_lsb(cb)`][`unsigned`][Returns the index of the least significant bit that is set. Only required when `B` is an integer type.]] -[[`eval_bit_test(cb, ui)`][`bool`][Returns true if `cb` has bit `ui` set. Only required when `B` is an integer type.]] -[[`eval_bit_set(b, ui)`][`void`][Sets the bit at index `ui` in `b`. Only required when `B` is an integer type.]] -[[`eval_bit_unset(b, ui)`][`void`][Unsets the bit at index `ui` in `b`. Only required when `B` is an integer type.]] -[[`eval_bit_flip(b, ui)`][`void`][Flips the bit at index `ui` in `b`. Only required when `B` is an integer type.]] -[[`eval_gcd(b, cb, cb2)`][`void`][Sets `b` to the greatest common divisor of `cb` and `cb2`. Only required when `B` is an integer type.]] -[[`eval_lcm(b, cb, cb2)`][`void`][Sets `b` to the least common multiple of `cb` and `cb2`. Only required when `B` is an integer type.]] + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_xor(b, cb, a)`.][[space]]] +[[`eval_left_shift(b, cb, ui)`][`void`][Computes `cb << ui` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_left_shift(b, a);`.][[space]]] +[[`eval_right_shift(b, cb, ui)`][`void`][Computes `cb >> ui` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_right_shift(b, a);`.][[space]]] +[[`eval_qr(cb, cb2, b, b2)`][`void`][Sets `b` to the result of `cb / cb2` and `b2` to the result of `cb % cb2`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.] + [`std::overflow_error` if `a` has the value zero.]] +[[`eval_integer_modulus(cb, ui)`][`unsigned`][Returns the result of `cb % ui`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.] + [`std::overflow_error` if `a` has the value zero.]] +[[`eval_lsb(cb)`][`unsigned`][Returns the index of the least significant bit that is set. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_bit_test(cb, ui)`][`bool`][Returns true if `cb` has bit `ui` set. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_bit_set(b, ui)`][`void`][Sets the bit at index `ui` in `b`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_bit_unset(b, ui)`][`void`][Unsets the bit at index `ui` in `b`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_bit_flip(b, ui)`][`void`][Flips the bit at index `ui` in `b`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_gcd(b, cb, cb2)`][`void`][Sets `b` to the greatest common divisor of `cb` and `cb2`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_lcm(b, cb, cb2)`][`void`][Sets `b` to the least common multiple of `cb` and `cb2`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_gcd(b, cb, a)`][`void`][Sets `b` to the greatest common divisor of `cb` and `cb2`. Only required when `B` is an integer type. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + The default version of this function calls `eval_gcd(b, cb, B(a))`.][[space]]] +[[`eval_lcm(b, cb, a)`][`void`][Sets `b` to the least common multiple of `cb` and `cb2`. Only required when `B` is an integer type. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + The default version of this function calls `eval_lcm(b, cb, B(a))`.][[space]]] +[[`eval_gcd(b, a, cb)`][`void`][Sets `b` to the greatest common divisor of `cb` and `a`. Only required when `B` is an integer type. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + The default version of this function calls `eval_gcd(b, cb, a)`.][[space]]] +[[`eval_lcm(b, a, cb)`][`void`][Sets `b` to the least common multiple of `cb` and `a`. Only required when `B` is an integer type. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + The default version of this function calls `eval_lcm(b, cb, a)`.][[space]]] +[[`eval_powm(b, cb, cb2, cb3)`][`void`][Sets `b` to the result of ['(cb^cb2)%cb3]. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_powm(b, cb, cb2, a)`][`void`][Sets `b` to the result of ['(cb^cb2)%a]. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types`. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_powm(b, cb, a, cb2)`][`void`][Sets `b` to the result of ['(cb^a)%cb2]. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types`. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_powm(b, cb, a, a2)`][`void`][Sets `b` to the result of ['(cb^a)%a2]. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types`. + The default version of this function is synthesised from other operations above.][[space]]] + +[[['Sign manipulation:]]] +[[`eval_abs(b, cb)`][`void`][Set `b` to the absolute value of `cb`. + The default version of this functions assigns `cb` to `b`, and then calls `b.negate()` if + `eval_get_sign(cb) < 0`.][[space]]] +[[`eval_fabs(b, cb)`][`void`][Set `b` to the absolute value of `cb`. + The default version of this functions assigns `cb` to `b`, and then calls `b.negate()` if + `eval_get_sign(cb) < 0`.][[space]]] + +[[['Floating point functions:]]] +[[`eval_fpclassify(cb)`][`int`][Returns one of the same values returned by `std::fpclassify`. Only required when `B` is an floating-point type. + The default version of this function will only test for zero `cb`.][[space]]] +[[`eval_trunc(b, cb)`][`void`][Performs the equivalent operation to `std::trunc` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_round(b, cb)`][`void`][Performs the equivalent operation to `std::round` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_exp(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_log(b, cb)`][`void`][Performs the equivalent operation to `std::log` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_log10(b, cb)`][`void`][Performs the equivalent operation to `std::log10` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_sin(b, cb)`][`void`][Performs the equivalent operation to `std::sin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_cos(b, cb)`][`void`][Performs the equivalent operation to `std::cos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_tan(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_asin(b, cb)`][`void`][Performs the equivalent operation to `std::asin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_acos(b, cb)`][`void`][Performs the equivalent operation to `std::acos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_atan(b, cb)`][`void`][Performs the equivalent operation to `std::atan` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_sinh(b, cb)`][`void`][Performs the equivalent operation to `std::sinh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_cosh(b, cb)`][`void`][Performs the equivalent operation to `std::cosh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_tanh(b, cb)`][`void`][Performs the equivalent operation to `std::tanh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_fmod(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::fmod` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_pow(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::pow` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_atan2(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::atan` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] ] -The tables above place no ['throws] requirements on any of the operations. It is up to each type modelling this concept to +When the tables above place no ['throws] requirements on an operation, then it is up to each type modelling this concept to decide when or whether throwing an exception is desirable. However, thrown exceptions should always either be the type, or inherit from the type `std::runtime_error`. For example, a floating point type might choose to throw `std::overflow_error` whenever the result of an operation would be infinite, and `std::underflow_error` whenever it would round to zero. diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 9a4e771b..dd745e04 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -2149,7 +2149,7 @@ void divide_unsigned_helper(cpp_int_backend* if(y == 0) { - BOOST_THROW_EXCEPTION(std::runtime_error("Integer Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Integer Division by zero.")); } // // Find the most significant word of numerator. @@ -2764,66 +2764,6 @@ inline unsigned eval_lsb(const cpp_int_backend::limb_bits; } -template -inline void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) -{ - int shift; - - cpp_int_backend u(a), v(b); - - int s = eval_get_sign(u); - - /* GCD(0,x) := x */ - if(s < 0) - { - u.negate(); - } - else if(s == 0) - { - result = v; - return; - } - s = eval_get_sign(v); - if(s < 0) - { - v.negate(); - } - else if(s == 0) - { - result = u; - return; - } - - /* Let shift := lg K, where K is the greatest power of 2 - dividing both u and v. */ - - unsigned us = eval_lsb(u); - unsigned vs = eval_lsb(v); - shift = (std::min)(us, vs); - eval_right_shift(u, us); - eval_right_shift(v, vs); - - do - { - /* Now u and v are both odd, so diff(u, v) is even. - Let u = min(u, v), v = diff(u, v)/2. */ - if(u.compare(v) > 0) - u.swap(v); - eval_subtract(v, u); - // Termination condition tries not to do a full compare if possible: - if(!v.limbs()[0] && eval_is_zero(v)) - break; - vs = eval_lsb(v); - eval_right_shift(v, vs); - BOOST_ASSERT((v.limbs()[0] & 1)); - BOOST_ASSERT((u.limbs()[0] & 1)); - } - while(true); - - result = u; - eval_left_shift(result, shift); -} - template inline bool eval_bit_test(const cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT { @@ -2884,25 +2824,6 @@ inline void eval_bit_flip(cpp_int_backend& va val.normalize(); } -template -inline void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) -{ - cpp_int_backend t; - eval_gcd(t, a, b); - - if(eval_is_zero(t)) - { - result = static_cast(0); - } - else - { - eval_divide(result, a, t); - eval_multiply(result, b); - } - if(eval_get_sign(result) < 0) - result.negate(); -} - template inline void eval_qr(const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& q, cpp_int_backend& r) BOOST_NOEXCEPT_IF(boost::is_void::value) diff --git a/include/boost/multiprecision/depricated/fixed_int.hpp b/include/boost/multiprecision/depricated/fixed_int.hpp index c12fa3a8..3595f27b 100644 --- a/include/boost/multiprecision/depricated/fixed_int.hpp +++ b/include/boost/multiprecision/depricated/fixed_int.hpp @@ -889,7 +889,7 @@ void divide_unsigned_helper(fixed_int& result, const fixed_int BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& o) { if(!*o.limbs()) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); *result.limbs() /= *o.limbs(); result.sign(result.sign() != o.sign()); } @@ -194,7 +194,7 @@ template BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& o) { if(!*o.limbs()) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); *result.limbs() /= *o.limbs(); } @@ -202,7 +202,7 @@ template BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& o) { if(!*o.limbs()) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); *result.limbs() %= *o.limbs(); result.sign(result.sign()); } diff --git a/include/boost/multiprecision/detail/integer_ops.hpp b/include/boost/multiprecision/detail/integer_ops.hpp index 4103d81b..ad041533 100644 --- a/include/boost/multiprecision/detail/integer_ops.hpp +++ b/include/boost/multiprecision/detail/integer_ops.hpp @@ -38,6 +38,88 @@ inline Integer eval_integer_modulus(const Backend& x, Integer val) return maybe_abs(result); } +template +inline void eval_gcd(B& result, const B& a, const B& b) +{ + using default_ops::eval_lsb; + using default_ops::eval_is_zero; + using default_ops::eval_get_sign; + + int shift; + + B u(a), v(b); + + int s = eval_get_sign(u); + + /* GCD(0,x) := x */ + if(s < 0) + { + u.negate(); + } + else if(s == 0) + { + result = v; + return; + } + s = eval_get_sign(v); + if(s < 0) + { + v.negate(); + } + else if(s == 0) + { + result = u; + return; + } + + /* Let shift := lg K, where K is the greatest power of 2 + dividing both u and v. */ + + unsigned us = eval_lsb(u); + unsigned vs = eval_lsb(v); + shift = (std::min)(us, vs); + eval_right_shift(u, us); + eval_right_shift(v, vs); + + do + { + /* Now u and v are both odd, so diff(u, v) is even. + Let u = min(u, v), v = diff(u, v)/2. */ + if(u.compare(v) > 0) + u.swap(v); + eval_subtract(v, u); + // Termination condition tries not to do a full compare if possible: + if(eval_is_zero(v)) + break; + vs = eval_lsb(v); + eval_right_shift(v, vs); + } + while(true); + + result = u; + eval_left_shift(result, shift); +} + +template +inline void eval_lcm(B& result, const B& a, const B& b) +{ + typedef typename typename mpl::front::type ui_type; + B t; + eval_gcd(t, a, b); + + if(eval_is_zero(t)) + { + result = static_cast(0); + } + else + { + eval_divide(result, a, t); + eval_multiply(result, b); + } + if(eval_get_sign(result) < 0) + result.negate(); +} + } template diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index b8d290f9..6a21bc86 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -570,7 +570,7 @@ template inline void eval_divide(gmp_float& result, const gmp_float& o) { if(eval_is_zero(o)) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpf_div(result.data(), result.data(), o.data()); } template @@ -592,7 +592,7 @@ template inline void eval_divide(gmp_float& result, unsigned long i) { if(i == 0) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpf_div_ui(result.data(), result.data(), i); } template @@ -622,7 +622,7 @@ template inline void eval_divide(gmp_float& result, long i) { if(i == 0) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpf_div_ui(result.data(), result.data(), std::abs(i)); if(i < 0) mpf_neg(result.data(), result.data()); @@ -741,21 +741,21 @@ template inline void eval_divide(gmp_float& a, const gmp_float& x, const gmp_float& y) { if(eval_is_zero(y)) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpf_div(a.data(), x.data(), y.data()); } template inline void eval_divide(gmp_float& a, const gmp_float& x, unsigned long y) { if(y == 0) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpf_div_ui(a.data(), x.data(), y); } template inline void eval_divide(gmp_float& a, const gmp_float& x, long y) { if(y == 0) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); if(y < 0) { mpf_div_ui(a.data(), x.data(), -y); @@ -768,14 +768,14 @@ template inline void eval_divide(gmp_float& a, unsigned long x, const gmp_float& y) { if(eval_is_zero(y)) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpf_ui_div(a.data(), x, y.data()); } template inline void eval_divide(gmp_float& a, long x, const gmp_float& y) { if(eval_is_zero(y)) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); if(x < 0) { mpf_ui_div(a.data(), -x, y.data()); @@ -1278,7 +1278,7 @@ inline void eval_multiply(gmp_int& t, const gmp_int& o) inline void eval_divide(gmp_int& t, const gmp_int& o) { if(eval_is_zero(o)) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpz_tdiv_q(t.data(), t.data(), o.data()); } inline void eval_modulus(gmp_int& t, const gmp_int& o) @@ -1304,7 +1304,7 @@ inline void eval_modulus(gmp_int& t, unsigned long i) inline void eval_divide(gmp_int& t, unsigned long i) { if(i == 0) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpz_tdiv_q_ui(t.data(), t.data(), i); } inline void eval_add(gmp_int& t, long i) @@ -1334,7 +1334,7 @@ inline void eval_modulus(gmp_int& t, long i) inline void eval_divide(gmp_int& t, long i) { if(i == 0) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpz_tdiv_q_ui(t.data(), t.data(), std::abs(i)); if(i < 0) mpz_neg(t.data(), t.data()); @@ -1390,7 +1390,7 @@ inline void eval_multiply(gmp_int& t, const gmp_int& p, const gmp_int& o) inline void eval_divide(gmp_int& t, const gmp_int& p, const gmp_int& o) { if(eval_is_zero(o)) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpz_tdiv_q(t.data(), p.data(), o.data()); } inline void eval_modulus(gmp_int& t, const gmp_int& p, const gmp_int& o) @@ -1416,7 +1416,7 @@ inline void eval_modulus(gmp_int& t, const gmp_int& p, unsigned long i) inline void eval_divide(gmp_int& t, const gmp_int& p, unsigned long i) { if(i == 0) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpz_tdiv_q_ui(t.data(), p.data(), i); } inline void eval_add(gmp_int& t, const gmp_int& p, long i) @@ -1446,7 +1446,7 @@ inline void eval_modulus(gmp_int& t, const gmp_int& p, long i) inline void eval_divide(gmp_int& t, const gmp_int& p, long i) { if(i == 0) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpz_tdiv_q_ui(t.data(), p.data(), std::abs(i)); if(i < 0) mpz_neg(t.data(), t.data()); @@ -1914,7 +1914,7 @@ inline void eval_multiply(gmp_rational& t, const gmp_rational& o) inline void eval_divide(gmp_rational& t, const gmp_rational& o) { if(eval_is_zero(o)) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpq_div(t.data(), t.data(), o.data()); } inline void eval_add(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) @@ -1932,7 +1932,7 @@ inline void eval_multiply(gmp_rational& t, const gmp_rational& p, const gmp_rati inline void eval_divide(gmp_rational& t, const gmp_rational& p, const gmp_rational& o) { if(eval_is_zero(o)) - BOOST_THROW_EXCEPTION(std::runtime_error("Division by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpq_div(t.data(), p.data(), o.data()); } diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index 06fe7eb1..57c4f6d4 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -154,7 +154,7 @@ inline void eval_divide(rational_adapter& result, const rational_ada using default_ops::eval_is_zero; if(eval_is_zero(o)) { - BOOST_THROW_EXCEPTION(std::runtime_error("Divide by zero.")); + BOOST_THROW_EXCEPTION(std::overflow_error("Divide by zero.")); } result.data() /= o.data(); } diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 0068ffde..6eb8e973 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -378,11 +378,17 @@ inline void eval_multiply(tommath_int& t, const tommath_int& o) } inline void eval_divide(tommath_int& t, const tommath_int& o) { + using default_ops::eval_is_zero; tommath_int temp; + if(eval_is_zero(o)) + BOOST_THROW_EXCEPTION(std::overflow_error("Integer division by zero")); detail::check_tommath_result(mp_div(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data(), &temp.data())); } inline void eval_modulus(tommath_int& t, const tommath_int& o) { + using default_ops::eval_is_zero; + if(eval_is_zero(o)) + BOOST_THROW_EXCEPTION(std::overflow_error("Integer division by zero")); bool neg = eval_get_sign(t) < 0; bool neg2 = eval_get_sign(o) < 0; detail::check_tommath_result(mp_mod(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data())); @@ -455,11 +461,17 @@ inline void eval_multiply(tommath_int& t, const tommath_int& p, const tommath_in } inline void eval_divide(tommath_int& t, const tommath_int& p, const tommath_int& o) { + using default_ops::eval_is_zero; tommath_int d; + if(eval_is_zero(o)) + BOOST_THROW_EXCEPTION(std::overflow_error("Integer division by zero")); detail::check_tommath_result(mp_div(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data(), &d.data())); } inline void eval_modulus(tommath_int& t, const tommath_int& p, const tommath_int& o) { + using default_ops::eval_is_zero; + if(eval_is_zero(o)) + BOOST_THROW_EXCEPTION(std::overflow_error("Integer division by zero")); bool neg = eval_get_sign(p) < 0; bool neg2 = eval_get_sign(o) < 0; detail::check_tommath_result(mp_mod(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data())); diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 71e49d19..e15efa6a 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -245,7 +245,7 @@ void test_integer_ops(const boost::mpl::int_ @@ -636,7 +636,7 @@ void test_float_ops(const boost::mpl::int_ Date: Thu, 16 Aug 2012 08:13:51 +0000 Subject: [PATCH 218/256] Big breaking change - make lossy construction explicit. [SVN r80058] --- .../concepts/mp_number_archetypes.hpp | 7 +- .../boost/multiprecision/cpp_dec_float.hpp | 10 + include/boost/multiprecision/cpp_int.hpp | 2 +- .../multiprecision/detail/integer_ops.hpp | 9 + .../boost/multiprecision/detail/no_et_ops.hpp | 60 ++-- .../multiprecision/detail/number_base.hpp | 100 +++--- include/boost/multiprecision/gmp.hpp | 39 ++- include/boost/multiprecision/mpfr.hpp | 23 +- include/boost/multiprecision/number.hpp | 166 +++++++--- .../boost/multiprecision/rational_adapter.hpp | 28 +- test/Jamfile.v2 | 12 + test/compile_fail/conv_fail_1.cpp | 17 + test/compile_fail/conv_fail_10.cpp | 14 + test/compile_fail/conv_fail_11.cpp | 14 + test/compile_fail/conv_fail_12.cpp | 14 + test/compile_fail/conv_fail_13.cpp | 14 + test/compile_fail/conv_fail_14.cpp | 14 + test/compile_fail/conv_fail_15.cpp | 14 + test/compile_fail/conv_fail_16.cpp | 14 + test/compile_fail/conv_fail_17.cpp | 15 + test/compile_fail/conv_fail_18.cpp | 16 + test/compile_fail/conv_fail_19.cpp | 15 + test/compile_fail/conv_fail_2.cpp | 14 + test/compile_fail/conv_fail_20.cpp | 16 + test/compile_fail/conv_fail_21.cpp | 16 + test/compile_fail/conv_fail_22.cpp | 16 + test/compile_fail/conv_fail_23.cpp | 16 + test/compile_fail/conv_fail_24.cpp | 16 + test/compile_fail/conv_fail_25.cpp | 16 + test/compile_fail/conv_fail_26.cpp | 16 + test/compile_fail/conv_fail_27.cpp | 16 + test/compile_fail/conv_fail_28.cpp | 16 + test/compile_fail/conv_fail_29.cpp | 14 + test/compile_fail/conv_fail_3.cpp | 14 + test/compile_fail/conv_fail_30.cpp | 14 + test/compile_fail/conv_fail_31.cpp | 14 + test/compile_fail/conv_fail_32.cpp | 14 + test/compile_fail/conv_fail_33.cpp | 14 + test/compile_fail/conv_fail_34.cpp | 14 + test/compile_fail/conv_fail_35.cpp | 14 + test/compile_fail/conv_fail_36.cpp | 14 + test/compile_fail/conv_fail_37.cpp | 14 + test/compile_fail/conv_fail_38.cpp | 14 + test/compile_fail/conv_fail_39.cpp | 14 + test/compile_fail/conv_fail_4.cpp | 14 + test/compile_fail/conv_fail_40.cpp | 14 + test/compile_fail/conv_fail_41.cpp | 14 + test/compile_fail/conv_fail_42.cpp | 14 + test/compile_fail/conv_fail_43.cpp | 14 + test/compile_fail/conv_fail_44.cpp | 14 + test/compile_fail/conv_fail_5.cpp | 14 + test/compile_fail/conv_fail_6.cpp | 14 + test/compile_fail/conv_fail_7.cpp | 14 + test/compile_fail/conv_fail_8.cpp | 14 + test/compile_fail/conv_fail_9.cpp | 14 + test/math/log1p_expm1_test.cpp | 2 +- test/math/powm1_sqrtp1m1_test.cpp | 2 +- test/math/table_type.hpp | 39 +++ test/math/test_bessel_i.cpp | 2 +- test/math/test_bessel_j.cpp | 2 +- test/math/test_bessel_k.cpp | 2 +- test/math/test_bessel_y.cpp | 2 +- test/math/test_beta.cpp | 2 +- test/math/test_binomial_coeff.cpp | 2 +- test/math/test_carlson.cpp | 2 +- test/math/test_cbrt.cpp | 2 +- test/math/test_digamma.cpp | 2 +- test/math/test_ellint_1.cpp | 2 +- test/math/test_ellint_2.cpp | 2 +- test/math/test_ellint_3.cpp | 2 +- test/math/test_erf.cpp | 2 +- test/math/test_expint.cpp | 2 +- test/math/test_gamma.cpp | 2 +- test/math/test_hermite.cpp | 2 +- test/math/test_ibeta.cpp | 2 +- test/math/test_ibeta_2.cpp | 2 +- test/math/test_ibeta_3.cpp | 2 +- test/math/test_ibeta_4.cpp | 2 +- test/math/test_ibeta_inv_1.cpp | 2 +- test/math/test_ibeta_inv_ab_4.cpp | 2 +- test/math/test_igamma.cpp | 2 +- test/math/test_igamma_inv.cpp | 2 +- test/math/test_igamma_inva.cpp | 2 +- test/math/test_laguerre.cpp | 2 +- test/math/test_legendre.cpp | 2 +- test/math/test_tgamma_ratio.cpp | 2 +- test/math/test_zeta.cpp | 2 +- test/test_acos.cpp | 26 +- test/test_arithmetic.cpp | 292 ++++++++++-------- test/test_asin.cpp | 12 +- test/test_atan.cpp | 4 +- test/test_constants.cpp | 6 +- test/test_cos.cpp | 22 +- test/test_cosh.cpp | 2 +- test/test_cpp_int.cpp | 8 +- test/test_exp.cpp | 22 +- test/test_float_io.cpp | 12 +- test/test_generic_conv.cpp | 12 +- test/test_gmp_conversions.cpp | 6 +- test/test_int_io.cpp | 4 +- test/test_log.cpp | 2 +- test/test_rational_io.cpp | 14 +- test/test_sin.cpp | 20 +- test/test_sinh.cpp | 2 +- test/test_sqrt.cpp | 2 +- test/test_tanh.cpp | 2 +- 106 files changed, 1273 insertions(+), 395 deletions(-) create mode 100644 test/compile_fail/conv_fail_1.cpp create mode 100644 test/compile_fail/conv_fail_10.cpp create mode 100644 test/compile_fail/conv_fail_11.cpp create mode 100644 test/compile_fail/conv_fail_12.cpp create mode 100644 test/compile_fail/conv_fail_13.cpp create mode 100644 test/compile_fail/conv_fail_14.cpp create mode 100644 test/compile_fail/conv_fail_15.cpp create mode 100644 test/compile_fail/conv_fail_16.cpp create mode 100644 test/compile_fail/conv_fail_17.cpp create mode 100644 test/compile_fail/conv_fail_18.cpp create mode 100644 test/compile_fail/conv_fail_19.cpp create mode 100644 test/compile_fail/conv_fail_2.cpp create mode 100644 test/compile_fail/conv_fail_20.cpp create mode 100644 test/compile_fail/conv_fail_21.cpp create mode 100644 test/compile_fail/conv_fail_22.cpp create mode 100644 test/compile_fail/conv_fail_23.cpp create mode 100644 test/compile_fail/conv_fail_24.cpp create mode 100644 test/compile_fail/conv_fail_25.cpp create mode 100644 test/compile_fail/conv_fail_26.cpp create mode 100644 test/compile_fail/conv_fail_27.cpp create mode 100644 test/compile_fail/conv_fail_28.cpp create mode 100644 test/compile_fail/conv_fail_29.cpp create mode 100644 test/compile_fail/conv_fail_3.cpp create mode 100644 test/compile_fail/conv_fail_30.cpp create mode 100644 test/compile_fail/conv_fail_31.cpp create mode 100644 test/compile_fail/conv_fail_32.cpp create mode 100644 test/compile_fail/conv_fail_33.cpp create mode 100644 test/compile_fail/conv_fail_34.cpp create mode 100644 test/compile_fail/conv_fail_35.cpp create mode 100644 test/compile_fail/conv_fail_36.cpp create mode 100644 test/compile_fail/conv_fail_37.cpp create mode 100644 test/compile_fail/conv_fail_38.cpp create mode 100644 test/compile_fail/conv_fail_39.cpp create mode 100644 test/compile_fail/conv_fail_4.cpp create mode 100644 test/compile_fail/conv_fail_40.cpp create mode 100644 test/compile_fail/conv_fail_41.cpp create mode 100644 test/compile_fail/conv_fail_42.cpp create mode 100644 test/compile_fail/conv_fail_43.cpp create mode 100644 test/compile_fail/conv_fail_44.cpp create mode 100644 test/compile_fail/conv_fail_5.cpp create mode 100644 test/compile_fail/conv_fail_6.cpp create mode 100644 test/compile_fail/conv_fail_7.cpp create mode 100644 test/compile_fail/conv_fail_8.cpp create mode 100644 test/compile_fail/conv_fail_9.cpp create mode 100644 test/math/table_type.hpp diff --git a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp index bb2c8678..f06c9577 100644 --- a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp @@ -197,7 +197,12 @@ inline int eval_fpclassify(const mp_number_backend_float_architype& arg) typedef boost::multiprecision::number mp_number_float_architype; -}}} // namespaces +} // namespace + +template<> +struct number_category : public mpl::int_{}; + +}} // namespaces namespace std{ diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index f8115b4a..7232fed8 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -26,6 +26,16 @@ namespace boost{ namespace multiprecision{ namespace backends{ +template +class cpp_dec_float; + +} // namespace + +template +struct number_category > : public mpl::int_{}; + +namespace backends{ + template class cpp_dec_float { diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index dd745e04..8e0a4574 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1943,7 +1943,7 @@ void divide_unsigned_helper(cpp_int_backend* // if(r_order <= y_order) { - if((r_order < y_order) || (r.compare(y) < 0)) + if((r_order < y_order) || (r.compare_unsigned(y) < 0)) { return; } diff --git a/include/boost/multiprecision/detail/integer_ops.hpp b/include/boost/multiprecision/detail/integer_ops.hpp index ad041533..08b66352 100644 --- a/include/boost/multiprecision/detail/integer_ops.hpp +++ b/include/boost/multiprecision/detail/integer_ops.hpp @@ -38,6 +38,11 @@ inline Integer eval_integer_modulus(const Backend& x, Integer val) return maybe_abs(result); } +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4127) +#endif + template inline void eval_gcd(B& result, const B& a, const B& b) { @@ -100,6 +105,10 @@ inline void eval_gcd(B& result, const B& a, const B& b) eval_left_shift(result, shift); } +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + template inline void eval_lcm(B& result, const B& a, const B& b) { diff --git a/include/boost/multiprecision/detail/no_et_ops.hpp b/include/boost/multiprecision/detail/no_et_ops.hpp index 28c7c6d4..23a8b4ac 100644 --- a/include/boost/multiprecision/detail/no_et_ops.hpp +++ b/include/boost/multiprecision/detail/no_et_ops.hpp @@ -40,7 +40,7 @@ inline number operator + (const number& a, const number -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator + (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -50,7 +50,7 @@ inline typename enable_if, number >::type return BOOST_MP_MOVE(result); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator + (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; @@ -71,7 +71,7 @@ inline number operator - (const number& a, const number -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator - (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -81,7 +81,7 @@ inline typename enable_if, number >::type return BOOST_MP_MOVE(result); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator - (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; @@ -102,7 +102,7 @@ inline number operator * (const number& a, const number -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator * (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -112,7 +112,7 @@ inline typename enable_if, number >::type return BOOST_MP_MOVE(result); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator * (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; @@ -133,7 +133,7 @@ inline number operator / (const number& a, const number -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator / (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -143,7 +143,7 @@ inline typename enable_if, number >::type return BOOST_MP_MOVE(result); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator / (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; @@ -164,7 +164,7 @@ inline number operator % (const number& a, const number -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator % (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -174,7 +174,7 @@ inline typename enable_if, number >::type return BOOST_MP_MOVE(result); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator % (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; @@ -195,7 +195,7 @@ inline number operator | (const number& a, const number -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator | (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -205,7 +205,7 @@ inline typename enable_if, number >::type return BOOST_MP_MOVE(result); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator | (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; @@ -226,7 +226,7 @@ inline number operator ^ (const number& a, const number -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator ^ (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -236,7 +236,7 @@ inline typename enable_if, number >::type return BOOST_MP_MOVE(result); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator ^ (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; @@ -257,7 +257,7 @@ inline number operator & (const number& a, const number -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator & (const number& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -267,7 +267,7 @@ inline typename enable_if, number >::type return BOOST_MP_MOVE(result); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator & (const V& a, const number& b) { typedef typename detail::canonical::type canonical_type; @@ -347,7 +347,7 @@ inline number operator + (number&& a, number&& b) return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator + (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -356,7 +356,7 @@ inline typename enable_if, number >::type return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator + (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; @@ -390,7 +390,7 @@ inline number operator - (number&& a, number&& b) return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator - (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -399,7 +399,7 @@ inline typename enable_if, number >::type return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator - (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; @@ -433,7 +433,7 @@ inline number operator * (number&& a, number&& b) return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator * (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -442,7 +442,7 @@ inline typename enable_if, number >::type return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator * (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; @@ -461,7 +461,7 @@ inline number operator / (number&& a, const number return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator / (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -480,7 +480,7 @@ inline number operator % (number&& a, const number return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator % (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -513,7 +513,7 @@ inline number operator | (number&& a, number&& b) return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator | (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -522,7 +522,7 @@ inline typename enable_if, number >::type return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator | (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; @@ -555,7 +555,7 @@ inline number operator ^ (number&& a, number&& b) return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator ^ (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -564,7 +564,7 @@ inline typename enable_if, number >::type return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator ^ (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; @@ -597,7 +597,7 @@ inline number operator & (number&& a, number&& b) return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator & (number&& a, const V& b) { typedef typename detail::canonical::type canonical_type; @@ -606,7 +606,7 @@ inline typename enable_if, number >::type return static_cast&&>(a); } template -inline typename enable_if, number >::type +inline typename enable_if >, number >::type operator & (const V& a, number&& b) { typedef typename detail::canonical::type canonical_type; diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp index 29f5379a..1c1267df 100644 --- a/include/boost/multiprecision/detail/number_base.hpp +++ b/include/boost/multiprecision/detail/number_base.hpp @@ -9,6 +9,7 @@ #include #include #include +#include #include namespace boost{ namespace multiprecision{ @@ -36,6 +37,14 @@ struct is_mp_number_expression : public mpl::false_ {}; template struct is_mp_number_expression > : public mpl::true_ {}; +template +struct is_compatible_arithmetic_type + : public mpl::bool_< + is_convertible::value + && !is_mp_number::value + && !is_mp_number_expression::value> +{}; + namespace detail{ // // Workaround for missing abs(long long) on some compilers: @@ -67,7 +76,7 @@ struct has_enough_bits template struct canonical_imp { - typedef Val type; + typedef typename decay::type type; }; template struct canonical_imp > @@ -604,13 +613,13 @@ inline detail::expression, number, number >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if >, detail::expression, V > >::type operator + (const number& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator + (const V& a, const number& b) { return detail::expression >(a, b); @@ -634,13 +643,13 @@ inline detail::expression, detail::expression >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if::result_type>, detail::expression, V > >::type operator + (const detail::expression& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if::result_type>, detail::expression > >::type operator + (const V& a, const detail::expression& b) { return detail::expression >(a, b); @@ -673,17 +682,23 @@ inline detail::expression, number, number >(b, a.left_ref()); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator + (const detail::expression >& a, const V& b) { return detail::expression >(b, a.left_ref()); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator + (const V& a, const detail::expression >& b) { return detail::expression, number >(a, b.left_ref()); } +template +inline detail::expression, number > > + operator + (const detail::expression >& a, const detail::expression >& b) +{ + return detail::expression, number > >(detail::expression, number >(a.left_ref(), b.left_ref())); +} // // Subtraction: // @@ -694,13 +709,13 @@ inline detail::expression, number, number >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if >, detail::expression, V > >::type operator - (const number& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator - (const V& a, const number& b) { return detail::expression >(a, b); @@ -724,13 +739,13 @@ inline detail::expression, detail::expression >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if::result_type>, detail::expression, V > >::type operator - (const detail::expression& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if::result_type>, detail::expression > >::type operator - (const V& a, const detail::expression& b) { return detail::expression >(a, b); @@ -765,13 +780,13 @@ inline detail::expression, number >(b, a.left_ref())); } template -inline typename enable_if, detail::expression, V > > >::type +inline typename enable_if >, detail::expression, V > > >::type operator - (const detail::expression >& a, const V& b) { return detail::expression, V > >(detail::expression, V >(a.left_ref(), b)); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator - (const V& a, const detail::expression >& b) { return detail::expression >(a, b.left_ref()); @@ -786,13 +801,13 @@ inline detail::expression, number, number >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if >, detail::expression, V > >::type operator * (const number& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator * (const V& a, const number& b) { return detail::expression >(a, b); @@ -816,13 +831,13 @@ inline detail::expression, detail::expression >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if::result_type>, detail::expression, V > >::type operator * (const detail::expression& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if::result_type>, detail::expression > >::type operator * (const V& a, const detail::expression& b) { return detail::expression >(a, b); @@ -859,14 +874,14 @@ inline detail::expression, number >(b, a.left_ref())); } template -inline typename enable_if, detail::expression, V > > >::type +inline typename enable_if >, detail::expression, V > > >::type operator * (const detail::expression >& a, const V& b) { return detail::expression, V > > ( detail::expression, V >(a.left_ref(), b)); } template -inline typename enable_if, detail::expression, V > > >::type +inline typename enable_if >, detail::expression, V > > >::type operator * (const V& a, const detail::expression >& b) { return detail::expression, V > >( @@ -882,13 +897,13 @@ inline detail::expression, number, number >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if >, detail::expression, V > >::type operator / (const number& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator / (const V& a, const number& b) { return detail::expression >(a, b); @@ -912,13 +927,13 @@ inline detail::expression, detail::expression >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if::result_type>, detail::expression, V > >::type operator / (const detail::expression& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if::result_type>, detail::expression > >::type operator / (const V& a, const detail::expression& b) { return detail::expression >(a, b); @@ -955,14 +970,14 @@ inline detail::expression, number >(a.left_ref(), b)); } template -inline typename enable_if, detail::expression, V > > >::type +inline typename enable_if >, detail::expression, V > > >::type operator / (const detail::expression >& a, const V& b) { return detail::expression, V > >( detail::expression, V>(a.left_ref(), b)); } template -inline typename enable_if, detail::expression > > >::type +inline typename enable_if >, detail::expression > > >::type operator / (const V& a, const detail::expression >& b) { return detail::expression > >( @@ -978,13 +993,13 @@ inline detail::expression, number, number >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if >, detail::expression, V > >::type operator % (const number& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator % (const V& a, const number& b) { return detail::expression >(a, b); @@ -1008,13 +1023,13 @@ inline detail::expression, detail::expression >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if::result_type>, detail::expression, V > >::type operator % (const detail::expression& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if::result_type>, detail::expression > >::type operator % (const V& a, const detail::expression& b) { return detail::expression >(a, b); @@ -1059,13 +1074,13 @@ inline detail::expression, numbe return detail::expression, number >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if >, detail::expression, V > >::type operator & (const number& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator & (const V& a, const number& b) { return detail::expression >(a, b); @@ -1089,13 +1104,13 @@ inline detail::expression, detail::expression >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if::result_type>, detail::expression, V > >::type operator & (const detail::expression& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if::result_type>, detail::expression > >::type operator & (const V& a, const detail::expression& b) { return detail::expression >(a, b); @@ -1110,13 +1125,13 @@ inline detail::expression, number return detail::expression, number >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if >, detail::expression, V > >::type operator| (const number& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator| (const V& a, const number& b) { return detail::expression >(a, b); @@ -1140,13 +1155,13 @@ inline detail::expression, detail::expression >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if::result_type>, detail::expression, V > >::type operator| (const detail::expression& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if::result_type>, detail::expression > >::type operator| (const V& a, const detail::expression& b) { return detail::expression >(a, b); @@ -1161,13 +1176,13 @@ inline detail::expression, numbe return detail::expression, number >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if >, detail::expression, V > >::type operator^ (const number& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if >, detail::expression > >::type operator^ (const V& a, const number& b) { return detail::expression >(a, b); @@ -1191,13 +1206,13 @@ inline detail::expression, detail::expression >(a, b); } template -inline typename enable_if, detail::expression, V > >::type +inline typename enable_if::result_type>, detail::expression, V > >::type operator^ (const detail::expression& a, const V& b) { return detail::expression, V >(a, b); } template -inline typename enable_if, detail::expression > >::type +inline typename enable_if::result_type>, detail::expression > >::type operator^ (const V& a, const detail::expression& b) { return detail::expression >(a, b); @@ -1208,6 +1223,7 @@ inline typename enable_if, detail::expression -struct number_category : public mpl::int_ {}; +struct number_category : public mpl::int_::is_integer ? number_kind_integer : (std::numeric_limits::max_exponent ? number_kind_floating_point : number_kind_unknown)> {}; template struct number_category > : public number_category{}; template diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 6a21bc86..cfdea145 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -29,7 +29,19 @@ namespace backends{ template struct gmp_float; +struct gmp_int; +struct gmp_rational; +} // namespace backends + +template<> +struct number_category : public mpl::int_{}; +template<> +struct number_category : public mpl::int_{}; +template +struct number_category > : public mpl::int_{}; + +namespace backends{ // // Within this file, the only functions we mark as noexcept are those that manipulate // (but don't create) an mpf_t. All other types may allocate at pretty much any time @@ -394,21 +406,21 @@ struct gmp_float : public detail::gmp_float_imp gmp_float& operator=(const gmp_float& o); gmp_float& operator=(const gmp_int& o); gmp_float& operator=(const gmp_rational& o); - gmp_float& operator=(const mpf_t& val) BOOST_NOEXCEPT + gmp_float& operator=(const mpf_t val) BOOST_NOEXCEPT { if(this->m_data[0]._mp_d == 0) mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); mpf_set(this->m_data, val); return *this; } - gmp_float& operator=(const mpz_t& val) BOOST_NOEXCEPT + gmp_float& operator=(const mpz_t val) BOOST_NOEXCEPT { if(this->m_data[0]._mp_d == 0) mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); mpf_set_z(this->m_data, val); return *this; } - gmp_float& operator=(const mpq_t& val) BOOST_NOEXCEPT + gmp_float& operator=(const mpq_t val) BOOST_NOEXCEPT { if(this->m_data[0]._mp_d == 0) mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); @@ -485,21 +497,21 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> } gmp_float& operator=(const gmp_int& o); gmp_float& operator=(const gmp_rational& o); - gmp_float& operator=(const mpf_t& val) + gmp_float& operator=(const mpf_t val) { if(this->m_data[0]._mp_d == 0) mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); mpf_set(this->m_data, val); return *this; } - gmp_float& operator=(const mpz_t& val) + gmp_float& operator=(const mpz_t val) { if(this->m_data[0]._mp_d == 0) mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); mpf_set_z(this->m_data, val); return *this; } - gmp_float& operator=(const mpq_t& val) + gmp_float& operator=(const mpq_t val) { if(this->m_data[0]._mp_d == 0) mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); @@ -1130,21 +1142,21 @@ struct gmp_int mpz_set_ui(m_data, 0); return *this; } - gmp_int& operator=(const mpf_t& val) + gmp_int& operator=(const mpf_t val) { if(m_data[0]._mp_d == 0) mpz_init(this->m_data); mpz_set_f(this->m_data, val); return *this; } - gmp_int& operator=(const mpz_t& val) + gmp_int& operator=(const mpz_t val) { if(m_data[0]._mp_d == 0) mpz_init(this->m_data); mpz_set(this->m_data, val); return *this; } - gmp_int& operator=(const mpq_t& val) + gmp_int& operator=(const mpq_t val) { if(m_data[0]._mp_d == 0) mpz_init(this->m_data); @@ -1789,14 +1801,14 @@ struct gmp_rational mpq_set_z(m_data, o.data()); return *this; } - gmp_rational& operator=(const mpq_t& o) + gmp_rational& operator=(const mpq_t o) { if(m_data[0]._mp_den._mp_d == 0) mpq_init(m_data); mpq_set(m_data, o); return *this; } - gmp_rational& operator=(const mpz_t& o) + gmp_rational& operator=(const mpz_t o) { if(m_data[0]._mp_den._mp_d == 0) mpq_init(m_data); @@ -2077,11 +2089,6 @@ struct component_type > typedef number type; }; -template<> -struct number_category : public mpl::int_{}; -template<> -struct number_category : public mpl::int_{}; - typedef number > mpf_float_50; typedef number > mpf_float_100; typedef number > mpf_float_500; diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 859e51b3..ce8209a6 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -23,6 +23,13 @@ namespace backends{ template struct mpfr_float_backend; +} // namespace backends + +template +struct number_category > : public mpl::int_{}; + +namespace backends{ + namespace detail{ inline long get_default_precision() { return 50; } @@ -387,22 +394,22 @@ struct mpfr_float_backend : public detail::mpfr_float_imp *static_cast*>(this) = v; return *this; } - mpfr_float_backend& operator=(const mpfr_t& val)BOOST_NOEXCEPT + mpfr_float_backend& operator=(const mpfr_t val)BOOST_NOEXCEPT { mpfr_set(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpf_t& val)BOOST_NOEXCEPT + mpfr_float_backend& operator=(const mpf_t val)BOOST_NOEXCEPT { mpfr_set_f(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpz_t& val)BOOST_NOEXCEPT + mpfr_float_backend& operator=(const mpz_t val)BOOST_NOEXCEPT { mpfr_set_z(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpq_t& val)BOOST_NOEXCEPT + mpfr_float_backend& operator=(const mpq_t val)BOOST_NOEXCEPT { mpfr_set_q(this->m_data, val, GMP_RNDN); return *this; @@ -508,22 +515,22 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> *static_cast*>(this) = v; return *this; } - mpfr_float_backend& operator=(const mpfr_t& val) BOOST_NOEXCEPT + mpfr_float_backend& operator=(const mpfr_t val) BOOST_NOEXCEPT { mpfr_set(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpf_t& val) BOOST_NOEXCEPT + mpfr_float_backend& operator=(const mpf_t val) BOOST_NOEXCEPT { mpfr_set_f(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpz_t& val) BOOST_NOEXCEPT + mpfr_float_backend& operator=(const mpz_t val) BOOST_NOEXCEPT { mpfr_set_z(this->m_data, val, GMP_RNDN); return *this; } - mpfr_float_backend& operator=(const mpq_t& val) BOOST_NOEXCEPT + mpfr_float_backend& operator=(const mpq_t val) BOOST_NOEXCEPT { mpfr_set_q(this->m_data, val, GMP_RNDN); return *this; diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index 15096180..40af6746 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -21,6 +21,7 @@ #include #include #include +#include #include // stream operators #include // EOF @@ -43,18 +44,38 @@ public: BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& e) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(e.m_backend){} template BOOST_FORCEINLINE number(V v, typename enable_if_c< - (boost::is_arithmetic::value || is_same::value || is_convertible::value) - && !is_convertible::type, Backend>::value >::type* = 0) + (boost::is_arithmetic::value || is_same::value || is_convertible::value) + && !is_convertible::type, Backend>::value + && !detail::is_restricted_conversion::type, Backend>::value + >::type* = 0) { m_backend = canonical_value(v); } template BOOST_FORCEINLINE BOOST_CONSTEXPR number(V v, typename enable_if_c< - (boost::is_arithmetic::value || is_same::value || is_convertible::value) - && is_convertible::type, Backend>::value >::type* = 0) + (boost::is_arithmetic::value || is_same::value || is_convertible::value) + && is_convertible::type, Backend>::value + && !detail::is_restricted_conversion::type, Backend>::value + >::type* = 0) : m_backend(canonical_value(v)) {} BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} + template + explicit BOOST_FORCEINLINE number(V v, typename enable_if_c< + (boost::is_arithmetic::value || is_same::value || is_convertible::value) + && !is_convertible::type, Backend>::value + && detail::is_restricted_conversion::type, Backend>::value + >::type* = 0) + { + m_backend = canonical_value(v); + } + template + explicit BOOST_FORCEINLINE BOOST_CONSTEXPR number(V v, typename enable_if_c< + (boost::is_arithmetic::value || is_same::value || is_convertible::value) + && is_convertible::type, Backend>::value + && detail::is_restricted_conversion::type, Backend>::value + >::type* = 0) + : m_backend(canonical_value(v)) {} /* // // This conflicts with component based initialization (for rational and complex types) @@ -71,12 +92,25 @@ public: BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} template - BOOST_FORCEINLINE number(const number& val, typename enable_if >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) + BOOST_FORCEINLINE number(const number& val, typename enable_if_c<(boost::is_convertible::value && !detail::is_restricted_conversion::value)>::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) { m_backend = val.backend(); } template - number(const number& val, typename disable_if >::type* = 0) + number(const number& val, typename enable_if_c<(!boost::is_convertible::value && !detail::is_restricted_conversion::value)>::type* = 0) + { + // + // Attempt a generic interconvertion: + // + detail::generic_interconvert(backend(), val.backend(), number_category(), number_category()); + } + template + explicit BOOST_FORCEINLINE number(const number& val, typename enable_if_c<(boost::is_convertible::value && detail::is_restricted_conversion::value)>::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) + { + m_backend = val.backend(); + } + template + explicit number(const number& val, typename enable_if_c<(!boost::is_convertible::value && detail::is_restricted_conversion::value)>::type* = 0) { // // Attempt a generic interconvertion: @@ -102,27 +136,40 @@ public: : m_backend(v){} template - number& operator=(const detail::expression& e) + typename enable_if::result_type, self_type>, number&>::type operator=(const detail::expression& e) { typedef typename is_same::result_type>::type tag_type; do_assign(e, tag_type()); return *this; } - + template + number& assign(const detail::expression& e) + { + typedef typename is_same::result_type>::type tag_type; + do_assign(e, tag_type()); + return *this; + } +/* BOOST_FORCEINLINE number& operator=(const number& e) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = e.m_backend; return *this; } - + */ template - BOOST_FORCEINLINE typename enable_if, is_same, is_convertible >, number& >::type + BOOST_FORCEINLINE typename enable_if, number& >::type operator=(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval::type>())) { m_backend = canonical_value(v); return *this; } - + template + BOOST_FORCEINLINE number& assign(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval::type>())) + { + m_backend = canonical_value(v); + return *this; + } + /* template BOOST_FORCEINLINE typename enable_if, mpl::not_, is_same, is_convertible > > >, number& >::type operator=(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) @@ -130,7 +177,6 @@ public: m_backend = v; return *this; } - template BOOST_FORCEINLINE number& operator=(const number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { @@ -145,6 +191,14 @@ public: m_backend = v.backend(); return *this; } + template + BOOST_FORCEINLINE typename enable_if, number& >::type + assign(const number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) + { + m_backend = v.backend(); + return *this; + } + */ template typename disable_if, number& >::type @@ -156,9 +210,19 @@ public: detail::generic_interconvert(backend(), v.backend(), number_category(), number_category()); return *this; } + template + typename disable_if, number& >::type + assign(const number& v) + { + // + // Attempt a generic interconvertion: + // + detail::generic_interconvert(backend(), v.backend(), number_category(), number_category()); + return *this; + } template - number(const detail::expression& e) + number(const detail::expression& e, typename enable_if_c::result_type, self_type>::value>::type* = 0) { *this = e; } @@ -196,7 +260,7 @@ public: } template - typename enable_if, number& >::type + typename enable_if, number& >::type operator+=(const V& v) { using default_ops::eval_add; @@ -210,24 +274,24 @@ public: return *this; } - template - number& operator-=(const detail::expression& e) + template + number& operator-=(const detail::expression& e) { // Create a copy if e contains this: if(contains_self(e)) { self_type temp(e); - do_subtract(temp, detail::terminal()); + do_subtract(detail::expression(temp), detail::terminal()); } else { - do_subtract(e, typename Exp::tag_type()); + do_subtract(e, typename detail::expression::tag_type()); } return *this; } template - typename enable_if, number& >::type + typename enable_if, number& >::type operator-=(const V& v) { using default_ops::eval_subtract; @@ -242,8 +306,8 @@ public: return *this; } - template - number& operator*=(const detail::expression& e) + template + number& operator*=(const detail::expression& e) { // Create a temporary if the RHS references *this, but not // if we're just doing an x *= x; @@ -254,13 +318,13 @@ public: } else { - do_multiplies(e, typename Exp::tag_type()); + do_multiplies(e, typename detail::expression::tag_type()); } return *this; } template - typename enable_if, number& >::type + typename enable_if, number& >::type operator*=(const V& v) { using default_ops::eval_multiply; @@ -274,24 +338,24 @@ public: do_modulus(detail::expression(e), detail::terminal()); return *this; } - template - number& operator%=(const detail::expression& e) + template + number& operator%=(const detail::expression& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); // Create a temporary if the RHS references *this: if(contains_self(e)) { self_type temp(e); - do_modulus(temp, detail::terminal()); + do_modulus(detail::expression(temp), detail::terminal()); } else { - do_modulus(e, typename Exp::tag_type()); + do_modulus(e, typename detail::expression::tag_type()); } return *this; } template - typename enable_if, number& >::type + typename enable_if, number& >::type operator%=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The modulus operation is only valid for integer types"); @@ -362,8 +426,8 @@ public: return *this; } - template - number& operator/=(const detail::expression& e) + template + number& operator/=(const detail::expression& e) { // Create a temporary if the RHS references *this: if(contains_self(e)) @@ -373,13 +437,13 @@ public: } else { - do_divide(e, typename Exp::tag_type()); + do_divide(e, typename detail::expression::tag_type()); } return *this; } template - BOOST_FORCEINLINE typename enable_if, number& >::type + BOOST_FORCEINLINE typename enable_if, number& >::type operator/=(const V& v) { using default_ops::eval_divide; @@ -394,8 +458,8 @@ public: return *this; } - template - number& operator&=(const detail::expression& e) + template + number& operator&=(const detail::expression& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); // Create a temporary if the RHS references *this, but not @@ -403,17 +467,17 @@ public: if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_bitwise_and(temp, detail::terminal()); + do_bitwise_and(detail::expression(temp), detail::terminal()); } else { - do_bitwise_and(e, typename Exp::tag_type()); + do_bitwise_and(e, typename detail::expression::tag_type()); } return *this; } template - BOOST_FORCEINLINE typename enable_if, number& >::type + BOOST_FORCEINLINE typename enable_if, number& >::type operator&=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); @@ -429,8 +493,8 @@ public: return *this; } - template - number& operator|=(const detail::expression& e) + template + number& operator|=(const detail::expression& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); // Create a temporary if the RHS references *this, but not @@ -438,17 +502,17 @@ public: if(contains_self(e) && !is_self(e)) { self_type temp(e); - do_bitwise_or(temp, detail::terminal()); + do_bitwise_or(detail::expression(temp), detail::terminal()); } else { - do_bitwise_or(e, typename Exp::tag_type()); + do_bitwise_or(e, typename detail::expression::tag_type()); } return *this; } template - BOOST_FORCEINLINE typename enable_if, number& >::type + BOOST_FORCEINLINE typename enable_if, number& >::type operator|=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); @@ -464,24 +528,24 @@ public: return *this; } - template - number& operator^=(const detail::expression& e) + template + number& operator^=(const detail::expression& e) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); if(contains_self(e)) { self_type temp(e); - do_bitwise_xor(temp, detail::terminal()); + do_bitwise_xor(detail::expression(temp), detail::terminal()); } else { - do_bitwise_xor(e, typename Exp::tag_type()); + do_bitwise_xor(e, typename detail::expression::tag_type()); } return *this; } template - BOOST_FORCEINLINE typename enable_if, number& >::type + BOOST_FORCEINLINE typename enable_if, number& >::type operator^=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); @@ -1535,6 +1599,8 @@ private: BOOST_FORCEINLINE BOOST_CONSTEXPR bool is_realy_self(const self_type& v)const BOOST_NOEXCEPT{ return &v == this; } static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& canonical_value(const self_type& v) BOOST_NOEXCEPT { return v.m_backend; } + template + static BOOST_FORCEINLINE BOOST_CONSTEXPR const B2& canonical_value(const number& v) BOOST_NOEXCEPT { return v.backend(); } template static BOOST_FORCEINLINE BOOST_CONSTEXPR typename detail::canonical::type canonical_value(const V& v) BOOST_NOEXCEPT { return static_cast::type>(v); } static BOOST_FORCEINLINE typename detail::canonical::type canonical_value(const std::string& v) BOOST_NOEXCEPT { return v.c_str(); } @@ -1583,7 +1649,7 @@ inline std::istream& operator >> (std::istream& is, number> s; - r = s; + r.assign(s); return is; } @@ -1613,7 +1679,7 @@ inline std::istream& operator >> (std::istream& is, rational> (std::istream& is, rational - typename enable_if, rational_adapter&>::type operator = (Arithmetic i) + template + typename enable_if, rational_adapter&>::type operator = (Int i) { m_value = i; return *this; } + template + typename enable_if, rational_adapter&>::type operator = (Float i) + { + int e; + Float f = std::frexp(i, &e); + f = std::ldexp(f, std::numeric_limits::digits); + e -= std::numeric_limits::digits; + integer_type num(f); + integer_type denom(1u); + if(e > 0) + { + num <<= e; + } + else if(e < 0) + { + denom <<= -e; + } + m_value.assign(num, denom); + return *this; + } rational_adapter& operator = (const char* s) { std::string s1; @@ -74,7 +94,7 @@ struct rational_adapter s1.append(1, c); ++s; } - v1 = s1; + v1.assign(s1); s1.erase(); if(c == '/') { @@ -86,7 +106,7 @@ struct rational_adapter s1.append(1, c); ++s; } - v2 = s1; + v2.assign(s1); } else v2 = 1; diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index abb83aa9..0acca17a 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -698,6 +698,14 @@ run test_rational_io.cpp gmp release # Otherwise runtime is slow : test_rational_io_mpz ; +run test_rational_io.cpp + : # command line + : # input files + : # requirements + TEST_CPP_INT + release # Otherwise runtime is slow + : test_rational_io_cpp_int ; + run test_generic_conv.cpp : # command line : # input files @@ -792,6 +800,10 @@ if $(enable-specfun) } } +for local source in [ glob compile_fail/*.cpp ] +{ + compile-fail $(source) ; +} if ! $(disable-concepts) { diff --git a/test/compile_fail/conv_fail_1.cpp b/test/compile_fail/conv_fail_1.cpp new file mode 100644 index 00000000..c5edc3b0 --- /dev/null +++ b/test/compile_fail/conv_fail_1.cpp @@ -0,0 +1,17 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +void foo(cpp_int i) +{ +} + +int main() +{ + foo(2.3); // conversion from float is explicit +} diff --git a/test/compile_fail/conv_fail_10.cpp b/test/compile_fail/conv_fail_10.cpp new file mode 100644 index 00000000..d4376a2b --- /dev/null +++ b/test/compile_fail/conv_fail_10.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i -= 2.3; +} diff --git a/test/compile_fail/conv_fail_11.cpp b/test/compile_fail/conv_fail_11.cpp new file mode 100644 index 00000000..b07a8b89 --- /dev/null +++ b/test/compile_fail/conv_fail_11.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i *= 2.3; +} diff --git a/test/compile_fail/conv_fail_12.cpp b/test/compile_fail/conv_fail_12.cpp new file mode 100644 index 00000000..fbaf8fae --- /dev/null +++ b/test/compile_fail/conv_fail_12.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i /= 2.3; +} diff --git a/test/compile_fail/conv_fail_13.cpp b/test/compile_fail/conv_fail_13.cpp new file mode 100644 index 00000000..1d705e7f --- /dev/null +++ b/test/compile_fail/conv_fail_13.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i %= 2.3; +} diff --git a/test/compile_fail/conv_fail_14.cpp b/test/compile_fail/conv_fail_14.cpp new file mode 100644 index 00000000..54b86232 --- /dev/null +++ b/test/compile_fail/conv_fail_14.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i |= 2.3; +} diff --git a/test/compile_fail/conv_fail_15.cpp b/test/compile_fail/conv_fail_15.cpp new file mode 100644 index 00000000..e225a870 --- /dev/null +++ b/test/compile_fail/conv_fail_15.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i ^= 2.3; +} diff --git a/test/compile_fail/conv_fail_16.cpp b/test/compile_fail/conv_fail_16.cpp new file mode 100644 index 00000000..0ba8c25b --- /dev/null +++ b/test/compile_fail/conv_fail_16.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i &= 2.3; +} diff --git a/test/compile_fail/conv_fail_17.cpp b/test/compile_fail/conv_fail_17.cpp new file mode 100644 index 00000000..0649a64d --- /dev/null +++ b/test/compile_fail/conv_fail_17.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(a); +} diff --git a/test/compile_fail/conv_fail_18.cpp b/test/compile_fail/conv_fail_18.cpp new file mode 100644 index 00000000..4335d975 --- /dev/null +++ b/test/compile_fail/conv_fail_18.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(2); + i = a; +} diff --git a/test/compile_fail/conv_fail_19.cpp b/test/compile_fail/conv_fail_19.cpp new file mode 100644 index 00000000..2315252e --- /dev/null +++ b/test/compile_fail/conv_fail_19.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(a + b); +} diff --git a/test/compile_fail/conv_fail_2.cpp b/test/compile_fail/conv_fail_2.cpp new file mode 100644 index 00000000..79ffff2f --- /dev/null +++ b/test/compile_fail/conv_fail_2.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i == 2.3; +} diff --git a/test/compile_fail/conv_fail_20.cpp b/test/compile_fail/conv_fail_20.cpp new file mode 100644 index 00000000..24a63fa2 --- /dev/null +++ b/test/compile_fail/conv_fail_20.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i = a * b; +} diff --git a/test/compile_fail/conv_fail_21.cpp b/test/compile_fail/conv_fail_21.cpp new file mode 100644 index 00000000..8c845f10 --- /dev/null +++ b/test/compile_fail/conv_fail_21.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i += a * b; +} diff --git a/test/compile_fail/conv_fail_22.cpp b/test/compile_fail/conv_fail_22.cpp new file mode 100644 index 00000000..d35e837e --- /dev/null +++ b/test/compile_fail/conv_fail_22.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i -= a * b; +} diff --git a/test/compile_fail/conv_fail_23.cpp b/test/compile_fail/conv_fail_23.cpp new file mode 100644 index 00000000..3e5a9f53 --- /dev/null +++ b/test/compile_fail/conv_fail_23.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i *= a * b; +} diff --git a/test/compile_fail/conv_fail_24.cpp b/test/compile_fail/conv_fail_24.cpp new file mode 100644 index 00000000..a2581052 --- /dev/null +++ b/test/compile_fail/conv_fail_24.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i /= a * b; +} diff --git a/test/compile_fail/conv_fail_25.cpp b/test/compile_fail/conv_fail_25.cpp new file mode 100644 index 00000000..694ee712 --- /dev/null +++ b/test/compile_fail/conv_fail_25.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i %= a * b; +} diff --git a/test/compile_fail/conv_fail_26.cpp b/test/compile_fail/conv_fail_26.cpp new file mode 100644 index 00000000..0df397f4 --- /dev/null +++ b/test/compile_fail/conv_fail_26.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i &= a * b; +} diff --git a/test/compile_fail/conv_fail_27.cpp b/test/compile_fail/conv_fail_27.cpp new file mode 100644 index 00000000..3995389d --- /dev/null +++ b/test/compile_fail/conv_fail_27.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i |= a * b; +} diff --git a/test/compile_fail/conv_fail_28.cpp b/test/compile_fail/conv_fail_28.cpp new file mode 100644 index 00000000..4133aa14 --- /dev/null +++ b/test/compile_fail/conv_fail_28.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i ^= a * b; +} diff --git a/test/compile_fail/conv_fail_29.cpp b/test/compile_fail/conv_fail_29.cpp new file mode 100644 index 00000000..854118fb --- /dev/null +++ b/test/compile_fail/conv_fail_29.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i + 3.3; +} diff --git a/test/compile_fail/conv_fail_3.cpp b/test/compile_fail/conv_fail_3.cpp new file mode 100644 index 00000000..0fe89320 --- /dev/null +++ b/test/compile_fail/conv_fail_3.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i != 2.3; +} diff --git a/test/compile_fail/conv_fail_30.cpp b/test/compile_fail/conv_fail_30.cpp new file mode 100644 index 00000000..4ba78fe5 --- /dev/null +++ b/test/compile_fail/conv_fail_30.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 + i; +} diff --git a/test/compile_fail/conv_fail_31.cpp b/test/compile_fail/conv_fail_31.cpp new file mode 100644 index 00000000..56a14828 --- /dev/null +++ b/test/compile_fail/conv_fail_31.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 - i; +} diff --git a/test/compile_fail/conv_fail_32.cpp b/test/compile_fail/conv_fail_32.cpp new file mode 100644 index 00000000..1769185f --- /dev/null +++ b/test/compile_fail/conv_fail_32.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i - 3.3; +} diff --git a/test/compile_fail/conv_fail_33.cpp b/test/compile_fail/conv_fail_33.cpp new file mode 100644 index 00000000..36758318 --- /dev/null +++ b/test/compile_fail/conv_fail_33.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i * 3.3; +} diff --git a/test/compile_fail/conv_fail_34.cpp b/test/compile_fail/conv_fail_34.cpp new file mode 100644 index 00000000..7d178c48 --- /dev/null +++ b/test/compile_fail/conv_fail_34.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 * i; +} diff --git a/test/compile_fail/conv_fail_35.cpp b/test/compile_fail/conv_fail_35.cpp new file mode 100644 index 00000000..67f6bdc8 --- /dev/null +++ b/test/compile_fail/conv_fail_35.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 / i; +} diff --git a/test/compile_fail/conv_fail_36.cpp b/test/compile_fail/conv_fail_36.cpp new file mode 100644 index 00000000..3b175be8 --- /dev/null +++ b/test/compile_fail/conv_fail_36.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i / 3.3; +} diff --git a/test/compile_fail/conv_fail_37.cpp b/test/compile_fail/conv_fail_37.cpp new file mode 100644 index 00000000..164db0b9 --- /dev/null +++ b/test/compile_fail/conv_fail_37.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i % 3.3; +} diff --git a/test/compile_fail/conv_fail_38.cpp b/test/compile_fail/conv_fail_38.cpp new file mode 100644 index 00000000..a905e20e --- /dev/null +++ b/test/compile_fail/conv_fail_38.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 % i; +} diff --git a/test/compile_fail/conv_fail_39.cpp b/test/compile_fail/conv_fail_39.cpp new file mode 100644 index 00000000..fa495d70 --- /dev/null +++ b/test/compile_fail/conv_fail_39.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 & i; +} diff --git a/test/compile_fail/conv_fail_4.cpp b/test/compile_fail/conv_fail_4.cpp new file mode 100644 index 00000000..6bd72119 --- /dev/null +++ b/test/compile_fail/conv_fail_4.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i <= 2.3; +} diff --git a/test/compile_fail/conv_fail_40.cpp b/test/compile_fail/conv_fail_40.cpp new file mode 100644 index 00000000..f3ccf05b --- /dev/null +++ b/test/compile_fail/conv_fail_40.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i & 3.3; +} diff --git a/test/compile_fail/conv_fail_41.cpp b/test/compile_fail/conv_fail_41.cpp new file mode 100644 index 00000000..67c30945 --- /dev/null +++ b/test/compile_fail/conv_fail_41.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i | 3.3; +} diff --git a/test/compile_fail/conv_fail_42.cpp b/test/compile_fail/conv_fail_42.cpp new file mode 100644 index 00000000..6ebe5f5b --- /dev/null +++ b/test/compile_fail/conv_fail_42.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 | i; +} diff --git a/test/compile_fail/conv_fail_43.cpp b/test/compile_fail/conv_fail_43.cpp new file mode 100644 index 00000000..cac2c020 --- /dev/null +++ b/test/compile_fail/conv_fail_43.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 ^ i; +} diff --git a/test/compile_fail/conv_fail_44.cpp b/test/compile_fail/conv_fail_44.cpp new file mode 100644 index 00000000..32a27593 --- /dev/null +++ b/test/compile_fail/conv_fail_44.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i ^ 3.3; +} diff --git a/test/compile_fail/conv_fail_5.cpp b/test/compile_fail/conv_fail_5.cpp new file mode 100644 index 00000000..23f49022 --- /dev/null +++ b/test/compile_fail/conv_fail_5.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i >= 2.3; +} diff --git a/test/compile_fail/conv_fail_6.cpp b/test/compile_fail/conv_fail_6.cpp new file mode 100644 index 00000000..78fea0f7 --- /dev/null +++ b/test/compile_fail/conv_fail_6.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i > 2.3; +} diff --git a/test/compile_fail/conv_fail_7.cpp b/test/compile_fail/conv_fail_7.cpp new file mode 100644 index 00000000..af4286f4 --- /dev/null +++ b/test/compile_fail/conv_fail_7.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i < 2.3; +} diff --git a/test/compile_fail/conv_fail_8.cpp b/test/compile_fail/conv_fail_8.cpp new file mode 100644 index 00000000..d741c613 --- /dev/null +++ b/test/compile_fail/conv_fail_8.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i = 2.3; +} diff --git a/test/compile_fail/conv_fail_9.cpp b/test/compile_fail/conv_fail_9.cpp new file mode 100644 index 00000000..29ce8b7b --- /dev/null +++ b/test/compile_fail/conv_fail_9.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i += 2.3; +} diff --git a/test/math/log1p_expm1_test.cpp b/test/math/log1p_expm1_test.cpp index 1754094c..4a53064b 100644 --- a/test/math/log1p_expm1_test.cpp +++ b/test/math/log1p_expm1_test.cpp @@ -46,7 +46,7 @@ #include #include -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #include "libs/math/test/log1p_expm1_test.hpp" diff --git a/test/math/powm1_sqrtp1m1_test.cpp b/test/math/powm1_sqrtp1m1_test.cpp index c3853651..db2621eb 100644 --- a/test/math/powm1_sqrtp1m1_test.cpp +++ b/test/math/powm1_sqrtp1m1_test.cpp @@ -46,7 +46,7 @@ #include #include -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #include "libs/math/test/powm1_sqrtp1m1_test.hpp" diff --git a/test/math/table_type.hpp b/test/math/table_type.hpp new file mode 100644 index 00000000..c3b5cee3 --- /dev/null +++ b/test/math/table_type.hpp @@ -0,0 +1,39 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_TABLE_TYPE + +#include +#include + +struct string_table_entry +{ +private: + const char* m_data; +public: + string_table_entry(const char* p) : m_data(p) {} + + template + operator T () const + { + return static_cast(m_data); + } +}; + +inline std::ostream& operator << (std::ostream& os, string_table_entry const & what) +{ + return os << static_cast(what); +} + +template +struct table_type > +{ + typedef string_table_entry type; +}; + +#define SC_(x) string_table_entry(BOOST_STRINGIZE(x)) + +#endif + diff --git a/test/math/test_bessel_i.cpp b/test/math/test_bessel_i.cpp index 3532f397..c9e7bb3c 100644 --- a/test/math/test_bessel_i.cpp +++ b/test/math/test_bessel_i.cpp @@ -41,7 +41,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#define SC_(x) static_cast::type>(BOOST_STRINGIZE(x)) #include #include "libs/math/test/test_bessel_i.hpp" diff --git a/test/math/test_bessel_j.cpp b/test/math/test_bessel_j.cpp index 931422aa..14c32412 100644 --- a/test/math/test_bessel_j.cpp +++ b/test/math/test_bessel_j.cpp @@ -41,7 +41,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #include #include "libs/math/test/test_bessel_j.hpp" diff --git a/test/math/test_bessel_k.cpp b/test/math/test_bessel_k.cpp index 856180e9..46ce61b9 100644 --- a/test/math/test_bessel_k.cpp +++ b/test/math/test_bessel_k.cpp @@ -42,7 +42,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #include #include "libs/math/test/test_bessel_k.hpp" diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp index dd9c99dd..2672d8bd 100644 --- a/test/math/test_bessel_y.cpp +++ b/test/math/test_bessel_y.cpp @@ -41,7 +41,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #include #include "libs/math/test/test_bessel_y.hpp" diff --git a/test/math/test_beta.cpp b/test/math/test_beta.cpp index b69c1808..39409cb7 100644 --- a/test/math/test_beta.cpp +++ b/test/math/test_beta.cpp @@ -41,7 +41,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #include #include "libs/math/test/test_beta.hpp" diff --git a/test/math/test_binomial_coeff.cpp b/test/math/test_binomial_coeff.cpp index 146b1af2..daae89b2 100644 --- a/test/math/test_binomial_coeff.cpp +++ b/test/math/test_binomial_coeff.cpp @@ -41,7 +41,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #include #include "libs/math/test/test_binomial_coeff.hpp" diff --git a/test/math/test_carlson.cpp b/test/math/test_carlson.cpp index 1aacc108..30f96116 100644 --- a/test/math/test_carlson.cpp +++ b/test/math/test_carlson.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_cbrt.cpp b/test/math/test_cbrt.cpp index b896d6d7..156e0dd6 100644 --- a/test/math/test_cbrt.cpp +++ b/test/math/test_cbrt.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_digamma.cpp b/test/math/test_digamma.cpp index 2d18eaa6..16653f83 100644 --- a/test/math/test_digamma.cpp +++ b/test/math/test_digamma.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_ellint_1.cpp b/test/math/test_ellint_1.cpp index c7da569a..b74c0f56 100644 --- a/test/math/test_ellint_1.cpp +++ b/test/math/test_ellint_1.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_ellint_2.cpp b/test/math/test_ellint_2.cpp index c07bddac..9529a21c 100644 --- a/test/math/test_ellint_2.cpp +++ b/test/math/test_ellint_2.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_ellint_3.cpp b/test/math/test_ellint_3.cpp index 9d3d6904..986b864b 100644 --- a/test/math/test_ellint_3.cpp +++ b/test/math/test_ellint_3.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_erf.cpp b/test/math/test_erf.cpp index 1b77e3a4..77db0a60 100644 --- a/test/math/test_erf.cpp +++ b/test/math/test_erf.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_expint.cpp b/test/math/test_expint.cpp index 0dbffc58..90b77e79 100644 --- a/test/math/test_expint.cpp +++ b/test/math/test_expint.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_gamma.cpp b/test/math/test_gamma.cpp index 44ca68be..a4df3f37 100644 --- a/test/math/test_gamma.cpp +++ b/test/math/test_gamma.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_hermite.cpp b/test/math/test_hermite.cpp index 271b8138..277e96a7 100644 --- a/test/math/test_hermite.cpp +++ b/test/math/test_hermite.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_ibeta.cpp b/test/math/test_ibeta.cpp index b78358f2..e48fb900 100644 --- a/test/math/test_ibeta.cpp +++ b/test/math/test_ibeta.cpp @@ -37,7 +37,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #define TEST_DATA 1 diff --git a/test/math/test_ibeta_2.cpp b/test/math/test_ibeta_2.cpp index 7dcc2fd8..212056a7 100644 --- a/test/math/test_ibeta_2.cpp +++ b/test/math/test_ibeta_2.cpp @@ -37,7 +37,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #define TEST_DATA 2 diff --git a/test/math/test_ibeta_3.cpp b/test/math/test_ibeta_3.cpp index d1f0d132..8bb2a9a9 100644 --- a/test/math/test_ibeta_3.cpp +++ b/test/math/test_ibeta_3.cpp @@ -37,7 +37,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #define TEST_DATA 3 diff --git a/test/math/test_ibeta_4.cpp b/test/math/test_ibeta_4.cpp index f71c117f..d4b224ff 100644 --- a/test/math/test_ibeta_4.cpp +++ b/test/math/test_ibeta_4.cpp @@ -37,7 +37,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #define TEST_DATA 4 diff --git a/test/math/test_ibeta_inv_1.cpp b/test/math/test_ibeta_inv_1.cpp index 88fc6184..54cb44eb 100644 --- a/test/math/test_ibeta_inv_1.cpp +++ b/test/math/test_ibeta_inv_1.cpp @@ -37,7 +37,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #define TEST_DATA 4 diff --git a/test/math/test_ibeta_inv_ab_4.cpp b/test/math/test_ibeta_inv_ab_4.cpp index e00fb612..e9916b96 100644 --- a/test/math/test_ibeta_inv_ab_4.cpp +++ b/test/math/test_ibeta_inv_ab_4.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #define TEST_DATA 4 diff --git a/test/math/test_igamma.cpp b/test/math/test_igamma.cpp index 429f1f40..50aff1c5 100644 --- a/test/math/test_igamma.cpp +++ b/test/math/test_igamma.cpp @@ -37,7 +37,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #include #include "libs/math/test/test_igamma.hpp" diff --git a/test/math/test_igamma_inv.cpp b/test/math/test_igamma_inv.cpp index 1bf31054..697b58fd 100644 --- a/test/math/test_igamma_inv.cpp +++ b/test/math/test_igamma_inv.cpp @@ -37,7 +37,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_igamma_inva.cpp b/test/math/test_igamma_inva.cpp index 09633434..8ff4e6d4 100644 --- a/test/math/test_igamma_inva.cpp +++ b/test/math/test_igamma_inva.cpp @@ -37,7 +37,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_laguerre.cpp b/test/math/test_laguerre.cpp index fe309c88..8f70b1ca 100644 --- a/test/math/test_laguerre.cpp +++ b/test/math/test_laguerre.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_legendre.cpp b/test/math/test_legendre.cpp index e3b26c51..7ec607ac 100644 --- a/test/math/test_legendre.cpp +++ b/test/math/test_legendre.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_tgamma_ratio.cpp b/test/math/test_tgamma_ratio.cpp index 7657e325..931ffe3c 100644 --- a/test/math/test_tgamma_ratio.cpp +++ b/test/math/test_tgamma_ratio.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/math/test_zeta.cpp b/test/math/test_zeta.cpp index 0c7976cd..1d2184ce 100644 --- a/test/math/test_zeta.cpp +++ b/test/math/test_zeta.cpp @@ -36,7 +36,7 @@ #include #endif -#define SC_(x) BOOST_STRINGIZE(x) +#include "table_type.hpp" #define TEST_UDT #include diff --git a/test/test_acos.cpp b/test/test_acos.cpp index b4dcc828..97cc96d2 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -53,21 +53,21 @@ void test() // static const boost::array, 13> exact_data = {{ - {{ 0.5, "1.04719755119659774615421446109316762806572313312503527365831486410260546876206966620934494178070568932738269550442743555" }}, - {{ 0.25, "1.31811607165281796574566425464604046984639096659071471685354851741333314266208327690226867044304393238598144034722708676" }}, - {{0.75, "0.722734247813415611178377352641333362025218486424440267626754132583707381914630264964827610939101303690078815991333621490" }}, - {{1 - std::ldexp(1.0, -20), "0.00138106804176241718210883847756746694048570648553426714212025111150044290934710742282266738617709904634187850607042604204" }}, - {{std::ldexp(1.0, -20), "1.57079537312058021283676140197495835299636605165647561806789944133748780804448843729970624018104090863783682329820313127" }}, - {{1, "0" }}, + {{ 0.5, static_cast("1.04719755119659774615421446109316762806572313312503527365831486410260546876206966620934494178070568932738269550442743555") }}, + {{ 0.25, static_cast("1.31811607165281796574566425464604046984639096659071471685354851741333314266208327690226867044304393238598144034722708676") }}, + {{0.75, static_cast("0.722734247813415611178377352641333362025218486424440267626754132583707381914630264964827610939101303690078815991333621490") }}, + {{1 - std::ldexp(1.0, -20), static_cast("0.00138106804176241718210883847756746694048570648553426714212025111150044290934710742282266738617709904634187850607042604204") }}, + {{std::ldexp(1.0, -20), static_cast("1.57079537312058021283676140197495835299636605165647561806789944133748780804448843729970624018104090863783682329820313127") }}, + {{1, static_cast("0") }}, - {{0, "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332" }}, + {{0, static_cast("1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332") }}, - {{ -0.5, "2.09439510239319549230842892218633525613144626625007054731662972820521093752413933241868988356141137865476539100885487110" }}, - {{ -0.25, "1.82347658193697527271697912863346241435077843278439110412139607489448326362412572172576615489907313559616664616605521989" }}, - {{-0.75, "2.41885840577637762728426603063816952217195091295066555334819045972410902437157873366320721440301576429206927052194868516" }}, - {{-1 + std::ldexp(1.0, -20), "3.14021158554803082128053454480193541725668369288957155383282434119631596337686189120521215795593996893580620800721188061" }}, - {{-std::ldexp(1.0, -20), "1.57079728046921302562588198130454453120080334771863020290704515097032859824172056132832858516107615934431126321507917538" }}, - {{-1, "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230665" }}, + {{ -0.5, static_cast("2.09439510239319549230842892218633525613144626625007054731662972820521093752413933241868988356141137865476539100885487110") }}, + {{ -0.25, static_cast("1.82347658193697527271697912863346241435077843278439110412139607489448326362412572172576615489907313559616664616605521989") }}, + {{-0.75, static_cast("2.41885840577637762728426603063816952217195091295066555334819045972410902437157873366320721440301576429206927052194868516") }}, + {{-1 + std::ldexp(1.0, -20), static_cast("3.14021158554803082128053454480193541725668369288957155383282434119631596337686189120521215795593996893580620800721188061") }}, + {{-std::ldexp(1.0, -20), static_cast("1.57079728046921302562588198130454453120080334771863020290704515097032859824172056132832858516107615934431126321507917538") }}, + {{-1, static_cast("3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230665") }}, }}; unsigned max_err = 0; for(unsigned k = 0; k < exact_data.size(); k++) diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index e15efa6a..99c1bb8b 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -64,16 +64,17 @@ #if defined(TEST_CPP_INT) || defined(TEST_CPP_INT_BR) #include #endif + +template +struct is_boost_rational : public boost::mpl::false_{}; + #if defined(TEST_TOMMATH_BOOST_RATIONAL) || defined(TEST_MPZ_BOOST_RATIONAL) #include #define NO_MIXED_OPS template -bool is_boost_rational(const boost::rational&) -{ - return true; -} +struct is_boost_rational > : public boost::mpl::true_{}; namespace boost{ namespace multiprecision{ @@ -138,7 +139,11 @@ struct is_twos_complement_integer : public boost #define BOOST_TEST_EQUAL(a, b) BOOST_TEST((a) == (b)) template -void test_comparisons(Val a, Val b) +void test_comparisons(Val, Val, const boost::mpl::false_) +{} + +template +void test_comparisons(Val a, Val b, const boost::mpl::true_) { Real r1(a); Real r2(b); @@ -222,14 +227,8 @@ void test_complement(Real, Real, Real, const boost::mpl::false_&) template void test_integer_ops(const T&){} -template -bool is_boost_rational(const T&) -{ - return false; -} - template -void test_integer_ops(const boost::mpl::int_&) +void test_rational(const boost::mpl::true_&) { Real a(2); a /= 3; @@ -240,16 +239,29 @@ void test_integer_ops(const boost::mpl::int_> b; + BOOST_CHECK_EQUAL(a, b); +} + +template +void test_rational(const boost::mpl::false_&) +{ + Real a(2); + a /= 3; + BOOST_TEST(numerator(a) == 2); + BOOST_TEST(denominator(a) == 3); + Real b(4); + b /= 6; + BOOST_TEST(a == b); + + BOOST_CHECK_THROW(Real(a / 0), std::overflow_error); + BOOST_CHECK_THROW(Real("3.14"), std::runtime_error); + b = Real("2/3"); + BOOST_CHECK_EQUAL(a, b); // // Check IO code: // @@ -259,6 +271,12 @@ void test_integer_ops(const boost::mpl::int_ +void test_integer_ops(const boost::mpl::int_&) +{ + test_rational(is_boost_rational()); +} + template void test_integer_ops(const boost::mpl::int_&) { @@ -661,6 +679,16 @@ void test_negative_mixed(boost::mpl::true_ const&) if(std::numeric_limits::is_specialized && !std::numeric_limits::is_signed) return; typedef typename lexical_cast_target_type::type target_type; + typedef typename boost::mpl::if_< + boost::is_convertible, + typename boost::mpl::if_c::value && (sizeof(Num) < sizeof(int)), int, Num>::type, + Real + >::type cast_type; + typedef typename boost::mpl::if_< + boost::is_convertible, + Num, + Real + >::type simple_cast_type; std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; Num n1 = -static_cast(1uLL << (std::numeric_limits::digits - 1)); Num n2 = -1; @@ -668,22 +696,22 @@ void test_negative_mixed(boost::mpl::true_ const&) Num n4 = -20; Num n5 = -8; - test_comparisons(n1, n2); - test_comparisons(n1, n3); - test_comparisons(n3, n1); - test_comparisons(n2, n1); - test_comparisons(n1, n1); - test_comparisons(n3, n3); + test_comparisons(n1, n2, boost::is_convertible()); + test_comparisons(n1, n3, boost::is_convertible()); + test_comparisons(n3, n1, boost::is_convertible()); + test_comparisons(n2, n1, boost::is_convertible()); + test_comparisons(n1, n1, boost::is_convertible()); + test_comparisons(n3, n3, boost::is_convertible()); // Default construct: - BOOST_TEST(Real(n1) == n1); - BOOST_TEST(Real(n2) == n2); - BOOST_TEST(Real(n3) == n3); - BOOST_TEST(Real(n4) == n4); - BOOST_TEST(n1 == Real(n1)); - BOOST_TEST(n2 == Real(n2)); - BOOST_TEST(n3 == Real(n3)); - BOOST_TEST(n4 == Real(n4)); + BOOST_TEST(Real(n1) == static_cast(n1)); + BOOST_TEST(Real(n2) == static_cast(n2)); + BOOST_TEST(Real(n3) == static_cast(n3)); + BOOST_TEST(Real(n4) == static_cast(n4)); + BOOST_TEST(static_cast(n1) == Real(n1)); + BOOST_TEST(static_cast(n2) == Real(n2)); + BOOST_TEST(static_cast(n3) == Real(n3)); + BOOST_TEST(static_cast(n4) == Real(n4)); BOOST_TEST(Real(n1).template convert_to() == n1); BOOST_TEST(Real(n2).template convert_to() == n2); BOOST_TEST(Real(n3).template convert_to() == n3); @@ -709,54 +737,54 @@ void test_negative_mixed(boost::mpl::true_ const&) BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, f)), 0); // Assignment: Real r(0); - BOOST_TEST(r != n1); - r = n1; - BOOST_TEST(r == n1); - r = n2; - BOOST_TEST(r == n2); - r = n3; - BOOST_TEST(r == n3); - r = n4; - BOOST_TEST(r == n4); + BOOST_TEST(r != static_cast(n1)); + r = static_cast(n1); + BOOST_TEST(r == static_cast(n1)); + r = static_cast(n2); + BOOST_TEST(r == static_cast(n2)); + r = static_cast(n3); + BOOST_TEST(r == static_cast(n3)); + r = static_cast(n4); + BOOST_TEST(r == static_cast(n4)); // Addition: - r = n2; - BOOST_TEST(r + n4 == n2 + n4); - BOOST_TEST(Real(r + n4) == n2 + n4); - r += n4; - BOOST_TEST(r == n2 + n4); + r = static_cast(n2); + BOOST_TEST(r + static_cast(n4) == static_cast(n2 + n4)); + BOOST_TEST(Real(r + static_cast(n4)) == static_cast(n2 + n4)); + r += static_cast(n4); + BOOST_TEST(r == static_cast(n2 + n4)); // subtraction: - r = n4; - BOOST_TEST(r - n5 == n4 - n5); - BOOST_TEST(Real(r - n5) == n4 - n5); - r -= n5; - BOOST_TEST(r == n4 - n5); + r = static_cast(n4); + BOOST_TEST(r - static_cast(n5) == static_cast(n4 - n5)); + BOOST_TEST(Real(r - static_cast(n5)) == static_cast(n4 - n5)); + r -= static_cast(n5); + BOOST_TEST(r == static_cast(n4 - n5)); // Multiplication: - r = n2; - BOOST_TEST(r * n4 == n2 * n4); - BOOST_TEST(Real(r * n4) == n2 * n4); - r *= n4; - BOOST_TEST(r == n2 * n4); + r = static_cast(n2); + BOOST_TEST(r * static_cast(n4) == static_cast(n2 * n4)); + BOOST_TEST(Real(r * static_cast(n4)) == static_cast(n2 * n4)); + r *= static_cast(n4); + BOOST_TEST(r == static_cast(n2 * n4)); // Division: - r = n1; - BOOST_TEST(r / n5 == n1 / n5); - BOOST_TEST(Real(r / n5) == n1 / n5); - r /= n5; - BOOST_TEST(r == n1 / n5); + r = static_cast(n1); + BOOST_TEST(r / static_cast(n5) == static_cast(n1 / n5)); + BOOST_TEST(Real(r / static_cast(n5)) == static_cast(n1 / n5)); + r /= static_cast(n5); + BOOST_TEST(r == static_cast(n1 / n5)); // // Extra cases for full coverage: // - r = Real(n4) + n5; - BOOST_TEST(r == n4 + n5); - r = n4 + Real(n5); - BOOST_TEST(r == n4 + n5); - r = Real(n4) - n5; - BOOST_TEST(r == n4 - n5); - r = n4 - Real(n5); - BOOST_TEST(r == n4 - n5); - r = n4 * Real(n5); - BOOST_TEST(r == n4 * n5); - r = (4 * n4) / Real(4); - BOOST_TEST(r == n4); + r = Real(n4) + static_cast(n5); + BOOST_TEST(r == static_cast(n4 + n5)); + r = static_cast(n4) + Real(n5); + BOOST_TEST(r == static_cast(n4 + n5)); + r = Real(n4) - static_cast(n5); + BOOST_TEST(r == static_cast(n4 - n5)); + r = static_cast(n4) - Real(n5); + BOOST_TEST(r == static_cast(n4 - n5)); + r = static_cast(n4) * Real(n5); + BOOST_TEST(r == static_cast(n4 * n5)); + r = static_cast(4 * n4) / Real(4); + BOOST_TEST(r == static_cast(n4)); } template @@ -768,6 +796,16 @@ template void test_mixed() { typedef typename lexical_cast_target_type::type target_type; + typedef typename boost::mpl::if_< + boost::is_convertible, + typename boost::mpl::if_c::value && (sizeof(Num) < sizeof(int)), int, Num>::type, + Real + >::type cast_type; + typedef typename boost::mpl::if_< + boost::is_convertible, + Num, + Real + >::type simple_cast_type; if(std::numeric_limits::digits < std::numeric_limits::digits) return; @@ -779,18 +817,18 @@ void test_mixed() Num n4 = 20; Num n5 = 8; - test_comparisons(n1, n2); - test_comparisons(n1, n3); - test_comparisons(n1, n1); - test_comparisons(n3, n1); - test_comparisons(n2, n1); - test_comparisons(n3, n3); + test_comparisons(n1, n2, boost::is_convertible()); + test_comparisons(n1, n3, boost::is_convertible()); + test_comparisons(n1, n1, boost::is_convertible()); + test_comparisons(n3, n1, boost::is_convertible()); + test_comparisons(n2, n1, boost::is_convertible()); + test_comparisons(n3, n3, boost::is_convertible()); // Default construct: - BOOST_TEST(Real(n1) == n1); - BOOST_TEST(Real(n2) == n2); - BOOST_TEST(Real(n3) == n3); - BOOST_TEST(Real(n4) == n4); + BOOST_TEST(Real(n1) == static_cast(n1)); + BOOST_TEST(Real(n2) == static_cast(n2)); + BOOST_TEST(Real(n3) == static_cast(n3)); + BOOST_TEST(Real(n4) == static_cast(n4)); BOOST_TEST(Real(n1).template convert_to() == n1); BOOST_TEST(Real(n2).template convert_to() == n2); BOOST_TEST(Real(n3).template convert_to() == n3); @@ -801,10 +839,10 @@ void test_mixed() BOOST_TEST(static_cast(Real(n3)) == n3); BOOST_TEST(static_cast(Real(n4)) == n4); #endif - BOOST_TEST(n1 == Real(n1)); - BOOST_TEST(n2 == Real(n2)); - BOOST_TEST(n3 == Real(n3)); - BOOST_TEST(n4 == Real(n4)); + BOOST_TEST(static_cast(n1) == Real(n1)); + BOOST_TEST(static_cast(n2) == Real(n2)); + BOOST_TEST(static_cast(n3) == Real(n3)); + BOOST_TEST(static_cast(n4) == Real(n4)); #if defined(TEST_MPFR) || defined(TEST_MPFR_50) Num tol = 10 * std::numeric_limits::epsilon(); #else @@ -820,50 +858,50 @@ void test_mixed() BOOST_TEST_CLOSE(n4, boost::lexical_cast(Real(n4).str(0, f)), 0); // Assignment: Real r(0); - BOOST_TEST(r != n1); - r = n1; - BOOST_TEST(r == n1); - r = n2; - BOOST_TEST(r == n2); - r = n3; - BOOST_TEST(r == n3); - r = n4; - BOOST_TEST(r == n4); + BOOST_TEST(r != static_cast(n1)); + r = static_cast(n1); + BOOST_TEST(r == static_cast(n1)); + r = static_cast(n2); + BOOST_TEST(r == static_cast(n2)); + r = static_cast(n3); + BOOST_TEST(r == static_cast(n3)); + r = static_cast(n4); + BOOST_TEST(r == static_cast(n4)); // Addition: - r = n2; - BOOST_TEST(r + n4 == n2 + n4); - BOOST_TEST(Real(r + n4) == n2 + n4); - r += n4; - BOOST_TEST(r == n2 + n4); + r = static_cast(n2); + BOOST_TEST(r + static_cast(n4) == static_cast(n2 + n4)); + BOOST_TEST(Real(r + static_cast(n4)) == static_cast(n2 + n4)); + r += static_cast(n4); + BOOST_TEST(r == static_cast(n2 + n4)); // subtraction: - r = n4; - BOOST_TEST(r - n5 == n4 - n5); - BOOST_TEST(Real(r - n5) == n4 - n5); - r -= n5; - BOOST_TEST(r == n4 - n5); + r = static_cast(n4); + BOOST_TEST(r - static_cast(n5) == static_cast(n4 - n5)); + BOOST_TEST(Real(r - static_cast(n5)) == static_cast(n4 - n5)); + r -= static_cast(n5); + BOOST_TEST(r == static_cast(n4 - n5)); // Multiplication: - r = n2; - BOOST_TEST(r * n4 == n2 * n4); - BOOST_TEST(Real(r * n4) == n2 * n4); - r *= n4; - BOOST_TEST(r == n2 * n4); + r = static_cast(n2); + BOOST_TEST(r * static_cast(n4) == static_cast(n2 * n4)); + BOOST_TEST(Real(r * static_cast(n4)) == static_cast(n2 * n4)); + r *= static_cast(n4); + BOOST_TEST(r == static_cast(n2 * n4)); // Division: - r = n1; - BOOST_TEST(r / n5 == n1 / n5); - BOOST_TEST(Real(r / n5) == n1 / n5); - r /= n5; - BOOST_TEST(r == n1 / n5); + r = static_cast(n1); + BOOST_TEST(r / static_cast(n5) == static_cast(n1 / n5)); + BOOST_TEST(Real(r / static_cast(n5)) == static_cast(n1 / n5)); + r /= static_cast(n5); + BOOST_TEST(r == static_cast(n1 / n5)); // // special cases for full coverage: // - r = n5 + Real(n4); - BOOST_TEST(r == n4 + n5); - r = n4 - Real(n5); - BOOST_TEST(r == n4 - n5); - r = n4 * Real(n5); - BOOST_TEST(r == n4 * n5); - r = (4 * n4) / Real(4); - BOOST_TEST(r == n4); + r = static_cast(n5) + Real(n4); + BOOST_TEST(r == static_cast(n4 + n5)); + r = static_cast(n4) - Real(n5); + BOOST_TEST(r == static_cast(n4 - n5)); + r = static_cast(n4) * Real(n5); + BOOST_TEST(r == static_cast(n4 * n5)); + r = static_cast(4 * n4) / Real(4); + BOOST_TEST(r == static_cast(n4)); test_negative_mixed(boost::mpl::bool_::is_signed>()); } diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 271172fe..2b56e062 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -53,12 +53,12 @@ void test() // static const boost::array, 6> exact_data = {{ - {{ 0.5, "0.523598775598298873077107230546583814032861566562517636829157432051302734381034833104672470890352844663691347752213717775" }}, - {{ 0.25, "0.252680255142078653485657436993710972252193733096838193633923778740575060481021222411748742228014601605092602909414066566" }}, - {{0.75, "0.848062078981481008052944338998418080073366213263112642860718163570200821228474234349189801731957230300995227265307531834" }}, - {{std::ldexp(1.0, -20), "9.53674316406394560289664793089102218648031077292419572854816420395098616062014311172490017625353237219958438022056661501e-7" }}, - {{ 1 - std::ldexp(1.0, -20), "1.56941525875313420204921285316218397515809899320201864334535204504240776023375739189119474528488143494473216475057072728" }}, - {{ 1, "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064" }}, + {{ 0.5, static_cast("0.523598775598298873077107230546583814032861566562517636829157432051302734381034833104672470890352844663691347752213717775") }}, + {{ 0.25, static_cast("0.252680255142078653485657436993710972252193733096838193633923778740575060481021222411748742228014601605092602909414066566") }}, + {{0.75, static_cast("0.848062078981481008052944338998418080073366213263112642860718163570200821228474234349189801731957230300995227265307531834") }}, + {{std::ldexp(1.0, -20), static_cast("9.53674316406394560289664793089102218648031077292419572854816420395098616062014311172490017625353237219958438022056661501e-7") }}, + {{ 1 - std::ldexp(1.0, -20), static_cast("1.56941525875313420204921285316218397515809899320201864334535204504240776023375739189119474528488143494473216475057072728") }}, + {{ 1, static_cast("1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064") }}, }}; unsigned max_err = 0; for(unsigned k = 0; k < exact_data.size(); k++) diff --git a/test/test_atan.cpp b/test/test_atan.cpp index 1b28a395..5e139fdf 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -123,7 +123,7 @@ void test() "1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017412671058533891074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730174305227163324106696803630124570637195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138", }}; - T arg = "1e-100"; + T arg = static_cast("1e-100"); unsigned max_err = 0; for(unsigned k = 0; k < data.size(); k++) @@ -149,7 +149,7 @@ void test() // // And again, but test all the phases of atan2: // - arg = "1e-100"; + arg = static_cast("1e-100"); unsigned err; for(unsigned k = 0; k < data.size(); k++) { diff --git a/test/test_constants.cpp b/test/test_constants.cpp index 4e72ca11..770b8721 100644 --- a/test/test_constants.cpp +++ b/test/test_constants.cpp @@ -172,13 +172,13 @@ void test() typedef typename T::backend_type backend_type; T num, expect; num.backend() = boost::multiprecision::default_ops::get_constant_pi(); - expect = pi; + expect = static_cast(pi); BOOST_CHECK_CLOSE_FRACTION(num, expect, std::numeric_limits::epsilon() * (is_mpfr(num) ? 1200 : 2)); num.backend() = boost::multiprecision::default_ops::get_constant_ln2(); - expect = ln2; + expect = static_cast(ln2); BOOST_CHECK_CLOSE_FRACTION(num, expect, std::numeric_limits::epsilon() * (is_mpfr(num) ? 30 : 1)); num.backend() = boost::multiprecision::default_ops::get_constant_e(); - expect = e; + expect = static_cast(e); BOOST_CHECK_CLOSE_FRACTION(num, expect, std::numeric_limits::epsilon() * (is_mpfr(num) ? 2 : 1)); } diff --git a/test/test_cos.cpp b/test/test_cos.cpp index 36488b1b..e429d06b 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -155,7 +155,7 @@ void test() boost::uintmax_t max_err = 0; for(unsigned k = 0; k < data.size(); k++) { - static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + static const T euler_gamma = static_cast("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); T val = cos(euler_gamma * ((100 * k) - 5000)); T e = relative_error(val, T(data[k])); unsigned err = e.template convert_to(); @@ -225,12 +225,12 @@ void test() "0.09655529472977379853549858833033074225823562054271495313739665642376685099661084023094270272485976247900824483810911634635819558334630910267353320029261330296977292720266655308513559530586843550229208517388789783011887450865488554143475302590353915732321663418057567573042594801866258948380684000769091353165879953111046260532796891917772727185993569684246844052518121013717183610828519193371796413317", }}; - T half_pi = "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064"; + T half_pi = static_cast("1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064"); max_err = 0; for(unsigned k = 0; k < near_one.size(); k++) { - static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + static const T euler_gamma = static_cast("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); T val = cos(half_pi - (euler_gamma + k) / 523); T e = relative_error(val, T(near_one[k])); unsigned err = e.template convert_to(); @@ -251,14 +251,14 @@ void test() // static const boost::array, 8> exact_data = {{ - {{ 0.5, "0.877582561890372716116281582603829651991645197109744052997610868315950763274213947405794184084682258355478400593109053993" }}, - {{ 0.25, "0.968912421710644784144595449494189199804134190287442831148128124288942561184523327264655202799685025510352709626116202617" }}, - {{0.75, "0.731688868873820886311838753000084543840541276050772482507683220220750082501569499540967562610201174960122884908227300721" }}, - {{std::ldexp(1.0, -20), "0.99999999999954525264911357034690133684385823577463126432241468890539365027135494672267164697779879113636143901797362388" }}, - {{ 2, "-0.416146836547142386997568229500762189766000771075544890755149973781964936124079169074531777860169140367366791365215728559" }}, - {{ 5, "0.283662185463226264466639171513557308334422592252215944930359066586151456767382702286176981668344573238827368717546699737" }}, - {{ 10, "-0.839071529076452452258863947824064834519930165133168546835953731048792586866270768400933712760422138927451054405350243624" }}, - {{ 8.5, "-0.60201190268482361534842652295699870029606776360435523539636606145572515876770619546025351418378467287262574566665150299" }} + {{ 0.5, static_cast("0.877582561890372716116281582603829651991645197109744052997610868315950763274213947405794184084682258355478400593109053993") }}, + {{ 0.25, static_cast("0.968912421710644784144595449494189199804134190287442831148128124288942561184523327264655202799685025510352709626116202617") }}, + {{0.75, static_cast("0.731688868873820886311838753000084543840541276050772482507683220220750082501569499540967562610201174960122884908227300721") }}, + {{std::ldexp(1.0, -20), static_cast("0.99999999999954525264911357034690133684385823577463126432241468890539365027135494672267164697779879113636143901797362388") }}, + {{ 2, static_cast("-0.416146836547142386997568229500762189766000771075544890755149973781964936124079169074531777860169140367366791365215728559") }}, + {{ 5, static_cast("0.283662185463226264466639171513557308334422592252215944930359066586151456767382702286176981668344573238827368717546699737") }}, + {{ 10, static_cast("-0.839071529076452452258863947824064834519930165133168546835953731048792586866270768400933712760422138927451054405350243624") }}, + {{ 8.5, static_cast("-0.60201190268482361534842652295699870029606776360435523539636606145572515876770619546025351418378467287262574566665150299") }} }}; max_err = 0; for(unsigned k = 0; k < exact_data.size(); k++) diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index 46900c40..b2c82e08 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -102,7 +102,7 @@ void test() "4.4466189016791091516801723880812533528438597080549410911235655611382010503145789286158745555771483577943662768773465284793798720178177605712848440200402906836390133865748188969184005230383247111166918721449908133920663776952786683837038180436264738937354101153867171804315769471050303182129269442292354388037298125177941217926845803005587166270803697433886463469168814941555804311717400657004050157245e1110", }}; - T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + T eg = static_cast("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); unsigned max_err = 0; for(unsigned k = 0; k < data.size(); k++) diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp index 9efa78a3..1ba8f9ec 100644 --- a/test/test_cpp_int.cpp +++ b/test/test_cpp_int.cpp @@ -72,10 +72,10 @@ void test() int si = d.convert_to(); unsigned ui = si; - test_type a1 = a.str(); - test_type b1 = b.str(); - test_type c1 = c.str(); - test_type d1 = d.str(); + test_type a1 = static_cast(a.str()); + test_type b1 = static_cast(b.str()); + test_type c1 = static_cast(c.str()); + test_type d1 = static_cast(d.str()); BOOST_CHECK_EQUAL(a.str(), a1.str()); BOOST_CHECK_EQUAL(b.str(), b1.str()); diff --git a/test/test_exp.cpp b/test/test_exp.cpp index 4167d4c7..424601dc 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -102,7 +102,7 @@ void test() "6.83336127500041943234365059231968669406267422759442985746460610830503287734479988530512309065240678799786759250323660701e3848", }}; - T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"; + T pi = static_cast("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"); unsigned max_err = 0; for(unsigned k = 0; k < data.size(); k++) @@ -127,16 +127,16 @@ void test() static const boost::array, 10> exact_data = {{ - {{ std::ldexp(1.0, -50), "1.00000000000000088817841970012562676935794497867573073630970950828771105957980924149923657574337470594698012676100224953" }}, - {{ std::ldexp(1.0, -20), "1.00000095367477115374544678824955687428365188553281789775169686343569285229334215539516690752571791280462887427635269562" }}, - {{ std::ldexp(1.0, -10), "1.00097703949241653524284529261160650646585162918174419940186408264916250428896869173656853690882467186075613761065459261" }}, - {{ 0.25, "1.28402541668774148407342056806243645833628086528146308921750729687220776586723800275330641943955356890166283174967968731" }}, - {{ 0.5, "1.64872127070012814684865078781416357165377610071014801157507931164066102119421560863277652005636664300286663775630779700" }}, - {{ 0.75, "2.11700001661267466854536981983709561013449158470240342177913303081098453336401282000279156026661579821888590471901551426" }}, - {{ 10, "22026.4657948067165169579006452842443663535126185567810742354263552252028185707925751991209681645258954515555010924578367" }}, - {{ 10.5, "36315.5026742466377389120269013166179689315579671275857607480190550842856628099187749764427758174866310742771977376827512" }}, - {{ 25, "7.20048993373858725241613514661261579152235338133952787362213864472320593107782569745000325654258093194727871848859163684e10" }}, - {{ 31.25, "3.72994612957188849046766396046821396700589012875701157893019118883826370993674081486706667149871508642909416337810227575e13" }}, + {{ std::ldexp(1.0, -50), static_cast("1.00000000000000088817841970012562676935794497867573073630970950828771105957980924149923657574337470594698012676100224953") }}, + {{ std::ldexp(1.0, -20), static_cast("1.00000095367477115374544678824955687428365188553281789775169686343569285229334215539516690752571791280462887427635269562") }}, + {{ std::ldexp(1.0, -10), static_cast("1.00097703949241653524284529261160650646585162918174419940186408264916250428896869173656853690882467186075613761065459261") }}, + {{ 0.25, static_cast("1.28402541668774148407342056806243645833628086528146308921750729687220776586723800275330641943955356890166283174967968731") }}, + {{ 0.5, static_cast("1.64872127070012814684865078781416357165377610071014801157507931164066102119421560863277652005636664300286663775630779700") }}, + {{ 0.75, static_cast("2.11700001661267466854536981983709561013449158470240342177913303081098453336401282000279156026661579821888590471901551426") }}, + {{ 10, static_cast("22026.4657948067165169579006452842443663535126185567810742354263552252028185707925751991209681645258954515555010924578367") }}, + {{ 10.5, static_cast("36315.5026742466377389120269013166179689315579671275857607480190550842856628099187749764427758174866310742771977376827512") }}, + {{ 25, static_cast("7.20048993373858725241613514661261579152235338133952787362213864472320593107782569745000325654258093194727871848859163684e10") }}, + {{ 31.25, static_cast("3.72994612957188849046766396046821396700589012875701157893019118883826370993674081486706667149871508642909416337810227575e13") }}, }}; max_err = 0; diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp index 410b531a..d2973446 100644 --- a/test/test_float_io.cpp +++ b/test/test_float_io.cpp @@ -172,18 +172,18 @@ void test() BOOST_CHECK_EQUAL(val.str(), "-inf"); BOOST_CHECK_EQUAL(val.str(0, std::ios_base::showpos), "-inf"); - val = "inf"; + val = static_cast("inf"); BOOST_CHECK_EQUAL(val, std::numeric_limits::infinity()); - val = "+inf"; + val = static_cast("+inf"); BOOST_CHECK_EQUAL(val, std::numeric_limits::infinity()); - val = "-inf"; + val = static_cast("-inf"); BOOST_CHECK_EQUAL(val, -std::numeric_limits::infinity()); } if(std::numeric_limits::has_quiet_NaN) { T val = std::numeric_limits::quiet_NaN(); BOOST_CHECK_EQUAL(val.str(), "nan"); - val = "nan"; + val = static_cast("nan"); BOOST_CHECK(boost::math::isnan(val)); } } @@ -246,9 +246,9 @@ void do_round_trip(const T& val, std::ios_base::fmtflags f) #endif ss.flags(f); ss << val; - T new_val = ss.str(); + T new_val = static_cast(ss.str()); BOOST_CHECK_EQUAL(new_val, val); - new_val = val.str(0, f); + new_val = static_cast(val.str(0, f)); BOOST_CHECK_EQUAL(new_val, val); } diff --git a/test/test_generic_conv.cpp b/test/test_generic_conv.cpp index a552a3cd..6664f4e9 100644 --- a/test/test_generic_conv.cpp +++ b/test/test_generic_conv.cpp @@ -91,18 +91,18 @@ int main() dec_float_500 tol("1e-500"); #ifdef TEST_GMP mpf = df; - mpf2 = df.str(); + mpf2 = static_cast(df.str()); BOOST_CHECK_EQUAL(mpf, mpf2); df = mpf; - df2 = mpf.str(); + df2 = static_cast(mpf.str()); BOOST_CHECK(fabs((df - df2) / df) < tol); #endif #ifdef TEST_MPFR mpfr = df; - mpfr2 = df.str(); + mpfr2 = static_cast(df.str()); BOOST_CHECK_EQUAL(mpfr, mpfr2); df = mpfr; - df2 = mpfr.str(); + df2 = static_cast(mpfr.str()); BOOST_CHECK(fabs((df - df2) / df) < tol); #endif // @@ -124,12 +124,12 @@ int main() // #ifdef TEST_GMP mpq = c; - mpq_rational mpq2 = c.str(); + mpq_rational mpq2 = static_cast(c.str()); BOOST_CHECK_EQUAL(mpq, mpq2); #endif #ifdef TEST_TOMMATH tr = c; - tom_rational tr2 = c.str(); + tom_rational tr2 = static_cast(c.str()); BOOST_CHECK_EQUAL(tr, tr2); #endif // diff --git a/test/test_gmp_conversions.cpp b/test/test_gmp_conversions.cpp index fad3d97d..8b1b2ec0 100644 --- a/test/test_gmp_conversions.cpp +++ b/test/test_gmp_conversions.cpp @@ -101,13 +101,13 @@ int main() rat = 2; BOOST_TEST(mpz_int(rat) == 2); iz = 3; - iz = f0; + iz = static_cast(f0); BOOST_TEST(iz == 2); iz = 3; - iz = f50; + iz = static_cast(f50); BOOST_TEST(iz == 2); iz = 3; - iz = rat; + iz = static_cast(rat); BOOST_TEST(iz == 2); BOOST_TEST(mpq_rational(mpz) == 2); diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp index 1f87a88c..b603fa88 100644 --- a/test/test_int_io.cpp +++ b/test/test_int_io.cpp @@ -66,9 +66,9 @@ void do_round_trip(const T& val, std::ios_base::fmtflags f) #endif ss.flags(f); ss << val; - T new_val = ss.str(); + T new_val = static_cast(ss.str()); BOOST_CHECK_EQUAL(new_val, val); - new_val = val.str(0, f); + new_val = static_cast(val.str(0, f)); BOOST_CHECK_EQUAL(new_val, val); } diff --git a/test/test_log.cpp b/test/test_log.cpp index 1d5f0342..6426e307 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -152,7 +152,7 @@ void test() "19.565410630120075532420489068555321524954362381908007338302983473268528473151341321768804731192210840056455228388636731122203200610869021021871133154865620432257415783302175345843898977949742849569372169004904667621738405749986270376895267386643049526766451459390277406632576412790748533372863644721976845168460840162066672290292749672668879524315410824251032084115058493720402881895485689493165441193", }}; - T pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"; + T pi = static_cast("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"); T tenth = 1; tenth /= 10; T logten = log(T(10)); diff --git a/test/test_rational_io.cpp b/test/test_rational_io.cpp index 8003d4f3..7b027cbf 100644 --- a/test/test_rational_io.cpp +++ b/test/test_rational_io.cpp @@ -9,9 +9,10 @@ # define _SCL_SECURE_NO_WARNINGS #endif -#if !defined(TEST_MPQ) && !defined(TEST_TOMMATH) +#if !defined(TEST_MPQ) && !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) # define TEST_MPQ # define TEST_TOMMATH +# define TEST_CPP_INT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -28,6 +29,9 @@ #if defined(TEST_TOMMATH) #include #endif +#ifdef TEST_CPP_INT +#include +#endif #include #include @@ -71,9 +75,9 @@ void do_round_trip(const T& val, std::ios_base::fmtflags f, const boost::mpl::tr #endif ss.flags(f); ss << val; - T new_val = ss.str(); + T new_val = static_cast(ss.str()); BOOST_CHECK_EQUAL(new_val, val); - new_val = val.str(0, f); + new_val = static_cast(val.str(0, f)); BOOST_CHECK_EQUAL(new_val, val); } @@ -132,6 +136,10 @@ int main() #ifdef TEST_TOMMATH test_round_trip >(); test_round_trip(); +#endif +#ifdef TEST_CPP_INT + test_round_trip >(); + test_round_trip(); #endif return boost::report_errors(); } diff --git a/test/test_sin.cpp b/test/test_sin.cpp index fef86827..78d1b620 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -155,7 +155,7 @@ void test() boost::uintmax_t max_err = 0; for(unsigned k = 0; k < data.size(); k++) { - static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + static const T euler_gamma = static_cast("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); T val = sin(euler_gamma * ((100 * k) - 5000)); T e = relative_error(val, T(data[k])); unsigned err = e.template convert_to(); @@ -228,7 +228,7 @@ void test() max_err = 0; for(unsigned k = 0; k < small_data.size(); k++) { - static const T euler_gamma = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + static const T euler_gamma = static_cast("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); T val = sin((euler_gamma + k) / 53); T e = relative_error(val, T(small_data[k])); unsigned err = e.template convert_to(); @@ -252,15 +252,15 @@ void test() // static const boost::array, 9> exact_data = {{ - {{ 0.5, "0.479425538604203000273287935215571388081803367940600675188616613125535000287814832209631274684348269086132091084505717418" }}, - {{ 0.25, "0.247403959254522929596848704849389195893390980386965810676544830494398136043486821690984848527973792338327197752176516138" }}, - {{0.75, "0.681638760023334166733241952779893935338382394659229909213625262151100388887003782753145274849781911981438190343146876189" }}, - {{std::ldexp(1.0, -20), "9.53674316406105439710335272649306549801506698739838753888815787489707114648106832493113326022411646219016312547902694921e-7" }}, - {{ 2, "0.909297426825681695396019865911744842702254971447890268378973011530967301540783544620126688924959380309967896742399486261" }}, - {{ 5, "-0.958924274663138468893154406155993973352461543964601778131672454235102558086559603076995955429532866596530638461663378937" }}, - {{ 10, "-0.544021110889369813404747661851377281683643012916223891574184012616757209640493425707075673894983216158293824238262832286" }}, + {{ 0.5, static_cast("0.479425538604203000273287935215571388081803367940600675188616613125535000287814832209631274684348269086132091084505717418") }}, + {{ 0.25, static_cast("0.247403959254522929596848704849389195893390980386965810676544830494398136043486821690984848527973792338327197752176516138") }}, + {{0.75, static_cast("0.681638760023334166733241952779893935338382394659229909213625262151100388887003782753145274849781911981438190343146876189") }}, + {{std::ldexp(1.0, -20), static_cast("9.53674316406105439710335272649306549801506698739838753888815787489707114648106832493113326022411646219016312547902694921e-7") }}, + {{ 2, static_cast("0.909297426825681695396019865911744842702254971447890268378973011530967301540783544620126688924959380309967896742399486261") }}, + {{ 5, static_cast("-0.958924274663138468893154406155993973352461543964601778131672454235102558086559603076995955429532866596530638461663378937") }}, + {{ 10, static_cast("-0.544021110889369813404747661851377281683643012916223891574184012616757209640493425707075673894983216158293824238262832286") }}, {{ 0, 0 }}, - {{ "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064", 1 }} + {{ static_cast("1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064"), 1 }} }}; max_err = 0; for(unsigned k = 0; k < exact_data.size(); k++) diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index 2a18c8b5..ae8f11d0 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -102,7 +102,7 @@ void test() "4.4466189016791091516801723880812533528438597080549410911235655611382010503145789286158745555771483577943662768773465284793798720178177605712848440200402906836390133865748188969184005230383247111166918721449908133920663776952786683837038180436264738937354101153867171804315769471050303182129269442292354388037298125177941217926845803005587166270803697433886463469168814941555804311717400657004050157245e1110", }}; - T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + T eg = static_cast("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); unsigned max_err = 0; for(unsigned k = 0; k < data.size(); k++) diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp index 57b84206..c59be223 100644 --- a/test/test_sqrt.cpp +++ b/test/test_sqrt.cpp @@ -152,7 +152,7 @@ void test() "17.7245385090551602729816748334114518279754945612238712821380778985291128459103218137495065673854466541622682362428257066623615286572442260252509370960278706846203769865310512284992517302895082622893209537926796280017463901535147972051670019018523401858544697449491264031392177552590621640541933250090639840761373347747515343366798978936585183640879545116516173876005906739343179133280985484624818490205465485219561325156164746751504273876105610799612710721006037204448367236529661370809432349883166842421384570960912042042778577806869476657000521830568512541339663694465418151071669388332194292935706226886522442054214994804992075648639887483850593064021821402928581123306497894520362114907896228738940324597819851313487126651250629326004465638210967502681249693059542046156076195221739152507020779275809905433290066222306761446966124818874306997883520506146444385418530797357425717918563595974995995226384924220388910396640644729397284134504300214056423343303926175613417633632001703765416347632066927654181283576249032690450848532013419243598973087119379948293873011126256165881888478597787596376136", }}; - T pi = "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913152"; + T pi = static_cast("3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913152"); unsigned max_err = 0; for(unsigned k = 0; k < data.size(); k++) diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index a76fbe48..623585ec 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -102,7 +102,7 @@ void test() "1.", }}; - T eg = "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"; + T eg = static_cast("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); unsigned max_err = 0; for(unsigned k = 0; k < data.size(); k++) From 1f35bfe581f8754fe54ae4f3f9072614196118ae Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 19 Aug 2012 16:39:24 +0000 Subject: [PATCH 219/256] Make some gmp constructors explicit. Add tests to verify that explicit conversions fail. Fix failures inside number.hpp. [SVN r80083] --- include/boost/multiprecision/gmp.hpp | 80 +++++++++++++++++++------ include/boost/multiprecision/number.hpp | 55 ++++++++++------- test/Jamfile.v2 | 5 +- test/compile_fail/conv_fail_45.cpp | 24 ++++++++ test/compile_fail/conv_fail_46.cpp | 23 +++++++ test/compile_fail/conv_fail_47.cpp | 24 ++++++++ test/compile_fail/conv_fail_48.cpp | 23 +++++++ test/test_gmp_conversions.cpp | 23 ++++++- 8 files changed, 213 insertions(+), 44 deletions(-) create mode 100644 test/compile_fail/conv_fail_45.cpp create mode 100644 test/compile_fail/conv_fail_46.cpp create mode 100644 test/compile_fail/conv_fail_47.cpp create mode 100644 test/compile_fail/conv_fail_48.cpp diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index cfdea145..ca328ab8 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -369,20 +369,22 @@ struct gmp_float : public detail::gmp_float_imp } gmp_float(const gmp_float& o) : detail::gmp_float_imp(o) {} template - gmp_float(const gmp_float& o); + gmp_float(const gmp_float& o, typename enable_if_c::type* = 0); + template + explicit gmp_float(const gmp_float& o, typename disable_if_c::type* = 0); gmp_float(const gmp_int& o); gmp_float(const gmp_rational& o); - gmp_float(mpf_t val) + gmp_float(const mpf_t val) { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); mpf_set(this->m_data, val); } - gmp_float(mpz_t val) + gmp_float(const mpz_t val) { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); mpf_set_z(this->m_data, val); } - gmp_float(mpq_t val) + gmp_float(const mpq_t val) { mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); mpf_set_q(this->m_data, val); @@ -442,17 +444,17 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> { mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); } - gmp_float(mpf_t val) + gmp_float(const mpf_t val) { mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); mpf_set(this->m_data, val); } - gmp_float(mpz_t val) + gmp_float(const mpz_t val) { mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); mpf_set_z(this->m_data, val); } - gmp_float(mpq_t val) + gmp_float(const mpq_t val) { mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); mpf_set_q(this->m_data, val); @@ -461,7 +463,7 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> template gmp_float(const gmp_float& o) { - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, mpf_get_prec(o.data())); mpf_set(this->m_data, o.data()); } #ifndef BOOST_NO_RVALUE_REFERENCES @@ -491,7 +493,13 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> gmp_float& operator=(const gmp_float& o) { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + { + mpf_init2(this->m_data, mpf_get_prec(o.data())); + } + else + { + mpf_set_prec(this->m_data, mpf_get_prec(o.data())); + } mpf_set(this->m_data, o.data()); return *this; } @@ -534,11 +542,11 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> } unsigned precision()const BOOST_NOEXCEPT { - return mpf_get_prec(this->m_data) * 301L / 1000 - 1; + return (mpf_get_prec(this->m_data) * 301L) / 1000 - 1; } void precision(unsigned digits10) BOOST_NOEXCEPT { - mpf_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); + mpf_set_prec(this->m_data, ((digits10 + 1) * 1000L) / 301); } }; @@ -977,27 +985,27 @@ struct gmp_int o.m_data[0]._mp_d = 0; } #endif - gmp_int(mpf_t val) + explicit gmp_int(const mpf_t val) { mpz_init(this->m_data); mpz_set_f(this->m_data, val); } - gmp_int(mpz_t val) + gmp_int(const mpz_t val) { mpz_init_set(this->m_data, val); } - gmp_int(mpq_t val) + explicit gmp_int(const mpq_t val) { mpz_init(this->m_data); mpz_set_q(this->m_data, val); } template - gmp_int(const gmp_float& o) + explicit gmp_int(const gmp_float& o) { mpz_init(this->m_data); mpz_set_f(this->m_data, o.data()); } - gmp_int(const gmp_rational& o); + explicit gmp_int(const gmp_rational& o); gmp_int& operator = (const gmp_int& o) { if(o.m_data[0]._mp_d) @@ -1659,12 +1667,12 @@ struct gmp_rational o.m_data[0]._mp_den._mp_d = 0; } #endif - gmp_rational(mpq_t o) + gmp_rational(const mpq_t o) { mpq_init(m_data); mpq_set(m_data, o); } - gmp_rational(mpz_t o) + gmp_rational(const mpz_t o) { mpq_init(m_data); mpq_set_z(m_data, o); @@ -1998,7 +2006,14 @@ inline void assign_components(gmp_rational& result, gmp_int const& v1, gmp_int c // template template -inline gmp_float::gmp_float(const gmp_float& o) +inline gmp_float::gmp_float(const gmp_float& o, typename enable_if_c::type*) +{ + mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); + mpf_set(this->m_data, o.data()); +} +template +template +inline gmp_float::gmp_float(const gmp_float& o, typename disable_if_c::type*) { mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); mpf_set(this->m_data, o.data()); @@ -2089,6 +2104,33 @@ struct component_type > typedef number type; }; +#ifdef BOOST_NO_SFINAE_EXPR + +namespace detail{ + +template<> +struct is_explicitly_convertible::type, gmp_int> : public mpl::true_ {}; +template<> +struct is_explicitly_convertible::type, gmp_int> : public mpl::true_ {}; +template +struct is_explicitly_convertible, gmp_int> : public mpl::true_ {}; +template<> +struct is_explicitly_convertible : public mpl::true_ {}; +template +struct is_explicitly_convertible, gmp_float > : public mpl::true_ {}; + +} + +#endif + +template<> +struct number_category::type> : public mpl::int_{}; +template<> +struct number_category::type> : public mpl::int_{}; +template<> +struct number_category >::type> : public mpl::int_{}; + + typedef number > mpf_float_50; typedef number > mpf_float_100; typedef number > mpf_float_500; diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index 40af6746..99ca7b19 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -43,7 +43,7 @@ public: BOOST_FORCEINLINE BOOST_CONSTEXPR number() BOOST_NOEXCEPT_IF(noexcept(Backend())) {} BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& e) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(e.m_backend){} template - BOOST_FORCEINLINE number(V v, typename enable_if_c< + BOOST_FORCEINLINE number(const V& v, typename enable_if_c< (boost::is_arithmetic::value || is_same::value || is_convertible::value) && !is_convertible::type, Backend>::value && !detail::is_restricted_conversion::type, Backend>::value @@ -52,28 +52,29 @@ public: m_backend = canonical_value(v); } template - BOOST_FORCEINLINE BOOST_CONSTEXPR number(V v, typename enable_if_c< - (boost::is_arithmetic::value || is_same::value || is_convertible::value) - && is_convertible::type, Backend>::value + BOOST_FORCEINLINE BOOST_CONSTEXPR number(const V& v, typename enable_if_c< + /*(boost::is_arithmetic::value || is_same::value || is_convertible::value) + &&*/ is_convertible::type, Backend>::value && !detail::is_restricted_conversion::type, Backend>::value >::type* = 0) : m_backend(canonical_value(v)) {} BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& e, unsigned digits10) : m_backend(e.m_backend, digits10){} template - explicit BOOST_FORCEINLINE number(V v, typename enable_if_c< + explicit BOOST_FORCEINLINE number(const V& v, typename enable_if_c< (boost::is_arithmetic::value || is_same::value || is_convertible::value) - && !is_convertible::type, Backend>::value + && !detail::is_explicitly_convertible::type, Backend>::value && detail::is_restricted_conversion::type, Backend>::value >::type* = 0) { m_backend = canonical_value(v); } template - explicit BOOST_FORCEINLINE BOOST_CONSTEXPR number(V v, typename enable_if_c< - (boost::is_arithmetic::value || is_same::value || is_convertible::value) - && is_convertible::type, Backend>::value - && detail::is_restricted_conversion::type, Backend>::value + explicit BOOST_FORCEINLINE BOOST_CONSTEXPR number(const V& v, typename enable_if_c< + /*(boost::is_arithmetic::value || is_same::value || is_convertible::value) + &&*/ detail::is_explicitly_convertible::type, Backend>::value + && (detail::is_restricted_conversion::type, Backend>::value + || !is_convertible::type, Backend>::value) >::type* = 0) : m_backend(canonical_value(v)) {} /* @@ -92,12 +93,16 @@ public: BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} template - BOOST_FORCEINLINE number(const number& val, typename enable_if_c<(boost::is_convertible::value && !detail::is_restricted_conversion::value)>::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) - { - m_backend = val.backend(); - } + BOOST_FORCEINLINE number(const number& val, + typename enable_if_c<(boost::is_convertible::value && !detail::is_restricted_conversion::value)>::type* = 0) + BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) + : m_backend(val.backend()) {} + template - number(const number& val, typename enable_if_c<(!boost::is_convertible::value && !detail::is_restricted_conversion::value)>::type* = 0) + number(const number& val, typename enable_if_c< + (!detail::is_explicitly_convertible::value + && !detail::is_restricted_conversion::value) + >::type* = 0) { // // Attempt a generic interconvertion: @@ -105,12 +110,17 @@ public: detail::generic_interconvert(backend(), val.backend(), number_category(), number_category()); } template - explicit BOOST_FORCEINLINE number(const number& val, typename enable_if_c<(boost::is_convertible::value && detail::is_restricted_conversion::value)>::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) - { - m_backend = val.backend(); - } + explicit BOOST_FORCEINLINE number(const number& val, typename enable_if_c< + (detail::is_explicitly_convertible::value + && (detail::is_restricted_conversion::value || !boost::is_convertible::value)) + >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) + : m_backend(val.backend()) {} + template - explicit number(const number& val, typename enable_if_c<(!boost::is_convertible::value && detail::is_restricted_conversion::value)>::type* = 0) + explicit number(const number& val, typename enable_if_c< + (!detail::is_explicitly_convertible::value + && detail::is_restricted_conversion::value) + >::type* = 0) { // // Attempt a generic interconvertion: @@ -130,11 +140,12 @@ public: assign_components(m_backend, v1.backend(), v2.backend()); } + /* template BOOST_FORCEINLINE BOOST_CONSTEXPR number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(v){} - + */ template typename enable_if::result_type, self_type>, number&>::type operator=(const detail::expression& e) { @@ -201,7 +212,7 @@ public: */ template - typename disable_if, number& >::type + typename disable_if, number& >::type operator=(const number& v) { // diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 0acca17a..994c4899 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -802,7 +802,10 @@ if $(enable-specfun) for local source in [ glob compile_fail/*.cpp ] { - compile-fail $(source) ; + compile-fail $(source) + : + [ check-target-builds ../config//has_gmp : TEST_GMP : ] + ; } if ! $(disable-concepts) diff --git a/test/compile_fail/conv_fail_45.cpp b/test/compile_fail/conv_fail_45.cpp new file mode 100644 index 00000000..5e2f813a --- /dev/null +++ b/test/compile_fail/conv_fail_45.cpp @@ -0,0 +1,24 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_GMP + +#include + +using namespace boost::multiprecision; + +void foo(mpz_int i); + +int main() +{ + mpf_t f + foo(f); +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/test/compile_fail/conv_fail_46.cpp b/test/compile_fail/conv_fail_46.cpp new file mode 100644 index 00000000..11530eb1 --- /dev/null +++ b/test/compile_fail/conv_fail_46.cpp @@ -0,0 +1,23 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_GMP + +#include + +using namespace boost::multiprecision; + +int main() +{ + mpf_t f; + mpz_int i; + i = f; +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/test/compile_fail/conv_fail_47.cpp b/test/compile_fail/conv_fail_47.cpp new file mode 100644 index 00000000..b385e988 --- /dev/null +++ b/test/compile_fail/conv_fail_47.cpp @@ -0,0 +1,24 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_GMP + +#include + +using namespace boost::multiprecision; + +void foo(mpf_float_50); + +int main() +{ + mpf_float_100 f(2); + foo(f); +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/test/compile_fail/conv_fail_48.cpp b/test/compile_fail/conv_fail_48.cpp new file mode 100644 index 00000000..66828ca3 --- /dev/null +++ b/test/compile_fail/conv_fail_48.cpp @@ -0,0 +1,23 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_GMP + +#include + +using namespace boost::multiprecision; + +int main() +{ + mpf_float_100 f(2); + mpf_float_50 f2; + f2 = f; +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/test/test_gmp_conversions.cpp b/test/test_gmp_conversions.cpp index 8b1b2ec0..1b724d80 100644 --- a/test/test_gmp_conversions.cpp +++ b/test/test_gmp_conversions.cpp @@ -86,16 +86,17 @@ int main() BOOST_TEST(mpz_int(mpz) == 2); BOOST_TEST(mpz_int(mpq) == 2); iz = 3; - iz = mpf; + iz = mpz_int(mpf); // explicit conversion only BOOST_TEST(iz == 2); iz = 3; iz = mpz; BOOST_TEST(iz == 2); iz = 4; - iz = mpq; + iz = mpz_int(mpq); // explicit conversion only BOOST_TEST(iz == 2); f0 = 2; f50 = 2; + BOOST_TEST(mpz_int(f0) == 2); BOOST_TEST(mpz_int(f50) == 2); rat = 2; @@ -128,6 +129,24 @@ int main() iz = denominator(rat); BOOST_TEST(iz == 1); + // + // Conversions involving precision only, + // note that mpf_t precisions are only approximate: + // + mpf_float::default_precision(30); + f50 = 2; + mpf_float_100 f100(3); + mpf_float f0a(4); + mpf_float f0b(f100); + BOOST_TEST(f0a.precision() >= 30); + BOOST_TEST(f0b.precision() >= 100); + f0a = f100; + BOOST_TEST(f0a == 3); + BOOST_TEST(f0a.precision() >= 100); + + f100 = f50; + BOOST_TEST(f100 == 2); + return boost::report_errors(); } From af9e0c2fe7e0297f3a79f8df2918cc050edfd2ca Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 21 Aug 2012 14:42:15 +0000 Subject: [PATCH 220/256] Add more explicit constructors and tests for them. Centralise digits10 to digits2 conversions. [SVN r80112] --- .../boost/multiprecision/cpp_dec_float.hpp | 28 +++- include/boost/multiprecision/cpp_int.hpp | 76 +++++++++++ .../boost/multiprecision/detail/digits.hpp | 23 ++++ include/boost/multiprecision/gmp.hpp | 79 ++++++------ include/boost/multiprecision/mpfr.hpp | 121 +++++++++++------- include/boost/multiprecision/number.hpp | 22 +--- test/Jamfile.v2 | 4 +- .../{conv_fail_1.cpp => conv_fail_01.cpp} | 0 .../{conv_fail_2.cpp => conv_fail_02.cpp} | 0 .../{conv_fail_3.cpp => conv_fail_03.cpp} | 0 .../{conv_fail_4.cpp => conv_fail_04.cpp} | 0 .../{conv_fail_5.cpp => conv_fail_05.cpp} | 0 .../{conv_fail_6.cpp => conv_fail_06.cpp} | 0 .../{conv_fail_7.cpp => conv_fail_07.cpp} | 0 .../{conv_fail_8.cpp => conv_fail_08.cpp} | 0 .../{conv_fail_9.cpp => conv_fail_09.cpp} | 0 test/compile_fail/conv_fail_49.cpp | 23 ++++ test/compile_fail/conv_fail_50.cpp | 22 ++++ test/compile_fail/conv_fail_51.cpp | 15 +++ test/compile_fail/conv_fail_52.cpp | 16 +++ test/compile_fail/conv_fail_53.cpp | 15 +++ test/compile_fail/conv_fail_54.cpp | 16 +++ test/compile_fail/conv_fail_55.cpp | 16 +++ test/compile_fail/conv_fail_56.cpp | 15 +++ test/compile_fail/conv_fail_57.cpp | 15 +++ test/compile_fail/conv_fail_58.cpp | 16 +++ test/math/test_bessel_j.cpp | 2 +- test/math/test_bessel_y.cpp | 2 +- test/math/test_erf.cpp | 2 +- test/math/test_gamma.cpp | 2 +- test/math/test_legendre.cpp | 2 +- test/test_cos.cpp | 2 +- test/test_cpp_dec_float_conv.cpp | 42 ++++++ test/test_cpp_int.cpp | 6 +- test/test_cpp_int_conv.cpp | 55 ++++++++ test/test_generic_conv.cpp | 32 ++--- test/test_mpfr_conversions.cpp | 18 +++ 37 files changed, 558 insertions(+), 129 deletions(-) create mode 100644 include/boost/multiprecision/detail/digits.hpp rename test/compile_fail/{conv_fail_1.cpp => conv_fail_01.cpp} (100%) rename test/compile_fail/{conv_fail_2.cpp => conv_fail_02.cpp} (100%) rename test/compile_fail/{conv_fail_3.cpp => conv_fail_03.cpp} (100%) rename test/compile_fail/{conv_fail_4.cpp => conv_fail_04.cpp} (100%) rename test/compile_fail/{conv_fail_5.cpp => conv_fail_05.cpp} (100%) rename test/compile_fail/{conv_fail_6.cpp => conv_fail_06.cpp} (100%) rename test/compile_fail/{conv_fail_7.cpp => conv_fail_07.cpp} (100%) rename test/compile_fail/{conv_fail_8.cpp => conv_fail_08.cpp} (100%) rename test/compile_fail/{conv_fail_9.cpp => conv_fail_09.cpp} (100%) create mode 100644 test/compile_fail/conv_fail_49.cpp create mode 100644 test/compile_fail/conv_fail_50.cpp create mode 100644 test/compile_fail/conv_fail_51.cpp create mode 100644 test/compile_fail/conv_fail_52.cpp create mode 100644 test/compile_fail/conv_fail_53.cpp create mode 100644 test/compile_fail/conv_fail_54.cpp create mode 100644 test/compile_fail/conv_fail_55.cpp create mode 100644 test/compile_fail/conv_fail_56.cpp create mode 100644 test/compile_fail/conv_fail_57.cpp create mode 100644 test/compile_fail/conv_fail_58.cpp create mode 100644 test/test_cpp_dec_float_conv.cpp create mode 100644 test/test_cpp_int_conv.cpp diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 7232fed8..bd70f8cd 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -192,15 +192,25 @@ public: prec_elem(f.prec_elem) { } template - cpp_dec_float(const cpp_dec_float& f) BOOST_NOEXCEPT : + cpp_dec_float(const cpp_dec_float& f, typename enable_if_c::type* = 0) BOOST_NOEXCEPT : + data(), + exp (f.exp), + neg (f.neg), + fpclass (static_cast(static_cast(f.fpclass))), + prec_elem(cpp_dec_float_elem_number) + { + std::copy(f.data.begin(), f.data.begin() + f.prec_elem, data.begin()); + } + template + explicit cpp_dec_float(const cpp_dec_float& f, typename disable_if_c::type* = 0) BOOST_NOEXCEPT : + data(), exp (f.exp), neg (f.neg), fpclass (static_cast(static_cast(f.fpclass))), prec_elem(cpp_dec_float_elem_number) { // TODO: this doesn't round! - std::copy(f.data.begin(), f.data.begin() + (std::min)(f.prec_elem, prec_elem), data.begin()); - precision((std::min)(f.prec_elem, prec_elem)); + std::copy(f.data.begin(), f.data.begin() + prec_elem, data.begin()); } template @@ -2855,6 +2865,18 @@ using boost::multiprecision::backends::cpp_dec_float; typedef number > cpp_dec_float_50; typedef number > cpp_dec_float_100; +#ifdef BOOST_NO_SFINAE_EXPR + +namespace detail{ + +template +struct is_explicitly_convertible, cpp_dec_float > : public mpl::true_ {}; + +} + +#endif + + }} namespace std diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 8e0a4574..baf1eb18 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -683,6 +683,10 @@ public: #ifndef BOOST_NO_RVALUE_REFERENCES BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT : base_type(static_cast(o)) {} #endif + // + // These are templates, so that only args that are *exactly* the types specified are allowed, and conversions + // are not considered. Without this, conversions may be ambiguous. + // template BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(LT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT : base_type(i) {} @@ -697,6 +701,67 @@ public: BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(SLT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT : base_type(i) {} #endif + + template + cpp_int_backend(const cpp_int_backend& other) + : base_type() + { + *this = static_cast< + typename detail::canonical< + typename cpp_int_backend::local_limb_type, + cpp_int_backend + >::type + >(*other.limbs()); + this->sign(other.sign()); + } + template + cpp_int_backend& operator=(const cpp_int_backend& other) + { + *this = static_cast< + typename detail::canonical< + typename cpp_int_backend::local_limb_type, + cpp_int_backend + >::type + >(*other.limbs()); + this->sign(other.sign()); + return *this; + } + + template + cpp_int_backend(const cpp_int_backend& other, + typename enable_if_c< + (Signed || !Signed2) + && (!is_void::value || (is_void::value && (MinBits >= MinBits2))) + >::type* = 0) + : base_type() + { + this->resize(other.size()); + std::copy(other.limbs(), other.limbs() + (std::min)(other.size(), this->size()), this->limbs()); + this->sign(other.sign()); + } + + template + explicit cpp_int_backend(const cpp_int_backend& other, + typename disable_if_c< + (Signed || !Signed2) + && (!is_void::value || (is_void::value && (MinBits >= MinBits2))) + >::type* = 0) + : base_type() + { + this->resize(other.size()); + std::copy(other.limbs(), other.limbs() + (std::min)(other.size(), this->size()), this->limbs()); + this->sign(other.sign()); + } + + template + cpp_int_backend& operator=(const cpp_int_backend& other) + { + this->resize(other.size()); + std::copy(other.limbs(), other.limbs() + (std::min)(other.size(), this->size()), this->limbs()); + this->sign(other.sign()); + return *this; + } + BOOST_FORCEINLINE cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { this->assign(o); @@ -2881,6 +2946,17 @@ typedef number, false> int1024_t; #pragma warning(pop) #endif +#ifdef BOOST_NO_SFINAE_EXPR + +namespace detail{ + +template +struct is_explicitly_convertible, cpp_int_backend > : public mpl::true_ {}; + +} + +#endif + }} // namespaces #include diff --git a/include/boost/multiprecision/detail/digits.hpp b/include/boost/multiprecision/detail/digits.hpp new file mode 100644 index 00000000..8752f5b5 --- /dev/null +++ b/include/boost/multiprecision/detail/digits.hpp @@ -0,0 +1,23 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_DIGITS_HPP +#define BOOST_MP_DIGITS_HPP + +namespace boost{ namespace multiprecision{ namespace detail{ + +inline unsigned long digits10_2_2(unsigned long d10) +{ + return (d10 * 1000uL) / 301uL + ((d10 * 1000uL) % 301 ? 2u : 1u); +} + +inline unsigned long digits2_2_10(unsigned long d2) +{ + return (d2 * 301uL) / 1000uL; +} + +}}} // namespaces + +#endif diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index ca328ab8..a0043ade 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -9,6 +9,7 @@ #include #include #include +#include #include #include #include @@ -67,7 +68,7 @@ struct gmp_float_imp // to get the right value, but if it's then used in further calculations // things go badly wrong!! // - mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); if(o.m_data[0]._mp_d) mpf_set(m_data, o.m_data); } @@ -81,7 +82,7 @@ struct gmp_float_imp gmp_float_imp& operator = (const gmp_float_imp& o) { if(m_data[0]._mp_d == 0) - mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); if(o.m_data[0]._mp_d) mpf_set(m_data, o.m_data); return *this; @@ -96,11 +97,11 @@ struct gmp_float_imp gmp_float_imp& operator = (unsigned long long i) { if(m_data[0]._mp_d == 0) - mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpf_t t; - mpf_init2(t, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(t, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); mpf_set_ui(m_data, 0); while(i) { @@ -118,7 +119,7 @@ struct gmp_float_imp { BOOST_MP_USING_ABS if(m_data[0]._mp_d == 0) - mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); bool neg = i < 0; *this = static_cast(abs(i)); if(neg) @@ -128,21 +129,21 @@ struct gmp_float_imp gmp_float_imp& operator = (unsigned long i) BOOST_NOEXCEPT { if(m_data[0]._mp_d == 0) - mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); mpf_set_ui(m_data, i); return *this; } gmp_float_imp& operator = (long i) BOOST_NOEXCEPT { if(m_data[0]._mp_d == 0) - mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); mpf_set_si(m_data, i); return *this; } gmp_float_imp& operator = (double d) BOOST_NOEXCEPT { if(m_data[0]._mp_d == 0) - mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); mpf_set_d(m_data, d); return *this; } @@ -153,7 +154,7 @@ struct gmp_float_imp using std::floor; if(m_data[0]._mp_d == 0) - mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); if (a == 0) { mpf_set_si(m_data, 0); @@ -198,7 +199,7 @@ struct gmp_float_imp gmp_float_imp& operator = (const char* s) { if(m_data[0]._mp_d == 0) - mpf_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); if(0 != mpf_set_str(m_data, s, 10)) BOOST_THROW_EXCEPTION(std::runtime_error(std::string("The string \"") + s + std::string("\"could not be interpreted as a valid floating point number."))); return *this; @@ -365,7 +366,7 @@ struct gmp_float : public detail::gmp_float_imp { gmp_float() { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); } gmp_float(const gmp_float& o) : detail::gmp_float_imp(o) {} template @@ -376,17 +377,17 @@ struct gmp_float : public detail::gmp_float_imp gmp_float(const gmp_rational& o); gmp_float(const mpf_t val) { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpf_set(this->m_data, val); } gmp_float(const mpz_t val) { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpf_set_z(this->m_data, val); } gmp_float(const mpq_t val) { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpf_set_q(this->m_data, val); } #ifndef BOOST_NO_RVALUE_REFERENCES @@ -411,21 +412,21 @@ struct gmp_float : public detail::gmp_float_imp gmp_float& operator=(const mpf_t val) BOOST_NOEXCEPT { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpf_set(this->m_data, val); return *this; } gmp_float& operator=(const mpz_t val) BOOST_NOEXCEPT { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpf_set_z(this->m_data, val); return *this; } gmp_float& operator=(const mpq_t val) BOOST_NOEXCEPT { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpf_set_q(this->m_data, val); return *this; } @@ -442,21 +443,21 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> { gmp_float() { - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); } gmp_float(const mpf_t val) { - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpf_set(this->m_data, val); } gmp_float(const mpz_t val) { - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpf_set_z(this->m_data, val); } gmp_float(const mpq_t val) { - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpf_set_q(this->m_data, val); } gmp_float(const gmp_float& o) : detail::gmp_float_imp<0>(o) {} @@ -473,7 +474,7 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> gmp_float(const gmp_rational& o); gmp_float(const gmp_float& o, unsigned digits10) { - mpf_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpf_set(this->m_data, o.data()); } @@ -508,21 +509,21 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> gmp_float& operator=(const mpf_t val) { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpf_set(this->m_data, val); return *this; } gmp_float& operator=(const mpz_t val) { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpf_set_z(this->m_data, val); return *this; } gmp_float& operator=(const mpq_t val) { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpf_set_q(this->m_data, val); return *this; } @@ -542,11 +543,11 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> } unsigned precision()const BOOST_NOEXCEPT { - return (mpf_get_prec(this->m_data) * 301L) / 1000 - 1; + return multiprecision::detail::digits2_2_10(mpf_get_prec(this->m_data)); } void precision(unsigned digits10) BOOST_NOEXCEPT { - mpf_set_prec(this->m_data, ((digits10 + 1) * 1000L) / 301); + mpf_set_prec(this->m_data, multiprecision::detail::digits10_2_2(digits10)); } }; @@ -2008,26 +2009,26 @@ template template inline gmp_float::gmp_float(const gmp_float& o, typename enable_if_c::type*) { - mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision())); mpf_set(this->m_data, o.data()); } template template inline gmp_float::gmp_float(const gmp_float& o, typename disable_if_c::type*) { - mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision())); mpf_set(this->m_data, o.data()); } template inline gmp_float::gmp_float(const gmp_int& o) { - mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision())); mpf_set_z(this->data(), o.data()); } template inline gmp_float::gmp_float(const gmp_rational& o) { - mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision())); mpf_set_q(this->data(), o.data()); } template @@ -2035,7 +2036,7 @@ template inline gmp_float& gmp_float::operator=(const gmp_float& o) { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision())); mpf_set(this->m_data, o.data()); return *this; } @@ -2043,7 +2044,7 @@ template inline gmp_float& gmp_float::operator=(const gmp_int& o) { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision())); mpf_set_z(this->data(), o.data()); return *this; } @@ -2051,31 +2052,31 @@ template inline gmp_float& gmp_float::operator=(const gmp_rational& o) { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, (((Digits10 ? Digits10 : this->get_default_precision()) + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(Digits10 ? Digits10 : this->get_default_precision())); mpf_set_q(this->data(), o.data()); return *this; } inline gmp_float<0>::gmp_float(const gmp_int& o) { - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpf_set_z(this->data(), o.data()); } inline gmp_float<0>::gmp_float(const gmp_rational& o) { - mpf_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpf_set_q(this->data(), o.data()); } inline gmp_float<0>& gmp_float<0>::operator=(const gmp_int& o) { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, ((this->get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(this->get_default_precision())); mpf_set_z(this->data(), o.data()); return *this; } inline gmp_float<0>& gmp_float<0>::operator=(const gmp_rational& o) { if(this->m_data[0]._mp_d == 0) - mpf_init2(this->m_data, ((this->get_default_precision() + 1) * 1000L) / 301L); + mpf_init2(this->m_data, multiprecision::detail::digits10_2_2(this->get_default_precision())); mpf_set_q(this->data(), o.data()); return *this; } @@ -2185,7 +2186,7 @@ public: { return -(max)(); } - BOOST_STATIC_CONSTEXPR int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); + BOOST_STATIC_CONSTEXPR int digits = static_cast((Digits10 * 1000L) / 301L + ((Digits10 * 1000L) % 301L ? 2 : 1)); BOOST_STATIC_CONSTEXPR int digits10 = Digits10; // Have to allow for a possible extra limb inside the gmp data structure: BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 2 + ((GMP_LIMB_BITS * 301L) / 1000L); diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index ce8209a6..98fa9334 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -12,6 +12,7 @@ #include #include #include +#include #include #include #include @@ -46,7 +47,7 @@ struct mpfr_float_imp mpfr_float_imp(const mpfr_float_imp& o) { - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); if(o.m_data[0]._mpfr_d) mpfr_set(m_data, o.m_data, GMP_RNDN); } @@ -60,7 +61,7 @@ struct mpfr_float_imp mpfr_float_imp& operator = (const mpfr_float_imp& o) BOOST_NOEXCEPT { if(m_data[0]._mpfr_d == 0) - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); if(o.m_data[0]._mpfr_d) mpfr_set(m_data, o.m_data, GMP_RNDN); return *this; @@ -76,14 +77,14 @@ struct mpfr_float_imp mpfr_float_imp& operator = (unsigned long long i) BOOST_NOEXCEPT { if(m_data[0]._mpfr_d == 0) - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); mpfr_set_uj(m_data, i, GMP_RNDN); return *this; } mpfr_float_imp& operator = (long long i) BOOST_NOEXCEPT { if(m_data[0]._mpfr_d == 0) - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); mpfr_set_sj(m_data, i, GMP_RNDN); return *this; } @@ -91,11 +92,11 @@ struct mpfr_float_imp mpfr_float_imp& operator = (unsigned long long i) { if(m_data[0]._mpfr_d == 0) - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); unsigned shift = 0; mpfr_t t; - mpfr_init2(t, (std::max)(static_cast(std::numeric_limits::digits), static_cast(((digits10 + 1) * 1000L) / 301L))); + mpfr_init2(t, (std::max)(static_cast(std::numeric_limits::digits), static_cast(multiprecision::detail::digits10_2_2(digits10)))); mpfr_set_ui(m_data, 0, GMP_RNDN); while(i) { @@ -113,7 +114,7 @@ struct mpfr_float_imp { BOOST_MP_USING_ABS if(m_data[0]._mpfr_d == 0) - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); bool neg = i < 0; *this = static_cast(abs(i)); if(neg) @@ -124,35 +125,35 @@ struct mpfr_float_imp mpfr_float_imp& operator = (unsigned long i) BOOST_NOEXCEPT { if(m_data[0]._mpfr_d == 0) - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); mpfr_set_ui(m_data, i, GMP_RNDN); return *this; } mpfr_float_imp& operator = (long i) BOOST_NOEXCEPT { if(m_data[0]._mpfr_d == 0) - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); mpfr_set_si(m_data, i, GMP_RNDN); return *this; } mpfr_float_imp& operator = (double d) BOOST_NOEXCEPT { if(m_data[0]._mpfr_d == 0) - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); mpfr_set_d(m_data, d, GMP_RNDN); return *this; } mpfr_float_imp& operator = (long double a) BOOST_NOEXCEPT { if(m_data[0]._mpfr_d == 0) - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); mpfr_set_ld(m_data, a, GMP_RNDN); return *this; } mpfr_float_imp& operator = (const char* s) { if(m_data[0]._mpfr_d == 0) - mpfr_init2(m_data, (((digits10 ? digits10 : get_default_precision()) + 1) * 1000L) / 301L); + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); if(mpfr_set_str(m_data, s, 10, GMP_RNDN) != 0) { BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Unable to parse string \"") + s + std::string("\"as a valid floating point number."))); @@ -328,52 +329,64 @@ struct mpfr_float_backend : public detail::mpfr_float_imp { mpfr_float_backend() { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); } mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp(static_cast&&>(o)) {} #endif template - mpfr_float_backend(const mpfr_float_backend& val) + mpfr_float_backend(const mpfr_float_backend& val, typename enable_if_c::type* = 0) { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set(this->m_data, val.data(), GMP_RNDN); } template - mpfr_float_backend(const gmp_float& val) + explicit mpfr_float_backend(const mpfr_float_backend& val, typename disable_if_c::type* = 0) { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); + mpfr_set(this->m_data, val.data(), GMP_RNDN); + } + template + mpfr_float_backend(const gmp_float& val, typename enable_if_c::type* = 0) + { + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); + mpfr_set_f(this->m_data, val.data(), GMP_RNDN); + } + template + mpfr_float_backend(const gmp_float& val, typename disable_if_c::type* = 0) + { + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_f(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend(const gmp_int& val) { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_z(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend(const gmp_rational& val) { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_q(this->m_data, val.data(), GMP_RNDN); } - mpfr_float_backend(mpfr_t val) + mpfr_float_backend(const mpfr_t val) { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set(this->m_data, val, GMP_RNDN); } - mpfr_float_backend(mpf_t val) + mpfr_float_backend(const mpf_t val) { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_f(this->m_data, val, GMP_RNDN); } - mpfr_float_backend(mpz_t val) + mpfr_float_backend(const mpz_t val) { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_z(this->m_data, val, GMP_RNDN); } - mpfr_float_backend(mpq_t val) + mpfr_float_backend(const mpq_t val) { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_q(this->m_data, val, GMP_RNDN); } mpfr_float_backend& operator=(const mpfr_float_backend& o) @@ -414,6 +427,7 @@ struct mpfr_float_backend : public detail::mpfr_float_imp mpfr_set_q(this->m_data, val, GMP_RNDN); return *this; } + // We don't change our precision here, this is a fixed precision type: template mpfr_float_backend& operator=(const mpfr_float_backend& val) BOOST_NOEXCEPT { @@ -443,26 +457,26 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> { mpfr_float_backend() { - mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); } - mpfr_float_backend(mpfr_t val) + mpfr_float_backend(const mpfr_t val) { - mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, mpfr_get_prec(val)); mpfr_set(this->m_data, val, GMP_RNDN); } - mpfr_float_backend(mpf_t val) + mpfr_float_backend(const mpf_t val) { - mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, mpf_get_prec(val)); mpfr_set_f(this->m_data, val, GMP_RNDN); } - mpfr_float_backend(mpz_t val) + mpfr_float_backend(const mpz_t val) { - mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpfr_set_z(this->m_data, val, GMP_RNDN); } - mpfr_float_backend(mpq_t val) + mpfr_float_backend(const mpq_t val) { - mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpfr_set_q(this->m_data, val, GMP_RNDN); } mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp<0>(o) {} @@ -471,29 +485,29 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> #endif mpfr_float_backend(const mpfr_float_backend& o, unsigned digits10) { - mpfr_init2(this->m_data, ((digits10 + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); *this = o; } template mpfr_float_backend(const mpfr_float_backend& val) { - mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, mpfr_get_prec(val.data())); mpfr_set(this->m_data, val.data(), GMP_RNDN); } template mpfr_float_backend(const gmp_float& val) { - mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, mpf_get_prec(val.data())); mpfr_set_f(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend(const gmp_int& val) { - mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpfr_set_z(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend(const gmp_rational& val) { - mpfr_init2(this->m_data, ((get_default_precision() + 1) * 1000L) / 301L); + mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpfr_set_q(this->m_data, val.data(), GMP_RNDN); } @@ -517,11 +531,13 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> } mpfr_float_backend& operator=(const mpfr_t val) BOOST_NOEXCEPT { + mpfr_set_prec(this->m_data, mpfr_get_prec(val)); mpfr_set(this->m_data, val, GMP_RNDN); return *this; } mpfr_float_backend& operator=(const mpf_t val) BOOST_NOEXCEPT { + mpfr_set_prec(this->m_data, mpf_get_prec(val)); mpfr_set_f(this->m_data, val, GMP_RNDN); return *this; } @@ -538,12 +554,14 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> template mpfr_float_backend& operator=(const mpfr_float_backend& val) BOOST_NOEXCEPT { + mpfr_set_prec(this->m_data, mpfr_get_prec(val.data())); mpfr_set(this->m_data, val.data(), GMP_RNDN); return *this; } template mpfr_float_backend& operator=(const gmp_float& val) BOOST_NOEXCEPT { + mpfr_set_prec(this->m_data, mpf_get_prec(val.data())); mpfr_set_f(this->m_data, val.data(), GMP_RNDN); return *this; } @@ -567,11 +585,11 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> } unsigned precision()const BOOST_NOEXCEPT { - return mpfr_get_prec(this->m_data) * 301L / 1000 - 1; + return multiprecision::detail::digits2_2_10(mpfr_get_prec(this->m_data)); } void precision(unsigned digits10) BOOST_NOEXCEPT { - mpfr_set_prec(this->m_data, (digits10 + 1) * 1000L / 301); + mpfr_set_prec(this->m_data, multiprecision::detail::digits2_2_10((digits10))); } }; @@ -1051,6 +1069,21 @@ inline void eval_tanh(mpfr_float_backend& result, const mpfr_float_bac } // namespace backends +#ifdef BOOST_NO_SFINAE_EXPR + +namespace detail{ + +template +struct is_explicitly_convertible, backends::mpfr_float_backend > : public mpl::true_ {}; + +} + +#endif + +template<> +struct number_category >::type> : public mpl::int_{}; + + using boost::multiprecision::backends::mpfr_float_backend; typedef number > mpfr_float_50; @@ -1119,7 +1152,7 @@ public: { return -(max)(); } - BOOST_STATIC_CONSTEXPR int digits = static_cast(((Digits10 + 1) * 1000L) / 301L); + BOOST_STATIC_CONSTEXPR int digits = static_cast((Digits10 * 1000L) / 301L + ((Digits10 * 1000L) % 301 ? 2 : 1)); BOOST_STATIC_CONSTEXPR int digits10 = Digits10; // Is this really correct??? BOOST_STATIC_CONSTEXPR int max_digits10 = Digits10 + 2; diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index 99ca7b19..a9ae4721 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -99,9 +99,8 @@ public: : m_backend(val.backend()) {} template - number(const number& val, typename enable_if_c< - (!detail::is_explicitly_convertible::value - && !detail::is_restricted_conversion::value) + explicit number(const number& val, typename enable_if_c< + (!detail::is_explicitly_convertible::value) >::type* = 0) { // @@ -116,17 +115,6 @@ public: >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) : m_backend(val.backend()) {} - template - explicit number(const number& val, typename enable_if_c< - (!detail::is_explicitly_convertible::value - && detail::is_restricted_conversion::value) - >::type* = 0) - { - // - // Attempt a generic interconvertion: - // - detail::generic_interconvert(backend(), val.backend(), number_category(), number_category()); - } template BOOST_FORCEINLINE number(V v1, V v2, typename enable_if, is_same, is_convertible > >::type* = 0) { @@ -210,7 +198,7 @@ public: return *this; } */ - +/* template typename disable_if, number& >::type operator=(const number& v) @@ -220,7 +208,7 @@ public: // detail::generic_interconvert(backend(), v.backend(), number_category(), number_category()); return *this; - } + }*/ template typename disable_if, number& >::type assign(const number& v) @@ -672,7 +660,7 @@ private: // create a temporary result and assign it to *this: typedef typename detail::expression::result_type temp_type; temp_type t(e); - *this = t; + this->assign(t); } diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 994c4899..d9a1af1c 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -738,6 +738,7 @@ run ../example/tommath_snips.cpp $(TOMMATH) : # requirements [ check-target-builds ../config//has_tommath : : no ] ; run ../example/floating_point_examples.cpp : : : gcc:-std=c++0x ; +run test_cpp_int_conv.cpp ; compile include_test/mpfr_include_test.cpp : # requirements @@ -804,7 +805,8 @@ for local source in [ glob compile_fail/*.cpp ] { compile-fail $(source) : - [ check-target-builds ../config//has_gmp : TEST_GMP : ] + [ check-target-builds ../config//has_gmp : TEST_GMP : ] + [ check-target-builds ../config//has_mpfr : TEST_MPFR : ] ; } diff --git a/test/compile_fail/conv_fail_1.cpp b/test/compile_fail/conv_fail_01.cpp similarity index 100% rename from test/compile_fail/conv_fail_1.cpp rename to test/compile_fail/conv_fail_01.cpp diff --git a/test/compile_fail/conv_fail_2.cpp b/test/compile_fail/conv_fail_02.cpp similarity index 100% rename from test/compile_fail/conv_fail_2.cpp rename to test/compile_fail/conv_fail_02.cpp diff --git a/test/compile_fail/conv_fail_3.cpp b/test/compile_fail/conv_fail_03.cpp similarity index 100% rename from test/compile_fail/conv_fail_3.cpp rename to test/compile_fail/conv_fail_03.cpp diff --git a/test/compile_fail/conv_fail_4.cpp b/test/compile_fail/conv_fail_04.cpp similarity index 100% rename from test/compile_fail/conv_fail_4.cpp rename to test/compile_fail/conv_fail_04.cpp diff --git a/test/compile_fail/conv_fail_5.cpp b/test/compile_fail/conv_fail_05.cpp similarity index 100% rename from test/compile_fail/conv_fail_5.cpp rename to test/compile_fail/conv_fail_05.cpp diff --git a/test/compile_fail/conv_fail_6.cpp b/test/compile_fail/conv_fail_06.cpp similarity index 100% rename from test/compile_fail/conv_fail_6.cpp rename to test/compile_fail/conv_fail_06.cpp diff --git a/test/compile_fail/conv_fail_7.cpp b/test/compile_fail/conv_fail_07.cpp similarity index 100% rename from test/compile_fail/conv_fail_7.cpp rename to test/compile_fail/conv_fail_07.cpp diff --git a/test/compile_fail/conv_fail_8.cpp b/test/compile_fail/conv_fail_08.cpp similarity index 100% rename from test/compile_fail/conv_fail_8.cpp rename to test/compile_fail/conv_fail_08.cpp diff --git a/test/compile_fail/conv_fail_9.cpp b/test/compile_fail/conv_fail_09.cpp similarity index 100% rename from test/compile_fail/conv_fail_9.cpp rename to test/compile_fail/conv_fail_09.cpp diff --git a/test/compile_fail/conv_fail_49.cpp b/test/compile_fail/conv_fail_49.cpp new file mode 100644 index 00000000..7f4bd612 --- /dev/null +++ b/test/compile_fail/conv_fail_49.cpp @@ -0,0 +1,23 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_MPFR + +#include + +using namespace boost::multiprecision; + +int main() +{ + mpfr_float_100 f(2); + mpfr_float_50 f2; + f2 = f; +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/test/compile_fail/conv_fail_50.cpp b/test/compile_fail/conv_fail_50.cpp new file mode 100644 index 00000000..d0a52a58 --- /dev/null +++ b/test/compile_fail/conv_fail_50.cpp @@ -0,0 +1,22 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_MPFR + +#include + +using namespace boost::multiprecision; + +int main() +{ + mpfr_float_100 f(2); + mpfr_float_50 f2 = f; +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/test/compile_fail/conv_fail_51.cpp b/test/compile_fail/conv_fail_51.cpp new file mode 100644 index 00000000..77441672 --- /dev/null +++ b/test/compile_fail/conv_fail_51.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_100 f(2); + cpp_dec_float_50 f2 = f; +} + diff --git a/test/compile_fail/conv_fail_52.cpp b/test/compile_fail/conv_fail_52.cpp new file mode 100644 index 00000000..0f9edfb5 --- /dev/null +++ b/test/compile_fail/conv_fail_52.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_100 f(2); + cpp_dec_float_50 f2; + f2 = f; +} + diff --git a/test/compile_fail/conv_fail_53.cpp b/test/compile_fail/conv_fail_53.cpp new file mode 100644 index 00000000..cd48feea --- /dev/null +++ b/test/compile_fail/conv_fail_53.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + int256_t i = 3; + int128_t j = i; +} + diff --git a/test/compile_fail/conv_fail_54.cpp b/test/compile_fail/conv_fail_54.cpp new file mode 100644 index 00000000..f7583363 --- /dev/null +++ b/test/compile_fail/conv_fail_54.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + int256_t i = 3; + int128_t j; + j = i; +} + diff --git a/test/compile_fail/conv_fail_55.cpp b/test/compile_fail/conv_fail_55.cpp new file mode 100644 index 00000000..680306f1 --- /dev/null +++ b/test/compile_fail/conv_fail_55.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + int256_t i = 3; + uint256_t j; + j = i; +} + diff --git a/test/compile_fail/conv_fail_56.cpp b/test/compile_fail/conv_fail_56.cpp new file mode 100644 index 00000000..f33e832d --- /dev/null +++ b/test/compile_fail/conv_fail_56.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + int256_t i = 3; + uint256_t j = i; +} + diff --git a/test/compile_fail/conv_fail_57.cpp b/test/compile_fail/conv_fail_57.cpp new file mode 100644 index 00000000..04dcb4cf --- /dev/null +++ b/test/compile_fail/conv_fail_57.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 3; + int256_t j = i; +} + diff --git a/test/compile_fail/conv_fail_58.cpp b/test/compile_fail/conv_fail_58.cpp new file mode 100644 index 00000000..00e09060 --- /dev/null +++ b/test/compile_fail/conv_fail_58.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 3; + int256_t j; + j = i; +} + diff --git a/test/math/test_bessel_j.cpp b/test/math/test_bessel_j.cpp index 14c32412..7738d5ae 100644 --- a/test/math/test_bessel_j.cpp +++ b/test/math/test_bessel_j.cpp @@ -87,7 +87,7 @@ void expected_results() ".*", // platform ".*", // test type(s) ".*JN.*Integer.*", // test data group - ".*", 40000, 10000); // test function + ".*", 50000, 15000); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp index 2672d8bd..adb472ca 100644 --- a/test/math/test_bessel_y.cpp +++ b/test/math/test_bessel_y.cpp @@ -107,7 +107,7 @@ void expected_results() ".*", // platform ".*", // test type(s) ".*", // test data group - ".*", 80, 40); // test function + ".*", 150, 60); // test function // // Finish off by printing out the compiler/stdlib/platform names, // we do this to make it easier to mark up expected error rates. diff --git a/test/math/test_erf.cpp b/test/math/test_erf.cpp index 77db0a60..3ce56dfc 100644 --- a/test/math/test_erf.cpp +++ b/test/math/test_erf.cpp @@ -75,7 +75,7 @@ void expected_results() ".*", // platform ".*", // test type(s) "Inverse Erf.*", // test data group - "boost::math::erfc?_inv", 35, 20); // test function + "boost::math::erfc?_inv", 60, 20); // test function // // Finish off by printing out the compiler/stdlib/platform names, // we do this to make it easier to mark up expected error rates. diff --git a/test/math/test_gamma.cpp b/test/math/test_gamma.cpp index a4df3f37..4e4d5636 100644 --- a/test/math/test_gamma.cpp +++ b/test/math/test_gamma.cpp @@ -68,7 +68,7 @@ void expected_results() ".*", // platform ".*", // test type(s) "factorials", // test data group - "boost::math::lgamma", 80, 40); // test function + "boost::math::lgamma", 750, 100); // test function add_expected_result( ".*", // compiler ".*", // stdlib diff --git a/test/math/test_legendre.cpp b/test/math/test_legendre.cpp index 7ec607ac..f855b9c3 100644 --- a/test/math/test_legendre.cpp +++ b/test/math/test_legendre.cpp @@ -54,7 +54,7 @@ void expected_results() ".*", // platform ".*", // test type(s) ".*", // test data group - ".*", 5000, 500); // test function + ".*", 6000, 500); // test function // // Finish off by printing out the compiler/stdlib/platform names, // we do this to make it easier to mark up expected error rates. diff --git a/test/test_cos.cpp b/test/test_cos.cpp index e429d06b..f31a3bfd 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -243,7 +243,7 @@ void test() max_err = err; } std::cout << "Max error was: " << max_err << std::endl; - BOOST_TEST(max_err < 500); + BOOST_TEST(max_err < 750); // // Test with some exact binary values as input - this tests our code diff --git a/test/test_cpp_dec_float_conv.cpp b/test/test_cpp_dec_float_conv.cpp new file mode 100644 index 00000000..d1c73064 --- /dev/null +++ b/test/test_cpp_dec_float_conv.cpp @@ -0,0 +1,42 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include +#include +#include "test.hpp" + +#include + +int main() +{ + using namespace boost::multiprecision; + // + // Test interconversions between different precisions: + // + cpp_dec_float_50 f1(2); + cpp_dec_float_100 f2(3); + + cpp_dec_float_100 f3 = f1; // implicit conversion OK + BOOST_TEST(f3 == 2); + cpp_dec_float_50 f4(f2); // explicit conversion OK + BOOST_TEST(f4 == 3); + + f2 = f1; + BOOST_TEST(f2 == 2); + f2 = 4; + f1 = static_cast(f2); + BOOST_TEST(f1 == 4); + + + return boost::report_errors(); +} + + + diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp index 1ba8f9ec..853249e1 100644 --- a/test/test_cpp_int.cpp +++ b/test/test_cpp_int.cpp @@ -281,9 +281,9 @@ void test() // also don't test for modulo types, as these may give a diffferent result from arbitrary // precision types: BOOST_CHECK_EQUAL(mpz_int(pow(d, ui % 19)).str(), test_type(pow(d1, ui % 19)).str()); - BOOST_CHECK_EQUAL(mpz_int(powm(a, b, c)).str(), test_type(powm(a, b, c)).str()); - BOOST_CHECK_EQUAL(mpz_int(powm(a, b, ui)).str(), test_type(powm(a, b, ui)).str()); - BOOST_CHECK_EQUAL(mpz_int(powm(a, ui, c)).str(), test_type(powm(a, ui, c)).str()); + BOOST_CHECK_EQUAL(mpz_int(powm(a, b, c)).str(), test_type(powm(a1, b1, c1)).str()); + BOOST_CHECK_EQUAL(mpz_int(powm(a, b, ui)).str(), test_type(powm(a1, b1, ui)).str()); + BOOST_CHECK_EQUAL(mpz_int(powm(a, ui, c)).str(), test_type(powm(a1, ui, c1)).str()); } if(last_error_count != (unsigned)boost::detail::test_errors()) diff --git a/test/test_cpp_int_conv.cpp b/test/test_cpp_int_conv.cpp new file mode 100644 index 00000000..60a93a7e --- /dev/null +++ b/test/test_cpp_int_conv.cpp @@ -0,0 +1,55 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include +#include +#include "test.hpp" + +#include + +int main() +{ + using namespace boost::multiprecision; + // + // Test interconversions between different precisions: + // + cpp_int i1(2); + int128_t i2(3); + int256_t i3(4); + number > i4(5); + + i1 = i3; + BOOST_TEST(i1 == 4); + i1 = i4; + BOOST_TEST(i1 == 5); + + i3 = -1234567; + i4 = -5677334; + i1 = i3; + BOOST_TEST(i1 == -1234567); + i1 = i4; + BOOST_TEST(i1 == -5677334); + + i3 = i2; + BOOST_TEST(i3 == 3); + + i3 = -1234567; + + uint128_t i5(i3); + BOOST_TEST(i5 == -1234567); + + int128_t i6(i4); + BOOST_TEST(i6 == -5677334); + + return boost::report_errors(); +} + + + diff --git a/test/test_generic_conv.cpp b/test/test_generic_conv.cpp index 6664f4e9..50169d73 100644 --- a/test/test_generic_conv.cpp +++ b/test/test_generic_conv.cpp @@ -43,16 +43,16 @@ int main() mpz_int z(c); cpp_int t(z); BOOST_CHECK_EQUAL(t, c); - z = -c; - t = -z; + z.assign(-c); + t.assign(-z); BOOST_CHECK_EQUAL(t, c); #endif #ifdef TEST_TOMMATH tom_int tom(c); cpp_int t2(tom); BOOST_CHECK_EQUAL(t2, c); - tom = -c; - t2 = -tom; + tom.assign(-c); + t2.assign(-tom); BOOST_CHECK_EQUAL(t2, c); #endif // @@ -62,7 +62,7 @@ int main() dec_float_500 df(c); dec_float_500 df2(c.str()); BOOST_CHECK_EQUAL(df, df2); - df = -c; + df.assign(-c); df2 = -df2; BOOST_CHECK_EQUAL(df, df2); #ifdef TEST_GMP @@ -70,7 +70,7 @@ int main() mpf_type mpf(c); mpf_type mpf2(c.str()); BOOST_CHECK_EQUAL(mpf, mpf2); - mpf = -c; + mpf.assign(-c); mpf2 = -mpf2; BOOST_CHECK_EQUAL(mpf, mpf2); #endif @@ -79,29 +79,29 @@ int main() mpfr_type mpfr(c); mpfr_type mpfr2(c.str()); BOOST_CHECK_EQUAL(mpfr, mpfr2); - mpfr = -c; + mpfr.assign(-c); mpfr2 = -mpfr2; BOOST_CHECK_EQUAL(mpfr, mpfr2); #endif // // Now float to float: // - df = c; + df.assign(c); df /= dec_float_500(gen()); dec_float_500 tol("1e-500"); #ifdef TEST_GMP - mpf = df; + mpf.assign(df); mpf2 = static_cast(df.str()); BOOST_CHECK_EQUAL(mpf, mpf2); - df = mpf; + df.assign(mpf); df2 = static_cast(mpf.str()); BOOST_CHECK(fabs((df - df2) / df) < tol); #endif #ifdef TEST_MPFR - mpfr = df; + mpfr.assign(df); mpfr2 = static_cast(df.str()); BOOST_CHECK_EQUAL(mpfr, mpfr2); - df = mpfr; + df.assign(mpfr); df2 = static_cast(mpfr.str()); BOOST_CHECK(fabs((df - df2) / df) < tol); #endif @@ -123,20 +123,20 @@ int main() // Integer to rational conversions: // #ifdef TEST_GMP - mpq = c; + mpq.assign(c); mpq_rational mpq2 = static_cast(c.str()); BOOST_CHECK_EQUAL(mpq, mpq2); #endif #ifdef TEST_TOMMATH - tr = c; + tr.assign(c); tom_rational tr2 = static_cast(c.str()); BOOST_CHECK_EQUAL(tr, tr2); #endif // // Rational to float: // - df = cppr; - df2 = numerator(cppr); + df.assign(cppr); + df2.assign(numerator(cppr)); df2 /= dec_float_500(denominator(cppr)); BOOST_CHECK(fabs(df - df2) / df2 < tol); } diff --git a/test/test_mpfr_conversions.cpp b/test/test_mpfr_conversions.cpp index cd11e638..1bc78f03 100644 --- a/test/test_mpfr_conversions.cpp +++ b/test/test_mpfr_conversions.cpp @@ -100,6 +100,24 @@ int main() BOOST_TEST(mpfr_float(gf) == 2); BOOST_TEST(mpfr_float_50(gf) == 2); + // + // Conversions involving precision only: + // + mpfr_float::default_precision(30); + f50 = 2; + mpfr_float_100 f100(3); + mpfr_float f0a(4); + mpfr_float f0b(f100); + BOOST_TEST(f0a.precision() == 30); + BOOST_TEST(f0b.precision() == 100); + f0a = f100; + BOOST_TEST(f0a == 3); + BOOST_TEST(f0a.precision() == 100); + + f100 = f50; + BOOST_TEST(f100 == 2); + + f50 = static_cast(f100); return boost::report_errors(); } From d609434125ac3f64409b3ac75c431bd8f679ee78 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 21 Aug 2012 15:47:32 +0000 Subject: [PATCH 221/256] Add missing files, fix the worst of the GCC build failures. [SVN r80114] --- include/boost/multiprecision/cpp_int.hpp | 4 +- .../multiprecision/detail/default_ops.hpp | 5 ++ .../multiprecision/detail/integer_ops.hpp | 2 +- .../traits/explicit_conversion.hpp | 45 +++++++++++++++++ .../traits/is_restricted_conversion.hpp | 48 +++++++++++++++++++ 5 files changed, 101 insertions(+), 3 deletions(-) create mode 100644 include/boost/multiprecision/traits/explicit_conversion.hpp create mode 100644 include/boost/multiprecision/traits/is_restricted_conversion.hpp diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index baf1eb18..36e0fc5e 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -707,7 +707,7 @@ public: : base_type() { *this = static_cast< - typename detail::canonical< + typename boost::multiprecision::detail::canonical< typename cpp_int_backend::local_limb_type, cpp_int_backend >::type @@ -718,7 +718,7 @@ public: cpp_int_backend& operator=(const cpp_int_backend& other) { *this = static_cast< - typename detail::canonical< + typename boost::multiprecision::detail::canonical< typename cpp_int_backend::local_limb_type, cpp_int_backend >::type diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index becb7cb4..4b7e7f9b 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -813,6 +813,11 @@ inline void eval_bit_unset(T& val, unsigned index) eval_bitwise_xor(val, mask); } +template +void eval_lcm(B& result, const B& a, const B& b); +template +void eval_gcd(B& result, const B& a, const B& b); + // // These have to implemented by the backend, declared here so that our macro generated code compiles OK. // diff --git a/include/boost/multiprecision/detail/integer_ops.hpp b/include/boost/multiprecision/detail/integer_ops.hpp index 08b66352..7cd7fb78 100644 --- a/include/boost/multiprecision/detail/integer_ops.hpp +++ b/include/boost/multiprecision/detail/integer_ops.hpp @@ -112,7 +112,7 @@ inline void eval_gcd(B& result, const B& a, const B& b) template inline void eval_lcm(B& result, const B& a, const B& b) { - typedef typename typename mpl::front::type ui_type; + typedef typename mpl::front::type ui_type; B t; eval_gcd(t, a, b); diff --git a/include/boost/multiprecision/traits/explicit_conversion.hpp b/include/boost/multiprecision/traits/explicit_conversion.hpp new file mode 100644 index 00000000..842d36d1 --- /dev/null +++ b/include/boost/multiprecision/traits/explicit_conversion.hpp @@ -0,0 +1,45 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright Vicente J. Botet Escriba 2009-2011 +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MP_EXPLICIT_CONVERTIBLE_HPP +#define BOOST_MP_EXPLICIT_CONVERTIBLE_HPP + +#include +#include + + +namespace boost{ namespace multiprecision{ namespace detail{ + +template +struct dummy_size{}; + +template +struct is_explicitly_convertible_imp +{ +#ifndef BOOST_NO_SFINAE_EXPR + template + static type_traits::yes_type selector(dummy_size(declval()))>*); + + template + static type_traits::no_type selector(...); + + static const bool value = sizeof(selector(0)) == sizeof(type_traits::yes_type); + + typedef boost::integral_constant type; +#else + typedef typename boost::is_convertible::type type; +#endif +}; + +template +struct is_explicitly_convertible : public is_explicitly_convertible_imp::type +{ +}; + +}}} // namespaces + +#endif + diff --git a/include/boost/multiprecision/traits/is_restricted_conversion.hpp b/include/boost/multiprecision/traits/is_restricted_conversion.hpp new file mode 100644 index 00000000..283f15ce --- /dev/null +++ b/include/boost/multiprecision/traits/is_restricted_conversion.hpp @@ -0,0 +1,48 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright Vicente J. Botet Escriba 2009-2011 +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MP_RESTRICTED_CONVERSION_HPP +#define BOOST_MP_RESTRICTED_CONVERSION_HPP + +#include +#include +#include + +namespace boost{ namespace multiprecision{ namespace detail{ + + +template +struct is_lossy_conversion +{ + typedef typename mpl::if_c< + ((number_category::value == number_kind_floating_point) && (number_category::value == number_kind_integer)) + || ((number_category::value == number_kind_floating_point) && (number_category::value == number_kind_rational)) + || ((number_category::value == number_kind_rational) && (number_category::value == number_kind_integer)) + || ((number_category::value == number_kind_fixed_point) && (number_category::value == number_kind_integer)) + || (number_category::value == number_kind_unknown) + || (number_category::value == number_kind_unknown), + mpl::true_, + mpl::false_ + >::type type; + static const bool value = type::value; +}; + +template +struct is_restricted_conversion +{ + typedef typename mpl::if_c< + ((is_explicitly_convertible::value && !is_convertible::value) + || is_lossy_conversion::value), + mpl::true_, + mpl::false_ + >::type type; + static const bool value = type::value; +}; + +}}} // namespaces + +#endif // BOOST_MP_RESTRICTED_CONVERSION_HPP + From 9d5a0bc87a30bf0d373a16b7d548157e41a0bf71 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 21 Aug 2012 16:24:05 +0000 Subject: [PATCH 222/256] Fix a few GCC warnings and errors [SVN r80115] --- .../multiprecision/detail/default_ops.hpp | 12 ++++--- .../detail/generic_interconvert.hpp | 1 + .../multiprecision/detail/integer_ops.hpp | 34 ++++++++++++------- 3 files changed, 30 insertions(+), 17 deletions(-) diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 4b7e7f9b..0fd06b26 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -725,10 +725,16 @@ inline void eval_round(T& result, const T& a) } } +template +void eval_lcm(B& result, const B& a, const B& b); +template +void eval_gcd(B& result, const B& a, const B& b); + template inline typename enable_if >::type eval_gcd(T& result, const T& a, const Arithmetic& b) { typedef typename boost::multiprecision::detail::canonical::type si_type; + using default_ops::eval_gcd; T t; t = static_cast(b); eval_gcd(result, a, t); @@ -742,6 +748,7 @@ template inline typename enable_if >::type eval_lcm(T& result, const T& a, const Arithmetic& b) { typedef typename boost::multiprecision::detail::canonical::type si_type; + using default_ops::eval_lcm; T t; t = static_cast(b); eval_lcm(result, a, t); @@ -813,11 +820,6 @@ inline void eval_bit_unset(T& val, unsigned index) eval_bitwise_xor(val, mask); } -template -void eval_lcm(B& result, const B& a, const B& b); -template -void eval_gcd(B& result, const B& a, const B& b); - // // These have to implemented by the backend, declared here so that our macro generated code compiles OK. // diff --git a/include/boost/multiprecision/detail/generic_interconvert.hpp b/include/boost/multiprecision/detail/generic_interconvert.hpp index 2cda6a6e..526ec86a 100644 --- a/include/boost/multiprecision/detail/generic_interconvert.hpp +++ b/include/boost/multiprecision/detail/generic_interconvert.hpp @@ -66,6 +66,7 @@ void generic_interconvert(To& to, const From& from, const mpl::int_::type limb_type; // get the corresponding type that we can assign to "To": diff --git a/include/boost/multiprecision/detail/integer_ops.hpp b/include/boost/multiprecision/detail/integer_ops.hpp index 7cd7fb78..9e53e094 100644 --- a/include/boost/multiprecision/detail/integer_ops.hpp +++ b/include/boost/multiprecision/detail/integer_ops.hpp @@ -309,7 +309,7 @@ void eval_powm(Backend& result, const Backend& a, const Backend& p, Integer c) } template -void eval_powm(Backend& result, const Backend& a, Integer b, const Backend& c) +typename enable_if >::type eval_powm(Backend& result, const Backend& a, Integer b, const Backend& c) { typedef typename canonical::type ui_type; typedef typename canonical::type i_type; @@ -320,11 +320,6 @@ void eval_powm(Backend& result, const Backend& a, Integer b, const Backend& c) using default_ops::eval_modulus; using default_ops::eval_right_shift; - if(b < 0) - { - BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); - } - Backend x, y(a); x = ui_type(1u); while(b > 0) @@ -341,8 +336,18 @@ void eval_powm(Backend& result, const Backend& a, Integer b, const Backend& c) eval_modulus(result, x, c); } +template +typename enable_if >::type eval_powm(Backend& result, const Backend& a, Integer b, const Backend& c) +{ + if(b < 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); + } + eval_powm(result, a, static_cast::type>(b), c); +} + template -void eval_powm(Backend& result, const Backend& a, Integer1 b, Integer2 c) +typename enable_if >::type eval_powm(Backend& result, const Backend& a, Integer1 b, Integer2 c) { typedef typename canonical::type ui_type; typedef typename canonical::type i1_type; @@ -354,11 +359,6 @@ void eval_powm(Backend& result, const Backend& a, Integer1 b, Integer2 c) using default_ops::eval_modulus; using default_ops::eval_right_shift; - if(b < 0) - { - BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); - } - Backend x, y(a); x = ui_type(1u); while(b > 0) @@ -375,6 +375,16 @@ void eval_powm(Backend& result, const Backend& a, Integer1 b, Integer2 c) eval_modulus(result, x, static_cast(c)); } +template +typename enable_if >::type eval_powm(Backend& result, const Backend& a, Integer1 b, Integer2 c) +{ + if(b < 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); + } + eval_powm(result, a, static_cast::type>(b), c); +} + struct powm_func { template From 615767497205a1436cf9e2704ca85ecd8ffa1106 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 21 Aug 2012 18:17:57 +0000 Subject: [PATCH 223/256] Fix rational_adapter's implicit/explicit constructors. Add converting constructors for trivial cpp_int's and test. Both fix GCC errors. [SVN r80120] --- include/boost/multiprecision/cpp_int.hpp | 61 +++++++++++++++++++ .../boost/multiprecision/rational_adapter.hpp | 27 ++++++++ test/test_cpp_int_conv.cpp | 3 + 3 files changed, 91 insertions(+) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 36e0fc5e..20e77d77 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1148,6 +1148,67 @@ public: this->sign(i < 0); return *this; } + + template + cpp_int_backend(const cpp_int_backend& other, + typename enable_if_c< + (sizeof(cpp_int_backend::local_limb_type) <= sizeof(typename cpp_int_backend::local_limb_type)) + && (Signed || !Signed2) + >::type* = 0) + : base_type() + { + *this = static_cast< + typename boost::multiprecision::detail::canonical< + typename cpp_int_backend::local_limb_type, + cpp_int_backend + >::type + >(*other.limbs()); + this->sign(other.sign()); + } + template + explicit cpp_int_backend(const cpp_int_backend& other, + typename disable_if_c< + (sizeof(cpp_int_backend::local_limb_type) <= sizeof(typename cpp_int_backend::local_limb_type)) + && (Signed || !Signed2) + >::type* = 0) + : base_type() + { + *this = static_cast< + typename boost::multiprecision::detail::canonical< + typename cpp_int_backend::local_limb_type, + cpp_int_backend + >::type + >(*other.limbs()); + this->sign(other.sign()); + } + template + cpp_int_backend& operator = (const cpp_int_backend& other) + { + *this = static_cast< + typename boost::multiprecision::detail::canonical< + typename cpp_int_backend::local_limb_type, + cpp_int_backend + >::type + >(*other.limbs()); + this->sign(other.sign()); + return *this; + } + template + explicit cpp_int_backend(const cpp_int_backend& other) + : base_type() + { + // We can only ever copy two limbs from other: + if(other.size() == 1) + { + *this->limbs() = *other.limbs(); + } + else + { + *this->limbs() = static_cast(*other.limbs()) | (static_cast(other.limbs()[1]) << (sizeof(limb_type) * CHAR_BIT)); + } + this->sign(other.sign()); + } + cpp_int_backend& operator = (const char* s) { try{ diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index 48d76b50..5e4ef673 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -34,6 +34,22 @@ struct rational_adapter m_value = o.m_value; } rational_adapter(const IntBackend& o) : m_value(o) {} + + template + rational_adapter(const U& u, typename enable_if_c::value>::type* = 0) + : m_value(IntBackend(u)){} + template + explicit rational_adapter(const U& u, + typename enable_if_c< + detail::is_explicitly_convertible::value && !is_convertible::value + >::type* = 0) + : m_value(IntBackend(u)){} + template + typename enable_if_c<(detail::is_explicitly_convertible::value && !is_arithmetic::value), rational_adapter&>::type operator = (const U& u) + { + m_value = IntBackend(u); + } + #ifndef BOOST_NO_RVALUE_REFERENCES rational_adapter(rational_adapter&& o) : m_value(o.m_value) {} rational_adapter(IntBackend&& o) : m_value(o) {} @@ -227,6 +243,17 @@ struct component_type > typedef number type; }; +#ifdef BOOST_NO_SFINAE_EXPR + +namespace detail{ + +template +struct is_explicitly_convertible > : public is_explicitly_convertible {}; + +} + +#endif + }} // namespaces diff --git a/test/test_cpp_int_conv.cpp b/test/test_cpp_int_conv.cpp index 60a93a7e..60c57d82 100644 --- a/test/test_cpp_int_conv.cpp +++ b/test/test_cpp_int_conv.cpp @@ -48,6 +48,9 @@ int main() int128_t i6(i4); BOOST_TEST(i6 == -5677334); + number, false> i7(i3); + BOOST_TEST(i7 == -1234567); + return boost::report_errors(); } From 145fa2cdd4fbe90e9796fddee1f7d28db985d121 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 23 Aug 2012 11:24:33 +0000 Subject: [PATCH 224/256] Inching closer to getting GCC to compile the tests again... [SVN r80153] --- include/boost/multiprecision/detail/number_base.hpp | 2 +- include/boost/multiprecision/mpfr.hpp | 1 - include/boost/multiprecision/number.hpp | 6 +++++- include/boost/multiprecision/rational_adapter.hpp | 4 ++-- 4 files changed, 8 insertions(+), 5 deletions(-) diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp index 1c1267df..0d7fe45a 100644 --- a/include/boost/multiprecision/detail/number_base.hpp +++ b/include/boost/multiprecision/detail/number_base.hpp @@ -76,7 +76,7 @@ struct has_enough_bits template struct canonical_imp { - typedef typename decay::type type; + typedef typename remove_cv::type>::type type; }; template struct canonical_imp > diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 98fa9334..cdbb8cfb 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -1083,7 +1083,6 @@ struct is_explicitly_convertible, backends::mpf template<> struct number_category >::type> : public mpl::int_{}; - using boost::multiprecision::backends::mpfr_float_backend; typedef number > mpfr_float_50; diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index a9ae4721..55b38314 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -1601,7 +1601,11 @@ private: template static BOOST_FORCEINLINE BOOST_CONSTEXPR const B2& canonical_value(const number& v) BOOST_NOEXCEPT { return v.backend(); } template - static BOOST_FORCEINLINE BOOST_CONSTEXPR typename detail::canonical::type canonical_value(const V& v) BOOST_NOEXCEPT { return static_cast::type>(v); } + static BOOST_FORCEINLINE BOOST_CONSTEXPR typename disable_if::type, V>, typename detail::canonical::type>::type + canonical_value(const V& v) BOOST_NOEXCEPT { return static_cast::type>(v); } + template + static BOOST_FORCEINLINE BOOST_CONSTEXPR typename enable_if::type, V>, const V&>::type + canonical_value(const V& v) BOOST_NOEXCEPT { return v; } static BOOST_FORCEINLINE typename detail::canonical::type canonical_value(const std::string& v) BOOST_NOEXCEPT { return v.c_str(); } static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const self_type& v) BOOST_NOEXCEPT { return v.backend(); } diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index 5e4ef673..6dd07d6f 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -41,11 +41,11 @@ struct rational_adapter template explicit rational_adapter(const U& u, typename enable_if_c< - detail::is_explicitly_convertible::value && !is_convertible::value + boost::multiprecision::detail::is_explicitly_convertible::value && !is_convertible::value >::type* = 0) : m_value(IntBackend(u)){} template - typename enable_if_c<(detail::is_explicitly_convertible::value && !is_arithmetic::value), rational_adapter&>::type operator = (const U& u) + typename enable_if_c<(boost::multiprecision::detail::is_explicitly_convertible::value && !is_arithmetic::value), rational_adapter&>::type operator = (const U& u) { m_value = IntBackend(u); } From d9901b51443b3b0613e9ec220f4365befd8233bb Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 24 Aug 2012 11:08:44 +0000 Subject: [PATCH 225/256] Fix remaining GCC C++11 failures. Fix buggy test cases. [SVN r80166] --- include/boost/multiprecision/cpp_int.hpp | 2 +- .../boost/multiprecision/detail/number_base.hpp | 10 ++++++++++ include/boost/multiprecision/number.hpp | 11 ++++++++--- test/test_arithmetic.cpp | 14 +++++++------- 4 files changed, 26 insertions(+), 11 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 20e77d77..23d91973 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -2811,7 +2811,7 @@ inline Integer negate_integer(Integer i, const mpl::true_&) BOOST_NOEXCEPT template inline Integer negate_integer(Integer i, const mpl::false_&) BOOST_NOEXCEPT { - return ~--i; + return ~(i-1); } template diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp index 0d7fe45a..ab3e34fe 100644 --- a/include/boost/multiprecision/detail/number_base.hpp +++ b/include/boost/multiprecision/detail/number_base.hpp @@ -78,6 +78,16 @@ struct canonical_imp { typedef typename remove_cv::type>::type type; }; +template +struct canonical_imp, Backend, Tag> +{ + typedef B type; +}; +template +struct canonical_imp, Backend, Tag> +{ + typedef B type; +}; template struct canonical_imp > { diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index 55b38314..b30e7891 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -112,7 +112,7 @@ public: explicit BOOST_FORCEINLINE number(const number& val, typename enable_if_c< (detail::is_explicitly_convertible::value && (detail::is_restricted_conversion::value || !boost::is_convertible::value)) - >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) + >::type* = 0) BOOST_NOEXCEPT_IF(noexcept(Backend(std::declval()))) : m_backend(val.backend()) {} template @@ -148,13 +148,13 @@ public: do_assign(e, tag_type()); return *this; } -/* + BOOST_FORCEINLINE number& operator=(const number& e) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) { m_backend = e.m_backend; return *this; } - */ + template BOOST_FORCEINLINE typename enable_if, number& >::type operator=(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval::type>())) @@ -603,6 +603,11 @@ explicit operator T()const { return this->template convert_to(); } +explicit operator bool()const +{ + using default_ops::eval_is_zero; + return !eval_is_zero(backend()); +} #endif // // Default precision: diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 99c1bb8b..4a6f102f 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -485,16 +485,16 @@ void test_integer_ops(const boost::mpl::int_::is_signed) { @@ -516,17 +516,17 @@ void test_integer_ops(const boost::mpl::int_ Date: Sun, 26 Aug 2012 16:46:44 +0000 Subject: [PATCH 226/256] Fix explicit conversion operators for GCC-4.6.x [SVN r80237] --- include/boost/multiprecision/number.hpp | 39 ++++++++++++++++++------- 1 file changed, 29 insertions(+), 10 deletions(-) diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index b30e7891..e7bbb7ee 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -598,16 +598,35 @@ public: return result; } #ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS -template -explicit operator T()const -{ - return this->template convert_to(); -} -explicit operator bool()const -{ - using default_ops::eval_is_zero; - return !eval_is_zero(backend()); -} +#if defined(__GNUC__) && (__GNUC__ == 4) && (__GNUC_MINOR__ < 7) + // + // Horrible workaround for gcc-4.6.x which always prefers the non-template + // operator bool() rather than the template operator when converting to + // an arithmetic type: + // + template , int>::type = 0> + explicit operator T ()const + { + using default_ops::eval_is_zero; + return !eval_is_zero(backend()); + } + template , int>::type = 0> + explicit operator T ()const + { + return this->template convert_to(); + } +#else + template + explicit operator T()const + { + return this->template convert_to(); + } + explicit operator bool()const + { + using default_ops::eval_is_zero; + return !eval_is_zero(backend()); + } +#endif #endif // // Default precision: From 6e58c919a60edcaabe5b782712ffb41d052f8858 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 27 Aug 2012 09:51:35 +0000 Subject: [PATCH 227/256] Delete dead code. [SVN r80248] --- include/boost/multiprecision/number.hpp | 53 +------------------------ 1 file changed, 2 insertions(+), 51 deletions(-) diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index e7bbb7ee..2a2f73fd 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -53,8 +53,7 @@ public: } template BOOST_FORCEINLINE BOOST_CONSTEXPR number(const V& v, typename enable_if_c< - /*(boost::is_arithmetic::value || is_same::value || is_convertible::value) - &&*/ is_convertible::type, Backend>::value + is_convertible::type, Backend>::value && !detail::is_restricted_conversion::type, Backend>::value >::type* = 0) : m_backend(canonical_value(v)) {} @@ -71,8 +70,7 @@ public: } template explicit BOOST_FORCEINLINE BOOST_CONSTEXPR number(const V& v, typename enable_if_c< - /*(boost::is_arithmetic::value || is_same::value || is_convertible::value) - &&*/ detail::is_explicitly_convertible::type, Backend>::value + detail::is_explicitly_convertible::type, Backend>::value && (detail::is_restricted_conversion::type, Backend>::value || !is_convertible::type, Backend>::value) >::type* = 0) @@ -128,12 +126,6 @@ public: assign_components(m_backend, v1.backend(), v2.backend()); } - /* - template - BOOST_FORCEINLINE BOOST_CONSTEXPR number(V v, typename enable_if, mpl::not_, is_same, is_convertible > > > >::type* = 0) - BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) - : m_backend(v){} - */ template typename enable_if::result_type, self_type>, number&>::type operator=(const detail::expression& e) { @@ -168,47 +160,6 @@ public: m_backend = canonical_value(v); return *this; } - /* - template - BOOST_FORCEINLINE typename enable_if, mpl::not_, is_same, is_convertible > > >, number& >::type - operator=(const V& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) - { - m_backend = v; - return *this; - } - template - BOOST_FORCEINLINE number& operator=(const number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) - { - m_backend = v.backend(); - return *this; - } - - template - BOOST_FORCEINLINE typename enable_if, number& >::type - operator=(const number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) - { - m_backend = v.backend(); - return *this; - } - template - BOOST_FORCEINLINE typename enable_if, number& >::type - assign(const number& v) BOOST_NOEXCEPT_IF(noexcept(std::declval() = static_cast(std::declval()))) - { - m_backend = v.backend(); - return *this; - } - */ -/* - template - typename disable_if, number& >::type - operator=(const number& v) - { - // - // Attempt a generic interconvertion: - // - detail::generic_interconvert(backend(), v.backend(), number_category(), number_category()); - return *this; - }*/ template typename disable_if, number& >::type assign(const number& v) From 1e00790703922627a72e36a57b9441098843d5d4 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 27 Aug 2012 12:30:53 +0000 Subject: [PATCH 228/256] Rename mp_number_archetype. Update docs with explicit conversion info. Regenerate docs. [SVN r80261] --- doc/html/boost_multiprecision/indexes.html | 2 +- .../boost_multiprecision/indexes/s01.html | 208 +++++------ .../boost_multiprecision/indexes/s02.html | 47 ++- .../boost_multiprecision/indexes/s03.html | 76 ++-- .../boost_multiprecision/indexes/s04.html | 333 ++++++++++-------- doc/html/boost_multiprecision/intro.html | 25 +- doc/html/boost_multiprecision/map.html | 2 +- doc/html/boost_multiprecision/map/ack.html | 4 +- doc/html/boost_multiprecision/map/hist.html | 30 +- doc/html/boost_multiprecision/map/todo.html | 19 +- doc/html/boost_multiprecision/perf.html | 2 +- .../perf/float_performance.html | 2 +- .../perf/int_real_world.html | 2 +- .../perf/integer_performance.html | 2 +- .../perf/rational_performance.html | 2 +- .../boost_multiprecision/perf/realworld.html | 2 +- doc/html/boost_multiprecision/ref.html | 4 +- .../boost_multiprecision/ref/backendconc.html | 45 +-- .../boost_multiprecision/ref/cpp_dec_ref.html | 8 +- .../boost_multiprecision/ref/cpp_int_ref.html | 6 +- .../boost_multiprecision/ref/gmp_int_ref.html | 2 +- .../boost_multiprecision/ref/headers.html | 2 +- .../boost_multiprecision/ref/internals.html | 94 +++++ .../boost_multiprecision/ref/mpf_ref.html | 2 +- .../boost_multiprecision/ref/mpfr_ref.html | 2 +- doc/html/boost_multiprecision/ref/number.html | 109 ++++-- .../boost_multiprecision/ref/tom_int_ref.html | 2 +- doc/html/boost_multiprecision/tut.html | 2 +- .../boost_multiprecision/tut/conversions.html | 91 +++-- doc/html/boost_multiprecision/tut/floats.html | 2 +- .../tut/floats/cpp_dec_float.html | 6 +- .../tut/floats/fp_eg.html | 2 +- .../tut/floats/fp_eg/aos.html | 2 +- .../tut/floats/fp_eg/gi.html | 2 +- .../tut/floats/fp_eg/jel.html | 2 +- .../tut/floats/fp_eg/nd.html | 2 +- .../tut/floats/fp_eg/poly_eg.html | 2 +- .../tut/floats/gmp_float.html | 10 +- .../tut/floats/mpfr_float.html | 10 +- doc/html/boost_multiprecision/tut/ints.html | 2 +- .../tut/ints/cpp_int.html | 8 +- .../boost_multiprecision/tut/ints/egs.html | 2 +- .../tut/ints/egs/bitops.html | 2 +- .../tut/ints/egs/factorials.html | 2 +- .../tut/ints/gmp_int.html | 8 +- .../tut/ints/tom_int.html | 6 +- .../boost_multiprecision/tut/primetest.html | 6 +- doc/html/boost_multiprecision/tut/random.html | 2 +- .../boost_multiprecision/tut/rational.html | 2 +- .../boost_multiprecision/tut/rational/br.html | 2 +- .../tut/rational/cpp_rational.html | 6 +- .../tut/rational/gmp_rational.html | 8 +- .../tut/rational/rational_adapter.html | 2 +- .../tut/rational/tommath_rational.html | 6 +- doc/html/index.html | 6 +- doc/multiprecision.qbk | 180 ++++++++-- .../concepts/mp_number_archetypes.hpp | 54 +-- test/test_acos.cpp | 2 +- test/test_arithmetic.cpp | 2 +- test/test_asin.cpp | 2 +- test/test_atan.cpp | 2 +- test/test_cos.cpp | 2 +- test/test_cosh.cpp | 2 +- test/test_exp.cpp | 2 +- test/test_fpclassify.cpp | 2 +- test/test_log.cpp | 2 +- test/test_numeric_limits.cpp | 2 +- test/test_pow.cpp | 2 +- test/test_round.cpp | 2 +- test/test_sin.cpp | 2 +- test/test_sinh.cpp | 2 +- test/test_sqrt.cpp | 2 +- test/test_tanh.cpp | 2 +- 73 files changed, 927 insertions(+), 576 deletions(-) create mode 100644 doc/html/boost_multiprecision/ref/internals.html diff --git a/doc/html/boost_multiprecision/indexes.html b/doc/html/boost_multiprecision/indexes.html index e3925a4f..8a9d13ce 100644 --- a/doc/html/boost_multiprecision/indexes.html +++ b/doc/html/boost_multiprecision/indexes.html @@ -3,7 +3,7 @@ Indexes - + diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index d414d97f..b72ad441 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -3,7 +3,7 @@ Function Index - + @@ -13,53 +13,59 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    +Function Index

    A B C D E F I L M P R S T Z

    -
    +
    A
    -
    B
    -

    -
    -

    [1] +

    +

    [1] The actual number generated will depend on the compiler, how well it optimises the code, and whether it supports rvalue references. The number of 11 temporaries was generated with Visual C++ 10

    -

    [2] +

    [2] Marc Glisse suggested pre-review that this could be reduced still further by careful use of rvalue-references and move semantics in the operator overloads. This will be investigated further at a later date. diff --git a/doc/html/boost_multiprecision/map.html b/doc/html/boost_multiprecision/map.html index 8edb89d1..5037bf2b 100644 --- a/doc/html/boost_multiprecision/map.html +++ b/doc/html/boost_multiprecision/map.html @@ -3,7 +3,7 @@ Roadmap - + diff --git a/doc/html/boost_multiprecision/map/ack.html b/doc/html/boost_multiprecision/map/ack.html index 4de1bb82..f437951a 100644 --- a/doc/html/boost_multiprecision/map/ack.html +++ b/doc/html/boost_multiprecision/map/ack.html @@ -3,7 +3,7 @@ Acknowledgements - + @@ -20,7 +20,7 @@

    This library would not have happened without:

    -
      +
      • Christopher Kormanyos' C++ decimal number code.
        • diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html index 70462181..157d4400 100644 --- a/doc/html/boost_multiprecision/map/hist.html +++ b/doc/html/boost_multiprecision/map/hist.html @@ -3,7 +3,7 @@ History - + @@ -17,7 +17,33 @@
        -
          +
          + + Post + review changes +
          +
            +
          • + Non-expression template operators further optimised with rvalue reference + support. +
            • +
          • + Many functions made made constexp? +
            • +
          • + Differentiate between explicit and implicit conversions in the number + constructor. +
            • +
          • + Removed "mp_" prefix from types. +
            • +
          +
          + + Pre-review + history +
          +
          • 2011-2012, John Maddock adds an expression template enabled front end to Christopher's code, and adds support for other backends. diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index 2877ef6c..d2ec17ec 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -3,7 +3,7 @@ TODO - + @@ -21,7 +21,7 @@ More a list of what could be done, rather than what should be done (which may be a much smaller list!).

            -
              +
              • Add back-end support for libdecNumber.
                • @@ -43,21 +43,10 @@
              - Pre-Review + Pre-Review Comments
              -
                -
              • - Can the non-expression template operators be further optimised with rvalue - reference support? -
                • -
              • - Can any functions - in particular value initialization - be made constexp? -
                • -
              • - Can we differentiate between explicit and implicit conversions in the - number constructor (may need some new type traits)? -
                • +
                • Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it. diff --git a/doc/html/boost_multiprecision/perf.html b/doc/html/boost_multiprecision/perf.html index 7a2b730a..530861ab 100644 --- a/doc/html/boost_multiprecision/perf.html +++ b/doc/html/boost_multiprecision/perf.html @@ -3,7 +3,7 @@ Performance Comparison - + diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html index d34ab87c..7117f46e 100644 --- a/doc/html/boost_multiprecision/perf/float_performance.html +++ b/doc/html/boost_multiprecision/perf/float_performance.html @@ -3,7 +3,7 @@ Float Algorithm Perfomance - + diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html index 353ab9ee..62aff8de 100644 --- a/doc/html/boost_multiprecision/perf/int_real_world.html +++ b/doc/html/boost_multiprecision/perf/int_real_world.html @@ -3,7 +3,7 @@ Integer Real World Tests - + diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html index 56ea5b0e..9b89b8e0 100644 --- a/doc/html/boost_multiprecision/perf/integer_performance.html +++ b/doc/html/boost_multiprecision/perf/integer_performance.html @@ -3,7 +3,7 @@ Integer Algorithm Perfomance - + diff --git a/doc/html/boost_multiprecision/perf/rational_performance.html b/doc/html/boost_multiprecision/perf/rational_performance.html index 98fb8836..509c5a2a 100644 --- a/doc/html/boost_multiprecision/perf/rational_performance.html +++ b/doc/html/boost_multiprecision/perf/rational_performance.html @@ -3,7 +3,7 @@ Rational Type Perfomance - + diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html index a084ecc1..b61c7c7f 100644 --- a/doc/html/boost_multiprecision/perf/realworld.html +++ b/doc/html/boost_multiprecision/perf/realworld.html @@ -3,7 +3,7 @@ Floating Point Real World Tests - + diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html index 0516caf6..8957bc6f 100644 --- a/doc/html/boost_multiprecision/ref.html +++ b/doc/html/boost_multiprecision/ref.html @@ -3,7 +3,7 @@ Reference - + @@ -25,6 +25,8 @@
                  gmp_float
                  mpfr_float_backend
                  cpp_dec_float
                  +
                  Internal Support + Code
                  Backend Requirements
                  Header File Structure
                diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index ab9600cb..3550a227 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -3,15 +3,15 @@ Backend Requirements - + - +
                -PrevUpHomeNext +PrevUpHomeNext

                @@ -20,10 +20,10 @@

                The requirements on the Backend template argument to number - are split up into sections: compulsary and optional. + are split up into sections: compulsory and optional.

                - Compulsary requirements have no default implementation in the library, therefore + Compulsory requirements have no default implementation in the library, therefore if the feature they implement is to be supported at all, then they must be implemented by the backend.

                @@ -34,20 +34,19 @@

                In the following tables, type B is the Backend - template arument to number, + template argument to number, b and b2 - are a variables of type B, cb - and cb2 are constant variables - of type const B, - rb is a variable of type - B&&, - a is a variable of Arithmetic - type, s is a variable of - type const char*, ui - is a variable of type unsigned, - bb is a variable of type - bool, pa - is a variable of type pointer-to-arithmetic-type, exp + are a variables of type B, cb, + cb2 and cb3 + are constant variables of type const + B, rb + is a variable of type B&&, + a and a2 + are variables of Arithmetic type, s + is a variable of type const char*, ui is a variable of type unsigned, bb + is a variable of type bool, + pa is a variable of type + pointer-to-arithmetic-type, exp is a variable of type B::exp_type, pexp is a variable of type B::exp_type*, i is a variable of type @@ -1075,7 +1074,9 @@

    Copy constructor from a different back-end type. When not provided, - a generic interconversion routine is used. + a generic interconversion routine is used. This constructor may + be explicit if the + corresponding frontend constructor should also be explicit.

    		@@ -2969,7 +2970,7 @@ eval_powm(b, cb, a, - a) + a2)

    		@@ -2980,7 +2981,7 @@

    Sets b to the result - of (cb^a)%a. The type of a + of (cb^a)%a2. The type of a shall be listed in one of the type lists B::signed_types, B::unsigned_types. The default version of this function is synthesised from other operations above. @@ -3612,7 +3613,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html index 8d84ad3d..76a9f702 100644 --- a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html @@ -3,15 +3,15 @@ cpp_dec_float - + - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -58,7 +58,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html index a302ef80..acc1b8c9 100644 --- a/doc/html/boost_multiprecision/ref/cpp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_int_ref.html @@ -3,7 +3,7 @@ cpp_int - + @@ -51,7 +51,7 @@

    -
    +
    Argument

    Meaning @@ -75,7 +75,7 @@

    The allocator used for dynamic memory allocation. This parameter can be void, in which case - no dymanic memory will ever be allocated. + no dynamic memory will ever be allocated.

    diff --git a/doc/html/boost_multiprecision/ref/gmp_int_ref.html b/doc/html/boost_multiprecision/ref/gmp_int_ref.html index 2f2655e7..d7eefd2d 100644 --- a/doc/html/boost_multiprecision/ref/gmp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/gmp_int_ref.html @@ -3,7 +3,7 @@ gmp_int - + diff --git a/doc/html/boost_multiprecision/ref/headers.html b/doc/html/boost_multiprecision/ref/headers.html index 87b88f8a..ab1a9f3d 100644 --- a/doc/html/boost_multiprecision/ref/headers.html +++ b/doc/html/boost_multiprecision/ref/headers.html @@ -3,7 +3,7 @@ Header File Structure - + diff --git a/doc/html/boost_multiprecision/ref/internals.html b/doc/html/boost_multiprecision/ref/internals.html new file mode 100644 index 00000000..b75aba98 --- /dev/null +++ b/doc/html/boost_multiprecision/ref/internals.html @@ -0,0 +1,94 @@ + + + +Internal Support Code + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + There are some traits classes which authors of new backends should be aware + of: +

    +
    namespace boost{ namespace multiprecision{ namespace detail{
+
+template<typename From, typename To>
+struct is_explicitly_convertible;
+
+}}}
+
    +

    + Inherits from boost::integral_constant<bool,true> if type From + has an explicit conversion from To. +

    +

    + For compilers that support C++11 SFINAE-expressions this trait should "just + work". Otherwise it inherits from boost::is_convertible<From, To>::type, and will need to be specialised for + Backends that have constructors marked as explicit. +

    +
    template <class From, class To>
+struct is_lossy_conversion
+{
+   static const bool value = see below;
+};
+
    +

    + Member value is true if the + conversion from From to + To would result in a loss + of precision, and false otherwise. +

    +

    + The default version of this trait simply checks whether the kind + of conversion (for example from a floating point to an integer type) is inherently + lossy. Note that if either of the types From + or To are of an unknown number + category (because number_category + is not specialised for that type) then this trait will be true. +

    +
    template<typename From, typename To>
+struct is_restricted_conversion
+{
+   static const bool value = see below;
+};
+
    +

    + Member value is true if From + is only explicitly convertible to To + and not implicitly convertible, or if is_lossy_conversion<From, To>::value is true. + Otherwise false. +

    +

    + Note that while this trait is the ultimate arbiter of which constructors + are marked as explicit in class + number, authors of backend + types should generally specialise one of the traits above, rather than this + one directly. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/ref/mpf_ref.html b/doc/html/boost_multiprecision/ref/mpf_ref.html index 02f8e03b..7bb0616a 100644 --- a/doc/html/boost_multiprecision/ref/mpf_ref.html +++ b/doc/html/boost_multiprecision/ref/mpf_ref.html @@ -3,7 +3,7 @@ gmp_float - + diff --git a/doc/html/boost_multiprecision/ref/mpfr_ref.html b/doc/html/boost_multiprecision/ref/mpfr_ref.html index a5e0ba30..45c7dbfe 100644 --- a/doc/html/boost_multiprecision/ref/mpfr_ref.html +++ b/doc/html/boost_multiprecision/ref/mpfr_ref.html @@ -3,7 +3,7 @@ mpfr_float_backend - + diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html index bf6d8b24..18b10bbc 100644 --- a/doc/html/boost_multiprecision/ref/number.html +++ b/doc/html/boost_multiprecision/ref/number.html @@ -3,7 +3,7 @@ number - + @@ -19,7 +19,7 @@
    - Synopsis + Synopsis 
    namespace boost{ namespace multiprecision{
 
@@ -29,6 +29,7 @@
    number();
    number(see-below);
    number& operator=(see-below);
+   number& assign(see-below);
 
    // Member operators
    number& operator+=(const see-below&);
@@ -69,7 +70,8 @@
    // Comparison:
    int compare(const number<Backend>& o)const;
    template <class V>
-   typename enable_if<is_arithmetic<V>, int>::type compare(const V& o)const;
+   typename enable_if<is_convertible<V, number<Backend, ExpressionTemplates> >, int>::type
+      compare(const V& o)const;
    // Access to the underlying implementation:
    Backend& backend();
    const Backend& backend()const;
@@ -198,7 +200,7 @@
    - Description + Description 
    template <class Backend, bool ExpressionTemplates = true>
 class number;
@@ -209,7 +211,7 @@
       
    
 
    
 
    
-
    
+
    
 
    Backend
    
 
    
               The actual arithmetic back-end that does all the work.
@@ -224,12 +226,13 @@
 
    number();
 number(see-below);
 number& operator=(see-below);
+number& assign(see-below);
 
    
 
    
         Type number is default constructible,
         and both copy constructible and assignable from:
       
    
-
      
+
        
 
      • 
             Itself.
           
        • 
@@ -237,14 +240,11 @@
             An expression template which is the result of one of the arithmetic operators.
           
 
      • 
-            Any builtin arithmetic type.
+            Any builtin arithmetic type, as long as the result would not be lossy
+            (for example float to integer conversion).
           
        • 
 
      • 
-            A std::string or any type which is convertible
-            to const char*.
-          
        • 
-
      • 
-            Any type that the Backend is constructible or assignable from.
+            Any type that the Backend is implicitly constructible or assignable from.
           
        • 
 
      • 
             An rvalue reference to another number.
@@ -253,7 +253,50 @@
             are always supported when the argument is an rvalue reference irrespective
             of the backend.
           
        • 
+
      • 
+            Any type in the same family, as long as no loss of precision is involved.
+            For example from int128
+            to int256, or cpp_dec_float_50 to cpp_dec_float_100.
+          
        • 
 
      
+
      
+        Type number is explicitly
+        constructible from:
+      
      
+
        
+
      • 
+            Any type mentioned above.
+          
        • 
+
      • 
+            A std::string or any type which is convertible
+            to const char*.
+          
        • 
+
      • 
+            Any arithmetic type (including those that would result in lossy conversions).
+          
        • 
+
      • 
+            Any type in the same family, including those that result in loss of precision.
+          
        • 
+
      • 
+            Any type that the Backend is explicitly constructible from.
+          
        • 
+
      • 
+            Any pair of types for which a generic interconversion exists: that is
+            from integer to integer, integer to rational, integer to float, rational
+            to rational, rational to float, or float to float.
+          
        • 
+
      
+
      
+        The assign member function is available for any type for which an explicit
+        converting constructor exists. It is intended to be used where a temporary
+        generated from an explicit assignment would be expensive, for example:
+      
      
+
      mpfr_float_50    f50;
+mpfr_float_100   f100;
+
+f50 = static_cast<mpfr_float_50>(f100);  // explicit cast create a temporary
+f50.assign(f100);                        // explicit call to assign create no temporary
+
      
 
      
         In addition, if the type has multiple components (for example rational or
         complex number types), then there is a two argument constructor:
@@ -286,16 +329,16 @@
 
      
         The arguments to these operators is either:
       
      
-
        
+
          
 
        • 
             Another number<Backend,
             ExpressionTemplates>.
           
          • 
 
        • 
-            A builtin arithmetic type.
+            An expression template derived from number<Backend>.
           
          • 
 
        • 
-            An expression template derived from number<Backend>.
+            Any type implicitly convertible to number<Backend, ExpressionTemplates>.
           
          • 
 
        
 
        
@@ -372,12 +415,13 @@
       
        
 
        int compare(const number<Backend, ExpressionTemplates>& o)const;
 template <class V>
-typename enable_if<is_arithmetic<V>, int>::type compare(const V& other)const;
+typename enable_if<is_convertible<V, number<Backend, ExpressionTemplates> >, int>::type
+   compare(const V& other)const;
 
        
 
        
         Returns:
       
        
-
          
+
            
 
          • 
             A value less that 0 for *this < other
           
            • 
@@ -397,7 +441,7 @@
       
            
 
            
 
-        Non-member
+        Non-member
         operators
       
            
 
            // Non member operators:
@@ -428,7 +472,7 @@
 
            
         The arguments to these functions must contain at least one of the following:
       
            
-
              
+
                
 
              • 
             A number.
           
                • 
@@ -442,7 +486,7 @@
 
                
         The return type of these operators is either:
       
                
-
                  
+
                    
 
                  • 
             An unmentionable-type expression template type when
             ExpressionTemplates is
@@ -471,7 +515,7 @@
       
                    
 
                    
 
-        swap
+        swap
       
                    
 
                    template <class Backend, ExpressionTemplates>
 void swap(number<Backend, ExpressionTemplates>& a, number<Backend, ExpressionTemplates>& b);
@@ -481,7 +525,7 @@
       
                    
 
                    
 
-        Iostream
+        Iostream
         Support
       
                    
 
                    template <class Backend, bool ExpressionTemplates>
@@ -502,7 +546,7 @@
       
                    
 
                    
 
-        Non-member
+        Non-member
         standard library function support
       
                    
 
                    unmentionable-expression-template-type    abs    (const number-or-expression-template-type&);
@@ -561,14 +605,14 @@
       
                    
 
                    
 
-        Traits Class
+        Traits Class
         Support
       
                    
 
                    template <class T>
 struct component_type;
 
                    
 
                    
-        If this is a type with mutiple components (for example rational or complex
+        If this is a type with multiple components (for example rational or complex
         types), then this trait has a single member type
         that is the type of those components.
       
                    
@@ -580,12 +624,15 @@
         where N is one of the enumerated
         values number_kind_integer,
         number_kind_floating_point,
-        number_kind_rational or
-        number_kind_fixed_point.
+        number_kind_rational, number_kind_fixed_point, or number_kind_unknown. This traits class
+        is specialized for any type that has std::numeric_limits
+        support as well as for classes in this library: which means it can be used
+        for generic code that must work with built in arithmetic types as well as
+        multiprecision ones.
       
                    
 
                    
 
-        Integer
+        Integer
         functions
       
                    
 
                    unmentionable-expression-template-type    pow(const number-or-expression-template-type& b, unsigned p);
@@ -666,7 +713,7 @@
       
                    
 
                    
 
-        Rational
+        Rational
         Number Functions
       
                    
 
                    typename component_type<number-or-expression-template-type>::type numerator  (const number-or-expression-template-type&);
@@ -678,7 +725,7 @@
       
                    
 
                    
 
-        Boost.Math
+        Boost.Math
         Interoperability Support
       
                    
 
                    namespace boost{ namespace math{
@@ -701,7 +748,7 @@
       
                    
 
                    
 
-        std::numeric_limits
+        std::numeric_limits
         support
       
                    
 
                    namespace std{
diff --git a/doc/html/boost_multiprecision/ref/tom_int_ref.html b/doc/html/boost_multiprecision/ref/tom_int_ref.html
index 5d7cf7bd..3134b00b 100644
--- a/doc/html/boost_multiprecision/ref/tom_int_ref.html
+++ b/doc/html/boost_multiprecision/ref/tom_int_ref.html
@@ -3,7 +3,7 @@
 
 tom_int
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html
index 8b64cd8e..1ed672ca 100644
--- a/doc/html/boost_multiprecision/tut.html
+++ b/doc/html/boost_multiprecision/tut.html
@@ -3,7 +3,7 @@
 
 Tutorial
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/conversions.html b/doc/html/boost_multiprecision/tut/conversions.html
index c288abe4..cb5c0664 100644
--- a/doc/html/boost_multiprecision/tut/conversions.html
+++ b/doc/html/boost_multiprecision/tut/conversions.html
@@ -3,7 +3,7 @@
 
 Constructing and Interconverting Between Number Types
 
-
+
 
 
 
@@ -22,14 +22,26 @@
         All of the number types that are based on number
         have certain conversion rules in common. In particular:
       
                    
-
                    • 
+
                      • 
             Any number type can be constructed (or assigned) from any builtin arithmetic
-            type:
+            type, as long as the conversion isn't lossy (for example float to int
+            conversion):
           
                      
 
                      cpp_dec_float_50 df(0.5); // OK construction from double
 cpp_int          i(450);  // OK constructs from signed int
+cpp_int          j = 3.14; // Error, lossy conversion.
 
                      
-
                      • 
+
                        • 
+            A number can be explicitly constructed from an arithmetic type, even
+            when the conversion is lossy:
+          
                        
+
                        cpp_int          i(3.14);  // OK explicit conversion
+i = static_cast<cpp_int>(3.14)  // OK explicit conversion
+i.assign(3.14);                 // OK, explicit assign and avoid a temporary from the cast above
+i = 3.14;                       // Error, no implicit assignment operator for lossy conversion.
+cpp_int          j = 3.14;      // Error, no implicit constructor for lossy conversion.
+
                        
+
                        • 
             A number can be converted
             to any built in type, via the convert_to
             member function:
@@ -40,7 +52,7 @@
 
                          
         Additional conversions may be supported by particular backends.
       
                          
-
                          • 
+
                            • 
             A number can be converted
             to any built in type, via an explicit conversion operator: this functionality
             is only available on compilers supporting C++11's explicit conversion
@@ -50,19 +62,25 @@
 int i = z;  // Error, implicit conversion not allowed.
 int j = static_cast<int>(z);  // OK explicit conversion.
 
                    
-
                    • 
-            Any number type can be constructed (or assigned) from a const char* or a std::string:
+
                      • 
+            Any number type can be explicitly constructed (or
+            assigned) from a const char*
+            or a std::string:
           
                      
 
                      // pi to 50 places from a string:
-cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
+cpp_dec_float_50 df("3.14159265358979323846264338327950288419716939937510");
 // Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly:
-cpp_int          i  = "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000";
+cpp_int          i("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000");
 // Invalid input always results in a std::runtime_error being thrown:
-i = std::string("3.14");
+i = static_cast<cpp_int>("3.14");
+// implicit conversions from strings are not allowed:
+i = "23"; // Error, no assignment operator for implicit conversion from string
+// assign member function, avoids having to create a temporary via a static_cast:
+i.assign("23");  // OK
 
                      
-
                      • 
-            Any number type will interoperate with the builtin type in arithmetic
-            expressions:
+
                        • 
+            Any number type will interoperate with the builtin types in arithmetic
+            expressions as long as the conversions are not lossy:
           
                        
 
                        // pi to 50 places from a string:
 cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
@@ -70,12 +88,11 @@
 // than constructing a temporary:
 df *= 2;
 
-// There is a need to be careful with integer types though:
+// You can't mix integer types with floats though:
 cpp_int i = 2;
-// Ooops, this really just multiplies by 3:
-i *= 3.14;
+i *= 3.14;  // Error, no *= operator will be found.
 
                        
-
                        • 
+
                          • 
             Any number type can be streamed to and from the C++ iostreams:
           
                          
 
                          cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
@@ -87,22 +104,40 @@
 // Now print in hex format with prefix:
 std::cout << std::hex << std::showbase << i << std::endl;
 
                          
-
                          • 
+
                            • 
+            Interconversions between number types of the same family are allowed
+            and are implicit conversions if no loss of precision is involved, and
+            explicit if it is:
+          
                            
+
                            int128       i128 = 0;
+int266       i256 = i128;  // OK implicit widening conversion
+i128              = i256;  // Error, no assignment operator found, narrowing conversion is explict
+i128              = static_cast<int128>(i256); // OK, explicit narrowing conversion
+
+mpz_int      z    = 0;
+mpf_float    f    = z;    // OK, GMP handles this conversion natively, and it's not lossy and therefore implicit
+
+mpf_float_50 f50  = 2;
+f                 = f50;  // OK, conversion from fixed to variable precision, f will have 50 digits precision.
+f50               = f;    // Error, conversion from variable to fixed precision is potentially lossy, explicit cast required.
+
                            
+
                            • 
             Some interconversions between number types are completely generic, and
-            are always available:
+            are always available, albeit the conversions are always explicit:
           
                            
 
                            cpp_int cppi(2);
 // We can always convert between numbers of the same category - 
-// int to int, rational to rational, or float to float, so this is OK:
-mpz_int z = cppi;
+// int to int, rational to rational, or float to float, so this is OK
+// as long as we use an explicit conversion:
+mpz_int z(cppi);
 // We can always promote from int to rational, int to float, or rational to float:
-cpp_rational     cppr = cppi;  // OK, int to rational
-cpp_dec_float_50 df =   cppi;  // OK, int to float
-df                  =   cppr;  // OK, rational to float
-// However narrowing conversions always fail:
+cpp_rational     cppr(cppi);  // OK, int to rational
+cpp_dec_float_50 df(cppi);    // OK, int to float
+df                  = static_cast<cpp_dec_float_50>(cppr);  // OK, explicit rational to float conversion
+// However narrowing and/or implicit conversions always fail:
 cppi                =   df;    // Compiler error, conversion not allowed
 
                            
-
                            • 
+
                              • 
             Other interconversions may be allowed as special cases, whenever the
             backend allows it:
           
                              
@@ -112,7 +147,9 @@
 
                    
 
                    
         More information on what additional types a backend supports conversions
-        from are given in the tutorial for each backend.
+        from are given in the tutorial for each backend. The converting constructor
+        will be implict if the backend's converting constructor is also implicit,
+        and explicit if the backends converting constructor is also explicit.
       
                    
 
                  
 
diff --git a/doc/html/boost_multiprecision/tut/floats.html b/doc/html/boost_multiprecision/tut/floats.html
index 45d29397..171fa60d 100644
--- a/doc/html/boost_multiprecision/tut/floats.html
+++ b/doc/html/boost_multiprecision/tut/floats.html
@@ -3,7 +3,7 @@
 Floating Point Numbers
-
+
diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html
index 268d472b..e0a56312 100644
--- a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html
+++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html
@@ -3,7 +3,7 @@
 cpp_dec_float
-
+
@@ -51,7 +51,7 @@
 
                  
           Things you should know when using this type:
         
                  
-
                    
+
                      
 
                    • 
               Default constructed cpp_dec_floats
               have a value of zero.
@@ -93,7 +93,7 @@
 
                    
 
                    
 
-          cpp_dec_float
+          cpp_dec_float
           example:
         
                    
 
                    
diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg.html
index 90d9d20f..238d5aff 100644
--- a/doc/html/boost_multiprecision/tut/floats/fp_eg.html
+++ b/doc/html/boost_multiprecision/tut/floats/fp_eg.html
@@ -3,7 +3,7 @@
 
 Examples
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html
index 46500c20..4a7b521e 100644
--- a/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html
+++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html
@@ -3,7 +3,7 @@
 
 Area of Circle
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html
index b7621a91..f5599b78 100644
--- a/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html
+++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html
@@ -3,7 +3,7 @@
 
 Calculating an Integral
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html
index e3e4c8e0..fbece29c 100644
--- a/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html
+++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html
@@ -3,7 +3,7 @@
 
 Defining a Lambda Function.
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html
index 71e7e9a9..75c6287d 100644
--- a/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html
+++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html
@@ -3,7 +3,7 @@
 
 Calculating a Derivative
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html
index 2c28c3be..2a6884ec 100644
--- a/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html
+++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html
@@ -3,7 +3,7 @@
 
 Polynomial Evaluation
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/floats/gmp_float.html b/doc/html/boost_multiprecision/tut/floats/gmp_float.html
index e60bb835..d420e0c4 100644
--- a/doc/html/boost_multiprecision/tut/floats/gmp_float.html
+++ b/doc/html/boost_multiprecision/tut/floats/gmp_float.html
@@ -3,7 +3,7 @@
 
 gmp_float
 
-
+
 
 
 
@@ -66,7 +66,7 @@
           of number<mpf_float<N> > are copy constructible and assignable
           from:
         
                    
-
                      
+
                        
 
                      • 
               The GMP native types mpf_t, mpz_t,
               mpq_t.
@@ -86,7 +86,7 @@
 
                        
           Things you should know when using this type:
         
                        
-
                          
+
                            
 
                          • 
               Default constructed gmp_floats
               have the value zero (this is the GMP
@@ -134,8 +134,8 @@
 
                          
 
                          
 
-          
-          GMP example:
+          
+          GMP example:
         
                          
 
                          
 
                          
diff --git a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html
index 183ccfdc..53692329 100644
--- a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html
+++ b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html
@@ -3,7 +3,7 @@
 
 mpfr_float
 
-
+
 
 
 
@@ -66,7 +66,7 @@
           of number<mpfr_float_backend<N> > are copy constructible and assignable
           from:
         
                          
-
                            
+
                              
 
                            • 
               The GMP native types mpf_t, mpz_t,
               mpq_t.
@@ -87,7 +87,7 @@
 
                              
           Things you should know when using this type:
         
                              
-
                                
+
                                  
 
                                • 
               A default constructed mpfr_float_backend
               is set to a NaN (this is the default MPFR
@@ -123,8 +123,8 @@
 
                                
 
                                
 
-          
-          MPFR example:
+          
+          MPFR example:
         
                                
 
                                
 
                                
diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html
index 754859f0..2494b3ac 100644
--- a/doc/html/boost_multiprecision/tut/ints.html
+++ b/doc/html/boost_multiprecision/tut/ints.html
@@ -3,7 +3,7 @@
 
 Integer Types
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html
index 65301980..c1be7123 100644
--- a/doc/html/boost_multiprecision/tut/ints/cpp_int.html
+++ b/doc/html/boost_multiprecision/tut/ints/cpp_int.html
@@ -3,7 +3,7 @@
 
 cpp_int
 
-
+
 
 
 
@@ -60,7 +60,7 @@
         
                                
 
                                
 
                                
-
                                
+
                                
 
                                MinBits
                                
 
                                
                 Determines the number of Bits to store directly within the object
@@ -91,7 +91,7 @@
 
                                
           Things you should know when using this type:
         
                                
-
                                  
+
                                    
 
                                  • 
               Default constructed cpp_int_backends
               have the value zero.
@@ -151,7 +151,7 @@
 
                                  
 
                                  
 
-          Example:
+          Example:
         
                                  
 
                                  
 
                                  
diff --git a/doc/html/boost_multiprecision/tut/ints/egs.html b/doc/html/boost_multiprecision/tut/ints/egs.html
index 145a22b2..bc357417 100644
--- a/doc/html/boost_multiprecision/tut/ints/egs.html
+++ b/doc/html/boost_multiprecision/tut/ints/egs.html
@@ -3,7 +3,7 @@
 
 Examples
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/ints/egs/bitops.html b/doc/html/boost_multiprecision/tut/ints/egs/bitops.html
index cd9dbdc3..9b061f26 100644
--- a/doc/html/boost_multiprecision/tut/ints/egs/bitops.html
+++ b/doc/html/boost_multiprecision/tut/ints/egs/bitops.html
@@ -3,7 +3,7 @@
 
 Bit Operations
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/ints/egs/factorials.html b/doc/html/boost_multiprecision/tut/ints/egs/factorials.html
index bc812cd7..76a984f4 100644
--- a/doc/html/boost_multiprecision/tut/ints/egs/factorials.html
+++ b/doc/html/boost_multiprecision/tut/ints/egs/factorials.html
@@ -3,7 +3,7 @@
 
 Factorials
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/ints/gmp_int.html b/doc/html/boost_multiprecision/tut/ints/gmp_int.html
index 75dfcbf9..cbb2d7f6 100644
--- a/doc/html/boost_multiprecision/tut/ints/gmp_int.html
+++ b/doc/html/boost_multiprecision/tut/ints/gmp_int.html
@@ -3,7 +3,7 @@
 
 gmp_int
 
-
+
 
 
 
@@ -41,7 +41,7 @@
           mpz_int is copy constructible
           and assignable from:
         
                                  
-
                                    
+
                                      
 
                                    • 
               The GMP native types: mpf_t, mpz_t,
               mpq_t.
@@ -59,7 +59,7 @@
 
                                      
           Things you should know when using this type:
         
                                      
-
                                        
+
                                          
 
                                        • 
               No changes are made to the GMP library's global settings - so you can
               safely mix this type with existing code that uses GMP.
@@ -97,7 +97,7 @@
 
                                        
 
                                        
 
-          Example:
+          Example:
         
                                        
 
                                        
 
                                        
diff --git a/doc/html/boost_multiprecision/tut/ints/tom_int.html b/doc/html/boost_multiprecision/tut/ints/tom_int.html
index b242c3f1..ac7f51bd 100644
--- a/doc/html/boost_multiprecision/tut/ints/tom_int.html
+++ b/doc/html/boost_multiprecision/tut/ints/tom_int.html
@@ -3,7 +3,7 @@
 
 tom_int
 
-
+
 
 
 
@@ -39,7 +39,7 @@
 
                                        
           Things you should know when using this type:
         
                                        
-
                                          
+
                                            
 
                                          • 
               Default constructed objects have the value zero (this is libtommath's
               default behavior).
@@ -71,7 +71,7 @@
 
                                          
 
                                          
 
-          Example:
+          Example:
         
                                          
 
                                          
 
                                          
diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html
index ae6e1e3f..baf4517d 100644
--- a/doc/html/boost_multiprecision/tut/primetest.html
+++ b/doc/html/boost_multiprecision/tut/primetest.html
@@ -3,7 +3,7 @@
 
 Primality Testing
 
-
+
 
 
 
@@ -35,8 +35,8 @@
         then n is prime with probability 0.25^trials.
         The algorithm used performs some trial divisions to exclude small prime factors,
         does one Fermat test to exclude many more composites, and then uses the Miller-Rabin
-        algorithm straight out of Knuth Vol 2, which recomends 25 trials for a pretty
-        strong likelyhood that n is prime.
+        algorithm straight out of Knuth Vol 2, which recommends 25 trials for a pretty
+        strong likelihood that n is prime.
       
                                          
 
                                          
         The third optional argument is for a Uniform Random Number Generator from
diff --git a/doc/html/boost_multiprecision/tut/random.html b/doc/html/boost_multiprecision/tut/random.html
index 6f0d438b..e52df62e 100644
--- a/doc/html/boost_multiprecision/tut/random.html
+++ b/doc/html/boost_multiprecision/tut/random.html
@@ -3,7 +3,7 @@
 
 Generating Random Numbers
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html
index 2f156532..9dcaf83e 100644
--- a/doc/html/boost_multiprecision/tut/rational.html
+++ b/doc/html/boost_multiprecision/tut/rational.html
@@ -3,7 +3,7 @@
 
 Rational Number Types
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/rational/br.html b/doc/html/boost_multiprecision/tut/rational/br.html
index 0f6c0044..c8802a42 100644
--- a/doc/html/boost_multiprecision/tut/rational/br.html
+++ b/doc/html/boost_multiprecision/tut/rational/br.html
@@ -3,7 +3,7 @@
 
 Use With Boost.Rational
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html
index 9c07ed72..445989b1 100644
--- a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html
+++ b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html
@@ -3,7 +3,7 @@
 
 cpp_rational
 
-
+
 
 
 
@@ -55,7 +55,7 @@
 
                                          
           Things you should know when using this type:
         
                                          
-
                                            
+
                                              
 
                                            • 
               Default constructed cpp_rationals
               have the value zero.
@@ -72,7 +72,7 @@
 
                                            
 
                                            
 
-          Example:
+          Example:
         
                                            
 
                                            
 
                                            
diff --git a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html
index f8e6dfc5..2d1f7fb8 100644
--- a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html
+++ b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html
@@ -3,7 +3,7 @@
 
 gmp_rational
 
-
+
 
 
 
@@ -41,7 +41,7 @@
           of number<gmp_rational>
           are copy constructible and assignable from:
         
                                            
-
                                              
+
                                                
 
                                              • 
               The GMP native types: mpz_t, mpq_t.
             
                                                • 
@@ -70,7 +70,7 @@
 
                                                
           Things you should know when using this type:
         
                                                
-
                                                  
+
                                                    
 
                                                  • 
               Default constructed mpq_rationals
               have the value zero (this is the GMP
@@ -98,7 +98,7 @@
 
                                                  
 
                                                  
 
-          Example:
+          Example:
         
                                                  
 
                                                  
 
                                                  
diff --git a/doc/html/boost_multiprecision/tut/rational/rational_adapter.html b/doc/html/boost_multiprecision/tut/rational/rational_adapter.html
index e377fe2e..5a7b69ec 100644
--- a/doc/html/boost_multiprecision/tut/rational/rational_adapter.html
+++ b/doc/html/boost_multiprecision/tut/rational/rational_adapter.html
@@ -3,7 +3,7 @@
 
 rational_adapter
 
-
+
 
 
 
diff --git a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html
index 11982c13..432d1012 100644
--- a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html
+++ b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html
@@ -3,7 +3,7 @@
 
 tommath_rational
 
-
+
 
 
 
@@ -51,7 +51,7 @@
 
                                                  
           Things you should know when using this type:
         
                                                  
-
                                
@@ -118,7 +120,7 @@
 
                                
 
                              
 
                  
 
 
 
 
 
 
 
 
 
 
                  
-
+
                  Last revised: August 09, 2012 at 17:32:59 GMT
                  Last revised: August 27, 2012 at 12:20:10 GMT
                  		
 
                  		
 
                  
 
                  
diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk
index c05e6e9a..bef12a15 100644
--- a/doc/multiprecision.qbk
+++ b/doc/multiprecision.qbk
@@ -134,7 +134,7 @@ However, there are still many simple expressions such as:
 
    a = b * c;
 
-Which don't noticably benefit from move support.  Therefore, optimal performance comes from having both
+Which don't noticeably benefit from move support.  Therefore, optimal performance comes from having both
 move-support, and expression templates enabled.
 
 Note that while "moved-from" objects are left in a sane state, they have an unspecified value, and the only permitted 
@@ -145,8 +145,6 @@ object's internal state), while maintaining usability in the standard library co
 
 [h4 Expression Templates]
 
-TODO: compare to rvalue refs.
-
 Class `number` is expression-template-enabled: that means that rather than having a multiplication
 operator that looks like this:
 
@@ -171,7 +169,7 @@ is.
 The great advantage of this method is the ['elimination of temporaries]: for example the "naive" implementation
 of `operator*` above, requires one temporary for computing the result, and at least another one to return it.  It's true 
 that sometimes this overhead can be reduced by using move-semantics, but it can't be eliminated completely.  For example, 
-lets suppose we're evaluating a polynomial via Horners method, something like this:
+lets suppose we're evaluating a polynomial via Horner's method, something like this:
 
     T a[7] = { /* some values */ };
     //....
@@ -887,10 +885,20 @@ So for example, given an integer back-end type `MyIntegerBackend`, the use would
 All of the number types that are based on `number` have certain conversion rules in common.
 In particular:
 
-* Any number type can be constructed (or assigned) from any builtin arithmetic type:
+* Any number type can be constructed (or assigned) from any builtin arithmetic type, as long
+  as the conversion isn't lossy (for example float to int conversion):
 
    cpp_dec_float_50 df(0.5); // OK construction from double
    cpp_int          i(450);  // OK constructs from signed int
+   cpp_int          j = 3.14; // Error, lossy conversion.
+
+* A number can be explicitly constructed from an arithmetic type, even when the conversion is lossy:
+
+   cpp_int          i(3.14);  // OK explicit conversion
+   i = static_cast(3.14)  // OK explicit conversion
+   i.assign(3.14);                 // OK, explicit assign and avoid a temporary from the cast above
+   i = 3.14;                       // Error, no implicit assignment operator for lossy conversion.
+   cpp_int          j = 3.14;      // Error, no implicit constructor for lossy conversion.
 
 * A `number` can be converted to any built in type, via the `convert_to` member function:
 
@@ -906,16 +914,21 @@ this functionality is only available on compilers supporting C++11's explicit co
    int i = z;  // Error, implicit conversion not allowed.
    int j = static_cast(z);  // OK explicit conversion.
 
-* Any number type can be constructed (or assigned) from a `const char*` or a `std::string`:
+* Any number type can be ['explicitly] constructed (or assigned) from a `const char*` or a `std::string`:
 
    // pi to 50 places from a string:
-   cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
+   cpp_dec_float_50 df("3.14159265358979323846264338327950288419716939937510");
    // Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly:
-   cpp_int          i  = "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000";
+   cpp_int          i("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000");
    // Invalid input always results in a std::runtime_error being thrown:
-   i = std::string("3.14");
+   i = static_cast("3.14");
+   // implicit conversions from strings are not allowed:
+   i = "23"; // Error, no assignment operator for implicit conversion from string
+   // assign member function, avoids having to create a temporary via a static_cast:
+   i.assign("23");  // OK
 
-* Any number type will interoperate with the builtin type in arithmetic expressions:
+* Any number type will interoperate with the builtin types in arithmetic expressions as long as the conversions
+are not lossy:
 
    // pi to 50 places from a string:
    cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
@@ -923,10 +936,9 @@ this functionality is only available on compilers supporting C++11's explicit co
    // than constructing a temporary:
    df *= 2;
 
-   // There is a need to be careful with integer types though:
+   // You can't mix integer types with floats though:
    cpp_int i = 2;
-   // Ooops, this really just multiplies by 3:
-   i *= 3.14;
+   i *= 3.14;  // Error, no *= operator will be found.
 
 * Any number type can be streamed to and from the C++ iostreams:
    
@@ -940,17 +952,33 @@ this functionality is only available on compilers supporting C++11's explicit co
    // Now print in hex format with prefix:
    std::cout << std::hex << std::showbase << i << std::endl;
 
-* Some interconversions between number types are completely generic, and are always available:
+* Interconversions between number types of the same family are allowed and are implicit conversions if no
+loss of precision is involved, and explicit if it is:
+
+   int128       i128 = 0;
+   int266       i256 = i128;  // OK implicit widening conversion
+   i128              = i256;  // Error, no assignment operator found, narrowing conversion is explict
+   i128              = static_cast(i256); // OK, explicit narrowing conversion
+
+   mpz_int      z    = 0;
+   mpf_float    f    = z;    // OK, GMP handles this conversion natively, and it's not lossy and therefore implicit
+   
+   mpf_float_50 f50  = 2;
+   f                 = f50;  // OK, conversion from fixed to variable precision, f will have 50 digits precision.
+   f50               = f;    // Error, conversion from variable to fixed precision is potentially lossy, explicit cast required.
+
+* Some interconversions between number types are completely generic, and are always available, albeit the conversions are always ['explicit]:
 
    cpp_int cppi(2);
    // We can always convert between numbers of the same category - 
-   // int to int, rational to rational, or float to float, so this is OK:
-   mpz_int z = cppi;
+   // int to int, rational to rational, or float to float, so this is OK
+   // as long as we use an explicit conversion:
+   mpz_int z(cppi);
    // We can always promote from int to rational, int to float, or rational to float:
-   cpp_rational     cppr = cppi;  // OK, int to rational
-   cpp_dec_float_50 df =   cppi;  // OK, int to float
-   df                  =   cppr;  // OK, rational to float
-   // However narrowing conversions always fail:
+   cpp_rational     cppr(cppi);  // OK, int to rational
+   cpp_dec_float_50 df(cppi);    // OK, int to float
+   df                  = static_cast(cppr);  // OK, explicit rational to float conversion
+   // However narrowing and/or implicit conversions always fail:
    cppi                =   df;    // Compiler error, conversion not allowed
 
 * Other interconversions may be allowed as special cases, whenever the backend allows it:
@@ -960,6 +988,8 @@ this functionality is only available on compilers supporting C++11's explicit co
    mpf_float i(m);        // copies the value of the native type.
 
 More information on what additional types a backend supports conversions from are given in the tutorial for each backend.
+The converting constructor will be implict if the backend's converting constructor is also implicit, and explicit if the
+backends converting constructor is also explicit.
 
 [endsect]
 
@@ -1010,7 +1040,7 @@ These functions perform a Miller-Rabin test for primality, if the result is `fal
 while if the result is `true` then /n/ is prime with probability ['0.25^trials].  The algorithm used performs some
 trial divisions to exclude small prime factors, does one Fermat test to exclude many more composites, and then
 uses the Miller-Rabin algorithm straight out of
-Knuth Vol 2, which recomends 25 trials for a pretty strong likelyhood that /n/ is prime.
+Knuth Vol 2, which recommends 25 trials for a pretty strong likelihood that /n/ is prime.
 
 The third optional argument is for a Uniform Random Number Generator from Boost.Random.  When not provided the `mt19937`
 generator is used.   Note that when producing random primes then you should probably use a different random number generator 
@@ -1039,6 +1069,7 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba
       number();
       number(see-below);
       number& operator=(see-below);
+      number& assign(see-below);
 
       // Member operators
       number& operator+=(const ``['see-below]``&);
@@ -1079,7 +1110,8 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba
       // Comparison:
       int compare(const number& o)const;
       template 
-      typename enable_if, int>::type compare(const V& o)const;
+      typename enable_if >, int>::type 
+         compare(const V& o)const;
       // Access to the underlying implementation:
       Backend& backend();
       const Backend& backend()const;
@@ -1221,17 +1253,38 @@ Class `number` has two template arguments:
    number();
    number(see-below);
    number& operator=(see-below);
+   number& assign(see-below);
 
 Type `number` is default constructible, and both copy constructible and assignable from:
 
 * Itself.
 * An expression template which is the result of one of the arithmetic operators.
-* Any builtin arithmetic type.
-* A `std::string` or any type which is convertible to `const char*`.
-* Any type that the Backend is constructible or assignable from.
+* Any builtin arithmetic type, as long as the result would not be lossy (for example float to integer conversion).
+* Any type that the Backend is implicitly constructible or assignable from.
 * An rvalue reference to another `number`.  Move-semantics are used for construction if the backend also
 supports rvalue reference construction.  In the case of assignment, move semantics are always supported
 when the argument is an rvalue reference irrespective of the backend.
+* Any type in the same family, as long as no loss of precision is involved.  For example from `int128` to `int256`,
+or `cpp_dec_float_50` to `cpp_dec_float_100`.
+
+Type `number` is explicitly constructible from:
+
+* Any type mentioned above.
+* A `std::string` or any type which is convertible to `const char*`.
+* Any arithmetic type (including those that would result in lossy conversions).
+* Any type in the same family, including those that result in loss of precision.
+* Any type that the Backend is explicitly constructible from.
+* Any pair of types for which a generic interconversion exists: that is from integer to integer, integer
+to rational, integer to float, rational to rational, rational to float, or float to float.
+
+The assign member function is available for any type for which an explicit converting constructor exists.
+It is intended to be used where a temporary generated from an explicit assignment would be expensive, for example:
+
+   mpfr_float_50    f50;
+   mpfr_float_100   f100;
+
+   f50 = static_cast(f100);  // explicit cast create a temporary
+   f50.assign(f100);                        // explicit call to assign create no temporary
 
 In addition, if the type has multiple components (for example rational or complex number types), then there is a
 two argument constructor:
@@ -1261,8 +1314,8 @@ These operators all take their usual arithmetic meanings.
 The arguments to these operators is either:
 
 * Another `number`.
-* A builtin arithmetic type.
 * An expression template derived from `number`.
+* Any type implicitly convertible to `number`.
 
 For the left and right shift operations, the argument must be a builtin
 integer type with a positive value (negative values result in a `std::runtime_error` being thrown).
@@ -1317,7 +1370,8 @@ the default precision and the precision of `*this` respectively.
 
       int compare(const number& o)const;
       template 
-      typename enable_if, int>::type compare(const V& other)const;
+      typename enable_if >, int>::type 
+         compare(const V& other)const;
 
 Returns:
 
@@ -1447,14 +1501,16 @@ such as fixed precision or complex types are added to the library later, then th
    template 
    struct component_type;
 
-If this is a type with mutiple components (for example rational or complex types), then this trait has a single member
+If this is a type with multiple components (for example rational or complex types), then this trait has a single member
 `type` that is the type of those components.
 
    template 
    struct number_category;
 
 A traits class that inherits from `mpl::int_` where `N` is one of the enumerated values `number_kind_integer`, `number_kind_floating_point`,
-`number_kind_rational` or `number_kind_fixed_point`.
+`number_kind_rational`, `number_kind_fixed_point`, or `number_kind_unknown`.  This traits class is specialized for any type that has
+`std::numeric_limits` support as well as for classes in this library: which means it can be used for generic code that must work
+with built in arithmetic types as well as multiprecision ones.
 
 
 [h4 Integer functions]
@@ -1595,7 +1651,7 @@ The template arguments are:
 [[Signed][When `true` the type is signed, otherwise unsigned.  Note that unsigned types are currently only 
       supported when the Allocator parameter is `void`.]]
 [[Allocator][The allocator used for dynamic memory allocation.  This parameter can be `void`, in which case
-      no dymanic memory will ever be allocated.]]
+      no dynamic memory will ever be allocated.]]
 ]
 
 The type of `number_category >::type` is `mpl::int_`.
@@ -1732,18 +1788,61 @@ More information on this type can be found in the [link boost_multiprecision.tut
 
 [endsect]
 
+[section:internals Internal Support Code]
+
+There are some traits classes which authors of new backends should be aware of:
+
+   namespace boost{ namespace multiprecision{ namespace detail{
+
+   template
+   struct is_explicitly_convertible;
+
+   }}}
+
+Inherits from `boost::integral_constant` if type `From` has an explicit conversion from `To`.
+
+For compilers that support C++11 SFINAE-expressions this trait should "just work".  Otherwise it inherits
+from `boost::is_convertible::type`, and will need to be specialised for Backends that have
+constructors marked as `explicit`.
+
+   template 
+   struct is_lossy_conversion
+   {
+      static const bool value = see below;
+   };
+
+Member `value` is true if the conversion from `From` to `To` would result in a loss of precision, and `false` otherwise.
+
+The default version of this trait simply checks whether the ['kind] of conversion (for example from a floating point to an integer type)
+is inherently lossy.  Note that if either of the types `From` or `To` are of an unknown number category (because `number_category` is not
+specialised for that type) then this trait will be `true`.
+
+   template
+   struct is_restricted_conversion
+   {
+      static const bool value = see below;
+   };
+
+Member `value` is `true` if `From` is only explicitly convertible to `To` and not implicitly convertible, or
+if `is_lossy_conversion::value` is `true`.  Otherwise `false`.
+
+Note that while this trait is the ultimate arbiter of which constructors are marked as `explicit` in class `number`,
+authors of backend types should generally specialise one of the traits above, rather than this one directly.
+
+[endsect]
+
 [section:backendconc Backend Requirements]
 
 The requirements on the `Backend` template argument to `number` are split up into
-sections: compulsary and optional.
+sections: compulsory and optional.
 
-Compulsary requirements have no default implementation in the library, therefore if the feature
+Compulsory requirements have no default implementation in the library, therefore if the feature
 they implement is to be supported at all, then they must be implemented by the backend.
 
 Optional requirements have default implementations that are called if the backend doesn't provide
 it's own.  Typically the backend will implement these to improve performance.
 
-In the following tables, type B is the `Backend` template arument to `number`, `b` and `b2` are
+In the following tables, type B is the `Backend` template argument to `number`, `b` and `b2` are
 a variables of type B, `cb`, `cb2` and `cb3` are constant variables of type `const B`,
 `rb` is a variable of type `B&&`, `a` and `a2` are variables of Arithmetic type, 
 `s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`,
@@ -1816,7 +1915,8 @@ of type B2.
 [[`B(a)`][`B`][Direct construction from an arithmetic type.  The type of `a` shall be listed in one of the type lists
             `B::signed_types`, `B::unsigned_types` or `B::float_types`.
             When not provided, this operation is simulated using default-construction followed by assignment.][[space]]]
-[[`B(b2)`][`B`][Copy constructor from a different back-end type.  When not provided, a generic interconversion routine is used.][[space]]]
+[[`B(b2)`][`B`][Copy constructor from a different back-end type.  When not provided, a generic interconversion routine is used.
+          This constructor may be `explicit` if the corresponding frontend constructor should also be `explicit`.][[space]]]
 [[`b = b2`][`b&`][Assignment operator from a different back-end type.  When not provided, a generic interconversion routine is used.][[space]]]
 [[`assign_components(b, a, a)`][`void`][Assigns to `b` the two components in the following arguments.  
                            Only applies to rational and complex number types.
@@ -2475,6 +2575,15 @@ Windows Vista machine.
 
 [section:hist History]
 
+[h4 Post review changes]
+
+* Non-expression template operators further optimised with rvalue reference support.
+* Many functions made made `constexp`?
+* Differentiate between explicit and implicit conversions in the number constructor.
+* Removed "mp_" prefix from types.
+
+[h4 Pre-review history]
+
 *2011-2012, John Maddock adds an expression template enabled front end to Christopher's code,
 and adds support for other backends.
 * 2011, Christopher Kormanyos publishes the decimal floating point code under the Boost
@@ -2500,9 +2609,6 @@ More a list of what ['could] be done, rather than what ['should] be done (which
 
 [h4 Pre-Review Comments]
 
-* Can the non-expression template operators be further optimised with rvalue reference support?
-* Can any functions - in particular value initialization - be made `constexp`?
-* Can we differentiate between explicit and implicit conversions in the number constructor (may need some new type traits)?
 * Can ring types (exact floating point types) be supported?  The answer should be yes, but someone needs to write it.
 * Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents.
 Open question - what should be the default - int32_t or int64_t?
diff --git a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp
index f06c9577..adc42b68 100644
--- a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp
+++ b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp
@@ -25,47 +25,47 @@ namespace concepts{
 #pragma warning(disable:4244)
 #endif
 
-struct mp_number_backend_float_architype
+struct number_backend_float_architype
 {
    typedef mpl::list                 signed_types;
    typedef mpl::list        unsigned_types;
    typedef mpl::list               float_types;
    typedef int                                  exponent_type;
 
-   mp_number_backend_float_architype()
+   number_backend_float_architype()
    {
       std::cout << "Default construct" << std::endl;
    }
-   mp_number_backend_float_architype(const mp_number_backend_float_architype& o)
+   number_backend_float_architype(const number_backend_float_architype& o)
    {
       std::cout << "Copy construct" << std::endl;
       m_value = o.m_value;
    }
-   mp_number_backend_float_architype& operator = (const mp_number_backend_float_architype& o)
+   number_backend_float_architype& operator = (const number_backend_float_architype& o)
    {
       m_value = o.m_value;
       std::cout << "Assignment (" << m_value << ")" << std::endl;
       return *this;
    }
-   mp_number_backend_float_architype& operator = (unsigned long long i)
+   number_backend_float_architype& operator = (unsigned long long i)
    {
       m_value = i;
       std::cout << "UInt Assignment (" << i << ")" << std::endl;
       return *this;
    }
-   mp_number_backend_float_architype& operator = (long long i)
+   number_backend_float_architype& operator = (long long i)
    {
       m_value = i;
       std::cout << "Int Assignment (" << i << ")" << std::endl;
       return *this;
    }
-   mp_number_backend_float_architype& operator = (long double d)
+   number_backend_float_architype& operator = (long double d)
    {
       m_value = d;
       std::cout << "long double Assignment (" << d << ")" << std::endl;
       return *this;
    }
-   mp_number_backend_float_architype& operator = (const char* s)
+   number_backend_float_architype& operator = (const char* s)
    {
       try
       {
@@ -78,7 +78,7 @@ struct mp_number_backend_float_architype
       std::cout << "const char* Assignment (" << s << ")" << std::endl;
       return *this;
    }
-   void swap(mp_number_backend_float_architype& o)
+   void swap(number_backend_float_architype& o)
    {
       std::cout << "Swapping (" << m_value << " with " << o.m_value << ")" << std::endl;
       std::swap(m_value, o.m_value);
@@ -108,7 +108,7 @@ struct mp_number_backend_float_architype
       std::cout << "Negating (" << m_value << ")" << std::endl;
       m_value = -m_value;
    }
-   int compare(const mp_number_backend_float_architype& o)const
+   int compare(const number_backend_float_architype& o)const
    {
       std::cout << "Comparison" << std::endl;
       return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0);
@@ -131,86 +131,86 @@ struct mp_number_backend_float_architype
    long double m_value;
 };
 
-inline void eval_add(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o)
+inline void eval_add(number_backend_float_architype& result, const number_backend_float_architype& o)
 {
    std::cout << "Addition (" << result.m_value << " += " << o.m_value << ")" << std::endl;
    result.m_value += o.m_value;
 }
-inline void eval_subtract(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o)
+inline void eval_subtract(number_backend_float_architype& result, const number_backend_float_architype& o)
 {
    std::cout << "Subtraction (" << result.m_value << " -= " << o.m_value << ")" << std::endl;
    result.m_value -= o.m_value;
 }
-inline void eval_multiply(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o)
+inline void eval_multiply(number_backend_float_architype& result, const number_backend_float_architype& o)
 {
    std::cout << "Multiplication (" << result.m_value << " *= " << o.m_value << ")" << std::endl;
    result.m_value *= o.m_value;
 }
-inline void eval_divide(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& o)
+inline void eval_divide(number_backend_float_architype& result, const number_backend_float_architype& o)
 {
    std::cout << "Division (" << result.m_value << " /= " << o.m_value << ")" << std::endl;
    result.m_value /= o.m_value;
 }
 
-inline void eval_convert_to(unsigned long long* result, const mp_number_backend_float_architype& val)
+inline void eval_convert_to(unsigned long long* result, const number_backend_float_architype& val)
 {
    *result = static_cast(val.m_value);
 }
-inline void eval_convert_to(long long* result, const mp_number_backend_float_architype& val)
+inline void eval_convert_to(long long* result, const number_backend_float_architype& val)
 {
    *result = static_cast(val.m_value);
 }
-inline void eval_convert_to(long double* result, mp_number_backend_float_architype& val)
+inline void eval_convert_to(long double* result, number_backend_float_architype& val)
 {
    *result = val.m_value;
 }
 
-inline void eval_frexp(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg, int* exp)
+inline void eval_frexp(number_backend_float_architype& result, const number_backend_float_architype& arg, int* exp)
 {
    result = std::frexp(arg.m_value, exp);
 }
 
-inline void eval_ldexp(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg, int exp)
+inline void eval_ldexp(number_backend_float_architype& result, const number_backend_float_architype& arg, int exp)
 {
    result = std::ldexp(arg.m_value, exp);
 }
 
-inline void eval_floor(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg)
+inline void eval_floor(number_backend_float_architype& result, const number_backend_float_architype& arg)
 {
    result = std::floor(arg.m_value);
 }
 
-inline void eval_ceil(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg)
+inline void eval_ceil(number_backend_float_architype& result, const number_backend_float_architype& arg)
 {
    result = std::ceil(arg.m_value);
 }
 
-inline void eval_sqrt(mp_number_backend_float_architype& result, const mp_number_backend_float_architype& arg)
+inline void eval_sqrt(number_backend_float_architype& result, const number_backend_float_architype& arg)
 {
    result = std::sqrt(arg.m_value);
 }
 
-inline int eval_fpclassify(const mp_number_backend_float_architype& arg)
+inline int eval_fpclassify(const number_backend_float_architype& arg)
 {
    return (boost::math::fpclassify)(arg.m_value);
 }
 
-typedef boost::multiprecision::number mp_number_float_architype;
+typedef boost::multiprecision::number mp_number_float_architype;
 
 } // namespace
 
 template<>
-struct number_category : public mpl::int_{};
+struct number_category : public mpl::int_{};
 
 }} // namespaces
 
 namespace std{
 
 template 
-class numeric_limits > : public std::numeric_limits
+class numeric_limits > : public std::numeric_limits
 {
    typedef std::numeric_limits base_type;
-   typedef boost::multiprecision::number number_type;
+   typedef boost::multiprecision::number number_type;
 public:
    static number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); }
    static number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); }
diff --git a/test/test_acos.cpp b/test/test_acos.cpp
index 97cc96d2..d0943592 100644
--- a/test/test_acos.cpp
+++ b/test/test_acos.cpp
@@ -89,7 +89,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index 4a6f102f..39af694c 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -1254,7 +1254,7 @@ int main()
    test > >();
 #endif
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_asin.cpp b/test/test_asin.cpp
index 2b56e062..3c913082 100644
--- a/test/test_asin.cpp
+++ b/test/test_asin.cpp
@@ -85,7 +85,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_atan.cpp b/test/test_atan.cpp
index 5e139fdf..cfb2de3d 100644
--- a/test/test_atan.cpp
+++ b/test/test_atan.cpp
@@ -231,7 +231,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_cos.cpp b/test/test_cos.cpp
index f31a3bfd..c9c51068 100644
--- a/test/test_cos.cpp
+++ b/test/test_cos.cpp
@@ -285,7 +285,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp
index b2c82e08..5e08ec0c 100644
--- a/test/test_cosh.cpp
+++ b/test/test_cosh.cpp
@@ -127,7 +127,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_exp.cpp b/test/test_exp.cpp
index 424601dc..f36d7c78 100644
--- a/test/test_exp.cpp
+++ b/test/test_exp.cpp
@@ -167,7 +167,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_fpclassify.cpp b/test/test_fpclassify.cpp
index b579daca..4ce78ec1 100644
--- a/test/test_fpclassify.cpp
+++ b/test/test_fpclassify.cpp
@@ -314,7 +314,7 @@ int main()
    test();
 #endif
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
    return boost::report_errors();
 }
diff --git a/test/test_log.cpp b/test/test_log.cpp
index 6426e307..5d6ea4e4 100644
--- a/test/test_log.cpp
+++ b/test/test_log.cpp
@@ -195,7 +195,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp
index 6d5c376d..4b95a19d 100644
--- a/test/test_numeric_limits.cpp
+++ b/test/test_numeric_limits.cpp
@@ -201,7 +201,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_pow.cpp b/test/test_pow.cpp
index 49762f90..6f489637 100644
--- a/test/test_pow.cpp
+++ b/test/test_pow.cpp
@@ -570,7 +570,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_round.cpp b/test/test_round.cpp
index d77f24be..f066a9d8 100644
--- a/test/test_round.cpp
+++ b/test/test_round.cpp
@@ -400,7 +400,7 @@ int main()
    test > >();
 #endif
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
    return boost::report_errors();
 }
diff --git a/test/test_sin.cpp b/test/test_sin.cpp
index 78d1b620..1d208575 100644
--- a/test/test_sin.cpp
+++ b/test/test_sin.cpp
@@ -279,7 +279,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp
index ae8f11d0..bb47e54f 100644
--- a/test/test_sinh.cpp
+++ b/test/test_sinh.cpp
@@ -203,7 +203,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp
index c59be223..cd66f169 100644
--- a/test/test_sqrt.cpp
+++ b/test/test_sqrt.cpp
@@ -173,7 +173,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();
diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp
index 623585ec..2860fde9 100644
--- a/test/test_tanh.cpp
+++ b/test/test_tanh.cpp
@@ -122,7 +122,7 @@ void test()
 int main()
 {
 #ifdef TEST_BACKEND
-   test >();
+   test >();
 #endif
 #ifdef TEST_MPF_50
    test();

From c7230f94ff7eee9b3430424451ad0975a8ccdc03 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Fri, 31 Aug 2012 11:57:55 +0000
Subject: [PATCH 229/256] Extra test cases for more complete coverage. Added
 test coverage makefile. Fixed errors from extra test cases. Rename a few
 traits.

[SVN r80328]
---
 .../boost_multiprecision/indexes/s01.html     |   4 +-
 .../boost_multiprecision/indexes/s02.html     |  12 +-
 .../boost_multiprecision/indexes/s03.html     |   4 +-
 .../boost_multiprecision/indexes/s04.html     |  14 +-
 doc/html/boost_multiprecision/intro.html      |   2 +-
 .../boost_multiprecision/ref/headers.html     |   2 +-
 doc/html/boost_multiprecision/ref/number.html |  18 +
 doc/html/index.html                           |   2 +-
 doc/multiprecision.qbk                        |  19 +-
 include/boost/multiprecision/cpp_int.hpp      |  77 +++-
 .../multiprecision/detail/default_ops.hpp     |   7 -
 .../multiprecision/detail/integer_ops.hpp     |  12 +-
 .../boost/multiprecision/detail/no_et_ops.hpp |   2 +
 .../multiprecision/detail/number_base.hpp     |  41 +-
 .../multiprecision/detail/number_compare.hpp  |  48 +--
 include/boost/multiprecision/gmp.hpp          |  18 +-
 include/boost/multiprecision/number.hpp       |  31 +-
 test/Jamfile.v2                               |  31 +-
 test/coverage/Makefile                        | 173 ++++++++
 test/test_arithmetic.cpp                      | 380 ++++++++++++++++--
 test/test_cpp_int_conv.cpp                    |  19 +
 test/test_int_io.cpp                          |   2 +
 test/test_rational_io.cpp                     |   6 +-
 23 files changed, 773 insertions(+), 151 deletions(-)
 create mode 100644 test/coverage/Makefile

diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html
index b72ad441..521ccd94 100644
--- a/doc/html/boost_multiprecision/indexes/s01.html
+++ b/doc/html/boost_multiprecision/indexes/s01.html
@@ -13,9 +13,9 @@
 
                  
 PrevUpHomeNext
 
                  
-
                  
+
                  
 
                  
-Function Index
                  
+Function Index
                
 
                A B C D E F I L M P R S T Z
                
 
                
 
                
diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html
index 06a7803d..11a14593 100644
--- a/doc/html/boost_multiprecision/indexes/s02.html
+++ b/doc/html/boost_multiprecision/indexes/s02.html
@@ -13,9 +13,9 @@
 
                
 PrevUpHomeNext
 
                
-
                
+
                
 
                
-Class Index
                
+Class Index
                
 
                C G I M N T
                
 
                
 
                
@@ -53,6 +53,14 @@
 
                
 
 
              • 
+
                is_number
                
+
                
+
                • 
+
              • 
+
                is_number_expression
                
+
                
+
                • 
+
              • 
 
                is_restricted_conversion
                
 
                
 
                • 
diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html
index f72413be..c96f5617 100644
--- a/doc/html/boost_multiprecision/indexes/s03.html
+++ b/doc/html/boost_multiprecision/indexes/s03.html
@@ -13,9 +13,9 @@
 
                
 PrevUpHomeNext
 
                
-
                
+
                
 
                
-Typedef Index
                
+Typedef Index
                
 
                C I L M T U
                
 
                
 
                
diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html
index b09b9e3b..070cf1bb 100644
--- a/doc/html/boost_multiprecision/indexes/s04.html
+++ b/doc/html/boost_multiprecision/indexes/s04.html
@@ -12,9 +12,9 @@
 
                
 PrevUpHome
 
                
-
                
+
                
 
                
-Index
                
+Index
                
 
                A B C D E F G I L M N O P R S T U Z
                
 
                
 
                
@@ -516,6 +516,14 @@
 
                
 
 
              • 
+
                is_number
                
+
                
+
                • 
+
              • 
+
                is_number_expression
                
+
                
+
                • 
+
              • 
 
                is_restricted_conversion
                
 
                
 
                • 
@@ -674,6 +682,8 @@
 
              • isinf
                • 
 
              • isnan
                • 
 
              • isnormal
                • 
+
              • is_number
                • 
+
              • is_number_expression
                • 
 
              • itrunc
                • 
 
              • llround
                • 
 
              • lltrunc
                • 
diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html
index 083e1186..16fb2968 100644
--- a/doc/html/boost_multiprecision/intro.html
+++ b/doc/html/boost_multiprecision/intro.html
@@ -256,7 +256,7 @@
       Will very likely result in obscure error messages inside the body of my_proc - since we've passed it an expression
       template type, and not a number type. Instead we probably need:
     
                
-
                my_proc(my_mp_number_type(a+b));
+
                my_proc(my_number_type(a+b));
 
                
 
                
       Having said that, these situations don't occur that often - or indeed not at
diff --git a/doc/html/boost_multiprecision/ref/headers.html b/doc/html/boost_multiprecision/ref/headers.html
index ab1a9f3d..29926494 100644
--- a/doc/html/boost_multiprecision/ref/headers.html
+++ b/doc/html/boost_multiprecision/ref/headers.html
@@ -166,7 +166,7 @@

    - concepts/mp_number_archetypes.hpp + concepts/number_archetypes.hpp

    		diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html index 18b10bbc..100989b0 100644 --- a/doc/html/boost_multiprecision/ref/number.html +++ b/doc/html/boost_multiprecision/ref/number.html @@ -148,6 +148,10 @@ struct component_type; template <class T> struct number_category; +template <class T> +struct is_number; +template <class T> +struct is_number_expression; // Integer specific functions: unmentionable-expression-template-type pow(const number-or-expression-template-type&, unsigned); @@ -630,6 +634,20 @@ for generic code that must work with built in arithmetic types as well as multiprecision ones.

    +
    template <class T>
+struct is_number;
+
    +

    + A traits class that inherits from mpl::true_ + if T is an instance of number<>, otherwise from mpl::false_. +

    +
    template <class T>
+struct is_number_expression;
+
    +

    + A traits class that inherits from mpl::true_ + if T is an expression template type derived from number<>, otherwise from mpl::false_. +

    Integer diff --git a/doc/html/index.html b/doc/html/index.html index 860f65f8..16147d66 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -120,7 +120,7 @@ - +

    Last revised: August 27, 2012 at 12:20:10 GMT

    Last revised: August 30, 2012 at 17:55:33 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index bef12a15..b94104f6 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -223,7 +223,7 @@ Then calling: Will very likely result in obscure error messages inside the body of `my_proc` - since we've passed it an expression template type, and not a number type. Instead we probably need: - my_proc(my_mp_number_type(a+b)); + my_proc(my_number_type(a+b)); Having said that, these situations don't occur that often - or indeed not at all for non-template functions. In addition, all the functions in the Boost.Math library will automatically convert expression-template arguments @@ -1188,6 +1188,10 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba struct component_type; template struct number_category; + template + struct is_number; + template + struct is_number_expression; // Integer specific functions: ``['unmentionable-expression-template-type]`` pow(const ``['number-or-expression-template-type]``&, unsigned); @@ -1512,6 +1516,17 @@ A traits class that inherits from `mpl::int_` where `N` is one of the enumera `std::numeric_limits` support as well as for classes in this library: which means it can be used for generic code that must work with built in arithmetic types as well as multiprecision ones. + template + struct is_number; + +A traits class that inherits from `mpl::true_` if T is an instance of `number<>`, otherwise from `mpl::false_`. + + template + struct is_number_expression; + +A traits class that inherits from `mpl::true_` if T is an expression template type derived from `number<>`, otherwise from `mpl::false_`. + + [h4 Integer functions] @@ -2196,7 +2211,7 @@ in point of fact this naming convention shouldn't be necessary, but rather works [[rational_adapter.hpp][Defines the `rational_adapter` backend.]] [[cpp_dec_float.hpp][Defines the `cpp_dec_float` backend.]] [[tommath.hpp][Defines the `tommath_int` backend.]] -[[concepts/mp_number_archetypes.hpp][Defines a backend concept architypes for testing use.]] +[[concepts/number_archetypes.hpp][Defines a backend concept architypes for testing use.]] ] [table Implementation Headers] diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 23d91973..39458f29 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1152,7 +1152,7 @@ public: template cpp_int_backend(const cpp_int_backend& other, typename enable_if_c< - (sizeof(cpp_int_backend::local_limb_type) <= sizeof(typename cpp_int_backend::local_limb_type)) + (MinBits2 <= MinBits) && (Signed || !Signed2) >::type* = 0) : base_type() @@ -1168,7 +1168,7 @@ public: template explicit cpp_int_backend(const cpp_int_backend& other, typename disable_if_c< - (sizeof(cpp_int_backend::local_limb_type) <= sizeof(typename cpp_int_backend::local_limb_type)) + (MinBits2 <= MinBits) && (Signed || !Signed2) >::type* = 0) : base_type() @@ -1209,17 +1209,6 @@ public: this->sign(other.sign()); } - cpp_int_backend& operator = (const char* s) - { - try{ - *this->limbs() = boost::lexical_cast(s); - } - catch(const std::exception&) - { - BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Could not interpret the string \"") + s + std::string("\" as a valid integer value."))); - } - return *this; - } BOOST_FORCEINLINE void swap(cpp_int_backend& o) BOOST_NOEXCEPT { this->do_swap(o); @@ -1228,11 +1217,13 @@ private: std::string str(std::ios_base::fmtflags f, const mpl::false_&)const { std::stringstream ss; - ss.flags(f); + ss.flags(f & ~std::ios_base::showpos); ss << *this->limbs(); std::string result; if(this->sign()) result += '-'; + else if(f & std::ios_base::showpos) + result += '+'; result += ss.str(); return result; } @@ -1314,6 +1305,58 @@ private: return result; } public: + cpp_int_backend& operator = (const char* s) + { + std::size_t n = s ? std::strlen(s) : 0; + *this->limbs() = 0; + unsigned radix = 10; + bool isneg = false; + if(n && (*s == '-')) + { + --n; + ++s; + isneg = true; + } + if(n && (*s == '0')) + { + if((n > 1) && ((s[1] == 'x') || (s[1] == 'X'))) + { + radix = 16; + s +=2; + n -= 2; + } + else + { + radix = 8; + n -= 1; + } + } + if(n) + { + unsigned val; + while(*s) + { + if(*s >= '0' && *s <= '9') + val = *s - '0'; + else if(*s >= 'a' && *s <= 'f') + val = 10 + *s - 'a'; + else if(*s >= 'A' && *s <= 'F') + val = 10 + *s - 'A'; + else + val = radix + 1; + if(val > radix) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string.")); + } + *this->limbs() *= radix; + *this->limbs() += val; + ++s; + } + } + if(isneg) + this->negate(); + return *this; + } std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const { #ifdef BOOST_MP_NO_DOUBLE_LIMB_TYPE_IO @@ -3045,9 +3088,9 @@ public: return number_type(0); } static number_type lowest() BOOST_NOEXCEPT { return (min)(); } - BOOST_STATIC_CONSTEXPR int digits = 0; - BOOST_STATIC_CONSTEXPR int digits10 = 0; - BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR int digits = INT_MAX; + BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L; + BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; BOOST_STATIC_CONSTEXPR bool is_signed = true; BOOST_STATIC_CONSTEXPR bool is_integer = true; BOOST_STATIC_CONSTEXPR bool is_exact = true; diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 0fd06b26..5029bf47 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -174,13 +174,6 @@ inline typename enable_if_c::value && is_convertible::val eval_complement(result, t); } -template -inline bool is_same_object(const T& u, const T&v) BOOST_NOEXCEPT -{ return &u == &v; } -template -BOOST_CONSTEXPR inline bool is_same_object(const T&, const U&) BOOST_NOEXCEPT -{ return false; } - // // Default versions of 3-arg arithmetic functions, these mostly just forward to the 2 arg versions: // diff --git a/include/boost/multiprecision/detail/integer_ops.hpp b/include/boost/multiprecision/detail/integer_ops.hpp index 9e53e094..c7ddffcb 100644 --- a/include/boost/multiprecision/detail/integer_ops.hpp +++ b/include/boost/multiprecision/detail/integer_ops.hpp @@ -401,17 +401,17 @@ inline typename enable_if< mpl::and_< mpl::bool_::value == number_kind_integer>, mpl::or_< - is_mp_number, - is_mp_number_expression + is_number, + is_number_expression >, mpl::or_< - is_mp_number, - is_mp_number_expression, + is_number, + is_number_expression, is_integral >, mpl::or_< - is_mp_number, - is_mp_number_expression, + is_number, + is_number_expression, is_integral > >, diff --git a/include/boost/multiprecision/detail/no_et_ops.hpp b/include/boost/multiprecision/detail/no_et_ops.hpp index 23a8b4ac..282f4fea 100644 --- a/include/boost/multiprecision/detail/no_et_ops.hpp +++ b/include/boost/multiprecision/detail/no_et_ops.hpp @@ -285,6 +285,7 @@ inline typename enable_if, number >::type { number result(a); using default_ops::eval_left_shift; + detail::check_shift_range(b, mpl::bool_<(sizeof(I) > sizeof(std::size_t))>(), is_signed()); eval_left_shift(result.backend(), b); return BOOST_MP_MOVE(result); } @@ -294,6 +295,7 @@ inline typename enable_if, number >::type { number result(a); using default_ops::eval_right_shift; + detail::check_shift_range(b, mpl::bool_<(sizeof(I) > sizeof(std::size_t))>(), is_signed()); eval_right_shift(result.backend(), b); return BOOST_MP_MOVE(result); } diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp index ab3e34fe..e5b46e6e 100644 --- a/include/boost/multiprecision/detail/number_base.hpp +++ b/include/boost/multiprecision/detail/number_base.hpp @@ -18,10 +18,10 @@ template class number; template -struct is_mp_number : public mpl::false_ {}; +struct is_number : public mpl::false_ {}; template -struct is_mp_number > : public mpl::true_ {}; +struct is_number > : public mpl::true_ {}; namespace detail{ @@ -32,17 +32,17 @@ struct expression; } // namespace detail template -struct is_mp_number_expression : public mpl::false_ {}; +struct is_number_expression : public mpl::false_ {}; template -struct is_mp_number_expression > : public mpl::true_ {}; +struct is_number_expression > : public mpl::true_ {}; template struct is_compatible_arithmetic_type : public mpl::bool_< is_convertible::value - && !is_mp_number::value - && !is_mp_number_expression::value> + && !is_number::value + && !is_number_expression::value> {}; namespace detail{ @@ -192,9 +192,9 @@ struct backend_type > template -struct is_mp_number : public mpl::false_{}; +struct is_number : public mpl::false_{}; template -struct is_mp_number > : public mpl::true_{}; +struct is_number > : public mpl::true_{}; template struct is_mp_number_exp : public mpl::false_{}; template @@ -594,6 +594,29 @@ void format_float_string(S& str, boost::intmax_t my_exp, boost::intmax_t digits, str.insert(0, 1, '+'); } +template +void check_shift_range(V val, const mpl::true_&, const mpl::true_&) +{ + if(val > (std::numeric_limits::max)()) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); + if(val < 0) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); +} +template +void check_shift_range(V val, const mpl::false_&, const mpl::true_&) +{ + if(val < 0) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); +} +template +void check_shift_range(V val, const mpl::true_&, const mpl::false_&) +{ + if(val > (std::numeric_limits::max)()) + BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); +} +template +void check_shift_range(V, const mpl::false_&, const mpl::false_&) BOOST_NOEXCEPT{} + } // namespace detail // @@ -701,7 +724,7 @@ template inline typename enable_if >, detail::expression > >::type operator + (const V& a, const detail::expression >& b) { - return detail::expression, number >(a, b.left_ref()); + return detail::expression >(a, b.left_ref()); } template inline detail::expression, number > > diff --git a/include/boost/multiprecision/detail/number_compare.hpp b/include/boost/multiprecision/detail/number_compare.hpp index 7b881d73..1450508f 100644 --- a/include/boost/multiprecision/detail/number_compare.hpp +++ b/include/boost/multiprecision/detail/number_compare.hpp @@ -74,7 +74,7 @@ inline bool operator == (const number& a, const nu return eval_eq(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator == (const number& a, const Arithmetic& b) { typedef typename detail::canonical::type ct; @@ -90,7 +90,7 @@ inline typename enable_if, typename return eval_eq(a.backend(), t.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator == (const Arithmetic& a, const number& b) { typedef typename detail::canonical::type ct; @@ -98,7 +98,7 @@ inline typename enable_if_c<(is_convertible -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator == (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; @@ -116,7 +116,7 @@ inline typename enable_if, typename return eval_eq(t.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator == (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; @@ -142,7 +142,7 @@ inline bool operator != (const number& a, const nu return !eval_eq(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator != (const number& a, const Arithmetic& b) { typedef typename detail::canonical::type ct; @@ -158,7 +158,7 @@ inline typename enable_if, typename return !eval_eq(a.backend(), t.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator != (const Arithmetic& a, const number& b) { typedef typename detail::canonical::type ct; @@ -166,7 +166,7 @@ inline typename enable_if_c<(is_convertible -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator != (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; @@ -184,7 +184,7 @@ inline typename enable_if, typename return !eval_eq(t.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator != (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; @@ -210,7 +210,7 @@ inline bool operator < (const number& a, const num return eval_lt(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator < (const number& a, const Arithmetic& b) { typedef typename detail::canonical::type ct; @@ -226,7 +226,7 @@ inline typename enable_if, typename return eval_lt(a.backend(), t.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator < (const Arithmetic& a, const number& b) { typedef typename detail::canonical::type ct; @@ -234,7 +234,7 @@ inline typename enable_if_c<(is_convertible -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator < (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; @@ -252,7 +252,7 @@ inline typename enable_if, typename return eval_lt(t.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator < (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; @@ -278,7 +278,7 @@ inline bool operator > (const number& a, const num return eval_gt(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator > (const number& a, const Arithmetic& b) { typedef typename detail::canonical::type ct; @@ -294,7 +294,7 @@ inline typename enable_if, typename return eval_gt(a.backend(), t.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator > (const Arithmetic& a, const number& b) { typedef typename detail::canonical::type ct; @@ -302,7 +302,7 @@ inline typename enable_if_c<(is_convertible -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator > (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; @@ -320,7 +320,7 @@ inline typename enable_if, typename return eval_gt(t.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator > (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; @@ -346,7 +346,7 @@ inline bool operator <= (const number& a, const nu return !eval_gt(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator <= (const number& a, const Arithmetic& b) { typedef typename detail::canonical::type ct; @@ -362,7 +362,7 @@ inline typename enable_if, typename return !eval_gt(a.backend(), t.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator <= (const Arithmetic& a, const number& b) { typedef typename detail::canonical::type ct; @@ -370,7 +370,7 @@ inline typename enable_if_c<(is_convertible -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator <= (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; @@ -388,7 +388,7 @@ inline typename enable_if, typename return !eval_gt(t.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator <= (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; @@ -414,7 +414,7 @@ inline bool operator >= (const number& a, const nu return !eval_lt(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator >= (const number& a, const Arithmetic& b) { typedef typename detail::canonical::type ct; @@ -430,7 +430,7 @@ inline typename enable_if, typename return !eval_lt(a.backend(), t.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type operator >= (const Arithmetic& a, const number& b) { typedef typename detail::canonical::type ct; @@ -438,7 +438,7 @@ inline typename enable_if_c<(is_convertible -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator >= (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; @@ -456,7 +456,7 @@ inline typename enable_if, typename return !eval_lt(t.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_mp_number_expression::value && !is_mp_number::value), bool>::type +inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type operator >= (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index a0043ade..719bb41c 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1534,19 +1534,23 @@ inline void eval_lcm(gmp_int& result, const gmp_int& a, const gmp_int& b) { mpz_lcm(result.data(), a.data(), b.data()); } -inline void eval_gcd(gmp_int& result, const gmp_int& a, const unsigned long b) +template +inline typename enable_if_c<(is_unsigned::value && (sizeof(I) <= sizeof(unsigned long)))>::type eval_gcd(gmp_int& result, const gmp_int& a, const I b) { mpz_gcd_ui(result.data(), a.data(), b); } -inline void eval_lcm(gmp_int& result, const gmp_int& a, const unsigned long b) +template +inline typename enable_if_c<(is_unsigned::value && (sizeof(I) <= sizeof(unsigned long)))>::type eval_lcm(gmp_int& result, const gmp_int& a, const I b) { mpz_lcm_ui(result.data(), a.data(), b); } -inline void eval_gcd(gmp_int& result, const gmp_int& a, const long b) +template +inline typename enable_if_c<(is_signed::value && (sizeof(I) <= sizeof(long)))>::type eval_gcd(gmp_int& result, const gmp_int& a, const I b) { mpz_gcd_ui(result.data(), a.data(), std::abs(b)); } -inline void eval_lcm(gmp_int& result, const gmp_int& a, const long b) +template +inline typename enable_if_c::value && ((sizeof(I) <= sizeof(long)))>::type eval_lcm(gmp_int& result, const gmp_int& a, const I b) { mpz_lcm_ui(result.data(), a.data(), std::abs(b)); } @@ -2464,9 +2468,9 @@ public: } static number_type lowest() BOOST_NOEXCEPT { return (min)(); } // Digits are unbounded, use zero for now: - BOOST_STATIC_CONSTEXPR int digits = 0; - BOOST_STATIC_CONSTEXPR int digits10 = 0; - BOOST_STATIC_CONSTEXPR int max_digits10 = 0; + BOOST_STATIC_CONSTEXPR int digits = INT_MAX; + BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L; + BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; BOOST_STATIC_CONSTEXPR bool is_signed = true; BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = true; diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index 2a2f73fd..a8fa5f44 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -356,7 +356,7 @@ public: BOOST_FORCEINLINE typename enable_if, number&>::type operator <<= (V val) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left-shift operation is only valid for integer types"); - check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); + detail::check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); eval_left_shift(m_backend, canonical_value(val)); return *this; } @@ -365,7 +365,7 @@ public: BOOST_FORCEINLINE typename enable_if, number&>::type operator >>= (V val) { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right-shift operation is only valid for integer types"); - check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); + detail::check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed()); eval_right_shift(m_backend, canonical_value(val)); return *this; } @@ -639,29 +639,6 @@ private: } - template - void check_shift_range(V val, const mpl::true_&, const mpl::true_&) - { - if(val > (std::numeric_limits::max)()) - BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); - if(val < 0) - BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); - } - template - void check_shift_range(V val, const mpl::false_&, const mpl::true_&) - { - if(val < 0) - BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a negative value.")); - } - template - void check_shift_range(V val, const mpl::true_&, const mpl::false_&) - { - if(val > (std::numeric_limits::max)()) - BOOST_THROW_EXCEPTION(std::out_of_range("Can not shift by a value greater than std::numeric_limits::max().")); - } - template - void check_shift_range(V, const mpl::false_&, const mpl::false_&) BOOST_NOEXCEPT{} - template void do_assign(const Exp& e, const detail::add_immediates&) { @@ -1072,6 +1049,7 @@ private: { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right shift operation is only valid for integer types"); using default_ops::eval_right_shift; + detail::check_shift_range(val, mpl::bool_<(sizeof(Val) > sizeof(std::size_t))>(), is_signed()); eval_right_shift(m_backend, canonical_value(e.value()), val); } @@ -1080,6 +1058,7 @@ private: { BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left shift operation is only valid for integer types"); using default_ops::eval_left_shift; + detail::check_shift_range(val, mpl::bool_<(sizeof(Val) > sizeof(std::size_t))>(), is_signed()); eval_left_shift(m_backend, canonical_value(e.value()), val); } @@ -1089,6 +1068,7 @@ private: BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The right shift operation is only valid for integer types"); using default_ops::eval_right_shift; self_type temp(e); + detail::check_shift_range(val, mpl::bool_<(sizeof(Val) > sizeof(std::size_t))>(), is_signed()); eval_right_shift(m_backend, temp.backend(), val); } @@ -1098,6 +1078,7 @@ private: BOOST_STATIC_ASSERT_MSG(number_category::value == number_kind_integer, "The left shift operation is only valid for integer types"); using default_ops::eval_left_shift; self_type temp(e); + detail::check_shift_range(val, mpl::bool_<(sizeof(Val) > sizeof(std::size_t))>(), is_signed()); eval_left_shift(m_backend, temp.backend(), val); } diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index d9a1af1c..e0fa0c37 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -135,8 +135,22 @@ run test_arithmetic.cpp : # command line : # input files : # requirements - TEST_CPP_INT - : test_arithmetic_cpp_int ; + TEST_CPP_INT_1 + : test_arithmetic_cpp_int_1 ; + +run test_arithmetic.cpp + : # command line + : # input files + : # requirements + TEST_CPP_INT_2 + : test_arithmetic_cpp_int_2 ; + +run test_arithmetic.cpp + : # command line + : # input files + : # requirements + TEST_CPP_INT_3 + : test_arithmetic_cpp_int_3 ; run test_arithmetic.cpp : # command line @@ -805,8 +819,8 @@ for local source in [ glob compile_fail/*.cpp ] { compile-fail $(source) : - [ check-target-builds ../config//has_gmp : TEST_GMP : ] - [ check-target-builds ../config//has_mpfr : TEST_MPFR : ] + [ check-target-builds ../config//has_gmp : TEST_GMP off : ] + [ check-target-builds ../config//has_mpfr : TEST_MPFR off : ] ; } @@ -820,51 +834,60 @@ if ! $(disable-concepts) : # requirements TEST_MPFR_50 [ check-target-builds ../config//has_mpfr : : no ] + off : $(source:B)_mpfr_50 ; compile $(source) mpfr : # requirements TEST_MPFR_6 [ check-target-builds ../config//has_mpfr : : no ] + off : $(source:B)_mpfr_6 ; compile $(source) mpfr : # requirements TEST_MPFR_15 [ check-target-builds ../config//has_mpfr : : no ] + off : $(source:B)_mpfr_15 ; compile $(source) mpfr : # requirements TEST_MPFR_17 [ check-target-builds ../config//has_mpfr : : no ] + off : $(source:B)_mpfr_17 ; compile $(source) mpfr : # requirements TEST_MPFR_30 [ check-target-builds ../config//has_mpfr : : no ] + off : $(source:B)_mpfr_30 ; compile $(source) gmp : # requirements TEST_MPF_50 [ check-target-builds ../config//has_gmp : : no ] + off : $(source:B)_mpf50 ; compile $(source) : # requirements TEST_CPP_DEC_FLOAT + off : $(source:B)_cpp_dec_float ; compile $(source) : # requirements TEST_CPP_DEC_FLOAT_NO_ET + off : $(source:B)_cpp_dec_float_no_et ; compile $(source) : # requirements TEST_BACKEND + off : $(source:B)_backend_concept ; } } diff --git a/test/coverage/Makefile b/test/coverage/Makefile new file mode 100644 index 00000000..5941c633 --- /dev/null +++ b/test/coverage/Makefile @@ -0,0 +1,173 @@ +# copyright John Maddock 2012 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + + +SOURCES=\ +../../../../boost/multiprecision/mpfr.hpp\ +../../../../boost/multiprecision/tommath.hpp\ +../../../../boost/multiprecision/number.hpp\ +../../../../boost/multiprecision/cpp_dec_float.hpp\ +../../../../boost/multiprecision/gmp.hpp\ +../../../../boost/multiprecision/random.hpp\ +../../../../boost/multiprecision/cpp_int.hpp\ +../../../../boost/multiprecision/miller_rabin.hpp\ +../../../../boost/multiprecision/rational_adapter.hpp\ +../../../../boost/multiprecision/concepts/mp_number_archetypes.hpp\ +../../../../boost/multiprecision/detail/big_lanczos.hpp\ +../../../../boost/multiprecision/detail/digits.hpp\ +../../../../boost/multiprecision/detail/no_et_ops.hpp\ +../../../../boost/multiprecision/detail/cpp_int_core.hpp\ +../../../../boost/multiprecision/detail/number_base.hpp\ +../../../../boost/multiprecision/detail/cpp_int_trivial_ops.hpp\ +../../../../boost/multiprecision/detail/generic_interconvert.hpp\ +../../../../boost/multiprecision/detail/number_compare.hpp\ +../../../../boost/multiprecision/detail/default_ops.hpp\ +../../../../boost/multiprecision/detail/integer_ops.hpp\ +../../../../boost/multiprecision/detail/functions/constants.hpp\ +../../../../boost/multiprecision/detail/functions/pow.hpp\ +../../../../boost/multiprecision/detail/functions/trig.hpp\ +../../../../boost/multiprecision/traits/explicit_conversion.hpp\ +../../../../boost/multiprecision/traits/is_restricted_conversion.hpp + +coverage : run + gcov test_arithmetic_cpp_int_1 test_arithmetic_cpp_int_2 test_arithmetic_cpp_int_3 test_arithmetic_cpp_dec_float test_arithmetic_concept test_arithmetic_mpz test_arithmetic_mpf test_arithmetic_mpf_50 test_arithmetic_mpq test_arithmetic_mpfr test_arithmetic_mpfr_50 test_cpp_int test_int_io test_float_io test_rational_io test_gmp_conversions test_mpfr_conversions test_cpp_int_conv + +test_arithmetic_cpp_int_1.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_1 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_1.o -c ../test_arithmetic.cpp + +test_arithmetic_cpp_int_1 : test_arithmetic_cpp_int_1.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_1 test_arithmetic_cpp_int_1.o + +test_arithmetic_cpp_int_2.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_2 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_2.o -c ../test_arithmetic.cpp + +test_arithmetic_cpp_int_2 : test_arithmetic_cpp_int_2.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_2 test_arithmetic_cpp_int_2.o + +test_arithmetic_cpp_int_3.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_3.o -c ../test_arithmetic.cpp + +test_arithmetic_cpp_int_3 : test_arithmetic_cpp_int_3.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_3 test_arithmetic_cpp_int_3.o + +test_arithmetic_cpp_dec_float.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_DEC_FLOAT --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_dec_float.o -c ../test_arithmetic.cpp + +test_arithmetic_cpp_dec_float : test_arithmetic_cpp_dec_float.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_dec_float test_arithmetic_cpp_dec_float.o + +test_arithmetic_concept.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_BACKEND --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_concept.o -c ../test_arithmetic.cpp + +test_arithmetic_concept : test_arithmetic_concept.o + g++ -std=gnu++0x --coverage -o test_arithmetic_concept test_arithmetic_concept.o + +test_arithmetic_mpz.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPZ --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpz.o -c ../test_arithmetic.cpp + +test_arithmetic_mpz : test_arithmetic_mpz.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpz test_arithmetic_mpz.o -lgmp + +test_arithmetic_mpf.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPF --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpf.o -c ../test_arithmetic.cpp + +test_arithmetic_mpf : test_arithmetic_mpf.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpf test_arithmetic_mpf.o -lgmp + +test_arithmetic_mpf_50.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPF_50 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpf_50.o -c ../test_arithmetic.cpp + +test_arithmetic_mpf_50 : test_arithmetic_mpf_50.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpf_50 test_arithmetic_mpf_50.o -lgmp + +test_arithmetic_mpq.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPQ --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpq.o -c ../test_arithmetic.cpp + +test_arithmetic_mpq : test_arithmetic_mpq.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpq test_arithmetic_mpq.o -lgmp + +test_arithmetic_mpfr.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPFR --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpfr.o -c ../test_arithmetic.cpp + +test_arithmetic_mpfr : test_arithmetic_mpfr.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpfr test_arithmetic_mpfr.o -lmpfr -lgmp + +test_arithmetic_mpfr_50.o : ../test_arithmetic.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPFR_50 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpfr_50.o -c ../test_arithmetic.cpp + +test_arithmetic_mpfr_50 : test_arithmetic_mpfr_50.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpfr_50 test_arithmetic_mpfr_50.o -lmpfr -lgmp + +test_cpp_int.o : ../test_cpp_int.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -g -I../../../.. -I../../../../../../trunk -o test_cpp_int.o -c ../test_cpp_int.cpp + +test_cpp_int : test_cpp_int.o + g++ -std=gnu++0x --coverage -o test_cpp_int test_cpp_int.o -lgmp + +test_int_io.o : ../test_int_io.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -DTEST_MPZ -DTEST_CPP_INT -g -I../../../.. -I../../../../../../trunk -o test_int_io.o -c ../test_int_io.cpp + +test_int_io : test_int_io.o + g++ -std=gnu++0x --coverage -o test_int_io test_int_io.o -lgmp + +test_float_io.o : ../test_float_io.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -g -I../../../.. -I../../../../../../trunk -o test_float_io.o -c ../test_float_io.cpp + +test_float_io : test_float_io.o + g++ -std=gnu++0x --coverage -o test_float_io test_float_io.o -lmpfr -lgmp + +test_rational_io.o : ../test_rational_io.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -DTEST_MPQ -DTEST_CPP_INT -g -I../../../.. -I../../../../../../trunk -o test_rational_io.o -c ../test_rational_io.cpp + +test_rational_io : test_rational_io.o + g++ -std=gnu++0x --coverage -o test_rational_io test_rational_io.o -lgmp + +test_gmp_conversions.o : ../test_gmp_conversions.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -g -I../../../.. -I../../../../../../trunk -o test_gmp_conversions.o -c ../test_gmp_conversions.cpp + +test_gmp_conversions : test_gmp_conversions.o + g++ -std=gnu++0x --coverage -o test_gmp_conversions test_gmp_conversions.o -lgmp + +test_mpfr_conversions.o : ../test_mpfr_conversions.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -g -I../../../.. -I../../../../../../trunk -o test_mpfr_conversions.o -c ../test_mpfr_conversions.cpp + +test_mpfr_conversions : test_mpfr_conversions.o + g++ -std=gnu++0x --coverage -o test_mpfr_conversions test_mpfr_conversions.o -lmpfr -lgmp + +test_cpp_int_conv.o : ../test_cpp_int_conv.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -g -I../../../.. -I../../../../../../trunk -o test_cpp_int_conv.o -c ../test_cpp_int_conv.cpp + +test_cpp_int_conv : test_cpp_int_conv.o + g++ -std=gnu++0x --coverage -o test_cpp_int_conv test_cpp_int_conv.o + +run : test_arithmetic_cpp_int_1 test_arithmetic_cpp_int_2 test_arithmetic_cpp_int_3 test_arithmetic_cpp_dec_float test_arithmetic_concept test_arithmetic_mpz test_arithmetic_mpf test_arithmetic_mpf_50 \ +test_arithmetic_mpq test_arithmetic_mpfr test_arithmetic_mpfr_50 test_cpp_int test_int_io test_float_io test_rational_io test_gmp_conversions test_mpfr_conversions test_cpp_int_conv + ./test_arithmetic_cpp_int_1 + ./test_arithmetic_cpp_int_2 + ./test_arithmetic_cpp_int_3 + ./test_arithmetic_cpp_dec_float + ./test_arithmetic_concept + ./test_arithmetic_mpz + ./test_arithmetic_mpf + ./test_arithmetic_mpf_50 + ./test_arithmetic_mpq + ./test_arithmetic_mpfr + ./test_arithmetic_mpfr_50 + ./test_cpp_int + ./test_int_io + ./test_float_io + ./test_rational_io + ./test_gmp_conversions + ./test_mpfr_conversions + ./test_cpp_int_conv + +clean : + rm -rf *.o *.gc* test_arithmetic_cpp_int_1 test_arithmetic_cpp_int_2 test_arithmetic_cpp_int_3 test_arithmetic_cpp_dec_float test_arithmetic_concept test_arithmetic_mpz \ + test_arithmetic_mpf test_arithmetic_mpf_50 test_arithmetic_mpq test_arithmetic_mpfr test_arithmetic_mpfr_50 test_cpp_int\ + test_int_io test_float_io test_rational_io test_gmp_conversions test_mpfr_conversions test_cpp_int_conv + + + + diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 39af694c..feb05b87 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -18,7 +18,8 @@ #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \ !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) \ && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\ - && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_BR) && !defined(TEST_ARITHMETIC_BACKEND) + && !defined(TEST_CPP_INT_1) && !defined(TEST_CPP_INT_2) && !defined(TEST_CPP_INT_3) \ + && !defined(TEST_CPP_INT_BR) && !defined(TEST_ARITHMETIC_BACKEND) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND @@ -28,7 +29,9 @@ # define TEST_CPP_DEC_FLOAT # define TEST_MPQ # define TEST_TOMMATH -# define TEST_CPP_INT +# define TEST_CPP_INT_1 +# define TEST_CPP_INT_2 +# define TEST_CPP_INT_3 # define TEST_CPP_INT_BR # define TEST_ARITHMETIC_BACKEND @@ -61,7 +64,7 @@ #include #include #endif -#if defined(TEST_CPP_INT) || defined(TEST_CPP_INT_BR) +#if defined(TEST_CPP_INT_1) || defined(TEST_CPP_INT_2) || defined(TEST_CPP_INT_3) || defined(TEST_CPP_INT_BR) #include #endif @@ -142,6 +145,11 @@ template void test_comparisons(Val, Val, const boost::mpl::false_) {} +int normalize_compare_result(int r) +{ + return r > 0 ? 1 : r < 0 ? -1 : 0; +} + template void test_comparisons(Val a, Val b, const boost::mpl::true_) { @@ -149,6 +157,8 @@ void test_comparisons(Val a, Val b, const boost::mpl::true_) Real r2(b); Real z(1); + int cr = a < b ? -1 : a > b ? 1 : 0; + BOOST_TEST_EQUAL(r1 == r2, a == b); BOOST_TEST_EQUAL(r1 != r2, a != b); BOOST_TEST_EQUAL(r1 <= r2, a <= b); @@ -204,6 +214,35 @@ void test_comparisons(Val a, Val b, const boost::mpl::true_) BOOST_TEST_EQUAL(a < r2*z, a < b); BOOST_TEST_EQUAL(a >= r2*z, a >= b); BOOST_TEST_EQUAL(a > r2*z, a > b); + + BOOST_TEST_EQUAL(normalize_compare_result(r1.compare(r2)), cr); + BOOST_TEST_EQUAL(normalize_compare_result(r2.compare(r1)), -cr); + BOOST_TEST_EQUAL(normalize_compare_result(r1.compare(b)), cr); + BOOST_TEST_EQUAL(normalize_compare_result(r2.compare(a)), -cr); +} + +template +void test_conditional(Real v, Exp e) +{ + // + // Verify that Exp is usable in Boolean contexts, and has the same value as v: + // + if(e) + { + BOOST_TEST(v); + } + else + { + BOOST_TEST(!v); + } + if(!e) + { + BOOST_TEST(!v); + } + else + { + BOOST_TEST(v); + } } template @@ -289,6 +328,15 @@ void test_integer_ops(const boost::mpl::int_::is_signed) { BOOST_TEST(-a % c == 0); @@ -326,6 +374,9 @@ void test_integer_ops(const boost::mpl::int_>= -20, std::out_of_range); + BOOST_TEST_THROW(Real(a << -20), std::out_of_range); + BOOST_TEST_THROW(Real(a >> -20), std::out_of_range); #ifndef BOOST_NO_LONG_LONG if(sizeof(long long) > sizeof(std::size_t)) { // extreme values should trigger an exception: BOOST_TEST_THROW(a >>= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); BOOST_TEST_THROW(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_TEST_THROW(a >>= -(1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_TEST_THROW(a <<= -(1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_TEST_THROW(a >>= (1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_TEST_THROW(a <<= (1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + // Unless they fit within range: + a = 2000L; + BOOST_TEST((a <<= 20uLL) == (2000L << 20)); + a = 2000; + BOOST_TEST((a <<= 20LL) == (2000L << 20)); + + BOOST_TEST_THROW(Real(a >> (1uLL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + BOOST_TEST_THROW(Real(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + BOOST_TEST_THROW(Real(a >>= -(1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + BOOST_TEST_THROW(Real(a <<= -(1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + BOOST_TEST_THROW(Real(a >>= (1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + BOOST_TEST_THROW(Real(a <<= (1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + // Unless they fit within range: + a = 2000L; + BOOST_TEST(Real(a << 20uLL) == (2000L << 20)); + a = 2000; + BOOST_TEST(Real(a << 20LL) == (2000L << 20)); } #endif a = 20; @@ -422,6 +496,11 @@ void test_integer_ops(const boost::mpl::int_(a, b, c, typename is_twos_complement_integer::type()); @@ -446,6 +525,11 @@ void test_integer_ops(const boost::mpl::int_::is_signed) + { + BOOST_TEST(gcd(a, -45) == boost::math::gcd(400, 45)); + BOOST_TEST(lcm(a, -45) == boost::math::lcm(400, 45)); + } + BOOST_TEST(gcd(a, 45u) == boost::math::gcd(400, 45)); + BOOST_TEST(lcm(a, 45u) == boost::math::lcm(400, 45)); BOOST_TEST(gcd(400, b) == boost::math::gcd(400, 45)); BOOST_TEST(lcm(400, b) == boost::math::lcm(400, 45)); + if(std::numeric_limits::is_signed) + { + BOOST_TEST(gcd(-400, b) == boost::math::gcd(400, 45)); + BOOST_TEST(lcm(-400, b) == boost::math::lcm(400, 45)); + } + BOOST_TEST(gcd(400u, b) == boost::math::gcd(400, 45)); + BOOST_TEST(lcm(400u, b) == boost::math::lcm(400, 45)); + + // + // Conditionals involving 2 arg functions: + // + test_conditional(Real(gcd(a, b)), gcd(a, b)); + Real r; divide_qr(a, b, c, r); BOOST_TEST(c == a / b); @@ -570,12 +680,48 @@ void test_integer_ops(const boost::mpl::int_ @@ -785,6 +931,95 @@ void test_negative_mixed(boost::mpl::true_ const&) BOOST_TEST(r == static_cast(n4 * n5)); r = static_cast(4 * n4) / Real(4); BOOST_TEST(r == static_cast(n4)); + + Real a, b, c; + a = 20; + b = 30; + c = -a + b; + BOOST_TEST(c == 10); + c = b + -a; + BOOST_TEST(c == 10); + n4 = 30; + c = -a + static_cast(n4); + BOOST_TEST(c == 10); + c = static_cast(n4) + -a; + BOOST_TEST(c == 10); + c = -a + -b; + BOOST_TEST(c == -50); + n4 = 4; + c = -(a + b) + static_cast(n4); + BOOST_TEST(c == -50+4); + n4 = 50; + c = (a + b) - static_cast(n4); + BOOST_TEST(c == 0); + c = (a + b) - static_cast(n4); + BOOST_TEST(c == 0); + c = a - -(b + static_cast(n4)); + BOOST_TEST(c == 20 - -(30 + 50)); + c = -(b + static_cast(n4)) - a; + BOOST_TEST(c == -(30 + 50) - 20); + c = a - -b; + BOOST_TEST(c == 50); + c = -a - b; + BOOST_TEST(c == -50); + c = -a - static_cast(n4); + BOOST_TEST(c == -20 - 50); + c = static_cast(n4) - -a; + BOOST_TEST(c == 50 + 20); + c = -(a + b) - Real(n4); + BOOST_TEST(c == -(20 + 30) - 50); + c = static_cast(n4) - (a + b); + BOOST_TEST(c == 0); + c = (a + b) * static_cast(n4); + BOOST_TEST(c == 50 * 50); + c = static_cast(n4) * (a + b); + BOOST_TEST(c == 50 * 50); + c = a * -(b + static_cast(n4)); + BOOST_TEST(c == 20 * -(30 + 50)); + c = -(b + static_cast(n4)) * a; + BOOST_TEST(c == 20 * -(30 + 50)); + c = a * -b; + BOOST_TEST(c == 20 * -30); + c = -a * b; + BOOST_TEST(c == 20 * -30); + c = -a * static_cast(n4); + BOOST_TEST(c == -20 * 50); + c = static_cast(n4) * -a; + BOOST_TEST(c == -20 * 50); + c = -(a + b) + a; + BOOST_TEST(-50 + 20); + c = static_cast(n4) - (a + b); + BOOST_TEST(c == 0); + Real d = 10; + c = (a + b) / d; + BOOST_TEST(c == 5); + c = (a + b) / (d + 0); + BOOST_TEST(c == 5); + c = (a + b) / static_cast(n4); + BOOST_TEST(c == 1); + c = static_cast(n4) / (a + b); + BOOST_TEST(c == 1); + d = 50; + c = d / -(a + b); + BOOST_TEST(c == -1); + c = -(a + b) / d; + BOOST_TEST(c == -1); + d = 2; + c = a / -d; + BOOST_TEST(c == 20 / -2); + c = -a / d; + BOOST_TEST(c == 20 / -2); + d = 50; + c = -d / static_cast(n4); + BOOST_TEST(c == -1); + c = static_cast(n4) / -d; + BOOST_TEST(c == -1); + c = static_cast(n4) + a; + BOOST_TEST(c == 70); + c = static_cast(n4) - a; + BOOST_TEST(c == 30); + c = static_cast(n4) * a; + BOOST_TEST(c == 50 * 20); } template @@ -793,7 +1028,12 @@ void test_negative_mixed(boost::mpl::false_ const&) } template -void test_mixed() +void test_mixed(const boost::mpl::false_&) +{ +} + +template +void test_mixed(const boost::mpl::true_&) { typedef typename lexical_cast_target_type::type target_type; typedef typename boost::mpl::if_< @@ -905,26 +1145,59 @@ void test_mixed() test_negative_mixed(boost::mpl::bool_::is_signed>()); } +template +void test_members(Real) +{ + // + // Test sign and zero functions: + // + Real a = 20; + Real b = 30; + BOOST_TEST(a.sign() > 0); + BOOST_TEST(!a.is_zero()); + if(std::numeric_limits::is_signed) + { + a = -20; + BOOST_TEST(a.sign() < 0); + BOOST_TEST(!a.is_zero()); + } + a = 0; + BOOST_TEST(a.sign() == 0); + BOOST_TEST(a.is_zero()); + + a = 20; + b = 30; + a.swap(b); + BOOST_TEST(a == 30); + BOOST_TEST(b == 20); +} + +template +void test_members(boost::rational v) +{ +} + template void test() { #ifndef NO_MIXED_OPS - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); - test_mixed(); + boost::multiprecision::is_number tag; + test_mixed(tag); + test_mixed(tag); + test_mixed(tag); + test_mixed(tag); + test_mixed(tag); + test_mixed(tag); + test_mixed(tag); + test_mixed(tag); + test_mixed(tag); #ifdef BOOST_HAS_LONG_LONG - test_mixed(); - test_mixed(); + test_mixed(tag); + test_mixed(tag); #endif - test_mixed(); - test_mixed(); - test_mixed(); + test_mixed(tag); + test_mixed(tag); + test_mixed(tag); #endif // // Integer only functions: @@ -1175,23 +1448,11 @@ void test() BOOST_TEST((72 < b+a) == false); BOOST_TEST((72 >= b+a) == true); BOOST_TEST((72 > b+a) == false); -#ifndef NO_MIXED_OPS + + test_members(a); // - // Test sign and zero functions, plus use in boolian context: + // Use in Boolean context: // - a = 20; - BOOST_TEST(a.sign() > 0); - BOOST_TEST(!a.is_zero()); - if(std::numeric_limits::is_signed) - { - a = -20; - BOOST_TEST(a.sign() < 0); - BOOST_TEST(!a.is_zero()); - } - a = 0; - BOOST_TEST(a.sign() == 0); - BOOST_TEST(a.is_zero()); -#endif a = 0; if(a) { @@ -1243,6 +1504,50 @@ void test() ss >> c; BOOST_TEST(c == 22); BOOST_TEST(c == a + b); + // + // More cases for complete code coverage: + // + a = 20; + b = 30; + swap(a, b); + BOOST_TEST(a == 30); + BOOST_TEST(b == 20); + a = 20; + b = 30; + std::swap(a, b); + BOOST_TEST(a == 30); + BOOST_TEST(b == 20); + a = 20; + b = 30; + a = a + b * 2; + BOOST_TEST(a == 20 + 30 * 2); + a = 100; + a = a - b * 2; + BOOST_TEST(a == 100 - 30 * 2); + a = 20; + a = a * (b + 2); + BOOST_TEST(a == 20 * (32)); + a = 20; + a = (b + 2) * a; + BOOST_TEST(a == 20 * (32)); + a = 90; + b = 2; + a = a / (b + 0); + BOOST_TEST(a == 45); + a = 20; + b = 30; + c = (a * b) + 22; + BOOST_TEST(c == 20 * 30 + 22); + c = 22 + (a * b); + BOOST_TEST(c == 20 * 30 + 22); + + // + // Test conditionals: + // + a = 20; + test_conditional(a, +a); + test_conditional(Real(-a), -a); + test_conditional(a, (a + 0)); } @@ -1291,20 +1596,23 @@ int main() #ifdef TEST_MPZ_BOOST_RATIONAL test >(); #endif -#ifdef TEST_CPP_INT +#ifdef TEST_CPP_INT_1 test(); test(); test(); +#endif +#ifdef TEST_CPP_INT_2 test(); test, false> >(); test > >(); - +#endif +#ifdef TEST_CPP_INT_3 // Again with "trivial" backends: test, false > >(); test, false > >(); #endif #ifdef TEST_CPP_INT_BR - test(); + test >(); #endif return boost::report_errors(); } diff --git a/test/test_cpp_int_conv.cpp b/test/test_cpp_int_conv.cpp index 60c57d82..b21d91a5 100644 --- a/test/test_cpp_int_conv.cpp +++ b/test/test_cpp_int_conv.cpp @@ -51,6 +51,25 @@ int main() number, false> i7(i3); BOOST_TEST(i7 == -1234567); + int256_t i8(i6); + BOOST_TEST(i8 == -5677334); + + i7.assign(4.0); + BOOST_TEST(i7 == 4); + + number, false> i9(-5677334); + i7 = i9; + BOOST_TEST(i7 == -5677334); + i7 = number, false>(i9); + BOOST_TEST(i7 == -5677334); + + i9 = static_cast, false> >(i7); + BOOST_TEST(i9 == -5677334); + + ++i9; + i7 = i9; + BOOST_TEST(i7 == 1 - 5677334); + return boost::report_errors(); } diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp index b603fa88..a17cfcf5 100644 --- a/test/test_int_io.cpp +++ b/test/test_int_io.cpp @@ -126,6 +126,8 @@ int main() test_round_trip > >(); test_round_trip > >(); test_round_trip > >(); + test_round_trip > >(); + test_round_trip > >(); #endif return boost::report_errors(); } diff --git a/test/test_rational_io.cpp b/test/test_rational_io.cpp index 7b027cbf..b954a0c4 100644 --- a/test/test_rational_io.cpp +++ b/test/test_rational_io.cpp @@ -94,14 +94,14 @@ void do_round_trip(const T& val, std::ios_base::fmtflags f, const boost::mpl::fa } template -struct is_mp_number : public boost::mpl::false_{}; +struct is_number : public boost::mpl::false_{}; template -struct is_mp_number > : public boost::mpl::true_{}; +struct is_number > : public boost::mpl::true_{}; template void do_round_trip(const T& val, std::ios_base::fmtflags f) { - do_round_trip(val, f, is_mp_number()); + do_round_trip(val, f, is_number()); } template From ce3354335c63facc219b2ef92fd33bb2b8c2f041 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 4 Sep 2012 08:20:26 +0000 Subject: [PATCH 230/256] Allow mixed precision binary operations. Add tests for basic mixed precision usage. [SVN r80394] --- include/boost/multiprecision/cpp_int.hpp | 9 +- .../multiprecision/detail/default_ops.hpp | 106 +-- .../boost/multiprecision/detail/et_ops.hpp | 691 ++++++++++++++++++ .../boost/multiprecision/detail/no_et_ops.hpp | 90 +-- .../multiprecision/detail/number_base.hpp | 644 +--------------- .../multiprecision/detail/number_compare.hpp | 205 +++--- include/boost/multiprecision/gmp.hpp | 14 +- include/boost/multiprecision/mpfr.hpp | 6 +- include/boost/multiprecision/number.hpp | 44 +- include/boost/multiprecision/tommath.hpp | 14 +- test/test_arithmetic.cpp | 86 ++- 11 files changed, 1045 insertions(+), 864 deletions(-) create mode 100644 include/boost/multiprecision/detail/et_ops.hpp diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 39458f29..17d97b72 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -3202,13 +3202,8 @@ public: static number_type val; if(!init) { - boost::multiprecision::limb_type l = ~static_cast(0); - unsigned c = MinBits / backend_type::limb_bits + (MinBits % backend_type::limb_bits ? 1 : 0); - for(unsigned i = 0; i < c; ++i) - { - val <<= backend_type::limb_bits; - val |= l; - } + boost::multiprecision::number, ExpressionTemplates> t(0); + val = ~t; init = true; } return val; diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 5029bf47..66f9731e 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -38,7 +38,7 @@ namespace boost{ namespace multiprecision{ namespace default_ops{ // of each depending on whether the backend can be directly constructed from type V: // template -inline typename enable_if_c::value && !is_convertible::value >::type +inline typename enable_if_c >::value && !is_convertible::value >::type eval_add(T& result, V const& v) { T t; @@ -46,14 +46,14 @@ inline typename enable_if_c::value && !is_convertible::va eval_add(result, t); } template -inline typename enable_if_c::value && is_convertible::value >::type +inline typename enable_if_c >::value && is_convertible::value >::type eval_add(T& result, V const& v) { T t(v); eval_add(result, t); } template -inline typename enable_if_c::value && !is_convertible::value>::type +inline typename enable_if_c >::value && !is_convertible::value>::type eval_subtract(T& result, V const& v) { T t; @@ -61,14 +61,14 @@ inline typename enable_if_c::value && !is_convertible::va eval_subtract(result, t); } template -inline typename enable_if_c::value && is_convertible::value>::type +inline typename enable_if_c >::value && is_convertible::value>::type eval_subtract(T& result, V const& v) { T t(v); eval_subtract(result, t); } template -inline typename enable_if_c::value && !is_convertible::value>::type +inline typename enable_if_c >::value && !is_convertible::value>::type eval_multiply(T& result, V const& v) { T t; @@ -76,14 +76,14 @@ inline typename enable_if_c::value && !is_convertible::va eval_multiply(result, t); } template -inline typename enable_if_c::value && is_convertible::value>::type +inline typename enable_if_c >::value && is_convertible::value>::type eval_multiply(T& result, V const& v) { T t(v); eval_multiply(result, t); } template -inline typename enable_if_c::value && !is_convertible::value>::type +inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide(T& result, V const& v) { T t; @@ -91,14 +91,14 @@ inline typename enable_if_c::value && !is_convertible::va eval_divide(result, t); } template -inline typename enable_if_c::value && is_convertible::value>::type +inline typename enable_if_c >::value && is_convertible::value>::type eval_divide(T& result, V const& v) { T t(v); eval_divide(result, t); } template -inline typename enable_if_c::value && !is_convertible::value>::type +inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus(T& result, V const& v) { T t; @@ -106,14 +106,14 @@ inline typename enable_if_c::value && !is_convertible::va eval_modulus(result, t); } template -inline typename enable_if_c::value && is_convertible::value>::type +inline typename enable_if_c >::value&& is_convertible::value>::type eval_modulus(T& result, V const& v) { T t(v); eval_modulus(result, t); } template -inline typename enable_if_c::value && !is_convertible::value>::type +inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_and(T& result, V const& v) { T t; @@ -121,14 +121,14 @@ inline typename enable_if_c::value && !is_convertible::va eval_bitwise_and(result, t); } template -inline typename enable_if_c::value && is_convertible::value>::type +inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_and(T& result, V const& v) { T t(v); eval_bitwise_and(result, t); } template -inline typename enable_if_c::value && !is_convertible::value>::type +inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_or(T& result, V const& v) { T t; @@ -136,14 +136,14 @@ inline typename enable_if_c::value && !is_convertible::va eval_bitwise_or(result, t); } template -inline typename enable_if_c::value && is_convertible::value>::type +inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_or(T& result, V const& v) { T t(v); eval_bitwise_or(result, t); } template -inline typename enable_if_c::value && !is_convertible::value>::type +inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_xor(T& result, V const& v) { T t; @@ -151,7 +151,7 @@ inline typename enable_if_c::value && !is_convertible::va eval_bitwise_xor(result, t); } template -inline typename enable_if_c::value && is_convertible::value>::type +inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_xor(T& result, V const& v) { T t(v); @@ -159,7 +159,7 @@ inline typename enable_if_c::value && is_convertible::val } template -inline typename enable_if_c::value && !is_convertible::value>::type +inline typename enable_if_c >::value && !is_convertible::value>::type eval_complement(T& result, V const& v) { T t; @@ -167,7 +167,7 @@ inline typename enable_if_c::value && !is_convertible::va eval_complement(result, t); } template -inline typename enable_if_c::value && is_convertible::value>::type +inline typename enable_if_c >::value && is_convertible::value>::type eval_complement(T& result, V const& v) { T t(v); @@ -195,20 +195,20 @@ inline void eval_add(T& t, const T& u, const T& v) } } template -inline typename enable_if_c::value && !is_convertible::value>::type eval_add(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_add(T& t, const T& u, const U& v) { T vv; vv = v; eval_add(t, u, vv); } template -inline typename enable_if_c::value && is_convertible::value>::type eval_add(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_add(T& t, const T& u, const U& v) { T vv(v); eval_add(t, u, vv); } template -inline typename enable_if_c::value>::type eval_add(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_add(T& t, const U& u, const T& v) { eval_add(t, v, u); } @@ -232,20 +232,20 @@ inline void eval_subtract(T& t, const T& u, const T& v) } } template -inline typename enable_if_c::value && !is_convertible::value>::type eval_subtract(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_subtract(T& t, const T& u, const U& v) { T vv; vv = v; eval_subtract(t, u, vv); } template -inline typename enable_if_c::value && is_convertible::value>::type eval_subtract(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_subtract(T& t, const T& u, const U& v) { T vv(v); eval_subtract(t, u, vv); } template -inline typename enable_if_c::value>::type eval_subtract(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_subtract(T& t, const U& u, const T& v) { eval_subtract(t, v, u); t.negate(); @@ -269,20 +269,20 @@ inline void eval_multiply(T& t, const T& u, const T& v) } } template -inline typename enable_if_c::value && !is_convertible::value>::type eval_multiply(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_multiply(T& t, const T& u, const U& v) { T vv; vv = v; eval_multiply(t, u, vv); } template -inline typename enable_if_c::value && is_convertible::value>::type eval_multiply(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_multiply(T& t, const T& u, const U& v) { T vv(v); eval_multiply(t, u, vv); } template -inline typename enable_if_c::value>::type eval_multiply(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_multiply(T& t, const U& u, const T& v) { eval_multiply(t, v, u); } @@ -305,27 +305,27 @@ inline void eval_divide(T& t, const T& u, const T& v) } } template -inline typename enable_if_c::value && !is_convertible::value>::type eval_divide(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide(T& t, const T& u, const U& v) { T vv; vv = v; eval_divide(t, u, vv); } template -inline typename enable_if_c::value && is_convertible::value>::type eval_divide(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_divide(T& t, const T& u, const U& v) { T vv(v); eval_divide(t, u, vv); } template -inline typename enable_if_c::value && !is_convertible::value>::type eval_divide(T& t, const U& u, const T& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide(T& t, const U& u, const T& v) { T uu; uu = u; eval_divide(t, uu, v); } template -inline typename enable_if_c::value && is_convertible::value>::type eval_divide(T& t, const U& u, const T& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_divide(T& t, const U& u, const T& v) { T uu(u); eval_divide(t, uu, v); @@ -350,27 +350,27 @@ inline void eval_modulus(T& t, const T& u, const T& v) } } template -inline typename enable_if_c::value && !is_convertible::value>::type eval_modulus(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus(T& t, const T& u, const U& v) { T vv; vv = v; eval_modulus(t, u, vv); } template -inline typename enable_if_c::value && is_convertible::value>::type eval_modulus(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_modulus(T& t, const T& u, const U& v) { T vv(v); eval_modulus(t, u, vv); } template -inline typename enable_if_c::value && !is_convertible::value>::type eval_modulus(T& t, const U& u, const T& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus(T& t, const U& u, const T& v) { T uu; uu = u; eval_modulus(t, uu, v); } template -inline typename enable_if_c::value && is_convertible::value>::type eval_modulus(T& t, const U& u, const T& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_modulus(T& t, const U& u, const T& v) { T uu(u); eval_modulus(t, uu, v); @@ -394,20 +394,20 @@ inline void eval_bitwise_and(T& t, const T& u, const T& v) } } template -inline typename enable_if_c::value && !is_convertible::value>::type eval_bitwise_and(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_and(T& t, const T& u, const U& v) { T vv; vv = v; eval_bitwise_and(t, u, vv); } template -inline typename enable_if_c::value && is_convertible::value>::type eval_bitwise_and(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_and(T& t, const T& u, const U& v) { T vv(v); eval_bitwise_and(t, u, vv); } template -inline typename enable_if_c::value>::type eval_bitwise_and(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_bitwise_and(T& t, const U& u, const T& v) { eval_bitwise_and(t, v, u); } @@ -430,20 +430,20 @@ inline void eval_bitwise_or(T& t, const T& u, const T& v) } } template -inline typename enable_if_c::value && !is_convertible::value>::type eval_bitwise_or(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_or(T& t, const T& u, const U& v) { T vv; vv = v; eval_bitwise_or(t, u, vv); } template -inline typename enable_if_c::value && is_convertible::value>::type eval_bitwise_or(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_or(T& t, const T& u, const U& v) { T vv(v); eval_bitwise_or(t, u, vv); } template -inline typename enable_if_c::value>::type eval_bitwise_or(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_bitwise_or(T& t, const U& u, const T& v) { eval_bitwise_or(t, v, u); } @@ -466,20 +466,20 @@ inline void eval_bitwise_xor(T& t, const T& u, const T& v) } } template -inline typename enable_if_c::value && !is_convertible::value>::type eval_bitwise_xor(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_xor(T& t, const T& u, const U& v) { T vv; vv = v; eval_bitwise_xor(t, u, vv); } template -inline typename enable_if_c::value && is_convertible::value>::type eval_bitwise_xor(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_xor(T& t, const T& u, const U& v) { T vv(v); eval_bitwise_xor(t, u, vv); } template -inline typename enable_if_c::value>::type eval_bitwise_xor(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_bitwise_xor(T& t, const U& u, const T& v) { eval_bitwise_xor(t, v, u); } @@ -580,13 +580,28 @@ struct calculate_next_larger_type >::type type; }; +template +inline bool check_in_range(const T& t) +{ + // Can t fit in an R? + if(std::numeric_limits::is_specialized && std::numeric_limits::is_bounded && (t > (std::numeric_limits::max)())) + return true; + return false; +} + +template +inline bool check_in_range(const terminal&) +{ + return false; +} + template inline void eval_convert_to(R* result, const B& backend) { typedef typename calculate_next_larger_type::type next_type; next_type n; eval_convert_to(&n, backend); - if(std::numeric_limits::is_specialized && (n > (std::numeric_limits::max)())) + if(check_in_range(n)) { *result = (std::numeric_limits::max)(); } @@ -1617,6 +1632,7 @@ inline multiprecision::number sinhc_pi(const multi // This has to come last of all: // #include +#include #endif diff --git a/include/boost/multiprecision/detail/et_ops.hpp b/include/boost/multiprecision/detail/et_ops.hpp new file mode 100644 index 00000000..35886a9b --- /dev/null +++ b/include/boost/multiprecision/detail/et_ops.hpp @@ -0,0 +1,691 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MP_ET_OPS_HPP +#define BOOST_MP_ET_OPS_HPP + +namespace boost{ namespace multiprecision{ + +// +// Non-member operators for number: +// +// Unary operators first: +// +template +inline const number& operator + (const number& v) { return v; } +template +inline const detail::expression& operator + (const detail::expression& v) { return v; } +template +inline detail::expression > operator - (const number& v) { return detail::expression >(v); } +template +inline detail::expression > operator - (const detail::expression& v) { return detail::expression >(v); } +template +inline detail::expression > operator ~ (const number& v) { return detail::expression >(v); } +template +inline detail::expression > operator ~ (const detail::expression& v) { return detail::expression >(v); } +// +// Then addition: +// +template +inline detail::expression, number > + operator + (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if >, detail::expression, V > >::type + operator + (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if >, detail::expression > >::type + operator + (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator + (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator + (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator + (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression, V > >::type + operator + (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression > >::type + operator + (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::expression, typename detail::expression::left_type > + operator + (const number& a, const detail::expression& b) +{ + return detail::expression, typename detail::expression::left_type >(a, b.left_ref()); +} +template +inline detail::expression, typename detail::expression::left_type > + operator + (const detail::expression& a, const number& b) +{ + return detail::expression, typename detail::expression::left_type >(b, a.left_ref()); +} +template +inline detail::expression, number > + operator + (const number& a, const detail::expression >& b) +{ + return detail::expression, number >(a, b.left_ref()); +} +template +inline detail::expression, number > + operator + (const detail::expression >& a, const number& b) +{ + return detail::expression, number >(b, a.left_ref()); +} +template +inline typename enable_if >, detail::expression > >::type + operator + (const detail::expression >& a, const V& b) +{ + return detail::expression >(b, a.left_ref()); +} +template +inline typename enable_if, number >, detail::expression, number > >::type + operator + (const detail::expression >& a, const number& b) +{ + return detail::expression, number >(b, a.left_ref()); +} +template +inline typename enable_if, number >, detail::expression, number > >::type + operator + (const number& a, const detail::expression >& b) +{ + return detail::expression, number >(a, b.left_ref()); +} +template +inline detail::expression, number > > + operator + (const detail::expression >& a, const detail::expression >& b) +{ + return detail::expression, number > >(detail::expression, number >(a.left_ref(), b.left_ref())); +} +// +// Subtraction: +// +template +inline detail::expression, number > + operator - (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if >, detail::expression, V > >::type + operator - (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if >, detail::expression > >::type + operator - (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator - (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator - (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator - (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression, V > >::type + operator - (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression > >::type + operator - (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::expression, typename detail::expression::left_type > + operator - (const number& a, const detail::expression& b) +{ + return detail::expression, typename detail::expression::left_type >(a, b.left_ref()); +} +template +inline detail::expression, typename detail::expression::left_type > > + operator - (const detail::expression& a, const number& b) +{ + return detail::expression, typename detail::expression::left_type > >( + detail::expression, typename detail::expression::left_type >(b, a.left_ref())); +} +template +inline detail::expression, number > + operator - (const number& a, const detail::expression >& b) +{ + return detail::expression, number >(a, b.left_ref()); +} +template +inline detail::expression, number > > + operator - (const detail::expression >& a, const number& b) +{ + return detail::expression, number > >( + detail::expression, number >(b, a.left_ref())); +} +template +inline typename enable_if >, detail::expression, V > > >::type + operator - (const detail::expression >& a, const V& b) +{ + return detail::expression, V > >(detail::expression, V >(a.left_ref(), b)); +} +template +inline typename enable_if, number >, detail::expression, number > > >::type + operator - (const detail::expression >& a, const number& b) +{ + return detail::expression, number > >(detail::expression, number >(a.left_ref(), b)); +} +template +inline typename enable_if >, detail::expression > >::type + operator - (const V& a, const detail::expression >& b) +{ + return detail::expression >(a, b.left_ref()); +} +template +inline typename enable_if, number >, detail::expression, number > >::type + operator - (const number& a, const detail::expression >& b) +{ + return detail::expression, number >(a, b.left_ref()); +} +// +// Multiplication: +// +template +inline detail::expression, number > + operator * (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if >, detail::expression, V > >::type + operator * (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if >, detail::expression > >::type + operator * (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator * (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator * (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator * (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression, V > >::type + operator * (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression > >::type + operator * (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::expression, typename detail::expression::left_type > > + operator * (const number& a, const detail::expression& b) +{ + return detail::expression, typename detail::expression::left_type > >( + detail::expression, typename detail::expression::left_type > (a, b.left_ref())); +} +template +inline detail::expression, typename detail::expression::left_type > > + operator * (const detail::expression& a, const number& b) +{ + return detail::expression, typename detail::expression::left_type > >( + detail::expression, typename detail::expression::left_type >(b, a.left_ref())); +} +template +inline detail::expression, number > > + operator * (const number& a, const detail::expression >& b) +{ + return detail::expression, number > >( + detail::expression, number >(a, b.left_ref())); +} +template +inline detail::expression, number > > + operator * (const detail::expression >& a, const number& b) +{ + return detail::expression, number > >( + detail::expression, number >(b, a.left_ref())); +} +template +inline typename enable_if >, detail::expression, V > > >::type + operator * (const detail::expression >& a, const V& b) +{ + return detail::expression, V > > ( + detail::expression, V >(a.left_ref(), b)); +} +template +inline typename enable_if, number >, detail::expression, number > > >::type + operator * (const detail::expression >& a, const number& b) +{ + return detail::expression, number > > ( + detail::expression, number >(a.left_ref(), b)); +} +template +inline typename enable_if >, detail::expression, V > > >::type + operator * (const V& a, const detail::expression >& b) +{ + return detail::expression, V > >( + detail::expression, V >(b.left_ref(), a)); +} +template +inline typename enable_if, number >, detail::expression, number > > >::type + operator * (const number& a, const detail::expression >& b) +{ + return detail::expression, number > >( + detail::expression, number >(b.left_ref(), a)); +} +// +// Division: +// +template +inline detail::expression, number > + operator / (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if >, detail::expression, V > >::type + operator / (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if >, detail::expression > >::type + operator / (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator / (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator / (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator / (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression, V > >::type + operator / (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression > >::type + operator / (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: +// +template +inline detail::expression, typename detail::expression::left_type > > + operator / (const number& a, const detail::expression& b) +{ + return detail::expression, typename detail::expression::left_type > >( + detail::expression, typename detail::expression::left_type >(a, b.left_ref())); +} +template +inline detail::expression::left_type, number > > + operator / (const detail::expression& a, const number& b) +{ + return detail::expression::left_type, number > >( + detail::expression::left_type, number >(a.left_ref(), b)); +} +template +inline detail::expression, number > > + operator / (const number& a, const detail::expression >& b) +{ + return detail::expression, number > >( + detail::expression, number >(a, b.left_ref())); +} +template +inline detail::expression, number > > + operator / (const detail::expression >& a, const number& b) +{ + return detail::expression, number > >( + detail::expression, number >(a.left_ref(), b)); +} +template +inline typename enable_if >, detail::expression, V > > >::type + operator / (const detail::expression >& a, const V& b) +{ + return detail::expression, V > >( + detail::expression, V>(a.left_ref(), b)); +} +template +inline typename enable_if, number >, detail::expression, number > > >::type + operator / (const detail::expression >& a, const number& b) +{ + return detail::expression, number > >( + detail::expression, number >(a.left_ref(), b)); +} +template +inline typename enable_if >, detail::expression > > >::type + operator / (const V& a, const detail::expression >& b) +{ + return detail::expression > >( + detail::expression >(a, b.left_ref())); +} +template +inline typename enable_if, number >, detail::expression, number > > >::type + operator / (const number& a, const detail::expression >& b) +{ + return detail::expression, number > >( + detail::expression, number >(a, b.left_ref())); +} +// +// Modulus: +// +template +inline detail::expression, number > + operator % (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if >, detail::expression, V > >::type + operator % (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if >, detail::expression > >::type + operator % (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator % (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator % (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator % (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression, V > >::type + operator % (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression > >::type + operator % (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Left shift: +// +template +inline typename enable_if, detail::expression, I > >::type + operator << (const number& a, const I& b) +{ + return detail::expression, I>(a, b); +} +template +inline typename enable_if, detail::expression, I> >::type + operator << (const detail::expression& a, const I& b) +{ + return detail::expression, I>(a, b); +} +// +// Right shift: +// +template +inline typename enable_if, detail::expression, I > >::type + operator >> (const number& a, const I& b) +{ + return detail::expression, I>(a, b); +} +template +inline typename enable_if, detail::expression, I> >::type + operator >> (const detail::expression& a, const I& b) +{ + return detail::expression, I>(a, b); +} +// +// Bitwise AND: +// +template +inline detail::expression, number > + operator & (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if >, detail::expression, V > >::type + operator & (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if >, detail::expression > >::type + operator & (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator & (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator & (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator & (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression, V > >::type + operator & (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression > >::type + operator & (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Bitwise OR: +// +template +inline detail::expression, number > + operator| (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if >, detail::expression, V > >::type + operator| (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if >, detail::expression > >::type + operator| (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator| (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator| (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator| (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression, V > >::type + operator| (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression > >::type + operator| (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} +// +// Bitwise XOR: +// +template +inline detail::expression, number > + operator^ (const number& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline typename enable_if >, detail::expression, V > >::type + operator^ (const number& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if >, detail::expression > >::type + operator^ (const V& a, const number& b) +{ + return detail::expression >(a, b); +} +template +inline detail::expression, detail::expression > + operator^ (const number& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline detail::expression, number > + operator^ (const detail::expression& a, const number& b) +{ + return detail::expression, number >(a, b); +} +template +inline detail::expression, detail::expression > + operator^ (const detail::expression& a, const detail::expression& b) +{ + return detail::expression, detail::expression >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression, V > >::type + operator^ (const detail::expression& a, const V& b) +{ + return detail::expression, V >(a, b); +} +template +inline typename enable_if::result_type>, detail::expression > >::type + operator^ (const V& a, const detail::expression& b) +{ + return detail::expression >(a, b); +} + +}} // namespaces + +#endif diff --git a/include/boost/multiprecision/detail/no_et_ops.hpp b/include/boost/multiprecision/detail/no_et_ops.hpp index 282f4fea..18728ea0 100644 --- a/include/boost/multiprecision/detail/no_et_ops.hpp +++ b/include/boost/multiprecision/detail/no_et_ops.hpp @@ -43,20 +43,18 @@ template inline typename enable_if >, number >::type operator + (const number& a, const V& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_add; - eval_add(result.backend(), a.backend(), static_cast(b)); + eval_add(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template inline typename enable_if >, number >::type operator + (const V& a, const number& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_add; - eval_add(result.backend(), b.backend(), static_cast(a)); + eval_add(result.backend(), b.backend(), number::canonical_value(a)); return BOOST_MP_MOVE(result); } // @@ -74,20 +72,18 @@ template inline typename enable_if >, number >::type operator - (const number& a, const V& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_subtract; - eval_subtract(result.backend(), a.backend(), static_cast(b)); + eval_subtract(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template inline typename enable_if >, number >::type operator - (const V& a, const number& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_subtract; - eval_subtract(result.backend(), static_cast(a), b.backend()); + eval_subtract(result.backend(), number::canonical_value(a), b.backend()); return BOOST_MP_MOVE(result); } // @@ -105,20 +101,18 @@ template inline typename enable_if >, number >::type operator * (const number& a, const V& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_multiply; - eval_multiply(result.backend(), a.backend(), static_cast(b)); + eval_multiply(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template inline typename enable_if >, number >::type operator * (const V& a, const number& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_multiply; - eval_multiply(result.backend(), b.backend(), static_cast(a)); + eval_multiply(result.backend(), b.backend(), number::canonical_value(a)); return BOOST_MP_MOVE(result); } // @@ -136,20 +130,18 @@ template inline typename enable_if >, number >::type operator / (const number& a, const V& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_divide; - eval_divide(result.backend(), a.backend(), static_cast(b)); + eval_divide(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template inline typename enable_if >, number >::type operator / (const V& a, const number& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_divide; - eval_divide(result.backend(), static_cast(a), b.backend()); + eval_divide(result.backend(), number::canonical_value(a), b.backend()); return BOOST_MP_MOVE(result); } // @@ -167,20 +159,18 @@ template inline typename enable_if >, number >::type operator % (const number& a, const V& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_modulus; - eval_modulus(result.backend(), a.backend(), static_cast(b)); + eval_modulus(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template inline typename enable_if >, number >::type operator % (const V& a, const number& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_modulus; - eval_modulus(result.backend(), static_cast(a), b.backend()); + eval_modulus(result.backend(), number::canonical_value(a), b.backend()); return BOOST_MP_MOVE(result); } // @@ -198,20 +188,18 @@ template inline typename enable_if >, number >::type operator | (const number& a, const V& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_bitwise_or; - eval_bitwise_or(result.backend(), a.backend(), static_cast(b)); + eval_bitwise_or(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template inline typename enable_if >, number >::type operator | (const V& a, const number& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_bitwise_or; - eval_bitwise_or(result.backend(), b.backend(), static_cast(a)); + eval_bitwise_or(result.backend(), b.backend(), number::canonical_value(a)); return BOOST_MP_MOVE(result); } // @@ -229,20 +217,18 @@ template inline typename enable_if >, number >::type operator ^ (const number& a, const V& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_bitwise_xor; - eval_bitwise_xor(result.backend(), a.backend(), static_cast(b)); + eval_bitwise_xor(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template inline typename enable_if >, number >::type operator ^ (const V& a, const number& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_bitwise_xor; - eval_bitwise_xor(result.backend(), b.backend(), static_cast(a)); + eval_bitwise_xor(result.backend(), b.backend(), number::canonical_value(a)); return BOOST_MP_MOVE(result); } // @@ -260,20 +246,18 @@ template inline typename enable_if >, number >::type operator & (const number& a, const V& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_bitwise_and; - eval_bitwise_and(result.backend(), a.backend(), static_cast(b)); + eval_bitwise_and(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template inline typename enable_if >, number >::type operator & (const V& a, const number& b) { - typedef typename detail::canonical::type canonical_type; number result; using default_ops::eval_bitwise_and; - eval_bitwise_and(result.backend(), b.backend(), static_cast(a)); + eval_bitwise_and(result.backend(), b.backend(), number::canonical_value(a)); return BOOST_MP_MOVE(result); } // @@ -352,18 +336,16 @@ template inline typename enable_if >, number >::type operator + (number&& a, const V& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_add; - eval_add(a.backend(), static_cast(b)); + eval_add(a.backend(), number::canonical_value(b)); return static_cast&&>(a); } template inline typename enable_if >, number >::type operator + (const V& a, number&& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_add; - eval_add(b.backend(), static_cast(a)); + eval_add(b.backend(), number::canonical_value(a)); return static_cast&&>(b); } // @@ -395,18 +377,16 @@ template inline typename enable_if >, number >::type operator - (number&& a, const V& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_subtract; - eval_subtract(a.backend(), static_cast(b)); + eval_subtract(a.backend(), number::canonical_value(b)); return static_cast&&>(a); } template inline typename enable_if >, number >::type operator - (const V& a, number&& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_subtract; - eval_subtract(b.backend(), static_cast(a)); + eval_subtract(b.backend(), number::canonical_value(a)); b.backend().negate(); return static_cast&&>(b); } @@ -438,18 +418,16 @@ template inline typename enable_if >, number >::type operator * (number&& a, const V& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_multiply; - eval_multiply(a.backend(), static_cast(b)); + eval_multiply(a.backend(), number::canonical_value(b)); return static_cast&&>(a); } template inline typename enable_if >, number >::type operator * (const V& a, number&& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_multiply; - eval_multiply(b.backend(), static_cast(a)); + eval_multiply(b.backend(), number::canonical_value(a)); return static_cast&&>(b); } // @@ -466,9 +444,8 @@ template inline typename enable_if >, number >::type operator / (number&& a, const V& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_divide; - eval_divide(a.backend(), static_cast(b)); + eval_divide(a.backend(), number::canonical_value(b)); return static_cast&&>(a); } // @@ -485,9 +462,8 @@ template inline typename enable_if >, number >::type operator % (number&& a, const V& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_modulus; - eval_modulus(a.backend(), static_cast(b)); + eval_modulus(a.backend(), number::canonical_value(b)); return static_cast&&>(a); } // @@ -518,18 +494,16 @@ template inline typename enable_if >, number >::type operator | (number&& a, const V& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_or; - eval_bitwise_or(a.backend(), static_cast(b)); + eval_bitwise_or(a.backend(), number::canonical_value(b)); return static_cast&&>(a); } template inline typename enable_if >, number >::type operator | (const V& a, number&& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_or; - eval_bitwise_or(b.backend(), static_cast(a)); + eval_bitwise_or(b.backend(), number::canonical_value(a)); return static_cast&&>(b); } // @@ -560,18 +534,16 @@ template inline typename enable_if >, number >::type operator ^ (number&& a, const V& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_xor; - eval_bitwise_xor(a.backend(), static_cast(b)); + eval_bitwise_xor(a.backend(), number::canonical_value(b)); return static_cast&&>(a); } template inline typename enable_if >, number >::type operator ^ (const V& a, number&& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_xor; - eval_bitwise_xor(b.backend(), static_cast(a)); + eval_bitwise_xor(b.backend(), number::canonical_value(a)); return static_cast&&>(b); } // @@ -602,18 +574,16 @@ template inline typename enable_if >, number >::type operator & (number&& a, const V& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_and; - eval_bitwise_and(a.backend(), static_cast(b)); + eval_bitwise_and(a.backend(), number::canonical_value(b)); return static_cast&&>(a); } template inline typename enable_if >, number >::type operator & (const V& a, number&& b) { - typedef typename detail::canonical::type canonical_type; using default_ops::eval_bitwise_and; - eval_bitwise_and(b.backend(), static_cast(a)); + eval_bitwise_and(b.backend(), number::canonical_value(a)); return static_cast&&>(b); } // diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp index e5b46e6e..8721991c 100644 --- a/include/boost/multiprecision/detail/number_base.hpp +++ b/include/boost/multiprecision/detail/number_base.hpp @@ -41,7 +41,7 @@ template struct is_compatible_arithmetic_type : public mpl::bool_< is_convertible::value - && !is_number::value + && !is_same::value && !is_number_expression::value> {}; @@ -221,6 +221,16 @@ struct combine_expression, number type; }; +template +struct combine_expression, number > +{ + typedef typename mpl::if_c< + is_convertible, number >::value, + number, + number + >::type type; +}; + template struct arg_type { @@ -619,638 +629,6 @@ void check_shift_range(V, const mpl::false_&, const mpl::false_&) BOOST_NOEXCEPT } // namespace detail -// -// Non-member operators for number: -// -// Unary operators first: -// -template -inline const number& operator + (const number& v) { return v; } -template -inline const detail::expression& operator + (const detail::expression& v) { return v; } -template -inline detail::expression > operator - (const number& v) { return detail::expression >(v); } -template -inline detail::expression > operator - (const detail::expression& v) { return detail::expression >(v); } -template -inline detail::expression > operator ~ (const number& v) { return detail::expression >(v); } -template -inline detail::expression > operator ~ (const detail::expression& v) { return detail::expression >(v); } -// -// Then addition: -// -template -inline detail::expression, number > - operator + (const number& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline typename enable_if >, detail::expression, V > >::type - operator + (const number& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if >, detail::expression > >::type - operator + (const V& a, const number& b) -{ - return detail::expression >(a, b); -} -template -inline detail::expression, detail::expression > - operator + (const number& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline detail::expression, number > - operator + (const detail::expression& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline detail::expression, detail::expression > - operator + (const detail::expression& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression, V > >::type - operator + (const detail::expression& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression > >::type - operator + (const V& a, const detail::expression& b) -{ - return detail::expression >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::expression, typename detail::expression::left_type > - operator + (const number& a, const detail::expression& b) -{ - return detail::expression, typename detail::expression::left_type >(a, b.left_ref()); -} -template -inline detail::expression, typename detail::expression::left_type > - operator + (const detail::expression& a, const number& b) -{ - return detail::expression, typename detail::expression::left_type >(b, a.left_ref()); -} -template -inline detail::expression, number > - operator + (const number& a, const detail::expression >& b) -{ - return detail::expression, number >(a, b.left_ref()); -} -template -inline detail::expression, number > - operator + (const detail::expression >& a, const number& b) -{ - return detail::expression, number >(b, a.left_ref()); -} -template -inline typename enable_if >, detail::expression > >::type - operator + (const detail::expression >& a, const V& b) -{ - return detail::expression >(b, a.left_ref()); -} -template -inline typename enable_if >, detail::expression > >::type - operator + (const V& a, const detail::expression >& b) -{ - return detail::expression >(a, b.left_ref()); -} -template -inline detail::expression, number > > - operator + (const detail::expression >& a, const detail::expression >& b) -{ - return detail::expression, number > >(detail::expression, number >(a.left_ref(), b.left_ref())); -} -// -// Subtraction: -// -template -inline detail::expression, number > - operator - (const number& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline typename enable_if >, detail::expression, V > >::type - operator - (const number& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if >, detail::expression > >::type - operator - (const V& a, const number& b) -{ - return detail::expression >(a, b); -} -template -inline detail::expression, detail::expression > - operator - (const number& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline detail::expression, number > - operator - (const detail::expression& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline detail::expression, detail::expression > - operator - (const detail::expression& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression, V > >::type - operator - (const detail::expression& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression > >::type - operator - (const V& a, const detail::expression& b) -{ - return detail::expression >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::expression, typename detail::expression::left_type > - operator - (const number& a, const detail::expression& b) -{ - return detail::expression, typename detail::expression::left_type >(a, b.left_ref()); -} -template -inline detail::expression, typename detail::expression::left_type > > - operator - (const detail::expression& a, const number& b) -{ - return detail::expression, typename detail::expression::left_type > >( - detail::expression, typename detail::expression::left_type >(b, a.left_ref())); -} -template -inline detail::expression, number > - operator - (const number& a, const detail::expression >& b) -{ - return detail::expression, number >(a, b.left_ref()); -} -template -inline detail::expression, number > > - operator - (const detail::expression >& a, const number& b) -{ - return detail::expression, number > >( - detail::expression, number >(b, a.left_ref())); -} -template -inline typename enable_if >, detail::expression, V > > >::type - operator - (const detail::expression >& a, const V& b) -{ - return detail::expression, V > >(detail::expression, V >(a.left_ref(), b)); -} -template -inline typename enable_if >, detail::expression > >::type - operator - (const V& a, const detail::expression >& b) -{ - return detail::expression >(a, b.left_ref()); -} -// -// Multiplication: -// -template -inline detail::expression, number > - operator * (const number& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline typename enable_if >, detail::expression, V > >::type - operator * (const number& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if >, detail::expression > >::type - operator * (const V& a, const number& b) -{ - return detail::expression >(a, b); -} -template -inline detail::expression, detail::expression > - operator * (const number& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline detail::expression, number > - operator * (const detail::expression& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline detail::expression, detail::expression > - operator * (const detail::expression& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression, V > >::type - operator * (const detail::expression& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression > >::type - operator * (const V& a, const detail::expression& b) -{ - return detail::expression >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::expression, typename detail::expression::left_type > > - operator * (const number& a, const detail::expression& b) -{ - return detail::expression, typename detail::expression::left_type > >( - detail::expression, typename detail::expression::left_type > (a, b.left_ref())); -} -template -inline detail::expression, typename detail::expression::left_type > > - operator * (const detail::expression& a, const number& b) -{ - return detail::expression, typename detail::expression::left_type > >( - detail::expression, typename detail::expression::left_type >(b, a.left_ref())); -} -template -inline detail::expression, number > > - operator * (const number& a, const detail::expression >& b) -{ - return detail::expression, number > >( - detail::expression, number >(a, b.left_ref())); -} -template -inline detail::expression, number > > - operator * (const detail::expression >& a, const number& b) -{ - return detail::expression, number > >( - detail::expression, number >(b, a.left_ref())); -} -template -inline typename enable_if >, detail::expression, V > > >::type - operator * (const detail::expression >& a, const V& b) -{ - return detail::expression, V > > ( - detail::expression, V >(a.left_ref(), b)); -} -template -inline typename enable_if >, detail::expression, V > > >::type - operator * (const V& a, const detail::expression >& b) -{ - return detail::expression, V > >( - detail::expression, V >(b.left_ref(), a)); -} -// -// Division: -// -template -inline detail::expression, number > - operator / (const number& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline typename enable_if >, detail::expression, V > >::type - operator / (const number& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if >, detail::expression > >::type - operator / (const V& a, const number& b) -{ - return detail::expression >(a, b); -} -template -inline detail::expression, detail::expression > - operator / (const number& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline detail::expression, number > - operator / (const detail::expression& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline detail::expression, detail::expression > - operator / (const detail::expression& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression, V > >::type - operator / (const detail::expression& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression > >::type - operator / (const V& a, const detail::expression& b) -{ - return detail::expression >(a, b); -} -// -// Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries: -// -template -inline detail::expression, typename detail::expression::left_type > > - operator / (const number& a, const detail::expression& b) -{ - return detail::expression, typename detail::expression::left_type > >( - detail::expression, typename detail::expression::left_type >(a, b.left_ref())); -} -template -inline detail::expression::left_type, number > > - operator / (const detail::expression& a, const number& b) -{ - return detail::expression::left_type, number > >( - detail::expression::left_type, number >(a.left_ref(), b)); -} -template -inline detail::expression, number > > - operator / (const number& a, const detail::expression >& b) -{ - return detail::expression, number > >( - detail::expression, number >(a, b.left_ref())); -} -template -inline detail::expression, number > > - operator / (const detail::expression >& a, const number& b) -{ - return detail::expression, number > >( - detail::expression, number >(a.left_ref(), b)); -} -template -inline typename enable_if >, detail::expression, V > > >::type - operator / (const detail::expression >& a, const V& b) -{ - return detail::expression, V > >( - detail::expression, V>(a.left_ref(), b)); -} -template -inline typename enable_if >, detail::expression > > >::type - operator / (const V& a, const detail::expression >& b) -{ - return detail::expression > >( - detail::expression >(a, b.left_ref())); -} -// -// Modulus: -// -template -inline detail::expression, number > - operator % (const number& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline typename enable_if >, detail::expression, V > >::type - operator % (const number& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if >, detail::expression > >::type - operator % (const V& a, const number& b) -{ - return detail::expression >(a, b); -} -template -inline detail::expression, detail::expression > - operator % (const number& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline detail::expression, number > - operator % (const detail::expression& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline detail::expression, detail::expression > - operator % (const detail::expression& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression, V > >::type - operator % (const detail::expression& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression > >::type - operator % (const V& a, const detail::expression& b) -{ - return detail::expression >(a, b); -} -// -// Left shift: -// -template -inline typename enable_if, detail::expression, I > >::type - operator << (const number& a, const I& b) -{ - return detail::expression, I>(a, b); -} -template -inline typename enable_if, detail::expression, I> >::type - operator << (const detail::expression& a, const I& b) -{ - return detail::expression, I>(a, b); -} -// -// Right shift: -// -template -inline typename enable_if, detail::expression, I > >::type - operator >> (const number& a, const I& b) -{ - return detail::expression, I>(a, b); -} -template -inline typename enable_if, detail::expression, I> >::type - operator >> (const detail::expression& a, const I& b) -{ - return detail::expression, I>(a, b); -} -// -// Bitwise AND: -// -template -inline detail::expression, number > - operator & (const number& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline typename enable_if >, detail::expression, V > >::type - operator & (const number& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if >, detail::expression > >::type - operator & (const V& a, const number& b) -{ - return detail::expression >(a, b); -} -template -inline detail::expression, detail::expression > - operator & (const number& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline detail::expression, number > - operator & (const detail::expression& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline detail::expression, detail::expression > - operator & (const detail::expression& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression, V > >::type - operator & (const detail::expression& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression > >::type - operator & (const V& a, const detail::expression& b) -{ - return detail::expression >(a, b); -} -// -// Bitwise OR: -// -template -inline detail::expression, number > - operator| (const number& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline typename enable_if >, detail::expression, V > >::type - operator| (const number& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if >, detail::expression > >::type - operator| (const V& a, const number& b) -{ - return detail::expression >(a, b); -} -template -inline detail::expression, detail::expression > - operator| (const number& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline detail::expression, number > - operator| (const detail::expression& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline detail::expression, detail::expression > - operator| (const detail::expression& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression, V > >::type - operator| (const detail::expression& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression > >::type - operator| (const V& a, const detail::expression& b) -{ - return detail::expression >(a, b); -} -// -// Bitwise XOR: -// -template -inline detail::expression, number > - operator^ (const number& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline typename enable_if >, detail::expression, V > >::type - operator^ (const number& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if >, detail::expression > >::type - operator^ (const V& a, const number& b) -{ - return detail::expression >(a, b); -} -template -inline detail::expression, detail::expression > - operator^ (const number& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline detail::expression, number > - operator^ (const detail::expression& a, const number& b) -{ - return detail::expression, number >(a, b); -} -template -inline detail::expression, detail::expression > - operator^ (const detail::expression& a, const detail::expression& b) -{ - return detail::expression, detail::expression >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression, V > >::type - operator^ (const detail::expression& a, const V& b) -{ - return detail::expression, V >(a, b); -} -template -inline typename enable_if::result_type>, detail::expression > >::type - operator^ (const V& a, const detail::expression& b) -{ - return detail::expression >(a, b); -} - // // Traits class, lets us know what kind of number we have, defaults to a floating point type: // diff --git a/include/boost/multiprecision/detail/number_compare.hpp b/include/boost/multiprecision/detail/number_compare.hpp index 1450508f..afeabbb3 100644 --- a/include/boost/multiprecision/detail/number_compare.hpp +++ b/include/boost/multiprecision/detail/number_compare.hpp @@ -19,14 +19,21 @@ inline bool eval_eq(const B& a, const B& b) { return a.compare(b) == 0; } +// +// For the default version which compares to some arbitrary type convertible to +// our number type, we don't know what value the ExpressionTemplates parameter to +// class number should be. We generally prefer ExpressionTemplates to be enabled +// in case type A is itself an expression template, but we need to test both options +// with is_convertible in case A has an implicit conversion operator to number. +// This is the case with many uBlas types for example. +// template inline bool eval_eq(const B& a, const A& b) { - typedef typename mpl::if_< - is_convertible >, - number, - number - >::type mp_type; + typedef typename mpl::if_c< + is_convertible >::value, + number, + number >::type mp_type; mp_type t(b); return eval_eq(a, t.backend()); } @@ -39,11 +46,10 @@ inline bool eval_lt(const B& a, const B& b) template inline bool eval_lt(const B& a, const A& b) { - typedef typename mpl::if_< - is_convertible >, - number, - number - >::type mp_type; + typedef typename mpl::if_c< + is_convertible >::value, + number, + number >::type mp_type; mp_type t(b); return eval_lt(a, t.backend()); } @@ -56,15 +62,38 @@ inline bool eval_gt(const B& a, const B& b) template inline bool eval_gt(const B& a, const A& b) { - typedef typename mpl::if_< - is_convertible >, - number, - number - >::type mp_type; + typedef typename mpl::if_c< + is_convertible >::value, + number, + number >::type mp_type; mp_type t(b); return eval_gt(a, t.backend()); } +} // namespace default_ops + +namespace detail{ + +template +struct is_valid_mixed_compare : public mpl::false_ {}; + +template +struct is_valid_mixed_compare, Val> : public is_convertible> {}; +/* +template +struct is_valid_mixed_compare > : public is_convertible> {}; +*/ +template +struct is_valid_mixed_compare, number > : public mpl::false_ {}; + +template +struct is_valid_mixed_compare, expression > + : public mpl::bool_, number >::value> {}; + +template +struct is_valid_mixed_compare, number > + : public mpl::bool_, number >::value> {}; + } template @@ -74,13 +103,13 @@ inline bool operator == (const number& a, const nu return eval_eq(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator == (const number& a, const Arithmetic& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_eq; - return eval_eq(a.backend(), ct(b)); + return eval_eq(a.backend(), number::canonical_value(b)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator == (const number& a, const detail::expression& b) @@ -89,24 +118,24 @@ inline typename enable_if, typename typename detail::expression::result_type t(b); return eval_eq(a.backend(), t.backend()); } +*/ template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator == (const Arithmetic& a, const number& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_eq; - return eval_eq(b.backend(), ct(a)); + return eval_eq(b.backend(), number::canonical_value(a)); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator == (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_eq; result_type t(b); - return eval_eq(t.backend(), ct(a)); + return eval_eq(t.backend(), result_type::canonical_value(a)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator == (const detail::expression& a, const number& b) @@ -114,16 +143,15 @@ inline typename enable_if, typename using default_ops::eval_eq; typename detail::expression::result_type t(a); return eval_eq(t.backend(), b.backend()); -} +}*/ template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator == (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_eq; result_type t(a); - return eval_eq(t.backend(), ct(b)); + return eval_eq(t.backend(), result_type::canonical_value(b)); } template inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type @@ -142,13 +170,13 @@ inline bool operator != (const number& a, const nu return !eval_eq(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator != (const number& a, const Arithmetic& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_eq; - return !eval_eq(a.backend(), ct(b)); + return !eval_eq(a.backend(), number::canonical_value(b)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator != (const number& a, const detail::expression& b) @@ -157,24 +185,24 @@ inline typename enable_if, typename typename detail::expression::result_type t(b); return !eval_eq(a.backend(), t.backend()); } +*/ template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator != (const Arithmetic& a, const number& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_eq; - return !eval_eq(b.backend(), ct(a)); + return !eval_eq(b.backend(), number::canonical_value(a)); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator != (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_eq; result_type t(b); - return !eval_eq(t.backend(), ct(a)); + return !eval_eq(t.backend(), result_type::canonical_value(a)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator != (const detail::expression& a, const number& b) @@ -182,16 +210,15 @@ inline typename enable_if, typename using default_ops::eval_eq; typename detail::expression::result_type t(a); return !eval_eq(t.backend(), b.backend()); -} +}*/ template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator != (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_eq; result_type t(a); - return !eval_eq(t.backend(), ct(b)); + return !eval_eq(t.backend(), result_type::canonical_value(b)); } template inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type @@ -210,13 +237,13 @@ inline bool operator < (const number& a, const num return eval_lt(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator < (const number& a, const Arithmetic& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_lt; - return eval_lt(a.backend(), ct(b)); + return eval_lt(a.backend(), number::canonical_value(b)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator < (const number& a, const detail::expression& b) @@ -225,24 +252,24 @@ inline typename enable_if, typename typename detail::expression::result_type t(b); return eval_lt(a.backend(), t.backend()); } +*/ template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator < (const Arithmetic& a, const number& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_gt; - return eval_gt(b.backend(), ct(a)); + return eval_gt(b.backend(), number::canonical_value(a)); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator < (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_gt; result_type t(b); - return eval_gt(t.backend(), ct(a)); + return eval_gt(t.backend(), result_type::canonical_value(a)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator < (const detail::expression& a, const number& b) @@ -251,15 +278,15 @@ inline typename enable_if, typename typename detail::expression::result_type t(a); return eval_lt(t.backend(), b.backend()); } +*/ template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator < (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_lt; result_type t(a); - return eval_lt(t.backend(), ct(b)); + return eval_lt(t.backend(), result_type::canonical_value(b)); } template inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type @@ -278,13 +305,13 @@ inline bool operator > (const number& a, const num return eval_gt(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator > (const number& a, const Arithmetic& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_gt; - return eval_gt(a.backend(), ct(b)); + return eval_gt(a.backend(), number::canonical_value(b)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator > (const number& a, const detail::expression& b) @@ -293,24 +320,24 @@ inline typename enable_if, typename typename detail::expression::result_type t(b); return eval_gt(a.backend(), t.backend()); } +*/ template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator > (const Arithmetic& a, const number& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_lt; - return eval_lt(b.backend(), ct(a)); + return eval_lt(b.backend(), number::canonical_value(a)); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator > (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_lt; result_type t(b); - return eval_lt(t.backend(), ct(a)); + return eval_lt(t.backend(), result_type::canonical_value(a)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator > (const detail::expression& a, const number& b) @@ -319,15 +346,15 @@ inline typename enable_if, typename typename detail::expression::result_type t(a); return eval_gt(t.backend(), b.backend()); } +*/ template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator > (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_gt; result_type t(a); - return eval_gt(t.backend(), ct(b)); + return eval_gt(t.backend(), result_type::canonical_value(b)); } template inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type @@ -346,13 +373,13 @@ inline bool operator <= (const number& a, const nu return !eval_gt(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator <= (const number& a, const Arithmetic& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_gt; - return !eval_gt(a.backend(), ct(b)); + return !eval_gt(a.backend(), number::canonical_value(b)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator <= (const number& a, const detail::expression& b) @@ -361,24 +388,24 @@ inline typename enable_if, typename typename detail::expression::result_type t(b); return !eval_gt(a.backend(), t.backend()); } +*/ template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator <= (const Arithmetic& a, const number& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_lt; - return !eval_lt(b.backend(), ct(a)); + return !eval_lt(b.backend(), number::canonical_value(a)); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator <= (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_lt; result_type t(b); - return !eval_lt(t.backend(), ct(a)); + return !eval_lt(t.backend(), result_type::canonical_value(a)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator <= (const detail::expression& a, const number& b) @@ -387,15 +414,15 @@ inline typename enable_if, typename typename detail::expression::result_type t(a); return !eval_gt(t.backend(), b.backend()); } +*/ template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator <= (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_gt; result_type t(a); - return !eval_gt(t.backend(), ct(b)); + return !eval_gt(t.backend(), result_type::canonical_value(b)); } template inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type @@ -414,13 +441,13 @@ inline bool operator >= (const number& a, const nu return !eval_lt(a.backend(), b.backend()); } template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator >= (const number& a, const Arithmetic& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_lt; - return !eval_lt(a.backend(), ct(b)); + return !eval_lt(a.backend(), number::canonical_value(b)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator >= (const number& a, const detail::expression& b) @@ -429,24 +456,24 @@ inline typename enable_if, typename typename detail::expression::result_type t(b); return !eval_lt(a.backend(), t.backend()); } +*/ template -inline typename enable_if_c<(is_convertible >::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c, Arithmetic>::value, bool>::type operator >= (const Arithmetic& a, const number& b) { - typedef typename detail::canonical::type ct; using default_ops::eval_gt; - return !eval_gt(b.backend(), ct(a)); + return !eval_gt(b.backend(), number::canonical_value(a)); } template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator >= (const Arithmetic& a, const detail::expression& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_gt; result_type t(b); - return !eval_gt(t.backend(), ct(a)); + return !eval_gt(t.backend(), result_type::canonical_value(a)); } +/* template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator >= (const detail::expression& a, const number& b) @@ -455,15 +482,15 @@ inline typename enable_if, typename typename detail::expression::result_type t(a); return !eval_lt(t.backend(), b.backend()); } +*/ template -inline typename enable_if_c<(is_convertible::result_type>::value && !is_number_expression::value && !is_number::value), bool>::type +inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator >= (const detail::expression& a, const Arithmetic& b) { typedef typename detail::expression::result_type result_type; - typedef typename detail::canonical::type ct; using default_ops::eval_lt; result_type t(a); - return !eval_lt(t.backend(), ct(b)); + return !eval_lt(t.backend(), result_type::canonical_value(b)); } template inline typename enable_if::result_type, typename detail::expression::result_type>, bool>::type diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 719bb41c..ba59df2c 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -331,7 +331,7 @@ struct gmp_float_imp return mpf_cmp_ui(m_data, i); } template - int compare(V v)const + typename enable_if, int>::type compare(V v)const { gmp_float d; d = v; @@ -552,17 +552,17 @@ struct gmp_float<0> : public detail::gmp_float_imp<0> }; template -inline typename disable_if, T>, bool>::type eval_eq(const gmp_float& a, const T& b) BOOST_NOEXCEPT +inline typename enable_if_c::value, bool>::type eval_eq(const gmp_float& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) == 0; } template -inline typename disable_if, T>, bool>::type eval_lt(const gmp_float& a, const T& b) BOOST_NOEXCEPT +inline typename enable_if_c::value, bool>::type eval_lt(const gmp_float& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) < 0; } template -inline typename disable_if, T>, bool>::type eval_gt(const gmp_float& a, const T& b) BOOST_NOEXCEPT +inline typename enable_if_c::value, bool>::type eval_gt(const gmp_float& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) > 0; } @@ -1265,17 +1265,17 @@ protected: }; template -inline typename disable_if, bool>::type eval_eq(const gmp_int& a, const T& b) +inline typename enable_if, bool>::type eval_eq(const gmp_int& a, const T& b) { return a.compare(b) == 0; } template -inline typename disable_if, bool>::type eval_lt(const gmp_int& a, const T& b) +inline typename enable_if, bool>::type eval_lt(const gmp_int& a, const T& b) { return a.compare(b) < 0; } template -inline typename disable_if, bool>::type eval_gt(const gmp_int& a, const T& b) +inline typename enable_if, bool>::type eval_gt(const gmp_int& a, const T& b) { return a.compare(b) > 0; } diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index cdbb8cfb..b3e4f14e 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -594,17 +594,17 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> }; template -inline typename disable_if, T>, bool>::type eval_eq(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT +inline typename enable_if, bool>::type eval_eq(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) == 0; } template -inline typename disable_if, T>, bool>::type eval_lt(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT +inline typename enable_if, bool>::type eval_lt(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) < 0; } template -inline typename disable_if, T>, bool>::type eval_gt(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT +inline typename enable_if, bool>::type eval_gt(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) > 0; } diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index a8fa5f44..e61372d9 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -161,7 +161,7 @@ public: return *this; } template - typename disable_if, number& >::type + typename disable_if, number& >::type assign(const number& v) { // @@ -540,12 +540,28 @@ public: { return m_backend.str(digits, f); } +private: + template + void convert_to_imp(T* result)const + { + using default_ops::eval_convert_to; + eval_convert_to(result, m_backend); + } + template + void convert_to_imp(number* result)const + { + result->assign(*this); + } + void convert_to_imp(std::string* result)const + { + *result = this->str(); + } +public: template T convert_to()const { - using default_ops::eval_convert_to; T result; - eval_convert_to(&result, m_backend); + convert_to_imp(&result); return result; } #ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS @@ -1553,6 +1569,20 @@ private: BOOST_FORCEINLINE BOOST_CONSTEXPR bool is_realy_self(const Val&)const BOOST_NOEXCEPT{ return false; } BOOST_FORCEINLINE BOOST_CONSTEXPR bool is_realy_self(const self_type& v)const BOOST_NOEXCEPT{ return &v == this; } + static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const self_type& v) BOOST_NOEXCEPT { return v.backend(); } + template + static BOOST_FORCEINLINE BOOST_CONSTEXPR const V& function_arg_value(const V& v) BOOST_NOEXCEPT { return v; } + template + static BOOST_FORCEINLINE const A1& function_arg_value(const detail::expression& exp) BOOST_NOEXCEPT { return exp.value(); } + template + static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const detail::expression, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value().backend(); } + Backend m_backend; + +public: + // + // These shouldn't really need to be public, or even member functions, but it makes implementing + // the non-member operators way easier if they are: + // static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& canonical_value(const self_type& v) BOOST_NOEXCEPT { return v.m_backend; } template static BOOST_FORCEINLINE BOOST_CONSTEXPR const B2& canonical_value(const number& v) BOOST_NOEXCEPT { return v.backend(); } @@ -1564,14 +1594,6 @@ private: canonical_value(const V& v) BOOST_NOEXCEPT { return v; } static BOOST_FORCEINLINE typename detail::canonical::type canonical_value(const std::string& v) BOOST_NOEXCEPT { return v.c_str(); } - static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const self_type& v) BOOST_NOEXCEPT { return v.backend(); } - template - static BOOST_FORCEINLINE BOOST_CONSTEXPR const V& function_arg_value(const V& v) BOOST_NOEXCEPT { return v; } - template - static BOOST_FORCEINLINE const A1& function_arg_value(const detail::expression& exp) BOOST_NOEXCEPT { return exp.value(); } - template - static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const detail::expression, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value().backend(); } - Backend m_backend; }; template diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 6eb8e973..6aef3e63 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -32,6 +32,11 @@ inline void check_tommath_result(unsigned v) } +struct tommath_int; + +void eval_multiply(tommath_int& t, const tommath_int& o); +void eval_add(tommath_int& t, const tommath_int& o); + struct tommath_int { typedef mpl::list signed_types; @@ -186,8 +191,6 @@ struct tommath_int // // We don't use libtommath's own routine because it doesn't error check the input :-( // - using default_ops::eval_multiply; - using default_ops::eval_add; if(m_data.dp == 0) detail::check_tommath_result(mp_init(&m_data)); std::size_t n = s ? std::strlen(s) : 0; @@ -279,8 +282,11 @@ struct tommath_int break; } } - eval_multiply(*this, block_mult); - eval_add(*this, block); + tommath_int t; + t = block_mult; + eval_multiply(*this, t); + t = block; + eval_add(*this, t); } } } diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index feb05b87..4a3e83b4 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -119,15 +119,31 @@ bool isfloat(double){ return true; } bool isfloat(long double){ return true; } template bool isfloat(T){ return false; } +namespace detail{ + +template +typename boost::disable_if, T>::type abs(T v) +{ + return v < 0 ? -v : v; +} +template +typename boost::enable_if, T>::type abs(T v) +{ + return v; +} + +} + #define BOOST_TEST_CLOSE(x, y, tol)\ + using std::abs; using detail::abs;\ if(x == 0){\ BOOST_TEST(y == 0); }\ else if(!isfloat(x)){\ BOOST_TEST(x == y); }\ - else if((x != y) && (::fabsl(static_cast((x-y)/x)) > tol))\ + else if((x != y) && (abs((x-y)/x) > tol))\ {\ BOOST_ERROR("Expected tolerance was exceeded: ");\ - BOOST_LIGHTWEIGHT_TEST_OSTREAM << std::setprecision(34) << "(x-y)/x = " << ::fabsl(static_cast((x-y)/x)) \ + BOOST_LIGHTWEIGHT_TEST_OSTREAM << std::setprecision(34) << "(x-y)/x = " << abs((x-y)/x) \ << " tolerance = " << tol << std::endl;\ } @@ -141,6 +157,58 @@ struct is_twos_complement_integer : public boost #define BOOST_TEST_EQUAL(a, b) BOOST_TEST((a) == (b)) + +template +struct related_type +{ + typedef T type; +}; + +#ifdef TEST_MPQ +template <> +struct related_type +{ + typedef boost::multiprecision::mpz_int type; +}; +#endif +#if defined(TEST_MPF_50) || defined(TEST_MPF) +template +struct related_type > > +{ + typedef boost::multiprecision::number< boost::multiprecision::gmp_float > type; +}; +template <> +struct related_type +{ + typedef boost::multiprecision::mpz_int type; +}; +#endif +#ifdef TEST_CPP_DEC_FLOAT +template +struct related_type > > +{ + typedef boost::multiprecision::number< boost::multiprecision::cpp_dec_float > type; +}; +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR) +template +struct related_type > > +{ + typedef boost::multiprecision::number< boost::multiprecision::mpfr_float_backend > type; +}; +#endif +#if defined(TEST_CPP_INT_1) || defined(TEST_CPP_INT_2) || defined(TEST_CPP_INT_3) || defined(TEST_CPP_INT_BR) +template <> +struct related_type +{ + typedef boost::multiprecision::int256_t type; +}; +template +struct related_type, ET> > +{ + typedef boost::multiprecision::number, ET> type; +}; +#endif template void test_comparisons(Val, Val, const boost::mpl::false_) {} @@ -836,7 +904,8 @@ void test_negative_mixed(boost::mpl::true_ const&) Real >::type simple_cast_type; std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; - Num n1 = -static_cast(1uLL << (std::numeric_limits::digits - 1)); + static const int left_shift = std::numeric_limits::digits - 1; + Num n1 = -static_cast(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10)); Num n2 = -1; Num n3 = 0; Num n4 = -20; @@ -1047,11 +1116,12 @@ void test_mixed(const boost::mpl::true_&) Real >::type simple_cast_type; - if(std::numeric_limits::digits < std::numeric_limits::digits) + if(std::numeric_limits::is_specialized && std::numeric_limits::is_bounded && std::numeric_limits::digits < std::numeric_limits::digits) return; std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; - Num n1 = static_cast(1uLL << (std::numeric_limits::digits - 1)); + static const int left_shift = std::numeric_limits::digits - 1; + Num n1 = static_cast(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10)); Num n2 = 1; Num n3 = 0; Num n4 = 20; @@ -1198,6 +1268,12 @@ void test() test_mixed(tag); test_mixed(tag); test_mixed(tag); + + typedef typename related_type::type related_type; + boost::mpl::bool_::value && !boost::is_same::value> tag2; + + test_mixed(tag2); + #endif // // Integer only functions: From 9edbdc0ca49ab3e6e0ef58cefa46d0671dbb52a6 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 4 Sep 2012 17:18:18 +0000 Subject: [PATCH 231/256] Enable optimisations in the GMP and MPFR backends for mixed mode arithmetic. Allow mixed arithmetic between two different expression templates. Change docs to indicate mixed arithmetic is allowed and rebuild. [SVN r80397] --- .../boost_multiprecision/indexes/s01.html | 4 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 4 +- doc/html/boost_multiprecision/intro.html | 27 ++- doc/html/boost_multiprecision/ref/number.html | 18 +- doc/html/index.html | 2 +- doc/multiprecision.qbk | 34 ++-- .../multiprecision/detail/default_ops.hpp | 157 ++++++++++++++---- include/boost/multiprecision/gmp.hpp | 96 +++++------ include/boost/multiprecision/mpfr.hpp | 96 +++++------ test/compile_fail/operator_fail_01.cpp | 17 ++ test/compile_fail/operator_fail_02.cpp | 18 ++ 13 files changed, 309 insertions(+), 172 deletions(-) create mode 100644 test/compile_fail/operator_fail_01.cpp create mode 100644 test/compile_fail/operator_fail_02.cpp diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 521ccd94..6657ceb9 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@ -
    +

    -Function Index

    +Function Index
    PrevUpHomeNext

    A B C D E F I L M P R S T Z

    diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index 11a14593..3e4124d3 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

    C G I M N T

    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index c96f5617..2cfc4d61 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    C I L M T U

    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 070cf1bb..d02da93c 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G I L M N O P R S T U Z

    diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index 16fb2968..8022566f 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -87,24 +87,39 @@ my_float a, b, c; // These variables have 300 decimal digits precision

    - Note that mixing arithmetic operations using types of different precision is - strictly forbidden: + We can also mix arithmetic operations between different types, provided there + is an unambiguous implicit conversion from one type to the other: 

    #include <boost/multiprecision/cpp_int.hpp>
 
 namespace mp = boost::multiprecision;     // Reduce the typing a bit later...
 
-mp::int128_t a(3), b(2);
+mp::int128_t a(3), b(4);
 mp::int512_t c(50), d;
 
-d = c * a;   // Compiler error
+d = c * a;   // OK, result of mixed arithmetic is an int512_t

    - However, conversions are allowed: + Conversions are also allowed: 

    d = a; // OK, widening conversion.
 d = a * b;  // OK, can convert from an expression template too.
-d = mp::int512_t(a) * c; // OK, all the types in the expression are the same now.
+
    +

    + However conversions that are inherently lossy are either declared explicit + or else forbidden altogether: +

    +
    d = 3.14;  // Error implicit conversion from float not allowed.
+d = static_cast<mp::int512_t>(3.14);  // OK explicit construction is allowed
+
    +

    + Mixed arithmetic will fail if the conversion is either ambiguous or explicit: +

    +
    number<cpp_int_backend<>, false> a(2);
+number<cpp_int_backend<>, true>  b(3);
+
+b = a * b; // Error, implicit conversion could go either way.
+b = a * 3.14; // Error, no operator overload if the conversion would be explicit.
    diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html index 100989b0..3c10b8c3 100644 --- a/doc/html/boost_multiprecision/ref/number.html +++ b/doc/html/boost_multiprecision/ref/number.html @@ -342,7 +342,8 @@ An expression template derived from number<Backend>.
  • - Any type implicitly convertible to number<Backend, ExpressionTemplates>. + Any type implicitly convertible to number<Backend, ExpressionTemplates>, including some other instance of + class number.

    • @@ -350,10 +351,6 @@ type with a positive value (negative values result in a std::runtime_error being thrown).

    -

    - Note that all the types involved in the expression must evaluate to the same - type - which is to say we cannot mix a number<B1> with a number<B2> where B1 and B2 are different types. - 

    operator convertible-to-bool-type()const;

    @@ -483,10 +480,11 @@

  • An expression template type derived from number.
    • +
  • + Any type for which number + has an implicit constructor - for example a builtin arithmetic type. +
    • -

    - In addition, one of the two arguments may be a builtin arithmetic type. -

    The return type of these operators is either:

    @@ -507,10 +505,6 @@ is a comparison operator. -

    - Note that all the types involved in the expression must evaluate to the same - type - which is to say we cannot mix a number<B1> with a number<B2> where B1 and B2 are different types. -

    Finally note that the second argument to the left and right shift operations must be a builtin integer type, and that the argument must be positive (negative diff --git a/doc/html/index.html b/doc/html/index.html index 16147d66..d7ce9ef1 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -120,7 +120,7 @@ - +

    Last revised: August 30, 2012 at 17:55:33 GMT

    Last revised: September 04, 2012 at 17:13:56 GMT

    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index b94104f6..b58cc69b 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -99,22 +99,35 @@ by passing a second template argument to `number`: my_float a, b, c; // These variables have 300 decimal digits precision -Note that mixing arithmetic operations using types of different precision is strictly forbidden: +We can also mix arithmetic operations between different types, provided there is an unambiguous implicit conversion from one +type to the other: #include namespace mp = boost::multiprecision; // Reduce the typing a bit later... - mp::int128_t a(3), b(2); + mp::int128_t a(3), b(4); mp::int512_t c(50), d; - d = c * a; // Compiler error + d = c * a; // OK, result of mixed arithmetic is an int512_t -However, conversions are allowed: +Conversions are also allowed: d = a; // OK, widening conversion. d = a * b; // OK, can convert from an expression template too. - d = mp::int512_t(a) * c; // OK, all the types in the expression are the same now. + +However conversions that are inherently lossy are either declared explicit or else forbidden altogether: + + d = 3.14; // Error implicit conversion from float not allowed. + d = static_cast(3.14); // OK explicit construction is allowed + +Mixed arithmetic will fail if the conversion is either ambiguous or explicit: + + number, false> a(2); + number, true> b(3); + + b = a * b; // Error, implicit conversion could go either way. + b = a * 3.14; // Error, no operator overload if the conversion would be explicit. [h4 Move Semantics] @@ -1319,14 +1332,11 @@ The arguments to these operators is either: * Another `number`. * An expression template derived from `number`. -* Any type implicitly convertible to `number`. +* Any type implicitly convertible to `number`, including some other instance of class `number`. For the left and right shift operations, the argument must be a builtin integer type with a positive value (negative values result in a `std::runtime_error` being thrown). -Note that all the types involved in the expression must evaluate to the same type - which is to say -we cannot mix a `number` with a `number` where B1 and B2 are different types. - operator ``['convertible-to-bool-type]``()const; Returns an ['unmentionable-type] that is usable in Boolean contexts (this allows `number` to be used in any @@ -1418,8 +1428,7 @@ The arguments to these functions must contain at least one of the following: * A `number`. * An expression template type derived from `number`. - -In addition, one of the two arguments may be a builtin arithmetic type. +* Any type for which `number` has an implicit constructor - for example a builtin arithmetic type. The return type of these operators is either: @@ -1427,9 +1436,6 @@ The return type of these operators is either: * Type `number` when `ExpressionTemplates` is `false`. * Type `bool` if the operator is a comparison operator. -Note that all the types involved in the expression must evaluate to the same type - which is to say -we cannot mix a `number` with a `number` where B1 and B2 are different types. - Finally note that the second argument to the left and right shift operations must be a builtin integer type, and that the argument must be positive (negative arguments result in a `std::runtime_error` being thrown). diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 66f9731e..79f98280 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -178,7 +178,7 @@ inline typename enable_if_c >::value && is_convertib // Default versions of 3-arg arithmetic functions, these mostly just forward to the 2 arg versions: // template -inline void eval_add(T& t, const T& u, const T& v) +inline void eval_add_default(T& t, const T& u, const T& v) { if(&t == &v) { @@ -195,26 +195,37 @@ inline void eval_add(T& t, const T& u, const T& v) } } template -inline typename enable_if_c >::value && !is_convertible::value>::type eval_add(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_add_default(T& t, const T& u, const U& v) { T vv; vv = v; eval_add(t, u, vv); } template -inline typename enable_if_c >::value && is_convertible::value>::type eval_add(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_add_default(T& t, const T& u, const U& v) { T vv(v); eval_add(t, u, vv); } template -inline typename enable_if_c >::value>::type eval_add(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_add_default(T& t, const U& u, const T& v) { eval_add(t, v, u); } +template +inline void eval_add_default(T& t, const U& u, const V& v) +{ + t = u; + eval_add(t, u); +} +template +inline void eval_add(T& t, const U& u, const V& v) +{ + eval_add_default(t, u, v); +} template -inline void eval_subtract(T& t, const T& u, const T& v) +inline void eval_subtract_default(T& t, const T& u, const T& v) { if(&t == &v) { @@ -232,27 +243,38 @@ inline void eval_subtract(T& t, const T& u, const T& v) } } template -inline typename enable_if_c >::value && !is_convertible::value>::type eval_subtract(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_subtract_default(T& t, const T& u, const U& v) { T vv; vv = v; eval_subtract(t, u, vv); } template -inline typename enable_if_c >::value && is_convertible::value>::type eval_subtract(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_subtract_default(T& t, const T& u, const U& v) { T vv(v); eval_subtract(t, u, vv); } template -inline typename enable_if_c >::value>::type eval_subtract(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_subtract_default(T& t, const U& u, const T& v) { eval_subtract(t, v, u); t.negate(); } +template +inline void eval_subtract_default(T& t, const U& u, const V& v) +{ + t = u; + eval_subtract(t, u); +} +template +inline void eval_subtract(T& t, const U& u, const V& v) +{ + eval_subtract_default(t, u, v); +} template -inline void eval_multiply(T& t, const T& u, const T& v) +inline void eval_multiply_default(T& t, const T& u, const T& v) { if(&t == &v) { @@ -269,26 +291,37 @@ inline void eval_multiply(T& t, const T& u, const T& v) } } template -inline typename enable_if_c >::value && !is_convertible::value>::type eval_multiply(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_multiply_default(T& t, const T& u, const U& v) { T vv; vv = v; eval_multiply(t, u, vv); } template -inline typename enable_if_c >::value && is_convertible::value>::type eval_multiply(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_multiply_default(T& t, const T& u, const U& v) { T vv(v); eval_multiply(t, u, vv); } template -inline typename enable_if_c >::value>::type eval_multiply(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_multiply_default(T& t, const U& u, const T& v) { eval_multiply(t, v, u); } +template +inline void eval_multiply_default(T& t, const U& u, const V& v) +{ + t = u; + eval_multiply(t, u); +} +template +inline void eval_multiply(T& t, const U& u, const V& v) +{ + eval_multiply_default(t, u, v); +} template -inline void eval_divide(T& t, const T& u, const T& v) +inline void eval_divide_default(T& t, const T& u, const T& v) { if(&t == &u) eval_divide(t, v); @@ -305,35 +338,45 @@ inline void eval_divide(T& t, const T& u, const T& v) } } template -inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide_default(T& t, const T& u, const U& v) { T vv; vv = v; eval_divide(t, u, vv); } template -inline typename enable_if_c >::value && is_convertible::value>::type eval_divide(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_divide_default(T& t, const T& u, const U& v) { T vv(v); eval_divide(t, u, vv); } template -inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide(T& t, const U& u, const T& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide_default(T& t, const U& u, const T& v) { T uu; uu = u; eval_divide(t, uu, v); } template -inline typename enable_if_c >::value && is_convertible::value>::type eval_divide(T& t, const U& u, const T& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_divide_default(T& t, const U& u, const T& v) { T uu(u); eval_divide(t, uu, v); } - +template +inline void eval_divide_default(T& t, const U& u, const V& v) +{ + t = u; + eval_divide(t, u); +} +template +inline void eval_divide(T& t, const U& u, const V& v) +{ + eval_divide_default(t, u, v); +} template -inline void eval_modulus(T& t, const T& u, const T& v) +inline void eval_modulus_default(T& t, const T& u, const T& v) { if(&t == &u) eval_modulus(t, v); @@ -350,34 +393,45 @@ inline void eval_modulus(T& t, const T& u, const T& v) } } template -inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus_default(T& t, const T& u, const U& v) { T vv; vv = v; eval_modulus(t, u, vv); } template -inline typename enable_if_c >::value && is_convertible::value>::type eval_modulus(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_modulus_default(T& t, const T& u, const U& v) { T vv(v); eval_modulus(t, u, vv); } template -inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus(T& t, const U& u, const T& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus_default(T& t, const U& u, const T& v) { T uu; uu = u; eval_modulus(t, uu, v); } template -inline typename enable_if_c >::value && is_convertible::value>::type eval_modulus(T& t, const U& u, const T& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_modulus_default(T& t, const U& u, const T& v) { T uu(u); eval_modulus(t, uu, v); } +template +inline void eval_modulus_default(T& t, const U& u, const V& v) +{ + t = u; + eval_modulus(t, u); +} +template +inline void eval_modulus(T& t, const U& u, const V& v) +{ + eval_modulus_default(t, u, v); +} template -inline void eval_bitwise_and(T& t, const T& u, const T& v) +inline void eval_bitwise_and_default(T& t, const T& u, const T& v) { if(&t == &v) { @@ -394,26 +448,37 @@ inline void eval_bitwise_and(T& t, const T& u, const T& v) } } template -inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_and(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_and_default(T& t, const T& u, const U& v) { T vv; vv = v; eval_bitwise_and(t, u, vv); } template -inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_and(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_and_default(T& t, const T& u, const U& v) { T vv(v); eval_bitwise_and(t, u, vv); } template -inline typename enable_if_c >::value>::type eval_bitwise_and(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_bitwise_and_default(T& t, const U& u, const T& v) { eval_bitwise_and(t, v, u); } +template +inline void eval_bitwise_and_default(T& t, const U& u, const V& v) +{ + t = u; + eval_bitwise_and(t, u); +} +template +inline void eval_bitwise_and(T& t, const U& u, const V& v) +{ + eval_bitwise_and_default(t, u, v); +} template -inline void eval_bitwise_or(T& t, const T& u, const T& v) +inline void eval_bitwise_or_default(T& t, const T& u, const T& v) { if(&t == &v) { @@ -430,26 +495,37 @@ inline void eval_bitwise_or(T& t, const T& u, const T& v) } } template -inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_or(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_or_default(T& t, const T& u, const U& v) { T vv; vv = v; eval_bitwise_or(t, u, vv); } template -inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_or(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_or_default(T& t, const T& u, const U& v) { T vv(v); eval_bitwise_or(t, u, vv); } template -inline typename enable_if_c >::value>::type eval_bitwise_or(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_bitwise_or_default(T& t, const U& u, const T& v) { eval_bitwise_or(t, v, u); } +template +inline void eval_bitwise_or_default(T& t, const U& u, const V& v) +{ + t = u; + eval_bitwise_or(t, u); +} +template +inline void eval_bitwise_or(T& t, const U& u, const V& v) +{ + eval_bitwise_or_default(t, u, v); +} template -inline void eval_bitwise_xor(T& t, const T& u, const T& v) +inline void eval_bitwise_xor_default(T& t, const T& u, const T& v) { if(&t == &v) { @@ -466,23 +542,34 @@ inline void eval_bitwise_xor(T& t, const T& u, const T& v) } } template -inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_xor(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_xor_default(T& t, const T& u, const U& v) { T vv; vv = v; eval_bitwise_xor(t, u, vv); } template -inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_xor(T& t, const T& u, const U& v) +inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_xor_default(T& t, const T& u, const U& v) { T vv(v); eval_bitwise_xor(t, u, vv); } template -inline typename enable_if_c >::value>::type eval_bitwise_xor(T& t, const U& u, const T& v) +inline typename enable_if_c >::value>::type eval_bitwise_xor_default(T& t, const U& u, const T& v) { eval_bitwise_xor(t, v, u); } +template +inline void eval_bitwise_xor_default(T& t, const U& u, const V& v) +{ + t = u; + eval_bitwise_xor(t, u); +} +template +inline void eval_bitwise_xor(T& t, const U& u, const V& v) +{ + eval_bitwise_xor_default(t, u, v); +} template inline void eval_increment(T& val) diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index ba59df2c..56834437 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -567,18 +567,18 @@ inline typename enable_if_c::value, bool>::type eval_gt(const g return a.compare(b) > 0; } -template -inline void eval_add(gmp_float& result, const gmp_float& o) BOOST_NOEXCEPT +template +inline void eval_add(gmp_float& result, const gmp_float& o) BOOST_NOEXCEPT { mpf_add(result.data(), result.data(), o.data()); } -template -inline void eval_subtract(gmp_float& result, const gmp_float& o) BOOST_NOEXCEPT +template +inline void eval_subtract(gmp_float& result, const gmp_float& o) BOOST_NOEXCEPT { mpf_sub(result.data(), result.data(), o.data()); } -template -inline void eval_multiply(gmp_float& result, const gmp_float& o) BOOST_NOEXCEPT +template +inline void eval_multiply(gmp_float& result, const gmp_float& o) BOOST_NOEXCEPT { mpf_mul(result.data(), result.data(), o.data()); } @@ -587,8 +587,8 @@ inline bool eval_is_zero(const gmp_float& val) BOOST_NOEXCEPT { return mpf_sgn(val.data()) == 0; } -template -inline void eval_divide(gmp_float& result, const gmp_float& o) +template +inline void eval_divide(gmp_float& result, const gmp_float& o) { if(eval_is_zero(o)) BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); @@ -651,31 +651,31 @@ inline void eval_divide(gmp_float& result, long i) // // Specialised 3 arg versions of the basic operators: // -template -inline void eval_add(gmp_float& a, const gmp_float& x, const gmp_float& y) BOOST_NOEXCEPT +template +inline void eval_add(gmp_float& a, const gmp_float& x, const gmp_float& y) BOOST_NOEXCEPT { mpf_add(a.data(), x.data(), y.data()); } -template -inline void eval_add(gmp_float& a, const gmp_float& x, unsigned long y) BOOST_NOEXCEPT +template +inline void eval_add(gmp_float& a, const gmp_float& x, unsigned long y) BOOST_NOEXCEPT { mpf_add_ui(a.data(), x.data(), y); } -template -inline void eval_add(gmp_float& a, const gmp_float& x, long y) BOOST_NOEXCEPT +template +inline void eval_add(gmp_float& a, const gmp_float& x, long y) BOOST_NOEXCEPT { if(y < 0) mpf_sub_ui(a.data(), x.data(), -y); else mpf_add_ui(a.data(), x.data(), y); } -template -inline void eval_add(gmp_float& a, unsigned long x, const gmp_float& y) BOOST_NOEXCEPT +template +inline void eval_add(gmp_float& a, unsigned long x, const gmp_float& y) BOOST_NOEXCEPT { mpf_add_ui(a.data(), y.data(), x); } -template -inline void eval_add(gmp_float& a, long x, const gmp_float& y) BOOST_NOEXCEPT +template +inline void eval_add(gmp_float& a, long x, const gmp_float& y) BOOST_NOEXCEPT { if(x < 0) { @@ -685,31 +685,31 @@ inline void eval_add(gmp_float& a, long x, const gmp_float& else mpf_add_ui(a.data(), y.data(), x); } -template -inline void eval_subtract(gmp_float& a, const gmp_float& x, const gmp_float& y) BOOST_NOEXCEPT +template +inline void eval_subtract(gmp_float& a, const gmp_float& x, const gmp_float& y) BOOST_NOEXCEPT { mpf_sub(a.data(), x.data(), y.data()); } -template -inline void eval_subtract(gmp_float& a, const gmp_float& x, unsigned long y) BOOST_NOEXCEPT +template +inline void eval_subtract(gmp_float& a, const gmp_float& x, unsigned long y) BOOST_NOEXCEPT { mpf_sub_ui(a.data(), x.data(), y); } -template -inline void eval_subtract(gmp_float& a, const gmp_float& x, long y) BOOST_NOEXCEPT +template +inline void eval_subtract(gmp_float& a, const gmp_float& x, long y) BOOST_NOEXCEPT { if(y < 0) mpf_add_ui(a.data(), x.data(), -y); else mpf_sub_ui(a.data(), x.data(), y); } -template -inline void eval_subtract(gmp_float& a, unsigned long x, const gmp_float& y) BOOST_NOEXCEPT +template +inline void eval_subtract(gmp_float& a, unsigned long x, const gmp_float& y) BOOST_NOEXCEPT { mpf_ui_sub(a.data(), x, y.data()); } -template -inline void eval_subtract(gmp_float& a, long x, const gmp_float& y) BOOST_NOEXCEPT +template +inline void eval_subtract(gmp_float& a, long x, const gmp_float& y) BOOST_NOEXCEPT { if(x < 0) { @@ -720,18 +720,18 @@ inline void eval_subtract(gmp_float& a, long x, const gmp_float -inline void eval_multiply(gmp_float& a, const gmp_float& x, const gmp_float& y) BOOST_NOEXCEPT +template +inline void eval_multiply(gmp_float& a, const gmp_float& x, const gmp_float& y) BOOST_NOEXCEPT { mpf_mul(a.data(), x.data(), y.data()); } -template -inline void eval_multiply(gmp_float& a, const gmp_float& x, unsigned long y) BOOST_NOEXCEPT +template +inline void eval_multiply(gmp_float& a, const gmp_float& x, unsigned long y) BOOST_NOEXCEPT { mpf_mul_ui(a.data(), x.data(), y); } -template -inline void eval_multiply(gmp_float& a, const gmp_float& x, long y) BOOST_NOEXCEPT +template +inline void eval_multiply(gmp_float& a, const gmp_float& x, long y) BOOST_NOEXCEPT { if(y < 0) { @@ -741,13 +741,13 @@ inline void eval_multiply(gmp_float& a, const gmp_float& x, else mpf_mul_ui(a.data(), x.data(), y); } -template -inline void eval_multiply(gmp_float& a, unsigned long x, const gmp_float& y) BOOST_NOEXCEPT +template +inline void eval_multiply(gmp_float& a, unsigned long x, const gmp_float& y) BOOST_NOEXCEPT { mpf_mul_ui(a.data(), y.data(), x); } -template -inline void eval_multiply(gmp_float& a, long x, const gmp_float& y) BOOST_NOEXCEPT +template +inline void eval_multiply(gmp_float& a, long x, const gmp_float& y) BOOST_NOEXCEPT { if(x < 0) { @@ -758,22 +758,22 @@ inline void eval_multiply(gmp_float& a, long x, const gmp_float -inline void eval_divide(gmp_float& a, const gmp_float& x, const gmp_float& y) +template +inline void eval_divide(gmp_float& a, const gmp_float& x, const gmp_float& y) { if(eval_is_zero(y)) BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpf_div(a.data(), x.data(), y.data()); } -template -inline void eval_divide(gmp_float& a, const gmp_float& x, unsigned long y) +template +inline void eval_divide(gmp_float& a, const gmp_float& x, unsigned long y) { if(y == 0) BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpf_div_ui(a.data(), x.data(), y); } -template -inline void eval_divide(gmp_float& a, const gmp_float& x, long y) +template +inline void eval_divide(gmp_float& a, const gmp_float& x, long y) { if(y == 0) BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); @@ -785,15 +785,15 @@ inline void eval_divide(gmp_float& a, const gmp_float& x, lo else mpf_div_ui(a.data(), x.data(), y); } -template -inline void eval_divide(gmp_float& a, unsigned long x, const gmp_float& y) +template +inline void eval_divide(gmp_float& a, unsigned long x, const gmp_float& y) { if(eval_is_zero(y)) BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); mpf_ui_div(a.data(), x, y.data()); } -template -inline void eval_divide(gmp_float& a, long x, const gmp_float& y) +template +inline void eval_divide(gmp_float& a, long x, const gmp_float& y) { if(eval_is_zero(y)) BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero.")); diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index b3e4f14e..7742c65c 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -609,23 +609,23 @@ inline typename enable_if, bool>::type eval_gt(const mpfr_float return a.compare(b) > 0; } -template -inline void eval_add(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT { mpfr_add(result.data(), result.data(), o.data(), GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT { mpfr_sub(result.data(), result.data(), o.data(), GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT { mpfr_mul(result.data(), result.data(), o.data(), GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& result, const mpfr_float_backend& o) +template +inline void eval_divide(mpfr_float_backend& result, const mpfr_float_backend& o) { mpfr_div(result.data(), result.data(), o.data(), GMP_RNDN); } @@ -682,31 +682,31 @@ inline void eval_divide(mpfr_float_backend& result, long i) // // Specialised 3 arg versions of the basic operators: // -template -inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_add(a.data(), x.data(), y.data(), GMP_RNDN); } -template -inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT { mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT { if(y < 0) mpfr_sub_ui(a.data(), x.data(), -y, GMP_RNDN); else mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_add(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } -template -inline void eval_add(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { if(x < 0) { @@ -716,31 +716,31 @@ inline void eval_add(mpfr_float_backend& a, long x, const mpfr_float_b else mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_sub(a.data(), x.data(), y.data(), GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT { mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT { if(y < 0) mpfr_add_ui(a.data(), x.data(), -y, GMP_RNDN); else mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { if(x < 0) { @@ -751,18 +751,18 @@ inline void eval_subtract(mpfr_float_backend& a, long x, const mpfr_fl mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_mul(a.data(), x.data(), y.data(), GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT { mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT { if(y < 0) { @@ -772,13 +772,13 @@ inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_back else mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { if(x < 0) { @@ -789,18 +789,18 @@ inline void eval_multiply(mpfr_float_backend& a, long x, const mpfr_fl mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) +template +inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) { mpfr_div(a.data(), x.data(), y.data(), GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) +template +inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) { mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, long y) +template +inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, long y) { if(y < 0) { @@ -810,13 +810,13 @@ inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backen else mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) +template +inline void eval_divide(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) { mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& a, long x, const mpfr_float_backend& y) +template +inline void eval_divide(mpfr_float_backend& a, long x, const mpfr_float_backend& y) { if(x < 0) { diff --git a/test/compile_fail/operator_fail_01.cpp b/test/compile_fail/operator_fail_01.cpp new file mode 100644 index 00000000..03dd4d46 --- /dev/null +++ b/test/compile_fail/operator_fail_01.cpp @@ -0,0 +1,17 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +using namespace boost::multiprecision; + +int main() +{ + number, true> a(2); + number, false> b(2); + + a = a + b; +} + diff --git a/test/compile_fail/operator_fail_02.cpp b/test/compile_fail/operator_fail_02.cpp new file mode 100644 index 00000000..cd422e74 --- /dev/null +++ b/test/compile_fail/operator_fail_02.cpp @@ -0,0 +1,18 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2); + cpp_int b(2); + + a = a + b; +} + From d561dfe50bb1e36a19a2f54dba513f7f09ebc0ed Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 5 Sep 2012 16:46:54 +0000 Subject: [PATCH 232/256] Allow mixed precision arithmetic in the cpp_int backend. [SVN r80408] --- include/boost/multiprecision/cpp_int.hpp | 340 +++++++++++++---------- 1 file changed, 187 insertions(+), 153 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 17d97b72..ba68478c 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1063,7 +1063,8 @@ public: } return result; } - int compare(const cpp_int_backend& o)const BOOST_NOEXCEPT + template + int compare(const cpp_int_backend& o)const BOOST_NOEXCEPT { if(this->sign() != o.sign()) return this->sign() ? -1 : 1; @@ -1075,7 +1076,8 @@ public: result = -result; return result; } - int compare_unsigned(const cpp_int_backend& o)const BOOST_NOEXCEPT + template + int compare_unsigned(const cpp_int_backend& o)const BOOST_NOEXCEPT { if(this->size() != o.size()) { @@ -1090,8 +1092,8 @@ public: } return 0; } - template - BOOST_FORCEINLINE typename enable_if, int>::type compare(Arithmatic i)const BOOST_NOEXCEPT + template + BOOST_FORCEINLINE typename enable_if, int>::type compare(Arithmetic i)const BOOST_NOEXCEPT { // braindead version: cpp_int_backend t; @@ -1377,8 +1379,8 @@ public: result = -result; return result; } - template - BOOST_FORCEINLINE typename enable_if, int>::type compare(Arithmatic i)const BOOST_NOEXCEPT + template + BOOST_FORCEINLINE typename enable_if, int>::type compare(Arithmetic i)const BOOST_NOEXCEPT { // braindead version: cpp_int_backend t; @@ -1394,6 +1396,13 @@ BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend +BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT +{ + return (a.sign() == b.sign()) + && (a.size() == b.size()) + && std::equal(a.limbs(), a.limbs() + a.size(), b.limbs()); +} template BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT { @@ -1504,13 +1513,13 @@ BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend 0 : eval_gt(a, static_cast(b)); // Use bit pattern of b for comparison. } -template -BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_add(result, result, o); } -template -inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { using std::swap; @@ -1528,10 +1537,10 @@ inline void add_unsigned(cpp_int_backend& res return; } result.resize(x); - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); - typename cpp_int_backend::const_limb_pointer pb = b.limbs(); - typename cpp_int_backend::limb_pointer pr = result.limbs(); - typename cpp_int_backend::limb_pointer pr_end = pr + m; + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr_end = pr + m; if(as < bs) swap(pa, pb); @@ -1541,7 +1550,7 @@ inline void add_unsigned(cpp_int_backend& res { carry += static_cast(*pa) + static_cast(*pb); *pr = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; ++pr, ++pa, ++pb; } pr_end += x - m; @@ -1556,21 +1565,21 @@ inline void add_unsigned(cpp_int_backend& res } carry += static_cast(*pa); *pr = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; ++pr, ++pa; } if(carry) { result.resize(x + 1); // We overflowed, need to add one more limb: - if(cpp_int_backend::variable || (result.size() > x)) + if(cpp_int_backend::variable || (result.size() > x)) result.limbs()[x] = static_cast(carry); } result.normalize(); result.sign(a.sign()); } -template -inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign() != b.sign()) { @@ -1580,22 +1589,22 @@ inline void eval_add(cpp_int_backend& result, add_unsigned(result, a, b); } -template -inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Addition using modular arithmatic. // Nothing fancy, just let uintmax_t take the strain: if(&result != &a) result.resize(a.size()); double_limb_type carry = o; - typename cpp_int_backend::limb_pointer pr = result.limbs(); - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); unsigned i = 0; for(; carry && (i < result.size()); ++i) { carry += static_cast(pa[i]); pr[i] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } if(&a != &result) { @@ -1607,7 +1616,7 @@ inline void add_unsigned(cpp_int_backend& res unsigned x = result.size(); result.resize(x + 1); // We overflowed, need to add one more limb: - if(cpp_int_backend::variable || (result.size() > x)) + if(cpp_int_backend::variable || (result.size() > x)) result.limbs()[x] = static_cast(carry); } result.normalize(); @@ -1623,8 +1632,8 @@ BOOST_FORCEINLINE void eval_add(cpp_int_backend -BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign()) { @@ -1642,8 +1651,8 @@ BOOST_FORCEINLINE void eval_add(cpp_int_backend 0) eval_add(result, static_cast(o)); } -template -BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o < 0) eval_subtract(result, a, static_cast(-o)); @@ -1692,8 +1701,8 @@ BOOST_FORCEINLINE void eval_subtract(cpp_int_backend -BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign()) { @@ -1716,8 +1725,8 @@ BOOST_FORCEINLINE void eval_subtract(cpp_int_backend(o)); } } -template -BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(o) { @@ -1751,13 +1760,13 @@ BOOST_FORCEINLINE void eval_decrement(cpp_int_backend -BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_subtract(result, result, o); } -template -inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { using std::swap; @@ -1788,9 +1797,9 @@ inline void subtract_unsigned(cpp_int_backend // Set up the result vector: result.resize(x); // Now that a, b, and result are stable, get pointers to their limbs: - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); - typename cpp_int_backend::const_limb_pointer pb = b.limbs(); - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); bool swapped = false; if(c < 0) { @@ -1809,7 +1818,7 @@ inline void subtract_unsigned(cpp_int_backend { borrow = static_cast(pa[i]) - static_cast(pb[i]) - borrow; pr[i] = static_cast(borrow); - borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; + borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; ++i; } // Now where only a has digits, only as long as we've borrowed: @@ -1817,7 +1826,7 @@ inline void subtract_unsigned(cpp_int_backend { borrow = static_cast(pa[i]) - borrow; pr[i] = static_cast(borrow); - borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; + borrow = (borrow >> cpp_int_backend::limb_bits) & 1u; ++i; } // Any remaining digits are the same as those in pa: @@ -1833,8 +1842,8 @@ inline void subtract_unsigned(cpp_int_backend if(swapped) result.negate(); } -template -BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign() != b.sign()) { @@ -1843,8 +1852,8 @@ BOOST_FORCEINLINE void eval_subtract(cpp_int_backend -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Very simple long multiplication, only usable for small numbers of limb_type's // but that's the typical use case for this type anyway: @@ -1853,8 +1862,8 @@ inline void eval_multiply(cpp_int_backend& re // unsigned as = a.size(); unsigned bs = b.size(); - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); - typename cpp_int_backend::const_limb_pointer pb = b.limbs(); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::const_limb_pointer pb = b.limbs(); if(as == 1) { bool s = b.sign() != a.sign(); @@ -1879,21 +1888,21 @@ inline void eval_multiply(cpp_int_backend& re return; } - if(&result == &a) + if((void*)&result == (void*)&a) { - cpp_int_backend t(a); + cpp_int_backend t(a); eval_multiply(result, t, b); return; } - if(&result == &b) + if((void*)&result == (void*)&b) { - cpp_int_backend t(b); + cpp_int_backend t(b); eval_multiply(result, a, t); return; } result.resize(as + bs); - typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); static const double_limb_type limb_max = ~static_cast(0u); static const double_limb_type double_limb_max = ~static_cast(0u); @@ -1903,19 +1912,22 @@ inline void eval_multiply(cpp_int_backend& re std::memset(pr, 0, result.size() * sizeof(limb_type)); for(unsigned i = 0; i < as; ++i) { - unsigned inner_limit = cpp_int_backend::variable ? bs : (std::min)(result.size() - i, bs); + unsigned inner_limit = cpp_int_backend::variable ? bs : (std::min)(result.size() - i, bs); for(unsigned j = 0; j < inner_limit; ++j) { BOOST_ASSERT(i+j < result.size()); - BOOST_ASSERT(!std::numeric_limits::is_specialized || ((std::numeric_limits::max)() - carry > static_cast(cpp_int_backend::max_limb_value) * static_cast(cpp_int_backend::max_limb_value))); + BOOST_ASSERT(!std::numeric_limits::is_specialized + || ((std::numeric_limits::max)() - carry + > + static_cast(cpp_int_backend::max_limb_value) * static_cast(cpp_int_backend::max_limb_value))); carry += static_cast(pa[i]) * static_cast(pb[j]); BOOST_ASSERT(!std::numeric_limits::is_specialized || ((std::numeric_limits::max)() - carry >= pr[i+j])); carry += pr[i + j]; pr[i + j] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; - BOOST_ASSERT(carry <= (cpp_int_backend::max_limb_value)); + carry >>= cpp_int_backend::limb_bits; + BOOST_ASSERT(carry <= (cpp_int_backend::max_limb_value)); } - if(cpp_int_backend::variable || (i + bs < result.size())) + if(cpp_int_backend::variable || (i + bs < result.size())) pr[i + bs] = static_cast(carry); carry = 0; } @@ -1925,41 +1937,41 @@ inline void eval_multiply(cpp_int_backend& re // result.sign(a.sign() != b.sign()); } -template -BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a) BOOST_NOEXCEPT_IF(boost::is_void::value) { eval_multiply(result, result, a); } -template -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(!val) { result = static_cast(0); return; } - if(&a != &result) + if((void*)&a != (void*)&result) result.resize(a.size()); double_limb_type carry = 0; - typename cpp_int_backend::limb_pointer p = result.limbs(); - typename cpp_int_backend::limb_pointer pe = result.limbs() + result.size(); - typename cpp_int_backend::const_limb_pointer pa = a.limbs(); + typename cpp_int_backend::limb_pointer p = result.limbs(); + typename cpp_int_backend::limb_pointer pe = result.limbs() + result.size(); + typename cpp_int_backend::const_limb_pointer pa = a.limbs(); while(p != pe) { carry += static_cast(*pa) * static_cast(val); *p = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; ++p, ++pa; } if(carry) { unsigned i = result.size(); result.resize(i + 1); - if(cpp_int_backend::variable || (result.size() > i)) + if(cpp_int_backend::variable || (result.size() > i)) result.limbs()[i] = static_cast(carry); } result.sign(a.sign()); - if(!cpp_int_backend::variable) + if(!cpp_int_backend::variable) result.normalize(); } template @@ -1967,8 +1979,8 @@ BOOST_FORCEINLINE void eval_multiply(cpp_int_backend -BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(val <= (std::numeric_limits::max)()) { @@ -1976,7 +1988,7 @@ BOOST_FORCEINLINE void eval_multiply(cpp_int_backend t(val); + cpp_int_backend t(val); eval_multiply(result, a, t); } } @@ -1985,8 +1997,8 @@ BOOST_FORCEINLINE void eval_multiply(cpp_int_backend -BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(val > 0) eval_multiply(result, a, static_cast(val)); @@ -2001,8 +2013,8 @@ BOOST_FORCEINLINE void eval_multiply(cpp_int_backend -inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const signed_double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const signed_double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(val > 0) { @@ -2018,7 +2030,7 @@ inline void eval_multiply(cpp_int_backend& re result.negate(); return; } - cpp_int_backend t(val); + cpp_int_backend t(val); eval_multiply(result, a, t); } template @@ -2027,18 +2039,21 @@ BOOST_FORCEINLINE void eval_multiply(cpp_int_backend -void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, const cpp_int_backend& y, cpp_int_backend& r) +template +void divide_unsigned_helper(cpp_int_backend* result, + const cpp_int_backend& x, + const cpp_int_backend& y, + cpp_int_backend& r) { - if((result == &x) || (&r == &x)) + if(((void*)result == (void*)&x) || ((void*)&r == (void*)&x)) { - cpp_int_backend t(x); + cpp_int_backend t(x); divide_unsigned_helper(result, t, y, r); return; } - if((result == &y) || (&r == &y)) + if(((void*)result == (void*)&y) || ((void*)&r == (void*)&y)) { - cpp_int_backend t(y); + cpp_int_backend t(y); divide_unsigned_helper(result, x, t, r); return; } @@ -2066,7 +2081,7 @@ void divide_unsigned_helper(cpp_int_backend* if(result == &r) { - cpp_int_backend rem; + cpp_int_backend rem; divide_unsigned_helper(result, x, y, rem); r = rem; return; @@ -2088,8 +2103,8 @@ void divide_unsigned_helper(cpp_int_backend* return; } - typename cpp_int_backend::const_limb_pointer px = x.limbs(); - typename cpp_int_backend::const_limb_pointer py = y.limbs(); + typename cpp_int_backend::const_limb_pointer px = x.limbs(); + typename cpp_int_backend::const_limb_pointer py = y.limbs(); limb_type r_order = x.size() - 1; if((r_order == 0) && (*px == 0)) @@ -2118,7 +2133,7 @@ void divide_unsigned_helper(cpp_int_backend* } } - cpp_int_backend t; + cpp_int_backend t; bool r_neg = false; // @@ -2134,9 +2149,9 @@ void divide_unsigned_helper(cpp_int_backend* else if(r_order == 1) { double_limb_type a, b; - a = (static_cast(px[1]) << cpp_int_backend::limb_bits) | px[0]; + a = (static_cast(px[1]) << cpp_int_backend::limb_bits) | px[0]; b = y_order ? - (static_cast(py[1]) << cpp_int_backend::limb_bits) | py[0] + (static_cast(py[1]) << cpp_int_backend::limb_bits) | py[0] : py[0]; if(result) *result = a / b; @@ -2148,9 +2163,10 @@ void divide_unsigned_helper(cpp_int_backend* // if(result) result->resize(1 + r_order - y_order); - typename cpp_int_backend::const_limb_pointer prem = r.limbs(); + typename cpp_int_backend::const_limb_pointer prem = r.limbs(); // This is initialised just to keep the compiler from emitting useless warnings later on: - typename cpp_int_backend::limb_pointer pr = typename cpp_int_backend::limb_pointer(); + typename cpp_int_backend::limb_pointer pr + = typename cpp_int_backend::limb_pointer(); if(result) { pr = result->limbs(); @@ -2168,10 +2184,10 @@ void divide_unsigned_helper(cpp_int_backend* if((prem[r_order] <= py[y_order]) && (r_order > 0)) { double_limb_type a, b, v; - a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; + a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; b = py[y_order]; v = a / b; - if(v > cpp_int_backend::max_limb_value) + if(v > cpp_int_backend::max_limb_value) guess = 1; else { @@ -2186,8 +2202,8 @@ void divide_unsigned_helper(cpp_int_backend* else { double_limb_type a, b, v; - a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; - b = (y_order > 0) ? (static_cast(py[y_order]) << cpp_int_backend::limb_bits) | py[y_order - 1] : (static_cast(py[y_order]) << cpp_int_backend::limb_bits); + a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1]; + b = (y_order > 0) ? (static_cast(py[y_order]) << cpp_int_backend::limb_bits) | py[y_order - 1] : (static_cast(py[y_order]) << cpp_int_backend::limb_bits); v = a / b; guess = static_cast(v); } @@ -2211,7 +2227,7 @@ void divide_unsigned_helper(cpp_int_backend* eval_subtract(*result, t); } } - else if(cpp_int_backend::max_limb_value - pr[shift] > guess) + else if(cpp_int_backend::max_limb_value - pr[shift] > guess) pr[shift] += guess; else { @@ -2228,15 +2244,15 @@ void divide_unsigned_helper(cpp_int_backend* // double_limb_type carry = 0; t.resize(y.size() + shift + 1); - bool truncated_t = !cpp_int_backend::variable && (t.size() != y.size() + shift + 1); - typename cpp_int_backend::limb_pointer pt = t.limbs(); + bool truncated_t = !cpp_int_backend::variable && (t.size() != y.size() + shift + 1); + typename cpp_int_backend::limb_pointer pt = t.limbs(); for(unsigned i = 0; i < shift; ++i) pt[i] = 0; for(unsigned i = 0; i < y.size(); ++i) { carry += static_cast(py[i]) * static_cast(guess); pt[i + shift] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } if(carry && !truncated_t) { @@ -2294,19 +2310,23 @@ void divide_unsigned_helper(cpp_int_backend* BOOST_ASSERT(r.compare_unsigned(y) < 0); // remainder must be less than the divisor or our code has failed } -template -void divide_unsigned_helper(cpp_int_backend* result, const cpp_int_backend& x, limb_type y, cpp_int_backend& r) +template +void divide_unsigned_helper( + cpp_int_backend* result, + const cpp_int_backend& x, + limb_type y, + cpp_int_backend& r) { - if((result == &x) || (&r == &x)) + if(((void*)result == (void*)&x) || ((void*)&r == (void*)&x)) { - cpp_int_backend t(x); + cpp_int_backend t(x); divide_unsigned_helper(result, t, y, r); return; } if(result == &r) { - cpp_int_backend rem; + cpp_int_backend rem; divide_unsigned_helper(result, x, y, rem); r = rem; return; @@ -2330,7 +2350,7 @@ void divide_unsigned_helper(cpp_int_backend* // r = x; r.sign(false); - typename cpp_int_backend::limb_pointer pr = r.limbs(); + typename cpp_int_backend::limb_pointer pr = r.limbs(); if((r_order == 0) && (*pr == 0)) { @@ -2365,7 +2385,7 @@ void divide_unsigned_helper(cpp_int_backend* else if(r_order == 1) { double_limb_type a; - a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[0]; + a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[0]; if(result) { *result = a / y; @@ -2377,7 +2397,7 @@ void divide_unsigned_helper(cpp_int_backend* } // This is initialised just to keep the compiler from emitting useless warnings later on: - typename cpp_int_backend::limb_pointer pres = typename cpp_int_backend::limb_pointer(); + typename cpp_int_backend::limb_pointer pres = typename cpp_int_backend::limb_pointer(); if(result) { result->resize(r_order + 1); @@ -2394,7 +2414,7 @@ void divide_unsigned_helper(cpp_int_backend* if((pr[r_order] < y) && r_order) { double_limb_type a, b; - a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[r_order - 1]; + a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[r_order - 1]; b = a % y; r.resize(r.size() - 1); --r_order; @@ -2438,32 +2458,36 @@ void divide_unsigned_helper(cpp_int_backend* BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed } -template -BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, + const cpp_int_backend& a, const cpp_int_backend& b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(&result, a, b, r); result.sign(a.sign() != b.sign()); } -template -BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, limb_type& b) +template +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, + const cpp_int_backend& a, limb_type& b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(&result, a, b, r); } -template -BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type& b) +template +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, + const cpp_int_backend& a, signed_limb_type& b) { - cpp_int_backend r; + cpp_int_backend r; divide_unsigned_helper(&result, a, std::abs(b), r); if(b < 0) result.negate(); } -template -BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& b) +template +BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, + const cpp_int_backend& b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); eval_divide(result, a, b); } template @@ -2480,27 +2504,32 @@ BOOST_FORCEINLINE void eval_divide(cpp_int_backend a(result); eval_divide(result, a, b); } -template -BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) +template +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, + const cpp_int_backend& a, + const cpp_int_backend& b) { - divide_unsigned_helper(static_cast* >(0), a, b, result); + divide_unsigned_helper(static_cast* >(0), a, b, result); result.sign(a.sign()); } -template -BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, limb_type b) +template +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, + const cpp_int_backend& a, limb_type b) { - divide_unsigned_helper(static_cast* >(0), a, b, result); + divide_unsigned_helper(static_cast* >(0), a, b, result); } -template -BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& a, signed_limb_type b) +template +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, + const cpp_int_backend& a, signed_limb_type b) { - divide_unsigned_helper(static_cast* >(0), a, static_cast(std::abs(b)), result); + divide_unsigned_helper(static_cast* >(0), a, static_cast(std::abs(b)), result); } -template -BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& b) +template +BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, + const cpp_int_backend& b) { // There is no in place divide: - cpp_int_backend a(result); + cpp_int_backend a(result); eval_modulus(result, a, b); } template @@ -2517,8 +2546,11 @@ BOOST_FORCEINLINE void eval_modulus(cpp_int_backend a(result); eval_modulus(result, a, b); } -template -void bitwise_op(cpp_int_backend& result, const cpp_int_backend& o, Op op) BOOST_NOEXCEPT +template +void bitwise_op( + cpp_int_backend& result, + const cpp_int_backend& o, + Op op) BOOST_NOEXCEPT { // // There are 4 cases: @@ -2537,8 +2569,8 @@ void bitwise_op(cpp_int_backend& result, cons unsigned m, x; minmax(rs, os, m, x); result.resize(x); - typename cpp_int_backend::limb_pointer pr = result.limbs(); - typename cpp_int_backend::const_limb_pointer po = o.limbs(); + typename cpp_int_backend::limb_pointer pr = result.limbs(); + typename cpp_int_backend::const_limb_pointer po = o.limbs(); for(unsigned i = rs; i < x; ++i) pr[i] = 0; @@ -2561,13 +2593,13 @@ void bitwise_op(cpp_int_backend& result, cons { carry += static_cast(~po[i]); pr[i] = op(pr[i], static_cast(carry)); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } for(unsigned i = os; i < x; ++i) { carry += static_cast(~limb_type(0)); pr[i] = op(pr[i], static_cast(carry)); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } // Set the overflow into the "extra" limb: carry += static_cast(~limb_type(0)); @@ -2584,13 +2616,13 @@ void bitwise_op(cpp_int_backend& result, cons { carry += static_cast(~pr[i]); pr[i] = op(static_cast(carry), po[i]); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } for(unsigned i = os; i < x; ++i) { carry += static_cast(~pr[i]); pr[i] = op(static_cast(carry), limb_type(0)); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } // Set the overflow into the "extra" limb: carry += static_cast(~limb_type(0)); @@ -2606,16 +2638,16 @@ void bitwise_op(cpp_int_backend& result, cons r_carry += static_cast(~pr[i]); o_carry += static_cast(~po[i]); pr[i] = op(static_cast(r_carry), static_cast(o_carry)); - r_carry >>= cpp_int_backend::limb_bits; - o_carry >>= cpp_int_backend::limb_bits; + r_carry >>= cpp_int_backend::limb_bits; + o_carry >>= cpp_int_backend::limb_bits; } for(unsigned i = os; i < x; ++i) { r_carry += static_cast(~pr[i]); o_carry += static_cast(~limb_type(0)); pr[i] = op(static_cast(r_carry), static_cast(o_carry)); - r_carry >>= cpp_int_backend::limb_bits; - o_carry >>= cpp_int_backend::limb_bits; + r_carry >>= cpp_int_backend::limb_bits; + o_carry >>= cpp_int_backend::limb_bits; } // Set the overflow into the "extra" limb: r_carry += static_cast(~limb_type(0)); @@ -2634,7 +2666,7 @@ void bitwise_op(cpp_int_backend& result, cons { carry += static_cast(~pr[i]); pr[i] = static_cast(carry); - carry >>= cpp_int_backend::limb_bits; + carry >>= cpp_int_backend::limb_bits; } } else @@ -2647,23 +2679,25 @@ struct bit_and{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCE struct bit_or { limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a | b; } }; struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a ^ b; } }; -template -BOOST_FORCEINLINE void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o)BOOST_NOEXCEPT_IF(is_void::value) +template +BOOST_FORCEINLINE void eval_bitwise_and( + cpp_int_backend& result, + const cpp_int_backend& o)BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_and()); } -template -BOOST_FORCEINLINE void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) +template +BOOST_FORCEINLINE void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_or()); } -template -BOOST_FORCEINLINE void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) +template +BOOST_FORCEINLINE void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_xor()); } -template -BOOST_FORCEINLINE void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +template +BOOST_FORCEINLINE void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Increment and negate: result = o; From 6dfcc7e526fc6e03223861c79e20badb8a45318d Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 6 Sep 2012 09:50:47 +0000 Subject: [PATCH 233/256] Big search and replace change of name for the ExpressionTemplates template parameter to class number. [SVN r80418] --- doc/multiprecision.qbk | 68 +-- .../concepts/mp_number_archetypes.hpp | 2 +- .../boost/multiprecision/cpp_dec_float.hpp | 48 +- include/boost/multiprecision/cpp_int.hpp | 158 +++---- .../depricated/arithmetic_backend.hpp | 2 +- .../multiprecision/depricated/fixed_int.hpp | 4 +- .../multiprecision/detail/big_lanczos.hpp | 2 +- .../multiprecision/detail/default_ops.hpp | 118 ++--- .../boost/multiprecision/detail/et_ops.hpp | 428 +++++++++--------- .../multiprecision/detail/integer_ops.hpp | 20 +- .../boost/multiprecision/detail/no_et_ops.hpp | 392 ++++++++-------- .../multiprecision/detail/number_base.hpp | 32 +- .../multiprecision/detail/number_compare.hpp | 88 ++-- include/boost/multiprecision/gmp.hpp | 142 +++--- include/boost/multiprecision/miller_rabin.hpp | 6 +- include/boost/multiprecision/mpfr.hpp | 96 ++-- include/boost/multiprecision/number.hpp | 38 +- include/boost/multiprecision/random.hpp | 14 +- .../boost/multiprecision/rational_adapter.hpp | 6 +- include/boost/multiprecision/tommath.hpp | 46 +- performance/arithmetic_backend.hpp | 2 +- performance/delaunay_test.cpp | 8 +- performance/miller_rabin_performance.cpp | 6 +- performance/sf_performance.cpp | 20 +- test/compile_fail/operator_fail_01.cpp | 4 +- test/concepts/number_concept_check.cpp | 2 +- test/concepts/sf_concept_check_basic.cpp | 2 +- test/concepts/sf_concept_check_bessel.cpp | 2 +- test/concepts/sf_concept_check_elliptic.cpp | 2 +- test/concepts/sf_concept_check_gamma.cpp | 2 +- test/concepts/sf_concept_check_poly.cpp | 2 +- test/include_test/cpp_int_include_test.cpp | 8 +- test/math/table_type.hpp | 2 +- test/test_arithmetic.cpp | 10 +- test/test_constexpr.cpp | 8 +- test/test_cpp_int_conv.cpp | 8 +- test/test_float_io.cpp | 6 +- test/ublas_interop/test1.hpp | 2 +- test/ublas_interop/test2.hpp | 2 +- test/ublas_interop/test3.hpp | 2 +- test/ublas_interop/test4.hpp | 2 +- test/ublas_interop/test5.hpp | 2 +- test/ublas_interop/test7.hpp | 2 +- 43 files changed, 911 insertions(+), 905 deletions(-) diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index b58cc69b..1446586a 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -95,7 +95,7 @@ by passing a second template argument to `number`: namespace mp = boost::multiprecision; // Reduce the typing a bit later... - typedef mp::number, false> my_float; + typedef mp::number, et_off> my_float; my_float a, b, c; // These variables have 300 decimal digits precision @@ -123,8 +123,8 @@ However conversions that are inherently lossy are either declared explicit or el Mixed arithmetic will fail if the conversion is either ambiguous or explicit: - number, false> a(2); - number, true> b(3); + number, et_off> a(2); + number, et_on> b(3); b = a * b; // Error, implicit conversion could go either way. b = a * 3.14; // Error, no operator overload if the conversion would be explicit. @@ -137,7 +137,7 @@ In addition the non-expression template operator overloads (see below) are move that look something like: template - number operator + (number&& a, const number& b) + number operator + (number&& a, const number& b) { return std::move(a += b); } @@ -336,16 +336,16 @@ The following back-ends provide integer arithmetic: typedef number cpp_rational; // arbitrary precision rational number // Fixed precision unsigned types: - typedef number, false> uint128_t; - typedef number, false> uint256_t; - typedef number, false> uint512_t; - typedef number, false> uint1024_t; + typedef number, et_off> uint128_t; + typedef number, et_off> uint256_t; + typedef number, et_off> uint512_t; + typedef number, et_off> uint1024_t; // Fixed precision signed types: - typedef number, false> int128_t; - typedef number, false> int256_t; - typedef number, false> int512_t; - typedef number, false> int1024_t; + typedef number, et_off> int128_t; + typedef number, et_off> int256_t; + typedef number, et_off> int512_t; + typedef number, et_off> int1024_t; }} // namespaces @@ -1043,10 +1043,10 @@ The library implements a Miller-Rabin test for primality: #include - template + template bool miller_rabin_test(const number& n, unsigned trials, Engine& gen); - template + template bool miller_rabin_test(const number& n, unsigned trials); These functions perform a Miller-Rabin test for primality, if the result is `false` then /n/ is definitely composite, @@ -1076,7 +1076,7 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba namespace boost{ namespace multiprecision{ - template + template class number { number(); @@ -1153,14 +1153,14 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba bool operator>=(const ``['see-below]``&, const ``['see-below]``&); // Swap: - template + template void swap(number& a, number& b); // iostream support: - template + template std::ostream& operator << (std::ostream& os, const number& r); std::ostream& operator << (std::ostream& os, const ``['unmentionable-expression-template-type]``& r); - template + template std::istream& operator >> (std::istream& is, number& r); // Non-member function standard library support: @@ -1209,7 +1209,7 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba // Integer specific functions: ``['unmentionable-expression-template-type]`` pow(const ``['number-or-expression-template-type]``&, unsigned); ``['unmentionable-expression-template-type]`` powm(const ``['number-or-expression-template-type]``& b, const ``['number-or-expression-template-type]``& p, const ``['number-or-expression-template-type]``& m); - template + template void divide_qr(const ``['number-or-expression-template-type]``& x, const ``['number-or-expression-template-type]``& y, number& q, number& r); template @@ -1247,7 +1247,7 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba // numeric_limits support: namespace std{ - template + template struct numeric_limits > { /* Usual members here */ @@ -1257,7 +1257,7 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba [h4 Description] - template + template class number; Class `number` has two template arguments: @@ -1433,7 +1433,7 @@ The arguments to these functions must contain at least one of the following: The return type of these operators is either: * An ['unmentionable-type] expression template type when `ExpressionTemplates` is `true`. -* Type `number` when `ExpressionTemplates` is `false`. +* Type `number` when `ExpressionTemplates` is `false`. * Type `bool` if the operator is a comparison operator. Finally note that the second argument to the left and right shift operations must be a builtin integer type, @@ -1448,11 +1448,11 @@ Swaps `a` and `b`. [h4 Iostream Support] - template + template std::ostream& operator << (std::ostream& os, const number& r); template std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r); - template + template inline std::istream& operator >> (std::istream& is, number& r) These operators provided formatted input-output operations on `number` types, and expression templates derived from them. @@ -1495,7 +1495,7 @@ this library support all of the iostream formatting flags, field width and preci ``['unmentionable-expression-template-type]`` atan2 (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); These functions all behave exactly as their standard library counterparts do: their argument is either an instance of `number` or -an expression template derived from it; If the argument is of type `number` then that is also the return type, +an expression template derived from it; If the argument is of type `number` then that is also the return type, otherwise the return type is an expression template. These functions are normally implemented by the Backend type. However, default versions are provided for Backend types that @@ -1545,7 +1545,7 @@ large as to take "effectively forever" to compute, or else simply run the host m Returns ['b[super p] mod m] as an expression template. - template + template bool divide_qr(const ``['number-or-expression-template-type]``& x, const ``['number-or-expression-template-type]``& y, number& q, number& r); @@ -1643,16 +1643,16 @@ whose precision can vary at compile time (such as `mpf_float`). typedef number cpp_rational; // arbitrary precision rational number // Fixed precision unsigned types: - typedef number, false> uint128_t; - typedef number, false> uint256_t; - typedef number, false> uint512_t; - typedef number, false> uint1024_t; + typedef number, et_off> uint128_t; + typedef number, et_off> uint256_t; + typedef number, et_off> uint512_t; + typedef number, et_off> uint1024_t; // Fixed precision signed types: - typedef number, false> int128_t; - typedef number, false> int256_t; - typedef number, false> int512_t; - typedef number, false> int1024_t; + typedef number, et_off> int128_t; + typedef number, et_off> int256_t; + typedef number, et_off> int512_t; + typedef number, et_off> int1024_t; }} // namespaces diff --git a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp index adc42b68..8884a9fa 100644 --- a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp @@ -206,7 +206,7 @@ struct number_category : public mpl::i namespace std{ -template +template class numeric_limits > : public std::numeric_limits { typedef std::numeric_limits base_type; diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index bd70f8cd..1a7241a5 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -2881,7 +2881,7 @@ struct is_explicitly_convertible, cpp_dec_float > : public namespace std { - template + template class numeric_limits, ExpressionTemplates> > { public: @@ -2922,49 +2922,49 @@ namespace std #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template +template BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::min_exponent; -template +template BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::min_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::max_exponent; -template +template BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::max_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template +template BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template +template BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif @@ -2974,7 +2974,7 @@ namespace boost{ namespace math{ namespace policies{ -template +template struct precision< boost::multiprecision::number, ExpressionTemplates>, Policy> { // Define a local copy of cpp_dec_float_digits10 because it might differ diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index ba68478c..6c5429d1 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -3069,16 +3069,16 @@ typedef rational_adapter > cpp_rational_backend; typedef number cpp_rational; // Fixed precision unsigned types: -typedef number, false> uint128_t; -typedef number, false> uint256_t; -typedef number, false> uint512_t; -typedef number, false> uint1024_t; +typedef number, et_off> uint128_t; +typedef number, et_off> uint256_t; +typedef number, et_off> uint512_t; +typedef number, et_off> uint1024_t; // Fixed precision signed types: -typedef number, false> int128_t; -typedef number, false> int256_t; -typedef number, false> int512_t; -typedef number, false> int1024_t; +typedef number, et_off> int128_t; +typedef number, et_off> int256_t; +typedef number, et_off> int512_t; +typedef number, et_off> int1024_t; #ifdef BOOST_MSVC #pragma warning(pop) @@ -3102,7 +3102,7 @@ struct is_explicitly_convertible +template class numeric_limits, ExpressionTemplates> > { typedef boost::multiprecision::number, ExpressionTemplates> number_type; @@ -3154,54 +3154,54 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template +template BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template +template BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif -template +template class numeric_limits, ExpressionTemplates> > { typedef boost::multiprecision::number, ExpressionTemplates> number_type; @@ -3273,59 +3273,59 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template +template const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template +template BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template +template BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif -template +template class numeric_limits, ExpressionTemplates> > { typedef boost::multiprecision::number, ExpressionTemplates> number_type; @@ -3401,54 +3401,54 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template +template const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template +template BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template +template BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif diff --git a/include/boost/multiprecision/depricated/arithmetic_backend.hpp b/include/boost/multiprecision/depricated/arithmetic_backend.hpp index 0f6e4c02..3dda99ac 100644 --- a/include/boost/multiprecision/depricated/arithmetic_backend.hpp +++ b/include/boost/multiprecision/depricated/arithmetic_backend.hpp @@ -127,7 +127,7 @@ using boost::multiprecision::backends::arithmetic_backend; namespace std{ -template +template class numeric_limits, ExpressionTemplates > > : public std::numeric_limits { typedef std::numeric_limits base_type; diff --git a/include/boost/multiprecision/depricated/fixed_int.hpp b/include/boost/multiprecision/depricated/fixed_int.hpp index 3595f27b..58ec099e 100644 --- a/include/boost/multiprecision/depricated/fixed_int.hpp +++ b/include/boost/multiprecision/depricated/fixed_int.hpp @@ -1517,7 +1517,7 @@ typedef number > int512_t; namespace std{ -template +template class numeric_limits, ExpressionTemplates> > { typedef boost::multiprecision::number, ExpressionTemplates> number_type; @@ -1591,7 +1591,7 @@ public: BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero; }; -template +template typename numeric_limits, ExpressionTemplates> >::initializer const numeric_limits, ExpressionTemplates> >::init; } diff --git a/include/boost/multiprecision/detail/big_lanczos.hpp b/include/boost/multiprecision/detail/big_lanczos.hpp index c3cb1461..094bcb02 100644 --- a/include/boost/multiprecision/detail/big_lanczos.hpp +++ b/include/boost/multiprecision/detail/big_lanczos.hpp @@ -16,7 +16,7 @@ namespace lanczos{ template struct lanczos; -template +template struct lanczos, Policy> { typedef typename boost::math::policies::precision, Policy>::type precision_type; diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 79f98280..a8b04623 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -945,7 +945,7 @@ namespace math{ // // Default versions of floating point classification routines: // -template +template inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number& arg) { using multiprecision::default_ops::eval_fpclassify; @@ -957,7 +957,7 @@ inline int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::det typedef typename multiprecision::detail::expression::result_type value_type; return fpclassify(value_type(arg)); } -template +template inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number& arg) { int v = fpclassify(arg); @@ -969,7 +969,7 @@ inline bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::deta typedef typename multiprecision::detail::expression::result_type value_type; return isfinite(value_type(arg)); } -template +template inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number& arg) { return fpclassify(arg) == FP_NAN; @@ -980,7 +980,7 @@ inline bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail: typedef typename multiprecision::detail::expression::result_type value_type; return isnan(value_type(arg)); } -template +template inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number& arg) { return fpclassify(arg) == FP_INFINITE; @@ -991,7 +991,7 @@ inline bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail: typedef typename multiprecision::detail::expression::result_type value_type; return isinf(value_type(arg)); } -template +template inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number& arg) { return fpclassify(arg) == FP_NORMAL; @@ -1013,7 +1013,7 @@ inline typename detail::expression::result_type trunc(const return BOOST_MP_MOVE(trunc(number_type(v), pol)); } -template +template inline number trunc(const number& v, const Policy&) { using default_ops::eval_trunc; @@ -1036,7 +1036,7 @@ inline int itrunc(const detail::expression& v) { return itrunc(v, boost::math::policies::policy<>()); } -template +template inline int itrunc(const number& v, const Policy& pol) { number r = trunc(v, pol); @@ -1044,7 +1044,7 @@ inline int itrunc(const number& v, const Policy& p return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } -template +template inline int itrunc(const number& v) { return itrunc(v, boost::math::policies::policy<>()); @@ -1063,7 +1063,7 @@ inline long ltrunc(const detail::expression& v) { return ltrunc(v, boost::math::policies::policy<>()); } -template +template inline long ltrunc(const number& v, const Policy& pol) { number r = trunc(v, pol); @@ -1071,7 +1071,7 @@ inline long ltrunc(const number& v, const Policy& pol) return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } -template +template inline long ltrunc(const number& v) { return ltrunc(v, boost::math::policies::policy<>()); @@ -1091,7 +1091,7 @@ inline long long lltrunc(const detail::expression& v) { return lltrunc(v, boost::math::policies::policy<>()); } -template +template inline long long lltrunc(const number& v, const Policy& pol) { number r = trunc(v, pol); @@ -1099,7 +1099,7 @@ inline long long lltrunc(const number& v, const Policy& return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } -template +template inline long long lltrunc(const number& v) { return lltrunc(v, boost::math::policies::policy<>()); @@ -1111,7 +1111,7 @@ inline typename detail::expression::result_type round(const typedef typename detail::expression::result_type number_type; return BOOST_MP_MOVE(round(static_cast(v), pol)); } -template +template inline number round(const number& v, const Policy&) { using default_ops::eval_round; @@ -1134,7 +1134,7 @@ inline int iround(const detail::expression& v) { return iround(v, boost::math::policies::policy<>()); } -template +template inline int iround(const number& v, const Policy& pol) { number r = round(v, pol); @@ -1142,7 +1142,7 @@ inline int iround(const number& v, const Policy& pol) return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0, pol).template convert_to(); return r.template convert_to(); } -template +template inline int iround(const number& v) { return iround(v, boost::math::policies::policy<>()); @@ -1161,7 +1161,7 @@ inline long lround(const detail::expression& v) { return lround(v, boost::math::policies::policy<>()); } -template +template inline long lround(const number& v, const Policy& pol) { number r = round(v, pol); @@ -1169,7 +1169,7 @@ inline long lround(const number& v, const Policy& pol) return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", 0, v, 0L, pol).template convert_to(); return r.template convert_to(); } -template +template inline long lround(const number& v) { return lround(v, boost::math::policies::policy<>()); @@ -1189,7 +1189,7 @@ inline long long llround(const detail::expression& v) { return llround(v, boost::math::policies::policy<>()); } -template +template inline long long llround(const number& v, const Policy& pol) { number r = round(v, pol); @@ -1197,7 +1197,7 @@ inline long long llround(const number& v, const Policy& return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", 0, v, 0LL, pol).template convert_to(); return r.template convert_to(); } -template +template inline long long llround(const number& v) { return llround(v, boost::math::policies::policy<>()); @@ -1241,9 +1241,9 @@ inline typename enable_if_c::value == category,\ detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , number > \ + , number > \ >::type \ -func(const number& arg)\ +func(const number& arg)\ {\ return detail::expression<\ detail::function\ @@ -1257,10 +1257,10 @@ func(const number& arg)\ template \ inline typename boost::enable_if_c<\ boost::multiprecision::number_category::value == category,\ - number >::type \ -func(const number& arg)\ + number >::type \ +func(const number& arg)\ {\ - number result;\ + number result;\ using default_ops::BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend());\ return BOOST_MP_MOVE(result);\ @@ -1296,10 +1296,10 @@ inline typename enable_if_c::value == category,\ detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , number \ - , number > \ + , number \ + , number > \ >::type \ -func(const number& arg, const number& a)\ +func(const number& arg, const number& a)\ {\ return detail::expression<\ detail::function\ @@ -1318,10 +1318,10 @@ inline typename enable_if_c<\ detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , number \ + , number \ , detail::expression > \ >::type \ -func(const number& arg, const detail::expression& a)\ +func(const number& arg, const detail::expression& a)\ {\ return detail::expression<\ detail::function\ @@ -1341,9 +1341,9 @@ inline typename enable_if_c<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , detail::expression \ - , number > \ + , number > \ >::type \ -func(const detail::expression& arg, const number& a)\ +func(const detail::expression& arg, const number& a)\ {\ return detail::expression<\ detail::function\ @@ -1384,11 +1384,11 @@ inline typename enable_if_c<\ detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , number \ + , number \ , Arithmetic\ > \ >::type \ -func(const number& arg, const Arithmetic& a)\ +func(const number& arg, const Arithmetic& a)\ {\ return detail::expression<\ detail::function\ @@ -1431,10 +1431,10 @@ inline typename enable_if_c<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ , Arithmetic \ - , number \ + , number \ > \ >::type \ -func(const Arithmetic& arg, const number& a)\ +func(const Arithmetic& arg, const number& a)\ {\ return detail::expression<\ detail::function\ @@ -1472,10 +1472,10 @@ func(const Arithmetic& arg, const detail::expression& a)\ }\ template \ inline typename enable_if_c<(number_category::value == category),\ - number >::type \ -func(const number& arg, const number& a)\ + number >::type \ +func(const number& arg, const number& a)\ {\ - number result;\ + number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), a.backend());\ return BOOST_MP_MOVE(result);\ @@ -1483,12 +1483,12 @@ func(const number& arg, const number& a)\ template \ inline typename enable_if_c<\ is_arithmetic::value && (number_category::value == category),\ - number \ + number \ >::type \ -func(const number& arg, const Arithmetic& a)\ +func(const number& arg, const Arithmetic& a)\ {\ typedef typename detail::canonical::type canonical_type;\ - number result;\ + number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), static_cast(a));\ return BOOST_MP_MOVE(result);\ @@ -1496,12 +1496,12 @@ func(const number& arg, const Arithmetic& a)\ template \ inline typename enable_if_c<\ is_arithmetic::value && (number_category::value == category),\ - number \ + number \ >::type \ -func(const Arithmetic& a, const number& arg)\ +func(const Arithmetic& a, const number& arg)\ {\ typedef typename detail::canonical::type canonical_type;\ - number result;\ + number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), static_cast(a), arg.backend());\ return BOOST_MP_MOVE(result);\ @@ -1536,10 +1536,10 @@ inline typename enable_if_c<\ detail::expression<\ detail::function\ , detail::BOOST_JOIN(func, _funct) \ - , number \ + , number \ , Arg2> \ >::type \ -func(const number& arg, Arg2 const& a)\ +func(const number& arg, Arg2 const& a)\ {\ return detail::expression<\ detail::function\ @@ -1555,10 +1555,10 @@ func(const number& arg, Arg2 const& a)\ template \ inline typename enable_if_c<\ (number_category::value == category),\ - number >::type \ -func(const number& arg, Arg2 const& a)\ + number >::type \ +func(const number& arg, Arg2 const& a)\ {\ - number result;\ + number result;\ using default_ops:: BOOST_JOIN(eval_,func);\ BOOST_JOIN(eval_,func)(result.backend(), arg.backend(), a);\ return BOOST_MP_MOVE(result);\ @@ -1614,23 +1614,23 @@ template inline detail::expression< detail::function , detail::abs_funct - , number > -abs(const number& arg) + , number > +abs(const number& arg) { return detail::expression< detail::function , detail::abs_funct - , number + , number >( detail::abs_funct() , arg ); } template -inline number -abs(const number& arg) +inline number +abs(const number& arg) { - number result; + number result; using default_ops::eval_abs; eval_abs(result.backend(), arg.backend()); return BOOST_MP_MOVE(result); @@ -1685,25 +1685,25 @@ namespace detail{ template T sinc_pi_imp(T); template T sinhc_pi_imp(T); } -template +template inline multiprecision::number sinc_pi(const multiprecision::number& x) { return BOOST_MP_MOVE(detail::sinc_pi_imp(x)); } -template +template inline multiprecision::number sinc_pi(const multiprecision::number& x, const Policy&) { return BOOST_MP_MOVE(detail::sinc_pi_imp(x)); } -template +template inline multiprecision::number sinhc_pi(const multiprecision::number& x) { return BOOST_MP_MOVE(detail::sinhc_pi_imp(x)); } -template +template inline multiprecision::number sinhc_pi(const multiprecision::number& x, const Policy&) { return BOOST_MP_MOVE(boost::math::sinhc_pi(x)); diff --git a/include/boost/multiprecision/detail/et_ops.hpp b/include/boost/multiprecision/detail/et_ops.hpp index 35886a9b..1e35c9be 100644 --- a/include/boost/multiprecision/detail/et_ops.hpp +++ b/include/boost/multiprecision/detail/et_ops.hpp @@ -13,46 +13,46 @@ namespace boost{ namespace multiprecision{ // // Unary operators first: // -template +template inline const number& operator + (const number& v) { return v; } template inline const detail::expression& operator + (const detail::expression& v) { return v; } template -inline detail::expression > operator - (const number& v) { return detail::expression >(v); } +inline detail::expression > operator - (const number& v) { return detail::expression >(v); } template inline detail::expression > operator - (const detail::expression& v) { return detail::expression >(v); } template -inline detail::expression > operator ~ (const number& v) { return detail::expression >(v); } +inline detail::expression > operator ~ (const number& v) { return detail::expression >(v); } template inline detail::expression > operator ~ (const detail::expression& v) { return detail::expression >(v); } // // Then addition: // template -inline detail::expression, number > - operator + (const number& a, const number& b) +inline detail::expression, number > + operator + (const number& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template -inline typename enable_if >, detail::expression, V > >::type - operator + (const number& a, const V& b) +inline typename enable_if >, detail::expression, V > >::type + operator + (const number& a, const V& b) { - return detail::expression, V >(a, b); + return detail::expression, V >(a, b); } template -inline typename enable_if >, detail::expression > >::type - operator + (const V& a, const number& b) +inline typename enable_if >, detail::expression > >::type + operator + (const V& a, const number& b) { - return detail::expression >(a, b); + return detail::expression >(a, b); } -template +template inline detail::expression, detail::expression > operator + (const number& a, const detail::expression& b) { return detail::expression, detail::expression >(a, b); } -template +template inline detail::expression, number > operator + (const detail::expression& a, const number& b) { @@ -79,82 +79,82 @@ inline typename enable_if +template inline detail::expression, typename detail::expression::left_type > operator + (const number& a, const detail::expression& b) { return detail::expression, typename detail::expression::left_type >(a, b.left_ref()); } -template +template inline detail::expression, typename detail::expression::left_type > operator + (const detail::expression& a, const number& b) { return detail::expression, typename detail::expression::left_type >(b, a.left_ref()); } template -inline detail::expression, number > - operator + (const number& a, const detail::expression >& b) +inline detail::expression, number > + operator + (const number& a, const detail::expression >& b) { - return detail::expression, number >(a, b.left_ref()); + return detail::expression, number >(a, b.left_ref()); } template -inline detail::expression, number > - operator + (const detail::expression >& a, const number& b) +inline detail::expression, number > + operator + (const detail::expression >& a, const number& b) { - return detail::expression, number >(b, a.left_ref()); + return detail::expression, number >(b, a.left_ref()); } template -inline typename enable_if >, detail::expression > >::type - operator + (const detail::expression >& a, const V& b) +inline typename enable_if >, detail::expression > >::type + operator + (const detail::expression >& a, const V& b) { - return detail::expression >(b, a.left_ref()); + return detail::expression >(b, a.left_ref()); } -template -inline typename enable_if, number >, detail::expression, number > >::type - operator + (const detail::expression >& a, const number& b) +template +inline typename enable_if, number >, detail::expression, number > >::type + operator + (const detail::expression >& a, const number& b) { - return detail::expression, number >(b, a.left_ref()); + return detail::expression, number >(b, a.left_ref()); } -template -inline typename enable_if, number >, detail::expression, number > >::type - operator + (const number& a, const detail::expression >& b) +template +inline typename enable_if, number >, detail::expression, number > >::type + operator + (const number& a, const detail::expression >& b) { - return detail::expression, number >(a, b.left_ref()); + return detail::expression, number >(a, b.left_ref()); } template -inline detail::expression, number > > - operator + (const detail::expression >& a, const detail::expression >& b) +inline detail::expression, number > > + operator + (const detail::expression >& a, const detail::expression >& b) { - return detail::expression, number > >(detail::expression, number >(a.left_ref(), b.left_ref())); + return detail::expression, number > >(detail::expression, number >(a.left_ref(), b.left_ref())); } // // Subtraction: // template -inline detail::expression, number > - operator - (const number& a, const number& b) +inline detail::expression, number > + operator - (const number& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template -inline typename enable_if >, detail::expression, V > >::type - operator - (const number& a, const V& b) +inline typename enable_if >, detail::expression, V > >::type + operator - (const number& a, const V& b) { - return detail::expression, V >(a, b); + return detail::expression, V >(a, b); } template -inline typename enable_if >, detail::expression > >::type - operator - (const V& a, const number& b) +inline typename enable_if >, detail::expression > >::type + operator - (const V& a, const number& b) { - return detail::expression >(a, b); + return detail::expression >(a, b); } -template +template inline detail::expression, detail::expression > operator - (const number& a, const detail::expression& b) { return detail::expression, detail::expression >(a, b); } -template +template inline detail::expression, number > operator - (const detail::expression& a, const number& b) { @@ -181,13 +181,13 @@ inline typename enable_if +template inline detail::expression, typename detail::expression::left_type > operator - (const number& a, const detail::expression& b) { return detail::expression, typename detail::expression::left_type >(a, b.left_ref()); } -template +template inline detail::expression, typename detail::expression::left_type > > operator - (const detail::expression& a, const number& b) { @@ -195,70 +195,70 @@ inline detail::expression, typename detail::expression::left_type >(b, a.left_ref())); } template -inline detail::expression, number > - operator - (const number& a, const detail::expression >& b) +inline detail::expression, number > + operator - (const number& a, const detail::expression >& b) { - return detail::expression, number >(a, b.left_ref()); + return detail::expression, number >(a, b.left_ref()); } template -inline detail::expression, number > > - operator - (const detail::expression >& a, const number& b) +inline detail::expression, number > > + operator - (const detail::expression >& a, const number& b) { - return detail::expression, number > >( - detail::expression, number >(b, a.left_ref())); + return detail::expression, number > >( + detail::expression, number >(b, a.left_ref())); } template -inline typename enable_if >, detail::expression, V > > >::type - operator - (const detail::expression >& a, const V& b) +inline typename enable_if >, detail::expression, V > > >::type + operator - (const detail::expression >& a, const V& b) { - return detail::expression, V > >(detail::expression, V >(a.left_ref(), b)); + return detail::expression, V > >(detail::expression, V >(a.left_ref(), b)); } -template -inline typename enable_if, number >, detail::expression, number > > >::type - operator - (const detail::expression >& a, const number& b) +template +inline typename enable_if, number >, detail::expression, number > > >::type + operator - (const detail::expression >& a, const number& b) { - return detail::expression, number > >(detail::expression, number >(a.left_ref(), b)); + return detail::expression, number > >(detail::expression, number >(a.left_ref(), b)); } template -inline typename enable_if >, detail::expression > >::type - operator - (const V& a, const detail::expression >& b) +inline typename enable_if >, detail::expression > >::type + operator - (const V& a, const detail::expression >& b) { - return detail::expression >(a, b.left_ref()); + return detail::expression >(a, b.left_ref()); } -template -inline typename enable_if, number >, detail::expression, number > >::type - operator - (const number& a, const detail::expression >& b) +template +inline typename enable_if, number >, detail::expression, number > >::type + operator - (const number& a, const detail::expression >& b) { - return detail::expression, number >(a, b.left_ref()); + return detail::expression, number >(a, b.left_ref()); } // // Multiplication: // template -inline detail::expression, number > - operator * (const number& a, const number& b) +inline detail::expression, number > + operator * (const number& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template -inline typename enable_if >, detail::expression, V > >::type - operator * (const number& a, const V& b) +inline typename enable_if >, detail::expression, V > >::type + operator * (const number& a, const V& b) { - return detail::expression, V >(a, b); + return detail::expression, V >(a, b); } template -inline typename enable_if >, detail::expression > >::type - operator * (const V& a, const number& b) +inline typename enable_if >, detail::expression > >::type + operator * (const V& a, const number& b) { - return detail::expression >(a, b); + return detail::expression >(a, b); } -template +template inline detail::expression, detail::expression > operator * (const number& a, const detail::expression& b) { return detail::expression, detail::expression >(a, b); } -template +template inline detail::expression, number > operator * (const detail::expression& a, const number& b) { @@ -285,14 +285,14 @@ inline typename enable_if +template inline detail::expression, typename detail::expression::left_type > > operator * (const number& a, const detail::expression& b) { return detail::expression, typename detail::expression::left_type > >( detail::expression, typename detail::expression::left_type > (a, b.left_ref())); } -template +template inline detail::expression, typename detail::expression::left_type > > operator * (const detail::expression& a, const number& b) { @@ -300,75 +300,75 @@ inline detail::expression, typename detail::expression::left_type >(b, a.left_ref())); } template -inline detail::expression, number > > - operator * (const number& a, const detail::expression >& b) +inline detail::expression, number > > + operator * (const number& a, const detail::expression >& b) { - return detail::expression, number > >( - detail::expression, number >(a, b.left_ref())); + return detail::expression, number > >( + detail::expression, number >(a, b.left_ref())); } template -inline detail::expression, number > > - operator * (const detail::expression >& a, const number& b) +inline detail::expression, number > > + operator * (const detail::expression >& a, const number& b) { - return detail::expression, number > >( - detail::expression, number >(b, a.left_ref())); + return detail::expression, number > >( + detail::expression, number >(b, a.left_ref())); } template -inline typename enable_if >, detail::expression, V > > >::type - operator * (const detail::expression >& a, const V& b) +inline typename enable_if >, detail::expression, V > > >::type + operator * (const detail::expression >& a, const V& b) { - return detail::expression, V > > ( - detail::expression, V >(a.left_ref(), b)); + return detail::expression, V > > ( + detail::expression, V >(a.left_ref(), b)); } -template -inline typename enable_if, number >, detail::expression, number > > >::type - operator * (const detail::expression >& a, const number& b) +template +inline typename enable_if, number >, detail::expression, number > > >::type + operator * (const detail::expression >& a, const number& b) { - return detail::expression, number > > ( - detail::expression, number >(a.left_ref(), b)); + return detail::expression, number > > ( + detail::expression, number >(a.left_ref(), b)); } template -inline typename enable_if >, detail::expression, V > > >::type - operator * (const V& a, const detail::expression >& b) +inline typename enable_if >, detail::expression, V > > >::type + operator * (const V& a, const detail::expression >& b) { - return detail::expression, V > >( - detail::expression, V >(b.left_ref(), a)); + return detail::expression, V > >( + detail::expression, V >(b.left_ref(), a)); } -template -inline typename enable_if, number >, detail::expression, number > > >::type - operator * (const number& a, const detail::expression >& b) +template +inline typename enable_if, number >, detail::expression, number > > >::type + operator * (const number& a, const detail::expression >& b) { - return detail::expression, number > >( - detail::expression, number >(b.left_ref(), a)); + return detail::expression, number > >( + detail::expression, number >(b.left_ref(), a)); } // // Division: // template -inline detail::expression, number > - operator / (const number& a, const number& b) +inline detail::expression, number > + operator / (const number& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template -inline typename enable_if >, detail::expression, V > >::type - operator / (const number& a, const V& b) +inline typename enable_if >, detail::expression, V > >::type + operator / (const number& a, const V& b) { - return detail::expression, V >(a, b); + return detail::expression, V >(a, b); } template -inline typename enable_if >, detail::expression > >::type - operator / (const V& a, const number& b) +inline typename enable_if >, detail::expression > >::type + operator / (const V& a, const number& b) { - return detail::expression >(a, b); + return detail::expression >(a, b); } -template +template inline detail::expression, detail::expression > operator / (const number& a, const detail::expression& b) { return detail::expression, detail::expression >(a, b); } -template +template inline detail::expression, number > operator / (const detail::expression& a, const number& b) { @@ -395,14 +395,14 @@ inline typename enable_if +template inline detail::expression, typename detail::expression::left_type > > operator / (const number& a, const detail::expression& b) { return detail::expression, typename detail::expression::left_type > >( detail::expression, typename detail::expression::left_type >(a, b.left_ref())); } -template +template inline detail::expression::left_type, number > > operator / (const detail::expression& a, const number& b) { @@ -410,79 +410,79 @@ inline detail::expression::left_type, number >(a.left_ref(), b)); } template -inline detail::expression, number > > - operator / (const number& a, const detail::expression >& b) +inline detail::expression, number > > + operator / (const number& a, const detail::expression >& b) { - return detail::expression, number > >( - detail::expression, number >(a, b.left_ref())); + return detail::expression, number > >( + detail::expression, number >(a, b.left_ref())); } template -inline detail::expression, number > > - operator / (const detail::expression >& a, const number& b) +inline detail::expression, number > > + operator / (const detail::expression >& a, const number& b) { - return detail::expression, number > >( - detail::expression, number >(a.left_ref(), b)); + return detail::expression, number > >( + detail::expression, number >(a.left_ref(), b)); } template -inline typename enable_if >, detail::expression, V > > >::type - operator / (const detail::expression >& a, const V& b) +inline typename enable_if >, detail::expression, V > > >::type + operator / (const detail::expression >& a, const V& b) { - return detail::expression, V > >( - detail::expression, V>(a.left_ref(), b)); + return detail::expression, V > >( + detail::expression, V>(a.left_ref(), b)); } -template -inline typename enable_if, number >, detail::expression, number > > >::type - operator / (const detail::expression >& a, const number& b) +template +inline typename enable_if, number >, detail::expression, number > > >::type + operator / (const detail::expression >& a, const number& b) { - return detail::expression, number > >( - detail::expression, number >(a.left_ref(), b)); + return detail::expression, number > >( + detail::expression, number >(a.left_ref(), b)); } template -inline typename enable_if >, detail::expression > > >::type - operator / (const V& a, const detail::expression >& b) +inline typename enable_if >, detail::expression > > >::type + operator / (const V& a, const detail::expression >& b) { - return detail::expression > >( - detail::expression >(a, b.left_ref())); + return detail::expression > >( + detail::expression >(a, b.left_ref())); } -template -inline typename enable_if, number >, detail::expression, number > > >::type - operator / (const number& a, const detail::expression >& b) +template +inline typename enable_if, number >, detail::expression, number > > >::type + operator / (const number& a, const detail::expression >& b) { - return detail::expression, number > >( - detail::expression, number >(a, b.left_ref())); + return detail::expression, number > >( + detail::expression, number >(a, b.left_ref())); } // // Modulus: // template -inline detail::expression, number > - operator % (const number& a, const number& b) +inline detail::expression, number > + operator % (const number& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template -inline typename enable_if >, detail::expression, V > >::type - operator % (const number& a, const V& b) +inline typename enable_if >, detail::expression, V > >::type + operator % (const number& a, const V& b) { - return detail::expression, V >(a, b); + return detail::expression, V >(a, b); } template -inline typename enable_if >, detail::expression > >::type - operator % (const V& a, const number& b) +inline typename enable_if >, detail::expression > >::type + operator % (const V& a, const number& b) { - return detail::expression >(a, b); + return detail::expression >(a, b); } template -inline detail::expression, detail::expression > - operator % (const number& a, const detail::expression& b) +inline detail::expression, detail::expression > + operator % (const number& a, const detail::expression& b) { - return detail::expression, detail::expression >(a, b); + return detail::expression, detail::expression >(a, b); } template -inline detail::expression, number > - operator % (const detail::expression& a, const number& b) +inline detail::expression, number > + operator % (const detail::expression& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template inline detail::expression, detail::expression > @@ -506,10 +506,10 @@ inline typename enable_if -inline typename enable_if, detail::expression, I > >::type - operator << (const number& a, const I& b) +inline typename enable_if, detail::expression, I > >::type + operator << (const number& a, const I& b) { - return detail::expression, I>(a, b); + return detail::expression, I>(a, b); } template inline typename enable_if, detail::expression, I> >::type @@ -521,10 +521,10 @@ inline typename enable_if, detail::expression -inline typename enable_if, detail::expression, I > >::type - operator >> (const number& a, const I& b) +inline typename enable_if, detail::expression, I > >::type + operator >> (const number& a, const I& b) { - return detail::expression, I>(a, b); + return detail::expression, I>(a, b); } template inline typename enable_if, detail::expression, I> >::type @@ -536,34 +536,34 @@ inline typename enable_if, detail::expression -inline detail::expression, number > - operator & (const number& a, const number& b) +inline detail::expression, number > + operator & (const number& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template -inline typename enable_if >, detail::expression, V > >::type - operator & (const number& a, const V& b) +inline typename enable_if >, detail::expression, V > >::type + operator & (const number& a, const V& b) { - return detail::expression, V >(a, b); + return detail::expression, V >(a, b); } template -inline typename enable_if >, detail::expression > >::type - operator & (const V& a, const number& b) +inline typename enable_if >, detail::expression > >::type + operator & (const V& a, const number& b) { - return detail::expression >(a, b); + return detail::expression >(a, b); } template -inline detail::expression, detail::expression > - operator & (const number& a, const detail::expression& b) +inline detail::expression, detail::expression > + operator & (const number& a, const detail::expression& b) { - return detail::expression, detail::expression >(a, b); + return detail::expression, detail::expression >(a, b); } template -inline detail::expression, number > - operator & (const detail::expression& a, const number& b) +inline detail::expression, number > + operator & (const detail::expression& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template inline detail::expression, detail::expression > @@ -587,34 +587,34 @@ inline typename enable_if -inline detail::expression, number > - operator| (const number& a, const number& b) +inline detail::expression, number > + operator| (const number& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template -inline typename enable_if >, detail::expression, V > >::type - operator| (const number& a, const V& b) +inline typename enable_if >, detail::expression, V > >::type + operator| (const number& a, const V& b) { - return detail::expression, V >(a, b); + return detail::expression, V >(a, b); } template -inline typename enable_if >, detail::expression > >::type - operator| (const V& a, const number& b) +inline typename enable_if >, detail::expression > >::type + operator| (const V& a, const number& b) { - return detail::expression >(a, b); + return detail::expression >(a, b); } template -inline detail::expression, detail::expression > - operator| (const number& a, const detail::expression& b) +inline detail::expression, detail::expression > + operator| (const number& a, const detail::expression& b) { - return detail::expression, detail::expression >(a, b); + return detail::expression, detail::expression >(a, b); } template -inline detail::expression, number > - operator| (const detail::expression& a, const number& b) +inline detail::expression, number > + operator| (const detail::expression& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template inline detail::expression, detail::expression > @@ -638,34 +638,34 @@ inline typename enable_if -inline detail::expression, number > - operator^ (const number& a, const number& b) +inline detail::expression, number > + operator^ (const number& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template -inline typename enable_if >, detail::expression, V > >::type - operator^ (const number& a, const V& b) +inline typename enable_if >, detail::expression, V > >::type + operator^ (const number& a, const V& b) { - return detail::expression, V >(a, b); + return detail::expression, V >(a, b); } template -inline typename enable_if >, detail::expression > >::type - operator^ (const V& a, const number& b) +inline typename enable_if >, detail::expression > >::type + operator^ (const V& a, const number& b) { - return detail::expression >(a, b); + return detail::expression >(a, b); } template -inline detail::expression, detail::expression > - operator^ (const number& a, const detail::expression& b) +inline detail::expression, detail::expression > + operator^ (const number& a, const detail::expression& b) { - return detail::expression, detail::expression >(a, b); + return detail::expression, detail::expression >(a, b); } template -inline detail::expression, number > - operator^ (const detail::expression& a, const number& b) +inline detail::expression, number > + operator^ (const detail::expression& a, const number& b) { - return detail::expression, number >(a, b); + return detail::expression, number >(a, b); } template inline detail::expression, detail::expression > diff --git a/include/boost/multiprecision/detail/integer_ops.hpp b/include/boost/multiprecision/detail/integer_ops.hpp index c7ddffcb..d01e92bb 100644 --- a/include/boost/multiprecision/detail/integer_ops.hpp +++ b/include/boost/multiprecision/detail/integer_ops.hpp @@ -131,7 +131,7 @@ inline void eval_lcm(B& result, const B& a, const B& b) } -template +template inline typename enable_if_c::value == number_kind_integer>::type divide_qr(const number& x, const number& y, number& q, number& r) @@ -140,7 +140,7 @@ inline typename enable_if_c::value == number_kind_integ eval_qr(x.backend(), y.backend(), q.backend(), r.backend()); } -template +template inline typename enable_if_c::value == number_kind_integer>::type divide_qr(const number& x, const multiprecision::detail::expression& y, number& q, number& r) @@ -148,7 +148,7 @@ inline typename enable_if_c::value == number_kind_integ divide_qr(x, number(y), q, r); } -template +template inline typename enable_if_c::value == number_kind_integer>::type divide_qr(const multiprecision::detail::expression& x, const number& y, number& q, number& r) @@ -156,7 +156,7 @@ inline typename enable_if_c::value == number_kind_integ divide_qr(number(x), y, q, r); } -template +template inline typename enable_if_c::value == number_kind_integer>::type divide_qr(const multiprecision::detail::expression& x, const multiprecision::detail::expression& y, number& q, number& r) @@ -164,7 +164,7 @@ inline typename enable_if_c::value == number_kind_integ divide_qr(number(x), number(y), q, r); } -template +template inline typename enable_if, mpl::bool_::value == number_kind_integer> >, Integer>::type integer_modulus(const number& x, Integer val) { @@ -180,7 +180,7 @@ inline typename enable_if, mpl::bool_ +template inline typename enable_if_c::value == number_kind_integer, unsigned>::type lsb(const number& x) { @@ -198,7 +198,7 @@ inline typename enable_if_c +template inline typename enable_if_c::value == number_kind_integer, bool>::type bit_test(const number& x, unsigned index) { @@ -216,7 +216,7 @@ inline typename enable_if_c +template inline typename enable_if_c::value == number_kind_integer, number&>::type bit_set(number& x, unsigned index) { @@ -225,7 +225,7 @@ inline typename enable_if_c::value == number_kind_integ return x; } -template +template inline typename enable_if_c::value == number_kind_integer, number&>::type bit_unset(number& x, unsigned index) { @@ -234,7 +234,7 @@ inline typename enable_if_c::value == number_kind_integ return x; } -template +template inline typename enable_if_c::value == number_kind_integer, number&>::type bit_flip(number& x, unsigned index) { diff --git a/include/boost/multiprecision/detail/no_et_ops.hpp b/include/boost/multiprecision/detail/no_et_ops.hpp index 18728ea0..49933a8f 100644 --- a/include/boost/multiprecision/detail/no_et_ops.hpp +++ b/include/boost/multiprecision/detail/no_et_ops.hpp @@ -15,16 +15,16 @@ namespace multiprecision{ // NOTE: these operators have to be defined after the methods in default_ops.hpp. // template -inline number operator - (const number& v) +inline number operator - (const number& v) { - number result(v); + number result(v); result.backend().negate(); return BOOST_MP_MOVE(result); } template -inline number operator ~ (const number& v) +inline number operator ~ (const number& v) { - number result; + number result; eval_complement(result.backend(), v.backend()); return BOOST_MP_MOVE(result); } @@ -32,252 +32,252 @@ inline number operator ~ (const number& v) // Addition: // template -inline number operator + (const number& a, const number& b) +inline number operator + (const number& a, const number& b) { - number result; + number result; using default_ops::eval_add; eval_add(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator + (const number& a, const V& b) +inline typename enable_if >, number >::type + operator + (const number& a, const V& b) { - number result; + number result; using default_ops::eval_add; - eval_add(result.backend(), a.backend(), number::canonical_value(b)); + eval_add(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator + (const V& a, const number& b) +inline typename enable_if >, number >::type + operator + (const V& a, const number& b) { - number result; + number result; using default_ops::eval_add; - eval_add(result.backend(), b.backend(), number::canonical_value(a)); + eval_add(result.backend(), b.backend(), number::canonical_value(a)); return BOOST_MP_MOVE(result); } // // Subtraction: // template -inline number operator - (const number& a, const number& b) +inline number operator - (const number& a, const number& b) { - number result; + number result; using default_ops::eval_subtract; eval_subtract(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator - (const number& a, const V& b) +inline typename enable_if >, number >::type + operator - (const number& a, const V& b) { - number result; + number result; using default_ops::eval_subtract; - eval_subtract(result.backend(), a.backend(), number::canonical_value(b)); + eval_subtract(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator - (const V& a, const number& b) +inline typename enable_if >, number >::type + operator - (const V& a, const number& b) { - number result; + number result; using default_ops::eval_subtract; - eval_subtract(result.backend(), number::canonical_value(a), b.backend()); + eval_subtract(result.backend(), number::canonical_value(a), b.backend()); return BOOST_MP_MOVE(result); } // // Multiply: // template -inline number operator * (const number& a, const number& b) +inline number operator * (const number& a, const number& b) { - number result; + number result; using default_ops::eval_multiply; eval_multiply(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator * (const number& a, const V& b) +inline typename enable_if >, number >::type + operator * (const number& a, const V& b) { - number result; + number result; using default_ops::eval_multiply; - eval_multiply(result.backend(), a.backend(), number::canonical_value(b)); + eval_multiply(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator * (const V& a, const number& b) +inline typename enable_if >, number >::type + operator * (const V& a, const number& b) { - number result; + number result; using default_ops::eval_multiply; - eval_multiply(result.backend(), b.backend(), number::canonical_value(a)); + eval_multiply(result.backend(), b.backend(), number::canonical_value(a)); return BOOST_MP_MOVE(result); } // // divide: // template -inline number operator / (const number& a, const number& b) +inline number operator / (const number& a, const number& b) { - number result; + number result; using default_ops::eval_divide; eval_divide(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator / (const number& a, const V& b) +inline typename enable_if >, number >::type + operator / (const number& a, const V& b) { - number result; + number result; using default_ops::eval_divide; - eval_divide(result.backend(), a.backend(), number::canonical_value(b)); + eval_divide(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator / (const V& a, const number& b) +inline typename enable_if >, number >::type + operator / (const V& a, const number& b) { - number result; + number result; using default_ops::eval_divide; - eval_divide(result.backend(), number::canonical_value(a), b.backend()); + eval_divide(result.backend(), number::canonical_value(a), b.backend()); return BOOST_MP_MOVE(result); } // // modulus: // template -inline number operator % (const number& a, const number& b) +inline number operator % (const number& a, const number& b) { - number result; + number result; using default_ops::eval_modulus; eval_modulus(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator % (const number& a, const V& b) +inline typename enable_if >, number >::type + operator % (const number& a, const V& b) { - number result; + number result; using default_ops::eval_modulus; - eval_modulus(result.backend(), a.backend(), number::canonical_value(b)); + eval_modulus(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator % (const V& a, const number& b) +inline typename enable_if >, number >::type + operator % (const V& a, const number& b) { - number result; + number result; using default_ops::eval_modulus; - eval_modulus(result.backend(), number::canonical_value(a), b.backend()); + eval_modulus(result.backend(), number::canonical_value(a), b.backend()); return BOOST_MP_MOVE(result); } // // Bitwise or: // template -inline number operator | (const number& a, const number& b) +inline number operator | (const number& a, const number& b) { - number result; + number result; using default_ops::eval_bitwise_or; eval_bitwise_or(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator | (const number& a, const V& b) +inline typename enable_if >, number >::type + operator | (const number& a, const V& b) { - number result; + number result; using default_ops::eval_bitwise_or; - eval_bitwise_or(result.backend(), a.backend(), number::canonical_value(b)); + eval_bitwise_or(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator | (const V& a, const number& b) +inline typename enable_if >, number >::type + operator | (const V& a, const number& b) { - number result; + number result; using default_ops::eval_bitwise_or; - eval_bitwise_or(result.backend(), b.backend(), number::canonical_value(a)); + eval_bitwise_or(result.backend(), b.backend(), number::canonical_value(a)); return BOOST_MP_MOVE(result); } // // Bitwise xor: // template -inline number operator ^ (const number& a, const number& b) +inline number operator ^ (const number& a, const number& b) { - number result; + number result; using default_ops::eval_bitwise_xor; eval_bitwise_xor(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator ^ (const number& a, const V& b) +inline typename enable_if >, number >::type + operator ^ (const number& a, const V& b) { - number result; + number result; using default_ops::eval_bitwise_xor; - eval_bitwise_xor(result.backend(), a.backend(), number::canonical_value(b)); + eval_bitwise_xor(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator ^ (const V& a, const number& b) +inline typename enable_if >, number >::type + operator ^ (const V& a, const number& b) { - number result; + number result; using default_ops::eval_bitwise_xor; - eval_bitwise_xor(result.backend(), b.backend(), number::canonical_value(a)); + eval_bitwise_xor(result.backend(), b.backend(), number::canonical_value(a)); return BOOST_MP_MOVE(result); } // // Bitwise and: // template -inline number operator & (const number& a, const number& b) +inline number operator & (const number& a, const number& b) { - number result; + number result; using default_ops::eval_bitwise_and; eval_bitwise_and(result.backend(), a.backend(), b.backend()); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator & (const number& a, const V& b) +inline typename enable_if >, number >::type + operator & (const number& a, const V& b) { - number result; + number result; using default_ops::eval_bitwise_and; - eval_bitwise_and(result.backend(), a.backend(), number::canonical_value(b)); + eval_bitwise_and(result.backend(), a.backend(), number::canonical_value(b)); return BOOST_MP_MOVE(result); } template -inline typename enable_if >, number >::type - operator & (const V& a, const number& b) +inline typename enable_if >, number >::type + operator & (const V& a, const number& b) { - number result; + number result; using default_ops::eval_bitwise_and; - eval_bitwise_and(result.backend(), b.backend(), number::canonical_value(a)); + eval_bitwise_and(result.backend(), b.backend(), number::canonical_value(a)); return BOOST_MP_MOVE(result); } // // shifts: // template -inline typename enable_if, number >::type - operator << (const number& a, const I& b) +inline typename enable_if, number >::type + operator << (const number& a, const I& b) { - number result(a); + number result(a); using default_ops::eval_left_shift; detail::check_shift_range(b, mpl::bool_<(sizeof(I) > sizeof(std::size_t))>(), is_signed()); eval_left_shift(result.backend(), b); return BOOST_MP_MOVE(result); } template -inline typename enable_if, number >::type - operator >> (const number& a, const I& b) +inline typename enable_if, number >::type + operator >> (const number& a, const I& b) { - number result(a); + number result(a); using default_ops::eval_right_shift; detail::check_shift_range(b, mpl::bool_<(sizeof(I) > sizeof(std::size_t))>(), is_signed()); eval_right_shift(result.backend(), b); @@ -297,313 +297,313 @@ inline typename enable_if, number >::type // semantics help a great deal in return by value, so performance is still pretty good... // template -inline number operator - (number&& v) +inline number operator - (number&& v) { v.backend().negate(); - return static_cast&&>(v); + return static_cast&&>(v); } template -inline number operator ~ (number&& v) +inline number operator ~ (number&& v) { eval_complement(v.backend(), v.backend()); - return static_cast&&>(v); + return static_cast&&>(v); } // // Addition: // template -inline number operator + (number&& a, const number& b) +inline number operator + (number&& a, const number& b) { using default_ops::eval_add; eval_add(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline number operator + (const number& a, number&& b) +inline number operator + (const number& a, number&& b) { using default_ops::eval_add; eval_add(b.backend(), a.backend()); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline number operator + (number&& a, number&& b) +inline number operator + (number&& a, number&& b) { using default_ops::eval_add; eval_add(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator + (number&& a, const V& b) +inline typename enable_if >, number >::type + operator + (number&& a, const V& b) { using default_ops::eval_add; - eval_add(a.backend(), number::canonical_value(b)); - return static_cast&&>(a); + eval_add(a.backend(), number::canonical_value(b)); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator + (const V& a, number&& b) +inline typename enable_if >, number >::type + operator + (const V& a, number&& b) { using default_ops::eval_add; - eval_add(b.backend(), number::canonical_value(a)); - return static_cast&&>(b); + eval_add(b.backend(), number::canonical_value(a)); + return static_cast&&>(b); } // // Subtraction: // template -inline number operator - (number&& a, const number& b) +inline number operator - (number&& a, const number& b) { using default_ops::eval_subtract; eval_subtract(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline number operator - (const number& a, number&& b) +inline number operator - (const number& a, number&& b) { using default_ops::eval_subtract; eval_subtract(b.backend(), a.backend()); b.backend().negate(); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline number operator - (number&& a, number&& b) +inline number operator - (number&& a, number&& b) { using default_ops::eval_subtract; eval_subtract(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator - (number&& a, const V& b) +inline typename enable_if >, number >::type + operator - (number&& a, const V& b) { using default_ops::eval_subtract; - eval_subtract(a.backend(), number::canonical_value(b)); - return static_cast&&>(a); + eval_subtract(a.backend(), number::canonical_value(b)); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator - (const V& a, number&& b) +inline typename enable_if >, number >::type + operator - (const V& a, number&& b) { using default_ops::eval_subtract; - eval_subtract(b.backend(), number::canonical_value(a)); + eval_subtract(b.backend(), number::canonical_value(a)); b.backend().negate(); - return static_cast&&>(b); + return static_cast&&>(b); } // // Multiply: // template -inline number operator * (number&& a, const number& b) +inline number operator * (number&& a, const number& b) { using default_ops::eval_multiply; eval_multiply(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline number operator * (const number& a, number&& b) +inline number operator * (const number& a, number&& b) { using default_ops::eval_multiply; eval_multiply(b.backend(), a.backend()); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline number operator * (number&& a, number&& b) +inline number operator * (number&& a, number&& b) { using default_ops::eval_multiply; eval_multiply(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator * (number&& a, const V& b) +inline typename enable_if >, number >::type + operator * (number&& a, const V& b) { using default_ops::eval_multiply; - eval_multiply(a.backend(), number::canonical_value(b)); - return static_cast&&>(a); + eval_multiply(a.backend(), number::canonical_value(b)); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator * (const V& a, number&& b) +inline typename enable_if >, number >::type + operator * (const V& a, number&& b) { using default_ops::eval_multiply; - eval_multiply(b.backend(), number::canonical_value(a)); - return static_cast&&>(b); + eval_multiply(b.backend(), number::canonical_value(a)); + return static_cast&&>(b); } // // divide: // template -inline number operator / (number&& a, const number& b) +inline number operator / (number&& a, const number& b) { using default_ops::eval_divide; eval_divide(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator / (number&& a, const V& b) +inline typename enable_if >, number >::type + operator / (number&& a, const V& b) { using default_ops::eval_divide; - eval_divide(a.backend(), number::canonical_value(b)); - return static_cast&&>(a); + eval_divide(a.backend(), number::canonical_value(b)); + return static_cast&&>(a); } // // modulus: // template -inline number operator % (number&& a, const number& b) +inline number operator % (number&& a, const number& b) { using default_ops::eval_modulus; eval_modulus(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator % (number&& a, const V& b) +inline typename enable_if >, number >::type + operator % (number&& a, const V& b) { using default_ops::eval_modulus; - eval_modulus(a.backend(), number::canonical_value(b)); - return static_cast&&>(a); + eval_modulus(a.backend(), number::canonical_value(b)); + return static_cast&&>(a); } // // Bitwise or: // template -inline number operator | (number&& a, const number& b) +inline number operator | (number&& a, const number& b) { using default_ops::eval_bitwise_or; eval_bitwise_or(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline number operator | (const number& a, number&& b) +inline number operator | (const number& a, number&& b) { using default_ops::eval_bitwise_or; eval_bitwise_or(b.backend(), a.backend()); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline number operator | (number&& a, number&& b) +inline number operator | (number&& a, number&& b) { using default_ops::eval_bitwise_or; eval_bitwise_or(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator | (number&& a, const V& b) +inline typename enable_if >, number >::type + operator | (number&& a, const V& b) { using default_ops::eval_bitwise_or; - eval_bitwise_or(a.backend(), number::canonical_value(b)); - return static_cast&&>(a); + eval_bitwise_or(a.backend(), number::canonical_value(b)); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator | (const V& a, number&& b) +inline typename enable_if >, number >::type + operator | (const V& a, number&& b) { using default_ops::eval_bitwise_or; - eval_bitwise_or(b.backend(), number::canonical_value(a)); - return static_cast&&>(b); + eval_bitwise_or(b.backend(), number::canonical_value(a)); + return static_cast&&>(b); } // // Bitwise xor: // template -inline number operator ^ (number&& a, const number& b) +inline number operator ^ (number&& a, const number& b) { using default_ops::eval_bitwise_xor; eval_bitwise_xor(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline number operator ^ (const number& a, number&& b) +inline number operator ^ (const number& a, number&& b) { using default_ops::eval_bitwise_xor; eval_bitwise_xor(b.backend(), a.backend()); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline number operator ^ (number&& a, number&& b) +inline number operator ^ (number&& a, number&& b) { using default_ops::eval_bitwise_xor; eval_bitwise_xor(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator ^ (number&& a, const V& b) +inline typename enable_if >, number >::type + operator ^ (number&& a, const V& b) { using default_ops::eval_bitwise_xor; - eval_bitwise_xor(a.backend(), number::canonical_value(b)); - return static_cast&&>(a); + eval_bitwise_xor(a.backend(), number::canonical_value(b)); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator ^ (const V& a, number&& b) +inline typename enable_if >, number >::type + operator ^ (const V& a, number&& b) { using default_ops::eval_bitwise_xor; - eval_bitwise_xor(b.backend(), number::canonical_value(a)); - return static_cast&&>(b); + eval_bitwise_xor(b.backend(), number::canonical_value(a)); + return static_cast&&>(b); } // // Bitwise and: // template -inline number operator & (number&& a, const number& b) +inline number operator & (number&& a, const number& b) { using default_ops::eval_bitwise_and; eval_bitwise_and(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline number operator & (const number& a, number&& b) +inline number operator & (const number& a, number&& b) { using default_ops::eval_bitwise_and; eval_bitwise_and(b.backend(), a.backend()); - return static_cast&&>(b); + return static_cast&&>(b); } template -inline number operator & (number&& a, number&& b) +inline number operator & (number&& a, number&& b) { using default_ops::eval_bitwise_and; eval_bitwise_and(a.backend(), b.backend()); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator & (number&& a, const V& b) +inline typename enable_if >, number >::type + operator & (number&& a, const V& b) { using default_ops::eval_bitwise_and; - eval_bitwise_and(a.backend(), number::canonical_value(b)); - return static_cast&&>(a); + eval_bitwise_and(a.backend(), number::canonical_value(b)); + return static_cast&&>(a); } template -inline typename enable_if >, number >::type - operator & (const V& a, number&& b) +inline typename enable_if >, number >::type + operator & (const V& a, number&& b) { using default_ops::eval_bitwise_and; - eval_bitwise_and(b.backend(), number::canonical_value(a)); - return static_cast&&>(b); + eval_bitwise_and(b.backend(), number::canonical_value(a)); + return static_cast&&>(b); } // // shifts: // template -inline typename enable_if, number >::type - operator << (number&& a, const I& b) +inline typename enable_if, number >::type + operator << (number&& a, const I& b) { using default_ops::eval_left_shift; eval_left_shift(a.backend(), b); - return static_cast&&>(a); + return static_cast&&>(a); } template -inline typename enable_if, number >::type - operator >> (number&& a, const I& b) +inline typename enable_if, number >::type + operator >> (number&& a, const I& b) { using default_ops::eval_right_shift; eval_right_shift(a.backend(), b); - return static_cast&&>(a); + return static_cast&&>(a); } #endif diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp index 8721991c..0f6ed2bd 100644 --- a/include/boost/multiprecision/detail/number_base.hpp +++ b/include/boost/multiprecision/detail/number_base.hpp @@ -14,13 +14,19 @@ namespace boost{ namespace multiprecision{ -template +enum expression_template_option +{ + et_off = 0, + et_on = 1 +}; + +template class number; template struct is_number : public mpl::false_ {}; -template +template struct is_number > : public mpl::true_ {}; namespace detail{ @@ -79,12 +85,12 @@ struct canonical_imp typedef typename remove_cv::type>::type type; }; template -struct canonical_imp, Backend, Tag> +struct canonical_imp, Backend, Tag> { typedef B type; }; template -struct canonical_imp, Backend, Tag> +struct canonical_imp, Backend, Tag> { typedef B type; }; @@ -178,7 +184,7 @@ struct function{}; template struct backend_type; -template +template struct backend_type > { typedef T type; @@ -193,7 +199,7 @@ struct backend_type > template struct is_number : public mpl::false_{}; -template +template struct is_number > : public mpl::true_{}; template struct is_mp_number_exp : public mpl::false_{}; @@ -203,25 +209,25 @@ struct is_mp_number_exp struct combine_expression; -template +template struct combine_expression, T2> { typedef number type; }; -template +template struct combine_expression > { typedef number type; }; -template +template struct combine_expression, number > { typedef number type; }; -template +template struct combine_expression, number > { typedef typename mpl::if_c< @@ -643,14 +649,14 @@ enum number_category_type template struct number_category : public mpl::int_::is_integer ? number_kind_integer : (std::numeric_limits::max_exponent ? number_kind_floating_point : number_kind_unknown)> {}; -template +template struct number_category > : public number_category{}; template struct number_category > : public number_category::result_type>{}; template struct component_type; -template +template struct component_type > : public component_type{}; template struct component_type > : public component_type::result_type>{}; @@ -668,7 +674,7 @@ struct promote_arg::result_type type; }; -template +template inline R real_cast(const boost::multiprecision::number& val) { return val.template convert_to(); diff --git a/include/boost/multiprecision/detail/number_compare.hpp b/include/boost/multiprecision/detail/number_compare.hpp index afeabbb3..ce7f622d 100644 --- a/include/boost/multiprecision/detail/number_compare.hpp +++ b/include/boost/multiprecision/detail/number_compare.hpp @@ -31,9 +31,9 @@ template inline bool eval_eq(const B& a, const A& b) { typedef typename mpl::if_c< - is_convertible >::value, - number, - number >::type mp_type; + is_convertible >::value, + number, + number >::type mp_type; mp_type t(b); return eval_eq(a, t.backend()); } @@ -47,9 +47,9 @@ template inline bool eval_lt(const B& a, const A& b) { typedef typename mpl::if_c< - is_convertible >::value, - number, - number >::type mp_type; + is_convertible >::value, + number, + number >::type mp_type; mp_type t(b); return eval_lt(a, t.backend()); } @@ -63,9 +63,9 @@ template inline bool eval_gt(const B& a, const A& b) { typedef typename mpl::if_c< - is_convertible >::value, - number, - number >::type mp_type; + is_convertible >::value, + number, + number >::type mp_type; mp_type t(b); return eval_gt(a, t.backend()); } @@ -77,32 +77,32 @@ namespace detail{ template struct is_valid_mixed_compare : public mpl::false_ {}; -template +template struct is_valid_mixed_compare, Val> : public is_convertible> {}; /* -template +template struct is_valid_mixed_compare > : public is_convertible> {}; */ -template +template struct is_valid_mixed_compare, number > : public mpl::false_ {}; -template +template struct is_valid_mixed_compare, expression > : public mpl::bool_, number >::value> {}; -template +template struct is_valid_mixed_compare, number > : public mpl::bool_, number >::value> {}; } -template +template inline bool operator == (const number& a, const number& b) { using default_ops::eval_eq; return eval_eq(a.backend(), b.backend()); } -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator == (const number& a, const Arithmetic& b) { @@ -110,7 +110,7 @@ inline typename enable_if_c::canonical_value(b)); } /* -template +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator == (const number& a, const detail::expression& b) { @@ -119,7 +119,7 @@ inline typename enable_if, typename return eval_eq(a.backend(), t.backend()); } */ -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator == (const Arithmetic& a, const number& b) { @@ -136,7 +136,7 @@ inline typename enable_if_c +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator == (const detail::expression& a, const number& b) { @@ -163,13 +163,13 @@ inline typename enable_if +template inline bool operator != (const number& a, const number& b) { using default_ops::eval_eq; return !eval_eq(a.backend(), b.backend()); } -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator != (const number& a, const Arithmetic& b) { @@ -177,7 +177,7 @@ inline typename enable_if_c::canonical_value(b)); } /* -template +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator != (const number& a, const detail::expression& b) { @@ -186,7 +186,7 @@ inline typename enable_if, typename return !eval_eq(a.backend(), t.backend()); } */ -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator != (const Arithmetic& a, const number& b) { @@ -203,7 +203,7 @@ inline typename enable_if_c +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator != (const detail::expression& a, const number& b) { @@ -230,13 +230,13 @@ inline typename enable_if +template inline bool operator < (const number& a, const number& b) { using default_ops::eval_lt; return eval_lt(a.backend(), b.backend()); } -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator < (const number& a, const Arithmetic& b) { @@ -244,7 +244,7 @@ inline typename enable_if_c::canonical_value(b)); } /* -template +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator < (const number& a, const detail::expression& b) { @@ -253,7 +253,7 @@ inline typename enable_if, typename return eval_lt(a.backend(), t.backend()); } */ -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator < (const Arithmetic& a, const number& b) { @@ -270,7 +270,7 @@ inline typename enable_if_c +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator < (const detail::expression& a, const number& b) { @@ -298,13 +298,13 @@ inline typename enable_if +template inline bool operator > (const number& a, const number& b) { using default_ops::eval_gt; return eval_gt(a.backend(), b.backend()); } -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator > (const number& a, const Arithmetic& b) { @@ -312,7 +312,7 @@ inline typename enable_if_c::canonical_value(b)); } /* -template +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator > (const number& a, const detail::expression& b) { @@ -321,7 +321,7 @@ inline typename enable_if, typename return eval_gt(a.backend(), t.backend()); } */ -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator > (const Arithmetic& a, const number& b) { @@ -338,7 +338,7 @@ inline typename enable_if_c +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator > (const detail::expression& a, const number& b) { @@ -366,13 +366,13 @@ inline typename enable_if +template inline bool operator <= (const number& a, const number& b) { using default_ops::eval_gt; return !eval_gt(a.backend(), b.backend()); } -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator <= (const number& a, const Arithmetic& b) { @@ -380,7 +380,7 @@ inline typename enable_if_c::canonical_value(b)); } /* -template +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator <= (const number& a, const detail::expression& b) { @@ -389,7 +389,7 @@ inline typename enable_if, typename return !eval_gt(a.backend(), t.backend()); } */ -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator <= (const Arithmetic& a, const number& b) { @@ -406,7 +406,7 @@ inline typename enable_if_c +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator <= (const detail::expression& a, const number& b) { @@ -434,13 +434,13 @@ inline typename enable_if +template inline bool operator >= (const number& a, const number& b) { using default_ops::eval_lt; return !eval_lt(a.backend(), b.backend()); } -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator >= (const number& a, const Arithmetic& b) { @@ -448,7 +448,7 @@ inline typename enable_if_c::canonical_value(b)); } /* -template +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator >= (const number& a, const detail::expression& b) { @@ -457,7 +457,7 @@ inline typename enable_if, typename return !eval_lt(a.backend(), t.backend()); } */ -template +template inline typename enable_if_c, Arithmetic>::value, bool>::type operator >= (const Arithmetic& a, const number& b) { @@ -474,7 +474,7 @@ inline typename enable_if_c +template inline typename enable_if, typename detail::expression::result_type>, bool>::type operator >= (const detail::expression& a, const number& b) { diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 56834437..6495445b 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -2151,7 +2151,7 @@ namespace std{ // // numeric_limits [partial] specializations for the types declared in this header: // -template +template class numeric_limits, ExpressionTemplates> > { typedef boost::multiprecision::number, ExpressionTemplates> number_type; @@ -2259,10 +2259,10 @@ private: static const data_initializer initializer; }; -template +template const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; -template +template class numeric_limits, ExpressionTemplates> > { typedef boost::multiprecision::number, ExpressionTemplates> number_type; @@ -2303,54 +2303,54 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template +template BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template +template BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif -template +template class numeric_limits > { typedef boost::multiprecision::number number_type; @@ -2401,54 +2401,54 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; -template +template BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; -template +template BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; #endif -template +template class numeric_limits > { typedef boost::multiprecision::number number_type; @@ -2500,49 +2500,49 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; -template +template BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; -template +template BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; #endif diff --git a/include/boost/multiprecision/miller_rabin.hpp b/include/boost/multiprecision/miller_rabin.hpp index f1961bf2..f9579532 100644 --- a/include/boost/multiprecision/miller_rabin.hpp +++ b/include/boost/multiprecision/miller_rabin.hpp @@ -11,7 +11,7 @@ namespace boost{ namespace multiprecision{ -template +template bool check_small_factors(const number& n) { static const boost::uint32_t small_factors1[] = { @@ -117,7 +117,7 @@ inline bool is_small_prime(unsigned n) return false; } -template +template typename enable_if_c::value == number_kind_integer, bool>::type miller_rabin_test(const number& n, unsigned trials, Engine& gen) { @@ -178,7 +178,7 @@ typename enable_if_c::value == number_kind_integer, boo #endif } -template +template bool miller_rabin_test(const number& x, unsigned trials) { static mt19937 gen; diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 7742c65c..ec3085c7 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -1103,7 +1103,7 @@ inline int digits() BOOST_NOEXCEPT return boost::multiprecision::backends::detail::get_default_precision(); } template <> -inline int digits, false> >() BOOST_NOEXCEPT +inline int digits, boost::multiprecision::et_off> >() BOOST_NOEXCEPT { return boost::multiprecision::backends::detail::get_default_precision(); } @@ -1117,7 +1117,7 @@ namespace std{ // // numeric_limits [partial] specializations for the types declared in this header: // -template +template class numeric_limits, ExpressionTemplates> > { typedef boost::multiprecision::number, ExpressionTemplates> number_type; @@ -1249,60 +1249,60 @@ private: static const data_initializer initializer; }; -template +template const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template +template BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent; -template +template BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent; -template +template BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template +template BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template +template BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif -template +template class numeric_limits, ExpressionTemplates> > { typedef boost::multiprecision::number, ExpressionTemplates> number_type; @@ -1343,49 +1343,49 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template +template BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template +template BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index e61372d9..2ec587b7 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -34,7 +34,7 @@ namespace boost{ namespace multiprecision{ #pragma warning(disable:4127 4714) #endif -template +template class number { typedef number self_type; @@ -87,16 +87,16 @@ public: m_backend = canonical_value(v); } */ - template + template BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} - template + template BOOST_FORCEINLINE number(const number& val, typename enable_if_c<(boost::is_convertible::value && !detail::is_restricted_conversion::value)>::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval() = std::declval())) : m_backend(val.backend()) {} - template + template explicit number(const number& val, typename enable_if_c< (!detail::is_explicitly_convertible::value) >::type* = 0) @@ -106,7 +106,7 @@ public: // detail::generic_interconvert(backend(), val.backend(), number_category(), number_category()); } - template + template explicit BOOST_FORCEINLINE number(const number& val, typename enable_if_c< (detail::is_explicitly_convertible::value && (detail::is_restricted_conversion::value || !boost::is_convertible::value)) @@ -119,7 +119,7 @@ public: using default_ops::assign_components; assign_components(m_backend, canonical_value(v1), canonical_value(v2)); } - template + template BOOST_FORCEINLINE number(const number& v1, const number& v2, typename enable_if >::type* = 0) { using default_ops::assign_components; @@ -547,7 +547,7 @@ private: using default_ops::eval_convert_to; eval_convert_to(result, m_backend); } - template + template void convert_to_imp(number* result)const { result->assign(*this); @@ -1584,7 +1584,7 @@ public: // the non-member operators way easier if they are: // static BOOST_FORCEINLINE BOOST_CONSTEXPR const Backend& canonical_value(const self_type& v) BOOST_NOEXCEPT { return v.m_backend; } - template + template static BOOST_FORCEINLINE BOOST_CONSTEXPR const B2& canonical_value(const number& v) BOOST_NOEXCEPT { return v.backend(); } template static BOOST_FORCEINLINE BOOST_CONSTEXPR typename disable_if::type, V>, typename detail::canonical::type>::type @@ -1596,7 +1596,7 @@ public: }; -template +template inline std::ostream& operator << (std::ostream& os, const number& r) { std::streamsize d = os.precision(); @@ -1625,7 +1625,7 @@ inline std::ostream& operator << (std::ostream& os, const expression +template inline std::istream& operator >> (std::istream& is, number& r) { std::string s; @@ -1634,7 +1634,7 @@ inline std::istream& operator >> (std::istream& is, number +template BOOST_FORCEINLINE void swap(number& a, number& b) { a.swap(b); @@ -1645,7 +1645,7 @@ BOOST_FORCEINLINE void swap(number& a, number class rational; -template +template inline std::istream& operator >> (std::istream& is, rational >& r) { std::string s1; @@ -1680,37 +1680,37 @@ inline std::istream& operator >> (std::istream& is, rational +template typename enable_if, bool>::type operator == (const rational >& a, const Arithmetic& b) { return a == multiprecision::number(b); } -template +template typename enable_if, bool>::type operator == (const Arithmetic& b, const rational >& a) { return a == multiprecision::number(b); } -template +template typename enable_if, bool>::type operator != (const rational >& a, const Arithmetic& b) { return a != multiprecision::number(b); } -template +template typename enable_if, bool>::type operator != (const Arithmetic& b, const rational >& a) { return a != multiprecision::number(b); } -template +template inline multiprecision::number numerator(const rational >& a) { return a.numerator(); } -template +template inline multiprecision::number denominator(const rational >& a) { return a.denominator(); @@ -1723,7 +1723,7 @@ namespace numeric { namespace ublas { template class sparse_vector_element; -template +template inline bool operator == (const sparse_vector_element& a, const ::boost::multiprecision::number& b) { typedef typename sparse_vector_element::const_reference ref_type; diff --git a/include/boost/multiprecision/random.hpp b/include/boost/multiprecision/random.hpp index d60cfb72..6d0518a6 100644 --- a/include/boost/multiprecision/random.hpp +++ b/include/boost/multiprecision/random.hpp @@ -17,7 +17,7 @@ namespace boost{ namespace random{ namespace detail{ // Need to find a better solution, like make Boost.Random safe to use with // UDT's and depricate/remove this header altogether. // -template +template boost::multiprecision::number generate_uniform_int(Engine& eng, const boost::multiprecision::number& min_value, const boost::multiprecision::number& max_value); @@ -30,7 +30,7 @@ namespace boost{ namespace random{ namespace detail{ -template +template struct subtract, true> { typedef boost::multiprecision::number result_type; @@ -39,7 +39,7 @@ struct subtract, tru } -template +template class independent_bits_engine > { public: @@ -198,7 +198,7 @@ private: Engine _base; }; -template +template class uniform_smallint > { public: @@ -381,7 +381,7 @@ private: namespace detail{ -template +template struct select_uniform_01 > { template @@ -391,7 +391,7 @@ struct select_uniform_01 +template boost::multiprecision::number generate_uniform_int( Engine& eng, const boost::multiprecision::number& min_value, const boost::multiprecision::number& max_value, @@ -557,7 +557,7 @@ boost::multiprecision::number } } -template +template inline boost::multiprecision::number generate_uniform_int(Engine& eng, const boost::multiprecision::number& min_value, const boost::multiprecision::number& max_value) { diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index 6dd07d6f..b7a37ed8 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -259,7 +259,7 @@ struct is_explicitly_convertible > : public is_e namespace std{ -template +template class numeric_limits, ExpressionTemplates> > : public std::numeric_limits > { typedef std::numeric_limits > base_type; @@ -280,9 +280,9 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; #endif diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 6aef3e63..a4e2e701 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -629,7 +629,7 @@ typedef number tom_rational; namespace std{ -template +template class numeric_limits > { typedef boost::multiprecision::number number_type; @@ -680,49 +680,49 @@ public: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::digits10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_digits10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_signed; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_integer; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_exact; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::radix; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::min_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent; -template +template BOOST_CONSTEXPR_OR_CONST int numeric_limits >::max_exponent10; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_infinity; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_quiet_NaN; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_signaling_NaN; -template +template BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits >::has_denorm; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::has_denorm_loss; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_iec559; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_bounded; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::is_modulo; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::traps; -template +template BOOST_CONSTEXPR_OR_CONST bool numeric_limits >::tinyness_before; -template +template BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits >::round_style; #endif diff --git a/performance/arithmetic_backend.hpp b/performance/arithmetic_backend.hpp index 3e9028a2..16aef4b1 100644 --- a/performance/arithmetic_backend.hpp +++ b/performance/arithmetic_backend.hpp @@ -522,7 +522,7 @@ inline double real_cast(concepts::real_concept r namespace std{ -template +template class numeric_limits, ExpressionTemplates > > : public std::numeric_limits { typedef std::numeric_limits base_type; diff --git a/performance/delaunay_test.cpp b/performance/delaunay_test.cpp index cb4ba42c..593fd5a4 100644 --- a/performance/delaunay_test.cpp +++ b/performance/delaunay_test.cpp @@ -270,14 +270,14 @@ int main() std::cout << "calculating...\n"; do_calc >("int64_t, int64_t"); - do_calc, false>, number, false> > >("arithmetic_backend"); + do_calc, et_off>, number, et_off> > >("arithmetic_backend"); do_calc >("int64_t, int128_t"); do_calc >("int64_t, int128_t"); - do_calc, true> > >("int64_t, int128_t (ET)"); + do_calc, et_on> > >("int64_t, int128_t (ET)"); do_calc >("int64_t, cpp_int"); - do_calc, false> > >("int64_t, cpp_int (no ET's)"); + do_calc, et_off> > >("int64_t, cpp_int (no ET's)"); do_calc > > >("int64_t, cpp_int(128-bit cache)"); - do_calc, false> > >("int64_t, cpp_int (128-bit Cache no ET's)"); + do_calc, et_off> > >("int64_t, cpp_int (128-bit Cache no ET's)"); return 0; } diff --git a/performance/miller_rabin_performance.cpp b/performance/miller_rabin_performance.cpp index fe202391..7dd4d49b 100644 --- a/performance/miller_rabin_performance.cpp +++ b/performance/miller_rabin_performance.cpp @@ -136,7 +136,7 @@ int main() { using namespace boost::multiprecision; #ifdef TEST_CPP_INT - test_miller_rabin, false> >("cpp_int (no Expression templates)"); + test_miller_rabin, et_off> >("cpp_int (no Expression templates)"); test_miller_rabin("cpp_int"); test_miller_rabin > >("cpp_int (128-bit cache)"); test_miller_rabin > >("cpp_int (256-bit cache)"); @@ -145,12 +145,12 @@ int main() test_miller_rabin("int1024_t"); #endif #ifdef TEST_MPZ - test_miller_rabin >("mpz_int (no Expression templates)"); + test_miller_rabin >("mpz_int (no Expression templates)"); test_miller_rabin("mpz_int"); std::cout << "Time for mpz_int (native Miller Rabin Test) = " << test_miller_rabin_gmp() << std::endl; #endif #ifdef TEST_TOMMATH - test_miller_rabin >("tom_int (no Expression templates)"); + test_miller_rabin >("tom_int (no Expression templates)"); test_miller_rabin("tom_int"); #endif mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index d2f95d07..5327e055 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -233,7 +233,7 @@ int main() std::cout << "Allocation Counts for Horner Evaluation:\n"; #ifdef TEST_MPFR basic_allocation_test("mpfr_float_50", mpfr_float_50(2)); - basic_allocation_test("mpfr_float_50 - no expression templates", number, false>(2)); + basic_allocation_test("mpfr_float_50 - no expression templates", number, et_off>(2)); #endif #ifdef TEST_MPFR_CLASS basic_allocation_test("mpfr_class", mpfr_class(2)); @@ -245,7 +245,7 @@ int main() std::cout << "Allocation Counts for boost::math::tools::evaluate_polynomial:\n"; #ifdef TEST_MPFR poly_allocation_test("mpfr_float_50", mpfr_float_50(2)); - poly_allocation_test("mpfr_float_50 - no expression templates", number, false>(2)); + poly_allocation_test("mpfr_float_50 - no expression templates", number, et_off>(2)); #endif #ifdef TEST_MPFR_CLASS poly_allocation_test("mpfr_class", mpfr_class(2)); @@ -261,12 +261,12 @@ int main() time_proc("Bessel Functions - double", test_bessel); time_proc("Bessel Functions - real_concept", test_bessel); time_proc("Bessel Functions - arithmetic_backend", test_bessel > >); - time_proc("Bessel Functions - arithmetic_backend - no expression templates", test_bessel, false> >); + time_proc("Bessel Functions - arithmetic_backend - no expression templates", test_bessel, et_off> >); time_proc("Non-central T - double", test_nct); time_proc("Non-central T - real_concept", test_nct); time_proc("Non-central T - arithmetic_backend", test_nct > >); - time_proc("Non-central T - arithmetic_backend - no expression templates", test_nct, false> >); + time_proc("Non-central T - arithmetic_backend - no expression templates", test_nct, et_off> >); #endif // @@ -288,7 +288,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_50", test_bessel, 3); - time_proc("mpf_float_50 (no expression templates", test_bessel, false> >, 3); + time_proc("mpf_float_50 (no expression templates", test_bessel, et_off> >, 3); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_bessel, 3); @@ -314,7 +314,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_100", test_bessel); - time_proc("mpf_float_100 (no expression templates", test_bessel, false> >); + time_proc("mpf_float_100 (no expression templates", test_bessel, et_off> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_bessel); @@ -341,7 +341,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_50", test_polynomial); - time_proc("mpf_float_50 (no expression templates", test_polynomial, false> >); + time_proc("mpf_float_50 (no expression templates", test_polynomial, et_off> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_polynomial); @@ -367,7 +367,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_100", test_polynomial); - time_proc("mpf_float_100 (no expression templates", test_polynomial, false> >); + time_proc("mpf_float_100 (no expression templates", test_polynomial, et_off> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_polynomial); @@ -393,7 +393,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_50", test_nct); - time_proc("mpf_float_50 (no expression templates", test_nct, false> >); + time_proc("mpf_float_50 (no expression templates", test_nct, et_off> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_nct); @@ -419,7 +419,7 @@ int main() #endif #ifdef TEST_MPF time_proc("mpf_float_100", test_nct); - time_proc("mpf_float_100 (no expression templates", test_nct, false> >); + time_proc("mpf_float_100 (no expression templates", test_nct, et_off> >); #endif #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_nct); diff --git a/test/compile_fail/operator_fail_01.cpp b/test/compile_fail/operator_fail_01.cpp index 03dd4d46..8b13b385 100644 --- a/test/compile_fail/operator_fail_01.cpp +++ b/test/compile_fail/operator_fail_01.cpp @@ -9,8 +9,8 @@ using namespace boost::multiprecision; int main() { - number, true> a(2); - number, false> b(2); + number, et_on> a(2); + number, et_off> b(2); a = a + b; } diff --git a/test/concepts/number_concept_check.cpp b/test/concepts/number_concept_check.cpp index 106fbe5a..ce7d5672 100644 --- a/test/concepts/number_concept_check.cpp +++ b/test/concepts/number_concept_check.cpp @@ -186,7 +186,7 @@ void foo() test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::number, false>()); + test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif } diff --git a/test/concepts/sf_concept_check_basic.cpp b/test/concepts/sf_concept_check_basic.cpp index 16cecfce..14244129 100644 --- a/test/concepts/sf_concept_check_basic.cpp +++ b/test/concepts/sf_concept_check_basic.cpp @@ -139,7 +139,7 @@ void foo() test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::number, false>()); + test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif } diff --git a/test/concepts/sf_concept_check_bessel.cpp b/test/concepts/sf_concept_check_bessel.cpp index 0c3c3935..e6670e25 100644 --- a/test/concepts/sf_concept_check_bessel.cpp +++ b/test/concepts/sf_concept_check_bessel.cpp @@ -104,7 +104,7 @@ void foo() test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::number, false>()); + test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif } diff --git a/test/concepts/sf_concept_check_elliptic.cpp b/test/concepts/sf_concept_check_elliptic.cpp index e55cace4..7365f89e 100644 --- a/test/concepts/sf_concept_check_elliptic.cpp +++ b/test/concepts/sf_concept_check_elliptic.cpp @@ -110,7 +110,7 @@ void foo() test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::number, false>()); + test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif } diff --git a/test/concepts/sf_concept_check_gamma.cpp b/test/concepts/sf_concept_check_gamma.cpp index 2dcdcaf8..9ab61912 100644 --- a/test/concepts/sf_concept_check_gamma.cpp +++ b/test/concepts/sf_concept_check_gamma.cpp @@ -126,7 +126,7 @@ void foo() test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::number, false>()); + test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif } diff --git a/test/concepts/sf_concept_check_poly.cpp b/test/concepts/sf_concept_check_poly.cpp index fff337e9..0bc21001 100644 --- a/test/concepts/sf_concept_check_poly.cpp +++ b/test/concepts/sf_concept_check_poly.cpp @@ -101,7 +101,7 @@ void foo() test_extra(boost::multiprecision::cpp_dec_float_50()); #endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET - test_extra(boost::multiprecision::number, false>()); + test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif } diff --git a/test/include_test/cpp_int_include_test.cpp b/test/include_test/cpp_int_include_test.cpp index 7e665657..a5f33323 100644 --- a/test/include_test/cpp_int_include_test.cpp +++ b/test/include_test/cpp_int_include_test.cpp @@ -8,9 +8,9 @@ using namespace boost::multiprecision; number > a; -number, false> b; -number, false> c; -number, false> d; -number, false> e; +number, et_off> b; +number, et_off> c; +number, et_off> d; +number, et_off> e; diff --git a/test/math/table_type.hpp b/test/math/table_type.hpp index c3b5cee3..a6a526e5 100644 --- a/test/math/table_type.hpp +++ b/test/math/table_type.hpp @@ -27,7 +27,7 @@ inline std::ostream& operator << (std::ostream& os, string_table_entry const & w return os << static_cast(what); } -template +template struct table_type > { typedef string_table_entry type; diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 4a3e83b4..f972d761 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -203,7 +203,7 @@ struct related_type { typedef boost::multiprecision::int256_t type; }; -template +template struct related_type, ET> > { typedef boost::multiprecision::number, ET> type; @@ -1654,7 +1654,7 @@ int main() #endif #ifdef TEST_CPP_DEC_FLOAT test(); - test, false> >(); + test, boost::multiprecision::et_off> >(); #endif #ifdef TEST_MPFR test(); @@ -1679,13 +1679,13 @@ int main() #endif #ifdef TEST_CPP_INT_2 test(); - test, false> >(); + test, boost::multiprecision::et_off> >(); test > >(); #endif #ifdef TEST_CPP_INT_3 // Again with "trivial" backends: - test, false > >(); - test, false > >(); + test, boost::multiprecision::et_off > >(); + test, boost::multiprecision::et_off > >(); #endif #ifdef TEST_CPP_INT_BR test >(); diff --git a/test/test_constexpr.cpp b/test/test_constexpr.cpp index 66e601b1..8669141b 100644 --- a/test/test_constexpr.cpp +++ b/test/test_constexpr.cpp @@ -31,9 +31,9 @@ void test3() using namespace boost::multiprecision; -template void test1, false> >(); -template void test1, false> >(); -template void test3, false> >(); -template void test2, false> >(); +template void test1, et_off> >(); +template void test1, et_off> >(); +template void test3, et_off> >(); +template void test2, et_off> >(); #endif \ No newline at end of file diff --git a/test/test_cpp_int_conv.cpp b/test/test_cpp_int_conv.cpp index b21d91a5..62b84e55 100644 --- a/test/test_cpp_int_conv.cpp +++ b/test/test_cpp_int_conv.cpp @@ -48,7 +48,7 @@ int main() int128_t i6(i4); BOOST_TEST(i6 == -5677334); - number, false> i7(i3); + number, et_off> i7(i3); BOOST_TEST(i7 == -1234567); int256_t i8(i6); @@ -57,13 +57,13 @@ int main() i7.assign(4.0); BOOST_TEST(i7 == 4); - number, false> i9(-5677334); + number, et_off> i9(-5677334); i7 = i9; BOOST_TEST(i7 == -5677334); - i7 = number, false>(i9); + i7 = number, et_off>(i9); BOOST_TEST(i7 == -5677334); - i9 = static_cast, false> >(i7); + i9 = static_cast, et_off> >(i7); BOOST_TEST(i9 == -5677334); ++i9; diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp index d2973446..591e550d 100644 --- a/test/test_float_io.cpp +++ b/test/test_float_io.cpp @@ -214,21 +214,21 @@ struct max_digits10_proxy static const unsigned value = std::numeric_limits::digits10 + 5; }; #ifdef TEST_CPP_DEC_FLOAT -template +template struct max_digits10_proxy, ET> > { static const unsigned value = std::numeric_limits, ET> >::max_digits10; }; #endif #ifdef TEST_MPF_50 -template +template struct max_digits10_proxy, ET> > { static const unsigned value = std::numeric_limits, ET> >::max_digits10; }; #endif #ifdef TEST_MPFR_50 -template +template struct max_digits10_proxy, ET> > { static const unsigned value = std::numeric_limits, ET> >::max_digits10; diff --git a/test/ublas_interop/test1.hpp b/test/ublas_interop/test1.hpp index db44c15f..b732c66e 100644 --- a/test/ublas_interop/test1.hpp +++ b/test/ublas_interop/test1.hpp @@ -19,7 +19,7 @@ #include -typedef boost::multiprecision::number, false> mp_test_type; +typedef boost::multiprecision::number, boost::multiprecision::et_off> mp_test_type; //typedef double mp_test_type; #define USE_RANGE diff --git a/test/ublas_interop/test2.hpp b/test/ublas_interop/test2.hpp index 8dfc0a61..232b7e2c 100644 --- a/test/ublas_interop/test2.hpp +++ b/test/ublas_interop/test2.hpp @@ -18,7 +18,7 @@ #include -typedef boost::multiprecision::number, false> mp_test_type; +typedef boost::multiprecision::number, boost::multiprecision::et_off> mp_test_type; //typedef double mp_test_type; #define USE_RANGE diff --git a/test/ublas_interop/test3.hpp b/test/ublas_interop/test3.hpp index e884d80c..97becba0 100644 --- a/test/ublas_interop/test3.hpp +++ b/test/ublas_interop/test3.hpp @@ -19,7 +19,7 @@ #include -typedef boost::multiprecision::number, false> mp_test_type; +typedef boost::multiprecision::number, boost::multiprecision::et_off> mp_test_type; //typedef double mp_test_type; #define USE_RANGE diff --git a/test/ublas_interop/test4.hpp b/test/ublas_interop/test4.hpp index 6001e9c4..c5ed3eba 100644 --- a/test/ublas_interop/test4.hpp +++ b/test/ublas_interop/test4.hpp @@ -19,7 +19,7 @@ #include -typedef boost::multiprecision::number, false> mp_test_type; +typedef boost::multiprecision::number, boost::multiprecision::et_off> mp_test_type; //typedef double mp_test_type; #define USE_RANGE diff --git a/test/ublas_interop/test5.hpp b/test/ublas_interop/test5.hpp index 639cecaf..dc345198 100644 --- a/test/ublas_interop/test5.hpp +++ b/test/ublas_interop/test5.hpp @@ -19,7 +19,7 @@ #include -typedef boost::multiprecision::number, false> mp_test_type; +typedef boost::multiprecision::number, boost::multiprecision::et_off> mp_test_type; //typedef double mp_test_type; #define USE_RANGE diff --git a/test/ublas_interop/test7.hpp b/test/ublas_interop/test7.hpp index 40546991..ad990859 100644 --- a/test/ublas_interop/test7.hpp +++ b/test/ublas_interop/test7.hpp @@ -19,7 +19,7 @@ #include -typedef boost::multiprecision::number, false> mp_test_type; +typedef boost::multiprecision::number, boost::multiprecision::et_off> mp_test_type; //typedef double mp_test_type; #define USE_RANGE From a2c8fc060fcd45828b3f08bd4a93dab5b05ea56c Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 6 Sep 2012 09:52:28 +0000 Subject: [PATCH 234/256] Rebuild docs. [SVN r80419] --- .../boost_multiprecision/indexes/s01.html | 4 ++-- .../boost_multiprecision/indexes/s02.html | 4 ++-- .../boost_multiprecision/indexes/s03.html | 4 ++-- .../boost_multiprecision/indexes/s04.html | 4 ++-- doc/html/boost_multiprecision/intro.html | 8 +++---- .../boost_multiprecision/ref/cpp_int_ref.html | 16 ++++++------- doc/html/boost_multiprecision/ref/number.html | 24 +++++++++---------- .../tut/ints/cpp_int.html | 16 ++++++------- .../boost_multiprecision/tut/primetest.html | 4 ++-- doc/html/index.html | 2 +- 10 files changed, 43 insertions(+), 43 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 6657ceb9..ad20bd40 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    +Function Index

    A B C D E F I L M P R S T Z

    diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index 3e4124d3..d1ad0b8d 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

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    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 2cfc4d61..1f790e8f 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    C I L M T U

    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index d02da93c..21e9dbb6 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G I L M N O P R S T U Z

    diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index 8022566f..699be148 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -82,7 +82,7 @@ namespace mp = boost::multiprecision; // Reduce the typing a bit later... -typedef mp::number<mp::mpfr_float_backend<300>, false> my_float; +typedef mp::number<mp::mpfr_float_backend<300>, et_off> my_float; my_float a, b, c; // These variables have 300 decimal digits precision @@ -115,8 +115,8 @@

    Mixed arithmetic will fail if the conversion is either ambiguous or explicit:

    -
    number<cpp_int_backend<>, false> a(2);
-number<cpp_int_backend<>, true>  b(3);
+
    number<cpp_int_backend<>, et_off> a(2);
+number<cpp_int_backend<>, et_on>  b(3);
 
 b = a * b; // Error, implicit conversion could go either way.
 b = a * 3.14; // Error, no operator overload if the conversion would be explicit.
@@ -135,7 +135,7 @@
       move aware and have overloads that look something like:
     
    
 
    template <class B>
-number<B, false> operator + (number&& a, const number& b)
+number<B, et_off> operator + (number&& a, const number& b)
 {
     return std::move(a += b);
 }
diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html
index acc1b8c9..0b84e4e9 100644
--- a/doc/html/boost_multiprecision/ref/cpp_int_ref.html
+++ b/doc/html/boost_multiprecision/ref/cpp_int_ref.html
@@ -27,16 +27,16 @@
 typedef number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
 
 // Fixed precision unsigned types:
-typedef number<cpp_int_backend<128, false, void>, false>   uint128_t;
-typedef number<cpp_int_backend<256, false, void>, false>   uint256_t;
-typedef number<cpp_int_backend<512, false, void>, false>   uint512_t;
-typedef number<cpp_int_backend<1024, false, void>, false>  uint1024_t;
+typedef number<cpp_int_backend<128, false, void>, et_off>   uint128_t;
+typedef number<cpp_int_backend<256, false, void>, et_off>   uint256_t;
+typedef number<cpp_int_backend<512, false, void>, et_off>   uint512_t;
+typedef number<cpp_int_backend<1024, false, void>, et_off>  uint1024_t;
 
 // Fixed precision signed types:
-typedef number<cpp_int_backend<128, true, void>, false>    int128_t;
-typedef number<cpp_int_backend<256, true, void>, false>    int256_t;
-typedef number<cpp_int_backend<512, true, void>, false>    int512_t;
-typedef number<cpp_int_backend<1024, true, void>, false>   int1024_t;
+typedef number<cpp_int_backend<128, true, void>, et_off>    int128_t;
+typedef number<cpp_int_backend<256, true, void>, et_off>    int256_t;
+typedef number<cpp_int_backend<512, true, void>, et_off>    int512_t;
+typedef number<cpp_int_backend<1024, true, void>, et_off>   int1024_t;
 
 }} // namespaces
 
    
diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html
index 3c10b8c3..3969151d 100644
--- a/doc/html/boost_multiprecision/ref/number.html
+++ b/doc/html/boost_multiprecision/ref/number.html
@@ -23,7 +23,7 @@
       
 
    namespace boost{ namespace multiprecision{
 
-template <class Backend, bool ExpressionTemplates = true>
+template <class Backend, expression_template_option ExpressionTemplates = true>
 class number
 {
    number();
@@ -100,14 +100,14 @@
 bool operator>=(const see-below&, const see-below&);
 
 // Swap:
-template <class Backend, bool ExpressionTemplates>
+template <class Backend, expression_template_option ExpressionTemplates>
 void swap(number<Backend, ExpressionTemplates>& a, number<Backend, ExpressionTemplates>& b);
 
 // iostream support:
-template <class Backend, bool ExpressionTemplates>
+template <class Backend, expression_template_option ExpressionTemplates>
 std::ostream& operator << (std::ostream& os, const number<Backend, ExpressionTemplates>& r);
 std::ostream& operator << (std::ostream& os, const unmentionable-expression-template-type& r);
-template <class Backend, bool ExpressionTemplates>
+template <class Backend, expression_template_option ExpressionTemplates>
 std::istream& operator >> (std::istream& is, number<Backend, ExpressionTemplates>& r);
 
 // Non-member function standard library support:
@@ -156,7 +156,7 @@
 // Integer specific functions:
 unmentionable-expression-template-type    pow(const number-or-expression-template-type&, unsigned);
 unmentionable-expression-template-type    powm(const number-or-expression-template-type& b, const number-or-expression-template-type& p, const number-or-expression-template-type& m);
-template <class Backend, bool ExpressionTemplates>
+template <class Backend, expression_template_option ExpressionTemplates>
 void divide_qr(const number-or-expression-template-type& x, const number-or-expression-template-type& y,
                number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r);
 template <class Integer>
@@ -194,7 +194,7 @@
 // numeric_limits support:
 namespace std{
 
-template <class Backend, bool ExpressionTemplates>
+template <class Backend, expression_template_option ExpressionTemplates>
 struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> >
 {
    /* Usual members here */
@@ -206,7 +206,7 @@
 
         Description
       
-
    template <class Backend, bool ExpressionTemplates = true>
+
    template <class Backend, expression_template_option ExpressionTemplates = true>
 class number;
 
    
 
    
@@ -496,7 +496,7 @@
           
 
  • 
             Type number<Backend,
-            false>
+            et_off>
             when ExpressionTemplates
             is false.
           
    • 
@@ -526,11 +526,11 @@
         Iostream
         Support
       
-
    template <class Backend, bool ExpressionTemplates>
+
    template <class Backend, expression_template_option ExpressionTemplates>
 std::ostream& operator << (std::ostream& os, const number<Backend, ExpressionTemplates>& r);
 template <class Unspecified...>
 std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r);
-template <class Backend, bool ExpressionTemplates>
+template <class Backend, expression_template_option ExpressionTemplates>
 inline std::istream& operator >> (std::istream& is, number<Backend, ExpressionTemplates>& r)
 
    
 
    
@@ -582,7 +582,7 @@
 
    
         These functions all behave exactly as their standard library counterparts
         do: their argument is either an instance of number
-        or an expression template derived from it; If the argument is of type number<Backend, false>
+        or an expression template derived from it; If the argument is of type number<Backend, et_off>
         then that is also the return type, otherwise the return type is an expression
         template.
       
    
@@ -660,7 +660,7 @@
 
    
         Returns bp mod m as an expression template.
       
    
-
    template <class Backend, bool ExpressionTemplates>
+
    template <class Backend, expression_template_option ExpressionTemplates>
 bool divide_qr(const number-or-expression-template-type& x, const number-or-expression-template-type& y,
                number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r);
 
    
diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html
index c1be7123..988e9909 100644
--- a/doc/html/boost_multiprecision/tut/ints/cpp_int.html
+++ b/doc/html/boost_multiprecision/tut/ints/cpp_int.html
@@ -32,16 +32,16 @@
 typedef number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
 
 // Fixed precision unsigned types:
-typedef number<cpp_int_backend<128, false, void>, false>   uint128_t;
-typedef number<cpp_int_backend<256, false, void>, false>   uint256_t;
-typedef number<cpp_int_backend<512, false, void>, false>   uint512_t;
-typedef number<cpp_int_backend<1024, false, void>, false>  uint1024_t;
+typedef number<cpp_int_backend<128, false, void>, et_off>   uint128_t;
+typedef number<cpp_int_backend<256, false, void>, et_off>   uint256_t;
+typedef number<cpp_int_backend<512, false, void>, et_off>   uint512_t;
+typedef number<cpp_int_backend<1024, false, void>, et_off>  uint1024_t;
 
 // Fixed precision signed types:
-typedef number<cpp_int_backend<128, true, void>, false>    int128_t;
-typedef number<cpp_int_backend<256, true, void>, false>    int256_t;
-typedef number<cpp_int_backend<512, true, void>, false>    int512_t;
-typedef number<cpp_int_backend<1024, true, void>, false>   int1024_t;
+typedef number<cpp_int_backend<128, true, void>, et_off>    int128_t;
+typedef number<cpp_int_backend<256, true, void>, et_off>    int256_t;
+typedef number<cpp_int_backend<512, true, void>, et_off>    int512_t;
+typedef number<cpp_int_backend<1024, true, void>, et_off>   int1024_t;
 
 }} // namespaces
 
    
diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html
index baf4517d..49006337 100644
--- a/doc/html/boost_multiprecision/tut/primetest.html
+++ b/doc/html/boost_multiprecision/tut/primetest.html
@@ -22,10 +22,10 @@
       
    
 
    #include <boost/multiprecision/miller_rabin.hpp>
 
-template <class Backend, bool ExpressionTemplates, class Engine>
+template <class Backend, expression_template_option ExpressionTemplates, class Engine>
 bool miller_rabin_test(const number<Backend, ExpressionTemplates>& n, unsigned trials, Engine& gen);
 
-template <class Backend, bool ExpressionTemplates, class Engine>
+template <class Backend, expression_template_option ExpressionTemplates, class Engine>
 bool miller_rabin_test(const number<Backend, ExpressionTemplates>& n, unsigned trials);
 
    
 
    
diff --git a/doc/html/index.html b/doc/html/index.html
index d7ce9ef1..57fb5f19 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -120,7 +120,7 @@
    - +

    Last revised: September 04, 2012 at 17:13:56 GMT

    Last revised: September 06, 2012 at 09:51:26 GMT
    From fc1cda1f6247b9253f63cc57877bfcde4d2e8984 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 7 Sep 2012 08:31:49 +0000 Subject: [PATCH 235/256] Largely cosmetic change - add two new template params to cpp_dec_float - one for the exponent type, and one for an optional allocator. [SVN r80431] --- .../boost_multiprecision/indexes/s01.html | 14 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 9 +- doc/html/boost_multiprecision/map/hist.html | 7 + doc/html/boost_multiprecision/map/todo.html | 12 +- doc/html/boost_multiprecision/ref/number.html | 313 +++++++- doc/html/boost_multiprecision/tut.html | 4 +- doc/html/boost_multiprecision/tut/floats.html | 74 +- .../tut/floats/cpp_dec_float.html | 46 +- .../tut/floats/fp_eg.html | 6 +- .../tut/floats/gmp_float.html | 6 +- .../tut/floats/mpfr_float.html | 6 +- .../boost_multiprecision/tut/rational.html | 72 +- .../tut/rational/cpp_rational.html | 8 +- .../tut/rational/gmp_rational.html | 8 +- .../tut/rational/tommath_rational.html | 6 +- doc/html/index.html | 6 +- doc/multiprecision.qbk | 246 ++++--- .../boost/multiprecision/cpp_dec_float.hpp | 686 +++++++++--------- test/math/log1p_expm1_test.cpp | 2 +- test/math/powm1_sqrtp1m1_test.cpp | 2 +- test/math/table_type.hpp | 2 +- test/math/test_bessel_i.cpp | 2 +- test/math/test_bessel_j.cpp | 2 +- test/math/test_bessel_k.cpp | 2 +- test/math/test_bessel_y.cpp | 2 +- test/math/test_beta.cpp | 2 +- test/math/test_binomial_coeff.cpp | 2 +- test/math/test_carlson.cpp | 2 +- test/math/test_cbrt.cpp | 2 +- test/math/test_digamma.cpp | 2 +- test/math/test_ellint_1.cpp | 2 +- test/math/test_ellint_2.cpp | 2 +- test/math/test_ellint_3.cpp | 2 +- test/math/test_erf.cpp | 2 +- test/math/test_expint.cpp | 2 +- test/math/test_gamma.cpp | 2 +- test/math/test_hermite.cpp | 2 +- test/math/test_ibeta.cpp | 2 +- test/math/test_ibeta_2.cpp | 2 +- test/math/test_ibeta_3.cpp | 2 +- test/math/test_ibeta_4.cpp | 2 +- test/math/test_ibeta_inv_1.cpp | 2 +- test/math/test_ibeta_inv_ab_4.cpp | 2 +- test/math/test_igamma.cpp | 2 +- test/math/test_igamma_inv.cpp | 2 +- test/math/test_igamma_inva.cpp | 2 +- test/math/test_laguerre.cpp | 2 +- test/math/test_legendre.cpp | 2 +- test/math/test_tgamma_ratio.cpp | 2 +- test/math/test_zeta.cpp | 2 +- test/test_acos.cpp | 8 +- test/test_arithmetic.cpp | 3 +- test/test_asin.cpp | 8 +- test/test_atan.cpp | 8 +- test/test_cos.cpp | 9 +- test/test_cosh.cpp | 8 +- test/test_exp.cpp | 9 +- test/test_log.cpp | 9 +- test/test_pow.cpp | 8 +- test/test_round.cpp | 8 +- test/test_sin.cpp | 9 +- test/test_sinh.cpp | 8 +- test/test_sqrt.cpp | 8 +- test/test_tanh.cpp | 8 +- 66 files changed, 1076 insertions(+), 636 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index ad20bd40..f8c6e580 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    +Function Index

    A B C D E F I L M P R S T Z

    @@ -55,10 +55,16 @@
    C
    -
    • +
      +
      • +
    • +

      cpp_dec_float

      +
      +
      • +
    D
    diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index d1ad0b8d..d8dacbad 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

    C G I M N T

    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 1f790e8f..42e8cba8 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    C I L M T U

    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 21e9dbb6..0deb96a1 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G I L M N O P R S T U Z

    @@ -98,6 +98,7 @@

  • cpp_dec_float

  • cpp_dec_float_100

  • cpp_dec_float_50

    • +

  • TODO

  • @@ -817,6 +818,10 @@
    • +

      TODO

      +
      +
      • +

    • tommath_int

      • diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html index 157d4400..f7102bd0 100644 --- a/doc/html/boost_multiprecision/map/hist.html +++ b/doc/html/boost_multiprecision/map/hist.html @@ -37,6 +37,13 @@
    • Removed "mp_" prefix from types.
      • +
    • + Allowed mixed precision arithmetic. +
      • +
    • + Changed ExpressionTemplates parameter to class number + to use enumerated values rather than true/false. +
    diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index d2ec17ec..e7fd11c7 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -54,7 +54,7 @@
  • Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents. Open question - what should - be the default - int32_t or int64_t? + be the default - int32_t or int64_t? (done 2012/09/06)
  • Document the size requirements of fixed precision ints. @@ -76,19 +76,21 @@ - min == -max etc.
  • - Document cpp_dec_float precision, rounding, and exponent size. + Document cpp_dec_float precision, rounding, and exponent size (done 2012/09/06).
  • - Can we be clearer in the docs that mixed arithmetic doesn't work? + Can we be clearer in the docs that mixed arithmetic doesn't work (no + longer applicable as of 2012/09/06)?
  • - Document round functions behaviour better (they behave as in C99). + Document round functions behaviour better (they behave as in C++11) (added + note 2012/09/06).
  • Should there be a choice of rounding mode (probably MPFR specific)?
  • - Document limits on size of cpp_dec_float. + Document limits on size of cpp_dec_float (done 2012/09/06).
    • diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html index 3969151d..b1f6dc2e 100644 --- a/doc/html/boost_multiprecision/ref/number.html +++ b/doc/html/boost_multiprecision/ref/number.html @@ -580,7 +580,7 @@ unmentionable-expression-template-type atan2 (const number-or-expression-template-type&, const number-or-expression-template-type&);

    - These functions all behave exactly as their standard library counterparts + These functions all behave exactly as their standard library C++11 counterparts do: their argument is either an instance of number or an expression template derived from it; If the argument is of type number<Backend, et_off> then that is also the return type, otherwise the return type is an expression @@ -601,6 +601,317 @@ library later, then these functions may be extended to support those number types).

    +

    + The precision of these functions is generally deterimined by the backend + implementation. For example the precision of these functions when used with + mpfr_float + is determined entirely by MPFR. + When these functions use our own implementations, the accuracy of the transcendal + functions is generally a few epsilon. Note however, that the trigonmetrical + functions incur the usual accuracy loss when reducing arguments by large + multiples of π. Also note that both __mpf_float and cpp_dec_float + have a number of guard digits beyond their stated precision, so the error + rates listed for these are in some sense artificially low. +

    +

    + The following table shows the error rates we observe for these functions + with various backend types, functions not listed here are exact (tested on + Win32 with VC++10, MPFR-3.0.0, MPIR-2.1.1): +

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Function +

    +     		+

    + mpfr_float_50 +

    +     		+

    + mpf_float_50 +

    +     		+

    + cpp_dec_float_50 +

    +
    +

    + sqrt +

    +     		+

    + 1eps +

    +     		+

    + 0eps +

    +     		+

    + 0eps +

    +
    +

    + exp +

    +     		+

    + 1eps +

    +     		+

    + 0eps +

    +     		+

    + 0eps +

    +
    +

    + log +

    +     		+

    + 1eps +

    +     		+

    + 0eps +

    +     		+

    + 0eps +

    +
    +

    + log10 +

    +     		+

    + 1eps +

    +     		+

    + 0eps +

    +     		+

    + 0eps +

    +
    +

    + cos +

    +     		+

    + 700eps +

    +     		+

    + 0eps +

    +     		+

    + 0eps +

    +
    +

    + sin +

    +     		+

    + 1eps +

    +     		+

    + 0eps +

    +     		+

    + 0eps +

    +
    +

    + tan +

    +     		+ + +
    +

    + acos +

    +     		+ + +
    +

    + asin +

    +     		+ + +
    +

    + atan +

    +     		+ + +
    +

    + cosh +

    +     		+ + +
    +

    + sinh +

    +     		+ + +
    +

    + tanh +

    +     		+ + +
    +

    + pow +

    +     		+ + +
    +

    + fmod +

    +     		+ + +
    +

    + atan2 +

    +     		+ + +
    Traits Class diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html index 1ed672ca..5ae44082 100644 --- a/doc/html/boost_multiprecision/tut.html +++ b/doc/html/boost_multiprecision/tut.html @@ -31,9 +31,9 @@
    Floating Point Numbers
    +
    cpp_dec_float
    gmp_float
    mpfr_float
    -
    cpp_dec_float
    Examples
    Area of @@ -50,8 +50,8 @@
    Rational Number Types
    -
    gmp_rational
    cpp_rational
    +
    gmp_rational
    tommath_rational
    Use With Boost.Rational
    rational_adapter
    diff --git a/doc/html/boost_multiprecision/tut/floats.html b/doc/html/boost_multiprecision/tut/floats.html index 171fa60d..bb8f542f 100644 --- a/doc/html/boost_multiprecision/tut/floats.html +++ b/doc/html/boost_multiprecision/tut/floats.html @@ -7,20 +7,20 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext
    +
    cpp_dec_float
    gmp_float
    mpfr_float
    -
    cpp_dec_float
    Examples
    Area of @@ -81,6 +81,39 @@
    • +

    + cpp_dec_float<N> +

    +     		+

    + boost/multiprecision/cpp_dec_float.hpp +

    +     		+

    + 10 +

    +     		+

    + None +

    +     		+

    + Header only, all C++ implementation. Boost licence. +

    +     		+

    + Approximately 2x slower than the MPFR + or GMP libraries. +

    +

    mpf_float<N> @@ -147,39 +180,6 @@

    -

    - cpp_dec_float<N> -

    -     		-

    - boost/multiprecision/cpp_dec_float.hpp -

    -     		-

    - 10 -

    -     		-

    - None -

    -     		-

    - Header only, all C++ implementation. Boost licence. -

    -     		-

    - Approximately 2x slower than the MPFR - or GMP libraries. -

    -
    @@ -193,7 +193,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html index e0a56312..5ceefb43 100644 --- a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html +++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html @@ -6,12 +6,12 @@ - - + +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -22,7 +22,7 @@ 

    namespace boost{ namespace multiprecision{
 
-template <unsigned Digits10>
+template <unsigned Digits10, class ExponentType = boost::int32_t, class Allocator = void>
 class cpp_dec_float;
 
 typedef number<cpp_dec_float<50> > cpp_dec_float_50;
@@ -42,7 +42,27 @@
           be used at fixed precision by specifying a non-zero Digits10
           template parameter. The typedefs cpp_dec_float_50
           and cpp_dec_float_100 provide
-          arithmetic types at 50 and 100 decimal digits precision respectively.
+          arithmetic types at 50 and 100 decimal digits precision respectively. Optionally,
+          you can specify an integer type to use for the exponent, this defaults
+          to a 32-bit integer type which is more than large enough for the vast majority
+          of use cases, but larger types such as long
+          long can also be specified if you
+          need a truely huge exponent range.
+        
    
+
    
+          Normally cpp_dec_float
+          allocates no memory: all of the space required for it's digits are allocated
+          directly within the class. As a result care should be taken not to use
+          the class with too high a digit count as stack space requirements can grow
+          out of control. If that represents a problem then providing an allocator
+          as the final template parameter causes cpp_dec_float
+          to dynamically allocate the memory it needs: this significantly reduces
+          the size of cpp_dec_float
+          and increases the viable upper limit on the number of digits at the expense
+          of performance. However, please bare in mind that arithmetic operations
+          rapidly become very expensive as the digit count grows:
+          the current implementation really isn't optimized or designed for large
+          digit counts.
         
    
 
    
           There is full standard library and numeric_limits
@@ -83,13 +103,25 @@
               Any number instantiated
               on this type, is convertible to any other number
               instantiated on this type - for example you can convert from number<cpp_dec_float<50> > to number<cpp_dec_float<SomeOtherValue> >.
-              Narrowing conversions are truncating.
+              Narrowing conversions are truncating and explicit.
             
 
  • 
               Conversion from a string results in a std::runtime_error
               being thrown if the string can not be interpreted as a valid floating
               point number.
             
    • 
+
  • 
+              The actual precision of a cpp_dec_float
+              is always slightly higher than the number of digits specified in the
+              template parameter, actually how much higher is an implementation detail
+              but is always at least 8 decimal digits.
+            
    • 
+
  • 
+              Operations involving cpp_dec_float
+              are always truncating. However, note that since their are guard digits
+              in effect, in practice this has no real impact on accuracy for most
+              use cases.
+            
    •

    @@ -131,7 +163,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg.html index 238d5aff..a2567273 100644 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg.html +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -40,7 +40,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/floats/gmp_float.html b/doc/html/boost_multiprecision/tut/floats/gmp_float.html index d420e0c4..a33583e7 100644 --- a/doc/html/boost_multiprecision/tut/floats/gmp_float.html +++ b/doc/html/boost_multiprecision/tut/floats/gmp_float.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -177,7 +177,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html index 53692329..40126cf1 100644 --- a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html +++ b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html @@ -7,11 +7,11 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -166,7 +166,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 9dcaf83e..712c33d3 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -7,19 +7,19 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext
    -
    gmp_rational
    cpp_rational
    +
    gmp_rational
    tommath_rational
    Use With Boost.Rational
    rational_adapter
    @@ -70,6 +70,38 @@ + +

    + cpp_rational +

    + + +

    + boost/multiprecision/cpp_int.hpp +

    + + +

    + 2 +

    + + +

    + None +

    + + +

    + An all C++ Boost-licensed implementation. +

    + + +

    + Slower than GMP. +

    + + +

    gmp_rational @@ -103,38 +135,6 @@ - -

    - cpp_rational -

    - - -

    - boost/multiprecision/cpp_int.hpp -

    - - -

    - 2 -

    - - -

    - None -

    - - -

    - An all C++ Boost-licensed implementation. -

    - - -

    - Slower than GMP. -

    - - -

    tommath_rational @@ -246,7 +246,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html index 445989b1..22bf2a4c 100644 --- a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html +++ b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html @@ -6,12 +6,12 @@ - - + +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -107,7 +107,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html index 2d1f7fb8..a317321b 100644 --- a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html +++ b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html @@ -6,12 +6,12 @@ - - + +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -138,7 +138,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html index 432d1012..4ce58b60 100644 --- a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html +++ b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -113,7 +113,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/index.html b/doc/html/index.html index 57fb5f19..2d72038a 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -46,9 +46,9 @@

    Floating Point Numbers
    +
    cpp_dec_float
    gmp_float
    mpfr_float
    -
    cpp_dec_float
    Examples
    Area of @@ -65,8 +65,8 @@
    Rational Number Types
    -
    gmp_rational
    cpp_rational
    +
    gmp_rational
    tommath_rational
    Use With Boost.Rational
    rational_adapter
    @@ -120,7 +120,7 @@
    - +

    Last revised: September 06, 2012 at 09:51:26 GMT

    Last revised: September 07, 2012 at 08:25:28 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 1446586a..e765f0e9 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -47,6 +47,16 @@ '''] +[def __cpp_int [link boost_multiprecision.tut.ints.cpp_int cpp_int]] +[def __gmp_int [link boost_multiprecision.tut.ints.gmp_int gmp_int]] +[def __tom_int [link boost_multiprecision.tut.ints.tom_int tom_int]] +[def __gmp_float [link boost_multiprecision.tut.floats.gmp_float gmp_float]] +[def __mpfr_float_backend [link boost_multiprecision.tut.floats.mpfr_float mpfr_float]] +[def __cpp_dec_float [link boost_multiprecision.tut.floats.cpp_dec_float cpp_dec_float]] +[def __gmp_rational [link boost_multiprecision.tut.rational.gmp_rational gmp_rational]] +[def __cpp_rational [link boost_multiprecision.tut.rational.cpp_rational cpp_rational]] +[def __tommath_rational [link boost_multiprecision.tut.rational.tommath_rational tommath_rational]] + [section:intro Introduction] The Multiprecision Library provides ['User-defined] integer, rational and floating-point C++ types which @@ -504,11 +514,73 @@ The following back-ends provide floating point arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] +[[`cpp_dec_float`][boost/multiprecision/cpp_dec_float.hpp][10][None][Header only, all C++ implementation. Boost licence.][Approximately 2x slower than the [mpfr] or [gmp] libraries.]] [[`mpf_float`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] [[`mpfr_float`][boost/multiprecision/mpfr.hpp][2][[gmp] and [mpfr]][Very fast and efficient back-end, with its own standard library implementation.][Dependency on GNU licensed [gmp] and [mpfr] libraries.]] -[[`cpp_dec_float`][boost/multiprecision/cpp_dec_float.hpp][10][None][Header only, all C++ implementation. Boost licence.][Approximately 2x slower than the [mpfr] or [gmp] libraries.]] ] +[section:cpp_dec_float cpp_dec_float] + +`#include ` + + namespace boost{ namespace multiprecision{ + + template + class cpp_dec_float; + + typedef number > cpp_dec_float_50; + typedef number > cpp_dec_float_100; + + }} // namespaces + +The `cpp_dec_float` back-end is used in conjunction with `number`: It acts as an entirely C++ (header only and dependency free) +real-number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision. + +Type `cpp_dec_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter. +The typedefs `cpp_dec_float_50` and `cpp_dec_float_100` provide arithmetic types at 50 and 100 decimal digits precision +respectively. Optionally, you can specify an integer type to use for the exponent, this defaults to a 32-bit integer type +which is more than large enough for the vast majority of use cases, but larger types such as `long long` can also be specified +if you need a truely huge exponent range. + +Normally `cpp_dec_float` allocates no memory: all of the space required for it's digits are allocated +directly within the class. As a result care should be taken not to use the class with too high a digit count +as stack space requirements can grow out of control. If that represents a problem then providing an allocator +as the final template parameter causes `cpp_dec_float` to dynamically allocate the memory it needs: this +significantly reduces the size of `cpp_dec_float` and increases the viable upper limit on the number of digits +at the expense of performance. However, please bare in mind that arithmetic operations rapidly become ['very] expensive +as the digit count grows: the current implementation really isn't optimized or designed for large digit counts. + +There is full standard library and `numeric_limits` support available for this type. + +Things you should know when using this type: + +* Default constructed `cpp_dec_float`s have a value of zero. +* The radix of this type is 10. As a result it can behave subtly differently from base-2 types. +* It is not possible to round-trip this type to and from a string and get back to exactly the same value +(this is a result of the type having some hidden internal guard digits). +* The type has a number of internal guard digits over and above those specified in the template argument. +Normally these should not be visible to the user. +* The type supports both infinities and NaN's. An infinity is generated whenever the result would overflow, +and a NaN is generated for any mathematically undefined operation. +* There is a `std::numeric_limits` specialisation for this type. +* Any `number` instantiated on this type, is convertible to any other `number` instantiated on this type - +for example you can convert from `number >` to `number >`. +Narrowing conversions are truncating and `explicit`. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. +* The actual precision of a `cpp_dec_float` is always slightly higher than the number of digits specified in +the template parameter, actually how much higher is an implementation detail but is always at least 8 decimal +digits. +* Operations involving `cpp_dec_float` are always truncating. However, note that since their are guard digits +in effect, in practice this has no real impact on accuracy for most use cases. + +[h5 cpp_dec_float example:] + +[cpp_dec_float_eg] + +[endsect] + [section:gmp_float gmp_float] `#include ` @@ -627,53 +699,6 @@ as a valid floating point number. [endsect] -[section:cpp_dec_float cpp_dec_float] - -`#include ` - - namespace boost{ namespace multiprecision{ - - template - class cpp_dec_float; - - typedef number > cpp_dec_float_50; - typedef number > cpp_dec_float_100; - - }} // namespaces - -The `cpp_dec_float` back-end is used in conjunction with `number`: It acts as an entirely C++ (header only and dependency free) -real-number type that is a drop-in replacement for the native C++ floating-point types, but with -much greater precision. - -Type `cpp_dec_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter. -The typedefs `cpp_dec_float_50` and `cpp_dec_float_100` provide arithmetic types at 50 and 100 decimal digits precision -respectively. - -There is full standard library and `numeric_limits` support available for this type. - -Things you should know when using this type: - -* Default constructed `cpp_dec_float`s have a value of zero. -* The radix of this type is 10. As a result it can behave subtly differently from base-2 types. -* It is not possible to round-trip this type to and from a string and get back to exactly the same value -(this is a result of the type having some hidden internal guard digits). -* The type has a number of internal guard digits over and above those specified in the template argument. -Normally these should not be visible to the user. -* The type supports both infinities and NaN's. An infinity is generated whenever the result would overflow, -and a NaN is generated for any mathematically undefined operation. -* There is a `std::numeric_limits` specialisation for this type. -* Any `number` instantiated on this type, is convertible to any other `number` instantiated on this type - -for example you can convert from `number >` to `number >`. -Narrowing conversions are truncating. -* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted -as a valid floating point number. - -[h5 cpp_dec_float example:] - -[cpp_dec_float_eg] - -[endsect] - [section:fp_eg Examples] [import ../example/floating_point_examples.cpp] @@ -723,13 +748,53 @@ The following back-ends provide rational number arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] -[[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] [[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licensed implementation.][Slower than [gmp].]] +[[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] [[`tommath_rational`][boost/multiprecision/tommath.hpp][2][[tommath]][All C/C++ implementation that's Boost Software Licence compatible.][Slower than [gmp].]] [[`rational_adapter`][boost/multiprecision/rational_adapter.hpp][N/A][none][All C++ adapter that allows any integer back-end type to be used as a rational type.][Requires an underlying integer back-end type.]] [[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `number` integer type.][The expression templates used by `number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]] ] +[section:cpp_rational cpp_rational] + +`#include ` + + namespace boost{ namespace multiprecision{ + + typedef rational_adapter > cpp_rational_backend; + + typedef number cpp_rational; + + }} // namespaces + +The `cpp_rational_backend` type is used via the typedef `boost::multiprecision::cpp_rational`. It provides +a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. + +As well as the usual conversions from arithmetic and string types, instances of `cpp_rational` are copy constructible +and assignable from type `cpp_int`. + +There is also a two argument constructor that accepts a numerator and denominator: both of type `cpp_int`. + +There are also non-member functions: + + cpp_int numerator(const cpp_rational&); + cpp_int denominator(const cpp_rational&); + +which return the numerator and denominator of the number. + +Things you should know when using this type: + +* Default constructed `cpp_rational`s have the value zero. +* Division by zero results in a `std::rumtime_error` being thrown. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be +interpreted as a valid rational number. + +[h5 Example:] + +[cpp_rational_eg] + +[endsect] + [section:gmp_rational gmp_rational] `#include ` @@ -778,46 +843,6 @@ interpreted as a valid rational number. [endsect] -[section:cpp_rational cpp_rational] - -`#include ` - - namespace boost{ namespace multiprecision{ - - typedef rational_adapter > cpp_rational_backend; - - typedef number cpp_rational; - - }} // namespaces - -The `cpp_rational_backend` type is used via the typedef `boost::multiprecision::cpp_rational`. It provides -a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. - -As well as the usual conversions from arithmetic and string types, instances of `cpp_rational` are copy constructible -and assignable from type `cpp_int`. - -There is also a two argument constructor that accepts a numerator and denominator: both of type `cpp_int`. - -There are also non-member functions: - - cpp_int numerator(const cpp_rational&); - cpp_int denominator(const cpp_rational&); - -which return the numerator and denominator of the number. - -Things you should know when using this type: - -* Default constructed `cpp_rational`s have the value zero. -* Division by zero results in a `std::rumtime_error` being thrown. -* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be -interpreted as a valid rational number. - -[h5 Example:] - -[cpp_rational_eg] - -[endsect] - [section:tommath_rational tommath_rational] `#include ` @@ -1494,7 +1519,7 @@ this library support all of the iostream formatting flags, field width and preci ``['unmentionable-expression-template-type]`` fmod (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); ``['unmentionable-expression-template-type]`` atan2 (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); -These functions all behave exactly as their standard library counterparts do: their argument is either an instance of `number` or +These functions all behave exactly as their standard library C++11 counterparts do: their argument is either an instance of `number` or an expression template derived from it; If the argument is of type `number` then that is also the return type, otherwise the return type is an expression template. @@ -1506,6 +1531,35 @@ used at variable precision. Also note that with the exception of `abs` that these functions can only be used with floating-point Backend types (if any other types such as fixed precision or complex types are added to the library later, then these functions may be extended to support those number types). +The precision of these functions is generally deterimined by the backend implementation. For example the precision +of these functions when used with __mpfr_float_backend is determined entirely by [mpfr]. When these functions use our own +implementations, the accuracy of the transcendal functions is generally a few epsilon. Note however, that the trigonmetrical +functions incur the usual accuracy loss when reducing arguments by large multiples of [pi]. Also note that both __mpf_float +and __cpp_dec_float have a number of guard digits beyond their stated precision, so the error rates listed for these +are in some sense artificially low. + +The following table shows the error rates we observe for these functions with various backend types, functions not listed +here are exact (tested on Win32 with VC++10, MPFR-3.0.0, MPIR-2.1.1): + +[table +[[Function][mpfr_float_50][mpf_float_50][cpp_dec_float_50]] +[[sqrt][1eps][0eps][0eps]] +[[exp][1eps][0eps][0eps]] +[[log][1eps][0eps][0eps]] +[[log10][1eps][0eps][0eps]] +[[cos][700eps][0eps][0eps]] +[[sin][1eps][0eps][0eps]] +[[tan][][][]] +[[acos][][][]] +[[asin][][][]] +[[atan][][][]] +[[cosh][][][]] +[[sinh][][][]] +[[tanh][][][]] +[[pow][][][]] +[[fmod][][][]] +[[atan2][][][]] +] [h4 Traits Class Support] template @@ -2602,6 +2656,8 @@ Windows Vista machine. * Many functions made made `constexp`? * Differentiate between explicit and implicit conversions in the number constructor. * Removed "mp_" prefix from types. +* Allowed mixed precision arithmetic. +* Changed ExpressionTemplates parameter to class `number` to use enumerated values rather than true/false. [h4 Pre-review history] @@ -2632,18 +2688,18 @@ More a list of what ['could] be done, rather than what ['should] be done (which * Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it. * Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents. -Open question - what should be the default - int32_t or int64_t? +Open question - what should be the default - int32_t or int64_t? (done 2012/09/06) * Document the size requirements of fixed precision ints. * Document std lib function accuracy. * Make fixed precision orthogonal to Allocator type in cpp_int. Possible solution - add an additional MaxBits template argument that defaults to 0 (meaning keep going till no more space/memory). * Add support for fused multiply add (and subtract). GMP mpz_t could use this. * Be a bit clearer on the effects of sign-magnitude representation of cpp_int - min == -max etc. -* Document cpp_dec_float precision, rounding, and exponent size. -* Can we be clearer in the docs that mixed arithmetic doesn't work? -* Document round functions behaviour better (they behave as in C99). +* Document cpp_dec_float precision, rounding, and exponent size (done 2012/09/06). +* Can we be clearer in the docs that mixed arithmetic doesn't work (no longer applicable as of 2012/09/06)? +* Document round functions behaviour better (they behave as in C++11) (added note 2012/09/06). * Should there be a choice of rounding mode (probably MPFR specific)? -* Document limits on size of cpp_dec_float. +* Document limits on size of cpp_dec_float (done 2012/09/06). [endsect] diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 1a7241a5..73f85bff 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -26,17 +26,28 @@ namespace boost{ namespace multiprecision{ namespace backends{ -template +template class cpp_dec_float; } // namespace -template -struct number_category > : public mpl::int_{}; +template +struct number_category > : public mpl::int_{}; namespace backends{ -template +namespace detail{ + +template +struct dynamic_array : public std::vector +{ + dynamic_array() + : std::vector(static_cast::size_type>(S), static_cast(0)) {} +}; + +} + +template class cpp_dec_float { private: @@ -46,18 +57,18 @@ public: typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list float_types; - typedef long long exponent_type; + typedef ExponentType exponent_type; static const boost::int32_t cpp_dec_float_radix = 10L; static const boost::int32_t cpp_dec_float_digits10_limit_lo = 9L; static const boost::int32_t cpp_dec_float_digits10_limit_hi = boost::integer_traits::const_max - 100; static const boost::int32_t cpp_dec_float_digits10 = ((cpp_dec_float_digits10_setting < cpp_dec_float_digits10_limit_lo) ? cpp_dec_float_digits10_limit_lo : ((cpp_dec_float_digits10_setting > cpp_dec_float_digits10_limit_hi) ? cpp_dec_float_digits10_limit_hi : cpp_dec_float_digits10_setting)); - static const boost::int64_t cpp_dec_float_max_exp10 = static_cast( 2776234983093287512LL); - static const boost::int64_t cpp_dec_float_min_exp10 = static_cast(-2776234983093287512LL); - static const boost::int64_t cpp_dec_float_max_exp = static_cast((cpp_dec_float_max_exp10 / 301LL) * 1000LL); - static const boost::int64_t cpp_dec_float_min_exp = static_cast((cpp_dec_float_min_exp10 / 301LL) * 1000LL); + static const ExponentType cpp_dec_float_max_exp10 = (static_cast(1) << (std::numeric_limits::digits - 5)); + static const ExponentType cpp_dec_float_min_exp10 = -cpp_dec_float_max_exp10; + static const ExponentType cpp_dec_float_max_exp = static_cast((cpp_dec_float_max_exp10 / 301LL) * 1000LL); + static const ExponentType cpp_dec_float_min_exp = static_cast((cpp_dec_float_min_exp10 / 301LL) * 1000LL); - BOOST_STATIC_ASSERT(cpp_dec_float_max_exp10 == -cpp_dec_float_min_exp10); + BOOST_STATIC_ASSERT((cpp_dec_float::cpp_dec_float_max_exp10 == -cpp_dec_float::cpp_dec_float_min_exp10)); private: static const boost::int32_t cpp_dec_float_elem_digits10 = 8L; @@ -89,10 +100,13 @@ private: } fpclass_type; - typedef boost::array array_type; + typedef typename mpl::if_, + boost::array, + detail::dynamic_array + >::type array_type; array_type data; - boost::int64_t exp; + ExponentType exp; bool neg; fpclass_type fpclass; boost::int32_t prec_elem; @@ -102,7 +116,7 @@ private: // cpp_dec_float(fpclass_type c) BOOST_NOEXCEPT : data(), - exp (static_cast(0)), + exp (static_cast(0)), neg (false), fpclass (c), prec_elem(cpp_dec_float_elem_number) { } @@ -114,23 +128,23 @@ private: { initializer() { - cpp_dec_float::nan(); - cpp_dec_float::inf(); - (cpp_dec_float::min)(); - (cpp_dec_float::max)(); - cpp_dec_float::zero(); - cpp_dec_float::one(); - cpp_dec_float::two(); - cpp_dec_float::half(); - cpp_dec_float::double_min(); - cpp_dec_float::double_max(); - cpp_dec_float::long_double_max(); - cpp_dec_float::long_double_min(); - cpp_dec_float::long_long_max(); - cpp_dec_float::long_long_min(); - cpp_dec_float::ulong_long_max(); - cpp_dec_float::eps(); - cpp_dec_float::pow2(0); + cpp_dec_float::nan(); + cpp_dec_float::inf(); + (cpp_dec_float::min)(); + (cpp_dec_float::max)(); + cpp_dec_float::zero(); + cpp_dec_float::one(); + cpp_dec_float::two(); + cpp_dec_float::half(); + cpp_dec_float::double_min(); + cpp_dec_float::double_max(); + cpp_dec_float::long_double_max(); + cpp_dec_float::long_double_min(); + cpp_dec_float::long_long_max(); + cpp_dec_float::long_long_min(); + cpp_dec_float::ulong_long_max(); + cpp_dec_float::eps(); + cpp_dec_float::pow2(0); } void do_nothing(){} }; @@ -141,14 +155,14 @@ public: // Constructors cpp_dec_float() BOOST_NOEXCEPT : data(), - exp (static_cast(0)), + exp (static_cast(0)), neg (false), fpclass (cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) { } cpp_dec_float(const char* s) : data(), - exp (static_cast(0)), + exp (static_cast(0)), neg (false), fpclass (cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) @@ -159,7 +173,7 @@ public: template cpp_dec_float(I i, typename enable_if >::type* = 0) BOOST_NOEXCEPT : data(), - exp (static_cast(0)), + exp (static_cast(0)), neg (false), fpclass (cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) @@ -170,7 +184,7 @@ public: template cpp_dec_float(I i, typename enable_if >::type* = 0) BOOST_NOEXCEPT : data(), - exp (static_cast(0)), + exp (static_cast(0)), neg (false), fpclass (cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) @@ -191,8 +205,8 @@ public: fpclass (f.fpclass), prec_elem(f.prec_elem) { } - template - cpp_dec_float(const cpp_dec_float& f, typename enable_if_c::type* = 0) BOOST_NOEXCEPT : + template + cpp_dec_float(const cpp_dec_float& f, typename enable_if_c::type* = 0) BOOST_NOEXCEPT : data(), exp (f.exp), neg (f.neg), @@ -201,8 +215,8 @@ public: { std::copy(f.data.begin(), f.data.begin() + f.prec_elem, data.begin()); } - template - explicit cpp_dec_float(const cpp_dec_float& f, typename disable_if_c::type* = 0) BOOST_NOEXCEPT : + template + explicit cpp_dec_float(const cpp_dec_float& f, typename disable_if_c::type* = 0) BOOST_NOEXCEPT : data(), exp (f.exp), neg (f.neg), @@ -216,7 +230,7 @@ public: template cpp_dec_float(const F val, typename enable_if >::type* = 0) BOOST_NOEXCEPT : data(), - exp (static_cast(0)), + exp (static_cast(0)), neg (false), fpclass (cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) @@ -224,7 +238,7 @@ public: *this = val; } - cpp_dec_float(const double val, long long exponent) BOOST_NOEXCEPT; + cpp_dec_float(const double val, ExponentType exponent) BOOST_NOEXCEPT; // Specific special values. static const cpp_dec_float& nan() BOOST_NOEXCEPT @@ -440,7 +454,7 @@ public: template int compare(const V& v)const BOOST_NOEXCEPT { - cpp_dec_float t; + cpp_dec_float t; t = v; return compare(t); } @@ -458,7 +472,7 @@ public: long double extract_long_double (void) const BOOST_NOEXCEPT; signed long long extract_signed_long_long (void) const BOOST_NOEXCEPT; unsigned long long extract_unsigned_long_long(void) const BOOST_NOEXCEPT; - void extract_parts (double& mantissa, boost::int64_t& exponent) const BOOST_NOEXCEPT; + void extract_parts (double& mantissa, ExponentType& exponent) const BOOST_NOEXCEPT; cpp_dec_float extract_integer_part (void) const BOOST_NOEXCEPT; void precision(const boost::int32_t prec_digits) BOOST_NOEXCEPT { @@ -475,13 +489,13 @@ public: } } static cpp_dec_float pow2(long long i) BOOST_NOEXCEPT; - long long order()const BOOST_NOEXCEPT + ExponentType order()const BOOST_NOEXCEPT { const bool bo_order_is_zero = ((!isfinite()) || (data[0] == static_cast(0u))); // // Binary search to find the order of the leading term: // - boost::uint32_t prefix = 0; + ExponentType prefix = 0; if(data[0] >= 100000UL) { @@ -523,7 +537,7 @@ public: } } - return (bo_order_is_zero ? static_cast(0) : static_cast(exp + prefix)); + return (bo_order_is_zero ? static_cast(0) : static_cast(exp + prefix)); } private: @@ -542,44 +556,44 @@ private: bool rd_string(const char* const s); - template + template friend class cpp_dec_float; }; -template -typename cpp_dec_float::initializer cpp_dec_float::init; +template +typename cpp_dec_float::initializer cpp_dec_float::init; -template -const boost::int32_t cpp_dec_float::cpp_dec_float_radix; -template -const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_setting; -template -const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_limit_lo; -template -const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_limit_hi; -template -const boost::int32_t cpp_dec_float::cpp_dec_float_digits10; -template -const boost::int64_t cpp_dec_float::cpp_dec_float_max_exp; -template -const boost::int64_t cpp_dec_float::cpp_dec_float_min_exp; -template -const boost::int64_t cpp_dec_float::cpp_dec_float_max_exp10; -template -const boost::int64_t cpp_dec_float::cpp_dec_float_min_exp10; -template -const boost::int32_t cpp_dec_float::cpp_dec_float_elem_digits10; -template -const boost::int32_t cpp_dec_float::cpp_dec_float_elem_number_request; -template -const boost::int32_t cpp_dec_float::cpp_dec_float_elem_number; -template -const boost::int32_t cpp_dec_float::cpp_dec_float_elem_mask; +template +const boost::int32_t cpp_dec_float::cpp_dec_float_radix; +template +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_setting; +template +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_limit_lo; +template +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10_limit_hi; +template +const boost::int32_t cpp_dec_float::cpp_dec_float_digits10; +template +const ExponentType cpp_dec_float::cpp_dec_float_max_exp; +template +const ExponentType cpp_dec_float::cpp_dec_float_min_exp; +template +const ExponentType cpp_dec_float::cpp_dec_float_max_exp10; +template +const ExponentType cpp_dec_float::cpp_dec_float_min_exp10; +template +const boost::int32_t cpp_dec_float::cpp_dec_float_elem_digits10; +template +const boost::int32_t cpp_dec_float::cpp_dec_float_elem_number_request; +template +const boost::int32_t cpp_dec_float::cpp_dec_float_elem_number; +template +const boost::int32_t cpp_dec_float::cpp_dec_float_elem_mask; -template -cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float& v) BOOST_NOEXCEPT +template +cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float& v) BOOST_NOEXCEPT { if(isnan()) { @@ -601,9 +615,9 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float } // Get the offset for the add/sub operation. - static const boost::int64_t max_delta_exp = static_cast((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); + static const ExponentType max_delta_exp = static_cast((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); - const boost::int64_t ofs_exp = static_cast(exp - v.exp); + const ExponentType ofs_exp = static_cast(exp - v.exp); // Check if the operation is out of range, requiring special handling. if(v.iszero() || (ofs_exp > max_delta_exp)) @@ -666,7 +680,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float { std::copy_backward(data.begin(), data.end() - static_cast(1u), data.end()); data[0] = carry; - exp += static_cast(cpp_dec_float_elem_digits10); + exp += static_cast(cpp_dec_float_elem_digits10); } } else @@ -748,7 +762,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float // This result of the subtraction is exactly zero. // Reset the sign and the exponent. neg = false; - exp = static_cast(0); + exp = static_cast(0); } else { @@ -758,7 +772,7 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float std::copy(data.begin() + static_cast(sj), data.end(), data.begin()); std::fill(data.end() - sj, data.end(), static_cast(0u)); - exp -= static_cast(sj * static_cast(cpp_dec_float_elem_digits10)); + exp -= static_cast(sj * static_cast(cpp_dec_float_elem_digits10)); } } } @@ -798,8 +812,8 @@ cpp_dec_float& cpp_dec_float::operator+=(const cpp_dec_float return *this; } -template -cpp_dec_float& cpp_dec_float::operator-=(const cpp_dec_float& v) BOOST_NOEXCEPT +template +cpp_dec_float& cpp_dec_float::operator-=(const cpp_dec_float& v) BOOST_NOEXCEPT { // Use *this - v = -(-*this + v). negate(); @@ -808,8 +822,8 @@ cpp_dec_float& cpp_dec_float::operator-=(const cpp_dec_float return *this; } -template -cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float& v) BOOST_NOEXCEPT +template +cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float& v) BOOST_NOEXCEPT { // Evaluate the sign of the result. const bool b_result_is_neg = (neg != v.neg); @@ -846,17 +860,17 @@ cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float } // Check for overflow or underflow. - const bool u_exp_is_neg = (exp < static_cast(0)); - const bool v_exp_is_neg = (v.exp < static_cast(0)); + const bool u_exp_is_neg = (exp < static_cast(0)); + const bool v_exp_is_neg = (v.exp < static_cast(0)); if(u_exp_is_neg == v_exp_is_neg) { // Get the unsigned base-10 exponents of *this and v and... - const boost::int64_t u_exp = ((!u_exp_is_neg) ? exp : static_cast( -exp)); - const boost::int64_t v_exp = ((!v_exp_is_neg) ? v.exp : static_cast(-v.exp)); + const ExponentType u_exp = ((!u_exp_is_neg) ? exp : static_cast( -exp)); + const ExponentType v_exp = ((!v_exp_is_neg) ? v.exp : static_cast(-v.exp)); // Check the range of the upcoming multiplication. - const bool b_result_is_out_of_range = (v_exp >= static_cast(cpp_dec_float_max_exp10 - u_exp)); + const bool b_result_is_out_of_range = (v_exp >= static_cast(cpp_dec_float_max_exp10 - u_exp)); if(b_result_is_out_of_range) { @@ -901,8 +915,8 @@ cpp_dec_float& cpp_dec_float::operator*=(const cpp_dec_float return *this; } -template -cpp_dec_float& cpp_dec_float::operator/=(const cpp_dec_float& v) BOOST_NOEXCEPT +template +cpp_dec_float& cpp_dec_float::operator/=(const cpp_dec_float& v) BOOST_NOEXCEPT { const bool u_and_v_are_finite_and_identical = ( isfinite() && (fpclass == v.fpclass) @@ -936,8 +950,8 @@ cpp_dec_float& cpp_dec_float::operator/=(const cpp_dec_float } } -template -cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const unsigned long long n) BOOST_NOEXCEPT +template +cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const unsigned long long n) BOOST_NOEXCEPT { // Multiply *this with a constant unsigned long long. @@ -991,7 +1005,7 @@ cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const u // Handle the carry and adjust the exponent. if(carry != static_cast(0u)) { - exp += static_cast(cpp_dec_float_elem_digits10); + exp += static_cast(cpp_dec_float_elem_digits10); // Shift the result of the multiplication one element to the right. std::copy_backward(data.begin(), @@ -1031,8 +1045,8 @@ cpp_dec_float& cpp_dec_float::mul_unsigned_long_long(const u return *this; } -template -cpp_dec_float& cpp_dec_float::div_unsigned_long_long(const unsigned long long n) BOOST_NOEXCEPT +template +cpp_dec_float& cpp_dec_float::div_unsigned_long_long(const unsigned long long n) BOOST_NOEXCEPT { // Divide *this by a constant unsigned long long. @@ -1097,7 +1111,7 @@ cpp_dec_float& cpp_dec_float::div_unsigned_long_long(const u if(data[0] == static_cast(0u)) { // Adjust the exponent - exp -= static_cast(cpp_dec_float_elem_digits10); + exp -= static_cast(cpp_dec_float_elem_digits10); // Shift result of the division one element to the left. std::copy(data.begin() + static_cast(1u), @@ -1120,8 +1134,8 @@ cpp_dec_float& cpp_dec_float::div_unsigned_long_long(const u return *this; } -template -cpp_dec_float& cpp_dec_float::calculate_inv() BOOST_NOEXCEPT +template +cpp_dec_float& cpp_dec_float::calculate_inv() BOOST_NOEXCEPT { // Compute the inverse of *this. const bool b_neg = neg; @@ -1155,17 +1169,17 @@ cpp_dec_float& cpp_dec_float::calculate_inv() BOOST_NOEXCEPT } // Save the original *this. - cpp_dec_float x(*this); + cpp_dec_float x(*this); // Generate the initial estimate using division. // Extract the mantissa and exponent for a "manual" // computation of the estimate. double dd; - boost::int64_t ne; + ExponentType ne; x.extract_parts(dd, ne); // Do the inverse estimate using double precision estimates of mantissa and exponent. - operator=(cpp_dec_float(1.0 / dd, -ne)); + operator=(cpp_dec_float(1.0 / dd, -ne)); // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration // is used. During the iterative steps, the precision of the calculation is limited @@ -1194,8 +1208,8 @@ cpp_dec_float& cpp_dec_float::calculate_inv() BOOST_NOEXCEPT return *this; } -template -cpp_dec_float& cpp_dec_float::calculate_sqrt(void) BOOST_NOEXCEPT +template +cpp_dec_float& cpp_dec_float::calculate_sqrt(void) BOOST_NOEXCEPT { // Compute the square root of *this. @@ -1211,17 +1225,17 @@ cpp_dec_float& cpp_dec_float::calculate_sqrt(void) BOOST_NOE } // Save the original *this. - cpp_dec_float x(*this); + cpp_dec_float x(*this); // Generate the initial estimate using division. // Extract the mantissa and exponent for a "manual" // computation of the estimate. double dd; - boost::int64_t ne; + ExponentType ne; extract_parts(dd, ne); // Force the exponent to be an even multiple of two. - if((ne % static_cast(2)) != static_cast(0)) + if((ne % static_cast(2)) != static_cast(0)) { ++ne; dd /= 10.0; @@ -1231,10 +1245,10 @@ cpp_dec_float& cpp_dec_float::calculate_sqrt(void) BOOST_NOE // Estimate the square root using simple manipulations. const double sqd = std::sqrt(dd); - *this = cpp_dec_float(sqd, static_cast(ne / static_cast(2))); + *this = cpp_dec_float(sqd, static_cast(ne / static_cast(2))); // Estimate 1.0 / (2.0 * x0) using simple manipulations. - cpp_dec_float vi(0.5 / sqd, static_cast(-ne / static_cast(2))); + cpp_dec_float vi(0.5 / sqd, static_cast(-ne / static_cast(2))); // Compute the square root of x. Coupled Newton iteration // as described in "Pi Unleashed" is used. During the @@ -1277,8 +1291,8 @@ cpp_dec_float& cpp_dec_float::calculate_sqrt(void) BOOST_NOE return *this; } -template -int cpp_dec_float::cmp_data(const array_type& vd) const BOOST_NOEXCEPT +template +int cpp_dec_float::cmp_data(const array_type& vd) const BOOST_NOEXCEPT { // Compare the data of *this with those of v. // Return +1 for *this > v @@ -1299,8 +1313,8 @@ int cpp_dec_float::cmp_data(const array_type& vd) const BOOST_NOEXCEPT } } -template -int cpp_dec_float::compare(const cpp_dec_float& v) const BOOST_NOEXCEPT +template +int cpp_dec_float::compare(const cpp_dec_float& v) const BOOST_NOEXCEPT { // Compare v with *this. // Return +1 for *this > v @@ -1377,8 +1391,8 @@ int cpp_dec_float::compare(const cpp_dec_float& v) const BOOST_NOEXCEP } } -template -bool cpp_dec_float::isone() const BOOST_NOEXCEPT +template +bool cpp_dec_float::isone() const BOOST_NOEXCEPT { // Check if the value of *this is identically 1 or very close to 1. @@ -1386,12 +1400,12 @@ bool cpp_dec_float::isone() const BOOST_NOEXCEPT if(not_negative_and_is_finite) { - if((data[0u] == static_cast(1u)) && (exp == static_cast(0))) + if((data[0u] == static_cast(1u)) && (exp == static_cast(0))) { const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); return (it_non_zero == data.end()); } - else if((data[0u] == static_cast(cpp_dec_float_elem_mask - 1)) && (exp == static_cast(-cpp_dec_float_elem_digits10))) + else if((data[0u] == static_cast(cpp_dec_float_elem_mask - 1)) && (exp == static_cast(-cpp_dec_float_elem_digits10))) { const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate); return (it_non_nine == data.end()); @@ -1401,14 +1415,14 @@ bool cpp_dec_float::isone() const BOOST_NOEXCEPT return false; } -template -bool cpp_dec_float::isint() const BOOST_NOEXCEPT +template +bool cpp_dec_float::isint() const BOOST_NOEXCEPT { if(fpclass != cpp_dec_float_finite) { return false; } if(iszero()) { return true; } - if(exp < static_cast(0)) { return false; } // |*this| < 1. + if(exp < static_cast(0)) { return false; } // |*this| < 1. const typename array_type::size_type offset_decimal_part = static_cast(exp / cpp_dec_float_elem_digits10) + 1u; @@ -1424,10 +1438,10 @@ bool cpp_dec_float::isint() const BOOST_NOEXCEPT return (it_non_zero == data.end()); } -template -void cpp_dec_float::extract_parts(double& mantissa, boost::int64_t& exponent) const BOOST_NOEXCEPT +template +void cpp_dec_float::extract_parts(double& mantissa, ExponentType& exponent) const BOOST_NOEXCEPT { - // Extract the approximate parts mantissa and base-10 exponent from the input cpp_dec_float value x. + // Extract the approximate parts mantissa and base-10 exponent from the input cpp_dec_float value x. // Extracts the mantissa and exponent. exponent = exp; @@ -1457,12 +1471,12 @@ void cpp_dec_float::extract_parts(double& mantissa, boost::int64_t& ex if(neg) { mantissa = -mantissa; } } -template -double cpp_dec_float::extract_double(void) const BOOST_NOEXCEPT +template +double cpp_dec_float::extract_double(void) const BOOST_NOEXCEPT { - // Returns the double conversion of a cpp_dec_float. + // Returns the double conversion of a cpp_dec_float. - // Check for non-normal cpp_dec_float. + // Check for non-normal cpp_dec_float. if(!isfinite()) { if(isnan()) @@ -1476,17 +1490,17 @@ double cpp_dec_float::extract_double(void) const BOOST_NOEXCEPT } } - cpp_dec_float xx(*this); + cpp_dec_float xx(*this); if(xx.isneg()) xx.negate(); - // Check if *this cpp_dec_float is zero. + // Check if *this cpp_dec_float is zero. if(iszero() || (xx.compare(double_min()) < 0)) { return 0.0; } - // Check if *this cpp_dec_float exceeds the maximum of double. + // Check if *this cpp_dec_float exceeds the maximum of double. if(xx.compare(double_max()) > 0) { return ((!neg) ? std::numeric_limits::infinity() @@ -1503,12 +1517,12 @@ double cpp_dec_float::extract_double(void) const BOOST_NOEXCEPT return d; } -template -long double cpp_dec_float::extract_long_double(void) const BOOST_NOEXCEPT +template +long double cpp_dec_float::extract_long_double(void) const BOOST_NOEXCEPT { - // Returns the long double conversion of a cpp_dec_float. + // Returns the long double conversion of a cpp_dec_float. - // Check if *this cpp_dec_float is subnormal. + // Check if *this cpp_dec_float is subnormal. if(!isfinite()) { if(isnan()) @@ -1522,17 +1536,17 @@ long double cpp_dec_float::extract_long_double(void) const BOOST_NOEXC } } - cpp_dec_float xx(*this); + cpp_dec_float xx(*this); if(xx.isneg()) xx.negate(); - // Check if *this cpp_dec_float is zero. + // Check if *this cpp_dec_float is zero. if(iszero() || (xx.compare(long_double_min()) < 0)) { return static_cast(0.0); } - // Check if *this cpp_dec_float exceeds the maximum of double. + // Check if *this cpp_dec_float exceeds the maximum of double. if(xx.compare(long_double_max()) > 0) { return ((!neg) ? std::numeric_limits::infinity() @@ -1549,14 +1563,14 @@ long double cpp_dec_float::extract_long_double(void) const BOOST_NOEXC return ld; } -template -signed long long cpp_dec_float::extract_signed_long_long(void) const BOOST_NOEXCEPT +template +signed long long cpp_dec_float::extract_signed_long_long(void) const BOOST_NOEXCEPT { // Extracts a signed long long from *this. // If (x > maximum of signed long long) or (x < minimum of signed long long), // then the maximum or minimum of signed long long is returned accordingly. - if(exp < static_cast(0)) + if(exp < static_cast(0)) { return static_cast(0); } @@ -1576,7 +1590,7 @@ signed long long cpp_dec_float::extract_signed_long_long(void) const B else { // Extract the data into an unsigned long long value. - cpp_dec_float xn(extract_integer_part()); + cpp_dec_float xn(extract_integer_part()); if(xn.isneg()) xn.negate(); @@ -1594,8 +1608,8 @@ signed long long cpp_dec_float::extract_signed_long_long(void) const B return ((!b_neg) ? static_cast(val) : static_cast(-static_cast(val))); } -template -unsigned long long cpp_dec_float::extract_unsigned_long_long(void) const BOOST_NOEXCEPT +template +unsigned long long cpp_dec_float::extract_unsigned_long_long(void) const BOOST_NOEXCEPT { // Extracts an unsigned long long from *this. // If x exceeds the maximum of unsigned long long, @@ -1608,12 +1622,12 @@ unsigned long long cpp_dec_float::extract_unsigned_long_long(void) con return static_cast(extract_signed_long_long()); } - if(exp < static_cast(0)) + if(exp < static_cast(0)) { return static_cast(0u); } - const cpp_dec_float xn(extract_integer_part()); + const cpp_dec_float xn(extract_integer_part()); unsigned long long val; @@ -1638,8 +1652,8 @@ unsigned long long cpp_dec_float::extract_unsigned_long_long(void) con return val; } -template -cpp_dec_float cpp_dec_float::extract_integer_part(void) const BOOST_NOEXCEPT +template +cpp_dec_float cpp_dec_float::extract_integer_part(void) const BOOST_NOEXCEPT { // Compute the signed integer part of x. @@ -1648,7 +1662,7 @@ cpp_dec_float cpp_dec_float::extract_integer_part(void) cons return *this; } - if(exp < static_cast(0)) + if(exp < static_cast(0)) { // The absolute value of the number is smaller than 1. // Thus the integer part is zero. @@ -1662,7 +1676,7 @@ cpp_dec_float cpp_dec_float::extract_integer_part(void) cons } // Make a local copy. - cpp_dec_float x = *this; + cpp_dec_float x = *this; // Clear out the decimal portion const size_t first_clear = (static_cast(x.exp) / static_cast(cpp_dec_float_elem_digits10)) + 1u; @@ -1673,8 +1687,8 @@ cpp_dec_float cpp_dec_float::extract_integer_part(void) cons return x; } -template -std::string cpp_dec_float::str(boost::intmax_t number_of_digits, std::ios_base::fmtflags f) const +template +std::string cpp_dec_float::str(boost::intmax_t number_of_digits, std::ios_base::fmtflags f) const { if(this->isinf()) { @@ -1692,7 +1706,7 @@ std::string cpp_dec_float::str(boost::intmax_t number_of_digits, std:: std::string str; boost::intmax_t org_digits(number_of_digits); - boost::int64_t my_exp = order(); + ExponentType my_exp = order(); if(number_of_digits == 0) number_of_digits = cpp_dec_float_total_digits10; if(f & std::ios_base::fixed) @@ -1701,14 +1715,14 @@ std::string cpp_dec_float::str(boost::intmax_t number_of_digits, std:: } else if(f & std::ios_base::scientific) ++number_of_digits; - // Determine the number of elements needed to provide the requested digits from cpp_dec_float. + // Determine the number of elements needed to provide the requested digits from cpp_dec_float. const std::size_t number_of_elements = (std::min)(static_cast((number_of_digits / static_cast(cpp_dec_float_elem_digits10)) + 2u), static_cast(cpp_dec_float_elem_number)); - // Extract the remaining digits from cpp_dec_float after the decimal point. + // Extract the remaining digits from cpp_dec_float after the decimal point. str = boost::lexical_cast(data[0]); - // Extract all of the digits from cpp_dec_float, beginning with the first data element. + // Extract all of the digits from cpp_dec_float, beginning with the first data element. for(std::size_t i = static_cast(1u); i < number_of_elements; i++) { std::stringstream ss; @@ -1826,8 +1840,8 @@ std::string cpp_dec_float::str(boost::intmax_t number_of_digits, std:: return str; } -template -bool cpp_dec_float::rd_string(const char* const s) +template +bool cpp_dec_float::rd_string(const char* const s) { try{ @@ -1837,7 +1851,7 @@ bool cpp_dec_float::rd_string(const char* const s) // the code complexity (and perhaps the run-time) of rd_string(). // Get a possible exponent and remove it. - exp = static_cast(0); + exp = static_cast(0); std::size_t pos; @@ -1846,7 +1860,7 @@ bool cpp_dec_float::rd_string(const char* const s) ) { // Remove the exponent part from the string. - exp = boost::lexical_cast(static_cast(str.c_str() + (pos + 1u))); + exp = boost::lexical_cast(static_cast(str.c_str() + (pos + 1u))); str = str.substr(static_cast(0u), pos); } @@ -1903,7 +1917,7 @@ bool cpp_dec_float::rd_string(const char* const s) } } - // Put the input string into the standard cpp_dec_float input form + // Put the input string into the standard cpp_dec_float input form // aaa.bbbbE+/-n, where aaa has 1...cpp_dec_float_elem_digits10, bbbb has an // even multiple of cpp_dec_float_elem_digits10 which are possibly zero padded // on the right-end, and n is a signed 64-bit integer which is an @@ -1948,7 +1962,7 @@ bool cpp_dec_float::rd_string(const char* const s) // Bring one single digit into the mantissa and adjust the exponent accordingly. str.erase(str.begin(), it_non_zero); str.insert(static_cast(1u), "."); - exp -= static_cast(delta_exp + 1u); + exp -= static_cast(delta_exp + 1u); } } else @@ -1959,11 +1973,11 @@ bool cpp_dec_float::rd_string(const char* const s) // Shift the decimal point such that the exponent is an even multiple of cpp_dec_float_elem_digits10. std::size_t n_shift = static_cast(0u); - const std::size_t n_exp_rem = static_cast(exp % static_cast(cpp_dec_float_elem_digits10)); + const std::size_t n_exp_rem = static_cast(exp % static_cast(cpp_dec_float_elem_digits10)); - if((exp % static_cast(cpp_dec_float_elem_digits10)) != static_cast(0)) + if((exp % static_cast(cpp_dec_float_elem_digits10)) != static_cast(0)) { - n_shift = ((exp < static_cast(0)) + n_shift = ((exp < static_cast(0)) ? static_cast(n_exp_rem + static_cast(cpp_dec_float_elem_digits10)) : static_cast(n_exp_rem)); } @@ -1987,7 +2001,7 @@ bool cpp_dec_float::rd_string(const char* const s) str.erase(pos, static_cast(1u)); - exp -= static_cast(n_shift); + exp -= static_cast(n_shift); } // Cut the size of the mantissa to <= cpp_dec_float_elem_digits10. @@ -2004,7 +2018,7 @@ bool cpp_dec_float::rd_string(const char* const s) str.erase(pos_plus_one, static_cast(1u)); - exp += static_cast(static_cast(n) * static_cast(cpp_dec_float_elem_digits10)); + exp += static_cast(static_cast(n) * static_cast(cpp_dec_float_elem_digits10)); } // Pad the decimal part such that its value is an even @@ -2031,7 +2045,7 @@ bool cpp_dec_float::rd_string(const char* const s) static_cast(pos_plus_one + max_dec)); } - // Now the input string has the standard cpp_dec_float input form. + // Now the input string has the standard cpp_dec_float input form. // (See the comment above.) // Set all the data elements to 0. @@ -2070,9 +2084,9 @@ bool cpp_dec_float::rd_string(const char* const s) if(exp == cpp_dec_float_min_exp10) { // Check for identity with the minimum value. - cpp_dec_float test = *this; + cpp_dec_float test = *this; - test.exp = static_cast(0); + test.exp = static_cast(0); if(test.isone()) { @@ -2098,15 +2112,15 @@ bool cpp_dec_float::rd_string(const char* const s) return true; } -template -cpp_dec_float::cpp_dec_float(const double mantissa, const long long exponent) BOOST_NOEXCEPT +template +cpp_dec_float::cpp_dec_float(const double mantissa, const ExponentType exponent) BOOST_NOEXCEPT : data (), - exp (static_cast(0)), + exp (static_cast(0)), neg (false), fpclass (cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) { - // Create *this cpp_dec_float from a given mantissa and exponent. + // Create *this cpp_dec_float from a given mantissa and exponent. // Note: This constructor does not maintain the full precision of double. const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits::min)() * (1.0 + std::numeric_limits::epsilon()))); @@ -2120,7 +2134,7 @@ cpp_dec_float::cpp_dec_float(const double mantissa, const long long ex const bool b_neg = (mantissa < 0.0); double d = ((!b_neg) ? mantissa : -mantissa); - boost::int64_t e = exponent; + ExponentType e = exponent; while(d > 10.0) { d /= 10.0; ++e; } while(d < 1.0) { d *= 10.0; --e; } @@ -2150,8 +2164,8 @@ cpp_dec_float::cpp_dec_float(const double mantissa, const long long ex } } -template -cpp_dec_float& cpp_dec_float::operator = (long double a) BOOST_NOEXCEPT +template +cpp_dec_float& cpp_dec_float::operator = (long double a) BOOST_NOEXCEPT { // Christopher Kormanyos's original code used a cast to long long here, but that fails // when long double has more digits than a long long. @@ -2200,12 +2214,12 @@ cpp_dec_float& cpp_dec_float::operator = (long double a) BOO return *this; } -template -void cpp_dec_float::from_unsigned_long_long(const unsigned long long u) BOOST_NOEXCEPT +template +void cpp_dec_float::from_unsigned_long_long(const unsigned long long u) BOOST_NOEXCEPT { std::fill(data.begin(), data.end(), static_cast(0u)); - exp = static_cast(0); + exp = static_cast(0); neg = false; fpclass = cpp_dec_float_finite; prec_elem = cpp_dec_float_elem_number; @@ -2225,15 +2239,15 @@ void cpp_dec_float::from_unsigned_long_long(const unsigned long long u if(i > static_cast(1u)) { - exp += static_cast((i - 1u) * static_cast(cpp_dec_float_elem_digits10)); + exp += static_cast((i - 1u) * static_cast(cpp_dec_float_elem_digits10)); } std::reverse(temp, temp + i); std::copy(temp, temp + (std::min)(i, static_cast(cpp_dec_float_elem_number)), data.begin()); } -template -boost::uint32_t cpp_dec_float::mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p) BOOST_NOEXCEPT +template +boost::uint32_t cpp_dec_float::mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p) BOOST_NOEXCEPT { // // There is a limit on how many limbs this algorithm can handle without dropping digits @@ -2261,8 +2275,8 @@ boost::uint32_t cpp_dec_float::mul_loop_uv(boost::uint32_t* const u, c return static_cast(carry); } -template -boost::uint32_t cpp_dec_float::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) BOOST_NOEXCEPT +template +boost::uint32_t cpp_dec_float::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) BOOST_NOEXCEPT { boost::uint64_t carry = static_cast(0u); @@ -2277,8 +2291,8 @@ boost::uint32_t cpp_dec_float::mul_loop_n(boost::uint32_t* const u, bo return static_cast(carry); } -template -boost::uint32_t cpp_dec_float::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) BOOST_NOEXCEPT +template +boost::uint32_t cpp_dec_float::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) BOOST_NOEXCEPT { boost::uint64_t prev = static_cast(0u); @@ -2292,14 +2306,14 @@ boost::uint32_t cpp_dec_float::div_loop_n(boost::uint32_t* const u, bo return static_cast(prev); } -template -cpp_dec_float cpp_dec_float::pow2(const long long p) BOOST_NOEXCEPT +template +cpp_dec_float cpp_dec_float::pow2(const long long p) BOOST_NOEXCEPT { // Create a static const table of p^2 for -128 < p < +128. // Note: The size of this table must be odd-numbered and // symmetric about 0. init.do_nothing(); - static const boost::array, 255u> p2_data = + static const boost::array, 255u> p2_data = {{ cpp_dec_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"), cpp_dec_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"), @@ -2558,90 +2572,90 @@ cpp_dec_float cpp_dec_float::pow2(const long long p) BOOST_N cpp_dec_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38") }}; - if((p > static_cast(-128)) && (p < static_cast(+128))) + if((p > static_cast(-128)) && (p < static_cast(+128))) { return p2_data[static_cast(p + ((p2_data.size() - 1u) / 2u))]; } // Compute and return 2^p. - if(p < static_cast(0)) + if(p < static_cast(0)) { - return pow2(static_cast(-p)).calculate_inv(); + return pow2(static_cast(-p)).calculate_inv(); } - else if(p < static_cast(std::numeric_limits::digits)) + else if(p < static_cast(std::numeric_limits::digits)) { const boost::uint64_t p2 = static_cast(static_cast(1uLL) << p); return cpp_dec_float(p2); } else { - cpp_dec_float t; + cpp_dec_float t; default_ops::detail::pow_imp(t, two(), p, mpl::true_()); return t; } } -template -inline void eval_add(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT +template +inline void eval_add(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT { result += o; } -template -inline void eval_subtract(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT +template +inline void eval_subtract(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT { result -= o; } -template -inline void eval_multiply(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT +template +inline void eval_multiply(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT { result *= o; } -template -inline void eval_divide(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT +template +inline void eval_divide(cpp_dec_float& result, const cpp_dec_float& o) BOOST_NOEXCEPT { result /= o; } -template -inline void eval_add(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT +template +inline void eval_add(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT { result.add_unsigned_long_long(o); } -template -inline void eval_subtract(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT +template +inline void eval_subtract(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT { result.sub_unsigned_long_long(o); } -template -inline void eval_multiply(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT +template +inline void eval_multiply(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT { result.mul_unsigned_long_long(o); } -template -inline void eval_divide(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT +template +inline void eval_divide(cpp_dec_float& result, const unsigned long long& o) BOOST_NOEXCEPT { result.div_unsigned_long_long(o); } -template -inline void eval_add(cpp_dec_float& result, long long o) BOOST_NOEXCEPT +template +inline void eval_add(cpp_dec_float& result, long long o) BOOST_NOEXCEPT { if(o < 0) result.sub_unsigned_long_long(-o); else result.add_unsigned_long_long(o); } -template -inline void eval_subtract(cpp_dec_float& result, long long o) BOOST_NOEXCEPT +template +inline void eval_subtract(cpp_dec_float& result, long long o) BOOST_NOEXCEPT { if(o < 0) result.add_unsigned_long_long(-o); else result.sub_unsigned_long_long(o); } -template -inline void eval_multiply(cpp_dec_float& result, long long o) BOOST_NOEXCEPT +template +inline void eval_multiply(cpp_dec_float& result, long long o) BOOST_NOEXCEPT { if(o < 0) { @@ -2651,8 +2665,8 @@ inline void eval_multiply(cpp_dec_float& result, long long o) BOOST_NO else result.mul_unsigned_long_long(o); } -template -inline void eval_divide(cpp_dec_float& result, long long o) BOOST_NOEXCEPT +template +inline void eval_divide(cpp_dec_float& result, long long o) BOOST_NOEXCEPT { if(o < 0) { @@ -2663,18 +2677,18 @@ inline void eval_divide(cpp_dec_float& result, long long o) BOOST_NOEX result.div_unsigned_long_long(o); } -template -inline void eval_convert_to(unsigned long long* result, const cpp_dec_float& val) BOOST_NOEXCEPT +template +inline void eval_convert_to(unsigned long long* result, const cpp_dec_float& val) BOOST_NOEXCEPT { *result = val.extract_unsigned_long_long(); } -template -inline void eval_convert_to(long long* result, const cpp_dec_float& val) BOOST_NOEXCEPT +template +inline void eval_convert_to(long long* result, const cpp_dec_float& val) BOOST_NOEXCEPT { *result = val.extract_signed_long_long(); } -template -inline void eval_convert_to(long double* result, cpp_dec_float& val) BOOST_NOEXCEPT +template +inline void eval_convert_to(long double* result, cpp_dec_float& val) BOOST_NOEXCEPT { *result = val.extract_long_double(); } @@ -2682,8 +2696,8 @@ inline void eval_convert_to(long double* result, cpp_dec_float& val) B // // Non member function support: // -template -inline int eval_fpclassify(const cpp_dec_float& x) BOOST_NOEXCEPT +template +inline int eval_fpclassify(const cpp_dec_float& x) BOOST_NOEXCEPT { if(x.isinf()) return FP_INFINITE; @@ -2694,31 +2708,31 @@ inline int eval_fpclassify(const cpp_dec_float& x) BOOST_NOEXCEPT return FP_NORMAL; } -template -inline void eval_abs(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT +template +inline void eval_abs(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT { result = x; if(x.isneg()) result.negate(); } -template -inline void eval_fabs(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT +template +inline void eval_fabs(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT { result = x; if(x.isneg()) result.negate(); } -template -inline void eval_sqrt(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT +template +inline void eval_sqrt(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT { result = x; result.calculate_sqrt(); } -template -inline void eval_floor(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT +template +inline void eval_floor(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT { result = x; if(!x.isfinite() || x.isint()) @@ -2727,12 +2741,12 @@ inline void eval_floor(cpp_dec_float& result, const cpp_dec_float::one(); + result -= cpp_dec_float::one(); result = result.extract_integer_part(); } -template -inline void eval_ceil(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT +template +inline void eval_ceil(cpp_dec_float& result, const cpp_dec_float& x) BOOST_NOEXCEPT { result = x; if(!x.isfinite() || x.isint()) @@ -2741,16 +2755,16 @@ inline void eval_ceil(cpp_dec_float& result, const cpp_dec_float::one(); + result += cpp_dec_float::one(); result = result.extract_integer_part(); } -template -inline void eval_trunc(cpp_dec_float& result, const cpp_dec_float& x) +template +inline void eval_trunc(cpp_dec_float& result, const cpp_dec_float& x) { if(!x.isfinite()) { - result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, number >(x), 0, boost::math::policies::policy<>()).backend(); + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, number >(x), 0, boost::math::policies::policy<>()).backend(); return; } else if(x.isint()) @@ -2761,15 +2775,17 @@ inline void eval_trunc(cpp_dec_float& result, const cpp_dec_float -inline void eval_ldexp(cpp_dec_float& result, const cpp_dec_float& x, long long e) BOOST_NOEXCEPT +template +inline void eval_ldexp(cpp_dec_float& result, const cpp_dec_float& x, ArgType e) BOOST_NOEXCEPT { + if((static_cast(e) > (std::numeric_limits::max)()) || (static_cast(e) < (std::numeric_limits::min)())) + BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Exponent value is out of range."))); result = x; - result *= cpp_dec_float::pow2(e); + result *= cpp_dec_float::pow2(e); } -template -inline void eval_frexp(cpp_dec_float& result, const cpp_dec_float& x, long long* e) +template +inline void eval_frexp(cpp_dec_float& result, const cpp_dec_float& x, ExponentType* e) { result = x; if(result.isneg()) @@ -2781,9 +2797,9 @@ inline void eval_frexp(cpp_dec_float& result, const cpp_dec_float::max)() / 1000)) + if(abs(t) < ((std::numeric_limits::max)() / 1000)) { t *= 1000; t /= 301; @@ -2794,7 +2810,7 @@ inline void eval_frexp(cpp_dec_float& result, const cpp_dec_float::pow2(-t); + result *= cpp_dec_float::pow2(-t); if(result.iszero() || result.isinf() || result.isnan()) { @@ -2803,32 +2819,32 @@ inline void eval_frexp(cpp_dec_float& result, const cpp_dec_float::pow2(-t); + result *= cpp_dec_float::pow2(-t); } BOOST_MP_USING_ABS if(abs(result.order()) > 5) { // If our first estimate doesn't get close enough then try recursion until we do: - long long e2; - cpp_dec_float r2; + ExponentType e2; + cpp_dec_float r2; eval_frexp(r2, result, &e2); // overflow protection: - if((t > 0) && (e2 > 0) && (t > (std::numeric_limits::max)() - e2)) + if((t > 0) && (e2 > 0) && (t > (std::numeric_limits::max)() - e2)) BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2.")); - if((t < 0) && (e2 < 0) && (t < (std::numeric_limits::min)() - e2)) + if((t < 0) && (e2 < 0) && (t < (std::numeric_limits::min)() - e2)) BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2.")); t += e2; result = r2; } - while(result.compare(cpp_dec_float::one()) >= 0) + while(result.compare(cpp_dec_float::one()) >= 0) { - result /= cpp_dec_float::two(); + result /= cpp_dec_float::two(); ++t; } - while(result.compare(cpp_dec_float::half()) < 0) + while(result.compare(cpp_dec_float::half()) < 0) { - result *= cpp_dec_float::two(); + result *= cpp_dec_float::two(); --t; } *e = t; @@ -2836,23 +2852,23 @@ inline void eval_frexp(cpp_dec_float& result, const cpp_dec_float -inline void eval_frexp(cpp_dec_float& result, const cpp_dec_float& x, int* e) +template +inline typename disable_if >::type eval_frexp(cpp_dec_float& result, const cpp_dec_float& x, int* e) { - long long t; + ExponentType t; eval_frexp(result, x, &t); - if(t > (std::numeric_limits::max)()) + if((t > (std::numeric_limits::max)()) || (t < (std::numeric_limits::min)())) BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is outside the range of an int")); *e = static_cast(t); } -template -inline bool eval_is_zero(const cpp_dec_float& val) BOOST_NOEXCEPT +template +inline bool eval_is_zero(const cpp_dec_float& val) BOOST_NOEXCEPT { return val.iszero(); } -template -inline int eval_get_sign(const cpp_dec_float& val) BOOST_NOEXCEPT +template +inline int eval_get_sign(const cpp_dec_float& val) BOOST_NOEXCEPT { return val.iszero() ? 0 : val.isneg() ? -1 : 1; } @@ -2869,8 +2885,8 @@ typedef number > cpp_dec_float_100; namespace detail{ -template -struct is_explicitly_convertible, cpp_dec_float > : public mpl::true_ {}; +template +struct is_explicitly_convertible, cpp_dec_float > : public mpl::true_ {}; } @@ -2881,8 +2897,8 @@ struct is_explicitly_convertible, cpp_dec_float > : public namespace std { - template - class numeric_limits, ExpressionTemplates> > + template + class numeric_limits, ExpressionTemplates> > { public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; @@ -2892,14 +2908,14 @@ namespace std BOOST_STATIC_CONSTEXPR bool is_bounded = true; BOOST_STATIC_CONSTEXPR bool is_modulo = false; BOOST_STATIC_CONSTEXPR bool is_iec559 = false; - BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; - BOOST_STATIC_CONSTEXPR int digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; - BOOST_STATIC_CONSTEXPR int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_total_digits10; - BOOST_STATIC_CONSTEXPR boost::int64_t min_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp; // Type differs from int. - BOOST_STATIC_CONSTEXPR boost::int64_t min_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp10; // Type differs from int. - BOOST_STATIC_CONSTEXPR boost::int64_t max_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp; // Type differs from int. - BOOST_STATIC_CONSTEXPR boost::int64_t max_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp10; // Type differs from int. - BOOST_STATIC_CONSTEXPR int radix = boost::multiprecision::cpp_dec_float::cpp_dec_float_radix; + BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; + BOOST_STATIC_CONSTEXPR int digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; + BOOST_STATIC_CONSTEXPR int max_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_total_digits10; + BOOST_STATIC_CONSTEXPR ExponentType min_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp; // Type differs from int. + BOOST_STATIC_CONSTEXPR ExponentType min_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_min_exp10; // Type differs from int. + BOOST_STATIC_CONSTEXPR ExponentType max_exponent = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp; // Type differs from int. + BOOST_STATIC_CONSTEXPR ExponentType max_exponent10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_max_exp10; // Type differs from int. + BOOST_STATIC_CONSTEXPR int radix = boost::multiprecision::cpp_dec_float::cpp_dec_float_radix; BOOST_STATIC_CONSTEXPR std::float_round_style round_style = std::round_to_nearest; BOOST_STATIC_CONSTEXPR bool has_infinity = true; BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true; @@ -2909,63 +2925,63 @@ namespace std BOOST_STATIC_CONSTEXPR bool traps = false; BOOST_STATIC_CONSTEXPR bool tinyness_before = false; - BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> (min) (void) { return (boost::multiprecision::cpp_dec_float::min)(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> (max) (void) { return (boost::multiprecision::cpp_dec_float::max)(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> lowest (void) { return boost::multiprecision::cpp_dec_float::zero(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> epsilon (void) { return boost::multiprecision::cpp_dec_float::eps(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> round_error (void) { return 0.5L; } - BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> infinity (void) { return boost::multiprecision::cpp_dec_float::inf(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> quiet_NaN (void) { return boost::multiprecision::cpp_dec_float::nan(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> signaling_NaN(void) { return boost::multiprecision::cpp_dec_float::zero(); } - BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> denorm_min (void) { return boost::multiprecision::cpp_dec_float::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> (min) (void) { return (boost::multiprecision::cpp_dec_float::min)(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> (max) (void) { return (boost::multiprecision::cpp_dec_float::max)(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> lowest (void) { return boost::multiprecision::cpp_dec_float::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> epsilon (void) { return boost::multiprecision::cpp_dec_float::eps(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> round_error (void) { return 0.5L; } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> infinity (void) { return boost::multiprecision::cpp_dec_float::inf(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> quiet_NaN (void) { return boost::multiprecision::cpp_dec_float::nan(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> signaling_NaN(void) { return boost::multiprecision::cpp_dec_float::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number, ExpressionTemplates> denorm_min (void) { return boost::multiprecision::cpp_dec_float::zero(); } }; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template -BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::min_exponent; -template -BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::min_exponent10; -template -BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::max_exponent; -template -BOOST_CONSTEXPR_OR_CONST boost::int64_t numeric_limits, ExpressionTemplates> >::max_exponent10; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +template +BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits, ExpressionTemplates> >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits, ExpressionTemplates> >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits, ExpressionTemplates> >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits, ExpressionTemplates> >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif } @@ -2974,12 +2990,12 @@ namespace boost{ namespace math{ namespace policies{ -template -struct precision< boost::multiprecision::number, ExpressionTemplates>, Policy> +template +struct precision< boost::multiprecision::number, ExpressionTemplates>, Policy> { // Define a local copy of cpp_dec_float_digits10 because it might differ // from the template parameter Digits10 for small or large digit counts. - static const boost::int32_t cpp_dec_float_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; + static const boost::int32_t cpp_dec_float_digits10 = boost::multiprecision::cpp_dec_float::cpp_dec_float_digits10; typedef typename Policy::precision_type precision_type; typedef digits2<((cpp_dec_float_digits10 + 1LL) * 1000LL) / 301LL> digits_2; diff --git a/test/math/log1p_expm1_test.cpp b/test/math/log1p_expm1_test.cpp index 4a53064b..4df662c6 100644 --- a/test/math/log1p_expm1_test.cpp +++ b/test/math/log1p_expm1_test.cpp @@ -140,7 +140,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test(number >(), "number >"); test(number >(), "number >"); - test(number >(), "number >"); + test(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/powm1_sqrtp1m1_test.cpp b/test/math/powm1_sqrtp1m1_test.cpp index db2621eb..1fa0f76d 100644 --- a/test/math/powm1_sqrtp1m1_test.cpp +++ b/test/math/powm1_sqrtp1m1_test.cpp @@ -132,7 +132,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_powm1_sqrtp1m1(number >(), "number >"); test_powm1_sqrtp1m1(number >(), "number >"); - test_powm1_sqrtp1m1(number >(), "number >"); + test_powm1_sqrtp1m1(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/table_type.hpp b/test/math/table_type.hpp index a6a526e5..0b78ec0f 100644 --- a/test/math/table_type.hpp +++ b/test/math/table_type.hpp @@ -27,7 +27,7 @@ inline std::ostream& operator << (std::ostream& os, string_table_entry const & w return os << static_cast(what); } -template +template struct table_type > { typedef string_table_entry type; diff --git a/test/math/test_bessel_i.cpp b/test/math/test_bessel_i.cpp index c9e7bb3c..4fc0c100 100644 --- a/test/math/test_bessel_i.cpp +++ b/test/math/test_bessel_i.cpp @@ -101,7 +101,7 @@ int test_main(int, char* []) test_bessel(number >(), "number >"); test_bessel(number >(), "number >"); test_bessel(number >(), "number >"); - test_bessel(number >(), "number >"); + test_bessel(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_bessel_j.cpp b/test/math/test_bessel_j.cpp index 7738d5ae..d0f2acd8 100644 --- a/test/math/test_bessel_j.cpp +++ b/test/math/test_bessel_j.cpp @@ -142,7 +142,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_bessel(number >(), "number >"); test_bessel(number >(), "number >"); - test_bessel(number >(), "number >"); + test_bessel(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_bessel_k.cpp b/test/math/test_bessel_k.cpp index 46ce61b9..8c4d8e54 100644 --- a/test/math/test_bessel_k.cpp +++ b/test/math/test_bessel_k.cpp @@ -115,7 +115,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_bessel(number >(), "number >"); test_bessel(number >(), "number >"); - test_bessel(number >(), "number >"); + test_bessel(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp index adb472ca..a3a7c91b 100644 --- a/test/math/test_bessel_y.cpp +++ b/test/math/test_bessel_y.cpp @@ -141,7 +141,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_bessel(number >(), "number >"); test_bessel(number >(), "number >"); - test_bessel(number >(), "number >"); + test_bessel(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_beta.cpp b/test/math/test_beta.cpp index 39409cb7..92d0fb77 100644 --- a/test/math/test_beta.cpp +++ b/test/math/test_beta.cpp @@ -127,7 +127,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_beta(number >(), "number >"); test_beta(number >(), "number >"); - test_beta(number >(), "number >"); + test_beta(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_binomial_coeff.cpp b/test/math/test_binomial_coeff.cpp index daae89b2..208c5dee 100644 --- a/test/math/test_binomial_coeff.cpp +++ b/test/math/test_binomial_coeff.cpp @@ -106,7 +106,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_binomial(number >(), "number >"); test_binomial(number >(), "number >"); - test_binomial(number >(), "number >"); + test_binomial(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_carlson.cpp b/test/math/test_carlson.cpp index 30f96116..d5936f38 100644 --- a/test/math/test_carlson.cpp +++ b/test/math/test_carlson.cpp @@ -98,7 +98,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_spots(number >(), "number >"); test_spots(number >(), "number >"); - test_spots(number >(), "number >"); + test_spots(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_cbrt.cpp b/test/math/test_cbrt.cpp index 156e0dd6..ca2af6d3 100644 --- a/test/math/test_cbrt.cpp +++ b/test/math/test_cbrt.cpp @@ -87,7 +87,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_cbrt(number >(), "number >"); test_cbrt(number >(), "number >"); - test_cbrt(number >(), "number >"); + test_cbrt(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_digamma.cpp b/test/math/test_digamma.cpp index 16653f83..a090081d 100644 --- a/test/math/test_digamma.cpp +++ b/test/math/test_digamma.cpp @@ -101,7 +101,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_digamma(number >(), "number >"); test_digamma(number >(), "number >"); - test_digamma(number >(), "number >"); + test_digamma(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_ellint_1.cpp b/test/math/test_ellint_1.cpp index b74c0f56..bf8eb4a3 100644 --- a/test/math/test_ellint_1.cpp +++ b/test/math/test_ellint_1.cpp @@ -94,7 +94,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_spots(number >(), "number >"); test_spots(number >(), "number >"); - test_spots(number >(), "number >"); + test_spots(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_ellint_2.cpp b/test/math/test_ellint_2.cpp index 9529a21c..d12c1d50 100644 --- a/test/math/test_ellint_2.cpp +++ b/test/math/test_ellint_2.cpp @@ -87,7 +87,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_spots(number >(), "number >"); test_spots(number >(), "number >"); - test_spots(number >(), "number >"); + test_spots(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_ellint_3.cpp b/test/math/test_ellint_3.cpp index 986b864b..abc6141a 100644 --- a/test/math/test_ellint_3.cpp +++ b/test/math/test_ellint_3.cpp @@ -108,7 +108,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_spots(number >(), "number >"); test_spots(number >(), "number >"); - test_spots(number >(), "number >"); + test_spots(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_erf.cpp b/test/math/test_erf.cpp index 3ce56dfc..e9308d8c 100644 --- a/test/math/test_erf.cpp +++ b/test/math/test_erf.cpp @@ -108,7 +108,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_erf(number >(), "number >"); test_erf(number >(), "number >"); - test_erf(number >(), "number >"); + test_erf(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_expint.cpp b/test/math/test_expint.cpp index 90b77e79..bf5b78eb 100644 --- a/test/math/test_expint.cpp +++ b/test/math/test_expint.cpp @@ -108,7 +108,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_expint(number >(), "number >"); test_expint(number >(), "number >"); - test_expint(number >(), "number >"); + test_expint(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_gamma.cpp b/test/math/test_gamma.cpp index 4e4d5636..c853bdb4 100644 --- a/test/math/test_gamma.cpp +++ b/test/math/test_gamma.cpp @@ -122,7 +122,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_gamma(number >(), "number >"); test_gamma(number >(), "number >"); - test_gamma(number >(), "number >"); + test_gamma(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_hermite.cpp b/test/math/test_hermite.cpp index 277e96a7..743a3de3 100644 --- a/test/math/test_hermite.cpp +++ b/test/math/test_hermite.cpp @@ -87,7 +87,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_hermite(number >(), "number >"); test_hermite(number >(), "number >"); - test_hermite(number >(), "number >"); + test_hermite(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_ibeta.cpp b/test/math/test_ibeta.cpp index e48fb900..2f6902e0 100644 --- a/test/math/test_ibeta.cpp +++ b/test/math/test_ibeta.cpp @@ -118,7 +118,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_beta(number >(), "number >"); test_beta(number >(), "number >"); - test_beta(number >(), "number >"); + test_beta(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_ibeta_2.cpp b/test/math/test_ibeta_2.cpp index 212056a7..72997385 100644 --- a/test/math/test_ibeta_2.cpp +++ b/test/math/test_ibeta_2.cpp @@ -118,7 +118,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_beta(number >(), "number >"); test_beta(number >(), "number >"); - test_beta(number >(), "number >"); + test_beta(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_ibeta_3.cpp b/test/math/test_ibeta_3.cpp index 8bb2a9a9..c6602542 100644 --- a/test/math/test_ibeta_3.cpp +++ b/test/math/test_ibeta_3.cpp @@ -104,7 +104,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_beta(number >(), "number >"); test_beta(number >(), "number >"); - test_beta(number >(), "number >"); + test_beta(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_ibeta_4.cpp b/test/math/test_ibeta_4.cpp index d4b224ff..c7a8b20f 100644 --- a/test/math/test_ibeta_4.cpp +++ b/test/math/test_ibeta_4.cpp @@ -111,7 +111,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_beta(number >(), "number >"); test_beta(number >(), "number >"); - test_beta(number >(), "number >"); + test_beta(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_ibeta_inv_1.cpp b/test/math/test_ibeta_inv_1.cpp index 54cb44eb..b9f052ca 100644 --- a/test/math/test_ibeta_inv_1.cpp +++ b/test/math/test_ibeta_inv_1.cpp @@ -97,7 +97,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_beta(number >(), "number >"); test_beta(number >(), "number >"); - test_beta(number >(), "number >"); + test_beta(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_ibeta_inv_ab_4.cpp b/test/math/test_ibeta_inv_ab_4.cpp index e9916b96..82eff4e6 100644 --- a/test/math/test_ibeta_inv_ab_4.cpp +++ b/test/math/test_ibeta_inv_ab_4.cpp @@ -90,7 +90,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_beta(number >(), "number >"); test_beta(number >(), "number >"); - test_beta(number >(), "number >"); + test_beta(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_igamma.cpp b/test/math/test_igamma.cpp index 50aff1c5..063cbeaf 100644 --- a/test/math/test_igamma.cpp +++ b/test/math/test_igamma.cpp @@ -94,7 +94,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_gamma(number >(), "number >"); test_gamma(number >(), "number >"); - test_gamma(number >(), "number >"); + test_gamma(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_igamma_inv.cpp b/test/math/test_igamma_inv.cpp index 697b58fd..5408444e 100644 --- a/test/math/test_igamma_inv.cpp +++ b/test/math/test_igamma_inv.cpp @@ -109,7 +109,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_gamma(number >(), "number >"); test_gamma(number >(), "number >"); - test_gamma(number >(), "number >"); + test_gamma(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_igamma_inva.cpp b/test/math/test_igamma_inva.cpp index 8ff4e6d4..fdd330e9 100644 --- a/test/math/test_igamma_inva.cpp +++ b/test/math/test_igamma_inva.cpp @@ -88,7 +88,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_gamma(number >(), "number >"); test_gamma(number >(), "number >"); - test_gamma(number >(), "number >"); + test_gamma(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_laguerre.cpp b/test/math/test_laguerre.cpp index 8f70b1ca..65840502 100644 --- a/test/math/test_laguerre.cpp +++ b/test/math/test_laguerre.cpp @@ -87,7 +87,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_laguerre(number >(), "number >"); test_laguerre(number >(), "number >"); - test_laguerre(number >(), "number >"); + test_laguerre(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_legendre.cpp b/test/math/test_legendre.cpp index f855b9c3..237310e6 100644 --- a/test/math/test_legendre.cpp +++ b/test/math/test_legendre.cpp @@ -87,7 +87,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_legendre_p(number >(), "number >"); test_legendre_p(number >(), "number >"); - test_legendre_p(number >(), "number >"); + test_legendre_p(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_tgamma_ratio.cpp b/test/math/test_tgamma_ratio.cpp index 931ffe3c..cae68344 100644 --- a/test/math/test_tgamma_ratio.cpp +++ b/test/math/test_tgamma_ratio.cpp @@ -101,7 +101,7 @@ int test_main(int, char* []) #ifdef TEST_CPP_DEC_FLOAT test_tgamma_ratio(number >(), "number >"); test_tgamma_ratio(number >(), "number >"); - test_tgamma_ratio(number >(), "number >"); + test_tgamma_ratio(number > >(), "number > >"); #endif return 0; } diff --git a/test/math/test_zeta.cpp b/test/math/test_zeta.cpp index 1d2184ce..4db422fe 100644 --- a/test/math/test_zeta.cpp +++ b/test/math/test_zeta.cpp @@ -96,7 +96,7 @@ int test_main(int, char* []) test_zeta(number >(), "number >"); test_zeta(number >(), "number >"); test_zeta(number >(), "number >"); - test_zeta(number >(), "number >"); + test_zeta(number > >(), "number > >"); #endif return 0; } diff --git a/test/test_acos.cpp b/test/test_acos.cpp index d0943592..c903613b 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -107,10 +107,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); #endif return boost::report_errors(); } diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index f972d761..26e624c6 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -1654,7 +1654,8 @@ int main() #endif #ifdef TEST_CPP_DEC_FLOAT test(); - test, boost::multiprecision::et_off> >(); + test, boost::multiprecision::et_off> >(); + test >, boost::multiprecision::et_on> >(); #endif #ifdef TEST_MPFR test(); diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 3c913082..3488f3d5 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -103,10 +103,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); // Check low multiprecision digit counts. test > >(); test > >(); diff --git a/test/test_atan.cpp b/test/test_atan.cpp index cfb2de3d..9888673d 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -249,10 +249,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); // Check low multiprecision digit counts. test > >(); test > >(); diff --git a/test/test_cos.cpp b/test/test_cos.cpp index c9c51068..55c6540b 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -47,6 +47,7 @@ template void test() { + std::cout << "Testing type " << typeid(T).name() << std::endl; static const boost::array data = {{ "-2.37609908807915949996042688873953402912174184373388399043229539427530802169622688886435380890546981798452174137747437590e-1", @@ -303,10 +304,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); #endif return boost::report_errors(); } diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index 5e08ec0c..f98f6cbc 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -145,10 +145,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); #endif return boost::report_errors(); } diff --git a/test/test_exp.cpp b/test/test_exp.cpp index f36d7c78..f9ca1cb1 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -47,6 +47,7 @@ template void test() { + std::cout << "Testing type " << typeid(T).name() << std::endl; static const boost::array data = {{ "1.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", @@ -185,10 +186,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); // Check low multiprecision digit counts. test > >(); test > >(); diff --git a/test/test_log.cpp b/test/test_log.cpp index 5d6ea4e4..12961093 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -47,6 +47,7 @@ template void test() { + std::cout << "Testing type " << typeid(T).name() << std::endl; static const boost::array data = {{ "-2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806", @@ -213,10 +214,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); // Check low multiprecision digit counts. test > >(); test > >(); diff --git a/test/test_pow.cpp b/test/test_pow.cpp index 6f489637..f269ddd6 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -588,10 +588,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); // Check low multiprecision digit counts. test > >(); test > >(); diff --git a/test/test_round.cpp b/test/test_round.cpp index f066a9d8..27fe149a 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -394,10 +394,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); #endif #ifdef TEST_BACKEND test >(); diff --git a/test/test_sin.cpp b/test/test_sin.cpp index 1d208575..571beb4f 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -47,6 +47,7 @@ template void test() { + std::cout << "Testing type: " << typeid(T).name() << std::endl; static const boost::array data = {{ "-9.71360659712083391437631022096936715962104815777147739346439739644168480837178969413799829610404829247283169084501281105e-1", @@ -297,10 +298,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); // Check low multiprecision digit counts. test > >(); test > >(); diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index bb47e54f..ec4f5365 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -221,10 +221,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); // Check low multiprecision digit counts. test > >(); test > >(); diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp index cd66f169..2ab95f28 100644 --- a/test/test_sqrt.cpp +++ b/test/test_sqrt.cpp @@ -191,10 +191,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); // Check low multiprecision digit counts. test > >(); test > >(); diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index 2860fde9..18478a7d 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -140,10 +140,10 @@ int main() test > >(); test > >(); test > >(); - test > >(); - test > >(); - test > >(); - test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); #endif return boost::report_errors(); } From 9f8b30fcdf7d17678681511d5ecca4f65b0be874 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 16 Sep 2012 12:25:14 +0000 Subject: [PATCH 236/256] Update docs with review comments. Update a few tests based on review comments. Regenerate docs. [SVN r80539] --- .../boost_multiprecision/indexes/s01.html | 4 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 4 +- doc/html/boost_multiprecision/map/todo.html | 106 ++- doc/html/boost_multiprecision/ref/number.html | 94 ++- .../tut/ints/cpp_int.html | 13 + doc/html/index.html | 2 +- doc/multiprecision.qbk | 79 ++- test/Jamfile.v2 | 23 + test/test_acos.cpp | 1 + test/test_asin.cpp | 1 + test/test_atan.cpp | 1 + test/test_cosh.cpp | 1 + test/test_pow.cpp | 1 + test/test_sinh.cpp | 1 + test/test_tan.cpp | 611 ++++++++++++++++++ test/test_tanh.cpp | 1 + 18 files changed, 915 insertions(+), 36 deletions(-) create mode 100644 test/test_tan.cpp diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index f8c6e580..6b1856e3 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    +Function Index

    A B C D E F I L M P R S T Z

    diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index d8dacbad..2706639a 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

    C G I M N T

    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 42e8cba8..12cee4d9 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    C I L M T U

    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 0deb96a1..862dddae 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G I L M N O P R S T U Z

    diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index e7fd11c7..5ab45fdb 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -17,6 +17,106 @@
    +

    + Things requested in review: +

    +
      +
    • + A 2's complement fixed precision int that uses exactly N bits and no + more. +
      • +
    • + A backend for an overflow aware integers. +
      • +
    • + Each back-end should document the requirements it satisfies (not currently + scheduled for inclusion: it's deliberately an implementation detail, + and "optional" requirements are optimisations which can't be + detected by the user). +
      • +
    • + IIUC convert_to is used to emulate in c++98 compilers C++11 explicit + conversions. Could the explicit conversion operator be added on compilers + supporting it? (Done 2012/09/15). +
      • +
    • + The front-end should make the differences between implicit and explicit + construction (Done 2012/09/15). +
      • +
    • + The use of bool in template parameters could be improved by the use of + an enum class which will be more explicit. E.g enum + class expression_template + {disabled, enabled}; enum class sign + {unsigned, signed}; (Partly done 2012/09/15). +
      • +
    • + The ExpresionTemplate parameter could be defaulted to a traits class + for more sensible defaults. +
      • +
    • + The library interface should use the noexcept (BOOST_NOEXCEPT, ...) facilities + (Done 2012/09/15). +
      • +
    • + It is unfortunate that the generic mp_number front end can not make use + contexpr as not all the backends can ensure this (done - we can go quite + a way). +
      • +
    • + literals: The library doesn't provide some kind of literals. I think + that the mp_number class should provide a way to create literals if the + backend is able to. (Done 2012/09/15). +
      • +
    • + The performances of mp_number<a_trivial_adaptor<float>, false>respect + to float and mp_number<a_trivial_adaptor<int>, false> and + int should be given to show the cost of using the generic interface (Mostly + done, just need to update docs to the latest results). +
      • +
    • + The documentation should contain Throws specification on the mp_number + and backend requirements operations. (Done 2012/09/15). +
      • +
    • + The tutorial should add more examples concerning implicit or explicit + conversions. (Done 2012/09/15). +
      • +
    • + The documentation must explain how move semantics helps in this domain + and what the backend needs to do to profit from this optimization. (Done + 2012/09/15). +
      • +
    • + The rounding applied when converting must be documented. +
      • +
    • + cpp_dec_float should round to nearest. +
      • +
    • + In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we + can optimise and eliminate one more temporary. +
      • +
    • + We can reuse temporaries in multiple subtrees (temporary caching). +
      • +
    • + Emphasise in the docs that ET's may reorder operations. +
      • +
    • + Document why we don't use proto (compile times). +
      • +
    • + Document what happens to small fixed precision cpp_int's. +
      • +
    • + Should we provide min/max overloads for expression templates? +
      • +
    • + Document why we don't abstract out addition/multiplication algorithms + etc. +
      • +

    More a list of what could be done, rather than what should be done (which may be a much smaller list!). @@ -57,10 +157,10 @@ be the default - int32_t or int64_t? (done 2012/09/06)

  • - Document the size requirements of fixed precision ints. + Document the size requirements of fixed precision ints (done 2012/09/15).
  • - Document std lib function accuracy. + Document std lib function accuracy (done 2012/09/15).
  • Make fixed precision orthogonal to Allocator type in cpp_int. Possible @@ -73,7 +173,7 @@
  • Be a bit clearer on the effects of sign-magnitude representation of cpp_int - - min == -max etc. + - min == -max etc - done.
  • Document cpp_dec_float precision, rounding, and exponent size (done 2012/09/06). diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html index b1f6dc2e..3c7994fc 100644 --- a/doc/html/boost_multiprecision/ref/number.html +++ b/doc/html/boost_multiprecision/ref/number.html @@ -787,10 +787,19 @@

    +

    + 0eps +

    +

    + 0eps +

    +

    + 0eps +

    @@ -800,10 +809,19 @@

    +

    + 0eps +

    +

    + 0eps +

    +

    + 0eps +

    @@ -813,10 +831,19 @@

    +

    + 0eps +

    +

    + 0eps +

    +

    + 0eps +

    @@ -826,10 +853,19 @@

    +

    + 1eps +

    +

    + 0eps +

    +

    + 0eps +

    @@ -839,10 +875,19 @@

    +

    + 1045eps[1] +

    +

    + 0eps +

    +

    + 0eps +

    @@ -852,10 +897,19 @@

    +

    + 2eps +

    +

    + 0eps +

    +

    + 0eps +

    @@ -865,10 +919,19 @@

    +

    + 1eps +

    +

    + 0eps +

    +

    + 0eps +

    @@ -877,24 +940,20 @@ pow

    - - - - - - - -

    - fmod + 0eps

    +

    + 4eps +

    - - +

    + 3eps +

    @@ -904,13 +963,26 @@

    +

    + 1eps +

    +

    + 0eps +

    +

    + 0eps +

    +

    [1] + It's likely that the inherent error in the input values to our + test cases are to blame here. +

    • diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html index 988e9909..fdfa36ff 100644 --- a/doc/html/boost_multiprecision/tut/ints/cpp_int.html +++ b/doc/html/boost_multiprecision/tut/ints/cpp_int.html @@ -148,6 +148,19 @@ of number on this backend move aware. +
  • + When used at fixed precision, the size of this type is always one machine + word larger than you would expect for an N-bit integer: the extra word + stores both the sign, and how many machine words in the integer are + actually in use. The latter is an optimisation for larger fixed precision + integers, so that a 1024-bit integer has almost the same performance + characterists as a 128-bit integer, rather than being 4 times slower + for addition and 16 times slower for multiplication (assuming the values + involved would always fit in 128 bits). Typically this means you can + use an integer type wide enough for the "worst case senario" + with only minor performance degradation even if most of the time the + arithmetic could in fact be done with a narrower type. +
    • diff --git a/doc/html/index.html b/doc/html/index.html index 2d72038a..6352948f 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -120,7 +120,7 @@ - +

    Last revised: September 07, 2012 at 08:25:28 GMT

    Last revised: September 16, 2012 at 12:00:51 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index e765f0e9..912cd037 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -406,6 +406,14 @@ the feature off. `uint128_t` then both `uint128_t(1)-4` and `-uint128(3)` would result in the value `0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD` of type `uint128_t`. * This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. +* When used at fixed precision, the size of this type is always one machine word larger than you would expect for an N-bit integer: +the extra word stores both the sign, and how many machine words in the integer are actually in use. +The latter is an optimisation for larger fixed precision integers, so that a 1024-bit integer has almost the same performance +characterists as a 128-bit integer, rather than being 4 times slower for addition and 16 times slower for multiplication + (assuming the values involved would always fit in 128 bits). +Typically this means you can use +an integer type wide enough for the "worst case senario" with only minor performance degradation even if most of the time +the arithmetic could in fact be done with a narrower type. [h5 Example:] @@ -1549,16 +1557,15 @@ here are exact (tested on Win32 with VC++10, MPFR-3.0.0, MPIR-2.1.1): [[log10][1eps][0eps][0eps]] [[cos][700eps][0eps][0eps]] [[sin][1eps][0eps][0eps]] -[[tan][][][]] -[[acos][][][]] -[[asin][][][]] -[[atan][][][]] -[[cosh][][][]] -[[sinh][][][]] -[[tanh][][][]] -[[pow][][][]] -[[fmod][][][]] -[[atan2][][][]] +[[tan][0eps][0eps][0eps]] +[[acos][0eps][0eps][0eps]] +[[asin][0eps][0eps][0eps]] +[[atan][1eps][0eps][0eps]] +[[cosh][1045eps[footnote It's likely that the inherent error in the input values to our test cases are to blame here.]][0eps][0eps]] +[[sinh][2eps][0eps][0eps]] +[[tanh][1eps][0eps][0eps]] +[[pow][0eps][4eps][3eps]] +[[atan2][1eps][0eps][0eps]] ] [h4 Traits Class Support] @@ -2675,6 +2682,52 @@ code. [section:todo TODO] +Things requested in review: + +* A 2's complement fixed precision int that uses exactly N bits and no more. +* A backend for an overflow aware integers. +* Each back-end should document the requirements it satisfies (not currently scheduled for inclusion: it's +deliberately an implementation detail, and "optional" requirements are optimisations which can't be detected +by the user). +* IIUC convert_to is used to emulate in c++98 compilers C++11 explicit +conversions. Could the explicit conversion operator be added on +compilers supporting it? (Done 2012/09/15). +* The front-end should make the differences between implicit and explicit +construction (Done 2012/09/15). +* The use of bool in template parameters could be improved by the use of +an enum class which will be more explicit. E.g `enum class expression_template {disabled, enabled}; +enum class sign {unsigned, signed};` (Partly done 2012/09/15). +* The ExpresionTemplate parameter could be defaulted to a traits class for more sensible defaults. +* The library interface should use the noexcept (BOOST_NOEXCEPT, ...) +facilities (Done 2012/09/15). +* It is unfortunate that the generic mp_number front end can not make use +contexpr as not all the backends can ensure this (done - we can go quite a way). +* literals: The library doesn't provide some kind of literals. I think that the +mp_number class should provide a way to create literals if the backend +is able to. (Done 2012/09/15). +* The performances of mp_number, false>respect to +float and mp_number, false> and int should be +given to show the cost of using the generic interface (Mostly done, just need to update docs to the latest results). +* The documentation should contain Throws specification on the mp_number +and backend requirements operations. (Done 2012/09/15). +* The tutorial should add more examples concerning implicit or explicit +conversions. (Done 2012/09/15). +* The documentation must explain how move semantics helps in this domain +and what the backend needs to do to profit from this optimization. (Done 2012/09/15). +* The rounding applied when converting must be documented. +* cpp_dec_float should round to nearest. +* In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we can optimise and eliminate one more temporary. +* We can reuse temporaries in multiple subtrees (temporary caching). +* Emphasise in the docs that ET's may reorder operations. +* Document why we don't use proto (compile times). +* Document what happens to small fixed precision cpp_int's. +* Should we provide min/max overloads for expression templates? +* Document why we don't abstract out addition/multiplication algorithms etc. + + + + + More a list of what ['could] be done, rather than what ['should] be done (which may be a much smaller list!). * Add back-end support for libdecNumber. @@ -2689,12 +2742,12 @@ More a list of what ['could] be done, rather than what ['should] be done (which * Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it. * Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents. Open question - what should be the default - int32_t or int64_t? (done 2012/09/06) -* Document the size requirements of fixed precision ints. -* Document std lib function accuracy. +* Document the size requirements of fixed precision ints (done 2012/09/15). +* Document std lib function accuracy (done 2012/09/15). * Make fixed precision orthogonal to Allocator type in cpp_int. Possible solution - add an additional MaxBits template argument that defaults to 0 (meaning keep going till no more space/memory). * Add support for fused multiply add (and subtract). GMP mpz_t could use this. -* Be a bit clearer on the effects of sign-magnitude representation of cpp_int - min == -max etc. +* Be a bit clearer on the effects of sign-magnitude representation of cpp_int - min == -max etc - done. * Document cpp_dec_float precision, rounding, and exponent size (done 2012/09/06). * Can we be clearer in the docs that mixed arithmetic doesn't work (no longer applicable as of 2012/09/06)? * Document round functions behaviour better (they behave as in C++11) (added note 2012/09/06). diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index e0fa0c37..ae17fbe4 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -496,6 +496,29 @@ run test_atan.cpp mpfr [ check-target-builds ../config//has_mpfr : : no ] : test_atan_mpfr_50 ; +run test_tan.cpp gmp + : # command line + : # input files + : # requirements + TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : no ] + : test_tan_mpf50 ; + +run test_tan.cpp + : # command line + : # input files + : # requirements + TEST_CPP_DEC_FLOAT + : test_tan_cpp_dec_float ; + +run test_tan.cpp mpfr + : # command line + : # input files + : # requirements + TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : no ] + : test_tan_mpfr_50 ; + run test_gmp_conversions.cpp gmp : # command line : # input files diff --git a/test/test_acos.cpp b/test/test_acos.cpp index c903613b..44bee8a5 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -47,6 +47,7 @@ template void test() { + std::cout << "Testing type: " << typeid(T).name() << std::endl; // // Test with some exact binary values as input - this tests our code // rather than the test data: diff --git a/test/test_asin.cpp b/test/test_asin.cpp index 3488f3d5..6f4acb22 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -47,6 +47,7 @@ template void test() { + std::cout << "Testing type: " << typeid(T).name() << std::endl; // // Test with some exact binary values as input - this tests our code // rather than the test data: diff --git a/test/test_atan.cpp b/test/test_atan.cpp index 9888673d..4e6d7552 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -68,6 +68,7 @@ struct is_mpfr_type void test() { + std::cout << "Testing type: " << typeid(T).name() << std::endl; static const boost::array data = {{ "9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999966666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-101", diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index f98f6cbc..68b4d838 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -47,6 +47,7 @@ template void test() { + std::cout << "Testing type: " << typeid(T).name() << std::endl; static const boost::array data = {{ "1.0560191127459844751259038114395241283965590525302917878166464679729562764239266483419824023679041866569431842053263976225991679105269492268050148624443706785607467750929028856273183654547152707568642275917435773104050171284580773949313906303074811586096214771879801872225500237540725592288167903987152007171391207680034517664218965133028298959753155835975555361514087618679892905973726581183754237665", diff --git a/test/test_pow.cpp b/test/test_pow.cpp index f269ddd6..07c770c5 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -48,6 +48,7 @@ template void test() { + std::cout << "Testing type: " << typeid(T).name() << std::endl; static const boost::array, 500> data = {{ {{ "9.85291419463953934609889984130859375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e4", "8.41670862661703722551465034484863281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e2", "8.66781019918879108354226292713799369912745098619466567318041467361236175866573114777000418440761829061824953361563557580935951901405814080757565313129904800947783606850513184296612628910656615168927761935861462770335134108408073175949783551491164949747086136599355880600420490275164555515512645668845e4202" }}, diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index ec4f5365..2c45eefb 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -47,6 +47,7 @@ template void test() { + std::cout << "Testing type: " << typeid(T).name() << std::endl; static const boost::array data = {{ "0.33937643772780730649735035088117439284797964277099188367427256402032493952288848579083622213428182842627923924487560393743204013166230906610274533504451302298480596207257724471359936027198954417317381228420986152562253196896619001418292769103034561794393400788635610424360775622370491149170501475453034747306600304507650361914904138327962144190354572359428689767990353722392457982930942617983634601752", diff --git a/test/test_tan.cpp b/test/test_tan.cpp new file mode 100644 index 00000000..341c4fbc --- /dev/null +++ b/test/test_tan.cpp @@ -0,0 +1,611 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include +#include +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) +# define TEST_MPF_50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFR_50 + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include +#endif +#if defined(TEST_MPFR_50) +#include +#endif +#ifdef TEST_BACKEND +#include +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include +#endif + +template +void test() +{ + std::cout << "Testing type: " << typeid(T).name() << std::endl; + static const boost::array, 500> data = + {{ + {{ "0", "0" }}, + {{ "0.03125", "0.03126017650125595642059651621507489147877835880393069701338513042228140662868270178810496567920444849" }}, + {{ "0.0625", "0.06258150756627501465828481747745378814263718044751609194477198396918772026898277636891147279909599223" }}, + {{ "0.09375", "0.09402562724573195576489755283678159034525247904824579838425258406126459673745015890895186868431790389" }}, + {{ "0.125", "0.1256551365751309677926782186297740007586657638922255426688666139272557034809288714758416649081949452" }}, + {{ "0.15625", "0.1575341073252716106852257741724104906661974475121544257009051769486388715993896887955248205741956572" }}, + {{ "0.1875", "0.1897286107180591328910833700730338162710122536010363055257273177325079653665703027537671734777793159" }}, + {{ "0.21875", "0.2223072805534313308722888175879995822319104918387718270273535559005416973923742249393961682186904743" }}, + {{ "0.25", "0.2553419212210362665044822364904736782042016388008226217404756502588831981346542579493165026310550454" }}, + {{ "0.28125", "0.2889081724405147260015884454642448286982056723714186732378896291489603033944207768995735063901118923" }}, + {{ "0.3125", "0.3230862443517455201183006557179619743037036164759656335249943943470835620899848486165999610265179128" }}, + {{ "0.34375", "0.3579617388480169983883959631794471406375375900948760280972554801967920011385682070576100261097824193" }}, + {{ "0.375", "0.3936265759256327582294137871012180981856966444080712949818309739116951585799388015457993878787997269" }}, + {{ "0.40625", "0.4301800474642300490203296054472752679963181652078151755042924196261397876727827800621729454863519218" }}, + {{ "0.4375", "0.467730025452391799921342706961992620413738282701114114727311802060193364671415150855360089743973883" }}, + {{ "0.46875", "0.5063943574962298120708227547071771387085972911587370796115595547436950963394141008177411206688111652" }}, + {{ "0.5", "0.5463024898437905132551794657802853832975517201797912461640913859329075105180258157151806482706562186" }}, + {{ "0.53125", "0.5875973675914432213941588631578976924522062928763012976297627647411436985181631978010052165746790249" }}, + {{ "0.5625", "0.630437673835884766852611429299775209903293946951939898251650513745196222165381994293674222073197888" }}, + {{ "0.59375", "0.6750004851442429076631779494777229128864061685897319107997999948317524157945835559284790797708856594" }}, + {{ "0.625", "0.7214844409909044199895178832795946807605892812145963657590722733756611374332889471678213489198161525" }}, + {{ "0.65625", "0.770113551344208705005983660052773240245517035179766333813336659352553100285016757206110401160028615" }}, + {{ "0.6875", "0.8211418015898941219114239653747117008753716453086877023306268412086961091026737960147423436480371207" }}, + {{ "0.71875", "0.874858760554482349539671907932155532231782257040588572549027780010892786023906162883923961511720127" }}, + {{ "0.75", "0.9315964599440724611652027565739364281886913399722189970823760758473440872606463942290222395451727347" }}, + {{ "0.78125", "0.9917378983632686802568573899299023689572109767948642785884455151680071204845003794305054375396567381" }}, + {{ "0.8125", "1.055727639411919906905928322585893795895648561782414602487481288436493656539800004691156074588329712" }}, + {{ "0.84375", "1.124085134704560944131255965236688143403009777898521429483610660496648114350313475950507899270640935" }}, + {{ "0.875", "1.197421629234347972339226617276609445975806623418086002265951386950959459751336541541255052511392263" }}, + {{ "0.90625", "1.276461828982383445402617843263224436254612963462020761243811395954456362359102470162910199798207331" }}, + {{ "0.9375", "1.362071976376228231137266640571127531383954502011184315622281795551984309995647087587519913956728759" }}, + {{ "0.96875", "1.455296662469072910283351203225910848640458285194500237036240390915811463257413817682188441906818248" }}, + {{ "1", "1.557407724654902230506974807458360173087250772381520038383946605698861397151727289555099965202242984" }}, + {{ "1.03125", "1.669970130353601668362228999287655840466243330137306547430306024592587314737242276409239980979443174" }}, + {{ "1.0625", "1.794932157265411111412512666640647365321540790157497713363548060626019826336277151761592643681562889" }}, + {{ "1.09375", "1.934751011916103924218794082343652203808222523749686394781135509079848569244264225172363092871198012" }}, + {{ "1.125", "2.092571276372179004423733981234886782259941716148720572913991515339894408382371607574079035650497628" }}, + {{ "1.15625", "2.272484060247449371554848155118626331407879143446651944395567708418983252993702557436552564850427597" }}, + {{ "1.1875", "2.479912917556758792437515574454698934001624072586467858166295252178386457324268836053055868956236971" }}, + {{ "1.21875", "2.722205296368710926927932441765877991142333599010908457349133016162381084884183783877142234320889929" }}, + {{ "1.25", "3.009569673862831288157563894386243931391637699606062181047618417194668052548525026087449023543493348" }}, + {{ "1.28125", "3.356619539863437446801254212059537717694035906934171604782430676182834617443082960603002796648697006" }}, + {{ "1.3125", "3.785038166535876194630450975067081020082611278470578710038656250838244608554256510046862645943214168" }}, + {{ "1.34375", "4.328443997051826678273102914917348524900160978527585314859991445919675557868173766988955991311583481" }}, + {{ "1.375", "5.04191525648136332110647205436422898660842030191113551461354742130497045161358084541551547909572374" }}, + {{ "1.40625", "6.02236781523945747670227618692239447637023828129226996489330674807031833318199939459376428890858723" }}, + {{ "1.4375", "7.457597366497314807346683309400119820853357043059007743950216525315136075258562571085388447049580691" }}, + {{ "1.46875", "9.765431722939984318153137075537986427219225446494026346174651506537333303940271000197727980305021618" }}, + {{ "1.5", "14.10141994717171938764608365198775644565954357723586186612326758608969627041415526864870292630944229" }}, + {{ "1.53125", "25.27361509038201021888564593774203447137999639112919943365223977030408052066444435679945642193151117" }}, + {{ "1.5625", "120.5325057225426126499709994255564804478992494692406282802019970839232698437518852292295322760051977" }}, + {{ "1.59375", "-43.55836040673973128976461522014256814059799632626649998645431997677346427573993827534701436489680689" }}, + {{ "1.625", "-18.43086276236962258434966752738448975654856844592479276671012332110139541995382323486170528839748939" }}, + {{ "1.65625", "-11.67374867215481348216513536293945130766869617358776549669176281104274968860961548954064974733991076" }}, + {{ "1.6875", "-8.529773993911653209272999783778324026196719414411590092375294867302897481134537117581472896391856125" }}, + {{ "1.71875", "-6.709482397820695376442251396240149572345307174060614879543507453718786710576833294867753884694537068" }}, + {{ "1.75", "-5.520379922509330168089935698420205500301122430036809938027371836902288281994865833387763391132527793" }}, + {{ "1.78125", "-4.681280325336429567316481395066494078522124421106252324368679821712511116596067067167862140573504461" }}, + {{ "1.8125", "-4.056414052170035671394695838412072312925972547334020477371203912084804008892977770267448199074447777" }}, + {{ "1.84375", "-3.572185661861125859870109039981697499670205624150737204067785923886464814599307447743073100872203818" }}, + {{ "1.875", "-3.185238919501229169914672833591055563068190813252958079987355697225012578404488535638528315769681186" }}, + {{ "1.90625", "-2.868371726567042158384165205507273428429609298347592604875428057959086996590505442480814626239318494" }}, + {{ "1.9375", "-2.603652912010850547260718033703880538638622594696262109914178307203938532760442947667909676035790898" }}, + {{ "1.96875", "-2.378782114044268462754557076702009514149544247914950239975234530609231791907385965883627186285245033" }}, + {{ "2", "-2.185039863261518991643306102313682543432017746227663164562955869966773747209194182319743542104728548" }}, + {{ "2.03125", "-2.016072402071886080344963601799448100479409508905552305715636690184075224937451135890591580854847922" }}, + {{ "2.0625", "-1.86713988123437020407782794323860043132451055327769468817959958079457004467338400013589662215485346" }}, + {{ "2.09375", "-1.734634103946532053863260773540976834775727590591832428183425859927779370855756294581920109583545138" }}, + {{ "2.125", "-1.615759423973460045704218998135983105718634789435135146363364502252797531256854000679335498343468236" }}, + {{ "2.15625", "-1.508315836353881219959349807787957061590021089263168744744644715237923771519750208817662219357365791" }}, + {{ "2.1875", "-1.410548011813148830578875195416796900655621273730614063607851296345238287109255775298602026828637775" }}, + {{ "2.21875", "-1.321038011883972941371242354544773427461451983076687172335288474134737150563349929598365091185906691" }}, + {{ "2.25", "-1.238627616224096475286573358483115818987811679840895892063010057942989763968416082248247538779346115" }}, + {{ "2.28125", "-1.162361144121629479886631062456510653121514437736910570208484412489182649570861593071569298439919991" }}, + {{ "2.3125", "-1.091442725473163592445273166049218471062020679322657236270267019564600575624640388147984118518979059" }}, + {{ "2.34375", "-1.025203931548868392935198625444103909279764848147237361743751176005185409221197679274034521026108332" }}, + {{ "2.375", "-0.9630789471610371325783309326887526239686440615099207880230611368370468000350460791927023591069451265" }}, + {{ "2.40625", "-0.9045853091742213054875350240709441597937968403208608690036487459318455608785453421438664490396695609" }}, + {{ "2.4375", "-0.8493088059488314622450104194218363224080665638942044768228802750401486144919082454646163741529209686" }}, + {{ "2.46875", "-0.7968915235352686521345041809817019192899787435677815043081356746793473472915009329509869865385574704" }}, + {{ "2.5", "-0.747022297238660279355352687825274557904116956883011279066593089700271855760843718388592769933778409" }}, + {{ "2.53125", "-0.699429020084844342139783831016239425344370000759297142831905446726651787263273111657622358057530982" }}, + {{ "2.5625", "-0.653872397910572369605836837404416068498526729423046632151562590225826018439381877458767572737519508" }}, + {{ "2.59375", "-0.6101408409895599924272199138429116429964861640554001463611527892708422318404310839955568952517348978" }}, + {{ "2.625", "-0.5680462555551780726648895974757705443146437970424414412380682777625097984947690751561280498460825515" }}, + {{ "2.65625", "-0.5274205529869757121326571336563206310413652365485599902702063856643631953989601868253259786432770197" }}, + {{ "2.6875", 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"15.15625", "-0.6154649762727536414801474029122625793755198617269250343988631456453788448149731706979351529235579577" }}, + {{ "15.1875", "-0.5731771332183040948793178896118867037269598773610412277642977614409075169432893108977656087532808068" }}, + {{ "15.21875", "-0.5323780107028691176788965668440942781647156607765742951342412648358988559400799809724920990286528734" }}, + {{ "15.25", "-0.4929146351866012621666401573415074523464609163340854530825224584649245974424596583470196176643838565" }}, + {{ "15.28125", "-0.4546489554738299415350063572461193751006928326854122963028434583535719327916356408447934270192962049" }}, + {{ "15.3125", "-0.4174557284251085623680148206370333657407709127949181945517726979253617292255491330234726669774559159" }}, + {{ "15.34375", "-0.3812207207302419203446046603506711987787377766806738457878506795815713138223264722913354548269137032" }}, + {{ "15.375", "-0.3458391695028422582485004568448026536356203654713446806415710694635885346246660520826948870993463705" }}, + {{ "15.40625", "-0.311214455551825073642663079591570618837743590849903018274057606911872122304533000910107606645650336" }}, + {{ "15.4375", "-0.2772569518534830079599506190692912755868921271423525814120233867695893487373304945292237740353757468" }}, + {{ "15.46875", "-0.2438830165543173054192587099181568413614402066070223778896735213919894343566763962867244846621486138" }}, + {{ "15.5", "-0.2110141052012553133863173741408514435037061655011970687100846880180438182550528565062101594891245018" }}, + {{ "15.53125", "-0.1785759811388596991279739233477573236616687666102227187311862264495771634608666297275574790232136991" }}, + {{ "15.5625", "-0.1464980063716879847555275878278898667317766571375499828106145375100216949704230935552550931052323183" }}, + {{ "15.59375", "-0.1147124978452713735943481847220917786442201384229215777788278473922030662630912256721375261600875605" }}, + }}; + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = tan(T(data[k][0])); + T e = relative_error(val, T(data[k][1])); + unsigned err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + val = tan(-T(data[k][0])); + e = relative_error(val, T(-T(data[k][1]))); + err = e.template convert_to(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; +} + + +int main() +{ +#ifdef TEST_BACKEND + test >(); +#endif +#ifdef TEST_MPF_50 + test(); + test(); +#endif +#ifdef TEST_MPFR_50 + test(); + test(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test(); + test(); + // Some "peculiar" digit counts which stress our code: + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > >(); + test > > >(); + test > > >(); + // Check low multiprecision digit counts. + test > >(); + test > >(); +#endif + return boost::report_errors(); +} + + + diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index 18478a7d..04d49f0a 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -47,6 +47,7 @@ template void test() { + std::cout << "Testing type: " << typeid(T).name() << std::endl; static const boost::array data = {{ "0.32137338579537729992840434899278935725496267444911714908205287462634251052210833615032073534299473485492692600156322137421801432333125051088723502425037485776412801577568405892077585206768190530859883094571475323319480739773193974206966728764224286661945738178210577326172938196062277314761537881936346874075881338768208490193827960565412814349738654540520356903367084438822830345189856017860672463017", From dd7ee604313e5a5dbb72023c79e933d6c37912ad Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 18 Sep 2012 16:47:03 +0000 Subject: [PATCH 237/256] Fix GCC C++11 mode failures. Tidy up TODO list. [SVN r80577] --- doc/multiprecision.qbk | 101 +++++++++--------- .../boost/multiprecision/cpp_dec_float.hpp | 13 ++- include/boost/multiprecision/cpp_int.hpp | 10 +- .../multiprecision/detail/default_ops.hpp | 24 +++++ test/test.hpp | 35 ++++-- test/test_arithmetic.cpp | 18 ++-- 6 files changed, 126 insertions(+), 75 deletions(-) diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 912cd037..b9772383 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -2682,50 +2682,6 @@ code. [section:todo TODO] -Things requested in review: - -* A 2's complement fixed precision int that uses exactly N bits and no more. -* A backend for an overflow aware integers. -* Each back-end should document the requirements it satisfies (not currently scheduled for inclusion: it's -deliberately an implementation detail, and "optional" requirements are optimisations which can't be detected -by the user). -* IIUC convert_to is used to emulate in c++98 compilers C++11 explicit -conversions. Could the explicit conversion operator be added on -compilers supporting it? (Done 2012/09/15). -* The front-end should make the differences between implicit and explicit -construction (Done 2012/09/15). -* The use of bool in template parameters could be improved by the use of -an enum class which will be more explicit. E.g `enum class expression_template {disabled, enabled}; -enum class sign {unsigned, signed};` (Partly done 2012/09/15). -* The ExpresionTemplate parameter could be defaulted to a traits class for more sensible defaults. -* The library interface should use the noexcept (BOOST_NOEXCEPT, ...) -facilities (Done 2012/09/15). -* It is unfortunate that the generic mp_number front end can not make use -contexpr as not all the backends can ensure this (done - we can go quite a way). -* literals: The library doesn't provide some kind of literals. I think that the -mp_number class should provide a way to create literals if the backend -is able to. (Done 2012/09/15). -* The performances of mp_number, false>respect to -float and mp_number, false> and int should be -given to show the cost of using the generic interface (Mostly done, just need to update docs to the latest results). -* The documentation should contain Throws specification on the mp_number -and backend requirements operations. (Done 2012/09/15). -* The tutorial should add more examples concerning implicit or explicit -conversions. (Done 2012/09/15). -* The documentation must explain how move semantics helps in this domain -and what the backend needs to do to profit from this optimization. (Done 2012/09/15). -* The rounding applied when converting must be documented. -* cpp_dec_float should round to nearest. -* In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we can optimise and eliminate one more temporary. -* We can reuse temporaries in multiple subtrees (temporary caching). -* Emphasise in the docs that ET's may reorder operations. -* Document why we don't use proto (compile times). -* Document what happens to small fixed precision cpp_int's. -* Should we provide min/max overloads for expression templates? -* Document why we don't abstract out addition/multiplication algorithms etc. - - - More a list of what ['could] be done, rather than what ['should] be done (which may be a much smaller list!). @@ -2736,22 +2692,69 @@ More a list of what ['could] be done, rather than what ['should] be done (which * Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. * Add assembly level routines to cpp_int_backend. * Add an all C++ binary floating point type. +* Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it, +the hard part is IO and binary-decimal convertion. +* Should there be a choice of rounding mode (probably MPFR specific)? + +Things requested in review: + +* A 2's complement fixed precision int that uses exactly N bits and no more. +* A backend for an overflow aware integers. +* Each back-end should document the requirements it satisfies (not currently scheduled for inclusion: it's +deliberately an implementation detail, and "optional" requirements are optimisations which can't be detected +by the user). +* The use of bool in template parameters could be improved by the use of +an enum class which will be more explicit. E.g `enum class expression_template {disabled, enabled}; +enum class sign {unsigned, signed};` (Partly done 2012/09/15). +* The ExpresionTemplate parameter could be defaulted to a traits class for more sensible defaults. +* The performances of mp_number, false>respect to +float and mp_number, false> and int should be +given to show the cost of using the generic interface (Mostly done, just need to update docs to the latest results). +* The rounding applied when converting must be documented. +* cpp_dec_float should round to nearest. +* In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we can optimise and eliminate one more temporary. +* We can reuse temporaries in multiple subtrees (temporary caching). +* Emphasise in the docs that ET's may reorder operations. +* Document why we don't use proto (compile times). +* Document what happens to small fixed precision cpp_int's. +* Should we provide min/max overloads for expression templates? +* Document why we don't abstract out addition/multiplication algorithms etc. +* IIUC convert_to is used to emulate in c++98 compilers C++11 explicit +conversions. Could the explicit conversion operator be added on +compilers supporting it? (Done 2012/09/15). +* The front-end should make the differences between implicit and explicit +construction (Done 2012/09/15). +* The tutorial should add more examples concerning implicit or explicit +conversions. (Done 2012/09/15). +* The documentation must explain how move semantics helps in this domain +and what the backend needs to do to profit from this optimization. (Done 2012/09/15). +* The documentation should contain Throws specification on the mp_number +and backend requirements operations. (Done 2012/09/15). +* The library interface should use the noexcept (BOOST_NOEXCEPT, ...) +facilities (Done 2012/09/15). +* It is unfortunate that the generic mp_number front end can not make use +contexpr as not all the backends can ensure this (done - we can go quite a way). +* literals: The library doesn't provide some kind of literals. I think that the +mp_number class should provide a way to create literals if the backend +is able to. (Done 2012/09/15). + + [h4 Pre-Review Comments] -* Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it. +* Make fixed precision orthogonal to Allocator type in cpp_int. Possible solution - add an additional MaxBits +template argument that defaults to 0 (meaning keep going till no more space/memory). +* Add support for fused multiply add (and subtract). GMP mpz_t could use this. +* Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it (Moved to TODO list). +* Should there be a choice of rounding mode (probably MPFR specific)? Moved to TODO list. * Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents. Open question - what should be the default - int32_t or int64_t? (done 2012/09/06) * Document the size requirements of fixed precision ints (done 2012/09/15). * Document std lib function accuracy (done 2012/09/15). -* Make fixed precision orthogonal to Allocator type in cpp_int. Possible solution - add an additional MaxBits -template argument that defaults to 0 (meaning keep going till no more space/memory). -* Add support for fused multiply add (and subtract). GMP mpz_t could use this. * Be a bit clearer on the effects of sign-magnitude representation of cpp_int - min == -max etc - done. * Document cpp_dec_float precision, rounding, and exponent size (done 2012/09/06). * Can we be clearer in the docs that mixed arithmetic doesn't work (no longer applicable as of 2012/09/06)? * Document round functions behaviour better (they behave as in C++11) (added note 2012/09/06). -* Should there be a choice of rounding mode (probably MPFR specific)? * Document limits on size of cpp_dec_float (done 2012/09/06). [endsect] diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index 73f85bff..e7264d17 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -16,6 +16,7 @@ #include #include #include +#include // // Headers required for Boost.Math integration: @@ -38,11 +39,17 @@ namespace backends{ namespace detail{ +template +struct rebind +{ + typedef typename Allocator::template rebind::other type; +}; + template -struct dynamic_array : public std::vector +struct dynamic_array : public std::vector::type> { dynamic_array() - : std::vector(static_cast::size_type>(S), static_cast(0)) {} + : std::vector::type>(static_cast::type>::size_type>(S), static_cast(0)) {} }; } @@ -1668,7 +1675,7 @@ cpp_dec_float cpp_dec_float= Digits10 - 1) + else if(exp >= static_cast(Digits10 - 1)) { // The number is too large to resolve the integer part. // Thus it is already a pure integer part. diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 6c5429d1..6e11c0b0 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -1702,7 +1702,7 @@ BOOST_FORCEINLINE void eval_subtract(cpp_int_backend -BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { if(a.sign()) { @@ -2682,22 +2682,22 @@ struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCE template BOOST_FORCEINLINE void eval_bitwise_and( cpp_int_backend& result, - const cpp_int_backend& o)BOOST_NOEXCEPT_IF(is_void::value) + const cpp_int_backend& o)BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_and()); } template -BOOST_FORCEINLINE void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) +BOOST_FORCEINLINE void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_or()); } template -BOOST_FORCEINLINE void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) +BOOST_FORCEINLINE void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value) { bitwise_op(result, o, bit_xor()); } template -BOOST_FORCEINLINE void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) +BOOST_FORCEINLINE void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) { // Increment and negate: result = o; diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index a8b04623..dfe1abca 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -177,6 +177,9 @@ inline typename enable_if_c >::value && is_convertib // // Default versions of 3-arg arithmetic functions, these mostly just forward to the 2 arg versions: // +template +void eval_add(T& t, const U& u, const V& v); + template inline void eval_add_default(T& t, const T& u, const T& v) { @@ -224,6 +227,9 @@ inline void eval_add(T& t, const U& u, const V& v) eval_add_default(t, u, v); } +template +void eval_subtract(T& t, const U& u, const V& v); + template inline void eval_subtract_default(T& t, const T& u, const T& v) { @@ -273,6 +279,9 @@ inline void eval_subtract(T& t, const U& u, const V& v) eval_subtract_default(t, u, v); } +template +void eval_multiply(T& t, const U& u, const V& v); + template inline void eval_multiply_default(T& t, const T& u, const T& v) { @@ -320,6 +329,9 @@ inline void eval_multiply(T& t, const U& u, const V& v) eval_multiply_default(t, u, v); } +template +void eval_divide(T& t, const U& u, const V& v); + template inline void eval_divide_default(T& t, const T& u, const T& v) { @@ -375,6 +387,9 @@ inline void eval_divide(T& t, const U& u, const V& v) eval_divide_default(t, u, v); } +template +void eval_modulus(T& t, const U& u, const V& v); + template inline void eval_modulus_default(T& t, const T& u, const T& v) { @@ -430,6 +445,9 @@ inline void eval_modulus(T& t, const U& u, const V& v) eval_modulus_default(t, u, v); } +template +void eval_bitwise_and(T& t, const U& u, const V& v); + template inline void eval_bitwise_and_default(T& t, const T& u, const T& v) { @@ -477,6 +495,9 @@ inline void eval_bitwise_and(T& t, const U& u, const V& v) eval_bitwise_and_default(t, u, v); } +template +void eval_bitwise_or(T& t, const U& u, const V& v); + template inline void eval_bitwise_or_default(T& t, const T& u, const T& v) { @@ -524,6 +545,9 @@ inline void eval_bitwise_or(T& t, const U& u, const V& v) eval_bitwise_or_default(t, u, v); } +template +void eval_bitwise_xor(T& t, const U& u, const V& v); + template inline void eval_bitwise_xor_default(T& t, const T& u, const T& v) { diff --git a/test/test.hpp b/test/test.hpp index 6e83d762..d707ccc0 100644 --- a/test/test.hpp +++ b/test/test.hpp @@ -14,19 +14,40 @@ #include #include #include +#include +#include + +namespace detail{ + +template +inline typename boost::disable_if, T>::type abs(const T& a) +{ + return a < 0 ? -a : a; +} + +template +inline typename boost::enable_if, T>::type abs(const T& a) +{ + return a; +} + +} template T relative_error(T a, T b) { + using std::abs; + using detail::abs; + T min_val = (std::numeric_limits::min)(); T max_val = (std::numeric_limits::max)(); if((a != 0) && (b != 0)) { // TODO: use isfinite: - if(fabs(b) >= max_val) + if(abs(b) >= max_val) { - if(fabs(a) >= max_val) + if(abs(a) >= max_val) return 0; // one infinity is as good as another! } // If the result is denormalised, treat all denorms as equivalent: @@ -38,17 +59,17 @@ T relative_error(T a, T b) b = min_val; else if((b > -min_val) && (b < 0)) b = -min_val; - return (std::max)(fabs((a-b)/a), fabs((a-b)/b)) / std::numeric_limits::epsilon(); + return (std::max)(abs(T((a-b)/a)), abs(T((a-b)/b))) / std::numeric_limits::epsilon(); } // Handle special case where one or both are zero: if(min_val == 0) - return fabs(a-b); - if(fabs(a) < min_val) + return abs(T(a-b)); + if(abs(a) < min_val) a = min_val; - if(fabs(b) < min_val) + if(abs(b) < min_val) b = min_val; - return (std::max)(fabs((a-b)/a), fabs((a-b)/b)) / std::numeric_limits::epsilon(); + return (std::max)(abs(T((a-b)/a)), abs(T((a-b)/b))) / std::numeric_limits::epsilon(); } enum diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 26e624c6..7128c20a 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -121,29 +121,25 @@ template bool isfloat(T){ return false; } namespace detail{ -template -typename boost::disable_if, T>::type abs(T v) +template +typename boost::multiprecision::detail::expression::result_type + abs(boost::multiprecision::detail::expression const& v) { - return v < 0 ? -v : v; -} -template -typename boost::enable_if, T>::type abs(T v) -{ - return v; + typedef typename boost::multiprecision::detail::expression::result_type result_type; + return v < 0 ? result_type(-v) : result_type(v); } } #define BOOST_TEST_CLOSE(x, y, tol)\ - using std::abs; using detail::abs;\ if(x == 0){\ BOOST_TEST(y == 0); }\ else if(!isfloat(x)){\ BOOST_TEST(x == y); }\ - else if((x != y) && (abs((x-y)/x) > tol))\ + else if((x != y) && (detail::abs((x-y)/x) > tol))\ {\ BOOST_ERROR("Expected tolerance was exceeded: ");\ - BOOST_LIGHTWEIGHT_TEST_OSTREAM << std::setprecision(34) << "(x-y)/x = " << abs((x-y)/x) \ + BOOST_LIGHTWEIGHT_TEST_OSTREAM << std::setprecision(34) << "(x-y)/x = " << detail::abs((x-y)/x) \ << " tolerance = " << tol << std::endl;\ } From 741f98585df4b1135d3c554dce11bc9d1bdf0a58 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 18 Sep 2012 17:02:45 +0000 Subject: [PATCH 238/256] Remove dead code. [SVN r80580] --- .../multiprecision/detail/number_compare.hpp | 123 +----------------- 1 file changed, 1 insertion(+), 122 deletions(-) diff --git a/include/boost/multiprecision/detail/number_compare.hpp b/include/boost/multiprecision/detail/number_compare.hpp index ce7f622d..dda75e64 100644 --- a/include/boost/multiprecision/detail/number_compare.hpp +++ b/include/boost/multiprecision/detail/number_compare.hpp @@ -79,10 +79,7 @@ struct is_valid_mixed_compare : public mpl::false_ {}; template struct is_valid_mixed_compare, Val> : public is_convertible> {}; -/* -template -struct is_valid_mixed_compare > : public is_convertible> {}; -*/ + template struct is_valid_mixed_compare, number > : public mpl::false_ {}; @@ -109,16 +106,6 @@ inline typename enable_if_c::canonical_value(b)); } -/* -template -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator == (const number& a, const detail::expression& b) -{ - using default_ops::eval_eq; - typename detail::expression::result_type t(b); - return eval_eq(a.backend(), t.backend()); -} -*/ template inline typename enable_if_c, Arithmetic>::value, bool>::type operator == (const Arithmetic& a, const number& b) @@ -135,15 +122,6 @@ inline typename enable_if_c -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator == (const detail::expression& a, const number& b) -{ - using default_ops::eval_eq; - typename detail::expression::result_type t(a); - return eval_eq(t.backend(), b.backend()); -}*/ template inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator == (const detail::expression& a, const Arithmetic& b) @@ -176,16 +154,6 @@ inline typename enable_if_c::canonical_value(b)); } -/* -template -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator != (const number& a, const detail::expression& b) -{ - using default_ops::eval_eq; - typename detail::expression::result_type t(b); - return !eval_eq(a.backend(), t.backend()); -} -*/ template inline typename enable_if_c, Arithmetic>::value, bool>::type operator != (const Arithmetic& a, const number& b) @@ -202,15 +170,6 @@ inline typename enable_if_c -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator != (const detail::expression& a, const number& b) -{ - using default_ops::eval_eq; - typename detail::expression::result_type t(a); - return !eval_eq(t.backend(), b.backend()); -}*/ template inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator != (const detail::expression& a, const Arithmetic& b) @@ -243,16 +202,6 @@ inline typename enable_if_c::canonical_value(b)); } -/* -template -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator < (const number& a, const detail::expression& b) -{ - using default_ops::eval_lt; - typename detail::expression::result_type t(b); - return eval_lt(a.backend(), t.backend()); -} -*/ template inline typename enable_if_c, Arithmetic>::value, bool>::type operator < (const Arithmetic& a, const number& b) @@ -269,16 +218,6 @@ inline typename enable_if_c -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator < (const detail::expression& a, const number& b) -{ - using default_ops::eval_lt; - typename detail::expression::result_type t(a); - return eval_lt(t.backend(), b.backend()); -} -*/ template inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator < (const detail::expression& a, const Arithmetic& b) @@ -311,16 +250,6 @@ inline typename enable_if_c::canonical_value(b)); } -/* -template -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator > (const number& a, const detail::expression& b) -{ - using default_ops::eval_gt; - typename detail::expression::result_type t(b); - return eval_gt(a.backend(), t.backend()); -} -*/ template inline typename enable_if_c, Arithmetic>::value, bool>::type operator > (const Arithmetic& a, const number& b) @@ -337,16 +266,6 @@ inline typename enable_if_c -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator > (const detail::expression& a, const number& b) -{ - using default_ops::eval_gt; - typename detail::expression::result_type t(a); - return eval_gt(t.backend(), b.backend()); -} -*/ template inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator > (const detail::expression& a, const Arithmetic& b) @@ -379,16 +298,6 @@ inline typename enable_if_c::canonical_value(b)); } -/* -template -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator <= (const number& a, const detail::expression& b) -{ - using default_ops::eval_gt; - typename detail::expression::result_type t(b); - return !eval_gt(a.backend(), t.backend()); -} -*/ template inline typename enable_if_c, Arithmetic>::value, bool>::type operator <= (const Arithmetic& a, const number& b) @@ -405,16 +314,6 @@ inline typename enable_if_c -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator <= (const detail::expression& a, const number& b) -{ - using default_ops::eval_gt; - typename detail::expression::result_type t(a); - return !eval_gt(t.backend(), b.backend()); -} -*/ template inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator <= (const detail::expression& a, const Arithmetic& b) @@ -447,16 +346,6 @@ inline typename enable_if_c::canonical_value(b)); } -/* -template -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator >= (const number& a, const detail::expression& b) -{ - using default_ops::eval_lt; - typename detail::expression::result_type t(b); - return !eval_lt(a.backend(), t.backend()); -} -*/ template inline typename enable_if_c, Arithmetic>::value, bool>::type operator >= (const Arithmetic& a, const number& b) @@ -473,16 +362,6 @@ inline typename enable_if_c -inline typename enable_if, typename detail::expression::result_type>, bool>::type - operator >= (const detail::expression& a, const number& b) -{ - using default_ops::eval_lt; - typename detail::expression::result_type t(a); - return !eval_lt(t.backend(), b.backend()); -} -*/ template inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type operator >= (const detail::expression& a, const Arithmetic& b) From 4f2738fd6f90ced9a24009d387d78eaed91c9788 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 20 Sep 2012 16:04:02 +0000 Subject: [PATCH 239/256] Add traits class to determine default ExpressionTemplate parameter value. Add support for fused-multiply-add/subtract. Optimise temporary usage when the LHS also appears on the RHS. [SVN r80607] --- .../boost_multiprecision/indexes/s01.html | 12 +- .../boost_multiprecision/indexes/s02.html | 13 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 19 +- doc/html/boost_multiprecision/map/hist.html | 11 + doc/html/boost_multiprecision/map/todo.html | 233 +++++++++--------- .../boost_multiprecision/ref/backendconc.html | 229 +++++++++++++++++ .../boost_multiprecision/ref/cpp_int_ref.html | 22 +- doc/html/boost_multiprecision/ref/number.html | 30 ++- .../tut/ints/cpp_int.html | 26 +- doc/html/index.html | 2 +- doc/multiprecision.qbk | 116 +++++++-- include/boost/multiprecision/cpp_int.hpp | 22 +- .../multiprecision/detail/default_ops.hpp | 184 +++++++++----- .../boost/multiprecision/detail/et_ops.hpp | 60 +++++ .../detail/functions/constants.hpp | 6 +- .../multiprecision/detail/functions/pow.hpp | 22 +- .../multiprecision/detail/functions/trig.hpp | 24 +- .../multiprecision/detail/number_base.hpp | 19 +- .../multiprecision/detail/number_compare.hpp | 4 +- include/boost/multiprecision/gmp.hpp | 58 ++++- include/boost/multiprecision/number.hpp | 60 ++++- .../boost/multiprecision/rational_adapter.hpp | 25 +- test/test_arithmetic.cpp | 161 +++++++++++- test/test_constants.cpp | 4 +- test/test_float_io.cpp | 4 +- 26 files changed, 1065 insertions(+), 305 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 6b1856e3..b8bcad1a 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    +Function Index

    A B C D E F I L M P R S T Z

    @@ -265,6 +265,14 @@
  • +

    eval_multiply_add

    +
    +
    • +
  • +

    eval_multiply_subtract

    +
    +
    • +

  • eval_pow

    • diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index 2706639a..29be2280 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,10 +13,10 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    -

    C G I M N T

    +Class Index
    +

    C E G I M N T

    C @@ -33,6 +33,13 @@
    +E +
    +
    • +

      expression_template_default

      +
      +
    +
    G
      diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 12cee4d9..dff01ef2 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
      PrevUpHomeNext
      -
      +

      -Typedef Index

      +Typedef Index

    C I L M T U

    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 862dddae..3030cc3f 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G I L M N O P R S T U Z

    @@ -347,6 +347,14 @@
  • +

    eval_multiply_add

    +
    +
    • +
  • +

    eval_multiply_subtract

    +
    +
    • +

  • eval_pow

    • @@ -400,6 +408,10 @@

    eval_trunc

    +
  • +

    expression_template_default

    +
    +
    • F @@ -676,6 +688,7 @@

  • component_type

  • default_precision

  • divide_qr

    • +

  • expression_template_default

  • fpclassify

  • integer_modulus

  • iround

    • @@ -746,6 +759,8 @@

  • eval_lt

  • eval_modulus

  • eval_multiply

    • +

  • eval_multiply_add

    • +

  • eval_multiply_subtract

  • eval_pow

  • eval_powm

  • eval_qr

    • diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html index f7102bd0..ca0c5cca 100644 --- a/doc/html/boost_multiprecision/map/hist.html +++ b/doc/html/boost_multiprecision/map/hist.html @@ -44,6 +44,17 @@ Changed ExpressionTemplates parameter to class number to use enumerated values rather than true/false. +
  • + Changed ExpressionTemplate parameter default value to use a traits class + so that the default value depends on the backend used. +
    • +
  • + Added support for fused-multiply-add/subtract with GMP support. +
    • +
  • + Tweaked expression template unpacking to use fewer temporaries when the + LHS also appears in the RHS. +
    • diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index 5ab45fdb..2abdc184 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -17,106 +17,6 @@
    -

    - Things requested in review: -

    -
      -
    • - A 2's complement fixed precision int that uses exactly N bits and no - more. -
      • -
    • - A backend for an overflow aware integers. -
      • -
    • - Each back-end should document the requirements it satisfies (not currently - scheduled for inclusion: it's deliberately an implementation detail, - and "optional" requirements are optimisations which can't be - detected by the user). -
      • -
    • - IIUC convert_to is used to emulate in c++98 compilers C++11 explicit - conversions. Could the explicit conversion operator be added on compilers - supporting it? (Done 2012/09/15). -
      • -
    • - The front-end should make the differences between implicit and explicit - construction (Done 2012/09/15). -
      • -
    • - The use of bool in template parameters could be improved by the use of - an enum class which will be more explicit. E.g enum - class expression_template - {disabled, enabled}; enum class sign - {unsigned, signed}; (Partly done 2012/09/15). -
      • -
    • - The ExpresionTemplate parameter could be defaulted to a traits class - for more sensible defaults. -
      • -
    • - The library interface should use the noexcept (BOOST_NOEXCEPT, ...) facilities - (Done 2012/09/15). -
      • -
    • - It is unfortunate that the generic mp_number front end can not make use - contexpr as not all the backends can ensure this (done - we can go quite - a way). -
      • -
    • - literals: The library doesn't provide some kind of literals. I think - that the mp_number class should provide a way to create literals if the - backend is able to. (Done 2012/09/15). -
      • -
    • - The performances of mp_number<a_trivial_adaptor<float>, false>respect - to float and mp_number<a_trivial_adaptor<int>, false> and - int should be given to show the cost of using the generic interface (Mostly - done, just need to update docs to the latest results). -
      • -
    • - The documentation should contain Throws specification on the mp_number - and backend requirements operations. (Done 2012/09/15). -
      • -
    • - The tutorial should add more examples concerning implicit or explicit - conversions. (Done 2012/09/15). -
      • -
    • - The documentation must explain how move semantics helps in this domain - and what the backend needs to do to profit from this optimization. (Done - 2012/09/15). -
      • -
    • - The rounding applied when converting must be documented. -
      • -
    • - cpp_dec_float should round to nearest. -
      • -
    • - In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we - can optimise and eliminate one more temporary. -
      • -
    • - We can reuse temporaries in multiple subtrees (temporary caching). -
      • -
    • - Emphasise in the docs that ET's may reorder operations. -
      • -
    • - Document why we don't use proto (compile times). -
      • -
    • - Document what happens to small fixed precision cpp_int's. -
      • -
    • - Should we provide min/max overloads for expression templates? -
      • -
    • - Document why we don't abstract out addition/multiplication algorithms - etc. -
      • -

    More a list of what could be done, rather than what should be done (which may be a much smaller list!). @@ -140,6 +40,114 @@

  • Add an all C++ binary floating point type.
    • +
  • + Can ring types (exact floating point types) be supported? The answer + should be yes, but someone needs to write it, the hard part is IO and + binary-decimal convertion. +
    • +
  • + Should there be a choice of rounding mode (probably MPFR specific)? +
    • + +

    + Things requested in review: +

    +
      +
    • + A 2's complement fixed precision int that uses exactly N bits and no + more. +
      • +
    • + A backend for an overflow aware integers. +
      • +
    • + Each back-end should document the requirements it satisfies (not currently + scheduled for inclusion: it's deliberately an implementation detail, + and "optional" requirements are optimisations which can't be + detected by the user). +
      • +
    • + The use of bool in template parameters could be improved by the use of + an enum class which will be more explicit. E.g enum + class expression_template + {disabled, enabled}; enum class sign + {unsigned, signed}; (Partly done 2012/09/15). +
      • +
    • + The performances of mp_number<a_trivial_adaptor<float>, false>respect + to float and mp_number<a_trivial_adaptor<int>, false> and + int should be given to show the cost of using the generic interface (Mostly + done, just need to update docs to the latest results). +
      • +
    • + The rounding applied when converting must be documented. +
      • +
    • + cpp_dec_float should round to nearest. +
      • +
    • + We can reuse temporaries in multiple subtrees (temporary caching). +
      • +
    • + Emphasise in the docs that ET's may reorder operations. +
      • +
    • + Document why we don't use proto (compile times). +
      • +
    • + Document what happens to small fixed precision cpp_int's. +
      • +
    • + Should we provide min/max overloads for expression templates? +
      • +
    • + Document why we don't abstract out addition/multiplication algorithms + etc. +
      • +
    • + IIUC convert_to is used to emulate in c++98 compilers C++11 explicit + conversions. Could the explicit conversion operator be added on compilers + supporting it? (Done 2012/09/15). +
      • +
    • + The front-end should make the differences between implicit and explicit + construction (Done 2012/09/15). +
      • +
    • + The tutorial should add more examples concerning implicit or explicit + conversions. (Done 2012/09/15). +
      • +
    • + The documentation must explain how move semantics helps in this domain + and what the backend needs to do to profit from this optimization. (Done + 2012/09/15). +
      • +
    • + The documentation should contain Throws specification on the mp_number + and backend requirements operations. (Done 2012/09/15). +
      • +
    • + The library interface should use the noexcept (BOOST_NOEXCEPT, ...) facilities + (Done 2012/09/15). +
      • +
    • + It is unfortunate that the generic mp_number front end can not make use + contexpr as not all the backends can ensure this (done - we can go quite + a way). +
      • +
    • + literals: The library doesn't provide some kind of literals. I think + that the mp_number class should provide a way to create literals if the + backend is able to. (Done 2012/09/15). +
      • +
    • + The ExpresionTemplate parameter could be defaulted to a traits class + for more sensible defaults (done 2012/09/20). +
      • +
    • + In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we + can optimise and eliminate one more temporary (done 2012/09/20). +
    @@ -147,9 +155,18 @@ Comments
      +
    • + Make fixed precision orthogonal to Allocator type in cpp_int. Possible + solution - add an additional MaxBits template argument that defaults + to 0 (meaning keep going till no more space/memory). +
    • Can ring types (exact floating point types) be supported? The answer - should be yes, but someone needs to write it. + should be yes, but someone needs to write it (Moved to TODO list). +
      • +
    • + Should there be a choice of rounding mode (probably MPFR specific)? Moved + to TODO list.
    • Make the exponent type for cpp_dec_float a templare parameter, maybe @@ -162,15 +179,6 @@
    • Document std lib function accuracy (done 2012/09/15).
      • -
    • - Make fixed precision orthogonal to Allocator type in cpp_int. Possible - solution - add an additional MaxBits template argument that defaults - to 0 (meaning keep going till no more space/memory). -
      • -
    • - Add support for fused multiply add (and subtract). GMP mpz_t could use - this. -
    • Be a bit clearer on the effects of sign-magnitude representation of cpp_int - min == -max etc - done. @@ -187,10 +195,11 @@ note 2012/09/06).
    • - Should there be a choice of rounding mode (probably MPFR specific)? + Document limits on size of cpp_dec_float (done 2012/09/06).
    • - Document limits on size of cpp_dec_float (done 2012/09/06). + Add support for fused multiply add (and subtract). GMP mpz_t could use + this (done 2012/09/20).
    diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index 3550a227..2f6d4b91 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -1810,6 +1810,235 @@ + +

    + eval_multiply_add(b, cb, cb2) +

    + + +

    + void +

    + + +

    + Multiplies cb by + cb2 and adds the + result to b. When + not provided does the equivalent of creating a temporary B t + and eval_multiply(t, cb, cb2) followed by eval_add(b, t). +

    + + +

    +   +

    + + + + +

    + eval_multiply_add(b, cb, a) +

    + + +

    + void +

    + + +

    + Multiplies a by + cb and adds the + result to b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided + does the equivalent of creating a temporary B + t and eval_multiply(t, cb, a) followed by eval_add(b, t). +

    + + +

    +   +

    + + + + +

    + eval_multiply_add(b, a, cb) +

    + + +

    + void +

    + + +

    + Multiplies a by + cb and adds the + result to b. The + type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided + does the equivalent of eval_multiply_add(b, cb, a). +

    + + +

    +   +

    + + + + +

    + eval_multiply_subtract(b, cb, cb2) +

    + + +

    + void +

    + + +

    + Multiplies cb by + cb2 and subtracts + the result from b. + When not provided does the equivalent of creating a temporary + B t + and eval_multiply(t, cb, cb2) followed by eval_subtract(b, t). +

    + + +

    +   +

    + + + + +

    + eval_multiply_subtract(b, cb, a) +

    + + +

    + void +

    + + +

    + Multiplies a by + cb and subtracts + the result from b. + The type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided + does the equivalent of creating a temporary B + t and eval_multiply(t, cb, a) followed by eval_subtract(b, t). +

    + + +

    +   +

    + + + + +

    + eval_multiply_subtract(b, a, cb) +

    + + +

    + void +

    + + +

    + Multiplies a by + cb and subtracts + the result from b. + The type of a shall + be listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. When not provided + does the equivalent of eval_multiply_subtract(b, cb, a). +

    + + +

    +   +

    + + + + +

    + eval_multiply_add(b, cb, cb2, cb3) +

    + + +

    + void +

    + + +

    + Multiplies cb by + cb2 and adds the + result to cb3 storing + the result in b. + When not provided does the equivalent of eval_multiply(b, cb, cb2) followed by eval_add(b, cb3). For brevity, only a version showing + all arguments of type B + is shown here, but you can replace up to any 2 of cb, cb2 + and cb3 with any + type type listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    + + +

    +   +

    + + + + +

    + eval_multiply_subtract(b, cb, cb2, cb3) +

    + + +

    + void +

    + + +

    + Multiplies cb by + cb2 and subtracts + from the result cb3 + storing the result in b. + When not provided does the equivalent of eval_multiply(b, cb, cb2) followed by eval_subtract(b, cb3). For brevity, only a version showing + all arguments of type B + is shown here, but you can replace up to any 2 of cb, cb2 + and cb3 with any + type type listed in one of the type lists B::signed_types, + B::unsigned_types or B::float_types. +

    + + +

    +   +

    + + +

    eval_divide(b, diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html index 0b84e4e9..f1dbd5df 100644 --- a/doc/html/boost_multiprecision/ref/cpp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_int_ref.html @@ -21,22 +21,28 @@ template <unsigned MinBits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> > struct cpp_int_backend; +// +// Expression templates default to et_off if there is no allocator: +// +template <unsigned MinDigits, bool Signed> +struct expression_template_default<cpp_int_backend<MinDigits, Signed, void> > +{ static const expression_template_option value = et_off; }; typedef number<cpp_int_backend<> > cpp_int; // arbitrary precision integer typedef rational_adapter<cpp_int_backend<> > cpp_rational_backend; typedef number<cpp_rational_backend> cpp_rational; // arbitrary precision rational number // Fixed precision unsigned types: -typedef number<cpp_int_backend<128, false, void>, et_off> uint128_t; -typedef number<cpp_int_backend<256, false, void>, et_off> uint256_t; -typedef number<cpp_int_backend<512, false, void>, et_off> uint512_t; -typedef number<cpp_int_backend<1024, false, void>, et_off> uint1024_t; +typedef number<cpp_int_backend<128, false, void> > uint128_t; +typedef number<cpp_int_backend<256, false, void> > uint256_t; +typedef number<cpp_int_backend<512, false, void> > uint512_t; +typedef number<cpp_int_backend<1024, false, void> > uint1024_t; // Fixed precision signed types: -typedef number<cpp_int_backend<128, true, void>, et_off> int128_t; -typedef number<cpp_int_backend<256, true, void>, et_off> int256_t; -typedef number<cpp_int_backend<512, true, void>, et_off> int512_t; -typedef number<cpp_int_backend<1024, true, void>, et_off> int1024_t; +typedef number<cpp_int_backend<128, true, void> > int128_t; +typedef number<cpp_int_backend<256, true, void> > int256_t; +typedef number<cpp_int_backend<512, true, void> > int512_t; +typedef number<cpp_int_backend<1024, true, void> > int1024_t; }} // namespaces diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html index 3c7994fc..de7a6cdc 100644 --- a/doc/html/boost_multiprecision/ref/number.html +++ b/doc/html/boost_multiprecision/ref/number.html @@ -23,7 +23,12 @@ 

    namespace boost{ namespace multiprecision{
 
-template <class Backend, expression_template_option ExpressionTemplates = true>
+enum expression_template_option { et_on = 1, et_off = 0 };
+
+template <class Backend> struct expression_template_default
+{ static const expression_template_option value = et_on; };
+
+template <class Backend, expression_template_option ExpressionTemplates = expression_template_default<Backend>::value>
 class number
 {
    number();
@@ -206,7 +211,20 @@
 
         Description
       
-
    template <class Backend, expression_template_option ExpressionTemplates = true>
+
    enum expression_template_option { et_on = 1, et_off = 0 };
+
    
+
    
+        This enumerated type is used to specify whether expression templates are
+        turned on (et_on) or turned off (et_off).
+      
    
+
    template <class Backend> struct expression_template_default
+{ static const expression_template_option value = et_on; };
+
    
+
    
+        This traits class specifies the default expression template option to be
+        used with a particular Backend type. It defaults to et_on.
+      
    
+
    template <class Backend, expression_template_option ExpressionTemplates = expression_template_default<Backend>::value>
 class number;
 
    
 
    
@@ -222,8 +240,12 @@
             
    
 
    ExpressionTemplates
    
 
    
-              A Boolean value: when true, then expression templates are enabled,
-              otherwise they are disabled.
+              A Boolean value: when et_on,
+              then expression templates are enabled, otherwise when set to et_off they are disabled. The default
+              for this parameter is computed via the traits class expression_template_default
+              whose member value
+              defaults to et_on unless
+              the the traits class is specialized for a particular backend.
             
    
 
 
diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html
index fdfa36ff..a220dc59 100644
--- a/doc/html/boost_multiprecision/tut/ints/cpp_int.html
+++ b/doc/html/boost_multiprecision/tut/ints/cpp_int.html
@@ -26,22 +26,28 @@
 
 template <unsigned MinDigits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
 class cpp_int_backend;
+//
+// Expression templates default to et_off if there is no allocator:
+//
+template <unsigned MinDigits, bool Signed>
+struct expression_template_default<cpp_int_backend<MinDigits, Signed, void> >
+{ static const expression_template_option value = et_off; };
 
-typedef number<cpp_int_backend<> >           cpp_int;    // arbitrary precision integer
+typedef number<cpp_int_backend<> >              cpp_int;    // arbitrary precision integer
 typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
-typedef number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
+typedef number<cpp_rational_backend>            cpp_rational; // arbitrary precision rational number
 
 // Fixed precision unsigned types:
-typedef number<cpp_int_backend<128, false, void>, et_off>   uint128_t;
-typedef number<cpp_int_backend<256, false, void>, et_off>   uint256_t;
-typedef number<cpp_int_backend<512, false, void>, et_off>   uint512_t;
-typedef number<cpp_int_backend<1024, false, void>, et_off>  uint1024_t;
+typedef number<cpp_int_backend<128, false, void> >   uint128_t;
+typedef number<cpp_int_backend<256, false, void> >   uint256_t;
+typedef number<cpp_int_backend<512, false, void> >   uint512_t;
+typedef number<cpp_int_backend<1024, false, void> >  uint1024_t;
 
 // Fixed precision signed types:
-typedef number<cpp_int_backend<128, true, void>, et_off>    int128_t;
-typedef number<cpp_int_backend<256, true, void>, et_off>    int256_t;
-typedef number<cpp_int_backend<512, true, void>, et_off>    int512_t;
-typedef number<cpp_int_backend<1024, true, void>, et_off>   int1024_t;
+typedef number<cpp_int_backend<128, true, void> >    int128_t;
+typedef number<cpp_int_backend<256, true, void> >    int256_t;
+typedef number<cpp_int_backend<512, true, void> >    int512_t;
+typedef number<cpp_int_backend<1024, true, void> >   int1024_t;
 
 }} // namespaces
 
    
diff --git a/doc/html/index.html b/doc/html/index.html
index 6352948f..0482b470 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -120,7 +120,7 @@
 
 
 
-
+
    Last revised: September 16, 2012 at 12:00:51 GMT
    Last revised: September 20, 2012 at 15:58:33 GMT
    		
 
    		
 
    
 
    
diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk
index b9772383..c9380777 100644
--- a/doc/multiprecision.qbk
+++ b/doc/multiprecision.qbk
@@ -340,22 +340,28 @@ The following back-ends provide integer arithmetic:
 
    template  >
    class cpp_int_backend;
+   //
+   // Expression templates default to et_off if there is no allocator:
+   //
+   template 
+   struct expression_template_default >
+   { static const expression_template_option value = et_off; };
 
-   typedef number >           cpp_int;    // arbitrary precision integer
+   typedef number >              cpp_int;    // arbitrary precision integer
    typedef rational_adapter >    cpp_rational_backend;
-   typedef number         cpp_rational; // arbitrary precision rational number
+   typedef number            cpp_rational; // arbitrary precision rational number
 
    // Fixed precision unsigned types:
-   typedef number, et_off>   uint128_t;
-   typedef number, et_off>   uint256_t;
-   typedef number, et_off>   uint512_t;
-   typedef number, et_off>  uint1024_t;
+   typedef number >   uint128_t;
+   typedef number >   uint256_t;
+   typedef number >   uint512_t;
+   typedef number >  uint1024_t;
 
    // Fixed precision signed types:
-   typedef number, et_off>    int128_t;
-   typedef number, et_off>    int256_t;
-   typedef number, et_off>    int512_t;
-   typedef number, et_off>   int1024_t;
+   typedef number >    int128_t;
+   typedef number >    int256_t;
+   typedef number >    int512_t;
+   typedef number >   int1024_t;
 
    }} // namespaces
 
@@ -1109,7 +1115,12 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba
 
    namespace boost{ namespace multiprecision{
 
-   template 
+   enum expression_template_option { et_on = 1, et_off = 0 };
+
+   template  struct expression_template_default 
+   { static const expression_template_option value = et_on; };
+
+   template ::value>
    class number
    {
       number();
@@ -1290,14 +1301,26 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba
 
 [h4 Description]
 
-   template 
+   enum expression_template_option { et_on = 1, et_off = 0 };
+
+This enumerated type is used to specify whether expression templates are turned on (et_on) or turned off (et_off).
+
+   template  struct expression_template_default 
+   { static const expression_template_option value = et_on; };
+
+This traits class specifies the default expression template option to be used with a particular Backend type.
+It defaults to `et_on`.
+
+   template ::value>
    class number;
 
 Class `number` has two template arguments:
 
 [variablelist
 [[Backend][The actual arithmetic back-end that does all the work.]]
-[[ExpressionTemplates][A Boolean value: when true, then expression templates are enabled, otherwise they are disabled.]]
+[[ExpressionTemplates][A Boolean value: when `et_on`, then expression templates are enabled, otherwise when set to `et_off` they are disabled.
+   The default for this parameter is computed via the traits class `expression_template_default` whose member `value` defaults to `et_on` unless
+   the the traits class is specialized for a particular backend.]]
 ]
 
    number();
@@ -1698,22 +1721,28 @@ whose precision can vary at compile time (such as `mpf_float`).
 
    template  >
    struct cpp_int_backend;
+   //
+   // Expression templates default to et_off if there is no allocator:
+   //
+   template 
+   struct expression_template_default >
+   { static const expression_template_option value = et_off; };
 
    typedef number >           cpp_int;    // arbitrary precision integer
    typedef rational_adapter >    cpp_rational_backend;
    typedef number         cpp_rational; // arbitrary precision rational number
 
    // Fixed precision unsigned types:
-   typedef number, et_off>   uint128_t;
-   typedef number, et_off>   uint256_t;
-   typedef number, et_off>   uint512_t;
-   typedef number, et_off>  uint1024_t;
+   typedef number >   uint128_t;
+   typedef number >   uint256_t;
+   typedef number >   uint512_t;
+   typedef number >  uint1024_t;
 
    // Fixed precision signed types:
-   typedef number, et_off>    int128_t;
-   typedef number, et_off>    int256_t;
-   typedef number, et_off>    int512_t;
-   typedef number, et_off>   int1024_t;
+   typedef number >    int128_t;
+   typedef number >    int256_t;
+   typedef number >    int512_t;
+   typedef number >   int1024_t;
 
    }} // namespaces
 
@@ -2080,6 +2109,42 @@ of type B2.
 [[`eval_multiply(b, a, cb)`][`void`][Multiplies `a` by `cb` and stores the result in `b`.  The type of `a` shall be listed in one of the type lists
             `B::signed_types`, `B::unsigned_types` or `B::float_types`.
             When not provided, does the equivalent of `eval_multiply(b, cb, a)`.][[space]]]
+[[`eval_multiply_add(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and adds the result to `b`.
+            When not provided does the equivalent of creating a temporary `B t` and `eval_multiply(t, cb, cb2)` followed by
+            `eval_add(b, t)`.][[space]]]
+[[`eval_multiply_add(b, cb, a)`][`void`][Multiplies `a` by `cb` and adds the result to `b`.
+            The type of `a` shall be listed in one of the type lists
+            `B::signed_types`, `B::unsigned_types` or `B::float_types`.
+            When not provided does the equivalent of creating a temporary `B t` and `eval_multiply(t, cb, a)` followed by
+            `eval_add(b, t)`.][[space]]]
+[[`eval_multiply_add(b, a, cb)`][`void`][Multiplies `a` by `cb` and adds the result to `b`.
+            The type of `a` shall be listed in one of the type lists
+            `B::signed_types`, `B::unsigned_types` or `B::float_types`.
+            When not provided does the equivalent of  `eval_multiply_add(b, cb, a)`.][[space]]]
+[[`eval_multiply_subtract(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and subtracts the result from `b`.
+            When not provided does the equivalent of creating a temporary `B t` and `eval_multiply(t, cb, cb2)` followed by
+            `eval_subtract(b, t)`.][[space]]]
+[[`eval_multiply_subtract(b, cb, a)`][`void`][Multiplies `a` by `cb` and subtracts the result from `b`.
+            The type of `a` shall be listed in one of the type lists
+            `B::signed_types`, `B::unsigned_types` or `B::float_types`.
+            When not provided does the equivalent of creating a temporary `B t` and `eval_multiply(t, cb, a)` followed by
+            `eval_subtract(b, t)`.][[space]]]
+[[`eval_multiply_subtract(b, a, cb)`][`void`][Multiplies `a` by `cb` and subtracts the result from `b`.
+            The type of `a` shall be listed in one of the type lists
+            `B::signed_types`, `B::unsigned_types` or `B::float_types`.
+            When not provided does the equivalent of  `eval_multiply_subtract(b, cb, a)`.][[space]]]
+[[`eval_multiply_add(b, cb, cb2, cb3)`][`void`][Multiplies `cb` by `cb2` and adds the result to `cb3` storing the result in `b`.
+            When not provided does the equivalent of `eval_multiply(b, cb, cb2)` followed by
+            `eval_add(b, cb3)`.
+            For brevity, only a version showing all arguments of type `B` is shown here, but you can replace up to any 2 of
+            `cb`, `cb2` and `cb3` with any type type listed in one of the type lists
+            `B::signed_types`, `B::unsigned_types` or `B::float_types`.][[space]]]
+[[`eval_multiply_subtract(b, cb, cb2, cb3)`][`void`][Multiplies `cb` by `cb2` and subtracts from the result `cb3` storing the result in `b`.
+            When not provided does the equivalent of `eval_multiply(b, cb, cb2)` followed by
+            `eval_subtract(b, cb3)`.
+            For brevity, only a version showing all arguments of type `B` is shown here, but you can replace up to any 2 of
+            `cb`, `cb2` and `cb3` with any type type listed in one of the type lists
+            `B::signed_types`, `B::unsigned_types` or `B::float_types`.][[space]]]
 [[`eval_divide(b, a)`][`void`][Divides `b` by `a`.  The type of `a` shall be listed in one of the type lists
             `B::signed_types`, `B::unsigned_types` or `B::float_types`.
             When not provided, the default version calls `eval_divide(b, B(a))`]
@@ -2665,6 +2730,9 @@ Windows Vista machine.
 * Removed "mp_" prefix from types.
 * Allowed mixed precision arithmetic.
 * Changed ExpressionTemplates parameter to class `number` to use enumerated values rather than true/false.
+* Changed ExpressionTemplate parameter default value to use a traits class so that the default value depends on the backend used.
+* Added support for fused-multiply-add/subtract with GMP support.
+* Tweaked expression template unpacking to use fewer temporaries when the LHS also appears in the RHS.
 
 [h4 Pre-review history]
 
@@ -2706,13 +2774,11 @@ by the user).
 * The use of bool in template parameters could be improved by the use of 
 an enum class which will be more explicit. E.g `enum class expression_template {disabled, enabled};
 enum class sign {unsigned, signed};`  (Partly done 2012/09/15).
-* The ExpresionTemplate parameter could be defaulted to a traits class for more sensible defaults.
 * The performances of mp_number, false>respect to 
 float and mp_number, false> and int should be 
 given to show the cost of using the generic interface (Mostly done, just need to update docs to the latest results).
 * The rounding applied when converting must be documented.
 * cpp_dec_float should round to nearest.
-* In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we can optimise and eliminate one more temporary.
 * We can reuse temporaries in multiple subtrees (temporary caching).
 * Emphasise in the docs that ET's may reorder operations.
 * Document why we don't use proto (compile times).
@@ -2737,6 +2803,8 @@ contexpr as not all the backends can ensure this (done - we can go quite a way).
 * literals: The library doesn't provide some kind of literals. I think that the 
 mp_number class should provide a way to create literals if the backend 
 is able to.  (Done 2012/09/15).
+* The ExpresionTemplate parameter could be defaulted to a traits class for more sensible defaults (done 2012/09/20).
+* In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we can optimise and eliminate one more temporary (done 2012/09/20).
 
 
 
@@ -2744,7 +2812,6 @@ is able to.  (Done 2012/09/15).
 
 * Make fixed precision orthogonal to Allocator type in cpp_int.  Possible solution - add an additional MaxBits 
 template argument that defaults to 0 (meaning keep going till no more space/memory).
-* Add support for fused multiply add (and subtract).  GMP mpz_t could use this.
 * Can ring types (exact floating point types) be supported?  The answer should be yes, but someone needs to write it (Moved to TODO list).
 * Should there be a choice of rounding mode (probably MPFR specific)?  Moved to TODO list.
 * Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents.
@@ -2756,6 +2823,7 @@ Open question - what should be the default - int32_t or int64_t?  (done 2012/09/
 * Can we be clearer in the docs that mixed arithmetic doesn't work (no longer applicable as of 2012/09/06)?
 * Document round functions behaviour better (they behave as in C++11) (added note 2012/09/06).
 * Document limits on size of cpp_dec_float (done 2012/09/06).
+* Add support for fused multiply add (and subtract).  GMP mpz_t could use this (done 2012/09/20).
 
 [endsect]
 
diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp
index 6e11c0b0..0436f657 100644
--- a/include/boost/multiprecision/cpp_int.hpp
+++ b/include/boost/multiprecision/cpp_int.hpp
@@ -3059,6 +3059,12 @@ BOOST_FORCEINLINE typename enable_if, Integer>::type eval_int
 
 } // namespace backends;
 
+template 
+struct expression_template_default >
+{
+   static const expression_template_option value = et_off;
+};
+
 using boost::multiprecision::backends::cpp_int_backend;
 
 template 
@@ -3069,16 +3075,16 @@ typedef rational_adapter >   cpp_rational_backend;
 typedef number        cpp_rational;
 
 // Fixed precision unsigned types:
-typedef number, et_off>   uint128_t;
-typedef number, et_off>   uint256_t;
-typedef number, et_off>   uint512_t;
-typedef number, et_off>  uint1024_t;
+typedef number >   uint128_t;
+typedef number >   uint256_t;
+typedef number >   uint512_t;
+typedef number >  uint1024_t;
 
 // Fixed precision signed types:
-typedef number, et_off>    int128_t;
-typedef number, et_off>    int256_t;
-typedef number, et_off>    int512_t;
-typedef number, et_off>   int1024_t;
+typedef number >    int128_t;
+typedef number >    int256_t;
+typedef number >    int512_t;
+typedef number >   int1024_t;
 
 #ifdef BOOST_MSVC
 #pragma warning(pop)
diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp
index dfe1abca..d83b336d 100644
--- a/include/boost/multiprecision/detail/default_ops.hpp
+++ b/include/boost/multiprecision/detail/default_ops.hpp
@@ -35,10 +35,16 @@ namespace boost{ namespace multiprecision{ namespace default_ops{
 //
 // Default versions of mixed arithmetic, these just construct a temporary
 // from the arithmetic value and then do the arithmetic on that, two versions
-// of each depending on whether the backend can be directly constructed from type V:
+// of each depending on whether the backend can be directly constructed from type V.
+//
+// Note that we have to provide *all* the template parameters to class number when used in
+// enable_if as MSVC-10 won't compile the code if we rely on a computed-default parameter.
+// Since the result of the test doesn't depend on whether expression templates are on or off
+// we just use et_on everywhere.  We could use a BOOST_WORKAROUND but that just obfuscates the
+// code even more....
 //
 template 
-inline typename enable_if_c >::value && !is_convertible::value >::type 
+inline typename enable_if_c >::value && !is_convertible::value >::type 
    eval_add(T& result, V const& v)
 {
    T t;
@@ -46,14 +52,14 @@ inline typename enable_if_c >::value && !is_converti
    eval_add(result, t);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value >::type 
+inline typename enable_if_c >::value && is_convertible::value >::type 
    eval_add(T& result, V const& v)
 {
    T t(v);
    eval_add(result, t);
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type
+inline typename enable_if_c >::value && !is_convertible::value>::type
    eval_subtract(T& result, V const& v)
 {
    T t;
@@ -61,14 +67,14 @@ inline typename enable_if_c >::value && !is_converti
    eval_subtract(result, t);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type
+inline typename enable_if_c >::value && is_convertible::value>::type
    eval_subtract(T& result, V const& v)
 {
    T t(v);
    eval_subtract(result, t);
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type
+inline typename enable_if_c >::value && !is_convertible::value>::type
    eval_multiply(T& result, V const& v)
 {
    T t;
@@ -76,14 +82,42 @@ inline typename enable_if_c >::value && !is_converti
    eval_multiply(result, t);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type
+inline typename enable_if_c >::value && is_convertible::value>::type
    eval_multiply(T& result, V const& v)
 {
    T t(v);
    eval_multiply(result, t);
 }
+
+template 
+void eval_multiply(T& t, const U& u, const V& v);
+
+template 
+inline typename disable_if_c::value && is_same::value>::type eval_multiply_add(T& t, const U& u, const V& v)
+{
+   T z;
+   eval_multiply(z, u, v);
+   eval_add(t, z);
+}
+template 
+inline typename enable_if_c::value && is_same::value>::type eval_multiply_add(T& t, const U& u, const V& v)
+{
+   eval_multiply_add(t, v, u);
+}
+template 
+inline typename disable_if_c::value && is_same::value>::type eval_multiply_subtract(T& t, const U& u, const V& v)
+{
+   T z;
+   eval_multiply(z, u, v);
+   eval_subtract(t, z);
+}
+template 
+inline typename enable_if_c::value && is_same::value>::type eval_multiply_subtract(T& t, const U& u, const V& v)
+{
+   eval_multiply_subtract(t, v, u);
+}
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type
+inline typename enable_if_c >::value && !is_convertible::value>::type
    eval_divide(T& result, V const& v)
 {
    T t;
@@ -91,14 +125,14 @@ inline typename enable_if_c >::value && !is_converti
    eval_divide(result, t);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type
+inline typename enable_if_c >::value && is_convertible::value>::type
    eval_divide(T& result, V const& v)
 {
    T t(v);
    eval_divide(result, t);
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type
+inline typename enable_if_c >::value && !is_convertible::value>::type
    eval_modulus(T& result, V const& v)
 {
    T t;
@@ -106,14 +140,14 @@ inline typename enable_if_c >::value && !is_converti
    eval_modulus(result, t);
 }
 template 
-inline typename enable_if_c >::value&& is_convertible::value>::type
+inline typename enable_if_c >::value&& is_convertible::value>::type
    eval_modulus(T& result, V const& v)
 {
    T t(v);
    eval_modulus(result, t);
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type
+inline typename enable_if_c >::value && !is_convertible::value>::type
    eval_bitwise_and(T& result, V const& v)
 {
    T t;
@@ -121,14 +155,14 @@ inline typename enable_if_c >::value && !is_converti
    eval_bitwise_and(result, t);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type
+inline typename enable_if_c >::value && is_convertible::value>::type
    eval_bitwise_and(T& result, V const& v)
 {
    T t(v);
    eval_bitwise_and(result, t);
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type
+inline typename enable_if_c >::value && !is_convertible::value>::type
    eval_bitwise_or(T& result, V const& v)
 {
    T t;
@@ -136,14 +170,14 @@ inline typename enable_if_c >::value && !is_converti
    eval_bitwise_or(result, t);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type
+inline typename enable_if_c >::value && is_convertible::value>::type
    eval_bitwise_or(T& result, V const& v)
 {
    T t(v);
    eval_bitwise_or(result, t);
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type
+inline typename enable_if_c >::value && !is_convertible::value>::type
    eval_bitwise_xor(T& result, V const& v)
 {
    T t;
@@ -151,7 +185,7 @@ inline typename enable_if_c >::value && !is_converti
    eval_bitwise_xor(result, t);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type
+inline typename enable_if_c >::value && is_convertible::value>::type
    eval_bitwise_xor(T& result, V const& v)
 {
    T t(v);
@@ -159,7 +193,7 @@ inline typename enable_if_c >::value && is_convertib
 }
 
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type
+inline typename enable_if_c >::value && !is_convertible::value>::type
    eval_complement(T& result, V const& v)
 {
    T t;
@@ -167,7 +201,7 @@ inline typename enable_if_c >::value && !is_converti
    eval_complement(result, t);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type
+inline typename enable_if_c >::value && is_convertible::value>::type
    eval_complement(T& result, V const& v)
 {
    T t(v);
@@ -198,20 +232,20 @@ inline void eval_add_default(T& t, const T& u, const T& v)
    }
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type eval_add_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && !is_convertible::value>::type eval_add_default(T& t, const T& u, const U& v)
 {
    T vv;
    vv = v;
    eval_add(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type eval_add_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && is_convertible::value>::type eval_add_default(T& t, const T& u, const U& v)
 {
    T vv(v);
    eval_add(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value>::type eval_add_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value>::type eval_add_default(T& t, const U& u, const T& v)
 {
    eval_add(t, v, u);
 }
@@ -249,20 +283,20 @@ inline void eval_subtract_default(T& t, const T& u, const T& v)
    }
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type eval_subtract_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && !is_convertible::value>::type eval_subtract_default(T& t, const T& u, const U& v)
 {
    T vv;
    vv = v;
    eval_subtract(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type eval_subtract_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && is_convertible::value>::type eval_subtract_default(T& t, const T& u, const U& v)
 {
    T vv(v);
    eval_subtract(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value>::type eval_subtract_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value>::type eval_subtract_default(T& t, const U& u, const T& v)
 {
    eval_subtract(t, v, u);
    t.negate();
@@ -279,9 +313,6 @@ inline void eval_subtract(T& t, const U& u, const V& v)
    eval_subtract_default(t, u, v);
 }
 
-template 
-void eval_multiply(T& t, const U& u, const V& v);
-
 template 
 inline void eval_multiply_default(T& t, const T& u, const T& v)
 {
@@ -300,20 +331,20 @@ inline void eval_multiply_default(T& t, const T& u, const T& v)
    }
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type eval_multiply_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && !is_convertible::value>::type eval_multiply_default(T& t, const T& u, const U& v)
 {
    T vv;
    vv = v;
    eval_multiply(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type eval_multiply_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && is_convertible::value>::type eval_multiply_default(T& t, const T& u, const U& v)
 {
    T vv(v);
    eval_multiply(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value>::type eval_multiply_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value>::type eval_multiply_default(T& t, const U& u, const T& v)
 {
    eval_multiply(t, v, u);
 }
@@ -329,6 +360,47 @@ inline void eval_multiply(T& t, const U& u, const V& v)
    eval_multiply_default(t, u, v);
 }
 
+template 
+inline typename disable_if_c::value && is_same::value>::type eval_multiply_add(T& t, const U& u, const V& v, const X& x)
+{
+   if((void*)&x == (void*)&t)
+   {
+      T z;
+      z = x;
+      eval_multiply_add(t, u, v, z);
+   }
+   else
+   {
+      eval_multiply(t, u, v);
+      eval_add(t, x);
+   }
+}
+template 
+inline typename enable_if_c::value && is_same::value>::type eval_multiply_add(T& t, const U& u, const V& v, const X& x)
+{
+   eval_multiply_add(t, v, u, x);
+}
+template 
+inline typename disable_if_c::value && is_same::value>::type eval_multiply_subtract(T& t, const U& u, const V& v, const X& x)
+{
+   if((void*)&x == (void*)&t)
+   {
+      T z;
+      z = x;
+      eval_multiply_subtract(t, u, v, z);
+   }
+   else
+   {
+      eval_multiply(t, u, v);
+      eval_subtract(t, x);
+   }
+}
+template 
+inline typename enable_if_c::value && is_same::value>::type eval_multiply_subtract(T& t, const U& u, const V& v, const X& x)
+{
+   eval_multiply_subtract(t, v, u, x);
+}
+
 template 
 void eval_divide(T& t, const U& u, const V& v);
 
@@ -350,27 +422,27 @@ inline void eval_divide_default(T& t, const T& u, const T& v)
    }
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide_default(T& t, const T& u, const U& v)
 {
    T vv;
    vv = v;
    eval_divide(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type eval_divide_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && is_convertible::value>::type eval_divide_default(T& t, const T& u, const U& v)
 {
    T vv(v);
    eval_divide(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value && !is_convertible::value>::type eval_divide_default(T& t, const U& u, const T& v)
 {
    T uu;
    uu = u;
    eval_divide(t, uu, v);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type eval_divide_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value && is_convertible::value>::type eval_divide_default(T& t, const U& u, const T& v)
 {
    T uu(u);
    eval_divide(t, uu, v);
@@ -408,27 +480,27 @@ inline void eval_modulus_default(T& t, const T& u, const T& v)
    }
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus_default(T& t, const T& u, const U& v)
 {
    T vv;
    vv = v;
    eval_modulus(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type eval_modulus_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && is_convertible::value>::type eval_modulus_default(T& t, const T& u, const U& v)
 {
    T vv(v);
    eval_modulus(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value && !is_convertible::value>::type eval_modulus_default(T& t, const U& u, const T& v)
 {
    T uu;
    uu = u;
    eval_modulus(t, uu, v);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type eval_modulus_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value && is_convertible::value>::type eval_modulus_default(T& t, const U& u, const T& v)
 {
    T uu(u);
    eval_modulus(t, uu, v);
@@ -466,20 +538,20 @@ inline void eval_bitwise_and_default(T& t, const T& u, const T& v)
    }
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_and_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_and_default(T& t, const T& u, const U& v)
 {
    T vv;
    vv = v;
    eval_bitwise_and(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_and_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_and_default(T& t, const T& u, const U& v)
 {
    T vv(v);
    eval_bitwise_and(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value>::type eval_bitwise_and_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value>::type eval_bitwise_and_default(T& t, const U& u, const T& v)
 {
    eval_bitwise_and(t, v, u);
 }
@@ -516,20 +588,20 @@ inline void eval_bitwise_or_default(T& t, const T& u, const T& v)
    }
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_or_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_or_default(T& t, const T& u, const U& v)
 {
    T vv;
    vv = v;
    eval_bitwise_or(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_or_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_or_default(T& t, const T& u, const U& v)
 {
    T vv(v);
    eval_bitwise_or(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value>::type eval_bitwise_or_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value>::type eval_bitwise_or_default(T& t, const U& u, const T& v)
 {
    eval_bitwise_or(t, v, u);
 }
@@ -566,20 +638,20 @@ inline void eval_bitwise_xor_default(T& t, const T& u, const T& v)
    }
 }
 template 
-inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_xor_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && !is_convertible::value>::type eval_bitwise_xor_default(T& t, const T& u, const U& v)
 {
    T vv;
    vv = v;
    eval_bitwise_xor(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_xor_default(T& t, const T& u, const U& v)
+inline typename enable_if_c >::value && is_convertible::value>::type eval_bitwise_xor_default(T& t, const T& u, const U& v)
 {
    T vv(v);
    eval_bitwise_xor(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value>::type eval_bitwise_xor_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value>::type eval_bitwise_xor_default(T& t, const U& u, const T& v)
 {
    eval_bitwise_xor(t, v, u);
 }
@@ -1272,7 +1344,7 @@ func(const number& arg)\
     return detail::expression<\
     detail::function\
   , detail::BOOST_JOIN(func, _funct) \
-  , number \
+  , number \
   >(\
         detail::BOOST_JOIN(func, _funct)() \
       , arg   \
@@ -1328,8 +1400,8 @@ func(const number& arg, const number& a)\
     return detail::expression<\
     detail::function\
   , detail::BOOST_JOIN(func, _funct) \
-  , number \
-  , number \
+  , number \
+  , number \
   >(\
         detail::BOOST_JOIN(func, _funct)() \
       , arg,\
@@ -1350,7 +1422,7 @@ func(const number& arg, const detail::expression \
-  , number \
+  , number \
   , detail::expression \
   >(\
         detail::BOOST_JOIN(func, _funct)() \
@@ -1373,7 +1445,7 @@ func(const detail::expression& arg, const number \
   , detail::expression \
-  , number \
+  , number \
   >(\
         detail::BOOST_JOIN(func, _funct)() \
       , arg,\
@@ -1417,7 +1489,7 @@ func(const number& arg, const Arithmetic& a)\
     return detail::expression<\
     detail::function\
   , detail::BOOST_JOIN(func, _funct) \
-  , number \
+  , number \
   , Arithmetic\
   >(\
         detail::BOOST_JOIN(func, _funct)() \
@@ -1464,7 +1536,7 @@ func(const Arithmetic& arg, const number& a)\
     detail::function\
   , detail::BOOST_JOIN(func, _funct) \
   , Arithmetic \
-  , number \
+  , number \
   >(\
         detail::BOOST_JOIN(func, _funct)() \
       , arg,\
@@ -1568,7 +1640,7 @@ func(const number& arg, Arg2 const& a)\
     return detail::expression<\
     detail::function\
   , detail::BOOST_JOIN(func, _funct) \
-  , number \
+  , number \
   , Arg2\
   >(\
         detail::BOOST_JOIN(func, _funct)() \
diff --git a/include/boost/multiprecision/detail/et_ops.hpp b/include/boost/multiprecision/detail/et_ops.hpp
index 1e35c9be..81fb9580 100644
--- a/include/boost/multiprecision/detail/et_ops.hpp
+++ b/include/boost/multiprecision/detail/et_ops.hpp
@@ -77,6 +77,66 @@ inline typename enable_if >(a, b);
 }
 //
+// Fused multiply add:
+//
+template 
+inline typename enable_if::result_type>, 
+   detail::expression::left_type, typename detail::expression::right_type, V> >::type
+   operator + (const V& a, const detail::expression& b)
+{
+   return detail::expression::left_type, typename detail::expression::right_type, V>(b.left(), b.right(), a);
+}
+template 
+inline typename enable_if::result_type>, 
+   detail::expression::left_type, typename detail::expression::right_type, V> >::type
+   operator + (const detail::expression& a, const V& b)
+{
+   return detail::expression::left_type, typename detail::expression::right_type, V>(a.left(), a.right(), b);
+}
+template 
+inline detail::expression::left_type, typename detail::expression::right_type, number >
+   operator + (const number& a, const detail::expression& b)
+{
+   return detail::expression::left_type, typename detail::expression::right_type, number >(b.left(), b.right(), a);
+}
+template 
+inline detail::expression::left_type, typename detail::expression::right_type, number >
+   operator + (const detail::expression& a, const number& b)
+{
+   return detail::expression::left_type, typename detail::expression::right_type, number >(a.left(), a.right(), b);
+}
+//
+// Fused multiply subtract:
+//
+template 
+inline typename enable_if::result_type>, 
+   detail::expression::left_type, typename detail::expression::right_type, V> > >::type
+   operator - (const V& a, const detail::expression& b)
+{
+   return detail::expression::left_type, typename detail::expression::right_type, V> >
+      (detail::expression::left_type, typename detail::expression::right_type, V>(b.left(), b.right(), a));
+}
+template 
+inline typename enable_if::result_type>, 
+   detail::expression::left_type, typename detail::expression::right_type, V> >::type
+   operator - (const detail::expression& a, const V& b)
+{
+   return detail::expression::left_type, typename detail::expression::right_type, V>(a.left(), a.right(), b);
+}
+template 
+inline detail::expression::left_type, typename detail::expression::right_type, number > >
+   operator - (const number& a, const detail::expression& b)
+{
+   return detail::expression::left_type, typename detail::expression::right_type, number > >
+      (detail::expression::left_type, typename detail::expression::right_type, number >(b.left(), b.right(), a));
+}
+template 
+inline detail::expression::left_type, typename detail::expression::right_type, number >
+   operator - (const detail::expression& a, const number& b)
+{
+   return detail::expression::left_type, typename detail::expression::right_type, number >(a.left(), a.right(), b);
+}
+//
 // Repeat operator for negated arguments: propagate the negation to the top level to avoid temporaries:
 //
 template 
diff --git a/include/boost/multiprecision/detail/functions/constants.hpp b/include/boost/multiprecision/detail/functions/constants.hpp
index 537b7bd1..b32f3f28 100644
--- a/include/boost/multiprecision/detail/functions/constants.hpp
+++ b/include/boost/multiprecision/detail/functions/constants.hpp
@@ -246,7 +246,7 @@ const T& get_constant_ln2()
    static bool b = false;
    if(!b)
    {
-      calc_log2(result, boost::multiprecision::detail::digits2 >::value);
+      calc_log2(result, boost::multiprecision::detail::digits2 >::value);
       b = true;
    }
 
@@ -262,7 +262,7 @@ const T& get_constant_e()
    static bool b = false;
    if(!b)
    {
-      calc_e(result, boost::multiprecision::detail::digits2 >::value);
+      calc_e(result, boost::multiprecision::detail::digits2 >::value);
       b = true;
    }
 
@@ -278,7 +278,7 @@ const T& get_constant_pi()
    static bool b = false;
    if(!b)
    {
-      calc_pi(result, boost::multiprecision::detail::digits2 >::value);
+      calc_pi(result, boost::multiprecision::detail::digits2 >::value);
       b = true;
    }
 
diff --git a/include/boost/multiprecision/detail/functions/pow.hpp b/include/boost/multiprecision/detail/functions/pow.hpp
index c0c2abc8..2ed9da1d 100644
--- a/include/boost/multiprecision/detail/functions/pow.hpp
+++ b/include/boost/multiprecision/detail/functions/pow.hpp
@@ -90,7 +90,7 @@ void hyp0F0(T& H0F0, const T& x)
    typedef typename mpl::front::type ui_type;
 
    BOOST_ASSERT(&H0F0 != &x);
-   long tol = boost::multiprecision::detail::digits2 >::value;
+   long tol = boost::multiprecision::detail::digits2 >::value;
    T t;
 
    T x_pow_n_div_n_fact(x);
@@ -146,7 +146,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x)
    eval_multiply(H1F0, pochham_a, x_pow_n_div_n_fact);
    eval_add(H1F0, si_type(1));
    T lim;
-   eval_ldexp(lim, H1F0, 1 - boost::multiprecision::detail::digits2 >::value);
+   eval_ldexp(lim, H1F0, 1 - boost::multiprecision::detail::digits2 >::value);
    if(eval_get_sign(lim) < 0)
       lim.negate();
 
@@ -154,7 +154,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x)
    T term, part;
 
    // Series expansion of hyperg_1f0(a; ; x).
-   for(n = 2; n < boost::multiprecision::detail::digits2 >::value + 10; n++)
+   for(n = 2; n < boost::multiprecision::detail::digits2 >::value + 10; n++)
    {
       eval_multiply(x_pow_n_div_n_fact, x);
       eval_divide(x_pow_n_div_n_fact, n);
@@ -167,7 +167,7 @@ void hyp1F0(T& H1F0, const T& a, const T& x)
       if(lim.compare(term) >= 0)
          break;
    }
-   if(n >= boost::multiprecision::detail::digits2 >::value + 10)
+   if(n >= boost::multiprecision::detail::digits2 >::value + 10)
       BOOST_THROW_EXCEPTION(std::runtime_error("H1F0 failed to converge"));
 }
 
@@ -193,7 +193,7 @@ void eval_exp(T& result, const T& x)
    bool isneg = eval_get_sign(x) < 0;
    if(type == FP_NAN)
    {
-      result = std::numeric_limits >::quiet_NaN().backend();
+      result = std::numeric_limits >::quiet_NaN().backend();
       return;
    }
    else if(type == FP_INFINITE)
@@ -218,7 +218,7 @@ void eval_exp(T& result, const T& x)
       xx.negate();
 
    // Check the range of the argument.
-   static const canonical_exp_type maximum_arg_for_exp = std::numeric_limits >::max_exponent == 0 ? (std::numeric_limits::max)() : std::numeric_limits >::max_exponent;
+   static const canonical_exp_type maximum_arg_for_exp = std::numeric_limits >::max_exponent == 0 ? (std::numeric_limits::max)() : std::numeric_limits >::max_exponent;
 
    if(xx.compare(maximum_arg_for_exp) >= 0)
    {
@@ -226,7 +226,7 @@ void eval_exp(T& result, const T& x)
       if(isneg)
          result = ui_type(0);
       else
-         result = std::numeric_limits >::has_infinity ? std::numeric_limits >::infinity().backend() : (std::numeric_limits >::max)().backend();
+         result = std::numeric_limits >::has_infinity ? std::numeric_limits >::infinity().backend() : (std::numeric_limits >::max)().backend();
       return;
    }
    if(xx.compare(si_type(1)) <= 0)
@@ -234,7 +234,7 @@ void eval_exp(T& result, const T& x)
       //
       // Use series for exp(x) - 1:
       //
-      T lim = std::numeric_limits >::epsilon().backend();
+      T lim = std::numeric_limits >::epsilon().backend();
       unsigned k = 2;
       exp_series = xx;
       result = si_type(1);
@@ -344,7 +344,7 @@ void eval_log(T& result, const T& arg)
    else
       eval_subtract(result, t);
 
-   eval_multiply(lim, result, std::numeric_limits >::epsilon().backend());
+   eval_multiply(lim, result, std::numeric_limits >::epsilon().backend());
    if(eval_get_sign(lim) < 0)
       lim.negate();
    INSTRUMENT_BACKEND(lim);
@@ -465,7 +465,7 @@ inline void eval_pow(T& result, const T& x, const T& a)
 
    if((eval_get_sign(x) < 0) && !bo_a_isint)
    {
-      result = std::numeric_limits >::quiet_NaN().backend();
+      result = std::numeric_limits >::quiet_NaN().backend();
    }
 
    T t, da;
@@ -564,7 +564,7 @@ namespace detail{
       ui_type k = 1;
 
       T lim(x);
-      eval_ldexp(lim, lim, 1 - boost::multiprecision::detail::digits2 >::value);
+      eval_ldexp(lim, lim, 1 - boost::multiprecision::detail::digits2 >::value);
 
       do
       {
diff --git a/include/boost/multiprecision/detail/functions/trig.hpp b/include/boost/multiprecision/detail/functions/trig.hpp
index 4e57b070..e4086427 100644
--- a/include/boost/multiprecision/detail/functions/trig.hpp
+++ b/include/boost/multiprecision/detail/functions/trig.hpp
@@ -36,7 +36,7 @@ void hyp0F1(T& result, const T& b, const T& x)
 
    T tol;
    tol = ui_type(1);
-   eval_ldexp(tol, tol, 1 - boost::multiprecision::detail::digits2 >::value);
+   eval_ldexp(tol, tol, 1 - boost::multiprecision::detail::digits2 >::value);
    eval_multiply(tol, result);
    if(eval_get_sign(tol) < 0)
       tol.negate();
@@ -87,7 +87,7 @@ void eval_sin(T& result, const T& x)
    {
    case FP_INFINITE:
    case FP_NAN:
-      result = std::numeric_limits >::quiet_NaN().backend();
+      result = std::numeric_limits >::quiet_NaN().backend();
       return;
    case FP_ZERO:
       result = ui_type(0);
@@ -233,7 +233,7 @@ void eval_cos(T& result, const T& x)
    {
    case FP_INFINITE:
    case FP_NAN:
-      result = std::numeric_limits >::quiet_NaN().backend();
+      result = std::numeric_limits >::quiet_NaN().backend();
       return;
    case FP_ZERO:
       result = ui_type(1);
@@ -391,7 +391,7 @@ void hyp2F1(T& result, const T& a, const T& b, const T& c, const T& x)
    eval_add(result, ui_type(1));
 
    T lim;
-   eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value);
+   eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value);
 
    if(eval_get_sign(lim) < 0)
       lim.negate();
@@ -447,7 +447,7 @@ void eval_asin(T& result, const T& x)
    {
    case FP_NAN:
    case FP_INFINITE:
-      result = std::numeric_limits >::quiet_NaN().backend();
+      result = std::numeric_limits >::quiet_NaN().backend();
       return;
    case FP_ZERO:
       result = ui_type(0);
@@ -464,7 +464,7 @@ void eval_asin(T& result, const T& x)
    int c = xx.compare(ui_type(1));
    if(c > 0)
    {
-      result = std::numeric_limits >::quiet_NaN().backend();
+      result = std::numeric_limits >::quiet_NaN().backend();
       return;
    }
    else if(c == 0)
@@ -524,7 +524,7 @@ void eval_asin(T& result, const T& x)
       eval_subtract(result, s);
 
       T lim;
-      eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value);
+      eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2 >::value);
       if(eval_get_sign(s) < 0)
          s.negate();
       if(eval_get_sign(lim) < 0)
@@ -546,7 +546,7 @@ inline void eval_acos(T& result, const T& x)
    {
    case FP_NAN:
    case FP_INFINITE:
-      result = std::numeric_limits >::quiet_NaN().backend();
+      result = std::numeric_limits >::quiet_NaN().backend();
       return;
    case FP_ZERO:
       result = get_constant_pi();
@@ -559,7 +559,7 @@ inline void eval_acos(T& result, const T& x)
 
    if(c > 0)
    {
-      result = std::numeric_limits >::quiet_NaN().backend();
+      result = std::numeric_limits >::quiet_NaN().backend();
       return;
    }
    else if(c == 0)
@@ -591,7 +591,7 @@ void eval_atan(T& result, const T& x)
    switch(eval_fpclassify(x))
    {
    case FP_NAN:
-      result = std::numeric_limits >::quiet_NaN().backend();
+      result = std::numeric_limits >::quiet_NaN().backend();
       return;
    case FP_ZERO:
       result = ui_type(0);
@@ -656,7 +656,7 @@ void eval_atan(T& result, const T& x)
    static const boost::int32_t double_digits10_minus_a_few = std::numeric_limits::digits10 - 3;
 
    T s, c, t;
-   for(boost::int32_t digits = double_digits10_minus_a_few; digits <= std::numeric_limits >::digits10; digits *= 2)
+   for(boost::int32_t digits = double_digits10_minus_a_few; digits <= std::numeric_limits >::digits10; digits *= 2)
    {
       eval_sin(s, result);
       eval_cos(c, result);
@@ -710,7 +710,7 @@ void eval_atan2(T& result, const T& y, const T& x)
       {
          if(eval_fpclassify(x) == FP_INFINITE)
          {
-            result = std::numeric_limits >::quiet_NaN().backend();
+            result = std::numeric_limits >::quiet_NaN().backend();
          }
          else
          {
diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp
index 0f6ed2bd..b6f9c65f 100644
--- a/include/boost/multiprecision/detail/number_base.hpp
+++ b/include/boost/multiprecision/detail/number_base.hpp
@@ -20,7 +20,13 @@ enum expression_template_option
    et_on   = 1
 };
 
-template 
+template 
+struct expression_template_default
+{
+   static const expression_template_option value = et_on;
+};
+
+template ::value>
 class number;
 
 template 
@@ -180,6 +186,8 @@ struct bitwise_or_immediates{};
 struct bitwise_xor_immediates{};
 struct complement_immediates{};
 struct function{};
+struct multiply_add{};
+struct multiply_subtract{};
 
 template 
 struct backend_type;
@@ -207,7 +215,14 @@ template 
 struct is_mp_number_exp > : public mpl::true_{};
 
 template 
-struct combine_expression;
+struct combine_expression
+{
+#ifdef BOOST_NO_DECLTYPE
+   typedef typename mpl::if_c sizeof(T2) ? T1, T2>::type type;
+#else
+   typedef decltype(T1() + T2()) type;
+#endif
+};
 
 template 
 struct combine_expression, T2>
diff --git a/include/boost/multiprecision/detail/number_compare.hpp b/include/boost/multiprecision/detail/number_compare.hpp
index dda75e64..00832838 100644
--- a/include/boost/multiprecision/detail/number_compare.hpp
+++ b/include/boost/multiprecision/detail/number_compare.hpp
@@ -152,14 +152,14 @@ inline typename enable_if_c& a, const Arithmetic& b)
 {
    using default_ops::eval_eq;
-   return !eval_eq(a.backend(), number::canonical_value(b));
+   return !eval_eq(a.backend(), number::canonical_value(b));
 }
 template 
 inline typename enable_if_c, Arithmetic>::value, bool>::type 
    operator != (const Arithmetic& a, const number& b)
 {
    using default_ops::eval_eq;
-   return !eval_eq(b.backend(), number::canonical_value(a));
+   return !eval_eq(b.backend(), number::canonical_value(a));
 }
 template 
 inline typename enable_if_c::result_type, Arithmetic>::value, bool>::type 
diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp
index 6495445b..5780cbe9 100644
--- a/include/boost/multiprecision/gmp.hpp
+++ b/include/boost/multiprecision/gmp.hpp
@@ -1288,6 +1288,14 @@ inline void eval_add(gmp_int& t, const gmp_int& o)
 {
    mpz_add(t.data(), t.data(), o.data());
 }
+inline void eval_multiply_add(gmp_int& t, const gmp_int& a, const gmp_int& b)
+{
+   mpz_addmul(t.data(), a.data(), b.data());
+}
+inline void eval_multiply_subtract(gmp_int& t, const gmp_int& a, const gmp_int& b)
+{
+   mpz_submul(t.data(), a.data(), b.data());
+}
 inline void eval_subtract(gmp_int& t, const gmp_int& o)
 {
    mpz_sub(t.data(), t.data(), o.data());
@@ -1310,6 +1318,14 @@ inline void eval_add(gmp_int& t, unsigned long i)
 {
    mpz_add_ui(t.data(), t.data(), i);
 }
+inline void eval_multiply_add(gmp_int& t, const gmp_int& a, unsigned long i)
+{
+   mpz_addmul_ui(t.data(), a.data(), i);
+}
+inline void eval_multiply_subtract(gmp_int& t, const gmp_int& a, unsigned long i)
+{
+   mpz_submul_ui(t.data(), a.data(), i);
+}
 inline void eval_subtract(gmp_int& t, unsigned long i)
 {
    mpz_sub_ui(t.data(), t.data(), i);
@@ -1335,6 +1351,20 @@ inline void eval_add(gmp_int& t, long i)
    else
       mpz_sub_ui(t.data(), t.data(), -i);
 }
+inline void eval_multiply_add(gmp_int& t, const gmp_int& a, long i)
+{
+   if(i > 0)
+      mpz_addmul_ui(t.data(), a.data(), i);
+   else
+      mpz_submul_ui(t.data(), a.data(), -i);
+}
+inline void eval_multiply_subtract(gmp_int& t, const gmp_int& a, long i)
+{
+   if(i > 0)
+      mpz_submul_ui(t.data(), a.data(), i);
+   else
+      mpz_addmul_ui(t.data(), a.data(), -i);
+}
 inline void eval_subtract(gmp_int& t, long i)
 {
    if(i > 0)
@@ -1895,19 +1925,6 @@ inline bool eval_is_zero(const gmp_rational& val)
 {
    return mpq_sgn(val.data()) == 0;
 }
-inline number numerator(const number& val)
-{
-   number result;
-   mpz_set(result.backend().data(), (mpq_numref(val.backend().data())));
-   return result;
-}
-inline number denominator(const number& val)
-{
-   number result;
-   mpz_set(result.backend().data(), (mpq_denref(val.backend().data())));
-   return result;
-}
-
 template 
 inline bool eval_eq(gmp_rational& a, const T& b)
 {
@@ -2109,6 +2126,21 @@ struct component_type >
    typedef number type;
 };
 
+template 
+inline number numerator(const number& val)
+{
+   number result;
+   mpz_set(result.backend().data(), (mpq_numref(val.backend().data())));
+   return result;
+}
+template 
+inline number denominator(const number& val)
+{
+   number result;
+   mpz_set(result.backend().data(), (mpq_denref(val.backend().data())));
+   return result;
+}
+
 #ifdef BOOST_NO_SFINAE_EXPR
 
 namespace detail{
diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp
index 2ec587b7..aae260c7 100644
--- a/include/boost/multiprecision/number.hpp
+++ b/include/boost/multiprecision/number.hpp
@@ -160,9 +160,9 @@ public:
       m_backend = canonical_value(v);
       return *this;
    }
-   template 
+   template 
    typename disable_if, number& >::type 
-      assign(const number& v)
+      assign(const number& v)
    {
       //
       // Attempt a generic interconvertion:
@@ -209,6 +209,17 @@ public:
       return *this;
    }
 
+   template 
+   number& operator+=(const detail::expression& e)
+   {
+      //
+      // Fused multiply-add:
+      //
+      using default_ops::eval_multiply_add;
+      eval_multiply_add(m_backend, canonical_value(e.left_ref()), canonical_value(e.right_ref()));
+      return *this;
+   }
+
    template 
    typename enable_if, number& >::type 
       operator+=(const V& v)
@@ -249,6 +260,17 @@ public:
       return *this;
    }
 
+   template 
+   number& operator-=(const detail::expression& e)
+   {
+      //
+      // Fused multiply-subtract:
+      //
+      using default_ops::eval_multiply_subtract;
+      eval_multiply_subtract(m_backend, canonical_value(e.left_ref()), canonical_value(e.right_ref()));
+      return *this;
+   }
+
 
    number& operator *= (const self_type& e)
    {
@@ -673,6 +695,18 @@ private:
       using default_ops::eval_multiply;
       eval_multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value()));
    }
+   template 
+   void do_assign(const Exp& e, const detail::multiply_add&)
+   {
+      using default_ops::eval_multiply_add;
+      eval_multiply_add(m_backend, canonical_value(e.left().value()), canonical_value(e.middle().value()), canonical_value(e.right().value()));
+   }
+   template 
+   void do_assign(const Exp& e, const detail::multiply_subtract&)
+   {
+      using default_ops::eval_multiply_subtract;
+      eval_multiply_subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.middle().value()), canonical_value(e.right().value()));
+   }
 
    template 
    void do_assign(const Exp& e, const detail::divide_immediates&)
@@ -710,13 +744,13 @@ private:
          // Ignore the right node, it's *this, just add the left:
          do_add(e.left(), typename left_type::tag_type());
       }
-      else if(bl || br)
+      else if(bl && br)
       {
          self_type temp(e);
          temp.m_backend.swap(this->m_backend);
       }
-      else if(left_depth >= right_depth)
-      {
+      else if(bl || (left_depth >= right_depth))
+      { // br is always false, but if bl is true we must take the this branch:
          do_assign(e.left(), typename left_type::tag_type());
          do_add(e.right(), typename right_type::tag_type());
       }
@@ -749,13 +783,13 @@ private:
          do_subtract(e.left(), typename left_type::tag_type());
          m_backend.negate();
       }
-      else if(bl || br)
+      else if(bl && br)
       {
          self_type temp(e);
          temp.m_backend.swap(this->m_backend);
       }
-      else if(left_depth >= right_depth)
-      {
+      else if(bl || (left_depth >= right_depth))
+      { // br is always false, but if bl is true we must take the this branch:
          do_assign(e.left(), typename left_type::tag_type());
          do_subtract(e.right(), typename right_type::tag_type());
       }
@@ -788,13 +822,13 @@ private:
          // Ignore the right node, it's *this, just add the left:
          do_multiplies(e.left(), typename left_type::tag_type());
       }
-      else if(bl || br)
+      else if(bl && br)
       {
          self_type temp(e);
          temp.m_backend.swap(this->m_backend);
       }
-      else if(left_depth >= right_depth)
-      {
+      else if(bl || (left_depth >= right_depth))
+      { // br is always false, but if bl is true we must take the this branch:
          do_assign(e.left(), typename left_type::tag_type());
          do_multiplies(e.right(), typename right_type::tag_type());
       }
@@ -818,7 +852,7 @@ private:
          // Ignore the left node, it's *this, just add the right:
          do_divide(e.right(), typename right_type::tag_type());
       }
-      else if(bl || br)
+      else if(br)
       {
          self_type temp(e);
          temp.m_backend.swap(this->m_backend);
@@ -848,7 +882,7 @@ private:
          // Ignore the left node, it's *this, just add the right:
          do_modulus(e.right(), typename right_type::tag_type());
       }
-      else if(bl || br)
+      else if(br)
       {
          self_type temp(e);
          temp.m_backend.swap(this->m_backend);
diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp
index b7a37ed8..b3f2ad16 100644
--- a/include/boost/multiprecision/rational_adapter.hpp
+++ b/include/boost/multiprecision/rational_adapter.hpp
@@ -213,17 +213,6 @@ inline int eval_get_sign(const rational_adapter& val)
    return eval_get_sign(val.data().numerator().backend());
 }
 
-template 
-inline number numerator(const number >& val)
-{
-   return val.backend().data().numerator();
-}
-template 
-inline number denominator(const number >& val)
-{
-   return val.backend().data().denominator();
-}
-
 template
 inline void assign_components(rational_adapter& result, const V& v1, const V& v2)
 {
@@ -232,6 +221,9 @@ inline void assign_components(rational_adapter& result, const V& v1,
 
 } // namespace backends
 
+template
+struct expression_template_default > : public expression_template_default {};
+   
 template
 struct number_category > : public mpl::int_{};
 
@@ -243,6 +235,17 @@ struct component_type >
    typedef number type;
 };
 
+template 
+inline number numerator(const number, ET>& val)
+{
+   return val.backend().data().numerator();
+}
+template 
+inline number denominator(const number, ET>& val)
+{
+   return val.backend().data().denominator();
+}
+
 #ifdef BOOST_NO_SFINAE_EXPR
 
 namespace detail{
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index 7128c20a..e38ea081 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -1085,6 +1085,79 @@ void test_negative_mixed(boost::mpl::true_ const&)
    BOOST_TEST(c == 30);
    c = static_cast(n4) * a;
    BOOST_TEST(c == 50 * 20);
+
+   n1 = -2;
+   n2 = -3;
+   n3 = -4;
+   a = static_cast(n1);
+   b = static_cast(n2);
+   c = static_cast(n3);
+   d = a + b * c;
+   BOOST_TEST(d == -2 + -3 * -4);
+   d = static_cast(n1) + b * c;
+   BOOST_TEST(d == -2 + -3 * -4);
+   d = a + static_cast(n2) * c;
+   BOOST_TEST(d == -2 + -3 * -4);
+   d = a + b * static_cast(n3);
+   BOOST_TEST(d == -2 + -3 * -4);
+   d = static_cast(n1) + static_cast(n2) * c;
+   BOOST_TEST(d == -2 + -3 * -4);
+   d = static_cast(n1) + b * static_cast(n3);
+   BOOST_TEST(d == -2 + -3 * -4);
+   a += static_cast(n2) * c;
+   BOOST_TEST(a == -2 + -3 * -4);
+   a = static_cast(n1);
+   a += b * static_cast(n3);
+   BOOST_TEST(a == -2 + -3 * -4);
+   a = static_cast(n1);
+
+   d = b * c + a;
+   BOOST_TEST(d == -2 + -3 * -4);
+   d = b * c + static_cast(n1);
+   BOOST_TEST(d == -2 + -3 * -4);
+   d = static_cast(n2) * c + a;
+   BOOST_TEST(d == -2 + -3 * -4);
+   d = b * static_cast(n3) + a;
+   BOOST_TEST(d == -2 + -3 * -4);
+   d = static_cast(n2) * c + static_cast(n1);
+   BOOST_TEST(d == -2 + -3 * -4);
+   d = b * static_cast(n3) + static_cast(n1);
+   BOOST_TEST(d == -2 + -3 * -4);
+
+   a = -20;
+   d = a - b * c;
+   BOOST_TEST(d == -20 - -3 * -4);
+   n1 = -20;
+   d = static_cast(n1) - b * c;
+   BOOST_TEST(d == -20 - -3 * -4);
+   d = a - static_cast(n2) * c;
+   BOOST_TEST(d == -20 - -3 * -4);
+   d = a - b * static_cast(n3);
+   BOOST_TEST(d == -20 - -3 * -4);
+   d = static_cast(n1) - static_cast(n2) * c;
+   BOOST_TEST(d == -20 - -3 * -4);
+   d = static_cast(n1) - b * static_cast(n3);
+   BOOST_TEST(d == -20 - -3 * -4);
+   a -= static_cast(n2) * c;
+   BOOST_TEST(a == -20 - -3 * -4);
+   a = static_cast(n1);
+   a -= b * static_cast(n3);
+   BOOST_TEST(a == -20 - -3 * -4);
+
+   a = -2;
+   d = b * c - a;
+   BOOST_TEST(d == -3 * -4 - -2);
+   n1 = -2;
+   d = b * c - static_cast(n1);
+   BOOST_TEST(d == -3 * -4 - -2);
+   d = static_cast(n2) * c - a;
+   BOOST_TEST(d == -3 * -4 - -2);
+   d = b * static_cast(n3) - a;
+   BOOST_TEST(d == -3 * -4 - -2);
+   d = static_cast(n2) * c - static_cast(n1);
+   BOOST_TEST(d == -3 * -4 - -2);
+   d = b * static_cast(n3) - static_cast(n1);
+   BOOST_TEST(d == -3 * -4 - -2);
 }
 
 template 
@@ -1209,6 +1282,77 @@ void test_mixed(const boost::mpl::true_&)
    r = static_cast(4 * n4) / Real(4);
    BOOST_TEST(r == static_cast(n4));
    test_negative_mixed(boost::mpl::bool_::is_signed>());
+
+   n1 = 2;
+   n2 = 3;
+   n3 = 4;
+   Real a(n1), b(n2), c(n3), d;
+   d = a + b * c;
+   BOOST_TEST(d == 2 + 3 * 4);
+   d = static_cast(n1) + b * c;
+   BOOST_TEST(d == 2 + 3 * 4);
+   d = a + static_cast(n2) * c;
+   BOOST_TEST(d == 2 + 3 * 4);
+   d = a + b * static_cast(n3);
+   BOOST_TEST(d == 2 + 3 * 4);
+   d = static_cast(n1) + static_cast(n2) * c;
+   BOOST_TEST(d == 2 + 3 * 4);
+   d = static_cast(n1) + b * static_cast(n3);
+   BOOST_TEST(d == 2 + 3 * 4);
+   a += static_cast(n2) * c;
+   BOOST_TEST(a == 2 + 3 * 4);
+   a = static_cast(n1);
+   a += b * static_cast(n3);
+   BOOST_TEST(a == 2 + 3 * 4);
+   a = static_cast(n1);
+
+   d = b * c + a;
+   BOOST_TEST(d == 2 + 3 * 4);
+   d = b * c + static_cast(n1);
+   BOOST_TEST(d == 2 + 3 * 4);
+   d = static_cast(n2) * c + a;
+   BOOST_TEST(d == 2 + 3 * 4);
+   d = b * static_cast(n3) + a;
+   BOOST_TEST(d == 2 + 3 * 4);
+   d = static_cast(n2) * c + static_cast(n1);
+   BOOST_TEST(d == 2 + 3 * 4);
+   d = b * static_cast(n3) + static_cast(n1);
+   BOOST_TEST(d == 2 + 3 * 4);
+
+   a = 20;
+   d = a - b * c;
+   BOOST_TEST(d == 20 - 3 * 4);
+   n1 = 20;
+   d = static_cast(n1) - b * c;
+   BOOST_TEST(d == 20 - 3 * 4);
+   d = a - static_cast(n2) * c;
+   BOOST_TEST(d == 20 - 3 * 4);
+   d = a - b * static_cast(n3);
+   BOOST_TEST(d == 20 - 3 * 4);
+   d = static_cast(n1) - static_cast(n2) * c;
+   BOOST_TEST(d == 20 - 3 * 4);
+   d = static_cast(n1) - b * static_cast(n3);
+   BOOST_TEST(d == 20 - 3 * 4);
+   a -= static_cast(n2) * c;
+   BOOST_TEST(a == 20 - 3 * 4);
+   a = static_cast(n1);
+   a -= b * static_cast(n3);
+   BOOST_TEST(a == 20 - 3 * 4);
+
+   a = 2;
+   d = b * c - a;
+   BOOST_TEST(d == 3 * 4 - 2);
+   n1 = 2;
+   d = b * c - static_cast(n1);
+   BOOST_TEST(d == 3 * 4 - 2);
+   d = static_cast(n2) * c - a;
+   BOOST_TEST(d == 3 * 4 - 2);
+   d = b * static_cast(n3) - a;
+   BOOST_TEST(d == 3 * 4 - a);
+   d = static_cast(n2) * c - static_cast(n1);
+   BOOST_TEST(d == 3 * 4 - 2);
+   d = b * static_cast(n3) - static_cast(n1);
+   BOOST_TEST(d == 3 * 4 - 2);
 }
 
 template 
@@ -1612,6 +1756,19 @@ void test()
    BOOST_TEST(c == 20 * 30 + 22);
    c = 22 + (a * b);
    BOOST_TEST(c == 20 * 30 + 22);
+   c = 10;
+   ac = a + b * c;
+   BOOST_TEST(ac == 20 + 30 * 10);
+   ac = b * c + a;
+   BOOST_TEST(ac == 20 + 30 * 10);
+   a = a + b * c;
+   BOOST_TEST(a == 20 + 30 * 10);
+   a = 20;
+   b = a + b * c;
+   BOOST_TEST(b == 20 + 30 * 10);
+   b = 30;
+   c = a + b * c;
+   BOOST_TEST(c == 20 + 30 * 10);
 
    //
    // Test conditionals:
@@ -1681,8 +1838,8 @@ int main()
 #endif
 #ifdef TEST_CPP_INT_3
    // Again with "trivial" backends:
-   test, boost::multiprecision::et_off > >();
-   test, boost::multiprecision::et_off > >();
+   test > >();
+   test > >();
 #endif
 #ifdef TEST_CPP_INT_BR
    test >();
diff --git a/test/test_constants.cpp b/test/test_constants.cpp
index 770b8721..b7f6afe9 100644
--- a/test/test_constants.cpp
+++ b/test/test_constants.cpp
@@ -159,8 +159,8 @@ inline bool is_mpfr(const T&)
    return false;
 }
 #if defined(TEST_MPFR_50)
-template 
-inline bool is_mpfr(const boost::multiprecision::number >&)
+template 
+inline bool is_mpfr(const boost::multiprecision::number, ET>&)
 {
    return true;
 }
diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp
index 591e550d..74ba8898 100644
--- a/test/test_float_io.cpp
+++ b/test/test_float_io.cpp
@@ -41,8 +41,8 @@
 #include 
 
 #if defined(TEST_MPF_50)
-template 
-bool is_mpf(const boost::multiprecision::number >&)
+template 
+bool is_mpf(const boost::multiprecision::number, ET>&)
 {  return true;  }
 #endif
 template 

From 5256e108a13835be2565380802bffd67c14a238f Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 20 Sep 2012 18:21:07 +0000
Subject: [PATCH 240/256] Fix Intel -x64 failures.

[SVN r80609]
---
 include/boost/multiprecision/cpp_int.hpp      | 44 +++++++++----------
 .../multiprecision/detail/number_base.hpp     |  2 +-
 .../multiprecision/detail/number_compare.hpp  |  2 +-
 test/test_arithmetic.cpp                      |  2 +-
 4 files changed, 25 insertions(+), 25 deletions(-)

diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp
index 0436f657..14141b2b 100644
--- a/include/boost/multiprecision/cpp_int.hpp
+++ b/include/boost/multiprecision/cpp_int.hpp
@@ -1156,15 +1156,10 @@ public:
       typename enable_if_c<
          (MinBits2 <= MinBits)
          && (Signed || !Signed2)
-      >::type* = 0) 
+      >::type* = 0) BOOST_NOEXCEPT
       : base_type()
    {
-       *this = static_cast<
-            typename boost::multiprecision::detail::canonical<
-               typename cpp_int_backend::local_limb_type, 
-               cpp_int_backend 
-            >::type
-         >(*other.limbs());
+      *this->limbs() = static_cast::local_limb_type>(*other.limbs());
       this->sign(other.sign());
    }
    template 
@@ -1172,31 +1167,21 @@ public:
       typename disable_if_c<
          (MinBits2 <= MinBits)
          && (Signed || !Signed2)
-      >::type* = 0) 
+      >::type* = 0) BOOST_NOEXCEPT
       : base_type()
    {
-       *this = static_cast<
-            typename boost::multiprecision::detail::canonical<
-               typename cpp_int_backend::local_limb_type, 
-               cpp_int_backend 
-            >::type
-         >(*other.limbs());
+      *this->limbs() = static_cast::local_limb_type>(*other.limbs());
       this->sign(other.sign());
    }
    template 
-   cpp_int_backend& operator = (const cpp_int_backend& other) 
+   cpp_int_backend& operator = (const cpp_int_backend& other)BOOST_NOEXCEPT
    {
-       *this = static_cast<
-            typename boost::multiprecision::detail::canonical<
-               typename cpp_int_backend::local_limb_type, 
-               cpp_int_backend 
-            >::type
-         >(*other.limbs());
+      *this->limbs() = static_cast::local_limb_type>(*other.limbs());
       this->sign(other.sign());
       return *this;
    }
    template 
-   explicit cpp_int_backend(const cpp_int_backend& other) 
+   explicit cpp_int_backend(const cpp_int_backend& other)BOOST_NOEXCEPT
       : base_type()
    {
       // We can only ever copy two limbs from other:
@@ -1210,6 +1195,21 @@ public:
       }
       this->sign(other.sign());
    }
+   template 
+   cpp_int_backend& operator=(const cpp_int_backend& other)BOOST_NOEXCEPT 
+   {
+      // We can only ever copy two limbs from other:
+      if(other.size() == 1)
+      {
+         *this->limbs() = *other.limbs();
+      }
+      else
+      {
+         *this->limbs() = static_cast(*other.limbs()) | (static_cast(other.limbs()[1]) << (sizeof(limb_type) * CHAR_BIT));
+      }
+      this->sign(other.sign());
+      return *this;
+   }
 
    BOOST_FORCEINLINE void swap(cpp_int_backend& o) BOOST_NOEXCEPT
    {
diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp
index b6f9c65f..37057c12 100644
--- a/include/boost/multiprecision/detail/number_base.hpp
+++ b/include/boost/multiprecision/detail/number_base.hpp
@@ -218,7 +218,7 @@ template 
 struct combine_expression
 {
 #ifdef BOOST_NO_DECLTYPE
-   typedef typename mpl::if_c sizeof(T2) ? T1, T2>::type type;
+   typedef typename mpl::if_c<(sizeof(T1() + T2()) == sizeof(T1)), T1, T2>::type type;
 #else
    typedef decltype(T1() + T2()) type;
 #endif
diff --git a/include/boost/multiprecision/detail/number_compare.hpp b/include/boost/multiprecision/detail/number_compare.hpp
index 00832838..bd01c3d6 100644
--- a/include/boost/multiprecision/detail/number_compare.hpp
+++ b/include/boost/multiprecision/detail/number_compare.hpp
@@ -78,7 +78,7 @@ template 
 struct is_valid_mixed_compare : public mpl::false_ {};
 
 template 
-struct is_valid_mixed_compare, Val> : public is_convertible> {};
+struct is_valid_mixed_compare, Val> : public is_convertible > {};
 
 template 
 struct is_valid_mixed_compare, number > : public mpl::false_ {};
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index e38ea081..ad1b78a6 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -1383,7 +1383,7 @@ void test_members(Real)
 }
 
 template 
-void test_members(boost::rational v)
+void test_members(boost::rational)
 {
 }
 

From a857186cb4749bdccf692eb5443551667447bad2 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Wed, 24 Oct 2012 16:00:05 +0000
Subject: [PATCH 241/256] Big "blow it away and start again" refactoring of
 cpp_int. Adds support for runtime checking, enumerated template params, fixed
 precision with allocator, and no "hidden" template parameters.

[SVN r81054]
---
 include/boost/multiprecision/cpp_int.hpp      | 3376 +++++------------
 include/boost/multiprecision/cpp_int/add.hpp  |  509 +++
 .../boost/multiprecision/cpp_int/bitwise.hpp  |  560 +++
 .../boost/multiprecision/cpp_int/checked.hpp  |  149 +
 .../multiprecision/cpp_int/comparison.hpp     |  389 ++
 .../multiprecision/cpp_int/cpp_int_config.hpp |  156 +
 .../boost/multiprecision/cpp_int/divide.hpp   |  618 +++
 .../boost/multiprecision/cpp_int/limits.hpp   |  215 ++
 include/boost/multiprecision/cpp_int/misc.hpp |  301 ++
 .../boost/multiprecision/cpp_int/multiply.hpp |  288 ++
 .../multiprecision/detail/cpp_int_core.hpp    |    2 +
 .../detail/cpp_int_trivial_ops.hpp            |   98 +-
 .../multiprecision/detail/default_ops.hpp     |   12 +-
 .../multiprecision/detail/integer_ops.hpp     |    8 +-
 .../boost/multiprecision/detail/no_et_ops.hpp |    4 +-
 .../multiprecision/detail/number_base.hpp     |   27 +-
 test/Jamfile.v2                               |   43 +
 test/include_test/cpp_int_include_test.cpp    |    6 +-
 test/test_arithmetic.cpp                      |  108 +-
 test/test_cpp_int.cpp                         |   22 +-
 test/test_cpp_int_conv.cpp                    |   10 +-
 test/test_int_io.cpp                          |   29 +-
 test/test_numeric_limits.cpp                  |    4 +-
 23 files changed, 4282 insertions(+), 2652 deletions(-)
 create mode 100644 include/boost/multiprecision/cpp_int/add.hpp
 create mode 100644 include/boost/multiprecision/cpp_int/bitwise.hpp
 create mode 100644 include/boost/multiprecision/cpp_int/checked.hpp
 create mode 100644 include/boost/multiprecision/cpp_int/comparison.hpp
 create mode 100644 include/boost/multiprecision/cpp_int/cpp_int_config.hpp
 create mode 100644 include/boost/multiprecision/cpp_int/divide.hpp
 create mode 100644 include/boost/multiprecision/cpp_int/limits.hpp
 create mode 100644 include/boost/multiprecision/cpp_int/misc.hpp
 create mode 100644 include/boost/multiprecision/cpp_int/multiply.hpp

diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp
index 14141b2b..c035de13 100644
--- a/include/boost/multiprecision/cpp_int.hpp
+++ b/include/boost/multiprecision/cpp_int.hpp
@@ -14,40 +14,148 @@
 #include 
 #include 
 #include 
-#include 
+#include 
 #include 
 #include 
+#include 
+#include 
+#include 
 
 namespace boost{
 namespace multiprecision{
+
 namespace backends{
 
 #ifdef BOOST_MSVC
 // warning C4127: conditional expression is constant
 #pragma warning(push)
-#pragma warning(disable:4127 4351)
+#pragma warning(disable:4127 4351 4293)
 #endif
 
-template , bool trivial = is_void::value && (MinBits <= sizeof(double_limb_type) * CHAR_BIT) >
+template  >
 struct cpp_int_backend;
 
-template , bool trivial = false>
+template 
 struct cpp_int_base;
+//
+// Traits class determines the maximum and minimum precision values:
+//
+template  struct max_precision;
 
-template 
-struct is_trivial_cpp_int;
-template 
-struct is_trivial_cpp_int >
+template 
+struct max_precision >
 {
-   typedef mpl::bool_ type;
+   static const unsigned value = is_void::value ?
+      static_unsigned_max::value
+      : (((MaxBits >= MinBits) && MaxBits) ? MaxBits : UINT_MAX);
 };
 
-template 
-struct cpp_int_base : private Allocator::template rebind::other
+template  struct min_precision;
+
+template 
+struct min_precision >
+{
+   static const unsigned value = (is_void::value ? static_unsigned_max::value : MinBits);
+};
+//
+// Traits class determines whether the number of bits precision requested could fit in a native type,
+// we call this a "trivial" cpp_int:
+//
+template 
+struct is_trivial_cpp_int
+{
+   static const bool value = false;
+};
+
+template 
+struct is_trivial_cpp_int >
+{
+   typedef cpp_int_backend self;
+   static const bool value = is_void::value && (max_precision::value <= (sizeof(double_limb_type) * CHAR_BIT) - (SignType == signed_packed ? 1 : 0));
+};
+
+template 
+struct is_trivial_cpp_int >
+{
+   static const bool value = true;
+};
+
+} // namespace backends
+//
+// Traits class to determine whether a cpp_int_backend is signed or not:
+//
+template 
+struct is_unsigned_number >
+   : public mpl::bool_<(SignType == unsigned_magnitude) || (SignType == unsigned_packed)>{};
+
+namespace backends{
+//
+// Traits class determines whether T should be implicitly convertible to U, or
+// whether the constructor should be made explicit.  The latter happens if we
+// are losing the sign, or have fewer digits precision in the target type:
+//
+template 
+struct is_implicit_cpp_int_conversion;
+
+template 
+struct is_implicit_cpp_int_conversion, cpp_int_backend >
+{
+   typedef cpp_int_backend t1;
+   typedef cpp_int_backend t2;
+   static const bool value =
+      (is_signed_number::value || !is_signed_number::value)
+      && (max_precision::value <= max_precision::value);
+};
+
+//
+// Traits class to determine whether operations on a cpp_int may throw:
+//
+template 
+struct is_non_throwing_cpp_int : public mpl::false_{};
+template 
+struct is_non_throwing_cpp_int > : public mpl::true_ {};
+
+//
+// Traits class, determines whether the cpp_int is fixed precision or not:
+//
+template 
+struct is_fixed_precision;
+template 
+struct is_fixed_precision >
+   : public mpl::bool_ >::value != UINT_MAX> {};
+
+namespace detail{
+
+inline void verify_new_size(unsigned new_size, unsigned min_size, const mpl::int_&)
+{
+   if(new_size < min_size)
+      BOOST_THROW_EXCEPTION(std::overflow_error("Unable to allocate sufficient storage for the value of the result: value overflows the maximum allowable magnitude."));
+}
+inline void verify_new_size(unsigned /*new_size*/, unsigned /*min_size*/, const mpl::int_&){}
+
+template 
+inline void verify_limb_mask(bool b, U limb, U mask, const mpl::int_&)
+{
+   // When we mask out "limb" with "mask", do we loose bits?  If so it's an overflow error:
+   if(b && (limb & ~mask))
+      BOOST_THROW_EXCEPTION(std::overflow_error("Overflow in cpp_int arithmetic: there is insufficient precision in the target type to hold all of the bits of the result."));
+}
+template 
+inline void verify_limb_mask(bool /*b*/, U /*limb*/, U /*mask*/, const mpl::int_&){}
+
+}
+
+//
+// Now define the various data layouts that are possible as partial specializations of the base class,
+// starting with the default arbitrary precision signed integer type:
+//
+template 
+struct cpp_int_base : private Allocator::template rebind::other
 {
    typedef typename Allocator::template rebind::other allocator_type;
    typedef typename allocator_type::pointer                      limb_pointer;
    typedef typename allocator_type::const_pointer                const_limb_pointer;
+   typedef mpl::int_                                    checked_type;
 
    //
    // Interface invariants:
@@ -65,14 +173,12 @@ public:
    BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT);
    BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast(0u));
    BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = 1u << (limb_bits - 1));
-   BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = 
-      MinBits 
-         ? MinBits / limb_bits + (MinBits % limb_bits ? 1 : 0) 
+   BOOST_STATIC_CONSTANT(unsigned, internal_limb_count =
+      MinBits
+         ? MinBits / limb_bits + (MinBits % limb_bits ? 1 : 0)
          : sizeof(limb_data) / sizeof(limb_type));
    BOOST_STATIC_CONSTANT(bool, variable = true);
 
-   BOOST_STATIC_ASSERT_MSG(Signed, "There is curently no support for unsigned arbitrary precision integers.");
-
 private:
    union data_type
    {
@@ -98,14 +204,14 @@ public:
    //
    // Direct construction:
    //
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT
       : m_data(i), m_limbs(1), m_sign(false), m_internal(true) { }
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT
       : m_data(i), m_limbs(1), m_sign(i < 0), m_internal(true) { }
 #if defined(BOOST_LITTLE_ENDIAN)
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT
       : m_data(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false), m_internal(true) { }
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT
       : m_data(i), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), m_sign(i < 0), m_internal(true) { }
 #endif
    //
@@ -118,9 +224,9 @@ public:
    BOOST_FORCEINLINE const_limb_pointer limbs()const  BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; }
    BOOST_FORCEINLINE unsigned capacity()const  BOOST_NOEXCEPT { return m_internal ? internal_limb_count : m_data.ld.capacity; }
    BOOST_FORCEINLINE bool sign()const  BOOST_NOEXCEPT { return m_sign; }
-   void sign(bool b)  BOOST_NOEXCEPT 
-   { 
-      m_sign = b; 
+   void sign(bool b)  BOOST_NOEXCEPT
+   {
+      m_sign = b;
       // Check for zero value:
       if(m_sign && (m_limbs == 1))
       {
@@ -128,12 +234,19 @@ public:
             m_sign = false;
       }
    }
-   void resize(unsigned new_size)
+   void resize(unsigned new_size, unsigned min_size)
    {
+      static const unsigned max_limbs = MaxBits / (CHAR_BIT * sizeof(limb_type)) + (MaxBits % (CHAR_BIT * sizeof(limb_type)) ? 1 : 0);
+      // We never resize beyond MaxSize:
+      if(new_size > max_limbs)
+         new_size = max_limbs;
+      detail::verify_new_size(new_size, min_size, checked_type());
+      // See if we have enough capacity already:
       unsigned cap = capacity();
       if(new_size > cap)
       {
-         cap = (std::max)(cap * 4, new_size);
+         // Allocate a new buffer and copy everything over:
+         cap = (std::min)((std::max)(cap * 4, new_size), max_limbs);
          limb_pointer pl = allocator().allocate(cap);
          std::copy(limbs(), limbs() + size(), pl);
          if(!m_internal)
@@ -157,12 +270,13 @@ public:
    BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1), m_sign(false), m_internal(true) {}
    BOOST_FORCEINLINE cpp_int_base(const cpp_int_base& o) : allocator_type(o), m_limbs(0), m_internal(true)
    {
-      resize(o.size());
+      resize(o.size(), o.size());
       std::copy(o.limbs(), o.limbs() + o.size(), limbs());
       m_sign = o.m_sign;
    }
 #ifndef BOOST_NO_RVALUE_REFERENCES
-   cpp_int_base(cpp_int_base&& o) BOOST_NOEXCEPT : allocator_type(static_cast(o)), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) 
+   cpp_int_base(cpp_int_base&& o) BOOST_NOEXCEPT
+      : allocator_type(static_cast(o)), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal)
    {
       if(m_internal)
       {
@@ -207,7 +321,7 @@ public:
       {
          static_cast(*this) = static_cast(o);
          m_limbs = 0;
-         resize(o.size());
+         resize(o.size(), o.size());
          std::copy(o.limbs(), o.limbs() + o.size(), limbs());
          m_sign = o.m_sign;
       }
@@ -224,7 +338,7 @@ public:
    }
    BOOST_FORCEINLINE bool isneg()const BOOST_NOEXCEPT
    {
-      return m_sign; 
+      return m_sign;
    }
    BOOST_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
    {
@@ -235,11 +349,39 @@ public:
    }
 };
 
-template 
-struct cpp_int_base
+#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
+
+template 
+const unsigned cpp_int_base::limb_bits;
+template 
+const limb_type cpp_int_base::max_limb_value;
+template 
+const limb_type cpp_int_base::sign_bit_mask;
+template 
+const unsigned cpp_int_base::internal_limb_count;
+template 
+const bool cpp_int_base::variable;
+
+#endif
+
+template 
+struct cpp_int_base : private Allocator::template rebind::other
+{
+   //
+   // There is currently no support for unsigned arbitrary precision arithmetic, largely
+   // because it's not clear what subtraction should do:
+   //
+   BOOST_STATIC_ASSERT_MSG(((sizeof(Allocator) == 0) && !is_void::value), "There is curently no support for unsigned arbitrary precision integers.");
+};
+//
+// Fixed precision (i.e. no allocator), signed-magnitude type with limb-usage count:
+//
+template 
+struct cpp_int_base
 {
    typedef limb_type*                      limb_pointer;
    typedef const limb_type*                const_limb_pointer;
+   typedef mpl::int_              checked_type;
 
    //
    // Interface invariants:
@@ -272,14 +414,14 @@ public:
    //
    // Direct construction:
    //
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT
       : m_wrapper(i), m_limbs(1), m_sign(false) {}
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT
       : m_wrapper(limb_type(i < 0 ? -i : i)), m_limbs(1), m_sign(i < 0) {}
 #if defined(BOOST_LITTLE_ENDIAN)
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT
       : m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false) {}
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT
       : m_wrapper(double_limb_type(i < 0 ? -i : i)), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), m_sign(i < 0) {}
 #endif
    //
@@ -290,8 +432,8 @@ public:
    BOOST_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; }
    BOOST_FORCEINLINE bool sign()const BOOST_NOEXCEPT { return m_sign; }
    BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT
-   { 
-      m_sign = b; 
+   {
+      m_sign = b;
       // Check for zero value:
       if(m_sign && (m_limbs == 1))
       {
@@ -299,13 +441,15 @@ public:
             m_sign = false;
       }
    }
-   BOOST_FORCEINLINE void resize(unsigned new_size) BOOST_NOEXCEPT
+   BOOST_FORCEINLINE void resize(unsigned new_size, unsigned min_size) BOOST_NOEXCEPT_IF((Checked == unchecked))
    {
       m_limbs = static_cast((std::min)(new_size, internal_limb_count));
+      detail::verify_new_size(m_limbs, min_size, checked_type());
    }
-   BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT
+   BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT_IF((Checked == unchecked))
    {
       limb_pointer p = limbs();
+      detail::verify_limb_mask(m_limbs == internal_limb_count, p[internal_limb_count-1], upper_limb_mask, checked_type());
       p[internal_limb_count-1] &= upper_limb_mask;
       while((m_limbs-1) && !p[m_limbs - 1])--m_limbs;
       if((m_limbs == 1) && (!*p)) m_sign = false; // zero is always unsigned
@@ -321,7 +465,7 @@ public:
    {
       if(this != &o)
       {
-         resize(o.size());
+         resize(o.size(), o.size());
          std::copy(o.limbs(), o.limbs() + o.size(), limbs());
          m_sign = o.m_sign;
       }
@@ -338,7 +482,7 @@ public:
    }
    BOOST_FORCEINLINE bool isneg()const BOOST_NOEXCEPT
    {
-      return m_sign; 
+      return m_sign;
    }
    BOOST_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
    {
@@ -348,12 +492,29 @@ public:
       std::swap(m_limbs, o.m_limbs);
    }
 };
+#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
 
-template 
-struct cpp_int_base
+template 
+const unsigned cpp_int_base::limb_bits;
+template 
+const limb_type cpp_int_base::max_limb_value;
+template 
+const limb_type cpp_int_base::sign_bit_mask;
+template 
+const unsigned cpp_int_base::internal_limb_count;
+template 
+const bool cpp_int_base::variable;
+
+#endif
+//
+// Fixed precision (i.e. no allocator), unsigned type with limb-usage count:
+//
+template 
+struct cpp_int_base
 {
    typedef limb_type*                      limb_pointer;
    typedef const limb_type*                const_limb_pointer;
+   typedef mpl::int_              checked_type;
 
    //
    // Interface invariants:
@@ -385,14 +546,14 @@ public:
    //
    // Direct construction:
    //
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT
       : m_wrapper(i), m_limbs(1) {}
-   BOOST_FORCEINLINE cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT
       : m_wrapper(limb_type(i < 0 ? -i : i)), m_limbs(1) { if(i < 0) negate(); }
 #ifdef BOOST_LITTLE_ENDIAN
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT
       : m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1) {}
-   BOOST_FORCEINLINE cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT
       : m_wrapper(double_limb_type(i < 0 ? -i : i)), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)) { if(i < 0) negate(); }
 #endif
    //
@@ -403,13 +564,15 @@ public:
    BOOST_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; }
    BOOST_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; }
    BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT {  if(b) negate(); }
-   BOOST_FORCEINLINE void resize(unsigned new_size) BOOST_NOEXCEPT
+   BOOST_FORCEINLINE void resize(unsigned new_size, unsigned min_size) BOOST_NOEXCEPT_IF((Checked == unchecked))
    {
       m_limbs = (std::min)(new_size, internal_limb_count);
+      detail::verify_new_size(m_limbs, min_size, checked_type());
    }
-   BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT
+   BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT_IF((Checked == unchecked))
    {
       limb_pointer p = limbs();
+      detail::verify_limb_mask(m_limbs == internal_limb_count, p[internal_limb_count-1], upper_limb_mask, checked_type());
       p[internal_limb_count-1] &= upper_limb_mask;
       while((m_limbs-1) && !p[m_limbs - 1])--m_limbs;
    }
@@ -424,26 +587,36 @@ public:
    {
       if(this != &o)
       {
-         resize(o.size());
+         resize(o.size(), o.size());
          std::copy(o.limbs(), o.limbs() + o.size(), limbs());
       }
    }
-   void negate() BOOST_NOEXCEPT
+private:
+   void check_negate(const mpl::int_&)
+   {
+      BOOST_THROW_EXCEPTION(std::range_error("Attempt to negate an unsigned number."));
+   }
+   void check_negate(const mpl::int_&){}
+public:
+   void negate() BOOST_NOEXCEPT_IF((Checked == unchecked))
    {
       // Not so much a negate as a complement - this gets called when subtraction
       // would result in a "negative" number:
       unsigned i;
+      if((m_limbs == 1) && (m_wrapper.m_data[0] == 0))
+         return; // negating zero is always zero, and always OK.
+      check_negate(checked_type());
       for(i = m_limbs; i < internal_limb_count; ++i)
          m_wrapper.m_data[i] = 0;
       m_limbs = internal_limb_count;
       for(i = 0; i < internal_limb_count; ++i)
          m_wrapper.m_data[i] = ~m_wrapper.m_data[i];
       normalize();
-      eval_increment(static_cast& >(*this));
+      eval_increment(static_cast& >(*this));
    }
    BOOST_FORCEINLINE BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT
    {
-      return false; 
+      return false;
    }
    BOOST_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
    {
@@ -452,7 +625,24 @@ public:
       std::swap(m_limbs, o.m_limbs);
    }
 };
+#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
 
+template 
+const unsigned cpp_int_base::limb_bits;
+template 
+const limb_type cpp_int_base::max_limb_value;
+template 
+const limb_type cpp_int_base::sign_bit_mask;
+template 
+const unsigned cpp_int_base::internal_limb_count;
+template 
+const bool cpp_int_base::variable;
+
+#endif
+//
+// Traits classes to figure out a native type with N bits, these vary from boost::uint_t only
+// because some platforms have native integer types longer than long long, "really long long" anyone??
+//
 template 
 struct trivial_limb_type_imp
 {
@@ -467,18 +657,16 @@ struct trivial_limb_type_imp
 
 template 
 struct trivial_limb_type : public trivial_limb_type_imp {};
-
-#ifdef BOOST_MSVC
-#pragma warning(push)
-#pragma warning(disable:4244 4293) // loss of data in initialization, shift count too large
-#endif
-
-template 
-struct cpp_int_base
+//
+// Backend for fixed precision signed-magnitude type which will fit entirely inside a "double_limb_type":
+//
+template 
+struct cpp_int_base
 {
    typedef typename trivial_limb_type::type  local_limb_type;
    typedef local_limb_type*                           limb_pointer;
    typedef const local_limb_type*                     const_limb_pointer;
+   typedef mpl::int_                         checked_type;
 protected:
    BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(local_limb_type) * CHAR_BIT);
    BOOST_STATIC_CONSTANT(local_limb_type, limb_mask = MinBits < limb_bits ? (local_limb_type(1) << MinBits) -1 : (~local_limb_type(0)));
@@ -490,20 +678,42 @@ private:
    // Interface invariants:
    //
    BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
+protected:
+   template 
+   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type)), T>::type check_in_range(T val, const mpl::int_&)
+   {
+      BOOST_MP_USING_ABS
+      typedef typename common_type::type common_type;
+
+      if(static_cast(abs(val)) > static_cast(limb_mask))
+         BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
+      return val;
+   }
+   template 
+   BOOST_CONSTEXPR T check_in_range(T val, const mpl::int_&)
+   {
+      return val;
+   }
+
+   template 
+   BOOST_CONSTEXPR T check_in_range(T val)
+   {
+      return check_in_range(val, checked_type());
+   }
 
 public:
    //
    // Direct construction:
    //
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT
-      : m_data(i < 0 ? -i : i), m_sign(i < 0) {}
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(check_in_range(i) < 0 ? static_cast(-i) : static_cast(i)), m_sign(i < 0) {}
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT
-      : m_data(i), m_sign(false) {}
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(static_cast(check_in_range(i))), m_sign(false) {}
    template 
-   BOOST_FORCEINLINE cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT
-      : m_data(std::fabs(i)), m_sign(i < 0) {}
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(static_cast(std::fabs(check_in_range(i)))), m_sign(i < 0) {}
    //
    // Helper functions for getting at our internal data, and manipulating storage:
    //
@@ -512,19 +722,23 @@ public:
    BOOST_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; }
    BOOST_FORCEINLINE bool sign()const BOOST_NOEXCEPT { return m_sign; }
    BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT
-   { 
-      m_sign = b; 
+   {
+      m_sign = b;
       // Check for zero value:
       if(m_sign && !m_data)
       {
          m_sign = false;
       }
    }
-   BOOST_FORCEINLINE void resize(unsigned new_size) BOOST_NOEXCEPT {}
-   BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT
+   BOOST_FORCEINLINE void resize(unsigned new_size, unsigned min_size)
    {
-      if(!m_data) 
+      detail::verify_new_size(2, min_size, checked_type());
+   }
+   BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT_IF((Checked == unchecked))
+   {
+      if(!m_data)
          m_sign = false; // zero is always unsigned
+      detail::verify_limb_mask(true, m_data, limb_mask, checked_type());
       m_data &= limb_mask;
    }
 
@@ -547,7 +761,7 @@ public:
    }
    BOOST_FORCEINLINE bool isneg()const BOOST_NOEXCEPT
    {
-      return m_sign; 
+      return m_sign;
    }
    BOOST_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
    {
@@ -555,38 +769,74 @@ public:
       std::swap(m_data, o.m_data);
    }
 };
-
-template 
-struct cpp_int_base
+//
+// Backend for unsigned fixed precision (i.e. no allocator) type which will fit entirely inside a "double_limb_type":
+//
+template 
+struct cpp_int_base
 {
    typedef typename trivial_limb_type::type  local_limb_type;
    typedef local_limb_type*                           limb_pointer;
    typedef const local_limb_type*                     const_limb_pointer;
 private:
    BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(local_limb_type) * CHAR_BIT);
-   BOOST_STATIC_CONSTANT(local_limb_type, limb_mask = MinBits < limb_bits ? (local_limb_type(1) << MinBits) -1 : (~local_limb_type(0)));
+   BOOST_STATIC_CONSTANT(local_limb_type, limb_mask = (~local_limb_type(0)) >> (limb_bits - MinBits));
 
    local_limb_type    m_data;
 
+   typedef mpl::int_                          checked_type;
+
    //
    // Interface invariants:
    //
    BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
+protected:
+   template 
+   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type)), T>::type check_in_range(T val, const mpl::int_&, const mpl::true_&)
+   {
+      typedef typename common_type::type common_type;
+
+      if(static_cast(val) > limb_mask)
+         BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
+   }
+   template 
+   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type)), T>::type check_in_range(T val, const mpl::int_&, const mpl::false_&)
+   {
+      typedef typename common_type::type common_type;
+
+      if(static_cast(val) > limb_mask)
+         BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
+      if(val < 0)
+         BOOST_THROW_EXCEPTION(std::range_error("The argument to an unsigned cpp_int constructor was negative."));
+      return val;
+   }
+   template 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR T check_in_range(T val, const mpl::int_&, const U&)
+   {
+      return val;
+   }
+
+   template 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR T check_in_range(T val)
+   {
+      return check_in_range(val, checked_type(), is_unsigned());
+   }
 
 public:
    //
    // Direct construction:
    //
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT
-      : m_data(i < 0 ? 1 + ~static_cast(-i) : static_cast(i)) {}
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(check_in_range(i) < 0 ? 1 + ~static_cast(-i) : static_cast(i)) {}
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT
-      : m_data(i) {}
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(static_cast(check_in_range(i))) {}
    template 
-   BOOST_FORCEINLINE cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT
-      : m_data(std::fabs(i)) 
+   BOOST_FORCEINLINE cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(static_cast(std::fabs(i)))
    {
+      check_in_range(i);
       if(i < 0)
          negate();
    }
@@ -602,9 +852,13 @@ public:
       if(b)
          negate();
    }
-   BOOST_FORCEINLINE void resize(unsigned new_size) BOOST_NOEXCEPT {}
-   BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT 
+   BOOST_FORCEINLINE void resize(unsigned new_size, unsigned min_size)
    {
+      detail::verify_new_size(2, min_size, checked_type());
+   }
+   BOOST_FORCEINLINE void normalize() BOOST_NOEXCEPT_IF((Checked == unchecked))
+   {
+      detail::verify_limb_mask(true, m_data, limb_mask, checked_type());
       m_data &= limb_mask;
    }
 
@@ -622,61 +876,70 @@ public:
    }
    BOOST_FORCEINLINE BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT
    {
-      return false; 
+      return false;
    }
    BOOST_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
    {
       std::swap(m_data, o.m_data);
    }
 };
-
-#ifdef BOOST_MSVC
-#pragma warning(pop)
+//
+// Traits class, lets us know whether type T can be directly converted to the base type,
+// used to enable/disable constructors etc:
+//
+template 
+struct is_allowed_cpp_int_base_conversion : public mpl::if_c<
+      is_same::value || is_same::value
+#ifdef BOOST_LITTLE_ENDIAN
+      || is_same::value || is_same::value
 #endif
-
-template 
-const unsigned cpp_int_base::limb_bits;
-template 
-const limb_type cpp_int_base::max_limb_value;
-template 
-const limb_type cpp_int_base::sign_bit_mask;
-template 
-const unsigned cpp_int_base::internal_limb_count;
-template 
-const bool cpp_int_base::variable;
-
-template 
-const unsigned cpp_int_base::limb_bits;
-template 
-const limb_type cpp_int_base::max_limb_value;
-template 
-const limb_type cpp_int_base::sign_bit_mask;
-template 
-const unsigned cpp_int_base::internal_limb_count;
-template 
-const bool cpp_int_base::variable;
-
-template 
-const unsigned cpp_int_base::limb_bits;
-template 
-const limb_type cpp_int_base::max_limb_value;
-template 
-const limb_type cpp_int_base::sign_bit_mask;
-template 
-const unsigned cpp_int_base::internal_limb_count;
-template 
-const bool cpp_int_base::variable;
-
-template 
-struct cpp_int_backend : public cpp_int_base
+      || (is_trivial_cpp_int::value && is_arithmetic::value),
+      mpl::true_,
+      mpl::false_
+   >::type
+{};
+//
+// Now the actual backend, normalising parameters passed to the base class:
+//
+template 
+struct cpp_int_backend
+   : public cpp_int_base<
+               min_precision >::value,
+               max_precision >::value,
+               SignType,
+               Checked,
+               Allocator,
+               is_trivial_cpp_int >::value>
 {
-   typedef cpp_int_backend               self_type;
-   typedef cpp_int_base                  base_type;
-   typedef typename is_trivial_cpp_int::type              trivial_tag;
+   typedef cpp_int_backend    self_type;
+   typedef cpp_int_base<
+               min_precision::value,
+               max_precision::value,
+               SignType,
+               Checked,
+               Allocator,
+               is_trivial_cpp_int::value>                 base_type;
+   typedef mpl::bool_::value>          trivial_tag;
 public:
-   typedef mpl::list      signed_types;
-   typedef mpl::list                    unsigned_types;
-   typedef mpl::list                                    float_types;
+   typedef typename mpl::if_<
+      trivial_tag,
+      mpl::list<
+      signed char, short, int, long,
+      long long, signed_double_limb_type>,
+      mpl::list
+   >::type                                                           signed_types;
+   typedef typename mpl::if_<
+      trivial_tag,
+      mpl::list,
+      mpl::list
+   >::type                                                           unsigned_types;
+   typedef typename mpl::if_<
+      trivial_tag,
+      mpl::list,
+      mpl::list
+   >::type                                                           float_types;
+   typedef mpl::int_                                        checked_type;
 
    BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{}
    BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) : base_type(o) {}
@@ -684,84 +947,207 @@ public:
    BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT : base_type(static_cast(o)) {}
 #endif
    //
-   // These are templates, so that only args that are *exactly* the types specified are allowed, and conversions
-   // are not considered.  Without this, conversions may be ambiguous.
+   // Direct construction from arithmetic type:
    //
-   template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(LT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT 
+   template 
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(Arg i, typename enable_if_c::value >::type const* = 0)BOOST_NOEXCEPT_IF((Checked == unchecked))
       : base_type(i) {}
-   template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(SLT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT 
-      : base_type(i) {}
-#if defined(BOOST_LITTLE_ENDIAN)
-   template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(LT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT 
-      : base_type(i) {}
-   template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(SLT i, typename enable_if >::type const* = 0)BOOST_NOEXCEPT 
-      : base_type(i) {}
-#endif
-   
-   template 
-   cpp_int_backend(const cpp_int_backend& other) 
+
+private:
+   template 
+   void do_assign(const cpp_int_backend& other, mpl::true_ const&, mpl::true_ const &)
+   {
+      // Assigning trivial type to trivial type:
+      this->check_in_range(*other.limbs());
+      *this->limbs() = static_cast(*other.limbs());
+      this->sign(other.sign());
+      this->normalize();
+   }
+   template 
+   void do_assign(const cpp_int_backend& other, mpl::true_ const&, mpl::false_ const &)
+   {
+      // non-trivial to trivial narrowing conversion:
+      double_limb_type v = *other.limbs();
+      if(other.size() > 1)
+      {
+         v |= static_cast(other.limbs()[1]) << bits_per_limb;
+         if((Checked == checked) && (other.size() > 2))
+         {
+            BOOST_THROW_EXCEPTION(std::range_error("Assignment of a cpp_int that is out of range for the target type."));
+         }
+      }
+      *this = v;
+      this->sign(other.sign());
+      this->normalize();
+   }
+   template 
+   void do_assign(const cpp_int_backend& other, mpl::false_ const&, mpl::true_ const &)
+   {
+      // trivial to non-trivial, treat the trivial argument as if it were an unsigned arithmetic type, then set the sign afterwards:
+       *this = static_cast<
+            typename boost::multiprecision::detail::canonical<
+               typename cpp_int_backend::local_limb_type,
+               cpp_int_backend
+            >::type
+         >(*other.limbs());
+       this->sign(other.sign());
+   }
+   template 
+   void do_assign(const cpp_int_backend& other, mpl::false_ const&, mpl::false_ const &)
+   {
+      // regular non-trivial to non-trivial assign:
+      this->resize(other.size(), other.size());
+      std::copy(other.limbs(), other.limbs() + (std::min)(other.size(), this->size()), this->limbs());
+      this->sign(other.sign());
+      this->normalize();
+   }
+public:
+   template 
+   cpp_int_backend(
+      const cpp_int_backend& other,
+      typename enable_if_c, self_type>::value>::type* = 0)
+      : base_type()
+   {
+      do_assign(
+         other,
+         mpl::bool_::value>(),
+         mpl::bool_ >::value>());
+   }
+   template 
+   explicit cpp_int_backend(
+      const cpp_int_backend& other,
+      typename disable_if_c, self_type>::value>::type* = 0)
+      : base_type()
+   {
+      do_assign(
+         other,
+         mpl::bool_::value>(),
+         mpl::bool_ >::value>());
+   }
+   template 
+   cpp_int_backend& operator=(
+      const cpp_int_backend& other)
+   {
+      do_assign(
+         other,
+         mpl::bool_::value>(),
+         mpl::bool_ >::value>());
+      return *this;
+   }
+#if 0
+   template 
+   cpp_int_backend(const cpp_int_backend& other, typename enable_if_c >::value >::type* = 0)
       : base_type()
    {
        *this = static_cast<
             typename boost::multiprecision::detail::canonical<
-               typename cpp_int_backend::local_limb_type, 
-               cpp_int_backend 
+               typename cpp_int_backend::local_limb_type,
+               cpp_int_backend
             >::type
          >(*other.limbs());
       this->sign(other.sign());
    }
-   template 
-   cpp_int_backend& operator=(const cpp_int_backend& other) 
+   template 
+   typename enable_if_c >::value, cpp_int_backend&>::type
+    operator=(const cpp_int_backend& other)
    {
        *this = static_cast<
             typename boost::multiprecision::detail::canonical<
-               typename cpp_int_backend::local_limb_type, 
-               cpp_int_backend 
+               typename cpp_int_backend::local_limb_type,
+               cpp_int_backend
             >::type
          >(*other.limbs());
       this->sign(other.sign());
       return *this;
    }
 
-   template 
-   cpp_int_backend(const cpp_int_backend& other, 
+   template 
+   cpp_int_backend(const cpp_int_backend& other,
       typename enable_if_c<
-         (Signed || !Signed2) 
+         ((is_signed_number >::value || !is_signed_number >::value)
          && (!is_void::value || (is_void::value && (MinBits >= MinBits2)))
-      >::type* = 0) 
+         && !is_trivial_cpp_int >::value
+         && !is_trivial_cpp_int >::value)
+      >::type* = 0)
       : base_type()
    {
-      this->resize(other.size());
+      this->resize(other.size(), other_size());
       std::copy(other.limbs(), other.limbs() + (std::min)(other.size(), this->size()), this->limbs());
       this->sign(other.sign());
    }
 
-   template 
-   explicit cpp_int_backend(const cpp_int_backend& other, 
-      typename disable_if_c<
-         (Signed || !Signed2) 
-         && (!is_void::value || (is_void::value && (MinBits >= MinBits2)))
-      >::type* = 0) 
+   template 
+   explicit cpp_int_backend(const cpp_int_backend& other,
+      typename enable_if_c<
+         (!((is_signed_number >::value || !is_signed_number >::value)
+         && (!is_void::value || (is_void::value && (MinBits >= MinBits2))))
+         && !is_trivial_cpp_int >::value
+         && is_trivial_cpp_int >::value)
+      >::type* = 0)
       : base_type()
    {
-      this->resize(other.size());
+      double_limb_type v = *other.limbs();
+      if(other.size() > 1)
+         v |= static_cast(other.limbs()[1]) << bits_per_limb;
+      *this = v;
+      this->sign(other.sign());
+   }
+
+   template 
+   explicit cpp_int_backend(const cpp_int_backend& other,
+      typename enable_if_c<
+         (!((is_signed_number >::value || !is_signed_number >::value))
+         && (!is_void::value || (is_void::value && (MinBits >= MinBits2)))
+         && !is_trivial_cpp_int >::value
+         && !is_trivial_cpp_int >::value)
+      >::type* = 0)
+      : base_type()
+   {
+      this->resize(other.size(), other.size());
       std::copy(other.limbs(), other.limbs() + (std::min)(other.size(), this->size()), this->limbs());
       this->sign(other.sign());
    }
 
-   template 
-   cpp_int_backend& operator=(const cpp_int_backend& other)
+   template 
+   explicit cpp_int_backend(const cpp_int_backend& other,
+      typename enable_if_c<
+         (!((is_signed_number >::value || !is_signed_number >::value))
+         && (!is_void::value || (is_void::value && (MinBits >= MinBits2)))
+         && !is_trivial_cpp_int >::value
+         && is_trivial_cpp_int >::value)
+      >::type* = 0)
+      : base_type()
    {
-      this->resize(other.size());
+      double_limb_type v = *other.limbs();
+      if(other.size() > 1)
+         v |= static_cast(other.limbs()[1]) << bits_per_limb;
+      *this = v;
+      this->sign(other.sign());
+   }
+
+   template 
+   typename enable_if_c<(!is_trivial_cpp_int >::value
+         && !is_trivial_cpp_int >::value), cpp_int_backend&>::type
+      operator=(const cpp_int_backend& other)
+   {
+      this->resize(other.size(), other.size());
       std::copy(other.limbs(), other.limbs() + (std::min)(other.size(), this->size()), this->limbs());
       this->sign(other.sign());
       return *this;
    }
 
+   template 
+   typename enable_if_c<(!is_trivial_cpp_int >::value
+         && is_trivial_cpp_int >::value), cpp_int_backend&>::type
+      operator=(const cpp_int_backend& other)
+   {
+      double_limb_type v = *other.limbs();
+      if(other.size() > 1)
+         v |= static_cast(other.limbs()[1]) << bits_per_limb;
+      *this = v;
+      this->sign(other.sign());
+   }
+#endif
    BOOST_FORCEINLINE cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
    {
       this->assign(o);
@@ -774,32 +1160,45 @@ public:
       return *this;
    }
 #endif
-   BOOST_FORCEINLINE cpp_int_backend& operator = (limb_type i) BOOST_NOEXCEPT
+private:
+   template 
+   typename enable_if >::type do_assign_arithmetic(A val, const mpl::true_&)
    {
-      this->resize(1);
+      this->check_in_range(val);
+      *this->limbs() = static_cast(val);
+      this->normalize();
+   }
+   template 
+   typename disable_if >::type do_assign_arithmetic(A val, const mpl::true_&)
+   {
+      this->check_in_range(val);
+      *this->limbs() = (val < 0) ? static_cast(-val) : static_cast(val);
+      this->sign(val < 0);
+      this->normalize();
+   }
+   BOOST_FORCEINLINE void do_assign_arithmetic(limb_type i, const mpl::false_&) BOOST_NOEXCEPT
+   {
+      this->resize(1, 1);
       *this->limbs() = i;
       this->sign(false);
-      return *this;
    }
-   BOOST_FORCEINLINE cpp_int_backend& operator = (signed_limb_type i) BOOST_NOEXCEPT
+   BOOST_FORCEINLINE void do_assign_arithmetic(signed_limb_type i, const mpl::false_&) BOOST_NOEXCEPT
    {
-      this->resize(1);
+      this->resize(1, 1);
       *this->limbs() = static_cast(std::abs(i));
       this->sign(i < 0);
-      return *this;
    }
-   cpp_int_backend& operator = (double_limb_type i) BOOST_NOEXCEPT_IF(MinBits <= sizeof(double_limb_type) * CHAR_BIT)
+   void do_assign_arithmetic(double_limb_type i, const mpl::false_&)
    {
       BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type));
       BOOST_STATIC_ASSERT(base_type::internal_limb_count >= 2);
       typename base_type::limb_pointer p = this->limbs();
       *p = static_cast(i);
       p[1] = static_cast(i >> base_type::limb_bits);
-      this->resize(p[1] ? 2 : 1);
+      this->resize(p[1] ? 2 : 1, p[1] ? 2 : 1);
       this->sign(false);
-      return *this;
    }
-   cpp_int_backend& operator = (signed_double_limb_type i) BOOST_NOEXCEPT_IF(MinBits <= sizeof(signed_double_limb_type) * CHAR_BIT)
+   void do_assign_arithmetic(signed_double_limb_type i, const mpl::false_&)
    {
       BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type));
       BOOST_STATIC_ASSERT(base_type::internal_limb_count >= 2);
@@ -814,12 +1213,11 @@ public:
       typename base_type::limb_pointer p = this->limbs();
       *p = static_cast(i);
       p[1] = static_cast(i >> base_type::limb_bits);
-      this->resize(p[1] ? 2 : 1);
+      this->resize(p[1] ? 2 : 1, p[1] ? 2 : 1);
       this->sign(s);
-      return *this;
    }
 
-   cpp_int_backend& operator = (long double a) BOOST_NOEXCEPT_IF(MinBits <= sizeof(long double) * CHAR_BIT)
+   void do_assign_arithmetic(long double a, const mpl::false_&)
    {
       using default_ops::eval_add;
       using default_ops::eval_subtract;
@@ -828,11 +1226,11 @@ public:
       using std::floor;
 
       if (a == 0) {
-         return *this = static_cast(0u);
+         *this = static_cast(0u);
       }
 
       if (a == 1) {
-         return *this = static_cast(1u);
+         *this = static_cast(1u);
       }
 
       BOOST_ASSERT(!(boost::math::isinf)(a));
@@ -863,9 +1261,67 @@ public:
          eval_left_shift(*this, e);
       else if(e < 0)
          eval_right_shift(*this, -e);
+   }
+public:
+   template 
+   BOOST_FORCEINLINE cpp_int_backend& operator = (Arithmetic val)
+   {
+      do_assign_arithmetic(val, trivial_tag());
       return *this;
    }
-   cpp_int_backend& operator = (const char* s)
+private:
+   void do_assign_string(const char* s, const mpl::true_&)
+   {
+      std::size_t n = s ? std::strlen(s) : 0;
+      *this->limbs() = 0;
+      unsigned radix = 10;
+      bool isneg = false;
+      if(n && (*s == '-'))
+      {
+         --n;
+         ++s;
+         isneg = true;
+      }
+      if(n && (*s == '0'))
+      {
+         if((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
+         {
+            radix = 16;
+            s +=2;
+            n -= 2;
+         }
+         else
+         {
+            radix = 8;
+            n -= 1;
+         }
+      }
+      if(n)
+      {
+         unsigned val;
+         while(*s)
+         {
+            if(*s >= '0' && *s <= '9')
+               val = *s - '0';
+            else if(*s >= 'a' && *s <= 'f')
+               val = 10 + *s - 'a';
+            else if(*s >= 'A' && *s <= 'F')
+               val = 10 + *s - 'A';
+            else
+               val = radix + 1;
+            if(val > radix)
+            {
+               BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
+            }
+            *this->limbs() = detail::checked_multiply(*this->limbs(), static_cast(radix), checked_type());
+            *this->limbs() = detail::checked_add(*this->limbs(), static_cast(val), checked_type());
+            ++s;
+         }
+      }
+      if(isneg)
+         this->negate();
+   }
+   void do_assign_string(const char* s, const mpl::false_&)
    {
       using default_ops::eval_multiply;
       using default_ops::eval_add;
@@ -961,14 +1417,121 @@ public:
       }
       if(isneg)
          this->negate();
+   }
+public:
+   cpp_int_backend& operator = (const char* s)
+   {
+      do_assign_string(s, trivial_tag());
       return *this;
    }
    BOOST_FORCEINLINE void swap(cpp_int_backend& o) BOOST_NOEXCEPT
    {
       this->do_swap(o);
    }
-   std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const
+private:
+   std::string do_get_trivial_string(std::ios_base::fmtflags f, const mpl::false_&)const
    {
+      if(this->sign() && (((f & std::ios_base::hex) == std::ios_base::hex) || ((f & std::ios_base::oct) == std::ios_base::oct)))
+         BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported."));
+      std::stringstream ss;
+      ss.flags(f & ~std::ios_base::showpos);
+      ss << *this->limbs();
+      std::string result;
+      if(this->sign())
+         result += '-';
+      else if(f & std::ios_base::showpos)
+         result += '+';
+      result += ss.str();
+      return result;
+   }
+   std::string do_get_trivial_string(std::ios_base::fmtflags f, const mpl::true_&)const
+   {
+      // Even though we have only one limb, we can't do IO on it :-(
+      int base = 10;
+      if((f & std::ios_base::oct) == std::ios_base::oct)
+         base = 8;
+      else if((f & std::ios_base::hex) == std::ios_base::hex)
+         base = 16;
+      std::string result;
+
+      unsigned Bits = base_type::limb_bits;
+
+      if(base == 8 || base == 16)
+      {
+         if(this->sign())
+            BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported."));
+         limb_type shift = base == 8 ? 3 : 4;
+         limb_type mask = static_cast((1u << shift) - 1);
+         typename base_type::local_limb_type v = *this->limbs();
+         result.assign(Bits / shift + (Bits % shift ? 1 : 0), '0');
+         int pos = result.size() - 1;
+         for(unsigned i = 0; i < Bits / shift; ++i)
+         {
+            char c = '0' + static_cast(v & mask);
+            if(c > '9')
+               c += 'A' - '9' - 1;
+            result[pos--] = c;
+            v >>= shift;
+         }
+         if(Bits % shift)
+         {
+            mask = static_cast((1u << (Bits % shift)) - 1);
+            char c = '0' + static_cast(v & mask);
+            if(c > '9')
+               c += 'A' - '9';
+            result[pos] = c;
+         }
+         //
+         // Get rid of leading zeros:
+         //
+         std::string::size_type n = result.find_first_not_of('0');
+         if(!result.empty() && (n == std::string::npos))
+            n = result.size() - 1;
+         result.erase(0, n);
+         if(f & std::ios_base::showbase)
+         {
+            const char* pp = base == 8 ? "0" : "0x";
+            result.insert(0, pp);
+         }
+      }
+      else
+      {
+         result.assign(Bits / 3 + 1, '0');
+         int pos = result.size() - 1;
+         typename base_type::local_limb_type v(*this->limbs());
+         bool neg = false;
+         if(this->sign())
+         {
+            neg = true;
+         }
+         while(v)
+         {
+            result[pos] = (v % 10) + '0';
+            --pos;
+            v /= 10;
+         }
+         unsigned n = result.find_first_not_of('0');
+         result.erase(0, n);
+         if(result.empty())
+            result = "0";
+         if(neg)
+            result.insert(0, 1, '-');
+         else if(f & std::ios_base::showpos)
+            result.insert(0, 1, '+');
+      }
+      return result;
+   }
+   std::string do_get_string(std::ios_base::fmtflags f, const mpl::true_&)const
+   {
+#ifdef BOOST_MP_NO_DOUBLE_LIMB_TYPE_IO
+      return do_get_trivial_string(f, mpl::bool_::value>());
+#else
+      return do_get_trivial_string(f, mpl::bool_());
+#endif
+   }
+   std::string do_get_string(std::ios_base::fmtflags f, const mpl::false_&)const
+   {
+      using default_ops::eval_get_sign;
       int base = 10;
       if((f & std::ios_base::oct) == std::ios_base::oct)
          base = 8;
@@ -1063,21 +1626,69 @@ public:
       }
       return result;
    }
-   template 
-   int compare(const cpp_int_backend& o)const BOOST_NOEXCEPT
+public:
+   std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const
+   {
+      return do_get_string(f, trivial_tag());
+   }
+   template 
+   typename enable_if_c<
+      !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value,
+      int
+   >::type compare(const cpp_int_backend& o)const BOOST_NOEXCEPT
    {
       if(this->sign() != o.sign())
          return this->sign() ? -1 : 1;
-      int result = 0;
+
       // Only do the compare if the same sign:
-      result = compare_unsigned(o);
+      int result = compare_unsigned(o);
 
       if(this->sign())
          result = -result;
       return result;
    }
-   template 
-   int compare_unsigned(const cpp_int_backend& o)const BOOST_NOEXCEPT
+   template 
+   typename enable_if_c<
+      is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value,
+      int
+   >::type compare(const cpp_int_backend& o)const
+   {
+      cpp_int_backend t(*this);
+      return t.compare(o);
+   }
+   template 
+   typename enable_if_c<
+      !is_trivial_cpp_int >::value && is_trivial_cpp_int >::value,
+      int
+   >::type compare(const cpp_int_backend& o)const
+   {
+      cpp_int_backend t(o);
+      return compare(t);
+   }
+   template 
+   typename enable_if_c<
+      is_trivial_cpp_int >::value && is_trivial_cpp_int >::value,
+      int
+   >::type compare(const cpp_int_backend& o)const BOOST_NOEXCEPT
+   {
+      if(this->sign())
+      {
+         if(o.sign())
+         {
+            return *this->limbs() < *o.limbs() ? 1 : (*this->limbs() > *o.limbs() ? -1 : 0);
+         }
+         else
+            return -1;
+      }
+      else
+      {
+         if(o.sign())
+            return 1;
+         return *this->limbs() < *o.limbs() ? -1 : (*this->limbs() > *o.limbs() ? 1 : 0);
+      }
+   }
+   template 
+   int compare_unsigned(const cpp_int_backend& o)const BOOST_NOEXCEPT
    {
       if(this->size() != o.size())
       {
@@ -1093,7 +1704,7 @@ public:
       return 0;
    }
    template 
-   BOOST_FORCEINLINE typename enable_if, int>::type compare(Arithmetic i)const BOOST_NOEXCEPT
+   BOOST_FORCEINLINE typename enable_if, int>::type compare(Arithmetic i)const
    {
       // braindead version:
       cpp_int_backend t;
@@ -1102,2363 +1713,72 @@ public:
    }
 };
 
-template 
-struct cpp_int_backend : public cpp_int_base
-{
-public:
-   typedef cpp_int_backend              self_type;
-   typedef cpp_int_base                 base_type;
-   typedef typename is_trivial_cpp_int::type              trivial_tag;
-   typedef mpl::list<
-      signed char, short, int, long, 
-      long long, signed_double_limb_type>                            signed_types;
-   typedef mpl::list                          unsigned_types;
-   typedef mpl::list                     float_types;
+} // namespace backends
 
-   BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(typename base_type::local_limb_type) * CHAR_BIT);
-
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{}
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT : base_type(o) {}
-   BOOST_FORCEINLINE cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_NOEXCEPT
-   {
-      this->assign(o);
-      return *this;
-   }
-
-   template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(A i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT
-      : base_type(i) {}
-
-   template 
-   BOOST_FORCEINLINE typename enable_if, cpp_int_backend&>::type operator = (SI i) BOOST_NOEXCEPT
-   {
-      *this->limbs() = static_cast(std::abs(i));
-      this->sign(i < 0);
-      return *this;
-   }
-   template 
-   BOOST_FORCEINLINE typename enable_if, cpp_int_backend&>::type operator = (UI i) BOOST_NOEXCEPT
-   {
-      *this->limbs() = static_cast(i);
-      return *this;
-   }
-   template 
-   BOOST_FORCEINLINE typename enable_if, cpp_int_backend&>::type operator = (F i) BOOST_NOEXCEPT
-   {
-      *this->limbs() = static_cast(std::abs(i));
-      this->sign(i < 0);
-      return *this;
-   }
-
-   template 
-   cpp_int_backend(const cpp_int_backend& other, 
-      typename enable_if_c<
-         (MinBits2 <= MinBits)
-         && (Signed || !Signed2)
-      >::type* = 0) BOOST_NOEXCEPT
-      : base_type()
-   {
-      *this->limbs() = static_cast::local_limb_type>(*other.limbs());
-      this->sign(other.sign());
-   }
-   template 
-   explicit cpp_int_backend(const cpp_int_backend& other, 
-      typename disable_if_c<
-         (MinBits2 <= MinBits)
-         && (Signed || !Signed2)
-      >::type* = 0) BOOST_NOEXCEPT
-      : base_type()
-   {
-      *this->limbs() = static_cast::local_limb_type>(*other.limbs());
-      this->sign(other.sign());
-   }
-   template 
-   cpp_int_backend& operator = (const cpp_int_backend& other)BOOST_NOEXCEPT
-   {
-      *this->limbs() = static_cast::local_limb_type>(*other.limbs());
-      this->sign(other.sign());
-      return *this;
-   }
-   template 
-   explicit cpp_int_backend(const cpp_int_backend& other)BOOST_NOEXCEPT
-      : base_type()
-   {
-      // We can only ever copy two limbs from other:
-      if(other.size() == 1)
-      {
-         *this->limbs() = *other.limbs();
-      }
-      else
-      {
-         *this->limbs() = static_cast(*other.limbs()) | (static_cast(other.limbs()[1]) << (sizeof(limb_type) * CHAR_BIT));
-      }
-      this->sign(other.sign());
-   }
-   template 
-   cpp_int_backend& operator=(const cpp_int_backend& other)BOOST_NOEXCEPT 
-   {
-      // We can only ever copy two limbs from other:
-      if(other.size() == 1)
-      {
-         *this->limbs() = *other.limbs();
-      }
-      else
-      {
-         *this->limbs() = static_cast(*other.limbs()) | (static_cast(other.limbs()[1]) << (sizeof(limb_type) * CHAR_BIT));
-      }
-      this->sign(other.sign());
-      return *this;
-   }
-
-   BOOST_FORCEINLINE void swap(cpp_int_backend& o) BOOST_NOEXCEPT
-   {
-      this->do_swap(o);
-   }
-private:
-   std::string str(std::ios_base::fmtflags f, const mpl::false_&)const
-   {
-      std::stringstream ss;
-      ss.flags(f & ~std::ios_base::showpos);
-      ss << *this->limbs();
-      std::string result;
-      if(this->sign())
-         result += '-';
-      else if(f & std::ios_base::showpos)
-         result += '+';
-      result += ss.str();
-      return result;
-   }
-   std::string str(std::ios_base::fmtflags f, const mpl::true_&)const
-   {
-      // Even though we have only one limb, we can't do IO on it :-(
-      int base = 10;
-      if((f & std::ios_base::oct) == std::ios_base::oct)
-         base = 8;
-      else if((f & std::ios_base::hex) == std::ios_base::hex)
-         base = 16;
-      std::string result;
-
-      unsigned Bits = base_type::limb_bits;
-
-      if(base == 8 || base == 16)
-      {
-         if(this->sign())
-            BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported."));
-         limb_type shift = base == 8 ? 3 : 4;
-         limb_type mask = static_cast((1u << shift) - 1);
-         typename base_type::local_limb_type v = *this->limbs();
-         result.assign(Bits / shift + (Bits % shift ? 1 : 0), '0');
-         int pos = result.size() - 1;
-         for(unsigned i = 0; i < Bits / shift; ++i)
-         {
-            char c = '0' + static_cast(v & mask);
-            if(c > '9')
-               c += 'A' - '9' - 1;
-            result[pos--] = c;
-            v >>= shift;
-         }
-         if(Bits % shift)
-         {
-            mask = static_cast((1u << (Bits % shift)) - 1);
-            char c = '0' + static_cast(v & mask);
-            if(c > '9')
-               c += 'A' - '9';
-            result[pos] = c;
-         }
-         //
-         // Get rid of leading zeros:
-         //
-         std::string::size_type n = result.find_first_not_of('0');
-         if(!result.empty() && (n == std::string::npos))
-            n = result.size() - 1;
-         result.erase(0, n);
-         if(f & std::ios_base::showbase)
-         {
-            const char* pp = base == 8 ? "0" : "0x";
-            result.insert(0, pp);
-         }
-      }
-      else
-      {
-         result.assign(Bits / 3 + 1, '0');
-         int pos = result.size() - 1;
-         typename base_type::local_limb_type v(*this->limbs());
-         bool neg = false;
-         if(this->sign())
-         {
-            neg = true;
-         }
-         while(v)
-         {
-            result[pos] = (v % 10) + '0';
-            --pos;
-            v /= 10;
-         }
-         unsigned n = result.find_first_not_of('0');
-         result.erase(0, n);
-         if(result.empty())
-            result = "0";
-         if(neg)
-            result.insert(0, 1, '-');
-         else if(f & std::ios_base::showpos)
-            result.insert(0, 1, '+');
-      }
-      return result;
-   }
-public:
-   cpp_int_backend& operator = (const char* s)
-   {
-      std::size_t n = s ? std::strlen(s) : 0;
-      *this->limbs() = 0;
-      unsigned radix = 10;
-      bool isneg = false;
-      if(n && (*s == '-'))
-      {
-         --n;
-         ++s;
-         isneg = true;
-      }
-      if(n && (*s == '0'))
-      {
-         if((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
-         {
-            radix = 16;
-            s +=2;
-            n -= 2;
-         }
-         else
-         {
-            radix = 8;
-            n -= 1;
-         }
-      }
-      if(n)
-      {
-         unsigned val;
-         while(*s)
-         {
-            if(*s >= '0' && *s <= '9')
-               val = *s - '0';
-            else if(*s >= 'a' && *s <= 'f')
-               val = 10 + *s - 'a';
-            else if(*s >= 'A' && *s <= 'F')
-               val = 10 + *s - 'A';
-            else
-               val = radix + 1;
-            if(val > radix)
-            {
-               BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
-            }
-            *this->limbs() *= radix;
-            *this->limbs() += val;
-            ++s;
-         }
-      }
-      if(isneg)
-         this->negate();
-      return *this;
-   }
-   std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const
-   {
-#ifdef BOOST_MP_NO_DOUBLE_LIMB_TYPE_IO
-      return str(f, mpl::bool_::value>());
-#else
-      return str(f, mpl::bool_());
-#endif
-   }
-   int compare(const cpp_int_backend& o)const BOOST_NOEXCEPT
-   {
-      if(this->sign() != o.sign())
-         return this->sign() ? -1 : 1;
-      int result = 0;
-      // Only do the compare if the same sign:
-      result = *this->limbs() == *o.limbs() ? 0 : *this->limbs() < *o.limbs() ? -1 : 1;
-
-      if(this->sign())
-         result = -result;
-      return result;
-   }
-   template 
-   BOOST_FORCEINLINE typename enable_if, int>::type compare(Arithmetic i)const BOOST_NOEXCEPT
-   {
-      // braindead version:
-      cpp_int_backend t;
-      t = i;
-      return compare(t);
-   }
-};
-
-template 
-BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
-{
-   return (a.sign() == b.sign())
-      && (a.size() == b.size())
-      && std::equal(a.limbs(), a.limbs() + a.size(), b.limbs());
-}
-template 
-BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
-{
-   return (a.sign() == b.sign())
-      && (a.size() == b.size())
-      && std::equal(a.limbs(), a.limbs() + a.size(), b.limbs());
-}
-template 
-BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
-{
-   return (a.sign() == false)
-      && (a.size() == 1)
-      && (*a.limbs() == b);
-}
-template 
-BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
-{
-   return (a.sign() == (b < 0))
-      && (a.size() == 1)
-      && (*a.limbs() == static_cast(std::abs(b)));
-}
-template 
-BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
-{
-   return (a.size() == 1)
-      && (*a.limbs() == b);
-}
-template 
-BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
-{
-   return (b < 0) ? eval_eq(a, cpp_int_backend(b)) : eval_eq(a, static_cast(b)); // Use bit pattern of b for comparison
-}
-
-template 
-BOOST_FORCEINLINE bool eval_lt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
-{
-   if(a.sign())
-      return true;
-   if(a.size() > 1)
-      return false;
-   return *a.limbs() < b;
-}
-template 
-inline bool eval_lt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
-{
-   if((b == 0) || (a.sign() != (b < 0)))
-      return a.sign();
-   if(a.sign())
-   {
-      if(a.size() > 1)
-         return true;
-      return *a.limbs() > static_cast(std::abs(b));
-   }
-   else
-   {
-      if(a.size() > 1)
-         return false;
-      return *a.limbs() < static_cast(b);
-   }
-}
-
-template 
-BOOST_FORCEINLINE bool eval_lt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
-{
-   if(a.size() > 1)
-      return false;
-   return *a.limbs() < b;
-}
-template 
-BOOST_FORCEINLINE bool eval_lt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
-{
-   return (b < 0) ? a.compare(b) < 0 : eval_lt(a, static_cast(b)); // Use bit pattern of b for comparison
-}
-
-template 
-BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
-{
-   if(a.sign())
-      return false;
-   if(a.size() > 1)
-      return true;
-   return *a.limbs() > b;
-}
-template 
-inline bool eval_gt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
-{
-   if(b == 0)
-      return !a.sign() && ((a.size() > 1) || *a.limbs());
-   if(a.sign() != (b < 0))
-      return !a.sign();
-   if(a.sign())
-   {
-      if(a.size() > 1)
-         return false;
-      return *a.limbs() < static_cast(std::abs(b));
-   }
-   else
-   {
-      if(a.size() > 1)
-         return true;
-      return *a.limbs() > static_cast(b);
-   }
-}
-
-template 
-BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
-{
-   if(a.size() > 1)
-      return true;
-   return *a.limbs() > b;
-}
-template 
-BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
-{
-   return (b < 0) ? a.compare(b) > 0 : eval_gt(a, static_cast(b)); // Use bit pattern of b for comparison.
-}
-
-template 
-BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   eval_add(result, result, o);
-}
-template 
-inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   using std::swap;
-
-   // Nothing fancy, just let uintmax_t take the strain:
-   double_limb_type carry = 0;
-   unsigned m, x;
-   unsigned as = a.size();
-   unsigned bs = b.size();
-   minmax(as, bs, m, x);
-   if(x == 1)
-   {
-      bool s = a.sign();
-      result = static_cast(*a.limbs()) + static_cast(*b.limbs());
-      result.sign(s);
-      return;
-   }
-   result.resize(x);
-   typename cpp_int_backend::const_limb_pointer pa = a.limbs();
-   typename cpp_int_backend::const_limb_pointer pb = b.limbs();
-   typename cpp_int_backend::limb_pointer pr = result.limbs();
-   typename cpp_int_backend::limb_pointer pr_end = pr + m;
-
-   if(as < bs)
-      swap(pa, pb);
-   
-   // First where a and b overlap:
-   while(pr != pr_end)
-   {
-      carry += static_cast(*pa) + static_cast(*pb);
-      *pr = static_cast(carry);
-      carry >>= cpp_int_backend::limb_bits;
-      ++pr, ++pa, ++pb;
-   }
-   pr_end += x - m;
-   // Now where only a has digits:
-   while(pr != pr_end)
-   {
-      if(!carry)
-      {
-         if(pa != pr)
-            std::copy(pa, pa + (pr_end - pr), pr);
-         break;
-      }
-      carry += static_cast(*pa);
-      *pr = static_cast(carry);
-      carry >>= cpp_int_backend::limb_bits;
-      ++pr, ++pa;
-   }
-   if(carry)
-   {
-      result.resize(x + 1);
-      // We overflowed, need to add one more limb:
-      if(cpp_int_backend::variable || (result.size() > x))
-         result.limbs()[x] = static_cast(carry);
-   }
-   result.normalize();
-   result.sign(a.sign());
-}
-template 
-inline void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(a.sign() != b.sign())
-   {
-      subtract_unsigned(result, a, b);
-      return;
-   }
-   add_unsigned(result, a, b);
-}
-
-template 
-inline void add_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   // Addition using modular arithmatic.
-   // Nothing fancy, just let uintmax_t take the strain:
-   if(&result != &a)
-      result.resize(a.size());
-   double_limb_type carry = o;
-   typename cpp_int_backend::limb_pointer pr = result.limbs();
-   typename cpp_int_backend::const_limb_pointer pa = a.limbs();
-   unsigned i = 0;
-   for(; carry && (i < result.size()); ++i)
-   {
-      carry += static_cast(pa[i]);
-      pr[i] = static_cast(carry);
-      carry >>= cpp_int_backend::limb_bits;
-   }
-   if(&a != &result)
-   {
-      for(; i < result.size(); ++i)
-         pr[i] = pa[i];
-   }
-   if(carry)
-   {
-      unsigned x = result.size();
-      result.resize(x + 1);
-      // We overflowed, need to add one more limb:
-      if(cpp_int_backend::variable || (result.size() > x))
-         result.limbs()[x] = static_cast(carry);
-   }
-   result.normalize();
-   result.sign(a.sign());
-}
-template 
-BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(result.sign())
-   {
-      subtract_unsigned(result, o);
-   }
-   else
-      add_unsigned(result, result, o);
-}
-template 
-BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(a.sign())
-   {
-      result = a;
-      subtract_unsigned(result, o);
-   }
-   else
-      add_unsigned(result, a, o);
-}
-template 
-BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(o < 0)
-      eval_subtract(result, static_cast(-o));
-   else if(o > 0)
-      eval_add(result, static_cast(o));
-}
-template 
-BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(o < 0)
-      eval_subtract(result, a, static_cast(-o));
-   else if(o > 0)
-      eval_add(result, a, static_cast(o));
-   else if(&result != &a)
-      result = a;
-}
-
-template 
-inline void subtract_unsigned(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   // Subtract one limb.
-   // Nothing fancy, just let uintmax_t take the strain:
-   BOOST_STATIC_CONSTANT(double_limb_type, borrow = static_cast(cpp_int_backend::max_limb_value) + 1);
-   typename cpp_int_backend::limb_pointer p = result.limbs();
-   if(*p > o)
-   {
-      *p -= o;
-   }
-   else if(result.size() == 1)
-   {
-      *p = o - *p;
-      result.negate();
-   }
-   else
-   {
-      *p = static_cast((borrow + *p) - o);
-      ++p;
-      while(!*p)
-      {
-         *p = cpp_int_backend::max_limb_value;
-         ++p;
-      }
-      --*p;
-      result.normalize();
-   }
-}
-template 
-BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(result.sign())
-   {
-      add_unsigned(result, result, o);
-   }
-   else
-      subtract_unsigned(result, o);
-}
-template 
-BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(a.sign())
-   {
-      add_unsigned(result, a, o);
-   }
-   else
-   {
-      result = a;
-      subtract_unsigned(result, o);
-   }
-}
-template 
-BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(o)
-   {
-      if(o < 0)
-         eval_add(result, static_cast(-o));
-      else
-         eval_subtract(result, static_cast(o));
-   }
-}
-template 
-BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(o)
-   {
-      if(o < 0)
-         eval_add(result, a, static_cast(-o));
-      else
-         eval_subtract(result, a, static_cast(o));
-   }
-   else if(&result != &a)
-      result = a;
-}
-template 
-BOOST_FORCEINLINE void eval_increment(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   static const limb_type one = 1;
-   if(!result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value))
-      ++result.limbs()[0];
-   else if(result.sign() && result.limbs()[0])
-      --result.limbs()[0];
-   else
-      eval_add(result, one);
-}
-template 
-BOOST_FORCEINLINE void eval_decrement(cpp_int_backend& result) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   static const limb_type one = 1;
-   if(!result.sign() && result.limbs()[0])
-      --result.limbs()[0];
-   else if(result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value))
-      ++result.limbs()[0];
-   else
-      eval_subtract(result, one);
-}
-template 
-BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   eval_subtract(result, result, o);
-}
-template 
-inline void subtract_unsigned(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   using std::swap;
-
-   // Nothing fancy, just let uintmax_t take the strain:
-   double_limb_type borrow = 0;
-   unsigned m, x;
-   minmax(a.size(), b.size(), m, x);
-   //
-   // special cases for small limb counts:
-   //
-   if(x == 1)
-   {
-      bool s = a.sign();
-      limb_type al = *a.limbs();
-      limb_type bl = *b.limbs();
-      if(bl > al)
-      {
-         std::swap(al, bl);
-         s = !s;
-      }
-      result = al - bl;
-      result.sign(s);
-      return;
-   }
-   // This isn't used till later, but comparison has to occur before we resize the result,
-   // as that may also resize a or b if this is an inplace operation:
-   int c = a.compare_unsigned(b);
-   // Set up the result vector:
-   result.resize(x);
-   // Now that a, b, and result are stable, get pointers to their limbs:
-   typename cpp_int_backend::const_limb_pointer pa = a.limbs();
-   typename cpp_int_backend::const_limb_pointer pb = b.limbs();
-   typename cpp_int_backend::limb_pointer pr = result.limbs();
-   bool swapped = false;
-   if(c < 0)
-   {
-      swap(pa, pb);
-      swapped = true;
-   }
-   else if(c == 0)
-   {
-      result = static_cast(0);
-      return;
-   }
-   
-   unsigned i = 0;
-   // First where a and b overlap:
-   while(i < m)
-   {
-      borrow = static_cast(pa[i]) - static_cast(pb[i]) - borrow;
-      pr[i] = static_cast(borrow);
-      borrow = (borrow >> cpp_int_backend::limb_bits) & 1u;
-      ++i;
-   }
-   // Now where only a has digits, only as long as we've borrowed:
-   while(borrow && (i < x))
-   {
-      borrow = static_cast(pa[i]) - borrow;
-      pr[i] = static_cast(borrow);
-      borrow = (borrow >> cpp_int_backend::limb_bits) & 1u;
-      ++i;
-   }
-   // Any remaining digits are the same as those in pa:
-   if((x != i) && (pa != pr))
-      std::copy(pa + i, pa + x, pr + i);
-   BOOST_ASSERT(0 == borrow);
-
-   //
-   // We may have lost digits, if so update limb usage count:
-   //
-   result.normalize();
-   result.sign(a.sign());
-   if(swapped)
-      result.negate();
-}
-template 
-BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(a.sign() != b.sign())
-   {
-      add_unsigned(result, a, b);
-      return;
-   }
-   subtract_unsigned(result, a, b);
-}
-template 
-inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   // Very simple long multiplication, only usable for small numbers of limb_type's
-   // but that's the typical use case for this type anyway:
-   //
-   // Special cases first:
-   //
-   unsigned as = a.size();
-   unsigned bs = b.size();
-   typename cpp_int_backend::const_limb_pointer pa = a.limbs();
-   typename cpp_int_backend::const_limb_pointer pb = b.limbs();
-   if(as == 1)
-   {
-      bool s = b.sign() != a.sign();
-      if(bs == 1)
-      {
-         result = static_cast(*pa) * static_cast(*pb);
-      }
-      else
-      {
-         limb_type l = *pa;
-         eval_multiply(result, b, l);
-      }
-      result.sign(s);
-      return;
-   }
-   if(bs == 1)
-   {
-      bool s = b.sign() != a.sign();
-      limb_type l = *pb;
-      eval_multiply(result, a, l);
-      result.sign(s);
-      return;
-   }
-
-   if((void*)&result == (void*)&a)
-   {
-      cpp_int_backend t(a);
-      eval_multiply(result, t, b);
-      return;
-   }
-   if((void*)&result == (void*)&b)
-   {
-      cpp_int_backend t(b);
-      eval_multiply(result, a, t);
-      return;
-   }
-
-   result.resize(as + bs);
-   typename cpp_int_backend::limb_pointer pr = result.limbs();
-
-   static const double_limb_type limb_max = ~static_cast(0u);
-   static const double_limb_type double_limb_max = ~static_cast(0u);
-   BOOST_STATIC_ASSERT(double_limb_max - 2 * limb_max >= limb_max * limb_max);
-
-   double_limb_type carry = 0;
-   std::memset(pr, 0, result.size() * sizeof(limb_type));
-   for(unsigned i = 0; i < as; ++i)
-   {
-      unsigned inner_limit = cpp_int_backend::variable ? bs : (std::min)(result.size() - i, bs);
-      for(unsigned j = 0; j < inner_limit; ++j)
-      {
-         BOOST_ASSERT(i+j < result.size());
-         BOOST_ASSERT(!std::numeric_limits::is_specialized 
-            || ((std::numeric_limits::max)() - carry 
-                  > 
-                static_cast(cpp_int_backend::max_limb_value) * static_cast(cpp_int_backend::max_limb_value)));
-         carry += static_cast(pa[i]) * static_cast(pb[j]);
-         BOOST_ASSERT(!std::numeric_limits::is_specialized || ((std::numeric_limits::max)() - carry >= pr[i+j]));
-         carry += pr[i + j];
-         pr[i + j] = static_cast(carry);
-         carry >>= cpp_int_backend::limb_bits;
-         BOOST_ASSERT(carry <= (cpp_int_backend::max_limb_value));
-      }
-      if(cpp_int_backend::variable || (i + bs < result.size()))
-         pr[i + bs] = static_cast(carry);
-      carry = 0;
-   }
-   result.normalize();
-   //
-   // Set the sign of the result:
-   //
-   result.sign(a.sign() != b.sign());
-}
-template 
-BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-    eval_multiply(result, result, a);
-}
-template 
-inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(!val)
-   {
-      result = static_cast(0);
-      return;
-   }
-   if((void*)&a != (void*)&result)
-      result.resize(a.size());
-   double_limb_type carry = 0;
-   typename cpp_int_backend::limb_pointer p = result.limbs();
-   typename cpp_int_backend::limb_pointer pe = result.limbs() + result.size();
-   typename cpp_int_backend::const_limb_pointer pa = a.limbs();
-   while(p != pe)
-   {
-      carry += static_cast(*pa) * static_cast(val);
-      *p = static_cast(carry);
-      carry >>= cpp_int_backend::limb_bits;
-      ++p, ++pa;
-   }
-   if(carry)
-   {
-      unsigned i = result.size();
-      result.resize(i + 1);
-      if(cpp_int_backend::variable || (result.size() > i))
-         result.limbs()[i] = static_cast(carry);
-   }
-   result.sign(a.sign());
-   if(!cpp_int_backend::variable)
-      result.normalize();
-}
-template 
-BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   eval_multiply(result, result, val);
-}
-template 
-BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(val <= (std::numeric_limits::max)())
-   {
-      eval_multiply(result, a, static_cast(val));
-   }
-   else
-   {
-      cpp_int_backend t(val);
-      eval_multiply(result, a, t);
-   }
-}
-template 
-BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   eval_multiply(result, result, val);
-}
-template 
-BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(val > 0)
-      eval_multiply(result, a, static_cast(val));
-   else
-   {
-      eval_multiply(result, a, static_cast(-val));
-      result.negate();
-   }
-}
-template 
-BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const signed_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   eval_multiply(result, result, val);
-}
-template 
-inline void eval_multiply(cpp_int_backend& result, const cpp_int_backend& a, const signed_double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(val > 0)
-   {
-      if(val <= (std::numeric_limits::max)())
-      {
-         eval_multiply(result, a, static_cast(val));
-         return;
-      }
-   }
-   else if(val >= -static_cast((std::numeric_limits::max)()))
-   {
-      eval_multiply(result, a, static_cast(-val));
-      result.negate();
-      return;
-   }
-   cpp_int_backend t(val);
-   eval_multiply(result, a, t);
-}
-template 
-BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const signed_double_limb_type& val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   eval_multiply(result, result, val);
-}
-
-template 
-void divide_unsigned_helper(cpp_int_backend* result, 
-   const cpp_int_backend& x, 
-   const cpp_int_backend& y, 
-   cpp_int_backend& r)
-{
-   if(((void*)result == (void*)&x) || ((void*)&r == (void*)&x))
-   {
-      cpp_int_backend t(x);
-      divide_unsigned_helper(result, t, y, r);
-      return;
-   }
-   if(((void*)result == (void*)&y) || ((void*)&r == (void*)&y))
-   {
-      cpp_int_backend t(y);
-      divide_unsigned_helper(result, x, t, r);
-      return;
-   }
-
-   /*
-    Very simple, fairly braindead long division.
-    Start by setting the remainder equal to x, and the
-    result equal to 0.  Then in each loop we calculate our
-    "best guess" for how many times y divides into r,
-    add our guess to the result, and subtract guess*y
-    from the remainder r.  One wrinkle is that the remainder
-    may go negative, in which case we subtract the current guess
-    from the result rather than adding.  The value of the guess
-    is determined by dividing the most-significant-limb of the
-    current remainder by the most-significant-limb of y.
-
-    Note that there are more efficient algorithms than this
-    available, in particular see Knuth Vol 2.  However for small
-    numbers of limbs this generally outperforms the alternatives
-    and avoids the normalisation step which would require extra storage.
-    */
-
-
-   using default_ops::eval_subtract;
-
-   if(result == &r)
-   {
-      cpp_int_backend rem;
-      divide_unsigned_helper(result, x, y, rem);
-      r = rem;
-      return;
-   }
-
-   //
-   // Find the most significant words of numerator and denominator.
-   //
-   limb_type y_order = y.size() - 1;
-
-   if(y_order == 0)
-   {
-      //
-      // Only a single non-zero limb in the denominator, in this case
-      // we can use a specialized divide-by-single-limb routine which is
-      // much faster.  This also handles division by zero:
-      //
-      divide_unsigned_helper(result, x, y.limbs()[y_order], r);
-      return;
-   }
-
-   typename cpp_int_backend::const_limb_pointer px = x.limbs();
-   typename cpp_int_backend::const_limb_pointer py = y.limbs();
-
-   limb_type r_order = x.size() - 1;
-   if((r_order == 0) && (*px == 0))
-   {
-      // x is zero, so is the result:
-      r = y;
-      if(result)
-         *result = x;
-      return;
-   }
-
-   r = x;
-   r.sign(false);
-   if(result)
-      *result = static_cast(0u);
-   //
-   // Check if the remainder is already less than the divisor, if so
-   // we already have the result.  Note we try and avoid a full compare
-   // if we can:
-   //
-   if(r_order <= y_order)
-   {
-      if((r_order < y_order) || (r.compare_unsigned(y) < 0))
-      {
-         return;
-      }
-   }
-
-   cpp_int_backend t;
-   bool r_neg = false;
-
-   //
-   // See if we can short-circuit long division, and use basic arithmetic instead:
-   //
-   if(r_order == 0)
-   {
-      if(result)
-         *result = px[0] / py[0];
-      r = px[0] % py[0];
-      return;
-   }
-   else if(r_order == 1)
-   {
-      double_limb_type a, b;
-      a = (static_cast(px[1]) << cpp_int_backend::limb_bits) | px[0];
-      b = y_order ? 
-         (static_cast(py[1]) << cpp_int_backend::limb_bits) | py[0] 
-         : py[0];
-      if(result)
-         *result = a / b;
-      r = a % b;
-      return;
-   }
-   //
-   // prepare result:
-   //
-   if(result)
-      result->resize(1 + r_order - y_order);
-   typename cpp_int_backend::const_limb_pointer prem = r.limbs();
-   // This is initialised just to keep the compiler from emitting useless warnings later on:
-   typename cpp_int_backend::limb_pointer pr 
-      = typename cpp_int_backend::limb_pointer();
-   if(result)
-   {
-      pr = result->limbs();
-      for(unsigned i = 1; i < 1 + r_order - y_order; ++i)
-         pr[i] = 0;
-   }
-   bool first_pass = true;
-
-   do
-   {
-      //
-      // Calculate our best guess for how many times y divides into r:
-      //
-      limb_type guess;
-      if((prem[r_order] <= py[y_order]) && (r_order > 0))
-      {
-         double_limb_type a, b, v;
-         a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1];
-         b = py[y_order];
-         v = a / b;
-         if(v > cpp_int_backend::max_limb_value)
-            guess = 1;
-         else
-         {
-            guess = static_cast(v);
-            --r_order;
-         }
-      }
-      else if(r_order == 0)
-      {
-         guess = prem[0] / py[y_order];
-      }
-      else
-      {
-         double_limb_type a, b, v;
-         a = (static_cast(prem[r_order]) << cpp_int_backend::limb_bits) | prem[r_order - 1];
-         b = (y_order > 0) ? (static_cast(py[y_order]) << cpp_int_backend::limb_bits) | py[y_order - 1] : (static_cast(py[y_order])  << cpp_int_backend::limb_bits);
-         v = a / b;
-         guess = static_cast(v);
-      }
-      BOOST_ASSERT(guess); // If the guess ever gets to zero we go on forever....
-      //
-      // Update result:
-      //
-      limb_type shift = r_order - y_order;
-      if(result)
-      {
-         if(r_neg)
-         {
-            if(pr[shift] > guess)
-               pr[shift] -= guess;
-            else
-            {
-               t.resize(shift + 1);
-               t.limbs()[shift] = guess;
-               for(unsigned i = 0; i < shift; ++i)
-                  t.limbs()[i] = 0;
-               eval_subtract(*result, t);
-            }
-         }
-         else if(cpp_int_backend::max_limb_value - pr[shift] > guess)
-            pr[shift] += guess;
-         else
-         {
-            t.resize(shift + 1);
-            t.limbs()[shift] = guess;
-            for(unsigned i = 0; i < shift; ++i)
-               t.limbs()[i] = 0;
-            eval_add(*result, t);
-         }
-      }
-      //
-      // Calculate guess * y, we use a fused mutiply-shift O(N) for this
-      // rather than a full O(N^2) multiply:
-      //
-      double_limb_type carry = 0;
-      t.resize(y.size() + shift + 1);
-      bool truncated_t = !cpp_int_backend::variable && (t.size() != y.size() + shift + 1);
-      typename cpp_int_backend::limb_pointer pt = t.limbs();
-      for(unsigned i = 0; i < shift; ++i)
-         pt[i] = 0;
-      for(unsigned i = 0; i < y.size(); ++i)
-      {
-         carry += static_cast(py[i]) * static_cast(guess);
-         pt[i + shift] = static_cast(carry);
-         carry >>= cpp_int_backend::limb_bits;
-      }
-      if(carry && !truncated_t)
-      {
-         pt[t.size() - 1] = static_cast(carry);
-      }
-      else if(!truncated_t)
-      {
-         t.resize(t.size() - 1);
-      }
-      //
-      // Update r:
-      //
-      eval_subtract(r, t);
-      if(r.isneg())
-      {
-         r.negate();
-         r_neg = !r_neg;
-      }
-      //
-      // First time through we need to strip any leading zero, otherwise
-      // the termination condition goes belly-up:
-      //
-      if(result && first_pass)
-      {
-         first_pass = false;
-         while(pr[result->size() - 1] == 0)
-            result->resize(result->size() - 1);
-      }
-      //
-      // Update r_order:
-      //
-      r_order = r.size() - 1;
-      if(r_order < y_order)
-         break;
-   }
-   // Termination condition is really just a check that r > y, but with a common
-   // short-circuit case handled first:
-   while((r_order > y_order) || (r.compare_unsigned(y) >= 0));
-
-   //
-   // We now just have to normalise the result:
-   //
-   if(r_neg && eval_get_sign(r))
-   {
-      // We have one too many in the result:
-      if(result)
-         eval_decrement(*result);
-      r.negate();
-      if(y.sign())
-         eval_subtract(r, y);
-      else
-         eval_add(r, y);
-   }
-
-   BOOST_ASSERT(r.compare_unsigned(y) < 0); // remainder must be less than the divisor or our code has failed
-}
-
-template 
-void divide_unsigned_helper(
-   cpp_int_backend* result, 
-   const cpp_int_backend& x, 
-   limb_type y, 
-   cpp_int_backend& r)
-{
-   if(((void*)result == (void*)&x) || ((void*)&r == (void*)&x))
-   {
-      cpp_int_backend t(x);
-      divide_unsigned_helper(result, t, y, r);
-      return;
-   }
-
-   if(result == &r)
-   {
-      cpp_int_backend rem;
-      divide_unsigned_helper(result, x, y, rem);
-      r = rem;
-      return;
-   }
-
-   // As above, but simplified for integer divisor:
-
-   using default_ops::eval_subtract;
-
-   if(y == 0)
-   {
-      BOOST_THROW_EXCEPTION(std::overflow_error("Integer Division by zero."));
-   }
-   //
-   // Find the most significant word of numerator.
-   //
-   limb_type r_order = x.size() - 1;
-
-   //
-   // Set remainder and result to their initial values:
-   //
-   r = x;
-   r.sign(false);
-   typename cpp_int_backend::limb_pointer pr = r.limbs();
-
-   if((r_order == 0) && (*pr == 0))
-   {
-      // All the limbs in x are zero, so is the result:
-      return;
-   }
-   //
-   // check for x < y, try to do this without actually having to 
-   // do a full comparison:
-   //
-   if((r_order == 0) && (*pr < y))
-   {
-      if(result)
-         *result = static_cast(0u);
-      return;
-   }
-
-   //
-   // See if we can short-circuit long division, and use basic arithmetic instead:
-   //
-   if(r_order == 0)
-   {
-      if(result)
-      {
-         *result = *pr / y;
-         result->sign(x.sign());
-      }
-      *pr %= y;
-      r.sign(x.sign());
-      return;
-   }
-   else if(r_order == 1)
-   {
-      double_limb_type a;
-      a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[0];
-      if(result)
-      {
-         *result = a / y;
-         result->sign(x.sign());
-      }
-      r = a % y;
-      r.sign(x.sign());
-      return;
-   }
-
-   // This is initialised just to keep the compiler from emitting useless warnings later on:
-   typename cpp_int_backend::limb_pointer pres = typename cpp_int_backend::limb_pointer();
-   if(result)
-   {
-      result->resize(r_order + 1);
-      pres = result->limbs();
-      if(result->size() > r_order)
-         pres[r_order] = 0;  // just in case we don't set the most significant limb below.
-   }
-
-   do
-   {
-      //
-      // Calculate our best guess for how many times y divides into r:
-      //
-      if((pr[r_order] < y) && r_order)
-      {
-         double_limb_type a, b;
-         a = (static_cast(pr[r_order]) << cpp_int_backend::limb_bits) | pr[r_order - 1];
-         b = a % y;
-         r.resize(r.size() - 1);
-         --r_order;
-         pr[r_order] = static_cast(b);
-         if(result)
-            pres[r_order] = static_cast(a / y);
-         if(r_order && pr[r_order] == 0)
-         {
-            --r_order;  // No remainder, division was exact.
-            r.resize(r.size() - 1);
-            if(result)
-               pres[r_order] = static_cast(0u);
-         }
-      }
-      else
-      {
-         if(result)
-            pres[r_order] = pr[r_order] / y;
-         pr[r_order] %= y;
-         if(r_order && pr[r_order] == 0)
-         {
-            --r_order;  // No remainder, division was exact.
-            r.resize(r.size() - 1);
-            if(result)
-               pres[r_order] = static_cast(0u);
-         }
-      }
-   }
-   // Termination condition is really just a check that r > y, but with two common
-   // short-circuit cases handled first:
-   while(r_order || (pr[r_order] > y));
-
-   if(result)
-   {
-      result->normalize();
-      result->sign(x.sign());
-   }
-   r.normalize();
-   r.sign(x.sign());
-
-   BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed
-}
-
-template 
-BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, 
-   const cpp_int_backend& a, const cpp_int_backend& b)
-{
-   cpp_int_backend r;
-   divide_unsigned_helper(&result, a, b, r);
-   result.sign(a.sign() != b.sign());
-}
-template 
-BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, 
-   const cpp_int_backend& a, limb_type& b)
-{
-   cpp_int_backend r;
-   divide_unsigned_helper(&result, a, b, r);
-}
-template 
-BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, 
-   const cpp_int_backend& a, signed_limb_type& b)
-{
-   cpp_int_backend r;
-   divide_unsigned_helper(&result, a, std::abs(b), r);
-   if(b < 0)
-      result.negate();
-}
-template 
-BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, 
-   const cpp_int_backend& b)
-{
-   // There is no in place divide:
-   cpp_int_backend a(result);
-   eval_divide(result, a, b);
-}
-template 
-BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, limb_type b)
-{
-   // There is no in place divide:
-   cpp_int_backend a(result);
-   eval_divide(result, a, b);
-}
-template 
-BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, signed_limb_type b)
-{
-   // There is no in place divide:
-   cpp_int_backend a(result);
-   eval_divide(result, a, b);
-}
-template 
-BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, 
-   const cpp_int_backend& a, 
-   const cpp_int_backend& b)
-{
-   divide_unsigned_helper(static_cast* >(0), a, b, result);
-   result.sign(a.sign());
-}
-template 
-BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, 
-   const cpp_int_backend& a, limb_type b)
-{
-   divide_unsigned_helper(static_cast* >(0), a, b, result);
-}
-template 
-BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, 
-   const cpp_int_backend& a, signed_limb_type b)
-{
-   divide_unsigned_helper(static_cast* >(0), a, static_cast(std::abs(b)), result);
-}
-template 
-BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, 
-   const cpp_int_backend& b)
-{
-   // There is no in place divide:
-   cpp_int_backend a(result);
-   eval_modulus(result, a, b);
-}
-template 
-BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, limb_type b)
-{
-   // There is no in place divide:
-   cpp_int_backend a(result);
-   eval_modulus(result, a, b);
-}
-template 
-BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, signed_limb_type b)
-{
-   // There is no in place divide:
-   cpp_int_backend a(result);
-   eval_modulus(result, a, b);
-}
-template 
-void bitwise_op(
-   cpp_int_backend& result, 
-   const cpp_int_backend& o, 
-   Op op) BOOST_NOEXCEPT
-{
-   //
-   // There are 4 cases:
-   // * Both positive.
-   // * result negative, o positive.
-   // * o negative, result positive.
-   // * Both negative.
-   //
-   // When one arg is negative we convert to 2's complement form "on the fly",
-   // and then convert back to signed-magnitude form at the end.
-   //
-   // First figure out how big the result needs to be and set up some data:
-   //
-   unsigned rs = result.size();
-   unsigned os = o.size();
-   unsigned m, x;
-   minmax(rs, os, m, x);
-   result.resize(x);
-   typename cpp_int_backend::limb_pointer pr = result.limbs();
-   typename cpp_int_backend::const_limb_pointer po = o.limbs();
-   for(unsigned i = rs; i < x; ++i)
-      pr[i] = 0;
-
-   limb_type next_limb = 0;
-
-   if(!result.sign())
-   {
-      if(!o.sign())
-      {
-         for(unsigned i = 0; i < os; ++i)
-            pr[i] = op(pr[i], po[i]);
-         for(unsigned i = os; i < x; ++i)
-            pr[i] = op(pr[i], limb_type(0));
-      }
-      else
-      {
-         // "o" is negative:
-         double_limb_type carry = 1;
-         for(unsigned i = 0; i < os; ++i)
-         {
-            carry += static_cast(~po[i]);
-            pr[i] = op(pr[i], static_cast(carry));
-            carry >>= cpp_int_backend::limb_bits;
-         }
-         for(unsigned i = os; i < x; ++i)
-         {
-            carry += static_cast(~limb_type(0));
-            pr[i] = op(pr[i], static_cast(carry));
-            carry >>= cpp_int_backend::limb_bits;
-         }
-         // Set the overflow into the "extra" limb:
-         carry += static_cast(~limb_type(0));
-         next_limb = op(limb_type(0), static_cast(carry));
-      }
-   }
-   else
-   {
-      if(!o.sign())
-      {
-         // "result" is negative:
-         double_limb_type carry = 1;
-         for(unsigned i = 0; i < os; ++i)
-         {
-            carry += static_cast(~pr[i]);
-            pr[i] = op(static_cast(carry), po[i]);
-            carry >>= cpp_int_backend::limb_bits;
-         }
-         for(unsigned i = os; i < x; ++i)
-         {
-            carry += static_cast(~pr[i]);
-            pr[i] = op(static_cast(carry), limb_type(0));
-            carry >>= cpp_int_backend::limb_bits;
-         }
-         // Set the overflow into the "extra" limb:
-         carry += static_cast(~limb_type(0));
-         next_limb = op(static_cast(carry), limb_type(0));
-      }
-      else
-      {
-         // both are negative:
-         double_limb_type r_carry = 1;
-         double_limb_type o_carry = 1;
-         for(unsigned i = 0; i < os; ++i)
-         {
-            r_carry += static_cast(~pr[i]);
-            o_carry += static_cast(~po[i]);
-            pr[i] = op(static_cast(r_carry), static_cast(o_carry));
-            r_carry >>= cpp_int_backend::limb_bits;
-            o_carry >>= cpp_int_backend::limb_bits;
-         }
-         for(unsigned i = os; i < x; ++i)
-         {
-            r_carry += static_cast(~pr[i]);
-            o_carry += static_cast(~limb_type(0));
-            pr[i] = op(static_cast(r_carry), static_cast(o_carry));
-            r_carry >>= cpp_int_backend::limb_bits;
-            o_carry >>= cpp_int_backend::limb_bits;
-         }
-         // Set the overflow into the "extra" limb:
-         r_carry += static_cast(~limb_type(0));
-         o_carry += static_cast(~limb_type(0));
-         next_limb = op(static_cast(r_carry), static_cast(o_carry));
-      }
-   }
-   //
-   // See if the result is negative or not:
-   //
-   if(static_cast(next_limb) < 0)
-   {
-      result.sign(true);
-      double_limb_type carry = 1;
-      for(unsigned i = 0; i < x; ++i)
-      {
-         carry += static_cast(~pr[i]);
-         pr[i] = static_cast(carry);
-         carry >>= cpp_int_backend::limb_bits;
-      }
-   }
-   else
-      result.sign(false);
-
-   result.normalize();
-}
-
-struct bit_and{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a & b; } };
-struct bit_or { limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a | b; } };
-struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a ^ b; } };
-
-template 
-BOOST_FORCEINLINE void eval_bitwise_and(
-   cpp_int_backend& result, 
-   const cpp_int_backend& o)BOOST_NOEXCEPT_IF(is_void::value)
-{
-   bitwise_op(result, o, bit_and());
-}
-template 
-BOOST_FORCEINLINE void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value)
-{
-   bitwise_op(result, o, bit_or());
-}
-template 
-BOOST_FORCEINLINE void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(is_void::value)
-{
-   bitwise_op(result, o, bit_xor());
-}
-template 
-BOOST_FORCEINLINE void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   // Increment and negate:
-   result = o;
-   eval_increment(result);
-   result.negate();
-}
-template 
-inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT
-{
-   if(!s)
-      return;
-
-   limb_type offset = static_cast(s / cpp_int_backend::limb_bits);
-   limb_type shift  = static_cast(s % cpp_int_backend::limb_bits);
-
-   if(offset > cpp_int_backend::internal_limb_count)
-   {
-      result = static_cast(0);
-      return;
-   }
-
-   unsigned ors = result.size();
-   if((ors == 1) && (!*result.limbs()))
-      return; // shifting zero yields zero.
-   unsigned rs = ors;
-   if(shift && (result.limbs()[ors - 1] >> (cpp_int_backend::limb_bits - shift)))
-      ++rs; // Most significant limb will overflow when shifted
-   rs += offset;
-   result.resize(rs);
-   bool truncated = result.size() != rs;
-   if(truncated)
-      rs = result.size();
-   typename cpp_int_backend::limb_pointer pr = result.limbs();
-
-   unsigned i = 0;
-   if(shift)
-   {
-      // This code only works when shift is non-zero, otherwise we invoke undefined behaviour!
-      i = 0;
-      if(!truncated)
-      {
-         if(rs > ors + offset)
-         {
-            pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift);
-            --rs;
-         }
-         else
-         {
-            pr[rs - 1 - i] = pr[ors - 1 - i] << shift;
-            if(ors > 1)
-               pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift);
-            ++i;
-         }
-      }
-      for(; ors > 1 + i; ++i)
-      {
-         pr[rs - 1 - i] = pr[ors - 1 - i] << shift;
-         pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift);
-      }
-      if(ors >= 1 + i)
-      {
-         pr[rs - 1 - i] = pr[ors - 1 - i] << shift;
-         ++i;
-      }
-      for(; i < rs; ++i)
-         pr[rs - 1 - i] = 0;
-   }
-   else
-   {
-      for(; i < ors; ++i)
-         pr[rs - 1 - i] = pr[ors - 1 - i];
-      for(; i < rs; ++i)
-         pr[rs - 1 - i] = 0;
-   }
-   //
-   // We may have shifted off the end and have leading zeros:
-   //
-   if(truncated)
-   {
-      result.normalize();
-   }
-}
-template 
-inline void eval_left_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(!s)
-      return;
-
-   limb_type offset = static_cast(s / cpp_int_backend::limb_bits);
-   limb_type shift  = static_cast(s % cpp_int_backend::limb_bits);
-
-   unsigned ors = result.size();
-   if((ors == 1) && (!*result.limbs()))
-      return; // shifting zero yields zero.
-   unsigned rs = ors;
-   if(shift && (result.limbs()[rs - 1] >> (cpp_int_backend::limb_bits - shift)))
-      ++rs; // Most significant limb will overflow when shifted
-   rs += offset;
-   result.resize(rs);
-   typename cpp_int_backend::limb_pointer pr = result.limbs();
-
-   unsigned i = 0;
-   if(shift)
-   {
-      // This code only works when shift is non-zero, otherwise we invoke undefined behaviour!
-      i = 0;
-      if(rs > ors + offset)
-      {
-         pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift);
-         --rs;
-      }
-      else
-      {
-         pr[rs - 1 - i] = pr[ors - 1 - i] << shift;
-         if(ors > 1)
-            pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift);
-         ++i;
-      }
-      for(; ors > 1 + i; ++i)
-      {
-         pr[rs - 1 - i] = pr[ors - 1 - i] << shift;
-         pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift);
-      }
-      if(ors >= 1 + i)
-      {
-         pr[rs - 1 - i] = pr[ors - 1 - i] << shift;
-         ++i;
-      }
-      for(; i < rs; ++i)
-         pr[rs - 1 - i] = 0;
-   }
-   else
-   {
-      for(; i < ors; ++i)
-         pr[rs - 1 - i] = pr[ors - 1 - i];
-      for(; i < rs; ++i)
-         pr[rs - 1 - i] = 0;
-   }
-}
-template 
-inline void eval_right_shift(cpp_int_backend& result, double_limb_type s) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if(!s)
-      return;
-
-   limb_type offset = static_cast(s / cpp_int_backend::limb_bits);
-   limb_type shift  = static_cast(s % cpp_int_backend::limb_bits);
-   unsigned ors = result.size();
-   unsigned rs = ors;
-   if(offset >= rs)
-   {
-      result = limb_type(0);
-      return;
-   }
-   rs -= offset;
-   typename cpp_int_backend::limb_pointer pr = result.limbs();
-   if((pr[ors - 1] >> shift) == 0)
-      --rs;
-   if(rs == 0)
-   {
-      result = limb_type(0);
-      return;
-   }
-   unsigned i = 0;
-   if(shift)
-   {
-      // This code only works for non-zero shift, otherwise we invoke undefined behaviour!
-      for(; i + offset + 1 < ors; ++i)
-      {
-         pr[i] = pr[i + offset] >> shift;
-         pr[i] |= pr[i + offset + 1] << (cpp_int_backend::limb_bits - shift);
-      }
-      pr[i] = pr[i + offset] >> shift;
-   }
-   else
-   {
-      for(; i < rs; ++i)
-         pr[i] = pr[i + offset];
-   }
-   result.resize(rs);
-}
-
-template 
-inline Integer negate_integer(Integer i, const mpl::true_&) BOOST_NOEXCEPT
-{
-   return -i;
-}
-template 
-inline Integer negate_integer(Integer i, const mpl::false_&) BOOST_NOEXCEPT
-{
-   return ~(i-1);
-}
-
-template 
-inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) BOOST_NOEXCEPT
-{
-   *result = static_cast(backend.limbs()[0]);
-   unsigned shift = cpp_int_backend::limb_bits;
-   for(unsigned i = 1; (i < backend.size()) && (shift < static_cast(std::numeric_limits::digits)); ++i)
-   {
-      *result += static_cast(backend.limbs()[i]) << shift;
-      shift += cpp_int_backend::limb_bits;
-   }
-   if(backend.sign())
-   {
-      *result = negate_integer(*result, mpl::bool_::is_signed>());
-   }
-}
-
-template 
-inline typename enable_if, void>::type eval_convert_to(R* result, const cpp_int_backend& backend) BOOST_NOEXCEPT
-{
-   typename cpp_int_backend::const_limb_pointer p = backend.limbs();
-   unsigned shift = cpp_int_backend::limb_bits;
-   *result = static_cast(*p);
-   for(unsigned i = 1; i < backend.size(); ++i)
-   {
-      *result += static_cast(std::ldexp(static_cast(p[i]), shift));
-      shift += cpp_int_backend::limb_bits;
-   }
-   if(backend.sign())
-      *result = -*result;
-}
-
-template 
-BOOST_FORCEINLINE bool eval_is_zero(const cpp_int_backend& val) BOOST_NOEXCEPT
-{
-   return (val.size() == 1) && (val.limbs()[0] == 0);
-}
-template 
-BOOST_FORCEINLINE int eval_get_sign(const cpp_int_backend& val) BOOST_NOEXCEPT
-{
-   return eval_is_zero(val) ? 0 : val.sign() ? -1 : 1;
-}
-template 
-BOOST_FORCEINLINE void eval_abs(cpp_int_backend& result, const cpp_int_backend& val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   result = val;
-   result.sign(false);
-}
-
-//
-// Get the location of the least-significant-bit:
-//
-template 
-inline unsigned eval_lsb(const cpp_int_backend& a) BOOST_NOEXCEPT
-{
-   BOOST_ASSERT(eval_get_sign(a) != 0);
-   
-   unsigned result = 0;
-   //
-   // Find the index of the least significant limb that is non-zero:
-   //
-   unsigned index = 0;
-   while(!a.limbs()[index] && (index < a.size()))
-      ++index;
-   //
-   // Find the index of the least significant bit within that limb:
-   //
-   limb_type l = a.limbs()[index];
-   while(!(l & 1u))
-   {
-      l >>= 1;
-      ++result;
-   }
-
-   return result + index * cpp_int_backend::limb_bits;
-}
-
-template 
-inline bool eval_bit_test(const cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT
-{
-   unsigned offset = index / cpp_int_backend::limb_bits;
-   unsigned shift = index % cpp_int_backend::limb_bits;
-   limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
-   if(offset >= val.size())
-      return false;
-   return val.limbs()[offset] & mask ? true : false;
-}
-
-template 
-inline void eval_bit_set(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   unsigned offset = index / cpp_int_backend::limb_bits;
-   unsigned shift = index % cpp_int_backend::limb_bits;
-   limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
-   if(offset >= val.size())
-   {
-      unsigned os = val.size();
-      val.resize(offset + 1);
-      if(offset >= val.size())
-         return;  // fixed precision overflow
-      for(unsigned i = os; i <= offset; ++i)
-         val.limbs()[i] = 0;
-   }
-   val.limbs()[offset] |= mask;
-}
-
-template 
-inline void eval_bit_unset(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT
-{
-   unsigned offset = index / cpp_int_backend::limb_bits;
-   unsigned shift = index % cpp_int_backend::limb_bits;
-   limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
-   if(offset >= val.size())
-      return;
-   val.limbs()[offset] &= ~mask;
-   val.normalize();
-}
-
-template 
-inline void eval_bit_flip(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   unsigned offset = index / cpp_int_backend::limb_bits;
-   unsigned shift = index % cpp_int_backend::limb_bits;
-   limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
-   if(offset >= val.size())
-   {
-      unsigned os = val.size();
-      val.resize(offset + 1);
-      if(offset >= val.size())
-         return;  // fixed precision overflow
-      for(unsigned i = os; i <= offset; ++i)
-         val.limbs()[i] = 0;
-   }
-   val.limbs()[offset] ^= mask;
-   val.normalize();
-}
-
-template 
-inline void eval_qr(const cpp_int_backend& x, const cpp_int_backend& y, 
-   cpp_int_backend& q, cpp_int_backend& r) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   divide_unsigned_helper(&q, x, y, r);
-   q.sign(x.sign() != y.sign());
-   r.sign(x.sign());
-}
-
-template 
-inline typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   if((sizeof(Integer) <= sizeof(limb_type)) || (val <= (std::numeric_limits::max)()))
-   {
-      cpp_int_backend d;
-      divide_unsigned_helper(static_cast*>(0), x, val, d);
-      return d.limbs()[0];
-   }
-   else
-   {
-      return default_ops::eval_integer_modulus(x, val);
-   }
-}
-template 
-BOOST_FORCEINLINE typename enable_if, Integer>::type eval_integer_modulus(const cpp_int_backend& x, Integer val) BOOST_NOEXCEPT_IF(boost::is_void::value)
-{
-   typedef typename make_unsigned::type unsigned_type;
-   return eval_integer_modulus(x, static_cast(std::abs(val)));
-}
-
-} // namespace backends;
-
-template 
-struct expression_template_default >
+template 
+struct expression_template_default >
 {
    static const expression_template_option value = et_off;
 };
 
 using boost::multiprecision::backends::cpp_int_backend;
 
-template 
-struct number_category > : public mpl::int_{};
+template 
+struct number_category > : public mpl::int_{};
 
-typedef number >          cpp_int;
-typedef rational_adapter >   cpp_rational_backend;
-typedef number        cpp_rational;
+typedef number >                   cpp_int;
+typedef rational_adapter >         cpp_rational_backend;
+typedef number                 cpp_rational;
 
 // Fixed precision unsigned types:
-typedef number >   uint128_t;
-typedef number >   uint256_t;
-typedef number >   uint512_t;
-typedef number >  uint1024_t;
+typedef number >   uint128_t;
+typedef number >   uint256_t;
+typedef number >   uint512_t;
+typedef number > uint1024_t;
 
 // Fixed precision signed types:
-typedef number >    int128_t;
-typedef number >    int256_t;
-typedef number >    int512_t;
-typedef number >   int1024_t;
+typedef number >    int128_t;
+typedef number >    int256_t;
+typedef number >    int512_t;
+typedef number >  int1024_t;
 
-#ifdef BOOST_MSVC
-#pragma warning(pop)
-#endif
+// Over again, but with checking enabled this time:
+typedef number >  checked_cpp_int;
+typedef rational_adapter >  checked_cpp_rational_backend;
+typedef number                 checked_cpp_rational;
+// Fixed precision unsigned types:
+typedef number >   checked_uint128_t;
+typedef number >   checked_uint256_t;
+typedef number >   checked_uint512_t;
+typedef number > checked_uint1024_t;
+
+// Fixed precision signed types:
+typedef number >    checked_int128_t;
+typedef number >    checked_int256_t;
+typedef number >    checked_int512_t;
+typedef number >  checked_int1024_t;
 
 #ifdef BOOST_NO_SFINAE_EXPR
 
 namespace detail{
 
-template
-struct is_explicitly_convertible, cpp_int_backend > : public mpl::true_ {};
+template
+struct is_explicitly_convertible, cpp_int_backend > : public mpl::true_ {};
 
 }
-
 #endif
 
 }} // namespaces
 
-#include 
-
-
-namespace std{
-
-template 
-class numeric_limits, ExpressionTemplates> >
-{
-   typedef boost::multiprecision::number, ExpressionTemplates> number_type;
-
-public:
-   BOOST_STATIC_CONSTEXPR bool is_specialized = true;
-   //
-   // Largest and smallest numbers are bounded only by available memory, set
-   // to zero:
-   //
-   static number_type (min)() BOOST_NOEXCEPT
-   {
-      return number_type(0);
-   }
-   static number_type (max)() BOOST_NOEXCEPT 
-   { 
-      return number_type(0);
-   }
-   static number_type lowest() BOOST_NOEXCEPT { return (min)(); }
-   BOOST_STATIC_CONSTEXPR int digits = INT_MAX;
-   BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L;
-   BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2;
-   BOOST_STATIC_CONSTEXPR bool is_signed = true;
-   BOOST_STATIC_CONSTEXPR bool is_integer = true;
-   BOOST_STATIC_CONSTEXPR bool is_exact = true;
-   BOOST_STATIC_CONSTEXPR int radix = 2;
-   static number_type epsilon() BOOST_NOEXCEPT { return 0; }
-   static number_type round_error() BOOST_NOEXCEPT { return 0; }
-   BOOST_STATIC_CONSTEXPR int min_exponent = 0;
-   BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
-   BOOST_STATIC_CONSTEXPR int max_exponent = 0;
-   BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
-   BOOST_STATIC_CONSTEXPR bool has_infinity = false;
-   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
-   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
-   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
-   BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
-   static number_type infinity() BOOST_NOEXCEPT { return 0; }
-   static number_type quiet_NaN() BOOST_NOEXCEPT { return 0; }
-   static number_type signaling_NaN() BOOST_NOEXCEPT { return 0; }
-   static number_type denorm_min() BOOST_NOEXCEPT { return 0; }
-   BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
-   BOOST_STATIC_CONSTEXPR bool is_bounded = false;
-   BOOST_STATIC_CONSTEXPR bool is_modulo = false;
-   BOOST_STATIC_CONSTEXPR bool traps = false;
-   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
-   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
-};
-
-#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
-
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN;
-template 
-BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before;
-template 
-BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style;
-
-#endif
-
-template 
-class numeric_limits, ExpressionTemplates> >
-{
-   typedef boost::multiprecision::number, ExpressionTemplates> number_type;
-
-   struct inititializer
-   {
-      inititializer()
-      {
-         (std::numeric_limits::max)();
-         (std::numeric_limits::min)();
-      }
-      void do_nothing()const{}
-   };
-
-   static const inititializer init;
-
-public:
-   BOOST_STATIC_CONSTEXPR bool is_specialized = true;
-   //
-   // Largest and smallest numbers are bounded only by available memory, set
-   // to zero:
-   //
-   static number_type (min)() BOOST_NOEXCEPT
-   {
-      return -(max)();
-   }
-   static number_type (max)() BOOST_NOEXCEPT 
-   {
-      typedef typename number_type::backend_type backend_type;
-      init.do_nothing();
-      static bool init = false;
-      static number_type val;
-      if(!init)
-      {
-         boost::multiprecision::number, ExpressionTemplates> t(0);
-         val = ~t;
-         init = true;
-      }
-      return val;
-   }
-   static number_type lowest() BOOST_NOEXCEPT { return (min)(); }
-   BOOST_STATIC_CONSTEXPR int digits = MinBits;
-   BOOST_STATIC_CONSTEXPR int digits10 = static_cast(MinBits * 301L / 1000L);
-   BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2;
-   BOOST_STATIC_CONSTEXPR bool is_signed = true;
-   BOOST_STATIC_CONSTEXPR bool is_integer = true;
-   BOOST_STATIC_CONSTEXPR bool is_exact = true;
-   BOOST_STATIC_CONSTEXPR int radix = 2;
-   static number_type epsilon() BOOST_NOEXCEPT { return 0; }
-   static number_type round_error() BOOST_NOEXCEPT { return 0; }
-   BOOST_STATIC_CONSTEXPR int min_exponent = 0;
-   BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
-   BOOST_STATIC_CONSTEXPR int max_exponent = 0;
-   BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
-   BOOST_STATIC_CONSTEXPR bool has_infinity = false;
-   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
-   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
-   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
-   BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
-   static number_type infinity() BOOST_NOEXCEPT { return 0; }
-   static number_type quiet_NaN() BOOST_NOEXCEPT { return 0; }
-   static number_type signaling_NaN() BOOST_NOEXCEPT { return 0; }
-   static number_type denorm_min() BOOST_NOEXCEPT { return 0; }
-   BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
-   BOOST_STATIC_CONSTEXPR bool is_bounded = true;
-   BOOST_STATIC_CONSTEXPR bool is_modulo = true;
-   BOOST_STATIC_CONSTEXPR bool traps = false;
-   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
-   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
-};
-
-template 
-const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init;
-
-#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
-
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::digits;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::digits10;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::max_digits10;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_signed;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_integer;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_exact;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::radix;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::min_exponent;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::min_exponent10;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::max_exponent;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::max_exponent10;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::has_infinity;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::has_quiet_NaN;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::has_signaling_NaN;
-template 
-BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates>  >::has_denorm;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::has_denorm_loss;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_iec559;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_bounded;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_modulo;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::traps;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::tinyness_before;
-template 
-BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates>  >::round_style;
-
-#endif
-
-template 
-class numeric_limits, ExpressionTemplates> >
-{
-   typedef boost::multiprecision::number, ExpressionTemplates> number_type;
-
-   struct inititializer
-   {
-      inititializer()
-      {
-         (std::numeric_limits::max)();
-      }
-      void do_nothing()const{}
-   };
-
-   static const inititializer init;
-
-public:
-   BOOST_STATIC_CONSTEXPR bool is_specialized = true;
-   //
-   // Largest and smallest numbers are bounded only by available memory, set
-   // to zero:
-   //
-   static number_type (min)() BOOST_NOEXCEPT
-   {
-      return number_type(0);
-   }
-   static number_type (max)() BOOST_NOEXCEPT 
-   {
-      typedef typename number_type::backend_type backend_type;
-      init.do_nothing();
-      static bool init = false;
-      static number_type val(0);
-      if(!init)
-      {
-         boost::multiprecision::limb_type l = ~static_cast(0);
-         unsigned c = MinBits / backend_type::limb_bits + (MinBits % backend_type::limb_bits ? 1 : 0);
-         for(unsigned i = 0; i < c; ++i)
-         {
-            val <<= backend_type::limb_bits;
-            val |= l;
-         }
-         init = true;
-      }
-      return val;
-   }
-   static number_type lowest() BOOST_NOEXCEPT { return (min)(); }
-   BOOST_STATIC_CONSTEXPR int digits = MinBits;
-   BOOST_STATIC_CONSTEXPR int digits10 = static_cast(MinBits * 301L / 1000L);
-   BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2;
-   BOOST_STATIC_CONSTEXPR bool is_signed = false;
-   BOOST_STATIC_CONSTEXPR bool is_integer = true;
-   BOOST_STATIC_CONSTEXPR bool is_exact = true;
-   BOOST_STATIC_CONSTEXPR int radix = 2;
-   static number_type epsilon() BOOST_NOEXCEPT { return 0; }
-   static number_type round_error() BOOST_NOEXCEPT { return 0; }
-   BOOST_STATIC_CONSTEXPR int min_exponent = 0;
-   BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
-   BOOST_STATIC_CONSTEXPR int max_exponent = 0;
-   BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
-   BOOST_STATIC_CONSTEXPR bool has_infinity = false;
-   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
-   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
-   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
-   BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
-   static number_type infinity() BOOST_NOEXCEPT { return 0; }
-   static number_type quiet_NaN() BOOST_NOEXCEPT { return 0; }
-   static number_type signaling_NaN() BOOST_NOEXCEPT { return 0; }
-   static number_type denorm_min() BOOST_NOEXCEPT { return 0; }
-   BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
-   BOOST_STATIC_CONSTEXPR bool is_bounded = true;
-   BOOST_STATIC_CONSTEXPR bool is_modulo = true;
-   BOOST_STATIC_CONSTEXPR bool traps = false;
-   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
-   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
-};
-
-template 
-const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init;
-
-#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
-
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::min_exponent10;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent;
-template 
-BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_exponent10;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN;
-template 
-BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps;
-template 
-BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before;
-template 
-BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style;
-
-#endif
-
-}
+//
+// Last of all we include the implementations of all the eval_* non member functions:
+//
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
 
 #endif
diff --git a/include/boost/multiprecision/cpp_int/add.hpp b/include/boost/multiprecision/cpp_int/add.hpp
new file mode 100644
index 00000000..068afc7d
--- /dev/null
+++ b/include/boost/multiprecision/cpp_int/add.hpp
@@ -0,0 +1,509 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// Comparison operators for cpp_int_backend:
+//
+#ifndef BOOST_MP_CPP_INT_ADD_HPP
+#define BOOST_MP_CPP_INT_ADD_HPP
+
+namespace boost{ namespace multiprecision{ namespace backends{
+
+//
+// This is the key addition routine where all the argument types are non-trivial cpp_int's:
+//
+template 
+inline void add_unsigned(CppInt1& result, const CppInt2& a, const CppInt3& b) BOOST_NOEXCEPT_IF(is_non_throwing_cpp_int::value)
+{
+   using std::swap;
+
+   // Nothing fancy, just let uintmax_t take the strain:
+   double_limb_type carry = 0;
+   unsigned m, x;
+   unsigned as = a.size();
+   unsigned bs = b.size();
+   minmax(as, bs, m, x);
+   if(x == 1)
+   {
+      bool s = a.sign();
+      result = static_cast(*a.limbs()) + static_cast(*b.limbs());
+      result.sign(s);
+      return;
+   }
+   result.resize(x, x);
+   typename CppInt2::const_limb_pointer pa = a.limbs();
+   typename CppInt3::const_limb_pointer pb = b.limbs();
+   typename CppInt1::limb_pointer pr = result.limbs();
+   typename CppInt1::limb_pointer pr_end = pr + m;
+
+   if(as < bs)
+      swap(pa, pb);
+   
+   // First where a and b overlap:
+   while(pr != pr_end)
+   {
+      carry += static_cast(*pa) + static_cast(*pb);
+      *pr = static_cast(carry);
+      carry >>= CppInt1::limb_bits;
+      ++pr, ++pa, ++pb;
+   }
+   pr_end += x - m;
+   // Now where only a has digits:
+   while(pr != pr_end)
+   {
+      if(!carry)
+      {
+         if(pa != pr)
+            std::copy(pa, pa + (pr_end - pr), pr);
+         break;
+      }
+      carry += static_cast(*pa);
+      *pr = static_cast(carry);
+      carry >>= CppInt1::limb_bits;
+      ++pr, ++pa;
+   }
+   if(carry)
+   {
+      // We overflowed, need to add one more limb:
+      result.resize(x + 1, x + 1);
+      if(CppInt1::variable || (result.size() > x))
+         result.limbs()[x] = static_cast(carry);
+   }
+   result.normalize();
+   result.sign(a.sign());
+}
+//
+// As above, but for adding a single limb to a non-trivial cpp_int:
+//
+template 
+inline void add_unsigned(CppInt1& result, const CppInt2& a, const limb_type& o) BOOST_NOEXCEPT_IF(is_non_throwing_cpp_int::value)
+{
+   // Addition using modular arithmatic.
+   // Nothing fancy, just let uintmax_t take the strain:
+   if(&result != &a)
+      result.resize(a.size(), a.size());
+   double_limb_type carry = o;
+   typename CppInt1::limb_pointer pr = result.limbs();
+   typename CppInt2::const_limb_pointer pa = a.limbs();
+   unsigned i = 0;
+   // Addition with carry until we either run out of digits or carry is zero:
+   for(; carry && (i < result.size()); ++i)
+   {
+      carry += static_cast(pa[i]);
+      pr[i] = static_cast(carry);
+      carry >>= CppInt1::limb_bits;
+   }
+   // Just copy any remaining digits:
+   if(&a != &result)
+   {
+      for(; i < result.size(); ++i)
+         pr[i] = pa[i];
+   }
+   if(carry)
+   {
+      // We overflowed, need to add one more limb:
+      unsigned x = result.size();
+      result.resize(x + 1, x + 1);
+      if(CppInt1::variable || (result.size() > x))
+         result.limbs()[x] = static_cast(carry);
+   }
+   result.normalize();
+   result.sign(a.sign());
+}
+//
+// Core subtraction routine for all non-trivial cpp_int's:
+//
+template 
+inline void subtract_unsigned(CppInt1& result, const CppInt2& a, const CppInt3& b) BOOST_NOEXCEPT_IF(is_non_throwing_cpp_int::value)
+{
+   using std::swap;
+
+   // Nothing fancy, just let uintmax_t take the strain:
+   double_limb_type borrow = 0;
+   unsigned m, x;
+   minmax(a.size(), b.size(), m, x);
+   //
+   // special cases for small limb counts:
+   //
+   if(x == 1)
+   {
+      bool s = a.sign();
+      limb_type al = *a.limbs();
+      limb_type bl = *b.limbs();
+      if(bl > al)
+      {
+         std::swap(al, bl);
+         s = !s;
+      }
+      result = al - bl;
+      result.sign(s);
+      return;
+   }
+   // This isn't used till later, but comparison has to occur before we resize the result,
+   // as that may also resize a or b if this is an inplace operation:
+   int c = a.compare_unsigned(b);
+   // Set up the result vector:
+   result.resize(x, x);
+   // Now that a, b, and result are stable, get pointers to their limbs:
+   typename CppInt2::const_limb_pointer pa = a.limbs();
+   typename CppInt3::const_limb_pointer pb = b.limbs();
+   typename CppInt1::limb_pointer pr = result.limbs();
+   bool swapped = false;
+   if(c < 0)
+   {
+      swap(pa, pb);
+      swapped = true;
+   }
+   else if(c == 0)
+   {
+      result = static_cast(0);
+      return;
+   }
+   
+   unsigned i = 0;
+   // First where a and b overlap:
+   while(i < m)
+   {
+      borrow = static_cast(pa[i]) - static_cast(pb[i]) - borrow;
+      pr[i] = static_cast(borrow);
+      borrow = (borrow >> CppInt1::limb_bits) & 1u;
+      ++i;
+   }
+   // Now where only a has digits, only as long as we've borrowed:
+   while(borrow && (i < x))
+   {
+      borrow = static_cast(pa[i]) - borrow;
+      pr[i] = static_cast(borrow);
+      borrow = (borrow >> CppInt1::limb_bits) & 1u;
+      ++i;
+   }
+   // Any remaining digits are the same as those in pa:
+   if((x != i) && (pa != pr))
+      std::copy(pa + i, pa + x, pr + i);
+   BOOST_ASSERT(0 == borrow);
+
+   //
+   // We may have lost digits, if so update limb usage count:
+   //
+   result.normalize();
+   result.sign(a.sign());
+   if(swapped)
+      result.negate();
+}
+//
+// And again to subtract a single limb:
+//
+template 
+inline void subtract_unsigned(CppInt1& result, const CppInt2& a, const limb_type& b) BOOST_NOEXCEPT_IF(is_non_throwing_cpp_int::value)
+{
+   // Subtract one limb.
+   // Nothing fancy, just let uintmax_t take the strain:
+   BOOST_STATIC_CONSTANT(double_limb_type, borrow = static_cast(CppInt1::max_limb_value) + 1);
+   result.resize(a.size(), a.size());
+   typename CppInt1::limb_pointer pr = result.limbs();
+   typename CppInt2::const_limb_pointer pa = a.limbs();
+   if(*pa > b)
+   {
+      *pr = *pa - b;
+      if(&result != &a)
+      {
+         std::copy(pa + 1, pa + a.size(), pr + 1);
+         result.sign(a.sign());
+      }
+   }
+   else if(result.size() == 1)
+   {
+      *pr = b - *pa;
+      result.sign(!a.sign());
+   }
+   else
+   {
+      *pr = static_cast((borrow + *pa) - b);
+      unsigned i = 1;
+      while(!pa[i])
+      {
+         pr[i] = CppInt1::max_limb_value;
+         ++i;
+      }
+      pr[i] = pa[i] - 1;
+      if(&result != &a)
+      {
+         ++i;
+         std::copy(pa + i, pa + a.size(), pr + i);
+      }
+      result.normalize();
+      result.sign(a.sign());
+   }
+}
+
+//
+// Now the actual functions called by the front end, all of which forward to one of the above:
+//
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_add(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   eval_add(result, result, o);
+}
+template 
+inline typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type
+   eval_add(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const cpp_int_backend& b) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(a.sign() != b.sign())
+   {
+      subtract_unsigned(result, a, b);
+      return;
+   }
+   add_unsigned(result, a, b);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_add(cpp_int_backend& result, const limb_type& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(result.sign())
+   {
+      subtract_unsigned(result, result, o);
+   }
+   else
+      add_unsigned(result, result, o);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_add(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const limb_type& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(a.sign())
+   {
+      subtract_unsigned(result, a, o);
+   }
+   else
+      add_unsigned(result, a, o);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_add(
+      cpp_int_backend& result, 
+      const signed_limb_type& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(o < 0)
+      eval_subtract(result, static_cast(-o));
+   else if(o > 0)
+      eval_add(result, static_cast(o));
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_add(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const signed_limb_type& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(o < 0)
+      eval_subtract(result, a, static_cast(-o));
+   else if(o > 0)
+      eval_add(result, a, static_cast(o));
+   else if(&result != &a)
+      result = a;
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_subtract(
+      cpp_int_backend& result, 
+      const limb_type& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(result.sign())
+   {
+      add_unsigned(result, result, o);
+   }
+   else
+      subtract_unsigned(result, result, o);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_subtract(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const limb_type& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(a.sign())
+   {
+      add_unsigned(result, a, o);
+   }
+   else
+   {
+      subtract_unsigned(result, a, o);
+   }
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_subtract(
+      cpp_int_backend& result, 
+      const signed_limb_type& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(o)
+   {
+      if(o < 0)
+         eval_add(result, static_cast(-o));
+      else
+         eval_subtract(result, static_cast(o));
+   }
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_subtract(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const signed_limb_type& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(o)
+   {
+      if(o < 0)
+         eval_add(result, a, static_cast(-o));
+      else
+         eval_subtract(result, a, static_cast(o));
+   }
+   else if(&result != &a)
+      result = a;
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_increment(cpp_int_backend& result) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   static const limb_type one = 1;
+   if(!result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value))
+      ++result.limbs()[0];
+   else if(result.sign() && result.limbs()[0])
+      --result.limbs()[0];
+   else
+      eval_add(result, one);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_decrement(cpp_int_backend& result) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   static const limb_type one = 1;
+   if(!result.sign() && result.limbs()[0])
+      --result.limbs()[0];
+   else if(result.sign() && (result.limbs()[0] < cpp_int_backend::max_limb_value))
+      ++result.limbs()[0];
+   else
+      eval_subtract(result, one);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_subtract(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   eval_subtract(result, result, o);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type
+   eval_subtract(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const cpp_int_backend& b) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(a.sign() != b.sign())
+   {
+      add_unsigned(result, a, b);
+      return;
+   }
+   subtract_unsigned(result, a, b);
+}
+
+//
+// Simple addition and subtraction routine for trivial cpp_int's come last:
+//
+// One of the arguments is signed:
+//
+template 
+inline typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && (is_signed_number >::value || is_signed_number >::value)
+         >::type 
+   eval_add(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(result.sign() != o.sign())
+   {
+      if(*o.limbs() > *result.limbs())
+      {
+         *result.limbs() = detail::checked_subtract(*o.limbs(), *result.limbs(), typename cpp_int_backend::checked_type());
+         result.negate();
+      }
+      else
+         *result.limbs() = detail::checked_subtract(*result.limbs(), *o.limbs(), typename cpp_int_backend::checked_type());
+   }
+   else
+      *result.limbs() = detail::checked_add(*result.limbs(), *o.limbs(), typename cpp_int_backend::checked_type());
+   result.normalize();
+}
+// Simple version for two unsigned arguments:
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
+         >::type 
+   eval_add(cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   *result.limbs() = detail::checked_add(*result.limbs(), *o.limbs(), typename cpp_int_backend::checked_type());
+   result.normalize();
+}
+
+// signed subtraction:
+template 
+inline typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && (is_signed_number >::value || is_signed_number >::value)
+         >::type 
+   eval_subtract(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(result.sign() != o.sign())
+   {
+      *result.limbs() = detail::checked_add(*result.limbs(), *o.limbs(), typename cpp_int_backend::checked_type());
+   }
+   else if(*result.limbs() < *o.limbs())
+   {
+      *result.limbs() = detail::checked_subtract(*o.limbs(), *result.limbs(), typename cpp_int_backend::checked_type());
+      result.negate();
+   }
+   else
+      *result.limbs() = detail::checked_subtract(*result.limbs(), *o.limbs(), typename cpp_int_backend::checked_type());
+   result.normalize();
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
+         >::type 
+   eval_subtract(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   *result.limbs() = detail::checked_subtract(*result.limbs(), *o.limbs(), typename cpp_int_backend::checked_type());
+   result.normalize();
+}
+
+}}} // namespaces
+
+#endif
diff --git a/include/boost/multiprecision/cpp_int/bitwise.hpp b/include/boost/multiprecision/cpp_int/bitwise.hpp
new file mode 100644
index 00000000..0d6db044
--- /dev/null
+++ b/include/boost/multiprecision/cpp_int/bitwise.hpp
@@ -0,0 +1,560 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// Comparison operators for cpp_int_backend:
+//
+#ifndef BOOST_MP_CPP_INT_BIT_HPP
+#define BOOST_MP_CPP_INT_BIT_HPP
+
+namespace boost{ namespace multiprecision{ namespace backends{
+
+template 
+void bitwise_op(
+   CppInt1& result, 
+   const CppInt2& o, 
+   Op op) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int::value))
+{
+   //
+   // There are 4 cases:
+   // * Both positive.
+   // * result negative, o positive.
+   // * o negative, result positive.
+   // * Both negative.
+   //
+   // When one arg is negative we convert to 2's complement form "on the fly",
+   // and then convert back to signed-magnitude form at the end.
+   //
+   // First figure out how big the result needs to be and set up some data:
+   //
+   unsigned rs = result.size();
+   unsigned os = o.size();
+   unsigned m, x;
+   minmax(rs, os, m, x);
+   result.resize(x, x);
+   typename CppInt1::limb_pointer pr = result.limbs();
+   typename CppInt2::const_limb_pointer po = o.limbs();
+   for(unsigned i = rs; i < x; ++i)
+      pr[i] = 0;
+
+   limb_type next_limb = 0;
+
+   if(!result.sign())
+   {
+      if(!o.sign())
+      {
+         for(unsigned i = 0; i < os; ++i)
+            pr[i] = op(pr[i], po[i]);
+         for(unsigned i = os; i < x; ++i)
+            pr[i] = op(pr[i], limb_type(0));
+      }
+      else
+      {
+         // "o" is negative:
+         double_limb_type carry = 1;
+         for(unsigned i = 0; i < os; ++i)
+         {
+            carry += static_cast(~po[i]);
+            pr[i] = op(pr[i], static_cast(carry));
+            carry >>= CppInt1::limb_bits;
+         }
+         for(unsigned i = os; i < x; ++i)
+         {
+            carry += static_cast(~limb_type(0));
+            pr[i] = op(pr[i], static_cast(carry));
+            carry >>= CppInt1::limb_bits;
+         }
+         // Set the overflow into the "extra" limb:
+         carry += static_cast(~limb_type(0));
+         next_limb = op(limb_type(0), static_cast(carry));
+      }
+   }
+   else
+   {
+      if(!o.sign())
+      {
+         // "result" is negative:
+         double_limb_type carry = 1;
+         for(unsigned i = 0; i < os; ++i)
+         {
+            carry += static_cast(~pr[i]);
+            pr[i] = op(static_cast(carry), po[i]);
+            carry >>= CppInt1::limb_bits;
+         }
+         for(unsigned i = os; i < x; ++i)
+         {
+            carry += static_cast(~pr[i]);
+            pr[i] = op(static_cast(carry), limb_type(0));
+            carry >>= CppInt1::limb_bits;
+         }
+         // Set the overflow into the "extra" limb:
+         carry += static_cast(~limb_type(0));
+         next_limb = op(static_cast(carry), limb_type(0));
+      }
+      else
+      {
+         // both are negative:
+         double_limb_type r_carry = 1;
+         double_limb_type o_carry = 1;
+         for(unsigned i = 0; i < os; ++i)
+         {
+            r_carry += static_cast(~pr[i]);
+            o_carry += static_cast(~po[i]);
+            pr[i] = op(static_cast(r_carry), static_cast(o_carry));
+            r_carry >>= CppInt1::limb_bits;
+            o_carry >>= CppInt1::limb_bits;
+         }
+         for(unsigned i = os; i < x; ++i)
+         {
+            r_carry += static_cast(~pr[i]);
+            o_carry += static_cast(~limb_type(0));
+            pr[i] = op(static_cast(r_carry), static_cast(o_carry));
+            r_carry >>= CppInt1::limb_bits;
+            o_carry >>= CppInt1::limb_bits;
+         }
+         // Set the overflow into the "extra" limb:
+         r_carry += static_cast(~limb_type(0));
+         o_carry += static_cast(~limb_type(0));
+         next_limb = op(static_cast(r_carry), static_cast(o_carry));
+      }
+   }
+   //
+   // See if the result is negative or not:
+   //
+   if(static_cast(next_limb) < 0)
+   {
+      result.sign(true);
+      double_limb_type carry = 1;
+      for(unsigned i = 0; i < x; ++i)
+      {
+         carry += static_cast(~pr[i]);
+         pr[i] = static_cast(carry);
+         carry >>= CppInt1::limb_bits;
+      }
+   }
+   else
+      result.sign(false);
+
+   result.normalize();
+}
+
+struct bit_and{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a & b; } };
+struct bit_or { limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a | b; } };
+struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a ^ b; } };
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_bitwise_and(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   bitwise_op(result, o, bit_and());
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_bitwise_or(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   bitwise_op(result, o, bit_or());
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_bitwise_xor(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   bitwise_op(result, o, bit_xor());
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type 
+   eval_complement(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   BOOST_STATIC_ASSERT_MSG(((Checked1 != checked) || (Checked2 != checked)), "Attempt to take the complement of a signed type results in undefined behavior.");
+   // Increment and negate:
+   result = o;
+   eval_increment(result);
+   result.negate();
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type 
+   eval_complement(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   unsigned os = o.size();
+   result.resize(UINT_MAX, os);
+   for(unsigned i = 0; i < os; ++i)
+      result.limbs()[i] = ~o.limbs()[i];
+   for(unsigned i = os; i < result.size(); ++i)
+      result.limbs()[i] = ~static_cast(0);
+}
+
+template 
+inline typename enable_if_c >::value>::type 
+   eval_left_shift(
+      cpp_int_backend& result, 
+      double_limb_type s) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(!s)
+      return;
+
+   limb_type offset = static_cast(s / cpp_int_backend::limb_bits);
+   limb_type shift  = static_cast(s % cpp_int_backend::limb_bits);
+
+   /*
+   static const unsigned max_bits = max_bits >::value;
+   static const unsigned max_limbs = max_bits / cpp_int_backend::limb_bits
+      + (max_bits % cpp_int_backend::limb_bits ? 1 : 0);
+   */
+
+   unsigned ors = result.size();
+   if((ors == 1) && (!*result.limbs()))
+      return; // shifting zero yields zero.
+   unsigned rs = ors;
+   if(shift && (result.limbs()[ors - 1] >> (cpp_int_backend::limb_bits - shift)))
+      ++rs; // Most significant limb will overflow when shifted
+   rs += offset;
+   result.resize(rs, rs);
+   bool truncated = result.size() != rs;
+   if(truncated)
+      rs = result.size();
+   typename cpp_int_backend::limb_pointer pr = result.limbs();
+
+   if(offset > rs)
+   {
+      // The result is shifted past the end of the result:
+      result = static_cast(0);
+      return;
+   }
+
+   unsigned i = 0;
+   if(shift)
+   {
+      // This code only works when shift is non-zero, otherwise we invoke undefined behaviour!
+      i = 0;
+      if(!truncated)
+      {
+         if(rs > ors + offset)
+         {
+            pr[rs - 1 - i] = pr[ors - 1 - i] >> (cpp_int_backend::limb_bits - shift);
+            --rs;
+         }
+         else
+         {
+            pr[rs - 1 - i] = pr[ors - 1 - i] << shift;
+            if(ors > 1)
+               pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift);
+            ++i;
+         }
+      }
+      for(; ors > 1 + i; ++i)
+      {
+         pr[rs - 1 - i] = pr[ors - 1 - i] << shift;
+         pr[rs - 1 - i] |= pr[ors - 2 - i] >> (cpp_int_backend::limb_bits - shift);
+      }
+      if(ors >= 1 + i)
+      {
+         pr[rs - 1 - i] = pr[ors - 1 - i] << shift;
+         ++i;
+      }
+      for(; i < rs; ++i)
+         pr[rs - 1 - i] = 0;
+   }
+   else
+   {
+      for(; i < ors; ++i)
+         pr[rs - 1 - i] = pr[ors - 1 - i];
+      for(; i < rs; ++i)
+         pr[rs - 1 - i] = 0;
+   }
+   //
+   // We may have shifted off the end and have leading zeros:
+   //
+   if(truncated)
+   {
+      result.normalize();
+   }
+}
+
+template 
+inline typename enable_if_c >::value>::type
+   eval_right_shift(
+      cpp_int_backend& result, 
+      double_limb_type s) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(!s)
+      return;
+
+   limb_type offset = static_cast(s / cpp_int_backend::limb_bits);
+   limb_type shift  = static_cast(s % cpp_int_backend::limb_bits);
+   unsigned ors = result.size();
+   unsigned rs = ors;
+   if(offset >= rs)
+   {
+      result = limb_type(0);
+      return;
+   }
+   rs -= offset;
+   typename cpp_int_backend::limb_pointer pr = result.limbs();
+   if((pr[ors - 1] >> shift) == 0)
+      --rs;
+   if(rs == 0)
+   {
+      result = limb_type(0);
+      return;
+   }
+   unsigned i = 0;
+   if(shift)
+   {
+      // This code only works for non-zero shift, otherwise we invoke undefined behaviour!
+      for(; i + offset + 1 < ors; ++i)
+      {
+         pr[i] = pr[i + offset] >> shift;
+         pr[i] |= pr[i + offset + 1] << (cpp_int_backend::limb_bits - shift);
+      }
+      pr[i] = pr[i + offset] >> shift;
+   }
+   else
+   {
+      for(; i < rs; ++i)
+         pr[i] = pr[i + offset];
+   }
+   result.resize(rs, rs);
+}
+
+//
+// Over agin for trivial cpp_int's:
+//
+template 
+BOOST_FORCEINLINE typename enable_if > >::type 
+   eval_left_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   *result.limbs() = detail::checked_left_shift(*result.limbs(), s, typename cpp_int_backend::checked_type());
+   result.normalize();
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if > >::type 
+   eval_right_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   // Nothing to check here... just make sure we don't invoke undefined behavior:
+   *result.limbs() = (static_cast(s) >= sizeof(*result.limbs()) * CHAR_BIT) ? 0 : *result.limbs() >>= s;
+}
+
+template 
+void is_valid_bitwise_op(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o, const mpl::int_&)
+{
+   if(result.sign() || o.sign())
+      BOOST_THROW_EXCEPTION(std::range_error("Bitwise operations on negative values results in undefined behavior."));
+}
+
+template 
+void is_valid_bitwise_op(
+      cpp_int_backend&, 
+      const cpp_int_backend& , const mpl::int_&){}
+
+template 
+inline typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && (is_signed_number >::value || is_signed_number >::value)
+         >::type 
+   eval_bitwise_and(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   is_valid_bitwise_op(result, o, typename cpp_int_backend::checked_type());
+
+   using default_ops::eval_bit_test;
+   using default_ops::eval_increment;
+
+   if(result.sign() || o.sign())
+   {
+      static const unsigned m = static_unsigned_max::value, static_unsigned_max::value>::value;
+      cpp_int_backend t1(result);
+      cpp_int_backend t2(o);
+      eval_bitwise_and(t1, t2);
+      bool s = eval_bit_test(t1, m + 1);
+      if(s)
+      {
+         eval_complement(t1, t1);
+         eval_increment(t1);
+      }
+      result = t1;
+      result.sign(s);
+   }
+   else
+   {
+      *result.limbs() &= *o.limbs();
+   }
+}
+
+template 
+inline typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
+         >::type 
+   eval_bitwise_and(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   *result.limbs() &= *o.limbs();
+}
+
+template 
+inline typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && (is_signed_number >::value || is_signed_number >::value)
+         >::type 
+   eval_bitwise_or(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   is_valid_bitwise_op(result, o, typename cpp_int_backend::checked_type());
+
+   using default_ops::eval_bit_test;
+   using default_ops::eval_increment;
+
+   if(result.sign() || o.sign())
+   {
+      static const unsigned m = static_unsigned_max::value, static_unsigned_max::value>::value;
+      cpp_int_backend t1(result);
+      cpp_int_backend t2(o);
+      eval_bitwise_or(t1, t2);
+      bool s = eval_bit_test(t1, m + 1);
+      if(s)
+      {
+         eval_complement(t1, t1);
+         eval_increment(t1);
+      }
+      result = t1;
+      result.sign(s);
+   }
+   else
+   {
+      *result.limbs() |= *o.limbs();
+      result.normalize();
+   }
+}
+
+template 
+inline typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
+         >::type 
+   eval_bitwise_or(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   *result.limbs() |= *o.limbs();
+}
+
+template 
+inline typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && (is_signed_number >::value || is_signed_number >::value)
+         >::type 
+   eval_bitwise_xor(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   is_valid_bitwise_op(result, o, typename cpp_int_backend::checked_type());
+
+   using default_ops::eval_bit_test;
+   using default_ops::eval_increment;
+
+   if(result.sign() || o.sign())
+   {
+      static const unsigned m = static_unsigned_max::value, static_unsigned_max::value>::value;
+      cpp_int_backend t1(result);
+      cpp_int_backend t2(o);
+      eval_bitwise_xor(t1, t2);
+      bool s = eval_bit_test(t1, m + 1);
+      if(s)
+      {
+         eval_complement(t1, t1);
+         eval_increment(t1);
+      }
+      result = t1;
+      result.sign(s);
+   }
+   else
+   {
+      *result.limbs() ^= *o.limbs();
+   }
+}
+
+template 
+inline typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
+         >::type 
+   eval_bitwise_xor(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   *result.limbs() ^= *o.limbs();
+}
+
+template 
+inline typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && (is_signed_number >::value || is_signed_number >::value)
+         >::type 
+   eval_complement(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   BOOST_STATIC_ASSERT_MSG(((Checked1 != checked) || (Checked2 != checked)), "Attempt to take the complement of a signed type results in undefined behavior.");
+   //
+   // If we're not checked then emulate 2's complement behavior:
+   //
+   if(o.sign())
+   {
+      *result.limbs() = *o.limbs() - 1;
+      result.sign(false);
+   }
+   else
+   {
+      *result.limbs() = 1 + *o.limbs();
+      result.sign(true);
+   }
+   result.normalize();
+}
+
+template 
+inline typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
+         >::type 
+   eval_complement(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   *result.limbs() = ~*o.limbs();
+}
+
+}}} // namespaces
+
+#endif
diff --git a/include/boost/multiprecision/cpp_int/checked.hpp b/include/boost/multiprecision/cpp_int/checked.hpp
new file mode 100644
index 00000000..a3eb5dcc
--- /dev/null
+++ b/include/boost/multiprecision/cpp_int/checked.hpp
@@ -0,0 +1,149 @@
+
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifndef BOOST_MP_CPP_INT_CHECKED_HPP
+#define BOOST_MP_CPP_INT_CHECKED_HPP
+
+namespace boost{ namespace multiprecision{ namespace backends{ namespace detail{
+
+//
+// Simple routines for performing checked arithmetic with a builtin arithmetic type.
+// Note that is is not a complete header, it must be included as part of boost/multiprecision/cpp_int.hpp.
+//
+
+inline void raise_overflow(std::string op)
+{
+   BOOST_THROW_EXCEPTION(std::overflow_error("overflow in " + op));
+}
+inline void raise_add_overflow()
+{
+   raise_overflow("addition");
+}
+inline void raise_subtract_overflow()
+{
+   raise_overflow("subtraction");
+}
+inline void raise_mul_overflow()
+{
+   raise_overflow("multiplication");
+}
+inline void raise_div_overflow()
+{
+   raise_overflow("division");
+}
+
+template 
+inline A checked_add_imp(A a, A b, const mpl::true_&)
+{
+   if(a > 0)
+   {
+      if((b > 0) && ((integer_traits::const_max - b) < a))
+         raise_add_overflow();
+   }
+   else
+   {
+      if((b < 0) && ((integer_traits::const_min - b) > a))
+         raise_add_overflow();
+   }
+   return a + b;
+}
+template 
+inline A checked_add_imp(A a, A b, const mpl::false_&)
+{
+   if((integer_traits::const_max - b) < a)
+      raise_add_overflow();
+   return a + b;
+}
+template 
+inline A checked_add(A a, A b, const mpl::int_&)
+{
+   return checked_add_imp(a, b, boost::is_signed());
+}
+template 
+inline A checked_add(A a, A b, const mpl::int_&)
+{
+   return a + b;
+}
+
+template 
+inline A checked_subtract_imp(A a, A b, const mpl::true_&)
+{
+   if(a > 0)
+   {
+      if((b < 0) && ((integer_traits::const_max + b) < a))
+         raise_subtract_overflow();
+   }
+   else
+   {
+      if((b > 0) && ((integer_traits::const_min + b) > a))
+         raise_subtract_overflow();
+   }
+   return a - b;
+}
+template 
+inline A checked_subtract_imp(A a, A b, const mpl::false_&)
+{
+   if(a < b)
+      raise_subtract_overflow();
+   return a - b;
+}
+template 
+inline A checked_subtract(A a, A b, const mpl::int_&)
+{
+   return checked_subtract_imp(a, b, boost::is_signed());
+}
+template 
+inline A checked_subtract(A a, A b, const mpl::int_&)
+{
+   return a - b;
+}
+
+template 
+inline A checked_multiply(A a, A b, const mpl::int_&)
+{
+   BOOST_MP_USING_ABS
+   if(a && (integer_traits::const_max / abs(a) < abs(b)))
+      raise_mul_overflow();
+   return a * b;
+}
+template 
+inline A checked_multiply(A a, A b, const mpl::int_&)
+{
+   return a * b;
+}
+
+template 
+inline A checked_divide(A a, A b, const mpl::int_&)
+{
+   if(b == 0)
+      raise_div_overflow();
+   return a / b;
+}
+template 
+inline A checked_divide(A a, A b, const mpl::int_&)
+{
+   return a / b;
+}
+
+template 
+inline A checked_left_shift(A a, unsigned long long shift, const mpl::int_&)
+{
+   if(a && shift)
+   {
+      if((shift > sizeof(A) * CHAR_BIT) || (a >> (sizeof(A) * CHAR_BIT - shift)))
+         BOOST_THROW_EXCEPTION(std::overflow_error("Shift out of range"));
+   }
+   return a << shift;
+}
+template 
+inline A checked_left_shift(A a, unsigned long long shift, const mpl::int_&)
+{
+   return (shift >= sizeof(A) * CHAR_BIT) ? 0 : a << shift;
+}
+
+}}}} // namespaces
+
+#endif
+
diff --git a/include/boost/multiprecision/cpp_int/comparison.hpp b/include/boost/multiprecision/cpp_int/comparison.hpp
new file mode 100644
index 00000000..32d6a470
--- /dev/null
+++ b/include/boost/multiprecision/cpp_int/comparison.hpp
@@ -0,0 +1,389 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// Comparison operators for cpp_int_backend:
+//
+#ifndef BOOST_MP_CPP_INT_COMPARISON_HPP
+#define BOOST_MP_CPP_INT_COMPARISON_HPP
+
+#include 
+
+namespace boost{ namespace multiprecision{ namespace backends{
+
+#ifdef BOOST_MSVC
+#pragma warning(push)
+#pragma warning(disable:4018 4389)
+#endif
+
+//
+// Start with non-trivial cpp_int's:
+//
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value, 
+      bool
+   >::type 
+   eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+{
+   return (a.sign() == b.sign())
+      && (a.size() == b.size())
+      && std::equal(a.limbs(), a.limbs() + a.size(), b.limbs());
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value 
+      && !is_trivial_cpp_int >::value,
+      bool
+   >::type 
+   eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+{
+   return (a.sign() == b.sign())
+      && (a.size() == b.size())
+      && std::equal(a.limbs(), a.limbs() + a.size(), b.limbs());
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
+{
+   return (a.sign() == false)
+      && (a.size() == 1)
+      && (*a.limbs() == b);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_eq(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
+{
+   return (a.sign() == (b < 0))
+      && (a.size() == 1)
+      && (*a.limbs() == static_cast(std::abs(b)));
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_eq(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
+{
+   return (a.size() == 1)
+      && (*a.limbs() == b);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_eq(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
+{
+   return (b < 0) ? eval_eq(a, cpp_int_backend(b)) : eval_eq(a, static_cast(b)); // Use bit pattern of b for comparison
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_lt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
+{
+   if(a.sign())
+      return true;
+   if(a.size() > 1)
+      return false;
+   return *a.limbs() < b;
+}
+template 
+inline typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_lt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
+{
+   if((b == 0) || (a.sign() != (b < 0)))
+      return a.sign();
+   if(a.sign())
+   {
+      if(a.size() > 1)
+         return true;
+      return *a.limbs() > static_cast(std::abs(b));
+   }
+   else
+   {
+      if(a.size() > 1)
+         return false;
+      return *a.limbs() < static_cast(b);
+   }
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_lt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
+{
+   if(a.size() > 1)
+      return false;
+   return *a.limbs() < b;
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_lt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
+{
+   return (b < 0) ? a.compare(b) < 0 : eval_lt(a, static_cast(b)); // Use bit pattern of b for comparison
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_gt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
+{
+   if(a.sign())
+      return false;
+   if(a.size() > 1)
+      return true;
+   return *a.limbs() > b;
+}
+template 
+inline typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_gt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
+{
+   if(b == 0)
+      return !a.sign() && ((a.size() > 1) || *a.limbs());
+   if(a.sign() != (b < 0))
+      return !a.sign();
+   if(a.sign())
+   {
+      if(a.size() > 1)
+         return false;
+      return *a.limbs() < static_cast(std::abs(b));
+   }
+   else
+   {
+      if(a.size() > 1)
+         return true;
+      return *a.limbs() > static_cast(b);
+   }
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_gt(const cpp_int_backend& a, limb_type b) BOOST_NOEXCEPT
+{
+   if(a.size() > 1)
+      return true;
+   return *a.limbs() > b;
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      !is_trivial_cpp_int >::value,
+      bool
+   >::type eval_gt(const cpp_int_backend& a, signed_limb_type b) BOOST_NOEXCEPT
+{
+   return (b < 0) ? a.compare(b) > 0 : eval_gt(a, static_cast(b)); // Use bit pattern of b for comparison.
+}
+//
+// And again for trivial cpp_ints:
+//
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_trivial_cpp_int >::value, 
+      bool
+   >::value eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+{
+   return (a.sign() == b.sign()) && (*a.limbs() == *b.limbs());
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_trivial_cpp_int >::value, 
+      bool
+   >::value eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+{
+   return *a.limbs() == *b.limbs();
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_unsigned::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_eq(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+{
+   return !a.sign() && (*a.limbs() == b);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_signed::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_eq(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+{
+   typedef typename make_unsigned::type ui_type;
+   return (a.sign() == (b < 0)) && (*a.limbs() == static_cast(std::abs(b)));
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_unsigned::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_eq(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+{
+   return *a.limbs() == b;
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_signed::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_eq(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+{
+   typedef typename make_unsigned::type ui_type;
+   if(b < 0)
+   {
+      cpp_int_backend t(b);
+      return *a.limbs() == *t.limbs();
+   }
+   else
+   {
+      return *a.limbs() == static_cast(b);
+   }
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_trivial_cpp_int >::value,
+      bool
+   >::type eval_lt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+{
+   if(a.sign() != b.sign())
+      return a.sign();
+   return a.sign() ? *a.limbs() > *b.limbs() : *a.limbs() < *b.limbs();
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_trivial_cpp_int >::value,
+      bool
+   >::type eval_lt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+{
+   return *a.limbs() < *b.limbs();
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_unsigned::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_lt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+{
+   if(a.sign())
+      return true;
+   return *a.limbs() < b;
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_signed::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_lt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+{
+   typedef typename make_unsigned::type ui_type;
+   if(a.sign() != (b < 0))
+      return a.sign();
+   return a.sign() ? (*a.limbs() > static_cast(std::abs(b))) : (*a.limbs() < static_cast(std::abs(b)));
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_unsigned::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_lt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+{
+   return *a.limbs() < b;
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_signed::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_lt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+{
+   typedef typename make_unsigned::type ui_type;
+   if(b < 0)
+   {
+      cpp_int_backend t(b);
+      return *a.limbs() < *t.limbs();
+   }
+   else
+   {
+      return *a.limbs() < static_cast(b);
+   }
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_trivial_cpp_int >::value,
+      bool
+   >::type eval_gt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+{
+   if(a.sign() != b.sign())
+      return !a.sign();
+   return a.sign() ? *a.limbs() < *b.limbs() : *a.limbs() > *b.limbs();
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_trivial_cpp_int >::value,
+      bool
+   >::type eval_gt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+{
+   return *a.limbs() > *b.limbs();
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_unsigned::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_gt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+{
+   if(a.sign())
+      return false;
+   return *a.limbs() > b;
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_signed::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_gt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+{
+   typedef typename make_unsigned::type ui_type;
+   if(a.sign() != (b < 0))
+      return !a.sign();
+   return a.sign() ? (*a.limbs() < static_cast(std::abs(b))) : (*a.limbs() > static_cast(std::abs(b)));
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_unsigned::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_gt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+{
+   return *a.limbs() > b;
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+      is_signed::value && is_trivial_cpp_int >::value, 
+      bool
+   >::type eval_gt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+{
+   typedef typename make_unsigned::type ui_type;
+   if(b < 0)
+   {
+      cpp_int_backend t(b);
+      return *a.limbs() > *t.limbs();
+   }
+   else
+   {
+      return *a.limbs() > static_cast(b);
+   }
+}
+
+#ifdef BOOST_MSVC
+#pragma warning(pop)
+#endif
+
+}}} // namespaces
+
+#endif
diff --git a/include/boost/multiprecision/cpp_int/cpp_int_config.hpp b/include/boost/multiprecision/cpp_int/cpp_int_config.hpp
new file mode 100644
index 00000000..2e829312
--- /dev/null
+++ b/include/boost/multiprecision/cpp_int/cpp_int_config.hpp
@@ -0,0 +1,156 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+#ifndef BOOST_MP_CPP_INT_CORE_HPP
+#define BOOST_MP_CPP_INT_CORE_HPP
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+
+namespace boost{ namespace multiprecision{
+
+namespace detail{
+
+//
+// These traits calculate the largest type in the list
+// [unsigned] ong long, long, int, which has the specified number
+// of bits.  Note that intN_t and boost::int_t find the first
+// member of the above list, not the last.  We want the last in the 
+// list to ensure that mixed arithmetic operations are as efficient 
+// as possible.
+//
+template 
+struct largest_signed_type
+{
+   typedef typename mpl::if_c<
+      1 + std::numeric_limits::digits == N,
+      long long,
+      typename mpl::if_c<
+         1 + std::numeric_limits::digits == N,
+         long,
+         typename mpl::if_c<
+            1 + std::numeric_limits::digits == N,
+            int,
+            typename boost::int_t::exact
+         >::type
+      >::type
+   >::type type;
+};
+
+template 
+struct largest_unsigned_type
+{
+   typedef typename mpl::if_c<
+      std::numeric_limits::digits == N,
+      unsigned long long,
+      typename mpl::if_c<
+         std::numeric_limits::digits == N,
+         unsigned long,
+         typename mpl::if_c<
+            std::numeric_limits::digits == N,
+            unsigned int,
+            typename boost::uint_t::exact
+         >::type
+      >::type
+   >::type type;
+};
+
+} // namepsace detail
+
+#if defined(__GNUC__) && ((__GNUC__ > 4) || ((__GNUC__ == 4) && (__GNUC_MINOR__ >= 6))) \
+   && !defined(BOOST_INTEL) && defined(__WORDSIZE) && (__WORDSIZE == 64)
+
+typedef detail::largest_unsigned_type<64>::type limb_type;
+typedef detail::largest_signed_type<64>::type signed_limb_type;
+typedef unsigned __int128 double_limb_type;
+typedef __int128 signed_double_limb_type;
+static const limb_type max_block_10 = 1000000000000000000uLL;
+static const limb_type digits_per_block_10 = 18;
+
+inline limb_type block_multiplier(unsigned count)
+{
+   static const limb_type values[digits_per_block_10] 
+      = { 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000 };
+   BOOST_ASSERT(count < digits_per_block_10);
+   return values[count];
+}
+
+// Can't do formatted IO on an __int128
+#define BOOST_MP_NO_DOUBLE_LIMB_TYPE_IO
+
+// Need to specialise integer_traits for __int128 as it's not a normal native type:
+} // namespace multiprecision
+
+template<>
+class integer_traits
+  : public std::numeric_limits,
+    public detail::integer_traits_base(0)>
+{ };
+template<>
+class integer_traits
+  : public std::numeric_limits,
+    public detail::integer_traits_base(static_cast(1) << 127), static_cast((~static_cast(0)) >> 1)>
+{ };
+
+namespace multiprecision{
+
+#else
+
+typedef detail::largest_unsigned_type<32>::type limb_type;
+typedef detail::largest_signed_type<32>::type signed_limb_type;
+typedef boost::uint64_t double_limb_type;
+typedef boost::int64_t signed_double_limb_type;
+static const limb_type max_block_10 = 1000000000;
+static const limb_type digits_per_block_10 = 9;
+
+inline limb_type block_multiplier(unsigned count)
+{
+   static const limb_type values[digits_per_block_10] 
+      = { 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 };
+   BOOST_ASSERT(count < digits_per_block_10);
+   return values[count];
+}
+
+#endif
+
+static const unsigned bits_per_limb = sizeof(limb_type) * CHAR_BIT;
+
+template 
+inline void minmax(const T& a, const T& b, T& aa, T& bb)
+{
+   if(a < b)
+   {
+      aa = a;
+      bb = b;
+   }
+   else
+   {
+      aa = b;
+      bb = a;
+   }
+}
+
+enum cpp_integer_type
+{
+   signed_magnitude,
+   unsigned_magnitude,
+   signed_packed,
+   unsigned_packed
+};
+
+enum cpp_int_check_type
+{
+   checked,
+   unchecked
+};
+
+}}
+
+#endif // BOOST_MP_CPP_INT_CORE_HPP
+
diff --git a/include/boost/multiprecision/cpp_int/divide.hpp b/include/boost/multiprecision/cpp_int/divide.hpp
new file mode 100644
index 00000000..5e1534e6
--- /dev/null
+++ b/include/boost/multiprecision/cpp_int/divide.hpp
@@ -0,0 +1,618 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// Comparison operators for cpp_int_backend:
+//
+#ifndef BOOST_MP_CPP_INT_DIV_HPP
+#define BOOST_MP_CPP_INT_DIV_HPP
+
+namespace boost{ namespace multiprecision{ namespace backends{
+
+template 
+void divide_unsigned_helper(
+   CppInt1* result, 
+   const CppInt2& x, 
+   const CppInt3& y, 
+   CppInt1& r)
+{
+   if(((void*)result == (void*)&x) || ((void*)&r == (void*)&x))
+   {
+      CppInt2 t(x);
+      divide_unsigned_helper(result, t, y, r);
+      return;
+   }
+   if(((void*)result == (void*)&y) || ((void*)&r == (void*)&y))
+   {
+      CppInt3 t(y);
+      divide_unsigned_helper(result, x, t, r);
+      return;
+   }
+
+   /*
+    Very simple, fairly braindead long division.
+    Start by setting the remainder equal to x, and the
+    result equal to 0.  Then in each loop we calculate our
+    "best guess" for how many times y divides into r,
+    add our guess to the result, and subtract guess*y
+    from the remainder r.  One wrinkle is that the remainder
+    may go negative, in which case we subtract the current guess
+    from the result rather than adding.  The value of the guess
+    is determined by dividing the most-significant-limb of the
+    current remainder by the most-significant-limb of y.
+
+    Note that there are more efficient algorithms than this
+    available, in particular see Knuth Vol 2.  However for small
+    numbers of limbs this generally outperforms the alternatives
+    and avoids the normalisation step which would require extra storage.
+    */
+
+
+   using default_ops::eval_subtract;
+
+   if(result == &r)
+   {
+      CppInt1 rem;
+      divide_unsigned_helper(result, x, y, rem);
+      r = rem;
+      return;
+   }
+
+   //
+   // Find the most significant words of numerator and denominator.
+   //
+   limb_type y_order = y.size() - 1;
+
+   if(y_order == 0)
+   {
+      //
+      // Only a single non-zero limb in the denominator, in this case
+      // we can use a specialized divide-by-single-limb routine which is
+      // much faster.  This also handles division by zero:
+      //
+      divide_unsigned_helper(result, x, y.limbs()[y_order], r);
+      return;
+   }
+
+   typename CppInt2::const_limb_pointer px = x.limbs();
+   typename CppInt3::const_limb_pointer py = y.limbs();
+
+   limb_type r_order = x.size() - 1;
+   if((r_order == 0) && (*px == 0))
+   {
+      // x is zero, so is the result:
+      r = y;
+      if(result)
+         *result = x;
+      return;
+   }
+
+   r = x;
+   r.sign(false);
+   if(result)
+      *result = static_cast(0u);
+   //
+   // Check if the remainder is already less than the divisor, if so
+   // we already have the result.  Note we try and avoid a full compare
+   // if we can:
+   //
+   if(r_order <= y_order)
+   {
+      if((r_order < y_order) || (r.compare_unsigned(y) < 0))
+      {
+         return;
+      }
+   }
+
+   CppInt1 t;
+   bool r_neg = false;
+
+   //
+   // See if we can short-circuit long division, and use basic arithmetic instead:
+   //
+   if(r_order == 0)
+   {
+      if(result)
+         *result = px[0] / py[0];
+      r = px[0] % py[0];
+      return;
+   }
+   else if(r_order == 1)
+   {
+      double_limb_type a, b;
+      a = (static_cast(px[1]) << CppInt1::limb_bits) | px[0];
+      b = y_order ? 
+         (static_cast(py[1]) << CppInt1::limb_bits) | py[0] 
+         : py[0];
+      if(result)
+         *result = a / b;
+      r = a % b;
+      return;
+   }
+   //
+   // prepare result:
+   //
+   if(result)
+      result->resize(1 + r_order - y_order, 1 + r_order - y_order);
+   typename CppInt1::const_limb_pointer prem = r.limbs();
+   // This is initialised just to keep the compiler from emitting useless warnings later on:
+   typename CppInt1::limb_pointer pr 
+      = typename CppInt1::limb_pointer();
+   if(result)
+   {
+      pr = result->limbs();
+      for(unsigned i = 1; i < 1 + r_order - y_order; ++i)
+         pr[i] = 0;
+   }
+   bool first_pass = true;
+
+   do
+   {
+      //
+      // Calculate our best guess for how many times y divides into r:
+      //
+      limb_type guess;
+      if((prem[r_order] <= py[y_order]) && (r_order > 0))
+      {
+         double_limb_type a, b, v;
+         a = (static_cast(prem[r_order]) << CppInt1::limb_bits) | prem[r_order - 1];
+         b = py[y_order];
+         v = a / b;
+         if(v > CppInt1::max_limb_value)
+            guess = 1;
+         else
+         {
+            guess = static_cast(v);
+            --r_order;
+         }
+      }
+      else if(r_order == 0)
+      {
+         guess = prem[0] / py[y_order];
+      }
+      else
+      {
+         double_limb_type a, b, v;
+         a = (static_cast(prem[r_order]) << CppInt1::limb_bits) | prem[r_order - 1];
+         b = (y_order > 0) ? (static_cast(py[y_order]) << CppInt1::limb_bits) | py[y_order - 1] : (static_cast(py[y_order])  << CppInt1::limb_bits);
+         v = a / b;
+         guess = static_cast(v);
+      }
+      BOOST_ASSERT(guess); // If the guess ever gets to zero we go on forever....
+      //
+      // Update result:
+      //
+      limb_type shift = r_order - y_order;
+      if(result)
+      {
+         if(r_neg)
+         {
+            if(pr[shift] > guess)
+               pr[shift] -= guess;
+            else
+            {
+               t.resize(shift + 1, shift + 1);
+               t.limbs()[shift] = guess;
+               for(unsigned i = 0; i < shift; ++i)
+                  t.limbs()[i] = 0;
+               eval_subtract(*result, t);
+            }
+         }
+         else if(CppInt1::max_limb_value - pr[shift] > guess)
+            pr[shift] += guess;
+         else
+         {
+            t.resize(shift + 1, shift + 1);
+            t.limbs()[shift] = guess;
+            for(unsigned i = 0; i < shift; ++i)
+               t.limbs()[i] = 0;
+            eval_add(*result, t);
+         }
+      }
+      //
+      // Calculate guess * y, we use a fused mutiply-shift O(N) for this
+      // rather than a full O(N^2) multiply:
+      //
+      double_limb_type carry = 0;
+      t.resize(y.size() + shift + 1, y.size() + shift + 1);
+      bool truncated_t = !CppInt1::variable && (t.size() != y.size() + shift + 1);
+      typename CppInt1::limb_pointer pt = t.limbs();
+      for(unsigned i = 0; i < shift; ++i)
+         pt[i] = 0;
+      for(unsigned i = 0; i < y.size(); ++i)
+      {
+         carry += static_cast(py[i]) * static_cast(guess);
+         pt[i + shift] = static_cast(carry);
+         carry >>= CppInt1::limb_bits;
+      }
+      if(carry && !truncated_t)
+      {
+         pt[t.size() - 1] = static_cast(carry);
+      }
+      else if(!truncated_t)
+      {
+         t.resize(t.size() - 1, t.size() - 1);
+      }
+      //
+      // Update r:
+      //
+      eval_subtract(r, t);
+      if(r.isneg())
+      {
+         r.negate();
+         r_neg = !r_neg;
+      }
+      //
+      // First time through we need to strip any leading zero, otherwise
+      // the termination condition goes belly-up:
+      //
+      if(result && first_pass)
+      {
+         first_pass = false;
+         while(pr[result->size() - 1] == 0)
+            result->resize(result->size() - 1, result->size() - 1);
+      }
+      //
+      // Update r_order:
+      //
+      r_order = r.size() - 1;
+      if(r_order < y_order)
+         break;
+   }
+   // Termination condition is really just a check that r > y, but with a common
+   // short-circuit case handled first:
+   while((r_order > y_order) || (r.compare_unsigned(y) >= 0));
+
+   //
+   // We now just have to normalise the result:
+   //
+   if(r_neg && eval_get_sign(r))
+   {
+      // We have one too many in the result:
+      if(result)
+         eval_decrement(*result);
+      r.negate();
+      if(y.sign())
+         eval_subtract(r, y);
+      else
+         eval_add(r, y);
+   }
+
+   BOOST_ASSERT(r.compare_unsigned(y) < 0); // remainder must be less than the divisor or our code has failed
+}
+
+template 
+void divide_unsigned_helper(
+   CppInt1* result, 
+   const CppInt2& x, 
+   limb_type y, 
+   CppInt1& r)
+{
+   if(((void*)result == (void*)&x) || ((void*)&r == (void*)&x))
+   {
+      CppInt2 t(x);
+      divide_unsigned_helper(result, t, y, r);
+      return;
+   }
+
+   if(result == &r)
+   {
+      CppInt1 rem;
+      divide_unsigned_helper(result, x, y, rem);
+      r = rem;
+      return;
+   }
+
+   // As above, but simplified for integer divisor:
+
+   using default_ops::eval_subtract;
+
+   if(y == 0)
+   {
+      BOOST_THROW_EXCEPTION(std::overflow_error("Integer Division by zero."));
+   }
+   //
+   // Find the most significant word of numerator.
+   //
+   limb_type r_order = x.size() - 1;
+
+   //
+   // Set remainder and result to their initial values:
+   //
+   r = x;
+   r.sign(false);
+   typename CppInt1::limb_pointer pr = r.limbs();
+
+   if((r_order == 0) && (*pr == 0))
+   {
+      // All the limbs in x are zero, so is the result:
+      return;
+   }
+   //
+   // check for x < y, try to do this without actually having to 
+   // do a full comparison:
+   //
+   if((r_order == 0) && (*pr < y))
+   {
+      if(result)
+         *result = static_cast(0u);
+      return;
+   }
+
+   //
+   // See if we can short-circuit long division, and use basic arithmetic instead:
+   //
+   if(r_order == 0)
+   {
+      if(result)
+      {
+         *result = *pr / y;
+         result->sign(x.sign());
+      }
+      *pr %= y;
+      r.sign(x.sign());
+      return;
+   }
+   else if(r_order == 1)
+   {
+      double_limb_type a;
+      a = (static_cast(pr[r_order]) << CppInt1::limb_bits) | pr[0];
+      if(result)
+      {
+         *result = a / y;
+         result->sign(x.sign());
+      }
+      r = a % y;
+      r.sign(x.sign());
+      return;
+   }
+
+   // This is initialised just to keep the compiler from emitting useless warnings later on:
+   typename CppInt1::limb_pointer pres = typename CppInt1::limb_pointer();
+   if(result)
+   {
+      result->resize(r_order + 1, r_order + 1);
+      pres = result->limbs();
+      if(result->size() > r_order)
+         pres[r_order] = 0;  // just in case we don't set the most significant limb below.
+   }
+
+   do
+   {
+      //
+      // Calculate our best guess for how many times y divides into r:
+      //
+      if((pr[r_order] < y) && r_order)
+      {
+         double_limb_type a, b;
+         a = (static_cast(pr[r_order]) << CppInt1::limb_bits) | pr[r_order - 1];
+         b = a % y;
+         r.resize(r.size() - 1, r.size() - 1);
+         --r_order;
+         pr[r_order] = static_cast(b);
+         if(result)
+            pres[r_order] = static_cast(a / y);
+         if(r_order && pr[r_order] == 0)
+         {
+            --r_order;  // No remainder, division was exact.
+            r.resize(r.size() - 1, r.size() - 1);
+            if(result)
+               pres[r_order] = static_cast(0u);
+         }
+      }
+      else
+      {
+         if(result)
+            pres[r_order] = pr[r_order] / y;
+         pr[r_order] %= y;
+         if(r_order && pr[r_order] == 0)
+         {
+            --r_order;  // No remainder, division was exact.
+            r.resize(r.size() - 1, r.size() - 1);
+            if(result)
+               pres[r_order] = static_cast(0u);
+         }
+      }
+   }
+   // Termination condition is really just a check that r > y, but with two common
+   // short-circuit cases handled first:
+   while(r_order || (pr[r_order] > y));
+
+   if(result)
+   {
+      result->normalize();
+      result->sign(x.sign());
+   }
+   r.normalize();
+   r.sign(x.sign());
+
+   BOOST_ASSERT(r.compare(y) < 0); // remainder must be less than the divisor or our code has failed
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type 
+   eval_divide(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const cpp_int_backend& b)
+{
+   cpp_int_backend r;
+   divide_unsigned_helper(&result, a, b, r);
+   result.sign(a.sign() != b.sign());
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_divide(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      limb_type& b)
+{
+   cpp_int_backend r;
+   divide_unsigned_helper(&result, a, b, r);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_divide(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      signed_limb_type& b)
+{
+   cpp_int_backend r;
+   divide_unsigned_helper(&result, a, static_cast(std::abs(b)), r);
+   if(b < 0)
+      result.negate();
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_divide(
+      cpp_int_backend& result, 
+      const cpp_int_backend& b)
+{
+   // There is no in place divide:
+   cpp_int_backend a(result);
+   eval_divide(result, a, b);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_divide(
+      cpp_int_backend& result, 
+      limb_type b)
+{
+   // There is no in place divide:
+   cpp_int_backend a(result);
+   eval_divide(result, a, b);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_divide(
+      cpp_int_backend& result, 
+      signed_limb_type b)
+{
+   // There is no in place divide:
+   cpp_int_backend a(result);
+   eval_divide(result, a, b);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type
+   eval_modulus(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const cpp_int_backend& b)
+{
+   divide_unsigned_helper(static_cast* >(0), a, b, result);
+   result.sign(a.sign());
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_modulus(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, limb_type b)
+{
+   divide_unsigned_helper(static_cast* >(0), a, b, result);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_modulus(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      signed_limb_type b)
+{
+   divide_unsigned_helper(static_cast* >(0), a, static_cast(std::abs(b)), result);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_modulus(
+      cpp_int_backend& result, 
+      const cpp_int_backend& b)
+{
+   // There is no in place divide:
+   cpp_int_backend a(result);
+   eval_modulus(result, a, b);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_modulus(
+      cpp_int_backend& result, 
+      limb_type b)
+{
+   // There is no in place divide:
+   cpp_int_backend a(result);
+   eval_modulus(result, a, b);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_modulus(
+      cpp_int_backend& result, 
+      signed_limb_type b)
+{
+   // There is no in place divide:
+   cpp_int_backend a(result);
+   eval_modulus(result, a, b);
+}
+
+//
+// Over again for trivial cpp_int's:
+//
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && (is_signed_number >::value 
+            || is_signed_number >::value)
+         >::type 
+   eval_divide(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o)
+{
+   if(!*o.limbs())
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   *result.limbs() /= *o.limbs();
+   result.sign(result.sign() != o.sign());
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
+      >::type 
+   eval_divide(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o)
+{
+   if(!*o.limbs())
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   *result.limbs() /= *o.limbs();
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+      >::type 
+   eval_modulus(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o)
+{
+   if(!*o.limbs())
+      BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
+   *result.limbs() %= *o.limbs();
+   result.sign(result.sign());
+}
+
+}}} // namespaces
+
+#endif
diff --git a/include/boost/multiprecision/cpp_int/limits.hpp b/include/boost/multiprecision/cpp_int/limits.hpp
new file mode 100644
index 00000000..0f80fccc
--- /dev/null
+++ b/include/boost/multiprecision/cpp_int/limits.hpp
@@ -0,0 +1,215 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// Comparison operators for cpp_int_backend:
+//
+#ifndef BOOST_MP_CPP_INT_LIM_HPP
+#define BOOST_MP_CPP_INT_LIM_HPP
+
+namespace std{
+
+namespace detail{
+
+template 
+inline boost::multiprecision::number, ExpressionTemplates>
+   get_min(const boost::mpl::true_&, const boost::mpl::true_&)
+{
+   // Bounded and signed.
+   typedef boost::multiprecision::number, ExpressionTemplates> result_type;
+   typedef boost::multiprecision::number, ExpressionTemplates> ui_type;
+   static const result_type val = -result_type(~ui_type(0));
+   return val;
+}
+
+template 
+inline boost::multiprecision::number, ExpressionTemplates>
+   get_min(const boost::mpl::true_&, const boost::mpl::false_&)
+{
+   // Bounded and unsigned:
+   static const boost::multiprecision::number, ExpressionTemplates> val(0u);
+   return val;
+}
+
+template 
+inline boost::multiprecision::number, ExpressionTemplates>
+   get_min(const boost::mpl::false_&, const boost::mpl::true_&)
+{
+   // Unbounded and signed.
+   // There is no minimum value, just return 0:
+   static const boost::multiprecision::number, ExpressionTemplates> val(0u);
+   return val;
+}
+
+template 
+inline boost::multiprecision::number, ExpressionTemplates>
+   get_min(const boost::mpl::false_&, const boost::mpl::false_&)
+{
+   // Unbound and unsigned:
+   static const boost::multiprecision::number, ExpressionTemplates> val(0u);
+   return val;
+}
+
+template 
+inline boost::multiprecision::number, ExpressionTemplates>
+   get_max(const boost::mpl::true_&, const boost::mpl::true_&)
+{
+   // Bounded and signed.
+   typedef boost::multiprecision::number, ExpressionTemplates> result_type;
+   typedef boost::multiprecision::number, ExpressionTemplates> ui_type;
+   static const result_type val = ~ui_type(0);
+   return val;
+}
+
+template 
+inline boost::multiprecision::number, ExpressionTemplates>
+   get_max(const boost::mpl::true_&, const boost::mpl::false_&)
+{
+   // Bound and unsigned:
+   typedef boost::multiprecision::number, ExpressionTemplates> result_type;
+   static const result_type val = ~result_type(0);
+   return val;
+}
+
+template 
+inline boost::multiprecision::number, ExpressionTemplates>
+   get_max(const boost::mpl::false_&, const boost::mpl::true_&)
+{
+   // Unbounded and signed.
+   // There is no maximum value, just return 0:
+   static const boost::multiprecision::number, ExpressionTemplates> val(0u);
+   return val;
+}
+
+template 
+inline boost::multiprecision::number, ExpressionTemplates>
+   get_max(const boost::mpl::false_&, const boost::mpl::false_&)
+{
+   // Unbound and unsigned:
+   static const boost::multiprecision::number, ExpressionTemplates> val(0u);
+   return val;
+}
+
+}
+
+template 
+class numeric_limits, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::cpp_int_backend backend_type;
+   typedef boost::multiprecision::number number_type;
+
+   struct inititializer
+   {
+      inititializer()
+      {
+         (std::numeric_limits::max)();
+         (std::numeric_limits::min)();
+      }
+      void do_nothing()const{}
+   };
+
+   static const inititializer init;
+
+public:
+   BOOST_STATIC_CONSTEXPR bool is_specialized = true;
+   //
+   // Largest and smallest numbers are bounded only by available memory, set
+   // to zero:
+   //
+   static number_type (min)() BOOST_NOEXCEPT
+   {
+      init.do_nothing();
+      return detail::get_min(boost::multiprecision::backends::is_fixed_precision(), boost::multiprecision::is_signed_number());
+   }
+   static number_type (max)() BOOST_NOEXCEPT 
+   { 
+      init.do_nothing();
+      return detail::get_max(boost::multiprecision::backends::is_fixed_precision(), boost::multiprecision::is_signed_number());
+   }
+   static number_type lowest() BOOST_NOEXCEPT { return (min)(); }
+   BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::backends::max_precision::value == UINT_MAX ? INT_MAX : boost::multiprecision::backends::max_precision::value;
+   BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L;
+   BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2;
+   BOOST_STATIC_CONSTEXPR bool is_signed = boost::multiprecision::is_signed_number::value;
+   BOOST_STATIC_CONSTEXPR bool is_integer = true;
+   BOOST_STATIC_CONSTEXPR bool is_exact = true;
+   BOOST_STATIC_CONSTEXPR int radix = 2;
+   static number_type epsilon() BOOST_NOEXCEPT { return 0; }
+   static number_type round_error() BOOST_NOEXCEPT { return 0; }
+   BOOST_STATIC_CONSTEXPR int min_exponent = 0;
+   BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
+   BOOST_STATIC_CONSTEXPR int max_exponent = 0;
+   BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
+   BOOST_STATIC_CONSTEXPR bool has_infinity = false;
+   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
+   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
+   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
+   BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
+   static number_type infinity() BOOST_NOEXCEPT { return 0; }
+   static number_type quiet_NaN() BOOST_NOEXCEPT { return 0; }
+   static number_type signaling_NaN() BOOST_NOEXCEPT { return 0; }
+   static number_type denorm_min() BOOST_NOEXCEPT { return 0; }
+   BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
+   BOOST_STATIC_CONSTEXPR bool is_bounded = boost::multiprecision::backends::is_fixed_precision::value;
+   BOOST_STATIC_CONSTEXPR bool is_modulo = (boost::multiprecision::backends::is_fixed_precision::value && (Checked == boost::multiprecision::unchecked));
+   BOOST_STATIC_CONSTEXPR bool traps = false;
+   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
+   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
+};
+
+template 
+const typename numeric_limits, ExpressionTemplates> >::inititializer numeric_limits, ExpressionTemplates> >::init;
+
+#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
+
+template 
+BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::digits;
+template 
+BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::digits10;
+template 
+BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::max_digits10;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_signed;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_integer;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_exact;
+template 
+BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::radix;
+template 
+BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::min_exponent;
+template 
+BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::min_exponent10;
+template 
+BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::max_exponent;
+template 
+BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates>  >::max_exponent10;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::has_infinity;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::has_quiet_NaN;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::has_signaling_NaN;
+template 
+BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates>  >::has_denorm;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::has_denorm_loss;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_iec559;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_bounded;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::is_modulo;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::traps;
+template 
+BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates>  >::tinyness_before;
+template 
+BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates>  >::round_style;
+
+#endif
+
+} // namespace std
+
+#endif
diff --git a/include/boost/multiprecision/cpp_int/misc.hpp b/include/boost/multiprecision/cpp_int/misc.hpp
new file mode 100644
index 00000000..cee2e386
--- /dev/null
+++ b/include/boost/multiprecision/cpp_int/misc.hpp
@@ -0,0 +1,301 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// Comparison operators for cpp_int_backend:
+//
+#ifndef BOOST_MP_CPP_INT_MISC_HPP
+#define BOOST_MP_CPP_INT_MISC_HPP
+
+namespace boost{ namespace multiprecision{ namespace backends{
+
+template 
+void check_in_range(const CppInt& val, const mpl::int_&)
+{
+   typedef typename boost::multiprecision::detail::canonical::type cast_type;
+   if(val.sign())
+   {
+      if(val.compare(static_cast((std::numeric_limits::min)())) < 0)
+         BOOST_THROW_EXCEPTION(std::overflow_error("Could not convert to the target type - -value is out of range."));
+   }
+   else
+   {
+      if(val.compare(static_cast((std::numeric_limits::max)())) > 0)
+         BOOST_THROW_EXCEPTION(std::overflow_error("Could not convert to the target type - -value is out of range."));
+   }
+}
+template 
+void check_in_range(const CppInt& /*val*/, const mpl::int_&) BOOST_NOEXCEPT {}
+
+void check_is_negative(const mpl::true_&) BOOST_NOEXCEPT {}
+void check_is_negative(const mpl::false_&)
+{
+   BOOST_THROW_EXCEPTION(std::domain_error("Attempt to assign a negative value to an unsigned type."));
+}
+
+template 
+inline Integer negate_integer(Integer i, const mpl::true_&) BOOST_NOEXCEPT
+{
+   return -i;
+}
+template 
+inline Integer negate_integer(Integer i, const mpl::false_&) BOOST_NOEXCEPT
+{
+   return ~(i-1);
+}
+
+template 
+inline typename enable_if_c::value && !is_trivial_cpp_int >::value, void>::type
+   eval_convert_to(R* result, const cpp_int_backend& backend) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   typedef mpl::int_ checked_type;
+   check_in_range(backend, checked_type());
+
+   *result = static_cast(backend.limbs()[0]);
+   unsigned shift = cpp_int_backend::limb_bits;
+   for(unsigned i = 1; (i < backend.size()) && (shift < static_cast(std::numeric_limits::digits)); ++i)
+   {
+      *result += static_cast(backend.limbs()[i]) << shift;
+      shift += cpp_int_backend::limb_bits;
+   }
+   if(backend.sign())
+   {
+      check_is_negative(boost::is_signed());
+      *result = negate_integer(*result, boost::is_signed());
+   }
+}
+
+template 
+inline typename enable_if_c::value && !is_trivial_cpp_int >::value, void>::type
+   eval_convert_to(R* result, const cpp_int_backend& backend) BOOST_NOEXCEPT
+{
+   typename cpp_int_backend::const_limb_pointer p = backend.limbs();
+   unsigned shift = cpp_int_backend::limb_bits;
+   *result = static_cast(*p);
+   for(unsigned i = 1; i < backend.size(); ++i)
+   {
+      *result += static_cast(std::ldexp(static_cast(p[i]), shift));
+      shift += cpp_int_backend::limb_bits;
+   }
+   if(backend.sign())
+      *result = -*result;
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value, bool>::type
+   eval_is_zero(const cpp_int_backend& val) BOOST_NOEXCEPT
+{
+   return (val.size() == 1) && (val.limbs()[0] == 0);
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value, int>::type
+   eval_get_sign(const cpp_int_backend& val) BOOST_NOEXCEPT
+{
+   return eval_is_zero(val) ? 0 : val.sign() ? -1 : 1;
+}
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type
+   eval_abs(cpp_int_backend& result, const cpp_int_backend& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   result = val;
+   result.sign(false);
+}
+
+//
+// Get the location of the least-significant-bit:
+//
+template 
+inline typename enable_if_c >::value, unsigned>::type
+   eval_lsb(const cpp_int_backend& a) BOOST_NOEXCEPT
+{
+   using default_ops::eval_get_sign;
+   BOOST_ASSERT(eval_get_sign(a) != 0);
+
+   unsigned result = 0;
+   //
+   // Find the index of the least significant limb that is non-zero:
+   //
+   unsigned index = 0;
+   while(!a.limbs()[index] && (index < a.size()))
+      ++index;
+   //
+   // Find the index of the least significant bit within that limb:
+   //
+   limb_type l = a.limbs()[index];
+   while(!(l & 1u))
+   {
+      l >>= 1;
+      ++result;
+   }
+
+   return result + index * cpp_int_backend::limb_bits;
+}
+
+template 
+inline typename enable_if_c >::value, bool>::type
+   eval_bit_test(const cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT
+{
+   unsigned offset = index / cpp_int_backend::limb_bits;
+   unsigned shift = index % cpp_int_backend::limb_bits;
+   limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
+   if(offset >= val.size())
+      return false;
+   return val.limbs()[offset] & mask ? true : false;
+}
+
+template 
+inline typename enable_if_c >::value>::type
+   eval_bit_set(cpp_int_backend& val, unsigned index)
+{
+   unsigned offset = index / cpp_int_backend::limb_bits;
+   unsigned shift = index % cpp_int_backend::limb_bits;
+   limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
+   if(offset >= val.size())
+   {
+      unsigned os = val.size();
+      val.resize(offset + 1, offset + 1);
+      if(offset >= val.size())
+         return;  // fixed precision overflow
+      for(unsigned i = os; i <= offset; ++i)
+         val.limbs()[i] = 0;
+   }
+   val.limbs()[offset] |= mask;
+}
+
+template 
+inline typename enable_if_c >::value>::type
+   eval_bit_unset(cpp_int_backend& val, unsigned index) BOOST_NOEXCEPT
+{
+   unsigned offset = index / cpp_int_backend::limb_bits;
+   unsigned shift = index % cpp_int_backend::limb_bits;
+   limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
+   if(offset >= val.size())
+      return;
+   val.limbs()[offset] &= ~mask;
+   val.normalize();
+}
+
+template 
+inline typename enable_if_c >::value>::type
+   eval_bit_flip(cpp_int_backend& val, unsigned index)
+{
+   unsigned offset = index / cpp_int_backend::limb_bits;
+   unsigned shift = index % cpp_int_backend::limb_bits;
+   limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
+   if(offset >= val.size())
+   {
+      unsigned os = val.size();
+      val.resize(offset + 1, offset + 1);
+      if(offset >= val.size())
+         return;  // fixed precision overflow
+      for(unsigned i = os; i <= offset; ++i)
+         val.limbs()[i] = 0;
+   }
+   val.limbs()[offset] ^= mask;
+   val.normalize();
+}
+
+template 
+inline typename enable_if_c >::value>::type
+   eval_qr(
+      const cpp_int_backend& x,
+      const cpp_int_backend& y,
+      cpp_int_backend& q,
+      cpp_int_backend& r) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   divide_unsigned_helper(&q, x, y, r);
+   q.sign(x.sign() != y.sign());
+   r.sign(x.sign());
+}
+
+template 
+inline typename enable_if_c::value && !is_trivial_cpp_int >::value, Integer>::type
+   eval_integer_modulus(const cpp_int_backend& x, Integer val)
+{
+   if((sizeof(Integer) <= sizeof(limb_type)) || (val <= (std::numeric_limits::max)()))
+   {
+      cpp_int_backend d;
+      divide_unsigned_helper(static_cast*>(0), x, static_cast(val), d);
+      return d.limbs()[0];
+   }
+   else
+   {
+      return default_ops::eval_integer_modulus(x, val);
+   }
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c::value && !is_trivial_cpp_int >::value, Integer>::type
+   eval_integer_modulus(const cpp_int_backend& x, Integer val)
+{
+   typedef typename make_unsigned::type unsigned_type;
+   return eval_integer_modulus(x, static_cast(std::abs(val)));
+}
+
+//
+// Now again for trivial backends:
+//
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type
+   eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+{
+   *result.limbs() = boost::math::gcd(*a.limbs(), *b.limbs());
+}
+// This one is only enabled for unchecked cpp_int's, for checked int's we need the checking in the default version:
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && (Checked1 == unchecked)>::type
+   eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   *result.limbs() = boost::math::lcm(*a.limbs(), *b.limbs());
+   result.normalize(); // result may overflow the specified number of bits
+}
+
+inline void conversion_overflow(const mpl::int_&)
+{
+   BOOST_THROW_EXCEPTION(std::overflow_error("Overflow in conversion to narrower type"));
+}
+inline void conversion_overflow(const mpl::int_&){}
+
+template 
+inline typename enable_if_c<
+            is_trivial_cpp_int >::value
+            && is_signed_number >::value
+         >::type
+   eval_convert_to(R* result, const cpp_int_backend& val)
+{
+   typedef typename common_type::local_limb_type>::type common_type;
+   if(std::numeric_limits::is_specialized && (static_cast(*val.limbs()) > static_cast((std::numeric_limits::max)())))
+   {
+      conversion_overflow(typename cpp_int_backend::checked_type());
+      *result = (std::numeric_limits::max)();
+   }
+   else
+      *result = static_cast(*val.limbs());
+   if(val.isneg())
+   {
+      check_is_negative(mpl::bool_::value || boost::is_floating_point::value>());
+      *result = negate_integer(*result, mpl::bool_::value || boost::is_floating_point::value>());
+   }
+}
+
+template 
+inline typename enable_if_c<
+            is_trivial_cpp_int >::value
+            && is_unsigned_number >::value
+         >::type
+   eval_convert_to(R* result, const cpp_int_backend& val)
+{
+   typedef typename common_type::local_limb_type>::type common_type;
+   if(std::numeric_limits::is_specialized && (static_cast(*val.limbs()) > static_cast((std::numeric_limits::max)())))
+   {
+      conversion_overflow(typename cpp_int_backend::checked_type());
+      *result = (std::numeric_limits::max)();
+   }
+   else
+      *result = static_cast(*val.limbs());
+}
+
+}}} // namespaces
+
+#endif
diff --git a/include/boost/multiprecision/cpp_int/multiply.hpp b/include/boost/multiprecision/cpp_int/multiply.hpp
new file mode 100644
index 00000000..630e7f91
--- /dev/null
+++ b/include/boost/multiprecision/cpp_int/multiply.hpp
@@ -0,0 +1,288 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// Comparison operators for cpp_int_backend:
+//
+#ifndef BOOST_MP_CPP_INT_MUL_HPP
+#define BOOST_MP_CPP_INT_MUL_HPP
+
+namespace boost{ namespace multiprecision{ namespace backends{
+
+template 
+inline typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_multiply(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(!val)
+   {
+      result = static_cast(0);
+      return;
+   }
+   if((void*)&a != (void*)&result)
+      result.resize(a.size(), a.size());
+   double_limb_type carry = 0;
+   typename cpp_int_backend::limb_pointer p = result.limbs();
+   typename cpp_int_backend::limb_pointer pe = result.limbs() + result.size();
+   typename cpp_int_backend::const_limb_pointer pa = a.limbs();
+   while(p != pe)
+   {
+      carry += static_cast(*pa) * static_cast(val);
+      *p = static_cast(carry);
+      carry >>= cpp_int_backend::limb_bits;
+      ++p, ++pa;
+   }
+   if(carry)
+   {
+      unsigned i = result.size();
+      result.resize(i + 1, i + 1);
+      if(cpp_int_backend::variable || (result.size() > i))
+         result.limbs()[i] = static_cast(carry);
+   }
+   result.sign(a.sign());
+   if(!cpp_int_backend::variable)
+      result.normalize();
+}
+
+//
+// resize_for_carry forces a resize of the underlying buffer only if a previous request
+// for "required" elements could possibly have failed, *and* we have checking enabled.
+// This will cause an overflow error inside resize():
+//
+template 
+inline void resize_for_carry(cpp_int_backend& /*result*/, unsigned /*required*/){}
+
+template 
+inline void resize_for_carry(cpp_int_backend& result, unsigned required)
+{
+   if(result.size() != required)
+      result.resize(required, required);
+}
+
+template 
+inline typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type
+   eval_multiply(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const cpp_int_backend& b) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   // Very simple long multiplication, only usable for small numbers of limb_type's
+   // but that's the typical use case for this type anyway:
+   //
+   // Special cases first:
+   //
+   unsigned as = a.size();
+   unsigned bs = b.size();
+   typename cpp_int_backend::const_limb_pointer pa = a.limbs();
+   typename cpp_int_backend::const_limb_pointer pb = b.limbs();
+   if(as == 1)
+   {
+      bool s = b.sign() != a.sign();
+      if(bs == 1)
+      {
+         result = static_cast(*pa) * static_cast(*pb);
+      }
+      else
+      {
+         limb_type l = *pa;
+         eval_multiply(result, b, l);
+      }
+      result.sign(s);
+      return;
+   }
+   if(bs == 1)
+   {
+      bool s = b.sign() != a.sign();
+      limb_type l = *pb;
+      eval_multiply(result, a, l);
+      result.sign(s);
+      return;
+   }
+
+   if((void*)&result == (void*)&a)
+   {
+      cpp_int_backend t(a);
+      eval_multiply(result, t, b);
+      return;
+   }
+   if((void*)&result == (void*)&b)
+   {
+      cpp_int_backend t(b);
+      eval_multiply(result, a, t);
+      return;
+   }
+
+   result.resize(as + bs, as + bs - 1);
+   typename cpp_int_backend::limb_pointer pr = result.limbs();
+
+   static const double_limb_type limb_max = ~static_cast(0u);
+   static const double_limb_type double_limb_max = ~static_cast(0u);
+   BOOST_STATIC_ASSERT(double_limb_max - 2 * limb_max >= limb_max * limb_max);
+
+   double_limb_type carry = 0;
+   std::memset(pr, 0, result.size() * sizeof(limb_type));
+   for(unsigned i = 0; i < as; ++i)
+   {
+      unsigned inner_limit = cpp_int_backend::variable ? bs : (std::min)(result.size() - i, bs);
+      for(unsigned j = 0; j < inner_limit; ++j)
+      {
+         BOOST_ASSERT(i+j < result.size());
+         BOOST_ASSERT(!std::numeric_limits::is_specialized 
+            || ((std::numeric_limits::max)() - carry 
+                  > 
+                static_cast(cpp_int_backend::max_limb_value) * static_cast(cpp_int_backend::max_limb_value)));
+         carry += static_cast(pa[i]) * static_cast(pb[j]);
+         BOOST_ASSERT(!std::numeric_limits::is_specialized || ((std::numeric_limits::max)() - carry >= pr[i+j]));
+         carry += pr[i + j];
+         pr[i + j] = static_cast(carry);
+         carry >>= cpp_int_backend::limb_bits;
+         BOOST_ASSERT(carry <= (cpp_int_backend::max_limb_value));
+      }
+      resize_for_carry(result, as + bs);  // May throw if checking is enabled
+      if(cpp_int_backend::variable || (i + bs < result.size()))
+         pr[i + bs] = static_cast(carry);
+      carry = 0;
+   }
+   result.normalize();
+   //
+   // Set the sign of the result:
+   //
+   result.sign(a.sign() != b.sign());
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_multiply(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+    eval_multiply(result, result, a);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_multiply(cpp_int_backend& result, const limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   eval_multiply(result, result, val);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_multiply(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const double_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(val <= (std::numeric_limits::max)())
+   {
+      eval_multiply(result, a, static_cast(val));
+   }
+   else
+   {
+      cpp_int_backend t(val);
+      eval_multiply(result, a, t);
+   }
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_multiply(cpp_int_backend& result, const double_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   eval_multiply(result, result, val);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_multiply(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const signed_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(val > 0)
+      eval_multiply(result, a, static_cast(val));
+   else
+   {
+      eval_multiply(result, a, static_cast(-val));
+      result.negate();
+   }
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_multiply(cpp_int_backend& result, const signed_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   eval_multiply(result, result, val);
+}
+
+template 
+inline typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+   eval_multiply(
+      cpp_int_backend& result, 
+      const cpp_int_backend& a, 
+      const signed_double_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   if(val > 0)
+   {
+      if(val <= (std::numeric_limits::max)())
+      {
+         eval_multiply(result, a, static_cast(val));
+         return;
+      }
+   }
+   else if(val >= -static_cast((std::numeric_limits::max)()))
+   {
+      eval_multiply(result, a, static_cast(-val));
+      result.negate();
+      return;
+   }
+   cpp_int_backend t(val);
+   eval_multiply(result, a, t);
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c >::value>::type 
+   eval_multiply(cpp_int_backend& result, const signed_double_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   eval_multiply(result, result, val);
+}
+
+//
+// Now over again for trivial cpp_int's:
+//
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && (is_signed_number >::value 
+            || is_signed_number >::value)
+         >::type 
+   eval_multiply(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   *result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), typename cpp_int_backend::checked_type());
+   result.sign(result.sign() != o.sign());
+   result.normalize();
+}
+
+template 
+BOOST_FORCEINLINE typename enable_if_c<
+         is_trivial_cpp_int >::value 
+         && is_trivial_cpp_int >::value
+         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
+         >::type 
+   eval_multiply(
+      cpp_int_backend& result, 
+      const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
+{
+   *result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), typename cpp_int_backend::checked_type());
+   result.normalize();
+}
+
+}}} // namespaces
+
+#endif
diff --git a/include/boost/multiprecision/detail/cpp_int_core.hpp b/include/boost/multiprecision/detail/cpp_int_core.hpp
index f2e86cf1..cf1a9b3b 100644
--- a/include/boost/multiprecision/detail/cpp_int_core.hpp
+++ b/include/boost/multiprecision/detail/cpp_int_core.hpp
@@ -98,6 +98,8 @@ inline limb_type block_multiplier(unsigned count)
 
 #endif
 
+static const unsigned bits_per_limb = sizeof(limb_type) * CHAR_BIT;
+
 template 
 inline void minmax(const T& a, const T& b, T& aa, T& bb)
 {
diff --git a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp
index 3213f6a6..7adbf872 100644
--- a/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp
+++ b/include/boost/multiprecision/detail/cpp_int_trivial_ops.hpp
@@ -19,112 +19,112 @@ namespace boost{ namespace multiprecision{ namespace backends{
 #endif
 
 template 
-BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE bool eval_eq(const old_cpp_int_backend& a, const old_cpp_int_backend& b) BOOST_NOEXCEPT
 {
    return (a.sign() == b.sign()) && (*a.limbs() == *b.limbs());
 }
 template 
-BOOST_FORCEINLINE bool eval_eq(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE bool eval_eq(const old_cpp_int_backend& a, const old_cpp_int_backend& b) BOOST_NOEXCEPT
 {
    return *a.limbs() == *b.limbs();
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const old_cpp_int_backend& a, U b) BOOST_NOEXCEPT
 {
    return !a.sign() && (*a.limbs() == b);
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const old_cpp_int_backend& a, S b) BOOST_NOEXCEPT
 {
    return (a.sign() == (b < 0)) && (*a.limbs() == std::abs(b));
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const old_cpp_int_backend& a, U b) BOOST_NOEXCEPT
 {
    return *a.limbs() == b;
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_eq(const old_cpp_int_backend& a, S b) BOOST_NOEXCEPT
 {
    return *a.limbs() == b;
 }
 
 template 
-BOOST_FORCEINLINE bool eval_lt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE bool eval_lt(const old_cpp_int_backend& a, const old_cpp_int_backend& b) BOOST_NOEXCEPT
 {
    if(a.sign() != b.sign())
       return a.sign();
    return a.sign() ? *a.limbs() > *b.limbs() : *a.limbs() < *b.limbs();
 }
 template 
-BOOST_FORCEINLINE bool eval_lt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE bool eval_lt(const old_cpp_int_backend& a, const old_cpp_int_backend& b) BOOST_NOEXCEPT
 {
    return *a.limbs() < *b.limbs();
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const old_cpp_int_backend& a, U b) BOOST_NOEXCEPT
 {
    if(a.sign())
       return true;
    return *a.limbs() < b;
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const old_cpp_int_backend& a, S b) BOOST_NOEXCEPT
 {
    if(a.sign() != (b < 0))
       return a.sign();
    return a.sign() ? (*a.limbs() > std::abs(b)) : (*a.limbs() < std::abs(b));
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const old_cpp_int_backend& a, U b) BOOST_NOEXCEPT
 {
    return *a.limbs() < b;
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_lt(const old_cpp_int_backend& a, S b) BOOST_NOEXCEPT
 {
    return *a.limbs() < b;
 }
 
 template 
-BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE bool eval_gt(const old_cpp_int_backend& a, const old_cpp_int_backend& b) BOOST_NOEXCEPT
 {
    if(a.sign() != b.sign())
       return !a.sign();
    return a.sign() ? *a.limbs() < *b.limbs() : *a.limbs() > *b.limbs();
 }
 template 
-BOOST_FORCEINLINE bool eval_gt(const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE bool eval_gt(const old_cpp_int_backend& a, const old_cpp_int_backend& b) BOOST_NOEXCEPT
 {
    return *a.limbs() > *b.limbs();
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const old_cpp_int_backend& a, U b) BOOST_NOEXCEPT
 {
    if(a.sign())
       return false;
    return *a.limbs() > b;
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const old_cpp_int_backend& a, S b) BOOST_NOEXCEPT
 {
    if(a.sign() != (b < 0))
       return !a.sign();
    return a.sign() ? (*a.limbs() < std::abs(b)) : (*a.limbs() > std::abs(b));
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, U b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const old_cpp_int_backend& a, U b) BOOST_NOEXCEPT
 {
    return *a.limbs() > b;
 }
 template 
-BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const cpp_int_backend& a, S b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE typename enable_if, bool>::type eval_gt(const old_cpp_int_backend& a, S b) BOOST_NOEXCEPT
 {
    return *a.limbs() > b;
 }
 
 template 
-inline void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+inline void eval_add(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
    if(result.sign() != o.sign())
    {
@@ -141,13 +141,13 @@ inline void eval_add(cpp_int_backend& result, const c
 }
 
 template 
-BOOST_FORCEINLINE void eval_add(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_add(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
    *result.limbs() += *o.limbs();
 }
 
 template 
-inline void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+inline void eval_subtract(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
    if(result.sign() != o.sign())
    {
@@ -163,26 +163,26 @@ inline void eval_subtract(cpp_int_backend& result, co
 }
 
 template 
-BOOST_FORCEINLINE void eval_subtract(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_subtract(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
    *result.limbs() -= *o.limbs();
 }
 
 template 
-BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_multiply(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
    *result.limbs() *= *o.limbs();
    result.sign(result.sign() != o.sign());
 }
 
 template 
-BOOST_FORCEINLINE void eval_multiply(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_multiply(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
    *result.limbs() *= *o.limbs();
 }
 
 template 
-BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& o)
+BOOST_FORCEINLINE void eval_divide(old_cpp_int_backend& result, const old_cpp_int_backend& o)
 {
    if(!*o.limbs())
       BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
@@ -191,7 +191,7 @@ BOOST_FORCEINLINE void eval_divide(cpp_int_backend& r
 }
 
 template 
-BOOST_FORCEINLINE void eval_divide(cpp_int_backend& result, const cpp_int_backend& o)
+BOOST_FORCEINLINE void eval_divide(old_cpp_int_backend& result, const old_cpp_int_backend& o)
 {
    if(!*o.limbs())
       BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
@@ -199,7 +199,7 @@ BOOST_FORCEINLINE void eval_divide(cpp_int_backend&
 }
 
 template 
-BOOST_FORCEINLINE void eval_modulus(cpp_int_backend& result, const cpp_int_backend& o)
+BOOST_FORCEINLINE void eval_modulus(old_cpp_int_backend& result, const old_cpp_int_backend& o)
 {
    if(!*o.limbs())
       BOOST_THROW_EXCEPTION(std::overflow_error("Division by zero."));
@@ -208,21 +208,21 @@ BOOST_FORCEINLINE void eval_modulus(cpp_int_backend
 }
 
 template 
-BOOST_FORCEINLINE void eval_left_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_left_shift(old_cpp_int_backend& result, T s) BOOST_NOEXCEPT
 {
    *result.limbs() <<= s;
 }
 
 template 
-BOOST_FORCEINLINE void eval_right_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_right_shift(old_cpp_int_backend& result, T s) BOOST_NOEXCEPT
 {
    *result.limbs() >>= s;
 }
 
 template 
-inline void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+inline void eval_bitwise_and(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
-   typename cpp_int_backend::local_limb_type a, b;
+   typename old_cpp_int_backend::local_limb_type a, b;
    a = *result.limbs();
    if(result.isneg())
    {
@@ -237,7 +237,7 @@ inline void eval_bitwise_and(cpp_int_backend& result,
    }
    a &= b;
    bool isneg = false;
-   static const typename cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1);
+   static const typename old_cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1);
    if(a & mask)
    {
       a = ~a;
@@ -249,15 +249,15 @@ inline void eval_bitwise_and(cpp_int_backend& result,
 }
 
 template 
-BOOST_FORCEINLINE void eval_bitwise_and(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_bitwise_and(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
    *result.limbs() &= *o.limbs();
 }
 
 template 
-inline void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+inline void eval_bitwise_or(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
-   typename cpp_int_backend::local_limb_type a, b;
+   typename old_cpp_int_backend::local_limb_type a, b;
    a = *result.limbs();
    if(result.isneg())
    {
@@ -272,7 +272,7 @@ inline void eval_bitwise_or(cpp_int_backend& result,
    }
    a |= b;
    bool isneg = false;
-   static const typename cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (sizeof(typename cpp_int_backend::local_limb_type) * CHAR_BIT - 1);
+   static const typename old_cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (sizeof(typename old_cpp_int_backend::local_limb_type) * CHAR_BIT - 1);
    if(a & mask)
    {
       a = ~a;
@@ -284,15 +284,15 @@ inline void eval_bitwise_or(cpp_int_backend& result,
 }
 
 template 
-BOOST_FORCEINLINE void eval_bitwise_or(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_bitwise_or(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
    *result.limbs() |= *o.limbs();
 }
 
 template 
-inline void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+inline void eval_bitwise_xor(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
-   typename cpp_int_backend::local_limb_type a, b;
+   typename old_cpp_int_backend::local_limb_type a, b;
    a = *result.limbs();
    if(result.isneg())
    {
@@ -307,7 +307,7 @@ inline void eval_bitwise_xor(cpp_int_backend& result,
    }
    a ^= b;
    bool isneg = false;
-   static const typename cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1);
+   static const typename old_cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1);
    if(a & mask)
    {
       a = ~a;
@@ -319,15 +319,15 @@ inline void eval_bitwise_xor(cpp_int_backend& result,
 }
 
 template 
-BOOST_FORCEINLINE void eval_bitwise_xor(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_bitwise_xor(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
    *result.limbs() ^= *o.limbs();
 }
 
 template 
-inline void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+inline void eval_complement(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
-   typename cpp_int_backend::local_limb_type a;
+   typename old_cpp_int_backend::local_limb_type a;
    a = *o.limbs();
    if(o.isneg())
    {
@@ -336,7 +336,7 @@ inline void eval_complement(cpp_int_backend& result,
    }
    a = ~a;
    bool isneg = false;
-   static const typename cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1);
+   static const typename old_cpp_int_backend::local_limb_type mask = static_cast::local_limb_type>(1) << (std::numeric_limits::local_limb_type>::digits - 1);
    if(a & mask)
    {
       a = ~a;
@@ -348,25 +348,25 @@ inline void eval_complement(cpp_int_backend& result,
 }
 
 template 
-BOOST_FORCEINLINE void eval_complement(cpp_int_backend& result, const cpp_int_backend& o) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_complement(old_cpp_int_backend& result, const old_cpp_int_backend& o) BOOST_NOEXCEPT
 {
    *result.limbs() = ~*o.limbs();
 }
 
 template 
-BOOST_FORCEINLINE void eval_gcd(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_gcd(old_cpp_int_backend& result, const old_cpp_int_backend& a, const old_cpp_int_backend& b) BOOST_NOEXCEPT
 {
    *result.limbs() = boost::math::gcd(*a.limbs(), *b.limbs());
 }
 
 template 
-BOOST_FORCEINLINE void eval_lcm(cpp_int_backend& result, const cpp_int_backend& a, const cpp_int_backend& b) BOOST_NOEXCEPT
+BOOST_FORCEINLINE void eval_lcm(old_cpp_int_backend& result, const old_cpp_int_backend& a, const old_cpp_int_backend& b) BOOST_NOEXCEPT
 {
    *result.limbs() = boost::math::lcm(*a.limbs(), *b.limbs());
 }
 
 template 
-inline void eval_convert_to(R* result, const cpp_int_backend& val)
+inline void eval_convert_to(R* result, const old_cpp_int_backend& val)
 {
    if(std::numeric_limits::is_specialized && (*val.limbs() > (std::numeric_limits::max)()))
       *result = (std::numeric_limits::max)();
@@ -377,7 +377,7 @@ inline void eval_convert_to(R* result, const cpp_int_backend
-inline void eval_convert_to(R* result, const cpp_int_backend& val)
+inline void eval_convert_to(R* result, const old_cpp_int_backend& val)
 {
    if(std::numeric_limits::is_specialized && (*val.limbs() > (std::numeric_limits::max)()))
       *result = (std::numeric_limits::max)();
diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp
index d83b336d..71ef9844 100644
--- a/include/boost/multiprecision/detail/default_ops.hpp
+++ b/include/boost/multiprecision/detail/default_ops.hpp
@@ -267,7 +267,7 @@ void eval_subtract(T& t, const U& u, const V& v);
 template 
 inline void eval_subtract_default(T& t, const T& u, const T& v)
 {
-   if(&t == &v)
+   if((&t == &v) && is_signed_number::value)
    {
       eval_subtract(t, u);
       t.negate();
@@ -296,16 +296,22 @@ inline typename enable_if_c >::value && is_co
    eval_subtract(t, u, vv);
 }
 template 
-inline typename enable_if_c >::value>::type eval_subtract_default(T& t, const U& u, const T& v)
+inline typename enable_if_c >::value && is_signed_number::value>::type eval_subtract_default(T& t, const U& u, const T& v)
 {
    eval_subtract(t, v, u);
    t.negate();
 }
+template 
+inline typename enable_if_c >::value && is_unsigned_number::value>::type eval_subtract_default(T& t, const U& u, const T& v)
+{
+   T temp(u);
+   eval_subtract(t, temp, v);
+}
 template 
 inline void eval_subtract_default(T& t, const U& u, const V& v)
 {
    t = u;
-   eval_subtract(t, u);
+   eval_subtract(t, v);
 }
 template 
 inline void eval_subtract(T& t, const U& u, const V& v)
diff --git a/include/boost/multiprecision/detail/integer_ops.hpp b/include/boost/multiprecision/detail/integer_ops.hpp
index d01e92bb..c58791f6 100644
--- a/include/boost/multiprecision/detail/integer_ops.hpp
+++ b/include/boost/multiprecision/detail/integer_ops.hpp
@@ -20,14 +20,10 @@ inline void eval_qr(const Backend& x, const Backend& y, Backend& q, Backend& r)
    eval_modulus(r, x, y);
 }
 
-template 
-inline typename enable_if, Integer>::type maybe_abs(Integer i) { return std::abs(i); }
-template 
-inline typename enable_if, Integer>::type maybe_abs(Integer i) { return i; }
-
 template 
 inline Integer eval_integer_modulus(const Backend& x, Integer val)
 {
+   BOOST_MP_USING_ABS
    using default_ops::eval_modulus;
    using default_ops::eval_convert_to;
    typedef typename boost::multiprecision::detail::canonical::type int_type;
@@ -35,7 +31,7 @@ inline Integer eval_integer_modulus(const Backend& x, Integer val)
    eval_modulus(t, x, static_cast(val));
    Integer result;
    eval_convert_to(&result, t);
-   return maybe_abs(result);
+   return abs(result);
 }
 
 #ifdef BOOST_MSVC
diff --git a/include/boost/multiprecision/detail/no_et_ops.hpp b/include/boost/multiprecision/detail/no_et_ops.hpp
index 49933a8f..82bb5e5c 100644
--- a/include/boost/multiprecision/detail/no_et_ops.hpp
+++ b/include/boost/multiprecision/detail/no_et_ops.hpp
@@ -359,7 +359,7 @@ inline number operator - (number&& a, const number&&>(a);
 }
 template 
-inline number operator - (const number& a, number&& b)
+inline typename enable_if, number >::type operator - (const number& a, number&& b)
 {
    using default_ops::eval_subtract;
    eval_subtract(b.backend(), a.backend());
@@ -382,7 +382,7 @@ inline typename enable_if >,
    return static_cast&&>(a);
 }
 template 
-inline typename enable_if >, number >::type
+inline typename enable_if_c<(is_compatible_arithmetic_type >::value && is_signed_number::value), number >::type
    operator - (const V& a, number&& b)
 {
    using default_ops::eval_subtract;
diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp
index 37057c12..e7244273 100644
--- a/include/boost/multiprecision/detail/number_base.hpp
+++ b/include/boost/multiprecision/detail/number_base.hpp
@@ -59,15 +59,20 @@ struct is_compatible_arithmetic_type
 
 namespace detail{
 //
-// Workaround for missing abs(long long) on some compilers:
+// Workaround for missing abs(long long) and abs(__int128) on some compilers:
 //
 template 
-typename boost::enable_if, T>::type abs(const T& t) BOOST_NOEXCEPT
+typename enable_if_c<(is_signed::value || is_floating_point::value), T>::type abs(T t) BOOST_NOEXCEPT
 {
    return t < 0 ? -t : t;
 }
+template 
+typename enable_if_c<(is_unsigned::value), T>::type abs(T t) BOOST_NOEXCEPT
+{
+   return t;
+}
 
-#define BOOST_MP_USING_ABS using std::abs; using boost::multiprecision::detail::abs;
+#define BOOST_MP_USING_ABS using boost::multiprecision::detail::abs;
 
 //
 // Move support:
@@ -205,15 +210,6 @@ struct backend_type >
 };
 
 
-template 
-struct is_number : public mpl::false_{};
-template 
-struct is_number > : public mpl::true_{};
-template 
-struct is_mp_number_exp : public mpl::false_{};
-template 
-struct is_mp_number_exp > : public mpl::true_{};
-
 template 
 struct combine_expression
 {
@@ -676,6 +672,13 @@ struct component_type > : public component_type
 struct component_type > : public component_type::result_type>{};
 
+template 
+struct is_unsigned_number : public mpl::false_{};
+template 
+struct is_unsigned_number > : public is_unsigned_number {};
+template 
+struct is_signed_number : public mpl::bool_::value> {};
+
 }} // namespaces
 
 namespace boost{ namespace math{ namespace tools{
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index ae17fbe4..65b162be 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -152,6 +152,27 @@ run test_arithmetic.cpp
 	      TEST_CPP_INT_3
         : test_arithmetic_cpp_int_3 ;
 
+run test_arithmetic.cpp
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_CPP_INT_1A
+        : test_arithmetic_cpp_int_1a ;
+
+run test_arithmetic.cpp
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_CPP_INT_2A
+        : test_arithmetic_cpp_int_2a ;
+
+run test_arithmetic.cpp
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_CPP_INT_3A
+        : test_arithmetic_cpp_int_3a ;
+
 run test_arithmetic.cpp
         : # command line
         : # input files
@@ -707,6 +728,28 @@ run test_cpp_int.cpp gmp
         : # requirements
          [ check-target-builds ../config//has_gmp : : no ]
          release  # otherwise runtime is too slow!! 
+         TEST1
+         : test_cpp_int_1
+         ;
+
+run test_cpp_int.cpp gmp
+        : # command line
+        : # input files
+        : # requirements
+         [ check-target-builds ../config//has_gmp : : no ]
+         release  # otherwise runtime is too slow!! 
+         TEST2
+         : test_cpp_int_2
+         ;
+
+run test_cpp_int.cpp gmp
+        : # command line
+        : # input files
+        : # requirements
+         [ check-target-builds ../config//has_gmp : : no ]
+         release  # otherwise runtime is too slow!! 
+         TEST3
+         : test_cpp_int_3
          ;
 
 run test_miller_rabin.cpp gmp
diff --git a/test/include_test/cpp_int_include_test.cpp b/test/include_test/cpp_int_include_test.cpp
index a5f33323..e3742612 100644
--- a/test/include_test/cpp_int_include_test.cpp
+++ b/test/include_test/cpp_int_include_test.cpp
@@ -9,8 +9,8 @@ using namespace boost::multiprecision;
 
 number > a;
 number, et_off> b;
-number, et_off> c;
-number, et_off> d;
-number, et_off> e;
+number, et_off> c;
+number, et_off> d;
+number, et_off> e;
 
 
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index ad1b78a6..1b047b1f 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -19,6 +19,7 @@
    !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) \
    && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\
    && !defined(TEST_CPP_INT_1) && !defined(TEST_CPP_INT_2) && !defined(TEST_CPP_INT_3) \
+   && !defined(TEST_CPP_INT_1A) && !defined(TEST_CPP_INT_2A) && !defined(TEST_CPP_INT_3A) \
    && !defined(TEST_CPP_INT_BR) && !defined(TEST_ARITHMETIC_BACKEND)
 #  define TEST_MPF_50
 #  define TEST_MPF
@@ -32,6 +33,9 @@
 #  define TEST_CPP_INT_1
 #  define TEST_CPP_INT_2
 #  define TEST_CPP_INT_3
+#  define TEST_CPP_INT_1A
+#  define TEST_CPP_INT_2A
+#  define TEST_CPP_INT_3A
 #  define TEST_CPP_INT_BR
 #  define TEST_ARITHMETIC_BACKEND
 
@@ -64,7 +68,7 @@
 #include 
 #include 
 #endif
-#if defined(TEST_CPP_INT_1) || defined(TEST_CPP_INT_2) || defined(TEST_CPP_INT_3) || defined(TEST_CPP_INT_BR)
+#if defined(TEST_CPP_INT_1) || defined(TEST_CPP_INT_2) || defined(TEST_CPP_INT_3) || defined(TEST_CPP_INT_BR) || defined(TEST_CPP_INT_1A) || defined(TEST_CPP_INT_2A) || defined(TEST_CPP_INT_3A)
 #include 
 #endif
 
@@ -150,6 +154,10 @@ struct is_twos_complement_integer : public boost::mpl::true_ {};
 template <>
 struct is_twos_complement_integer : public boost::mpl::false_ {};
 #endif
+#if defined(TEST_CPP_INT_1) || defined(TEST_CPP_INT_2) || defined(TEST_CPP_INT_3) || defined(TEST_CPP_INT_BR) || defined(TEST_CPP_INT_1A) || defined(TEST_CPP_INT_2A) || defined(TEST_CPP_INT_3A)
+template 
+struct is_twos_complement_integer, ExpressionTemplates> > : public boost::mpl::false_ {};
+#endif
 
 #define BOOST_TEST_EQUAL(a, b) BOOST_TEST((a) == (b))
 
@@ -193,16 +201,16 @@ struct related_type > type;
 };
 #endif
-#if defined(TEST_CPP_INT_1) || defined(TEST_CPP_INT_2) || defined(TEST_CPP_INT_3) || defined(TEST_CPP_INT_BR)
+#if defined(TEST_CPP_INT_1) || defined(TEST_CPP_INT_2) || defined(TEST_CPP_INT_3) || defined(TEST_CPP_INT_BR) || defined(TEST_CPP_INT_1A) || defined(TEST_CPP_INT_2A) || defined(TEST_CPP_INT_3A)
 template <>
 struct related_type
 {
    typedef boost::multiprecision::int256_t type;
 };
-template 
-struct related_type, ET> >
+template 
+struct related_type, ET> >
 {
-   typedef boost::multiprecision::number, ET> type;
+   typedef boost::multiprecision::number, ET> type;
 };
 #endif
 template 
@@ -315,11 +323,18 @@ void test_complement(Real a, Real b, Real c, const boost::mpl::true_&)
    int i = 1020304;
    int j = 56789123;
    int sign_mask = ~0;
-   BOOST_TEST(~a == (~i & sign_mask));
-   c = a & ~b;
-   BOOST_TEST(c == (i & (~j & sign_mask)));
-   c = ~(a | b);
-   BOOST_TEST(c == (~(i | j) & sign_mask));
+   if(std::numeric_limits::is_signed)
+   {
+      BOOST_TEST(~a == (~i & sign_mask));
+      c = a & ~b;
+      BOOST_TEST(c == (i & (~j & sign_mask)));
+      c = ~(a | b);
+      BOOST_TEST(c == (~(i | j) & sign_mask));
+   }
+   else
+   {
+      BOOST_TEST((~a & a) == 0);
+   }
 }
 
 template 
@@ -710,7 +725,10 @@ void test_integer_ops(const boost::mpl::int_::is_signed || is_twos_complement_integer::value)
+   {
+      ac = a;
+      ac -= c - b;
+      BOOST_TEST(ac == 8 - (500-64));
+      ac = a;
+      ac -= b*c;
+      BOOST_TEST(ac == 8 - 500*64);
    }
-   ac = a;
-   ac -= c - b;
-   BOOST_TEST(ac == 8 - (500-64));
-   ac = a;
-   ac -= b*c;
-   BOOST_TEST(ac == 8 - 500*64);
    ac = a;
    ac += ac * b;
    BOOST_TEST(ac == 8 + 8 * 64);
-   ac = a;
-   ac -= ac * b;
-   BOOST_TEST(ac == 8 - 8 * 64);
+   if(std::numeric_limits::is_signed || is_twos_complement_integer::value)
+   {
+      ac = a;
+      ac -= ac * b;
+      BOOST_TEST(ac == 8 - 8 * 64);
+   }
    ac = a * 8;
    ac *= +a;
    BOOST_TEST(ac == 64 * 8);
    ac = a;
-   ac *= -a;
-   BOOST_TEST(ac == -64);
-   ac = a;
    ac *= b * c;
    BOOST_TEST(ac == 8 * 64 * 500);
    ac = a;
@@ -1583,6 +1604,9 @@ void test()
       ac = b;
       ac /= -a;
       BOOST_TEST(ac == -8);
+      ac = a;
+      ac *= -a;
+      BOOST_TEST(ac == -64);
    }
    ac = b;
    ac /= b / a;
@@ -1775,7 +1799,10 @@ void test()
    //
    a = 20;
    test_conditional(a, +a);
-   test_conditional(Real(-a), -a);
+   if(std::numeric_limits::is_signed || is_twos_complement_integer::value)
+   {
+      test_conditional(Real(-a), -a);
+   }
    test_conditional(a, (a + 0));
 }
 
@@ -1828,18 +1855,35 @@ int main()
 #endif
 #ifdef TEST_CPP_INT_1
    test();
-   test();
-   test();
+   test();
+   test();
+#endif
+#ifdef TEST_CPP_INT_1A
+   test();
+   test();
+   test();
 #endif
 #ifdef TEST_CPP_INT_2
    test();
    test, boost::multiprecision::et_off> >();
-   test > >();
+   test > >();
+#endif
+#ifdef TEST_CPP_INT_2A
+   test();
+   test, boost::multiprecision::et_off> >();
+   test > >();
 #endif
 #ifdef TEST_CPP_INT_3
    // Again with "trivial" backends:
-   test > >();
-   test > >();
+   test > >();
+   test > >();
+   test > >();
+#endif
+#ifdef TEST_CPP_INT_3A
+   // Again with "trivial" checked backends:
+   test > >();
+   test > >();
+   test > >();
 #endif
 #ifdef TEST_CPP_INT_BR
    test >();
diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp
index 853249e1..164833d5 100644
--- a/test/test_cpp_int.cpp
+++ b/test/test_cpp_int.cpp
@@ -57,6 +57,8 @@ void test()
 {
    using namespace boost::multiprecision;
    typedef Number test_type;
+   typedef typename test_type::backend_type::checked_type checked;
+
    unsigned last_error_count = 0;
    boost::timer tim;
 
@@ -242,7 +244,7 @@ void test()
       BOOST_CHECK_EQUAL(mpz_int(gcd(a, -b)).str(), test_type(gcd(a1, -b1)).str());
       BOOST_CHECK_EQUAL(mpz_int(lcm(c, -d)).str(), test_type(lcm(c1, -d1)).str());
 
-      if(std::numeric_limits::is_modulo)
+      if(std::numeric_limits::is_modulo && checked::value)
       {
          static mpz_int m = mpz_int(1) << std::numeric_limits::digits;
          mpz_int t(a);
@@ -327,7 +329,7 @@ void test()
       // Tests run on the compiler farm time out after 300 seconds, 
       // so don't get too close to that:
       //
-      if(tim.elapsed() > 100)
+      if(tim.elapsed() > 200)
       {
          std::cout << "Timeout reached, aborting tests now....\n";
          break;
@@ -336,11 +338,25 @@ void test()
    }
 }
 
+#if !defined(TEST1) && !defined(TEST2) && !defined(TEST3)
+#define TEST1
+#define TEST2
+#define TEST3
+#endif
+
 int main()
 {
    using namespace boost::multiprecision;
+#ifdef TEST1
    test();
-   test > >();
+#endif
+#ifdef TEST2
+   test > >();
+#endif
+#ifdef TEST3
+   // Unchecked test verifies modulo arithmetic:
+   test > >();
+#endif
    return boost::report_errors();
 }
 
diff --git a/test/test_cpp_int_conv.cpp b/test/test_cpp_int_conv.cpp
index 62b84e55..d5a8e2a3 100644
--- a/test/test_cpp_int_conv.cpp
+++ b/test/test_cpp_int_conv.cpp
@@ -23,7 +23,7 @@ int main()
    cpp_int    i1(2);
    int128_t   i2(3);
    int256_t   i3(4);
-   number > i4(5);
+   number > i4(5);
 
    i1 = i3;
    BOOST_TEST(i1 == 4);
@@ -48,7 +48,7 @@ int main()
    int128_t   i6(i4);
    BOOST_TEST(i6 == -5677334);
 
-   number, et_off> i7(i3);
+   number, et_off> i7(i3);
    BOOST_TEST(i7 == -1234567);
 
    int256_t   i8(i6);
@@ -57,13 +57,13 @@ int main()
    i7.assign(4.0);
    BOOST_TEST(i7 == 4);
 
-   number, et_off> i9(-5677334);
+   number, et_off> i9(-5677334);
    i7 = i9;
    BOOST_TEST(i7 == -5677334);
-   i7 = number, et_off>(i9);
+   i7 = number, et_off>(i9);
    BOOST_TEST(i7 == -5677334);
 
-   i9 = static_cast, et_off> >(i7);
+   i9 = static_cast, et_off> >(i7);
    BOOST_TEST(i9 == -5677334);
 
    ++i9;
diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp
index a17cfcf5..6d9d0a76 100644
--- a/test/test_int_io.cpp
+++ b/test/test_int_io.cpp
@@ -40,12 +40,27 @@
 #include 
 #include 
 
+template 
+struct unchecked_type{ typedef T type; };
+
+#ifdef TEST_CPP_INT
+template 
+struct unchecked_type, ExpressionTemplates> >
+{
+   typedef boost::multiprecision::number, ExpressionTemplates> type;
+};
+#endif
+
 template 
 T generate_random()
 {
-   static boost::random::uniform_int_distribution ui(0, 20);
+   typedef typename unchecked_type::type unchecked_T;
+
+   static const unsigned limbs = std::numeric_limits::is_specialized && std::numeric_limits::is_bounded ? std::numeric_limits::digits / std::numeric_limits::digits + 3 : 20;
+
+   static boost::random::uniform_int_distribution ui(0, limbs);
    static boost::random::mt19937 gen;
-   T val = gen();
+   unchecked_T val = gen();
    unsigned lim = ui(gen);
    for(unsigned i = 0; i < lim; ++i)
    {
@@ -123,11 +138,11 @@ int main()
    test_round_trip();
 #endif
 #ifdef TEST_CPP_INT
-   test_round_trip > >();
-   test_round_trip > >();
-   test_round_trip > >();
-   test_round_trip > >();
-   test_round_trip > >();
+   test_round_trip();
+   test_round_trip();
+   test_round_trip();
+   test_round_trip > >();
+   test_round_trip > >();
 #endif
    return boost::report_errors();
 }
diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp
index 4b95a19d..7b262ddc 100644
--- a/test/test_numeric_limits.cpp
+++ b/test/test_numeric_limits.cpp
@@ -239,8 +239,8 @@ int main()
    test();
    test();
    test();
-   test > >();
-   test > >();
+   test > >();
+   test > >();
 #endif
    return boost::report_errors();
 }

From 82409d86a0ec83c3b8249b980077cc0bd17dba0a Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 25 Oct 2012 09:29:04 +0000
Subject: [PATCH 242/256] Minor changes for __int128 support and fix some C++0x
 issues

[SVN r81062]
---
 .../multiprecision/cpp_int/cpp_int_config.hpp | 19 +++++++++----------
 test/test_constexpr.cpp                       | 10 +++++-----
 2 files changed, 14 insertions(+), 15 deletions(-)

diff --git a/include/boost/multiprecision/cpp_int/cpp_int_config.hpp b/include/boost/multiprecision/cpp_int/cpp_int_config.hpp
index 2e829312..ae74d3b9 100644
--- a/include/boost/multiprecision/cpp_int/cpp_int_config.hpp
+++ b/include/boost/multiprecision/cpp_int/cpp_int_config.hpp
@@ -63,13 +63,12 @@ struct largest_unsigned_type
 
 } // namepsace detail
 
-#if defined(__GNUC__) && ((__GNUC__ > 4) || ((__GNUC__ == 4) && (__GNUC_MINOR__ >= 6))) \
-   && !defined(BOOST_INTEL) && defined(__WORDSIZE) && (__WORDSIZE == 64)
+#if defined(BOOST_HAS_INT128)
 
 typedef detail::largest_unsigned_type<64>::type limb_type;
 typedef detail::largest_signed_type<64>::type signed_limb_type;
-typedef unsigned __int128 double_limb_type;
-typedef __int128 signed_double_limb_type;
+typedef boost::uint128_type double_limb_type;
+typedef boost::int128_type signed_double_limb_type;
 static const limb_type max_block_10 = 1000000000000000000uLL;
 static const limb_type digits_per_block_10 = 18;
 
@@ -88,14 +87,14 @@ inline limb_type block_multiplier(unsigned count)
 } // namespace multiprecision
 
 template<>
-class integer_traits
-  : public std::numeric_limits,
-    public detail::integer_traits_base(0)>
+class integer_traits
+  : public std::numeric_limits,
+    public detail::integer_traits_base(0)>
 { };
 template<>
-class integer_traits
-  : public std::numeric_limits,
-    public detail::integer_traits_base(static_cast(1) << 127), static_cast((~static_cast(0)) >> 1)>
+class integer_traits
+  : public std::numeric_limits,
+    public detail::integer_traits_base((static_cast(1) << 127)), static_cast(((~static_cast(0)) >> 1))>
 { };
 
 namespace multiprecision{
diff --git a/test/test_constexpr.cpp b/test/test_constexpr.cpp
index 8669141b..fb4fff44 100644
--- a/test/test_constexpr.cpp
+++ b/test/test_constexpr.cpp
@@ -31,9 +31,9 @@ void test3()
 
 using namespace boost::multiprecision;
 
-template void test1, et_off> >();
-template void test1, et_off> >();
-template void test3, et_off> >();
-template void test2, et_off> >();
+template void test1, et_off> >();
+template void test1, et_off> >();
+template void test3, et_off> >();
+template void test2, et_off> >();
 
-#endif
\ No newline at end of file
+#endif

From e3b56e3f7c66122db8449d589e5fc0eda21c7dd6 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 25 Oct 2012 11:53:25 +0000
Subject: [PATCH 243/256] Fix constexpr support.

[SVN r81063]
---
 include/boost/multiprecision/cpp_int.hpp | 61 +++++++++++++-----------
 test/test_constexpr.cpp                  | 15 ++++++
 2 files changed, 49 insertions(+), 27 deletions(-)

diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp
index c035de13..68594089 100644
--- a/include/boost/multiprecision/cpp_int.hpp
+++ b/include/boost/multiprecision/cpp_int.hpp
@@ -680,25 +680,21 @@ private:
    BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
 protected:
    template 
-   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type)), T>::type check_in_range(T val, const mpl::int_&)
+   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type)), void>::type check_in_range(T val, const mpl::int_&)
    {
       BOOST_MP_USING_ABS
       typedef typename common_type::type common_type;
 
       if(static_cast(abs(val)) > static_cast(limb_mask))
          BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
-      return val;
    }
    template 
-   BOOST_CONSTEXPR T check_in_range(T val, const mpl::int_&)
-   {
-      return val;
-   }
+   void check_in_range(T val, const mpl::int_&){}
 
    template 
-   BOOST_CONSTEXPR T check_in_range(T val)
+   void check_in_range(T val)
    {
-      return check_in_range(val, checked_type());
+      check_in_range(val, checked_type());
    }
 
 public:
@@ -706,14 +702,23 @@ public:
    // Direct construction:
    //
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
-      : m_data(check_in_range(i) < 0 ? static_cast(-i) : static_cast(i)), m_sign(i < 0) {}
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if_c::value && (Checked == unchecked) >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(i < 0 ? static_cast(-i) : static_cast(i)), m_sign(i < 0) {}
+   template 
+   BOOST_FORCEINLINE cpp_int_base(SI i, typename enable_if_c::value && (Checked == checked) >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(i < 0 ? static_cast(-i) : static_cast(i)), m_sign(i < 0) { check_in_range(i); }
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
-      : m_data(static_cast(check_in_range(i))), m_sign(false) {}
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if_c::value && (Checked == unchecked)>::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(static_cast(i)), m_sign(false) {}
+   template 
+   BOOST_FORCEINLINE cpp_int_base(UI i, typename enable_if_c::value && (Checked == checked)>::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(static_cast(i)), m_sign(false) { check_in_range(i); }
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
-      : m_data(static_cast(std::fabs(check_in_range(i)))), m_sign(i < 0) {}
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(F i, typename enable_if_c::value && (Checked == unchecked)>::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(static_cast(std::fabs(i))), m_sign(i < 0) {}
+   template 
+   BOOST_FORCEINLINE cpp_int_base(F i, typename enable_if_c::value && (Checked == checked)>::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(static_cast(std::fabs(i))), m_sign(i < 0) { check_in_range(i); }
    //
    // Helper functions for getting at our internal data, and manipulating storage:
    //
@@ -792,7 +797,7 @@ private:
    BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
 protected:
    template 
-   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type)), T>::type check_in_range(T val, const mpl::int_&, const mpl::true_&)
+   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type))>::type check_in_range(T val, const mpl::int_&, const mpl::true_&)
    {
       typedef typename common_type::type common_type;
 
@@ -800,7 +805,7 @@ protected:
          BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
    }
    template 
-   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type)), T>::type check_in_range(T val, const mpl::int_&, const mpl::false_&)
+   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type))>::type check_in_range(T val, const mpl::int_&, const mpl::false_&)
    {
       typedef typename common_type::type common_type;
 
@@ -808,18 +813,14 @@ protected:
          BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
       if(val < 0)
          BOOST_THROW_EXCEPTION(std::range_error("The argument to an unsigned cpp_int constructor was negative."));
-      return val;
    }
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR T check_in_range(T val, const mpl::int_&, const U&)
-   {
-      return val;
-   }
+   BOOST_FORCEINLINE void check_in_range(T val, const mpl::int_&, const U&){}
 
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR T check_in_range(T val)
+   BOOST_FORCEINLINE void check_in_range(T val)
    {
-      return check_in_range(val, checked_type(), is_unsigned());
+      check_in_range(val, checked_type(), is_unsigned());
    }
 
 public:
@@ -827,11 +828,17 @@ public:
    // Direct construction:
    //
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
-      : m_data(check_in_range(i) < 0 ? 1 + ~static_cast(-i) : static_cast(i)) {}
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename enable_if_c::value && (Checked == unchecked) >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(i < 0 ? 1 + ~static_cast(-i) : static_cast(i)) {}
+   template 
+   BOOST_FORCEINLINE cpp_int_base(SI i, typename enable_if_c::value && (Checked == checked) >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(i < 0 ? 1 + ~static_cast(-i) : static_cast(i)) { check_in_range(i); }
    template 
-   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
-      : m_data(static_cast(check_in_range(i))) {}
+   BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename enable_if_c::value && (Checked == unchecked) >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(static_cast(i)) {}
+   template 
+   BOOST_FORCEINLINE cpp_int_base(UI i, typename enable_if_c::value && (Checked == checked) >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
+      : m_data(static_cast(i)) { check_in_range(i); }
    template 
    BOOST_FORCEINLINE cpp_int_base(F i, typename enable_if >::type const* = 0) BOOST_NOEXCEPT_IF((Checked == unchecked))
       : m_data(static_cast(std::fabs(i)))
diff --git a/test/test_constexpr.cpp b/test/test_constexpr.cpp
index fb4fff44..ca84ad3e 100644
--- a/test/test_constexpr.cpp
+++ b/test/test_constexpr.cpp
@@ -7,6 +7,9 @@
 
 #ifndef BOOST_NO_CONSTEXPR
 
+template 
+void silence_unused(const T&){}
+
 template 
 void test1()
 {
@@ -14,6 +17,11 @@ void test1()
    constexpr T i2;
    constexpr T i3 = -3;
    constexpr T i4(i1);
+
+   silence_unused(i1);
+   silence_unused(i2);
+   silence_unused(i3);
+   silence_unused(i4);
 }
 template 
 void test2()
@@ -21,12 +29,19 @@ void test2()
    constexpr T i1 = 2u;
    constexpr T i2;
    constexpr T i3 = -3;
+
+   silence_unused(i1);
+   silence_unused(i2);
+   silence_unused(i3);
 }
 template 
 void test3()
 {
    constexpr T i1 = 2u;
    constexpr T i2;
+
+   silence_unused(i1);
+   silence_unused(i2);
 }
 
 using namespace boost::multiprecision;

From 645fe8865c9d8db83d963a0f0e2979b8056fa442 Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Sat, 27 Oct 2012 17:48:33 +0000
Subject: [PATCH 244/256] Add tests for checked ints and fix failures. Make
 negating an unsigned int an error, and fix resulting test failures. Change
 allocator defaults to be void when the allocator is not actually required.

[SVN r81070]
---
 include/boost/multiprecision/cpp_int.hpp      |  24 +-
 .../boost/multiprecision/cpp_int/bitwise.hpp  | 125 +++----
 .../boost/multiprecision/cpp_int/checked.hpp  |   2 +-
 .../multiprecision/cpp_int/cpp_int_config.hpp |  12 +-
 .../boost/multiprecision/cpp_int/limits.hpp   |   7 +-
 .../boost/multiprecision/detail/et_ops.hpp    |  12 +-
 .../boost/multiprecision/detail/no_et_ops.hpp |   2 +
 test/Jamfile.v2                               |   2 +
 test/compile_fail/cpp_int_complement.cpp      |  14 +
 test/compile_fail/cpp_int_negate_1.cpp        |  14 +
 test/compile_fail/cpp_int_negate_2.cpp        |  14 +
 test/test.hpp                                 |   7 +-
 test/test_arithmetic.cpp                      | 331 +++++++++---------
 test/test_checked_cpp_int.cpp                 | 116 ++++++
 test/test_cpp_int.cpp                         |  71 ++--
 test/test_int_io.cpp                          |  38 +-
 16 files changed, 504 insertions(+), 287 deletions(-)
 create mode 100644 test/compile_fail/cpp_int_complement.cpp
 create mode 100644 test/compile_fail/cpp_int_negate_1.cpp
 create mode 100644 test/compile_fail/cpp_int_negate_2.cpp
 create mode 100644 test/test_checked_cpp_int.cpp

diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp
index 68594089..4f84e881 100644
--- a/include/boost/multiprecision/cpp_int.hpp
+++ b/include/boost/multiprecision/cpp_int.hpp
@@ -32,7 +32,7 @@ namespace backends{
 #pragma warning(disable:4127 4351 4293)
 #endif
 
-template  >
+template  >::type >
 struct cpp_int_backend;
 
 template 
@@ -680,7 +680,8 @@ private:
    BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
 protected:
    template 
-   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type)), void>::type check_in_range(T val, const mpl::int_&)
+   typename disable_if_c::is_specialized && (std::numeric_limits::digits <= MinBits)>::type
+      check_in_range(T val, const mpl::int_&)
    {
       BOOST_MP_USING_ABS
       typedef typename common_type::type common_type;
@@ -797,7 +798,8 @@ private:
    BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
 protected:
    template 
-   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type))>::type check_in_range(T val, const mpl::int_&, const mpl::true_&)
+   typename disable_if_c::is_specialized && (std::numeric_limits::digits <= MinBits)>::type
+      check_in_range(T val, const mpl::int_&, const mpl::false_&)
    {
       typedef typename common_type::type common_type;
 
@@ -805,7 +807,7 @@ protected:
          BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
    }
    template 
-   typename disable_if_c::value && (sizeof(T) <= sizeof(local_limb_type))>::type check_in_range(T val, const mpl::int_&, const mpl::false_&)
+   void check_in_range(T val, const mpl::int_&, const mpl::true_&)
    {
       typedef typename common_type::type common_type;
 
@@ -814,13 +816,13 @@ protected:
       if(val < 0)
          BOOST_THROW_EXCEPTION(std::range_error("The argument to an unsigned cpp_int constructor was negative."));
    }
-   template 
-   BOOST_FORCEINLINE void check_in_range(T val, const mpl::int_&, const U&){}
+   template 
+   BOOST_FORCEINLINE void check_in_range(T val, const mpl::int_&, const mpl::bool_&){}
 
    template 
    BOOST_FORCEINLINE void check_in_range(T val)
    {
-      check_in_range(val, checked_type(), is_unsigned());
+      check_in_range(val, checked_type(), is_signed());
    }
 
 public:
@@ -878,6 +880,10 @@ public:
    }
    BOOST_FORCEINLINE void negate() BOOST_NOEXCEPT
    {
+      if(Checked == checked)
+      {
+         BOOST_THROW_EXCEPTION(std::range_error("Attempt to negate an unsigned type."));
+      }
       m_data = ~m_data;
       ++m_data;
    }
@@ -1316,7 +1322,7 @@ private:
                val = 10 + *s - 'A';
             else
                val = radix + 1;
-            if(val > radix)
+            if(val >= radix)
             {
                BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
             }
@@ -1377,7 +1383,7 @@ private:
                      val = 10 + *s - 'A';
                   else
                      val = base_type::max_limb_value;
-                  if(val > radix)
+                  if(val >= radix)
                   {
                      BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
                   }
diff --git a/include/boost/multiprecision/cpp_int/bitwise.hpp b/include/boost/multiprecision/cpp_int/bitwise.hpp
index 0d6db044..7909cba3 100644
--- a/include/boost/multiprecision/cpp_int/bitwise.hpp
+++ b/include/boost/multiprecision/cpp_int/bitwise.hpp
@@ -10,10 +10,24 @@
 
 namespace boost{ namespace multiprecision{ namespace backends{
 
+template 
+void is_valid_bitwise_op(
+      cpp_int_backend& result,
+      const cpp_int_backend& o, const mpl::int_&)
+{
+   if(result.sign() || o.sign())
+      BOOST_THROW_EXCEPTION(std::range_error("Bitwise operations on negative values results in undefined behavior."));
+}
+
+template 
+void is_valid_bitwise_op(
+      cpp_int_backend&,
+      const cpp_int_backend& , const mpl::int_&){}
+
 template 
 void bitwise_op(
-   CppInt1& result, 
-   const CppInt2& o, 
+   CppInt1& result,
+   const CppInt2& o,
    Op op) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int::value))
 {
    //
@@ -26,6 +40,11 @@ void bitwise_op(
    // When one arg is negative we convert to 2's complement form "on the fly",
    // and then convert back to signed-magnitude form at the end.
    //
+   // Note however, that if the type is checked, then bitwise ops on negative values
+   // are not permitted and an exception will result.
+   //
+   is_valid_bitwise_op(result, o, typename CppInt1::checked_type());
+   //
    // First figure out how big the result needs to be and set up some data:
    //
    unsigned rs = result.size();
@@ -144,36 +163,36 @@ struct bit_or { limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCE
 struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a ^ b; } };
 
 template 
-BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type
    eval_bitwise_and(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    bitwise_op(result, o, bit_and());
 }
 
 template 
-BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type
    eval_bitwise_or(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    bitwise_op(result, o, bit_or());
 }
 
 template 
-BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value >::type
    eval_bitwise_xor(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    bitwise_op(result, o, bit_xor());
 }
 
 template 
-BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type
    eval_complement(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    BOOST_STATIC_ASSERT_MSG(((Checked1 != checked) || (Checked2 != checked)), "Attempt to take the complement of a signed type results in undefined behavior.");
@@ -184,9 +203,9 @@ BOOST_FORCEINLINE typename enable_if_c
-BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type 
+BOOST_FORCEINLINE typename enable_if_c >::value && !is_trivial_cpp_int >::value && !is_trivial_cpp_int >::value >::type
    eval_complement(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    unsigned os = o.size();
@@ -195,12 +214,13 @@ BOOST_FORCEINLINE typename enable_if_c(0);
+   result.normalize();
 }
 
 template 
-inline typename enable_if_c >::value>::type 
+inline typename enable_if_c >::value>::type
    eval_left_shift(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       double_limb_type s) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    if(!s)
@@ -287,7 +307,7 @@ inline typename enable_if_c
 inline typename enable_if_c >::value>::type
    eval_right_shift(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       double_limb_type s) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    if(!s)
@@ -334,7 +354,7 @@ inline typename enable_if_c
-BOOST_FORCEINLINE typename enable_if > >::type 
+BOOST_FORCEINLINE typename enable_if > >::type
    eval_left_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    *result.limbs() = detail::checked_left_shift(*result.limbs(), s, typename cpp_int_backend::checked_type());
@@ -342,35 +362,21 @@ BOOST_FORCEINLINE typename enable_if
-BOOST_FORCEINLINE typename enable_if > >::type 
+BOOST_FORCEINLINE typename enable_if > >::type
    eval_right_shift(cpp_int_backend& result, T s) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    // Nothing to check here... just make sure we don't invoke undefined behavior:
    *result.limbs() = (static_cast(s) >= sizeof(*result.limbs()) * CHAR_BIT) ? 0 : *result.limbs() >>= s;
 }
 
-template 
-void is_valid_bitwise_op(
-      cpp_int_backend& result, 
-      const cpp_int_backend& o, const mpl::int_&)
-{
-   if(result.sign() || o.sign())
-      BOOST_THROW_EXCEPTION(std::range_error("Bitwise operations on negative values results in undefined behavior."));
-}
-
-template 
-void is_valid_bitwise_op(
-      cpp_int_backend&, 
-      const cpp_int_backend& , const mpl::int_&){}
-
 template 
 inline typename enable_if_c<
-         is_trivial_cpp_int >::value 
+         is_trivial_cpp_int >::value
          && is_trivial_cpp_int >::value
          && (is_signed_number >::value || is_signed_number >::value)
-         >::type 
+         >::type
    eval_bitwise_and(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    is_valid_bitwise_op(result, o, typename cpp_int_backend::checked_type());
@@ -401,13 +407,13 @@ inline typename enable_if_c<
 
 template 
 inline typename enable_if_c<
-         is_trivial_cpp_int >::value 
+         is_trivial_cpp_int >::value
          && is_trivial_cpp_int >::value
-         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
          && is_unsigned_number >::value
-         >::type 
+         >::type
    eval_bitwise_and(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    *result.limbs() &= *o.limbs();
@@ -415,12 +421,12 @@ inline typename enable_if_c<
 
 template 
 inline typename enable_if_c<
-         is_trivial_cpp_int >::value 
+         is_trivial_cpp_int >::value
          && is_trivial_cpp_int >::value
          && (is_signed_number >::value || is_signed_number >::value)
-         >::type 
+         >::type
    eval_bitwise_or(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    is_valid_bitwise_op(result, o, typename cpp_int_backend::checked_type());
@@ -452,13 +458,13 @@ inline typename enable_if_c<
 
 template 
 inline typename enable_if_c<
-         is_trivial_cpp_int >::value 
+         is_trivial_cpp_int >::value
          && is_trivial_cpp_int >::value
-         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
          && is_unsigned_number >::value
-         >::type 
+         >::type
    eval_bitwise_or(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    *result.limbs() |= *o.limbs();
@@ -466,12 +472,12 @@ inline typename enable_if_c<
 
 template 
 inline typename enable_if_c<
-         is_trivial_cpp_int >::value 
+         is_trivial_cpp_int >::value
          && is_trivial_cpp_int >::value
          && (is_signed_number >::value || is_signed_number >::value)
-         >::type 
+         >::type
    eval_bitwise_xor(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    is_valid_bitwise_op(result, o, typename cpp_int_backend::checked_type());
@@ -502,13 +508,13 @@ inline typename enable_if_c<
 
 template 
 inline typename enable_if_c<
-         is_trivial_cpp_int >::value 
+         is_trivial_cpp_int >::value
          && is_trivial_cpp_int >::value
-         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
          && is_unsigned_number >::value
-         >::type 
+         >::type
    eval_bitwise_xor(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    *result.limbs() ^= *o.limbs();
@@ -516,12 +522,12 @@ inline typename enable_if_c<
 
 template 
 inline typename enable_if_c<
-         is_trivial_cpp_int >::value 
+         is_trivial_cpp_int >::value
          && is_trivial_cpp_int >::value
          && (is_signed_number >::value || is_signed_number >::value)
-         >::type 
+         >::type
    eval_complement(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    BOOST_STATIC_ASSERT_MSG(((Checked1 != checked) || (Checked2 != checked)), "Attempt to take the complement of a signed type results in undefined behavior.");
@@ -543,16 +549,17 @@ inline typename enable_if_c<
 
 template 
 inline typename enable_if_c<
-         is_trivial_cpp_int >::value 
+         is_trivial_cpp_int >::value
          && is_trivial_cpp_int >::value
-         && is_unsigned_number >::value 
+         && is_unsigned_number >::value
          && is_unsigned_number >::value
-         >::type 
+         >::type
    eval_complement(
-      cpp_int_backend& result, 
+      cpp_int_backend& result,
       const cpp_int_backend& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value))
 {
    *result.limbs() = ~*o.limbs();
+   result.normalize();
 }
 
 }}} // namespaces
diff --git a/include/boost/multiprecision/cpp_int/checked.hpp b/include/boost/multiprecision/cpp_int/checked.hpp
index a3eb5dcc..5217ffe8 100644
--- a/include/boost/multiprecision/cpp_int/checked.hpp
+++ b/include/boost/multiprecision/cpp_int/checked.hpp
@@ -23,7 +23,7 @@ inline void raise_add_overflow()
 }
 inline void raise_subtract_overflow()
 {
-   raise_overflow("subtraction");
+   BOOST_THROW_EXCEPTION(std::range_error("Subtraction resulted in a negative value, but the type is unsigned"));
 }
 inline void raise_mul_overflow()
 {
diff --git a/include/boost/multiprecision/cpp_int/cpp_int_config.hpp b/include/boost/multiprecision/cpp_int/cpp_int_config.hpp
index ae74d3b9..5c05d5ae 100644
--- a/include/boost/multiprecision/cpp_int/cpp_int_config.hpp
+++ b/include/boost/multiprecision/cpp_int/cpp_int_config.hpp
@@ -137,16 +137,16 @@ inline void minmax(const T& a, const T& b, T& aa, T& bb)
 
 enum cpp_integer_type
 {
-   signed_magnitude,
-   unsigned_magnitude,
-   signed_packed,
-   unsigned_packed
+   signed_magnitude = 1,
+   unsigned_magnitude = 0,
+   signed_packed = 3,
+   unsigned_packed = 2
 };
 
 enum cpp_int_check_type
 {
-   checked,
-   unchecked
+   checked = 1,
+   unchecked = 0
 };
 
 }}
diff --git a/include/boost/multiprecision/cpp_int/limits.hpp b/include/boost/multiprecision/cpp_int/limits.hpp
index 0f80fccc..7f7d7476 100644
--- a/include/boost/multiprecision/cpp_int/limits.hpp
+++ b/include/boost/multiprecision/cpp_int/limits.hpp
@@ -18,7 +18,7 @@ inline boost::multiprecision::number, ExpressionTemplates> result_type;
-   typedef boost::multiprecision::number, ExpressionTemplates> ui_type;
+   typedef boost::multiprecision::number, ExpressionTemplates> ui_type;
    static const result_type val = -result_type(~ui_type(0));
    return val;
 }
@@ -57,7 +57,7 @@ inline boost::multiprecision::number, ExpressionTemplates> result_type;
-   typedef boost::multiprecision::number, ExpressionTemplates> ui_type;
+   typedef boost::multiprecision::number, ExpressionTemplates> ui_type;
    static const result_type val = ~ui_type(0);
    return val;
 }
@@ -68,7 +68,8 @@ inline boost::multiprecision::number, ExpressionTemplates> result_type;
-   static const result_type val = ~result_type(0);
+   typedef boost::multiprecision::number, ExpressionTemplates> ui_type;
+   static const result_type val = ~ui_type(0);
    return val;
 }
 
diff --git a/include/boost/multiprecision/detail/et_ops.hpp b/include/boost/multiprecision/detail/et_ops.hpp
index 81fb9580..9808a6aa 100644
--- a/include/boost/multiprecision/detail/et_ops.hpp
+++ b/include/boost/multiprecision/detail/et_ops.hpp
@@ -18,9 +18,17 @@ inline const number& operator + (const number
 inline const detail::expression& operator + (const detail::expression& v) { return v; }
 template 
-inline detail::expression > operator - (const number& v) { return detail::expression >(v); }
+inline detail::expression > operator - (const number& v) 
+{
+   BOOST_STATIC_ASSERT_MSG(is_signed_number::value, "Negating an unsigned type results in ill-defined behavior.");
+   return detail::expression >(v); 
+}
 template 
-inline detail::expression > operator - (const detail::expression& v) { return detail::expression >(v); }
+inline detail::expression > operator - (const detail::expression& v) 
+{ 
+   BOOST_STATIC_ASSERT_MSG((is_signed_number::result_type>::value), "Negating an unsigned type results in ill-defined behavior.");
+   return detail::expression >(v); 
+}
 template 
 inline detail::expression > operator ~ (const number& v) { return detail::expression >(v); }
 template 
diff --git a/include/boost/multiprecision/detail/no_et_ops.hpp b/include/boost/multiprecision/detail/no_et_ops.hpp
index 82bb5e5c..df27544c 100644
--- a/include/boost/multiprecision/detail/no_et_ops.hpp
+++ b/include/boost/multiprecision/detail/no_et_ops.hpp
@@ -17,6 +17,7 @@ namespace multiprecision{
 template 
 inline number operator - (const number& v) 
 {
+   BOOST_STATIC_ASSERT_MSG(is_signed_number::value, "Negating an unsigned type results in ill-defined behavior.");
    number result(v);
    result.backend().negate();
    return BOOST_MP_MOVE(result); 
@@ -299,6 +300,7 @@ inline typename enable_if, number >::type
 template 
 inline number operator - (number&& v) 
 {
+   BOOST_STATIC_ASSERT_MSG(is_signed_number::value, "Negating an unsigned type results in ill-defined behavior.");
    v.backend().negate();
    return static_cast&&>(v); 
 }
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 65b162be..08cf87c7 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -752,6 +752,8 @@ run test_cpp_int.cpp gmp
          : test_cpp_int_3
          ;
 
+run test_checked_cpp_int.cpp ;
+
 run test_miller_rabin.cpp gmp
         : # command line
         : # input files
diff --git a/test/compile_fail/cpp_int_complement.cpp b/test/compile_fail/cpp_int_complement.cpp
new file mode 100644
index 00000000..195d94e7
--- /dev/null
+++ b/test/compile_fail/cpp_int_complement.cpp
@@ -0,0 +1,14 @@
+///////////////////////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include 
+
+using namespace boost::multiprecision;
+
+int main()
+{
+   checked_int256_t i;
+   i = ~i;
+}
diff --git a/test/compile_fail/cpp_int_negate_1.cpp b/test/compile_fail/cpp_int_negate_1.cpp
new file mode 100644
index 00000000..35fa0abc
--- /dev/null
+++ b/test/compile_fail/cpp_int_negate_1.cpp
@@ -0,0 +1,14 @@
+///////////////////////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include 
+
+using namespace boost::multiprecision;
+
+int main()
+{
+   checked_uint256_t i;
+   i = -i;
+}
diff --git a/test/compile_fail/cpp_int_negate_2.cpp b/test/compile_fail/cpp_int_negate_2.cpp
new file mode 100644
index 00000000..5b75cf09
--- /dev/null
+++ b/test/compile_fail/cpp_int_negate_2.cpp
@@ -0,0 +1,14 @@
+///////////////////////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include 
+
+using namespace boost::multiprecision;
+
+int main()
+{
+   number, et_on> i;
+   i = -i;
+}
diff --git a/test/test.hpp b/test/test.hpp
index d707ccc0..d8606f45 100644
--- a/test/test.hpp
+++ b/test/test.hpp
@@ -16,17 +16,20 @@
 #include 
 #include 
 #include 
+#include 
 
 namespace detail{
 
 template 
-inline typename boost::disable_if, T>::type abs(const T& a)
+inline typename boost::disable_if_c::value || boost::multiprecision::is_unsigned_number::value, T>::type 
+   abs(const T& a)
 {
    return a < 0 ? -a : a;
 }
 
 template 
-inline typename boost::enable_if, T>::type abs(const T& a)
+inline typename boost::enable_if_c::value || boost::multiprecision::is_unsigned_number::value, T>::type 
+   abs(const T& a)
 {
    return a;
 }
diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp
index 1b047b1f..32f5a9d0 100644
--- a/test/test_arithmetic.cpp
+++ b/test/test_arithmetic.cpp
@@ -395,9 +395,118 @@ void test_integer_ops(const boost::mpl::int_(is_boost_rational());
 }
 
+template 
+void test_signed_integer_ops(const boost::mpl::true_&)
+{
+   Real a(20);
+   Real b(7);
+   Real c(5);
+   BOOST_TEST(-a % c == 0);
+   BOOST_TEST(-a % b == -20 % 7);
+   BOOST_TEST(-a % -b == -20 % -7);
+   BOOST_TEST(a % -b == 20 % -7);
+   BOOST_TEST(-a % 7 == -20 % 7);
+   BOOST_TEST(-a % -7 == -20 % -7);
+   BOOST_TEST(a % -7 == 20 % -7);
+   BOOST_TEST(-a % 7u == -20 % 7);
+   BOOST_TEST(-a % a == 0);
+   BOOST_TEST(-a % 5 == 0);
+   BOOST_TEST(-a % -5 == 0);
+   BOOST_TEST(a % -5 == 0);
+
+   b = -b;
+   BOOST_TEST(a % b == 20 % -7);
+   a = -a;
+   BOOST_TEST(a % b == -20 % -7);
+   BOOST_TEST(a % -7 == -20 % -7);
+   b = 7;
+   BOOST_TEST(a % b == -20 % 7);
+   BOOST_TEST(a % 7 == -20 % 7);
+   BOOST_TEST(a % 7u == -20 % 7);
+
+   a = 20;
+   a %= b;
+   BOOST_TEST(a == 20 % 7);
+   a = -20;
+   a %= b;
+   BOOST_TEST(a == -20 % 7);
+   a = 20;
+   a %= -b;
+   BOOST_TEST(a == 20 % -7);
+   a = -20;
+   a %= -b;
+   BOOST_TEST(a == -20 % -7);
+   a = 5;
+   a %= b - a;
+   BOOST_TEST(a == 5 % (7-5));
+   a = -20;
+   a %= 7;
+   BOOST_TEST(a == -20 % 7);
+   a = 20;
+   a %= -7;
+   BOOST_TEST(a == 20 % -7);
+   a = -20;
+   a %= -7;
+   BOOST_TEST(a == -20 % -7);
+#ifndef BOOST_NO_LONG_LONG
+   a = -20;
+   a %= 7uLL;
+   BOOST_TEST(a == -20 % 7);
+   a = 20;
+   a %= -7LL;
+   BOOST_TEST(a == 20 % -7);
+   a = -20;
+   a %= -7LL;
+   BOOST_TEST(a == -20 % -7);
+#endif
+   a = 400;
+   b = 45;
+   BOOST_TEST(gcd(a, -45) == boost::math::gcd(400, 45));
+   BOOST_TEST(lcm(a, -45) == boost::math::lcm(400, 45));
+   BOOST_TEST(gcd(-400, b) == boost::math::gcd(400, 45));
+   BOOST_TEST(lcm(-400, b) == boost::math::lcm(400, 45));
+   a = -20;
+   BOOST_TEST(abs(a) == 20);
+   BOOST_TEST(abs(-a) == 20);
+   BOOST_TEST(abs(+a) == 20);
+   a = 20;
+   BOOST_TEST(abs(a) == 20);
+   BOOST_TEST(abs(-a) == 20);
+   BOOST_TEST(abs(+a) == 20);
+   a = -400;
+   b = 45;
+   BOOST_TEST(gcd(a, b) == boost::math::gcd(-400, 45));
+   BOOST_TEST(lcm(a, b) == boost::math::lcm(-400, 45));
+   BOOST_TEST(gcd(a, 45) == boost::math::gcd(-400, 45));
+   BOOST_TEST(lcm(a, 45) == boost::math::lcm(-400, 45));
+   BOOST_TEST(gcd(-400, b) == boost::math::gcd(-400, 45));
+   BOOST_TEST(lcm(-400, b) == boost::math::lcm(-400, 45));
+   Real r;
+   divide_qr(a, b, c, r);
+   BOOST_TEST(c == a / b);
+   BOOST_TEST(r == a % b);
+   BOOST_TEST(integer_modulus(a, 57) == abs(a % 57));
+   b = -57;
+   divide_qr(a, b, c, r);
+   BOOST_TEST(c == a / b);
+   BOOST_TEST(r == a % b);
+   BOOST_TEST(integer_modulus(a, -57) == abs(a % -57));
+   a = 458;
+   divide_qr(a, b, c, r);
+   BOOST_TEST(c == a / b);
+   BOOST_TEST(r == a % b);
+   BOOST_TEST(integer_modulus(a, -57) == abs(a % -57));
+}
+template 
+void test_signed_integer_ops(const boost::mpl::false_&)
+{
+}
+
 template 
 void test_integer_ops(const boost::mpl::int_&)
 {
+   test_signed_integer_ops(boost::mpl::bool_::is_signed>());
+
    Real a(20);
    Real b(7);
    Real c(5);
@@ -416,79 +525,14 @@ void test_integer_ops(const boost::mpl::int_::is_signed)
-   {
-      BOOST_TEST(-a % c == 0);
-      BOOST_TEST(-a % b == -20 % 7);
-      BOOST_TEST(-a % -b == -20 % -7);
-      BOOST_TEST(a % -b == 20 % -7);
-      BOOST_TEST(-a % 7 == -20 % 7);
-      BOOST_TEST(-a % -7 == -20 % -7);
-      BOOST_TEST(a % -7 == 20 % -7);
-      BOOST_TEST(-a % 7u == -20 % 7);
-      BOOST_TEST(-a % a == 0);
-      BOOST_TEST(-a % 5 == 0);
-      BOOST_TEST(-a % -5 == 0);
-      BOOST_TEST(a % -5 == 0);
-
-      b = -b;
-      BOOST_TEST(a % b == 20 % -7);
-      a = -a;
-      BOOST_TEST(a % b == -20 % -7);
-      BOOST_TEST(a % -7 == -20 % -7);
-      b = 7;
-      BOOST_TEST(a % b == -20 % 7);
-      BOOST_TEST(a % 7 == -20 % 7);
-      BOOST_TEST(a % 7u == -20 % 7);
-
-      a = 20;
-      a %= b;
-      BOOST_TEST(a == 20 % 7);
-      a = -20;
-      a %= b;
-      BOOST_TEST(a == -20 % 7);
-      a = 20;
-      a %= -b;
-      BOOST_TEST(a == 20 % -7);
-      a = -20;
-      a %= -b;
-      BOOST_TEST(a == -20 % -7);
-      a = 5;
-      a %= b - a;
-      BOOST_TEST(a == 5 % (7-5));
-   }
 
    a = 20;
    a %= 7;
    BOOST_TEST(a == 20 % 7);
-   if(std::numeric_limits::is_signed)
-   {
-      a = -20;
-      a %= 7;
-      BOOST_TEST(a == -20 % 7);
-      a = 20;
-      a %= -7;
-      BOOST_TEST(a == 20 % -7);
-      a = -20;
-      a %= -7;
-      BOOST_TEST(a == -20 % -7);
-   }
 #ifndef BOOST_NO_LONG_LONG
    a = 20;
    a %= 7uLL;
    BOOST_TEST(a == 20 % 7);
-   if(std::numeric_limits::is_signed)
-   {
-      a = -20;
-      a %= 7uLL;
-      BOOST_TEST(a == -20 % 7);
-      a = 20;
-      a %= -7LL;
-      BOOST_TEST(a == 20 % -7);
-      a = -20;
-      a %= -7LL;
-      BOOST_TEST(a == -20 % -7);
-   }
 #endif
    a = 20;
    BOOST_TEST(++a == 21);
@@ -649,20 +693,10 @@ void test_integer_ops(const boost::mpl::int_::is_signed)
-   {
-      BOOST_TEST(gcd(a, -45) == boost::math::gcd(400, 45));
-      BOOST_TEST(lcm(a, -45) == boost::math::lcm(400, 45));
-   }
    BOOST_TEST(gcd(a, 45u) == boost::math::gcd(400, 45));
    BOOST_TEST(lcm(a, 45u) == boost::math::lcm(400, 45));
    BOOST_TEST(gcd(400, b) == boost::math::gcd(400, 45));
    BOOST_TEST(lcm(400, b) == boost::math::lcm(400, 45));
-   if(std::numeric_limits::is_signed)
-   {
-      BOOST_TEST(gcd(-400, b) == boost::math::gcd(400, 45));
-      BOOST_TEST(lcm(-400, b) == boost::math::lcm(400, 45));
-   }
    BOOST_TEST(gcd(400u, b) == boost::math::gcd(400, 45));
    BOOST_TEST(lcm(400u, b) == boost::math::lcm(400, 45));
 
@@ -685,39 +719,6 @@ void test_integer_ops(const boost::mpl::int_::is_signed)
-   {
-      a = -20;
-      BOOST_TEST(abs(a) == 20);
-      BOOST_TEST(abs(-a) == 20);
-      BOOST_TEST(abs(+a) == 20);
-      a = 20;
-      BOOST_TEST(abs(a) == 20);
-      BOOST_TEST(abs(-a) == 20);
-      BOOST_TEST(abs(+a) == 20);
-      a = -400;
-      b = 45;
-      BOOST_TEST(gcd(a, b) == boost::math::gcd(-400, 45));
-      BOOST_TEST(lcm(a, b) == boost::math::lcm(-400, 45));
-      BOOST_TEST(gcd(a, 45) == boost::math::gcd(-400, 45));
-      BOOST_TEST(lcm(a, 45) == boost::math::lcm(-400, 45));
-      BOOST_TEST(gcd(-400, b) == boost::math::gcd(-400, 45));
-      BOOST_TEST(lcm(-400, b) == boost::math::lcm(-400, 45));
-      divide_qr(a, b, c, r);
-      BOOST_TEST(c == a / b);
-      BOOST_TEST(r == a % b);
-      BOOST_TEST(integer_modulus(a, 57) == abs(a % 57));
-      b = -57;
-      divide_qr(a, b, c, r);
-      BOOST_TEST(c == a / b);
-      BOOST_TEST(r == a % b);
-      BOOST_TEST(integer_modulus(a, -57) == abs(a % -57));
-      a = 458;
-      divide_qr(a, b, c, r);
-      BOOST_TEST(c == a / b);
-      BOOST_TEST(r == a % b);
-      BOOST_TEST(integer_modulus(a, -57) == abs(a % -57));
-   }
    for(unsigned i = 0; i < 20; ++i)
    {
       if(std::numeric_limits::is_specialized && (!std::numeric_limits::is_bounded || ((int)i * 17 < std::numeric_limits::digits)))
@@ -904,8 +905,6 @@ struct lexical_cast_target_type
 template 
 void test_negative_mixed(boost::mpl::true_ const&)
 {
-   if(std::numeric_limits::is_specialized && !std::numeric_limits::is_signed)
-      return;
    typedef typename lexical_cast_target_type::type target_type;
    typedef typename boost::mpl::if_<
          boost::is_convertible, 
@@ -1299,7 +1298,12 @@ void test_mixed(const boost::mpl::true_&)
    BOOST_TEST(r == static_cast(n4 * n5));
    r = static_cast(4 * n4) / Real(4);
    BOOST_TEST(r == static_cast(n4));
-   test_negative_mixed(boost::mpl::bool_::is_signed>());
+
+   typedef boost::mpl::bool_<
+      (!std::numeric_limits::is_specialized || std::numeric_limits::is_signed)
+      && (!std::numeric_limits::is_specialized || std::numeric_limits::is_signed)> signed_tag;
+
+   test_negative_mixed(signed_tag());
 
    n1 = 2;
    n2 = 3;
@@ -1405,6 +1409,53 @@ void test_members(boost::rational)
 {
 }
 
+template 
+void test_signed_ops(const boost::mpl::true_&)
+{
+   Real a(8);
+   Real b(64);
+   Real c(500);
+   Real d(1024);
+   Real ac;
+   BOOST_TEST(-a == -8);
+   ac = a;
+   ac = ac - b;
+   BOOST_TEST(ac == 8 - 64);
+   ac = a;
+   ac -= a + b;
+   BOOST_TEST(ac == -64);
+   ac = a;
+   ac -= b - a;
+   BOOST_TEST(ac == 16 - 64);
+   ac = -a;
+   BOOST_TEST(ac == -8);
+   ac = a;
+   ac -= -a;
+   BOOST_TEST(ac == 16);
+   ac = a;
+   ac += -a;
+   BOOST_TEST(ac == 0);
+   ac = b;
+   ac /= -a;
+   BOOST_TEST(ac == -8);
+   ac = a;
+   ac *= -a;
+   BOOST_TEST(ac == -64);
+   ac = a + -b;
+   BOOST_TEST(ac == 8 - 64);
+   ac = -a + b;
+   BOOST_TEST(ac == -8+64);
+   ac = -a + -b;
+   BOOST_TEST(ac == -72);
+   ac = a + - + -b; // lots of unary operators!!
+   BOOST_TEST(ac == 72);
+   test_conditional(Real(-a), -a);
+}
+template 
+void test_signed_ops(const boost::mpl::false_&)
+{
+}
+
 template 
 void test()
 {
@@ -1462,10 +1513,6 @@ void test()
    BOOST_TEST(a == 8);
    Real ac(a);
    BOOST_TEST(ac == a);
-   if(std::numeric_limits::is_signed)
-   {
-      BOOST_TEST(-a == -8);
-   }
    ac = a * c;
    BOOST_TEST(ac == 8*500L);
    ac = 8*500L;
@@ -1509,12 +1556,6 @@ void test()
    ac = a;
    ac = a + ac;
    BOOST_TEST(ac == 16);
-   if(std::numeric_limits::is_signed)
-   {
-      ac = a;
-      ac = ac - b;
-      BOOST_TEST(ac == 8 - 64);
-   }
    ac = a;
    ac = a - ac;
    BOOST_TEST(ac == 0);
@@ -1524,22 +1565,8 @@ void test()
    ac = a;
    ac += b + a;
    BOOST_TEST(ac == 80);
-   if(std::numeric_limits::is_signed)
-   {
-      ac = a;
-      ac -= a + b;
-      BOOST_TEST(ac == -64);
-      ac = a;
-      ac -= b - a;
-      BOOST_TEST(ac == 16 - 64);
-   }
    ac = +a;
    BOOST_TEST(ac == 8);
-   if(std::numeric_limits::is_signed)
-   {
-      ac = -a;
-      BOOST_TEST(ac == -8);
-   }
    ac = 8;
    ac = a * ac;
    BOOST_TEST(ac == 8*8);
@@ -1558,14 +1585,6 @@ void test()
    ac -= +a;
    BOOST_TEST(ac == 0);
    ac = a;
-   if(std::numeric_limits::is_signed)
-   {
-      ac -= -a;
-      BOOST_TEST(ac == 16);
-      ac = a;
-      ac += -a;
-      BOOST_TEST(ac == 0);
-   }
    if(std::numeric_limits::is_signed || is_twos_complement_integer::value)
    {
       ac = a;
@@ -1599,15 +1618,6 @@ void test()
    ac = b;
    ac /= +a;
    BOOST_TEST(ac == 8);
-   if(std::numeric_limits::is_signed)
-   {
-      ac = b;
-      ac /= -a;
-      BOOST_TEST(ac == -8);
-      ac = a;
-      ac *= -a;
-      BOOST_TEST(ac == -64);
-   }
    ac = b;
    ac /= b / a;
    BOOST_TEST(ac == 64 / (64/8));
@@ -1625,17 +1635,6 @@ void test()
    BOOST_TEST(ac == 72);
    ac = +a + +b;
    BOOST_TEST(ac == 72);
-   if(std::numeric_limits::is_signed)
-   {
-      ac = a + -b;
-      BOOST_TEST(ac == 8 - 64);
-      ac = -a + b;
-      BOOST_TEST(ac == -8+64);
-      ac = -a + -b;
-      BOOST_TEST(ac == -72);
-      ac = a + - + -b; // lots of unary operators!!
-      BOOST_TEST(ac == 72);
-   }
    ac = a;
    ac = b / ac;
    BOOST_TEST(ac == b / a);
@@ -1799,11 +1798,9 @@ void test()
    //
    a = 20;
    test_conditional(a, +a);
-   if(std::numeric_limits::is_signed || is_twos_complement_integer::value)
-   {
-      test_conditional(Real(-a), -a);
-   }
    test_conditional(a, (a + 0));
+
+   test_signed_ops(boost::mpl::bool_::is_signed>());
 }
 
 
diff --git a/test/test_checked_cpp_int.cpp b/test/test_checked_cpp_int.cpp
new file mode 100644
index 00000000..847760d2
--- /dev/null
+++ b/test/test_checked_cpp_int.cpp
@@ -0,0 +1,116 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+
+//
+// Compare arithmetic results using fixed_int to GMP results.
+//
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#include 
+#include "test.hpp"
+
+template 
+void test()
+{
+   using namespace boost::multiprecision;
+   typedef Number test_type;
+
+   if(std::numeric_limits::is_bounded)
+   {
+      test_type val = (std::numeric_limits::max)();
+      BOOST_CHECK_THROW(++val, std::overflow_error);
+      val = (std::numeric_limits::max)();
+      BOOST_CHECK_THROW(test_type(1 + val), std::overflow_error);
+      BOOST_CHECK_THROW(test_type(val + 1), std::overflow_error);
+      BOOST_CHECK_THROW(test_type(2 * val), std::overflow_error);
+      val /= 2;
+      val += 1;
+      BOOST_CHECK_THROW(test_type(2 * val), std::overflow_error);
+
+      if(std::numeric_limits::is_signed)
+      {
+         val = (std::numeric_limits::min)();
+         BOOST_CHECK_THROW(--val, std::overflow_error);
+         val = (std::numeric_limits::min)();
+         BOOST_CHECK_THROW(test_type(val - 1), std::overflow_error);
+         BOOST_CHECK_THROW(test_type(2 * val), std::overflow_error);
+         val /= 2;
+         val -= 1;
+         BOOST_CHECK_THROW(test_type(2 * val), std::overflow_error);
+      }
+      else
+      {
+         val = (std::numeric_limits::min)();
+         BOOST_CHECK_THROW(--val, std::range_error);
+         val = (std::numeric_limits::min)();
+         BOOST_CHECK_THROW(test_type(val - 1), std::range_error);
+      }
+   }
+
+   if(std::numeric_limits::is_signed)
+   {
+      test_type a = -1;
+      test_type b = 1;
+      BOOST_CHECK_THROW(test_type(a | b), std::range_error);
+      BOOST_CHECK_THROW(test_type(a & b), std::range_error);
+      BOOST_CHECK_THROW(test_type(a ^ b), std::range_error);
+   }
+   else
+   {
+      // Constructing from a negative value is not allowed:
+      BOOST_CHECK_THROW(test_type(-2), std::range_error);
+      BOOST_CHECK_THROW(test_type("-2"), std::range_error);
+   }
+   if(std::numeric_limits::digits < std::numeric_limits::digits)
+   {
+      long long llm = (std::numeric_limits::max)();
+      test_type t;
+      BOOST_CHECK_THROW(t = llm, std::range_error);
+      BOOST_CHECK_THROW(t = static_cast(llm), std::range_error);
+      unsigned long long ullm = (std::numeric_limits::max)();
+      BOOST_CHECK_THROW(t = ullm, std::range_error);
+      BOOST_CHECK_THROW(t = static_cast(ullm), std::range_error);
+
+      static const checked_uint512_t big = (std::numeric_limits::max)();
+      BOOST_CHECK_THROW(t = static_cast(big), std::range_error);
+   }
+   //
+   // String errors:
+   //
+   BOOST_CHECK_THROW(test_type("12A"), std::runtime_error);
+   BOOST_CHECK_THROW(test_type("0658"), std::runtime_error);
+
+   if(std::numeric_limits::is_signed)
+   {
+      BOOST_CHECK_THROW(test_type(-2).str(0, std::ios_base::hex), std::runtime_error);
+      BOOST_CHECK_THROW(test_type(-2).str(0, std::ios_base::oct), std::runtime_error);
+   }
+}
+
+int main()
+{
+   using namespace boost::multiprecision;
+
+   test > >();
+   test();
+   test();
+   test > >();
+   test > >();
+
+   //
+   // We also need to test type with "odd" bit counts in order to ensure full code coverage:
+   //
+   test > >();
+   test > >();
+   test > >();
+   test > >();
+   return boost::report_errors();
+}
+
+
+
diff --git a/test/test_cpp_int.cpp b/test/test_cpp_int.cpp
index 164833d5..4b7b74f0 100644
--- a/test/test_cpp_int.cpp
+++ b/test/test_cpp_int.cpp
@@ -52,6 +52,11 @@ T generate_random(unsigned bits_wanted)
    return val;
 }
 
+template 
+struct is_checked_cpp_int : public boost::mpl::false_ {};
+template 
+struct is_checked_cpp_int, ET> > : public boost::mpl::true_ {};
+
 template 
 void test()
 {
@@ -115,28 +120,37 @@ void test()
       // bitwise ops:
       BOOST_CHECK_EQUAL(mpz_int(a|b).str(), test_type(a1 | b1).str());
       BOOST_CHECK_EQUAL((mpz_int(a)|=b).str(), (test_type(a1) |= b1).str());
-      BOOST_CHECK_EQUAL(mpz_int(-a|b).str(), test_type(-a1 | b1).str());
-      BOOST_CHECK_EQUAL((mpz_int(-a)|=b).str(), (test_type(-a1) |= b1).str());
-      BOOST_CHECK_EQUAL(mpz_int(a|-b).str(), test_type(a1 | -b1).str());
-      BOOST_CHECK_EQUAL((mpz_int(a)|=-b).str(), (test_type(a1) |= -b1).str());
-      BOOST_CHECK_EQUAL(mpz_int(-a|-b).str(), test_type(-a1 | -b1).str());
-      BOOST_CHECK_EQUAL((mpz_int(-a)|=-b).str(), (test_type(-a1) |= -b1).str());
+      if(!is_checked_cpp_int::value)
+      {
+         BOOST_CHECK_EQUAL(mpz_int(-a|b).str(), test_type(-a1 | b1).str());
+         BOOST_CHECK_EQUAL((mpz_int(-a)|=b).str(), (test_type(-a1) |= b1).str());
+         BOOST_CHECK_EQUAL(mpz_int(a|-b).str(), test_type(a1 | -b1).str());
+         BOOST_CHECK_EQUAL((mpz_int(a)|=-b).str(), (test_type(a1) |= -b1).str());
+         BOOST_CHECK_EQUAL(mpz_int(-a|-b).str(), test_type(-a1 | -b1).str());
+         BOOST_CHECK_EQUAL((mpz_int(-a)|=-b).str(), (test_type(-a1) |= -b1).str());
+      }
       BOOST_CHECK_EQUAL(mpz_int(a&b).str(), test_type(a1 & b1).str());
       BOOST_CHECK_EQUAL((mpz_int(a)&=b).str(), (test_type(a1) &= b1).str());
-      BOOST_CHECK_EQUAL(mpz_int(-a&b).str(), test_type(-a1 & b1).str());
-      BOOST_CHECK_EQUAL((mpz_int(-a)&=b).str(), (test_type(-a1) &= b1).str());
-      BOOST_CHECK_EQUAL(mpz_int(a&-b).str(), test_type(a1 & -b1).str());
-      BOOST_CHECK_EQUAL((mpz_int(a)&=-b).str(), (test_type(a1) &= -b1).str());
-      BOOST_CHECK_EQUAL(mpz_int(-a&-b).str(), test_type(-a1 & -b1).str());
-      BOOST_CHECK_EQUAL((mpz_int(-a)&=-b).str(), (test_type(-a1) &= -b1).str());
+      if(!is_checked_cpp_int::value)
+      {
+         BOOST_CHECK_EQUAL(mpz_int(-a&b).str(), test_type(-a1 & b1).str());
+         BOOST_CHECK_EQUAL((mpz_int(-a)&=b).str(), (test_type(-a1) &= b1).str());
+         BOOST_CHECK_EQUAL(mpz_int(a&-b).str(), test_type(a1 & -b1).str());
+         BOOST_CHECK_EQUAL((mpz_int(a)&=-b).str(), (test_type(a1) &= -b1).str());
+         BOOST_CHECK_EQUAL(mpz_int(-a&-b).str(), test_type(-a1 & -b1).str());
+         BOOST_CHECK_EQUAL((mpz_int(-a)&=-b).str(), (test_type(-a1) &= -b1).str());
+      }
       BOOST_CHECK_EQUAL(mpz_int(a^b).str(), test_type(a1 ^ b1).str());
       BOOST_CHECK_EQUAL((mpz_int(a)^=b).str(), (test_type(a1) ^= b1).str());
-      BOOST_CHECK_EQUAL(mpz_int(-a^b).str(), test_type(-a1 ^ b1).str());
-      BOOST_CHECK_EQUAL((mpz_int(-a)^=b).str(), (test_type(-a1) ^= b1).str());
-      BOOST_CHECK_EQUAL(mpz_int(a^-b).str(), test_type(a1 ^ -b1).str());
-      BOOST_CHECK_EQUAL((mpz_int(a)^=-b).str(), (test_type(a1) ^= -b1).str());
-      BOOST_CHECK_EQUAL(mpz_int(-a^-b).str(), test_type(-a1 ^ -b1).str());
-      BOOST_CHECK_EQUAL((mpz_int(-a)^=-b).str(), (test_type(-a1) ^= -b1).str());
+      if(!is_checked_cpp_int::value)
+      {
+         BOOST_CHECK_EQUAL(mpz_int(-a^b).str(), test_type(-a1 ^ b1).str());
+         BOOST_CHECK_EQUAL((mpz_int(-a)^=b).str(), (test_type(-a1) ^= b1).str());
+         BOOST_CHECK_EQUAL(mpz_int(a^-b).str(), test_type(a1 ^ -b1).str());
+         BOOST_CHECK_EQUAL((mpz_int(a)^=-b).str(), (test_type(a1) ^= -b1).str());
+         BOOST_CHECK_EQUAL(mpz_int(-a^-b).str(), test_type(-a1 ^ -b1).str());
+         BOOST_CHECK_EQUAL((mpz_int(-a)^=-b).str(), (test_type(-a1) ^= -b1).str());
+      }
       // Shift ops:
       for(unsigned i = 0; i < 128; ++i)
       {
@@ -185,15 +199,18 @@ void test()
       BOOST_CHECK_EQUAL((mpz_int(a)%=-si).str(), (test_type(a1) %= -si).str());
       BOOST_CHECK_EQUAL((mpz_int(-a)%=si).str(), (test_type(-a1) %= si).str());
       BOOST_CHECK_EQUAL((mpz_int(-a)%=-si).str(), (test_type(-a1) %= -si).str());
-      BOOST_CHECK_EQUAL(mpz_int(a|si).str(), test_type(a1 | si).str());
-      BOOST_CHECK_EQUAL((mpz_int(a)|=si).str(), (test_type(a1) |= si).str());
-      BOOST_CHECK_EQUAL(mpz_int(a&si).str(), test_type(a1 & si).str());
-      BOOST_CHECK_EQUAL((mpz_int(a)&=si).str(), (test_type(a1) &= si).str());
-      BOOST_CHECK_EQUAL(mpz_int(a^si).str(), test_type(a1 ^ si).str());
-      BOOST_CHECK_EQUAL((mpz_int(a)^=si).str(), (test_type(a1) ^= si).str());
-      BOOST_CHECK_EQUAL(mpz_int(si|a).str(), test_type(si|a1).str());
-      BOOST_CHECK_EQUAL(mpz_int(si&a).str(), test_type(si&a1).str());
-      BOOST_CHECK_EQUAL(mpz_int(si^a).str(), test_type(si^a1).str());
+      if((si > 0) || !is_checked_cpp_int::value)
+      {
+         BOOST_CHECK_EQUAL(mpz_int(a|si).str(), test_type(a1 | si).str());
+         BOOST_CHECK_EQUAL((mpz_int(a)|=si).str(), (test_type(a1) |= si).str());
+         BOOST_CHECK_EQUAL(mpz_int(a&si).str(), test_type(a1 & si).str());
+         BOOST_CHECK_EQUAL((mpz_int(a)&=si).str(), (test_type(a1) &= si).str());
+         BOOST_CHECK_EQUAL(mpz_int(a^si).str(), test_type(a1 ^ si).str());
+         BOOST_CHECK_EQUAL((mpz_int(a)^=si).str(), (test_type(a1) ^= si).str());
+         BOOST_CHECK_EQUAL(mpz_int(si|a).str(), test_type(si|a1).str());
+         BOOST_CHECK_EQUAL(mpz_int(si&a).str(), test_type(si&a1).str());
+         BOOST_CHECK_EQUAL(mpz_int(si^a).str(), test_type(si^a1).str());
+      }
       BOOST_CHECK_EQUAL(mpz_int(gcd(a, b)).str(), test_type(gcd(a1, b1)).str());
       BOOST_CHECK_EQUAL(mpz_int(lcm(c, d)).str(), test_type(lcm(c1, d1)).str());
       BOOST_CHECK_EQUAL(mpz_int(gcd(-a, b)).str(), test_type(gcd(-a1, b1)).str());
diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp
index 6d9d0a76..ed92c6b6 100644
--- a/test/test_int_io.cpp
+++ b/test/test_int_io.cpp
@@ -98,6 +98,31 @@ void do_round_trip(const T& val)
    }
 }
 
+template 
+void negative_round_trip(T val, const boost::mpl::true_&)
+{
+   do_round_trip(T(-val));
+}
+template 
+void negative_round_trip(T, const boost::mpl::false_&)
+{
+}
+
+template 
+void negative_spots(const boost::mpl::true_&)
+{
+   BOOST_CHECK_EQUAL(T(-1002).str(), "-1002");
+   if(!std::numeric_limits::is_modulo)
+   {
+      BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::oct), std::runtime_error);
+      BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::hex), std::runtime_error);
+   }
+}
+template 
+void negative_spots(const boost::mpl::false_&)
+{
+}
+
 template 
 void test_round_trip()
 {
@@ -105,16 +130,11 @@ void test_round_trip()
    {
       T val = generate_random();
       do_round_trip(val);
-      if(std::numeric_limits::is_signed)
-         do_round_trip(T(-val));
+      negative_round_trip(val, boost::mpl::bool_::is_signed>());
    }
 
    BOOST_CHECK_EQUAL(T(1002).str(), "1002");
    BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::showpos), "+1002");
-   if(std::numeric_limits::is_signed)
-   {
-      BOOST_CHECK_EQUAL(T(-1002).str(), "-1002");
-   }
    BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::oct), "1752");
    BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::oct|std::ios_base::showbase), "01752");
    BOOST_CHECK_EQUAL(boost::to_lower_copy(T(1002).str(0, std::ios_base::hex)), "3ea");
@@ -122,11 +142,7 @@ void test_round_trip()
    BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::dec), "1002");
    BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::dec|std::ios_base::showbase), "1002");
 
-   if(std::numeric_limits::is_signed && !std::numeric_limits::is_modulo)
-   {
-      BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::oct), std::runtime_error);
-      BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::hex), std::runtime_error);
-   }
+   negative_spots(boost::mpl::bool_::is_signed>());
 }
 
 int main()

From c587f1550b59af4f42bd22962b1414ed6addf08e Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Wed, 31 Oct 2012 17:06:33 +0000
Subject: [PATCH 245/256] Update and regenerate docs. Fix error in expression
 template unpacking that occasionally caused variable over-writes. Update Math
 lib tests to test at least one non-ET type.

[SVN r81121]
---
 .../boost_multiprecision/indexes/s01.html     |   8 +-
 .../boost_multiprecision/indexes/s02.html     |  12 +-
 .../boost_multiprecision/indexes/s03.html     |  48 ++-
 .../boost_multiprecision/indexes/s04.html     |  74 +++-
 doc/html/boost_multiprecision/intro.html      | 118 +++++--
 doc/html/boost_multiprecision/map/hist.html   |   6 +-
 doc/html/boost_multiprecision/map/todo.html   |  42 +--
 .../boost_multiprecision/ref/cpp_int_ref.html | 102 ++++--
 .../boost_multiprecision/ref/headers.html     | 118 ++++++-
 .../boost_multiprecision/ref/internals.html   |  11 +
 doc/html/boost_multiprecision/ref/number.html |   7 +-
 .../boost_multiprecision/tut/conversions.html |  20 +-
 .../tut/floats/cpp_dec_float.html             |   6 +-
 .../tut/floats/gmp_float.html                 |   8 +-
 .../tut/ints/cpp_int.html                     | 226 +++++++++++--
 .../tut/ints/gmp_int.html                     |   2 +-
 .../tut/ints/tom_int.html                     |   2 +-
 .../tut/rational/cpp_rational.html            |   2 +-
 .../tut/rational/gmp_rational.html            |   2 +-
 .../tut/rational/tommath_rational.html        |   2 +-
 doc/html/index.html                           |   2 +-
 doc/multiprecision.qbk                        | 317 ++++++++++++------
 include/boost/multiprecision/cpp_int/misc.hpp |   2 +-
 include/boost/multiprecision/number.hpp       |  12 +-
 performance/sf_performance.cpp                |   7 +
 test/math/log1p_expm1_test.cpp                |   2 +
 test/math/powm1_sqrtp1m1_test.cpp             |   2 +
 test/math/test_bessel_i.cpp                   |   2 +
 test/math/test_bessel_j.cpp                   |   2 +
 test/math/test_bessel_k.cpp                   |   2 +
 test/math/test_bessel_y.cpp                   |   2 +
 test/math/test_beta.cpp                       |   2 +
 test/math/test_binomial_coeff.cpp             |   2 +
 test/math/test_carlson.cpp                    |   2 +
 test/math/test_cbrt.cpp                       |   2 +
 test/math/test_digamma.cpp                    |   2 +
 test/math/test_ellint_1.cpp                   |   2 +
 test/math/test_ellint_2.cpp                   |   2 +
 test/math/test_ellint_3.cpp                   |   2 +
 test/math/test_erf.cpp                        |   2 +
 test/math/test_expint.cpp                     |   2 +
 test/math/test_gamma.cpp                      |   2 +
 test/math/test_hermite.cpp                    |   2 +
 test/math/test_ibeta.cpp                      |   2 +
 test/math/test_ibeta_2.cpp                    |   2 +
 test/math/test_ibeta_3.cpp                    |   2 +
 test/math/test_ibeta_4.cpp                    |   2 +
 test/math/test_ibeta_inv_1.cpp                |   2 +
 test/math/test_ibeta_inv_ab_4.cpp             |   2 +
 test/math/test_igamma.cpp                     |   2 +
 test/math/test_igamma_inv.cpp                 |   2 +
 test/math/test_igamma_inva.cpp                |   2 +
 test/math/test_laguerre.cpp                   |   2 +
 test/math/test_legendre.cpp                   |   2 +
 test/math/test_tgamma_ratio.cpp               |   2 +
 test/math/test_zeta.cpp                       |   2 +
 56 files changed, 943 insertions(+), 275 deletions(-)

diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html
index b8bcad1a..af78fb53 100644
--- a/doc/html/boost_multiprecision/indexes/s01.html
+++ b/doc/html/boost_multiprecision/indexes/s01.html
@@ -13,9 +13,9 @@
 
-
    
+
    
 
    
-Function Index
    
+Function Index
    
 
    A B C D E F I L M P R S T Z
    
 
    
 
    
@@ -23,6 +23,10 @@
 
    
 
      
 
    • 
+
      abs
      
+
      
+
      • 
+
    • 
 
      assign
      
 
      
 
      • 
diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html
index 29be2280..2df7fd66 100644
--- a/doc/html/boost_multiprecision/indexes/s02.html
+++ b/doc/html/boost_multiprecision/indexes/s02.html
@@ -13,9 +13,9 @@
 
      
 PrevUpHomeNext
 
      
-
      
+
      
 
      
-Class Index
      
+Class Index
    
 
    C E G I M N T
    
 
    
 
    
@@ -71,6 +71,14 @@
 
    is_restricted_conversion
    
 
    
 
+
  • 
+
    is_signed_number
    
+
    
+
    • 
+
  • 
+
    is_unsigned_number
    
+
    
+
    • 
 
    
 
    
 M
diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html
index dff01ef2..be23bda1 100644
--- a/doc/html/boost_multiprecision/indexes/s03.html
+++ b/doc/html/boost_multiprecision/indexes/s03.html
@@ -13,9 +13,9 @@
 
    
 PrevUpHomeNext
 
    
-
    
+
    
 
    
-Typedef Index
    
+Typedef Index
    
 
    C I L M T U
    
 
    
 
    
@@ -23,6 +23,50 @@
 
    
 
      
 
    • 
+
      checked_cpp_int
      
+
      
+
      • 
+
    • 
+
      checked_cpp_rational
      
+
      
+
      • 
+
    • 
+
      checked_cpp_rational_backend
      
+
      
+
      • 
+
    • 
+
      checked_int1024_t
      
+
      
+
      • 
+
    • 
+
      checked_int128_t
      
+
      
+
      • 
+
    • 
+
      checked_int256_t
      
+
      
+
      • 
+
    • 
+
      checked_int512_t
      
+
      
+
      • 
+
    • 
+
      checked_uint1024_t
      
+
      
+
      • 
+
    • 
+
      checked_uint128_t
      
+
      
+
      • 
+
    • 
+
      checked_uint256_t
      
+
      
+
      • 
+
    • 
+
      checked_uint512_t
      
+
      
+
      • 
+
    • 
 
      cpp_dec_float_100
      
 
      
 
      • 
diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html
index 3030cc3f..7a5144be 100644
--- a/doc/html/boost_multiprecision/indexes/s04.html
+++ b/doc/html/boost_multiprecision/indexes/s04.html
@@ -12,9 +12,9 @@
 
      
 PrevUpHome
 
      
-
      
+
      
 
      
-Index
      
+Index
    
 
    A B C D E F G I L M N O P R S T U Z
    
 
    
 
    
@@ -22,6 +22,10 @@
 
    
 
      
 
    • 
+
      abs
      
+
      
+
      • 
+
    • 
 
      assign
      
 
      
 
      • 
@@ -64,6 +68,50 @@
 
      
 
 
    • 
+
      checked_cpp_int
      
+
      
+
      • 
+
    • 
+
      checked_cpp_rational
      
+
      
+
      • 
+
    • 
+
      checked_cpp_rational_backend
      
+
      
+
      • 
+
    • 
+
      checked_int1024_t
      
+
      
+
      • 
+
    • 
+
      checked_int128_t
      
+
      
+
      • 
+
    • 
+
      checked_int256_t
      
+
      
+
      • 
+
    • 
+
      checked_int512_t
      
+
      
+
      • 
+
    • 
+
      checked_uint1024_t
      
+
      
+
      • 
+
    • 
+
      checked_uint128_t
      
+
      
+
      • 
+
    • 
+
      checked_uint256_t
      
+
      
+
      • 
+
    • 
+
      checked_uint512_t
      
+
      
+
      • 
+
    • 
 
      compare
      
 
      
 
      • 
@@ -112,6 +160,17 @@
 
    • 
 
      cpp_int
      
 
      
 
      • 
 
    • 
@@ -541,6 +602,14 @@
 
      
 
      • 
 
    • 
+
      is_signed_number
      
+
      
+
      • 
+
    • 
+
      is_unsigned_number
      
+
      
+
      • 
+
    • 
 
      itrunc
      
 
      
 
      • 
@@ -679,6 +748,7 @@
 
    • 
 
      number
      
 
        
+
      • abs
        • 
 
      • assign
        • 
 
      • bit_flip
        • 
 
      • bit_set
        • 
diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html
index 699be148..66275daf 100644
--- a/doc/html/boost_multiprecision/intro.html
+++ b/doc/html/boost_multiprecision/intro.html
@@ -155,10 +155,11 @@
       Note that while "moved-from" objects are left in a sane state, they
       have an unspecified value, and the only permitted operations on them are destruction
       or the assignment of a new value. Any other operation should be considered
-      a programming error and many backends will trigger an assertion if any other
-      operation is attempted. This behavior allows for optimal performance on move-construction
-      (i.e. no allocation required, we just take ownership of the existing object's
-      internal state), while maintaining usability in the standard library containers.
+      a programming error and all of our backends will trigger an assertion if any
+      other operation is attempted. This behavior allows for optimal performance
+      on move-construction (i.e. no allocation required, we just take ownership of
+      the existing object's internal state), while maintaining usability in the standard
+      library containers.
     
        
 
        
 
@@ -217,9 +218,36 @@
       performed rather than the number of temporaries directly, note also that the
       mpf_class
       wrapper that will be supplied with GMP-5.1 reduces the number of temporaries
-      to pretty much zero). Finally if we use this library with expression templates
-      disabled, we still only generate 11 temporaries [1] [2].
+      to pretty much zero). Note that if we compile with expression templates disabled
+      and rvalue-reference support on, then actually still have no wasted memory
+      allocations as even though temporaries are created, their contents are moved
+      rather than copied. [1]
     
        
+
        
+
+
+
+
+
+
        [Important]Important
        
+
        
+        Expression templates can radically reorder the operations in an expression,
+        for example:
+      
        
+
        
+        a = (b * c) * a;
+      
        
+
        
+        Will get transformed into:
+      
        
+
        
+        a *= c; a *= b;
+      
        
+
        
+        If this is likely to be an issue for a particular application, then they
+        should be disabled.
+      
        
+
        
 
        
       This library also extends expression template support to standard library functions
       like abs or sin
@@ -411,7 +439,7 @@
 
      
 
      
       Finally, note that number takes
-      a second template argument, which, when set to false
+      a second template argument, which, when set to et_off
       disables all the expression template machinery. The result is much faster to
       compile, but slower at runtime.
     
      
@@ -421,9 +449,6 @@
       to carry out the underlying arithmetic, and all are operating at the same precision
       (50 decimal digits):
     
      
-
      
-      TODO: Update, compare to rvalue refs but no ET's as well.
-    
      
 
      
 
      Table 1.2. Evaluation of Boost.Math's Bessel function test data
      
 
      
@@ -453,17 +478,35 @@
 
+
+
+
+
+
@@ -475,12 +518,12 @@
             
@@ -492,12 +535,12 @@
             
@@ -538,12 +581,30 @@
             
+
+
+
+
+
@@ -555,12 +616,12 @@
             
@@ -572,30 +633,29 @@
             
      
 
               
      
-                number
+                mpfr_float_50
               
      
                   		
 
               
      
-                1.0 (6.21s)
+                1.0 (5.66s)
               
      
                   		
 
               
      
-                1.0 (2685469)
+                1.0 (1611963)
+              
      
+            
      
+              
      
+                number<mpfr_float_backend<50>, et_off>
       (but with
+                rvalue reference support)
+              
      
+                  		
+              
      
+                1.10 (6.25s)
+              
      
+                  		
+              
      
+                2.64 (4260868)
               
      
                   		
 
      
 
      
               
      
-                1.04 (6.45s)
+                1.09 (6.16s)
               
      
                   		
 
               
      
-                1.47 (3946007)
+                2.45 (3948316)
               
      
                   		
 
      
 
      
               
      
-                1.53 (9.52s)
+                1.65 (9.34s)
               
      
                   		
 
               
      
-                4.92 (13222940)
+                8.21 (13226029)
               
      
                   		
 
      
 
      
               
      
-                1.0 (269s)
+                1.0 (257s)
               
      
                   		
 
               
      
-                1.0 (139082551)
+                1.0 (127710873)
+              
      
+            
      
+              
      
+                number<mpfr_float_backend<50>, et_off>
       (but with
+                rvalue reference support)
+              
      
+                  		
+              
      
+                1.0 (257s)
+              
      
+                  		
+              
      
+                1.2 (156797871)
               
      
                   		
 
      
 
      
               
      
-                1.04 (278s)
+                1.1 (280s)
               
      
                   		
 
               
      
-                1.81 (252400791)
+                2.1 (268336640)
               
      
                   		
 
      
 
      
               
      
-                1.49 (401s)
+                1.4 (363s)
               
      
                   		
 
               
      
-                3.22 (447009280)
+                3.6 (466960653)
               
      
                   		
 
      
       
 
      
 
      
-
      
+
      
+      The above results were generated on Win32 compiling with Visual C++ 2010, all
+      optimizations on (/Ox), with MPFR 3.0 and MPIR 2.3.0.
+    
      
+
      
 
      
 
      [1] 
         The actual number generated will depend on the compiler, how well it optimises
         the code, and whether it supports rvalue references. The number of 11 temporaries
         was generated with Visual C++ 10
       
      
-
      [2] 
-        Marc Glisse suggested pre-review that this could be reduced still further
-        by careful use of rvalue-references and move semantics in the operator overloads.
-        This will be investigated further at a later date.
-      
      
 
      
 
      
 
diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html
index ca0c5cca..7c4b992f 100644
--- a/doc/html/boost_multiprecision/map/hist.html
+++ b/doc/html/boost_multiprecision/map/hist.html
@@ -28,7 +28,7 @@
             support.
           
    • 
-            Many functions made made constexp?
+            Many functions made constexp.
           
    • 
             Differentiate between explicit and implicit conversions in the number
@@ -55,6 +55,10 @@
             Tweaked expression template unpacking to use fewer temporaries when the
             LHS also appears in the RHS.
           
      • 
+
    • 
+            Refactored cpp_int_backend
+            based on review comments with new template parameter structure.
+          
      • 
 
diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html
index 2abdc184..585439d0 100644
--- a/doc/html/boost_multiprecision/map/todo.html
+++ b/doc/html/boost_multiprecision/map/todo.html
@@ -57,22 +57,6 @@
             A 2's complement fixed precision int that uses exactly N bits and no
             more.
           
-
    • 
-            A backend for an overflow aware integers.
-          
      • 
-
    • 
-            Each back-end should document the requirements it satisfies (not currently
-            scheduled for inclusion: it's deliberately an implementation detail,
-            and "optional" requirements are optimisations which can't be
-            detected by the user).
-          
      • 
-
    • 
-            The use of bool in template parameters could be improved by the use of
-            an enum class which will be more explicit. E.g enum
-            class expression_template
-            {disabled, enabled}; enum class sign
-            {unsigned, signed}; (Partly done 2012/09/15).
-          
      • 
 
    • 
             The performances of mp_number<a_trivial_adaptor<float>, false>respect
             to float and mp_number<a_trivial_adaptor<int>, false> and
@@ -94,9 +78,6 @@
 
    • 
             Document why we don't use proto (compile times).
           
      • 
-
    • 
-            Document what happens to small fixed precision cpp_int's.
-          
      • 
 
    • 
             Should we provide min/max overloads for expression templates?
           
      • 
@@ -104,6 +85,27 @@
             Document why we don't abstract out addition/multiplication algorithms
             etc.
           
+
    • 
+            Document what happens to small fixed precision cpp_int's (done 2012/10/31).
+          
      • 
+
    • 
+            The use of bool in template parameters could be improved by the use of
+            an enum class which will be more explicit. E.g enum
+            class expression_template
+            {disabled, enabled}; enum class sign
+            {unsigned, signed}; (Partly done 2012/09/15, done 2012/10/31).
+          
      • 
+
    • 
+            Each back-end should document the requirements it satisfies (not currently
+            scheduled for inclusion: it's deliberately an implementation detail,
+            and "optional" requirements are optimisations which can't be
+            detected by the user). Not done: this is an implementation detail, the
+            exact list of requirements satisfied is purely an optimimization, not
+            something the user can detect.
+          
      • 
+
    • 
+            A backend for an overflow aware integers (done 2012/10/31).
+          
      • 
 
    • 
             IIUC convert_to is used to emulate in c++98 compilers C++11 explicit
             conversions. Could the explicit conversion operator be added on compilers
@@ -158,7 +160,7 @@
 
    • 
             Make fixed precision orthogonal to Allocator type in cpp_int. Possible
             solution - add an additional MaxBits template argument that defaults
-            to 0 (meaning keep going till no more space/memory).
+            to 0 (meaning keep going till no more space/memory). Done.
           
      • 
 
    • 
             Can ring types (exact floating point types) be supported? The answer
diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html
index f1dbd5df..36391a56 100644
--- a/doc/html/boost_multiprecision/ref/cpp_int_ref.html
+++ b/doc/html/boost_multiprecision/ref/cpp_int_ref.html
@@ -19,30 +19,56 @@
 
      • namespace boost{ namespace multiprecision{
 
-template <unsigned MinBits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
-struct cpp_int_backend;
+typedef unspecified-type limb_type;
+
+enum cpp_integer_type    { signed_magnitude, unsigned_magnitude };
+enum cpp_int_check_type  { checked, unchecked };
+
+template <unsigned MinDigits = 0,
+          unsigned MaxDits = 0,
+          cpp_integer_type SignType = signed_magnitude,
+          cpp_int_check_type Checked = unchecked,
+          class Allocator = std::allocator<limb_type> >
+class cpp_int_backend;
 //
 // Expression templates default to et_off if there is no allocator:
 //
-template <unsigned MinDigits, bool Signed>
-struct expression_template_default<cpp_int_backend<MinDigits, Signed, void> >
+template <unsigned MinDigits, unsigned MaxDigits, cpp_integer_type SignType, cpp_int_check_type Checked>
+struct expression_template_default<cpp_int_backend<MinDigits, MaxDigits, SignType, Checked, void> >
 { static const expression_template_option value = et_off; };
 
-typedef number<cpp_int_backend<> >           cpp_int;    // arbitrary precision integer
+typedef number<cpp_int_backend<> >              cpp_int;    // arbitrary precision integer
 typedef rational_adapter<cpp_int_backend<> >    cpp_rational_backend;
-typedef number<cpp_rational_backend>         cpp_rational; // arbitrary precision rational number
+typedef number<cpp_rational_backend>            cpp_rational; // arbitrary precision rational number
 
 // Fixed precision unsigned types:
-typedef number<cpp_int_backend<128, false, void> >   uint128_t;
-typedef number<cpp_int_backend<256, false, void> >   uint256_t;
-typedef number<cpp_int_backend<512, false, void> >   uint512_t;
-typedef number<cpp_int_backend<1024, false, void> >  uint1024_t;
+typedef number<cpp_int_backend<128, 128, unsigned_magnitude, unchecked, void> >   uint128_t;
+typedef number<cpp_int_backend<256, 256, unsigned_magnitude, unchecked, void> >   uint256_t;
+typedef number<cpp_int_backend<512, 512, unsigned_magnitude, unchecked, void> >   uint512_t;
+typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, unchecked, void> > uint1024_t;
 
 // Fixed precision signed types:
-typedef number<cpp_int_backend<128, true, void> >    int128_t;
-typedef number<cpp_int_backend<256, true, void> >    int256_t;
-typedef number<cpp_int_backend<512, true, void> >    int512_t;
-typedef number<cpp_int_backend<1024, true, void> >   int1024_t;
+typedef number<cpp_int_backend<128, 128, signed_magnitude, unchecked, void> >     int128_t;
+typedef number<cpp_int_backend<256, 256, signed_magnitude, unchecked, void> >     int256_t;
+typedef number<cpp_int_backend<512, 512, signed_magnitude, unchecked, void> >     int512_t;
+typedef number<cpp_int_backend<1024, 1024, signed_magnitude, unchecked, void> >   int1024_t;
+
+// Over again, but with checking enabled this time:
+typedef number<cpp_int_backend<0, 0, signed_magnitude, checked> >                 checked_cpp_int;
+typedef rational_adapter<cpp_int_backend<0, 0, signed_magnitude, checked> >       checked_cpp_rational_backend;
+typedef number<cpp_rational_backend>                                              checked_cpp_rational;
+
+// Checked fixed precision unsigned types:
+typedef number<cpp_int_backend<128, 128, unsigned_magnitude, checked, void> >     checked_uint128_t;
+typedef number<cpp_int_backend<256, 256, unsigned_magnitude, checked, void> >     checked_uint256_t;
+typedef number<cpp_int_backend<512, 512, unsigned_magnitude, checked, void> >     checked_uint512_t;
+typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, checked, void> >   checked_uint1024_t;
+
+// Fixed precision signed types:
+typedef number<cpp_int_backend<128, 128, signed_magnitude, checked, void> >       checked_int128_t;
+typedef number<cpp_int_backend<256, 256, signed_magnitude, checked, void> >       checked_int256_t;
+typedef number<cpp_int_backend<512, 512, signed_magnitude, checked, void> >       checked_int512_t;
+typedef number<cpp_int_backend<1024, 1024, signed_magnitude, checked, void> >     checked_int1024_t;
 
 }} // namespaces
 
      
@@ -58,30 +84,44 @@
 
      
 
      
 
      
-
      Argument
      
-
      
-              Meaning
-            
      
 
      MinBits
      
 
      
-              The number of Bits to reserve inside the class's internal cache. When
-              constructing a value, the object will use this internal cache if possible
-              before resorting to dynamic memory allocation. When this value is zero,
-              then the size of the internal cache is 2*sizeof(void*)*CHAR_BIT.
-              When the Allocator argument is void,
-              then this parameter determines the precision of the type.
+              Determines the number of Bits to store directly within the object before
+              resorting to dynamic memory allocation. When zero, this field is determined
+              automatically based on how many bits can be stored in union with the
+              dynamic storage header: setting a larger value may improve performance
+              as larger integer values will be stored internally before memory allocation
+              is required.
             
      
-
      Signed
      
+
      MaxBits
      
 
      
-              When true the type is
-              signed, otherwise unsigned. Note that unsigned types are currently
-              only supported when the Allocator parameter is void.
+              Determines the maximum number of bits to be stored in the type: resulting
+              in a fixed precision type. When this value is the same as MinBits,
+              then the Allocator parameter is ignored, as no dynamic memory allocation
+              will ever be performed: in this situation the Allocator parameter should
+              be set to type void. Note
+              that this parameter should not be used simply to prevent large memory
+              allocations, not only is that role better performed by the allocator,
+              but fixed precision integers have a tendency to allocate all of MaxBits
+              of storage more often than one would expect.
+            
      
+
      SignType
      
+
      
+              Determines whether the resulting type is signed or not. Note that for
+              arbitrary
+              precision types this parameter must be signed_magnitude.
+              For fixed precision types then this type may be either signed_magnitude or unsigned_magnitude.
+            
      
+
      Checked
      
+
      
+              This parameter has two values: checked
+              or unchecked. See the
+              tutorial
+              for more information.
             
      
 
      Allocator
      
 
      
-              The allocator used for dynamic memory allocation. This parameter can
-              be void, in which case
-              no dynamic memory will ever be allocated.
+              The allocator to use for dynamic memory allocation, or type void if MaxBits == MinBits.
             
      
 
      
 
      
diff --git a/doc/html/boost_multiprecision/ref/headers.html b/doc/html/boost_multiprecision/ref/headers.html
index 29926494..4e55c754 100644
--- a/doc/html/boost_multiprecision/ref/headers.html
+++ b/doc/html/boost_multiprecision/ref/headers.html
@@ -64,18 +64,6 @@
               
-
-
-
-
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/doc/html/boost_multiprecision/ref/internals.html b/doc/html/boost_multiprecision/ref/internals.html
index b75aba98..8a6e979a 100644
--- a/doc/html/boost_multiprecision/ref/internals.html
+++ b/doc/html/boost_multiprecision/ref/internals.html
@@ -77,6 +77,17 @@
         types should generally specialise one of the traits above, rather than this
         one directly.
       
      
+
      template <class T>
+is_signed_number;
+template <class T>
+is_unsigned_number;
+
      
+
      
+        These two traits inherit from either mpl::true_
+        or mpl::false_, by default types are assumed to
+        be signed unless is_unsigned_number
+        is specialized for that type.
+      
      
 
 
 
 
 
 
      
 
      
-                
      
-                  integer_ops.hpp
-                
      
-                    		
-                
      
-                  Integer specific non-member functions.
-                
      
-              
      
 
                 
      
                   miller_rabin.hpp
@@ -201,25 +189,121 @@
 
      
 
                 
      
-                  detail/big_lanczos.hpp
+                  cpp_int/add.hpp
                 
      
                     		
 
                 
      
-                  Lanczos support for Boost.Math integration.
+                  Add and subtract operators for cpp_int_backend.
                 
      
                     		
 
      
 
      
 
                 
      
-                  detail/cpp_int_core.hpp
+                  cpp_int/bitwise.hpp
                 
      
                     		
 
                 
      
-                  Platform and peformance tuning for the cpp_int
-                  backend.
+                  Bitwise operators for cpp_int_backend.
+                
      
+              
      
+                
      
+                  cpp_int/checked.hpp
+                
      
+                    		
+                
      
+                  Helper functions for checked arithmetic for cpp_int_backend.
+                
      
+              
      
+                
      
+                  cpp_int/comparison.hpp
+                
      
+                    		
+                
      
+                  Comparison operators for cpp_int_backend.
+                
      
+              
      
+                
      
+                  cpp_int/cpp_int_config.hpp
+                
      
+                    		
+                
      
+                  Basic setup and configuration for cpp_int_backend.
+                
      
+              
      
+                
      
+                  cpp_int/divide.hpp
+                
      
+                    		
+                
      
+                  Division and modulus operators for cpp_int_backend.
+                
      
+              
      
+                
      
+                  cpp_int/limits.hpp
+                
      
+                    		
+                
      
+                  numeric_limits
+                  support for cpp_int_backend.
+                
      
+              
      
+                
      
+                  cpp_int/misc.hpp
+                
      
+                    		
+                
      
+                  Miscellaneous operators for cpp_int_backend.
+                
      
+              
      
+                
      
+                  cpp_int/multiply.hpp
+                
      
+                    		
+                
      
+                  Multiply operators for cpp_int_backend.
+                
      
+              
      
+                
      
+                  detail/big_lanczos.hpp
+                
      
+                    		
+                
      
+                  Lanczos support for Boost.Math integration.
                 
      
                     		
 
      
 
 
      
diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html
index de7a6cdc..69b8a905 100644
--- a/doc/html/boost_multiprecision/ref/number.html
+++ b/doc/html/boost_multiprecision/ref/number.html
@@ -281,8 +281,8 @@
           
    • 
             Any type in the same family, as long as no loss of precision is involved.
-            For example from int128
-            to int256, or cpp_dec_float_50 to cpp_dec_float_100.
+            For example from int128_t
+            to int256_t, or cpp_dec_float_50 to cpp_dec_float_100.
           
      • 
@@ -631,7 +631,8 @@
         When these functions use our own implementations, the accuracy of the transcendal
         functions is generally a few epsilon. Note however, that the trigonmetrical
         functions incur the usual accuracy loss when reducing arguments by large
-        multiples of π. Also note that both __mpf_float and cpp_dec_float
+        multiples of π. Also note that both gmp_float
+        and cpp_dec_float
         have a number of guard digits beyond their stated precision, so the error
         rates listed for these are in some sense artificially low.
       
      
diff --git a/doc/html/boost_multiprecision/tut/conversions.html b/doc/html/boost_multiprecision/tut/conversions.html
index cb5c0664..29ca1eff 100644
--- a/doc/html/boost_multiprecision/tut/conversions.html
+++ b/doc/html/boost_multiprecision/tut/conversions.html
@@ -27,15 +27,15 @@
             type, as long as the conversion isn't lossy (for example float to int
             conversion):
           
-
      cpp_dec_float_50 df(0.5); // OK construction from double
-cpp_int          i(450);  // OK constructs from signed int
-cpp_int          j = 3.14; // Error, lossy conversion.
+
      cpp_dec_float_50 df(0.5);   // OK construction from double
+cpp_int          i(450);    // OK constructs from signed int
+cpp_int          j = 3.14;  // Error, lossy conversion.
 
      
 
      • 
             A number can be explicitly constructed from an arithmetic type, even
             when the conversion is lossy:
           
      
-
      cpp_int          i(3.14);  // OK explicit conversion
+
      cpp_int          i(3.14);       // OK explicit conversion
 i = static_cast<cpp_int>(3.14)  // OK explicit conversion
 i.assign(3.14);                 // OK, explicit assign and avoid a temporary from the cast above
 i = 3.14;                       // Error, no implicit assignment operator for lossy conversion.
@@ -59,8 +59,8 @@
             syntax.
           
 
      mpz_int z(2);
-int i = z;  // Error, implicit conversion not allowed.
-int j = static_cast<int>(z);  // OK explicit conversion.
+int i = z;                     // Error, implicit conversion not allowed.
+int j = static_cast<int>(z);   // OK explicit conversion.
 
      
 
      • 
             Any number type can be explicitly constructed (or
@@ -109,10 +109,10 @@
             and are implicit conversions if no loss of precision is involved, and
             explicit if it is:
           
      
-
      int128       i128 = 0;
-int266       i256 = i128;  // OK implicit widening conversion
-i128              = i256;  // Error, no assignment operator found, narrowing conversion is explict
-i128              = static_cast<int128>(i256); // OK, explicit narrowing conversion
+
      int128_t     i128 = 0;
+int266_t     i256 = i128;  // OK implicit widening conversion
+i128_t            = i256;  // Error, no assignment operator found, narrowing conversion is explict
+i128_t            = static_cast<int128_t>(i256); // OK, explicit narrowing conversion
 
 mpz_int      z    = 0;
 mpf_float    f    = z;    // OK, GMP handles this conversion natively, and it's not lossy and therefore implicit
diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html
index 5ceefb43..f3909b91 100644
--- a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html
+++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html
@@ -33,9 +33,9 @@
 
      
           The cpp_dec_float back-end
           is used in conjunction with number:
-          It acts as an entirely C++ (header only and dependency free) real-number
-          type that is a drop-in replacement for the native C++ floating-point types,
-          but with much greater precision.
+          It acts as an entirely C++ (header only and dependency free) floating-point
+          number type that is a drop-in replacement for the native C++ floating-point
+          types, but with much greater precision.
         
      
 
      
           Type cpp_dec_float can
diff --git a/doc/html/boost_multiprecision/tut/floats/gmp_float.html b/doc/html/boost_multiprecision/tut/floats/gmp_float.html
index a33583e7..566ffc47 100644
--- a/doc/html/boost_multiprecision/tut/floats/gmp_float.html
+++ b/doc/html/boost_multiprecision/tut/floats/gmp_float.html
@@ -110,9 +110,9 @@
 
    • 
               Since the underlying GMP types
               have no notion of infinities or NaN's, care should be taken to avoid
-              numeric overflow or division by zero. That latter will trigger a hardware
-              exception, while generating excessively large exponents may result
-              in instability of the underlying GMP
+              numeric overflow or division by zero. That latter will result in a
+              std::overflow_error being thrown, while generating excessively large
+              exponents may result in instability of the underlying GMP
               library (in testing, converting a number with an excessively large
               or small exponent to a string caused GMP
               to segfault).
@@ -128,7 +128,7 @@
               point number.
             
      • 
 
    • 
-              Division by zero results in a std::runtime_error
+              Division by zero results in a std::overflow_error
               being thrown.
             
      • 
 
diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html
index a220dc59..68c0d7be 100644
--- a/doc/html/boost_multiprecision/tut/ints/cpp_int.html
+++ b/doc/html/boost_multiprecision/tut/ints/cpp_int.html
@@ -24,13 +24,20 @@
 
 typedef unspecified-type limb_type;
 
-template <unsigned MinDigits = 0, bool Signed = true, class Allocator = std::allocator<limb_type> >
+enum cpp_integer_type    { signed_magnitude, unsigned_magnitude };
+enum cpp_int_check_type  { checked, unchecked };
+
+template <unsigned MinDigits = 0,
+          unsigned MaxDits = 0,
+          cpp_integer_type SignType = signed_magnitude,
+          cpp_int_check_type Checked = unchecked,
+          class Allocator = std::allocator<limb_type> >
 class cpp_int_backend;
 //
 // Expression templates default to et_off if there is no allocator:
 //
-template <unsigned MinDigits, bool Signed>
-struct expression_template_default<cpp_int_backend<MinDigits, Signed, void> >
+template <unsigned MinDigits, unsigned MaxDigits, cpp_integer_type SignType, cpp_int_check_type Checked>
+struct expression_template_default<cpp_int_backend<MinDigits, MaxDigits, SignType, Checked, void> >
 { static const expression_template_option value = et_off; };
 
 typedef number<cpp_int_backend<> >              cpp_int;    // arbitrary precision integer
@@ -38,31 +45,45 @@
 typedef number<cpp_rational_backend>            cpp_rational; // arbitrary precision rational number
 
 // Fixed precision unsigned types:
-typedef number<cpp_int_backend<128, false, void> >   uint128_t;
-typedef number<cpp_int_backend<256, false, void> >   uint256_t;
-typedef number<cpp_int_backend<512, false, void> >   uint512_t;
-typedef number<cpp_int_backend<1024, false, void> >  uint1024_t;
+typedef number<cpp_int_backend<128, 128, unsigned_magnitude, unchecked, void> >   uint128_t;
+typedef number<cpp_int_backend<256, 256, unsigned_magnitude, unchecked, void> >   uint256_t;
+typedef number<cpp_int_backend<512, 512, unsigned_magnitude, unchecked, void> >   uint512_t;
+typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, unchecked, void> > uint1024_t;
 
 // Fixed precision signed types:
-typedef number<cpp_int_backend<128, true, void> >    int128_t;
-typedef number<cpp_int_backend<256, true, void> >    int256_t;
-typedef number<cpp_int_backend<512, true, void> >    int512_t;
-typedef number<cpp_int_backend<1024, true, void> >   int1024_t;
+typedef number<cpp_int_backend<128, 128, signed_magnitude, unchecked, void> >     int128_t;
+typedef number<cpp_int_backend<256, 256, signed_magnitude, unchecked, void> >     int256_t;
+typedef number<cpp_int_backend<512, 512, signed_magnitude, unchecked, void> >     int512_t;
+typedef number<cpp_int_backend<1024, 1024, signed_magnitude, unchecked, void> >   int1024_t;
+
+// Over again, but with checking enabled this time:
+typedef number<cpp_int_backend<0, 0, signed_magnitude, checked> >                 checked_cpp_int;
+typedef rational_adapter<cpp_int_backend<0, 0, signed_magnitude, checked> >       checked_cpp_rational_backend;
+typedef number<cpp_rational_backend>                                              checked_cpp_rational;
+
+// Checked fixed precision unsigned types:
+typedef number<cpp_int_backend<128, 128, unsigned_magnitude, checked, void> >     checked_uint128_t;
+typedef number<cpp_int_backend<256, 256, unsigned_magnitude, checked, void> >     checked_uint256_t;
+typedef number<cpp_int_backend<512, 512, unsigned_magnitude, checked, void> >     checked_uint512_t;
+typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, checked, void> >   checked_uint1024_t;
+
+// Fixed precision signed types:
+typedef number<cpp_int_backend<128, 128, signed_magnitude, checked, void> >       checked_int128_t;
+typedef number<cpp_int_backend<256, 256, signed_magnitude, checked, void> >       checked_int256_t;
+typedef number<cpp_int_backend<512, 512, signed_magnitude, checked, void> >       checked_int512_t;
+typedef number<cpp_int_backend<1024, 1024, signed_magnitude, checked, void> >     checked_int1024_t;
 
 }} // namespaces
 
      
 
      
           The cpp_int_backend type
-          is used via one of the typedefs boost::multiprecision::cpp_int,
-          boost::multiprecision::uint128_t, boost::multiprecision::uint256_t,
-          boost::multiprecision::uint512_t, boost::multiprecision::int128_t,
-          boost::multiprecision::int256_t or boost::multiprecision::int512_t.
+          is normally used via one of the convenience typedefs given above.
         
      
 
      
           This back-end is the "Swiss Army Knife" of integer types as it
           can represent both fixed and arbitrary
           precision integer types, and both signed and unsigned types. There
-          are three template arguments:
+          are five template arguments:
         
      
 
      
 
      
@@ -74,26 +95,143 @@
                 is determined automatically based on how many bits can be stored
                 in union with the dynamic storage header: setting a larger value
                 may improve performance as larger integer values will be stored internally
-                before memory allocation is required. When the Allocator parameter
-                is type void, then this
-                field determines the total number of bits in the resulting fixed
-                precision type.
+                before memory allocation is required.
               
      
-
      Signed
      
+
      MaxBits
      
+
      
+                Determines the maximum number of bits to be stored in the type: resulting
+                in a fixed precision type. When this value is the same as MinBits,
+                then the Allocator parameter is ignored, as no dynamic memory allocation
+                will ever be performed: in this situation the Allocator parameter
+                should be set to type void.
+                Note that this parameter should not be used simply to prevent large
+                memory allocations, not only is that role better performed by the
+                allocator, but fixed precision integers have a tendency to allocate
+                all of MaxBits of storage more often than one would expect.
+              
      
+
      SignType
      
 
      
                 Determines whether the resulting type is signed or not. Note that
                 for arbitrary
-                precision types (where the Allocator parameter is non-void),
-                then this parameter must be true.
-                For fixed precision types then this type may be either true (type is signed), or false (type is unsigned).
+                precision types this parameter must be signed_magnitude.
+                For fixed precision types then this type may be either signed_magnitude or unsigned_magnitude.
+              
      
+
      Checked
      
+
      
+                This parameter has two values: checked
+                or unchecked. See
+                below.
               
      
 
      Allocator
      
 
      
-                The allocator to use for dynamic memory allocation, or type void if this is to be a fixed precision
-                type.
+                The allocator to use for dynamic memory allocation, or type void if MaxBits == MinBits.
               
      
 
 
      
+
      
+          When the template parameter Checked is set to checked
+          then the result is a checked-integer, checked and
+          unchecked integers have the following properties:
+        
      
+
      
 
 
 
 
      
+++++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
      




      
+                  
      
+                    Condition
+                  
      
+                      		
+                  
      
+                    Checked-Integer
+                  
      
+                      		
+                  
      
+                    Unchecked-Integer
+                  
      
+                
      
+                  
      
+                    Numeric overflow in fixed precision arithmetic
+                  
      
+                      		
+                  
      
+                    Throws a std::overflow_error.
+                  
      
+                      		
+                  
      
+                    Performs arithmetic modulo 2MaxBits
+                  
      
+                
      
+                  
      
+                    Constructing an integer from a value that can not be represented
+                    in the target type
+                  
      
+                      		
+                  
      
+                    Throws a std::range_error.
+                  
      
+                      		
+                  
      
+                    Converts the value modulo 2MaxBits, signed to unsigned conversions
+                    extract the last MaxBits bits of the 2's complement representation
+                    of the input value.
+                  
      
+                
      
+                  
      
+                    Unsigned subtraction yielding a negative value.
+                  
      
+                      		
+                  
      
+                    Throws a std::range_error.
+                  
      
+                      		
+                  
      
+                    Yields the value that would result from treating the unsigned
+                    type as a 2's complement signed type.
+                  
      
+                
      
+                  
      
+                    Attempting a bitwise operation on a negative value.
+                  
      
+                      		
+                  
      
+                    Throws a std::range_error
+                  
      
+                      		
+                  
      
+                    Yields the value, but not the bit pattern, that would result
+                    from performing the operation on a 2's complement integer type.
+                  
      
+                
    
 
    
           Things you should know when using this type:
         
    
@@ -103,7 +241,7 @@
               have the value zero.
             
 
  • 
-              Division by zero results in a std::runtime_error
+              Division by zero results in a std::overflow_error
               being thrown.
             
    • 
 
  • 
@@ -135,19 +273,26 @@
               being thrown, this is a direct consequence of the sign-magnitude representation.
             
    • 
 
  • 
-              The fixed precision types mp_[u]intXXX_t
-              have expression template support turned off - it seems to make little
-              difference to the performance of these types either way - so we may
-              as well have the faster compile times by turning the feature off.
+              The fixed precision types [checked_][u]intXXX_t have expression template
+              support turned off - it seems to make little difference to the performance
+              of these types either way - so we may as well have the faster compile
+              times by turning the feature off.
             
    • 
 
  • 
-              Unsigned types support subtraction, and unary negation - the result
-              is "as if" a 2's complement operation had been performed
-              - in other words they behave pretty much as a built in integer type
-              would in this situation. So for example if we were using uint128_t then both uint128_t(1)-4
-              and -uint128(3)
+              Unsigned types support subtraction - the result is "as if"
+              a 2's complement operation had been performed as long as they are not
+              checked-integers (see above). In other words they
+              behave pretty much as a built in integer type would in this situation.
+              So for example if we were using uint128_t
+              then uint128_t(1)-4
               would result in the value 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD
               of type uint128_t.
+              However, had this operation been performed on checked_uint128_t
+              then a std::range_error would have been thrown.
+            
    • 
+
  • 
+              Unary negation of unsigned types results in a compiler error (static
+              assertion).
             
    • 
 
  • 
               This backend supports rvalue-references and is move-aware, making instantiations
@@ -167,6 +312,15 @@
               with only minor performance degradation even if most of the time the
               arithmetic could in fact be done with a narrower type.
             
    • 
+
  • 
+              When used at fixed precision and MaxBits is smaller than the number
+              of bits in the largest native integer type, then internally cpp_int_backend switches to a "trivial"
+              implementation where it is just a thin wrapper around a single integer.
+              Note that it will still be slightly slower than a bare native integer,
+              as it emulates a signed-magnitude representation rather than simply
+              using the platforms native sign representation: this ensures there
+              is no step change in behavior as a cpp_int grows in size.
+            
    • 
 
    
 
    
 
diff --git a/doc/html/boost_multiprecision/tut/ints/gmp_int.html b/doc/html/boost_multiprecision/tut/ints/gmp_int.html
index cbb2d7f6..385392f9 100644
--- a/doc/html/boost_multiprecision/tut/ints/gmp_int.html
+++ b/doc/html/boost_multiprecision/tut/ints/gmp_int.html
@@ -80,7 +80,7 @@
               being thrown if the string can not be interpreted as a valid integer.
             
 
  • 
-              Division by zero results in a std::runtime_error
+              Division by zero results in a std::overflow_error
               being thrown.
             
    • 
 
  • 
diff --git a/doc/html/boost_multiprecision/tut/ints/tom_int.html b/doc/html/boost_multiprecision/tut/ints/tom_int.html
index ac7f51bd..62e8c343 100644
--- a/doc/html/boost_multiprecision/tut/ints/tom_int.html
+++ b/doc/html/boost_multiprecision/tut/ints/tom_int.html
@@ -65,7 +65,7 @@
               being thrown if the string can not be interpreted as a valid integer.
             
    • 
 
  • 
-              Division by zero results in a std::runtime_error
+              Division by zero results in a std::overflow_error
               being thrown.
             
    • 
 
    
diff --git a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html
index 22bf2a4c..cb140646 100644
--- a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html
+++ b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html
@@ -61,7 +61,7 @@
               have the value zero.
             
 
  • 
-              Division by zero results in a std::rumtime_error
+              Division by zero results in a std::overflow_error
               being thrown.
             
    • 
 
  • 
diff --git a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html
index a317321b..9e78cecf 100644
--- a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html
+++ b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html
@@ -77,7 +77,7 @@
               default behavior).
             
    • 
 
  • 
-              Division by zero results in a std::runtime_error
+              Division by zero results in a std::overflow_error
               being thrown.
             
    • 
 
  • 
diff --git a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html
index 4ce58b60..12377a87 100644
--- a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html
+++ b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html
@@ -57,7 +57,7 @@
               have the value zero (this the inherited Boost.Rational behavior).
             
    • 
 
  • 
-              Division by zero results in a std::runtime_error
+              Division by zero results in a std::overflow_error
               being thrown.
             
    • 
 
  • 
diff --git a/doc/html/index.html b/doc/html/index.html
index 0482b470..07802bad 100644
--- a/doc/html/index.html
+++ b/doc/html/index.html
@@ -120,7 +120,7 @@
 
 
 
-
+
    Last revised: September 20, 2012 at 15:58:33 GMT
    Last revised: October 31, 2012 at 16:58:22 GMT
    		
 
    		
 
    
 
    
diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk
index c9380777..210fefe3 100644
--- a/doc/multiprecision.qbk
+++ b/doc/multiprecision.qbk
@@ -51,6 +51,7 @@
 [def __gmp_int [link boost_multiprecision.tut.ints.gmp_int gmp_int]]
 [def __tom_int [link boost_multiprecision.tut.ints.tom_int tom_int]]
 [def __gmp_float [link boost_multiprecision.tut.floats.gmp_float gmp_float]]
+[def __mpf_float [link boost_multiprecision.tut.floats.gmp_float gmp_float]]
 [def __mpfr_float_backend [link boost_multiprecision.tut.floats.mpfr_float mpfr_float]]
 [def __cpp_dec_float [link boost_multiprecision.tut.floats.cpp_dec_float cpp_dec_float]]
 [def __gmp_rational [link boost_multiprecision.tut.rational.gmp_rational gmp_rational]]
@@ -162,7 +163,7 @@ move-support, and expression templates enabled.
 
 Note that while "moved-from" objects are left in a sane state, they have an unspecified value, and the only permitted 
 operations on them are destruction or the assignment of a new value.  Any other operation should be considered
-a programming error and many backends will trigger an assertion if any other operation is attempted.  This behavior
+a programming error and all of our backends will trigger an assertion if any other operation is attempted.  This behavior
 allows for optimal performance on move-construction (i.e. no allocation required, we just take ownership of the existing
 object's internal state), while maintaining usability in the standard library containers.
 
@@ -204,12 +205,24 @@ temporaries (this is true even though [mpfr_class] does use expression templates
 we used an even simpler wrapper around [mpfr] like [mpreal] things would have been even worse and no less that 24 temporaries
 are created for this simple expression (note - we actually measure the number of memory allocations performed rather than 
 the number of temporaries directly, note also that the [mpf_class] wrapper that will be supplied with GMP-5.1 reduces the number of 
-temporaries to pretty much zero).  Finally if we use this library with expression templates disabled, we still only generate 11
-temporaries
+temporaries to pretty much zero).  Note that if we compile with expression templates disabled and rvalue-reference support
+on, then actually still have no wasted memory allocations as even though temporaries are created, their contents are moved
+rather than copied.
 [footnote The actual number generated will depend on the compiler, how well it optimises the code, and whether it supports
 rvalue references.  The number of 11 temporaries was generated with Visual C++ 10]
-[footnote Marc Glisse suggested pre-review that this could be reduced still further by careful use of rvalue-references
-and move semantics in the operator overloads.  This will be investigated further at a later date.].
+
+[important
+Expression templates can radically reorder the operations in an expression, for example:
+
+   a = (b * c) * a;
+
+Will get transformed into:
+
+   a *= c;
+   a *= b;
+
+If this is likely to be an issue for a particular application, then they should be disabled.
+]
 
 This library also extends expression template support to standard library functions like `abs` or `sin` with `number`
 arguments.  This means that an expression such as:
@@ -288,29 +301,34 @@ magic by converting out-of-place operators to in-place ones, we necessarily take
 transformation is more efficient than creating the extra temporary variable, just not by as much as
 one would hope.
 
-Finally, note that `number` takes a second template argument, which, when set to `false` disables all
+Finally, note that `number` takes a second template argument, which, when set to `et_off` disables all
 the expression template machinery.  The result is much faster to compile, but slower at runtime.
 
 We'll conclude this section by providing some more performance comparisons between these three libraries,
 again, all are using [mpfr] to carry out the underlying arithmetic, and all are operating at the same precision
 (50 decimal digits):
 
-TODO: Update, compare to rvalue refs but no ET's as well.
-
 [table Evaluation of Boost.Math's Bessel function test data
 [[Library][Relative Time][Relative Number of Memory Allocations]]
-[[number][1.0 (6.21s)][1.0 (2685469)]]
-[[[mpfr_class]][1.04 (6.45s)][1.47 (3946007)]]
-[[[mpreal]][1.53 (9.52s)][4.92 (13222940)]]
+[[mpfr_float_50]                            [1.0 (5.66s)] [1.0 (1611963)]]
+[[number, et_off>[br](but with rvalue reference support)]   
+                                            [1.10 (6.25s)][2.64 (4260868)]]
+[[[mpfr_class]]                             [1.09 (6.16s)][2.45 (3948316)]]
+[[[mpreal]]                                 [1.65 (9.34s)][8.21 (13226029)]]
 ]
 
 [table Evaluation of Boost.Math's Non-Central T distribution test data
 [[Library][Relative Time][Relative Number of Memory Allocations]]
-[[number][1.0 (269s)][1.0 (139082551)]]
-[[[mpfr_class]][1.04 (278s)][1.81 (252400791)]]
-[[[mpreal]][1.49 (401s)][3.22 (447009280)]]
+[[number]                                   [1.0 (257s)][1.0 (127710873)]]
+[[number, et_off>[br](but with rvalue reference support)]   
+                                            [1.0 (257s)][1.2 (156797871)]]
+[[[mpfr_class]]                             [1.1 (280s)][2.1 (268336640)]]
+[[[mpreal]]                                 [1.4 (363s)][3.6 (466960653)]]
 ]
 
+The above results were generated on Win32 compiling with Visual C++ 2010, all optimizations on (/Ox),
+with MPFR 3.0 and MPIR 2.3.0.
+
 [endsect]
 
 [section:tut Tutorial]
@@ -338,13 +356,20 @@ The following back-ends provide integer arithmetic:
 
    typedef unspecified-type limb_type;
 
-   template  >
+   enum cpp_integer_type    { signed_magnitude, unsigned_magnitude };
+   enum cpp_int_check_type  { checked, unchecked };
+
+   template  >
    class cpp_int_backend;
    //
    // Expression templates default to et_off if there is no allocator:
    //
-   template 
-   struct expression_template_default >
+   template 
+   struct expression_template_default >
    { static const expression_template_option value = et_off; };
 
    typedef number >              cpp_int;    // arbitrary precision integer
@@ -352,46 +377,80 @@ The following back-ends provide integer arithmetic:
    typedef number            cpp_rational; // arbitrary precision rational number
 
    // Fixed precision unsigned types:
-   typedef number >   uint128_t;
-   typedef number >   uint256_t;
-   typedef number >   uint512_t;
-   typedef number >  uint1024_t;
+   typedef number >   uint128_t;
+   typedef number >   uint256_t;
+   typedef number >   uint512_t;
+   typedef number > uint1024_t;
 
    // Fixed precision signed types:
-   typedef number >    int128_t;
-   typedef number >    int256_t;
-   typedef number >    int512_t;
-   typedef number >   int1024_t;
+   typedef number >     int128_t;
+   typedef number >     int256_t;
+   typedef number >     int512_t;
+   typedef number >   int1024_t;
+
+   // Over again, but with checking enabled this time:
+   typedef number >                 checked_cpp_int;
+   typedef rational_adapter >       checked_cpp_rational_backend;
+   typedef number                                              checked_cpp_rational;
+
+   // Checked fixed precision unsigned types:
+   typedef number >     checked_uint128_t;
+   typedef number >     checked_uint256_t;
+   typedef number >     checked_uint512_t;
+   typedef number >   checked_uint1024_t;
+
+   // Fixed precision signed types:
+   typedef number >       checked_int128_t;
+   typedef number >       checked_int256_t;
+   typedef number >       checked_int512_t;
+   typedef number >     checked_int1024_t;
 
    }} // namespaces
 
-The `cpp_int_backend` type is used via one of the typedefs `boost::multiprecision::cpp_int`, 
-`boost::multiprecision::uint128_t`, `boost::multiprecision::uint256_t`,
-`boost::multiprecision::uint512_t`, `boost::multiprecision::int128_t`, `boost::multiprecision::int256_t`
-or `boost::multiprecision::int512_t`.  
+The `cpp_int_backend` type is normally used via one of the convenience typedefs given above.  
 
 This back-end is the "Swiss Army Knife" of integer types as it can represent both fixed and 
 [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision]
-integer types, and both signed and unsigned types.  There are three template arguments:
+integer types, and both signed and unsigned types.  There are five template arguments:
 
 [variablelist
 [[MinBits][Determines the number of Bits to store directly within the object before resorting to dynamic memory
            allocation.  When zero, this field is determined automatically based on how many bits can be stored
            in union with the dynamic storage header: setting a larger value may improve performance as larger integer
-           values will be stored internally before memory allocation is required.  
-           When the Allocator parameter is type `void`, then this field
-           determines the total number of bits in the resulting fixed precision type.]]
-[[Signed][Determines whether the resulting type is signed or not.  Note that for 
+           values will be stored internally before memory allocation is required.]]
+[[MaxBits][Determines the maximum number of bits to be stored in the type: resulting in a fixed precision type.
+           When this value is the same as MinBits, then the Allocator parameter is ignored, as no dynamic
+           memory allocation will ever be performed: in this situation the Allocator parameter should be set to
+           type `void`.  Note that this parameter should not be used simply to prevent large memory
+           allocations, not only is that role better performed by the allocator, but fixed precision
+           integers have a tendency to allocate all of MaxBits of storage more often than one would expect.]]
+[[SignType][Determines whether the resulting type is signed or not.  Note that for 
 [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] types
-          (where the Allocator parameter is non-void), then this parameter must be `true`.  For fixed precision
-          types then this type may be either `true` (type is signed), or `false` (type is unsigned).]]
-[[Allocator][The allocator to use for dynamic memory allocation, or type `void` if this is to be a fixed precision type.]]
+          this parameter must be `signed_magnitude`.  For fixed precision
+          types then this type may be either `signed_magnitude` or `unsigned_magnitude`.]]
+[[Checked][This parameter has two values: `checked` or `unchecked`.  See below.]]
+[[Allocator][The allocator to use for dynamic memory allocation, or type `void` if MaxBits == MinBits.]]
+]
+
+When the template parameter Checked is set to `checked` then the result is a ['checked-integer], checked 
+and unchecked integers have the following properties:
+
+[table
+[[Condition][Checked-Integer][Unchecked-Integer]]
+[[Numeric overflow in fixed precision arithmetic][Throws a `std::overflow_error`.][Performs arithmetic modulo 2[super MaxBits]]]
+[[Constructing an integer from a value that can not be represented in the target type][Throws a `std::range_error`.]
+[Converts the value modulo 2[super MaxBits], signed to unsigned conversions extract the last MaxBits bits of the
+2's complement representation of the input value.]]
+[[Unsigned subtraction yielding a negative value.][Throws a `std::range_error`.][Yields the value that would
+result from treating the unsigned type as a 2's complement signed type.]]
+[[Attempting a bitwise operation on a negative value.][Throws a `std::range_error`][Yields the value, but not the bit pattern,
+that would result from performing the operation on a 2's complement integer type.]]
 ]
 
 Things you should know when using this type:
 
 * Default constructed `cpp_int_backend`s have the value zero.
-* Division by zero results in a `std::runtime_error` being thrown.
+* Division by zero results in a `std::overflow_error` being thrown.
 * Construction from a string that contains invalid non-numeric characters results in a `std::runtime_error` being thrown.
 * Since the precision of `cpp_int_backend` is necessarily limited when the allocator parameter is void, 
 care should be taken to avoid numeric overflow when using this type
@@ -404,13 +463,16 @@ That said it should be noted that there's no requirement for built-in types to b
 is the most common format by far.
 * Attempting to print negative values as either an Octal or Hexadecimal string results in a `std::runtime_error` being thrown,
 this is a direct consequence of the sign-magnitude representation.
-* The fixed precision types `mp_[u]intXXX_t` have expression template support turned off - it seems to make little 
+* The fixed precision types `[checked_][u]intXXX_t` have expression template support turned off - it seems to make little 
 difference to the performance of these types either way - so we may as well have the faster compile times by turning
 the feature off.
-* Unsigned types support subtraction, and unary negation - the result is "as if" a 2's complement operation had been performed
- - in other words they behave pretty much as a built in integer type would in this situation.  So for example if we were using
- `uint128_t` then both `uint128_t(1)-4` and `-uint128(3)` would result in the value `0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD`
- of type `uint128_t`.
+* Unsigned types support subtraction - the result is "as if" a 2's complement operation had been performed as long as they are not 
+ ['checked-integers] (see above).
+ In other words they behave pretty much as a built in integer type would in this situation.  So for example if we were using
+ `uint128_t` then `uint128_t(1)-4` would result in the value `0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD`
+ of type `uint128_t`.  However, had this operation been performed on `checked_uint128_t` then a `std::range_error` would have
+ been thrown.
+* Unary negation of unsigned types results in a compiler error (static assertion).
 * This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware.
 * When used at fixed precision, the size of this type is always one machine word larger than you would expect for an N-bit integer: 
 the extra word stores both the sign, and how many machine words in the integer are actually in use.  
@@ -420,6 +482,11 @@ characterists as a 128-bit integer, rather than being 4 times slower for additio
 Typically this means you can use
 an integer type wide enough for the "worst case senario" with only minor performance degradation even if most of the time
 the arithmetic could in fact be done with a narrower type.
+* When used at fixed precision and MaxBits is smaller than the number of bits in the largest native integer type, then
+internally `cpp_int_backend` switches to a "trivial" implementation where it is just a thin wrapper around a single
+integer.  Note that it will still be slightly slower than a bare native integer, as it emulates a 
+signed-magnitude representation rather than simply using the platforms native sign representation: this ensures
+there is no step change in behavior as a cpp_int grows in size.
  
 
 [h5 Example:]
@@ -460,7 +527,7 @@ as a result performing formatted output on this type when the argument is negati
 `std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown.
 * Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted 
 as a valid integer.
-* Division by zero results in a `std::runtime_error` being thrown.
+* Division by zero results in a `std::overflow_error` being thrown.
 * Although this type is a wrapper around [gmp] it will work equally well with [mpir].  Indeed use of [mpir]
 is recommended on Win32.
 * This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware.
@@ -498,7 +565,7 @@ as a result performing formatted output on this type when the argument is negati
 `std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown.
 * Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted 
 as a valid integer.
-* Division by zero results in a `std::runtime_error` being thrown.
+* Division by zero results in a `std::overflow_error` being thrown.
 
 [h5 Example:]
 
@@ -548,7 +615,7 @@ The following back-ends provide floating point arithmetic:
    }} // namespaces
 
 The `cpp_dec_float` back-end is used in conjunction with `number`: It acts as an entirely C++ (header only and dependency free)
-real-number type that is a drop-in replacement for the native C++ floating-point types, but with 
+floating-point number type that is a drop-in replacement for the native C++ floating-point types, but with 
 much greater precision.
 
 Type `cpp_dec_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter.  
@@ -641,7 +708,7 @@ existing [gmp] code.
 * It is not possible to round-trip objects of this type to and from a string and get back
 exactly the same value.  This appears to be a limitation of [gmp].
 * Since the underlying [gmp] types have no notion of infinities or NaN's, care should be taken
-to avoid numeric overflow or division by zero.  That latter will trigger a hardware exception, 
+to avoid numeric overflow or division by zero.  That latter will result in a std::overflow_error being thrown, 
 while generating excessively large exponents may result in instability of the underlying [gmp]
 library (in testing, converting a number with an excessively large or small exponent 
 to a string caused [gmp] to segfault).
@@ -649,7 +716,7 @@ to a string caused [gmp] to segfault).
 the recommended option on Win32.
 * Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted 
 as a valid floating point number.
-* Division by zero results in a `std::runtime_error` being thrown.
+* Division by zero results in a `std::overflow_error` being thrown.
 
 [h5 [gmp] example:]
 
@@ -799,7 +866,7 @@ which return the numerator and denominator of the number.
 Things you should know when using this type:
 
 * Default constructed `cpp_rational`s have the value zero.
-* Division by zero results in a `std::rumtime_error` being thrown.
+* Division by zero results in a `std::overflow_error` being thrown.
 * Conversion from a string results in a `std::runtime_error` being thrown if the string can not be
 interpreted as a valid rational number.
 
@@ -844,7 +911,7 @@ It's also possible to access the underlying `mpq_t` via the `data()` member func
 Things you should know when using this type:
 
 * Default constructed `mpq_rational`s have the value zero (this is the [gmp] default behavior).
-* Division by zero results in a `std::runtime_error` being thrown.
+* Division by zero results in a `std::overflow_error` being thrown.
 * Conversion from a string results in a `std::runtime_error` being thrown if the string can not be
 interpreted as a valid rational number.
 * No changes are made to the [gmp] library's global settings, so this type can coexist with existing
@@ -885,7 +952,7 @@ which return the numerator and denominator of the number.
 Things you should know when using this type:
 
 * Default constructed `tom_rational`s have the value zero (this the inherited Boost.Rational behavior).
-* Division by zero results in a `std::runtime_error` being thrown.
+* Division by zero results in a `std::overflow_error` being thrown.
 * Conversion from a string results in a `std::runtime_error` being thrown if the string can not be
 interpreted as a valid rational number.
 * No changes are made to [tommath]'s global state, so this type can safely coexist with other [tommath] code.
@@ -940,13 +1007,13 @@ In particular:
 * Any number type can be constructed (or assigned) from any builtin arithmetic type, as long
   as the conversion isn't lossy (for example float to int conversion):
 
-   cpp_dec_float_50 df(0.5); // OK construction from double
-   cpp_int          i(450);  // OK constructs from signed int
-   cpp_int          j = 3.14; // Error, lossy conversion.
+   cpp_dec_float_50 df(0.5);   // OK construction from double
+   cpp_int          i(450);    // OK constructs from signed int
+   cpp_int          j = 3.14;  // Error, lossy conversion.
 
 * A number can be explicitly constructed from an arithmetic type, even when the conversion is lossy:
 
-   cpp_int          i(3.14);  // OK explicit conversion
+   cpp_int          i(3.14);       // OK explicit conversion
    i = static_cast(3.14)  // OK explicit conversion
    i.assign(3.14);                 // OK, explicit assign and avoid a temporary from the cast above
    i = 3.14;                       // Error, no implicit assignment operator for lossy conversion.
@@ -963,8 +1030,8 @@ Additional conversions may be supported by particular backends.
 this functionality is only available on compilers supporting C++11's explicit conversion syntax.
 
    mpz_int z(2);
-   int i = z;  // Error, implicit conversion not allowed.
-   int j = static_cast(z);  // OK explicit conversion.
+   int i = z;                     // Error, implicit conversion not allowed.
+   int j = static_cast(z);   // OK explicit conversion.
 
 * Any number type can be ['explicitly] constructed (or assigned) from a `const char*` or a `std::string`:
 
@@ -1007,10 +1074,10 @@ are not lossy:
 * Interconversions between number types of the same family are allowed and are implicit conversions if no
 loss of precision is involved, and explicit if it is:
 
-   int128       i128 = 0;
-   int266       i256 = i128;  // OK implicit widening conversion
-   i128              = i256;  // Error, no assignment operator found, narrowing conversion is explict
-   i128              = static_cast(i256); // OK, explicit narrowing conversion
+   int128_t     i128 = 0;
+   int266_t     i256 = i128;  // OK implicit widening conversion
+   i128_t            = i256;  // Error, no assignment operator found, narrowing conversion is explict
+   i128_t            = static_cast(i256); // OK, explicit narrowing conversion
 
    mpz_int      z    = 0;
    mpf_float    f    = z;    // OK, GMP handles this conversion natively, and it's not lossy and therefore implicit
@@ -1337,7 +1404,7 @@ Type `number` is default constructible, and both copy constructible and assignab
 * An rvalue reference to another `number`.  Move-semantics are used for construction if the backend also
 supports rvalue reference construction.  In the case of assignment, move semantics are always supported
 when the argument is an rvalue reference irrespective of the backend.
-* Any type in the same family, as long as no loss of precision is involved.  For example from `int128` to `int256`,
+* Any type in the same family, as long as no loss of precision is involved.  For example from `int128_t` to `int256_t`,
 or `cpp_dec_float_50` to `cpp_dec_float_100`.
 
 Type `number` is explicitly constructible from:
@@ -1719,30 +1786,56 @@ whose precision can vary at compile time (such as `mpf_float`).
 
    namespace boost{ namespace multiprecision{
 
-   template  >
-   struct cpp_int_backend;
+   typedef unspecified-type limb_type;
+
+   enum cpp_integer_type    { signed_magnitude, unsigned_magnitude };
+   enum cpp_int_check_type  { checked, unchecked };
+
+   template  >
+   class cpp_int_backend;
    //
    // Expression templates default to et_off if there is no allocator:
    //
-   template 
-   struct expression_template_default >
+   template 
+   struct expression_template_default >
    { static const expression_template_option value = et_off; };
 
-   typedef number >           cpp_int;    // arbitrary precision integer
+   typedef number >              cpp_int;    // arbitrary precision integer
    typedef rational_adapter >    cpp_rational_backend;
-   typedef number         cpp_rational; // arbitrary precision rational number
+   typedef number            cpp_rational; // arbitrary precision rational number
 
    // Fixed precision unsigned types:
-   typedef number >   uint128_t;
-   typedef number >   uint256_t;
-   typedef number >   uint512_t;
-   typedef number >  uint1024_t;
+   typedef number >   uint128_t;
+   typedef number >   uint256_t;
+   typedef number >   uint512_t;
+   typedef number > uint1024_t;
 
    // Fixed precision signed types:
-   typedef number >    int128_t;
-   typedef number >    int256_t;
-   typedef number >    int512_t;
-   typedef number >   int1024_t;
+   typedef number >     int128_t;
+   typedef number >     int256_t;
+   typedef number >     int512_t;
+   typedef number >   int1024_t;
+
+   // Over again, but with checking enabled this time:
+   typedef number >                 checked_cpp_int;
+   typedef rational_adapter >       checked_cpp_rational_backend;
+   typedef number                                              checked_cpp_rational;
+
+   // Checked fixed precision unsigned types:
+   typedef number >     checked_uint128_t;
+   typedef number >     checked_uint256_t;
+   typedef number >     checked_uint512_t;
+   typedef number >   checked_uint1024_t;
+
+   // Fixed precision signed types:
+   typedef number >       checked_int128_t;
+   typedef number >       checked_int256_t;
+   typedef number >       checked_int512_t;
+   typedef number >     checked_int1024_t;
 
    }} // namespaces
 
@@ -1753,16 +1846,22 @@ to change.
 The template arguments are:
 
 [variablelist
-[[Argument][Meaning]]
-[[MinBits]
-   [The number of Bits to reserve inside the class's internal cache.  When constructing a value,
-    the object will use this internal cache if possible before resorting to dynamic memory allocation.
-    When this value is zero, then the size of the internal cache is `2*sizeof(void*)*CHAR_BIT`.
-    When the Allocator argument is `void`, then this parameter determines the precision of the type.]]
-[[Signed][When `true` the type is signed, otherwise unsigned.  Note that unsigned types are currently only 
-      supported when the Allocator parameter is `void`.]]
-[[Allocator][The allocator used for dynamic memory allocation.  This parameter can be `void`, in which case
-      no dynamic memory will ever be allocated.]]
+[[MinBits][Determines the number of Bits to store directly within the object before resorting to dynamic memory
+           allocation.  When zero, this field is determined automatically based on how many bits can be stored
+           in union with the dynamic storage header: setting a larger value may improve performance as larger integer
+           values will be stored internally before memory allocation is required.]]
+[[MaxBits][Determines the maximum number of bits to be stored in the type: resulting in a fixed precision type.
+           When this value is the same as MinBits, then the Allocator parameter is ignored, as no dynamic
+           memory allocation will ever be performed: in this situation the Allocator parameter should be set to
+           type `void`.  Note that this parameter should not be used simply to prevent large memory
+           allocations, not only is that role better performed by the allocator, but fixed precision
+           integers have a tendency to allocate all of MaxBits of storage more often than one would expect.]]
+[[SignType][Determines whether the resulting type is signed or not.  Note that for 
+[@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] types
+          this parameter must be `signed_magnitude`.  For fixed precision
+          types then this type may be either `signed_magnitude` or `unsigned_magnitude`.]]
+[[Checked][This parameter has two values: `checked` or `unchecked`.  See the [link boost_multiprecision.tut.ints.cpp_int tutorial] for more information.]]
+[[Allocator][The allocator to use for dynamic memory allocation, or type `void` if MaxBits == MinBits.]]
 ]
 
 The type of `number_category >::type` is `mpl::int_`.
@@ -1940,6 +2039,14 @@ if `is_lossy_conversion::value` is `true`.  Otherwise `false`.
 Note that while this trait is the ultimate arbiter of which constructors are marked as `explicit` in class `number`,
 authors of backend types should generally specialise one of the traits above, rather than this one directly.
 
+   template 
+   is_signed_number;
+   template 
+   is_unsigned_number;
+
+These two traits inherit from either `mpl::true_` or `mpl::false_`, by default types are assumed to be signed unless
+`is_unsigned_number` is specialized for that type.
+
 [endsect]
 
 [section:backendconc Backend Requirements]
@@ -2335,7 +2442,6 @@ in point of fact this naming convention shouldn't be necessary, but rather works
 [[Header][Contains]]
 [[cpp_int.hpp][The `cpp_int` backend type.]]
 [[gmp.hpp][Defines all [gmp] related backends.]]
-[[integer_ops.hpp][Integer specific non-member functions.]]
 [[miller_rabin.hpp][Miller Rabin primality testing code.]]
 [[number.hpp][Defines the `number` backend, is included by all the backend headers.]]
 [[mpfr.hpp][Defines the mpfr_float_backend backend.]]
@@ -2348,8 +2454,16 @@ in point of fact this naming convention shouldn't be necessary, but rather works
 
 [table Implementation Headers]
 [[Header][Contains]]
+[[cpp_int/add.hpp][Add and subtract operators for `cpp_int_backend`.]]
+[[cpp_int/bitwise.hpp][Bitwise operators for `cpp_int_backend`.]]
+[[cpp_int/checked.hpp][Helper functions for checked arithmetic for `cpp_int_backend`.]]
+[[cpp_int/comparison.hpp][Comparison operators for `cpp_int_backend`.]]
+[[cpp_int/cpp_int_config.hpp][Basic setup and configuration for `cpp_int_backend`.]]
+[[cpp_int/divide.hpp][Division and modulus operators for `cpp_int_backend`.]]
+[[cpp_int/limits.hpp][`numeric_limits` support for `cpp_int_backend`.]]
+[[cpp_int/misc.hpp][Miscellaneous operators for `cpp_int_backend`.]]
+[[cpp_int/multiply.hpp][Multiply operators for `cpp_int_backend`.]]
 [[detail/big_lanczos.hpp][Lanczos support for Boost.Math integration.]]
-[[detail/cpp_int_core.hpp][Platform and peformance tuning for the `cpp_int` backend.]]
 [[detail/default_ops.hpp][Default versions of the optional backend non-member functions.]]
 [[detail/generic_interconvert.hpp][Generic interconversion routines.]]
 [[detail/number_base.hpp][All the expression template code, metaprogramming, and operator overloads for `number`.]]
@@ -2725,7 +2839,7 @@ Windows Vista machine.
 [h4 Post review changes]
 
 * Non-expression template operators further optimised with rvalue reference support.
-* Many functions made made `constexp`?
+* Many functions made `constexp`.
 * Differentiate between explicit and implicit conversions in the number constructor.
 * Removed "mp_" prefix from types.
 * Allowed mixed precision arithmetic.
@@ -2733,6 +2847,7 @@ Windows Vista machine.
 * Changed ExpressionTemplate parameter default value to use a traits class so that the default value depends on the backend used.
 * Added support for fused-multiply-add/subtract with GMP support.
 * Tweaked expression template unpacking to use fewer temporaries when the LHS also appears in the RHS.
+* Refactored `cpp_int_backend` based on review comments with new template parameter structure.
 
 [h4 Pre-review history]
 
@@ -2763,28 +2878,30 @@ More a list of what ['could] be done, rather than what ['should] be done (which
 * Can ring types (exact floating point types) be supported?  The answer should be yes, but someone needs to write it, 
 the hard part is IO and binary-decimal convertion.
 * Should there be a choice of rounding mode (probably MPFR specific)?
+* We can reuse temporaries in multiple subtrees (temporary caching).
 
 Things requested in review:
 
 * A 2's complement fixed precision int that uses exactly N bits and no more.
-* A backend for an overflow aware integers.
-* Each back-end should document the requirements it satisfies (not currently scheduled for inclusion: it's
-deliberately an implementation detail, and "optional" requirements are optimisations which can't be detected
-by the user).
-* The use of bool in template parameters could be improved by the use of 
-an enum class which will be more explicit. E.g `enum class expression_template {disabled, enabled};
-enum class sign {unsigned, signed};`  (Partly done 2012/09/15).
 * The performances of mp_number, false>respect to 
 float and mp_number, false> and int should be 
 given to show the cost of using the generic interface (Mostly done, just need to update docs to the latest results).
 * The rounding applied when converting must be documented.
 * cpp_dec_float should round to nearest.
-* We can reuse temporaries in multiple subtrees (temporary caching).
-* Emphasise in the docs that ET's may reorder operations.
 * Document why we don't use proto (compile times).
-* Document what happens to small fixed precision cpp_int's.
 * Should we provide min/max overloads for expression templates?
 * Document why we don't abstract out addition/multiplication algorithms etc.
+* We can reuse temporaries in multiple subtrees (temporary caching)  Moved to TODO list.
+* Emphasise in the docs that ET's may reorder operations (done 2012/10/31).
+* Document what happens to small fixed precision cpp_int's (done 2012/10/31).
+* The use of bool in template parameters could be improved by the use of 
+an enum class which will be more explicit. E.g `enum class expression_template {disabled, enabled};
+enum class sign {unsigned, signed};`  (Partly done 2012/09/15, done 2012/10/31).
+* Each back-end should document the requirements it satisfies (not currently scheduled for inclusion: it's
+deliberately an implementation detail, and "optional" requirements are optimisations which can't be detected
+by the user).  Not done: this is an implementation detail, the exact list of requirements satisfied is purely
+an optimimization, not something the user can detect.
+* A backend for an overflow aware integers (done 2012/10/31).
 * IIUC convert_to is used to emulate in c++98 compilers C++11 explicit 
 conversions. Could the explicit conversion operator be added on 
 compilers supporting it?  (Done 2012/09/15).
@@ -2811,7 +2928,7 @@ is able to.  (Done 2012/09/15).
 [h4 Pre-Review Comments]
 
 * Make fixed precision orthogonal to Allocator type in cpp_int.  Possible solution - add an additional MaxBits 
-template argument that defaults to 0 (meaning keep going till no more space/memory).
+template argument that defaults to 0 (meaning keep going till no more space/memory).  Done.
 * Can ring types (exact floating point types) be supported?  The answer should be yes, but someone needs to write it (Moved to TODO list).
 * Should there be a choice of rounding mode (probably MPFR specific)?  Moved to TODO list.
 * Make the exponent type for cpp_dec_float a templare parameter, maybe include support for big-integer exponents.
diff --git a/include/boost/multiprecision/cpp_int/misc.hpp b/include/boost/multiprecision/cpp_int/misc.hpp
index cee2e386..04178687 100644
--- a/include/boost/multiprecision/cpp_int/misc.hpp
+++ b/include/boost/multiprecision/cpp_int/misc.hpp
@@ -31,7 +31,7 @@ void check_in_range(const CppInt& /*val*/, const mpl::int_&) BOOST_NO
 void check_is_negative(const mpl::true_&) BOOST_NOEXCEPT {}
 void check_is_negative(const mpl::false_&)
 {
-   BOOST_THROW_EXCEPTION(std::domain_error("Attempt to assign a negative value to an unsigned type."));
+   BOOST_THROW_EXCEPTION(std::range_error("Attempt to assign a negative value to an unsigned type."));
 }
 
 template 
diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp
index aae260c7..51bd8fb1 100644
--- a/include/boost/multiprecision/number.hpp
+++ b/include/boost/multiprecision/number.hpp
@@ -749,7 +749,7 @@ private:
          self_type temp(e);
          temp.m_backend.swap(this->m_backend);
       }
-      else if(bl || (left_depth >= right_depth))
+      else if(!br && (bl || (left_depth >= right_depth)))
       { // br is always false, but if bl is true we must take the this branch:
          do_assign(e.left(), typename left_type::tag_type());
          do_add(e.right(), typename right_type::tag_type());
@@ -788,7 +788,7 @@ private:
          self_type temp(e);
          temp.m_backend.swap(this->m_backend);
       }
-      else if(bl || (left_depth >= right_depth))
+      else if(!br && (bl || (left_depth >= right_depth)))
       { // br is always false, but if bl is true we must take the this branch:
          do_assign(e.left(), typename left_type::tag_type());
          do_subtract(e.right(), typename right_type::tag_type());
@@ -827,7 +827,7 @@ private:
          self_type temp(e);
          temp.m_backend.swap(this->m_backend);
       }
-      else if(bl || (left_depth >= right_depth))
+      else if(!br && (bl || (left_depth >= right_depth)))
       { // br is always false, but if bl is true we must take the this branch:
          do_assign(e.left(), typename left_type::tag_type());
          do_multiplies(e.right(), typename right_type::tag_type());
@@ -927,7 +927,7 @@ private:
       {
          do_bitwise_and(e.left(), typename left_type::tag_type());
       }
-      else if(left_depth >= right_depth)
+      else if(!br && (bl || (left_depth >= right_depth)))
       {
          do_assign(e.left(), typename left_type::tag_type());
          do_bitwise_and(e.right(), typename right_type::tag_type());
@@ -972,7 +972,7 @@ private:
       {
          do_bitwise_or(e.left(), typename left_type::tag_type());
       }
-      else if(left_depth >= right_depth)
+      else if(!br && (bl || (left_depth >= right_depth)))
       {
          do_assign(e.left(), typename left_type::tag_type());
          do_bitwise_or(e.right(), typename right_type::tag_type());
@@ -1017,7 +1017,7 @@ private:
       {
          do_bitwise_xor(e.left(), typename left_type::tag_type());
       }
-      else if(left_depth >= right_depth)
+      else if(!br && (bl || (left_depth >= right_depth)))
       {
          do_assign(e.left(), typename left_type::tag_type());
          do_bitwise_xor(e.right(), typename right_type::tag_type());
diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp
index 5327e055..08c2e726 100644
--- a/performance/sf_performance.cpp
+++ b/performance/sf_performance.cpp
@@ -282,8 +282,10 @@ int main()
 #ifdef TEST_MPFR
 #if MPFR_VERSION, 1);
+   time_proc("mpfr_float_50 (no expression templates", test_bessel, et_off> >, 1);
 #else
    time_proc("mpfr_float_50", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1);
+   time_proc("mpfr_float_50 (no expression templates", test_bessel, et_off> >, mpfr_buildopt_tls_p() ? 3 : 1);
 #endif
 #endif
 #ifdef TEST_MPF
@@ -311,6 +313,7 @@ int main()
 #endif
 #ifdef TEST_MPFR
    time_proc("mpfr_float_100", test_bessel);
+   time_proc("mpfr_float_100 (no expression templates", test_bessel, et_off> >);
 #endif
 #ifdef TEST_MPF
    time_proc("mpf_float_100", test_bessel);
@@ -338,6 +341,7 @@ int main()
 #endif
 #ifdef TEST_MPFR
    time_proc("mpfr_float_50", test_polynomial);
+   time_proc("mpfr_float_50 (no expression templates", test_polynomial, et_off> >);
 #endif
 #ifdef TEST_MPF
    time_proc("mpf_float_50", test_polynomial);
@@ -364,6 +368,7 @@ int main()
 #endif
 #ifdef TEST_MPFR
    time_proc("mpfr_float_100", test_polynomial);
+   time_proc("mpfr_float_100 (no expression templates", test_polynomial, et_off> >);
 #endif
 #ifdef TEST_MPF
    time_proc("mpf_float_100", test_polynomial);
@@ -390,6 +395,7 @@ int main()
 #endif
 #ifdef TEST_MPFR
    time_proc("mpfr_float_50", test_nct);
+   time_proc("mpfr_float_50 (no expression templates", test_nct, et_off> >);
 #endif
 #ifdef TEST_MPF
    time_proc("mpf_float_50", test_nct);
@@ -416,6 +422,7 @@ int main()
 #endif
 #ifdef TEST_MPFR
    time_proc("mpfr_float_100", test_nct);
+   time_proc("mpfr_float_100 (no expression templates", test_nct, et_off> >);
 #endif
 #ifdef TEST_MPF
    time_proc("mpf_float_100", test_nct);
diff --git a/test/math/log1p_expm1_test.cpp b/test/math/log1p_expm1_test.cpp
index 4df662c6..9472123d 100644
--- a/test/math/log1p_expm1_test.cpp
+++ b/test/math/log1p_expm1_test.cpp
@@ -131,6 +131,8 @@ int test_main(int, char* [])
    test(number >(), "number >");
    test(number >(), "number >");
    test(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test(number >(), "number >");
diff --git a/test/math/powm1_sqrtp1m1_test.cpp b/test/math/powm1_sqrtp1m1_test.cpp
index 1fa0f76d..a5850b3d 100644
--- a/test/math/powm1_sqrtp1m1_test.cpp
+++ b/test/math/powm1_sqrtp1m1_test.cpp
@@ -123,6 +123,8 @@ int test_main(int, char* [])
    //test_powm1_sqrtp1m1(number >(), "number >");
    test_powm1_sqrtp1m1(number >(), "number >");
    test_powm1_sqrtp1m1(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_powm1_sqrtp1m1(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_powm1_sqrtp1m1(number >(), "number >");
diff --git a/test/math/test_bessel_i.cpp b/test/math/test_bessel_i.cpp
index 4fc0c100..a058c070 100644
--- a/test/math/test_bessel_i.cpp
+++ b/test/math/test_bessel_i.cpp
@@ -91,6 +91,8 @@ int test_main(int, char* [])
    //test_bessel(number >(), "number >");
    test_bessel(number >(), "number >");
    test_bessel(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_bessel(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_bessel(number >(), "number >");
diff --git a/test/math/test_bessel_j.cpp b/test/math/test_bessel_j.cpp
index d0f2acd8..0cdd5f51 100644
--- a/test/math/test_bessel_j.cpp
+++ b/test/math/test_bessel_j.cpp
@@ -133,6 +133,8 @@ int test_main(int, char* [])
    //test_bessel(number >(), "number >");
    test_bessel(number >(), "number >");
    test_bessel(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_bessel(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_bessel(number >(), "number >");
diff --git a/test/math/test_bessel_k.cpp b/test/math/test_bessel_k.cpp
index 8c4d8e54..0fa9dc3b 100644
--- a/test/math/test_bessel_k.cpp
+++ b/test/math/test_bessel_k.cpp
@@ -106,6 +106,8 @@ int test_main(int, char* [])
    test_bessel(number >(), "number >");
    test_bessel(number >(), "number >");
    test_bessel(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_bessel(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_bessel(number >(), "number >");
diff --git a/test/math/test_bessel_y.cpp b/test/math/test_bessel_y.cpp
index a3a7c91b..8e39e399 100644
--- a/test/math/test_bessel_y.cpp
+++ b/test/math/test_bessel_y.cpp
@@ -132,6 +132,8 @@ int test_main(int, char* [])
    //test_bessel(number >(), "number >");
    test_bessel(number >(), "number >");
    test_bessel(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_bessel(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_bessel(number >(), "number >");
diff --git a/test/math/test_beta.cpp b/test/math/test_beta.cpp
index 92d0fb77..a372f704 100644
--- a/test/math/test_beta.cpp
+++ b/test/math/test_beta.cpp
@@ -118,6 +118,8 @@ int test_main(int, char* [])
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_beta(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_beta(number >(), "number >");
diff --git a/test/math/test_binomial_coeff.cpp b/test/math/test_binomial_coeff.cpp
index 208c5dee..01c7ad44 100644
--- a/test/math/test_binomial_coeff.cpp
+++ b/test/math/test_binomial_coeff.cpp
@@ -97,6 +97,8 @@ int test_main(int, char* [])
    test_binomial(number >(), "number >");
    test_binomial(number >(), "number >");
    test_binomial(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_binomial(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_binomial(number >(), "number >");
diff --git a/test/math/test_carlson.cpp b/test/math/test_carlson.cpp
index d5936f38..2680c392 100644
--- a/test/math/test_carlson.cpp
+++ b/test/math/test_carlson.cpp
@@ -89,6 +89,8 @@ int test_main(int, char* [])
    test_spots(number >(), "number >");
    test_spots(number >(), "number >");
    test_spots(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_spots(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_spots(number >(), "number >");
diff --git a/test/math/test_cbrt.cpp b/test/math/test_cbrt.cpp
index ca2af6d3..ac07d662 100644
--- a/test/math/test_cbrt.cpp
+++ b/test/math/test_cbrt.cpp
@@ -78,6 +78,8 @@ int test_main(int, char* [])
    test_cbrt(number >(), "number >");
    test_cbrt(number >(), "number >");
    test_cbrt(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_cbrt(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_cbrt(number >(), "number >");
diff --git a/test/math/test_digamma.cpp b/test/math/test_digamma.cpp
index a090081d..86b8f00a 100644
--- a/test/math/test_digamma.cpp
+++ b/test/math/test_digamma.cpp
@@ -92,6 +92,8 @@ int test_main(int, char* [])
    test_digamma(number >(), "number >");
    test_digamma(number >(), "number >");
    test_digamma(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_digamma(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_digamma(number >(), "number >");
diff --git a/test/math/test_ellint_1.cpp b/test/math/test_ellint_1.cpp
index bf8eb4a3..bc843e30 100644
--- a/test/math/test_ellint_1.cpp
+++ b/test/math/test_ellint_1.cpp
@@ -85,6 +85,8 @@ int test_main(int, char* [])
    test_spots(number >(), "number >");
    test_spots(number >(), "number >");
    test_spots(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_spots(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_spots(number >(), "number >");
diff --git a/test/math/test_ellint_2.cpp b/test/math/test_ellint_2.cpp
index d12c1d50..bd8c01cf 100644
--- a/test/math/test_ellint_2.cpp
+++ b/test/math/test_ellint_2.cpp
@@ -78,6 +78,8 @@ int test_main(int, char* [])
    test_spots(number >(), "number >");
    test_spots(number >(), "number >");
    test_spots(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_spots(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_spots(number >(), "number >");
diff --git a/test/math/test_ellint_3.cpp b/test/math/test_ellint_3.cpp
index abc6141a..49ffdc31 100644
--- a/test/math/test_ellint_3.cpp
+++ b/test/math/test_ellint_3.cpp
@@ -99,6 +99,8 @@ int test_main(int, char* [])
    test_spots(number >(), "number >");
    test_spots(number >(), "number >");
    test_spots(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_spots(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_spots(number >(), "number >");
diff --git a/test/math/test_erf.cpp b/test/math/test_erf.cpp
index e9308d8c..925b72a4 100644
--- a/test/math/test_erf.cpp
+++ b/test/math/test_erf.cpp
@@ -99,6 +99,8 @@ int test_main(int, char* [])
    test_erf(number >(), "number >");
    test_erf(number >(), "number >");
    test_erf(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_erf(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_erf(number >(), "number >");
diff --git a/test/math/test_expint.cpp b/test/math/test_expint.cpp
index bf5b78eb..c134390b 100644
--- a/test/math/test_expint.cpp
+++ b/test/math/test_expint.cpp
@@ -99,6 +99,8 @@ int test_main(int, char* [])
    test_expint(number >(), "number >");
    test_expint(number >(), "number >");
    test_expint(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_expint(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_expint(number >(), "number >");
diff --git a/test/math/test_gamma.cpp b/test/math/test_gamma.cpp
index c853bdb4..7e944a91 100644
--- a/test/math/test_gamma.cpp
+++ b/test/math/test_gamma.cpp
@@ -113,6 +113,8 @@ int test_main(int, char* [])
    test_gamma(number >(), "number >");
    test_gamma(number >(), "number >");
    test_gamma(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_gamma(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_gamma(number >(), "number >");
diff --git a/test/math/test_hermite.cpp b/test/math/test_hermite.cpp
index 743a3de3..bb1c3ac1 100644
--- a/test/math/test_hermite.cpp
+++ b/test/math/test_hermite.cpp
@@ -78,6 +78,8 @@ int test_main(int, char* [])
    test_hermite(number >(), "number >");
    test_hermite(number >(), "number >");
    test_hermite(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_hermite(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_hermite(number >(), "number >");
diff --git a/test/math/test_ibeta.cpp b/test/math/test_ibeta.cpp
index 2f6902e0..2e2233c0 100644
--- a/test/math/test_ibeta.cpp
+++ b/test/math/test_ibeta.cpp
@@ -109,6 +109,8 @@ int test_main(int, char* [])
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_beta(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_beta(number >(), "number >");
diff --git a/test/math/test_ibeta_2.cpp b/test/math/test_ibeta_2.cpp
index 72997385..e885e095 100644
--- a/test/math/test_ibeta_2.cpp
+++ b/test/math/test_ibeta_2.cpp
@@ -109,6 +109,8 @@ int test_main(int, char* [])
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_beta(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_beta(number >(), "number >");
diff --git a/test/math/test_ibeta_3.cpp b/test/math/test_ibeta_3.cpp
index c6602542..bc685922 100644
--- a/test/math/test_ibeta_3.cpp
+++ b/test/math/test_ibeta_3.cpp
@@ -95,6 +95,8 @@ int test_main(int, char* [])
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_beta(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_beta(number >(), "number >");
diff --git a/test/math/test_ibeta_4.cpp b/test/math/test_ibeta_4.cpp
index c7a8b20f..754f6b59 100644
--- a/test/math/test_ibeta_4.cpp
+++ b/test/math/test_ibeta_4.cpp
@@ -102,6 +102,8 @@ int test_main(int, char* [])
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_beta(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_beta(number >(), "number >");
diff --git a/test/math/test_ibeta_inv_1.cpp b/test/math/test_ibeta_inv_1.cpp
index b9f052ca..47cd48f7 100644
--- a/test/math/test_ibeta_inv_1.cpp
+++ b/test/math/test_ibeta_inv_1.cpp
@@ -88,6 +88,8 @@ int test_main(int, char* [])
    //test_beta(number >(), "number >");
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_beta(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_beta(number >(), "number >");
diff --git a/test/math/test_ibeta_inv_ab_4.cpp b/test/math/test_ibeta_inv_ab_4.cpp
index 82eff4e6..60bd3930 100644
--- a/test/math/test_ibeta_inv_ab_4.cpp
+++ b/test/math/test_ibeta_inv_ab_4.cpp
@@ -81,6 +81,8 @@ int test_main(int, char* [])
    //test_beta(number >(), "number >");
    test_beta(number >(), "number >");
    test_beta(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_beta(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_beta(number >(), "number >");
diff --git a/test/math/test_igamma.cpp b/test/math/test_igamma.cpp
index 063cbeaf..5f544f4f 100644
--- a/test/math/test_igamma.cpp
+++ b/test/math/test_igamma.cpp
@@ -85,6 +85,8 @@ int test_main(int, char* [])
    test_gamma(number >(), "number >");
    test_gamma(number >(), "number >");
    test_gamma(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_gamma(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_gamma(number >(), "number >");
diff --git a/test/math/test_igamma_inv.cpp b/test/math/test_igamma_inv.cpp
index 5408444e..2cb4c4d9 100644
--- a/test/math/test_igamma_inv.cpp
+++ b/test/math/test_igamma_inv.cpp
@@ -100,6 +100,8 @@ int test_main(int, char* [])
    test_gamma(number >(), "number >");
    test_gamma(number >(), "number >");
    test_gamma(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_gamma(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_gamma(number >(), "number >");
diff --git a/test/math/test_igamma_inva.cpp b/test/math/test_igamma_inva.cpp
index fdd330e9..5724ed7d 100644
--- a/test/math/test_igamma_inva.cpp
+++ b/test/math/test_igamma_inva.cpp
@@ -79,6 +79,8 @@ int test_main(int, char* [])
    test_gamma(number >(), "number >");
    test_gamma(number >(), "number >");
    test_gamma(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_gamma(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_gamma(number >(), "number >");
diff --git a/test/math/test_laguerre.cpp b/test/math/test_laguerre.cpp
index 65840502..6b6aab15 100644
--- a/test/math/test_laguerre.cpp
+++ b/test/math/test_laguerre.cpp
@@ -78,6 +78,8 @@ int test_main(int, char* [])
    test_laguerre(number >(), "number >");
    test_laguerre(number >(), "number >");
    test_laguerre(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_laguerre(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_laguerre(number >(), "number >");
diff --git a/test/math/test_legendre.cpp b/test/math/test_legendre.cpp
index 237310e6..6143b020 100644
--- a/test/math/test_legendre.cpp
+++ b/test/math/test_legendre.cpp
@@ -78,6 +78,8 @@ int test_main(int, char* [])
    test_legendre_p(number >(), "number >");
    test_legendre_p(number >(), "number >");
    test_legendre_p(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_legendre_p(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_legendre_p(number >(), "number >");
diff --git a/test/math/test_tgamma_ratio.cpp b/test/math/test_tgamma_ratio.cpp
index cae68344..5c27f269 100644
--- a/test/math/test_tgamma_ratio.cpp
+++ b/test/math/test_tgamma_ratio.cpp
@@ -92,6 +92,8 @@ int test_main(int, char* [])
    test_tgamma_ratio(number >(), "number >");
    test_tgamma_ratio(number >(), "number >");
    test_tgamma_ratio(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_tgamma_ratio(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_tgamma_ratio(number >(), "number >");
diff --git a/test/math/test_zeta.cpp b/test/math/test_zeta.cpp
index 4db422fe..003f7abf 100644
--- a/test/math/test_zeta.cpp
+++ b/test/math/test_zeta.cpp
@@ -86,6 +86,8 @@ int test_main(int, char* [])
    test_zeta(number >(), "number >");
    test_zeta(number >(), "number >");
    test_zeta(number >(), "number >");
+   // there should be at least one test with expression templates off:
+   test_zeta(number, et_off>(), "number, et_off>");
 #endif
 #ifdef TEST_MPFR_50
    test_zeta(number >(), "number >");

From d1336b5f635d97f7906f5f51906945c1de4cc5ef Mon Sep 17 00:00:00 2001
From: John Maddock 
Date: Thu, 1 Nov 2012 11:19:59 +0000
Subject: [PATCH 246/256] More doc updates. Regenerate docs.

[SVN r81133]
---
 .../boost_multiprecision/indexes/s01.html     |   5 +-
 .../boost_multiprecision/indexes/s02.html     |   4 +-
 .../boost_multiprecision/indexes/s03.html     |   4 +-
 .../boost_multiprecision/indexes/s04.html     |  15 +-
 doc/html/boost_multiprecision/map.html        |   1 +
 doc/html/boost_multiprecision/map/ack.html    |   6 +-
 doc/html/boost_multiprecision/map/faq.html    | 111 +++++++++++
 doc/html/boost_multiprecision/map/todo.html   |  36 ++--
 doc/html/boost_multiprecision/ref.html        |   6 +-
 doc/html/boost_multiprecision/tut.html        |   3 +
 doc/html/boost_multiprecision/tut/lits.html   |  63 ++++++
 .../boost_multiprecision/tut/primetest.html   |   6 +-
 .../boost_multiprecision/tut/rounding.html    | 182 ++++++++++++++++++
 doc/html/index.html                           |   6 +-
 doc/multiprecision.qbk                        | 100 +++++++++-
 15 files changed, 509 insertions(+), 39 deletions(-)
 create mode 100644 doc/html/boost_multiprecision/map/faq.html
 create mode 100644 doc/html/boost_multiprecision/tut/lits.html
 create mode 100644 doc/html/boost_multiprecision/tut/rounding.html

diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html
index af78fb53..680560fd 100644
--- a/doc/html/boost_multiprecision/indexes/s01.html
+++ b/doc/html/boost_multiprecision/indexes/s01.html
@@ -13,9 +13,9 @@
 
    
 PrevUpHomeNext
 
    
-
    
+
    
 
    
-Function Index
    
+Function Index
    
 
    A B C D E F I L M P R S T Z
    
 
    
 
    
@@ -421,6 +421,7 @@
 
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    precision
    
 
    
diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html
index 2df7fd66..d15a40c9 100644
--- a/doc/html/boost_multiprecision/indexes/s02.html
+++ b/doc/html/boost_multiprecision/indexes/s02.html
@@ -13,9 +13,9 @@
 
    
 PrevUpHomeNext
 
    
-
    
+
    
 
    
-Class Index
    
+Class Index
    • 
 
    C E G I M N T
    
 
    
 
    
diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html
index be23bda1..729668d3 100644
--- a/doc/html/boost_multiprecision/indexes/s03.html
+++ b/doc/html/boost_multiprecision/indexes/s03.html
@@ -13,9 +13,9 @@
 
    
 PrevUpHomeNext
 
    
-
    
+
    
 
    
-Typedef Index
    
+Typedef Index
    
 
    C I L M T U
    
 
    
 
    
diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html
index 7a5144be..adbddd56 100644
--- a/doc/html/boost_multiprecision/indexes/s04.html
+++ b/doc/html/boost_multiprecision/indexes/s04.html
@@ -12,9 +12,9 @@
 
    
 PrevUpHome
 
    
-
    
+
    
 
    
-Index
    
+Index
    
 
    A B C D E F G I L M N O P R S T U Z
    
 
    
 
    
@@ -475,10 +475,16 @@
 
    
 F
 
    
-
    
 
    
 G
 
    
@@ -859,6 +865,7 @@
 
  • 
 
    precision
    
 
    
diff --git a/doc/html/boost_multiprecision/map.html b/doc/html/boost_multiprecision/map.html
index 5037bf2b..9521a6be 100644
--- a/doc/html/boost_multiprecision/map.html
+++ b/doc/html/boost_multiprecision/map.html
@@ -20,6 +20,7 @@
 
    
 
    History
    
 
    TODO
    
+
    FAQ
    
 
    Acknowledgements
    
 
    
 
    • 
diff --git a/doc/html/boost_multiprecision/map/ack.html b/doc/html/boost_multiprecision/map/ack.html
index f437951a..0dc685f5 100644
--- a/doc/html/boost_multiprecision/map/ack.html
+++ b/doc/html/boost_multiprecision/map/ack.html
@@ -6,12 +6,12 @@
 
 
 
-
+
 
 
 
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -49,7 +49,7 @@
 
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/html/boost_multiprecision/map/faq.html b/doc/html/boost_multiprecision/map/faq.html
new file mode 100644
index 00000000..887b9ad4
--- /dev/null
+++ b/doc/html/boost_multiprecision/map/faq.html
@@ -0,0 +1,111 @@
+
+
+
+FAQ
+
+
+
+
+
+
+
+
+
    
+PrevUpHomeNext
+
    
+
    
+
    
+FAQ
+
    
+
    
+
    
+
    
+
    Why do I get compiler errors when passing a number
+          to a template function?
    
+
    
+              Most likely you are actually passing an expression template type to
+              the function and template-argument-deduction deduces the "wrong"
+              type. Try casting the arguments involving expressions to the actual
+              number type, or as a last resort turning off expression template support
+              in the number type you are using.
+            
    
+
    When is expression template support a performance gain?
    
+
    
+              As a general rule, expression template support adds a small runtime
+              overhead creating and unpacking the expression templates, but greatly
+              reduces the number of temporaries created. So it's most effective in
+              improving performance when the cost of creating a temporary is high:
+              for example when creating a temporary involves a memory allocation.
+              It is least effective (and may even be a dis-optimisation) when temporaries
+              are cheap: for example if the number type is basically a thin wrapper
+              around a native arithmetic type. In addition, since the library makes
+              extensive use of thin inline wrapper functions, turning on compiler
+              optimization is essential to achieving high performance.
+            
    
+
    Do expression templates reorder operations?
    
+
    
+              Yes they do, sometimes quite radically so, if this is a concern then
+              they should be turned off for the number type you are using.
+            
    
+
    I can't construct my number type from some other type,
+          but the docs indicate that the conversion should be allowed, what's up?
    
+
    
+              Some conversions are explicit, that includes construction
+              from a string, or constructing from any type that may result in loss
+              of precision (for example constructing an integer type from a float).
+            
    
+
    Why do I get an exception thrown (or the program crash due to an
+          uncaught exception) when using the bitwise operators on a checked cpp_int?
    
+
    
+              Bitwise operations on negative values (or indeed any signed integer
+              type) are unspecified by the standard. As a result any attempt to carry
+              out a bitwise operation on a negative checked-integer will result in
+              a std::range_error being thrown.
+            
    
+
    Why do I get compiler errors when trying to use the complement operator?
    
+
    
+              Use of the complement operator on signed types is problematic as the
+              result is unspecified by the standard, and is further complicated by
+              the fact that most extended precision integer types use a sign-magnitude
+              representation rather than the 2's complement one favored by most native
+              integer types. As a result the complement operator is deliberately
+              disabled for checked cpp_int's.
+              Unchecked cpp_int's
+              give the same valued result as a 2's complement type would, but not
+              the same bit-pattern.
+            
    
+
    Why can't I negate an unsigned type?
    
+
    
+              The unary negation operator is deliberately disabled for unsigned integer
+              types as it's use would almost always be a programming error.
+            
    
+
    Why doesn't the library use proto?
    
+
    
+              A very early version of the library did use proto, but compile times
+              became too slow for the library to be usable. Since the library only
+              required a tiny fraction of what proto has to offer anyway, a lightweight
+              expression template mechanism was used instead. Compile times are still
+              too slow...
+            
    
+
    Why not abstract out addition/multiplication algorithms?
    
+
    
+              This was deamed not to be practical: these algorithms are intimately
+              tied to the actual data representation used.
+            
    
+
    
+
    
+
    
+
+
+
+
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos
    
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      
    
+
    
+
    
+
    
+PrevUpHomeNext
+
    
+
+
diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html
index 585439d0..8f453970 100644
--- a/doc/html/boost_multiprecision/map/todo.html
+++ b/doc/html/boost_multiprecision/map/todo.html
@@ -7,11 +7,11 @@
 
 
 
-
+
 
 
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -48,6 +48,9 @@
 
  • 
             Should there be a choice of rounding mode (probably MPFR specific)?
           
    • 
+
  • 
+            We can reuse temporaries in multiple subtrees (temporary caching).
+          
    • 
 
    
 
    
         Things requested in review:
@@ -63,27 +66,28 @@
             int should be given to show the cost of using the generic interface (Mostly
             done, just need to update docs to the latest results).
           
    • 
-
  • 
-            The rounding applied when converting must be documented.
-          
    • 
 
  • 
             cpp_dec_float should round to nearest.
           
    • 
-
  • 
-            We can reuse temporaries in multiple subtrees (temporary caching).
-          
    • 
-
  • 
-            Emphasise in the docs that ET's may reorder operations.
-          
    • 
-
  • 
-            Document why we don't use proto (compile times).
-          
    • 
 
  • 
             Should we provide min/max overloads for expression templates?
           
    • 
+
  • 
+            The rounding applied when converting must be documented (Done).
+          
    • 
 
  • 
             Document why we don't abstract out addition/multiplication algorithms
-            etc.
+            etc. (done - FAQ)
+          
    • 
+
  • 
+            Document why we don't use proto (compile times) (Done).
+          
    • 
+
  • 
+            We can reuse temporaries in multiple subtrees (temporary caching) Moved
+            to TODO list.
+          
    • 
+
  • 
+            Emphasise in the docs that ET's may reorder operations (done 2012/10/31).
           
    • 
 
  • 
             Document what happens to small fixed precision cpp_int's (done 2012/10/31).
@@ -215,7 +219,7 @@
 
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html
index 8957bc6f..a77e8169 100644
--- a/doc/html/boost_multiprecision/ref.html
+++ b/doc/html/boost_multiprecision/ref.html
@@ -6,12 +6,12 @@
 
 
 
-
+
 
 
 
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -41,7 +41,7 @@
 
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html
index 5ae44082..906d8213 100644
--- a/doc/html/boost_multiprecision/tut.html
+++ b/doc/html/boost_multiprecision/tut.html
@@ -60,6 +60,9 @@
       Interconverting Between Number Types
    • 
 PrevUpHomeNext
    Generating Random Numbers
    Primality Testing
    +
    Literal Types and constexpr Support
    +
    Rounding Rules for + Conversions

    In order to use this library you need to make two choices: what kind of number diff --git a/doc/html/boost_multiprecision/tut/lits.html b/doc/html/boost_multiprecision/tut/lits.html new file mode 100644 index 00000000..b64f2793 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/lits.html @@ -0,0 +1,63 @@ + + + +Literal Types and constexpr Support + + + + + + + + +

    +PrevUpHomeNext +
    +
    +
    +

    + There is limited support for constexpr + in the library, currently the number + front end supports constexpr + on default construction and all forwarding constructors, but not on any of + the non-member operators. So if some type B + is a literal type, then number<B> + is also a literal type, and you will be able to compile-time-construct such + a type from any literal that B + is compile-time-constructible from. However, you will not be able to perform + compile-time arithmetic on such types. +

    +

    + Currently the only backend type provided by the library that is also a literal + type are instantiations of cpp_int_backend + where the Allocator parameter is type void, + and the Checked parameter is boost::multiprecision::unchecked. +

    +

    + For example: +

    +
    using namespace boost::multiprecision;
+
+constexpr int128_t            i = 0;     // OK, fixed precision int128_t has no allocator.
+constexpr uint1024_t          j = 0xFFFFFFFF00000000uLL;  // OK, fixed precision uint1024_t has no allocator.
+
+constexpr checked_uint128_t   k = -1; // Error, checked type is not a literal type as we need runtime error checking.
+constexpr cpp_int             l = 2;  // Error, type is not a literal as it performs memory management.
+
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html index 49006337..fb38c41b 100644 --- a/doc/html/boost_multiprecision/tut/primetest.html +++ b/doc/html/boost_multiprecision/tut/primetest.html @@ -7,11 +7,11 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -103,7 +103,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/rounding.html b/doc/html/boost_multiprecision/tut/rounding.html new file mode 100644 index 00000000..84dcc3f6 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/rounding.html @@ -0,0 +1,182 @@ + + + +Rounding Rules for Conversions + + + + + + + + +
    +PrevUpHomeNext +
    +
    +
    +

    + As a general rule, all conversions between unrelated types are performed + using basic arithmetic operations, therefore conversions are either exact, + or follow the same rounding rules as arithmetic for the type in question. +

    +

    + The following table summarises the situation for conversions from native + types: +

    +
    ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Backend +

    +     		+

    + Rounding Rules +

    +
    +

    + cpp_int +

    +     		+

    + Conversions from integer types are exact if the target has sufficient + precision, otherwise they truncate to the first 2^MaxBits bits + (modulo arithmetic). Conversions from floating point types are + truncating to the nearest integer. +

    +
    +

    + gmp_int +

    +     		+

    + Conversions are performed by the GMP library except for conversion + from long double + which is truncating. +

    +
    +

    + tom_int +

    +     		+

    + Conversions from floating point types are truncating, all others + are performed by libtommath and are exact. +

    +
    +

    + gmp_float +

    +     		+

    + Conversions are performed by the GMP library except for conversion + from long double + which should be exact provided the target type has as much precision + as a long double. +

    +
    +

    + mpfr_float +

    +     		+

    + All conversions are performed by the underlying MPFR library. +

    +
    +

    + cpp_dec_float +

    +     		+

    + All conversions are performed using basic arithmetic operations + and are truncating. +

    +
    +

    + gmp_rational +

    +     		+

    + See gmp_int +

    +
    +

    + cpp_rational +

    +     		+

    + See cpp_int +

    +
    +

    + tommath_rational +

    +     		+

    + See tom_int +

    +
    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/index.html b/doc/html/index.html index 07802bad..3373c51d 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -75,6 +75,9 @@ Interconverting Between Number Types
    Generating Random Numbers
    Primality Testing
    +
    Literal Types and constexpr Support
    +
    Rounding Rules for + Conversions
    Reference
    @@ -107,6 +110,7 @@
    History
    TODO
    +
    FAQ
    Acknowledgements
    Indexes
    @@ -120,7 +124,7 @@

    - +

    Last revised: October 31, 2012 at 16:58:22 GMT

    Last revised: November 01, 2012 at 11:12:34 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 210fefe3..d2ff465f 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -1172,6 +1172,55 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba [endsect] +[section:lits Literal Types and `constexpr` Support] + +There is limited support for `constexpr` in the library, currently the `number` front end supports `constexpr` +on default construction and all forwarding constructors, but not on any of the non-member operators. So if +some type `B` is a literal type, then `number` is also a literal type, and you will be able to +compile-time-construct such a type from any literal that `B` is compile-time-constructible from. +However, you will not be able to perform compile-time arithmetic on such types. + +Currently the only backend type provided by the library that is also a literal type are instantiations +of `cpp_int_backend` where the Allocator parameter is type `void`, and the Checked parameter is +`boost::multiprecision::unchecked`. + +For example: + + using namespace boost::multiprecision; + + constexpr int128_t i = 0; // OK, fixed precision int128_t has no allocator. + constexpr uint1024_t j = 0xFFFFFFFF00000000uLL; // OK, fixed precision uint1024_t has no allocator. + + constexpr checked_uint128_t k = -1; // Error, checked type is not a literal type as we need runtime error checking. + constexpr cpp_int l = 2; // Error, type is not a literal as it performs memory management. + +[endsect] + +[section:rounding Rounding Rules for Conversions] + +As a general rule, all conversions between unrelated types are performed using basic arithmetic operations, therefore +conversions are either exact, or follow the same rounding rules as arithmetic for the type in question. + +The following table summarises the situation for conversions from native types: + +[table +[[Backend][Rounding Rules]] +[[__cpp_int][Conversions from integer types are exact if the target has sufficient precision, otherwise they + truncate to the first 2^MaxBits bits (modulo arithmetic). Conversions from floating point types + are truncating to the nearest integer.]] +[[__gmp_int][Conversions are performed by the GMP library except for conversion from `long double` which is truncating.]] +[[__tom_int][Conversions from floating point types are truncating, all others are performed by libtommath and are exact.]] +[[__gmp_float][Conversions are performed by the GMP library except for conversion from `long double` which should be exact + provided the target type has as much precision as a `long double`.]] +[[__mpfr_float_backend][All conversions are performed by the underlying MPFR library.]] +[[__cpp_dec_float][All conversions are performed using basic arithmetic operations and are truncating.]] +[[__gmp_rational][See __gmp_int]] +[[__cpp_rational][See __cpp_int]] +[[__tommath_rational][See __tom_int]] +] + +[endsect] + [endsect] [section:ref Reference] @@ -2886,11 +2935,11 @@ Things requested in review: * The performances of mp_number, false>respect to float and mp_number, false> and int should be given to show the cost of using the generic interface (Mostly done, just need to update docs to the latest results). -* The rounding applied when converting must be documented. * cpp_dec_float should round to nearest. -* Document why we don't use proto (compile times). * Should we provide min/max overloads for expression templates? -* Document why we don't abstract out addition/multiplication algorithms etc. +* The rounding applied when converting must be documented (Done). +* Document why we don't abstract out addition/multiplication algorithms etc. (done - FAQ) +* Document why we don't use proto (compile times) (Done). * We can reuse temporaries in multiple subtrees (temporary caching) Moved to TODO list. * Emphasise in the docs that ET's may reorder operations (done 2012/10/31). * Document what happens to small fixed precision cpp_int's (done 2012/10/31). @@ -2944,6 +2993,51 @@ Open question - what should be the default - int32_t or int64_t? (done 2012/09/ [endsect] +[section:faq FAQ] + +[variablelist +[[Why do I get compiler errors when passing a `number` to a template function?] + [Most likely you are actually passing an expression template type to the function and + template-argument-deduction deduces the "wrong" type. Try casting the arguments + involving expressions to the actual number type, or as a last resort turning off + expression template support in the number type you are using.]] +[[When is expression template support a performance gain?] + [As a general rule, expression template support adds a small runtime overhead + creating and unpacking the expression templates, but greatly reduces the number of + temporaries created. So it's most effective in improving performance when the cost + of creating a temporary is high: for example when creating a temporary involves a memory + allocation. It is least effective (and may even be a dis-optimisation) when temporaries + are cheap: for example if the number type is basically a thin wrapper around a native + arithmetic type. In addition, since the library makes extensive use of thin inline wrapper + functions, turning on compiler optimization is essential to achieving high performance.]] +[[Do expression templates reorder operations?] + [Yes they do, sometimes quite radically so, if this is a concern then they should be turned + off for the number type you are using.]] +[[I can't construct my number type from ['some other type], but the docs indicate that the conversion should be allowed, what's up?] + [Some conversions are ['explicit], that includes construction from a string, or constructing from any type + that may result in loss of precision (for example constructing an integer type from a float).]] +[[Why do I get an exception thrown (or the program crash due to an uncaught exception) when using the bitwise operators on a checked `cpp_int`?] + [Bitwise operations on negative values (or indeed any signed integer type) are unspecified by the standard. As a result + any attempt to carry out a bitwise operation on a negative checked-integer will result in a `std::range_error` being thrown.]] +[[Why do I get compiler errors when trying to use the complement operator?] + [Use of the complement operator on signed types is problematic as the result is unspecified by the standard, and is further + complicated by the fact that most extended precision integer types use a sign-magnitude representation rather than the 2's + complement one favored by most native integer types. As a result the complement operator is deliberately disabled for + checked `cpp_int`'s. Unchecked `cpp_int`'s give the same valued result as a 2's complement type would, but not the same bit-pattern.]] +[[Why can't I negate an unsigned type?] + [The unary negation operator is deliberately disabled for unsigned integer types as it's use would almost always be a programming error.]] +[[Why doesn't the library use proto?] + [A very early version of the library did use proto, but compile times became too slow + for the library to be usable. Since the library only required a tiny fraction of what + proto has to offer anyway, a lightweight expression template mechanism was used instead. + Compile times are still too slow...]] +[[Why not abstract out addition/multiplication algorithms?] + [This was deamed not to be practical: these algorithms are intimately + tied to the actual data representation used.]] +] + +[endsect] + [section:ack Acknowledgements] This library would not have happened without: From b640732abd0ebeb99ff77aa3190b0a135e77110e Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 1 Nov 2012 19:01:08 +0000 Subject: [PATCH 247/256] Add additional template parameter to mpfr_float_backend to allow stack-based floats. [SVN r81135] --- .../boost_multiprecision/indexes/s01.html | 4 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 19 +- .../boost_multiprecision/indexes/s04.html | 14 +- doc/html/boost_multiprecision/map/hist.html | 4 + .../tut/floats/mpfr_float.html | 23 +- doc/html/index.html | 2 +- doc/multiprecision.qbk | 20 +- include/boost/multiprecision/mpfr.hpp | 802 ++++++++++++------ test/test_arithmetic.cpp | 1 + 10 files changed, 617 insertions(+), 276 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 680560fd..dcd3d39e 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    +Function Index

    A B C D E F I L M P R S T Z

    diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index d15a40c9..41276154 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

    C E G I M N T

    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 729668d3..bbdea96e 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,10 +13,10 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    -

    C I L M T U

    +Typedef Index
    +

    C I L M S T U

    C @@ -198,6 +198,19 @@
    +S +
    +
    +
    T
      diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index adbddd56..9d0e47c3 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
      PrevUpHome
      -
      +

      -Index

      +Index

    A B C D E F G I L M N O P R S T U Z

    @@ -670,6 +670,8 @@

  • mpfr_float_50

  • mpfr_float_500

  • mpfr_float_backend

    • +

  • static_mpfr_float_100

    • +

  • static_mpfr_float_50

  • @@ -897,6 +899,14 @@
    • +

      static_mpfr_float_100

      +
      +
      • +
    • +

      static_mpfr_float_50

      +
      +
      • +

    • str

      • diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html index 7c4b992f..eec38fe9 100644 --- a/doc/html/boost_multiprecision/map/hist.html +++ b/doc/html/boost_multiprecision/map/hist.html @@ -59,6 +59,10 @@ Refactored cpp_int_backend based on review comments with new template parameter structure. +
    • + Added additional template parameter to mpfr_float_backend + to allow stack-based allocation. +
    diff --git a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html index 40126cf1..29355351 100644 --- a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html +++ b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html @@ -22,7 +22,13 @@ 

    namespace boost{ namespace multiprecision{
 
-template <unsigned Digits10>
+enum mpfr_allocation_type
+{
+   allocate_stack,
+   allocate_dynamic
+};
+
+template <unsigned Digits10, mpfr_allocation_type AllocateType = allocate_dynamic>
 class mpfr_float_backend;
 
 typedef number<mpfr_float_backend<50> >    mpfr_float_50;
@@ -31,6 +37,9 @@
 typedef number<mpfr_float_backend<1000> >  mpfr_float_1000;
 typedef number<mpfr_float_backend<0> >     mpfr_float;
 
+typedef number<mpfr_float_backend<50, allocate_stack> >    static_mpfr_float_50;
+typedef number<mpfr_float_backend<100, allocate_stack> >   static_mpfr_float_100;
+
 }} // namespaces

    @@ -51,6 +60,18 @@ whose precision can be controlled via the numbers member functions.

    +

    + In addition the second template parameter lets you choose between dynamic + allocation (the default, and uses MPFR's normal allocation routines), or + stack allocation (where all the memory required for the underlying data + types is stored within mpfr_float_backend). + The latter option can result in significantly faster code, at the expense + of growing the size of mpfr_float_backend. + It can only be used at fixed precision, and should only be used for lower + digit counts. Note that we can not guarentee that using allocate_stack + won't cause any calls to mpfr's allocation routines, as mpfr may call these + inside it's own code. +

    diff --git a/doc/html/index.html b/doc/html/index.html index 3373c51d..0c8517c2 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -124,7 +124,7 @@
    [Note]
    - +

    Last revised: November 01, 2012 at 11:12:34 GMT

    Last revised: November 01, 2012 at 18:56:42 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index d2ff465f..64829ae8 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -730,7 +730,13 @@ as a valid floating point number. namespace boost{ namespace multiprecision{ - template + enum mpfr_allocation_type + { + allocate_stack, + allocate_dynamic + }; + + template class mpfr_float_backend; typedef number > mpfr_float_50; @@ -739,6 +745,9 @@ as a valid floating point number. typedef number > mpfr_float_1000; typedef number > mpfr_float; + typedef number > static_mpfr_float_50; + typedef number > static_mpfr_float_100; + }} // namespaces The `mpfr_float_backend` type is used in conjunction with `number`: It acts as a thin wrapper around the [mpfr] `mpfr_t` @@ -751,6 +760,14 @@ mpfr_float_500, mpfr_float_1000 provide arithmetic types at 50, 100, 500 and 100 respectively. The typedef mpfr_float provides a variable precision type whose precision can be controlled via the `number`s member functions. +In addition the second template parameter lets you choose between dynamic allocation (the default, +and uses MPFR's normal allocation routines), +or stack allocation (where all the memory required for the underlying data types is stored +within `mpfr_float_backend`). The latter option can result in significantly faster code, at the +expense of growing the size of `mpfr_float_backend`. It can only be used at fixed precision, and +should only be used for lower digit counts. Note that we can not guarentee that using `allocate_stack` +won't cause any calls to mpfr's allocation routines, as mpfr may call these inside it's own code. + [note This type only provides `numeric_limits` support when the precision is fixed at compile time.] As well as the usual conversions from arithmetic and string types, instances of `number >` are @@ -2897,6 +2914,7 @@ Windows Vista machine. * Added support for fused-multiply-add/subtract with GMP support. * Tweaked expression template unpacking to use fewer temporaries when the LHS also appears in the RHS. * Refactored `cpp_int_backend` based on review comments with new template parameter structure. +* Added additional template parameter to `mpfr_float_backend` to allow stack-based allocation. [h4 Pre-review history] diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index ec3085c7..7924b414 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -17,17 +17,24 @@ #include #include -namespace boost{ +namespace boost{ namespace multiprecision{ + +enum mpfr_allocation_type +{ + allocate_stack, + allocate_dynamic +}; + namespace backends{ -template +template struct mpfr_float_backend; } // namespace backends -template -struct number_category > : public mpl::int_{}; +template +struct number_category > : public mpl::int_{}; namespace backends{ @@ -35,15 +42,25 @@ namespace detail{ inline long get_default_precision() { return 50; } +template +struct mpfr_float_imp; + template -struct mpfr_float_imp +struct mpfr_float_imp { typedef mpl::list signed_types; typedef mpl::list unsigned_types; typedef mpl::list float_types; typedef long exponent_type; - mpfr_float_imp() BOOST_NOEXCEPT {} + mpfr_float_imp() + { + mpfr_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : get_default_precision())); + } + mpfr_float_imp(unsigned prec) + { + mpfr_init2(m_data, prec); + } mpfr_float_imp(const mpfr_float_imp& o) { @@ -281,7 +298,8 @@ struct mpfr_float_imp BOOST_ASSERT(m_data[0]._mpfr_d); mpfr_neg(m_data, m_data, GMP_RNDN); } - int compare(const mpfr_float_backend& o)const BOOST_NOEXCEPT + template + int compare(const mpfr_float_backend& o)const BOOST_NOEXCEPT { BOOST_ASSERT(m_data[0]._mpfr_d && o.m_data[0]._mpfr_d); return mpfr_cmp(m_data, o.m_data); @@ -299,19 +317,19 @@ struct mpfr_float_imp template int compare(V v)const BOOST_NOEXCEPT { - mpfr_float_backend d; + mpfr_float_backend d; d = v; return compare(d); } - mpfr_t& data() BOOST_NOEXCEPT - { + mpfr_t& data() BOOST_NOEXCEPT + { BOOST_ASSERT(m_data[0]._mpfr_d); - return m_data; + return m_data; } - const mpfr_t& data()const BOOST_NOEXCEPT - { + const mpfr_t& data()const BOOST_NOEXCEPT + { BOOST_ASSERT(m_data[0]._mpfr_d); - return m_data; + return m_data; } protected: mpfr_t m_data; @@ -322,89 +340,344 @@ protected: } }; -} // namespace detail +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4127) // Conditional expression is constant +#endif template -struct mpfr_float_backend : public detail::mpfr_float_imp +struct mpfr_float_imp { - mpfr_float_backend() + typedef mpl::list signed_types; + typedef mpl::list unsigned_types; + typedef mpl::list float_types; + typedef long exponent_type; + + static const unsigned digits2 = (digits10 * 1000uL) / 301uL + ((digits10 * 1000uL) % 301 ? 2u : 1u); + static const unsigned limb_count = mpfr_custom_get_size(digits2) / sizeof(mp_limb_t); + + mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); + mpfr_custom_init(m_buffer, digits2); + mpfr_custom_init_set(m_data, MPFR_NAN_KIND, 0, digits2, m_buffer); } - mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp(o) {} + + mpfr_float_imp(const mpfr_float_imp& o) + { + mpfr_custom_init(m_buffer, digits2); + mpfr_custom_init_set(m_data, MPFR_NAN_KIND, 0, digits2, m_buffer); + mpfr_set(m_data, o.m_data, GMP_RNDN); + } + mpfr_float_imp& operator = (const mpfr_float_imp& o) BOOST_NOEXCEPT + { + mpfr_set(m_data, o.m_data, GMP_RNDN); + return *this; + } +#ifdef _MPFR_H_HAVE_INTMAX_T + mpfr_float_imp& operator = (unsigned long long i) BOOST_NOEXCEPT + { + mpfr_set_uj(m_data, i, GMP_RNDN); + return *this; + } + mpfr_float_imp& operator = (long long i) BOOST_NOEXCEPT + { + mpfr_set_sj(m_data, i, GMP_RNDN); + return *this; + } +#else + mpfr_float_imp& operator = (unsigned long long i) + { + unsigned long long mask = ((1uLL << std::numeric_limits::digits) - 1); + unsigned shift = 0; + mpfr_t t; + mp_limb_t t_limbs[limb_count]; + mpfr_custom_init(t_limbs, digits2); + mpfr_custom_init_set(t, MPFR_NAN_KIND, 0, digits2, t_limbs); + mpfr_set_ui(m_data, 0, GMP_RNDN); + while(i) + { + mpfr_set_ui(t, static_cast(i & mask), GMP_RNDN); + if(shift) + mpfr_mul_2exp(t, t, shift, GMP_RNDN); + mpfr_add(m_data, m_data, t, GMP_RNDN); + shift += std::numeric_limits::digits; + i >>= std::numeric_limits::digits; + } + return *this; + } + mpfr_float_imp& operator = (long long i) + { + BOOST_MP_USING_ABS + bool neg = i < 0; + *this = static_cast(abs(i)); + if(neg) + mpfr_neg(m_data, m_data, GMP_RNDN); + return *this; + } +#endif + mpfr_float_imp& operator = (unsigned long i) BOOST_NOEXCEPT + { + mpfr_set_ui(m_data, i, GMP_RNDN); + return *this; + } + mpfr_float_imp& operator = (long i) BOOST_NOEXCEPT + { + mpfr_set_si(m_data, i, GMP_RNDN); + return *this; + } + mpfr_float_imp& operator = (double d) BOOST_NOEXCEPT + { + mpfr_set_d(m_data, d, GMP_RNDN); + return *this; + } + mpfr_float_imp& operator = (long double a) BOOST_NOEXCEPT + { + mpfr_set_ld(m_data, a, GMP_RNDN); + return *this; + } + mpfr_float_imp& operator = (const char* s) + { + if(mpfr_set_str(m_data, s, 10, GMP_RNDN) != 0) + { + BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Unable to parse string \"") + s + std::string("\"as a valid floating point number."))); + } + return *this; + } + void swap(mpfr_float_imp& o) BOOST_NOEXCEPT + { + // We have to swap by copying: + mpfr_float_imp t(*this); + *this = o; + o = t; + } + std::string str(std::streamsize digits, std::ios_base::fmtflags f)const + { + BOOST_ASSERT(m_data[0]._mpfr_d); + + bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; + bool fixed = (f & std::ios_base::fixed) == std::ios_base::fixed; + + std::streamsize org_digits(digits); + + if(scientific && digits) + ++digits; + + std::string result; + mp_exp_t e; + if(mpfr_inf_p(m_data)) + { + if(mpfr_sgn(m_data) < 0) + result = "-inf"; + else if(f & std::ios_base::showpos) + result = "+inf"; + else + result = "inf"; + return result; + } + if(mpfr_nan_p(m_data)) + { + result = "nan"; + return result; + } + if(mpfr_zero_p(m_data)) + { + e = 0; + result = "0"; + } + else + { + char* ps = mpfr_get_str (0, &e, 10, static_cast(digits), m_data, GMP_RNDN); + --e; // To match with what our formatter expects. + if(fixed && e != -1) + { + // Oops we actually need a different number of digits to what we asked for: + mpfr_free_str(ps); + digits += e + 1; + if(digits == 0) + { + // We need to get *all* the digits and then possibly round up, + // we end up with either "0" or "1" as the result. + ps = mpfr_get_str (0, &e, 10, 0, m_data, GMP_RNDN); + --e; + unsigned offset = *ps == '-' ? 1 : 0; + if(ps[offset] > '5') + { + ++e; + ps[offset] = '1'; + ps[offset + 1] = 0; + } + else if(ps[offset] == '5') + { + unsigned i = offset + 1; + bool round_up = false; + while(ps[i] != 0) + { + if(ps[i] != '0') + { + round_up = true; + break; + } + } + if(round_up) + { + ++e; + ps[offset] = '1'; + ps[offset + 1] = 0; + } + else + { + ps[offset] = '0'; + ps[offset + 1] = 0; + } + } + else + { + ps[offset] = '0'; + ps[offset + 1] = 0; + } + } + else if(digits > 0) + { + ps = mpfr_get_str (0, &e, 10, static_cast(digits), m_data, GMP_RNDN); + --e; // To match with what our formatter expects. + } + else + { + ps = mpfr_get_str (0, &e, 10, 1, m_data, GMP_RNDN); + --e; + unsigned offset = *ps == '-' ? 1 : 0; + ps[offset] = '0'; + ps[offset + 1] = 0; + } + } + result = ps ? ps : "0"; + if(ps) + mpfr_free_str(ps); + } + boost::multiprecision::detail::format_float_string(result, e, org_digits, f, 0 != mpfr_zero_p(m_data)); + return result; + } + void negate() BOOST_NOEXCEPT + { + mpfr_neg(m_data, m_data, GMP_RNDN); + } + template + int compare(const mpfr_float_backend& o)const BOOST_NOEXCEPT + { + return mpfr_cmp(m_data, o.m_data); + } + int compare(long i)const BOOST_NOEXCEPT + { + return mpfr_cmp_si(m_data, i); + } + int compare(unsigned long i)const BOOST_NOEXCEPT + { + return mpfr_cmp_ui(m_data, i); + } + template + int compare(V v)const BOOST_NOEXCEPT + { + mpfr_float_backend d; + d = v; + return compare(d); + } + mpfr_t& data() BOOST_NOEXCEPT + { + return m_data; + } + const mpfr_t& data()const BOOST_NOEXCEPT + { + return m_data; + } +protected: + mpfr_t m_data; + mp_limb_t m_buffer[limb_count]; +}; + +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + +} // namespace detail + +template +struct mpfr_float_backend : public detail::mpfr_float_imp +{ + mpfr_float_backend() : detail::mpfr_float_imp() {} + mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp(static_cast&&>(o)) {} + mpfr_float_backend(mpfr_float_backend&& o) : detail::mpfr_float_imp(static_cast&&>(o)) {} #endif template mpfr_float_backend(const mpfr_float_backend& val, typename enable_if_c::type* = 0) + : detail::mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set(this->m_data, val.data(), GMP_RNDN); } template explicit mpfr_float_backend(const mpfr_float_backend& val, typename disable_if_c::type* = 0) + : detail::mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set(this->m_data, val.data(), GMP_RNDN); } template mpfr_float_backend(const gmp_float& val, typename enable_if_c::type* = 0) + : detail::mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_f(this->m_data, val.data(), GMP_RNDN); } template mpfr_float_backend(const gmp_float& val, typename disable_if_c::type* = 0) + : detail::mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_f(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend(const gmp_int& val) + : detail::mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_z(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend(const gmp_rational& val) + : detail::mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_q(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend(const mpfr_t val) + : detail::mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set(this->m_data, val, GMP_RNDN); } mpfr_float_backend(const mpf_t val) + : detail::mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_f(this->m_data, val, GMP_RNDN); } mpfr_float_backend(const mpz_t val) + : detail::mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_z(this->m_data, val, GMP_RNDN); } mpfr_float_backend(const mpq_t val) + : detail::mpfr_float_imp() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); mpfr_set_q(this->m_data, val, GMP_RNDN); } mpfr_float_backend& operator=(const mpfr_float_backend& o) { - *static_cast*>(this) = static_cast const&>(o); + *static_cast*>(this) = static_cast const&>(o); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES mpfr_float_backend& operator=(mpfr_float_backend&& o) BOOST_NOEXCEPT { - *static_cast*>(this) = static_cast&&>(o); + *static_cast*>(this) = static_cast&&>(o); return *this; } #endif template mpfr_float_backend& operator=(const V& v) { - *static_cast*>(this) = v; + *static_cast*>(this) = v; return *this; } mpfr_float_backend& operator=(const mpfr_t val)BOOST_NOEXCEPT @@ -453,80 +726,78 @@ struct mpfr_float_backend : public detail::mpfr_float_imp }; template <> -struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> +struct mpfr_float_backend<0, allocate_dynamic> : public detail::mpfr_float_imp<0, allocate_dynamic> { - mpfr_float_backend() - { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); - } + mpfr_float_backend() : detail::mpfr_float_imp<0, allocate_dynamic>() {} mpfr_float_backend(const mpfr_t val) + : detail::mpfr_float_imp<0, allocate_dynamic>(mpfr_get_prec(val)) { - mpfr_init2(this->m_data, mpfr_get_prec(val)); mpfr_set(this->m_data, val, GMP_RNDN); } mpfr_float_backend(const mpf_t val) + : detail::mpfr_float_imp<0, allocate_dynamic>(mpf_get_prec(val)) { - mpfr_init2(this->m_data, mpf_get_prec(val)); mpfr_set_f(this->m_data, val, GMP_RNDN); } mpfr_float_backend(const mpz_t val) + : detail::mpfr_float_imp<0, allocate_dynamic>() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpfr_set_z(this->m_data, val, GMP_RNDN); } mpfr_float_backend(const mpq_t val) + : detail::mpfr_float_imp<0, allocate_dynamic>() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpfr_set_q(this->m_data, val, GMP_RNDN); } - mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp<0>(o) {} + mpfr_float_backend(const mpfr_float_backend& o) : detail::mpfr_float_imp<0, allocate_dynamic>(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - mpfr_float_backend(mpfr_float_backend&& o) BOOST_NOEXCEPT : detail::mpfr_float_imp<0>(static_cast&&>(o)) {} + mpfr_float_backend(mpfr_float_backend&& o) BOOST_NOEXCEPT : detail::mpfr_float_imp<0, allocate_dynamic>(static_cast&&>(o)) {} #endif - mpfr_float_backend(const mpfr_float_backend& o, unsigned digits10) + mpfr_float_backend(const mpfr_float_backend& o, unsigned digits10) + : detail::mpfr_float_imp<0, allocate_dynamic>(digits10) { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(digits10)); *this = o; } template mpfr_float_backend(const mpfr_float_backend& val) + : detail::mpfr_float_imp<0, allocate_dynamic>(mpfr_get_prec(val.data())) { - mpfr_init2(this->m_data, mpfr_get_prec(val.data())); mpfr_set(this->m_data, val.data(), GMP_RNDN); } template mpfr_float_backend(const gmp_float& val) + : detail::mpfr_float_imp<0, allocate_dynamic>(mpf_get_prec(val.data())) { - mpfr_init2(this->m_data, mpf_get_prec(val.data())); mpfr_set_f(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend(const gmp_int& val) + : detail::mpfr_float_imp<0, allocate_dynamic>() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpfr_set_z(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend(const gmp_rational& val) + : detail::mpfr_float_imp<0, allocate_dynamic>() { - mpfr_init2(this->m_data, multiprecision::detail::digits10_2_2(get_default_precision())); mpfr_set_q(this->m_data, val.data(), GMP_RNDN); } mpfr_float_backend& operator=(const mpfr_float_backend& o) { - *static_cast*>(this) = static_cast const&>(o); + mpfr_set_prec(this->m_data, mpfr_get_prec(o.data())); + mpfr_set(this->m_data, o.data(), GMP_RNDN); return *this; } #ifndef BOOST_NO_RVALUE_REFERENCES mpfr_float_backend& operator=(mpfr_float_backend&& o) BOOST_NOEXCEPT { - *static_cast*>(this) = static_cast &&>(o); + *static_cast*>(this) = static_cast &&>(o); return *this; } #endif template mpfr_float_backend& operator=(const V& v) { - *static_cast*>(this) = v; + *static_cast*>(this) = v; return *this; } mpfr_float_backend& operator=(const mpfr_t val) BOOST_NOEXCEPT @@ -593,87 +864,87 @@ struct mpfr_float_backend<0> : public detail::mpfr_float_imp<0> } }; -template -inline typename enable_if, bool>::type eval_eq(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT +template +inline typename enable_if, bool>::type eval_eq(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) == 0; } -template -inline typename enable_if, bool>::type eval_lt(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT +template +inline typename enable_if, bool>::type eval_lt(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) < 0; } -template -inline typename enable_if, bool>::type eval_gt(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT +template +inline typename enable_if, bool>::type eval_gt(const mpfr_float_backend& a, const T& b) BOOST_NOEXCEPT { return a.compare(b) > 0; } -template -inline void eval_add(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT { mpfr_add(result.data(), result.data(), o.data(), GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT { mpfr_sub(result.data(), result.data(), o.data(), GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& result, const mpfr_float_backend& o) BOOST_NOEXCEPT { mpfr_mul(result.data(), result.data(), o.data(), GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& result, const mpfr_float_backend& o) +template +inline void eval_divide(mpfr_float_backend& result, const mpfr_float_backend& o) { mpfr_div(result.data(), result.data(), o.data(), GMP_RNDN); } -template -inline void eval_add(mpfr_float_backend& result, unsigned long i) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& result, unsigned long i) BOOST_NOEXCEPT { mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& result, unsigned long i) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& result, unsigned long i) BOOST_NOEXCEPT { mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& result, unsigned long i) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& result, unsigned long i) BOOST_NOEXCEPT { mpfr_mul_ui(result.data(), result.data(), i, GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& result, unsigned long i) +template +inline void eval_divide(mpfr_float_backend& result, unsigned long i) { mpfr_div_ui(result.data(), result.data(), i, GMP_RNDN); } -template -inline void eval_add(mpfr_float_backend& result, long i) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& result, long i) BOOST_NOEXCEPT { if(i > 0) mpfr_add_ui(result.data(), result.data(), i, GMP_RNDN); else mpfr_sub_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& result, long i) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& result, long i) BOOST_NOEXCEPT { if(i > 0) mpfr_sub_ui(result.data(), result.data(), i, GMP_RNDN); else mpfr_add_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& result, long i) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& result, long i) BOOST_NOEXCEPT { mpfr_mul_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); if(i < 0) mpfr_neg(result.data(), result.data(), GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& result, long i) +template +inline void eval_divide(mpfr_float_backend& result, long i) { mpfr_div_ui(result.data(), result.data(), std::abs(i), GMP_RNDN); if(i < 0) @@ -682,31 +953,31 @@ inline void eval_divide(mpfr_float_backend& result, long i) // // Specialised 3 arg versions of the basic operators: // -template -inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_add(a.data(), x.data(), y.data(), GMP_RNDN); } -template -inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT { mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT { if(y < 0) mpfr_sub_ui(a.data(), x.data(), -y, GMP_RNDN); else mpfr_add_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_add(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } -template -inline void eval_add(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_add(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { if(x < 0) { @@ -716,31 +987,31 @@ inline void eval_add(mpfr_float_backend& a, long x, const mpfr_float_backend else mpfr_add_ui(a.data(), y.data(), x, GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_sub(a.data(), x.data(), y.data(), GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT { mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT { if(y < 0) mpfr_add_ui(a.data(), x.data(), -y, GMP_RNDN); else mpfr_sub_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); } -template -inline void eval_subtract(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_subtract(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { if(x < 0) { @@ -751,18 +1022,18 @@ inline void eval_subtract(mpfr_float_backend& a, long x, const mpfr_float_ba mpfr_ui_sub(a.data(), x, y.data(), GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_mul(a.data(), x.data(), y.data(), GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) BOOST_NOEXCEPT { mpfr_mul_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend& x, long y) BOOST_NOEXCEPT { if(y < 0) { @@ -772,13 +1043,13 @@ inline void eval_multiply(mpfr_float_backend& a, const mpfr_float_backend -inline void eval_multiply(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); } -template -inline void eval_multiply(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT +template +inline void eval_multiply(mpfr_float_backend& a, long x, const mpfr_float_backend& y) BOOST_NOEXCEPT { if(x < 0) { @@ -789,18 +1060,18 @@ inline void eval_multiply(mpfr_float_backend& a, long x, const mpfr_float_ba mpfr_mul_ui(a.data(), y.data(), x, GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) +template +inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, const mpfr_float_backend& y) { mpfr_div(a.data(), x.data(), y.data(), GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) +template +inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, unsigned long y) { mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, long y) +template +inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& x, long y) { if(y < 0) { @@ -810,13 +1081,13 @@ inline void eval_divide(mpfr_float_backend& a, const mpfr_float_backend& else mpfr_div_ui(a.data(), x.data(), y, GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) +template +inline void eval_divide(mpfr_float_backend& a, unsigned long x, const mpfr_float_backend& y) { mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); } -template -inline void eval_divide(mpfr_float_backend& a, long x, const mpfr_float_backend& y) +template +inline void eval_divide(mpfr_float_backend& a, long x, const mpfr_float_backend& y) { if(x < 0) { @@ -827,19 +1098,19 @@ inline void eval_divide(mpfr_float_backend& a, long x, const mpfr_float_back mpfr_ui_div(a.data(), x, y.data(), GMP_RNDN); } -template -inline bool eval_is_zero(const mpfr_float_backend& val) BOOST_NOEXCEPT +template +inline bool eval_is_zero(const mpfr_float_backend& val) BOOST_NOEXCEPT { return 0 != mpfr_zero_p(val.data()); } -template -inline int eval_get_sign(const mpfr_float_backend& val) BOOST_NOEXCEPT +template +inline int eval_get_sign(const mpfr_float_backend& val) BOOST_NOEXCEPT { return mpfr_sgn(val.data()); } -template -inline void eval_convert_to(unsigned long* result, const mpfr_float_backend& val) +template +inline void eval_convert_to(unsigned long* result, const mpfr_float_backend& val) { if(mpfr_nan_p(val.data())) { @@ -847,8 +1118,8 @@ inline void eval_convert_to(unsigned long* result, const mpfr_float_backend -inline void eval_convert_to(long* result, const mpfr_float_backend& val) +template +inline void eval_convert_to(long* result, const mpfr_float_backend& val) { if(mpfr_nan_p(val.data())) { @@ -857,8 +1128,8 @@ inline void eval_convert_to(long* result, const mpfr_float_backend& va *result = mpfr_get_si(val.data(), GMP_RNDN); } #ifdef _MPFR_H_HAVE_INTMAX_T -template -inline void eval_convert_to(unsigned long long* result, const mpfr_float_backend& val) +template +inline void eval_convert_to(unsigned long long* result, const mpfr_float_backend& val) { if(mpfr_nan_p(val.data())) { @@ -866,8 +1137,8 @@ inline void eval_convert_to(unsigned long long* result, const mpfr_float_backend } *result = mpfr_get_uj(val.data(), GMP_RNDN); } -template -inline void eval_convert_to(long long* result, const mpfr_float_backend& val) +template +inline void eval_convert_to(long long* result, const mpfr_float_backend& val) { if(mpfr_nan_p(val.data())) { @@ -876,13 +1147,13 @@ inline void eval_convert_to(long long* result, const mpfr_float_backend -inline void eval_convert_to(double* result, const mpfr_float_backend& val) BOOST_NOEXCEPT +template +inline void eval_convert_to(double* result, const mpfr_float_backend& val) BOOST_NOEXCEPT { *result = mpfr_get_d(val.data(), GMP_RNDN); } -template -inline void eval_convert_to(long double* result, const mpfr_float_backend& val) BOOST_NOEXCEPT +template +inline void eval_convert_to(long double* result, const mpfr_float_backend& val) BOOST_NOEXCEPT { *result = mpfr_get_ld(val.data(), GMP_RNDN); } @@ -890,45 +1161,45 @@ inline void eval_convert_to(long double* result, const mpfr_float_backend -inline void eval_sqrt(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT +template +inline void eval_sqrt(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_sqrt(result.data(), val.data(), GMP_RNDN); } -template -inline void eval_abs(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT +template +inline void eval_abs(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_abs(result.data(), val.data(), GMP_RNDN); } -template -inline void eval_fabs(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT +template +inline void eval_fabs(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_abs(result.data(), val.data(), GMP_RNDN); } -template -inline void eval_ceil(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT +template +inline void eval_ceil(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_ceil(result.data(), val.data()); } -template -inline void eval_floor(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT +template +inline void eval_floor(mpfr_float_backend& result, const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_floor(result.data(), val.data()); } -template -inline void eval_trunc(mpfr_float_backend& result, const mpfr_float_backend& val) +template +inline void eval_trunc(mpfr_float_backend& result, const mpfr_float_backend& val) { if(0 == mpfr_number_p(val.data())) { - result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, number >(val), 0, boost::math::policies::policy<>()).backend(); + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, number >(val), 0, boost::math::policies::policy<>()).backend(); return; } mpfr_trunc(result.data(), val.data()); } -template -inline void eval_ldexp(mpfr_float_backend& result, const mpfr_float_backend& val, long e) BOOST_NOEXCEPT +template +inline void eval_ldexp(mpfr_float_backend& result, const mpfr_float_backend& val, long e) BOOST_NOEXCEPT { if(e > 0) mpfr_mul_2exp(result.data(), val.data(), e, GMP_RNDN); @@ -937,29 +1208,29 @@ inline void eval_ldexp(mpfr_float_backend& result, const mpfr_float_ba else result = val; } -template -inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_backend& val, int* e) BOOST_NOEXCEPT +template +inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_backend& val, int* e) BOOST_NOEXCEPT { long v; mpfr_get_d_2exp(&v, val.data(), GMP_RNDN); *e = v; eval_ldexp(result, val, -v); } -template -inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_backend& val, long* e) BOOST_NOEXCEPT +template +inline void eval_frexp(mpfr_float_backend& result, const mpfr_float_backend& val, long* e) BOOST_NOEXCEPT { mpfr_get_d_2exp(e, val.data(), GMP_RNDN); return eval_ldexp(result, val, -*e); } -template -inline int eval_fpclassify(const mpfr_float_backend& val) BOOST_NOEXCEPT +template +inline int eval_fpclassify(const mpfr_float_backend& val) BOOST_NOEXCEPT { return mpfr_inf_p(val.data()) ? FP_INFINITE : mpfr_nan_p(val.data()) ? FP_NAN : mpfr_zero_p(val.data()) ? FP_ZERO : FP_NORMAL; } -template -inline void eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const mpfr_float_backend& e) BOOST_NOEXCEPT +template +inline void eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const mpfr_float_backend& e) BOOST_NOEXCEPT { mpfr_pow(result.data(), b.data(), e.data(), GMP_RNDN); } @@ -970,99 +1241,99 @@ inline void eval_pow(mpfr_float_backend& result, const mpfr_float_back // certain other enable_if usages are defined first. It's a capricious // and rather annoying compiler bug in other words.... // -# define BOOST_MP_ENABLE_IF_WORKAROUND (Digits10 || !Digits10) && +# define BOOST_MP_ENABLE_IF_WORKAROUND (Digits10 || !Digits10) && #else #define BOOST_MP_ENABLE_IF_WORKAROUND #endif -template -inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) BOOST_NOEXCEPT +template +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) BOOST_NOEXCEPT { mpfr_pow_si(result.data(), b.data(), e, GMP_RNDN); } -template -inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) BOOST_NOEXCEPT +template +inline typename enable_if, mpl::bool_ > >::type eval_pow(mpfr_float_backend& result, const mpfr_float_backend& b, const Integer& e) BOOST_NOEXCEPT { mpfr_pow_ui(result.data(), b.data(), e, GMP_RNDN); } #undef BOOST_MP_ENABLE_IF_WORKAROUND -template -inline void eval_exp(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_exp(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_exp(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_log(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_log(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_log(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_log10(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_log10(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_log10(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_sin(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_sin(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_sin(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_cos(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_cos(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_cos(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_tan(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_tan(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_tan(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_asin(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_asin(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_asin(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_acos(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_acos(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_acos(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_atan(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_atan(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_atan(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_atan2(mpfr_float_backend& result, const mpfr_float_backend& arg1, const mpfr_float_backend& arg2) BOOST_NOEXCEPT +template +inline void eval_atan2(mpfr_float_backend& result, const mpfr_float_backend& arg1, const mpfr_float_backend& arg2) BOOST_NOEXCEPT { mpfr_atan2(result.data(), arg1.data(), arg2.data(), GMP_RNDN); } -template -inline void eval_sinh(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_sinh(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_sinh(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_cosh(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_cosh(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_cosh(result.data(), arg.data(), GMP_RNDN); } -template -inline void eval_tanh(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT +template +inline void eval_tanh(mpfr_float_backend& result, const mpfr_float_backend& arg) BOOST_NOEXCEPT { mpfr_tanh(result.data(), arg.data(), GMP_RNDN); } @@ -1073,8 +1344,8 @@ inline void eval_tanh(mpfr_float_backend& result, const mpfr_float_bac namespace detail{ -template -struct is_explicitly_convertible, backends::mpfr_float_backend > : public mpl::true_ {}; +template +struct is_explicitly_convertible, backends::mpfr_float_backend > : public mpl::true_ {}; } @@ -1091,6 +1362,9 @@ typedef number > mpfr_float_500; typedef number > mpfr_float_1000; typedef number > mpfr_float; +typedef number > static_mpfr_float_50; +typedef number > static_mpfr_float_100; + } // namespace multiprecision namespace math{ @@ -1117,14 +1391,14 @@ namespace std{ // // numeric_limits [partial] specializations for the types declared in this header: // -template -class numeric_limits, ExpressionTemplates> > +template +class numeric_limits, ExpressionTemplates> > { - typedef boost::multiprecision::number, ExpressionTemplates> number_type; + typedef boost::multiprecision::number, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT - { + { initializer.do_nothing(); static std::pair value; if(!value.first) @@ -1136,7 +1410,7 @@ public: return value.second; } BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT - { + { initializer.do_nothing(); static std::pair value; if(!value.first) @@ -1159,8 +1433,8 @@ public: BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR int radix = 2; - BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT - { + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT + { initializer.do_nothing(); static std::pair value; if(!value.first) @@ -1172,8 +1446,8 @@ public: return value.second; } // What value should this be???? - BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT - { + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT + { // returns epsilon/2 initializer.do_nothing(); static std::pair value; @@ -1194,8 +1468,8 @@ public: BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; - BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT - { + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT + { // returns epsilon/2 initializer.do_nothing(); static std::pair value; @@ -1207,8 +1481,8 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT - { + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT + { // returns epsilon/2 initializer.do_nothing(); static std::pair value; @@ -1220,9 +1494,9 @@ public: } return value.second; } - BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT - { - return number_type(0); + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT + { + return number_type(0); } BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return number_type(0); } BOOST_STATIC_CONSTEXPR bool is_iec559 = false; @@ -1237,72 +1511,72 @@ private: { data_initializer() { - std::numeric_limits > >::epsilon(); - std::numeric_limits > >::round_error(); - (std::numeric_limits > >::min)(); - (std::numeric_limits > >::max)(); - std::numeric_limits > >::infinity(); - std::numeric_limits > >::quiet_NaN(); + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); + std::numeric_limits > >::infinity(); + std::numeric_limits > >::quiet_NaN(); } void do_nothing()const{} }; static const data_initializer initializer; }; -template -const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; +template +const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; -template -BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; -template -BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent; -template -BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent10; -template -BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent; -template -BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent10; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; -template -BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; -template -BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; -template -BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +template +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST long numeric_limits, ExpressionTemplates> >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; #endif -template +template class numeric_limits, ExpressionTemplates> > { typedef boost::multiprecision::number, ExpressionTemplates> number_type; diff --git a/test/test_arithmetic.cpp b/test/test_arithmetic.cpp index 32f5a9d0..dd97caf4 100644 --- a/test/test_arithmetic.cpp +++ b/test/test_arithmetic.cpp @@ -1839,6 +1839,7 @@ int main() #endif #ifdef TEST_MPFR_50 test(); + test(); #endif #ifdef TEST_TOMMATH test(); From 3080df73d9ad6dbb2783b127e3a4dcfbaf4e3df3 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 2 Nov 2012 13:07:39 +0000 Subject: [PATCH 248/256] Update MPFR docs with performance comparison. [SVN r81146] --- .../boost_multiprecision/indexes/s01.html | 4 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 4 +- .../tut/floats/mpfr_float.html | 81 ++++++++++++++++++- doc/html/index.html | 2 +- doc/multiprecision.qbk | 10 +++ performance/sf_performance.cpp | 6 +- 8 files changed, 104 insertions(+), 11 deletions(-) diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index dcd3d39e..dd045fea 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
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    diff --git a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html index 29355351..2bee41f5 100644 --- a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html +++ b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html @@ -70,8 +70,81 @@ It can only be used at fixed precision, and should only be used for lower digit counts. Note that we can not guarentee that using allocate_stack won't cause any calls to mpfr's allocation routines, as mpfr may call these - inside it's own code. + inside it's own code. The following table gives an idea of the performance + tradeoff's at 50 decimal digits precision[2]:

    +
    ++++ + + + + + + + + + + + + + + + + + + + + + + +
    +

    + Type +

    +     		+

    + Bessel function evaluation, relative times +

    +
    +

    + number<mpfr_float_backend<50, allocate_static>, + et_on> +

    +     		+

    + 1.0 (5.5s) +

    +
    +

    + number<mpfr_float_backend<50, allocate_static>, + et_off> +

    +     		+

    + 1.05 (5.8s) +

    +
    +

    + number<mpfr_float_backend<50, allocate_dynamic>, + et_on> +

    +     		+

    + 1.05 (5.8s) +

    +
    +

    + number<mpfr_float_backend<50, allocate_dynamic>, + et_off> +

    +     		+

    + 1.16 (6.4s) +

    +
    @@ -176,6 +249,12 @@

    +
    +
    +

    [2] + Compiled with VC++10 and /Ox, with MPFR-3.0.0 and MPIR-2.3.0 +

    +
    [Note]
    diff --git a/doc/html/index.html b/doc/html/index.html index 0c8517c2..a919dfc2 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -124,7 +124,7 @@
    - +

    Last revised: November 01, 2012 at 18:56:42 GMT

    Last revised: November 02, 2012 at 13:02:30 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 64829ae8..b23a001a 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -767,6 +767,16 @@ within `mpfr_float_backend`). The latter option can result in significantly fas expense of growing the size of `mpfr_float_backend`. It can only be used at fixed precision, and should only be used for lower digit counts. Note that we can not guarentee that using `allocate_stack` won't cause any calls to mpfr's allocation routines, as mpfr may call these inside it's own code. +The following table gives an idea of the performance tradeoff's at 50 decimal digits +precision[footnote Compiled with VC++10 and /Ox, with MPFR-3.0.0 and MPIR-2.3.0]: + +[table +[[Type][Bessel function evaluation, relative times]] +[[`number, et_on>`][1.0 (5.5s)]] +[[`number, et_off>`][1.05 (5.8s)]] +[[`number, et_on>`][1.05 (5.8s)]] +[[`number, et_off>`][1.16 (6.4s)]] +] [note This type only provides `numeric_limits` support when the precision is fixed at compile time.] diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index 08c2e726..11c60ac6 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -282,10 +282,14 @@ int main() #ifdef TEST_MPFR #if MPFR_VERSION, 1); - time_proc("mpfr_float_50 (no expression templates", test_bessel, et_off> >, 1); + time_proc("mpfr_float_50 (no expression templates)", test_bessel, et_off> >, 1); + time_proc("static_mpfr_float_50", test_bessel, et_on> >, 1); + time_proc("static_mpfr_float_50 (no expression templates)", test_bessel, et_off> >, 1); #else time_proc("mpfr_float_50", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); time_proc("mpfr_float_50 (no expression templates", test_bessel, et_off> >, mpfr_buildopt_tls_p() ? 3 : 1); + time_proc("static_mpfr_float_50", test_bessel, et_on> >, mpfr_buildopt_tls_p() ? 3 : 1); + time_proc("static_mpfr_float_50 (no expression templates)", test_bessel, et_off> >, mpfr_buildopt_tls_p() ? 3 : 1); #endif #endif #ifdef TEST_MPF From 788449ffa564f27ca5a9eea0a99561a224aaa923 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 2 Nov 2012 19:13:50 +0000 Subject: [PATCH 249/256] Add non-member functions for mixed precision arithmetic + tests for same. Fix a couple of bugs discovered along the way. [SVN r81151] --- .../boost/multiprecision/cpp_dec_float.hpp | 6 +- include/boost/multiprecision/cpp_int.hpp | 4 +- .../multiprecision/detail/default_ops.hpp | 74 ++++++++++++++-- test/Jamfile.v2 | 11 ++- test/test_mixed_cpp_int.cpp | 85 +++++++++++++++++++ test/test_mixed_float.cpp | 57 +++++++++++++ 6 files changed, 225 insertions(+), 12 deletions(-) create mode 100644 test/test_mixed_cpp_int.cpp create mode 100644 test/test_mixed_float.cpp diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp index e7264d17..3e31b257 100644 --- a/include/boost/multiprecision/cpp_dec_float.hpp +++ b/include/boost/multiprecision/cpp_dec_float.hpp @@ -376,8 +376,10 @@ public: exp = f.exp; neg = f.neg; fpclass = static_cast(static_cast(f.fpclass)); - std::copy(f.data.begin(), f.data.begin() + (std::min)(f.prec_elem, prec_elem), data.begin()); - precision((std::min)(f.prec_elem, prec_elem)); + unsigned elems = (std::min)(f.prec_elem, cpp_dec_float_elem_number); + std::copy(f.data.begin(), f.data.begin() + elems, data.begin()); + std::fill(data.begin() + elems, data.end(), 0); + prec_elem = cpp_dec_float_elem_number; return *this; } cpp_dec_float& operator= (long long v) BOOST_NOEXCEPT diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 4f84e881..8401be6c 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -690,7 +690,7 @@ protected: BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent.")); } template - void check_in_range(T val, const mpl::int_&){} + void check_in_range(T, const mpl::int_&){} template void check_in_range(T val) @@ -817,7 +817,7 @@ protected: BOOST_THROW_EXCEPTION(std::range_error("The argument to an unsigned cpp_int constructor was negative.")); } template - BOOST_FORCEINLINE void check_in_range(T val, const mpl::int_&, const mpl::bool_&){} + BOOST_FORCEINLINE void check_in_range(T, const mpl::int_&, const mpl::bool_&){} template BOOST_FORCEINLINE void check_in_range(T val) diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 71ef9844..88c762f2 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -253,7 +253,7 @@ template inline void eval_add_default(T& t, const U& u, const V& v) { t = u; - eval_add(t, u); + eval_add(t, v); } template inline void eval_add(T& t, const U& u, const V& v) @@ -358,7 +358,7 @@ template inline void eval_multiply_default(T& t, const U& u, const V& v) { t = u; - eval_multiply(t, u); + eval_multiply(t, v); } template inline void eval_multiply(T& t, const U& u, const V& v) @@ -457,7 +457,7 @@ template inline void eval_divide_default(T& t, const U& u, const V& v) { t = u; - eval_divide(t, u); + eval_divide(t, v); } template inline void eval_divide(T& t, const U& u, const V& v) @@ -515,7 +515,7 @@ template inline void eval_modulus_default(T& t, const U& u, const V& v) { t = u; - eval_modulus(t, u); + eval_modulus(t, v); } template inline void eval_modulus(T& t, const U& u, const V& v) @@ -565,7 +565,7 @@ template inline void eval_bitwise_and_default(T& t, const U& u, const V& v) { t = u; - eval_bitwise_and(t, u); + eval_bitwise_and(t, v); } template inline void eval_bitwise_and(T& t, const U& u, const V& v) @@ -615,7 +615,7 @@ template inline void eval_bitwise_or_default(T& t, const U& u, const V& v) { t = u; - eval_bitwise_or(t, u); + eval_bitwise_or(t, v); } template inline void eval_bitwise_or(T& t, const U& u, const V& v) @@ -665,7 +665,7 @@ template inline void eval_bitwise_xor_default(T& t, const U& u, const V& v) { t = u; - eval_bitwise_xor(t, u); + eval_bitwise_xor(t, v); } template inline void eval_bitwise_xor(T& t, const U& u, const V& v) @@ -1108,6 +1108,66 @@ inline bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::deta } // namespace math namespace multiprecision{ +template +inline number& add(number& result, const number& a, const number& b) +{ + BOOST_STATIC_ASSERT_MSG((is_convertible::value), "No conversion to the target of a mixed precision addition exists"); + BOOST_STATIC_ASSERT_MSG((is_convertible::value), "No conversion to the target of a mixed precision addition exists"); + using default_ops::eval_add; + eval_add(result.backend(), a.backend(), b.backend()); + return result; +} + +template +inline number& subtract(number& result, const number& a, const number& b) +{ + BOOST_STATIC_ASSERT_MSG((is_convertible::value), "No conversion to the target of a mixed precision addition exists"); + BOOST_STATIC_ASSERT_MSG((is_convertible::value), "No conversion to the target of a mixed precision addition exists"); + using default_ops::eval_subtract; + eval_subtract(result.backend(), a.backend(), b.backend()); + return result; +} + +template +inline number& multiply(number& result, const number& a, const number& b) +{ + BOOST_STATIC_ASSERT_MSG((is_convertible::value), "No conversion to the target of a mixed precision addition exists"); + BOOST_STATIC_ASSERT_MSG((is_convertible::value), "No conversion to the target of a mixed precision addition exists"); + using default_ops::eval_multiply; + eval_multiply(result.backend(), a.backend(), b.backend()); + return result; +} + +template +inline typename enable_if_c::value, number&>::type + add(number& result, const I& a, const I& b) +{ + using default_ops::eval_add; + typedef typename detail::canonical::type canonical_type; + eval_add(result.backend(), static_cast(a), static_cast(b)); + return result; +} + +template +inline typename enable_if_c::value, number&>::type + subtract(number& result, const I& a, const I& b) +{ + using default_ops::eval_subtract; + typedef typename detail::canonical::type canonical_type; + eval_subtract(result.backend(), static_cast(a), static_cast(b)); + return result; +} + +template +inline typename enable_if_c::value, number&>::type + multiply(number& result, const I& a, const I& b) +{ + using default_ops::eval_multiply; + typedef typename detail::canonical::type canonical_type; + eval_multiply(result.backend(), static_cast(a), static_cast(b)); + return result; +} + template inline typename detail::expression::result_type trunc(const detail::expression& v, const Policy& pol) { diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 08cf87c7..5178e124 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -820,7 +820,16 @@ run ../example/tommath_snips.cpp $(TOMMATH) : # requirements [ check-target-builds ../config//has_tommath : : no ] ; run ../example/floating_point_examples.cpp : : : gcc:-std=c++0x ; -run test_cpp_int_conv.cpp ; +run test_cpp_int_conv.cpp; + +run test_mixed_cpp_int.cpp ; +run test_mixed_float.cpp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : TEST_GMP gmp : ] + [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr gmp : ] ; + compile include_test/mpfr_include_test.cpp : # requirements diff --git a/test/test_mixed_cpp_int.cpp b/test/test_mixed_cpp_int.cpp new file mode 100644 index 00000000..ff47ac3a --- /dev/null +++ b/test/test_mixed_cpp_int.cpp @@ -0,0 +1,85 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include +#include "test.hpp" + +template +void test() +{ + using namespace boost::multiprecision; + typedef Number test_type; + + test_type h = (std::numeric_limits::max)(); + test_type l = (std::numeric_limits::max)(); + BigNumber r; + + add(r, h, h); + BOOST_CHECK_EQUAL(r, cpp_int(h) + cpp_int(h)); + + multiply(r, h, h); + BOOST_CHECK_EQUAL(r, cpp_int(h) * cpp_int(h)); + + if(std::numeric_limits::is_signed) + { + subtract(r, l, h); + BOOST_CHECK_EQUAL(r, cpp_int(l) - cpp_int(h)); + subtract(r, h, l); + BOOST_CHECK_EQUAL(r, cpp_int(h) - cpp_int(l)); + multiply(r, l, l); + BOOST_CHECK_EQUAL(r, cpp_int(l) * cpp_int(l)); + } + + // + // Try again with integer types as the source: + // + static const unsigned max_digits = std::numeric_limits::is_signed ? std::numeric_limits::digits : std::numeric_limits::digits; + static const unsigned require_digits = std::numeric_limits::digits <= 2 * max_digits ? std::numeric_limits::digits / 2 : max_digits; + typedef typename boost::mpl::if_c::is_signed, typename boost::int_t::least, typename boost::uint_t::least>::type i_type; + + i_type ih = (std::numeric_limits::max)(); + i_type il = (std::numeric_limits::max)(); + + add(r, ih, ih); + BOOST_CHECK_EQUAL(r, cpp_int(ih) + cpp_int(ih)); + + multiply(r, ih, ih); + BOOST_CHECK_EQUAL(r, cpp_int(ih) * cpp_int(ih)); + + if(std::numeric_limits::is_signed) + { + subtract(r, il, ih); + BOOST_CHECK_EQUAL(r, cpp_int(il) - cpp_int(ih)); + subtract(r, ih, il); + BOOST_CHECK_EQUAL(r, cpp_int(ih) - cpp_int(il)); + multiply(r, il, il); + BOOST_CHECK_EQUAL(r, cpp_int(il) * cpp_int(il)); + } +} + +int main() +{ + using namespace boost::multiprecision; + + test(); + test(); + test, et_off>, checked_int512_t>(); + + test(); + test(); + test, et_off>, checked_uint512_t>(); + return boost::report_errors(); +} + + + diff --git a/test/test_mixed_float.cpp b/test/test_mixed_float.cpp new file mode 100644 index 00000000..2b5aa6ff --- /dev/null +++ b/test/test_mixed_float.cpp @@ -0,0 +1,57 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#ifdef TEST_GMP +#include +#endif +#ifdef TEST_MPFR +#include +#endif +#include +#include "test.hpp" + +template +void test() +{ + using namespace boost::multiprecision; + typedef Number test_type; + + test_type a = 1; + a /= 3; + test_type b = -a; + + BigNumber r; + BOOST_CHECK_EQUAL(add(r, a, a), BigNumber(a) + BigNumber(a)); + BOOST_CHECK_EQUAL(subtract(r, a, b), BigNumber(a) - BigNumber(b)); + BOOST_CHECK_EQUAL(subtract(r, b, a), BigNumber(b) - BigNumber(a)); + BOOST_CHECK_EQUAL(multiply(r, a, a), BigNumber(a) * BigNumber(a)); +} + +int main() +{ + using namespace boost::multiprecision; + + test(); + +#ifdef TEST_GMP + test(); +#endif +#ifdef TEST_MPFR + test(); +#endif + + return boost::report_errors(); +} + + + From da40611f5796e10d32ad4c0e1b4e8ed55dc80476 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 3 Nov 2012 18:27:11 +0000 Subject: [PATCH 250/256] Fix mpfr_float_backend interconversions. Update docs and regenerate. [SVN r81163] --- .../boost_multiprecision/indexes/s01.html | 32 +++- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 42 ++++- doc/html/boost_multiprecision/map/hist.html | 4 + doc/html/boost_multiprecision/ref.html | 6 +- doc/html/boost_multiprecision/ref/number.html | 50 +++++- doc/html/boost_multiprecision/tut.html | 1 + doc/html/boost_multiprecision/tut/mixed.html | 169 ++++++++++++++++++ .../boost_multiprecision/tut/rounding.html | 6 +- doc/html/index.html | 3 +- doc/multiprecision.qbk | 103 +++++++++++ example/mixed_integer_arithmetic.cpp | 58 ++++++ include/boost/multiprecision/mpfr.hpp | 12 +- 14 files changed, 465 insertions(+), 29 deletions(-) create mode 100644 doc/html/boost_multiprecision/tut/mixed.html create mode 100644 example/mixed_integer_arithmetic.cpp diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index dd045fea..95db893b 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
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    +Function Index

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    @@ -27,6 +27,14 @@
  • +

    add

    +
    +
    • +

  • assign

    • @@ -403,13 +411,22 @@
    M
    -
    P
    @@ -449,6 +466,13 @@
  • +

    subtract

    +
    +
    • +

  • swap

    • diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index 9d2ed9e1..74da4b03 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

    C E G I M N T

    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index c7a71b66..0aea103d 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    C I L M S T U

    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index a13e6c88..77ea931e 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G I L M N O P R S T U Z

    @@ -26,6 +26,14 @@
  • +

    add

    +
    +
    • +

  • assign

    • @@ -661,6 +669,14 @@
  • +

    Mixed Precision Arithmetic

    +
    +
    • +

  • mpfr_float

    • +
  • +

    multiply

    +
    +
    • N @@ -757,6 +780,7 @@

    number

    @@ -911,6 +937,13 @@
  • +

    subtract

    +
    +
    • +

  • swap

    • @@ -921,7 +954,10 @@

    • TODO

      -
      +

    • tommath_int

      diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html index eec38fe9..8a324bdd 100644 --- a/doc/html/boost_multiprecision/map/hist.html +++ b/doc/html/boost_multiprecision/map/hist.html @@ -63,6 +63,10 @@ Added additional template parameter to mpfr_float_backend to allow stack-based allocation.
      • +
    • + Added section on mixed precision arithmetic, and added support for operations + yielding a higher precision result than either of the arguments. +
    diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html index a77e8169..c3d58d48 100644 --- a/doc/html/boost_multiprecision/ref.html +++ b/doc/html/boost_multiprecision/ref.html @@ -6,12 +6,12 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -41,7 +41,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html index 69b8a905..77aeb478 100644 --- a/doc/html/boost_multiprecision/ref/number.html +++ b/doc/html/boost_multiprecision/ref/number.html @@ -115,6 +115,14 @@ template <class Backend, expression_template_option ExpressionTemplates> std::istream& operator >> (std::istream& is, number<Backend, ExpressionTemplates>& r); +// Arithmetic with a higher precision result: +template <class ResultType, class Source1 class Source2> +ResultType& add(ResultType& result, const Source1& a, const Source2& b); +template <class ResultType, class Source1 class Source2> +ResultType& subtract(ResultType& result, const Source1& a, const Source2& b); +template <class ResultType, class Source1 class Source2> +ResultType& multiply(ResultType& result, const Source1& a, const Source2& b); + // Non-member function standard library support: unmentionable-expression-template-type abs (const number-or-expression-template-type&); unmentionable-expression-template-type fabs (const number-or-expression-template-type&); @@ -566,6 +574,38 @@

    + Arithmetic + with a higher precision result +
    +
    template <class ResultType, class Source1 class Source2>
+ResultType& add(ResultType& result, const Source1& a, const Source2& b);
+
+template <class ResultType, class Source1 class Source2>
+ResultType& subtract(ResultType& result, const Source1& a, const Source2& b);
+
+template <class ResultType, class Source1 class Source2>
+ResultType& multiply(ResultType& result, const Source1& a, const Source2& b);
+
    +

    + These functions apply the named operator to the arguments a + and b and store the result in result, + returning result. In all cases they behave "as + if" arguments a and b were + first promoted to type ResultType + before applying the operator, though particular backends may well avoid that + step by way of an optimization. +

    +

    + The type ResultType must + be an instance of class number, + and the types Source1 and + Source2 may be either instances + of class number or native + integer types. The latter is an optimization that allows arithmetic to be + performed on native integer types producing an extended precision result. +

    +
    + Non-member standard library function support
    @@ -1008,7 +1048,7 @@

    - + Traits Class Support
    @@ -1049,7 +1089,7 @@ if T is an expression template type derived from number<>, otherwise from mpl::false_.

    - + Integer functions
    @@ -1130,7 +1170,7 @@ composite less than 0.25^trials.

    - + Rational Number Functions
    @@ -1142,7 +1182,7 @@ respectively.

    - + Boost.Math Interoperability Support
    @@ -1165,7 +1205,7 @@ to ensure interoperability.

    - + std::numeric_limits support
    diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html index 906d8213..a54194d1 100644 --- a/doc/html/boost_multiprecision/tut.html +++ b/doc/html/boost_multiprecision/tut.html @@ -63,6 +63,7 @@
    Literal Types and constexpr Support
    Rounding Rules for Conversions
    +
    Mixed Precision Arithmetic

    In order to use this library you need to make two choices: what kind of number diff --git a/doc/html/boost_multiprecision/tut/mixed.html b/doc/html/boost_multiprecision/tut/mixed.html new file mode 100644 index 00000000..8b609e43 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/mixed.html @@ -0,0 +1,169 @@ + + + +Mixed Precision Arithmetic + + + + + + + + +

    +PrevUpHomeNext +
    +
    +
    +

    + Mixed precision arithmetic is fully supported by the library, there are two + different forms: +

    +
      +
    • + Where the operands are of different precision. +
      • +
    • + Where the operands are of the same precision, but yield a higher precision + result. +
      • +
    +
    + + Mixing + Operands of Differing Precision +
    +

    + If the arguments to a binary operator are of different precision, then the + operation is allowed as long as there is an unambiguous implicit conversion + from one argument type to the other. In all cases the arithmetic is performed + "as if" the lower precision type is promoted to the higher precision + type before applying the operator. However, particular backends may optimise + this and avoid actually creating a temporary if they are able to do so. +

    +

    + For example: +

    +
    mpfr_float_50         a(2), b;
+mpfr_float_100        c(3), d;
+static_mpfr_float_50  e(5), f;
+mpz_int               i(20);
+
+d = a * c;  // OK, result of operand is an mpfr_float_100.
+b = a * c;  // Error, can't convert the result to an mpfr_float_50 as it will lose digits.
+f = a * e;  // Error, operator is ambiguous, result could be of either type.
+f = e * i;  // OK, unambiguous conversion from mpz_int to static_mpfr_float_50
+
    +
    + + Operands + of the Same Precision +
    +

    + Sometimes you want to apply an operator to two arguments of the same precision + in such a way as to obtain a result of higher precision. The most common + situation occurs with fixed precision integers, where you want to multiply + two N-bit numbers to obtain a 2N-bit result. This is supported in this library + by the following free functions: +

    +
    template <class ResultType, class Source1 class Source2>
+ResultType& add(ResultType& result, const Source1& a, const Source2& b);
+
+template <class ResultType, class Source1 class Source2>
+ResultType& subtract(ResultType& result, const Source1& a, const Source2& b);
+
+template <class ResultType, class Source1 class Source2>
+ResultType& multiply(ResultType& result, const Source1& a, const Source2& b);
+
    +

    + These functions apply the named operator to the arguments a + and b and store the result in result, + returning result. In all cases they behave "as + if" arguments a and b were + first promoted to type ResultType + before applying the operator, though particular backends may well avoid that + step by way of an optimization. +

    +

    + The type ResultType must + be an instance of class number, + and the types Source1 and + Source2 may be either instances + of class number or native + integer types. The latter is an optimization that allows arithmetic to be + performed on native integer types producing an extended precision result. +

    +

    + For example: +

    +

    +

    +
    #include <boost/multiprecision/cpp_int.hpp>
+
+using namespace boost::multiprecision;
+
+boost::uint64_t i = (std::numeric_limits<boost::uint64_t>::max)();
+boost::uint64_t j = 1;
+
+uint128_t ui128;
+uint256_t ui256;
+//
+// Start by performing arithmetic on 64-bit integers to yield 128-bit results:
+//
+std::cout << std::hex << std::showbase << i << std::endl;
+std::cout << std::hex << std::showbase << add(ui128, i, j) << std::endl;
+std::cout << std::hex << std::showbase << multiply(ui128, i, i) << std::endl;
+//
+// The try squaring a 128-bit integer to yield a 256-bit result:
+//
+ui128 = (std::numeric_limits<uint128_t>::max)();
+std::cout << std::hex << std::showbase << multiply(ui256, ui128, ui128) << std::endl;
+
    +

    +

    +

    + Produces the output: +

    +

    +

    +
    0xffffffffffffffff
+0x10000000000000000
+0xFFFFFFFFFFFFFFFE0000000000000001
+0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE00000000000000000000000000000001
+
    +

    +

    +
    + + Backends + With Optimized Mixed Precision Arithmetic +
    +

    + The following backends have at least some direct support for mixed precision + arithmetic, and therefore avoid creating unnecessary temporaries when using + the interfaces above. Therefore when using these types it's more efficient + to use mixed precision arithmetic, than it is to explicitly cast the operands + to the result type: +

    +

    + mpfr_float, + gmp_float, + cpp_int. +

    +
    + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/rounding.html b/doc/html/boost_multiprecision/tut/rounding.html index 84dcc3f6..1b64cfc3 100644 --- a/doc/html/boost_multiprecision/tut/rounding.html +++ b/doc/html/boost_multiprecision/tut/rounding.html @@ -7,11 +7,11 @@ - +
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -176,7 +176,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/index.html b/doc/html/index.html index a919dfc2..0e5cb43d 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -78,6 +78,7 @@
    Literal Types and constexpr Support
    Rounding Rules for Conversions
    +
    Mixed Precision Arithmetic

    Reference
    @@ -124,7 +125,7 @@ - +

    Last revised: November 02, 2012 at 13:02:30 GMT

    Last revised: November 03, 2012 at 18:24:27 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index b23a001a..1b4c2f9b 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -26,6 +26,7 @@ [import ../example/cpp_int_snips.cpp] [import ../example/random_snips.cpp] [import ../example/safe_prime.cpp] +[import ../example/mixed_integer_arithmetic.cpp] [template mpfr[] [@http://www.mpfr.org MPFR]] [template gmp[] [@http://gmplib.org GMP]] @@ -1248,6 +1249,78 @@ The following table summarises the situation for conversions from native types: [endsect] +[section:mixed Mixed Precision Arithmetic] + +Mixed precision arithmetic is fully supported by the library, there are two different forms: + +* Where the operands are of different precision. +* Where the operands are of the same precision, but yield a higher precision result. + +[h4 Mixing Operands of Differing Precision] + +If the arguments to a binary operator are of different precision, then the operation is allowed +as long as there is an unambiguous implicit conversion from one argument type to the other. +In all cases the arithmetic is performed "as if" the lower precision type is promoted to the +higher precision type before applying the operator. However, particular backends may optimise +this and avoid actually creating a temporary if they are able to do so. + +For example: + + mpfr_float_50 a(2), b; + mpfr_float_100 c(3), d; + static_mpfr_float_50 e(5), f; + mpz_int i(20); + + d = a * c; // OK, result of operand is an mpfr_float_100. + b = a * c; // Error, can't convert the result to an mpfr_float_50 as it will lose digits. + f = a * e; // Error, operator is ambiguous, result could be of either type. + f = e * i; // OK, unambiguous conversion from mpz_int to static_mpfr_float_50 + +[h4 Operands of the Same Precision] + +Sometimes you want to apply an operator to two arguments of the same precision in +such a way as to obtain a result of higher precision. The most common situation +occurs with fixed precision integers, where you want to multiply two N-bit numbers +to obtain a 2N-bit result. This is supported in this library by the following +free functions: + + template + ResultType& add(ResultType& result, const Source1& a, const Source2& b); + + template + ResultType& subtract(ResultType& result, const Source1& a, const Source2& b); + + template + ResultType& multiply(ResultType& result, const Source1& a, const Source2& b); + +These functions apply the named operator to the arguments ['a] and ['b] and store the +result in ['result], returning ['result]. In all cases they behave "as if" +arguments ['a] and ['b] were first promoted to type `ResultType` before applying the +operator, though particular backends may well avoid that step by way of an optimization. + +The type `ResultType` must be an instance of class `number`, and the types `Source1` and `Source2` +may be either instances of class `number` or native integer types. The latter is an optimization +that allows arithmetic to be performed on native integer types producing an extended precision result. + +For example: + +[mixed_eg] + +Produces the output: + +[mixed_output] + +[h4 Backends With Optimized Mixed Precision Arithmetic] + +The following backends have at least some direct support for mixed precision arithmetic, +and therefore avoid creating unnecessary temporaries when using the interfaces above. +Therefore when using these types it's more efficient to use mixed precision arithmetic, +than it is to explicitly cast the operands to the result type: + +__mpfr_float_backend, __mpf_float, __cpp_int. + +[endsect] + [endsect] [section:ref Reference] @@ -1350,6 +1423,14 @@ The following table summarises the situation for conversions from native types: template std::istream& operator >> (std::istream& is, number& r); + // Arithmetic with a higher precision result: + template + ResultType& add(ResultType& result, const Source1& a, const Source2& b); + template + ResultType& subtract(ResultType& result, const Source1& a, const Source2& b); + template + ResultType& multiply(ResultType& result, const Source1& a, const Source2& b); + // Non-member function standard library support: ``['unmentionable-expression-template-type]`` abs (const ``['number-or-expression-template-type]``&); ``['unmentionable-expression-template-type]`` fabs (const ``['number-or-expression-template-type]``&); @@ -1659,6 +1740,26 @@ These operators provided formatted input-output operations on `number` types, an It's down to the back-end type to actually implement string conversion. However, the back-ends provided with this library support all of the iostream formatting flags, field width and precision settings. +[h4 Arithmetic with a higher precision result] + + template + ResultType& add(ResultType& result, const Source1& a, const Source2& b); + + template + ResultType& subtract(ResultType& result, const Source1& a, const Source2& b); + + template + ResultType& multiply(ResultType& result, const Source1& a, const Source2& b); + +These functions apply the named operator to the arguments ['a] and ['b] and store the +result in ['result], returning ['result]. In all cases they behave "as if" +arguments ['a] and ['b] were first promoted to type `ResultType` before applying the +operator, though particular backends may well avoid that step by way of an optimization. + +The type `ResultType` must be an instance of class `number`, and the types `Source1` and `Source2` +may be either instances of class `number` or native integer types. The latter is an optimization +that allows arithmetic to be performed on native integer types producing an extended precision result. + [h4 Non-member standard library function support] ``['unmentionable-expression-template-type]`` abs (const ``['number-or-expression-template-type]``&); @@ -2925,6 +3026,8 @@ Windows Vista machine. * Tweaked expression template unpacking to use fewer temporaries when the LHS also appears in the RHS. * Refactored `cpp_int_backend` based on review comments with new template parameter structure. * Added additional template parameter to `mpfr_float_backend` to allow stack-based allocation. +* Added section on mixed precision arithmetic, and added support for operations yielding a higher precision result +than either of the arguments. [h4 Pre-review history] diff --git a/example/mixed_integer_arithmetic.cpp b/example/mixed_integer_arithmetic.cpp new file mode 100644 index 00000000..7348b474 --- /dev/null +++ b/example/mixed_integer_arithmetic.cpp @@ -0,0 +1,58 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include + +int main() +{ + //[mixed_eg + //=#include + + using namespace boost::multiprecision; + + boost::uint64_t i = (std::numeric_limits::max)(); + boost::uint64_t j = 1; + + uint128_t ui128; + uint256_t ui256; + // + // Start by performing arithmetic on 64-bit integers to yield 128-bit results: + // + std::cout << std::hex << std::showbase << i << std::endl; + std::cout << std::hex << std::showbase << add(ui128, i, j) << std::endl; + std::cout << std::hex << std::showbase << multiply(ui128, i, i) << std::endl; + // + // The try squaring a 128-bit integer to yield a 256-bit result: + // + ui128 = (std::numeric_limits::max)(); + std::cout << std::hex << std::showbase << multiply(ui256, ui128, ui128) << std::endl; + + //] + + return 0; +} + +/* + +Program output: + +//[mixed_output + +0xffffffffffffffff +0x10000000000000000 +0xFFFFFFFFFFFFFFFE0000000000000001 +0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE00000000000000000000000000000001 + +//] +*/ + diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index 7924b414..dac44984 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -608,14 +608,14 @@ struct mpfr_float_backend : public detail::mpfr_float_imp(static_cast&&>(o)) {} #endif - template - mpfr_float_backend(const mpfr_float_backend& val, typename enable_if_c::type* = 0) + template + mpfr_float_backend(const mpfr_float_backend& val, typename enable_if_c::type* = 0) : detail::mpfr_float_imp() { mpfr_set(this->m_data, val.data(), GMP_RNDN); } - template - explicit mpfr_float_backend(const mpfr_float_backend& val, typename disable_if_c::type* = 0) + template + explicit mpfr_float_backend(const mpfr_float_backend& val, typename disable_if_c::type* = 0) : detail::mpfr_float_imp() { mpfr_set(this->m_data, val.data(), GMP_RNDN); @@ -701,8 +701,8 @@ struct mpfr_float_backend : public detail::mpfr_float_imp - mpfr_float_backend& operator=(const mpfr_float_backend& val) BOOST_NOEXCEPT + template + mpfr_float_backend& operator=(const mpfr_float_backend& val) BOOST_NOEXCEPT { mpfr_set(this->m_data, val.data(), GMP_RNDN); return *this; From e599ca723ca6bdfed618535063081223dd552dd4 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 4 Nov 2012 12:08:37 +0000 Subject: [PATCH 251/256] Fix missing typename. [SVN r81169] --- include/boost/multiprecision/cpp_int.hpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 8401be6c..09bf8c99 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -32,7 +32,7 @@ namespace backends{ #pragma warning(disable:4127 4351 4293) #endif -template >::type > +template >::type > struct cpp_int_backend; template From 836d7652430f6bd596f1df8bde67dbd8f973ebd9 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 4 Nov 2012 12:14:22 +0000 Subject: [PATCH 252/256] Fix Jamfile SNAFU. [SVN r81170] --- test/Jamfile.v2 | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 5178e124..8b3328d5 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -820,7 +820,7 @@ run ../example/tommath_snips.cpp $(TOMMATH) : # requirements [ check-target-builds ../config//has_tommath : : no ] ; run ../example/floating_point_examples.cpp : : : gcc:-std=c++0x ; -run test_cpp_int_conv.cpp; +run test_cpp_int_conv.cpp ; run test_mixed_cpp_int.cpp ; run test_mixed_float.cpp From e3deed1fdf3e22ac55f3d6820638317b98ea2579 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 5 Nov 2012 12:36:25 +0000 Subject: [PATCH 253/256] Optimize cpp_int multiplication with precision extension. Turn off some warnings. [SVN r81200] --- .../concepts/mp_number_archetypes.hpp | 1 - .../boost/multiprecision/cpp_int/multiply.hpp | 153 +++++++++++++++++- .../depricated/arithmetic_backend.hpp | 1 - .../multiprecision/detail/default_ops.hpp | 1 - .../multiprecision/detail/number_base.hpp | 7 + include/boost/multiprecision/gmp.hpp | 8 +- include/boost/multiprecision/mpfr.hpp | 1 - .../boost/multiprecision/rational_adapter.hpp | 8 +- include/boost/multiprecision/tommath.hpp | 1 - performance/delaunay_test.cpp | 19 ++- test/test_mixed_cpp_int.cpp | 7 +- 11 files changed, 192 insertions(+), 15 deletions(-) diff --git a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp index 8884a9fa..6c33ee76 100644 --- a/include/boost/multiprecision/concepts/mp_number_archetypes.hpp +++ b/include/boost/multiprecision/concepts/mp_number_archetypes.hpp @@ -11,7 +11,6 @@ #include #include #include -#include #include #include #include diff --git a/include/boost/multiprecision/cpp_int/multiply.hpp b/include/boost/multiprecision/cpp_int/multiply.hpp index 630e7f91..2559cead 100644 --- a/include/boost/multiprecision/cpp_int/multiply.hpp +++ b/include/boost/multiprecision/cpp_int/multiply.hpp @@ -271,9 +271,7 @@ BOOST_FORCEINLINE typename enable_if_c< template BOOST_FORCEINLINE typename enable_if_c< is_trivial_cpp_int >::value - && is_trivial_cpp_int >::value && is_unsigned_number >::value - && is_unsigned_number >::value >::type eval_multiply( cpp_int_backend& result, @@ -283,6 +281,157 @@ BOOST_FORCEINLINE typename enable_if_c< result.normalize(); } +template +BOOST_FORCEINLINE typename enable_if_c< + is_trivial_cpp_int >::value + && is_trivial_cpp_int >::value + && (is_signed_number >::value + || is_signed_number >::value) + >::type + eval_multiply( + cpp_int_backend& result, + const cpp_int_backend& a, + const cpp_int_backend& b) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value)) +{ + *result.limbs() = detail::checked_multiply(*a.limbs(), *b.limbs(), typename cpp_int_backend::checked_type()); + result.sign(a.sign() != b.sign()); + result.normalize(); +} + +template +BOOST_FORCEINLINE typename enable_if_c< + is_trivial_cpp_int >::value + && is_unsigned_number >::value + >::type + eval_multiply( + cpp_int_backend& result, + const cpp_int_backend& a, + const cpp_int_backend& b) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int >::value)) +{ + *result.limbs() = detail::checked_multiply(*a.limbs(), *b.limbs(), typename cpp_int_backend::checked_type()); + result.normalize(); +} + +// +// Special routines for multiplying two integers to obtain a multiprecision result: +// +template +BOOST_FORCEINLINE typename enable_if_c< + !is_trivial_cpp_int >::value + >::type + eval_multiply( + cpp_int_backend& result, + signed_double_limb_type a, signed_double_limb_type b) +{ + static const signed_double_limb_type mask = ~static_cast(0); + static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT; + bool s = false; + double_limb_type w, x, y, z; + if(a < 0) + { + a = -a; + s = true; + } + if(b < 0) + { + b = -b; + s = !s; + } + w = a & mask; + x = a >> limb_bits; + y = b & mask; + z = b >> limb_bits; + + result.resize(4, 4); + limb_type* pr = result.limbs(); + + double_limb_type carry = w * y; + pr[0] = static_cast(carry); + carry >>= limb_bits; + carry += w * z + x * y; + pr[1] = static_cast(carry); + carry >>= limb_bits; + carry += x * z; + pr[2] = static_cast(carry); + pr[3] = static_cast(carry >> limb_bits); + + result.sign(s); + result.normalize(); +} + +template +BOOST_FORCEINLINE typename enable_if_c< + !is_trivial_cpp_int >::value + >::type + eval_multiply( + cpp_int_backend& result, + double_limb_type a, double_limb_type b) +{ + static const signed_double_limb_type mask = ~static_cast(0); + static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT; + + double_limb_type w, x, y, z; + w = a & mask; + x = a >> limb_bits; + y = b & mask; + z = b >> limb_bits; + + result.resize(4, 4); + limb_type* pr = result.limbs(); + + double_limb_type carry = w * y; + pr[0] = static_cast(carry); + carry >>= limb_bits; + carry += w * z; + pr[1] = static_cast(carry); + carry >>= limb_bits; + pr[2] = static_cast(carry); + carry = x * y + pr[1]; + pr[1] = static_cast(carry); + carry >>= limb_bits; + carry += pr[2] + x * z; + pr[2] = static_cast(carry); + pr[3] = static_cast(carry >> limb_bits); + + result.sign(false); + result.normalize(); +} + +template +BOOST_FORCEINLINE typename enable_if_c< + !is_trivial_cpp_int >::value + && is_trivial_cpp_int >::value + && is_trivial_cpp_int >::value + >::type + eval_multiply( + cpp_int_backend& result, + cpp_int_backend const& a, + cpp_int_backend const& b) +{ + typedef typename boost::multiprecision::detail::canonical::local_limb_type, cpp_int_backend >::type canonical_type; + eval_multiply(result, static_cast(*a.limbs()), static_cast(*b.limbs())); + result.sign(a.sign() != b.sign()); +} + +template +BOOST_FORCEINLINE typename enable_if_c::value && (sizeof(SI) <= sizeof(signed_double_limb_type) / 2)>::type + eval_multiply( + cpp_int_backend& result, + SI a, SI b) +{ + result = static_cast(a) * static_cast(b); +} + +template +BOOST_FORCEINLINE typename enable_if_c::value && (sizeof(UI) <= sizeof(signed_double_limb_type) / 2)>::type + eval_multiply( + cpp_int_backend& result, + UI a, UI b) +{ + result = static_cast(a) * static_cast(b); +} + }}} // namespaces #endif diff --git a/include/boost/multiprecision/depricated/arithmetic_backend.hpp b/include/boost/multiprecision/depricated/arithmetic_backend.hpp index 3dda99ac..7a13c476 100644 --- a/include/boost/multiprecision/depricated/arithmetic_backend.hpp +++ b/include/boost/multiprecision/depricated/arithmetic_backend.hpp @@ -10,7 +10,6 @@ #include #include #include -#include #include namespace boost{ diff --git a/include/boost/multiprecision/detail/default_ops.hpp b/include/boost/multiprecision/detail/default_ops.hpp index 88c762f2..d93c0276 100644 --- a/include/boost/multiprecision/detail/default_ops.hpp +++ b/include/boost/multiprecision/detail/default_ops.hpp @@ -9,7 +9,6 @@ #include #include #include -#include #include #include #include diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp index e7244273..2e9a29f9 100644 --- a/include/boost/multiprecision/detail/number_base.hpp +++ b/include/boost/multiprecision/detail/number_base.hpp @@ -10,7 +10,14 @@ #include #include #include +#ifdef BOOST_MSVC +# pragma warning(push) +# pragma warning(disable:4307) +#endif #include +#ifdef BOOST_MSVC +# pragma warning(pop) +#endif namespace boost{ namespace multiprecision{ diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 5780cbe9..6df42b62 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -12,8 +12,14 @@ #include #include #include -#include +#ifdef BOOST_MSVC +# pragma warning(push) +# pragma warning(disable:4127) +#endif #include +#ifdef BOOST_MSVC +# pragma warning(pop) +#endif #include #include #include diff --git a/include/boost/multiprecision/mpfr.hpp b/include/boost/multiprecision/mpfr.hpp index dac44984..4ee9e2d7 100644 --- a/include/boost/multiprecision/mpfr.hpp +++ b/include/boost/multiprecision/mpfr.hpp @@ -10,7 +10,6 @@ #include #include #include -#include #include #include #include diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index b3f2ad16..1c8a69cb 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -10,9 +10,15 @@ #include #include #include -#include #include +#ifdef BOOST_MSVC +# pragma warning(push) +# pragma warning(disable:4512) +#endif #include +#ifdef BOOST_MSVC +# pragma warning(pop) +#endif namespace boost{ namespace multiprecision{ diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index a4e2e701..686ef7e8 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -11,7 +11,6 @@ #include #include #include -#include #include #include #include diff --git a/performance/delaunay_test.cpp b/performance/delaunay_test.cpp index 593fd5a4..d6fff135 100644 --- a/performance/delaunay_test.cpp +++ b/performance/delaunay_test.cpp @@ -135,6 +135,12 @@ BOOST_FORCEINLINE void mul_2n(R& r, const T& a, const T& b) r *= b; } +template +BOOST_FORCEINLINE void mul_2n(boost::multiprecision::number& r, const T& a, const T& b) +{ + multiply(r, a, b); +} + BOOST_FORCEINLINE void mul_2n(int128_t& r, const boost::int64_t& a, const boost::int64_t& b) { r = mult_64x64_to_128(a, b); @@ -270,10 +276,15 @@ int main() std::cout << "calculating...\n"; do_calc >("int64_t, int64_t"); - do_calc, et_off>, number, et_off> > >("arithmetic_backend"); - do_calc >("int64_t, int128_t"); - do_calc >("int64_t, int128_t"); - do_calc, et_on> > >("int64_t, int128_t (ET)"); + do_calc, et_off>, number, et_off> > >("arithmetic_backend, arithmetic_backend"); + do_calc, et_off> > >("int64_t, arithmetic_backend"); + do_calc, et_off>, number, et_off> > >("multiprecision::int64_t, multiprecision::int64_t"); + + do_calc >("int64_t, int128_t"); + do_calc >("int64_t, boost::multiprecision::int128_t"); + do_calc, et_on> > >("int64_t, int128_t (ET)"); + do_calc, et_off>, boost::multiprecision::int128_t > >("multiprecision::int64_t, multiprecision::int128_t"); + do_calc >("int64_t, cpp_int"); do_calc, et_off> > >("int64_t, cpp_int (no ET's)"); do_calc > > >("int64_t, cpp_int(128-bit cache)"); diff --git a/test/test_mixed_cpp_int.cpp b/test/test_mixed_cpp_int.cpp index ff47ac3a..7d12eba9 100644 --- a/test/test_mixed_cpp_int.cpp +++ b/test/test_mixed_cpp_int.cpp @@ -73,11 +73,14 @@ int main() test(); test(); - test, et_off>, checked_int512_t>(); + test, et_off>, checked_int128_t>(); + test(); test(); test(); - test, et_off>, checked_uint512_t>(); + test, et_off>, checked_uint128_t>(); + test(); + return boost::report_errors(); } From a9bcf67b4b9a4f3a1a2ab983c78c0b67075d11a0 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 5 Nov 2012 19:05:31 +0000 Subject: [PATCH 254/256] Fix errors resulting from incorrect noexcept specifications and no numeric_limits support for __int128 [SVN r81211] --- include/boost/multiprecision/cpp_int.hpp | 38 +++++++++++-------- .../multiprecision/detail/number_base.hpp | 28 +++++++++----- 2 files changed, 42 insertions(+), 24 deletions(-) diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 09bf8c99..12b056be 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -212,7 +212,8 @@ public: BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT : m_data(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false), m_internal(true) { } BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT - : m_data(i), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), m_sign(i < 0), m_internal(true) { } + : m_data(i), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), + m_sign(i < 0), m_internal(true) { } #endif // // Helper functions for getting at our internal data, and manipulating storage: @@ -275,7 +276,7 @@ public: m_sign = o.m_sign; } #ifndef BOOST_NO_RVALUE_REFERENCES - cpp_int_base(cpp_int_base&& o) BOOST_NOEXCEPT + cpp_int_base(cpp_int_base&& o) : allocator_type(static_cast(o)), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal) { if(m_internal) @@ -422,7 +423,9 @@ public: BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT : m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false) {} BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT - : m_wrapper(double_limb_type(i < 0 ? -i : i)), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), m_sign(i < 0) {} + : m_wrapper(double_limb_type(i < 0 ? -i : i)), + m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)), + m_sign(i < 0) {} #endif // // Helper functions for getting at our internal data, and manipulating storage: @@ -548,12 +551,12 @@ public: // BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT : m_wrapper(i), m_limbs(1) {} - BOOST_FORCEINLINE cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT_IF((Checked == unchecked)) : m_wrapper(limb_type(i < 0 ? -i : i)), m_limbs(1) { if(i < 0) negate(); } #ifdef BOOST_LITTLE_ENDIAN BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT : m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1) {} - BOOST_FORCEINLINE cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT + BOOST_FORCEINLINE cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT_IF((Checked == unchecked)) : m_wrapper(double_limb_type(i < 0 ? -i : i)), m_limbs(i < 0 ? (-i > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)) { if(i < 0) negate(); } #endif // @@ -563,7 +566,7 @@ public: BOOST_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; } BOOST_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; } BOOST_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; } - BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT { if(b) negate(); } + BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT_IF((Checked == unchecked)) { if(b) negate(); } BOOST_FORCEINLINE void resize(unsigned new_size, unsigned min_size) BOOST_NOEXCEPT_IF((Checked == unchecked)) { m_limbs = (std::min)(new_size, internal_limb_count); @@ -577,8 +580,10 @@ public: while((m_limbs-1) && !p[m_limbs - 1])--m_limbs; } - BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_wrapper(limb_type(0u)), m_limbs(1) {} - BOOST_FORCEINLINE cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_limbs(o.m_limbs) + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT + : m_wrapper(limb_type(0u)), m_limbs(1) {} + BOOST_FORCEINLINE cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT + : m_limbs(o.m_limbs) { std::copy(o.limbs(), o.limbs() + o.size(), limbs()); } @@ -749,7 +754,8 @@ public: } BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() : m_data(0), m_sign(false) {} - BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_data(o.m_data), m_sign(o.m_sign) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT + : m_data(o.m_data), m_sign(o.m_sign) {} //~cpp_int_base() BOOST_NOEXCEPT {} BOOST_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT { @@ -856,7 +862,7 @@ public: BOOST_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; } BOOST_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; } BOOST_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; } - BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT + BOOST_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT_IF((Checked == unchecked)) { if(b) negate(); @@ -872,13 +878,14 @@ public: } BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() : m_data(0) {} - BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT : m_data(o.m_data) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT + : m_data(o.m_data) {} //~cpp_int_base() BOOST_NOEXCEPT {} BOOST_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT { m_data = o.m_data; } - BOOST_FORCEINLINE void negate() BOOST_NOEXCEPT + BOOST_FORCEINLINE void negate() BOOST_NOEXCEPT_IF((Checked == unchecked)) { if(Checked == checked) { @@ -957,7 +964,8 @@ public: BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{} BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_NOEXCEPT_IF(boost::is_void::value) : base_type(o) {} #ifndef BOOST_NO_RVALUE_REFERENCES - BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT : base_type(static_cast(o)) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT + : base_type(static_cast(o)) {} #endif // // Direct construction from arithmetic type: @@ -1195,7 +1203,7 @@ private: *this->limbs() = i; this->sign(false); } - BOOST_FORCEINLINE void do_assign_arithmetic(signed_limb_type i, const mpl::false_&) BOOST_NOEXCEPT + BOOST_FORCEINLINE void do_assign_arithmetic(signed_limb_type i, const mpl::false_&) BOOST_NOEXCEPT_IF((Checked == unchecked)) { this->resize(1, 1); *this->limbs() = static_cast(std::abs(i)); @@ -1467,7 +1475,7 @@ private: base = 16; std::string result; - unsigned Bits = base_type::limb_bits; + unsigned Bits = sizeof(typename base_type::local_limb_type) * CHAR_BIT; if(base == 8 || base == 16) { diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp index 2e9a29f9..54afe583 100644 --- a/include/boost/multiprecision/detail/number_base.hpp +++ b/include/boost/multiprecision/detail/number_base.hpp @@ -57,11 +57,11 @@ template struct is_number_expression > : public mpl::true_ {}; template -struct is_compatible_arithmetic_type +struct is_compatible_arithmetic_type : public mpl::bool_< - is_convertible::value - && !is_same::value - && !is_number_expression::value> + is_convertible::value + && !is_same::value + && !is_number_expression::value> {}; namespace detail{ @@ -90,11 +90,21 @@ typename enable_if_c<(is_unsigned::value), T>::type abs(T t) BOOST_NOEXCEPT # define BOOST_MP_MOVE(x) x #endif +template +struct bits_of +{ + BOOST_STATIC_ASSERT(is_integral::value || std::numeric_limits::is_specialized); + static const unsigned value = + std::numeric_limits::is_specialized ? + std::numeric_limits::digits + : sizeof(T) * CHAR_BIT - (is_signed::value ? 1 : 0); +}; + template struct has_enough_bits { template - struct type : public mpl::bool_::digits >= b>{}; + struct type : public mpl::bool_::value>= b>{}; }; template @@ -115,7 +125,7 @@ struct canonical_imp, Backend, Tag> template struct canonical_imp > { - typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename has_enough_bits::value>::template type pred_type; typedef typename mpl::find_if< typename Backend::signed_types, pred_type @@ -125,7 +135,7 @@ struct canonical_imp > template struct canonical_imp > { - typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename has_enough_bits::value>::template type pred_type; typedef typename mpl::find_if< typename Backend::unsigned_types, pred_type @@ -135,7 +145,7 @@ struct canonical_imp > template struct canonical_imp > { - typedef typename has_enough_bits::digits>::template type pred_type; + typedef typename has_enough_bits::value>::template type pred_type; typedef typename mpl::find_if< typename Backend::float_types, pred_type @@ -393,7 +403,7 @@ struct expression typedef typename middle_type::result_type middle_result_type; typedef typename right_type::result_type right_result_type; typedef typename combine_expression< - left_result_type, + left_result_type, typename combine_expression::type >::type result_type; typedef tag tag_type; From 3430188795544c87c7efc258bb792216dfd36d98 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 9 Nov 2012 18:55:19 +0000 Subject: [PATCH 255/256] Add overloads of the integer-only functions which work with native integer types. Ensure powm promotes fixed precision types to avoid numeric overflow. Allow the Miller-Rabin code to be used by native integers. Fix Miller Rabin tests to actually return the test result! Fix some bugs in cpp_int unsigned arithmetic, and ensure the Miller Rabin and random number code can be safely used with checked fixed precision integers. [SVN r81269] --- doc/multiprecision.qbk | 4 +- include/boost/multiprecision/cpp_int.hpp | 27 ++- .../multiprecision/cpp_int/comparison.hpp | 2 +- .../boost/multiprecision/cpp_int/divide.hpp | 22 ++- include/boost/multiprecision/cpp_int/misc.hpp | 9 +- .../multiprecision/detail/integer_ops.hpp | 84 +++++---- include/boost/multiprecision/gmp.hpp | 9 + include/boost/multiprecision/integer.hpp | 174 ++++++++++++++++++ include/boost/multiprecision/miller_rabin.hpp | 53 ++++-- include/boost/multiprecision/number.hpp | 2 +- include/boost/multiprecision/random.hpp | 14 +- include/boost/multiprecision/tommath.hpp | 9 + test/Jamfile.v2 | 1 + test/test_miller_rabin.cpp | 43 ++++- test/test_native_integer.cpp | 79 ++++++++ 15 files changed, 463 insertions(+), 69 deletions(-) create mode 100644 include/boost/multiprecision/integer.hpp create mode 100644 test/test_native_integer.cpp diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 1b4c2f9b..051ff313 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -1874,7 +1874,7 @@ large as to take "effectively forever" to compute, or else simply run the host m Returns ['b[super p] mod m] as an expression template. template - bool divide_qr(const ``['number-or-expression-template-type]``& x, const ``['number-or-expression-template-type]``& y, + void divide_qr(const ``['number-or-expression-template-type]``& x, const ``['number-or-expression-template-type]``& y, number& q, number& r); Divides x by y and returns both the quotient and remainder. After the call `q = x / y` and `r = x % y`. @@ -1888,6 +1888,8 @@ Returns the absolute value of `x % val`. Returns the index of the least significant bit that is set to 1. +Throws a `std::range_error` if the argument is <= 0. + template bool bit_test(const number& val, unsigned index); diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index 12b056be..d2397f85 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -29,7 +29,7 @@ namespace backends{ #ifdef BOOST_MSVC // warning C4127: conditional expression is constant #pragma warning(push) -#pragma warning(disable:4127 4351 4293) +#pragma warning(disable:4127 4351 4293 4996 4307) #endif template >::type > @@ -1736,6 +1736,31 @@ public: } // namespace backends +namespace detail{ + +template +struct double_precision_type; + +template +struct double_precision_type > +{ + typedef typename mpl::if_c< + backends::is_fixed_precision >::value, + backends::cpp_int_backend< + (is_void::value ? + 2 * backends::max_precision >::value + : MinBits), + 2 * backends::max_precision >::value, + SignType, + Checked, + Allocator>, + backends::cpp_int_backend + >::type type; +}; + + +} + template struct expression_template_default > { diff --git a/include/boost/multiprecision/cpp_int/comparison.hpp b/include/boost/multiprecision/cpp_int/comparison.hpp index 32d6a470..8ad701dc 100644 --- a/include/boost/multiprecision/cpp_int/comparison.hpp +++ b/include/boost/multiprecision/cpp_int/comparison.hpp @@ -14,7 +14,7 @@ namespace boost{ namespace multiprecision{ namespace backends{ #ifdef BOOST_MSVC #pragma warning(push) -#pragma warning(disable:4018 4389) +#pragma warning(disable:4018 4389 4996) #endif // diff --git a/include/boost/multiprecision/cpp_int/divide.hpp b/include/boost/multiprecision/cpp_int/divide.hpp index 5e1534e6..c2afc7ec 100644 --- a/include/boost/multiprecision/cpp_int/divide.hpp +++ b/include/boost/multiprecision/cpp_int/divide.hpp @@ -215,7 +215,7 @@ void divide_unsigned_helper( // rather than a full O(N^2) multiply: // double_limb_type carry = 0; - t.resize(y.size() + shift + 1, y.size() + shift + 1); + t.resize(y.size() + shift + 1, y.size() + shift); bool truncated_t = !CppInt1::variable && (t.size() != y.size() + shift + 1); typename CppInt1::limb_pointer pt = t.limbs(); for(unsigned i = 0; i < shift; ++i) @@ -235,12 +235,18 @@ void divide_unsigned_helper( t.resize(t.size() - 1, t.size() - 1); } // - // Update r: + // Update r in a way that won't actually produce a negative result + // in case the argument types are unsigned: // - eval_subtract(r, t); - if(r.isneg()) + if(r.compare(t) > 0) { - r.negate(); + eval_subtract(r, t); + } + else + { + r.swap(t); + eval_subtract(r, t); + prem = r.limbs(); r_neg = !r_neg; } // @@ -272,11 +278,13 @@ void divide_unsigned_helper( // We have one too many in the result: if(result) eval_decrement(*result); - r.negate(); if(y.sign()) + { + r.negate(); eval_subtract(r, y); + } else - eval_add(r, y); + eval_subtract(r, y, r); } BOOST_ASSERT(r.compare_unsigned(y) < 0); // remainder must be less than the divisor or our code has failed diff --git a/include/boost/multiprecision/cpp_int/misc.hpp b/include/boost/multiprecision/cpp_int/misc.hpp index 04178687..b440aab8 100644 --- a/include/boost/multiprecision/cpp_int/misc.hpp +++ b/include/boost/multiprecision/cpp_int/misc.hpp @@ -110,7 +110,14 @@ inline typename enable_if_c& a) BOOST_NOEXCEPT { using default_ops::eval_get_sign; - BOOST_ASSERT(eval_get_sign(a) != 0); + if(eval_get_sign(a) == 0) + { + BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand.")); + } + if(a.sign()) + { + BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined.")); + } unsigned result = 0; // diff --git a/include/boost/multiprecision/detail/integer_ops.hpp b/include/boost/multiprecision/detail/integer_ops.hpp index c58791f6..06df91ab 100644 --- a/include/boost/multiprecision/detail/integer_ops.hpp +++ b/include/boost/multiprecision/detail/integer_ops.hpp @@ -241,6 +241,16 @@ inline typename enable_if_c::value == number_kind_integ namespace detail{ +// +// Within powm, we need a type with twice as many digits as the argument type, define +// a traits class to obtain that type: +// +template +struct double_precision_type +{ + typedef Backend type; +}; + // // Calculate (a^p)%c: // @@ -253,29 +263,34 @@ void eval_powm(Backend& result, const Backend& a, const Backend& p, const Backen using default_ops::eval_modulus; using default_ops::eval_right_shift; - typedef typename canonical::type ui_type; + typedef typename double_precision_type::type double_type; + typedef typename canonical::type ui_type; - Backend x, y(a), b(p); + double_type x, y(a), b(p), t; x = ui_type(1u); + while(eval_get_sign(b) > 0) { if(eval_bit_test(b, 0)) { - eval_multiply(result, x, y); - eval_modulus(x, result, c); + eval_multiply(t, x, y); + eval_modulus(x, t, c); } - eval_multiply(result, y, y); - eval_modulus(y, result, c); + eval_multiply(t, y, y); + eval_modulus(y, t, c); eval_right_shift(b, ui_type(1)); } - eval_modulus(result, x, c); + Backend x2(x); + eval_modulus(result, x2, c); } template void eval_powm(Backend& result, const Backend& a, const Backend& p, Integer c) { - typedef typename canonical::type ui_type; - typedef typename canonical::type i_type; + typedef typename double_precision_type::type double_type; + typedef typename canonical::type ui_type; + typedef typename canonical::type i1_type; + typedef typename canonical::type i2_type; using default_ops::eval_bit_test; using default_ops::eval_get_sign; @@ -288,27 +303,29 @@ void eval_powm(Backend& result, const Backend& a, const Backend& p, Integer c) BOOST_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent.")); } - Backend x, y(a), b(p); + double_type x, y(a), b(p), t; x = ui_type(1u); + while(eval_get_sign(b) > 0) { if(eval_bit_test(b, 0)) { - eval_multiply(result, x, y); - eval_modulus(x, result, static_cast(c)); + eval_multiply(t, x, y); + eval_modulus(x, t, static_cast(c)); } - eval_multiply(result, y, y); - eval_modulus(y, result, static_cast(c)); + eval_multiply(t, y, y); + eval_modulus(y, t, static_cast(c)); eval_right_shift(b, ui_type(1)); } - eval_modulus(result, x, static_cast(c)); + Backend x2(x); + eval_modulus(result, x2, static_cast(c)); } template typename enable_if >::type eval_powm(Backend& result, const Backend& a, Integer b, const Backend& c) { - typedef typename canonical::type ui_type; - typedef typename canonical::type i_type; + typedef typename double_precision_type::type double_type; + typedef typename canonical::type ui_type; using default_ops::eval_bit_test; using default_ops::eval_get_sign; @@ -316,20 +333,22 @@ typename enable_if >::type eval_powm(Backend& result, const using default_ops::eval_modulus; using default_ops::eval_right_shift; - Backend x, y(a); + double_type x, y(a), t; x = ui_type(1u); + while(b > 0) { if(b & 1) { - eval_multiply(result, x, y); - eval_modulus(x, result, c); + eval_multiply(t, x, y); + eval_modulus(x, t, c); } - eval_multiply(result, y, y); - eval_modulus(y, result, c); + eval_multiply(t, y, y); + eval_modulus(y, t, c); b >>= 1; } - eval_modulus(result, x, c); + Backend x2(x); + eval_modulus(result, x2, c); } template @@ -345,8 +364,9 @@ typename enable_if >::type eval_powm(Backend& result, const B template typename enable_if >::type eval_powm(Backend& result, const Backend& a, Integer1 b, Integer2 c) { - typedef typename canonical::type ui_type; - typedef typename canonical::type i1_type; + typedef typename double_precision_type::type double_type; + typedef typename canonical::type ui_type; + typedef typename canonical::type i1_type; typedef typename canonical::type i2_type; using default_ops::eval_bit_test; @@ -355,20 +375,22 @@ typename enable_if >::type eval_powm(Backend& result, cons using default_ops::eval_modulus; using default_ops::eval_right_shift; - Backend x, y(a); + double_type x, y(a), t; x = ui_type(1u); + while(b > 0) { if(b & 1) { - eval_multiply(result, x, y); - eval_modulus(x, result, static_cast(c)); + eval_multiply(t, x, y); + eval_modulus(x, t, static_cast(c)); } - eval_multiply(result, y, y); - eval_modulus(y, result, static_cast(c)); + eval_multiply(t, y, y); + eval_modulus(y, t, static_cast(c)); b >>= 1; } - eval_modulus(result, x, static_cast(c)); + Backend x2(x); + eval_modulus(result, x2, static_cast(c)); } template diff --git a/include/boost/multiprecision/gmp.hpp b/include/boost/multiprecision/gmp.hpp index 6df42b62..e09c2bdc 100644 --- a/include/boost/multiprecision/gmp.hpp +++ b/include/boost/multiprecision/gmp.hpp @@ -1593,6 +1593,15 @@ inline typename enable_if_c::value && ((sizeof(I) <= sizeof(long))) inline unsigned eval_lsb(const gmp_int& val) { + int c = eval_get_sign(val); + if(c == 0) + { + BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand.")); + } + if(c < 0) + { + BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined.")); + } return mpz_scan1(val.data(), 0); } diff --git a/include/boost/multiprecision/integer.hpp b/include/boost/multiprecision/integer.hpp new file mode 100644 index 00000000..0e0075fb --- /dev/null +++ b/include/boost/multiprecision/integer.hpp @@ -0,0 +1,174 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_INTEGER_HPP +#define BOOST_MP_INTEGER_HPP + +#include + +namespace boost{ +namespace multiprecision{ + +template +typename enable_if_c::value && is_integral::value, Integer>::type + multiply(Integer& result, const I2& a, const I2& b) +{ + return result = static_cast(a) * static_cast(b); +} +template +typename enable_if_c::value && is_integral::value, Integer>::type + add(Integer& result, const I2& a, const I2& b) +{ + return result = static_cast(a) + static_cast(b); +} +template +typename enable_if_c::value && is_integral::value, Integer>::type + subtract(Integer& result, const I2& a, const I2& b) +{ + return result = static_cast(a) - static_cast(b); +} + +template +typename enable_if_c::value>::type divide_qr(const Integer& x, const Integer& y, Integer& q, Integer& r) +{ + q = x / y; + r = x % y; +} + +template +typename enable_if_c::value && is_integral::value, I2>::type integer_modulus(const I1& x, I2 val) +{ + return static_cast(x % val); +} + +namespace detail{ +// +// Figure out the kind of integer that has twice as many bits as some builtin +// integer type I. Use a native type if we can (including types which may not +// be recognised by boost::int_t because they're larger than long long), +// otherwise synthesize a cpp_int to do the job. +// +template +struct double_integer +{ + static const unsigned int_t_digits = + 2 * sizeof(I) <= sizeof(long long) ? std::numeric_limits::digits * 2 : 1; + + typedef typename mpl::if_c< + 2 * sizeof(I) <= sizeof(long long), + typename mpl::if_c< + is_signed::value, + typename boost::int_t::least, + typename boost::uint_t::least + >::type, + typename mpl::if_c< + 2 * sizeof(I) <= sizeof(double_limb_type), + typename mpl::if_c< + is_signed::value, + signed_double_limb_type, + double_limb_type + >::type, + number::value ? signed_magnitude : unsigned_magnitude), unchecked, void> > + >::type + >::type type; +}; + +} + +template +typename enable_if_c::value && is_integral::value && is_integral::value, I1>::type + powm(const I1& a, I2 b, I3 c) +{ + typedef typename detail::double_integer::type double_type; + + I1 x(1), y(a); + double_type result; + + while(b > 0) + { + if(b & 1) + { + multiply(result, x, y); + x = integer_modulus(result, c); + } + multiply(result, y, y); + y = integer_modulus(result, c); + b >>= 1; + } + return x % c; +} + +template +typename enable_if_c::value, unsigned>::type lsb(const Integer& val) +{ + if(val == 0) + { + BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand.")); + } + if(val < 0) + { + BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined.")); + } + unsigned index = 0; + Integer mask = 1; + + while(((mask & val) == 0) && (index < sizeof(Integer) * CHAR_BIT)) + { + ++index; + mask <<= 1; + } + return index; +} + +template +typename enable_if_c::value, bool>::type bit_test(const Integer& val, unsigned index) +{ + Integer mask = 1; + if(index >= sizeof(Integer) * CHAR_BIT) + return 0; + if(index) + mask <<= index; + return val & mask ? true : false; +} + +template +typename enable_if_c::value, Integer&>::type bit_set(Integer& val, unsigned index) +{ + Integer mask = 1; + if(index >= sizeof(Integer) * CHAR_BIT) + return val; + if(index) + mask <<= index; + val |= mask; + return val; +} + +template +typename enable_if_c::value, Integer&>::type bit_unset(Integer& val, unsigned index) +{ + Integer mask = 1; + if(index >= sizeof(Integer) * CHAR_BIT) + return val; + if(index) + mask <<= index; + val &= ~mask; + return val; +} + +template +typename enable_if_c::value, Integer&>::type bit_flip(Integer& val, unsigned index) +{ + Integer mask = 1; + if(index >= sizeof(Integer) * CHAR_BIT) + return val; + if(index) + mask <<= index; + val ^= mask; + return val; +} + +}} // namespaces + +#endif diff --git a/include/boost/multiprecision/miller_rabin.hpp b/include/boost/multiprecision/miller_rabin.hpp index f9579532..f386c5c3 100644 --- a/include/boost/multiprecision/miller_rabin.hpp +++ b/include/boost/multiprecision/miller_rabin.hpp @@ -7,12 +7,14 @@ #define BOOST_MP_MR_HPP #include +#include namespace boost{ namespace multiprecision{ +namespace detail{ -template -bool check_small_factors(const number& n) +template +bool check_small_factors(const I& n) { static const boost::uint32_t small_factors1[] = { 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u }; @@ -117,22 +119,37 @@ inline bool is_small_prime(unsigned n) return false; } -template -typename enable_if_c::value == number_kind_integer, bool>::type - miller_rabin_test(const number& n, unsigned trials, Engine& gen) +template +typename enable_if_c::value, unsigned>::type + cast_to_unsigned(const I& val) +{ + return static_cast(val); +} +template +typename disable_if_c::value, unsigned>::type + cast_to_unsigned(const I& val) +{ + return val.template convert_to(); +} + +} // namespace detail + +template +typename enable_if_c::value == number_kind_integer, bool>::type + miller_rabin_test(const I& n, unsigned trials, Engine& gen) { #ifdef BOOST_MSVC #pragma warning(push) #pragma warning(disable:4127) #endif - typedef number number_type; + typedef I number_type; if(n <= 227) - return is_small_prime(n.template convert_to()); + return detail::is_small_prime(detail::cast_to_unsigned(n)); if((n & 1) == 0) return false; - if(!check_small_factors(n)) + if(!detail::check_small_factors(n)) return false; number_type nm1 = n - 1; @@ -144,15 +161,12 @@ typename enable_if_c::value == number_kind_integer, boo if(x != 1u) return false; - q = (n - 1) >> 1; - unsigned k = 1; - while((q & 1) == 0) - { - q >>= 1; - ++k; - } + q = n - 1; + unsigned k = lsb(q); + q >>= k; + // Declare our random number generator: - boost::random::uniform_int_distribution dist(0, n); + boost::random::uniform_int_distribution dist(2, n - 2); // // Execute the trials: // @@ -169,7 +183,7 @@ typename enable_if_c::value == number_kind_integer, boo return false; // test failed if(++j == k) return false; // failed - y = (y * y) % n; + y = powm(y, 2, n); } } return true; // Yeheh! probably prime. @@ -178,8 +192,9 @@ typename enable_if_c::value == number_kind_integer, boo #endif } -template -bool miller_rabin_test(const number& x, unsigned trials) +template +typename enable_if_c::value == number_kind_integer, bool>::type + miller_rabin_test(const I& x, unsigned trials) { static mt19937 gen; return miller_rabin_test(x, trials, gen); diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index 51bd8fb1..26571832 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -88,7 +88,7 @@ public: } */ template - BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.m_backend) {} + BOOST_FORCEINLINE BOOST_CONSTEXPR number(const number& val) BOOST_NOEXCEPT_IF(noexcept(Backend(static_cast(std::declval())))) : m_backend(val.backend()) {} template BOOST_FORCEINLINE number(const number& val, diff --git a/include/boost/multiprecision/random.hpp b/include/boost/multiprecision/random.hpp index 6d0518a6..fefba1b9 100644 --- a/include/boost/multiprecision/random.hpp +++ b/include/boost/multiprecision/random.hpp @@ -8,6 +8,11 @@ #ifndef BOOST_MP_RANDOM_HPP #define BOOST_MP_RANDOM_HPP +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4127) +#endif + #include namespace boost{ namespace random{ namespace detail{ @@ -50,7 +55,10 @@ public: { return 0; } // This is the only function we modify compared to the primary template: static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () - { return (result_type(1) << w) - 1; } + { + // This expression allows for the possibility that w == std::numeric_limits::digits: + return (((result_type(1) << (w - 1)) - 1) << 1) + 1; + } independent_bits_engine() { } @@ -572,4 +580,8 @@ inline boost::multiprecision::number }} // namespaces +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + #endif diff --git a/include/boost/multiprecision/tommath.hpp b/include/boost/multiprecision/tommath.hpp index 686ef7e8..0b7fe911 100644 --- a/include/boost/multiprecision/tommath.hpp +++ b/include/boost/multiprecision/tommath.hpp @@ -588,6 +588,15 @@ inline void eval_qr(const tommath_int& x, const tommath_int& y, inline unsigned eval_lsb(const tommath_int& val) { + int c = eval_get_sign(val); + if(c == 0) + { + BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand.")); + } + if(c < 0) + { + BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined.")); + } return mp_cnt_lsb(const_cast< ::mp_int*>(&val.data())); } diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 8b3328d5..8d9cc239 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -821,6 +821,7 @@ run ../example/tommath_snips.cpp $(TOMMATH) [ check-target-builds ../config//has_tommath : : no ] ; run ../example/floating_point_examples.cpp : : : gcc:-std=c++0x ; run test_cpp_int_conv.cpp ; +run test_native_integer.cpp ; run test_mixed_cpp_int.cpp ; run test_mixed_float.cpp diff --git a/test/test_miller_rabin.cpp b/test/test_miller_rabin.cpp index d8f9f9a2..ec12ab8b 100644 --- a/test/test_miller_rabin.cpp +++ b/test/test_miller_rabin.cpp @@ -3,14 +3,21 @@ // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + #include +#include #include #include #include #include #include "test.hpp" -int main() + +template +void test() { // // Very simple test program to verify that the GMP's Miller-Rabin @@ -22,7 +29,14 @@ int main() using namespace boost::random; using namespace boost::multiprecision; - independent_bits_engine gen; + typedef I test_type; + + static const unsigned test_bits = + std::numeric_limits::digits && (std::numeric_limits::digits <= 256) + ? std::numeric_limits::digits + : 128; + + independent_bits_engine gen; // // We must use a different generator for the tests and number generation, otherwise // we get false positives. Further we use the same random number engine for the @@ -35,16 +49,17 @@ int main() // for(unsigned i = 1; i < boost::math::max_prime; ++i) { - BOOST_TEST(miller_rabin_test(mpz_int(boost::math::prime(i)), 25, gen)); + BOOST_TEST(miller_rabin_test(test_type(boost::math::prime(i)), 25, gen)); + BOOST_TEST(mpz_probab_prime_p(mpz_int(boost::math::prime(i)).backend().data(), 25)); } // // Now test some random values and compare GMP's native routine with ours. // for(unsigned i = 0; i < 10000; ++i) { - mpz_int n = gen(); + test_type n = gen(); bool is_prime_boost = miller_rabin_test(n, 25, gen2); - bool is_gmp_prime = mpz_probab_prime_p(n.backend().data(), 25); + bool is_gmp_prime = mpz_probab_prime_p(mpz_int(n).backend().data(), 25) ? true : false; if(is_prime_boost && is_gmp_prime) { std::cout << "We have a prime: " << std::hex << std::showbase << n << std::endl; @@ -53,7 +68,23 @@ int main() std::cout << std::hex << std::showbase << "n = " << n << std::endl; BOOST_CHECK_EQUAL(is_prime_boost, is_gmp_prime); } - return 0; +} + +int main() +{ + using namespace boost::multiprecision; + + test(); + test >(); + test(); + test(); + + test(); + test, et_off> >(); + test(); + test(); + + return boost::report_errors(); } diff --git a/test/test_native_integer.cpp b/test/test_native_integer.cpp new file mode 100644 index 00000000..7ed79323 --- /dev/null +++ b/test/test_native_integer.cpp @@ -0,0 +1,79 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include +#include "test.hpp" + +#ifdef BOOST_MSVC +#pragma warning(disable:4146) +#endif + +template +void test() +{ + using namespace boost::multiprecision; + + I i(0); + + BOOST_CHECK_THROW(lsb(i), std::range_error); + BOOST_CHECK(bit_test(bit_set(i, 0), 0)); + BOOST_CHECK_EQUAL(bit_set(i, 0), 1); + BOOST_CHECK_EQUAL(bit_unset(i, 0), 0); + BOOST_CHECK_EQUAL(bit_flip(bit_set(i, 0), 0), 0); + + unsigned max_index = (std::numeric_limits::digits) - 1; + BOOST_CHECK(bit_test(bit_set(i, max_index), max_index)); + BOOST_CHECK_EQUAL(bit_unset(i, max_index), 0); + BOOST_CHECK_EQUAL(bit_flip(bit_set(i, max_index), max_index), 0); + + if(std::numeric_limits::is_signed) + { + i = -1; + BOOST_CHECK_THROW(lsb(i), std::range_error); + } + + H mx = (std::numeric_limits::max)(); + + BOOST_CHECK_EQUAL(multiply(i, mx, mx), static_cast(mx) * static_cast(mx)); + BOOST_CHECK_EQUAL(add(i, mx, mx), static_cast(mx) + static_cast(mx)); + if(std::numeric_limits::is_signed) + { + BOOST_CHECK_EQUAL(subtract(i, mx, static_cast(-mx)), static_cast(mx) - static_cast(-mx)); + BOOST_CHECK_EQUAL(add(i, static_cast(-mx), static_cast(-mx)), static_cast(-mx) + static_cast(-mx)); + } + + i = (std::numeric_limits::max)(); + I j = 12345; + I r, q; + divide_qr(i, j, q, r); + BOOST_CHECK_EQUAL(q, i / j); + BOOST_CHECK_EQUAL(r, i % j); + BOOST_CHECK_EQUAL(integer_modulus(i, j), i % j); + I p = 456; + BOOST_CHECK_EQUAL(powm(i, p, j), pow(cpp_int(i), static_cast(p)) % j); +} + +int main() +{ + using namespace boost::multiprecision; + + test(); + test(); + test(); + test(); + + return boost::report_errors(); +} + + + From 4071dd8d59b0310450367edbd917893e31040abc Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 13 Nov 2012 17:12:19 +0000 Subject: [PATCH 256/256] Fix missing number constructor. Fix is_explicitly_convertible to take account of the generic conversions. Change sf_performance to use multiple files so we can actually compile the thing! Minor doc updates. Suppress some more warnings. [SVN r81324] --- .../boost_multiprecision/indexes/s01.html | 4 +- .../boost_multiprecision/indexes/s02.html | 4 +- .../boost_multiprecision/indexes/s03.html | 4 +- .../boost_multiprecision/indexes/s04.html | 4 +- doc/html/boost_multiprecision/intro.html | 7 + doc/html/boost_multiprecision/map/faq.html | 2 +- doc/html/boost_multiprecision/map/hist.html | 3 + doc/html/boost_multiprecision/map/todo.html | 17 +- doc/html/boost_multiprecision/ref/number.html | 24 +- .../tut/floats/cpp_dec_float.html | 9 +- doc/html/index.html | 2 +- doc/multiprecision.qbk | 34 +- include/boost/multiprecision/cpp_int.hpp | 2 +- include/boost/multiprecision/cpp_int/misc.hpp | 9 + .../detail/generic_interconvert.hpp | 2 +- include/boost/multiprecision/number.hpp | 7 + .../boost/multiprecision/rational_adapter.hpp | 2 +- .../traits/explicit_conversion.hpp | 37 +- performance/Jamfile.v2 | 4 +- performance/sf_performance.cpp | 412 +----------------- performance/sf_performance_basic.cpp | 49 +++ performance/sf_performance_bessel.cpp | 42 ++ performance/sf_performance_bessel1.cpp | 23 + performance/sf_performance_bessel2.cpp | 17 + performance/sf_performance_bessel3.cpp | 16 + performance/sf_performance_bessel4.cpp | 15 + performance/sf_performance_bessel5.cpp | 17 + performance/sf_performance_bessel6.cpp | 19 + performance/sf_performance_nct.cpp | 39 ++ performance/sf_performance_nct1.cpp | 15 + performance/sf_performance_nct2.cpp | 14 + performance/sf_performance_nct3.cpp | 22 + performance/sf_performance_nct4.cpp | 15 + performance/sf_performance_nct5.cpp | 14 + performance/sf_performance_nct6.cpp | 22 + performance/sf_performance_poly.cpp | 66 +++ test/test_atan.cpp | 4 + test/test_float_io.cpp | 6 +- test/test_int_io.cpp | 4 + test/test_native_integer.cpp | 2 +- test/test_numeric_limits.cpp | 4 + test/test_rational_io.cpp | 1 - test/test_round.cpp | 4 + 43 files changed, 564 insertions(+), 455 deletions(-) create mode 100644 performance/sf_performance_basic.cpp create mode 100644 performance/sf_performance_bessel.cpp create mode 100644 performance/sf_performance_bessel1.cpp create mode 100644 performance/sf_performance_bessel2.cpp create mode 100644 performance/sf_performance_bessel3.cpp create mode 100644 performance/sf_performance_bessel4.cpp create mode 100644 performance/sf_performance_bessel5.cpp create mode 100644 performance/sf_performance_bessel6.cpp create mode 100644 performance/sf_performance_nct.cpp create mode 100644 performance/sf_performance_nct1.cpp create mode 100644 performance/sf_performance_nct2.cpp create mode 100644 performance/sf_performance_nct3.cpp create mode 100644 performance/sf_performance_nct4.cpp create mode 100644 performance/sf_performance_nct5.cpp create mode 100644 performance/sf_performance_nct6.cpp create mode 100644 performance/sf_performance_poly.cpp diff --git a/doc/html/boost_multiprecision/indexes/s01.html b/doc/html/boost_multiprecision/indexes/s01.html index 95db893b..6f80e7e7 100644 --- a/doc/html/boost_multiprecision/indexes/s01.html +++ b/doc/html/boost_multiprecision/indexes/s01.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
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    +

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    diff --git a/doc/html/boost_multiprecision/indexes/s02.html b/doc/html/boost_multiprecision/indexes/s02.html index 74da4b03..5cb232f6 100644 --- a/doc/html/boost_multiprecision/indexes/s02.html +++ b/doc/html/boost_multiprecision/indexes/s02.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
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    diff --git a/doc/html/boost_multiprecision/indexes/s03.html b/doc/html/boost_multiprecision/indexes/s03.html index 0aea103d..f5f32e2a 100644 --- a/doc/html/boost_multiprecision/indexes/s03.html +++ b/doc/html/boost_multiprecision/indexes/s03.html @@ -13,9 +13,9 @@
    PrevUpHomeNext
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    +

    -Typedef Index

    +Typedef Index

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    diff --git a/doc/html/boost_multiprecision/indexes/s04.html b/doc/html/boost_multiprecision/indexes/s04.html index 77ea931e..fee56997 100644 --- a/doc/html/boost_multiprecision/indexes/s04.html +++ b/doc/html/boost_multiprecision/indexes/s04.html @@ -12,9 +12,9 @@
    PrevUpHome
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    +Index

    A B C D E F G I L M N O P R S T U Z

    diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index 66275daf..9f845bbe 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -47,6 +47,13 @@ back-ends rely on 3rd party libraries, but a header-only Boost license version is always available (if somewhat slower).

    +

    + Should you just wish to cut to the chase and use a fully Boost-licensed number + type, then skip to cpp_int + for multiprecision integers, cpp_dec_float + for multiprecision floating point types and cpp_rational + for rational types. +

    The library is often used via one of the predefined typedefs: for example if you wanted an arbitrary diff --git a/doc/html/boost_multiprecision/map/faq.html b/doc/html/boost_multiprecision/map/faq.html index 887b9ad4..5df05580 100644 --- a/doc/html/boost_multiprecision/map/faq.html +++ b/doc/html/boost_multiprecision/map/faq.html @@ -77,7 +77,7 @@

    Why can't I negate an unsigned type?

    The unary negation operator is deliberately disabled for unsigned integer - types as it's use would almost always be a programming error. + types as its use would almost always be a programming error.

    Why doesn't the library use proto?

    diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html index 8a324bdd..bb5e3493 100644 --- a/doc/html/boost_multiprecision/map/hist.html +++ b/doc/html/boost_multiprecision/map/hist.html @@ -67,6 +67,9 @@ Added section on mixed precision arithmetic, and added support for operations yielding a higher precision result than either of the arguments. +

  • + Added overloads of integer-specific functions for built in integer types. +
    • diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index 8f453970..f8aa94a5 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -51,15 +51,18 @@
  • We can reuse temporaries in multiple subtrees (temporary caching).
    • +
  • + cpp_dec_float should round to nearest. +
    • +
  • + A 2's complement fixed precision int that uses exactly N bits and no + more. +

    • Things requested in review:

      -
    • - A 2's complement fixed precision int that uses exactly N bits and no - more. -
    • The performances of mp_number<a_trivial_adaptor<float>, false>respect to float and mp_number<a_trivial_adaptor<int>, false> and @@ -67,10 +70,8 @@ done, just need to update docs to the latest results).
    • - cpp_dec_float should round to nearest. -
      • -
    • - Should we provide min/max overloads for expression templates? + Should we provide min/max overloads for expression templates? (Not done + - we can't overload functions declared in the std namespace :-( ).
    • The rounding applied when converting must be documented (Done). diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html index 77aeb478..e1c5c399 100644 --- a/doc/html/boost_multiprecision/ref/number.html +++ b/doc/html/boost_multiprecision/ref/number.html @@ -1093,21 +1093,33 @@ Integer functions
    +

    + In addition to functioning with types from this library, these functions + are also overloaded for built in integer types if you include <boost/multiprecision/integer.hpp>. + Further, when used with fixed precision types (whether built in integers + or multiprecision ones), the functions will promote to a wider type internally + when the algorithm requires it. Versions overloaded for built in integer + types return that integer type rather than an expression template. + 

    unmentionable-expression-template-type    pow(const number-or-expression-template-type& b, unsigned p);

    Returns bp as an expression template. Note that this function should be used with extreme care as the result can grow so large as to take "effectively forever" to compute, or else simply run - the host machine out of memory. + the host machine out of memory. This is the one function in this category + that is not overloaded for built in integer types, further, it's probably + not a good idea to use it with fixed precision cpp_int's + either. 

    unmentionable-expression-template-type    powm(const number-or-expression-template-type& b, const number-or-expression-template-type& p, const number-or-expression-template-type& m);

    - Returns bp mod m as an expression template. + Returns bp mod m as an expression template. Fixed precision + types are promoted internally to ensure accuracy. 

    template <class Backend, expression_template_option ExpressionTemplates>
-bool divide_qr(const number-or-expression-template-type& x, const number-or-expression-template-type& y,
+void divide_qr(const number-or-expression-template-type& x, const number-or-expression-template-type& y,
                number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r);

    @@ -1128,6 +1140,9 @@

    Returns the index of the least significant bit that is set to 1.

    +

    + Throws a std::range_error if the argument is <= 0. + 

    template <class Backend, class ExpressionTemplates>
 bool bit_test(const number<Backend, ExpressionTemplates>& val, unsigned index);
    @@ -1167,7 +1182,8 @@ Miller-Rabin tests. Returns false if n is definitely composite, or true if n is probably prime with the probability of it being - composite less than 0.25^trials. + composite less than 0.25^trials. Fixed precision types are promoted internally + to ensure accuracy.

    diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html index f3909b91..b671a7b9 100644 --- a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html +++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html @@ -51,7 +51,7 @@

    Normally cpp_dec_float - allocates no memory: all of the space required for it's digits are allocated + allocates no memory: all of the space required for its digits are allocated directly within the class. As a result care should be taken not to use the class with too high a digit count as stack space requirements can grow out of control. If that represents a problem then providing an allocator @@ -59,7 +59,7 @@ to dynamically allocate the memory it needs: this significantly reduces the size of cpp_dec_float and increases the viable upper limit on the number of digits at the expense - of performance. However, please bare in mind that arithmetic operations + of performance. However, please bear in mind that arithmetic operations rapidly become very expensive as the digit count grows: the current implementation really isn't optimized or designed for large digit counts. @@ -80,11 +80,6 @@ The radix of this type is 10. As a result it can behave subtly differently from base-2 types. -

  • - It is not possible to round-trip this type to and from a string and - get back to exactly the same value (this is a result of the type having - some hidden internal guard digits). -
  • The type has a number of internal guard digits over and above those specified in the template argument. Normally these should not be visible diff --git a/doc/html/index.html b/doc/html/index.html index 0e5cb43d..8445dad1 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -125,7 +125,7 @@ - +

    Last revised: November 03, 2012 at 18:24:27 GMT

    Last revised: November 12, 2012 at 19:14:07 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index 051ff313..131b5ccc 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -80,6 +80,10 @@ where possible, but provides Boost license alternatives for users who must have unconstrained license. Which is to say some back-ends rely on 3rd party libraries, but a header-only Boost license version is always available (if somewhat slower). +Should you just wish to cut to the chase and use a fully Boost-licensed number type, then skip to +__cpp_int for multiprecision integers, __cpp_dec_float for multiprecision floating point types +and __cpp_rational for rational types. + The library is often used via one of the predefined typedefs: for example if you wanted an [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] integer type using [gmp] as the underlying implementation then you could use: @@ -625,12 +629,12 @@ respectively. Optionally, you can specify an integer type to use for the expone which is more than large enough for the vast majority of use cases, but larger types such as `long long` can also be specified if you need a truely huge exponent range. -Normally `cpp_dec_float` allocates no memory: all of the space required for it's digits are allocated +Normally `cpp_dec_float` allocates no memory: all of the space required for its digits are allocated directly within the class. As a result care should be taken not to use the class with too high a digit count as stack space requirements can grow out of control. If that represents a problem then providing an allocator as the final template parameter causes `cpp_dec_float` to dynamically allocate the memory it needs: this significantly reduces the size of `cpp_dec_float` and increases the viable upper limit on the number of digits -at the expense of performance. However, please bare in mind that arithmetic operations rapidly become ['very] expensive +at the expense of performance. However, please bear in mind that arithmetic operations rapidly become ['very] expensive as the digit count grows: the current implementation really isn't optimized or designed for large digit counts. There is full standard library and `numeric_limits` support available for this type. @@ -639,8 +643,6 @@ Things you should know when using this type: * Default constructed `cpp_dec_float`s have a value of zero. * The radix of this type is 10. As a result it can behave subtly differently from base-2 types. -* It is not possible to round-trip this type to and from a string and get back to exactly the same value -(this is a result of the type having some hidden internal guard digits). * The type has a number of internal guard digits over and above those specified in the template argument. Normally these should not be visible to the user. * The type supports both infinities and NaN's. An infinity is generated whenever the result would overflow, @@ -1864,14 +1866,22 @@ A traits class that inherits from `mpl::true_` if T is an expression template ty [h4 Integer functions] +In addition to functioning with types from this library, these functions are also overloaded for built in integer +types if you include ``. Further, when used with fixed precision types (whether +built in integers or multiprecision ones), the functions will promote to a wider type internally when the algorithm +requires it. Versions overloaded for built in integer types return that integer type rather than an expression +template. + ``['unmentionable-expression-template-type]`` pow(const ``['number-or-expression-template-type]``& b, unsigned p); Returns ['b[super p]] as an expression template. Note that this function should be used with extreme care as the result can grow so -large as to take "effectively forever" to compute, or else simply run the host machine out of memory. +large as to take "effectively forever" to compute, or else simply run the host machine out of memory. This is the one function in +this category that is not overloaded for built in integer types, further, it's probably not a good idea to use it with +fixed precision `cpp_int`'s either. ``['unmentionable-expression-template-type]`` powm(const ``['number-or-expression-template-type]``& b, const ``['number-or-expression-template-type]``& p, const ``['number-or-expression-template-type]``& m); -Returns ['b[super p] mod m] as an expression template. +Returns ['b[super p] mod m] as an expression template. Fixed precision types are promoted internally to ensure accuracy. template void divide_qr(const ``['number-or-expression-template-type]``& x, const ``['number-or-expression-template-type]``& y, @@ -1917,7 +1927,8 @@ Flips the bit at /index/ in /val/, and returns /val/. Tests to see if the number /n/ is probably prime - the test excludes the vast majority of composite numbers by excluding small prime factors and performing a single Fermat test. Then performs /trials/ Miller-Rabin tests. Returns `false` if /n/ is definitely composite, or `true` if /n/ is probably prime with the -probability of it being composite less than 0.25^trials. +probability of it being composite less than 0.25^trials. Fixed precision types are promoted internally +to ensure accuracy. [h4 Rational Number Functions] @@ -3030,6 +3041,7 @@ Windows Vista machine. * Added additional template parameter to `mpfr_float_backend` to allow stack-based allocation. * Added section on mixed precision arithmetic, and added support for operations yielding a higher precision result than either of the arguments. +* Added overloads of integer-specific functions for built in integer types. [h4 Pre-review history] @@ -3061,15 +3073,15 @@ More a list of what ['could] be done, rather than what ['should] be done (which the hard part is IO and binary-decimal convertion. * Should there be a choice of rounding mode (probably MPFR specific)? * We can reuse temporaries in multiple subtrees (temporary caching). +* cpp_dec_float should round to nearest. +* A 2's complement fixed precision int that uses exactly N bits and no more. Things requested in review: -* A 2's complement fixed precision int that uses exactly N bits and no more. * The performances of mp_number, false>respect to float and mp_number, false> and int should be given to show the cost of using the generic interface (Mostly done, just need to update docs to the latest results). -* cpp_dec_float should round to nearest. -* Should we provide min/max overloads for expression templates? +* Should we provide min/max overloads for expression templates? (Not done - we can't overload functions declared in the std namespace :-( ). * The rounding applied when converting must be documented (Done). * Document why we don't abstract out addition/multiplication algorithms etc. (done - FAQ) * Document why we don't use proto (compile times) (Done). @@ -3158,7 +3170,7 @@ Open question - what should be the default - int32_t or int64_t? (done 2012/09/ complement one favored by most native integer types. As a result the complement operator is deliberately disabled for checked `cpp_int`'s. Unchecked `cpp_int`'s give the same valued result as a 2's complement type would, but not the same bit-pattern.]] [[Why can't I negate an unsigned type?] - [The unary negation operator is deliberately disabled for unsigned integer types as it's use would almost always be a programming error.]] + [The unary negation operator is deliberately disabled for unsigned integer types as its use would almost always be a programming error.]] [[Why doesn't the library use proto?] [A very early version of the library did use proto, but compile times became too slow for the library to be usable. Since the library only required a tiny fraction of what diff --git a/include/boost/multiprecision/cpp_int.hpp b/include/boost/multiprecision/cpp_int.hpp index d2397f85..be4cfcca 100644 --- a/include/boost/multiprecision/cpp_int.hpp +++ b/include/boost/multiprecision/cpp_int.hpp @@ -29,7 +29,7 @@ namespace backends{ #ifdef BOOST_MSVC // warning C4127: conditional expression is constant #pragma warning(push) -#pragma warning(disable:4127 4351 4293 4996 4307) +#pragma warning(disable:4127 4351 4293 4996 4307 4702) #endif template >::type > diff --git a/include/boost/multiprecision/cpp_int/misc.hpp b/include/boost/multiprecision/cpp_int/misc.hpp index b440aab8..217c9f8c 100644 --- a/include/boost/multiprecision/cpp_int/misc.hpp +++ b/include/boost/multiprecision/cpp_int/misc.hpp @@ -8,6 +8,11 @@ #ifndef BOOST_MP_CPP_INT_MISC_HPP #define BOOST_MP_CPP_INT_MISC_HPP +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4702) +#endif + namespace boost{ namespace multiprecision{ namespace backends{ template @@ -303,6 +308,10 @@ inline typename enable_if_c< *result = static_cast(*val.limbs()); } +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + }}} // namespaces #endif diff --git a/include/boost/multiprecision/detail/generic_interconvert.hpp b/include/boost/multiprecision/detail/generic_interconvert.hpp index 526ec86a..63ec0191 100644 --- a/include/boost/multiprecision/detail/generic_interconvert.hpp +++ b/include/boost/multiprecision/detail/generic_interconvert.hpp @@ -77,7 +77,7 @@ void generic_interconvert(To& to, const From& from, const mpl::int_(0); + limb_type mask = static_cast(~static_cast(0)); From fl; eval_bitwise_and(fl, t, mask); eval_convert_to(&limb, fl); diff --git a/include/boost/multiprecision/number.hpp b/include/boost/multiprecision/number.hpp index 26571832..b408a36f 100644 --- a/include/boost/multiprecision/number.hpp +++ b/include/boost/multiprecision/number.hpp @@ -176,6 +176,13 @@ public: { *this = e; } + template + explicit number(const detail::expression& e, + typename enable_if_c::result_type, self_type>::value + && boost::multiprecision::detail::is_explicitly_convertible::result_type, self_type>::value>::type* = 0) + { + assign(e); + } #ifndef BOOST_NO_RVALUE_REFERENCES BOOST_FORCEINLINE BOOST_CONSTEXPR number(number&& r) BOOST_NOEXCEPT : m_backend(static_cast(r.m_backend)){} diff --git a/include/boost/multiprecision/rational_adapter.hpp b/include/boost/multiprecision/rational_adapter.hpp index 1c8a69cb..d2c5c3b7 100644 --- a/include/boost/multiprecision/rational_adapter.hpp +++ b/include/boost/multiprecision/rational_adapter.hpp @@ -13,7 +13,7 @@ #include #ifdef BOOST_MSVC # pragma warning(push) -# pragma warning(disable:4512) +# pragma warning(disable:4512 4127) #endif #include #ifdef BOOST_MSVC diff --git a/include/boost/multiprecision/traits/explicit_conversion.hpp b/include/boost/multiprecision/traits/explicit_conversion.hpp index 842d36d1..b4cd8215 100644 --- a/include/boost/multiprecision/traits/explicit_conversion.hpp +++ b/include/boost/multiprecision/traits/explicit_conversion.hpp @@ -16,6 +16,40 @@ namespace boost{ namespace multiprecision{ namespace detail{ template struct dummy_size{}; +template +struct has_generic_interconversion +{ + typedef typename mpl::if_c< + is_number::value && is_number::value, + typename mpl::if_c< + number_category::value == number_kind_integer, + typename mpl::if_c< + number_category::value == number_kind_integer + || number_category::value == number_kind_floating_point + || number_category::value == number_kind_rational + || number_category::value == number_kind_fixed_point, + mpl::true_, + mpl::false_ + >::type, + typename mpl::if_c< + number_category::value == number_kind_rational, + typename mpl::if_c< + number_category::value == number_kind_rational + || number_category::value == number_kind_rational, + mpl::true_, + mpl::false_ + >::type, + typename mpl::if_c< + number_category::value == number_kind_floating_point, + mpl::true_, + mpl::false_ + >::type + >::type + >::type, + mpl::false_ + >::type type; +}; + template struct is_explicitly_convertible_imp { @@ -30,7 +64,8 @@ struct is_explicitly_convertible_imp typedef boost::integral_constant type; #else - typedef typename boost::is_convertible::type type; + typedef typename has_generic_interconversion::type gen_type; + typedef mpl::bool_::value || gen_type::value> type; #endif }; diff --git a/performance/Jamfile.v2 b/performance/Jamfile.v2 index eb349c69..f97fb89c 100644 --- a/performance/Jamfile.v2 +++ b/performance/Jamfile.v2 @@ -62,7 +62,9 @@ exe miller_rabin_performance : miller_rabin_performance.cpp /boost/system//boost TEST_CPP_INT ; -exe sf_performance : sf_performance.cpp /boost/system//boost_system /boost/chrono//boost_chrono /boost/thread//boost_thread +exe sf_performance : sf_performance.cpp sf_performance_basic.cpp sf_performance_bessel.cpp + sf_performance_nct.cpp sf_performance_poly.cpp + /boost/system//boost_system /boost/chrono//boost_chrono /boost/thread//boost_thread : release [ check-target-builds ../config//has_gmp : TEST_MPF TEST_MPZ gmp : ] [ check-target-builds ../config//has_mpfr : TEST_MPFR mpfr : ] diff --git a/performance/sf_performance.cpp b/performance/sf_performance.cpp index 11c60ac6..95c08d18 100644 --- a/performance/sf_performance.cpp +++ b/performance/sf_performance.cpp @@ -3,152 +3,7 @@ // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ -#define BOOST_MATH_MAX_ROOT_ITERATION_POLICY 500 -#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false - -#if !defined(TEST_MPFR) && !defined(TEST_MPREAL) && !defined(TEST_MPF) && !defined(TEST_MPREAL) \ - && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_CLASS) && !defined(TEST_FLOAT) -# define TEST_MPFR -# define TEST_MPF -# define TEST_CPP_DEC_FLOAT -# define TEST_MPFR_CLASS -# define TEST_MPREAL -# define TEST_FLOAT -#endif - -#ifdef TEST_FLOAT -#include "arithmetic_backend.hpp" -#endif -#ifdef TEST_MPFR_CLASS -#include -#endif -#ifdef TEST_MPFR -#include -#endif -#ifdef TEST_MPREAL -#include -#endif -#ifdef TEST_MPF -#include -#endif -#ifdef TEST_CPP_DEC_FLOAT -#include -#endif -#include -#include -#include -#include -#include -#include -#include - -template -Real test_bessel(); - -template -struct stopwatch -{ - typedef typename Clock::duration duration; - stopwatch() - { - m_start = Clock::now(); - } - duration elapsed() - { - return Clock::now() - m_start; - } - void reset() - { - m_start = Clock::now(); - } - -private: - typename Clock::time_point m_start; -}; - -template -Real test_bessel() -{ - try{ -# define T double -# define SC_(x) x -# include "libs/math/test/bessel_i_int_data.ipp" -# include "libs/math/test/bessel_i_data.ipp" - - Real r; - - for(unsigned i = 0; i < bessel_i_int_data.size(); ++i) - { - r += boost::math::cyl_bessel_i(Real(bessel_i_int_data[i][0]), Real(bessel_i_int_data[i][1])); - } - for(unsigned i = 0; i < bessel_i_data.size(); ++i) - { - r += boost::math::cyl_bessel_i(Real(bessel_i_data[i][0]), Real(bessel_i_data[i][1])); - } - -#include "libs/math/test/bessel_j_int_data.ipp" - for(unsigned i = 0; i < bessel_j_int_data.size(); ++i) - { - r += boost::math::cyl_bessel_j(Real(bessel_j_int_data[i][0]), Real(bessel_j_int_data[i][1])); - } - -#include "libs/math/test/bessel_j_data.ipp" - for(unsigned i = 0; i < bessel_j_data.size(); ++i) - { - r += boost::math::cyl_bessel_j(Real(bessel_j_data[i][0]), Real(bessel_j_data[i][1])); - } - -#include "libs/math/test/bessel_j_large_data.ipp" - for(unsigned i = 0; i < bessel_j_large_data.size(); ++i) - { - r += boost::math::cyl_bessel_j(Real(bessel_j_large_data[i][0]), Real(bessel_j_large_data[i][1])); - } - -#include "libs/math/test/sph_bessel_data.ipp" - for(unsigned i = 0; i < sph_bessel_data.size(); ++i) - { - r += boost::math::sph_bessel(static_cast(sph_bessel_data[i][0]), Real(sph_bessel_data[i][1])); - } - - return r; - } - catch(const std::exception& e) - { - std::cout << e.what() << std::endl; - } - return 0; -} - -template -Real test_polynomial() -{ - static const unsigned t[] = { - 2, 3, 4, 5, 6, 7, 8 }; - Real result = 0; - for(Real k = 2; k < 1000; ++k) - result += boost::math::tools::evaluate_polynomial(t, k); - - return result; -} - -template -Real test_nct() -{ -#define T double -#include "libs/math/test/nct.ipp" - - Real result = 0; - for(unsigned i = 0; i < nct.size(); ++i) - { - try{ - result += quantile(boost::math::non_central_t_distribution(nct[i][0], nct[i][1]), nct[i][3]); - } - catch(const std::exception&) - {} - result += cdf(boost::math::non_central_t_distribution(nct[i][0], nct[i][1]), nct[i][2]); - } - return result; -} +#include "sf_performance.hpp" unsigned allocation_count = 0; @@ -173,273 +28,18 @@ void * realloc_func(void * p, size_t old, size_t n) return (*realloc_func_ptr)(p, old, n); } -template -void basic_allocation_test(const char* name, Real x) -{ - static const unsigned a[] = { 2, 3, 4, 5, 6, 7, 8 }; - allocation_count = 0; - Real result = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; - std::cout << "Allocation count for type " << name << " = " << allocation_count << std::endl; -} - -template -void poly_allocation_test(const char* name, Real x) -{ - static const unsigned a[] = { 2, 3, 4, 5, 6, 7, 8 }; - allocation_count = 0; - Real result = boost::math::tools::evaluate_polynomial(a, x); - std::cout << "Allocation count for type " << name << " = " << allocation_count << std::endl; -} - -template -void time_proc(const char* name, Real (*proc)(), unsigned threads = 1) -{ - try{ - static Real total = 0; - allocation_count = 0; - boost::chrono::duration time; - stopwatch c; - total += proc(); - time = c.elapsed(); - std::cout << "Time for " << name << " = " << time << std::endl; - std::cout << "Total allocations for " << name << " = " << allocation_count << std::endl; - - for(unsigned thread_count = 1; thread_count < threads; ++thread_count) - { - c.reset(); - boost::thread_group g; - for(unsigned i = 0; i <= thread_count; ++i) - g.create_thread(proc); - g.join_all(); - time = c.elapsed(); - std::cout << "Time for " << name << " (" << (thread_count + 1) << " threads) = " << time << std::endl; - std::cout << "Total allocations for " << name << " = " << allocation_count << std::endl; - } - } - catch(const std::exception& e) - { - std::cout << e.what() << std::endl; - } -} - int main() { using namespace boost::multiprecision; + #if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) || defined(TEST_MPREAL) || defined(TEST_MPF) mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); mp_set_memory_functions(&alloc_func, &realloc_func, &free_func); #endif - std::cout << "Allocation Counts for Horner Evaluation:\n"; -#ifdef TEST_MPFR - basic_allocation_test("mpfr_float_50", mpfr_float_50(2)); - basic_allocation_test("mpfr_float_50 - no expression templates", number, et_off>(2)); -#endif -#ifdef TEST_MPFR_CLASS - basic_allocation_test("mpfr_class", mpfr_class(2)); -#endif -#ifdef TEST_MPREAL - basic_allocation_test("mpfr::mpreal", mpfr::mpreal(2)); -#endif - - std::cout << "Allocation Counts for boost::math::tools::evaluate_polynomial:\n"; -#ifdef TEST_MPFR - poly_allocation_test("mpfr_float_50", mpfr_float_50(2)); - poly_allocation_test("mpfr_float_50 - no expression templates", number, et_off>(2)); -#endif -#ifdef TEST_MPFR_CLASS - poly_allocation_test("mpfr_class", mpfr_class(2)); -#endif -#ifdef TEST_MPREAL - poly_allocation_test("mpfr::mpreal", mpfr::mpreal(2)); -#endif - - // - // Comparison for builtin floats: - // -#ifdef TEST_FLOAT - time_proc("Bessel Functions - double", test_bessel); - time_proc("Bessel Functions - real_concept", test_bessel); - time_proc("Bessel Functions - arithmetic_backend", test_bessel > >); - time_proc("Bessel Functions - arithmetic_backend - no expression templates", test_bessel, et_off> >); - - time_proc("Non-central T - double", test_nct); - time_proc("Non-central T - real_concept", test_nct); - time_proc("Non-central T - arithmetic_backend", test_nct > >); - time_proc("Non-central T - arithmetic_backend - no expression templates", test_nct, et_off> >); -#endif - - // - // 50 digits first: - // - std::cout << "Testing Bessel Functions at 50 digits....." << std::endl; -#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) - mpfr_set_default_prec(50 * 1000L / 301L); -#endif -#ifdef TEST_MPREAL - mpfr::mpreal::set_default_prec(50 * 1000L / 301L); -#endif -#ifdef TEST_MPFR -#if MPFR_VERSION, 1); - time_proc("mpfr_float_50 (no expression templates)", test_bessel, et_off> >, 1); - time_proc("static_mpfr_float_50", test_bessel, et_on> >, 1); - time_proc("static_mpfr_float_50 (no expression templates)", test_bessel, et_off> >, 1); -#else - time_proc("mpfr_float_50", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); - time_proc("mpfr_float_50 (no expression templates", test_bessel, et_off> >, mpfr_buildopt_tls_p() ? 3 : 1); - time_proc("static_mpfr_float_50", test_bessel, et_on> >, mpfr_buildopt_tls_p() ? 3 : 1); - time_proc("static_mpfr_float_50 (no expression templates)", test_bessel, et_off> >, mpfr_buildopt_tls_p() ? 3 : 1); -#endif -#endif -#ifdef TEST_MPF - time_proc("mpf_float_50", test_bessel, 3); - time_proc("mpf_float_50 (no expression templates", test_bessel, et_off> >, 3); -#endif -#ifdef TEST_CPP_DEC_FLOAT - time_proc("cpp_dec_float_50", test_bessel, 3); -#endif -#ifdef TEST_MPFR_CLASS - time_proc("mpfr_class", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); -#endif -#ifdef TEST_MPREAL - time_proc("mpfr::mpreal", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); -#endif - // - // Then 100 digits: - // - std::cout << "Testing Bessel Functions at 100 digits....." << std::endl; -#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) - mpfr_set_default_prec(100 * 1000L / 301L); -#endif -#ifdef TEST_MPREAL - mpfr::mpreal::set_default_prec(100 * 1000L / 301L); -#endif -#ifdef TEST_MPFR - time_proc("mpfr_float_100", test_bessel); - time_proc("mpfr_float_100 (no expression templates", test_bessel, et_off> >); -#endif -#ifdef TEST_MPF - time_proc("mpf_float_100", test_bessel); - time_proc("mpf_float_100 (no expression templates", test_bessel, et_off> >); -#endif -#ifdef TEST_CPP_DEC_FLOAT - time_proc("cpp_dec_float_100", test_bessel); -#endif -#ifdef TEST_MPFR_CLASS - time_proc("mpfr_class", test_bessel); -#endif -#ifdef TEST_MPREAL - time_proc("mpfr::mpreal", test_bessel); -#endif - - // - // 50 digits first: - // - std::cout << "Testing Polynomial Evaluation at 50 digits....." << std::endl; -#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) - mpfr_set_default_prec(50 * 1000L / 301L); -#endif -#ifdef TEST_MPREAL - mpfr::mpreal::set_default_prec(50 * 1000L / 301L); -#endif -#ifdef TEST_MPFR - time_proc("mpfr_float_50", test_polynomial); - time_proc("mpfr_float_50 (no expression templates", test_polynomial, et_off> >); -#endif -#ifdef TEST_MPF - time_proc("mpf_float_50", test_polynomial); - time_proc("mpf_float_50 (no expression templates", test_polynomial, et_off> >); -#endif -#ifdef TEST_CPP_DEC_FLOAT - time_proc("cpp_dec_float_50", test_polynomial); -#endif -#ifdef TEST_MPFR_CLASS - time_proc("mpfr_class", test_polynomial); -#endif -#ifdef TEST_MPREAL - time_proc("mpfr::mpreal", test_polynomial); -#endif - // - // Then 100 digits: - // - std::cout << "Testing Polynomial Evaluation at 100 digits....." << std::endl; -#ifdef TEST_MPFR_CLASS - mpfr_set_default_prec(100 * 1000L / 301L); -#endif -#ifdef TEST_MPREAL - mpfr::mpreal::set_default_prec(100 * 1000L / 301L); -#endif -#ifdef TEST_MPFR - time_proc("mpfr_float_100", test_polynomial); - time_proc("mpfr_float_100 (no expression templates", test_polynomial, et_off> >); -#endif -#ifdef TEST_MPF - time_proc("mpf_float_100", test_polynomial); - time_proc("mpf_float_100 (no expression templates", test_polynomial, et_off> >); -#endif -#ifdef TEST_CPP_DEC_FLOAT - time_proc("cpp_dec_float_100", test_polynomial); -#endif -#ifdef TEST_MPFR_CLASS - time_proc("mpfr_class", test_polynomial); -#endif -#ifdef TEST_MPREAL - time_proc("mpfr::mpreal", test_polynomial); -#endif - // - // 50 digits first: - // - std::cout << "Testing Non-Central T at 50 digits....." << std::endl; -#ifdef TEST_MPFR_CLASS - mpfr_set_default_prec(50 * 1000L / 301L); -#endif -#ifdef TEST_MPREAL - mpfr::mpreal::set_default_prec(50 * 1000L / 301L); -#endif -#ifdef TEST_MPFR - time_proc("mpfr_float_50", test_nct); - time_proc("mpfr_float_50 (no expression templates", test_nct, et_off> >); -#endif -#ifdef TEST_MPF - time_proc("mpf_float_50", test_nct); - time_proc("mpf_float_50 (no expression templates", test_nct, et_off> >); -#endif -#ifdef TEST_CPP_DEC_FLOAT - time_proc("cpp_dec_float_50", test_nct); -#endif -#ifdef TEST_MPFR_CLASS - time_proc("mpfr_class", test_nct); -#endif -#ifdef TEST_MPREAL - time_proc("mpfr::mpreal", test_nct); -#endif - // - // Then 100 digits: - // - std::cout << "Testing Non-Central T at 100 digits....." << std::endl; -#ifdef TEST_MPFR_CLASS - mpfr_set_default_prec(100 * 1000L / 301L); -#endif -#ifdef TEST_MPREAL - mpfr::mpreal::set_default_prec(100 * 1000L / 301L); -#endif -#ifdef TEST_MPFR - time_proc("mpfr_float_100", test_nct); - time_proc("mpfr_float_100 (no expression templates", test_nct, et_off> >); -#endif -#ifdef TEST_MPF - time_proc("mpf_float_100", test_nct); - time_proc("mpf_float_100 (no expression templates", test_nct, et_off> >); -#endif -#ifdef TEST_CPP_DEC_FLOAT - time_proc("cpp_dec_float_100", test_nct); -#endif -#ifdef TEST_MPFR_CLASS - time_proc("mpfr_class", test_nct); -#endif -#ifdef TEST_MPREAL - time_proc("mpfr::mpreal", test_nct); -#endif + basic_tests(); + bessel_tests(); + poly_tests(); + nct_tests(); } diff --git a/performance/sf_performance_basic.cpp b/performance/sf_performance_basic.cpp new file mode 100644 index 00000000..d079fc99 --- /dev/null +++ b/performance/sf_performance_basic.cpp @@ -0,0 +1,49 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void basic_tests() +{ + + std::cout << "Allocation Counts for Horner Evaluation:\n"; +#ifdef TEST_MPFR + basic_allocation_test("mpfr_float_50", mpfr_float_50(2)); + basic_allocation_test("mpfr_float_50 - no expression templates", number, et_off>(2)); +#endif +#ifdef TEST_MPFR_CLASS + basic_allocation_test("mpfr_class", mpfr_class(2)); +#endif +#ifdef TEST_MPREAL + basic_allocation_test("mpfr::mpreal", mpfr::mpreal(2)); +#endif + + std::cout << "Allocation Counts for boost::math::tools::evaluate_polynomial:\n"; +#ifdef TEST_MPFR + poly_allocation_test("mpfr_float_50", mpfr_float_50(2)); + poly_allocation_test("mpfr_float_50 - no expression templates", number, et_off>(2)); +#endif +#ifdef TEST_MPFR_CLASS + poly_allocation_test("mpfr_class", mpfr_class(2)); +#endif +#ifdef TEST_MPREAL + poly_allocation_test("mpfr::mpreal", mpfr::mpreal(2)); +#endif + + // + // Comparison for builtin floats: + // +#ifdef TEST_FLOAT + time_proc("Bessel Functions - double", test_bessel); + time_proc("Bessel Functions - real_concept", test_bessel); + time_proc("Bessel Functions - arithmetic_backend", test_bessel > >); + time_proc("Bessel Functions - arithmetic_backend - no expression templates", test_bessel, et_off> >); + + time_proc("Non-central T - double", test_nct); + time_proc("Non-central T - real_concept", test_nct); + time_proc("Non-central T - arithmetic_backend", test_nct > >); + time_proc("Non-central T - arithmetic_backend - no expression templates", test_nct, et_off> >); +#endif +} diff --git a/performance/sf_performance_bessel.cpp b/performance/sf_performance_bessel.cpp new file mode 100644 index 00000000..817f5a56 --- /dev/null +++ b/performance/sf_performance_bessel.cpp @@ -0,0 +1,42 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_1(); +void bessel_tests_2(); +void bessel_tests_3(); +void bessel_tests_4(); +void bessel_tests_5(); +void bessel_tests_6(); + +void bessel_tests() +{ + // + // 50 digits first: + // + std::cout << "Testing Bessel Functions at 50 digits....." << std::endl; +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) + mpfr_set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(50 * 1000L / 301L); +#endif + + bessel_tests_1(); + bessel_tests_2(); + bessel_tests_3(); + + // + // Then 100 digits: + // + std::cout << "Testing Bessel Functions at 100 digits....." << std::endl; +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) + mpfr_set_default_prec(100 * 1000L / 301L); +#endif + bessel_tests_4(); + bessel_tests_5(); + bessel_tests_6(); +} diff --git a/performance/sf_performance_bessel1.cpp b/performance/sf_performance_bessel1.cpp new file mode 100644 index 00000000..6c13315f --- /dev/null +++ b/performance/sf_performance_bessel1.cpp @@ -0,0 +1,23 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_1() +{ +#ifdef TEST_MPFR +#if MPFR_VERSION, 1); + time_proc("mpfr_float_50 (no expression templates)", test_bessel, et_off> >, 1); + time_proc("static_mpfr_float_50", test_bessel, et_on> >, 1); + time_proc("static_mpfr_float_50 (no expression templates)", test_bessel, et_off> >, 1); +#else + time_proc("mpfr_float_50", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); + time_proc("mpfr_float_50 (no expression templates", test_bessel, et_off> >, mpfr_buildopt_tls_p() ? 3 : 1); + time_proc("static_mpfr_float_50", test_bessel, et_on> >, mpfr_buildopt_tls_p() ? 3 : 1); + time_proc("static_mpfr_float_50 (no expression templates)", test_bessel, et_off> >, mpfr_buildopt_tls_p() ? 3 : 1); +#endif +#endif +} diff --git a/performance/sf_performance_bessel2.cpp b/performance/sf_performance_bessel2.cpp new file mode 100644 index 00000000..3eecda8e --- /dev/null +++ b/performance/sf_performance_bessel2.cpp @@ -0,0 +1,17 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_2() +{ +#ifdef TEST_MPF + time_proc("mpf_float_50", test_bessel, 3); + time_proc("mpf_float_50 (no expression templates", test_bessel, et_off> >, 3); +#endif +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_50", test_bessel, 3); +#endif +} diff --git a/performance/sf_performance_bessel3.cpp b/performance/sf_performance_bessel3.cpp new file mode 100644 index 00000000..67ee0fba --- /dev/null +++ b/performance/sf_performance_bessel3.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_3() +{ +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_bessel, mpfr_buildopt_tls_p() ? 3 : 1); +#endif +} diff --git a/performance/sf_performance_bessel4.cpp b/performance/sf_performance_bessel4.cpp new file mode 100644 index 00000000..108d62e1 --- /dev/null +++ b/performance/sf_performance_bessel4.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_4() +{ +#ifdef TEST_MPFR + time_proc("mpfr_float_100", test_bessel); + time_proc("mpfr_float_100 (no expression templates", test_bessel, et_off> >); + time_proc("static_mpfr_float_100", test_bessel); +#endif +} diff --git a/performance/sf_performance_bessel5.cpp b/performance/sf_performance_bessel5.cpp new file mode 100644 index 00000000..f1154b59 --- /dev/null +++ b/performance/sf_performance_bessel5.cpp @@ -0,0 +1,17 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_5() +{ +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPF + time_proc("mpf_float_100", test_bessel); + time_proc("mpf_float_100 (no expression templates", test_bessel, et_off> >); +#endif +} diff --git a/performance/sf_performance_bessel6.cpp b/performance/sf_performance_bessel6.cpp new file mode 100644 index 00000000..f9c61cd2 --- /dev/null +++ b/performance/sf_performance_bessel6.cpp @@ -0,0 +1,19 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_6() +{ +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_100", test_bessel); +#endif +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_bessel); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_bessel); +#endif +} diff --git a/performance/sf_performance_nct.cpp b/performance/sf_performance_nct.cpp new file mode 100644 index 00000000..c0a713ba --- /dev/null +++ b/performance/sf_performance_nct.cpp @@ -0,0 +1,39 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_1(); +void nct_tests_2(); +void nct_tests_3(); +void nct_tests_4(); +void nct_tests_5(); +void nct_tests_6(); + +void nct_tests() +{ + // + // 50 digits first: + // + std::cout << "Testing Non-Central T at 50 digits....." << std::endl; +#ifdef TEST_MPFR_CLASS + mpfr_set_default_prec(50 * 1000L / 301L); +#endif + + nct_tests_1(); + nct_tests_2(); + nct_tests_3(); + + // + // Then 100 digits: + // + std::cout << "Testing Non-Central T at 100 digits....." << std::endl; +#ifdef TEST_MPFR_CLASS + mpfr_set_default_prec(100 * 1000L / 301L); +#endif + nct_tests_4(); + nct_tests_5(); + nct_tests_6(); +} diff --git a/performance/sf_performance_nct1.cpp b/performance/sf_performance_nct1.cpp new file mode 100644 index 00000000..cde285c9 --- /dev/null +++ b/performance/sf_performance_nct1.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_1() +{ +#ifdef TEST_MPFR + time_proc("mpfr_float_50", test_nct); + time_proc("mpfr_float_50 (no expression templates", test_nct, et_off> >); + time_proc("static_mpfr_float_50", test_nct); +#endif +} diff --git a/performance/sf_performance_nct2.cpp b/performance/sf_performance_nct2.cpp new file mode 100644 index 00000000..76142bea --- /dev/null +++ b/performance/sf_performance_nct2.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_2() +{ +#ifdef TEST_MPF + time_proc("mpf_float_50", test_nct); + time_proc("mpf_float_50 (no expression templates", test_nct, et_off> >); +#endif +} diff --git a/performance/sf_performance_nct3.cpp b/performance/sf_performance_nct3.cpp new file mode 100644 index 00000000..714831b8 --- /dev/null +++ b/performance/sf_performance_nct3.cpp @@ -0,0 +1,22 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_3() +{ +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_50", test_nct); +#endif +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_nct); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_nct); +#endif +} diff --git a/performance/sf_performance_nct4.cpp b/performance/sf_performance_nct4.cpp new file mode 100644 index 00000000..1ad30271 --- /dev/null +++ b/performance/sf_performance_nct4.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_4() +{ +#ifdef TEST_MPFR + time_proc("mpfr_float_100", test_nct); + time_proc("mpfr_float_100 (no expression templates", test_nct, et_off> >); + time_proc("static_mpfr_float_100", test_nct); +#endif +} diff --git a/performance/sf_performance_nct5.cpp b/performance/sf_performance_nct5.cpp new file mode 100644 index 00000000..c098ab20 --- /dev/null +++ b/performance/sf_performance_nct5.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_5() +{ +#ifdef TEST_MPF + time_proc("mpf_float_100", test_nct); + time_proc("mpf_float_100 (no expression templates", test_nct, et_off> >); +#endif +} diff --git a/performance/sf_performance_nct6.cpp b/performance/sf_performance_nct6.cpp new file mode 100644 index 00000000..76e0a7e1 --- /dev/null +++ b/performance/sf_performance_nct6.cpp @@ -0,0 +1,22 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_6() +{ +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_100", test_nct); +#endif +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_nct); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_nct); +#endif +} diff --git a/performance/sf_performance_poly.cpp b/performance/sf_performance_poly.cpp new file mode 100644 index 00000000..138a39bd --- /dev/null +++ b/performance/sf_performance_poly.cpp @@ -0,0 +1,66 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void poly_tests() +{ + // + // 50 digits first: + // + std::cout << "Testing Polynomial Evaluation at 50 digits....." << std::endl; +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) + mpfr_set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPFR + time_proc("mpfr_float_50", test_polynomial); + time_proc("mpfr_float_50 (no expression templates", test_polynomial, et_off> >); + time_proc("static_mpfr_float_50", test_polynomial); +#endif +#ifdef TEST_MPF + time_proc("mpf_float_50", test_polynomial); + time_proc("mpf_float_50 (no expression templates", test_polynomial, et_off> >); +#endif +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_50", test_polynomial); +#endif +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_polynomial); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_polynomial); +#endif + // + // Then 100 digits: + // + std::cout << "Testing Polynomial Evaluation at 100 digits....." << std::endl; +#ifdef TEST_MPFR_CLASS + mpfr_set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPFR + time_proc("mpfr_float_100", test_polynomial); + time_proc("mpfr_float_100 (no expression templates", test_polynomial, et_off> >); + time_proc("static_mpfr_float_100", test_polynomial); +#endif +#ifdef TEST_MPF + time_proc("mpf_float_100", test_polynomial); + time_proc("mpf_float_100 (no expression templates", test_polynomial, et_off> >); +#endif +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_100", test_polynomial); +#endif +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_polynomial); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_polynomial); +#endif +} diff --git a/test/test_atan.cpp b/test/test_atan.cpp index 4e6d7552..07ed5b10 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -44,6 +44,10 @@ #include #endif +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + template T atan2_def(T y, T x) { diff --git a/test/test_float_io.cpp b/test/test_float_io.cpp index 74ba8898..ad66dac3 100644 --- a/test/test_float_io.cpp +++ b/test/test_float_io.cpp @@ -40,6 +40,10 @@ #include #include +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + #if defined(TEST_MPF_50) template bool is_mpf(const boost::multiprecision::number, ET>&) @@ -286,12 +290,10 @@ int main() #ifdef TEST_CPP_DEC_FLOAT test(); test(); - // cpp_dec_float has extra guard digits that messes this up: test_round_trip(); test_round_trip(); - #endif #ifdef TEST_MPF_50 test(); diff --git a/test/test_int_io.cpp b/test/test_int_io.cpp index ed92c6b6..2b615fdc 100644 --- a/test/test_int_io.cpp +++ b/test/test_int_io.cpp @@ -40,6 +40,10 @@ #include #include +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + template struct unchecked_type{ typedef T type; }; diff --git a/test/test_native_integer.cpp b/test/test_native_integer.cpp index 7ed79323..0e55822a 100644 --- a/test/test_native_integer.cpp +++ b/test/test_native_integer.cpp @@ -38,7 +38,7 @@ void test() if(std::numeric_limits::is_signed) { - i = -1; + i = static_cast(-1); BOOST_CHECK_THROW(lsb(i), std::range_error); } diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index 7b262ddc..8b32f8a7 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -51,6 +51,10 @@ #include #endif +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + #define PRINT(x)\ std::cout << BOOST_STRINGIZE(x) << " = " << std::numeric_limits::x << std::endl; diff --git a/test/test_rational_io.cpp b/test/test_rational_io.cpp index b954a0c4..34e66e6d 100644 --- a/test/test_rational_io.cpp +++ b/test/test_rational_io.cpp @@ -36,7 +36,6 @@ #include #include #include -#include #include #include "test.hpp" #include diff --git a/test/test_round.cpp b/test/test_round.cpp index 27fe149a..fd72c2e0 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -43,6 +43,10 @@ #include #endif +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + boost::mt19937 rng; template